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Marko Hočevar

Introduction to turbine machinery

Ljubljana, 2016

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Contents

Contents ............................................................................................................................................ 3

Nomenclature ................................................................................................................................. 7

Foreword and acknowledgments ............................................................................................ 8

Topics for seminars ...................................................................................................................... 9

Dictionary ..................................................................................................................................... 10

1 Introduction .............................................................................................................................. 13

1.1 WORKING PRINCIPLE ....................................................................................................... 13 1.2 TYPES OF TURBINE MACHINERY ......................................................................................... 14

1.2.1 Classification to enclosed or open turbine machines ......................................... 15 1.2.2 Classification regarding direction of the flow .................................................... 16 1.2.3 Classification regarding energy conversion direction ........................................ 18 1.2.4 Classification regarding application type .......................................................... 19 1.2.5 Classification regarding physical action ............................................................ 20

1.3 TURBINE MACHINERY PRODUCTION IN SLOVENIA .................................................................. 20 1.4 APPROACHES TO TURBINE MACHINERY OPERATION ............................................................... 21 1.5 NOMENCLATURE ............................................................................................................ 23

2. Thermodynamics and efficiencies .................................................................................. 24

2.1 FIRST LAW OF THERMODYNAMICS ...................................................................................... 24 2.2 EFFICIENCY.................................................................................................................... 28

2.2.1 Efficiency in steam and gas turbines ................................................................. 30 2.2.2 Efficiency in water turbines................................................................................ 32 2.2.3 Efficiency of pumps and compressors ................................................................ 33 2.2.4 Polytropic efficiency ........................................................................................... 34

3 Control volume approach to turbine machinery ........................................................ 35

3.1 CONTROL VOLUME ......................................................................................................... 35 3.2 STATIONARY CASE OF OPERATION ...................................................................................... 39

4 Differential approach to turbine machinery ................................................................ 40

5 Euler approach to fluid flow in turbine machinery ................................................... 43

5.1 ENERGY TRANSFER AND TRIANGLES OF VELOCITY ................................................................... 43

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5.1.1 Triangles of velocity in the runner ..................................................................... 43 5.2 ENTHALPY AND PRESSURE CHANGES IN TURBINE MACHINERY ................................................... 45

5.2.1 Enthalpy and pressure rise in radial compressor ............................................... 45 5.2.2 Entalpy and pressure reduction in radial turbine............................................... 48 5.2.3 Enthalpy and pressure rise in axial compressor ................................................. 50 5.2.4 Enthalpy and pressure reduction in axial turbine .............................................. 51

5.3 TORQUE ON THE BLADES OF THE TURBINE MACHINE RUNNER .................................................. 53 5.4 EULER EQUATION FOR TURBINE MACHINERY ........................................................................ 56 5.5 RADIAL FLOW COMPRESSORS AND PUMPS ........................................................................... 58

5.5.1 Triangles of velocity in radial compressors and pumps ..................................... 58 5.5.2 Second form of Euler equation .......................................................................... 62 5.5.3 Reactivity ........................................................................................................... 64 5.5.4 Radial runner characteristics ............................................................................. 68 5.5.5 Radial runner power and torque ........................................................................ 70 5.5.6 Radial runner static pressure ............................................................................. 71 5.5.7 Radial runner real pressure characteristics ....................................................... 71

5.6 AXIAL FLOW VENTILATORS, FANS, COMPRESORS AND PUMPS................................................... 73 5.6.1 Euler equation for axial turbine machinery ....................................................... 75

6 Similarity theory and dimensional analysis of turbine machinery ..................... 77

6.1 SIMPLE APPROACH TO OF SELECTION OF DIMENSIONLESS NUMBERS .......................................... 78 6.2 USE OF DIMENSIONLESS NUMBERS ..................................................................................... 81 6.3 FUNDAMENTAL APPROACH TO SELECTION OF DIMENSIONLESS NUMBERS ................................... 83

7 Water turbines ......................................................................................................................... 85

7.1 WATER TURBINE CLASSIFICATION ....................................................................................... 87 7.2 CRITERIA FOR WATER TURBINE CLASSIFICATION WITH RESPECT TO THE SPECIFIC SPEED (NS) ............ 88 7.3 PELTON TURBINE ............................................................................................................ 90 7.4 FRANCIS WATER TURBINES ............................................................................................... 94 7.5 KAPLAN WATER TURBINES ................................................................................................ 99 7.6 TUBULAR TURBINES ...................................................................................................... 102

7.6.1 Bulb turbine ..................................................................................................... 104 7.6.2 Pit turbine ........................................................................................................ 105 7.6.3 Tubular turbine S ............................................................................................. 105 7.6.4 Axial turbine with a vertical shaft – Saxo turbine ............................................ 106

7.7 OTHER TYPE OF WATER TURBINES .................................................................................... 107

8 Other elements of hydro power plants ......................................................................... 110

8.1 WATER INTAKE SYSTEM ................................................................................................. 110 8.1.1 Dams ................................................................................................................ 110 8.1.2 Teeth and trash racks ...................................................................................... 111

8.2 WATER SUPPLY SYSTEM ................................................................................................. 113

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8.2.1 Headrace channels and tunnels ....................................................................... 113 8.2.2 Surge tank ........................................................................................................ 113 8.2.3 Penstock ........................................................................................................... 115 8.2.4 Bypass valve or pressure regulator .................................................................. 115 8.2.5 Ball valve or butterfly valve in and bypass pipeline ......................................... 116 8.2.6 Gates ................................................................................................................ 117

8.3 POWERHOUSE EQUIPMENT ............................................................................................ 118 8.3.1 Spiral casing ..................................................................................................... 119 8.3.2 Stay vanes and guide vanes ............................................................................. 119 8.3.3 Turbine runner, turbine cover, anti-lifting plate and system for air blowing... 120 8.3.4 Shaft ................................................................................................................. 122 8.3.5 Ležaji ................................................................................................................ 122 8.3.6 Shaft seal ......................................................................................................... 125 8.3.7 Creep detector ................................................................................................. 125 8.3.8 Governing of the angle of guide vanes and runner blades .............................. 126 8.3.9 Inverter ............................................................................................................ 128 8.3.10 Brakes ............................................................................................................ 129 8.3.11 Generator and its electric equipment ............................................................ 129

8.4 OTHER SYSTEMS IN THE POWERPLANT .............................................................................. 131 8.4.1 Spillways and spillway gates ............................................................................ 132 8.4.2 Sump pumps .................................................................................................... 134 8.4.3 Fish passages ................................................................................................... 134

9 Manufacture of runners of water turbines.................................................................. 138

9.1 MANUFACTURE OF PELTON TURBINE RUNNERS .................................................................. 139 9.2 MANUFACTURE OF FRANCIS TURBINE RUNNERS.................................................................. 141 9.3 MANUFACTURE OF RUNNERS OF KAPLAN TURBINES ............................................................ 145 9.4 PRE ASSEMBLY, ASSEMBLY AND INSTALLATION OF WATER TURBINES ....................................... 146

10 The properties of operation of water power plants .............................................. 148

10.1 CHARACTERISTICS AND HILL DIAGRAM OF TURBINES........................................................... 150 10.1.1 Characteristics of water turbines ................................................................... 150 10.1.2 Hill diagram ................................................................................................... 153

10.2 PUMP/TURBINE OPERATION IN FOUR QUADRANTS (EXTENDED RANGE OF OPERATION) ............. 157

10 Cavitation in water turbines and pumps ................................................................... 159

10.1 INTRODUCTION TO CAVITATION ..................................................................................... 159 10.2 RELATION TO THE OPERATING POINT OF THE TURBINE MACHINE........................................... 161

10.2.1 In Kaplan turbine ........................................................................................... 161 10.2.2 In Francis turbine ........................................................................................... 163

10.2.3 IN CENTRIFUGAL PUMP ............................................................................................. 164 10.3 CAVITATION AND NPSH/NPSE CHARACTERISTICS ............................................................ 165

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10.3.1 In pumps ........................................................................................................ 166 10.3.2 In turbines ...................................................................................................... 168

10.4 PREVENTION OF CAVITATION EFFECTS IN WATER TURBINES ................................................. 170 10.5 INFLUENCE OF PARTICLES IN THE FLOW ON CAVITATION IN WATER TURBINES .......................... 171 10.6 RUNNER EROSION DUE TO SOLID DISPERSED PARTICLES ...................................................... 172

References .................................................................................................................................. 173

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Nomenclature

simbol pomen enota

indeksi pomen

okrajšave pomen

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Foreword and acknowledgments

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Topics for seminars

We encourage students to make seminars and present them to colleagues.

