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Waterjet-Hull Interaction

door Tom J.C. van Terwisga

Samenvatting

Doelstelling van dit werk is het ontwikkelen en valideren van gereedschappen voorde analyse van waterjet-romp interactie.

Hoewel er reeds een aanzienlijke hoeveelheid kennis bestaat omtrent deafzonderlijke componenten in het waterjet-romp systeem, bestaat er een hiaat inonze kennis met betrekking tot de wederzijdse interactie. Als gevoig daarvanworden verschillen in het vermogen-snelheidsverband tussen prototype envoorspelling vaak aan interactie toegeschreven.

Een van de belangrijkste oorzaken voor misverstanden op het gebied van waterjetvoortstuwing lijkt de afwezigheid van duidelijke definities te zijn. Hoofdstuk i laatzien dat er in de literatuur veel verwarring bestaat over definities en beschrijvingvan waterjet-romp interactie. Dit werk begint derhalve met een theoretisch modelwaarmee een complete beschrijving van waterjet-romp interactie mogelijk is. Hetinteractie effect op de romp wordt uitgedrukt in een 'resistance increment' factor.Het interactie effect van de waterjet wordt uitgedrukt in een 'thrust deduction'factor en een impuls interactie- en een energie interactie-efficiency. De beidelaatste rendementen verdisconteren de verandering in ingenomen impuls- enenergieflux ten gevolge van de verstoring door de romp.

Hoewel een ruwe procedure voor voortstuwingsproeven met waterjets reedsvoorgesteld is door de ITTC in 1987, leidt deze aanpak gemakkelijk tot grotesystematische fouten, waardoor het nut van de proeven dubieus wordt. Bovendienwas de voorgestelde verwerkingsprocedure gebaseerd op een incompleettheoretisch model. In dit werk wordt een verbeterde experimentele procedurebeschreven die gebaseerd is op ijking van de opnemers tijdens een paaltrek proef,tezamen met een verwerkingsprocedure die bepaling van de interactie factorenmogelijk maakt.

Gedetailleerde stromingsberekeningen en LDV metingen zijn gemaakt aan destroming in en rondom de intake. De resultaten geven inzicht in de geldigheid vande aannames die gemaakt zijn in de verwerkingsprocedure van voort-stuwingsproeven. Zij tonen aan dat een rechthoekige dwarsdoorsnede van destroombuis met een breedte die 30% groter is dan de geometrische intake breedte,

een adequate representatie van de ingenomen stroming geeft. Zij tonen eveneensaan dat de 'thrust deduction' factor tijdens het droogvaren van de spiegel nietverwaarloosbaar is.

Berekeningen met een potentiaalprogramma en de methode van Savitsky zijngedaan voor een berekening van de interactie effecten. De resultaten hiervankomen echter niet bevredigend overeen met de experimentele resultaten. Eenempirisch model wordt aangeraden voor een bepaling van interactie effecten invoorlopige vermogensberekeningen.

Dit werk biedt een consistente verzameling van definities en relaties, waarmeezowel de voortstuwingseigenschappen van de romp en de waterjet, als ook huninteractie termen volledig beschreven worden. Een experimentele methode met eengroter betrouwbaarheidsniveau dan tot nu toe beschreven in de openbare literatuurwordt eveneens voorgesteld. Deze resultaten kunnen bijdragen tot een bredereacceptatie van het waterjet systeem en tot een betere afwikkeling van contractueleonderhandelingen. Immers, de te verwachten voortstuwingseigenschappen van hetschip zijn hierdoor beter voorspelbaar.

STELLINGEN

De interactie tussen de romp en het waterjet systeem kan het gevraagdemotorvermogen tot meer dan 20% beïnvloeden.

Voor een juiste selectie van voortstuwer systeem voor een bepaaldetoepassing, dienen de effecten van romp-voortstuwer interactie meegewogente worden.

De interactie term 'thrust deduction' suggereert dat de stuwkracht verminderdwordt als gevoig van de aanwezige romp. Bij een waterjet-romp systeem isdit deels het geval. Bij een schroef-romp systeem is dit echter per definitieonj uist.

De beschrijving van waterjet-romp interactie met dezelfde interactie termenzoals algemeen aanvaard voor de beschrijving van propeller-romp interactie,is principieel onjuist.

Waterjet-romp interactie effecten worden bet meest nauwkeurig bepaald doormiddel van modeiproeven.

In een potentiaalstroming is er in het algemeen meer nul dan je denkt. Doorbet toenemend gebruik van numerieke analyse methoden wordt dit steedsvaker over bet hoofd gezien.

Interactie-verschijnselen zijn effecten die bij de gratie van door de mensgeschapen (te) simpele denkmodellen in het technisch jargon bestaan. Denatuur zelf kent ze niet.

AIs we het vanzelfsprekend vinden dat met name jongeren fouten makenwaarvan ze kunnen leren, dan moeten we het ook accepteren dat eencomplexe en jonge organisatie als de VN fouten maakt. Een opvoeder die ditproces bewaakt is echter onontbeerlijk. De afwezigheid hiervan vormt daaromhet grootste probleem bij bet voiwassen worden van de VN.

Het zou het welzijn van de individuen van beide seksen als ook die vanorganisaties ten goede komen, wanneer we de psychologische verschillentussen mannen en vrouwen niet krampachtig ontkennen, doch er dankbaargebruik van maken.

10 Eén van de meest gemaakte menselijke fouten is het oordelen op basis vaneen té eenvoudig denkmodel van de werkelijkheid. Als deze fout tijdens eenborrel gemaakt wordt is er een excuus, zijn de consequenties gering en kanhet de gezelligheid stimuleren. Bij alle andere gelegenheden kan het echterverstrekkende gevolgen voor ons welzijn hebben.

De volgende redeneer mechanismen kunnen naar afnemende mate vanbetrouwbaarheid van het resultaat genoemd worden: wiskunde, statistiek,fuzzy reasoning, en 'no reasoning at all'. Het redeneren van de mens bevindtzich in het algemeen tussen de twee laatstgenoemde mechanismen.

Door de complexiteit en de veelheid van processen in het menselijk lichaam,zijn er talrijke mogelijkheden voor ongewenste interacties tussen dezeprocessen en medicijnen. Door gebruik te maken van de lichaamseigenprocessen, geeft de horneopathie inherent een kleinere kans op bijwerkingendan de allopathie.

Het succes van het in de logistiek gehanteerde JIT principe (Just In Time)leidt tot een groter aantal vrachtwagenkilometers per ton produkt. Dit leidt toteen grotere stroperigheid en verstoppingskans van bet verkeer, waardoor hetuT principe uiteindelijk via het JTL (Just Too Late) principe za] overgaan inhet NNA (Not Needed Anymore) principe.

Het veelgehoorde argument '1k heb geen tijd', heeft pas enigeovertuigingskracht nadat de spreker ervan is overleden. En zeifs dan is hetdiscutabel.

Stellingen behorend bij het proefschrift van T.J.C. van Terwisga: "Waterjet-HullInteraction'. 25 april 1996


Torn J.C. van Terwisga

TECHNISCHE UVERSITETt.aboratorium voor

ScheepshydromechanicaArchief

Mekeiweg 2, 2628 CD Deft11L015-786873-Fax 015-781333

Printed by:Grafisch Bedrijf Ponsen & Looijen BV, Wageningen


Proefschrift

ter verkrijging van de graad van doctoraan de Technische Universiteit Deift,

op gezag van de Rector Magnificus Prof.ir. K.F. Wakker,in het openbaar te verdedigen ten overstaan van een commissie,

door het College van Dekanen aangewezen,op donderdag 25 aprii te 13.30 uur

door

Thomas Jan Cornelis VAN TERWISGA

scheepsbouwkundig ingenieur

geboren te Sneek

Dit proefschrift is goedgekeurd door de promotor:

Prof.dr.ir. G. Kuiper

Samenstelling promotiecommissie:

Rector Magnificus, voorzitterProf.dr.ir. G. Kuiper, TU Deift, promotorProf.dr.ir. J. Pinkster, TU DeiftProf.Dr.Dipl.-Ing. C. Gallin, TU DeiftProf.dr.ir. A. Hermans, TU DeiftProf.dr.ir. L. van Wijngaarden, U-TwenteProf.Dr.-Ing. C. Kruppa, TU BerlinDr. A.J. Bowen, Canterbury University, New Zealand

ISBN 90-75757-01-8

Aan mijn oudersfac intha

Table of Contents

2

Introduction1 .1 Aim and motivation1 .2 Historic setting1.3 Outline of work1.4 Description of waterjet system1.5 Relations with other propulsors

1.5.1 Comparison with propeller1.5.2 Comparison with gasturbine jet system

1.6 Review of previous work1.6.1 Parametric models1.6.2 Experimental procedures1 .6.3 Computational procedures

1 .7 Summary of present work1.7.1 Theoretical model1.7.2 Experimental procedure1.7.3 Computational analysis

Theoretical model2.1 Systems decomposition

2.1.1 Definition of jet system control volume2. 1.2 Analysis of overall powering characteristics

2.2 Basic equations2.2.1 Thrust2.2.2 Power2.2.3 Free stream conditions2.2.4 Lift

2.3 Interaction2.3.1 Momentum interaction efficiency2.3.2 Energy interaction efficiency2.3.3 Quantitative assessment and comparison with previous

work2.3.4 Hull resistance increment

2.4 Conclusions

i248

13

13

172223344348484950

5353545864656871

78808 1

88

909496

3 Experimental analysis 993.1 Propulsion test procedure 993.2 Flow rate measurement 105

3.2.1 Flowmeter selection 1063.2.2 Calibration procedure 119

3.2.3 Bollard pull verification tests 139

3.3 Uncertainty analysis 144

3.4 Propulsion test results 154

3.4.1 Thrust deduction 155

3.4.2 Momentum and energy interaction efficiencies 164

3.5 Extrapolation method 166

3.6 Conclusions 168

4 Computational analysis 171

4. 1 Free stream intake analysis 171

4.1.1 Intake flow analysis 172

4.1.2 Intake induced drag and lift 189

4.2 Computational prediction of interaction 196

4.2.1 Resistance increment for hump speed 197

4.2.2 Resistance increment for design speed 2104.3 Analysis of propulsion test procedure 215

4.3.1 Effect of intake geometry on interaction efficiency . . . . 2164.3.2 Effect of hull and free surface effects on t1 assumption 219

5 Conclusions and recommendations 229

5.1 Methods and tools 230

5.2 Physical mechanisms 233

Appendices

Al Derivation of relations for ideal efficiency 235

A2 Expressions for the computation of cm and Ce 239

A3 Outline of uncertainty analysis 243

A4 Description of facilities and models used for experiments 253

AS Description of potential flow panel codes HESM' and DAWSON 259

A6 Description of performance prediction code PLANE' 263

A7 Description of LDV experiments in the MARIN large cavitation tunnel 265

References 271

Nomenclature 23

Summary 291

Acknowledgement 293

Curriculum Vitae 295

Chapter 1

1 Introduction1.1 Aim and motivation

Aim of this work is 'the development and validation of tools to analyze inter-action effects in powering characteristics of waterjet-hull systems'.

Interaction may be regarded as the phenomenon that is responsible for devi-ations in the actual characteristics of two or more integrated subsystems, from asynthesis of properties of the merely matched subsystems. Interaction phenom-ena are only revealed after one has a theoretical model to derive interactionterms, or after one has the means to observe interaction effects from measure-ments. And interaction is only explained and used effectively in design, afterone has the tools to analyze the responsible mechanisms in detail. The searchfor the aforementioned instruments forms the incentive of this work.

What's new? Propeller-hull interaction is a well developed field of research inpropulsion hydrodynamics where many researchers have made useful contribu-tions, see e.g. Morgan [1992]. What makes waterjet-hull interaction different isthe degree of integration of hull and propulsor system, rendering the definitionof interaction less straightforward, causing complications in experimental tech-niques, and finally, rendering the interaction mechanisms different from thoseobserved with propeller-hull operation.

Chapter 1 Introduction

During the first propulsion tests with waterjet propelled hulls, it appeared thatwaterjet-hull interaction could affect the overall efficiency by well over 20%.This finding in itself would probably be sufficient to justify research on thistopic. Moreover, the interaction effect on thrust sometimes appears to create anunfortunate combination of working regions for both the pump of the jet systemand the hull. Such a combination may prohibit the jet-hull combination to reachits design working point and may result in a maximum speed of the craft that isseveral knots lower than could be expected from pure matching of the twosingle systems.

Apart from this technical motivation, an economic motivation may be extractedfrom present industrial developments. A growing number of waterjet applica-tions and waterjet manufacturers can be observed from the literature. Apartfrom the increase of these numbers, there is also an increase in waterjet sizeperceptible. And with this increase in scale, one can simply see the growingfinancial risks and the consequent request for performance warrants.

1.2 Historic setting

An obvious question one may ask when being confronted with such an effortinto waterjet-hull interaction, is the one on 'Why it is only now that interactionraises this interest'. The following section seeks for a plausible explanation.

In the development of a new concept, technicians are initially only concernedwith the performance and the relations governing the isolated system. Interac-tion between this new system and other systems is consequently neglected. Assuch, the development of the waterjet-hull system can be regarded to havealready started in the ancient times during the development of the first hullforms. The first achievement was the actual building and operation of thecorresponding vessel. Building and operation were based on experience, necess-arily gained after having learnt how certain ideas failed to work. Improvementswere gradually implemented after an empirical evaluation of the new idea.

Archimedes (287-212 BC), presumably puzzled by the appearance of floatingvessels, found a rational theory to describe this phenomenon. With his theory,new ideas and improvements could more easily, and with greater certainty beevaluated. His contribution undoubtedly speeded up the development in naviga-tion and shipbuilding. In the course of times, a wealth of knowledge becameavailable on the subsystem 'hull'.

2

1.2 Historic setting

Another historical event of probably similar importance, was the developmentof mechanical ship propulsion. This could be achieved after the availability ofmechanical power, which came within reach with the introduction of steamengines. Talented engineers subsequently concentrated on the propulsor systemto convert the available mechanical power from the engine to a propelling forcefor the ship.

Since the beginning of the 17th Century, written reference is made to waterjetpropulsion. In 1631, a Scot called David Ramsey acquired English Patent No.50, which included an invention to make Boates, Shippes and Barges goeagainst Stronge Winde and Tyde". This was at a time when there was greatinterest in using steam to raise water and to operate fountains, so there is goodreason to suppose Ramsey had a type of waterjet in mind' (Dickinson [19381)...

A more explicit reference to the waterjet is made in a patent granted toToogood and Hayes [1661] for their invention of "Forceing Water by Bellowes

together with a particular way of Forceing water through the Bottome orSides of Shipps belowe the Surface or Toppe of the Water, which may be ofsinguler Use and Ease in Navagacon".

'The theory of waterjet propulsion was subsequently investigated and discussedby the Frenchman Daniel Bernoulli in 1753. He suggested (Flexner [1944]) thatif a stream of water was driven out of the stern of a boat below the waterline,its reaction on the body of water in which the boat floated would drive thevessel forward. By pouring water into an L-shaped pipe stretching to the aftend, Bernoulli's simple model experiment confirmed the principle of waterjetpropulsion, yet left others to determine how to force the water from the vessel'(Roy [1994]).

Up until the mid-nineteenth century, there has been little or no development onwaterjet propulsors. 'Because of the limitations of technology and lack ofunderstanding of the principles of propulsion , waterjet propulsors wereunable to compete with paddle wheels and, later, propellers' (Allison [1993]).

From the early days of waterjet development, attempts to improve the propulsorconcentrated on a better understanding and a consequent improved design of thepropulsor system itself. Interaction effects may not have been noted due to alimited accuracy of measurements or due to the absence of a physical modelwhich showed that the effect searched for, could only be explained by interac-tiOfl.

3


As with the first propeller propelled vessels, waterjet systems have long beenused successfully before technical interest focused on a proper description andprediction of interaction effects between propulsor and hull. This interest couldalso have been slumbering for quite a period, because the first waterjet projectsoften allowed for extensive trials or initial model testing. Problems due tointeraction effects could thus timely be solved experimentally.

Nowadays, the design procedure of a waterjet propelled vessel is different.Because of the availability of a large number of well developed waterjet sys-tems, the designer is confronted with a selection of existing waterjet units, morethan with the integrated design of the waterjet itself. Due to the success ofwaterjet propulsion development, times and budgets available for the vesseldevelopment have been reduced significantly.

Having less time available, it is the responsibility of the ship designer to selectthe most appropriate waterjet system for the vessel under development. For anoptimal selection of the propulsor installation, the evaluation of candidatesshould not only be made on an evaluation of separate systems, but should alsotake into account possible interaction phenomena that interfere with the vesselsoverall performance.

1.3 Outline of work

Philosophy in approach

The basic philosophy underlying this study is taken from what is called SystemsTheory.

'For centuries, science has sought for insight by analysing, by breaking downmore complex matters into series of simpler problems. The solution of the totalproblem would then be equal to the sum of the solutions of the partial prob-lems. Partial problems are thereby studied independently. More and more, alsobasic, elements being identified. At the same time, the field of science iswidened, causing a growth in the amount of phenomena that need to beexplained. The analysis getting keener and deeper. Caused by this increasingamount of knowledge, spread over numerous disciplines, synthesis has becomeincreasingly difficult.

These days, the subsystems or elements are largely known and their propertieshave been well investigated. Various combinations of elements or systems arebeing studied now. But often, insight in the mutual interaction between

4

elements is limited. This is partly caused by the classical scientific dogma:'Only change one variable at a time'.' (translated from [In't Veld, 1981]).

Description of concepts

Systems may be described by an enumeration of their constituting elements, orby a set of properties or 'attributes' of the system. This latter way is appropriatewhen interaction between systems is to be described.

According to the concepts adopted in Systems Theory, 'interaction' betweentwo (sub)systems occurs when the attributes of one system are affected by theattributes of the other system. The distortion causing the interaction, is passedthrough by the environment of the subject system. Analogous to the way inwhich interaction occurs between two systems, it may occur directly betweenthe system and its environment (see e.g. In 't Veld [1981]).

The attributes are quantified by the so-called 'state variables'. A set of statevariable values consequently defines the 'state' of the system. The values ofthese state variables are constrained by the set of relations governing the systemin its environment.

To be able to quantify interaction, the 'isolated' system's condition is intro-duced (Fig. 1.1). This condition is defined by the set of attributes and relationsdescribing the system in a predefined undisturbed environment. The undisturbedenvironment will in this work be referred to as the 'free stream condition'.Examples of free stream conditions are the later defined free stream conditionfor the waterjet system and the 'open water' condition for propellers.

Before looking at a complete integration of two systems with mutual interac-tion, an intermediate system's condition is introduced. In this so-calledmatched condition', there is no interaction between the two systems yet. The

systems do however limit the range of values of the state variables of eachsystem. The state itself is not affected, only the number of states that can occuris limited. The possible states are governed by the 'matching relations'.

The situation in which interaction occurs is referred to as the 'united condition'of the combined system. In addition to matching relations, 'interaction relations'determine the possible states of the systems involved. It can be inferred fromFig. 1.1 that interaction between two systems is caused by a change in the envi-ronment through the action of the other system.

1.3. Outline of work

5


6

Isolated Condition

Matched Condition

United Condition

Fig. I I Relation between the degree of integration and interaction between two systems

Waterjet-hull interaction as meant throughout this work, refers to the interactionbetween the waterjet system and the hull system only. That is, to a change invalues of the relevant attributes due to the presence of the other system.

The following gives an example on the use of the three conditions describedabove. The isolated systems condition or free stream condition is used for thequantification of the bare hull resistance as a function of speed. Similarly, thejet system's thrust production can be determined in its isolated condition forvarying values of flow velocity and flow rate. In the matched condition, thethrust of the waterjet should balance the resistance of the hull. However, nointeraction effects on thrust or resistance are accounted for yet. We speak of theunited condition after interaction effects have been accounted for. In this situ-

ation, the resistance of the hull is affected by the distorted flow due to thewaterjet action, and vice versa, the thrust delivered by the waterjet for a certainimpeller rotation rate is affected by the hull distortion in ingested flow.

It should be noted that the matched condition is a conceptual condition whichonly occurs in reality when it coincides with the united condition. This is wheninteraction between both systems does not occur. The reason for consideringthis condition is that a rough indication of the attributes of the combined systemcan easily be obtained during synthesis activities. A second reason is that foranalysis activities the concept of interaction is defined more precisely.

Scope

This thesis deals with interaction effects in the hydrodynamic relations that mayoccur in the relations of either the jet or the hull system. Interaction effects inthe geometrical or constructional relations of either system are consequently notdealt with.

We speak of hydrodynamic interaction when for instance the equilibrium posi-tion of the jet-hull system is different from that of the bare hull resistance test.This change in balance is caused by the jet action, causing a change in thehull's environment. Interaction effects can be described in terms of integratedvariables, such as in the above example. They can however also be expressed interms of state variables of the environment, such as fluid pressures and veloc-ities.

The present work is concerned only with steady operation of the jet-hull sys-tem. Unsteady operation occurs for instance during acceleration of the vesseland during operation in a seaway. Unsteady operations can initially beapproached by a quasi-steady analysis for each time step considered. 1f such anapproach does not yield the requested correspondence with experimental obser-vations. the next step would be to also take into account time derivatives of thestate variables. However, as a first step, we will concentrate here on interactionduring steady operation.

Although the above limitations are considered necessary from a practical pointof view, it should at the same time be realized that the quasi-steady approachshould be considered with care. Doctors et aI. [19721 for example, show thatboth the height and the corresponding Froude number of the hump in thewavemaking drag of a Surface Effect Ship depend on the acceleration of thevessel. This change in resistance characteristics may consequently lead to achange in thrust requirements.

1.3. Outline of work

7


Up to now, the unsteady type of operation during acceleration (anddeceleration) has not emerged to the author as a field of industrial interest.

This is different for the unsteady operation of a vessel in a seaway. Enginedamage problems have been reported on High Speed Marine Vehicles by Meek-Hansen [1991]. Possible reasons for these damage problems are believed to becaused by either air ingestion by the intake, by separation of the flow in theintake or by a combination of both (ITTC [1993]).

Waterjet systems occur with various versions of the intake geometry. The threebasic configurations are shown in Fig. 1.3, viz, the flush type intake, the ramtype and the scoop type intake. This work is restricted to waterjet systems witha flush type intake. The theoretical model describing waterjet-hull interaction, aswell as the experimental procedures can however be used for ram and scooptype intakes as well, with only minor modifications.

1.4 Description of waterjet system

General principle

The general principle underlying the thrust production of the jet propulsor istersely summarized in the conservation law of momentum. A consequence ofthis physical law is, that an action force is required to accelerate a certainamount of fluid. This action force is exerted on the fluid by an actuator. For awaterjet system, the actuator normally consists of a mechanical pump. In steadyconditions, the action force has to be counterbalanced by a reaction forceexerted by the fluid on the actuator. This reaction force can be identified as a

thrust vector Tg:

Tg 4mnmi

where = momentum flux vectorsubscripts n and i denote the nozzle and intake area respectively.

The minus sign for the gross thrust has been added because the thrust is definedas the reaction force to the force associated with the increase in momentum.

The momentum flux for a uniform flow can be written as:

fll = P (1.2)

8

Fig. 1.2 GeneraI scheme of waterjet propulsor

Water from the jet system's environment is ingested by the intake, acceleratedby the actuator and discharged through the nozzle. The actuator usually consistsof a mechanical pump, which may have a range of characteristics. The firstwaterjet systems were primarily equipped with centrifugal pumps, offering arelatively low pump efficiency. Modern waterjet systems mostly apply axialflow or mixed flow type pumps at improved pump efficiencies. An alternative

1 .4 Description of waterjet system

9

where p= specific mass of fluidvolume flow rate through control volume

u,n = momentum velocity vector.

Although various propulsor concepts acting in a fluid or a mixture of fluids areavailable, they all share this common principle. Examples of such propulsorsare for instance the classical propeller and all its derivatives, the gasturbine jetused in airplanes and the waterjet for marine applications. Analogies inpropulsor-hull interaction with propellers and gasturbines will be discussed inthe next section, to ensure that research results on propulsor-hull interaction forsimilar propulsors are used whenever possible.

To obtain a better understanding of the way in which interaction occurs andhow it can be treated, a description of the waterjet system is provided in thefollowing. The elements and fundamental processes are shortly addressed,without pursuing completeness.

Description of waterjet system

A general scheme of the waterjet propulsor is presented in Fig. 1 .2. A suitablecontrol volume that is required for e.g. the thrust computation from eq. (1.1), isdiscussed in detail in Chapter 2.


actuator that has recently raised some interest is the Magneto HydrodynamicPump [Doss and Geyer, 1993] and [Tasaki et al., 1991]. Due to its current lowefficiency, it has only been applied in experimental craft.

A further distinction of waterjet systems can be made after the type of intakeapplied. Two basic types of intake exist. One being an intake with an openingthat is situated flush in the vessel's hull and consequently approximately paral-lel to the local flow. The other being an intake with an opening that is situatedat approximate right angles to the local flow. Based on these two basic con-cepts, various hybrid forms may be conceived. The basic concepts are sketchedin Fig. 1.3.

lo

flush intake

ram intake

planing scoop intake scoop intake

Fig. 1.3 Basic intake concepts (from Kruppa et al. [1968])

Both types of intake have their specific area of application. An advantage of theflush intake is that it does not suffer from any drag due to protruding parts, asin the case of a ram type intake. Due to its position in the hull's bottom how-ever, it may become subject to air ingestion, either caused by large relativemotions and a shallow submergence, or by entrained air in the flow under thehull. These disadvantages are avoided with a ram type intake, which can besituated at a more favourable position in the flow.

The flush type intake is presently the most frequently applied intake. Ramintakes are mounted in Hydrofoil craft or in other craft where the flush intakewould be situated too close to the water surface. Hybrid forms are not oftenapplied any more. They may be used wherever the disadvantages of flush typeintakes are considered too serious, but the drastic ram intake solution is con-sidered overdone.

Process per element

The most important part of the jet system governing both the size of the unitand its overall efficiency, is the nozzle. This part of the jet system converts thepotential (pressure) energy in the flow, added by the pump, into kinetic energy,used for thrust production.

For a given thrust and speed requirement, the nozzle area determines the thrustloading coefficient CT,,:

CT,, =Tg

(1.3)-p UA

where = gross thrust as defined by eq. (1.1)o = ship speed or free stream velocity

= nozzle exit area.

lt will be demonstrated in Chapter 2 that the ideal efficiency of the jet systemonly depends on the magnitude of CT,,. The ideal efficiency largely determinesthe overall efficiency. Thus, in analogy with propellers, the lower the thrustloading, the higher the efficiency of the system. This implies an increase inefficiency with increasing nozzle area.

The nozzle is usually shaped such as to have the vena contracta of the dis-charged jet coinciding with the nozzle exit. The vena contracta of the jetcoincides with the position where the average static pressure in the jet equals

1.4 Description of waterjet system

11


the ambient pressure of the medium in which it is discharged. Some jets areequipped with a clearly converging or Pelton type nozzle, causing the venacontracta of the jet to be situated outside the physical boundaries of the jetsystem (Fig. 1.4).

12

jet boundary jet boundary

Vena contractaFig. 1.4 Distinct nozzle geometries

The function of the pump in the waterjet system is to add potential energy tothe flow, resulting in a pressure rise over the pump. The most suitable type ofpump depends on the jet's thrust loading coefficient CTfl. For high thrust load-ing coefficients, the ratio between nozzle velocity and free stream velocity islarge, causing a relatively high head at low flow rate requirement. In extremecases, the radial flow pump would offer the best pump efficiency. Nowadays,jet systems are usually selected at a lower thrust loading coefficient to obtainthe highest efficiency. This design condition demands a high pump efficiency ata relatively low head but large flow rate. For these requirements, the mixedflow and the axial flow pump offer a better performance.

The function of the intake and consecutive ducting to the pump inlet area is toprovide sufficient flow to the pump. Intake design requirements relate to amaximum energy recovery from the flow about the hull and minimum energylosses within the intake. Another important requirement for the intake is that itshould present, as good as possible, a homogeneous flow to the pump. Theintake should further be as small as possible to minimize the weight of itsconstruction and of the ingested water.

The intake and ducting mostly feature bends and a diffusing or contractingcross sectional area along the intake/ducting. It should be noted that for most

parallel throat nozzle Pelton type nozzle

operational conditions, diffusion or contraction of the ingested flow alreadystarts ahead of the intake.

1.5 Relations with other propulsors

The waterjet, the marine propeller and the aeronautical jet engine share thesame principle for thrust production. The latter two propulsors have furthermorebeen subject to a longer time of scientific interest than the marine waterjet. Inthis period, well established theories of and procedures for the assessment ofinteraction effects have become available. When investigating interaction effectsin and about waterjets, due attention has therefore to be paid to these relatedpropulsors.

Before discussing interaction aspects of the propeller and the gasturbine jet, themost salient similarities and differences between the propulsors are discussed.

1.5.1 Comparison with propeller

The major hydrodynamic difference between a propeller and a waterjet systemoccurs in the state of the flow passing the actuator, and therefore the risk ofcavitation. The state of flow can be characterized by the state variables staticpressure and velocity as a function of their position.

Restricting ourselves to the steady process, we are not concerned with vari-ations of these parameters in time. Averaging these parameters over the diskarea just in front of the actuator, yields the two parameters that govern thecavitation number G:

where = vapour pressure.

i-pv±p22

1 .4 Description of waterjet system

(1.4)

The higher this cavitation number, the better the resistance in the actuator diskagainst cavitation.

Using a required thrust production at a given speed as a starting point for ourcomparison, the cavitation number of the propeller can only be increased bydecreasing the velocity through its disk area. This conclusion is simply verifiedthrough the use of Bernoulli's theorem. Lowering the velocity through the diskarea can only be accomplished by increasing the disk area.

13


The cavitation number just in front of the impeller disk of the waterjet is simi-larly controlled by the average velocity through this disk. This average velocityis however not only controlled by the impeller diameter itself, but also by thenozzle diameter. This is because the flow rate through the impeller disk iscontrolled by the nozzle area. For this resulting flow rate, the average velocitythrough the actuator disk is subsequently controlled by the impeller diameter.The smaller the nozzle area, the smaller the flow rate. And the bigger theimpeller diameter, the lower the average velocity.

As we have seen in the preceding section, decreasing the nozzle area results ina decrease of ideal efficiency. This process of increasing the resistance againstcavitation by decreasing the flow rate through the system is consequently at thecost of efficiency. This implies that when the jet is designed such as to have abetter resistance against cavitation than the propeller, the propeller shows thebetter efficiency.

This lower efficiency of the waterjet is partly compensated for by the absenceof appendage drag, which does occur for submerged propellers. This appendagedrag can reach values at high hull speeds of over 20% of the bare hull drag,causing a major effect in power requirements.

Fig. 1.5 shows the trends in thrust loading coefficient CTfl and non-dimensionalappendage drag as a function of the non-dimensional speed FnL.

14

tL)

Io

Fig. I .5 Thrust loading coefficient and appendage drag contribution as a function of non-dimensional speed

06

o

0.2 1.2 1.40.4 0.6 0.8 1

FnL I-t

12 0.25

1 .5 Relation with other propulsors

As discussed before, the decreasing thrust coefficient results in an increase inwaterjet efficiency. At the same time, the increasing importance of the append-age drag to the overall efficiency benefits the waterjet. If one furthermoreconsiders the deteriorating effects of cavitation at the higher speeds on overallpowering performance, it becomes clear that the waterjet system is especiallysuitable for the higher speeds, when purely evaluated in terms of cavitation andefficiency.

Propeller-hull interaction

The most frequently used model for the description of propeller-hull poweringperformance is based on the overall performance of the combined system, andthe performance of the isolated systems in predefined conditions. This theoreti-cal model provides a parametric description of the interaction. For this reason, itis a suitable model for application in preliminary ship design. A short descrip-tion of the model is given below.

The powering characteristics of the isolated hull are either computed ormeasured during a resistance test. The powering characteristics of the isolatedpropeller are measured or computed for a uniform inflow. The performancecharacteristics of the propeller are then represented in a so-called hopen waterdiagram'. This diagram provides the relations between non-dimensional propel-ler speed of advance J, with non-dimensional thrust KT and torque KQ.

Considering the combined propeller-hull system, the propeller normally operatesin the wake of the hull. The effective propeller inflow velocity thereby differsfrom the ship speed. By definition, the relation between thrust coefficient andpropeller advance speed is set equal to that in free stream conditions. Theadvance ratio subsequently derived from the thrust coefficient as obtained fromself propulsion tests, can now be compared with that based on ship speed (seeFig. 1.6, Newman [19891). The difference with the corresponding advance ratioas obtained from the open water characteristics is accounted for in the 'Taylorwake fraction' WT according to:

U = UO(l-wT) (1.5)

where U = effective propeller speed of advanceU0 = free stream velocity or ship speed.

15


16

I I

i difference in US-* 1 W = UEI/UMODEL»1

I I

I I difference in KQ S * (KQ ) O

I (KQ)SP

KT = thrust coefficientKQ = torque coefficient

SubscriptsO = open water conditionSP = self propelled condition

Fig. 1.6 Relationship between self propelled and open water propeller characteristics (fromNewman [1989])

Because the propeller open water characteristics may differ from the propellercharacteristics in the 'behind hull' condition, and because we have assumedidentical thrust coefficients KT in both conditions for a given advance ratio J, agenerally small discrepancy occurs in the torque coefficient KQ. This discrep-ancy is accounted for by the relative rotative efficiency iR (see Fig. 1.6):

iRK20

KQ

SQSPs.

where K0 = propeller torque coefficientsubscript O indicates open water conditions.

Usually, a discrepancy exists between the thrust T delivered by the propellerand the resistance R that was measured during the resistance test. This discrep-ancy is accounted for by the thrust deduction fraction t:

(1.6)

U- nD

UEJ UMODEL

i .5 Relation with other propulsors

17

(T-R)(1.7)

T

The overall efficiency fluA can now be obtained from the open water efficiencyand the interaction contribution

flOA 1Oib1NT

where ib = open water efficiencyfl/NT = interaction efficiency,

and the interaction efficiency can subsequently be written as:

(l-t)flINT - fiR

(1 WT)

The fraction occurring on the right-hand side of this equation is often referredto as the hull efficiency flH

As can be observed from the above model, the interaction between the propellerand the supporting hull is defined on a basis of the propeller open water charac-teristics. Characteristics that were obtained from thrust and torque measure-ments or computations. The idea of relating interaction to the free stream char-acteristics of the systems involved can also be used in a model for the descrip-tion of waterjet-hull interaction. But because the waterjet free stream character-istics are obtained in a different way than practised for propeller propulsion, itis not obvious to use the same terminology and relations.

1.5.2 Comparison with gasturbine jet system

First, a short description of the basic elements and processes of the gasturbinejet will be given. Having reviewed the working principle, a comparison is madebetween the elementary processes of the waterjet and the gasturbine jet. Finally,the applicability of the analogy with waterjet-hull interaction is addressed.

The description of aeronautical or gasturbine jet systems will be concentratedon subsonic jet engines. The physics involved in the corresponding processes isbetter comparable to those of waterjet systems because of the absence of shockwaves.

(1.8)

(1.9)


Although the jet-fuselage configuration is not directly comparable to jet-hullsystems, similarities occur. Hush intake type waterjets may be compared withsimilar intakes of jet engines embedded in the fuselage. Ram intake typewaterjets as occur on hydrofoil craft may be compared with podded jet enginesunderneath the wings or mounted on the fuselage.

Description of gasturbine jet

A general scheme of the gasturbine jet is presented in Fig. 1.7.

a 1 2 34intake compressor combustion camber turbine nozzle

18

p(N/m2)

volume

a

o S(J/(kgK))entropy

a-1 ram.effect2 adiabatic compression

2 . 3 : continuous burning at evenpressure

3 .4 : adiabatic expension4 . 5 adiabatic expansion in a

convergent or convergent-divergent nozzle to excitionof jet

Fig. 1.7 GeneraI scheme of gasturbine jet system (Bodegom, W. Van [19981)

In the actuator of a gasturbine jet (viz, the combustion chamber), chemicalenergy is directly converted into kinetic and internal energy in an essentiallyisobar process (path 2-3 in Fig. 1.7). By expanding the exhaust gases in the aftpart of the jet system, most of the internal energy is converted into kineticenergy that can be used for thrust production (path 5-6 in Fig. 1.7).

This direct conversion of chemical energy within the jet can only occur in acompressible fluid, governed by thermodynamic principles. Burning fuel in theactuator of the waterjet would initially only result in a rise of the water tem-perature, without the flow being able to retrieve this energy for thrust purposes.

1.5 Relation with other propulsors

Because of the compressibility of air, the distinct elements constituting thegasturbine jet system are characterized by a greater variety of physical pro-cesses than in the case of waterjet propulsion. These processes are schemati-cally presented in the ideal pV and TS-diagrams shown in Fig. 1.7.

The function of the ram intake of the gasturbine jet is to ingest the requiredmass flow from the external flow at a maximum energy recovery. Apart frommaximum energy recovery at a minimal external drag, another conditionimposed on inlet design relates to an even velocity distribution in front of thecompressor mouth, so that an even force distribution on the compressor isobtained. At subsonic airspeeds, the process of air ingestion and compression inthe intake is isentropic (path a-I in Fig. 1.7). Analogous to the waterjet intake,diffusion or contraction of the ingested flow already starts upstream of thephysical intake opening.

Before entering the combustion chamber, the ingested air is further compressedby a compressor, performing an adiabatic compression (path 1-2 in Fig. 1.7). Ahigh pressure of the ingested air is favourable for the thermodynamic efficiencyof the combustion process.

The pressure increase in inlet and compressor is of great importance to the totalefficiency. The pressure rise in the intake is about 1 .6 times the free streampressure. The pressure increase over the compressor is subsequently 12-15 timesthe pressure just in front of the compressor. For supersonic speeds, the pressurerise over the intake alone can even reach values in excess of 20 times the freestream pressure.

After the combustion chamber, the flow enters the turbine, where part of theenergy is converted into mechanical power (path 3-4 in Fig. 1.7). This power isused to drive the upstream compressor. In the turbine, the exhaust gas isexpanded, resulting in a decrease of gas temperature and pressure and anincrease of flow velocity.

The final stage of the jet system consists of the nozzle, in which the potentialenergy of the flow is completely converted into kinetic energy (path 4-5 inFig. 1.7). The discharged exhaust gases adopt the ambient pressure at a highertemperature (or internal energy) than ambient.

Comparison with waterjet

A remarkable difference with the waterjet propulsor is the conversion process ofchemical into kinetic and potential energy. incorporated within the jet system

19


itself. As a consequence, the ingested medium is not equal to the dischargedmedium. The ingested flows consist of air and fuel, the discharged flow ofexhaust gases.

The ingestion of a uniform velocity distribution by the intake is more importantthan it is for waterjets. The origin for this difference is that the specific mass ofthe ingested flow rate increases with speed, due to the compressibility of airand the increasing ram pressure with speed. This effect results in a thrust-speedrelation that is markedly distinct from the same relation for waterjets (seeFig. 1.8). Increasing the mass flow through the system for a given speed andthrust requirement, decreases the nozzle velocity ratio NVR. And a decrease ofthis parameter implies a higher ideal efficiency, as will be discussed further inChapter 2.

thrust - speed relation for thrust - speed relation forincompressible fluid compressible fluid(waterjet) (gasturbine jet)

20

E

E-

ingested watervelocity

Resultant of A & B

Fig. 1.8 Thrust-speed relations for waterjet and gasturbine jet system

ingested airvelocity

The compressor, mainly responsible for the pressure rise, requires a uniforminflow for an efficient and balanced performance. As a consequence of thisuniform flow requirement, the inlets are either podded or fuselage integrated insuch a way that no appreciable amount of low energy or vortex flow is likely tobe ingested (Antonatos et al. [1972]). This is contrary to what is practised inmarine jets (see Photo 1.1).

Despite the aforementioned differences, a remarkable correspondence occurs inoperational conditions, expressed in Nozzle Velocity Ratio values NVR. Oper-ational values for this ratio occur between 1.5 and 5 for both jet systems (Borget al. [19931). Consequently, their ideal efficiencies are comparable.

Courtesy Royal Dutch Air Force

Courtesy Lips Jets BV

Photo 1 .1 Comparison of intakes of a gasturbine jet and a waterjet

1.5 Relation with other propulsors

21


It is concluded that the compressibility of air causes major differences in theprocesses of the gasturbine and the waterjet. Additional complications for themarine jet are furthermore the possibility of cavitation and consequent perform-ance degradation, and the presence of an interface between the two media(water and air) in which the vessel operates.

Analogy with aeronautical jet-fuselage interaction

Fuselage interference effects on jet performance are of prime importance foraircraft designed for supersonic speeds. Due to the close interrelation betweenfuselage and jet engine in the case of flush intakes, the jet system design isclosely integrated in the whole aircraft design process (Ferri [1972]).

To the knowledge of the author, there are no parametric models available toquantify jet-fuselage interaction effects for airplanes. Taking into account thebroad attention that is paid to the jet-fuselage integration in the design process,and the requirement for uniform flow ingestion, the need for such a descriptionmay not be so evident.

Due to the marked differences in processes taking place in the marine jet andthe aeronautical jet, as discussed in this section, aerodynamic publications havea limited significance as far as the marine jet is concerned. Nevertheless, sorneuseful information can be obtained from this discipline. The work of Mossmanet al. [1948] on flush type intakes may in this respect serve as a classicalexample.

1.6 Review of previous work

A large number of publications dealing with the hydrodynamics or aerodynam-ics of jet propulsion has been published since jet propulsion started to raiseinterest. Because the interest was first excited in aeronautics, the first publica-tions have an aeronautical origin. As concluded in Section 1.5, these publica-tions have only a limited significance for the present work.

Waterjet technology has in the past particularly been pushed in Germany, Italy,New Zealand, the United States and Sweden. These countries have providedalso most of the available literature.

This review of previous work is split up into a review of parametric models,experimental procedures and numerical procedures.

22

1.6.1 Parametric models

For a meaningful set up of procedures and interpretation of the experimentaland numerical information, parametric models are indispensable.

Description of parametric models

A parametric model is a special form of a more generic theoretical model. Atheoretical model is a set of symbols and relations, describing both the elementsand the processes occurring in the systems considered. The Navier-Stokesequations are generally considered as a basic theoretical model governing allflows that may be described as a continuum. These equations can be written ina differential form, describing the equations of motion for an infinitesimalvolume, or in its integral form, describing the equations of motion for a certaincontrol volume (Fig. 1.9).

Newton's second law as applied to fluid mechanics

Differential equation (Flow field) analysis Integral analysis

Non-viscous flow Viscous flow

Navier-Stokes equations

Differential form Integral form

parametric model

1

CFD applications

Fig. 1.9 Place and relevance of a parametric model in fluid dynamics

A parametric model of these equations can be extracted from the integral formfor a simplified description of specific processes. This is done by substitutingparametric expressions for integral expressions. Such a model is useful to gaininsight in the relevant physics for a given process. It furthermore allows for anefficient storage of data on the process, consequently allowing for empirical

1 .6 Review of previous work

Insight in relevant physicsStorage of data for empirical useAnalysis of model tests

23


approaches. A third application of such a model is the analysis of data obtainedfrom model tests.

Organization of review

As can be inferred from Fig. 1. 1, a complete description of interaction phenom-ena is only obtained after the subsystems involved are completely defined. Thisincludes their relations with the undisturbed environment.

This condition is considered to be satisfied for the powering characteristics ofthe hull system. The hull's resistance has been studied for many decades now.An example of a detailed analysis of the hull's resistance is given by Paffett[1972]. Model test procedures for measurement of the hull's resistance are welldefined (see e.g. HSMV report of ITTC [1987]).

The definition of the powering characteristics of the waterjet system in anundisturbed environment is more complicated however. This is illustrated by theconfusion that exists in the literature about the control volume defining thewaterjet system and the corresponding intake drag of flush waterjet systems.This consequently results in confusion about the defined gross thrust (eq. 1.1)and the actual net thrust that is available to propel the hull.

Interaction is originated at the boundaries of the system and appears as achange of powering characteristics. A change in environment results in achange in stress distribution on, and changes in mass, momentum and energyfluxes through its boundaries. The attention related to interaction on waterjetperformance will therefore be discussed first in terms of definitions of controlvolume and free stream characteristics, and subsequently in terms of changes instresses and fluxes due to the hull action.

Although there seems to be little specific interest in jet-hull interaction in theliterature, the subject is addressed several times as part of an overall perform-ance description. Within the themes mentioned in the preceding paragraph, theliterature is reviewed in temporal sequence.

In reviewing the work that has been done on parametric models, we will con-centrate on jet-hull interaction for flush intakes, in line with the rest of thiswork. Subsequently, due attention will be paid to jet-hull interaction for ramintake systems. We will close the review on parametric models with a consider-ation of an original contribution by Schmiechen to the field of propulsor-hullinteraction.

24

Flush waterjet system

Definition of jet system and free stream powering characteristics

The generally quoted waterjet gross thrust T is usually defined as the force thatresults from the change in momentum fiu through a certain control volume(eq. 1.1). The selected control volume also determines the difference betweendefined gross thrust and actual net thrust exerted by the jet upon the hull. Alogical first step in defining jet system characteristics therefore seems to be anexplicit definition of this control volume. Such a definition has long beenmissing in literature however.