Possible topics for seminars are:

- history of turbine machinery,

- manufacture of hydraulic turbine machinery,

- acceptance test of turbine machinery,

- wind turbines,

- various other topics, related to turbine machinery, suggested by students.

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Dictionary

slovenski izraz angleški izraz

Banki turbina cross-flow turbine

bruto padec gross head

cevna turbina s hruško bulb turbine

cevna turbina v jašku pit turbine

čep vodilne lopatice guide vane pivot pin

čistilni stroj cleaning machine

črpalna vodna elektrarna pump turbine

delna obremenitev partial load

dovodni kanal head race channel

dovodni rov head race tunnel

drenažna črpalka sump pump

gonilna lopatica runner blade

gonilnik runner

gred shaft

iglasti ventil needle valve

iztočni kanal tailrace channel

iztočni rov tailrace tunnel

jašek shaft

jez dam

kavitacija cavitation

kavitacijski vrtinec cavitation vortex

ležaj bearing

lopatica turbine turbine blade, pri Peltonovih turbinah

se lopatice imenujejo tudi buckets

navitje rotorja rotor winding

navitje statorja stator winding

neto padec net head

nosilni ležaj support bearing ali thrust bearing

neto pozitivna sesalna višina neto positive suction head

obvod bypass

odklonilo deflector

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peskolov sand trap

pesto hub, boss

pobežna vrtilna frekvenca runaway speed

pokrov generatorja generator cover

potopitev submersion

predturbinski ventil ball valve ali butterfly valve

predvodilna lopatica stay vane

predvodilnik stay ring

prelivno polje spilway

pretočno število discharge coefficient

pretok discharge

prevzemni preizkus acceptance test

propeler propeller

razbremenilni ventil bypass valve ali pressure regulator

razbremenitev turbine load rejection

rešetka trash rack

ribja steza fish passage

ribam prijazna turbina fish friendly turbine

roka bracket

sesalna cev draft tube

sistem krmiljenja governor

specifična hitrost specific speed

spiralno ohišje spiral casing, scroll casing

spodnji akumulacijski zbiralnik lower reservoir

školjčni diagram hill diagram ali performance diagram

šoba nozzle ali injector

tesnilka seal

tesnilka gredi shaft seal

tlačni cevovod penstock

tlačni udar water hammer

tlačno število pressure coefficient

turbinski pokrov turbine cover

venec rim ali tip

vodilna lopatica guide vane

vodilni ležaj guide bearing

vodilni obroč guide vane ring ali guide vane wheel

vodilnik wicket gate

vodni padec head

vodostan surge tank ali surge chamber

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vstop vode water inlet

vtočni sistem water intake system

vzbujanje excitation

vztrajnik flywheel

začetna kavitacija incipient cavitation

zapornica gate

zavore brakes

zaznavalo premikanja creep detection sensor

zgornji akumulacijski zbiralnik upper reservoir

udarne izgube

trenjske izgube

optimalna delovna točka best efficiency point

notranje izgube inner losses, internal losses

vijak (ladijski) screw (ship), marine propeller

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1 Introduction

Turbine machinery is a subject of great importance today. People's life is

greatly influenced by use of electric energy. Extensive use of electric energy

has dramatically changed everyone's life. We are almost unable to imagine life

without use of electric motors, domestic appliances and consumer electronics.

Clothes washing and drying machines, refridgerators, microwave ovens,

television sets, audio and video electronics, air conditioning and computers

fall in this category. Almost all of the available electric energy nowadays is

produced with the use of turbine machinery. Turbine machinery is also used

for aero and naval propulsion and in internal combustion engines featuring

turbochargers.

Turbine machinery is a machine, where a continuous energy transfer is

present between fluid and an element of the machine, which rotates around its

axis. This element of the turbine machine is common for all turbine machines

and is called an impeller, also turbine wheel, rotor, screw or runner.

Turbine machines are pumps, fans, compressors, water turbines, gas turbines,

steam turbines, wind turbines, aircraft and marine propellers, torque

converters, hydrodynamic clutches etc.

This textbook is about principles of turbine machinery. Only in the section

about water turbines we will review technical aspects of the machinery more

in detail.

1.1 Working principle Turbine machinery and piston machinery perform similar task, but they differ

in the type of energy conversion. The operation of a reciprocating piston

engine is immediately apparent to understand. With Fp we denote the force on

the piston, for which we can write the equation

𝐹p = 𝑝𝑆 . (1)

Here p is pressure and S surface of the piston. With the movement of the

piston by dl, the work performed by the piston may be described by

d𝐴 = 𝐹pd𝑙 = 𝑝𝑆d𝑙 = 𝑝d𝑉 . (2)

In agreement with the above equation, work performed by piston is connected

with the change of the fluid volume.

In the turbine machinery the energy conversion is indirect and always takes

place through the change of kinetic energy of the fluid. For this we may

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consider Fig. below. In the turbine the fluid flows from the pressure penstock

into the turbine machine and first flows through a cascade of guide vanes. In

the cascade of guide vanes flow velocity and with it connected kinetic energy

increases at the expense of reduction of pressure or potential energy. At the

same time the shape and direction of guide vanes direct the flow in the

tangential direction of the runner. However, only tangential velocity can

increase, the axial velocity can not increase due to consersvation of the mass

flow rate. The cross section can not change much due to problems of flow

separation. In the runner, the fluid transfers its kinetic energy to the runner by

changing its direction. This decreases the tangential velocity, while again axial

velocity does not change much. The flow exits the turbine with reduced energy

ob the suction side of the turbine.

In pumps, ventilators, fans and comporessors, the procedure is the opposite.

We will consider the radial pump from Fig. below. The fluid flows in the

runner with negligible tangential velocity. In the runner the tangential velocity

is increased due to the torque of the shaft. However, due to conservation of the

mass flow rate, radial velocity is related to the axial velocity from the inlet

considering ratio of both cross sections. At the exit from the runner, the flow

has the energy, given by the shaft, mostly in the form of tangential velocity. To

decrease the flow and change the velocity into pressure, in the vaned difussor,

the tangential flow is slowed down and the shaft torque is converted into

pressure.

Fig. 1: Turbine machinery working principle, left: axial turbine and right:

radial pump, above: turbine machine diagram, below: runner and

guide vanes

1.2 Types of turbine machinery All turbine machinery works on the above mentioned principle of energy

transfer through velocity. However, many variants exist and several different

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classifications of turbine machines are possible. Turbine machines can be

classified according to several principles as follows:

- enclosed or open,

- direction of the fluid flow,

- energy conversion direction,

- application type and

- physical action.

Above mentioned classification will be explained below.

1.2.1 Classification to enclosed or open turbine machines Regarding whether fluid is enclosed within the turbine machine casing or not

(Fig. below) we distinguish:

- enclosed (water turbines, pumps, gas and steam turbines, ducted fans,

compressors) or

- open (propellers, screws, windmills, unshrouded fans, propfan engines,

wind turbines)

Open machines act on an infinite extent of fluid, whereas closed machines

operate on a finite quantity of fluid as it passes through a housing or casing.

Fig. below (left) shows an offshore 5 MW wind turbine. With wind turbines,

not all the energy of blowing wind can be used. Conservation of mass requires

that the amount of air entering and exiting a turbine must be equal.

Accordingly, Betz's law gives the maximal achievable extraction of wind

power by a wind turbine as 16/27 (59,3 %) of the total kinetic energy of the

air flowing through the turbine.

In Fig. below (right) a Francis water turbine is shown. Water is contained in

housing throughout the turbine.

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Fig. 2: Example of open (left, 5 MW offshore wind turbine Senvion, North

Sea) and enclosed turbine machinery (right, Francis turbine, HPP

Hubelj, Slovenia), source: Wikipedia.

1.2.2 Classification regarding direction of the flow Regarding direction of the flow (Fig. below) turbine machines are

- axial,

- diagonal,

- mixed flow,

- radial,

- tangential and

- cross flow turbine machines.

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Fig. 3: Flow through turbine machine. Left: pressure type (from top radial

flow turbine, diagonal turbine, axial turbine and cross flow fan),

right: impulse Pelton turbine (tangential flow)

When the path of the through-flow is wholly or mainly parallel to the axis of

rotation, the device is termed an axial flow turbomachine. The axial water

turbine shown in Fig. below (left) is a bulb turbine Dubrava, Croatia. HPP

Dubrava has max. head 18,8 m, max. flow rate 250 m3/s and max. power per

unit 43,5 MW. Bulb turbines are suitable for low head applications for lower

courses of rivers.

When the path of the through-flow is wholly or mainly in a plane

perpendicular to the rotation axis, the device is termed a radial flow

turbomachine.

When axial and radial flows are both present and neither is negligible, the

device is termed a mixed flow turbomachine. It combines flow and force

components of both radial and axial types. The Francis and Kaplan turbine

may be viewed as radial or mixed flow turbine, in Fig. below (right) is show

Francis turbine Doblar I.

In literature, there is often confusion about the direction of the flow within the

machine. Sometimes direction of the flow is taken with regard to the machine

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(turbine machine comprises among others of casing, guide vanes and runner)

or with regard to the runner only. For instance, inflow into the Kaplan turbine

is radial, while inflow onto the Kaplan turbine runner is axial. Outflow from

Kaplan turbine is for both cases axial.

Fig. 4: Example of axial and mixed flow water turbine. Left: flow tract of

axial water turbine HPP Dubrava, Croatia. The man standing in

front of turbine shows axial arrangement of elements of bulb

turbine. Right: Kaplan axial/mixed/radial flow water turbine HPP

Doblar I, Slovenia.

1.2.3 Classification regarding energy conversion direction Regarding purpose whether the runner gives energy to the fluid (machinery)

or takes energy from the fluid (engine) one may classify turbine machines as:

- machinery, runner gives energy to the fluid (pumps, propellers,

ventilators, fans, compressors, etc.),

- engine, runner takes energy from the fluid (water turbines, steam

turbines, gas turbines),

- combination of engines and machinery, runner takes energy from the

fluid and returns it to the fluid (fluid couplings, transmissions,

hydrodynamic clutchs and torque converters).

Fig. below (left) shows a low pressure 175 kW compressor HV Turbo for air

compression to provide aeration to aeration panels for secondary treatment of

municipal and industrial wastewater with up to 0,7 bar pressure difference.

The rotational speed gearbox multiplicator is used between the electric motor

and compressor runner. The air enters the compressor through the

rectangular filter, flows through the guide vane ring, through the runner,

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diffuser and volute chamber and exits the machine at the end of compressor

and leaves through the diffuser directed downwards in front of the

compressor. The runner gives the air tangential kinetic energy, a velocity that

is later in the diffuser and volute chamber reduced and pressure recovered.

Fig. 5: Turbine machines can provide energy to the flow or get energy

from the flow. Left: 175 kW compressor HV Turbo, Danemark (Now

Siemens Energy), wastewater treatment plant Domžale Kamnik.

Right: 42 MW gas turbine SGT 800, Siemens, TPP Šoštanj, Slovenia.

The SGT 800 turbine is designed for combined heat and power and combined-

cycle applications. The airflow enters turbine through filter and flows through

multistage axial compressor. Each stage of compressor comprises of a runner

and guide vane, acting as diffuser directing and slowing down the flow. At the

exit from compressor compressed air enters the combustion chamber. In

combustion chamber the fuel/air mix is burned. The exhaust gases exit the

turbine through the multistage axial turbine. Eaxh turbine stage is comprised

of runner and guide vane, similar like in compressor. The useful torque of

turbine blades is converted to electric power.

1.2.4 Classification regarding application type Installation type may be on of the following

- marine propulsion,

- aircraft propulsion,

- land vehicle installation,

- energy production and

- industrial applications.

Other installations are also possible.

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1.2.5 Classification regarding physical action Turbine machines can be classified according the relative magnitude of the

pressure changes across each stage. According to this classification we

distinguish impulse and pressure types of turbine machines

Impulse turbine machines operate by accelerating and possibly changing the

flow direction of fluid through a stationary nozzle onto the runner blade. In

such configuration, the nozzle functions as a stator or guide vane blade. In the

nozzle the incoming pressure is transformed into velocity, or the enthalpy of

the fluid decreases as the velocity increases. Pressure and enthalpy drop over

the runner blades is minimal, while velocity will decrease while in contact

with the runner almost to standstill. Impulse turbomachines do not necessarly

require a casing around the nozzle and runner. Usually they still have a casing

to prevent water spilling around the turbine machinery building. In most

cases, air pressure within the casing is atmospheric pressure. A Pelton turbine

is an example of an impulse turbine.

Reaction turbine machine operates by reacting to the flow of fluid through

runner and stator blade stages. Pressure and enthalpy consistently decrease

through the stages.

Fig. 6: Classification of turbine machines according to physical action.

Left: 46,2 MW impulse Pelton turbine spining in open, view from

below, Lünnersee, Austria, right: reaction 600 MW Alstom axial

steam turbine unit 6, Šoštanj, Slovenia

1.3 Turbine machinery production in Slovenia The whole engineering field of turbine machinery in Slovenia is well

developed. In year 1897 started operation the first hydraulic power plant on

Ljubljanica river, supplying electricity to paper mill company Vevče. HE

Završnica was built in 1915 as first public hydraulic power plant in Slovenia.

First very large power plant in Slovenia was HE Fala, built in 1918.

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The main companies in Slovenia in the field of manufacture of water turbines

are:

- Litostroj Power d. o. o. (Already supplied more than 500 water turbines in

more than 50 countries, over 18 GW of installed power)

- Kolektor Turboinštitut d. o. o.,

- Andino d. o. o.,

- Vodosil d. o. o., Laško

- Hidropower d. o. o., Idrija,

- Ligres d. o. o.,

- Hydro Hit Gameljne, Ljubljana,

- TPS Turbine, Celje,

- Siapro d. o. o., Most na Soci,

- S.var d. o. o., Godovič,

- Tinck Engineering d. o. o., Cerkno,

- MBM energy d. o. o., Šentjanž.

The main companies in Slovenia in the field of manufacture of water turbines

are:

- IMP Pumps,

- Litostroj Power d. o. o.,

- Kolektor Turboinštitut d. o. o.,

- Elko Elektrokovina d.o.o.,

- Ydria motors.

The main companies in Slovenia in the field of manufacture of fans are:

- Hidria Rotomatika,

- Domel,

- Tehnovent s.p.

- Systemair,

- Lindab IMP Klima,

- Ydria motors,

- Klima Celje,

- Gros,

- Rotometal,

- Agromehanika,

- Zupan sprayers,

- LF AIR, itd.

There are no producers of gas or steam turbines in Slovenia.

1.4 Approaches to turbine machinery operation Several approaches (i.e. theories) of turbine machinery operation exist.

Among them are:

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- thermodynamic (chapter 2),

- control volume (chapter 3),

- differential CFD (chapter 4),

- Euler (chapter 5),

- linear momentum,

- blade element and

- blade element momentum approach.

Thermodynamic approach is useful if we treat the turbine machine as a black

box and want to evaluate efficiency of turbine machine.

In linear momentum approach (also called actuator disk approach), for

instance for a propeller, we consider axial flow velocity far away before and

far away after the propeller. From the change of axial velocity we calculate

force 𝐹 = 𝑚𝑣̇ by which a propeller acts on the fluid and vice versa.

In blade momentum approach for instance for a axial fan, we calculate lift and

drag forces on the runner blades in a similar way as for

Blade element momentum theory is a combination of momentum and blade

element theories.

We will in most cases in this book use Euler approach, where in contrast to the

blade element theory we follow the fluid flow. In Euler approcah we consider

flow velocity and angular momentum at the entrance and exit from the

turbine machinery runner. From the change of tangential velocity we calculate

the power, pressure rise etc. We can think of the change of velocity in

tangential direction as a consequence of the runner acting with force on the

fluid flow (see connection to the blade element theory).

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Fig. 7: Approaches to turbine machinery

For differential CFD approach we calculate Navier stokes equations of the flow

inside turbine machinery. For this we divide the flow tract in the very large

number of cells. From pressures, calculated from cells on runner surfaces,

among others we calculate torque and power on the runner and shaft.

Allthough all aproaches are valid and useful, for teaching purposes the Euler

approach is most general for all turbine machinery and provides good

understanding to students.

1.5 Nomenclature Thoughout the textbook we will use terms turbine, turbine machine,

aerodynamic machine and hydraulic machine. Turbine machinery will be a

term generally used. With the term aerodynamic machines we will name low

pressure fans, and the term hydraulic machines we will use for pumps and

water turbines, in all these cases no heat exchange in the turbine will accur

and in most case flow will be non-compressible.

In the following we will first review types of turbine machinery, and then we

will consider ideal performance laws. In te last part, we will consider different

types of turbine machinery.

Througt the textbook we will use nomenclature, as explained in separate

section about nomenclature.

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2. Thermodynamics and efficiencies

In this section we will review thermodynamic properties of turbine

machinery. We will present first law of thermodynamics, adapted for the use

in turbine machinery. Later, we will present thermodynamic view on

efficiency of turbine machinery. In the third subsection we will later present

mechanic equations of turbine machinery and will merge both

representations in section 4.