Early parametric models for the description of waterjet performance are givenby e.g. Brandau [1967], Kruppa et al. [1968] and Gao et al. [1969]. Emphasisin these theoretical models is put on the description of powering characteristicsof the jet system in free stream conditions. Explicit definitions of control vol-umes are omitted, but implicit reference is made to a control volume with anintake area infinitely far upstream (control volume A in Fig. 1.10).

To the knowledge of the author, Bowen [1971] was the first author in the mar-ine field, to bring about a discussion on the control volume that should beconsidered as a model of the jet system with flush intake. He discusses thedifference between a generally applied definition of gross thrust and the actualthrust acting upon the hull. Analogous to the practice in the aeronautical field(Jakobsson [1951]), he designates the difference between these definitions as a'pre-entry thrust', and derives an estimate of this thrust contribution for raminlets. Bowen thereby also applies Control Volume A (Fig. 1.10) for thedescription of the jet system.

An early parametric model including an explicit definition of the waterjetcontrol volume is presented by Etter et al. [1980]. The definition of their con-trol volume corresponds to volume C (Fig. 1.10). The free stream characteristicsof the waterjet system are not elaborated. The emphasis is placed on a separ-ation of jet system net thrust and hull resistance.

The discrepancy between jet system gross thrust and the bare hull resistance isexpressed in an inlet system drag. This intake drag is derived from model testswith a self propelled model, and therefore also incorporates a change in hullresistance due to the jet action.

in a recent publication by Allison [1993], a complete review of existing rela-tions to describe waterjet performance is given, including a review of interac-


25


tion effects. Implicit use is made of control volume A (Fig. 1.10). Allisonincludes an inlet drag allowance in the jet efficiency, to allow for the differencebetween gross and net thrust, but omits a definition. He mentions that this termtends to zero for truly flush intakes.

26

pump

X4

fixed (material) boundaries

A = intake leading edge (imaginary)= ramp tangency point

I'BC = lower dividing streamlineC = stagnation pointD = intake trailing edge or outer lip tangency pointEE intake throat area

Possible waterjet control volumes:

CV A : II'CFF'ICV B : A'FF'ACVC : A'B'CFF'A'

Fig. 1.10 Definitions of jet system's control volume used in the literature (see also fold-outat the back)

Intake drag

Many authors refer to the difference between defined gross thrust and a netthrust acting upon the hull as an intake drag. Although the intake drag is

yz

/y

/AA //

r ///

B' B

variable (imaginary) boundaries in the flow


addressed several times (e.g. Mossman et al. [1948], Arcand et al. [1968],Hoshino et al. [19841), little attention is paid to its definition. An exception tothis rule is the contribution by Etter et al. [1980], as discussed in the previoussection.

Mossman and Randall [1948] determine the intake drag for a number of flushtype intakes in a wind tunnel. They implicitly use control volume A (Fig. 1.10).It will be shown in Section 4.1.2 however, that their intake drag consequentlyincludes a significant frictional drag contribution of the tunnel wall in front ofthe intake.

Arcand and Comolli [1968] use the same definition in their data reduction.They state however that they believe that a better definition of the 'real externaldrag' of the intake is possible. Although their idea is not elaborated in detail, itcan be inferred that their improved definition gets rid of the major part of thetunnel wall contribution.

Hoshino and Baba [19841 define the intake drag as the difference between grossthrust required to propel the ship and its bare hull resistance. This intake dragconsequently not only accounts for a discrepancy between gross and net thrustfor the jet system, but also for a change in hull drag due to the jet action. Theauthors implicitly use Control Volume A (Fig. 1.10) for the definition of grossthrust.

Confusion about external intake drag and internal jet system forces is illustratedby statements in Okamoto et al. [1993] and Kim et al. [1994]. Okamoto et al.state that 'the intake duct shows a thrust generation mechanism' for certainoperational conditions. Whereas Kim et al. state that 'the pressure distributionalong the intake lip is responsible for additional appendage drag'.

Interaction effects

Effects on thrust and power

Using an equal flow rate through the system as a basis for comparison, bothdistortions in the local velocity distribution and distortions in the local pressuresaffect the ingested and the discharged momentum and energy fluxes through thewaterjet system. These fluxes govern the associated thrust production and thepower requirement respectively.

Only a few publications address the problem of waterjet-hull interaction indetail. The first accounts of interaction effects on waterjet performance relate to

27


the ingestion of boundary layer flow. This flow shows a decelerated velocityrelative to the free stream velocity.

Although the effects of pressure distortions on jet performance are acknowl-edged in an early stage (see e.g. Kruppa [19681), much confusion arises as tohow it should be accounted for in a parametric model, as noticed by Kruppa[1992].

Kruppa et al. [1968] account in their parametric model for the effect of theboundary layer velocity distribution on the ingested momentum and energy flux.The authors introduce momentum and energy wake fractions. The authors notethat, whenever a pressure gradient occurs between the undisturbed free streamand the intake area of the waterjet, these wake fractions should be corrected forpressure terms. The correction for the momentum wake fraction is not elabor-ated however. The difference between gross thrust and bare hull resistance isreferred to as a parasitic drag. This parasitic drag consequently includes a dragcontribution of the intake and a change in hull resistance due to the waterjetaction.

Wilson [1977] gives a detailed account of the state of the art knowledge onwaterjet-hull interaction in that time. The parametric model used by Wilson isbased on schemes presented by Johnson et al. [1972] and Barr [1974]. Theessential relationships are outlined by Miller [1977].

Miller describes waterjet-hull interaction in terms of ingested momentum andenergy velocities, accounting for differences in the respective fluxes relative tothe corresponding free stream fluxes. The effects considered are solely causedby the boundary layer velocity profile. The other interaction parameter isreferred to as an intake drag, being equal to the difference in net thrust andcalculated gross thrust. The intake drag is to be determined experimentally,implying that this drag component not only accounts for a net force acting onthe intake part of the jet, but that it also accounts for a change in hull drag dueto the jet action.

A more complete description of the parametric model by Miller is presented byEtter et al. [1980]. This model is adopted by the High Speed Marine VehicleCommittee of the 18th ITTC [1987]. The model describes the powering per-formance of the combined jet-hull system. without breaking it down in the per-formances of the isolated systems and their mutual interaction. The relationbetween intake drag and a thrust deduction fraction is elaborated.

28


Haglund et al. [1982] express a waterjet-hull interaction efficiency as a hullefficiency, analogous to the same efficiency used in propeller-hull theory. Thesame control volume for the waterjet system is used as described by Etter et al.[19801 (CV C in Fig. 1.10). The effect of the boundary layer velocity profile onmomentum and energy flux is only taken into account by the use of an averagevolumetric intake velocity.

Later, Svensson [1989] includes a pressure term in the jet efficiency, accountingfor the static pressure contribution in the ingested energy flux.

Hoshino et al. [19841 only account for interaction by using a thrust effective-ness (1-t). The authors do not account for the ingested boundary layer flow.

As a further development to the model proposed by Kruppa et al. [1968],Masilge [1991] breaks the distortions in ingested momentum and energy fluxesdown into a pressure contribution and a velocity contribution. The requirementfor a pressure term in the ingested fluxes was also noted and a model suggestedby Van Terwisga [1991].

As a sequel to their 1968 paper, Kruppa [19921 presents a relation for overallefficiency based on thrust (thrust power efficiency), in which he incorporatesthe potential flow and viscous flow interaction effects separately, as proposedearlier by Van Terwisga [1991]. He notes the lack of a pressure term in themomentum equation for thrust and consequently observes that the equations forthrust power efficiency for ram type inlets on the one hand and flush type inletson the other hand are not compatible. Based on this observation, Kruppa queriesa conclusion by Svensson [19891, where the positive effect of a retarded poten-tial flow wake on thrust power efficiency is noted.

Allison [1993] gives a review of interaction effects. Similar to the hull-effi-ciency in propeller-hull interaction, an interaction efficiency is used in theoverall efficiency equation, according to:

(l-t)11=

(1-w)

where t = thrust deduction fractionw = volumetric wake fraction.

lt is emphasized by Allison that this efficiency is not directly comparable to thehull efficiency used in propeller-hull theory. Contrary to the model for propel-

(1.10)

29


1cr-hull interaction, where no interaction terms occur in the propeller efficiency,interaction terms remain present in the efficiency of the jet system.

Effects on lift

Svensson [1989] mentions a net lifting force on the stern of the vessel withactive waterjet. This conclusion was obtained from pressure measurements onthe hull in the vicinity of the waterjet system (see Fig. 1.11). He states that 'thetotal lifting force generated by the inlets can be in excess of 5% of the displace-ment for a high speed craft. The total lifting force can thus exceed the weightof the units. This will be recognized as a negative thrust deduction caused by areduction of the vessels resistance'.

BOTTOM PLATING B = I .5D

BOTTOMPLATING

B= D

30

INLET INLET VELOCITY RATIO (IV R)D = NOMINAL INLET DIAMETERB = BREADTH OF BOTTOM PLATING

Fig. I Il Lifting force due to pressure on the bottom plating and inlet for a KaMeWawaterjet installation (from Svensson [1989])

The issue of lift production caused by waterjet-hull interaction will be treated inChapter 2. It will be shown that the jet system itself does not generate a liftforce, provided the jet is discharged parallel to the hull's bottom.

Determination of ingested momentum and energy fluxes

An important problem in determining interaction effects on the waterjet per-formance, is the assessment of ingested amount of momentum and energy for aflush intake operating in a non-uniform velocity field. For this particular prob-lem, a strong analogy occurs between the flow in and about a flush intake of awaterjet system and the intake of a condenser scoop system.

Spannhake [1951] presents a detailed theoretical analysis of the flow through acondenser scoop system. He defines clear control volumes for both the inlet andthe outlet scoop. He also introduces an expression for the imaginary intake areaof the protruding streamtube (area AB in Fig. 1.10). This expression is based ondata obtained from flow visualisation studies about the intake as published byHewins et al. [1940].

Quantitative experimental information on the shape of this imaginary upstreamintake area for a waterjet is provided by Alexander et al. [1993]. These datawill be reviewed in more detail in Section 4.3.1 of this work.

Interaction effects ou hull performance

Interaction effects on the hull are caused by a change in the flow about the hulldue to the jet action. It can be expressed as a change in the hull resistance. Thischange in resistance is in the literature expressed in a thrust deduction fractionor an intake drag, as discussed in the foregoing. A possible change in lift pro-duction on the hull as mentioned by Svensson [19891 could, if present, also beascribed to interaction.

Several authors, e.g. Hothersall [19921, Allison [1993], Van Terwisga [1992],mention the effect of waterjet weight on the hull performance. The weight ofthe jet system does not affect the hydrodynamic environment for a given hullloading condition, and does therefore not cause a true hydrodynamic interactioneffect. As it does affect the vessel's weight breakdown, one should account forit in the jet selection process.

Interaction in ram type intake jets

Sherman and Lincoln [1969] discuss the optimization of the ram type intake forwaterjet systems in detail. They include clear definitions of the net and grossthrust and the external drag of the jet system. They thereby implicitly considerthe control volume AHFF'H'A' (see Fig. 1.12).


31


nozzleF

strut

The net thrust, available to propel the hull is obtained from the vector summa-tion of gross thrust and external drag:

Tnet Tg+D ext

where Tnet = net thrustTg = gross thrustDext = external drag.

Their gross thrust is defined as:

Tg mnniO+(PnPO)An (1.12)

32

hull

A

F -- .

where = momentum fluxp = pressureA = nozzle areasubscript n = nozzle

O = free stream condition.


This definition grossly corresponds to the basic definition given in eq. (1.1), butis extended with a pressure force term over the nozzle area. It will be demon-strated in Chapter 2 that this term is also present for flush waterjet intakes, butis included in a thrust deduction fraction t there.

The external drag of the system consists of the sum of the external force FEXT,a so-called pre-entry drag DPE and a possible interference drag DINT:

DEXT FEXT+DPE+DINT (1.13)

The external force FEXT acts on the material external part of the waterjet system(AHH'A' in Fig. 1.12). It is obtained from the summation of all pressure andfrictional forces in x-direction, associated with the ram inlet system from thestagnation line around the external surface to the termination of the system.

The pre-entry drag DPE acts on the protruding part of the streamtube ahead ofthe material intake. This is the same component that was introduced in thediscussion on the net thrust of flush type waterjets by Bowen [1971] and dis-cussed in the foregoing. It is caused by external diffusion or contraction of theingested streamtube. As a consequence thereof, a discrepancy occurs betweenthe actual net thrust and the defined gross thrust after the external force FEXTand a possible interference drag DINT have been accounted for.

The interference drag DINT can be interpreted as a drag component accountingfor a change in hull drag due to the presence of the waterjet.

A discussion on the subject of thrust definition and actual net thrust was heldduring the 20th ITTC in and about the Report of the High Speed MarineVehicle Committee {ITTC, 1993].

Because the flow is ingested at a certain distance from the hull, interactionbetween hull and intake is usually small. The hull drag may be affected by thepressure distortion by the intake or by an interference drag due to the strutpiercing through the hull.

Parametric model due to Scizmniechen

An original approach to the propulsor-hull interaction problem is due toSchmiechen [1968, 1970]. He presents a generic system of criteria to evaluatethe powering performance of propulsor-hull systems. He separates thepropulsor-hull system, thereby only providing a definition of the propulsor

33

Chapter 1 introduction

system. A definition of the hull system is not presented explicitly. As a conse-quence, a physical interpretation of the concept of resistance is not clear.

The propulsor system in free stream conditions is defined as an actuator throughwhich the same mass flow rate is flowing and the same power is absorbed asfor this system integrated in the combined propulsor-hull system. A physicalsystem boundary is only described in broad terms. The outlet plane throughwhich mass flow, momentum and energy fluxes are discharged, is situated inthe far field for both the isolated and the integrated propulsor system. Theintake boundary is not clearly defined in geometrical terms, but is to be solvedfor any particular case.

His definitions of efficiency that are introduced are not directly related to aneffective/absorbed power ratio. The concepts of power that are introduced dofurthermore not all have a physical interpretation, as momentum and energyfluxes are used indifferently. If one allows for this new-speak, it is probablypossible to use these definitions in a system of relations that is consistent initself.

Conclusions

It is concluded from the review of parametric models, that there is no modelavailable that explicitly and completely accounts for waterjet-hull interactionwith flush type intake. The usefulness of such a model is illustrated by thegenerally accepted parametric model for propeller-hull interaction, as discussedin Section 1.5.1.

Probably due to the absence of explicit relations for waterjet-hull interaction,there is widespread confusion about the effect of interaction between a flushtype waterjet and its supporting hull. This confusion becomes apparent in theuse of intake drag, thrust deduction, lift production and interaction effects onwaterjet performance.

1.6.2 Experimental procedures

An analysis of model tests with a self propelled model provides quantitativeinformation on interaction. Such an analysis involves a comparison of theresults of the combined system with measured or computed properties of theconstituting systems, viz, hull and waterjet(s). The work reviewed here concen-trates on procedures for propulsion tests.

Bare hull resistance tests are conducted by a wide variety of towing tanks and

34

various procedures have been published (see e.g. Reports of the ITTC Resis-tance Committee or the High Speed Marine Vehicle Committee).

Performance tests of isolated waterjet systems are less common. Although thislatter type of tests is not considered to be part of this work, it is addressedshortly in this section for the sake of completeness. This deliberate thrift isjustified by the fact that jet manufacturers have usually done extensive compu-tations and measurements on their designs.

Propulsion tests

The High Speed Marine Vehicle (HSMV) Committee of the 18th ITTC [1987]provides a procedure for propulsion tests with waterjets. This procedure isbased on the measurement of flow rate and the subsequent reduction of momen-tum and energy fluxes in and out of the jet system contained by the hull. Theprocedure is schematically presented in Fig. 1.13 and is outlined below.

The HSMV Committee states that the ship model should be equipped withscaled waterjet inlet and nozzle systems. They emphasize the needlessness ofgeometric scaling of the jet systems pump. A pump able to provide the requiredflow rate through the inlet and nozzle system is sufficient. This approach couldbe referred to as a 'black box' approach, as the precise characteristics of thepump are not relevant.

The HSMV Committee furthermore emphasizes the importance of an accurateflow rate measurement as the basis for meaningful thrust and power values.Apart from flow rate measurements, the ingested velocity profile ahead of theintake opening should be measured or estimated. This information is essential toderive ingested momentum and energy fluxes from the measured flow rate.Thrust and power data can subsequently be obtained from these fluxes.

In addition to flow rate transducers, the committee states that the model shouldalso be equipped for measurements of impeller thrust, torque, rate of revol-utions, and hull towing force and running trim.

The Committee recommends a sequence of two similar tests after calibration ofthe flow rate transducers. In the first series of tests, the required flow rateshould be measured at the pump rate of revolutions causing a residual towingforce to the model equal to the calculated one. This force can be calculatedwith e.g. the procedure presented by Savitsky et al. [19811. In the second series,at pre-set model speed and impeller rotation rate, the velocity profile ahead ofthe intake should be measured with the Prandtl tube rake.


35


E

36

EXPERIMENT

Q-calibration

Propulsion test i

Propulsion test 2

1

Jet system tests

DATA PROCESSING RESULTS

Data reductionmethod

Extrapol. method

Matching prop& jet system data

- VREF

VREF - VM

u(z) - VM

T(VM), 's (Vs)

T(V), JSE (Vs)

KH KM as f(KQ)

'ir. (Vs), n(V5)

Fig. I .1 3 Basic propulsion test procedure as recommended by the 18th ITTC


In contrast with this 'black box' approach, there are a few accounts of propul-sion tests with completely scaled waterjet units. Mavlyudov et al. [1975] andLazarov et al. [1987] report of propulsion tests where the jet system wasmounted rigidly within the hull. A set-up which does not allow for a separatethrust measurement of the jet-unit through force transducers. This set-up issupposed to allow for a measurement of required power on the pump impellerthat can directly be extrapolated to full scale.

Mavlyudov et al. [1975] determine the discharged momentum fluxes from thenozzle and the intake through total pressure measurements with pitot rakes inthe respective areas. An effective nozzle area is determined from a bollard pulltest, where both the pulling force and the average velocity through the nozzleare measured.

In an alternative experimental set-up, forces between the jet unit and the hullare passed through by force transducers. All other connections between the jetunit and the hull are made flexible, so as to prevent them from passing throughany forces or moments. Such attempts are reported to have been pursued byMARIN (ITTC [1987]) and Bassin d'Essais des Carènes (ITTC [1993]). A fullscale experiment with this set-up is reported by Coop et al. [1992].

Flow rate measurements

Haglund et al. [1982] report on tests of a waterjet mounted on top of acavitation tunnel and on full scale tests. They measured the local velocitydistribution in front of the impeller disk (no impeller present). The flow ratewas subsequently found from integration over the gauged cross section. As acheck on this procedure, static pressures were also measured between the nozzlearea and the stator. By applying the continuity equation and Bernoulli's theorembetween the measuring section and the nozzle outlet, the flow rate could becalculated. The two methods were reported to give practically the same result.

Hoshino et al. [1984] consider three ways of flow rate measurement:

The discharged flow rate from the nozzle is collected over a certain timeinterval, and the weight of water over this time interval is measured.These measurements provide a mass and, after accounting for specificmass, a volume flow rate.

2. Measurement of the jet velocity distribution through a pitot rake. Afterintegration of the velocity field over the nozzle area a flow rate isobtained. This method is comparable to the one applied by Haglund et al.11982].

37

Chapter i Introduction

3. Direct measurement of the discharged momentum flux from the nozzle bymeasurement of a reaction force on a so-called reaction elbow. Thisprocedure has been evaluated for a specific test set up by Eilers et al.[1977].

The authors selected procedure i because of its simplicity and accuracy ofmeasurement. A sketch of the test set-up is shown in Fig. 1.14.

Towing Carriage

38

Craft Model

Guidea

Propeller

Jet

Rudder

Flow Measurement Tank

Fig. 1.14 Test set-up for flow rate measurement: water collecting tank (from Hoshima et al.[19841)

As a check, they also conducted a bollard pull test at zero forward speed andcompared the measured pulling force with the computed thrust. The results ofthis comparison are presented in Fig. 1.15. Although computed and measuredthrust are within 2% for one model, they differ some 20% for the other model.This discrepancy is ascribed to a scatter in the discharged jetfiow. The discrep-ancy between thrust derived from the flow rate measurements and the directlymeasured thrust was accounted for by the introduction of an effective nozzlearea in the thrust derived from flow rate measurements.

The HSMV Committee of the 18th ITTC [19871 also mentions three techniquesfor flow rate measurements:

1. Determination of an average nozzle velocity through venturi pressure tapsin the nozzle.

Measurement of flow rate through paddle wheels or turbine flow ratetransducers in the outlet nozzle.Weighing the discharged flow from the nozzle that is collected in a tankbehind the model over a certain time interval.

10

-4

=5LL

0 5 10

et = PQÜn [kgf]

Fig. 1 .15 Comparison of thrust derived from flow rate measurement and directly measuredthrust at bollard pull test (Hoshino et al. [1984])

Method 3, where a collecting tank is used, is reported to be an accurate method.It is however only a suitable method if the nozzle is sufficiently free from thewater, so as to avoid a distortion of the water collecting gear on the flow aboutthe ship model. This implies that this method is not suitable for low speeds orfor arrangements where the water is leaving the nozzle at or below the watersurface.

It is suggested by Rönnquist Il983I1 to apply a convenient combination of acalibration of flow rate transducers at speed zero with a water collecting tank,and an actual flow rate measurement with these calibrated transducers duringthe propulsion test. It is suggested that either venturi pressure taps or paddlewheels be used for this procedure.

The HSMV Committee of the 20th ITTC [19931 mentions that 'major diffi-culties are experienced in flow rate measurements during self propulsion testswith waterjets'.


39


Flow rate measurements at SSPA (Swedish Model Basin) are reported to consistof flow rate calibrations at speed zero (Allenström [1990]). The flow rate cali-bration is conducted by weighing the collected water over a certain time inter-val. This measured flow rate is calibrated with pressure taps in the nozzle and apaddle wheel imbedded in the wall of the nozzle. During the actual self propul-sion tests, the calibrated relation from speed zero is used to derive actual flowrates.

Flow rate measurements at MARINTEK (Norwegian Model Basin) are alsobased on calibrations using a water collecting tank (Aarsnes [1991]). Themeasured flow rate is calibrated with three pitot tubes, situated in the intake andyielding an average local velocity. This local velocity was found to be moresuitable for reference purposes than impeller rotation rate. Calibration betweenflow rate and these pitot signals is conducted for a range of speeds and impellerrotation rates, so that the actual propulsion test condition is covered. This wasdeemed necessary as deviations in the calibrated relation appeared for differentspeeds and impeller rates. After the calibration has been finished, free runningpropulsion tests are conducted.

The HSMV Committee flotes the difficulty in assessing the ingested momentumand energy fluxes when a clear three-dimensional flow about the intake isexperienced. Such a flow condition is likely to occur if the intake is situated inlarge deadrise bottoms of e.g. SES or catamarans.

In their contribution to the workshop on waterjets of the 20th ITTC, Hoshino etal. [19931 present a number of procedures applied during several propulsiontests conducted in Japan. Apart from techniques that have already been men-tioned in the foregoing, he gives an account of propulsion tests on a ram typeintake. Apart from a venturi type velocity transducer, working over two distinctcross sections in the nozzle, the reaction force acting on a wedge situated in thedischarged jet was measured (Fig. 1.16). The relation between the reaction forceand the waterjet thrust had been calibrated at bollard pull condition. The authorsstate that the agreement in derived thrust from both measurements was good.

The difficulty of a good flow rate measurement is clearly illustrated by thelarge number of different flow rate measuring procedures. Up until the time thisreview was prepared, there does not seem to be consent over a robust andvalidated flow rate measurement technique.

40

Lifter

Towing Carriage

L:i1r-


Inlet

Fig. 1. 16 Arrangement of venturi type velocity transducer and reaction force transducer for apod-strut with a waterjet system (Hoshino et al. [1993])

Extrapolation method

Having addressed the issue of propulsion test procedures, the issue of extrapo-lating the model powering data to full scale values remains. The power demandby the waterjets is most logically obtained from the effective power demand bythe full scale hull, the full scale jet powering characteristics and the full scaleinteraction effects. The corresponding powering data obtained from the modelcould be scaled with Froude's scaling principle, provided no scale effects werepresent. This procedure warrants dynamic similitude between gravitation andinertia forces.

The HSMV Committee of the 18th ITTC [19871 considers two scale effectsimportant. One relates to the difference in frictional resistance, which isaccounted for by an additional towing force during the propulsion test. A sec-ond scale effect relates to the difference in ingested boundary layer. The fullscale boundary layer thickness and velocity distribution should be obtained fromcomputations to allow for this difference.

The difference in bare hull resistance and measured thrust, accounted for by thethrust deduction fraction, is assumed to be free of scale effects and thus retainsthe same value for both model and full scale.

41

I L-

Load Cell Pressure Gauges Dummy Hull

Waterj' / /P pump Motor

Wedge Load Cell


From the above assumption, the full scale thrust can be obtained from themeasured thrust on model scale. With an extrapolated boundary layer velocityprofile just ahead of the waterjet intakes, the flow rate can be determined that isrequired to generate this full scale thrust. Once the flow rate and the full scalejet system and interaction characteristics are known, the required pump headcan be determined. Flow rate and pump head subsequently determine the work-ing point of the pump, and with that, the efficiency and power requirement.

Jet system tests

The HSMV Committee of the 18th ITTC [1987] provides two different testingtechniques to determine the powering characteristics of the jet system.

The first one is a procedure where the jet characteristics are obtained frompropulsion tests with a waterjet-hull model. The hull can either be a model ofthe actual hull or a model of a specific test boat. For this purpose, all compo-nents of the jet system incorporated in the hull need to be scaled geometrically.This is in contrast with the black box approach, where only overall or interac-tion effects are studied.

Basic measurements for the determination of the jet system's powering charac-teristics are the flow rate, impeller torque and rotation rate. For a proper reduc-tion of the jet system's free stream characteristics, it is essential to know thevelocity profile ahead of the intake. Although not mentioned by the ITTC[1987], interaction effects should be accounted for in the derivation of themeasured results to free stream characteristics.

The second procedure consists of tests on the isolated waterjet system in awater or cavitation tunnel. This set-up has the advantage that free stream condi-tions are approached, so that corrections for jet-hull interaction or jet-set-upinteraction are small, and consequently so for the corresponding errors.

Conclusions

It is concluded from the review on experimental procedures that a broad pro-cedure for self propulsion tests with waterjet propelled models is proposed bythe ITTC [1987]. Within this procedure there is uncertainty about:

- robust and accurate flow rate measurement procedures;- the relation between flow rate and ingested momentum and energy flux,

and thus thrust and power;- assumptions in the extrapolation method, especially with regard to the

42

absence of scale effects in the thrust deduction fraction;- isolation of waterjet-hull interaction effects.

The latter uncertainty has been treated in the previous section.

1.6.3 Computational procedures

Similar to the objective of experimental procedures, computational proceduresseek to quantify interaction effects. In addition to propulsion tests, where inte-gral quantities are obtained, computational methods provide a detailed insight inthe flow phenomena. Often this latter aspect is worth the trouble of goingthrough all the work, despite the sometimes doubtful quantitative results.

This review will first address the CFD work related to the analysis of thewaterjet's free stream characteristics, which is addressed by the majority of theliterature. Secondly, the literature dealing with a prediction of waterjet-hullinteraction effects is discussed.

Free stream intake characteristics

Most publications on a computational analysis of the free stream characteristicsaddress the performance of the intake. Initially, attention has been focused on aprediction of the pressure distribution along the intake ramp and the intake lip.This information is relevant for a prediction on the occurrence of cavitation,which may occur in the initial part of the intake. Nowadays, now that fullRANS codes are available, attention is extended to the prediction of boundarylayer separation, which may occur at the intake ramp, and the prediction ofviscous energy losses and flow field at the pump inlet. A review of the relevantpublications is given in this section, in an order of increasing complexity andpotential resemblance with reality.

One of the first publications providing computed streamlines in the intakeregion is due to Kruppa et al. [19681. These authors compute the flowlines near2D scoop and flush intakes through a conformal mapping procedure. Thisprocedure allows for a limited number of mathematically defined intakegeometries.

Kashiwadani [1985, 19861 presents well documented results on a potential panelcode for 2D intake geometries. The purpose of his work is to analyze andoptimize the initial part of the waterjet intake (ramp and lip) for cavitation freeoperation at high speeds. The author has developed a potential flow code wherea continuous description of the geometry of the intake is obtained with a rda-


43


lively small number of points. In this respect, his method differs from the workof Hess and Smith [1966] and Ishikawa [1983]. The limited number of inputpoints was desired for geometry optimization.

The continuous surface description was desired for a continuous and accuratepressure computation on the jet surface. The original method by Hess andSmith has been demonstrated to be less accurate for internal flows, such asoccur in the waterjet intake (Hess [1975]). The original method applies a sur-face description by a distribution of quadrilateral panels. Each panel uses aconstant source strength distribution over its surface. The boundary conditionsare imposed in the so-called null point of each element. This point is taken asthe point where the element itself has no effect on the tangential velocity. Thevelocities are computed only in these null points and velocities at other posi-tions on the surface are obtained from interpolation in the known null points.

Kashiwadani [1985] uses a 2D integral equation to describe the source distribu-tion over the material boundaries. The flow velocity vector iZ(x,y) is then givenby the following equation:

r(x,y) = U T-_ +Jf(s)L ds (1.14)

2m

where s = girth length along the boundary C (see Fig. 1.17)= position vector from (x,y) to point on boundary C= position vector from (x,y) to suction source with strength Q

i = unit vector in x-direction.

C

44

-U

Fig. 1.17 Nomenclature and definitions in waterjet model used by Kashiwadani [19851)


Although the method compares good with an exact solution and with the resultsfrom Ishikawa [1983], a rather poor correlation with experimental results from awind tunnel set-up is reported. Wind tunnel tests with a model having an aspectratio of the intake throat of w(h=2 (compared to for the 2D computations)were conducted. The differences in pressure distribution are considered to becaused by 3D effects during the experiments and by viscosity effects, not pres-ent in the potential flow computations. The discrepancies within the intake arefurthermore more significant than those just outside the intake. The supposedlarge effects of viscosity and 3D flow are enforced by the infinitely small lipradius of the tested model.

In a second report, Kashiwadani [19861 optimized the 2D intake on a maximuminception speed criterion. The optimized geometry showed a more rounded lip.This optimized geometry was again tested in a wind tunnel set-up, where alarge number of static pressures was measured along the centreline of theintake. The correspondence between measured and computed pressures justoutside the intake area appeared to be good, whereas correspondence within theducting was poor again, except for the trends. The difference in C value withinthe ducting appeared to be similar for both cases (approx. 0.7). The effect ofthree-dimensionality of the flow was checked by sparse pressure transducers offthe centreline. These transducers showed similar signals to the centreline oneshowever. The aspect ratio of the duct w/h was approx. 3 this time.

Førde et al. [1991] attempt to compute the flow field in the intake and thepertinent energy losses. They solve the Euler equations with a code suitable forboth internal and external compressible flows. The time dependent Euler equa-tions are solved by a time marching method. Grid generation is done by a multiblock transfinite algebraic method. A geometry generation procedure has beendeveloped by the authors, based on a simple description by three characteristiccontour lines. A surface is subsequently modelled between the defined linesusing Bezier surfaces.

In an attempt to compute the viscous losses in the intake as well, a thin layerNavier-Stokes code has been used. No further description of this method isgiven however. In their discussion on results, the authors conclude that the gridthat was used is probably too coarse to give a representative computation of theviscous losses. The analysis of results is partly biased by a misconception onthe ingested momentum by the intake. The authors correct the ingested momen-tum for the angle of the mean ingested flow vector. It will be shown in Chapter2 however, that there is no loss in momentum associated with the angle underwhich the flow is ingested for a flush type intake.

45


Pylkkänen [1994] has analyzed a 2D intake with a RANS solver (FLOW3D).His main purpose was to find out whether the flow in the intake would cavitateor whether separation would occur. He verified whether a satisfactory solutionin the 2D domain was obtained by checking the computed results with windtunnel measurements on 2 intake geometries. He found deviations in staticpressure between computations and measurements from 2 to 15% on the rampand on the lip. The agreement on the ramp was generally better than on the lipsurfaces. The measured top speeds at the impeller plane were further l-11%higher than predicted by the 2D calculations. Pylkkänen presumed that thedeviations were caused by the typical 3D flow ingestion, which is not modelledin the 2D computations. He further presumes that the impeller shaft should bemodelled in order to find reliable predictions.

The reported deviations in the internal pressure coefficient Gp as obtained fromthe viscous computations by Pylkkänen, are significantly better than the devi-ations obtained from the 2D potential computations by Kashiwadani. This indi-cates that the neglect of viscous effects has a bigger effect on the results (on thecentreline intake) than the 2D modelling of the reality.

Waterjet-hull interaction

Kim et al. 111994] perform potential flow computations on a waterjet-hull com-bination. Their objective is to determine the pressure distribution and cavitationinception characteristics in the intake. To this end, the authors consider a math-ematical hull form and an intake built up from cylindrical sections. The freesurface boundary condition is approximated by its high speed limit:

46

where = perturbation potential function.

Special attention has been paid to an accurate representation of the geometry bythe use of higher order boundary elements. These elements use cubic splineinterpolation functions for the source distribution over each panel.

The authors conclude that the pressure distribution is strongly affected by theship's hull. They furthermore conclude that the pressure distribution along theramp centreline is more critical to cavitation inception than along the lip. Theystate that the pressure distribution along the lip is directly responsible for addi-tional appendage drag.

on z=O (1.15)


Their conclusion about the importance of the ship's hull on the intake's pres-sure distribution is likely to be caused by either the mathematical hull form, notrepresentative for realistic hulls, or by the computational method. From experi-ments at MARIN, changes in velocity near the intake due to the hull appear toreach maximum values of approx. 5%, whereas the authors show a value of14% at the nose of the intake ramp (ramp tangency point), increasing to adifference of 22% with free stream velocities further along the ramp.

Their conclusion about the effect of the lip's pressure distribution on appendagedrag is incorrect as will be discussed in Chapters 2 and 4.

Latorre et al. [1995] study the intake flow from a waterjet-hull combination.They consider the effect of trim on intake pressure distribution and cavitationinception by using a 2D RANS code, described by Miyata [1988]. The authorsfound a significant reduction in the minimum C (approx. 0.4) on the internalpart of the intake lip due to a change in trim by the hull.

The paper suggests that the distance from the keel to the lower boundary of thecomputational domain is only some 20% of the hull's length. This, togetherwith the 2D approach and the relatively short length of the hull in front of theintake is likely to cause significant deviations from representative 'real world'conditions. The authors furthermore conclude a significant influence on intakeefficiency, which is not justifiable from the presented results.

Okamoto et al. [19931 present pressure measurements in the intake of a jet-hullmodel, measured during propulsion tests. Although these data cannot be inter-preted to overall performance, as is done by the authors, they may serve apurpose in the validation of CFD results.

Conclusions

It is concluded from the review on computational procedures, that most of thecomputational work is directed towards intake flow analysis. Aspects of interestare the viscous energy losses, the flow field at the pump inlet and the detectionof cavitation inception. A few attempts are reported that deal with waterjet-hullinteraction. The conclusions drawn from these computations are not in agree-ment with the experience and insight that is obtained from the present workhowever.

47


1.7 Summary of present work

When starting an investigation into a rather abstract physical phenomenon, suchas waterjet-hull interaction, one first needs to search for tools. A theoreticalmodel providing a description of a phenomenon can in this respect be regardedas an essential tool. Other tools that are considered essential are experimentaland computational procedures.

To illustrate the strong interrelation between a theoretical model and an experi-mental procedure, we consider the following approach for an investigation. Onecould, for example, start observing by experimenting. From these observations alot can be leaint about the adequacy of an available physical or theoreticalmodel. After a subsequent evaluation of experimental results one may have toadapt the theoretical model, and after having done this, one may be forced torevise the experimental procedure. It is this iterative way of working that hasbeen gone throughout the present work. For the readers tranquillity of mind, heor she will not be teased with a presentation of this work in a similar whimsicalway.

After having done the first propulsion tests with waterjet propelled models,three conclusions gradually emanated. One conclusion referred to the difficultyof the experimental procedure required to measure the powering characteristicsof a waterjet propelled model. A second conclusion referred to the absence of atheoretical model, fully and explicitly expressing the interaction effects. Andfinally as a third conclusion, interaction appeared to be able to affect therequired power with well over 20%.

1.7.1 Theoretical model

Because of the observed lack of a theoretical model describing all possibleinteraction effects on hull resistance, jet system thrust, power required and thusoverall efficiency, such a model is discussed first. Perhaps the main differencebetween this model and previously published models is that waterjet-hull inter-action effects are accounted for completely and explicitly. As part of the model,a clear definition of the jet system's free stream conditions is proposed, togetherwith a definition of the bare hull powering characteristics. These definitions linkup with those proposed by the High Speed Marine Vehicle Committee of the18th ITTC [198711.

In the proposed theoretical model, the difference between waterjet gross thrustand net thrust is accounted for by a true thrust deduction fraction t1, which is aproperty of the jet's free stream characteristics. This thrust deduction fraction is

48

thus not an interaction parameter, contrary to the generally applied definition ofthrust deduction in propeller-hull theory. The thrust deduction fraction as intro-duced here, may be subject to interaction effects itself. The change in hullresistance due to the jet action is captured in a so-called resistance incrementfraction r.

The flow that is ingested by the intake and sometimes the flow that is dis-charged from the nozzle area, is affected by the presence of the hull. Thesedistorted flow effects are accounted for by so-called momentum and energyinteraction efficiencies. These efficiencies account for the effect that is causedby distorted ambient velocities and pressures on momentum and energy fluxes,relative to those in the free stream condition.

Explicit relations for the thrust deduction fraction, resistance increment fractionand momentum and energy intake efficiencies are derived from integral con-siderations of the conservation laws of momentum and energy. Consistentrelations are derived for the free stream characteristics of the jet system.

1.7.2 Experimental procedure

Having constructed a theoretical framework, quantification of the relevantparameters is a logical next step. Before starting a detailed analysis of allpossible contributions, it is preferable to obtain quantitative information on themajor parameters, indicating the overall significance of interaction. This overallquantification of interaction is obtained from model propulsion tests.

Despite the well developed procedures for propulsion tests with propeller pro-pulsion, such procedures cannot be applied for waterjet propelled models. Themain reason for this set-back is the close integration between waterjet and hullsystem. The forces on the impeller of the jet only partly account for the power-ing characteristics of the complete jet system. Forces are also passed through tothe hull by the ducting and pumphousing. The delivered power by the impelleris furthermore only representative for the prototype delivered power if a com-pletely scaled jet system has been used in the model tests. In addition, such amodel jet would need to be sufficiently large to avoid uncontrollable scaleeffects.

During propulsion tests with waterjet propulsors, a geometrically scaled hullmodel with a model stock jet having geometrically scaled intake and nozzleopenings proceeds at a scaled speed through the model basin. As will be dis-cussed in Chapter 3, the most effective way to measure powering characteristicsof a waterjet system is to measure volumetric, momentum and energy fluxes

1 .7 Summary of present work

49


through intake and nozzle areas. This requires a highly accurate method for themeasurement of flow rate through the waterjet model.

A satisfactory technique to do this is searched for and various options experi-mentally evaluated. One method, using a built-in averaging static pitot tube wasselected as most reliable and accurate transducer for flow rate measurements. Adiscussion on accuracy and reliability of the methods considered is presented inChapter 3.

Three sources for scale effects can be acknowledged when extrapolating modelpropulsion tests. One source for scale effects is the hull's resistance. The othersource is embedded in the powering characteristics of the model jet system. Athird source is formed by the interaction effects between jet system and hull.

As for the extrapolation of the hull performance, a wealth of information andprocedures is available to make satisfactory assessments of possible scaleeffects. Therefore no specific attention will be paid to this subject in the presentwork.

After more knowledge on the jet system free stream characteristics and thewaterjet-hull interaction mechanism became available during the project, abetter assessment of possible scale effects came into reach. This knowledge isreworked in both the experimental and extrapolation procedure. The proposedITTC procedure for propulsion tests (ITTC [19871) is hereby used as a startingpoint. The assumptions in this model are checked and procedures are elaboratedin more detail.

In addition to an extensive discussion on the experimental procedures con-sidered, some quantitative results from the propulsion tests are discussed. Thisdiscussion serving the purpose of directing further research.

1.7.3 Computational analysis

Three incentives for a detailed computational flow analysis grew during thestudy. These incentives are:

- The requirement for a detailed insight in the jet system free stream char-acteristics.

- The urge to assess the validity of computational procedures for a deter-mination of the overall powering characteristics and separate interactioneffects.

50

1.7 Summary of present work

- The necessity to study the validity of initial simplifications and assump-tions that are made in the propulsion test procedure.

Insight in the jet system free stream characteristics is needed to identify andquantify possible sources for interaction. It is also required to investigate thevalidity of assumptions in the extrapolation procedure proposed by the ITTC[19871.

A potential flow panel code for the analysis of non-viscous flows is used tostudy the flow in the intake region. A validation study was conducted usingdetailed flow measurements on a flush intake in the MARIN large cavitationtunnel. From this validation study, it appears that for an important range ofworking conditions, a satisfactory prediction of the flow just outside the intakecan be obtained. The results are also used in an assessment of the jet's thrustdeduction fraction t1. The computed results are furthermore used to gain knowl-edge about the virtual intake area of the chosen control volume.

A potential flow code incorporating linearized free surface effects, is used tostudy the effect of flow ingestion by the intake on the equilibrium position andthe pressure drag of the hull. For the higher speed region, a modified Savitskymethod is used for this purpose.

For the reduction of thrust, power and efficiency, from propulsion tests,assumptions need to be made with regard to the relation between volume flowrate and ingested momentum and energy fluxes. For such relations and for abetter understanding of the relation between gross and net thrust of the jetsystem, a detailed study of the flow in and around the flush intake is conducted.

51

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Chapter 2

2 Theoretical model2.1 Systems decomposition

In analysing complex systems, but also in designing them, decomposing thetotal system leads to a better insight in the performance of the constitutingsystems. In decomposing a complex overall problem into smaller partial prob-lems, mutual constraints between the partial problems have to be acknowledged,so as to guarantee a proper functioning of the overall system.

For the present case, the waterjet-hull system is decomposed into a bare hulland a waterjet system. The bare hull is equal to the hull of the combined sys-tem with the exception that the waterjet is not present. The weight and theposition of the centre of gravity however correspond to those of the combinedsystem in operation. The weight of the hull thus includes the jet system'sweight including entrained water. This definition corresponds to the proposedITTC procedure for model propulsion tests (ITTC [19871).

The waterjet system can be subdivided into a pump system and a ductingsystem. The pump system is the driving heart of the waterjet, converting mech-anical power into hydraulic power. The ducting system leads the required flowrate from the external tiow to and from the pump again into the environment.

53

Chapter 2 Theoretical model

The pump and ducting system of the waterjet are usually an integral part of thehull. Therefore, the total jet thrust exerted on the hull and the correspondingrequired power cannot be measured or computed so easily as in the case ofpropeller propulsion. An indirect way of measuring thrust and power has to befollowed. In doing so, it appears that the powering characteristics are mostappropriately obtained from integral considerations of the conservation lawsover a suitably chosen control volume.

Although the overall powering characteristics are basically independent of thesubdivision of the total system, clear definitions of the subsystems are essentialin avoiding inconsistencies in the description of interaction.

2.1.1 Definition of jet system control volume

Control volumes are preferably chosen such that the required forces are passedby. or required fluxes are passing through their boundaries. Furthermore, theboundaries are chosen such that knowledge about forces or fluxes acting onthem or passing through them is obtained easily. Apart from these theoreticalconsiderations, one may impose that the control volume selected for a waterjetsystem corresponds to that part of the flow that is strongly affected by thewaterjet system. In this way, interaction effects between the flow about the hulland that through the waterjet are relatively small. Consequently, the overallperformance of the composed system is largely determined by the performanceof the individual systems.

The working point of the waterjet-hull system is determined by the thrustrequired by the hull and the net thrust delivered by the waterjet system. Havingdefined a control volume, the thrust generated over this volume can be obtainedfrom the conservation law of momentum. An obvious definition of thrust isthen given by the net rate of change of the momentum flux in x-direction. Thisso-called gross thrust Tg is generally not equal to the thrust acting on the hullhowever. This latter thrust is made up from the total hydrodynamic stresses(both normal and tangential) acting directly upon the material (fixed) boundariesof the waterjet system. It will be referred to as net thrust Tnet in the following.

General agreement seems to exist in the marine literature on the definition ofgross thrust T. Most definitions correspond to the one used by the High SpeedMarine Vehicle Committee of the 18th ITTC [1987]:

Tg = tnni: - mix(2.1)

54

2.1 Systems decomposition

55

where = momentum (m) flux from the nozzle (n) in x-directionmix momentum flux ingested through the intake area (i) in x-

direction.

Less agreement is found however on the boundaries over which the integralconsideration is made, as was discussed in Section 1.5.1. This can easily lead toserious differences in results.

One of the possible control volumes is designated volume A in Fig. Fig. 2.1.This control volume is used by a.o. Bowen [1971]. An advantage of this controlvolume is the knowledge that is available on the flow characteristics in theintake region. A disadvantage is however, that a large part of the jet system isnow positioned along the hull and in the hull affected stream. As a conse-quence, external forces can affect the thus defined internal jet flow over a largepart of the jet system's boundaries, resulting in a strong dependency of the jetsystem's performance on the hull containing the jet.