For additional topics about thermodynamics, available textbooks about

turbine machinery often review equation of continuity, first and second law of

thermodynamics, steady flow energy equation, momentum equation, Euler

equation, Bernoulli equation, compressible flow equations etc. During your

study, this was covered in previous courses. In this textbook we will consider

that students are to some extent familiar with topics about thermodynamics.

Those students who want to study it again, are invited to consider a very good

textbook about energy machinery with good sections about thermodynamics

and turbine machinery [Tuma and Sekavčnik, 2005].

2.1 First law of thermodynamics The first law of thermodynamics describes conservation of energy for the case

of thermodynamic systems. The law of conservation of energy states that the

total energy of a thermodynamic isolated system is constant; energy can be

transformed from one form to another, but cannot be created or destroyed.

Total energy change of the system E is a sum of all work 𝐴 and heat 𝑄 supplied

to the system

𝐸 = 𝑄 − 𝐴 . (3)

For the sign of work 𝐴 we will use Clausius convention. By Clausius

convention, heat transfer in the system is positive and work done by the

system (in our case turbine machine) is also positive. IUPAC convention is

however different. As the flow through the turbine machine is continuous, we

may also use time derivatives. According to figure below

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Fig. 8: First law of thermodynamics (left) and the same adapted for the

case of turbine machinery (right). Shown are flows into and out

of the turbine machine. Here we consider entire turbine machine,

not just runner like in the case of Euler equations.

we have :

- fluid flow into the turbine machine (inlet, index 1),

- fluid flow out of the turbine machine (outlet, index 2),

- heat flow in or out of the turbine machine and

- work flow (power) in or out from the turbine machine (shaft).

The first law of thermodynamics for the turbine machine is therefore

𝐸 = 𝑄 − 𝐴 = 𝐸𝑓𝑙𝑢𝑖𝑑 𝑝𝑜𝑤𝑒𝑟 𝑜𝑢𝑡 2 − 𝐸𝑓𝑙𝑢𝑖𝑑 𝑝𝑜𝑤𝑒𝑟 𝑖𝑛 1 . (4)

We write expressions for energy 𝐸 for the fluid flow flowing into and out of

the turbine machine, composed of the following parts:

- internal specific energy u,

- pressure p,

- velocity c and

- elevation z.

In the following we will often use small letters for variables per unit mass,

for instance we write here specific internal energy as u, which is internal

energy U per unit mass. The total specific fluid energy comprises of specific

internal energy 𝑢, specific flow work 𝑝𝑣, specific kinetic energy 1

2𝑐2 and

specific potential energy 𝑔𝑧

𝑒 = 𝑢 + 𝑝𝑣 +1

2𝑐2 + 𝑔𝑧 . (5)

For a steady uniform flow, the first law of thermodynamics has a form

26

�̇� (𝑢1 + 𝑝1𝑣1 +1

2𝑐12 + 𝑔𝑧1) + �̇�

= �̇� (𝑢2 + 𝑝2𝑣2 +1

2𝑐22 + 𝑔𝑧2) + �̇�

(6)

In the above equation we have considered the entire turbine machine, while

later we will write equations that consider only runners (Euler equations). In

the parenthesis on the left and on the right we have specific internal energy u,

pressure part pv, specific kinetic energy 1

2𝑐2 and specific potential energy gz. v

is specific volume per unit mass. The term pv represents the work done by the

fluid inside the control volume to move the fluid in or out out of the control

volume. The equation can be extended to multiple inlets and outlets.

Remember that both parentheses correspond to the fluid flow in and out of

the turbine machine, as shown in Fig. 8 above.

The sum of specific internal energy and specific flow work is specific enthalpy

[𝑚2

𝑠2]

ℎ = 𝑢 + 𝑝𝑣 . (7)

We can further complicate the issue with specific variables and divide the

equation above with �̇�. The first law of thermodynamics for turbine

machinery becomes

ℎ1 +1

2𝑐12 + 𝑔𝑧1 + 𝑞 = ℎ2 +

1

2𝑐22 + 𝑔𝑧2 + 𝑎 . (8)

where 𝑞 =�̇�

�̇� and 𝑎 =

�̇�

�̇�.

Sum of specific internal energy, specific flow work and specific kinetic energy

and specific potential energy is called stagnation enthalpy or total enthalpy

ℎ0 = 𝑢 + 𝑝𝑣 + 1

2𝑐2 . (9)

The first law of thermodynamics can be written as

ℎ01 + 𝑔𝑧1 + 𝑞 = ℎ02 + 𝑔𝑧2 + 𝑎 . (10)

q and a are specific heat and a specific work (per unit mass). In

turbomachinery, flows are nearly adiabatic and temperature inside the

turbine machine is for stationary operation nearly constant, thus q = 0 and we

27

can write first law of thermodynamics for turbine (𝑎 > 0), remember, work

done by the system is positive.

In the similar was as total enthalpy, we may also introduce total pressure.

Total pressure is a static pressure, increased for a velocity term, which we in

this case call dynamic pressure (total pressure = static pressure + dynamic

pressure). We can elso neglect potential energy terms to get

𝑎 = ℎ01 − ℎ02 . (11)

and for compressors and pumps (𝑎 < 0), but we can also write

𝑎 = ℎ02 − ℎ01 . (12)

In the equation above we have ignored the convention of thermodynamics of

denoting work out from a system as positive and work in as negative, and the

equations are written in a form that gives a positive value for work, for both a

turbine and a compressor (it is easier for the lecturer and students also...).

Later we will very much rely on the first law of thermodynamics, when we will

discuss efficiency of turbine machinery.

In this textbook we will in most cases consider systems, where the heat is not

supplied or extracted from the system like water turbines, water pumps and

low pressure fans. This is because within the Slovenian industry there are

many manufacturers with long history in mentioned fields but much less for

thermal turbine machines. For such case we substitute enthalpy with pressure

and we write first law of thermodynamics for various machines in the

following ways:

1. For general case of turbine machines (energy per unit mass)

𝑒 =𝐸

𝑚= 𝑌 = 𝑔𝐻 =

𝑝2𝜌+1

2𝑣22 + 𝑔𝑧2 −

𝑝1𝜌−1

2𝑣12 − 𝑔𝑧1 (13)

2. For low pressure fans with no compressibility effects (energy per unit

volume) we prefer to operate with pressures

𝐸

𝑉= 𝑝2 +

1

2𝜌𝑣2

2 + 𝜌𝑔𝑧2 − 𝑝1 −1

2𝜌𝑣1

2 − 𝜌𝑔𝑧1 (14)

3. For pumps (energy per unit weight) we prefer to operate with heights

(elevations above a selected level) 𝑧

28

𝐸

𝑚𝑔=𝑌

𝑔= 𝐻 =

𝑝2𝜌𝑔+1

2

𝑣22

𝑔+ 𝑧2 −

𝑝1𝜌𝑔−1

2

𝑣12

𝑔− 𝑧1 (15)

The reason why we do so is that the pumping height (usually called head) is

for the case of turbine pumps the same regardless of the fluid. For instance,

pump pumping water with the head 123 m will pump oil with the same head

123 m. The pumping pressure will be however different, because densities of

fluids are different.

2.2 Efficiency Efficiency is often the most important parameter of turbine machinery, think

of a water turbine with 600 MW power operating continuously, how much

additional energy and income is generated in 50 years of operation if

efficiency is improved by 0.1 %.

In this subsection we will write the efficiency in a thermodynamic way,

without any consideration of flows inside the runner and stator. This falls

within the thermodynamic approach as discussed in section 1.4.

Efficiencies in turbine machinery are shown in Fig. below. Turbines are

designed to convert the available power of a flowing fluid 𝑃𝑎𝑣𝑎𝑖𝑙 into useful

mechanical power delivered at the coupling of the output shaft Pelect. Pumps

and fans operate in the opposite way; they transform useful mechanical power

delivered at the coupling of the input shaft Pelect into power of the fluid P.

Fig. 9: Efficiencies in turbine machinery

The overall efficiency 𝜂 of such energy transformation is for the turbines set

with eq. 16

29

𝜂 =𝑃𝑒𝑙𝑒𝑐𝑡𝑃𝑎𝑣𝑎𝑖𝑙

(16)

and for pumps and fans with eq. 17

𝜂 =𝑃𝑎𝑣𝑎𝑖𝑙

𝑃𝑒𝑙𝑒𝑐𝑡 . (17)

Thermal turbine machines feature in addition the thermal efficiency 𝜂𝑡

𝜂𝑡 =𝑃𝑎𝑣𝑎𝑖𝑙

�̇� . (18)

Heat flow �̇� is supplied to thermal turbine machines. Thermal efficiency 𝜂𝑡

considers irreversible losses because of energy conversions in thermal cycle.

Thermal efficiencies have approximate value from 0.5 to 0.6 (Tuma and

Sekavčnik, 2005). Thermal efficiency 𝜂𝑡 is set as a ratio or power of ideally

reversible machine working with ideal thermal cycle and the heat supplied to

this machine. The highest thermal efficiency 𝜂𝑡 has Carnot cycle. The term

thermal efficiency only applies to thermal processes and is not relevant at all

with hydraulic and aerodynamic machines. To avoid thermal efficiency, we

therefore in eq. 16 in denominator write available power 𝑃𝑎𝑣𝑎𝑖𝑙. The

mechanical power at output shaft coupling is usually power available to the

electric generator 𝑃𝑒𝑙𝑒𝑐𝑡.

To cover losses in the flow tract including the runner and stator, we introduce

internal or isentropic or hydraulic (Dixon and Hall, 2010) efficiency 𝜂𝑖 (slo.:

notranji izkoristek), which is set by eq. 17 for turbines as the ratio of

mechanical power of the runner and maximum power possible for the fluid

𝜂i =𝑃𝑠ℎ𝑎𝑓𝑡

𝑃𝑎𝑣𝑎𝑖𝑙 (19)

and with eq. 20 for fans and pumps

𝜂i =𝑃𝑎𝑣𝑎𝑖𝑙𝑃𝑠ℎ𝑎𝑓𝑡

. (20)

We will study more in details the internal losses in the following chapters.

Mechanical losses are represented by mechanical efficiency 𝜂𝑚𝑒𝑐ℎ. Mechanical

losses occur between the turbine runner and the generator/electric motor

shaft coupling. This is the result of the work done against friction at the

30

glands, bearings, seals, auxiliary equipment, radiation losses etc. The amount

of mechanical losses is for small machines up to 5 %, while for large machines

it is well below 1 % (Dixon and Hall, 2010). For turbines we may write

mechanical efficiency 𝜂𝑚 as a ratio of electric power to the power of the shaft

𝜂m = 𝑃elect𝑃𝑠ℎ𝑎𝑓𝑡

, (21)

while eq. 22 is used for fans and pumps

𝜂m =𝑃𝑠ℎ𝑎𝑓𝑡

𝑃elect . (22)

One may separately introduce also other types of efficiencies, for instance due

to thermal losses, radiation losses, volumetric losses, bearing cooling loses,

draft tube losses, aerodynamic losses etc. In this textbook we will not go into

details regarding efficiency.

2.2.1 Efficiency in steam and gas turbines

We will consider efficiency in steam and gas turbines based on Mollier

diagram shown in Fig. 10. Line 1-2 shows actual expansion and line 1-2s

shows ideal adiabatic reversible expansion. We may notice that for any useful

installation of steam and gas turbines potential energy terms may be

negligible. The actual work rate of a steam or gas turbine may be written using

this simplification as

�̇�

�̇�= ℎ01 − ℎ02 = (ℎ1 − ℎ2) +

1

2 (𝑐1

2 − 𝑐22) . (23)

On the right hand side of eq. 23 we have have written stagnation enthalpy as a

sum of enthalpy and velocity terms. This is because fluid velocities at entry

and exit from the turbine are high. Turbines differ depending on the use of exit

kinetic energy. In some turbines exit kinetic velocities is lost, while at others it

is not. In the case that it is not lost, ideal work rate output is obtained between

states 01 and 02s according to eq. 24 (Dixon and Hall, 2010)

�̇�𝑚𝑎𝑥�̇�

= ℎ01 − ℎ02𝑠 = (ℎ1 − ℎ2𝑠) + 1

2 (𝑐1

2 − 𝑐2𝑠2 ) . (24)

We may now write internal efficiency (eq. 25) using eq. 23 and eq. 24

(remember we discussed earlier that internal efficiency represents losses

inside the flow tract)

31

η𝑖 =𝐴

𝐴max=ℎ01 − ℎ02ℎ01 − ℎ02𝑠

. (25)

If the difference in inlet and exit velocity is not significant (c1~c2), we may

write eq. 25 without kinetic energy terms with enthalpies instead of

stagnation enthalpies

η𝑖 =𝐴

𝐴max=ℎ1 − ℎ2ℎ1 − ℎ2𝑠

. (26)

Kinetic energy at the exit from turbine is not wasted in aircraft engines, where

exhaust gas from last turbine stage contributes to overall engine thrust. Also,

kinetic energy from one stage is available in the next stage of multistage

turbine.

If the exhaust kinetic energy can not be used and is entirely wasted, we have

the case, where the ideal expansion is to the same static pressure as the actual

process, but with zero exit kinetic energy. The maximum possible work is in

this case obtained between 01 and 2s

�̇�𝑚𝑎𝑥�̇�

= ℎ01 − ℎ2𝑠 = (ℎ1 − ℎ2𝑠) + 1

2 𝑐12 (27)

and corresponding internal efficiency is total to static effiency

η𝑖 =𝐴

𝐴max=ℎ01 − ℎ02ℎ01 − ℎ2𝑠

. (28)

Like before, if the difference in inlet and exit velocity is not significant (c1~c2),

we may write the above equation for internal efficiency

η𝑖 =𝐴

𝐴max=

ℎ1 − ℎ2

ℎ1 − ℎ2𝑠 +12𝑐12 . (29)

Total to static internal efficiency is always lower than total to total internal

efficiency. Total to total internal efficiency relates to internal losses in the

runner due to creation of vortices, etc., while in addition total to static internal

efficiency includes additional loss of kinetic energy at the exit of the turbine.

32

Fig. 10: Enthalpy in adiabatic turbine and adiabatic compressor. Variables

having zeros in the index represent stagnation specific enthalpies,

while those without represent specific enthalpies. Dashed line

corersponds to total to total and full line to static to static

efficiency.

2.2.2 Efficiency in water turbines

Water turbines are an example of turbine machines, where the fluid is not

compressible. The other examples are low pressure fans and ventilators.

Modern water turbines are very efficient machines. They feature large draft

tubes, which serve as difusors. Within draft tubes, flow is decelerated to near

zero velocity.

Before, we have argued, that gas and steam turbines due to the properties of

steam or gas cycle and thermal efficiency 𝜂𝑡 are only available to use energy

rate �̇� ∙ 𝜂𝑡. Something similar may be written for water turbines, however it

does not have same root cause as with steam or gas turbines. The water

turbines use water from upper accumulation and release it to the lower

accumulation. Mechanical part of water turbines starts at the end of penstock

with the turbine valve, if the water turbine has one. Some energy is lost in the

water conduit from the upper accumulation to the end of penstock, resulting

from friction in the upper accumulation intake, trash rack, channel, tunnel,

gates, surge tank itd. Losses from similar causes appear also in the flow tract

from the turbine to the lower accumulation. These losses are somehow

equivalent to the thermal efficiency of the gas or steam turbine, as they are not

related to the mechanical engineering part of the (water) power plant, instead

33

they are civil engineering part of the water turbine design and very much cost

related.

Additional losses of course appear in the flow tract (internal efficiency 𝜂𝑖) of

the mechanical part of the water turbine (from the end of penstock to the end

of draft tube) and due to friction of mechanical parts of the water turbine

(mechanical efficiency 𝜂𝑚).

We will in the relevant section about water turbines go more in detail into

efficiency of water turbines.

2.2.3 Efficiency of pumps and compressors

We have described in section 1.3 the overall efficiency of pumps and

compressors with equation above as a ratio of work transferred to the fluid

and work at the shaft coupling and internal efficiency by equation above as a

ratio of work transferred to the fluid and work available to the runner. For a

complete adiabatic compression process (Fig. above), we write equation for

the specific work

�̇�

�̇�= (ℎ02 − ℎ01) + 𝑔(𝑧2 − 𝑧1) . (30)

Fig. above shows real compression process (going from state 1 to state 2) and

ideal (which we may also call minimum) compression process (going from

state 1 to state 2s). Based on the Mollier diagram in Fig. above, for a

compressor the height term on the right of Eq. above is usually negligible and

we may write internal efficiency as

η𝑖 =𝑊𝑚𝑖𝑛𝑊

=ℎ02𝑠 − ℎ01ℎ02 − ℎ01

. (31)

Similar as with turbines, if the difference in inlet and exit velocity is not

significant (c1~c2), we may write Eq. 24 without kinetic energy terms with

enthalpies instead of stagnation enthalpies

η𝑖 =𝑊𝑚𝑖𝑛𝑊

=ℎ2𝑠 − ℎ1ℎ2 − ℎ1

. (32)

For low pressure ventilators, fans and water pumps the flow is

incompressible, therefore ideal specific work may be written as

34

�̇�

�̇�=(𝑝2 − 𝑝1)

𝜌+1

2(𝑐22 − 𝑐1

2) + 𝑔(𝑧2 − 𝑧1) = 𝑔(𝐻2 −𝐻1)

= 𝑔𝐻 . (33)

With H we denote pump head. Because 𝑝 = 𝜌𝑔𝐻, using head H instead of

pressure is a very useful for pumps. A pump, rotating at the same rotational

speed, delivers same head regardless of the pumping medium. For instance,

pump pumping water will pump water, oil or air to the same height, however

pressures will be different. With ventilators and fans we usually denote

performance instead of with head with total pressure (se ponavlja).