A second alternative is represented by control volume B, spanned by the pointsA'DCFF'A' (Fig. 2.1). This is a practical definition of the control volume whenthrust measurements are obtained from a set-up where the complete waterjet(model) is separated from the hull model and only attached to it through forcetransducers. A description of such a set-up is for example given by the ITTC[1987] and Alexander et al. [1993]. If the required power is to be measuredfrom model tests, a proper model of the complete waterjet unit is required. Thesize of the jet model needs to be sufficiently large so as to avoid large scaleeffects in the internal flow, hampering a proper scaling of measured inputpower.

In this definition of waterjet control volume, the gross thrust is identical to thenet thrust acting upon the hull (provided no net force results from the pressureterms over the nozzle area). It is difficult however to determine the thrust frommomentum flux considerations on the ingested flow, as the velocity distributionin the intake area A'D is highly irregular. For this reason, and because thepressure in this area shows a similar irregularity, estimates of power throughevaluation of the net change of energy fluxes is also difficult and inaccurate.

The most frequently used control volume is referred to as volume C, and isrepresented by the points A'B'CFF'A'. The intake area A'B' is typically situatedat the intake's ramp tangency point A'. This control volume is implicitly usedby Wilson [1977] and Miller [1977]. A more accurate description of the controlvolume and appropriate theoretical model is presented by Etter et al. [1980],which is also used by the ITTC [1987].


8

56

4

zr

A' A

-Jl

fixed (material) boundaries

variable (imaginary) boundaries in the flow

A = intake leading edge (imaginary)A' = ramp tangency pointI'BC lower dividing streamlineC = stagnation pointD = intake trailing edge or outer lip tangency pointEE' = intake throat area

Area I A1 = imaginary intake areaArea 2 = A2 dividing stream surfaceArea 4 = A4 = outer lip surfaceArea 6 = A6 = internal material jet boudaryArea 7 A-j = boudary area of pump control volumeArea 8 = 8 = nozzle discharge areaVolume P = Vp = pump control volume

Suitable waterjet control volumes:CVA: II'CFF'ICVB: A'DCFF'A'CV C: A'B'CFF'A'CV D: ABCFF'A

Fig. 2.1 Definition of jet system's control volume (see also fold-out at the back)

I

U0


This control volume offers good possibilities for a survey of the flow in theintake region A'B'. The material (fixed) boundary of the waterjet system doesnot coincide with the external hull, and the jet system boundary exposed to theexternal flow is relatively small.

A more uniform velocity distribution in the intake area A'B' is obtained whenthe intake area is shifted slightly ahead of the intake's ramp tangency point(A'). In this way, most of the effect of the intake ramp curvature on the flow inthe intake area is avoided. It is furthermore more logical that the flow stronglyaffected by the waterjet geometry, belongs to its internal flow. The correspon-ding control volume is designated volume D (Fig. 2.1).

Although the extent of the ramp curvature effect is a function of the curvature,the distance A'A may be more uniquely defined as a part of the intake lengthA'D. Point D is determined by the intake geometry and is referred to as theintake trailing edge or outer lip tangency point. From potential flow computa-tions and Laser Doppler Measurements that were made at MARIN on an intakewith a relatively small radius of curvature, it was concluded that a distance A'Aof 10% of the intake length A'D is efficient in smoothing the 3-D velocityprofile in the intake area. The resulting velocity field is presented in Section4.1.1.

Having selected control volume D, the ducting system is partly defined by thefixed (material) boundaries of the jet system, partly by a dividing stream sur-face ahead of the physical intake opening. This dividing stream surface (A2 inFig. 2.1) is an imaginary surface in the flow, through which no transport ofmass occurs by definition.

The geometry of the areas 1 and 2 depends on the point of operation of thewaterjet. It may also be affected by the external flow, e.g. in the case where alongitudinal pressure gradient exists.

The flow is discharged through area 8, representing the nozzle area. Further-more, the flow is bounded by area 6, representing the physical ducting of thewaterjet system. All forces, including pump forces, exerted by the waterjetsystem on the hull can only be passed through this area and through the pumpcontrol volume VP.

An interesting observation can be made when the control volume A is studiedin a free potential flow. This is a potential flow that is not distorted by the hullnor by free surface effects. In this particular case, it can be demonstrated thatthe net thrust, is equal to the gross thrust (Van Gent, [1993]). This observation

57


is used in the derivation of the ideal efficiency as discussed in the previous sec-tion. It can also be used for the derivation of an expression for the thrust deduc-tion fraction t., both in free stream and operational conditions. Using theserelations, it wili be demonstrated in Section 2.3.1 that under certain conditions,the gross thrust of control volume A equals the net thrust in operational condi-tions.

2.1.2 Analysis of overall powering characteristics

Dominant parameters in the powering characteristics are thrust and power. Theworking point of the jet system is determined by the equilibrium between therequired thrust by the hull, and the actually delivered thrust by the jet.

The effective power delivered by a system is often expressed in its non-dimen-sional form. An efficiency is thus obtained that can generally be defined as:

'doute (2.2)

where '3oute = effective power delivered by systemPin = power input in system P, =

loss = power losses.

The efficiency of the overall system can be obtained from the efficiencies of thesubsystems from which it is composed. The process of energy conversionthrough each subsystem of the combined waterjet-hull system is sketched inFig. 2.2, and will be discussed in the following.

When matching two distinct subsystems, the overall performance is generallynot equal to the overall performance that results from the free stream character-istics after matching both systems. The difference being referred to as interac-tion. For the purpose of design or analysis of such a combined system, it isdesirable to have the interaction effects explicitly defined. The overall effi-ciency of the combined system can then be obtained from the free streamefficiency n0 and an interaction efficiency nINT according to:

OA = nonlNT (2.3)

58

pump system

jet system11et U

ducting system

bare hull system

Fig. 2.2 Decomposition of energy fluxes through waterjet-hull system

The performance of the jet system in free stream conditions will now beworked out first, followed by an analysis of the waterjet-hull interaction compo-nents.

Jet system

The actual thrust delivered by the waterjet should match the required thrust bythe hull. Usually, a gross thrust Tg is introduced, which generally differs fromthe actual thrust Tnet. The reason for the introduction of a new definition ofthrust is that this thrust is more easily computed or measured over a suitablychosen control volume.

To facilitate conversion from gross thrust to net thrust, these two definitions ofthrust can be related to each other by a single parameter. A logical reference tothis parameter is thrust deduction fraction' t1, according to:

Tg(l t1) = Tnet (2.4)

A simple expression for the quantification of the jet's thrust deduction fractionwill be discussed in the applications section.

The thrust deduction has been used here in the same form as it is commonlyused in propeller-hull theory. The distinction is that the thrust deduction fractionaccounts here only for the difference in gross and net thrust of a waterjet oper-

2. 1 Systems decomposition

JSE

TE

59

mIl+r hei


ating in free stream conditions. In propeller-hull theory, the thrust deductionfraction accounts for the additional resistance of the hull due to the propelleraction, and as such, is an interaction parameter.

The primary objective of the jet system is to convert the hydraulic powerdelivered by the jet system JSE into a thrust acting on the hull. The effectivejet system power J5E can be regarded as the power required to transport acertain flow rate Q from the intake (AB) to the nozzle, and can be obtainedfrom:

JSE = QH5 (2.5)

where Hjs = waterjet system head.

The appropriate energy levels at the nozzle and the intake, determining the jetsystem head, are strongly affected by the flow conditions in the environment ofthe waterjet system.

The power appropriate to the jet system's thrust production can be designatedas effective thrust power PTE:

TE TnetU (2.6)

where U0 = hull's speed or free stream velocity.

The conversion from hydraulic power to thrust power is accompanied by axialkinetic energy losses, which are usually accounted for in a so-called momentumor jet efficiency. The jet efficiency used by Etter et al. [19801, is defined as:

T,U011JET - Dr JSE

where Tg = gross thrust.

The free stream condition of the waterjet system is now defined as the condi-tion where the jet operates in an undisturbed flow with uniform velocity U0 inx-direction. Such a condition can for example be created in CFD codes or on atest stand in a water tunnel. The centre of the nozzle area is situated on the freesurface.

For this condition, the product of jet efficiency and thrust effectiveness (1-t1)can be transformed into the ideal efficiency Ti,:

60

(2.7)

TgOUØ(1-t10)1i

= JSE0

where subscript O indicates free stream conditions.

The advantage of selecting the free stream conditions such that this productdevelops into the ideal efficiency, is that two simple relations can be derivedfor this efficiency:

iii

nl =2

i +NVR

where NVR = nozzle velocity ratio; NVR = u,/U0or

4

3+Jl +2CT

where CTfl thrust loading coefficient; CTfl = T/(½pUO2A)A = nozzle area.


(2.8)

(2.9)

(2.10)

The efficiency of the conversion process by the jet system from hydraulic jetsystem power JSE to effective thrust power ATE' is thus expressed by the idealefficiency 1:

Iii =TEO (2.11)JSE0

This ideal efficiency represents an important part of the overall efficiency of thejet-hull system.

The hydraulic jet system power JSE results from the effective pump power PEafter accounting for the energy losses due to the ducting. The energy lossesoccurring in the ducting system can be accounted for by a ducting efficiency1ducr

'3JSE (2.12)PE

61


The pump system converts the delivered mechanical power D into hydraulicpower, designated here as the effective pump power PE The efficiency appro-priate to this conversion process is designated pump efficiency rjp:

Interaction

So far, the hull and the waterjet system have been discussed from the viewpointof free stream characteristics. When these two systems are fit together, theyinterfere with each others performance.

The bare hull resistance is changed due to a distortion in the flow about the aftbody. At higher speeds, this distortion can furthermore cause a distinct equilib-rium position of the hull, thus causing another change in resistance. In anequilibrium situation, the actual resistance of the hull balances the net thrustdelivered by the jet system. The change in hull resistance can now be expressedby a 'resistance increment' factor I +r, according to:

PElip -

1D

62

Tneti +7 =

RBH

(2.13)

(2.14)

Similarly, the jet system performance is affected by the flow distortion causedby the hull. Due to this distortion, a boundary layer is ingested through theintake area and the local flow velocity is likely to differ from the free stream orthe hull's velocity. This affects the ingested momentum and energy fluxes, andthus the delivered thrust and power. Analogous to interaction effects in theintake region, interaction effects may also occur in the nozzle region. Thisoccurs for instance when the nozzle is submerged in the transom flow insteadof in air. Corrections on these fluxes can be applied by introducing a momen-tum interaction and an energy interaction efficiency respectively.

Interaction effects on momentum fluxes affect the thrust production. They canbe accounted for by a momentum interaction efficiency 1lmI according to:

Tnet (2.15)T,11

Interaction effects on the energy tiuxes directly affect the power balance. Theseeffects can be accounted for by an energy interaction efficiency 11e1' accordingto:

= JSEO (2.16)JSE

The overall efficiency of the waterjet-hull system can be defined in the usualway, according to:

and

lOA =PE (2.17)"D

where E = effective hull power; E = RBHUO.

After substitution of equations (2.6) and (2.11) to (2.16), the following relationfor the overall efficiency is obtained:

110 = lIli ductlP

11e!li/NT

(1 +rYq,1

11e!10A = li1 ductlP (1 +r)lj


(2.18)

This overall efficiency may subsequently be decomposed into the product of thefree stream efficiency 1lü and the interaction efficiency 11JNT' where

(2.19)

(2.20)

Note that a change in net thrust, expressed here in r, also affects the idealefficiency. This is caused by a corresponding change in thrust loading coeffi-cient. This could be regarded as a secondary interaction effect, which is notincorporated in the interaction efficiency.

63


2.2 Basic equations

Relations for the delivered thrust and corresponding required power will now bederived from the conservation laws of momentum and energy respectively. Forthis derivation, we will consider the conservation laws in their integral form, fora control volume fixed in the coordinate system. A body-fixed Cartesiancoordinate system is used, with the x-ordinate oriented parallel to the localbuttock (parallel to AD) and the z-ordinate pointing downward (Fig. 2.3). Forreasons of simplicity, it is assumed here that the jet, discharged from the nozzlearea FF' is oriented parallel to the x-ordinate.

x, y, zX', y', z'

Fig. 2.3 Definition of coordinate systems

Tensor notation is used throughout the equations with the Cartesian summationconvention. In any product of terms, a repeated suffix is held to be summedover its three values 1, 2 and 3 (or x, y and z). A suffix not repeated in anyproduct can take any of the values 1, 2 or 3.

The pump system of the waterjet is represented by a system of one or moreactuator disks. They are contained in control volume V and exert a forceper unit mass on the fluid and deliver a power D to the fluid.

64

hull fixed coordinate systemearth fixed coordinate systemrotated coordinate system x, y. z (hull fixed)

z

2.2.1 Thrust

The thrust is a force vector that can be quantified through use of the conserva-tion law of momentum.

The conservation law of momentum in words reads that the net rate of changeof momentum for a given control volume equals the sum of the forces exertedby surface forces and volume forces. This yields for a stationary situation, thefollowing momentum equation in i-direction, in its integral form:

J J pu(u)dA = f J (2.21)A1+A8 A1A2A6A8 V1 V

where ¡Ip u(uknk)dA = net momentum flux through control volumeffodA = external force acting on surface of the control vol-

umeIffpFdV = external force acting on the mass contained in the

control volumefIfpF1dV = pump force acting on fluid

Fig. 2.1 lists the designations of the surfaces and volumes.

In examining eq. (2.21), note that by convention, the normal vector on a surfacealways points in a direction out of the control volume. Hence, when i also

points out of the control volume, the product un is positive. The flow is thenphysically leaving the control volume, i.e. it is an outflow. An inflow in thecontrol volume consequently shows a negative contribution.

The external force acting on the surface is made up from the total mean stressin a turbulent flow:

2.2. Basic equations

JJYdA = JJn1dA

where = total mean stress; -p& +p = time averaged pressure

= Kronecker delta (equal to 1 if i=j and O otherwise)= total shear stress tensor; t1' +

t11' = viscous stress; 2pSp = dynamic viscosity of fluid

(2.22)

65


66

Sf,, = time averaged rate of strain= contribution of turbulent motion to the stress tensor; Reynolds

stress tensor.

Because the surface normal vector is positive when pointing out of the controlvolume, an external pressure force acting upon this volume is positive (becauseof the minus sign of p in The sign of the force that occurs in the equationwhen written in Cartesian coordinates, depends on the direction of this force inthe coordinate system.

In search for a relation between the physical flow model (streamtube) and thegeometrical model (waterjet surface), we will now consider the momentumbalance in x-direction. We will define the thrust pertinent to the streamtube asgross thrust:

The gross thrust Tg is defined as the force vector pertinent to the change inmoinen turn flux over the selected control volume, acting on its environment.

Because we are mainly interested in the x-component of this thrust, the grossthrust will refer in the following to the x-component of this force vector Tgtand will shortly be written as Tg This definition of gross thrust correspondsessentially to that proposed by the ITTC [1987]. The definition of gross thrustin tensor notation subsequently reads:

Tg= J puX(uk)dA (2.23)

A1 +A

The minus sign in the right-hand term occurs because the gross thrust is definedas the reaction force that is exerted by the control volume on its environment.In this way, the gross and the net thrust point in the same direction.

Similarly, the net thrust vector refers to the material boundaries of the waterjet:

The net thrust Tnet is defined as the force vector acting upon the materialboundaries of the waterjet system, directly passing the force through to the hull.

Analogous to the adopted symbol for the gross thrust, we will consider here thecomponent of the net thrust in x-direction Tnetx, which will be abbreviated toTnet in the following. A possible lift exerted by the jet on the hull (Tnetz or L)will be discussed later.

The definition of net thrust in tensor notation subsequently reads:

Tuer= J J dA-JJJpFdV (2.24)

A4A6 VP

The minus sign in the right-hand term occurs because of the orientation of thenormal vectors, pointing out of the flow or control volumes.

With the adoption of the above definitions of gross and net thrust, we maywrite eq. (2.21) as

- Tg = Tnet+J f dA -JJcYdA +JjjpgdV (225)A1+A,+A A4 V

The mass force acting on the fluid in the volume V is the gravity force; F. = g.

The difference between the net thrust and the gross thrust can now be expressedin a true thrust deduction fraction, which is defined by the following relation:

Tnet = Tg(l -t1) (2.4)

This thrust deduction fraction t1 can consequently be written in terms of forcesacting on the streamtube model, by using eq. (2.25):

= _L{f J dA-JJodA+JjJpgdVl (2.27)g A1+A2+A8 A4 V

The thrust deduction expresses the discrepancy between the gross thrust Tg andthe net thrust T,iet. The net thrust is smaller than the gross thrust whenever apositive thrust deduction occurs. This is the case when the total stress force actsin negative x-direction upon the combined protruding streamtube boundaries(A1A2-f A8) and in positive direction on the material jet boundary (A4) respect-ively.

It should be noted that the thrust deduction fraction t., as defined above, isdifferent from the same used in propeller-hull theory. ?n the latter, t accounts(by definition) for the increase in hull resistance, caused by the propeller action.In this context it merely accounts for the difference between the actual netthrust acting on the hull, and the defined gross thrust.


67


2.2.2 Power

In analogy with the derivation of the thrust equation, the equation for therequired power is derived from the conservation law of energy.

The conservation law of energy in words reads that the rate of change of thetotal energy per unit time for a certain amount of mass equals the sum of thework per unit time, done by the forces acting on the surface, and the amount ofexternal energy that is supplied per unit time.

The total energy e per unit mass can be written as:

e = ek. e ein pot tnt(2.28)

The following observations and assumptions have been made in the derivationof this relation:

The potential energy e0 is determined solely from the gravity field; li=-gz',where the z' ordinate is pointing vertically downward.

68

cc l, ccj j p(......0

J J(-pun+ut1JnJ)dA+PD

A1A2+A8

(2.30)

where ekfl = kinetic energy; ½u2ep0, = potential energy

= internal energy.

The conservation law of energy can now be written in the following integralform:

JJJP.±dV = JjuojdA+jjJpqdV (2.29)

where f//p(de/dt) dV = rate of change of total energy contained in volumeV

ffuo dA = rate of work done on the volume's surfacefffpq dV = rate of external energy exchange with volume.

For a waterjet system in a stationary incompressible flow, this equation can bereworked into:


Because transport of mass only occurs through the areas A1 and A8, only theseareas contribute to the transport of kinetic and potential energy through thevolume boundaries.

The rate of change of internal energy for an incompressible fluid can be writtenas:

Wdiss = fJjlt ,u dV (2.31)

This term represents the viscous energy losses within the flow, which are con-verted into heat.

The contribution of the work done by surface forces, acting on the boundariesof the control volume, is represented by the first term on the right-hand side ofeq. (2.30). No work is done by the surface tension forces dA within the duct-ing of the waterjet, due to the non-slip condition at the corresponding surfaces.A similar observation can be made for the pressure forces acting perpendicularto the dividing stream surface.

If it is furthermore assumed that there is no exchange of heat through thevolume boundaries, the external rate of change of energy that is supplied to thesystem is therefore solely due to the pump, and can be referred to as

Pump system

In the following, we will write the velocity and normal vectors in the compo-nents of a new Cartesian coordinate system. to better distinguish between theuseful and the lost kinetic energy. The new Cartesian coordinate system isobtained from the body-fixed system x,y,z by rotating the system about the y-axis until the e-axis is aligned with the local centreline intake (see Fig. 2.3).

The input power D is given by eq. (2.30). The effective power delivered bythe pump PE can be described as the power required to deliver a pressure headfor a certain flow rate:

cc 1 2PE = jjp(_u-

A7

+J)undAp

(2.32)

The first term in the right-hand side of eq. (2.32) represents the change in kin-etic energy in axial direction. The second term represents the change in poten-tial energy, and the third term in the same integrand represents the transport ofenergy by the pressure p.

69


The power losses associated with the pump can be written as:

loss JJp (-u +u)undA Wdjss _JJ(u t)ndA (2.33)A7

The first term on the right-hand side of eq. (2.33) represents the kineticrotational and radial losses and the second term '1Jd55 represents the viscousenergy losses. The third term represents the transport of mean flow energy bythe total stress t, representing both viscous shear and turbulent flow stresses.

Ducting system

The effective power that is delivered by the jet system JSE is analogous to theeffective pump power:

JSE J J (2.34)

The power losses in the ducting system are given by an equation similar to eq.(2. 33), with the relevant system boundaries applied:

Pi055= J J J (2.35)

A1--A,+A8

The last term in equation (2.35) not only yields a contribution over the intakeand nozzle area A1 and A8 respectively, but also over the dividing streamplaneA2.

Jet system

The power output by the jet system is given by:

TgV0 (2.36)

where Tcan be referred to as thrust power. The gross thrust in this power

term is defined by eq. (2.23).

70

The jet efficiency can subsequently be defined as:

11JET (2.37)JSE

If the average pressure p in the intake is equal to that in the nozzle area aftercorrection for submergence, and the nozzle centreline is situated in the freestream water surface, the jet efficiency reduces to the often quoted ideal effi-ciency ,. This will be illustrated in Section 2.2.3.

2.2.3 Free stream conditions

Before treating the subject of interaction, let us first have a closer look at thewaterjet system in free stream conditions. The objective of doing so is to obtaina better insight in the mechanisms governing thrust and power, and to aim atsimplifications in the relations discussed in the previous sections.

Let us define the free stream condition for the waterjet system as the conditionwhere a waterjet, mounted on an infinitely extended flat plate, operates in auniform velocity U0 (Fig. 2.4). The flat mounting plate is situated in the x-yplane, which coincides with the horizontal plane x'-y'. The nozzle centre issituated in the free stream surface (z0=O).

The free stream velocity is directed in x-direction. The pressure at the freesurface is designated Po and the potential force field N' is made up from thegravity:

N' = -gz (2.38)

Although the free stream flow is fully viscous, viscous energy losses caused bythe jet system's environment do not occur by definition. If they do occur in apractical test set-up, for instance in a tunnel, correction for these energy andmomentum losses should be made.

Thrust

One of the most intriguing issues related to waterjet thrust, is the relationbetween gross and net thrust. For gross thrust is easily computed or derivedfrom measurements, but it is the net thrust that should be matched with thehull's resistance.


71


free stream condition

operational condition

Fig. 2.4 Difference between free stream and operational condition

Thrust deduction

The relation between net thrust and gross thrust is defined by eq. (2.26). Thethrust deduction fraction is expressed in terms of force contributions by eq.(2.27). For reasons of simplicity, the change in resistance due to the missingsurface force on the nozzle area A8 is transferred to the relation for the jet'sthrust deduction fraction t. This step will be explained in Section 2.3.4 on thehull's resistance increment. Equation (2.27) then develops into:

= _{J J (2.39)g A1+A, A8 A4 V

where 5 = total mean stress tensor in x-direction, acting upon the hull forthe flow condition without waterjet mounted.

If we consider the jet system's free stream conditions, the integrand for thenozzle area A8 equates to zero, because This follows directly from thedefinition of free stream conditions.

X

72

j..!IziO 4

--I U0

-yzi

z = O, p0

Z = O, Po

ZflO = O4


Furthermore the volume force due to the gravity term g vanishes, as there is nogravity term in the horizontal x-direction.

The remaining contribution to the jet system's thrust deduction fraction, nowreferred to as t is the force in x-direction, acting upon the protruding part ofthe streamtube and the part of the intake lip that is exposed to the externalflow. We will refer to this force as FXABCD in the following:

FBcD = -JJdA +J J dA (2.40)A4 A1+A.,

A positive value of FBcD can be interpreted as an intake drag D, pertinent tothe jet system. The relation between intake drag and thrust deduction in freestream conditions is now given by:

D. = t10Tgo (2.41)

Intake drag

As indicated in Section 1.5 (review of previous work), several authors haveaddressed the issue on intake drag. Intake drag for flush intakes as meant in thepresent context, is perhaps most completely treated by Mossman and Randall[1948]. These authors derive an intake drag from wake survey measurements ona number of flush intake geometries. It will be demonstrated in Section 4.1.2that their definition of intake drag includes a significant contribution of thetunnel wall in front of the intake area. It will be demonstrated here that theintake drag FßcD of a flush intake in a potential flow equals zero for a suit-ably chosen control volume of the waterjet.

Let us consider a flush intake operating in a potential flow. It was noted byVan Gent [19931 that the net force, acting upon the dividing streamline in x-direction, should be zero according to the Paradox of d'Alembert. Van Gentnoted the similarity between the dividing streamline and a flow line in the fieldmade up by a source in a uniform flow (see Fig. 2.5).

73


F

-Q

Fx s ink

Fxl

Fig. 2.5 Flow line about a single sink in a uniform onflow

The dividing streamline I'C (Fig. 2.1) and part CD of the intake lip prone to theexternal flow, can now be modelled by a flow line in a field consisting of asuitable set of sinks and sources in a uniform flow. A double model of thisflow line is shown in Fig. 2.6, where the streamline is minored about a hori-zontal line through the stagnation point C. We have now obtained a half opensymmetrical flow line model.

Fig. 2.6 Double model of streamline I'CD

For a study on the net pressure force on the half body, we will study a similarbody that is built up from one sink. Fig. 2.5 shows a resulting flow line, wherepoint C is the stagnation point again. We can now study the momentum balancefor the inner part of the half body. The integrated pressure forces on the upperand lower streamlines of the half body are designated and F respectively.For symmetry reasons, these two pressure force components are identical. Thesink with strength -Q, exerts an internal force on the control volume, which canbe obtained from Lagally's theorem (Weinblum [1951]):

FXSjflk = -pQU0 (2.42)

74

Centre Line

Uo

mix

The momentum balance for the internal control volume subsequently reads:

= F +F +Fmix xsink xu xl


(2.43)

Because 4,nix equals the force exerted by the sink, the sum of the pressureforces on the half body equals zero. As these forces are equal, the individualcomponents should also be equal to zero. In the same way, it can be shown thatthe momentum balance can be written in the same form for any set of sinks andsources. The internal sinklsource forces are simply obtained from the sum ofthe Lagally forces. The interaction forces between the distinct sinks and sourcescancel each other. The momentum flux is in the same way built up from thesum of momentum fluxes of the individual sinks and sources, so that the netpressure force on the flow lines equals zero for any half open body.Consequently, the force FBcD equals zero in free stream conditions, providedthe imaginary intake area AB is situated outside the jet systems flow distortion.

An important consequence of the above observation is that the net thrust isequal to the gross thrust for control volume A. We will refer to the gross thrustpertinent to this control volume as Tg in the following, and write this con-clusion as:

Tpîet = Tgoj (2.44)

where subscript O indicates free stream conditions; indicates the imaginaryintake area AB to be positioned infinitely far upstream.

Note that the gross thrust for Control Volume A (Tg) is equal for both freestream conditions and operational conditions. The index O for free streamconditions will therefore be omitted.

For intake areas that are situated more closely to the intake's ramp tangencypoint, such as for the selected control volume D in Fig. 2.1, the flow distortionby the intake causes the mean momentum velocity through the intake area todeviate from the free stream velocity. It will be shown in Section 4.1.1, thateven in the case where the intake area is situated 10% of the physical intakelength A'D in front of the ramp tangency point, the average intake velocitydeviates noticeably from the free stream velocity.

For this case, we can find an expression for the thrust deduction fraction orfor the intake drag, from a consideration of the force acting on the streamlineI'BCDJ (Fig. 2.1) and a momentum consideration on control volume II'BAI.

75


The resulting expression for the thrust deduction then reads:

where IVR0 = intake velocity ratio through area AB; uK/UO= mean volumetric velocity through intake area

NVR = nozzle velocity ratio.

Strictly speaking, we would have to use the mean momentum velocity throughthe intake area in the above expression. Assuming a small difference betweenthe minimum and maximum velocity in this area however, the differencebetween the mean volumetric and the mean momentum velocity is negligible.

It is seen from eq. (2.45) that for an imaginary intake situated in the undis-turbed flow, the thrust deduction t0 becomes zero. This corresponds to theprevious observation that the gross thrust equals the net thrust.

Power

It will be shown in the following, that the product of jet efficiency as used byEtter et al. [19801 and thrust deduction factor (1-ti) reduces to the ideal effi-ciency for the selected Control Volume D in free stream conditions.

For these conditions, the relation for the effective jet system power JSE0reduces to:

JSE0 =pnO I -, Pio (2.46)

where e= average energy velocity

p = pressurez = vertical distance from free surfaceU0 = uniform free stream velocitysubscript n denotes nozzle area (area 8), i denotes intake area (area 1)and O denotes free stream conditions.

For the sake of simplicity, it will be assumed that the nozzle is completelyeffective in converting pressure energy into kinetic energy, so that the pressureat the nozzle area equals the ambient pressure p0, provided the jet is discharged

76

i -IVR0(2.45)

NVR -I VR0

1-2 Pio 1_uj0+__gzj0 = _U(f.

Iii =U0(iZm U0)

1 -" 2......(u -U0)


in air. Should this not be the case, the mean nozzle velocity should be replacedby the mean jet velocity that occurs in the vena contracta. Consequently, the jetarea in this vena contracta should be used instead of the nozzle area.

The flow in front of the intake was defined as a non-viscous flow. The energylevel at the intake in this free stream condition can now be expressed in freestream variables using Bernoulli's theorem:

(2.47)

The effective jet system power in free stream conditions JSEO can then berewritten into

JSEO = pQ!(ii-U)+pQ(-gz0) (2.48)

It is seen from eq. (2.48) that the potential force field N' only contributes to thepower demand if the centre of the nozzle area does not coincide with the free(undisturbed) surface (z0=O). By defining the free stream condition as thecondition where the centre nozzle is situated in the free stream surface, thegravity term is cancelled.

The jet efficiency JET consequently reduces to the ideal efficiency 1:

(2.49)

If the nozzle centreline is oriented parallel to the x-ordinate and the velocitydistribution in the nozzle area is uniform, the ideal efficiency can be reduced toeither of the following relations:

= 2 (2.50)1 +N%/R

where NVR = nozzle velocity ratio; NVR=u,/U0

or

77


ri1 =4

3 Ii +2CT,1

where CTfl = thrust loading coefficient; CTfl=TgJ(½PUO2Afl)A = nozzle area.

(2.51)

A derivation of these relations for the ideal efficiency is given in Appendix 1.

2.2.4 Lift

A net lifting force on the stem of the vessel with an active waterjet has beensuggested by Svensson [1989. This conclusion was obtained from pressuremeasurements in the intake and on the hull in the vicinity of the intake.According to Svensson, this lifting force, generated by the inlets, can be inexcess of 5% of the displacement of a high speed craft.

This section aims to explain that there is no net lift contribution from the pres-sure field about the intakes, as long as the bottom plating about the intake issufficiently wide.

To study the net lift production of a waterjet unit in free stream conditions, wewill mount the unit on an infinitely large horizontal plate and let it operate in apotential flow. A potential flow assures a proper modelling of the flow, pro-vided the boundary layer about the real hull is thin. This is a realistic assump-tion for most hull forms fitted with waterjets. And because we focus on theinduced lift production by the intake, we consider the jet to be dischargedhorizontally again.

To find an expression for the net lift force on the jet-plate system (or z-compo-nent of the net thrust vector), we consider the momentum balance for the con-trol volumes indicated in Fig. 2.7. Because there is no change in the verticalmomentum flux for Control Volume A, the sum of the vertical forces acting

upon this volume equals zero:

FZJAF/Fc+FzJ/c = o (2.52)

where subscript z denotes the force component and capitals refer to the corre-sponding lines in Fig. 2.7.

78

J.,

Fig. 2.7 Control volumes used for derivation of intake drag and lift

A similar momentum balance can be worked out for Control Volume i Incontrast to Control Volume A, there needs to be an exchange of mass throughthe lower boundary J"..!', to replenish the flow rate Q that is ingested by theintake. This replenishment cannot take place through the downstream boundaryJ"J, as there needs to be a uniform velocity field at this boundary, for we haveseen in Section 2.2.3 that there is no net horizontal force acting within the con-trol volume.

The momentum balance for Volume i subsequently reads:

pump

cv i

CVA- //

L

A /7 1.1


in order to find a parametric description for the lift force on the hull, we willwrite the vertical momentum flux as:

where = momentum flux velocity coefficient in a potential flow.

The mean z-component of the velocity ¿ is obtained from the conservationlaw of mass:

79

FZCDJ+FZ (2.53)

nzi'j PQmpI4z (2.54)

Q (2.55)AJ//J//


The net lift force Tnetz is made up from the sum of the vertical forces FZIAFFCand FZCDJ, which can now be written as:

Tnetz = PQCmpl7z (2.56)

To study the behaviour of the lift force, a non-dimensional lift coefficient CL isintroduced:

TCL

pQU0(2.57)

Keeping in mind that the flow rate Q can be expressed as the product of theintake throat area the intake velocity ratio lVR and the free stream velocityU0, we have found an expression for the lift coefficient CL as a function of theratio between intake throat area and plane area A1:

80

Cml VRA itCL- -

/-Il II(2.58)

The momentum velocity coefficient Cm has a value less than one for a non-uniform velocity field (see also Appendix 2). Representative values for theintake velocity ratio IVRE are of 0(1). It can thus easily be seen that the liftcoefficient CL vanishes for sufficiently large areas ¡"J' in relation to the intakethroat area.

The net lift force on the waterjet-hull configuration may attain finite valueswhen the bottom plane is limited. This situation may for example occur inactual vessels, where the intake is situated just in front of the transom stem. Aquantitative discussion on this phenomenon is postponed to Chapter 4.

2.3 Interaction

As we have seen in Section 2.1, the interaction effects in the powering charac-teristics can be expressed in the momentum and energy interaction efficienciesfor the effect on waterjet performance, and in resistance increment for the effecton hull performance. Parametric expressions that can be used in either a compu-tational or an experimental study will be derived in the following.

2.3.1 Momentum interaction efficiency

Hull interaction effects on waterjet thrust are accounted for in the so-calledmomentum interaction efficiency, which is defined by (see also Section 2.1.2):

TnetüTI mi

Tnet

with

and

/ lITI = fl,11,11,111

/ Tg-Tg

i, (l-t10)

= (l-;)

subscript O indicates free stream conditions.

It will be shown in the following that, for control volume D in a potential flow,the net thrust in free stream conditions equals the net thrust in operationalconditions for the same flow rate and a negligible free surface induced pressuregradient over AD. As a result, the momentum interaction efficiency equalsunity.

Contributions to the thrust deduction by the nozzle area A8 and the trim angle(eq. (2.39)) are thereby neglected. which is a good approximation for mostoperational conditions. The effect of this simplification will be discussed inSection 4.3.2.

2.3 Interaction

(2.59)

(2.61)

(2.62)

(2.63)

81

For reasons discussed in Section 2.1, the net thrust is most practically obtainedfrom the product of gross thrust Tg and jet system thrust deduction t:

Tnet = Tg(l_tj) (2.4)

As a consequence, the momentum interaction efficiency can be written as:


Momentum interaction efficiency TI,,ÇJ

To get rid of the integral term in the definition of the gross thrust (eq. (2.23)),the momentum flux mj through the intake area A1 will be expressed in globalflow parameters and coefficients:

dmi = PQUmjx (2.64)

where

mix = CvpCmUø (2.65)

and = potential flow velocity coefficient; U/U0momentum velocity coefficient due to boundary layer velocitydistributionlocal potential flow velocity outside the boundary layerfree stream velocity in x-direction.

Expressions for the momentum velocity coefficient as a function of the bound-ary layer parameters are given in Appendix 2.

Assuming an effectively uniform velocity profile in the jet at the nozzle exit,the discharged momentum flux can be written as:

= p Qu,71 (2.66)

where i7, = mean nozzle velocity at nozzle exit area 8.

Substituting the above parametric expressions in the first term of the momentuminteraction efficiency r,, we obtain:

82

/ NVR-1l_lin! = NVR I VR mi

(2.67)

where IVR,77 = intake momentum velocity ratio through intake area A1;u1JU0.

Momentum interaction efficiency rÇj

Let us now consider the second term of the momentum interaction efficiency;r. This term is defined by eq. (2.63). An expression for the thrust deduction

Cm =

U =U0 =

2.3 Interaction

fraction in free stream conditions t was already derived in Section 2.2.3 eq.(2.45).

We will now focus on a relation for the thrust deduction fraction t1 in oper-ational conditions. The basic equation for t1 is given in eq. (2.39). We willrestrict ourselves to the first integral term over the protruding part of thestreamtube and intake lip (ABCD in Fig. 2.1). The integral terms over thenozzle area and the enclosed volume are assumed to be negligible here.

To simplify the study of t. in operational conditions, let us break down the totalflow field into a flow fiel1d pertinent to the jet action in free stream conditions,a flow field pertinent to a double model of the hull without free surface effects,and into a flow field consisting of the free surface distortion. In the potentialflow considered, the total flow field potential function consists of the sum ofthe individual potential functions. Hence, the resulting velocity fields may besummed.

We will first consider a two-dimensional double model (mirrored about the freesurface) of a waterjet-hull system in a potential flow (Fig. 2.8). This conditionleaves free surface effects out of consideration. Depending on the hull shape,the jet system may be operating in an accelerated or a decelerated flow.

From its definition, the following expression for the thrust deduction fraction t1can be derived (see eqs. (2.39) and (2.40)):

(2.68)T

where FABcD = external force acting in x-direction on the protruding partof the intake (see Fig. 2.8).

A suitable expression for FßcD can be obtained from a consideration of theforce in x-direction acting upon the streamline I'BCDJ and a momentum con-sideration on the control volume II'BASI forward of the imaginary intake areaAB.

The force on the streamline part BCD can be obtained from a consideration ofthe pressure force on the streamline I'BCDJ. Using the paradox of d'Alembertor Lagally's theorem, it can again be derived that the net pressure force in x-direction, acting upon this streamline equals zero. Consequently, the force onBCD can be written as:

83


J

84

Flow about isolated body

4-U0

po

A' A

-J---B

FXBCD =

where

F = f_Pflx

and p = pressure= x-component of normal vector

ds = infinitesimal line element.

-X

+

Fig. 2.8 Flow field decomposition for a waterjet-hull configuration

In the above expression, use is made of the adopted constraint that n equals

zero along line element DJ.

From a momentum balance over the control volume Il'BASI, we find:

(2.69)

(2,70)

I,///U0

Waterjet in free stream

p, 4-U0

2.3 Interaction

FBcD = -pQ(U-U0)+ I -Pn dsJASJ

P

The integral term over AS! can now be written as:

J pn ds JSAPOflS JSAISA X

(2.72)

It should be noted here that the force over AB as mentioned in eq. (2.71) whereit acts upon control volume II'BASI changes sign when we consider the cone-sponding reaction force acting upon control volume ABCFF'A. In a steadyflow, its magnitude remains the same.

If the integral term over the streamline ASI in the right-hand side of this equa-tion would be negligibly small, we would have obtained a simple expression forthe thrust deduction. To study the character of this integral term, we decomposethe total flow field into a free stream field for the jet system mounted on a flatplate, and the flow field about the hull without jet (see Fig. 2.8). The total pres-sure p can now be linearized as the sum of the pressure p0, occurring when thehalf body is positioned in the free stream, and a perturbation pressure p', causedby the intake action:

(2.73)

(2.74)

With Lagally's theorem, it can again be shown that the first integral term on theright-hand side of this equation equals zero if the body contour part AJ isoriented parallel to the x-coordinate. This condition is usually fulfilled for hullforms fitted with waterjets.

The second integral term on the right-hand side, or perturbation term due to thejet action, can be neglected whenever either the perturbation pressure p' isnegligibly small, or whenever the normal in x-direction is negligibly small inthe area where p' cannot be neglected. The first condition is a condition

85

pQ(U-U0) = FsJ+FXßA-FBcD (2.71)

where the pressure forces F are the forces acting upon the control volume.

The force FBcD can now be obtained from eq. (2.71), and reads:


imposed on the flow induced by the intake, and is an argument to position theimaginary intake area AB slightly ahead of the ramp tangency point A'. Thesecond condition imposes a geometrical constraint on the body containing thejet.

It is to be noted that the total pressure can only be obtained from the sum ofthe pressures of both flow fields, if one of the perturbation pressures is small.

With the neglect of the pressure integral over AS!, we have obtained a simpleexpression in terms of u,, U0 and NVR for the thrust deduction fraction t1 inoperational conditions without free surface effects:

I -1VR(2.75)

NVR-1VR

A similar relation was found for the thrust deduction fraction in free streamconditions t10 eq. (2.45).

We will now add the free surface velocity field. We will thereby consider theflow in the protruding part of the streamtube, configuring the jet system withintake AB (Control Volume D in Fig. 2.1). Using Bernoulli's theorem, freesurface effects may be interpreted as a change in the relation between themagnitude of the velocity u and the pressure p due to the wave height Ç:

p = co_pu2_gÇ (2.76)

where co = constant, determined by U0, p0 and z0wave height (positive downward).

A constant change in wave height over the intake length AD results in a uni-form change in pressure. Because the pressure integral over part ABCD is notaffected by a uniform change in pressure, such a free surface effect does notaffect the thrust deduction t3. Only in case a pressure gradient (or varying waveheight Ç) over AD occurs, the thrust deduction will be affected. We willinitially neglect the effect of a free surface induced pressure gradient. Its effecton the thrust deduction t1 for a representative case will be discussed in Section4.3.2, where more information about the dividing streamlines and a possiblepressure gradient is available.

86

2.3 Interaction

Substituting now eq. (2.45) and eq. (2.75) in eq. (2.61) shows that the contribu-tions of îj and T1 neutralize each other, leading to a momentum interactionefficiency equal to unity in a potential flow.

Implications for net-gross thrust relation

The interpretation of the above discussion is that, as long as the pressure inte-gral over AS! is negligible, the net thrust in operational conditions equals thenet thrust of the jet system in free stream conditions for identical NVR value.The integral term is either negligible for an imaginary intake of the jet that issufficiently far upstream of the ramp tangency point, or for a hull form in frontof the intake area AB with a negligible component of the normal in thrust (x)direction. In case this integral term is not negligible, part of the hull's resistanceis found back in the jet system's thrust or vice versa. This will lead to a redis-tribution in the values of the momentum interaction efficiency and the hull'sresistance increment. The power requirement will however not be affectedbecause there is no loss of energy involved.

An important implication for the computation of net thrust in a potential flowis, that the net thrust is equal to the gross thrust pertinent to control volume A(Fig. 2.1):

Tnet = Tgoo (2.77)

For a viscous flow, the ingested momentum should be corrected for a momen-tum deficit in the intake area AB, due to the viscous stresses acting on the hullbounded part of streamtube lI'BAI. The net thrust in a viscous flow canconsequently be obtained from:

Tg=, = pQU0(NVR-c7) (2.78)

Because substantial deviations from the neglects of the nozzle contribution to t1may occur during transom clearing (Section 4.3.2), we will use Tgoo as a goodapproximation of the net thrust over the greater part of the speed range. Theparametric relation for the momentum interaction efficiency can now be writtenas:

l-c7- 1+

11ml NVR-1(2.79)

87


2.3.2 Energy interaction efficiency

Analogous to the definition of momentum interaction, hull interaction effects onwaterjet power are accounted for in the so-called energy interaction efficiency.This efficiency is defined by (see also Section 2.1.2):

11e! =JSEO (2.80)JSE

where JSE = effective jet system (hydraulic) power.

As in the case of the momentum interaction efficiency, both the power in thefree stream and in the operational condition refer to the same flow rate Q

through the jet system. Introducing an average energy velocity iZ,, the effectivejet system power can be written as:

JSE = Q{p -p g(z -z) (p -p)} (2.81)

In order to find a parametric expression for the energy interaction efficiency,the kinetic energy flux through the intake area will be written as:

88

1 2224eki PQCvpÇUj0 (2.82)

where Ce = energy velocity coefficient due to the boundary layer velocitydistribution

= potential flow velocity coefficient; u/u0u = local potential flow velocity, just outside the boundary layer

= free stream velocity in x-direction through intake area.

The energy velocity coefficient can be determined when the ratio between theingested flow rate and the flow rate that can be absorbed from the boundarylayer are known. Appropriate relations are given in Appendix 2.

The effective jet system power in free stream conditions JSEO can be obtainedfrom eq. (2.48):

JSEO = pQ(ii-U) (2.83)

We will now again assume that for operational conditions, the nozzle is com-pletely effective in converting the pressure energy into kinetic energy, so thatthe pressure outside the nozzle is equal to the ambient pressure p0. ApplyingBernoulli's theorem and taking into consideration that the centrepoint nozzle issituated on the water surface in free stream conditions, the following relationfor the effective jet power is found:

JSE = JSEOP Qgz (2.84)

where = sinkage of the nozzle centrepoint relative to the free (undis-turbed) surface.

The energy interaction efficiency 1e1 in a potential flow can subsequently bewritten as:

1e1 = 1+pQgz

(2.85)JSE

It is seen that the energy interaction efficiency adopts a value greater than i ifthe sinkage of the nozzle is positive (downward).

Applying the energy velocity coefficients Ce and cv,, the energy interactionefficiency in a viscous flow can be written as:

i gz cIVR(C-l)Thi U(NVR2_l) (NVR2-1)

2

The second term on the right-hand side may be regarded as a typical potentialflow effect in the interaction efficiency, which is caused by the change inelevation of the nozzle. This term may also be written as the ratio between thenozzle elevation Zn and the required pump head H0 in free stream conditions,expressed in meters water column mwc; z,/H0.

The third term on the right-hand side represents viscous effects in the interac-tion efficiency. if there is no boundary layer present (Ce=l), this term vanishes.The potential flow velocity coefficient is seen to diminish the effect of thefrictional boundary layer losses in a retarded potential flow. This can be under-stood if one recalls that the frictional energy losses are related to the kineticenergy contents. If all energy would be stored in potential pressure energy,there would be no viscous losses.

2.3 Interaction

(2.86)

89


Similar to the validity of the parametric relation for the momentum interactionefficiency î, the above relation is valid as soon as the nozzle discharges inair. 1f the jet is discharged in a separated flow, Bernoulli's theorem is notapplicable any more and corrections should be made.

2.3.3 Quantitative assessment and comparison with previouswork

Now that we have obtained parametric expressions for the interaction effects ofthe hull on the jet performance, we can make an assessment of its magnitude.Moreover, we can compare these findings with results obtained from modelspublished by other authors. We will thus study first the interaction effects on jetperformance in a potential flow, followed by viscous flow considerations.

In his search for a better physical understanding of waterjet-hull interaction, JonHamilton [1994] put the following thought experiment forward. 'imagine aninfinitesimal wate rjet near the stagnation point of the hull. How will this affectthe interaction efficiency?'.

This limiting case is considered a good test case for the aforementioned para-metric models governing the overall efficiency. To keep the comparison as pureas possible, we will consider the jet-hull operating in a potential flow. As aconsequence, the ducting losses are zero. It is furthermore assumed that thepump efficiency equals unity, that the nozzle centreline remains at the freestream water surface and that the resistance increment of the hull (1 +r) equalszero.

The overall efficiency lOA by Svensson [1989] now reduces to the followingrelation:

where p hull speed I nozzle velocity ratio; U./uc = potential flow velocity coefficient w'L70.

The wake fraction w, used by many authors, relates for a potential flow to thevelocity coefficient in the following way:

= l-w (2.88)

90

10A2p(l -c1,)

l-p2(2.87)

2Gp = 1Cvp

2ifluA

1

11e!110A = ll

where

2

= 1+NVR

NVR = nozzle velocity ratio u,/U0 or i/p.

Because we consider a potential flow, the momentum velocity coefficient Cm

equals unity. A representative value for IVR0 of 1.03 has been used.

The results of the above efficiency relations are plotted in Fig. 2.9 for a rangeof jet operating conditions (expressed in NVR value) and a strong flow retarda-tion (c=O.l). lt can be seen that three of the quoted efficiency relations predictvalues for the overall efficiency in excess of 1.0, which is unrealistic. Thiswould imply that we had found an original realization of the perpetuum mobile.The parametric expression that is discussed here shows values not exceedingunity, which is more realistic.

The effect of the above models on the interaction efficiency for a representativeflow retardation (c =0.95) is shown in Fig. 2.10. Although not explicitly givenin the efficiency reIìtions of other authors, the interaction efficiency flINT couldbe computed from the following relation:

flINT =fi OA (2.93)Iii

2.3 Interaction

A relation between the pressure coefficient G used by Svensson and the veloc-ity coefficient can be found using Bernoufi's theorem:

(2.89)

Similarly, the relation for overall efficiency 11OA by Dyne et al. l994] reducesto:

(2.90)

From the breakdown of the overall efficiency as proposed in this work, thefollowing terms remain:

91

(2.91)

(2.92)


92

2

o

0

1.2

1.15

Ez1.05

0.95

- - . - Svensson

Dyne [1994]

- -. Terwisga- modified

[1989]

[1993]

model

-- . -

- -.

Svensson [1989]

Dyne [1994]

Terwisga [1993]

modified model

-

*-

S,.'

-

05 15 2 25 35NVR [-I

Cvp = 0. 1. w= 0.9nozzle elevation, intake, pump and nozzle losses equal zero

Fig. 2.9 Computed overall efficiencies for an infinitesimal waterjet near the stagnation point

05 15 2 2.5 3 3.5

NVR [-1

Cvp 0.95, w = 0.05nozzle elevation, intake, pump and nozzle losses equal zero

Fig. 2.10 Computed interaction efficiencies for a waterjet in a retarded potential flow

Realizing that representative NVR values range from approx. 1.5 to 3, errors ininteraction (and thus in overall efficiency) occur from 1.5 to 2.5% (Dyne[19941) to 2.5 to 10% (Svensson [19891 and Van Terwisga [1993]). The para-metric model presented in this work yields an interaction efficiency with aconstant value of 1.0.

With the aid of eqs. (2.79) and (2.86), the effect of distortions in the viscousflow can be studied independently. This is done for a value of the NVR of 1.7,which is representative for design conditions. The velocity profile in the bound-ary layer is assumed to follow the n-th power law.

An example of the effect of the ingestion of boundary layer is given inFig. 2.11, where the overall interaction efficiency is plotted as a function of theratio of required flow rate and flow rate available from the boundary layer.Potential flow distortions are supposed to be absent. A maximum value in thiscase for the interaction efficiency due to the boundary layer of 1.06 is found forthe condition where a maximum of boundary layer flow is captured (in this casethe ingested flow rate amounts to 60% of the attainable flow rate from theboundary layer). For increasing flow rates at equal boundary layer flow rate, theinteraction efficiency approaches a value of I asyniptotically.

1.25

1.20

.15

1.10

I.05

1.00

0.95

0.90

0.85

0.800.5 1.5 2 25

Q1QbI

3 35

2.3 Interaction

4

93

Fig. 2.11 Effect of boundary layer height/ingested flow rate ratio Q'QhI on interaction effi-ciency

NVR= 1.7n=9

I '11m1

OINT

leI


2.3.4 Hull resistance increment

In a steady situation, the net thrust Tnet is counterbalanced by an effectiveresistance RE. This equilibrium of forces yields:

RE Tnet (2.94)

The effective resistance with active waterjet mounted, can be derived from thebare hull resistance in the following way:

RE = (2.95)A3 A8

where total mean stress tensor in x-direction for the flow conditionwithout waterjet mounted

AR = change in hull resistance due to waterjet action.

The integral terms in eq. (2.95) represent the effect of the change in hullgeometry on the hull's resistance, due to the waterjet. It is again assumed herethat the orientation of the x-ordinate is parallel to the hull's speed vector.

The integral over area A3 refers to the missing surface in the intake projected inthe hull plane. This area is referred to as projected intake area. The integralterm over the nozzle area A8 refers to a similar absence of area, where therewould be a pressure force acting during a resistance test.

For reasons of simplicity, we will transfer the latter change in resistance due tothe missing surface force on the nozzle area A8, to the relation between grossand net thrust. This results in an additional term in the relation for the thrustdeduction fraction t1 (eq. (2.27)), which subsequently becomes:

t1 _LJ J dA +JJ(-o)dA -JJcYdA +JJJp gd%' (2.39)X A+A2 A8 A4 V

A non-dimensional change in resistance or resistance increment fraction r wasdefined in Section 2.1.2 as:

94

'!

r----

r = _!_-f jYodA +AR}RBH

A1

where the resistance increment can now be written as:

Tnet1 +r =

RBH

2.3 Interaction

(2.97)

(2.98)

The resistance increment factor (1+r) is caused solely by the waterjet actionand geometry, and can therefore be regarded as a factor accounting for a trueinteraction effect of the waterjet on the hull performance.

Apart from the change in resistance due to the geometrical changes as discussedabove, the waterjet action causes a change in the local flow about the aftbody.This will change the pressure field, resulting in changes in wavemaking resis-tance. It may furthermore affect the equilibrium position of the hull. When thishappens, an additional change in global flow pattern about the hull occurs and achange in overall hull resistance occurs.

The jet induced hull resistance increment (AR) may be estimated from potentialflow panel codes, as will be discussed in Chapter 4.

An alternative method is provided by a set of resistance tests. For an estimateof the change in hull resistance due to the waterjet action (AR), we may assumethat this change is built up from two independent contributions. One contribu-tion being due to a change in the local flow pattern about the intake, the othercontribution being due to a change in global flow pattern about the hull. Thelatter contribution is caused by a change in equilibrium position of the hull dueto the jet action, and can be expressed in a change in rise of the hull (dz) and ina change in running trim angle (d'r).

The change in local flow about the intake, for a given intake geometry, isstrongly dependent on the ingested flow rate Q. Assuming free stream condi-tions, and neglecting viscous effects, the flow pattern is uniquely determined bythe intake velocity ratio ¡VR.

If the assumption on the independence between the changes in resistance due tothe local and the global flow appears to be true, the change in resistance can beestimated from a linear development in a Taylor series:

95


96

AR(Q,dz,d'r) = AR(Q,0,0) _(Q,0 ,0)dz (2.99)

A further simplification may consist from the assumption that the derivatives ofAR to the rise and trim angle are independent of the flow rate Q, so that wemay write:

(Q,0,0) = (0,0,0) (2.100)

and

(Q,0,0) = .(0,0,0) (2.10 1)

The partial derivatives of the resistance to the change in rise and trim angle cannow be obtained from resistance tests at varied displacement and position of thecentre of gravity. This procedure will be used in Section 3.4.

2.4 Conclusions

A systematic separation between waterjet and hull system appears to be poss-ible. This results in a set of parametric relations, explicitly describing the freestream characteristics of the subsystems and their mutual interaction effects.

The overall powering characteristics and interaction effects are essentiallyindependent of the choice of control volume, modelling the jet system. A skilfulchoice does however enhance the accuracy of measurements or needs fewerassumptions and simplifications in the derivation of the powering characteris-tics. The control volumes A and D in Fig. 2.1 are demonstrated to have usefulhydrodynamic properties. Control volume B will be demonstrated in Section 4.2to be advantageous in modelling the intake in computations.

The following conclusions relative to the physical interpretation of jet-hullinteraction are drawn. These conclusions contradict many statements in the openliterature.

There is no intake drag for a flush type intake operating in a potentialflow.

2.4 Conclusions

There is no interaction effect of the potential flow distortion by the hullon the jet performance, provided there is no hull induced pressuregradient over the intake area AD (Fig. 2.1). Additional conditions arethat the flow about the nozzle is not affected by the hull and that thehull has zero dynamic trim (see Section 4.3.2).There is no net contribution of the intake induced flow on the total liftforce of the jet-hull system. provided the area around the flush intakeopening is sufficiently extended.

97

Chapter 3

3 Experimental analysisThe objectives of the present chapter are threefold. First, a propulsion testprocedure is presented which deviates from the ITTC [1987] proposal (see Fig.1.13) on a number of points. Major differences occur in the flow rate calibra-tion procedure and the data reduction method. The modifications yield animprovement in both uncertainty and time required for the execution of thetests. This first objective is dealt with in the first two sections of this chapter.Secondly, an uncertainty analysis is presented in Section 3.3 with the aim toquantify the uncertainty in model propulsion tests, and to acknowledge thosefactors that dominate the resulting uncertainty. And thirdly, a selection ofsalient results will be presented in Section 3.4 that has been collected during thecourse of the present study. The physical interpretation of these results will bediscussed, providing a natural transition to Chapter 4, where we will take acloser look at the mechanisms of waterjet-hull interaction.

3.1 Propulsion test procedure

Model propulsion tests provide a means to obtain an accurate assessment of thepowering characteristics of the combined waterjet-hull system. Furthermore, itprovides a means to separate the interaction effects if the powering characteris-tics of both systems in their isolated condition are known. We will refer tothese latter characteristics as the free stream characteristics.

99

Chapter 3 Experimental analysis

In the present context, the term powering characteristics refers to thrust, deliveredpower and impeller rotation rate as a function of vessel speed. Thesecharacteristics of the combined system are preferably determined from a synthesisof the free stream attributes. That is; without interaction effects. The overallcharacteristics of the combined system can however not merely be obtained frommatching the attributes of the isolated systems.

The propulsion test procedure as recommended by the HSMV Committee of the18th ITTC [19871 has been used as a starting point. An argumentation for thischoice and some remarks on this procedure are given in this section.

The basic ITTC procedure is presented in Fig. 1.13 (Section 1.6.2). The procedureis based on a black box approach as far as the pump of the jet system isconcerned. The pump mounted in the model does not need to be scaled, but needsto be capable of delivering the required flow rate. Before focusing on thepropulsion test procedure, this black box approach is discussed in comparison topropulsion tests with a completely scaled pump unit.

Selection of test set-up

Two possibilities to model the waterjet system in the model hull are schematicallypresented in Fig. 3.1. In option 1, mass, momentum and energy flux through thewaterjet system boundaries are determined from measurements on flow rate andvelocity distribution in the intake. The corresponding thrust and power requirementis obtained from the relations discussed in Chapter 2, Sections 2.3.1 and 2.3.2.

In option 2, the thrust and power delivered to the impeller are measured directlythrough force and torque transducers. The free stream powering characteristics ofthe jet system are then expressed in a similar manner as propeller open watercharacteristics. In this procedure, interaction effects can only be related to resultinginteraction effects on the pump characteristics. This method prohibits a break downof interaction in terms of hull effects and waterjet system effects, because theboundaries between the two systems are situated well within the jet system. Moreprecisely about the pump. A breakdown between jet system and hull isnevertheless desirable for an effective use of interaction data in preliminary shipdesign.

The latter option also imposes severe constraints to the test set-up. To be able todetermine the powering characteristics of the combined waterjet-hull system, a hullmodel with an integrated and properly scaled waterjet unit should be used. Thismodel should be large enough to avoid uncontrollable scale effects within thewaterjet system.

100

u(z)

Fig 3.1 Possible approaches for waterjet modelling in propulsion tests

The delivered power to the impeller and impeller rotation rate are now measureddirectly. Correction for internal scale effects in the jet are necessary to arrive at afull scale prediction.

A practical disadvantage of option 2 is that a direct measurement of the thrust iscomplicated. This is because the total force of the waterjet system acting upon thehull is passed through to the hull through all points in which both systems areconnected to each other. A solution to this problem is to put the complete waterjetsystem, including the driving motor, on a force measuring frame. Special careshould be taken that the flexible connections between jet system and hull areunable to pass forces. These connections should be watertight sealings to avoidleakage. Fig 3.2 shows a set-up based on this modelling procedure that has beenused in the early days of waterjet testing at MARiN. Because of its complexity,the adverse dynamic mass-spring characteristics of the measuring frame and thecosts involved, it was decided to abandon further developments in this direction.

It may be clear from the description of the test set-up of option 2, that thisprocedure is both expensive and time consuming. Due to its technical complexity,it is sensitive to bias errors during the tests. Furthermore, it does not directly giveinteraction data between the bare hull and the jet system. Data which are usefulin the selection of existing waterjet systems. For those reasons, this test set-up isnot considered further in this work.


I) See Appendix 3 for definitions on accuracy and related terminology.

101

Option i Option 2Scaled intake and nozzle Fully scaled waterjet systemblack box pump

Flow rate Q


102

forcebalance

connection to ship model

/

equipment frame

flexible seal

drivemotor

>seal

flexible seal

ibase line

i

Fig 3.2 Test set-up for complete model of waterjet system

Description of propulsion test procedure

The same modelling of the jet system and the same sequence of activities asproposed by the HSMV Committee of the 18th ITTC is used throughout this work(see Fig. 1.13, Section 1.6.2). The experimental method that results from theinvestigation described in this chapter, differs from the aforementioned ITTCprocedure in essentially the flow rate calibration procedure and the data reductionmethod. A further deviation occurs in the way in which characteristics of theingested flow are measured.

Flow rate measurement

The flow rate measurement procedure is extensively treated in Section 3.2.

Propulsion tests

After having a flow rate measurement procedure, the ITTC {1987] proposes twodistinct propulsion tests (see Fig. 1.13). The first propulsion test in the ITTCprocedure is meant to determine the impeller rotation rate and the flow ratethrough the jet system. A second propulsion test is subsequently proposed wherethe velocity profile just in front of the open intake is measured with a pitot staticrake. The velocity profile measurement is to be done with preset impeller rotation

rate, as obtained from the first propulsion test. This is because minor differencesin impeller rotation rate in the self propulsion point could occur because of theadded resistance of the pitot rake.

It has been demonstrated in Section 2.3 however, that it is essentially the viscousenergy and momentum deficit that needs to be measured during the propulsiontests. The simplest way to do this is to measure the velocity profile in theboundary layer. The boundary layer thickness can be obtained by fitting atheoretical velocity profile through the experimental data (see Fig 3.3).

1.1

1 .0

u . u


(3.1)

103

0.9

0.8

0.7

Measured

- Computed

model boundary layer: n = 7

I j

0 0.5 1 1.5 2

z/ö [-J

Fig 3.3 Example fit between measured and computed boundary layer velocity profile

A suitable model for this velocity profile is given by the power law:

u(z) (Z I/fl

-u


Because the intake area AB (Fig. 2.1) is situated in the flow region with lowintake induced velocities, the boundary layer characteristics can also be measuredduring a resistance test. That is; with closed intakes. Analogous to the vocabularyused in propeller hydrodynamics, we could speak here about the nominal wakefield for the waterjet intake.

An alternative procedure is provided by Dyne et al. [1994]. These authors proposeto determine a momentum and an energy frictional wake fraction from a set ofvelocity and pressure measurements. This method is however more elaborate andis unlikely to contribute to a lower uncertainty for the so-called thin boundarylayers. In this context, a boundary layer is called thin if the pressure gradientperpendicular to the wall is negligible. This can be assumed for almost all waterjetpropelled hull forms.

We have seen in Section 2.3 that the potential flow velocity just in front of theintake does not play an important role in overall powering characteristics. Only amodest contribution in the energy interaction efficiency could be discerned(eq. 2.86). If the potential flow component is obtained from measurements, oneshould take care that the intake induced velocity is not included, as this is notcontributing to the interaction. It is therefore better to use the nominal wakevelocity distribution, measured during the resistance test.

Data reduction method

The difference between the data reduction method proposed in this work and theITTC [19781 procedure is mainly caused by the difference in parametric model(Chapter 2) and the different flow rate calibration procedures used. The datareduction method resulting from this work is schematized in Fig 3.4. The numbersin parentheses, given for the key data, refer to the relations needed for theircomputation.

Extrapolation method

The extrapolation method is discussed in Section 3.5

Final prediction

A final prediction of powering characteristics in terms of power delivered to thepump impeller and impeller rotation rate involves incorporation of the internal jetsystem characteristics. These characteristics can be obtained from experiments onthe isolated jet system and matching of jet system data with extrapolatedpropulsion test data, as indicated in Fig. 1.13.

104

Model Geometry

Wi

Calibration5et' a0, a1

Propulsion test

Data Analysis

u(z)

RBH u(z)

cm(App.2)

t (3.39)

TgL (3.10)

Dp U0


U01_ p

Ce (App.2)

A0

JSE (3.36)

1e1 (2.86)

1NT(4.42) 11

numbers in brackets refer to equation numbers

Fig 3.4 Flow chart of data required for propulsion test analysis

3.2 Flow rate measurement

As can be concluded from the HSMV Committee reports of the 18th [1987] and20th [1993] ITTC meetings, it is difficult to carry out flow rate measurements withsufficient accuracy. This section gives an account of the search for such a method.

en

Z

1 0

en Z0


3.2.1 Flowmeter selection

There are well over one hundred different types of flowmeters currently availableand several other techniques are the subject of R&D around the world. Such awide variety is making meter selection and correct application increasingly difficult(Fumess [1990]). The purpose of the work addressed in this section is to identifythe most promising flowmeter in waterjet propulsion tests.

Three aspects in the selection of a flowmeter have been considered here:

Performance considerationsInstallation considerationsEconomic considerations.

As to the economic aspects of a flowmeter, acquisition, operational andmaintenance costs determine the overall costs. The operational costs refer to thecosts required for the installation of the meter, its calibration for each set ofexperiments and its reliability. To keep the costs as low as possible, it was decidedto initially focus in this work on robust flowmeters for which relatively muchexperience is available. Mainly for these reasons, attention was limited to theflowmeters from the Groups 1, 2 and 4 from Table 3.1.

Table 3.1Classification of flowmeters (BSJ Guide 7405 [199 lJ)*

* refers to endnote on page 169

106

Group Flowmeter description

I Orifices, venturis and nozzles

2 Other differential pressure types

3 Positive displacement types

4 Rotary turbine types

5 Fluid oscillatory types

6 Electromagnetic types

7 Ultrasonic types

8 Direct and indirect mass types

9 Thermal types

10 Miscellaneous types

The first two groups consist of differential pressure transducers, Group 4 consistsof rotary turbine type meters. Two of the three flowmeters mentioned by theHSMV committee (venturi pressure taps and paddle wheels) belong to theseselected groups (Groups i and 4 respectively). The third meter, a water collectingcontainer is not treated by the BSI. This type of flow measurement will beaddressed in the section on flow rate calibration, together with an alternative 'weir'method.

We will concentrate in this section on reference flowmeters for installation withinthe model jet. In line with the ITTC recommendations, the flowmeter will beseparately calibrated for each jet.

Performance considerations

Performance considerations deal with the required accuracy2" of the flowmeter andthe expected range of flowrates to be measured. In the case of waterjet propulsion,the required accuracy is determined by the accuracy that is required for the thrustdeduced from the propulsion tests. The model thrust is a suitable performanceindicator, as this variable plays a dominant role in the extrapolation procedure andhence in the final power-speed prediction. As a first aspiration level for theaccuracy of the thrust measurement, the error in direct thrust measurement on apropeller may be taken. To this end, we will use an estimate on the experimentalstandard error for propeller thrust measurements from model propulsion tests(ITTC [1978]), which is derived to be approx. i to 2% of the mean value.

To study the relation between uncertainty in waterjet thrust and flow rate, we willconsider the relative sensitivity 06 pertinent to gross thrust, defined by:

¿ET -0' (T) = _-__g

QTg

where the overbars denote average values.

This relative sensitivity is a measure for the propagation of an error in flow rateto the error in thrust. The relative sensitivity is a non-dimensional quantity, relatingthe non-dimensional error in flow rate to the non-dimensional error in thrust. Amore detailed explanation on the propagation of errors is given in Appendix 3.

3.2 Flow rate measurements

(3.2)

2) See Appendix 3 for definitions on accuracy and related terminology.

107


To find the sensitivity of thrust for errors in flow rate, we will use the followingrelation between thrust and flow rate (from eq. (2.78)):

P(QCmt1O) (3.3)n

where p = mass density of waterQ = flow rateA,1 = nozzle areac,,1 = momentum velocity coefficient due to the velocity distribution in

the intakeU0 = free stream velocity.

The relative sensitivity of thrust for an error in flow rate is now found to be:

2NVR-ce'(T) 'nQ g NVRCm

where NVR =nozzle velocity ratio; u/U0.

A similar exercise for the effective jet system power JSE can be made, using eq.(2.81). After neglecting the contribution of the sinkage of the nozzle, we find:

3NVR 2_c2

0(JsE)= 2

(35)NVR Ce

Fig 3.5 shows the relative sensitivities of net thrust Tnet and effective jet systempower JSE for errors in flow rate, as a function of the nozzle velocity ratio NVR.Representative values for the momentum velocity coefficient Cm and energyvelocity coefficient c of 0.9 have been applied here.

It is seen that the relative sensitivity of the thrust increases drastically for ¡'[VRvalues smaller than about 2. Consequently, for most waterjet operational conditionswhere NVR adopts values between 1.5 and 3, an error of 1% in flow rate alreadycauses an error of 3.5 to 2.4% in derived thrust. For the effective jet system power

JSE errors between 4.3 and 3.2% would result.

108

(3.4)

15

o


109

I

I

- 8'Q (Tnet)

- - 9'Q (JSE

IIL-Cm = 0.9, Ce2 = 0.9

o 2 3 4

NVR [-1

Fig 3.5 Relative sensitivities of thrust and power for flow rate

These values of the relative sensitivity emphasize the importance of an accurateprocedure for the flow rate measurement.

Table 3.2 lists the performance for various types of flowmeters. Based on thisreview and the aforementioned economical considerations, it was decided to focusin some more detail on the venturi type flowmeter, using the nozzle geometry asventuri (Group 1), to the averaging pitot (Group 2), and to the insertion turbineflowmeter (Group 4).

Installation considerations

For a further selection of flowmeters, we will consider the installationconsiderations here.

Two installation constraints that should be met by the selected flowmeter can beacknowledged. One constraint is imposed by the jet model. It limits the allowableflowmeter distortion in order to have a reliable flow model for the full scalewaterjet without flowmeter. The other constraint is imposed by the flowmeter inorder to obtain reliable signals.


Table 3.2Performance factors in flowmeter selection (from BSI Guide 7405 [199 lI)*

110

Group Type Linearity [%] Repeatability [%] RangeahilityPressure I)

drop atmaximum

flow

1 Orifice # # 3 or 4: I 3/4Venturi # 3 or 4: 1 2Nozzle 3 or 4: I 2/3

2 Variable area ±1 to ±5% FS ±0.5 to ±1% FS 10: 1 3

Target NS NS 3: I 3

Averaging pitot # ±0.05 to ±0.2% R # 1/2Sonic nozzle ±0.25% ±0.1% 100: 1 3/4

3 Sliding vane ±0.1 to ±0.3% R ±0.01 to ±0.05% R 10 to 20: 1 4/5Oval gear ±0.25% R ±0.05 to ±0.1% R 4

Rotary piston ±0.5 to ±1% R ±0.2 R 10 to 250: 1 4/5Gas diaphragm No data No data 100: 1 2

Rotary gas ±1% ±0.2% 25: 1 2

4 Turbine ±0.15 to ±1% R ±0.02 to ±0.5% R 5 to 10: 1 3

Pelton ±0.25 to ±0.2% R ±0.1 to ±0.25% R 4 to 10: 1 4

Mechanical meter No data ±1% ES 10 to 280: 1 3

Insertion turbine ±0.25 to ±5% R ±0.1 to ±2% R 10 to 40: 1 1/2

5 Vortex ±1% R ±0.1 to ±1% 1/ 4to 40: 1 3

Swirlmeter < ±2% R NS 10 to 30: 1 3

Insertion vortex ±2% ±0.1% R 15 to 30: 1

6 Electromagnetic ±0.5 to ±1% R ±0.1% R to 0.2% FS lOto 100: I

Insertion electro-magnetic

±2.5 to ±4% R ±0.1% R 10: 1

7 Doppler No data ±0.2% FS 5 to 25: 1 I

Transit time ±0.1 io 1% R ±0.2% R to ±1% F5 10 io 300: 1

8 Coriolis NS ±0.1 to ±0.25% R 10 to 100: 1 2/5Twin rotor No data No data 10 to 20: 1 3/4

9 Anemometer No data ±0.2% PS 10 to 40: 1 2Thermal mass ±0.5 to ±2% FS ±0.2% F5 to ±1% R 10 to 500: 1 2

IO Tracer No data No data Up to 1000: 1 iLaser No data ±05% R Up to 2500: I I

Key:% R is the percentage flow rate% ES is the percentage full scaleNS indicates not specified

is dependent on differential pressure measurement

U lis low; Sis high

Let us first address the constraints imposed by the waterjet system on theflowmeter. It is important that the flowmeter should not change the relationbetween the flow rate and thrust developed by the jet. This consequently impliesthat the influence of the flowmeter on the velocity distribution and the staticpressure in the intake and the nozzle should be negligible. Another constraint isthat it should not have large external protrusions that create additional drag. Thismay especially be important at the lower speeds, where the nozzle is fully orpartially submerged.

Let us secondly consider the constraints imposed by the flowmeter. There are twomain types of disturbances affecting the flowmeter performance; flow profiledistortion and swirl' (Fumess [19901). Many flowmeters require therefore a certainundisturbed upstream pipe length in the order of JO diameters or more in front ofthe meter. A somewhat smaller length is usually required downstream of the meter(see Table 3.3). Often a flow straightener is required as well.

Profile distortions may for example be caused by an obstruction partially blockingthe conduit, such as e.g. large flow separation or cavitation in the waterjet intake.Swirl may be generated by e.g. an impeller, a turbine or a stator. lt may also becaused by the ingestion of axial vorticity from the external flow, caused byappendages or chines ahead of the intakes (see e.g. Brennen [19941). Swirl is farmore difficult to correct for than velocity profile distortion. Fig 3.6 shows that aswirl angle of 1 deg already causes a deviation in the calibration coefficient of aturbine meter of approx. 2%, leading to a similar deviation in flow rate. In contrastto the sensitivity of the turbine meter, Fig. 3.7 shows that a multiport averagingpitot has a tolerance of an angle of approximately 3 deg with the onset flow.

12

loLiquid turbinemeter

Vo

L)

VL) 4

2Q-)

Q-3

o

C-)

Swirl angle, degrees

Fig 3.6 Effect of swirl on turbine meters (from BSI Guide 7405 [1991])*


Gas turbinemeter

111

5010 20 30 40


Table 3.3Flowmeter installation constraints (from BSI Guide 7405 [19911*

112

Group Type Orientation DirectionQuoted rangeof upstream

lengths

Quotedrange of

minimumdownstream

lengths

Fil-ter

Pipebore range

[mm]

I OrificeVenturiNozzle

H, VU, VD, IH, VU, VD, IH, VU, VD, I

U, BU

U

SD/80D0.5D/29.5D3D/SOD

2D/8D4D2D18D

NN

6 to 2600> 6

2 Variable areaTargetAveraging pitotSonic nozzle

VUH, VU, VD, IH, VU, VD, IH, VU, VD, I

U

U

U, BU

OD

6D/2OD2D/25D> 5D

OD

3.5D/4.5D2D/4D> OD

PNPN

2 to 60012 to 100> 25

5

3 Sliding vaneOval gearRotary pistonGas diaphragmRotary gas

H, VU. VD. IHH, VU. VD, IHH. VU, VD, I

U

UUU

U, B

OD

OD

OD

OD

OD/IOD

OD

OD

OD

OD

OD/3D

RRRNR

25 to 2504 to 4006 to 100020 to lOO50 to 400

4 TurhincPeltonMechanicalmeterInsertion turhinc

H. VU, VD. IH. VU, VD. IH, VU, VD, I

H, VU, VD, I

U, BUU

U. B

5D/2OD5D3D/IOD

JODI8OD

3D/1ODSDID/5D5

D/IOD

PRR

P

5 to 6004 to 2012 to 1800

> 75

5 VortexSwirlmeterInsertion vortex

H. VU. VD, IH, VU, VD, IH, VU. VD, I

U

UU

lD/4OD3D20D

SDIDSD

NNN

12 to 20012 to 400> 200

6 ElectromagneticInsertion electro-magnetic

H, VU, VD, IH, VU, VD, 1

U, BU, B

OD/IOD25D

OD/5D3D

NN

2 to 3000> WO

7 DopplerTransit time

H. VU. VD, IH. VU, VD. I

U. BU, B

IODOD/5OD

SD2D/5D

N

N> 25> 4

X CoriolisTwin rotor

H, VU, VD, IH, VU, VD, ¡

UU

OD

2OD

OD

SDNN

6 to 1506 to 150

9 AnemometerThermal mass

H. VU, VD, IH. VU, VD, I

U, BU

IOD/4OD

No dataNo dataNo data

R

R

> 252 to 300

(1 TracerLaser

H. VU, VD, IH. VU, VD, I

U, BU, B

#OD

#OD

NP

Unlimited

Key:H is horizontal flow U is uni-d irectional flowVU is upward vertical flow B is bi-directional flowVD is downward vertical flow R is recommended

is inclined flow N is not necessary# is mixing length P is possible

o

3.2 Flow rate measurement..

Fig. 3.7 Installation guidelines for multiport averaging static pitot tube (from BSI Guide 7405[199 1I)*

Considering the installation constraints for the waterjet system, it soon becomesclear that in no part of the system a developed, swirl free and undisturbed velocityprofile will occur. This observation implies that the fiowmeter used should becalibrated under the conditions for which it is used, and that it should show littlesensitivity to flow profile distortions and swirl. Ideally, this means that beforeconducting the actual propulsion test, first a calibration test should be made at thesame model speed and impeller rotation rate. This procedure is followed by theNorwegian towing tank, where pitot tubes in the intake are used as flowmeters(ITTC [1993]).

Flow rate calibration at non-zero speeds is a complicated and time consuming taskhowever. We will therefore consider the consequences of calibrating the flow rateat zero speed in the following. It is thereby noted that the flowmeter is calibratedin its actual position, but at a slightly different operating condition of the jet.

Calibrating at zero model speed only yields reliable results if the distinct operatingcondition does not introduce significant deviations in the flowmeter reading. Thisis an essential constraint, because minor deviations in the pump's working pointare known to occur due to this change in operation, which may consequently causea minor change in velocity profile as well as in swirl.

113

Q

t,

I.

'i,

o o


Apart from small variations in pump working point, deviations in the jet velocityprofile may also occur through the occurrence of separation in the intake andchanges in the ingested boundary layer (or velocity profile).

To minimize the effect of large changes in velocity profile, the best position forthe flowmeter is situated between the stator of the pump and the nozzle exit area.Initial disturbances in the ingested flow are thus levelled out by the impeller andstator action.

Based on observed differences in working point between bollard pull andpropulsion tests and the consequent deviations in swirl, it was decided to stopfurther evaluation of the insertion turbine meter at this point.

Jet velocity profile study

To obtain more insight in the differences occurring in velocity profile between thespeed zero or bollard pull condition and the operational condition at non-zerospeed, velocity measurements with a five fingered pitot static rake were conducted.To this end, the pitot rake was mounted in such a way that the stagnation pressureis measured in the nozzle discharge area (A8 in Fig. 2.1). A sketch of this set-upis shown in Fig 3.8.

Fig 3.8 Nozzle geometry and pitot static rake position used for the jet velocity profilemeasurements

114

Fig 3.9 Positions of venturi pressure taps and asp

The relation between reference velocity and local velocity in the nozzle was foreach position found from linear regression analysis.

A review of the experimental programme on the jet velocity profile measurementsis given in Table 3.4.

Impeller rotation rates at the self propulsion point of ship were selected, becausethis is the operating condition in which the flow rate is to be measured.


The shift in pump working point that occurs for changing model speeds (resultingin a change in non-dimensional flow rate K0), causes a change in the relationbetween flow rate and impeller rotation rate. To ensure that the velocity profile iscompared at equal flow rate, a reference velocity transducer was mounted. Therelation between flow rate and reference velocity was thereby assumed to beindependent of model speed.

The reference velocity signal was obtained from a venturi flowmeter. The venturifiowmeter consisted of four circumferential pressure tappings at each of twodistinct cross sections in the nozzle (see Fig 3.9).

115


The results of the velocity profile comparison between zero and non-zero speed atequal flow rate are presented in Fig 3.10. The measured velocity u in the jet ateach of the five positions is expressed in the corresponding velocity u thatwould have occurred during the bollard pull test at speed zero. The latter velocitywas obtained from the linear regression formulas. The local velocities for the twohighest impeller rotation rates in the vertical cut are obtained by extrapolation ofthe linear regression relation.

116

0.60

Table 3.4Review of jet velocity profile measurements

vertical plane1.6

-e-- n=2600, Vm=3.l-o.. -- n=3600, Vm=4.7

20 40 60 80

1.0

0.85100 0

horizontal plane

- -- n=2600, Vm=3.l- -4- n3 100, Vm=3.7

20 40 60 80 100

Type of testCondition

V [rn/sini Impeller n [rpm]

Horizontal plan 0 8001200160026003100

3.1 26003.7 3100

Vertical plan 0 80016002400

2600 (2*)3.1 26003.7 31004.7 3600

radial position from radial position fromupper nozzle wall [mmj portside nozzle wall [mm]

Fig 3.10 Effect of model speed on jet velocity profile


For all pitot positions, all measurements could be used for the regression analysis,with the exception of the point in the vertical cut at a radial position of 68 mm.For this point, the two lowest impeller rotation rates were skipped because theydisproportionally increased the standard error in the regression coefficient.

With these results, the deviation in average (momentum) velocity in the nozzle canbe assessed when a five port averaging static pitot ('asp') would be used for flowrate measurements that is calibrated at speed zero. The mean momentum velocityis obtained from the square root of the asp pressure differential.

Because the signal of the asp is made up from the average of the local velocitypressures, this signal can be written as:

Lu (3.6)DPasp =

where Ç = asp calibration coefficient= local velocity at position i

n = number of ports on asp.

The calibration coefficient Ç is supposed to be independent of model speed. Theeffect of model speed on the average momentum velocity can now be assessed bystudying the ratio of the asp pressure differentials between bollard pull andpropulsion test. In the case of true independency, the following equation shouldhold:

117

u)2/, = 1 (3.7)

jr1 UI?/?

Table 3.5 shows the results of the computed pressure ratio values.

It is seen from this table that all values are within 1% deviation, except for themeasurements in the vertical cut at a model speed of 3.1 mIs, where a deviationof some 4% occurs. A similar exceptional behaviour is observed from Fig 3.10 forthis condition.


Table 3.5Results on five port asp check

No simple explanation for the exceptional behaviour at this single point is readilyavailable. It should be noted however, that due to the relatively large nozzleopening (see Fig 3.9), the pump is operating outside its design range, resulting ina lightly loaded pump operating at low efficiency. This condition may result in anunstable flow in the impeller, leading to more than one possible velocity field inthe nozzle. The resulting deviation in velocity profile is clearly not sufficientlyhandled by a five port asp.

Flowrneter evaluation

Taking the preceding considerations on flowmeters into account, two types offlowmeters were tested on their suitability. These types are:

One and four tap venturis, making use of the nozzle contractionMultiport averaging pitot tube.

The positions where these transducers were installed in the nozzle are depicted inFig 3.9.

Both venturi meters showed to be very sensitive to local distortions caused byother transducers. Similar distortions may occur in the lower speed region wherethe nozzle is not yet completely ventilated. These conditions would subsequentlyaffect the relation between flow rate and venturi signal. The one tap venturi metershowed a greater sensitivity than the 4 tap meter, as could be expected.

118

Type of testModel speed

Vm [mIsi

/V[E(u/u1 bp)2'1

Horizontal cut3.1 0.9903.7 1.002

Vertical cut3.1 1.0423.7 1.0094.7 1.008


Furthermore, the precision error of the venturi meter signal appeared to be approx.twice the precision error of the asp signal (2% versus 1% of the mean signal).

In addition to the lower quality of the signal, the venturi meter is more prone tosystematic errors due to a skewed velocity profile relative to the calibrationsituation, as can be inferred from Fig 3.10.

The averaging static pitot (asp) was selected as the most promising flowmeter forthe following reasons:

The asp only interferes to a limited extent with the flow in the nozzle area(A8 in Fig. 2.1).The precision error of the asp signal appeared to be approximately half theerror of the 4 tap venturi meter. It furthermore showed to be less sensitiveto local flow distortions.The sensitivity of the asp for local flow distortions has been studiedthrough the determination of the nozzle velocity profile and turned out toresult in bias errors within 1%, where deviations in local flow velocity upto 10% occurred (Fig 3.10). According to the BSI Guide [1991],deviations in angle of attack (on the asp cross section) up to 3 deg due toswirl for example, do not significantly affect the meter calibration.

3.2.2 Calibration procedure

Before conducting the propulsion test, the selected flowmeter needs to becalibrated, as mentioned in the previous section. From the summary of previouswork on flow rate measurement (Section 1.6.2), it is concluded that almost allprocedures suggested in the course of time, attempt to accurately measure the flowrate, in order to derive the thrust. A similar procedure was also attempted in thebeginning of the present work. The uncertainty of propulsion test results however,largely depends on the uncertainty of the flow rate calibration. It appeared aftermany attempts, that although sufficiently accurate results were incidentallyobtained, the uncertainty of this 'flow rate calibration procedure' is unacceptablyhigh.

As a consequence, direct calibration of the thrust from the nozzle during a bollardpull test was attempted. This procedure will be referred to as 'thrust calibrationprocedure'. It appeared to significantly improve the accuracy of the thrust derivedfrom propulsion tests.

119


A broad outline of both calibration procedures will be given first. Subsequently,each procedure will be described in more detail and obtained results will bediscussed in terms of their contribution to the overall uncertainty. Finally, anevaluation of both procedures is made, based on the estimated uncertainty of theirresults, and the propagation of errors in the final thrust and power prediction.

Outline of Jlowmeter calibration procedures

Fig 3.11 shows schematically the activities and the results for both calibrationprocedures.

120

FLOW RATE CALIBRATION

Flow rate calibration- V-notch weir- WC Container

+Bollard pull test

+Propulsion test

Fig 3.11 Scheme of flowmeter calibration procedures

The 'flow rate calibration procedure' consists of three activities. The first activityis the actual flow rate calibration. This calibration determines the relation betweenthe flow rate Q and the differential pressure Dp from the asp. The obtained relationis subsequently used in the bollard pull test (second activity), resulting in a thrustderived from the asp signal and a pulling force, directly measured on the model.A bollard pull thrust deduction fraction tbp is obtained, which is defined as:

P TJetx

THRUST CALIBRATION

Bollard pull thrustcalibration

+

(3.8)

Propulsion test - T-V

Q-Dp

__-ø tp tbp

- T-V


where T. = thrust from jet (from discharged momentum) in x-direction'xbp = pulling force acting on model in x-direction at bollard pull.

This bollard pull thrust deduction was used as a check on the thrust derived fromthe asp. Based on experience with propeller driven hulls, it was known thatrepresentative values for the thrust deduction fraction should not be much higherthan 0.05. If the bollard puil thrust deduction fraction met this empirical criterion,the flowmeter calibration was considered successful.

The relation between flow rate and asp signal was subsequently used in thepropulsion tests, where the waterjet net thrust could be derived from the relationfor gross thrust (see Section 2.3.1):

Tg COSOnPQCmUO (3.9)

where O, = nozzle centreline inclination relative to vessel fixed x-ordinate(see Fig. 2.3).

It will be derived and experimentally demonstrated later however (Section 3.2.3),that for most configurations, the thrust deduction fraction for a waterjet driven hullin bollard pull condition should approximately equal zero. With this knowledge,

a direct relation between the asp-signal and the momentum flux from the nozzle,

or jet thrust Tjetx could be obtained. Using eq. (3.9), the net thrust during thepropulsion test can be approximated from:

Tgoo ietxCn1UOTietxPA,i

cosO(3.10)

Apart from the net thrust, the effective jet system power JSE can be obtainedfrom either the flow rate or the bollard pull thrust.

In the substitution of flow rate for jet thrust in the relations for net thrust andpower, it is assumed that the jet velocity profile is sufficiently uniform to equatethe mean momentum and energy velocities to the mean volumetric velocity.Should this not be the case, the differences in mean velocities can be accountedfor with momentum and energy velocity coefficients (Cm and Ce), as introduced inSection 2.3. The relation between jet thrust and flow rate is then given by:

121


where c,, = momentum velocity coefficient in nozzle discharge area.

Flow rate calibration

A number of methods to measure the flow rate with the greatest possible accuracyand certainty have been investigated. The methods considered (in arbitrary order)are:

calibrated flowmeter in a straight pipe sectiondirect mass flow measurement through weighing of collected waterintegration of velocity profile in the jetV-notch weir.

Calibrated flowmeter in a straight pipe

A calibrated flowmeter in a straight pipe can be used in a set-up where the pipeis connected to the nozzle of the waterjet unit. An advantage of this method is thatan accurate flowmeter can be selected and can be mounted in line with theappropriate installation constraints. Disadvantages are:

a relatively complicated test set-up for calibration is neededmore than one pipe diameter and flowmeter may be necessary to cover therequired range of flow rates (a range of 5 - 70 lIs was required).

Provided the installation constraints pertinent to the flowmeter are met (Section3.2.1), this method of calibration is potentially satisfactory. The complexity of therequired test set-up and the acquisition costs were initially considered prohibitivefor successful application.

This method has been used once in this work to calibrate a V-notch weir, whichwill be discussed later in this section. For this purpose, a turbine flowmeter was

used.

et-

CnmA

(3.11)

122

Mass flow measurement through weighing

Collecting the water discharged from the nozzle and weighing it as a function oftime has been used by several institutions (see e.g. ITTC [1993]). This method hasbeen applied in the present work in two different set-ups.

The first set-up consisted of a large container, suitable of collecting water for asteady period of about 10 seconds at a flow rate of approx. 70 1/s. Because of thedimensions and the weight of the replenished container, this flow rate calibrationcould only take place at zero speed of the ship model. A practical disadvantagewas furthermore that the container had to be emptied at regular intervals, makingthe whole calibration procedure time consuming.

Later on during this work, a smaller water collecting container (WC container) wasdesigned for a smaller maximum flow rate calibration. This WC container had theadvantage that it was so small and light that it could be mounted onto the carriageof the basin, thus allowing for a calibration at speed. Another advantage was theautomated valve in the container, which could be adjusted to collect water overany required time interval. The valve opening angle could be measured as afunction of time, thus giving the possibility to estimate the errors due to the lapseof time during opening and closing of the valve.

The WC container has been used during one sequence of tests, with the aim toobtain an indication of the start and stop errors, of the sensitivity to differences incollecting time and the repeatability of the measurements. A photograph of the WCcontainer in operation is shown in Photo 3.1. The photo illustrates the whiskerspray over the box, which potentially leads to a bias error. It can furthermore beseen that the sealing of the valve was not sufficiently adequate to guide the full jetinto the container without losses. The corresponding leakage losses were estimatedto amount to approx. 0.3 L's.

Fig 3.12 shows some of the results obtained with the WC container. In this graph,the flow rate obtained from the WC container is plotted against the square root ofthe asp pressure reading. It clearly shows the scatter of the data, which wasconsidered unacceptably large for accurate thrust measurements. Although theabove mentioned defects could probably be reduced to a certain extent, theinherent uncertainty of the set-up was considered too large to render this apromising method.