The internal efficiency of a pump pumping incompressible medium is thus

η𝑖 =𝑊𝑚𝑖𝑛𝑊

=𝑔𝐻

𝑊 . (34)

2.2.4 Polytropic efficiency

text

Fig. 11: Small stages compression process

35

3 Control volume approach to turbine machinery

In the previous section we have studied the turbine machine in a black box

approach and without much insight to the flow inside the machine. Now we

want to investigate it deeper and we will consider the runner of the turbine

machine.

In fluid mechanics we can approach the turbine machine runner in an integral

way. By doing so we will consider a control volume (Fig. below), which is set

around the turbine machine. Only the shaft of the turbine machine extends out

of the control volume. All equations, describing the turbine machine with the

control volume approach, are based on Reynolds transport equation

[Laksmiranayana, 1996]. The control volume approach is also applied to basic

laws of conservation of mass, momentum and energy. In the following of this

section we will deliberately not be mathematically concise and will trade

concisity for som additional clarity.

3.1 Control volume The control volume approach does not allow analysis of flow properties inside

the control volume; however it provides basic understanding of turbine

machinery operation. The control volume approach is limited to simple

geometries, that may lead to simplified analytical solutions. In comparison

with approach from previous chapter, runner operation is addressed.

We consider a turbine machine, which is enclosed in a control volume (Fig.

below). The control volume is fixed around the turbine machine and does not

move. Fluid and heat flow across the control volume surface is allowed, while

work is suplied only through the shaft, penetrating accross the control colume

to the turbine runner, enclosed within the control volume. Fig. below shows

an imaginary control volume, while on it's right is more realistic

implementation of the control volume, adapted for the use with turbine

machinery.

36

Fig. 12: Control volume around a turbine machine. Only the shaft of a

turbine extends out of the turbine machine. Fluid and heat flow

across the control volume surface is allowed.

The generalized equation of laws of fluid mechanics for such case is given for

arbitrary property N. The N is an extensive property (magnitude is dependent

of the size of the system, or additive) like mass, linear momentum, angular

momentum or energy. The generalized equation is

𝑑𝑁

𝑑𝑡= ∬ 𝑛𝜌𝑐 ∙ 𝑑𝑆

𝑆

+𝜕

𝜕𝑡 ∭ 𝑛𝜌𝑑𝑉

𝑉

.

(

𝑟𝑎𝑡𝑒 𝑜𝑓𝑐ℎ𝑎𝑛𝑔𝑒 𝑜𝑓 𝑁𝑓𝑜𝑟 𝑡ℎ𝑒 𝑠𝑦𝑠𝑡𝑒𝑚

) = (𝑓𝑙𝑢𝑥 𝑜𝑓𝑁 𝑜𝑣𝑒𝑟 𝑡ℎ𝑒

𝑐𝑜𝑛𝑡𝑟𝑜𝑙 𝑠𝑢𝑟𝑓𝑎𝑐𝑒) + (

𝑟𝑎𝑡𝑒 𝑜𝑓 𝑐ℎ𝑎𝑛𝑔𝑒𝑜𝑓 𝑁 𝑖𝑛𝑠𝑖𝑑𝑒

𝑐𝑜𝑛𝑡𝑟𝑜𝑙 𝑣𝑜𝑙𝑢𝑚𝑒

)

(35)

On the left hand side of equation above, there is a rate of change of property N

for the system. The first term on the right hand side of equation above is flux

of property N through the control surface. The last term in equation above is

rate of change of property N inside the control volume. We denote integration

over the closed surface with two integration signs and integration over closed

volume with three integration signs. With n we denote specific property of N

by unit mass.

The equations for mass (continuity), linear momentum, angular momentum

and energy are based on equation above.

To get continuity equation we must substitute the property N with m and n

with n = m/m = 1 and we get

0 =∬ 𝜌𝑐 ∙ 𝑑𝑆𝑆

+𝜕

𝜕𝑡 ∭ 𝜌𝑑𝑉

𝑉

. (36)

37

0 = (

𝑡ℎ𝑒 𝑛𝑒𝑡 𝑜𝑢𝑡𝑓𝑙𝑜𝑤 𝑟𝑎𝑡𝑒 𝑜𝑓 𝑚𝑎𝑠𝑠 𝑡ℎ𝑟𝑜𝑢𝑔ℎ 𝑡ℎ𝑒 𝑐𝑜𝑛𝑡𝑟𝑜𝑙 𝑠𝑢𝑟𝑓𝑎𝑐𝑒

) + (𝑡ℎ𝑒 𝑝𝑟𝑜𝑑𝑢𝑐𝑡𝑖𝑜𝑛 𝑟𝑎𝑡𝑒𝑜𝑓 𝑚𝑎𝑠𝑠 𝑖𝑛 𝑡ℎ𝑒𝑐𝑜𝑛𝑡𝑟𝑜𝑙 𝑣𝑜𝑙𝑢𝑚𝑒

)

On the left hand side of equation we get zero because of conservation of mass.

The unit of continuity equation is [kg/s].

For linear momentum, we substitute n for velocity 𝑐

𝑛 → 𝑐 . (37)

On the left handside of equation above we must in addition of substitution

above also multiply with mass, while on the right handside we directly

substitute equation above into equation above to get equation of linear

momentum for control volume

∬ �⃗�𝑑𝑆𝑆

+∭ �⃗⃗�𝜌𝑑𝑉𝑉

=

∬ 𝑐(𝜌𝑐 ∙ 𝑑𝑆)𝑆

+𝜕

𝜕𝑡 ∭ 𝑐(𝜌𝑑𝑉)

𝑉

(𝑠𝑢𝑟𝑓𝑎𝑐𝑒 𝑓𝑜𝑟𝑐𝑒𝑠

𝑎𝑐𝑡𝑖𝑛𝑔 𝑜𝑛 𝑡ℎ𝑒 𝑚𝑎𝑡𝑡𝑒𝑟 𝑖𝑛 𝑡ℎ𝑒 𝑐𝑜𝑛𝑡𝑟𝑜𝑙 𝑣𝑜𝑙𝑢𝑚𝑒

) + (𝑏𝑜𝑑𝑦 𝑓𝑜𝑟𝑐𝑒𝑠

𝑎𝑐𝑡𝑖𝑛𝑔 𝑜𝑛 𝑡ℎ𝑒 𝑚𝑎𝑡𝑡𝑒𝑟 𝑖𝑛 𝑡ℎ𝑒 𝑐𝑜𝑛𝑡𝑟𝑜𝑙 𝑣𝑜𝑙𝑢𝑚𝑒

)

= (

𝑛𝑒𝑡 𝑜𝑢𝑡𝑓𝑙𝑜𝑤 𝑟𝑎𝑡𝑒 𝑜𝑓 𝑚𝑜𝑚𝑒𝑛𝑡𝑢𝑚

𝑡ℎ𝑟𝑜𝑢𝑔ℎ 𝑐𝑜𝑛𝑡𝑟𝑜𝑙 𝑠𝑢𝑟𝑓𝑎𝑐𝑒)+ (

𝑡𝑖𝑚𝑒 𝑟𝑎𝑡𝑒 𝑜𝑓 𝑐ℎ𝑎𝑛𝑔𝑒𝑜𝑓 𝑚𝑜𝑚𝑒𝑛𝑡𝑢𝑚

𝑖𝑛 𝑐𝑜𝑛𝑡𝑟𝑜𝑙 𝑣𝑜𝑙𝑢𝑚𝑒

)

(38)

On the left hand side we have a total derivative of velocity, acceleration which

is related to the force acting upon the fluid. In this was we may see the above

linear momentum equation as an application of Newton's second law of

motion. Total derivative in fluid mechanics is for time derivation of a variable,

following motion of the parcel, while partial derivative is for the time

derivative in fixed point in space. In the above linear momentum equation for

control volume we have surface force �⃗� (normalized per unit area) acting per

unit area dS, which represent normal and tangential surface forces, acting on

the surface of the control volume. As usual for turbine machines, normal

forces correspond to pressure forces and tangential forces correspond to

viscous and turbulent stresses, acting on the control surface surface. �⃗⃗� are all

body forces (normalized per unit mass, also called mass forces), acting on the

fluid inside the measurement volume. Examples of these forces are

gravitational force and electromagnetic forces.