123


124

Photo 3.1 The water collecting container in operation

16

14

12

lo


16 18 20 22 24 26

V Dp asp [cmwcl

Fig 3.12 Comparison of flow rates WC container and bollard pull calibration

Integration of velocity profile

Based on the measurements mentioned in Section 3.2.1 on the jet velocity profilein the nozzle, an estimate of the discharged flow rate can be obtained from anintegration of the measured velocity profile over the nozzle area. To this end, thepitot static rake was set at four different angular positions in the jet. The resultingvelocity profiles are presented in Fig 3.13.

Due to the non-uniform and non-symmetric character of the velocity profile andthe limited number of measured positions, the uncertainty in the velocity profilewas considered too big to allow for an accurate flow rate from velocity integration.An important contribution to this uncertainty is due to the asymmetry of the axialvelocity close to the nozzle centre (Fig 3.13). Both the symmetry and theuniformity of the velocity profile are expected to improve for smaller nozzle/pumpdiameter ratios. A further improvement is expected when the pump operates closerto or in its design range of working points.

125

Aa WCC. Vm=0, n=2500

o D WCC, Vm=0, n=3200

G WCC. Vm=2.53 / 5.36o

jet thrust, Vm=0

R


126

1.2

1.1

0.9

0.8

0.7

£. £j

D

.o

D4Sdeg

O 90deg

£ I35deg -

l8Odeg

£O

o

-0.5 0.5

Fig 3.13 Measured velocity profile at nozzle discharge opening

From the limited set of experiments conducted, it is concluded that flow ratemeasurement through velocity field integration is time consuming for sufficientaccuracy. Furthermore, one should be ascertained of a steady and stable flowpattern in the nozzle if the velocity field is measured by timewise sequentialvelocity measurements.

V-notch weir

Flow rate measurement through weirs is common practice in civil engineering tomeasure flow rates through open channels. This technique is furthermoreunderstood to be applied by pump manufacturers for accurate flow ratemeasurements.

A wide variety of weir types exists (see e.g. Bos [1990]). Of these types, the'sharp crested V-notch weir' (Fig 3.14) was selected, because of its simplicity, itsrangeability (5-70 1/s was required) and its expected accuracy.

For use in the calibration of jet discharged flow rate, the weir is mounted in a 4m long container, as shown in Fig 3.14. The weir is mounted at one end of thecontainer. The water supply is positioned at the other end. Two plates weremounted just after the water supply, to damp the turbulence and wave generationcreated by this supply.

Source publication LRI no. 20International Institute for Land Reclamationand Improvement Copyright:

dimensions in Em]

Q Ç 2.5(2g) tan(_) h2


Fig 3.14 V-notch sharp crested weir (from Bos [1990]); V-notch weir container

Two distinct notches could be mounted, one having a notch angle O of 90 deg, theother having an angle corresponding to a quarter of the tangent of 90 deg (28 deg).This latter notch is considered more accurate for the flow rates in the lower range.

The flow rate for a V-notch weir (fully contracted) is obtained from:

(3.12)

where Ce = coefficient of discharge; Ce =f(h1/p1, p1/B1 and O) (see Fig 3.14)= notch angle

he = effective head; he = hj+Khh1 = actual discharge head (see Fig 3.14)K17 = coefficient representing the combined effects of fluid properties.

By measuring the discharge height h1, the flow rate through the weir can becalculated.

Because of the importance of accurate flow measurements, the weir itself has beencalibrated in order to reduce the bias error in the flow rate (Willemsen et al.[19921). Calibration of the weir was done with a certificated turbine flowmeter.This flowmeter was reported to have an uncertainty of 0.03% in calibrationcoefficient.

The uncertainty of the flow rate measurement through a weir can now be estimatedfrom its calibration. The flow rate in an arbitrary weir test can be obtained from:

127


128

90 deg notch 28 deg notch

Completesample

Falling waterlevel

Completesample

Falling waterlevel

average Cweir []

cwe,r

1.3420.202

1.3390.252

1.4160.533

1.3960.061

Qm = Cweirh (3.13)

where Qrn measured flow rateCweir = calibrated weir coefficienth = measured water level height.

The coefficient Cweir is determined from the weir calibration and only depends onthe weir geometry. The water level height was measured through a wave probe.The zero height reference level is determined at the beginning of each testingsequence. The height obtained from the wave probe signal can subsequently bewritten as:

h = a1&-h0 (3.14)

where a1 = linear wave probe calibration coefficient= measured voltage over wave probe

h0 = zero flow rate adjustment weir.

C weit uncertainty

The results of the weir coefficient from calibration are plotted in Fig 3.15. Thefigure clearly shows that the scatter in calibration coefficient for the 28 deg notchis clearly higher for a rising water level (increasing pump rotation rate) than fora falling level. This observation corresponds with a recommendation for the waveprobe calibration procedure which suggests that the probe should be calibrated forfalling water levels only.

The precision error in the weir coefficient could now be calculated from thesample presented in Fig 3.15. The results are summarized in Table 3.6.

Table 3.6Precision of the V-notch weir coefficient

0.98


129

L0 90 deg, mer. rpm

90 deg, deer rpm

L 28 deg, incr. rpm

28 deg, deer. rpm

L

LL

L

oo DL..otò n

. s

O 2 4

Thousands

impeller rotation rate [rpm]

Fig 3.15 V-notch weir calibration results

Precision of height measurement

The precision error of the height measurements is evaluated from three wave probecalibration experiments, each experiment consisting of 8 to 14 points. The averagebest estimate of the standard deviation of the height measurements of threecalibration experiments on two distinct wave probes has been used.

h0 uncertainty

An estimate of the bias error in the zero adjustment of the weir was obtained froma number of repeated zero settings with the weir. The zero adjustment was visuallyread on the manometer scale. From these repeated zero readings, a bias error ofapprox. 1 .5 mm was estimated.

The results of the above uncertainty analysis in the flow rate as measured from theweir are summarized in Table 3.7.

The importance of the scatter in the height measurements by the wave probe isclearly illustrated. Improvements in flow rate uncertainty by improving theuncertainty of the water height measurements is considered possible.

Fig 3.16 shows an example of typical bollard pull thrust deduction fractions tbpthat were obtained from the above flow rate calibration procedure. Taking into

1.08

1.06


consideration that the uncertainty in the bollard pull thrust is twice the uncer-tainty in flow rate due to the corresponding sensitivity, the shown deviationsfrom zero thrust deduction are explained by the uncertainty analysis from Table3.7.

Table 3.7Uncertainty analysis of flow rate measurement from V-notch weir

Thrust calibration

With regard to the large uncertainty in the flow rate measurement from the weir,and the difficulties experienced in using other methods, the idea originated tocalibrate the discharged momentum flux directly through pulling forcemeasurements on the model. For such a procedure we need some knowledge aboutthe thrust deduction in bollard pull condition.

Hypothesis on thrust deduction

From simple potential flow considerations on the flow field about the intake duringbollard pull condition, one can derive that the ingested momentum flux in x-direction for an arbitrary intake mounted on a flat plate equals zero (Fig 3.17).

130

3) Errors are expressed as a percentage of the Reading (R), unless indicated otherwise.

Error source ErrorRelative

sensitivity0 [-1

Bias error

b [%J3)

Precisionerror

;[%f3)

- cweir

- precision of heightmeasurement fromwave probe

- zero height setting h0

Totals

Bho'l.S mm

1.0

2.5

-2.5 0.54

1.35

0.25

1.0

2.51

URSS Qweir @ 95% 5.2%

Example dataQm15 I/se=28 degh=279 mm

0. 1

0.05

-0.05

-0.!

R

o

qj(xj,O) A'N

D

Fig 3.17 F!ow field about an arbitrary intake at boflard pu!! condition


A/P

R I''½Ae

131

---t

i' e test 50231, 1.19A0

-o- test 50231,

1000 500 2000 2500 3000 3500 4000

n [rpm]

Fig 3.16 Typical bollard pull thrust deduction fractions obtained from V-notch weircalibrations


To illustrate this, let us consider a 2-dimensional intake in the x-z plane. The flowfield can be modelled by a suitable set of sinks on the x-abscissa. Each sink hasa strength -q and a potential p and is located in (x,O). The potential of the totalflow field can be written as the sum of the potentials of the individual sinks:

= (3.15)

We would like to demonstrate that the ingested momentum flux 4)m3x through area3 in x-direction equals zero at U0=O. Let us therefore first consider the circularcontrol volume, spanned by the area Ae, containing the set of sinks representingthe intake. The circle has a radius R, with the origin at the centre of gravity of thesink distribution. The momentum balance for this control volume can now bewritten as:

4)mex = JpndA (3.16)Ae

The external force in the right-hand side of the equation, is built up from thepressure force acting upon the external boundary Ae and the forces on thesingularities representing the intake. These latter forces can be computed withLagally's theorem. But because the free stream velocity equals zero in the bollardpull condition, the net Lagally force on the sink distribution equals zero. Internalforces between the sinks neutralize each other.

For an arbitrary distribution of n sinks on the x-abscissa. we can write themomentum flux in polar coordinates:

mex = -J(v2cosO-7rVesin O)rdO (3.17)

where Vr = radial velocityV9 = angular velocity.

The second term in the integrand is caused by the fact that the potential functionis made up from a sink distribution instead of one sink point. For increasing radiiR, this second term quickly diminishes because of the vanishing contribution of y9.

132

The radial velocity Vr can be obtained from the potential function:

Vr =¿fr

(3.18)

Remembering the potential function of a single sink in polar coordinates:

the following relation for the momentum flux through Ae can be derived:

,nex

q1(R-xcosO)]2RcosOdø (3.20)

o ' 4it(R 2+x22x1RcosO)5/2

This integral approaches zero if the term in brackets becomes independent of thepolar coordinate O. This situation occurs for x.cR or for q1cQ.

This implies that if R is sufficiently large with respect to the intake length, themomentum flux in x-direction through Ae equals zero, and consequently the netpressure force acting upon Ac equals zero (eq. (3.16)).

To find the momentum flux Pm3x' we will now consider half the circular controlvolume spanned by Ac. The new boundary is situated just underneath the x-abscissa so that the set of sinks is just out of the control volume. The newboundary is made up from the plating area A and the projected intake area A3.The circumferential area is one half the original circumferential area Ae. Themomentum balance for this volume reads:

2it

-q(p1 =

47tr1

ìn3xmex J pndA+ J pndAA+A3

2e


(3.19)

(3.21)

Use has been made of symmetry of the flowfield about the x abscissa. We haveseen that both the momentum flux and the external net force in x-direction on theexternal area Ae vanish for a sufficiently large radius of the control volume R.Furthermore, the contributions of the surface forces on the surfaces A and A3

133


equal zero because n equals zero. Equation (3.21) consequently reduces to:

4m3x = (3.22)

Therefore, the net thrust during bollard pull is given by:

Tnet = Tjetx

where Tietx is the discharged momentum flux from the nozzle:

Tjetx -- cosOA ,

It is assumed in the above relation that the velocity distribution in the jet issufficiently uniform to neglect differences in mean volumetric and meanmomentum velocities. If this is not the case, a similar momentum velocitycoefficient c1 can be introduced as has been done to account for this effect in theingested momentum flux in the intake (see Appendix 2).

Despite the above argumentation, differences between the jet thrust Tjetx and themeasured pulling force on the model may occur for the following reasons:

The discharged jet induces a non-zero force in x-direction.The limited bottom area about the intake affects the intake flow.The viscous stresses acting on the bottom plating exert a non-zerocomponent in x-direction.

These effects are assumed negligible in eq. (3.23).

Model tests have been conducted to check this assumption. The test set-up and theresults will be described in the next section (Section 3.2.3). We will continue firstwith an estimate of the uncertainty in measured jet thrust Tjetx.

Thrust deduction uncertainty

The jet thrust can be obtained from a pulling force measurement during bollardpull conditions:

134

(3.23)

(3.24)


It is noted that the precision error estimates for calibration and measurement arenot copied. The authors cited take the measurement error as the precision error ofthe instantaneous signal, whereas we are only interested in the average of one

135

Error sources80 N Transducer 800 N Transducer

Bias error B1 Prec. error S Bias error B Prec. error S-

- Transducer & A-Dconverter linearity error

- A-D digital error- Calibration- Filter- Measurement error

Total (Ftneas=52.8 N)

1.60 102 N2.15 l02 N

1.64 10-2 N

0.1%

4.0 102 N

2.6 10-2 N

0.1%

1.60 lO N2.15 lO N

1.64 10-2 N

0.5%

4.0 10' N

2.6 l02 N

0.76%

URSS F,nea @ 95% 0.2% 1.6%

Tietx =Fx,neas

(3.25)

The uncertainty in jet thrust acting upon the hull is consequently built up from theparameters that occur in this relation.

The quintessential assumption in the 'thrust calibration' procedure is theassumption that the jet thrust deduction fraction tbp is negligible. Based on the testsdiscussed in the next section, it is estimated that the bias error, due to thisassumption is about 1% of the jet thrust.

Pulling force uncertainty

Generally speaking, an accurate force measurement is a much easier task toaccomplish than an accurate flow rate measurement. This is expressed in thesmaller uncertainty of a careful force measurement. For an estimate of thisuncertainty, the error sources and much of the corresponding estimates areborrowed from the report of the High Speed Marine Vehicle Committee of the20th ITTC 1993], and listed in Table 3.8.

Table 3.8Estimates of uncertainty for measured force Fmeas

for two transducers with different capacity


'run', consisting of a large number of samples. Also the precision error in forceestimate from the calibration test is considered to be too pessimistic. The valuesgiven here are based on standard MARIN practice. They also show a betteragreement with the data presented by Lin et al. [19901

To illustrate the effect of a small and a large capacity transducer, an 80 N (fullscale) force transducer and an 800 N transducer are considered.

The foregoing table shows that the difference in uncertainty between the small andthe large capacity transducers is caused largely by the precision error incalibration. We will assume that the most appropriate transducer has been fittedfor the thrust calibration and consequently use the smallest uncertainty value.

The resulting uncertainty in jet thrust Tjetx is summarized in the Table 3.9.

Table 3.9Uncertainty in jet thrust for calibration input

Evaluation of procedures

Performance considerations should play a dominant role in the selection of themost suitable procedure, apart from economic considerations. To this end, we willuse uncertainty in net thrust as a performance indicator. Consequently, both theprecision and bias errors, as well as their propagation into the uncertainty of thenet thrust should play a role in the selection of calibration procedure.

136

4) This estimate is based on the repeatability of the bollard pull force measurements inSection 3.2.3.

Error source ErrorRelative

sensitivity0 [-1

Bias error

b [%]

Precisionerror

s [%]

- Thrust deduction tb Sect. 3.2.3 1.0 1.0

- Transducer force Fmeas Table 3.8 1.0 0.1

Total 1.1 0.1

URSS 1il @ 95% 1.1%

The non-dimensional confidence level for the result u, covering 95% probability,is given by (see also Appendix 3):

RSS= /bk2+(too25(v)sk)2 @ 95%

where b? = non-dimensional bias error in result= non-dimensional precision error in result.

The non-dimensional error in the result is caused by a propagation of several errorsources occurring in the experimental procedure. The bias error in the result canbe obtained from the following relation:


(3.26)

137

h

= (3.27)

N i=I

where 0 = relative sensitivity of result for parameter i (see Appendix 3)b = non-dimensional bias error in parameter i.

A similar relation is found for the non-dimensional precision error.

The error source parameters follow from the parametric relations for the net thrust(equations (3.9) and (3.10) respectively). The uncertainties for flow rate and jetthrust that are used as input signals in the calibration procedure have beendiscussed in the preceding. We will now systematically compare othercontributions to the sensitivity of both calibration procedures.

Starting from the equations (3.9) and (3.10), the relative sensitivities 0 can beexpressed as functions of the nozzle velocity ratio NVR and the momentumvelocity coefficient in the intake Cm. The relative sensitivity for an error in theflow rate 0 can now be compared to the relative sensitivity for an error in the jetthrust 0etx This is done in Fig 3.18 for a representative value of c,= 0.9. Thisfigure shows that the jet thrust procedure shows a sensitivity that is half thesensitivity of the flow rate procedure over the complete NVR range.

A similar comparison on the relative sensitivity of net thrust can be made for theerror contributions of the nozzle area A and the specific mass of water p. Thesensitivity of both procedures for A is plotted in Fig 3. 18 for both calibrationprocedures. It shows that the difference between thrust calibration and flow rate


calibration is here considerable in the NVR region of practical interest (roughly forl.5<.NVR<3). With regard to the uncertainty in nozzle area, it is noted that thetolerance (bias error) in the nozzle diameter manufacture is about 0.05 to 0.1 mm.An additional error may however be caused by a possible vena contracta behindthe nozzle discharge area (A8 in Fig. 2.1).

138

jet thrust calibration- - - flow rate calibration

Cm = 0.9

jetflow rate calibration

thrust calibration- - -

e'Q

Cm0.

jet thrust calibrationrate calibration- - - flow

Cm =0. - - - - - -

o 2 3 4 o 2 3 4

NVR[-] NVR [-J

o 2 3 4NVR[-]

Fig 3.18 Relative sensitivities for bollard pull thrust and flow rate, for nozzle area A and formass density p

A comparison on the relative sensitivity of net thrust for errors in specific mass isgiven in Fig 3.18. Again, the thrust calibration procedure shows the lowersensitivity in the practical NVR range. As regards the uncertainty in specific mass,it is noted that during a number of flow rate calibration tests with the V-notchweir, air bubbles were observed at the water supply in the container. Although thesource of the air leakage was not revealed, it could have affected the specific masswithin the waterjet. The risk for different values of specific mass in the flow ratecalibration procedure is higher than it is in the thrust calibration procedure. This

is especially caused by the fact that the pump operating point differs more fromthe working point during the propulsion test in the first procedure. This is causedby the additional pump head by the hose between nozzle and container and theadditional height recovery.

The relative sensitivities of net thrust for the model velocity U0 and Cm show asimilar relation with NVR, due to the similar form in which the source parametersoccur in the thrust equations for both procedures. The uncertainties for both errorsources are furthermore independent of the calibration procedure.

in summary, the uncertainty in jet thrust (input in thrust calibration procedure) isonly some 20% of the uncertainty in flow rate (input in flow rate calibrationprocedure). Furthermore, the thrust calibration procedure shows a favourablebehaviour in propagating the errors in all error source parameters for the jet'soperating region of practical interest. For these reasons, it was decided to select thethrust calibration procedure as the most accurate and reliable calibration procedure.

3.2.3 Bollard pull verification tests

In the 'thrust calibration procedure', a necessary hypothesis was made that thethrust deduction fraction in bollard pull conditions equals zero for a hull withrepresentative transom fitted waterjets. To verify this hypothesis, a series of bollardpull tests has been conducted.

The objective of these tests is to quantify the effects of the ingested flow in theintake and the discharged flow from the nozzle on the relation between thrust fromthe nozzle (1jetx or nozzle momentum flux) and measured pulling force actingupon the hull model.

The experiments consisted of a series of bollard pull tests on four modelconfigurations, viz.:

Bare hull modelModel with stern plate between jet and transomModel with intake pipeModel with both stern plate and intake pipe.

The second configuration consists of the bare hull with a so-called 'stern plate'.This plate is mounted on a separate transducer frame and positioned in betweenthe discharged jet from the nozzle and the hull's transom (Fig 3.19).


139


This 'stern plate' configuration enables the measurement of the jet induced forceon a transom-like area. This submerged area is approx. 13 times the submergedtransom area. The slot between the nozzle and the circular gap in the plate throughwhich it protrudes is only 0.3 to 0.4 mm after fitting. The angle between the x-reference of the plate transducer frame and the baseline of the model wasmeasured with an inclinometer to be only 0°40'.

transom

140

IL-hull -

Istat.O

base line

uil

72197

plate

stiffener

forcetransducer

-.

dimensions in [mm] for model

Fig 3.19 Test set-up for Hamilton test boat with stern plate

The third configuration consists of the bare hull with a so-called 'intake pipe'. Acylindrical pipe enclosing the intake and protruding vertically downward with alength of 2.7 times the local hull draft (Fig 3.20). The 'intake pipe' should warranta symmetrical ingestion of the flow without inducing a flow about the hull. Underthis condition, the ingested momentum flux in x-direction equals zero, and the jetdelivered thrust consequently consists from the discharged jet contribution pluspossible induced hull forces only.

The fourth configuration consists of the bare hull fitted with both the stern plateand the intake pipe. This configuration enables us to measure the pure thrust from

750

¡ stat. O

0 210

intake pipe

Fig 3.20 Test set-up for Hamilton test boat with intake pipe

To increase the precision of the experiments, and to get a better understanding ofpossible bias errors, a number of static load and repeat tests were conducted. Thefull testing program is given in Table 3.10.

Fig 3.21 shows that the forces measured on the stern plate are about 1.5% of thepulling force measured on the model. Test No. 50708 (with stern plate) shows anerratic behaviour in Fpiate. which is possibly due to unstable circulation about theplate. Coincidentally, this test happened to be the first test of the day. Itfurthermore appears that the additional fitting of the intake pipe does not affect themeasured plate forces.


the nozzle Tjetx after accounting for a possible induced force on the stern plateExpiate:

Tjetx = Fxmeas Fxpiate (3.28)

The tests have been conducted with the Hamilton Jet test boat. A brief descriptionof this boat and its waterjet installation is given in Appendix 4.

141


Notes: - The asp angle of attack (relative to centreline nozzle) was changed in between TestNos.50712 and 50713 from 25 deg to 10 deg.

- The static load tests with the stern plate mounted were conducted at impeller rotationrates of 0, 1500 and 2500 rpm.

- The baseline of the model was kept horizontal during all tests.- The impeller rotation rate was increased during the tests from 1500 up to 3500 rpm

during all bollard pull tests, except for Test No. 50717, where it was decreased from3500 rpm downward.

142

0.05

0.04

0.03

V- 0.02

0.01

O

Table 3.10Review of bollard pull verification tests

TestNo.

Type of test

50706 - bare hull50707 - static load on 6 comp. frame transducer50708 - with stem plate50709 - with stern plate and intake pipe50710 - with intake pipe50711 - bare hull50712 - with stern plate50713 - bare hull50714 - static load immediately on 6 comp. measuring frame plate, no stern plate

mounted50715 - static load on 6 comp. frame, stern plate mounted again50716 - with stern plate50717 - bare hull

-- test nr 50708 / sternplate

-- test nr 50712 / sternplate

--- test nr 50709 / sternplate & intakepipe

9 testnr5ø7ló/sternplate

'WAI A1000 1500 2000 2500 3000 3500 4000

n [rpm]

Fig 3.21 Measured Fxpiaje forces as a function of impeller rotation rate

Fig 3.22 shows a comparison of the pulling forces Fxmeas that were measured onthe hull model. These forces are normalized with the force from Test No. 50706with the bare hull model. It shows that the average difference in measured pullingforce between the tests with and without stern plate is some 1.5%, the pullingforce with stern plate being lower. This difference corresponds to the forcemeasured directly on the stern plate. The configurations with intake pipe (TestsNo. 50709 and 50710) do not show any significant difference with similarconfigurations without intake pipe.

CC

S

1.04

1.03

1.02

1.01

0.99


143

test no. 50708test no. 50709

i test no. 50710

withoutsternplate --

plate-'I1000 1500 2000 2500 3000 3500 4000

n [rpm]

Fig 3.22 Comparison of measured pulling forces Fxmeas as a function of impeller rotation rate

With regard to the uncertainty in the measured pulling force Fxnieaç the followingobservation is made. The scatter in Fxmeas for similar configurations appears to bewithin approx. 0.5% for impeller rotation rates in excess of 2000 (Fxmeas>lS% FS(Full Scale)). This is somewhat higher than the estimated uncertainty in Fneas inTable 3.8 of the previous section. The additional error contribution is attributed tothe condition of the flow. The importance of the flow condition is also illustratedby the greater deviation in Test No. 50708 which also showed an erratic behaviour


in plate force Fxpiate.

Based on the above observations, it is concluded that the momentum flux throughthe intake (area A'D in Fig. 2.1) in bollard pull conditions equals zero for thesubject model. This observation is likely to have a general validity, as the subjectintake is mounted close to the transom stern in comparison to other representativewaterjet systems. Especially the bigger mixed flow pump waterjets need totransport the ingested water to a higher level in the hull, consequently leading toa further separation of intake trailing edge and transom.

The jet induced force acting upon the stern plate amounts to approx. 1.5% of themeasured pulling force. Because the submerged part of the stem plate is approx.13 times the submerged transom area, it is assumed that the actual jet inducedforce on the transom is generally within 1%. The distance of the nozzle dischargeto the transom plate s,, is considered to be representative for most cases(s,/D=1.7).

3.3 Uncertainty analysis

The importance of subjective judgement in uncertainty analysis is tersely expressedby P.H. Meyers. In the 1930's, he and his team had put several years of hard workat NBS into the determination of the specific heat of ammonia. They finallyarrived at a value and reported the result in a paper. Toward the end of the paper,Meyers is said to have declared (Abernethy et al. [1985]):

"We think our reported value is good to one part in 10,000; we are willing to betour own money at even odds that it is correct to two parts in 10,000; furthermore,f by any chance our value is shown to be in error by more than one part in 1000,we are prepared to eat our apparatus and drink the ammonia!'

Despite the important role of subjective judgement, uncertainty analysis is regardedas an effective means to demonstrate the relative importance of each errorcontribution. Furthermore, it allows for an improved interpretation of the results.

To arrive at a realistic estimate of the uncertainty in the net thrust and effective jetsystem power, derived from model propulsion tests, a complete review of therelevant relations and their parameters is now discussed. Figure 3.4 shows the datarequired to analyze the powering characteristics of the model based on the signalsmeasured during the propulsion test. The data are classified after their origin andtheir relations are indicated.

144

We will use the data analysis category as a starting point for the derivation of theuncertainty in net thrust prediction. The error contributions of each parameter willbe discussed in the following. The propagation of the error sources into theapproximation of net thrust Tg, is given by the relative sensitivities O', that can bederived from the following rèlation:

Tgoo = TjetxC mU

where Tjetx = thrust from nozzle in x-direction.

The uncertainty analysis is elaborated for a representative case, of which theresults are presented in Tables 3.11 through 3.14. The case is characterized by anozzle velocity ratio NVR=2 and an ingested flow rate to boundary layer flow rateratio of 1.5.

The error contributions quoted in Table 3.11 are briefly discussed per source in thefollowing. Table 3.11 presents the final uncertainty estimate in net thrust T,iet. TheTables 3.12 and 3.13 present the intermediate uncertainty results in j et thrust Tietand intake momentum coefficient c,, respectively.

Derived jet thrust Tjetx

The value of T,ierx from the propulsion test is obtained from the following linearrelation, obtained from a regression analysis on the bollard pull results:

Tjetx a0±a1Dp (3.30)

where a1 = regression coefficientDp = differential pressure signal from 'asp'.


TjetxPAn (3.10)cosO

145


Table 3.11Uncertainty analysis Tnet

Table 3.12Uncertainty analysis from propulsion tests

146

Error Error s (0'b') + (t 0's')2source [% R] [% R]

Tetx See Table 3.13 1.41 1.50 0.26 5.01From ITTC [1993] -0.82 0.08 0.09 0.03

Cm See Table 3.14 -0.82 2.20 0.02 3.25p From ITTC [1993], S=l.82102 0.41 0 0

B(D,)=0.2 mm 0.41 0.80 0.11B=0.1 deg. 2.00 0

Totals 2.80 0.37

UÇ,5 @ 95% 2.90

Example data.9 80NVR =2

C 4 60

U' = 5mis 40O, =Sdeg -D =50mm 20

T:eto = 98 N oTjetx Uo Cm P A 0n

Error source

Error source o; s (0'b') + (t 0's')2[%R] [%R]

a0 0.01 20.00 0.10a 1.00 0.20 0.16lIp 1.00 1.00 0.04 1.01

calibration 1.00 1.10 1.21

Totals 1.49 0.26

U, @ 95% 1.57

Example data

= aaiD60 -- -

=375 o20

-

I IT. =80Njex Io

a a1 !) 1petcalibration

Error source

Table 3.13Uncertainty analysis Cm


The precision error of consequently follows from the precision errors in thecoefficients a and Dp. xpressions for the precision errors of the coefficients aregiven by (Barford [1987]):

147

Error source Error 0 b

[%RIs

[%R](O'b')2 + (t e's')2

Error QblU0 I .00 0.08 0.09 0.04

¡.1 <J< 1.5 1.00 10.00 100.001.00 10.00 100.00

n 0.13 20.00 6.25

Totals 14.36 0.09

URSS @ 95% 14.36

Example data: n = 7.00

Error Q

etx 1.00 1.49 0.26 2.48

Totals 1.49 0.26

URSS @ 95% 1.57

Error Qb,'QQ -1.00 1.49 0.26 2.48

Qh/ 1.00 14.36 0.09 206.29

Totals 14.44 0.27

URSS @ 14.45

Error Cmn 0.09 20.00 0 3.49Q11/Q -0.08 14.44 0.27 1.35

Totals 2.20 0.02

URSS @ 95% 2.20

Example data: Q/Q11 = I .5


where

n 22)=

2()2 [nv-x>y]2nx 2_2

148

S0(a0) =

\/n(n-2)[nx 2(x)2J

S0(a1) =n,1(y)

(n-2)nx 2(Ex)2]

Estimates of the precision errors are based on the results of the bollard pull testsreported in Section 3.2.3, and are listed in Table 3.14.

Table 3.14Precision errors in Tjett regression coefficients

(3.31)

(3.32)

(3.33)

When analysing the following data, it is seen that the a0 coefficient of Test No.50713 does not compare well with that of Test No. 50717. This is attributed to thefact that this bollard pull test was the first test in the morning. At the lowerimpeller rotation rates the asp signal appeared to be l-2% lower than thecorresponding signal from the subsequent tests. It should furthermore be noted thatthe coefficients of the first tests (50706 and 50711) are not directly comparable tothat of the last tests (50713 and 50717) due to the fact that the orientation of theasp with respect to the mean flow was changed.

Test No. n s, (a0)[%J

s,Ç (a1)

[%]a0[N]

a1

[N/cmwk]

50706 12 21 0.19 -0.833 0.25150711 8 22 0.15 -0.711 0.25250713 9 13 0.18 1.467 0.26650717 8 196 0.20 -0.106 0.267

Estimatedmean value

37 20 0.2


The large precision error in a0 (196%) for test No. 50713 is caused by the smallvalue of the coefficient itself. When comparing the absolute value of the precisionerror, it is of a similar magnitude as the error from the other tests.

For the contribution of asp signal Dp, the precision error of the average Pp valuefrom a propulsion test is taken. This error appears to be negligible with a value of0.04%.

Little information is available on the bias error in the asp pressure Dp. A bias errormay occur if either the angle of attack or the velocity profile on the asp is changedrelative to the calibration test. Such a change may occur if the working point ofthe pump is changed (expressed e.g. in a change in flow rate coefficient KQ) ormay be due to the ingested boundary layer, which was not present during thecalibration test.

Two experimental observations on this issue have been made. The first observationwas made during the systematic series of bollard pull tests, where it was shownthat the average asp signal decreased with some 7% after an axial rotation of theasp over 15 deg. The second observation relates to the degree of correspondencebetween two propulsion tests on the Hamilton test boat (see Section 3.4). Thesecond series of tests were conducted about half a year after the first series, anda new asp was used for the second tests. The pressure ports in this new aspshowed a distinct distribution over the length of the asp, and it was positionedunder an angle of attack of 10 deg with the centreline nozzle instead of 25 deg asused during the first test. Despite these modifications to the asp, the deviation infinal thrust values was within 1.5% of the original values. Based on this experienceand experience with other propulsion tests, a bias error in Dp of approx. 1% hasbeen assumed. This is believed to be a conservative estimate in most cases.

An additional bias error is present in the regression relation for jet thrust Tier. Thiserror occurs during the bollard pull calibration test and is not incorporated in theuncertainty analysis of the coefficients a. The magnitude of the error is taken fromTable 3.9, and is estimated to be about 1%.

Table 3.12 clearly shows the importance of the bias errors in the asp signal Dp andthe jet thrust T1 from the calibration. These errors contribute respectively approx.40 and 50% to the total uncertainty in the jet thrust as derived from the propulsiontest.

149


Hull speed U0

Both the bias and the precision error for the hull speed have been borrowed fromthe HSMV Report of the 20th ITTC [1993], for a model speed of 5 mIs.

Momentum velocity coefficient Cm

For the selected case where the required flow rate Q exceeds the flow rate that isingested from the boundary layer Q,1, the momentum velocity coefficient Cm isgiven by (see Appendix 2):

wherew=geometric intake width

width effectiveness factor, due to the flow contraction ahead of the intake=:boundary layer thickness

n =power from velocity profile power law.

The results of the uncertainty analysis on Cm are presented in Table 3.13. Theestimates are based on a procedure where the boundary layer parameters and nare obtained from semi-empirical relations, as for instance given by Hoerner[19651. It is observed that the major uncertainty contributions to are again madeby the bias error estimates on the width effectiveness factorf, the boundary layerthickness and the velocity profile power n. The latter contribution was estimatedat 20% resulting in an uncertainty contribution of approx. 75% in c,. Theestimated bias error in the velocity power n results in values on model scale thatare situated in the range from 5.6 to 8.4. A mean value of 7 has been used here(see e.g. Schlichting [1979]). At full scale, this power value will be closer to 9.

The estimated bias errors in J, and contribute equally to the uncertainty inboundary layer flow rate Qbl' but finally only contribute about 25% to the totaluncertainty in Cm.

150

Cm 1- QhI

n +2 Q

and the flow rate ingested from the boundary layer Qbj is given by:

nQbI = UofwWi

11+1

(3.34)

(3.35)

If the boundary layer parameters ö and n are obtained from a curve fitting processon a series of pitot rake measurements in the boundary layer, the bias errors in nand boundary layer thickness are estimated to reduce from 20 and 10%respectively to about 5%. An example of a curve fitting result on the boundarylayer profile measurements is given in Fig 3.3.

The uncertainty in c,,7 decreases from 2.2% to a value of 1.0% due to the boundarylayer measurements. This results in an improvement of the Tnet uncertainty from2.9% to 2.4%. It is to be noted that the sensitivity for errors in c,,7 increases for thelower NVR values, consequently increasing the improvement in uncertainty.

Specific mass p

The precision error in the specific mass is borrowed from the HSMV committeereport [1993] and is due to a precision error in the measurement of the watertemperature.

As discussed in Section 3.2.3 on the thrust calibration procedure, a bias erroroccurs when during the bollard pull calibration a different amount of air is ingestedthan during the propulsion test. As the working point of the pump is approximatelythe same in both conditions for the proposed procedure however, this is not likelyto happen. A bias error is therefore not further considered.

Nozzle area A,,

A manufacturing tolerance of 0.2 mm in diameter is assumed.

Nozzle inclination angle O,,

The nozzle inclination angle is assumed to be measured with the inclinometer. Thismeter has a tolerance of approx. 0.1%. Hence a bias error of similar magnitudeis assumed.

Uncertainty in net thrust Tnet

Table 3.11 clearly shows that the bias error contributions by Tiet and cm govern theuncertainty in 1. The greatest contribution (approx. 60%) is provided by the biaserror in the derived jet thrust Tj,. from the propulsion tests.

The total precision error in net thrust is assessed to amount to approx. 0.4%. Thisis of a similar order as the precision error quoted by English [19951 for propellerthrust measurements on slender monohulls. It is consequently concluded that the


151


precision of the instrumentation used during the propulsion tests is satisfactory.Great care is to be practised during both the calibration procedure and thepropulsion test, so as to notice possibly unforeseen bias errors.

A total uncertainty in net thrust of approx. 3% results for an NVR value of 2. Thisassessment is however based on uncertain bias error estimates, especially in aspsignal from the propulsion test and in jet thrust during the calibration procedure.The author is therefore not prepared to drink the model basin, nor is he preparedto eat the carriage should the uncertainty turn out to be slightly different.

Uncertainty in effective jet system power JSE

A similar procedure as applied to the uncertainty prediction in Tnet can be followedfor the power JSE Because the bias error in Tiet appears to be the dominantcontribution in net thrust, and because the net thrust also largely determines therequired power, we will focus here on the jet thrust contribution. Analogous to theform of the net thrust in eq. (3.10), the corresponding power JSE can he writtenas:

JSE =Tieti.AnP jetx - 'cU-gzjcos e 2pA,7cose,7

(3.36)

The relative sensitivity e' for an error in Tje is consequently 1.8 for the presentcase (NVR=2, c'0.9). This is some 30% higher than the sensitivity for the netthrust.

Judgernent criteria for bias errors

As we have seen from the preceding uncertainty analysis, the major contributionsto the final error are caused by bias errors. Errors that can only be prevented oracknowledged if sufficient knowledge on the physical process and the propertiesof the test set-up is available. To increase the certainty of the results in and

JSE' derived from the experiments, a number of criteria can be defined that shouldbe met.

A good check on the net thrust data is obtained after a comparison of the thrustwith the bare hull resistance. If a number of propulsion test results is available, themargins within which the resistance increment r should lie are roughly given.Furthermore, if more knowledge on the physical mechanism causing the resistanceincrement is available, one could probably narrow this bandwidth.

152

A second criterion is the physical requirement that the resistance increment fractionr should show a faired character when plotted against speed. Outliers in the resultsare easily identified in this way.

A third acceptance criterion is formed by the overloading and underloading tests,that are normally conducted for one or two speeds of interest. During these tests,typically 3 to 4 impeller rotation rates are adjusted for one speed. This gives arelation between thrust and pulling force FD as presented in Fig 3.23. If the pullingforces are varied within reasonable limits, a straight line is usually discernedthrough the self propulsion point of ship, defined by the coordinates (FDTSP). Thepoint where this line intersects the thrust abscissa is the self propulsion point ofmodel Tm. The line intersects the pulling force abscissa through a point that isusually situated close but not exactly on the value of the model resistance Rm. Thispoint is referred to as FTO.

T

Tm

FD

= + ir aT

s''s

s'N

NN

NN

NN

N

Rm FTOF

Fig 3.23 Thrust-Force diagram from overloading and underloading tests

If the intersection with the pulling force abscissa is assumed to be sufficientlyclose to the bare hull resistance, the line can consequently be expressed as:

T T,-F(l+r) (3.37)

It can now be observed that the resistance increment fraction r can be obtainedfrom the inclination of the loading variation line, which can be determined throughregression analysis. The resistance increment fraction is then obtained from:

r JT (3.38)


153


The resistance increment fraction that can be obtained from these overloading andunderloading tests should approximately match the corresponding values from thespeed variation tests at the self propulsion point ship. To this end, the pulling force

D should be adjusted as close as possible to its required value. Residualdiscrepancies between the actual pulling force and the required force ED shouldbe corrected for, using the overloading and underloading relation obtained from theexperiments.

3.4 Propulsion test results

This section presents collected results on interaction data obtained from a selectionof propulsion tests that have been conducted at MARIN. The set of hull formsinvolved covers a wide variety, ranging from a low LIB monohull (L/B=3) to ahigh L/B catamaran (L/B demihull =15), and ranging from a small 7 m to a large80 m vessel. The objective of this review is to give an idea of the importance ofinteraction. Due to the non-systematic nature of the data, it is not meant to providedesign guidance.

The overall interaction effect is quantified by the interaction efficiency Theenvelope area, comprising all values of this interaction efficiency obtained fromthe above selection of waterjet propulsion tests, is plotted in Fig 3.24.

154

115

LOS

0.95

0.85

0.750 00 0.50 1 00 1 50

FnL H

Fig 3.24 Collected total interaction efficiencies 1JNT as a function of Froude number

3.4.1 Thrust deduction

A total thrust deduction fraction t is obtained from resistance and propulsiontests in a straightforward manner. This total thrust deduction links the grossthrust Tg to the bare hull resistance RBH in the following way:

T(l-t) RBH (3.39)

To link up with the existing nomenclature in propeller hydrodynamics, we mayrefer to the resistance increment as the hull's thrust deduction fraction tr Acorresponding thrust deduction factor may subsequently be defined as:

ltr_l+r

This thrust deduction is built up from the jet system's thrust deduction fractiont1 and the hull's resistance increment t,. (see Section 4.3.2):

t = tj+tJ. (4.34)

Using the results from Section 2.3.1 where it was concluded that the thrustdeduction fraction t1 equals zero under certain conditions, the total thrust deduc-tion t may be regarded representative for the hull's resistance incrementexpressed in tr It will be shown in Section 4.3.2 that this assumption is validover most of the speed range of interest. Significant deviations between t and trmay occur in the hump speed region however.

Fig 3.25 shows the total thrust deduction t plotted against Froude number basedon waterline length (at zero speed). Although a wide variety of hull forms isincorporated, some general trends can be observed:

- Relatively high thrust deduction values are obtained for speeds in the regionof the hump in the wavemaking resistance (around FnL=O.S). The thrustdeduction shows the highest values (up to t=O.25) for the short L/B hullsand the lowest values for the high L/B hulls. The variation in t is large.

- For higher speeds in excess of FnL=O.S, all t values appear to be slightlynegative, indicating a decrease in hull resistance. The bandwidth of themodels indicated is about 5% of the total thrust.


(4.32)

155


- For speeds corresponding to FnL>l, the total thrust deduction increases withincreasing speed again.

156

0.3

0.2

0.l

o

-0.1O 0.5 15

FnL H

Fig 3.25 Collected total thrust deduction values t as a function of Froude number FnL

To unravel the mechanism governing t, further experimental analysis is pursuedalong the lines proposed in Section 2.3.4. It was suggested there to decompose theresistance increment into independent contributions of flow rate and hullequilibrium position. With the insight from this experimental analysis, a hypothesisis posed for the mechanism governing the resistance increment. This hypothesisis evaluated further in Chapter 4.

Mechanism of resistance increment

An experimental study was conducted with the aim to get a better understandingof the mechanism of the hull's resistance increment. To this end, a series ofpropulsion and resistance tests has been conducted. Systematic LCG variation testswere conducted during the resistance tests in an attempt to assess the hull'sresistance increment from variations in hull equilibrium position. These variationshave been made at two speeds, corresponding to Froude numbers of FnL=O.SO and1.19. The experimental study was conducted with the HAMILTON Test Boat (seeAppendix 4 for a description of the model).

The total thrust deduction fraction t, as obtained from two independent propulsiontests under the same condition is presented in Fig. 3.26. It should be noted that thetwo tests indicated in the figure were conducted with about half a year interval,with distinct asp tubes, mounted at different angles of attack. The discrepancybetween both tests attains a maximum at the higher speeds, where it amounts toapprox. 1.5% of the thrust. This discrepancy is well within the uncertainty in thrust(approx. 3%) found in Section 3.3. It is probably caused by an extrapolation of theflow rate-Dp (asp) relation in the upper flow rate regime (Fig. 3.27).

0.3

0.2

0.1

O

-0.1

.

-e- test no. 48820

-+- test no. 50781


157

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

FnL HResults based on asp readings and jet thrust calibration

Fig 3.26 Hull thrust deduction for the HAMILTON Test Boat

Fig. 3.28 shows a comparison of the thrust deduction fraction t and the change intrim and sinkage due to the jet action. A remarkable correspondence in tendenciesis found at the steep fall of the thrust deduction at FnL=O.S. In the higher speedrange, the relation between the tendencies in t, and equilibrium position becomesless clear. It is inferred from this plot that, at least for the lower speeds, the hullequilibrium is strongly related to the thrust deduction.

The photo series presented in Photographs 3.2 and 3.3 show that the steep declinein t and the clearing of the stern coincide.


158

FnL = 0.43

FnL = 0.50

FnL 0.56

Photo 3.2 Wave patern of Hamilton Test Boat for Speeds coinciding with the steep declinein thrust deduction t


FnL = 0.43

= 0.50

FnL = 0.56

Photo 3.3 Underwater photographs of Hamilton Test Boat for Speeds coinciding with thesteep decline in thrust deduction t

159


160

15 0.8

-0.8

I dz

range used in propulsion tests

Regression obtained frombollard pull test 50780

0.2

*-0.2

D-0.4I-

D? 0.6

C,

-0.810 15 20 25 30 35

VDp [cmwcl

Fig 3.27 Coverage of the calibrated asp signal with that obtained from the propulsion tests

0.2 0.4 0.6 0.8 1.2 1.4 1.6

FnL [}

Res, test nr. 50221 and Prop. test. nr. 50208

Fig 3.28 Comparison of the total thrust deduction t with the change in trim and sinkage dueto the waterjet action

10 0.4

s)

to-0.4

5

o

-5

A linearized estimate for the hull's resistance increment as a function of equi-librium position (see Section 2.3.4), can now be obtained from the LCG vari-ations in the resistance test. A review of the series of tests is given in Table3.15.

Table 3.15Review of resistance test variations on HAMILTON Test Boat


Originally two displacement variations were tested as well, because at this timeit was thought that the jet system could contribute to a significant lift forceacting upon the hull (Alexander et al. [1994]). However, as the induced lift onthe hull is approximately zero (Section 2.2.4), it can be argued that the changein dynamic position of the hull should preferably be obtained at the samedisplacement.

To this end, regression analysis was applied to find the coefficients in thefollowing linearized relation for the resistance increment:

1+r ao+ai(t-'to)+a2(za-zau) (3.32)

where 't =trim angle (dynamic plus static)za =sinkage of transom stern (dynamic plus static)subscript O indicates value at the resistance test.