38

Turbine machinery gives energy to the fluid by rotation or gets it from the

fluid. Using linear momentum may therefore be awkward and it is better to

use angular momentum instead. We use

𝑛 → 𝑟 × 𝑐 . (39)

The 𝑟 is radius vector from the origin of coordinate system. We get angular

momentum equation for control volume

∬ 𝑟 × �⃗�𝑑𝑆𝑆

+∭ (𝑟 × �⃗⃗�)𝜌𝑑𝑉𝑉

=

∬ (𝑟 × 𝑐)(𝜌𝑐 ∙ 𝑑𝑆)𝑆

+𝜕

𝜕𝑡 ∭ (𝑟 × 𝑐)(𝜌𝑑𝑉)

𝑉

(𝑠𝑢𝑟𝑓𝑎𝑐𝑒 𝑡𝑜𝑟𝑞𝑢𝑒

𝑎𝑐𝑡𝑖𝑛𝑔 𝑜𝑛 𝑡ℎ𝑒 𝑚𝑎𝑡𝑡𝑒𝑟 𝑖𝑛 𝑡ℎ𝑒 𝑐𝑜𝑛𝑡𝑟𝑜𝑙 𝑣𝑜𝑙𝑢𝑚𝑒

) + (𝑏𝑜𝑑𝑦 𝑡𝑜𝑟𝑞𝑢𝑒

𝑎𝑐𝑡𝑖𝑛𝑔 𝑜𝑛 𝑡ℎ𝑒 𝑚𝑎𝑡𝑡𝑒𝑟 𝑖𝑛 𝑡ℎ𝑒 𝑐𝑜𝑛𝑡𝑟𝑜𝑙 𝑣𝑜𝑙𝑢𝑚𝑒

)

= (

𝑛𝑒𝑡 𝑜𝑢𝑡𝑓𝑙𝑜𝑤 𝑟𝑎𝑡𝑒 𝑜𝑓 𝑎𝑛𝑔𝑢𝑙𝑎𝑟 𝑚𝑜𝑚𝑒𝑛𝑡𝑢𝑚 𝑡ℎ𝑟𝑜𝑢𝑔ℎ 𝑐𝑜𝑛𝑡𝑟𝑜𝑙 𝑠𝑢𝑟𝑓𝑎𝑐𝑒

) + (𝑡𝑖𝑚𝑒 𝑟𝑎𝑡𝑒 𝑜𝑓 𝑐ℎ𝑎𝑛𝑔𝑒𝑜𝑓 𝑎𝑛𝑔𝑢𝑙𝑎𝑟 𝑚𝑜𝑚𝑒𝑛𝑡𝑢𝑚𝑖𝑛 𝑐𝑜𝑛𝑡𝑟𝑜𝑙 𝑣𝑜𝑙𝑢𝑚𝑒

)

(40)

On the left hand side of the equation above same principles apply as

mentioned regarding momentum equation. First term on the left can be

replaced by shaft torque.

For energy equation we substitute n → e and we get energy equation for the

control volume. In this was enery equation is similar to the first law of

thermodynamics that we introduced in the previous chapter. We will

therefore not write the energy equation again here. The work transferred to

the fluid (or from) may be of many forms, but in turbine machinery the most

dominant form is through the turbine shaft. The rate of work on the turbine

shaft is power Ps and is a product of torque M and rotational speed

𝑃𝑠 = 𝑀𝜔 . (41)

The second way, how work can be transferred to the fluid inside control

volume, is by a normal stress. The third way, how work is transferred to the

fluid, is by tangential stresses. Work done by tangential stresses is low in

comparison with work done by a shaft and by normal stresses.

In the following, we will write equations for stationary case.

39

3.2 Stationary case of operation In this section we will skip linear momentum equations, because the angular

momentum equation is more suitable for turbine machinery. This is because

the turbine machine rotor is rotating along it's axis.

We will also consider stationary operation of turbine machinery. This is usual

operation of turbine machinery. Terms involving partial time derivative are

then equal to 0. The stationary form of continuity equation is

0 =∬ 𝜌𝑐 ∙ 𝑑𝑆𝑆

. (42)

The stationary case of angular momentum equation is

∬ 𝑟 × �⃗�𝑑𝑆𝑆

+∭ (𝑟 × �⃗⃗�)𝜌𝑑𝑉𝑉

=∬ (𝑟 × 𝑐)(𝜌𝑐 ∙ 𝑑𝑆)𝑆

. (43)

Forces �⃗� acting per unit area dS represent normal and tangential surface

forces, acting on the surface of the control volume. As usual for turbine

machines, normal forces correspond to pressure forces and tangential forces

correspond to viscous and turbulent stresses, acting on the control surface.

The first term on the left side in the above equation represents angular

momentum/torque of all surface forces acting on control surface. The second

term on the left hand side of equation above represents total angular

momentum/torque of all body forces and the term on the right represents

total flux of angular momentum across control surfaces. Usually, only the

torque with respect to shaft rotation is important. The left term involving

surface integration of 𝑟 × �⃗� is a momentum of force on the shaft of turbine

machine. The left term can be thus for turbine machines replaced by torque

Mshaft.

40

4 Differential approach to turbine machinery

As discussed above, control volume approach is unable to provide information

about flow properties inside the control volume. For a more in depth analysis,

we must switch to differential approach. Differential approach leads to general

equations of the flow, which are Navier Stokes equations. Differential

approach enables calculation of properties of the flow in every single point

inside control volume. Such approach forms the core of any commercial

computer fluid dynamics CFD software solution. Continuity, momentum

equations and energy equation form a system of differential equations. This

system is not closed and additional assumptions are required. Such systems

can only be solved if suitable initial and boundary conditions are available.

Solved problems are accurate solutions for variables like velocity, pressure,

temperature etc. in every point inside turbine machine.

The differential approach enables analysis of:

- local velocity fields,

- local pressure fields,

- local temperature fields,

- forces on the solid boundaries,

- local entropy generation,

- etc.

The differential equations may be derived from control volume equations

using Gauss divergence theorem, that relates the flow (that is, flux) of a vector

field through a surface to the behavior of the vector field inside the surface. By

using Gauss divergence theorem, we get for instance in linear momentum

equation all terms with volume integrals. In this textbook we will not perform

derivation of equations of motion, reader should consider books about fluid

mechanics [Schlichting, 1979].

The equations of motion for compressible viscous flow in differential form are

continuity equation [Lakshmiranayana, 1996]

𝜕𝜌

𝜕𝑡+ ∇⃗⃗⃗ ∙ (𝜌𝑐) = 0 (44)

41

and three linear momentum equations for each direction [Lakshmiranayana,

1996]

𝑑𝜌𝑐

𝑑𝑡= (𝑐 ∙ ∇⃗⃗⃗)𝜌𝑐 +

𝜕𝜌𝑐

𝜕𝑡= −∇𝑝 + 𝜌�⃗� + ∇⃗⃗⃗ ∙ 𝜏

(1) (2) (3) (4) (5) (6)

(45)

The 6 terms in linear momentum equations are:

- (1) total acceleration,

- (2) convective acceleration,

- (3) local acceleration,

- (4) pressure force term,

- (5) gravitational force term and

- (6) viscous stress tensor.

For incompressible, laminar flow, the density and viscosity are constant. For

inviscid flow, last term is zero. Under such assumptions, these equations

represent a complete set of equations for the four unknowns (pressure and

three velocity components), also meaning that fourth energy equation is not

required. In most situations, the fifth term 𝜌�⃗� is neglected.

For further discussion about linear momentum equations in various forms,

energy equation and rate of work done by shear stresses, readers should see

[Lakshmiranayana, 1996].

The diferential governing equations of the flow are most often simplified to

such extent, that they enable engineering analysis of turbine machinery. Often,

the flow is:

- incompressible,

- viscosity gradients are small and

- gravitational effects can be neglected.

Density is constant in the case of water turbines and low pressure ventilators

and fans. The assumption of constant density can not be used for steam and

gas turbines and high pressure compressors. In the mentioned case of

constant density and low viscous gradients the following simplifications:

- density is constant and may be omitted from equations where applicable,

- viscous terms in momentum equations are simplified and

- energy equation is not needed because of density is treated as constant

and we need one equation less.

The continuity equation becomes

∇⃗⃗⃗ ∙ 𝑐 = 0 , (46)

42

telling us that divergence of velocity is zero for such case of the flow (constant

density, simplified viscous terms). Linear momentum equations become

𝜌𝑑𝑐

𝑑𝑡= −∇𝑝 + 𝜇∇2𝑐

(1) (2) (3)

(47)

The above equations are called thin layer Navier stokes equations for

incompressible flow. In the above equation on the left we have acceleration

while on the right hand side of equation we have forces acting on the fluid.