The results of the regression analysis and a comparison of the linearized esti-mate of r with that obtained from the propulsion tests is given in Table 3.16:

161

Condition Speed range tested[kni

Remarks Test No.

A0, LCG0 6.5 - 9.5 Baseline condition 5020815.0 - 22.0

LCG variation testsA, LCGJ 7.5. 18 'r0-1.0 deg 50211A0, LCG2 t00.5 deg 50212¿ LCG3 to+O.5 deg 50213A0, LCG4 to+1.0 deg

c is trim angle for baselinecondition at speed O

50214


Table 3.16Comparison of linearized estimate and experimentallydetermined values for the hull's resistance increment

Table 3.16 shows that a reasonable correspondence occurs between the linearizedestimate and the experimental value for the highest Froude number of 1.19. Thecorrespondence for the lowest Froude number of 0.50 is poor however. It is to benoted here that the expression for the resistance increment proposed in Section2.3.4, also included a resistance term depending on the flow rate Q. This term hasbeen neglected in the preceding consideration, but may become important for thelower speeds.

One way to include the effect of local flow contributions to the change in hullresistance is to perform potential flow computations including free surface effects.This approach will be considered further in Chapter 4.

Some thoughts on the physical mechanism controlling the hull's resistanceincrement are now put forward. The same three speed regions as discussed beforewill be used.

Hump speed region

Thrust deduction fractions t may reach significant values (up to 0.25 has beenderived from propulsion tests). The behaviour of t with speed is similar to that ofthe transom sinkage in this region. The resistance increment consists largely oftransom pressure drag and wavemaking drag. The local flow distortion in theaftbody, depending on aftbody geometry and ingested flow rate Q, plays animportant role in the resistance increment.

162

FnL=O.50 FnL= 1.19

Regression results

a0 1.008 1.004a1 5.33 l0 2.11 102a2 8.37 l0 -2.29 l0S(y) 7.10 l0 4.90 10

Estimated l+r 1.06 1.00

Experimental result

Derived 1+r 1.17 0.99

Post hump speeds up till FnLl

Thrust deduction fractions t show mainly negative values between O and -5% ofthe bare hull resistance. This is the speed region where the wavemaking resistancecontribution decreases and the frictional and spray resistance become moreimportant. The transom stem is fully ventilated and the viscous pressure drag bythe transom is hence equal to zero.

For speeds just above FnLO.S, the wavemaking resistance is sufficiently sensitiveto show the effect of local flow distortions in the aftbody. With increasing speeds,this sensitivity decreases and the equilibrium position of the hull becomes moreimportant in the determination of the wavemaking resistance or pressure drag.

lt is an empirical finding, that in this speed region, a lower hull resistance can beobtained by decreasing the aftbody volume and by decreasing the running trimangle. By mounting an active waterjet (at equal hull displacement), an effectivedecrease in aftbody volume is obtained. Furthermore, the waterjet action oftendecreases the running trim angle. These two mechanisms are considered to beresponsible for the negative resistance increment of the hull.

Planing speeds FnL>l

The total thrust deduction t starts to increase again. In this speed region, the hullresistance is primarily affected by hull equilibrium position. For prismatic hullforms, the wavemaking resistance or pressure drag is simply obtained from:

R/) = Ltant (3.43)

where t =trim angle (in earth-fixed coordinate system).

It is an empirical finding that a certain optimal trim angle exists from theresistance point of view. This trim angle being hull form dependent. For lowertrim angles, the resistance caused by the spray at the bow (both pressure andfrictional resistance) increases. For higher trim angles, the pressure drag expressedby eq. (3.43) increases. It should also be noticed that the wetted surface areachanges with changing equilibrium position. hence changing the frictional drag.

If the trim angle is optimized based on resistance considerations withoutaccounting for the effect of the jet on running trim, the usual decrease in trimangle due to the jet action will cause an increase in hull resistance.


163


3.4.2 Momentum and energy interaction efficiencies

The collected values of momentum and energy interaction efficiencies are plottedas a function of the Nozzle Velocity Ratio NVR in Fig. 3.29 and Fig. 3.30respectively.

164

E

1.2

1.15

0.95I 00 2.00 3.00 4.00 5.00

NVR l-1

Fig 3.29 Collected momentum interaction efficiencies as a function of Nozzle VelocityRatio NVR

Fig. 3.29 shows that the trend for all cases is similar. Some scatter in the absolutevalues occurs, which is due to differences in ratio between required flow rate andboundary layer flow rate Qb1 The effect of this ratio is shown in Fig. 2.11. Thecase with the lowest lÍq,711 values featured a ratio of approx. 3, whereas thecase with the highest values showed a QQb/ ratio less than 1.

Similar observations can be made from Fig 3.30. Contrary to the momentuminteraction efficiency however, which is only controlled by viscous effects, theenergy interaction efficiency is also affected by potential flow effects. This effectis expressed as a function of the nozzle sinkage relative to the still waterline (seeSection 2.3.2). Hence the greater scatter in absolute values of T1eJ

To obtain an indication of the importance of both the potential and the viscouscontributions, the case with the highest values and the one with the lowest valuesof lei are studied in more detail. To this end, two speeds per case are considered.One speed being around hump speed (FnLO.5). the other speed being the designspeed.

1.05

0.95

0.9

0.85


Q; oQ

QQ

C_) -0.15

0.04

o

.0.04

165

loo 2.00 3.00 4.00 5,00

NVR [-]

Fig 3,30 Collected energy interaction efficiencies as a function of nozzle velocity ratioNVR

The results are presented in Fig 3.31. It is seen that the potential part maycontribute as much as 10% to the energy interaction efficiency. This occurs forthe lower speed, where the transom sinkage is relatively large. For increasingspeeds, the transom sinkage decreases as well as the flow rate ratio QQb1 Thislatter phenomenon causes the viscous contribution to increase. It should also benoticed that the potential and viscous contributions counteract each other, thepotential contribution contributing to a higher interaction efficiency (notice thatthe reciprocal value of 1e1 is plotted).

0.43 0.89 0.40 1.34

Fn [-] Fn [-1

Fig 3.31 Subdivision of potential and viscous contributions to energy interaction efficiency


3.5 Extrapolation method

Extrapolation is required for the powering data representing the waterjet system,the hull and the mutual interaction. Specific tests on the waterjet system have beenshortly addressed in Section 1.5.2. The full scale data are further considered to beavailable here. Extrapolation of the bare hull resistance is a daily task for modelbasins and is therefore also not further elaborated. This leaves the extrapolation ofthe interaction data, expressed in hull thrust deduction tr momentum and energyinteraction efficiencies.

The basic principles for extrapolation as proposed by the HSMV of the 18th ITTC[1987] are followed. With the relations developed in Chapter 2 of this work, theeffect of extrapolation on the interaction data can be explicitly evaluated.

The extrapolation procedure is schematized in Fig 3.32. The procedure uses theFroude scaling principle as a starting point and applies corrections for viscousscale effects. Such corrections are necessary on the viscous part of the bare hullresistance, and consequently on the boundary layer thickness and velocity profilewithin this layer.

RBHSi

Hull thrust deduction t,.

Analogous to the proposal by the ITTC [19871, the hull thrust deduction fractionis considered free of scale effects. This assumption, made without justification bythe ITTC [1987], is justified here with reference to the hypothesis on the hullthrust deduction as discussed in the previous section. Studying the definition of the

166

'jr

Cm. Ce

JI,

flml flel

Fig 3.32 Scheme of extrapolation procedure

RB Hm ö1. u(z) model

E,. u(z) full scale

'Ir

Qbl

3.5 Extrapolation method

resistance increment (eq. (2.97)) (equivalent to the hull thrust deduction), showsthat at least one term prone to viscous scale effects consists:

Jfxo' (3.44)A3

which represents the change in hull resistance due to the missing area projected inthe hull plane. As this contribution is 0(1%) of the bare hull resistance, and thescale effect on resistance, expressed in FD is typically of 0 (10%) of the resistance,the viscous scale effect on the intake plane contribution is neglected.

Moinentun and energy interaction efficiency

The momentum and the energy interaction efficiencies and Tle/ are given by theequations (2.79) and (2.86) respectively (Section 2.3). The momentum interactionefficiency is seen to be a function of NVR and momentum velocity coefficient Cm.For a given waterjet system, the nozzle velocity ratio depends on the flow rate Qand the hull velocity U0. The flow rate is governed by the thrust requirement, asexpressed in eq. (2.78). It is to a lesser extent affected by the momentum velocitycoefficient Cm which in turn depends on the flow rate and the boundary layercharacteristics. Consequently, an iteration process is required to match flow rate,net thrust requirement and momentum velocity coefficient (see Fig 3.32).

The boundary layer characteristics in tetijis of thickness S and velocity distributionu(z) within the boundary layer can be measured on the model with a closed intake(nominal intake field). Alternatively, the boundary layer characteristics can beestimated from a semi-empirical formula. In the latter case, care should be takenthat the uncertainty in the estimate does not dominate the overall uncertainty in theexperiment (see Section 3.3).

Extrapolation of the boundary layer characteristics is done through a Reynoldsdependent relation for the thickness. The velocity profile is considered to followthe power law, where the local velocity can be found from eq. 3.1. The powercoefficient n for the model can be matched from the measured velocity profile inthe imaginary intake area. A power value for n of approx. 9 for the full scalesituation is suggested.

After the flow rate is solved from the above process, the energy velocitycoefficient is readily available. The nozzle sinkage term in the energy velocitycoefficient is considered free of scale effects and is therefore simply obtained fromFroude scaling.

167


3.6 Conclusions

An accurate (high precision) and robust (small risk of bias errors) procedure forthe experimental determination of waterjet-hufl powering characteristics has beensearched for. The following conclusions can be drawn from this study:

In selecting a flowmeter for reference measurements during the actualpropulsion test, one should take into consideration that both the swirl and thevelocity profile in any place in the jet system may differ from acorresponding condition during speed zero. The reference flowmeter shouldtherefore show a low sensitivity to changes in flow pattern. It is concludedthat an averaging static pitot tube (asp) meets this criterion. lt has proven tobe a reliable transducer during many propulsion tests.Calibrating the reference velocity transducer in the jet system with flow rateeasily leads to uncertainties that render the meaning of propulsion testsdoubtful. Calibrating it with model pulling force during bollard pullconditions yields both a better uncertainty in calibration input signal, but alsoprovides a much weaker, or at most an equal propagation of all relevant errorsources into the final thrust and power prediction.Applying the thrust calibration procedure, the errors in jet thrust (momentumflux from the nozzle) and in ingested momentum flux or cause the largesterrors in the final results. Their relative contributions have been quantified inSection 3.3.

The results of a selected set of waterjet-hull combinations, incorporating monohullsand catamarans from 7 up till 80 m length, show that the total interactionefficiency lINT may reach values between 0.75 and 1.15. The lower values occurin the hump speed region, around FnL=O.S. For slightly higher Froude numbers,the interaction efficiencies adopt values in between 1.0 and 1.15 (see also Fig.3.24).

Based on the trends observed in the hull's resistance increment and anexperimental study on a possible mechanism, a hypothesis for the resistanceincrement mechanism is put forward. Based on this hypothesis and on themechanisms governing the momentum and energy interaction efficiencies, scaleeffects in the extrapolation method can be identified.

168

Extracts from BS 7405 1991 are reproduced with the permission of BSL Completeeditions of the standards can be obtained by post from BSI Customer Services, 389Chiswick High Road, London W4 4AL or through national standards bodies

169

170


Chapter 4

4 Computational analysisThe global objective of this work is 'the development and validation of tools'.It would however be of little use to study the validity of an arbitrary set ofavailable tools without giving due consideration to the problem that is to besolved. Keeping in mind that the problem definition should be the driving forcebehind the selection of tools, this chapter is subdivided into three problemareas, viz:

Analysis of free stream intake characteristicsComputational prediction of interaction effectsValidity of assumptions and simplifications made in propulsion tests.

Each of the above problem areas has been analyzed with computational toolsthat are available at MARIN. To validate the detailed flow characteristics thatbecome available from CFD calculations, detailed LDV flow measurements ona representative intake have been conducted. Integral properties following fromthe computations are compared to results obtained from propulsion tests. Final-ly, due attention is given to a physical interpretation of results.

4.1 Free stream intake analysis

A full comprehension of the waterjet free stream characteristics, as defined in

171

Chapter 4 Computational analysis

Chapter 2, is not obvious. Misunderstandings on intake drag occur frequently inthe literature (Sections 1.6.1 and 2.2.3). Supposed intake induced lift forceshave been published in recent literature (Section 1.6.1), whereas it is demon-strated in Section 2.2.4 that there is no intake induced lift in free stream condi-tions.

4.1.1 Intake flow analysis

For the present work, a better understanding of the external flow pattern and theinternal flow pattern in the initial part of the intake is indispensable. This flowpattern needs to be known to quantify the difference in intake characteristicsbetween free stream and operational conditions. Furthermore, a detailed knowl-edge about the local flow in the intake region is necessary to simplify the intakemodel in CFD computations on jet-hull interaction.

Taking the above requirements in mind, it was decided to use the MARINpotential flow code HESM. This panel code uses a flat panel distribution tomodel the intake geometry with a constant source strength per panel (zero orderpanel code). Experiments were conducted in the MARIN large cavitation tunnelon the same intake as computed, to validate the results of this panel code.These experiments resulted in pressure readings along the intake and detailedvelocity fields measured with 3D LDV equipment.

The comparison between the potential flow results and the full viscous experi-mental results provided insight in the importance of viscous effects in freestream conditions. Furthermore, the intake drag could be determined in a vis-cous flow. It was already demonstrated in Section 2.2.3 that there is no intakedrag in a potential flow.

A description of the potential flow panel code HESM is given in Appendix 5.The LDV tests and set-up are briefly described in Appendix 7. This section firstdeals with a validation of the computed results with the LDV measurements,and subsequently discusses the interpretation of the results.

Modelling of problem in HESM

The intake geometry that has been used, together with the 2D planes in whichthe flow has been computed andlor measured is presented in Fig. 4.1.

HESM computations were made on two panel distributions representing theintake geometry. One coarser distribution consisting of a total of 931 panels andone fine distribution of 2018 panels (see Fig. 4.2).

172


z

oE

E

Fig. 4. i Intake geometry analysed by HESM computations and LDV measurements

E-

E-

>

173

Li Li Li


Fig. 4.2 Panel distribution on intake model (2018 panels)

The most difficult region to model is the intake lip. In this region a large veloc-ity gradient occurs, necessitating a fine grid. Details of the lip region for thefine panel representation are given in Fig. 4.3.

Fig. 4.3 Panel distribution on intake lip

174


The operating condition of the intake in a potential flow is defined by theintake velocity ratio in the intake throat ¡VR,. Two operating conditions havebeen computed, representative for design speed and hump speed (IVR,=0.6 and0.9 respectively).

The requested operating condition was adjusted by a so-called 'propeller disk',positioned at the end of the intake (Fig. 4.4). This disk is covered with a dis-tributioji of source (or sink) panels of constant strength. The source strengthvaries in radial direction, corresponding to the thrust distribution of a represen-tative propeller.

source distribution in propellerdisk for smaller IVRt

Fig. 4.4 Modelling of pump through a source disk in the intake

The strength of the propeller disk is adjusted through a thrust loading coeffi-cient CT,,:

Tpropeiier

p (4.1)pUA

It is to be noted here that the relation between propeller force and source dis-tribution in the present model is not as simple as that between the thrust andsource strength for a propeller in a free stream. This is caused by the flowthrough the propeller disk, which is not purely axial here (Fig. 4.4). This flowdirection causes radial components that need to be incorporated in the Bernoulliequation, in order to find the pressure jump over the propeller disk. Therequired IVR, ratios have consequently been obtained from interpolation in theempirical relation between CT,, and JVR,. Thrust loading coefficients CT,, of -4.6and +4.6 were required for ¡VR, values of 0.6 and 0.9 respectively.

i 75


Sensitivity of leakage for panel density

Two distinct planes in the intake have been used to check the volume flow ratethrough the intake. These planes are designated plane 1 and 2 in Fig. 4.5. Hessand Smith [1966] already noted that their method is less accurate for concavestreamlines and internal flows. To account for the lesser accuracy, they advisedto take a finer panel distribution for these type of flow problems.

176

-300

-200

EE -100N

O

100

symmetric plane waterjetpropellerdiskplane Iplane 2intake area (Ait)

0 -100 -200 -300 -4(X) -500

x [mml

Fig. 4.5 Definition of cross sectional planes within the intake

The effect of the number of panels on the flow rate through the planes i and 2has been studied. The results of which are presented in the Table 4.1 below.

Table 4.1Computed flow rates through two cross sections for two distinct panel distributions. The flow

rates are given relative to the flow rate in plane 2 with the 2018 panels

IVRE = 0.6 !VR1 = 0.9

Plane I Plane 2 Plane I Plane 2

931 panels2018 panels

0.870.85

1.021.00

1.031.02

0.991.00


lt is observed that the difference in flow rates for the two panel distributions iswithin 2%. A discrepancy of some 15% in flow rate through plane 1 and 2

occurs however for the condition where IVR1=0.6.

This discrepancy is attributed to the proximity of plane 1 to the boundaries ofthe elements modelling the intake. These boundaries are singularities in themathematical model, causing unrealistic velocities in their proximity. This effectgets stronger when the source strengths of neighbouring panels differ stronger.This effect causes the deviation for the IVRE of 0.6, where a strong pressuregradient over plane I exists (Fig. 4.6), whereas this gradient is much smaller forthe condition where IVR=0.9 (Fig. 4.7).

Validation of internal intake flow

The computed pressures will be compared with pressure readings from theintake ramp and lip centrelines. The results are shown in Fig. 4.8 for a designIVR1=O.62 and in Fig. 4.9 for an off-design IVR=O.94.

Fig. 4.8 shows that the results for the ramp agree qualitatively, but that the dis-crepancy between measured and computed pressure increases when travellinginward. A maximum difference in C, value of about 0.4 is found. At the lip,the computed results do not show the drop in G downstream of the stagnationpoint as shown by the experimental results. A maximum difference in G,between measured and computed results of approx. 0.7 occurs. This poor corre-lation shows a remarkable correspondence with the results of Kashiwadani[1986] for his 2D potential flow code. He made a similar comparison for anÍVR1 of 0.68.

Fig. 4.9 shows a comparison as in Fig. 4.8 at an IVR=O.94. The comparison ofthe pressures at the ramp and at the lip show the same trend. The difference inC, value is larger here however (maximum difference in C is about 1.2).

The difference in computed and measured G is likely to be caused by differentpositions of the stagnation point at the lip. The experimental stagnation point islikely to be somewhat more outside the intake, causing a suction peak just onthe inner side of the intake lip. The suction peak is clearly present in theexperimental results for an IVR,=0.94 (Fig. 4.9), but a similar tendency can beobserved from Fig. 4.8 for the IVR=0.62.

177


178

0.500

0.000

-0.200

,--.---- -

Fig. 4.6 Comparison of measured and computed C1!, distribution in centreplane VL1 forIVR=O.6


- -r-. --t--s--._

Fig. 4.7 Comparison of measured and computed Ç distribution in centreplane VL I forIVR=O.9

179


U

0.8

-0.8

180

Ramp, IVRt = 0.62

-100 0 200

1.5

o

400 -60

Intake lip, IVRt = 0.62

0 40 80

0.4- -

o

computed

measured

TL)

O

-0.8

girth coordinate from girth coordinate fromramp LE [mm model] lip LE [mm model]

Fig. 4.8 Comparison of measured and computed static pressures for iVRO.62

Ramp, IVRt = 0.94 Intake lip, IVRt = 0.94

-lOO 0 200 400 -60 0 40 80

girth coordinate from girth coordinate fromramp LE [mm model] lip LE [mm model]

Fig. 4.9 Comparison of measured and computed static pressures for IVR,=0.94

The more outward stagnation point in the tests can be attributed to the displace-ment effect of the boundary layer at the ramp, which is not accounted for in thecomputations. This displacement effect causes a reduction of effective area inthe throat of the intake. At an equal flow rate, the intake will therefore effec-tively operate at a slightly higher IVRE than for the corresponding computations.

Another viscous effect that is not included in the potential flow computations isthe vortex that is shed from the sharp lateral edge of the intake. This vortex hasbeen observed from the LDV measurements in the internal transverse planeVT5 (Fig. 4.1). Fig. 4.10 clearly shows the clockwise rotation just in the intake,downstream of the lateral edge. It also shows the decelerated axial velocity inthe nucleus of the vortex.

- computedmeasured

.

- computedmeasured

.

A

- - computedo measured

0

i-10N

-20t-

o -30o

-40 -

-50

transverse coordinate y [mm]

-60 -50 -40 -30 -20 -IO O

\\\\ \ \

HI I

-60o

N 10

-20ooo

. -30

>

-40


transverse coordinate y [mm]

-50 -40 -30 -20 -IO O

Fig. 4.10 Measured velocity distribution in internal plane VT5 for IVR=0.62

Kashiwadani [1985, 1986] explained the discrepancy between calculated andmeasured static pressure within the intake by viscous and 3D flow effects. Hedid not measure a significant rotation within the intake however (Kashiwadani[1986]). He also found no significant deviations in the off-centreline pressuretransducers compared to the centreline transducers. Thus, the hypothesis on theimportance of 3D flow effects was not confirmed.

Kashiwadani subsequently hypothesized that the discrepancy in static pressurewas mainly caused by the quickly increasing boundary layer displacementthickness near the intake throat. This effect causes a decrease of effective intakethroat area, causing an increase in average flow velocity and therefore adecrease in static pressure. A comparison of measured and computed velocityprofiles in the intake throat by Kashiwadani is presented in Figure 4.11.

Conclusions

It is now concluded that the zero order panel method as implemented in HESMyields results that give comparable deviations as the higher order method devel-oped by Kashiwadani [1985]. The discrepancies with the measurements in theinternal part of the intake are caused by the absence of viscous effects in the

181


calculations. These begin to play a dominant role in the internal pressure andvelocity distribution.

182

(side view)

1.5

1.0

0.5

MeasuredCalculated

U0

0.5 1.0

ramp wall lip wall

Fig. 4.11 Comparison of measured and computed velocity profiles in intake throat area A4for various IVRE values (from Kashiwadani [19861)

Validation of external intake flow

It has been demonstrated in the preceding observations that the validity of thepotential panel code HESM is limited as far as the internal intake flow is con-cerned. Because viscous effects are considered less important in the flow justoutside the intake, a better correspondence between experiments and computedresults is expected here. This expectation is confirmed by the findings byKashiwadani [198611 (see Section 1.6.3).


To validate the HESM results, LDV measurements have been made for a num-ber of 2D planes just outside the intake. The results for two vertical longitudi-nal planes (VL1 and VL2) and one horizontal plane Hl will be presented here(see Fig. 4.1).

A comparison of the C distribution in plane VL1 for IVRE values of 0.6 and0.9 is presented in the Figs. 4.6 and 4.7 respectively. It can be observed fromthese figures that a broad correspondence appears between the computed andthe measured results. Noticeable differences occur at the ramp in the boundarylayer and near the stagnation point on the intake lip. The outward shift of thestagnation point from the measurements in comparison to the computed resultscan be observed.

Fig. 4.12 shows a comparison of the C distribution in the horizontal plane Hlfor an IVRE of 0.6. This plane is situated at the very beginning of the intake, inthe region where viscous effects just start to become important. The same trendas observed for plane VL1 is noticeable here. The extent of the acceleratedregion at the ramp is about equal for both the measured and computed results.Toward the lip, the computed results show a stronger deceleration, correspon-ding to the more inward position of the stagnation point. The slightly highervelocities at the lateral edge are likely to be caused by the flow ingested overthe sharp edge. This accelerated region is situated slightly away from the lateraledge in the measured results, likely to be due to the presence of the boundarylayer.

The correspondence of the measured and computed C distribution in theimaginary intake area (plane VTO) for IVR=O.6 can be observed from Fig. 4.13.

A more detailed comparison of results is obtained when we compare the shapeand pressure distribution of the dividing streamlines. The streamlines can betraced from the detailed flow fields available by considering the stream functioniii. The stream function is defined such that no transport of mass occurs throughlines (or planes) of equal value. Hence, the dividing streamlines can be obtainedby solving the differential equation:

¿h

where s = girth coordinate.

(4.2)

183


I0500

0 000

-0 200

------5-\ 1 --u

- ---- --il i'Li -1 _u_ur . j

r ,/L!L ...--

wIlrrhulLrniw

Fig. 4.12 Comparison of measured and computed C,, distribution in horizontal plane HI forJVR=O.6

184

cp


0. 000

-0.220

C p_p r

II. 1 79

0.000

-0.176

Fig. 4. 13 Comparison of measured and computed ('i, distribution in vertical plane VTO forJVR=O.6

185


In the x-z plane, this equation can be written as:

aN! dx dz = oaxds azds

The following relations can be obtained from the continuity equation:

&NJ aN!_=-w and =uax az

where u and w are the x and z-components of the local velocity. After substi-tution in equation (4.3) we find:

dz w (4.5)dx u

This equation can now be solved for any 2D x-z plane.

As a starting point for a dividing streamline, the point with the highest G1,, valuein the lip area was searched for. Starting from this point eq. (4.5) was numeri-cally solved in the following way. Because a residual velocity was available inthe point with the highest GP, the velocity gradient w/u could be obtained. Thenext point for which eq. (4.5) is solved, is found by searching the two nearestpoints following (see Fig. 4.14). The velocities pertinent to this point areobtained by interpolating in these two neighbouring points. This process isrepeated several times until the required streamline is found up to the desiredlength.

Dividing streamline tracing was performed for both the set of computed andexperimental data. The resulting streamlines are presented in Fig. 4.15 for JVRvalues of 0.6 and 0.9 respectively. It is seen that the dividing streamlines almostcoincide at the imaginary intake area AB, but that the streamline from theexperimental data is positioned lower in the flow further downstream. The linesfrom computed and experimental data seem to approach each other again nearthe stagnation point. This discrepancy is in line with the findings from theinternal flow. It has been found there that the displacement thickness of theboundary layer on the ramp quickly increases toward the intake throat. Thisincreasing displacement thickness forces the dividing streamline further out-ward.

186

(4.3)

(4.4)

300

O

100

computation - - -.experiment - -

300

O

100


computation - - -.experiment - -

187

-J- grid point t velocity vector in z-direction

dividing streamline velocity vector in x-direction

Fig. 4.14 Tracing of dividing streamlines

IVRt=0.6 IVRt=0.9

o -500 O -500x [mm] x [mm]

Fig. 4. 15 Comparison of dividing streamlines traced from HESM and LDV results (/VR0.6and 0.9)

The pressure coefficient G pertinent to the dividing streamlines is plotted forboth the computed and experimental data in Fig. 4.16, again for IVRE values of0.6 and 0.9. Maximum deviations in Gr, of the order of 0.1 occur in the sameregion where deviations in streamline position were found.

To provide some more insight in the change of dividing streamlines with lateralposition, the streamlines for the three computed planes VL1 through 3 (Fig. 4.1)are plotted in Fig. 4.17. It is observed that at the lowest IVR1 of 0.6, the divid-ing streamline approaches the intake lip from the inside of the intake, whereas

E

N


for the higher IVRE of 0.9, the dividing streamline shows a rather straight char-acter, approaching the lip from the outside.

EE

N

188

300

100

Fig. 4.16 Computed and measured pressure distribution along dividing streamline in planeVL1 (IVR=O.6 and 0.9)

plane VLIplane VL2 - -plane VL3

-0.4

300

100

o

-.

plane VLI - - -.plane VL2 - -plane VL3

Fig. 4.17 Dividing streamlines traced from HESM results for three longitudinal planesVLI,2 and 3 (IVR=0.6 and 0.9)

The results on the external flow fields will be used in the following sections.

Conclusions

The potential flow panel code HESM yields acceptable results for the externalflow about a waterjet intake, if the ingested boundary layer is relatively thin(Q1QhI> approx. 1).

1.0

ç-)

O

IVR=0.61.0

IVRt=0.9

computation - - - computation - -experiment experiment

IVRt = 0.6 TVR1 = 0.9

o -500 o -500

x [mm] x [mm]

-0.4-100 -500 -100 -500

x [mm] x [mm]

4.1.2 Intake induced drag and lift

Intake induced drag

Many authors refer to an intake drag which makes up for the differencebetween a particular definition of gross thrust and some net thrust acting uponthe hull. Although the intake drag is addressed several times, for example byMossman et al. [19481, Arcand et al. [1968] and Hoshino et al. [1984], littleattention is paid to its definition. An exception to this rule is the contribution byEtter et al. [1980].

The intake drag is defined as the difference between the gross thrust and the netthrust acting upon the hull (Section 2.2.3). The control volume representing thehydrodynamic jet model is selected to be volume D (Fig. 2.1) in Section 2.1.1.The definition of intake drag does not refer to the bare hull resistance, so itdoes not include a change in hull resistance due to the jet action.

The jet system's thrust deduction fraction t1, as introduced in Chapter 2, repre-sents the non-dimensional intake drag D.:

t. -J Tg

It has been demonstrated in Chapter 2 that the intake drag equals zero for apotential flow in free stream conditions.

As a step further, let us consider the isolated waterjet operating in a viscousflow. This condition is less accessible to the simple arguments used in Chapter2. To get a proper idea of the viscous intake drag, a wake survey analysis ofexperimental data was considered to be one of the most accurate methods.

To this end, detailed velocity measurements in plane VT3 (Fig. 4.1) wereobtained from the LDV experiments in the MARIN large cavitation tunnel. Theexperimental set-up is described in Appendix 7. The operational condition ofthe intake, governing its drag, is characterized by the intake velocity ratio in theintake throat IVRE, by the ratio of ingested flow rate to flow rate ingested fromthe boundary layer Q'QbI and by the Reynolds number of the intake throat Rn.The test conditions are specified in Fig. 4.18.

The same two operational conditions have been used as in the preceding analy-sis, representative for modern jet system operations, viz. IVRE values of 0.62and 0.94.


(4.6)

189


190

0.6

0.4

0.2

o

-0.2

-0.4

-0.6

-0.8o

CDj=+l.9 1O for IVR=0.62

CDj=-3.l 1O for IVR= 0.94

yI½w [-]

Fig. 4.18 Momentum thickness distribution in plane VT3

Noting that there is no viscous contribution to FB, the intake drag can bewritten as (see also Section 2.2.3):

FXBC+FCD (4.7)

The forces FXBC and FXCD act upon the protruding streamtube of the jet system.

The viscous component of the intake drag can be obtained from a momentumconsideration of Control Volume i in Fig. 4.19. The momentum balance in x-.direction reads:

JJp u(u-Uo)dA = -FXDJ-FXcD-Fxßc-FJ ¡B (4.8)A2

It is noted with the above equation that there is no net contribution of the ambi-ent pressure p0 over the control volume. The force contributions in the right-hand term are reactions on the action forces acting on the bottom plating (posi-tive drag) and the streamtube (positive intake drag).

-- IVRt=0.62e- IVR=0.94

2

Rn 5 * 1O

0.5 1.5 2

J

A


191

.4

F'pump X

U0cv i

Fig. 4.19 Control volumes used for derivation of intake drag and lift

Using the definitions of the boundary layer displacement thickness 2 (Appen-dix 2) and the intake drag eq. (4.7), eq. (4.8) can be rewritten into

wp

--D1 = 2pU fô2dy-FXJIB-FXDJ

(4.9)

y=o

where w,, = width of the wake survey plane= displacement thickness of boundary layer.

The viscous force FXDJ will be neglected in the following because of the smalldistance DJ in the test set-up. The force FJB equals zero when the dividingstreamline is outside the boundary layer. When it gets within the boundarylayer, its value increases up to a maximum value at the bottom plane IA. Anestimate for the frictional force term when the streamline I'B is completelyattached to the wall of the tunnel can be obtained from the boundary layermomentum thickness outside the intake affected flow region. For this purpose,the most outward boundary layer thickness value was selected and designated

I, z


A non-dimensional intake drag coefficient can now be defined as the ratiobetween intake drag and ingested momentum flux:

192

DCD'=

pQU0

Using eq. (4.9) and (4.10), we find the following expression for the intake dragcoefficient:

2w

(4.10)

where =displacement thickness with active intake mounted

(y) =displacement thickness caused by frictional force FXJB.

It should be noted that there is a gradual transition in 6 from O to S2(w).Because the form of this transition is not known, an abrupt change in is

imposed at the lateral y-position of the geometric intake edge. Hence, theoriginal displacement thickness ö is set zero over the width of the intake, andis set equal to the most outward 2 value for the other points.

The difference in measured displacement thicknesses (2-6) is presented as afunction of the transverse y-coordinate in Fig. 4.18, which also lists the dragcoefficients. It can be concluded from these values and the uncertainty in Snear the intake lateral edge, that the viscous intake drag is effectively zero.

Mossman and Randall [1948] do not account for the change in FX1B with lateralposition. Instead, they take the full displacement thickness measured withoutintake. Their intake drag coefficients consist consequently largely from thefrictional drag coefficient of the tunnel wall.

CD= AVR

(4.11)

Çv) = o for ylw

= 2(w) for y>±w

Intake induced lift

An intake induced lift force on the stern of a vessel with an active waterjet hasbeen suggested by Svensson [1989]. It has also been demonstrated in Section2.2.4 that there is no intake induced lift for a jet operating in free stream condi-tions. Consequently, if an intake induced lift does exist, it must be caused bythe limited bottom plating about the intake.

To study the above paradox, we will consider an intake operating in free streamconditions. To model the operational condition, part of the bottom plating aft ofthe intake is removed. The flow about the intake is left unchanged however. Anestimate of the intake induced lift can thus be obtained from the free streamflow, by simply adding the geometric condition imposed by the hull.

The results from the HESM flow computations about the intake have been usedto assess the lift effect. As demonstrated in the preceding section. a potentialflow model provides a realistic flow outside the intake, provided the boundarylayer at the hull is thin. This is a valid assumption for most hull forms fittedwith waterjets. Because we focus on the induced lift production by the intake,the jet is considered to be discharged horizontally.

An estimate of the lift has been obtained by integration of pressures over thebottom area, starting at the most aftward point on the plate and heading towardthe intake lip. The thus obtained cumulative lift L(x) gives an indication of theforce that is absent when the hull ends at a short distance behind the intake lip.

Typical transverse pressure distributions behind the lip are presented in Fig.4.20. lt is seen here that the pressure at the lateral edge of the plating has notfully converged to zero pressure. This is considered to be partly caused by theasymptotic behaviour of the pressure with increasing distance from the intake,partly with the accuracy of the panel method. To get rid of this boundary effect,all pressures c(xy) have been reduced with the pressure at the lateral edgeC1(x, ½w1,).

The cumulative lift force L(x) has been non-dimensionalized with the ingestedmomentum flux in the following way (see Fig. 4.21):

4. 1 Free stream intake analysis

CL(x)L(x)

pQU0(4.12)

193


194

0.15

0.1

0.05

y = ½ Wp

L (X)

transverse coordinate yI½w [-J

Fig. 4.20 Transverse pressure distributions behind an intake

3 ii

IntakeLip

yCp(x,w)

Fig. 4.21 Geometry and nomenclature used in lift deficit computation

x =0 (lip TE)

X = 0.16 i

X = 0.33 Ii

x = 3.06 I

o 2 3 4

The lift coefficient CL(x) could subsequently be obtained from:

WJ)y

x 2

CL(X) J J Cp(x,y)-C(x,)}dydxIVRA vø

0.06

0.04

-0.02

-0.04


where C(xv) = bottom pressure coefficient dependent on positionw = width bottom plating used in HESM free stream model.

The results are presented in Fig. 4.22 for two distinct IVRE values, viz. 0.6 and0.9. It is seen that the lift L(x) only amounts to approx. 2% of the ingestedmomentum flux in x-direction. This only provides a lift force of 0(0. 1 %) of thehull's displacement. The corresponding trimming moment would result in achange in running trim of 0(0.01) deg for the Hamilton test boat. This result isnot in agreement with the lift reported by Svensson and not in agreement withthe experimentally observed trim and sinkage (Chapter 3).

0.02

o

-0.06O 3

Aftward distance from intake trailing edge I intake length [- I

Fig. 4.22 Transverse pressure distributions behind an intake

(4.13)

195

IVR=0.63- - IVR=0.94

width nelwidth intake


Conclusions

The following conclusions are drawn from the presented study on intakeinduced drag and lift:

The tested intake has no intake drag for the definition used here. Someauthors refer to the ingested momentum as intake drag. This ingestedmomentum is regarded as part of the propulsor action throughout thiswork however, and is therefore incorporated in the thrust.A significant net lifting force induced by the intake can not be discernedfrom an intake in a free stream flow, matched with a geometric hullcondition. Although it is demonstrated that missing lift due to a limitedbottom area behind the intake lip occurs, which changes sign with IVRE,its magnitude is too small to give a noticeable contribution to the changein hull equilibrium position. As a result, the change in hull equilibriummust be caused by interaction effects in the local flow.

4.2 Computational prediction of interaction

A computed prediction of the interaction effects is desirable when its magnitudeis uncertain. On the other hand, a computational prediction often improves theunderstanding of the phenomena involved and can be used for a further analysisof propulsion test data. This section deals with the predictive power of a fewselected tools. Section 4.3 deals with a further analysis of propulsion test data.

A complete prediction of waterjet-hull interaction effects on the poweringcharacteristics includes a prediction of the hull's resistance increment r and thejet system's interaction efficiencies Ti,711 and 11e1 Relations for the jet system'sinteraction efficiencies are given in Chapter 2. For a given flow rate, theseinteraction parameters are determined by the boundary layer characteristics andthe nozzle sinkage. Many relations are available for a prediction of the bound-ary layer characteristics in terms of thickness and velocity profile (see e.g.Schlichting [197911). We will concentrate in this section on a prediction of theresistance increment r and the nozzle sinkage.

For the evaluation of tools, we will use the case with the Hamilton Test Boat(see Section 3.4). The resistance increment will be discussed for two distinctspeeds, corresponding to Froude numbers of 0.50 and 1.19 respectively. Thiscase is selected because of the representative shape of the thrust deductionfraction with speed and because of the amount of information available.

196


Based on the discussion on results in Chapter 3, it is deemed important that theselected code should be able to compute the equilibrium position of the hull fora successful prediction of the resistance increment. It is furthermore deemedimportant that the code be able to compute the effect of ingested flow rate onthe pressure distribution and hence the wavemaking resistance. This lattercriterion is assumed to be particularly important in the lower speed range (FnL< approx. 1). The hypothesis on the potential flow character of the resistanceincrement (Section 3.4.1) is used here in the selection process.

The available programs that met the above constraints are the MARIN programsDAWSON/RAPID and PLANE. Descriptions of these programs are given in theAppendices 5 and 6 respectively.

4.2.1 Resistance increment for hump speed

Selection of code

The hump speed regime is particularly suitable for analysis with a free surfacepotential flow code such as e.g. DAWSON with linearized free surface condi-tions. An improved method is implemented in RAPID where the non-linear freesurface conditions are solved. The RAPID code furthermore has the advantagethat the equilibrium position of the hull is iteratively determined, which is notthe case in DAWSON. Because of convergence problems with the RAPID codefor the present case however, the results that are presented here have beenproduced by DAWSON. The intermediate RAPID results that became availableindicated nonetheless similar values of the integral quantities (such as e.g. theresistance components).

It is noted here that viscous phenomena such as occur in breaking bow wavesand in the separated flow behind the stern before it gets ventilated, are notaccounted for in either method.

Modelling of problem

The modelling of the waterjet intake was done in a simple but representativeway. Contrary to the work by Kim et al. [1994] and Latorre et al. [1995], theinternal flow in the waterjet was not modelled. Instead, when a suitable condi-tion in a boundary plane between external and internal flow is imposed, theproblem is considered to be sufficiently well modelled for a study of interactionphenomena. For the boundary plane, the projected intake plane A'D can be used(see Fig. 4.23).

197


The proper boundary condition in this plane was obtained by specifying thetotal required flow rate Q flowing through this projected intake area. In addi-tion, the normal velocity distribution should be representative for an intakeoperating at the corresponding IVR1.

4x 2VpLi flip

VP Zy

198

B B

A A

4UI,

D A3

Suitable waterjet control volumes:

CV A: II'CFF'ICVB: A'DCFF'A'CVC: A'B'CFF'A'CV D: ABCFF'A

A3 projected intake area

Fig. 4.23 Control volume representing the waterjet system in the DAWSON/PLANE compu-tations

The vertical velocity distribution in the projected intake area was obtained fromthe LDV measurements in the horizontal plane Hl (see Fig. 4.1), for the IVREof 0.94. The IVRE obtained for the test boat from the propulsion tests at thisFroude number was 0.89, sufficiently close to the LDV condition. The normalvelocity distribution from the LDV tests is presented in Fig. 4.24 for 3 longi-tudinal cuts. This velocity profile has been represented in DAWSON by aconstant normal velocity over the projected intake area AD' (see Fig. 4.25).

In modelling the intake this way, care should be taken that the resulting liftforce due to the ingested vertical momentum flux is cancelled by an equal butopposite lift force within the jet (see Section 2.2.4). This neutralizing internalforce is not modelled in the panel model, but should be accounted for in theobtained results, as will be demonstrated later in the discussion on trim andsinkage.


199

- yI½w=0. y/½w = 0.58.*- y/½w=O.8

_rA" = intake

= intakeLE in DAWSONTE (lip) in

modelDAWSON________ D'

la

model

--

transom

Q shaft50

____._.l_

p* FQofship

A"

02 O -0.2 -0.4 -0.6 -0.8 -1.0 -1.2

D' xiii [-J A"

Fig. 4.24 Normal velocity distribution in projected intake area for an IVR=0.94 obtainedfrom LDV measurements

ord. O ord. I

Fig. 4.25 Relation between actual waterjet intake and projected intake area A'' D' as used inthe DAWSON computations

Results pressure distribution

To check the results of the rather coarse DAWSON model we will first studythe computed pressure distribution. Fig. 4.26 shows the C1 distribution over thecentreline of the intake. This distribution is compared with those obtained from

1.4

1.2

1.0

N

N

0.8

0.6

0.4

02


the LDV measurements and the corresponding HESM computations. It is notedthat the first pressure distribution belongs to an operational condition, whereasthe latter two distributions belong to an intake in free stream conditions.

200

0.8

0.4

-0.4

-0.8

Fig. 4.26 Comparison of computed and measured C distribution over centrehne intake

The pressure distribution from the DAWSON results has been deduced from thepressure distributions of the bare hull and the combined jet-hull system. To thisend, the velocity field pertinent to the bare hull is subtracted from the field ofthe combined jet-hull system:

t7jet) = i(hull+jet)-(hul1) at any position (4.14)

It is observed from Fig. 4.26, that there is qualitative correlation. It is also seenthat the DAWSON model does not follow the higher frequency peaks in G.This effect is ascribed to the relatively coarse panel distribution used.

Centreline G distributions for the bare hull (free stream condition) and thehull-jet combination (operational condition) are plotted in Fig. 4.27. A compari-son of the C distribution over the complete aftbody is presented in Fig. 4.28. Itcan be observed from these comparisons that significant differences in pressuredistribution occur in the intake region, due to the jet action. It can also be

DAWSON wjet IVRt = 0.89

. LDV wjet IVRt = 0.94

.*- HESMwjetIVRt=0.90

.

L

o -2

observed however that the influence of the intake on the C, distribution islimited to an area which roughly extends between approximately one intakelength ahead of the ramp tangency point and aft of the intake lip, and oneintake width next to each lateral edge of the intake. Due to the nature of thepotential function of sinks and sources, the influence of the intake on the pres-sure distribution decays asymptotically with hr2 for non-zero hull speeds,where r is the distance between the point considered and the centre of gravityof the sink distribution modelling the intake.


201

-ca-

-*-

aftbody

waterjet

hull-jet

LwerJetDAWiJ

- DAWSON

IVR = 0.9 - LDV- DAWSON.,,

_WI-rO -2 -4 -6 -8

x/I1 [-1

Fig. 4.27 Comparison of computed C distributions over centreline aftbody for the isolatedhull and the hull-jet combination

Fig. 4.29 shows that the wave profile that is generated by the hull with activewaterjet resembles closely the wave profile without jet. Relative to the profileof the bare hull, the water level slightly falls along the aftbody, to subsequentlygive a slightly higher stern wave. It is to be noted that both computations aremade at an equal equilibrium position of the hull, so that only the local suctioneffect of the intake on the profile is visualized.

0.6

0.4

0.2

-0.2

-0.4

-0.6


202

Fig. 4.28 C distribution over complete hull with and without waterjet intake for FnL=O.5Oand IVR=O.9

Results resistance computation

An important objective of the DAWSON computations is to predict the resis-tance increment of the hull due to the jet action. The relation for the resistanceincrement given in Chapter 2 (eq. 2.97) shows that the r is basically built upfrom two contributions. One is due to a change in frictional drag, caused by themissing part of the projected intake area A3 in the wetted surface. The other isdue to a change in hull resistance, caused by a change in tangential stresses andnormal pressures over the remaining wetted area (S-A3).

Let us first consider the contribution in frictional drag due to the missing intakearea A3. A first estimate is made by assuming that the same frictional coeffi-cient can be used for the total wetted area S as for the intake area A3. The con-tribution to the resistance increment r can then be written as:

A3 CFr = --SCT

where S = total wetted surface of the hull (excluding transom area)C1 = mean frictional drag coefficient

= total drag coefficient.

(4.15)

203


0.4

0.3

' 0.2-

-0.1

-0.2

-03

Fig. 4.29

¡ I

-AP

fr. -1

-

J I J

J J J J

FPfr. 8

without waterjet

J

-- - with waterjet

J I I

1.4 1.2 1.0 0.8 0.6 0.4 0.2 0.0 -0.2 -0.4

x/L

Comparison of wave profile along the hull with and without waterjet

-0.6


For the present case (hull form and speed), it appears that the frictional contri-bution of the missing area A3 to r is approx. 0.002. It can consequently beneglected here.

The hull frictional resistance is furthermore assumed to remain effectivelyunchanged and is left out of the following discussion.

The normal pressure drag R that is provided by DAWSON is computed from:

The first term on the right-hand side is referred to as the dynamic pressure Pdvn'the second term is the hydrostatic pressure. The normal pressure drag R cannow be broken down into a component due to the hydrodynamic pressure, anda component due to a hydrostatic pressure. For conventional ships withoutventilated stern or flow separation, the hydrostatic pressure does not exert a netforce in x-direction. In case of a ventilated stern, it does exert a force however.This contribution is referred to as transom drag, and in the fully ventilated case,is obtained from:

Rr = JjpgzdA (4.18)A Tr

where ATr =ventilated transom area up to the undisturbed free surface.

The remaining pressure drag component due to the hydrodynamic pressure isreferred to as wavemaking resistance' R. The residual resistance as obtainedfrom resistance tests can directly be compared to the total pressure dragobtained from DAWSON.

204

R = jf(PPo)ndA (4.16)

where p = pressurep0 ambient pressureS = wetted surface up to undisturbed waterplane

= x-component of unit normal vector at wetted surface S.

The pressure p can be rewritten with Bernoulli's theorem into:

P-P0 p(U_u2)+pgz (4.17)


The computed resistance results in their non-dimensional form are summarizedin the table below and compared with the experimental resistance values:

Table 4.2Comparison of computed resistance with experimental data

All tgures refer to full scale. The above resistance coefficients all refer to theexperimental wetted surface area S=l3.3 m2.

It is important to note with the above table that the DAWSON results wereobtained for the experimental trim and sinkage data. These data have been usedbecause the hull equilibrium was not sufficiently accurate computed byDAWSON, whereas its importance for the final results was recognized.

We will now express the computed resistance increment in a fraction tr for acomparison with the total thrust deduction t as obtained from the experiments.The resistance increment t, (Section 3.4) can be expressed in CT, according to:

CT(hulljet)-Cl(hulI)r - C-(hul1+Iet)

The tr fraction can now be computed with the data from Table 4.2.

Table 4.3 shows a comparison between the resistance increment tr and the totalthrust deduction t. The resistance increment value obtained from the series ofresistance tests (Section 3.4) is added for completeness.

(4.19)

205

Resistancecomponent

DAWSON Resistance testhull

Hull HulI+jet

C lO 215 187

CTr lO 1688 1944

CRes lO 2306CF 267 267 267

CT l0 2170 2398 2573


206

Table 4.3Comparison of computed resistance increment tr

with total thrust deduction t from experiments

The following observations can be made on the thrust deduction fraction tr:

Almost the complete contribution to the computed tr consists of achange in transom drag (110% of tr).The wavemaking drag furnishes a negative contribution to ç.

The importance of the transom drag contribution to the resistance increment isconfirmed by the finding that the thrust deduction fraction t for lowLength/Beam ratio hulls is usually significantly higher than the values for slen-der hull forms.

It is to be noted with Table 4.3 that the DAWSON predicted transom drag istoo high, when the transom is not yet fully ventilated in reality. This is becauseit is assumed in the calculations that the transom is completely ventilated. Thismay partly explain the discrepancy in computed tr with that obtained from thesystematic resistance tests. The resistance increment from these tests onlyexplains about 45% of the experimental thrust deduction, whereas theDAWSON results explain about 65%. If however, the transom is not yet fullyventilated, which can be concluded from Photo 3.2, the true resistanceincrement will have a somewhat lower value than the DAWSON prediction.

lt is concluded that a reasonable agreement exists between the computed resis-tance increment fraction and the experimental value for t,.. It is also concludedthat a significant gap between the total thrust deduction and the resistanceincrement still exists. One should note however, that the total thrust deductionis composed from the resistance increment contribution t,., and the jet system'sthrust deduction t1. The effect of thïs latter contribution is discussed in Section4.3.2.

Source of t t t,. tít[-1 [-1 [1

Propulsion/resistance tests 0.143 100DAWSON computations 0.095 66Resistance test regression 0.057 44

Results trim and sinkage

As demonstrated in the preceding discussion on the resistance increment, anaccurate prediction of trim and sinkage is of paramount importance. This sec-tion will first provide the relations in the computational model that govern theequilibrium of the hull. Subsequently, the results that were obtained withDAWSON are discussed.

As mentioned in the discussion on the modelling of the problem, the waterjet isrepresented by control volume D in Fig. 4.23.

In order to find the change in trim and sinkage due to the jet action, we need toknow the change in hull lift and trimming moment. The relations determiningthe vertical and pitch equilibrium are found from similar considerations as usedin the derivation of the resistance increment in Chapter 2.

In the next discussion, we will use the earth-fixed coordinate system x',y',z'.

The hydromechanic force acting upon the hull in vertical direction (z') can nowbe written as:

Fo = jJG..odA +jjcYodA (4.20)S A3


= vertical force acting upon bare hull (including weight of jetsystem)

= wetted surface of hull excluding the projected waterjet intakearea A3

= projected waterjet intake area (see Fig. 4.23)= total stress acting in z'-direction (see Section 2.2.1).

The hull's vertical equilibrium position is found by matching the abovehydromechanic force (including both hydrostatic and hydrodynamic pressures)with the combined weight of the jet-hull combination.

During the propulsion test (operational condition), the jet intake is open and theweight of the jet system is not part of the hull displacement any more. To findthe total hydromechanic force acting upon the hull, we consequently have toconsider the hull and the jet system separately. The total vertical force is thenobtained by adding the vertical forces on both systems.

207

where F:,0

s

A3G..'


The hydromechanic vertical force on the jet system can be obtained from themomentum balance for control volume D in vertical direction:

mnz'miz' = z'netJ J +JjJpgdV (4.21)A3+A8 V

where Fnet = net vertical force acting upon the hull.

It is to be noted with the above equation that the net vertical force F.,net hasbeen given a negative sign. This is because it represents the force acting uponthe hull. Its reaction force (equal magnitude but opposite sign) acts upon thestreamtube for which the momentum balance is constructed.

The hydromechanic force acting directly upon the hull system in the operationalcondition subsequently reads:

JJcdA (4.22)

The total vertical hydromechanic force acting upon the hull system in theoperational condition consequently reads:

F +F, = J(L'dA mnz' miz' + J dA J"Jj g7dV (4.23)S A3+A8 V

Again, the vertical equilibrium position of the hull is found by matching thevertical hydromechanic force with the weight of the hull system. It should benoted that the weight of the entrained water in the jet system should not beused again to balance the hydromechanic force, as the jet system force (includ-ing entrained water) is already accounted for by Fznej

Similar relations can be found for the momentum moment balance, determiningthe pitch equilibrium.

From an analysis of the difference in resulting equilibrium position of the hullbetween the resistance test and the corresponding DAWSON computation, areasonable correspondence occurs. The deviations in trim and sinkage are listedin the Table 4.4:

208

The DAWSON results relative to the change in hull equilibrium caused by thejet action, are listed in the table below:

Table 4.5Change in trim and sinkage due to the waterjet action

relative to the resistance test condition (full scale values)


Table 4.4Deviation in computed hull equilibrium position relative to

resistance test result (computation-experiment, full scale values)

Table 4.5 shows the agreement in the trends for transom sinkage and trim. Thecomputed values however, are only some 30 and 20% respectively of theexperimental values for sinkage and trim. Although the computed values arestill too low, they are much closer to the experimental values than the trim andsinkage prediction from the free stream jet consideration in Section 4.1.2. Thesevalues appeared to be an order of magnitude smaller.

From a comparison of the errors presented in the Tables 4.4 and 4.5, it is notedthat they are of the same order of magnitude. Although the errors in hull equi-libriuin for the resistance condition are small in absolute terms, they are too bigwhen used for a prediction of the resistance increment caused by the jet action.

Conclusions

lt is concluded from the above results, that the DAWSON program provides asuitable tool for the analysis of the physical mechanisms involved in the changeof hull behaviour due to the jet action. The prediction of the equilibrium posi-

209

Experiments DAWSON Error

Resulting sinkage at transom (dz [ml,positive downward)Resulting trim (dt [degi, positive bowdown)

0.03

-0.57

0.01

-0.11

0.02

-0.46

- Error in transom sinkage (z [m], positive downward) 0.01- Error in trim (&r [degi positive bow up) 0.15


tion of the hull is not sufficiently accurate for a prediction of resistanceincrement. The error with the experimental data causes a large error in thecalculated resistance increment.

Possible reasons for the error in hull equilibrium position are:

The inadequacy of the flow model describing the transom clearance.The steepness of the wake is underestimated, causing a computedpressure at the transom that is relatively too high.The neglect of viscous effects in transom clearing.The coarseness of the panel distribution and the corresponding inac-curacy in the lift force obtained from pressure integration.

4.2.2 Resistance increment for design speed

Selection of code

For a study of the resistance increment at high Froude numbers (FnL>l), theSavitsky method is used. This popular resistance prediction method is recom-mended in a review paper by Altmeter [1993] for typical high speed monohulls.

The Savitsky method is implemented in the MARIN program PLANE. Thisprogram has been adapted to allow for the free stream forces and momentsintroduced with waterjet propulsion. No allowance is consequently made forpossible interaction effects in the pressure distribution about the intake, such ascomputed in DAWSON.

Modelling of problem

The same control volume as applied in the DAWSON model can be effectivelyused here to determine the jet system's net forces and moments (see Fig 4.23).As derived in Section 2.3.1, the net thrust of a jet system on a flat plate isapproximated by:

Tg = cosOn-pQcmUo (3.9)

where O,, = nozzle inclination relative to hull-fixed coordinate system.

Because the net force on the protruding streamtube plus external part of theintake lip equals zero, we can derive:

210


7CoB = Centre of BuoyancyCoF = Centre of FlotationCoG = Centre of GravityFT = Towing forceRT = Total dragA = Displacement weightV = Displacement volume

Fig. 4.30 Forces acting on the hull-jet system as modelled in the computer program PLANE

Results

To check the validity of the computed results, they were compared with theexperimental results. Both the resistance and propulsion test conditions werecomputed, to find the resistance increment and the change in trim and sinkage.

211

,n3x = pQc,U0 (4.25)

The point of application of the ingested momentum follows from a momentummoment balance. Without detailed elaboration of this balance, this point isassumed to be in the centroid of the intake area.

As demonstrated in Section 2.2.4, the jet system in free stream conditions doesnot exert an intake induced lift force upon the hull.

Fig. 4.30 shows the forces that are modelled in the PLANE program. Resistancetests can be modelled by applying the pulling force in the actual towing pointduring the tests. The equilibrium position of the hull is obtained by solving theforce and moment balance for each speed and condition.


A comparison of the measured and the computed resistance is presented in Fig.4.31. It can be observed that the trend in computed resistance corresponds wellwith that of the measured resistance. Taking the limitations of the resistanceprediction algorithm into account, the absolute values of the resistance in thelower speed range correspond surprisingly well with the measured values. Forthe higher speed range however, a discrepancy of some 10% with the measuredresistance occurs.

212

6

5

FnL [1

Fig. 4.31 Comparison of computed and measured resistance data

Fig. 4.32 shows a comparison of trim and sinkage data. Significant discrep-ancies in trim data occur over almost the entire speed range (up to 1.3 degdifference in trim angle). The correspondence in sinkage of the Centre of Grav-ity is satisfactory.

A computed resistance increment factor t,. could be derived from the resistanceand propulsion computations, according to:

RBHr T

net

(4.26)

0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6


213

/ .I.I _A

4AAAA

/- tPLANEA riseCGexp

-- riseCGPLANE

0.3 lo

80.2

6

0.1

4

o2

-0.1 o

0.2 0.4 0.6 0.8 I 1.2 1.4 .6

FflL [1

Fig. 4.32 Comparison of computed and measured trim and sinkage data

This resistance increment factor tr is compared to the total thrust deductionfraction t in Fig. 4.33. It is to be noted that the thrust deduction fraction fromthe experiments consists essentially from a hull resistance increment, except atthe point where the transom clears. This issue will be discussed in Section4.3.2.

It is shown that the level of the thrust deduction fraction and the resistanceincrement factor roughly correspond for FnL 1. For increasing speeds however,the thrust deduction fraction t increases more rapidly than the computed resis-tance increment factor. A strong discrepancy occurs for the lower speed regionas could be expected.

To investigate whether the discrepancy between t and computed t,. would main-ly be caused by a discrepancy in hull equilibrium position, the relationsbetween running trim and thrust deduction were compared (Fig. 4.34). Despitethe fact that the level of computed Ir-values roughly corresponds with theexperimental values for the higher speed regime, large discrepancies occur incorresponding change in running trim dt.


214

0.2

0.1

0

-0.1

0.04

0.02

O

-0.02

-0.04

-0.06

1.6

Experiment

PLANE

u

u

u

.U.

/Experiment -PLANE

-0.6 -0.4 -0.2 O 0.2

dt (prop-res) [deg]

Fig. 4.34 Comparison of computed and measured thrust deduction fraction as a function ofchange in trim angle

A similar exercise was conducted to check whether the agreement in measuredand computed resistance would improve if the computed running trim angle wasbrought in correspondence with the measured trim angle. This was achieved byadjusting the LCG value so as to obtain approximately equal running trim

0.2 0.4 0.6 0.8 1 1.2 1.4

FflL []

Fig. 4.33 Comparison of computed and measured thrast deduction fraction

angles at FnL' 1. Although the computed resistance at this speed more closelyapproached the experimental value, there is still some 6% discrepancy. More-over. the trend of both resistance and running trim with speed, which closelyresembled the experimental trend for the uncorrected LCG position, clearlydiffered from the experimental trend for this case. Adjusting the running trimangle therefore does not seem to improve the predictive power of PLANE overa certain speed range.

Conclusions

It is concluded from the above study that the Savitsky method, extended with ajet model consisting of free stream forces and moments, does not give a goodcorrelation with the model tests. The trends in hull equilibrium and resistanceincrement are weakly shown, but the quantitative correspondence is poor.

4.3 Analysis of propulsion test procedure

In the data reduction applied in Chapter 3, a few assumptions and neglects havebeen made. This section will review the consequences of these simplificationsand assess their importance.

In the determination of the ingested momentum and energy fluxes by the intake,it has been assumed that the imaginary intake area featured a rectangular crosssection with a width that is 30% wider than the geometric width of the intake.The consequences of this assumption will be studied in Section 4.3.1.

In the derivation of the net thrust from the gross thrust, necessary to find theresistance increment of the hull, all integral terms in the relation for the thrustdeduction t1 have been neglected. As a consequence, this thrust deduction wasequal to zero. Part of this simplification was already justified for a potentialflow in Section 2.3.1.

The magnitude of the other contributions can now be assessed, as detailedinformation on both the integral quantities obtained from the propulsion tests, aswell as detailed information from the flow field about the hull-jet system isavailable. The following contributions are addressed in Section 4.3.2:

Effect of free surface induced pressure gradient over protruding part ofstreamtube BCD (Fig. 2.1).Effect of a clearing transom stern.Effect of a running trim angle.


215


4.3.1 Effect of intake geometry on interaction efficiency

The geometry of the imaginary intake area is important in the determination ofthe ingested momentum and energy fluxes for a given flow rate Q, as is dis-cussed in the Chapters 2 and 3. In the reduction of experimental powering data,many authors use a rectangular cross section with an effective width that isslightly wider than the geometric width of the projected intake area (see e.g.ITTC [1987]). An effective width factor f for this cross section is oftendefined as:

JwWe (4.27)w

where we = effective width of imaginary intake cross section (AB in Fig. 2.1)w, = geometric width of projected intake area.

It is easily seen that an increase of the effective width factor leads to a decreasein flow rate ratio Q'Qbl' consequently leading to an increase in the viscouscontribution to the interaction efficiency TÌINT This effect is explained in Sec-tion 2.3.3.

The value of the flow rate ratio Q'Qbl depends on the shape of the imaginaryintake area, as do the momentum and energy coefficients c,71 and c. Thereforean attempt is made here to obtain more knowledge about the true shape of theintake. Subsequently the effect of the assumption of a rectangular intake shapeon interaction data is studied. This is done through a comparison of interactionefficiencies for the most likely intake shape and a simplified shape with rec-tangular cross section.

Information on the shape of the imaginary intake area can be found in e.g.Spannhake [1951] and Alexander et al. [1994]. Spannhake concludes from databy Hewins and Reilly [1940] that the imaginary intake area for flush intakes ofcondensers resembles a half ellipsoid. It is to be noted that condenser inletscoops have a similar geometry as flush waterjet intakes, but that their oper-ational condition is typically at much lower flow rate ratios Q'Qhl This ellipsoi-dal shape of the imaginary intake is confirmed for flush waterjet intakes byAlexander et al. [1994]. These authors state that the width of the imaginaryintake was found to be approximately 50% greater than the width of thewaterjet intake. They furthermore report that the width was largely independentof the craft speed over the range investigated. The change in non-dimensionalflow rate was effectuated through a change in height of the semi-ellipsoid.

216


The data from Alexander et al. [1994] are plotted in Fig. 4.35, together with theprofile that is inferred from the HESM results by the traced dividing stream-lines. It is seen from this figure that both the experimental data from Alexanderet al. and the computed data by HESM are close to a semi-ellipsoid with amaximum width equal to about 1 .5 times the geometric intake width.

0O

y/(½ w) [-1

Fig. 4.35 Comparison of elliptic intake profile with HESM results

The effect of using an ellipsoid intake with a width factor f=l .5 instead ofusing a rectangular intake cross section with f,=l.3 will now be investigated.To this end, the momentum and energy coefficients c,77 and c are numericallyevaluated for both intake geometries. General expressions for these coefficientsin their integral form are given in Appendix 2.

The shape of the imaginary intake geometry is not only determined by theaforementioned width factor but also by the power r of the following gen-eral geometrical relation:

(

max=

W2e

where We = maximum width of imaginary intake area= maximum height of imaginary intake area.

A value for r of 2 corresponds to a semi-ellipsoid streamtube cross section, avalue of 1000 corresponds to a rectangular section.

(4.28)

217

o-o

HESM IVRt = 0.6Elliptic profileHESM IVRt = 0.9Alexander etal ['941

o

n

0.5 1.5 2

1.2

.0

0.8

' 0.6

0.4

0.2


Other non-dimensional parameters determining the amount of ingested boundarylayer are a non-dimensional height of the imaginary intake hmi and a non-dimensional boundary layer thickness 5/w.

A non-dimensional flow rate can now be defined that is related to hull speedand intake width, according to:

The effect of the shape of the imaginary intake area is now studied for equalingested flow rate, or equal flow rate coefficient C0. The results are plotted inFig. 4.36. The variations in CQ have been obtainedby variations in non-dimen-sional height of the intake The non-dimensional boundary layer thick-ness ö/w was fixed at a value of 0.5, which is considered to be a relativelylarge value. In other words, the effect of ingested boundary layer is relativelylarge.

218

1.5

1.4

1.3

1.2

0.9

-Q2

U0w(4.29)

I i I

NVR=1.7= 1.3 (rect), 1.5 (ellips)

öI = 0.5= 9

r = 1000 (rect), 2 (ellips)

-- -°

1mmT / rectangle

lumi / ellips11INT / rectangle

lINT' chips

-c - - o

0 2 3

Cq (Q/(UoW2) []

Fig. 4.36 Effect of imaginary intake geometry on interaction.

Fig. 4.36 shows, however, that the effect of the intake shape on total interactionefficiency rl/NT is within 0.5% over the complete range of flow rates. The effectis most pronounced at values of CQ around 0.75. corresponding to flow rate


ratios Q'QhI of approx. 1.2. For decreasing flow rate ratios, the effect of intakeshape diminishes again.

The effect of intake shape on thrust, expressed in momentum interaction effi-ciency 1L is seen to amount to a maximum of approx. 1.5%. The effect is mostpronounced around CQvalues of 0.75 again.

It is concluded from this sensitivity study that an imaginary intake of rectangu-lar shape with a width factor f=1.3 gives a good approximation in the reduc-tion of propulsion test data. Maximum bias errors in power due to the actualshape of the intake geometry are expected to be within 0.5%. Bias errors in netthrust due to the intake geometry are not expected to exceed 1.5%. These errorscan be avoided by taking into account the best estimate for the intake area,being a semi-ellipsoid with a width factorf=1.5.

4.3.2 Effect of hull and free surface effects on t3 assumption

The relation between the gross thrust that is derived from propulsion tests orcomputations, and the net thrust, acting upon the hull is discussed in Section2.2.3. The effect of jet-hull interaction on this relation is discussed subsequentlyin Section 2.3.1. The present section deals with a quantitative assessment of theterms and conditions derived in the above sections.

A total thrust deduction fraction t is obtained from propulsion tests in a straight-forward manner. This thrust deduction links the gross thrust Tg to the bare hullresistance REH in the following way:

Tgoo(l_t) = RBH (3.39)

This total thrust deduction contains consequently a jet system thrust deductiont, to convert gross thrust to net thrust, and a hull resistance increment r. Torink up with the existing nomenclature in propeller hydrodynamics, we mayrefer to the resistance increment as the hull's thrust deduction fraction tr Acorresponding thrust deduction factor may subsequently be defined as:

T,iet(ltr) = RBH (4.31)

so that

ltr =1+r

(4.32)

219


Consistent with the definitions introduced in Chapter 2, we may write eq. (4.31)as:

Tgoo(ltj)(Itr) RBH (4.33)

Neglecting second order terms, we may write the total thrust deduction t as thesum of the jet system thrust deduction t1 and the hull's resistance increment tr:

t = tjt/ (4.34)

It is seen that, in order to derive the hull's resistance increment from propulsiontests, an estimate on t should be made.

The jet system's thrust deduction fraction t1 was derived to read (eq. 2.39):

ti = JJ G/IA+JJ( -a 0)dA +JJJpgdv) (4.35)A1+A2-A4 V

The first integral term on the right-hand side is the force acting on the protrud-ing part of the intake (see also Fig. 2.1). The second integral term is a contribu-tion over the nozzle area A8, and the third integral term is a contribution of theentrained water weight when the jet is positioned under an angle. These threecontributions will be addressed separately in the following.

Free surface induced pressure gradient over protruding streaintube

The first integral term on the right-hand side is the force acting on the protrud-ing part of the jet system, defined by A1+A2+A4 (see Fig. 2.1). This force wasderived to equal zero in a potential flow with free surface (see Section 2.3.1).In this derivation, the assumption is necessary that the contribution of the freesurface induced pressure gradient in x-direction acting over BCD (Fig. 2.1) isnegligible. This assumption will be validated here.

The additional force FXABCD due to the free surface pressure gradient wouldhowever affect the relation between bare hull resistance and gross thrust. Let usdesignate the contribution to t1 that is considered here as t.

The value of the thrust deduction component t» can be obtained after the divid-ing stream surface and the local pressure gradient are known:

220

fr. -1

0.1

o

-0.1

-0.2

-0.3

-0.4

-0.5


AFTBODY GEOMETRY

A /Q of ship

fr. i

Fig. 4.37 Representative dividing streamline in aftbody induced pressure field of the Hamil-ton Test Boat (Fn=0.5)

221

ti1 -_ f Pfl (4.36)g°°ABCD

Information on the shape of the protruding part of the waterjet streamtube ispresented in the preceding Section 4.2.1. The pressure gradient due to the barehull (without waterjet) and free surface effects is computed by DAWSON forthe Hamilton test boat at a Froude number FnL=O.5 (see also Section 4.2). Thepressure distribution over the aftbody together with the position and the shapeof the dividing streamline of the waterjet on its centreline, discussed in theprevious section, is given in Fig. 4.37 Although the waterjet geometry used forthe computation of the dividing streamline is not the one actually mounted inthe test boat, the operational condition of the intake is equal to that measuredduring the propulsion test during this speed (IVR=O.9).


The strongest pressure gradient over the intake is preferably selected for anindication of its effect on thrust deduction. This condition will occur at thepoint where the flow about the transom stem gets fully ventilated. Pressuregradients in an unbounded flow occur where the streamlines are curved. Thestronger the curvature, the higher the pressure gradient. The flowlines off thetransom show only a weak curvature at low speeds, where a dead- water zoneis entrained. This dead water zone is bounded by the transom stem and the con-tinuous streamlines. At higher speeds, when the transom stern is fully venti-lated, the curvature decreases with increasing speed. This effect is observed asthe smoothing of the rooster tail occurring behind the transom with increasingspeed. In the transition regime, where the actual clearing of the transom occurs,a strong curvature of the streamlines occurs.

Little is known about this transition regime, probably caused by the stronginteraction between the viscous dominated dead-water zone and the potentialdominated streamlines. Also wave breaking mechanisms are expected to affecttransom clearing (see e.g. Raven [1993]).

Although the pressure distribution on the aftbody is difficult to compute, theabsolute value of the pressure is given by the condition that the static pressureat the transom edge cannot be lower than atmospheric pressure. It thus solelydepends on the sinkage of the transom.

Because we consider a hull running at FnL=O.S, in the speed regime where thetransom is clearing (observed from model tests, see Section 3.4.1) and wheretransom sinkage is about maximum, the situation considered is close to a worstcase regarding the additional pressure force on the waterjet streamtube.

An estimate of the magnitude of the thrust deduction t» can now be obtainedfrom a 2D consideration of the known dividing streamlines. Neglecting thecontribution on the outer part of the intake lip CD, the 2D version of eq. (4.36)is found to read:

where CPh = hull induced pressure coefficientA designates the longitudinal position of the imaginary intake

AB¡VR0 = intake velocity ratio in imaginary intake area AB (see Fig.

2.1)h. = height of ingested streamtube at imaginary intake area AB.

222

1

= 21 VR 0h (NVR - I J ph -Cph(A))nxdsAC

(4.37)


The viscous momentum deficit in the intake area, expressed by Cm has beenneglected.

To convert eq. (4.36) to its 2D counterpart, the required 2D flow rate has beenwritten as:

Q = U0! VR 0h (4.38)

The results obtained for the three longitudinal planes considered (Fig. 4.1) aresummarized in Table 4.6.

Table 4.6Results of 2D estimates of thrust deduction induced by free surface effects in hump speed

region (FnL=O.5) at an /VR=0.9

It is inferred from the above table thatto the aftbody induced pressure fieldshould be noticed that this contributionthe NVR value is decreased at equaloccur when a bigger nozzle diameterintake throat area.

the 3D thrust deduction fraction t» dueis within 1% for the present case. Itmay increase up to a few percent whenIVRr Such condition will for instanceis used in combination with a smaller

If a bigger jet system is used to produce the same thrust, both the NVR and theIVRE value will decrease. These effects counteract each other in t11. An indica-tion of their possible net effect is given in Table 4.7.

223

JVR [-1 0.90IVR0 [-j 1.03NVR [-1 4.51I/wi [-j 2.85

Plane VL1 Plane VL2 Plane VL3

ìii 102 [] 17.2 12.6 1.601II/c1nds l0 [-] 12.3 8.07 0.84

t.1 102 [1 0.99 0.88 0.73


Table 4.7Results of 2D estimates of thrust deduction t induced by free surface effects in the hump

speed region at an IVR1=0.6 and an NVR=3

lt is concluded from the above table that the magnitude of the thrust deductiont» is not very sensitive to the size of the jet unit. Contributions to t» of 0(0.01)are computed for the present case.

If however, a non-zero external force would exist, it would not have an effecton overall efficiency nor would it have an effect on required power. This isunderstood when one takes into consideration that the pressure force acts per-pendicular to the internal flow in the jet system. Hence no energy is exchangedbetween external and internal flow.

Clearing effect of transom stern

The second term in the right-hand side of eq. (4.35) is zero by definition in freestream conditions. It equals zero in operational conditions if the ambient pres-sure about the nozzle and the corresponding height at the transom stern of thehull are identical. This is a valid assumption if the transom stern and thewaterjet nozzle are both ventilated (acting in air). The assumption is no longervalid when the projected nozzle position at the transom is ventilated, whereasthe nozzle itself is still submerged. This condition occurs during the clearing ofthe transom stern, when the nozzle still protrudes in the following stern wave.

Let us designate the contribution to the thrust deduction that is considered hereas t». This component can be obtained from the following relation:

IVRE [-1 0.60IVR0 [-1 1.03

NVR [-1 3.00l/w1 [-1 2.85

Plane VL1 Plane VL2 Plane VL3

h1/! 102 [I 12.0 9.90 1.00

I/1/CPhnXds [-1 6.81 5.32 0.47

t» 102 [] 1.38 1.30 1.12

it12 TgJJAA8

It can be seen from this relation, that whenever the nozzle protrudes in thefollowing stern wave whereas the projected nozzle position at the transom isalready ventilated, a positive contribution to t12 occurs (both the integral termand Tg are negative, see Section 2.2.1).

To study the character of t12 and to obtain an indication of the contribution tothe total thrust deduction t, a simple model of the falling water level behind thestern is made. Before the simple model will be explained, one should bear inmind that the Froude number can be written as:

FnL =IX

2ic L

where A. = wave length of transverse waveL = characteristic length for the generation of transverse waves.

It is thus seen that the Froude number can be interpreted as a non-dimensionalwave length, as well as a non-dimensional ship speed. We will use this interpre-tation in the assessment of the difference in Froude number between transomand nozzle ventilation, and in a judgement of the wave steepness just behindthe transom. The latter is adjusted so as to bridge the gap between the experi-mental t-value and the computed t,. from Section 4.2.1.

The height from the nozzle centre to the free surface at the Froude numberFnL=O.5O is used to compute the pressure at the nozzle before ventilation. Fig.4.38 shows that the nozzle position at the stern becomes ventilated at a lowerFroude number than the nozzle discharge centre, because of the smaller wavelength required. This consideration neglects the effect of the transom stern onthe local wave. The difference in FflL at which ventilation occurs can thus beestimated from the length of the protruding nozzle AX, the characteristic hulllength and the Froude number of the hull. The difference in ventilation isestimated from:

AXAFnL =


L 4f

(4.39)

(4.40)

(4.41)

225


226

z=0 '

½A L

= stern wave length0.03 L

0.07 L

Hamilton test boat at FflL = 0.5

Fig. 4.38 Waves relevant in the model for clearing of stern and nozzle

The falling rate of the water with increasing Froude number is supposed tofollow a sinusoidal function (sinusoidal wave). Because of the transom stem,the wave behind the transom will be much steeper than the dominant transversewave pertinent to FnL=O.S. The wave steepness during clearing is determinedby both potential flow and viscous flow effects (see e.g. Raven [1993]). To theknowledge of the author, there is no proper model available to describe thisclearing process. Observations of the breaking stern wave behind the transomdo indeed indicate a much larger steepness.

The wave length coming off the transom stem is determined iteratively, so as tofill the gap between the computed tr and the measured t as discussed in Section4.2.1. The wave length at which a required t12 of approx. 0.05 was found isindicated in Fig. 4.38. It is noted that when the height of the transom stemwave is increased, which is a realistic thought, the contribution of t1 will

increase.

The relation between t1 and FnL that results from this model is presented inFig. 4.39. The sharp peaked character of t1 corresponds remarkably well withthat of the experimental thrust deduction t, as found from the propulsion tests(see Figs. 3.25 and 3.26).

Apart from the aforementioned effect on thrust deduction fraction (or onthe dead- water zone behind the transom also affects the parametric relation for

the energy interaction efficiency r. This is because viscous energy lossesoccur in the dead- water zone behind the stern. Because of these viscous losses,the Bernoulli equation for a potential flow is not valid any more. This equationhas been used in the derivation of the parametric relation for the energy interac-tion efficiency (Section 2.3.2). A correction for viscous effects is thus needed.


227

transom- - nozzle

-*- tj2 computed

0.06 0.12E

o004 . 0.08

uNN

li

0.04

O o0.35 04 0.45 0.5 0.55

FflL []

Fig. 4.39 Effect of transom clearing on thrust deduction fraction j2

Trim effect on entrained water weight

A third contribution to the thrust deduction fraction t1 is given by the third termin the right-hand side of eq. (4.35). lt is referred to as tß. Analogous to thevalue of t12 in free stream conditions, this term equals zero by definition in suchconditions. When the hull operates at a running trim angle and the ingestedwater weight is not negligible compared to the vessel's overall resistance, thisterm cannot be neg'ected beforehand.

The value of t from the experiments with the Hamilton test boat amounted tomaximum values of approx. -0.01.

Conclusion on t1

The effects discussed in this section are quantified for the Hamilton test boatoperating at a Froude number Fn L=0 .5. The results are listed in the Table 4.8. It


is to be noted that the most important contribution to t1 has not been obtainedfrom measurements, but has been quantified so as to close the gap between thetotal thrust deduction and the resistance increment as obtained from theDAWSON computations.

Table 4.8Comparison of computed and measured contributions to the thrust deduction fraction r

It is concluded from the above study of the jet system's thrust deduction frac-tion t1, that deviations from zero may especially occur around the speed wherethe transom is clearing. For higher speeds, this fraction is practically zero(Tg,=Tnet). Hence, the experimentally derived thrust deduction t is a goodmeasure for the hull's resistance increment for the higher speeds, but may needcorrection at speeds around transom clearing. Such corrections could beobtained from resistance and propulsion experiments when the static pressure atthe projected position at the transom (resistance test) and in the nozzle dis-charge (propulsion test) are measured.

If the information to break the total thrust deduction fraction t down into a trand a t. component is lacking, the contribution of t1 to the momentum interac-tion effticiency rl, can be incorporated in the total thrust deduction fraction r.The total interaction efficiency TIJNT subsequently follows from:

fl/NT = (1-t) el (4.42)

where t is obtained from the propulsion and resistance tests (eq. (3.39)), and themomentum and energy interaction efficiencies are obtained from the equations(2.79) and (2.86) respectively.

228

Source of r t.

[-1f

tr[-1

t

[-1

rit¡1%]

Contribution protr. streamtube r» 0(0.01) 7Contribution clearing stern 0(0.04) 28Contribution by entrained water t» 0(-0.01) -7

DAWSON computations 0.095 66Resistance test regression 0.057 44

Propulsion/ resistance tests 0.143 100

229

Chapter 5

5 Conclusions and recommendations

This chapter is split into three parts. The introduction summarizes the mainconclusions, followed by recommendations for future work. Section 5.1 lists themore detailed conclusions that were drawn from the development and validationwork on tools for the analysis of waterjet-hull interaction. Section 5.2 lists theconclusions on the physical mechanisms governing waterjet-hull interaction thatwere revealed in passing.

The following main conclusions are drawn from this work:

A parametric model for the description of the powering characteristics ofa hull-waterjet system is proposed, allowing for a separate identificationof the complete waterjet-hull interaction terms. This model has resultedin a better insight in the physical mechanism governing interaction.

0 An experimental procedure is proposed and validated to determine thecomplete waterjet-hull interaction terms. This method offers a higheraccuracy (high precision) and robustness (little risk for bias errors) thanmethods that can hitherto be found in the existing literature.The resolution of the computational tools studied is not sufficient to givea meaningful estimate of the waterjet-hull interaction terms. The mainasset of the computational analysis is that it enhances the understandingof interaction mechanisms.

Chapter 5 Conclusions and recommendations

230

As a result, the following recommendations are proposed:

Because of the complex flow phenomena that determine the interactioneffects (especially the hull's resistance increment and nozzle sinkage), itis likely that interaction effects are most accurately determined throughmodel propulsion tests for the next decade or longer. A computationalprediction method for interaction effects that can be used in preliminarydesign stages is therefore best based on an empirical approach. Based onthe insight gained in the mechanisms of interaction and based on collecteddata on a wide variety of jet-hull combinations, an empirical predictionmodel can be derived. The data supplied in this work form a first step toarrive at such a prediction model.The accuracy of model propulsion results should be improved byascertaining and possibly reducing the bias error in the experimentalresults. This is effectively done through the collection and analysis ofcarefully conducted propulsion tests.

5.1 Methods and tools

Parametric model

1. A systematic separation between waterjet and hull appears to be possible,leading to a set of parametric relations that describe the free streamcharacteristics and their interaction effects explicitly. (Chapter 2)

A thrust deduction t is introduced that not only accounts for the hull'sresistance increment, such as in propeller hydrodynamics, but also for thedifference between gross thrust and net thrust. This latter component isexpressed in the jet system's thrust deduction t3 and is also prone tointeraction. (Chapter 2)

The powering characteristics of the overall hull-jet system are essentiallyindependent on the choice of control volume modelling the jet system. Askilful selection of control volume does however allow for an accuratequantification of both the individual and the combined poweringcharacteristics. (Chapter 2)

4. To represent the hydrodynamic model of the jet system, control VolumeD (Fig. 2.1) meets the constraints that should be imposed to allow for aseparation of jet system and hull characteristics. For the computation ofgross and net thrust in a potential flow with free surface effects however,

5.1 Methods and tools

control volume A (Fig. 2.1) appears to yield simpler relations. Thisvolume has its (imaginary) intake situated in the free stream. In a viscousflow, simple corrections on net thrust and power are necessary to accountfor the viscous stresses exerted by the hull on part of the streamtube.(Chapter 2)

Experiin entai procedure

The velocity profile and the swirl in any place in the jet system maychange with model speed. A reference flowmeter should therefore showa low sensitivity to changes in flow pattern. An 'averaging static pitottube' meets this criterion. It has proven to be a reliable transducer duringmany propulsion tests. (Chapter 3)

Calibration of the reference fiowmeter with flow rate easily leads touncertainties that render the meaning of propulsion tests doubtful.Calibrating it with model pulling force during bollard pull conditionsyields both a better uncertainty in calibration input signal, but alsoprovides a much weaker, or at most an equal propagation of all relevanterror sources into the final thrust and power prediction. (Chapter 3)

Applying the above thrust calibration procedure, the errors in jet thrust(momentum flux from the nozzle) and ingested momentum flux orcause the biggest errors. Their relative contributions are quantified inSection 3.3.

Based on the experimental trends observed in the hull's resistanceincrement and an experimental and computational study on a possiblemechanism, it is concluded that the resistance increment of the hulllargely consists of a potential flow contribution. The viscous effects in themomentum and energy interaction efficiencies are quantified. Thesefindings confirm the assumptions made in the ITTC'87 extrapolationmethod. (Section 3.5)

It has been proven that it is essentially the viscous momentum and energyloss in the imaginary intake that affect the thrust and power characteristicsof the jet-hull combination. These viscous losses can be determined duringresistance tests. (Chapters 2 and 3)

231


Computational tools

Free stream characteristics

10. Potential flow methods, including higher order methods, do not givesatisfactory predictions of the flow field within the intake. Deviations incomputed C with experimental data of 0(0.5) occur. Potential flowmethods do give satisfactory predictions for flow fields outside the intakehowever. Maximum deviations in Cp along the dividing streamline werefound to be approx. 0.1. (Section 4.1.1)

Computational prediction of interaction

li. The DAWSON potential flow panel code provides a suitable means foranalysis of the physical mechanisms involved in the change of hullbehaviour due to the jet action. The prediction of the equilibrium positionof the hull is not sufficiently accurate for a prediction of the resistanceincrement. The resulting deviation with the experimental data causes alarge error in the resistance increment. (Section 4.2.1)

The 'Savitsky' resistance prediction method, extended with a jet modelrepresenting the free stream jet forces and moments, does not give a goodcorrelation with the experimental results. The trends in hull equilibriumand resistance increment are weakly shown, but the quantitativecorrespondence is poor. (Section 4.2.2)

Analysis of propulsion test procedure

The imaginary intake area AB (Fig. 2.1) is adequately represented by arectangular shape with a width of 1.3 times the geometrical width of theintake area, for the derivation of ingested momentum and energy fluxes.Maximum bias errors in power due to the actual shape of the intakegeometry are demonstrated to be within 0.5%. These errors can beavoided by using the best estimate for the intake area, being a semi-ellipsoid with a width of approx. 1.5 times the geometrical width. (Section4.3.1)

4. The pressure gradient over the protruding part of the streamtube (BD ofControl Volume D in Fig. 2.1) may cause a contribution to the jet thrustdeduction of 0(1%) of the thrust. This effect is quantified by t11. It showsa maximum in the hump speed region. (Section 4.3.2)

5.2 Physical mechanisms

The results of a selected set of waterjet-hull combinations, incorporatingmonohulls and catamarans from 7 up till 80 m length, show that the totalinteraction efficiency rl!NT may reach values between 0.75 and 1.15. Thelower values occur in the hump speed region, around FnL=O.S. Forslightly higher Froude numbers, the interaction efficiencies adopt valuesin between 1.0 and 1.15 (see also Fig. 3.24). (Section 3.4)

The resistance increment of the hull due to the jet action is dominated bypressure drag. For Froude numbers below approx. 1, this pressure drag islargely governed by the transom sinkage. For higher Froude numbers thetrim angle becomes more important. The increasing importance of theforward sinkage is likely to be caused by the growing importance of spraydrag from the forebody. (Section 4.2)

There is no intake drag for a flush type intake operating in a potentialtiow. The viscous drag of a representative intake appears to be negligiblefrom wake survey measurements. It can thus be concluded that areasonably designed waterjet intake does not experience a drag force.(Sections 2.2 and 4.1.2)

There is no net contribution by the intake induced flow on the total liftforce acting on the jet-hull system, provided the area around the flushintake opening is sufficiently large. (Section 2.2.4)

The net induced lift force that is obtained from free stream considerationsby integrating the loss of lift due to the absence of plate area behind theintake lip, does not explain the experimentally observed trim and sinkage.As a consequence, the pressure distribution of the combined waterjet-hullsystem is not adequately represented by the sum of pressures of bothindividual systems in their free stream condition. (Section 4.1.2)

The sharp peak in thrust deduction fraction t as a function of Froudenumber is caused by the clearing of the transom stem. This is caused bythe difference in water column present at the nozzle and the projectednozzle position at the stern. The effect is quantified by t1. Thiscontribution is also noticeable in the overall efficiency. If this contributionis to be obtained explicitly from propulsion tests, average static pressuresshould be measured in the nozzle discharge and at the projected nozzlearea at the transom during the propulsion and resistance tests respectively.(Section 4.3.2)

5.2 Physical mechanisms

233


21. The gravity acceleration typically increases the net thrust with acontribution of 0(1%) for a given flow rate. Consequently, it reduces thepower requirement by the same amount. The effect is quantified by t.(Section 4.3.2)

234

Appendix i

Al Derivation of relations for idealefficiency

In the derivation of relations for the ideal efficiency î, we will consider a waterjetunit operating in a free stream condition. This condition is defined as the conditionwhere the jet system operates in an undisturbed flow with uniform velocity U0 inx-direction. The centre of the nozzle area is situated on the free surface. The intakeplane AD is situated in the horizontal x-y plane (see Fig. 2.1).

We will consider Control Volume D, defined by the points ABCFF'A as a modelof the jet system. The part CD of the intake lip, exposed to the external flow isincluded in the jet system. A possible force in x-direction, acting upon CD,contributes therefore to the net thrust production by the jet system.

The ideal efficiency is generally defined as the ratio of the work done by the jet'sthrust per unit time (effective thrust power TE) and the required hydraulic power

JSE in a potential flow:

T0U0-t10)

- JSE0

where Tg = gross thrustt1 = jet system's thrust deduction fraction

(All)

235

Appendix 1

236

U0 = free stream velocityJsE = effective jet system power (hydraulic power)

subscript O indicates free stream conditions.

This definition corresponds to the similar r definition used in propellerhydrodynamics.

It is demonstrated in Chapter 2 that the effective thrust power in free streamconditions for control volume D is identical to the thrust power for control volumeA (II'CFF'I in Fig. 2.1). The same holds for the effective jet system power JSE

The ideal efficiency can consequently be written as:

TgooUo

- D' iSEO

where Tg = gross thrust for control volume A.

It is also demonstrated in Chapter 2 that the gross thrust Tg is identical to the netthrust Tnet delivered by the jet system.

The gross thrust Tg can be found from a momentum consideration on controlvolume A:

Tgoo = pQ(u-U0) (Al.3)

where p = mass density of fluidQ = flow rate through jet systemu = mean velocity in nozzle discharge area FF'.

It is hereby assumed that the nozzle is completely effective in converting thepressure energy into kinetic energy, so that the pressure at the nozzle area equalsthe ambient pressure p0, provided the jet is discharged in air. Should this not bethe case, the mean nozzle velocity should be replaced by the mean jet velocity thatoccurs in the vena contracta. Consequently, the jet area in this vena contractashould be used instead of the nozzle area.

The effective jet system power J5E can be found from an energy considerationon control volume A:

(Al.2)

Derivation of relations for ideal efficiency

Tgoo

n

-p UA,1

Substituting eq. Al.8 into Al.3 yields:

NVR = !+!/l+2CT2 2

(Al.7)

The relation between this thrust loading coefficient CT and the nozzle velocityratio NVR is given through the momentum balance over control volume A (eq.Al.3). In addition, the conservation law of mass provides a relation between flowrate Q and nozzle velocity u:

Q = uA (A1.8)

(Al.9)

The ideal efficiency expressed in the thrust loading coefficient is now obtained bysubstituting eq. AL9 into eq. A 1.6:

237

JSE = Q±p(u,U) (Al.4)

If we define the nozzle velocity ratio as:

uNVR = _-- (Al.5)

U0

we can rewrite eq. Al.2 into its often quoted form:

nl =2 (A1.6)

The disadvantage of this form is that the NVR value needs to be computed fromthe required net thrust Tnet and the nozzle discharge area A. A direct relationbetween the ideal efficiency and these geometrical parameters is found by defininga thrust loading coefficient CTfl, according to:

Appendix i

23

4Tli =

3 +/i +2cm(A 1.10)

Appendix 2

A2 Expressions for the computationof Cm and Ce

The momentum and energy coefficients C,17 and Ce have a simple relation withthe generally used displacement, momentum and energy thicknesses in bound-ary layer theory. Provided the intake height exceeds the boundary layer thick-ness O (h>O), the following relations can be found:

02Cm for hO (A2. 1)

h-01

and

2 03c = 1-for h0 (A2.2)

(A2.3)

e

where the displacement thickness is defined as

=

o

the momentum thickness O as

239

Appendix 2

= J(l-)_dz- o

and the energy thickness E as

=

o

(A2.4)

(A2.5)

If the boundary layer velocity profile can be represented by the n-tb power law,simple expressions for c, and Ce can be found as a function of the power n,and the flow rate ratio QIQ111. The flow rate Qbl denotes the flow rate that canbe absorbed from the complete boundary layer. The flow rate ratio shows thefollowing relation with the height over which the flow is absorbed by theintake:

17

240

h for h (A2.6)

(A2.7)

Qbl

and

h n for h

The boundary layer flow rate can be obtained from

Qbl = Uw(6-1)

where

=

(A2.8)

(A2.9)n + i

The following relations for cm can be derived:

Cm for h6 (A2. 10)

?2±2 Qbl

and

and

Cm = i -__(.) for hn+2 Q

Similarly, the following relations for Ce are found:

2

2 n+l Q)fl+1C e n+3Qbl

Expressions for the computation of C1 and

flThj ?

for h

c2 = i for h

(A2.1l)

(A2.12)

(A2.13)

241

Appendix 3

A3 Outline of uncertainty analysisA3-1 Introduction

This appendix provides a summary of the uncertainty analysis, as used in thevalidation of experimental or numerical procedures throughout this work. Thecontents are based on the report of the Validation Panel of the 19th ITTC (Lin etal. [19901), to which frequent reference will be made.

The following concepts are of importance for a good understanding of uncertainty:

'Accuracy' is the qualitative expression for the closeness of a measuredvalue to the true value. The quantitative expression of accuracy should bein terms of uncertainty. Good accuracy implies small uncertainty.'Uncertainty analysis' is the means of quantifying and expressing 'howvalid' the method (measurement, calculation etc.) is in estimating therequired true value. A complete uncertainty analysis would define theprobability distribution that the error (true value - estimate produced bythe method) could take. Inevitably, it will often be necessary to deal with'partial' validation and uncertainty analysis applied to only parts of thetotal method. Such activities may be perfectly acceptable, providing thebasis and assumptions are clearly defined.'Repeatability of a measurement' is the quantitative expression of thecloseness of agreement between successive measurements of the samevalue of the same quantity carried out by the same method with the samemeasuring instrument at the same location at appropriately short intervals

243

Appendix 3

244

of time.s 'Repeatability of a measuring instrument' is the quantity which

characterizes the ability of a measuring instrument to give identicalindications or responses for repeated applications of the same value of thequantity measured under stated conditions of use.

s 'Linearity of a meter' is the deviation (within preset limits) of aflowmeter's performance from the ideal straight line relationship betweenmeter output and flow rate.

s 'Validation' refers to the total process of confirming that the estimate(model test, numerical calculation, full-scale measurement, test-rigmeasurement, data base prediction, etc.) is properly related to the truevalue of the parameter in question. Validation includes all aspects frommodelling assumptions, through measurement techniques and numericalmethods to the production of the final estimate.

s 'Verification' is to be used in a specific way to describe checking that aparticular requirement in the method is implemented correctly. Incomputational methods its use is to be confined to checking that the codecorrectly performs the solution of the chosen equation by the chosentechnique. (Lin et al. [19901).

The above definitions were adopted from the BSI Guide [19911 and Kline [19851.A review of literature in the field of uncertainty analysis is presented by Lin et al.[19901. The recommendations of the validation panel to the 19th ITTC follow thelines of the ISO/ANSI standard. Abernethy and Ringhiser [19851 give furtherbackground information relative to the development of an internationallyacceptable methodology.

A3-2 Guidelines for uncertainty analysis ofmeasurements

The objective of uncertainty analysis, is to construct an uncertainty interval for anymeasurement, within which the true value (by definition unknown) will lie witha chosen confidence (usually 95%, which is also adopted here).

A3-2.1 Types of error

'Only two types of error exist in a well-controlled activity: precision errors(random or repeatability), and bias errors (systematic or fixed). (The relation ofthese errors to the true value is illustrated in Fig. A3.1.) We need only add to thediscussion that, in general, it is presumed that major mistakes and malfunctions are

true value

biaserror (B)

tota]error

trueaverage

(JI)

measuredvalue (x)

Fig. A3. I Designation of errors

A3-2.2 Outline of methodology

The following stages are proposed by Lin et al. [19901:

- Identify all error sources.- Determine the individual precision (statistically) and bias errors (by

judgement) for each source from 1.- Determine the sensitivity of each error source (from 2) to the end

result.- Create the total precision uncertainty interval from 2 and 3.- Create the total bias uncertainty interval from 2 and 3.- Combine the tota! precision and bias uncertainty intervals from 4 and

5 respective!y

It is stressed by Lin et al. [19901 that the results of step 4, 5 and 6 should bedeclared separately.

Outline of uncertainty analysis

absent from data subject to such scrutiny. If such errors do exist, they may ofcourse contribute grossly to the two types of error and may well render theexercise meaningless. Monitoring of data and engineering judgement may benecessary to eliminate such errors, but this must be done by rational and not justcareless discarding of 'rogue' or 'outlying' data points. Care is needed under thesecond type if it is known that the limits of bias error are not symmetric.' (Lin etal. [19901).

measurementpopulation

precisionerror

245

I Appendix 3

A3-2.3 Calculation methods

A3-2.3.1 Elemental precision estimates (step 2)

'The object is to determine the precision index S of a particular elemental errorsource. S is an estimate of the standard deviation of the scatter that would beobtained if the measurement x were repeated a number of times. If an end resultis influenced by k elemental measurements, x.(i_-1,k), then at this point, theobject is to estimate the value S, that accompanies x Combining the k errorsources follows later. If the basic measurement can be repeated N times, thenan estimate of the true' standard deviation (only obtainable from an infinite setof measurements) is available, usually called the 'experimental' standard devi-ation:

246

si =(x-i

j=1 (N-l)(A3.l)

where i, = average value of the N measurements.

The larger the value of N, the more accurate S. will be.' (Lin et al. [19901.

The precision index S. of the average value ï of a set of measurements isalways less than that of an individual measurement, according to:

ss- = _±.xiv

A3-2.3.2 Elemental bias estimates (step 2)

The basic independent measurements x discussed in the previous section, mayhave a bias error in addition to the precision errors. Unfortunately, this errortype is not amenable to statistical analysis. Remember that all known offsetsand corrections that can be applied are assumed to have been implemented, soonly residual unknown bias errors remain. Examples might include: the accu-racy to which calibration coefficients can be calculated and applied; the preci-sion with which zero settings can be made; perhaps the knowledge that a meanmeasurement (say force or pressure) may be biased by the intensity of fluctu-

(A3.2)

ation (but having no direct measurement of the intensity); and, straying into acomputational area, perhaps the knowledge that a particular integration or grid-based calculation tends to consistently underestimate or overestimate the 'true'value.

The limits to this bias error should be estimated with a 'confidence' level that isequivalent to 95 percent. (Note - the literature stresses that a normal humanfailing is to underestimate the size of these errors).' (Lin et al. [19901).

A3-2.3.3 Propagation of errors (step 3)

The parameters x that can be regarded as error sources, were already intro-duced in Section A3-2.3.1. The final result R of a test or prediction can bewritten as a function of the k independent variables x:

R = R(xl,x2,...xk) (A3.3)

For a small deviation Axt, a Taylor expansion about the point x can be writtenas:

R(x+Ax) = R(x)+Ax2

2R 3)

x1 7? - 2-. dx

The error in the result can therefore be approximated for small deviations of Ax.by:

R(x+Ax)-R(x) (A3.5)

Analogous to this result for one value of the parameter x, a similar result canbe derived for the precision error of the result:


(A3.4)

247

k

result = (O1S)2 (A3.6)

i- J

where O = sensitivity

Appendix 3

Similarly, we can write for the bias errors:

248

¡ öxj

A similar result is found when eq. A3.7 is non-dimensionalized.

The usefulness of the non-dimensional sensitivity 0 is illustrated with thefollowing example. Consider two transducers, giving a linear relation throughthe origin between the result R and the signal x

R = (A3.1O)

The coefficient a1 of transducer i is smaller than a2 of transducer 2. Thedimensional sensitivity O of x for both transducers reads:

O = a (A3.11)

where

and

s =

S'it =

non-dimensional precision

o =L

(A3.8)

error; Sj/i,

(A3.9)

k

Bresuit = (OB (A3 .7)

N i=1

If unsymmetric bias limits occur, upper and lower values for Bresult will have tobe calculated.

Instead of using the dimensional sensitivity as introduced above, it is oftenmore convenient to use a non-dimensional sensitivity 0, relating the non-dimensional error in the result to the non-dimensional deviation in the sourceparameter x. Non-dimesionalizing eq. A3.6, we find:

Transducer 2 consequently shows the greater sensitivity for deviations in x, thusincreasing the error in R. When we consider the non-dimensional sensitivity e;however, we find this to equal unity. This implies that both transducers showthe same percentage deviation in the result for equal deviation in x, despite thedifferences in dimensional sensitivity 01. The non-dimensional sensitivity e; willbe referred to as relative sensitivity in the following. Calculation of the sensitiv-ity can either be done analytically or numerically.

It is emphasized that only factors with uncorrelated errors can be introduced inequations A3.6 and A3.8.

A3-2.3.4 Total uncertainty interval for precision and bias errors (steps5 and 6)

'The random uncertainty interval is now given by:

t±95


(A3.12)

where M is the number of times the test is repeated and t95 is the Student's tdistribution associated with 95% probability. If Sreuit is based on reliable S.values (large degree of freedom v, where v=N-1), then t95 can be approxi-mated by 2. If relatively few samples (<30) contributed to the individual S.estimates, t95 may be larger than 2 as a result of the limited degree of freedomfor each estimate. But as t95 is an overall value, requiring an 'average' degreeof freedom to be attached to the final result, it needs to be weighted by themagnitude of the S values and their individual degrees of freedom v. This isdone by the Welch-Satterthwaite approximation:

4SR

V result =(0S)'4

in V1

(A3.13)

The bias uncertainty interval is such that the true value of the result Rtrue lieswithin

R±BR (A3.14)

249

Appendix 3

250

or, if unsymmetric bias errors are identified:'

R BR<Rtrue<R+BR (A3.15)

(Lin et aL [1990]).

A3-2.3.5 Total uncertainty (step 6)

'If a single number U is needed to express a reasonable limit of error for a givenparameter, then some model for combining the bias and precision errors must beadopted, where the interval

x±U (A3. 16)

represents a band within which the true value of the parameter is expected to liefor a specified coverage.

While no rigorous confidence level can be associated with the uncertainty U,coverages analogous to 95 percent and 99 percent confidence levels can be givenfor two recommended uncertainty models respectively:

UR RSS= /B+(tSR)2 @ 95%

(A3.17)

orUR ADD = BR+rSR @ 99% (A3.18)

Note that upper and lower limits should be constructed using B and Bj if theseare different.'

A3-3 List of symbols

B - bias error of parameter xM - number of repeat testsN - number of measurements of parameter xR - result of a test or calculationS. - precision error (or index) or 'experimental' standard deviation of

parameter x


s non-dimensional precision error (or index) or experimental stan-dard deviation of parameter x

U - uncertainty limit pertinent to a chosen uncertainty level (mostly 95or 99%)

- average value of parameter x-x, - j-th value of parameter x-O sensitivity for error in result due to error in x

non-dimensional or relative sensitivity

251

252


Appendix 4

A4 Description of facilities and modelsused for experiments

253

Appendix 4

A4-1 Deep Water Towing Tank

251

INSTRUMENTATION

MODEL SIZE RANGE

E

DIMENSIONS 250 mx 10.5 m, 5.5 m deep.CARRIAGE Manned, motor driven, four drive wheels, four pairs of horizontal

guide wheels.

TYPE OF DRIVE SYSTEM ANDTOTAL POWER Thyrister controlled power Supply. 4x 46kW.

MAXIMUM CARRIAGE SPEED Bm/o.OTHER CAPABILITIES VerricaI/horzontal PMM. wind-force dynarnorrreter set-up.

BasinTowing carriageDrive wheelsHarbourPassage to workshop

105m

Dynamometers with strain gauge transducers in propeller hub.wind-force dynamometer, 6-component force balance dynamometer,5-hole pitot tube, laser doppler velocity scanner, underwater photographicand video tape Systems, pressure transducer for wave cut experiments.1.5- 10m.

Description of facilities and models used for experiments

A4-2 HAMILTON Jet Test Boat

The following table presents the main particulars of the full scale test boat at theparent condition LCG:

Fig. A4. I presents the hull's body plan and stem and stern contours. The jet modelconfiguration as built in the hull model is presented in Fig. A4.2. The asp positionas used in the first propulsion test (Test No. 48820) is presented in Fig. A4.3.Finally, the block marker distribution used for a precise determination of thewetted surface at speed is presented in Fig. A4.4.

A plywood model has been manufactured according to a scale factor of 3.00. Themodel was designated model No. 7386.

255

Description Symbol Magnitude Unit

Length between perpendiculars (Fr-i - 8) 7.27 mLength on waterline LWL 6.27 mHull beam at draught moulded at midship B 2.226 mDraught moulded on FP TF 0.386 niDraught moulded on AP TA 0.424 mDisplacement volume moulded y 2.798 m3Displacement mass in sea water 2.868 t

Wetted surface area bare hull at rest S 13.264 m2LCB position aft of frame 8 LCB 4.58 mSlenderness ratio L1v"3 5.16 -Length-beam ratio LJIB 3.27 -Beam-draught ratio B/TM 5.50 -

Appendix 4

256

ofship

FR. -1= AP FR. 8 = FP

Fig. A4. i Body plan, stem and stern profiles and sectional area curve of model

A B fr. O C fr .1

A B fr.O

Fig. A4.2 Waterjet intake opening i for modelDimensions are given in mm for ship

qN

&

Description of facilities and models used for experiments

Fig. A4.3 Position of ASP for ship model No. 7386Dimensions are given in mm for ship

rarw-

7

Fig. A4.4 Block marker distribution of ship model No. 7386

257

Appendix 5

AS Description of potential flow panelcodes 'HESM' and 'DAWSON'

A5-1 Introduction

The MARIN computer codes 'HESM' and 'DAWSON' solve the potential flowproblem for an arbitrary 3D body. HESM solves the potential flow equations fora fluid without free surface. DAWSON can be regarded as an extension of theformer code, including free surface conditions. The methods are based on work byHess and Smith [1964] and Dawson [1977] respectively.

A5-2 HESM

Mathematical statement of problem

The first problem considered is that of a steady flow of an unbounded perfect fluid

about a 3D body. The state parameters describing the flow (V and p for anincompressible potential flow) can be obtained once the potential function cI in the

fluid domain R' is known. The fluid velocity vector V at any point can then beexpressed as:

(A5.l)

259

Appendix 5

The unknown potential function ct must satisfy three conditions in an unboundedflow. It must satisfy Laplace's equation in the external fluid domain R' (outside thebody), it must have a zero normal derivative on the body surface S, and it mustapproach the uniform stream potential at infinity. Symbolically:

A0 mR' (A5.2)

=0 onS (A5.3)

- (A5.4)

The above equations are conveniently solved when the total potential function cIis written as the sum of the free stream potential p and the perturbation potentialdue to the body :

= (p00+(p (A5.5)

In order to solve the perturbation potential (p, it will be represented as the potentialof a source density distribution over the surface S. The potential at a point P inspace with coordinates x,y,z due to a unit point source located at a point q on thesurface S is 1/r(P,q), where r(P,q) is the distance between the points P and q.Accordingly, the perturbation potential at P due to the complete source distributionover the body S is:

260

(p(x,y,z) =(q) dS

r(P,q)(A5.6)

It can be demonstrated that the above equation satisfies the conditions given by eq.(A5.2) and (A5.4) for any source distribution. The source distribution (q) isconsequently determined from the normal derivative boundary condition eq.(AS .3).An expression for the normal derivative of the potential function is found from thelimit where the point P in the fluid approaches the point p on the surface. Carefulevaluation of this limit is required because the integrand in the right-hand sideterm becomes singular if the surface is approached. The limit of the normalderivative is found to consist of two terms:

Description of potential flow panel codes HESMand DAWSON

=I )(q)dS

òn r(p,q)

The first term on the right-hand side is the contribution to the normal derivativeof the portion of S in the immediate neighbourhood of p, the second term is thecontribution of the remainder of S. Substituting the above equation in eq. (3),yields an integral equation for that needs to be solved:

Numerical method of solution

The basic problem in the method is the numerical solution of eq. A5.8. Thisrequires an approximate evaluation of the relevant integral and an approximaterepresentation of the body surface. Of several solutions possible Hess and Smith[1964] choose a method that consists of an approximation of the body surface bya large number of plane quadrilateral elements. The source density over eachelement is assumed constant. Eq. A5.8 can now be replaced by a set of linearalgebraic equations from which the value of each source element is to be solved.

On each element one point is selected where the fluid velocity normal to theelement is required to vanish and where tangential velocity and pressure areeventually evaluated. This point is taken as the point where the element itself hasno effect on the tangential velocity, i.e. the point where the element gives rise tono velocity in its own plane. This point is designated the 'null point' of theelement.

Once the values of the source density on the quadrilateral elements have beenobtained, the fluid velocities at points away from the body surface may also becalculated. The velocities at points on the body surface other than the null pointscannot be calculated directly, but must be obtained by interpolation of thevelocities at the null points. A similar strategy is required for points just off thebody surface. This restriction is imposed by the form of the approximation of thebody surface. For example, direct calculation by summing the contributions of thequadrilateral elements gives an infinite velocity at a point on an edge of one of theelements.

2TccY(p)-( )(q)dS = -(p).Vr(p,q)

(A5.7)

(A5.8)

261

Appendix 5

Algebraic equations can also be derived for the velocity induced by a quadrilateralsource element in an arbitrary point in the fluid domain. Because of the complexcharacter of these equations, Hess and Smith approximate the induced velocitieswith a multipole expansion through the second order if the point P is sufficientlyfar from the relevant source element. Such an expansion is known to converge ifthe point P is farther from the centroid of the source element than any point of thequadrilateral is. The designation 'multipole expansion' arises from the fact that thevarious terms in this expansion may be interpreted as the potentials of pointsingularities of various orders, located at the elements centroid.

By applying the above approximation only for points that are farther from thesurface than a given criterion, Hess and Smith demonstrate that the additional lossof accuracy is negligible compared to the basic approximation of the body surfaceby plane quadrilateral elements with constant values of source density.

A5-3 DAWSON and RAPID

If the fluid is bounded by a free surface, a wave pattern on this surface occurswhen the body under consideration translates through or in the vicinity of thissurface. This problem gives rise to additional 'free surface conditions' (FSC's),that need to be fulfilled apart from the conditions for an unbounded potential flow(see Section A5-2).

On the free surface, a kinematic boundary condition is to be satisfied, requiringthat the flow is tangential to the wave surface:

= O on free suiface y=T (A5.9)

The dynamic boundary condition ensures that the pressure in the flow at the freesurface equals the atmospheric pressure:

= O (A5.lO)

The most important difference between the DAWSON and RAPID code is the wayin which the free surface conditions are modelled. In linearized methods, such asapplied in DAWSON, the boundary conditions are applied at the undisturbed freesurface. In the non-linear method applied in RAPID, the boundary conditions aresatisfied on the actual free surface. Additionally, the boundary conditions on thehull form are satisfied also above the undisturbed free surface.

262

Appendix 6

A6 Description of performanceprediction code 'PLANE'

A6-1 Introduction

The MARIN computer code 'PLANE' determines the equilibrium position of thehull and corresponding drag, lift and thrust forces for a prismatic planing hullform. The method is based on the work by Savitsky [1964].

A6-2 Statement of problem

To determine the required power or thrust of a prismatic planing hull form for agiven speed, the equations of motion in three degrees of freedom are solved, sothat equilibrium is attained in vertical, horizontal and pitch motion. The relevantforces and their points of application are identified in Fig. A6. 1.

From a systematic series of tests on various prismatic hull forms, Savitsky hasderived empirical relations for lift, drag, wetted area, centre of pressure andporpoising stability limits as a function of speed, trim angle, deadrise angle andloading.

With these empirical relations, the three equations of motion can be solved,rendering the hull's trim angle. Once the trim angle is known, the total drag andthe hull's sinkage can be determined.

263

Appendix 6

264

mn

CoB = Centre of BuoyancyCoF = Centre of FlotationCoG = Centre of Gravity

FT = Towing forceR1 = Total dragA = Displacement weight

V = Displacement volume

Fig. A6.1 Force acting on the hull-jet system as modelled in the computerprogram PLANE

A6-3 Limitations

It is to be emphasized that the empirical planing equations are only for hull formshaving a constant deadrise, constant beam and constant trim angle over the entirewetted planing area. Most practical planing hull designs do have some longitudinalvariation in these dimensions. According to Savitsky, deadrise angle and beamshould in these cases be taken as the average in the stagnation line area of the hull.The trim angle should be taken as the average of the keel and chine buttock lines.It should also be noted that the empirical relations are not applicable to the lowerspeed range, where the forward pulled-up bow sections of the hull become wetted.In this situation, strong variations in deadrise and buttock lines with length occur.

To extend the prediction model to the lower speed range (below FnL 0.9), anempirical correction proposed by Blount and Fox has been added to the program(Blount [1976]). This so-called M-factor is a simple correction factor to force theresistance curve at the experimental curve in the hump speed region (FnL 0.5-0.9).

Appendix 7

A7 Description of LDV experiments inthe MARIN large cavitation tunnel

The objective of the LDV experiments on a waterjet intake was to obtain a betterknowledge about the free stream characteristics of an intake, and to obtainvalidation material for CFD computations on an intake. To this end, arepresentative intake geometry was mounted to the sidewall of the tunnel. TheLDV measurements were conducted for two operational conditions. One beingrepresentative for design conditions (IVR1=OE6), the other being representative foroff-design conditions, such as occur in the hump speed region (IVR=O.9).

Description of model

A geometric description of the intake model is given in Fig. A7.l. The flush intakeis characterized by sharp edged and parallel side walls in the bottom plane.Furthermore relatively small radii of curvature are used for the intake lip and thetransition from bottom plane into intake ramp.

Description of test set-up

The intake was mounted on the sidewall of the MARIN large cavitation tunnel. Awaterjet pump was fitted to the intake, followed by a retour conduit, leading theingested flow back into the tunnel. A calibrated asp was used to measure the flowrate through the retour conduit.

265

Appendix 7

Fig. A7.2 shows a sketch of the LDV head, mounted on top of the tunnel. Thelaser beams were transmitted under a fixed angle of approx. 30 deg. Variationsin transverse position of the measuring volume were obtained through verticaltranslations of the laser head. The measuring volume that could be covered inthis way is indicated in the figure.

Prior to the tests, the boundary layer velocity profile was measured at threelongitudinal positions ahead of the intake Leading Edge LE (see Fig. A7.3). Atthe two foremost positions, measurements were done in three transverse sta-tions. The boundary layer profile measurements were done both with and with-out turbulence stimulation strip (Fig. A7.4). This strip had a width of 3 timesthe geometrical intake width, and was situated 1.5 times the intake length aheadof the intake Leading Edge. Based on these measurements, it was decided to dothe actual LDV tests with the turbulence stimulation strip mounted. The result-ing velocity profile at 70% of the intake length ahead of the intake LE is pres-ented in Fig. A7.5 for three transverse positions. It appears that the boundarylayer at the centreline of the intake is consequently thicker than at the other twolocations. This phenomenon is ascribed to the wake of one of the guiding vanesof the tunnel, upstream of the intake.

Review of tests

The velocity distribution has been measured in a number of 2D planes, indi-cated in Fig. A7. 1. The velocity distribution has been measured for two oper-ational conditions of the intake, viz. IVR0.62 and 0.94. The first condition isrepresentative for design speeds, the second for conditions where the propulsoris more heavily loaded, such as for instance occurs around hump speeds(FnL=O.S). Apart from these LDV measurements, the pressures in the initial partof the intake were measured at the centreline intake. The positions of the pres-sure transducers are also indicated in Fig. A7.1.

266

Description of LDV experiments in the MARIN large cavitation tunnel

I// S

_44 III-all/li-llviIIIIlI1uir-tiiiiiJ1VIlT4'iraiI

L

/ÏIIt m'iiLU

>

>

>

uoE

EE=

ooouE

-o

o

>

*

Fig. A7. I Intake geometry analysed by HESM computations and LDV measurements

267

Appendix 7

268

A = 150.0B = 94.0

window 300

Fig. A7.2 Limitations in the measuring volumeDimensions are given in rum

optical head

z

yJ

176.0

,'1aser beams

Description of LDV experiments in the MARIN large cavitation tunnel

518mm

GL...Bj

Fig. A7.3 Designation of strips for boundary layer measurements

LE. intake

40 mm

Fig. A7.4 Position and geometry of turbulence stimulation strips

UJ-

reference point

30mm

269

EGL...A_1 GL..B_1

QGL. B 2

GL...A_2

GE. .B 3Q

-GL...A_3

l (A'Dfig.2.1) = 339 mm

Appendix 7

270

1.0

0.9

0.8

0.7

1.0

0.9

0.8

0.7

0 20 40 60 80 100

z [mm]

Strip GL3AG-3

/

0.8I

0.70 20 40 60 80 100

z [mm]

bi. parameters

n=9Cvp = 1.02

Strip GL3AG-1 Strip GL3AG-2

0 20 40 60 80 100

z [mm]

Fig. A7.5 Boundary layer velocity profilesUo = 3 m/s, stimulated turbulenceposition X = -667.5 mro

1.0

0.9

References

References of Chapter 1

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274

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275

References

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BOWEN, G.L.; "The net thrust relationship for waterjet-propelled craft", HoveringCraft Hydrofoil 10, Jan. 1971, pp.14-15.

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276

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ITTC 1987; Report of the High Speed Marine Vehicle Committee, 18th Interna-tional Towing Tank Conference 1987, pp. 304-313.

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MOSS MAN, E.A. and RANDALL, L.M.; "An experimental investigation of thedesign variables for NACA RM No. A7130", Jan. 1948.

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TERWISGA, T. VAN; "A theoretical model for the powering characteristics ofwaterjet-hull systems", FAST'93 Conference, Yokohama, Dec. 1993.

WEINBLUM, G.P.; "The thrust deduction", American Society of Naval Engin-eers, Vol. 63, 1951.

WILSON, M.B.: "A survey of propulsion-vehicle interactions on high-pe,form-ance marine craft", Proceedings of 18th ATTC, Aug. 23-25, 1977.


ABERNETHY, RB.. BENEDICT, R.P. and DOWDELL, R.B. "ASMEmeasurement uncertainty", Journal of Fluids Engineering, Vol. 107, June 1985.

ALEXANDER, K.V., COOP, H. and TERWISGA, T. VAN; "Waterjet-hullinteraction: Recent experimental results", SNAME Annual Meeting, NewOrleans, Nov. 1994.

B ARFORD, N.C.; "Experimental measurements: Precision, error and truth ",2nd edition, John Wiley and Sons, 1987.

Chapter 2/3

277

References

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BSI Guide BS7405: "Guide to selection and application of jlowmeters for themeasurement of fluid flow in closed conduits", 1991.

DYNE, G. and LINDELL, P.; "Waterjet testing in the SSPA towing tank",International Symposium on Waterjet Propulsion, Royal Institution of NavalArchitects, London, Dec. 1994.

ENGLISH, J.W.; "Ship model propulsion experiments analysis and randomuncertainly", preprint published for written discussion, The Institute of MarineEngineers, Jan. 1995.

FURNESS, R. A.; "Modern flowmeter applications ", KIVI/NIRIA studiedag'Flowmeting nu en morgen', Amsterdam, Oct. 31, 1990.

HOERNER, S.F.; "Fluid dynamic drag", published by the author, 1965.

ITTC 1978; Report of the Peiforinance Committee, 15th International Towing TankConference, The Hague, The Netherlands.

ITTC 1987; Report of the High Speed Marine Vehicle Committee, 18thInternational Towing Tank Conference 1987, pp. 304-313.

ITTC 1993; Report of the High Speed Marine Vehicles Committee, 20thInternational Towing Tank Conference, San Francisco, 1993.

LIN, W.C. et al.; "Report of the panel on validation procedures", 19th ITTC,Madrid, Sept. 1990.

WILLEMSEN, H. and TERWISGA, T. VAN; "liking van de Thomson goot alsinstrument voor het meten van debieten", MARIN Report No. 52227-1-SRD, Dec.1992 (proprietary, in Dutch).

278


ALEXANDER, K.V., COOP, H. and TERWISGA, T. VAN; "Waterjet-hullinteraction: Recent experimental results", SNAME Annual Meeting, New Orleans,Nov. 1994.

ALTMETER, iM.; "Resistance prediction of planing hulls: State of the art",Marine Technology, Vol. 30, No. 4, Oct. 1993.

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ETTER, R.J., KRISHNAMOORTHY, V. and SCHERER, JO.; "Model testing ofwaterjet propelled craft", Proceedings of the 19th ATTC, 1980.

HESS, J.L. and SMITH, A.M.O.; "Calculation of potential flow about arbitrarybodies", Progress in Aeronautical Sciences, Vol. 8, Pergamon Press, 1966.

HEWINS, E.F. and REILLY, J.R.; "Condenser scoop design", TransactionsSNAME, 1940, pp. 277-304.

HOSHINO, T. and BABA, E.; "Self propulsion test of a se,ni-displacement craftmodel with a waterjet propulsor", Journal of the Society of Naval Architects ofJapan, Vol. 155, June 1984.

ITTC 1987; Report of the High Speed Marine Vehicle Committee, 18thInternational Towing Tank Conference 1987.

KASHIWADANI, T.; "The study on the configuration of waterjet inlet (istReport)", Journal of the Society of Naval Architects of Japan, Vol. 157, 1985.

KASHIWADANI, T.; "The study on the configuration of waterjet inlet (2ndReport)", Journal of the Society of Naval Architects of Japan, Vol. 159, 1986.

KIM, K.S., HONG, S.Y. and CHOI, H.S.; "Analysis of the wate rjet-propelled ship.tlow by a higher order boundary element method", NAV'94 InternationalConference on Ship and Marine Research, Rome, Oct. 1994.

LATORRE. R. and KAWAMURA, T.; "CFD investigation of trim influence onwaterjet pressure distribution and cavitation ", International Symposium onCavitation CAV95, Deauville, May 1995.

Chapter 4

279

References

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References of Appendix 3

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BOS, M.G. et al.; "Discharge measurement structures", 3rd revised edition, ILRIpublication 20, Wageningen 1989.

LIN, W.C. et al.; "Report of the panel on validation procedures", 19th ITTC,Madrid, Sept. 1990.

KLINE, S.J.; "The purposes of uncertainty analysis", Journal of FluidsEngineering, Vol. 107, pp. 153-160, 1985.

280


HESS J.L. and SMITH, A.M.O.; "Calculation of nonlifting potential flow aboutarbitrary three-dimensional bodies", Journal of Ship Research, Sept. 1964.

RAVEN, H.C.; "Adequacy of free suiface conditions for the wave resistanceproblem", 18th Symposium on Naval Hydrodynamics, Washington, 1991.

RAVEN, H.C.; "Nonlinear ship wave calculations using the RAPID method",6th International Conference on Numerical Ship Hydrodynamics', Iowa City,August 1993.

DAWSON, C.W.; A practical computer method for solving ship-wave prob-lems". Second International Conference on Ship Hydrodynamics, Berkeley,1977.


BLOUNT, D.L.; "Small-craft power prediction", Marine Technology, Vol. 13,No. 1, Jan. 1976.

SAVITSKY, D.; "Hydrodvnamic design of planing hulls ", Marine Technology,Oct. 1964.

Appendix 5/6

281

282


Nomenclature

A control surface

A intake area (default: area lin Fig. 2.1)

A1 intake throat area (area 5 in Fig. 2.1)

A,1 nozzle area (area 8 in Fig. 2.1)

Ap propeller disk area

AT1 transom area below undisturbed free surface

A3 projected intake area in bottom plane (Fig. 2.1)

B. bias error of parameter x (Appendix 3)

b non-dimensional bias error of parameter x (Appendix 3)

CDj intake drag coefficient; CDj=D/(p QU0)

CF mean frictional drag coefficient

CL lift coefficient; CL=II(p QU0)

pressure coefficient; C13 = I

CPh hull induced pressure coefficient

CQ flow rate coefficient; CQ=Q/(U0w)

GRey residual drag coefficient; GR=RR/(½p U)

CT total drag coefficient; CT=Rl/('½pUS)

283

Nomenclature

CTfl thrust loading coefficient; CTfl=T/(½PUAfl)

CT propeller thrust loading coefficient; CTp=Tpropelle/(½PUAp)

CTr transom drag coefficient; CTr=RT/(½PUS)

C wavemaking drag coefficient; Cw=Rv/('/2pUS)

ce energy velocity coefficient due to boundary layer velocity distribu-

tion (Appendix 2)

Cm momentum velocity coefficient due to boundary layer velocity dis-

tribution (Appendix 2)

Cmn momentum velocity coefficient in nozzle discharge area

potential flow velocity coefficient; cV/)= U/U0

Cweir calibrated weir coefficient

D diameter or impeller diameter

D. intake drag

D nozzle diameter

Dp differential pressure

dz change in rise of hull due to waterjet action

dz change in trim angle of hull due to waterjet action

e total energy per unit mass

e1 internal energy per unit mass

ekfl kinetic energy per unit mass; ekfl=½u2

e0 potential energy per unit mass; e0=W

F force

FD residual pulling force on model to compensate for scale effect in hull

resistance during propulsion test

F pressure force

FXbp pulling force experienced by hull-jet system in bollard pull condition

(acting in x-direction)

FT towing force applied to model during propulsion or resistance test

284

Nomenclature

Fxmeas measured pulling force acting in x-direction

Fxpiate measured force on 'stern' plate acting in x-direction

Fznet net force in z-direction acting on hull-jet system

FnL Froude number based on waterline length

f effective width factor intake; f=w/w

g gravity acceleration component in i-direction

waterjet system head

H pump head

Ii height over which the flow is ingested

h1 geometric height of intake throat cross section

Ii, maximum height of imaginary intake area

IVR Intake Velocity Ratio at some intake; default IVR=i71/U0 (see Fig.

2.1)

JVR1 Intake Velocity Ratio in intake throat (area 5 in Fig. 2.1)

KH head coefficient; KH=H/(pn2D2)

KM impeller torque coefficient; KM=M/(pn2D5)

KQ flow rate coeffient; KQ=Q/(nD3)

L lift

geometric intake length (AD in Fig. 2.1)

M impeller torque

NVR Nozzle Velocity Ratio; NVR=u/U0

n impeller rotation rate

n value of power law describing boundary layer velocity profile

n unit normal vector component in i-direction

delivered power to pump impeller

effective power; PE=RBHVS

P, power input

285

Nomenclature

286

JsE effective jet system power; PJSE=QHJS

loss power loss

soute effective power output

PE effective pump power; PPE=QHP

thrust power; P7_TgUo

TE effective thrust power; TE TnetV

p pressure (time averaged)

Q flow rate

Qbl maximum flow rate that can be obtained from the boundary layer

q rate of external energy exchange per unit mass

q source point

RAPP appendage drag

RBH bare hull resistance

RE effective or actual hull resistance

R pressure drag

RRES residual drag

RT total drag

RTR transom drag

Rw wavemaking drag

Rn Reynolds number of intake; Rn=UoJVRVA/v

r resistance increment fraction; RBH(]+r)=T,let

S total wetted surface of the hull (excluding transom area)

S. precision error of parameter x (Appendix 3)

S11 rate of strain tensor (time averaged)

s girth coordinate

s non-dimensional precision error of parameter x- (Appendix 3)

s,, distance from nozzle discharge to 'stern' plate

TgT gross thrust

Nomenclature

Tgoo gross thrust for a control volume with the imaginary intake area

infinitely far upstream, corrected for viscous losses (eq. (2.78))

Tjetx thrust from nozzle in x-direction; Tjetx_,n,.

Tm net thrust in self propulsion point model

Tnet net thrust, passed through to the hull

net thrust in self propulsion point ship

tbp bollard pull thrust deduction fraction; Tietx(Jtbp)'xmeas

t total thrust deduction fraction; Tg(lt)=RßH

jet system thrust deduction fraction; Tg(ltj)=Tnet

t» jet thrust deduction accounting for force on protruding streamtube

ABCD (Fig. 2.1)

tj2 jet thrust deduction accounting for force acting on nozzle area A8

(Fig. 2.1)

tj3 jet thrust deduction accounting for gravity force

tr resistance increment fraction; Tflet(ltr)=RßH

U local potential flow velocity in x-direction

UR RSS uncertainty limit for 95% confidence level in result R (Appendix 3)

U0 free stream velocity in x-direction or hull speed

u magnitude of velocity

u1,u2,u3 mean velocity components in x,y,z direction

mean energy velocity in i-direction

mean momentum velocity in i-direction

mean volumetric nozzle velocity

V control volume

V, ship model speed

V ship speed

w volumetric wake fraction

287

Nomenclature

We effective width of imaginary intake AB (Fig. 2.1)

w geometric intake width

w width bottom plating or wake survey plane

WT Taylor wake fraction used in propeller hydrodynamics

x,y,z Cartesian hull-fixed coordinates

x1,x2,x3 Cartesian hull-fixed coordinates (identical to x,y,z)

z, sinkage of the nozzle centre relative to free stream conditions

A displacement weight of hull or hull-jet system

AR change in hull resistance due to waterjet action; RE=RBH+AR

6 boundary layer thickness

Kronecker delta

deviation in computed sinkage relative to experimental value

deviation in computed trim angle relative to experimental value

boundary layer displacement thickness

62 boundary layer momentum thickness

63 boundary layer energy thickness

flduct ducting efficiency; lduct= JSF/PE

leí energy interaction efficiency; JSEYJSE

ideal jet system efficiency; 11/=Tgo(]tjo)U/PJsEo

flINT interaction efficiency; rIJNTr/((I + r)flmj)

RiET jet efficiency; 1JETTg'(/PJSE

jet system efficiency; lJs=JsFY'D

TlmI momentum interaction efficiency; n ,

first order momentum interaction efficiency; fl,7j=Tgc/Tg

second order momentum interaction efficiency;

loA overall efficiency; loA =F/D

pump efficiency; 11 PP PP/PD

288

free stream efficiency; flo=flpfldt1]Jweir V-notch angle

nozzle centreline inclination to x-ordinate

B. sensitivity of result R for an error in dependent parameter x (Appen-

dix 3)

non-dimensional sensitivity or relative sensitivity (Appendix 3)

p dynamic viscosity of fluid

p hull speed! nozzle velocity ratio; p=U-/u

V kinematic viscosity

E.r1. Ç Cartesian material bound coordinates

p specific mass of fluid

standard deviation

total mean stress tensor;

t hull trim angle

total shear stress tensor;

viscous stress;

Reynolds stress tensor

eki kinetic energy flux through area i

momentum flux through area i in j-direction

total velocity potential

disturbance velocity potential

potential force field

w stream function

Wiliss rate of change of internal energy through dissipation

Nomenclature

289

Nomenclature

subscripts:

sequence of subscripts with flow state parameters: e.g. Uabcd

where

a denotes type of flux; volumetric (-), momentum (m) or energy (e)

b denotes area to which it refers

C. component (e.g. x,y or z)

d conditions (e.g. O for free stream)

bp bollard pull condition

i intake

i,j,k tensor indices denoting the ordinate

m model

n nozzle

s full scale (ship)

t intake throat (area 5 in Fig. 2.1)

x,y,z vector indices denoting the ordinate, hull-fixed coordinate system

x',y',z' vector indices denoting the ordinate, space-fixed coordinate system

vector indices denoting the ordinate, material-bound coordinate sys-

tem

O free stream conditions

290

Summary

The main objective of this work is to develop and validate tools for the analysisof interaction effects in the powering characteristics of jet propelled vessels.

Despite our knowledge about the hull and the waterjet in isolated conditions, a lackin knowledge with regard to the interference between hull system and jet systemseems to exist. Many discrepancies between computed and actually measuredpower-speed relation of the prototype vessel are ascribed to interaction. Littleknowledge is available on the mechanisms and the magnitude of these effectshowever.

Misunderstandings in the field of jet propulsion are believed to often originatefrom a lack of clear definitions of concepts. It is demonstrated in Chapter 1 thata great deal of confusion can be found in the existing literature on definition anddescription of jet-hull interaction. Hence, this work starts with a theoretical modeldescribing the complete waterjet-hull interaction. The effect of interaction on thehull is expressed in a hull resistance increment. The effect of interaction on the jetperformance is expressed in a thrust deduction and so-called momentum andenergy interaction efficiencies. The latter efficiencies account for the change iningested momentum and energy flux due to the presence of the hull.

Although a rough procedure for model propulsion tests was provided by the ITTCin 1987, this procedure was found to easily lead to large systematic errors,rendering the results of the tests doubtful. In addition, the data reduction procedurewas based on an incomplete theoretical model. An improved experimentalprocedure based on thrust calibration through bollard pull tests is developed,together with a data reduction procedure that allows for quantification of theinteraction parameters.

291

Summary

Detailed computations and LDV measurements were made on the flow in theintake and aftbody region. They give insight into the validity of assumptions madein the experimental data reduction procedure. They show that a rectangular crosssection of the imaginary streamtube upstream of the intake with an effective widthof 1.3 times the geometric width, provides an adequate representation of theingested flow. They also indicate that the jet system's thrust deduction fraction isnot negligible in the speed range where the transom clears.

Computations were conducted with a potential flow code and a Savitsky method,aimed at a direct computation of interaction. These computations did not show asatisfactory agreement with the experimental results. An empirical predictionmodel based on test results is recommended for preliminary power-speedcomputations.

The present work provides a consistent set of definitions for a complete descriptionof both the powering characteristics of the isolated hull system and jet system, andtheir interaction. An experimental procedure with a lower uncertainty level thanhitherto published in the open literature is proposed for their quantification. Theresults of this work are hoped to contribute to a wider acceptation of the waterjetsystem and to smoother contractual negotiations, as the final performance of thehull-jet system is better predictable.

292

Acknowledgement

The more comprehensive our knowledge gets, the more teamwork is required toadvance this knowledge. The present work could only be achieved through thecontributions of numerous people. Contributions which are gratefully ac-knowledged.

I would like to thank my promotor Prof. Gert Kuiper, who has enthusiasticallysupported this work from the beginning. Furthermore, I am indebted to theMARIN Management Team for their permission to undertake this work and topublish the results in the form of a thesis.

Other people as well have made decisive contributions. Jouke van der Baan'senthusiasm for the subject has played a key role in the early hours of this study.Do Ligtelijn and Ubald Nienhuis have contributed greatly by allowing me the timerequired, despite the work load for our department they often had to negotiate.This appreciation is extended to my colleagues, whose work load will have beenincreased from time to time because of this work. Harry Willemsen isacknowledged for his contribution in tediously analysing the heaps of experimentaldata.

Special mention is due to the contributions of various people at Hamilton Jets ofNew Zealand. The numerous discussions with them have greatly contributed to myunderstanding of the jet-hull interaction mechanism. I am furthermore indebted totheir permission to use data on their test boat for this thesis. A special word ofthanks is extended to Mr. Jon Hamilton. I will always remember his brainenergizing thought-experiments.

A personal word of appreciation goes to the trio that prepared the manuscript forprinting. The illustrations by Gerrit Radstaat and the text processing and layoutwork by Manette Drinóczy-Jansen and Gerard Trouerbach have made it apresentable piece of work.

Finally, I warmly thank Jacintha for keeping up with me and my frequent absent-mindedness. She did a great job in timely pulling me out of the attic. Hercontribution is not only indirectly reflected in the contents of this work, but alsophysically present in the front cover.

293

Curriculum Vitae

Tom van Terwisga was born on October 16, 1959 in Sneek in The Netherlands.He attended secondary school at the RSG in Heerenveen, from 1972-1978. Hestarted studying Naval Architecture at Deift University of Technology in 1978. In1985, he finished his studies in hydrodynamics on the development of a poweringprediction model for SES craft. After obtaining his master's degree, he wasemployed by the Maritime Research Institute Netherlands (MARIN) inWageningen, where he worked in the R&D Department on developments inhydrodynamic tools and designs for special vessels. In 1990 he moved to the ShipResearch Department where he conducted projects on high speed vessels and theirpropulsion. He is currently involved in research projects on propulsorhydrodynamics.

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