In this case we may see the above simplified linear momentum equation as a

development of Newton second law of motion 𝑚 ∙ 𝑎 = 𝐹, density 𝜌 being used

instead of mass m, 𝑑𝑐

𝑑𝑡 being used instead of acceleration a and −∇𝑝 + 𝜇∇2𝑐

being used instead of force F. Individual terms in the above equation represent

- (1) local and convective acceleration,

- (2) pressure gradient and

- (3) viscous forces.

Simplification of viscous terms is already incorporated in the above equation.

In most cases of development and use of turbine machines the thickness of the

boundary layer is small compared to the overall characteristic dimension of

turbine machine. In such case, viscosity perpendicular to the element of

volume (y in equation below) is much more important than viscosity in the

two other directions (x and z in equation below)

𝜇∂2𝑐

∂𝑦2≫ 𝜇(

∂2𝑐

∂𝑥2+∂2𝑐

∂𝑧2) (48)

This assumption was already incorporated in linear momentum equation

above.

We can make further simplifications, from which we can derive Bernoulli

equation, potential flow equations etc. [Lakshminarayana, 1996].

43

5 Euler approach to fluid flow in turbine machinery

In this section we will discuss turbine machinery performance, pressure

characteristics, Euler equation, etc. We will assume, that the flow is ideal and

no energy is lost due to friction, turbulence decay etc. By considering the ideal

turbine machines we will for instance neglect any losses in guide vanes,

diffusor or spiral casing.

In this chapter, we will consider energy conversions in radial compressors,

radial turbines, axial comporessors and axial turbines. In the end we will

discuss local properties of the real flow in the turbine machinery runners.

5.1 Energy transfer and triangles of velocity In turbomachinery energy transfer takes place across one or more blade row

in a continuously flowing fluid. Energy is transferred to (pumps, compressors)

or from a fluid (turbines). During this process energy and angular momentum

of the fluid is changed.

5.1.1 Triangles of velocity in the runner Velocities of the flow in turbine machines we will denote with the following

symbols and indexes:

- c is absolute velocity of the flow in the stationary absolute coordinate

system,

- ca is axial velocity of the flow in the direction of the axis of the turbine

machine in the stationary absolute coordinate system,

- cr is radial velocity of the flow in the direction of the radius vector in the

stationary absolute coordinate system,

- u is circumferential velocity of the runner in the stationary absolute

coordinate system,

- cu is projection of absolute velocity onto the circumferential velocity of the

runner in the stationary absolute coordinate system,

- cm is meridional velocity of the flow and is vector sum of axial and radial

velocity in the stationary absolute coordinate system,

- w is relative velocity of the flow in relative rotating coordinate system.

For the meridional velocity 𝑐m of the flow we can write the following:

44

- for radial turbine machine 𝑐m ≈ 𝑐r,

- for axial turbine machine 𝑐m ≈ 𝑐a and

- for diagonal turbine machine 𝑐m ≈ √𝑐a2 + 𝑐r

2 .

Meridional velocity cm is a measure of the volume flow rate of fluid, therefore

it is for instance comprised almost entirely on the radial velocity for the radial

machine. For meridional velocity and volume flow rate we can write the

following equation

�̇� = 𝑐m 𝑆 . (49)

Here S is a cross section of the flow channel of the turbine machine in the

location where the meridional velocity is measured. For the circumferential

velocity we write the basic equation of physics, here 𝜔 is rotational frequency

and r radius, where circumferential speed is determined 𝑢 = 𝜔𝑟. For the

relation between absolute, relative and circumferential speed we can write the

following equation (50), which is the basic kinematic equation of the fluid flow

inside turbine machinery

𝑐 = �⃗⃗⃗� + �⃗⃗� . (50)

Absolute velocity of the flow 𝑐 is vector sum of relative velocity of the flow �⃗⃗⃗�

and circumferential velocity of the runner �⃗⃗�. With angle we will later denote

angles of the absolute flow and with the angle we will denote angles of

relative fluid flow (also angle of blades for best efficiency point). For the

indexes we will use the notation from Figure below. That means that entrance

to the runner will be denoted by index 1 and exit with index 2. Other authors

may use different notation. For instance standard about acceptance tests for

water turbine and pump models [IEC 600193, 1999] uses index 1 for high

pressure part (for turbine inlet, for compressors exit) and index 2 for low

pressure part (for turbine exit, for compressors inlet). Sometimes also indexes

0 and 3 are used, denoting flow conditions just before the runner (index 0)

and 3 just outside the runner.

45

Fig. 13: Triangles of velocity for a cascade. Index 1 relates to entrance to the runner and index 2 to the exit.

5.2 Enthalpy and pressure changes in turbine machinery In this subsection we will show enthalpy changes in both axial and radial

compressors and turbines.

5.2.1 Enthalpy and pressure rise in radial compressor Radial compressor is a turbine machine, in which fluid medium flows in radial

or in axial direction and exits in radial direction. They are also called

centrifugal compressors. They achieve relatively high pressure rise in a single

stage. Further stages can be added in series if a higher pressure is required.

For instance, compressors of aircraft engines feature more than 10 stages. A

three stage radial compressor is shown in Figure below.

46

Fig. 14: Radial air compressor of producer Man with three stages. Each

runner stage is followed by a radial difussor. Each runner stage has

thinner flow channels; this is because the air is compressible.

Succesive stages have slightly smaller inlet diameter. Last stage (on

the left) has larger exit diameter for high exit speed and higher

pressure, also diffuser is longer.

Mechanical work, supplied to the runner by the turbine shaft, is converted into

stagnation increase of pressure, angular momentum and enthalpy. Radial

compressors have usually much higher pressure rise than axial compressors

for the reasons which we will discuss later. Let's describe flow properties

inside the compressor shown in Fig. below.

At the entrance to the runner with inducer, flow direction is mostly oriented

axially. At this point, the flow enters the inducer. The inducer is build as the

first part of compressor runner and extends to the point, where the flow starts

to flow predominanty in radial direction. Some runners have inducer only on

for instance every second blade and not all compressors have an inducer.

Mechanical work is transferred from the internal combustion engine or

electric motor through shaft on the compressor blades. This work is converted

into angular momentum, stagnation pressure, head, and enthalpy rise.

Throughout the compressor runner blade passage these variables gradually

rise as shown in Fig. below (left). Runners without inducer are noisy because

flow separation occurs, causing turbulent mixing and vortices generation near

the leading edge.

In the runner, the static enthalpy, total enthalpy and pressure gradually rise.

This is because work is transferred from the runner to the fluid. Tangential

velocity of the flow is increased. The reader should remember, that in the

introduction we mentioned, that in turbine machines, energy transforms takes

47

place through changes of velocity. Meridional velocity (a vector sum of axial

and radial velocity, both contributing to the volume flow rate) depends on the

cross sections changes, but does not change much. This is because continuity

of mass flow rate applies. Rapid changes of velocity are also not desirable

because we want to prevent transverse pressure gradients, leading to flow

separation and vortices generation. Cross sections of flow channels in turbine

machinery therefore do not change much and also not suddenly.

At the exit from the runner, the flow has substantial amount of the kinetic

energy in the form of tangential velocity. Much less kinetic energy is related to

the radial, axial or meridional velocity.

In the difusser, which is usually designed as a stator with a cascade of stator

vanes, but may also be vaneless radial diffuser, the flow is decelerated in

tangential direction. Therefore, in the diffuser both static enthalpy and static

pressure rise. Stagnation enthalpy does not rise, because no work is done in

the difusser (contrary to the runner).

In the volute casing or spiral casing, the flow is further decelerated, while static

enthalpy rises further. The stagnation enthalpy does not change. The most

important task of volute casing is to direct the flow from the circumference of

the runner to the flange and pressure piping, if the compresor delivers the

compressed fluid into the pipe. Many applications exist, where there is no

need to pump the fluid in the pipe, instead the fluid is pumped in the volute.

48

Fig. 15: Enthalpy and stagnation enthalpy rise in runner, diffusor and

volute casing of centrifugal compressor. Shown is the runner with

inducer.

5.2.2 Entalpy and pressure reduction in radial turbine The opposite process as described in subsection above is happening in the

radial turbine. Among them, we will consider Francis water turbine. Francis

turbine is water turbine and the water as a medium is not compressible.

In the Francis turbine, water flows from the upper reservoir through the

pressure penstock to the turbine. In the upper reservoir, the water has

potential energy. At the end of penstock, the potential energy is transformed

to pressure energy. The water at the end of the penstock (end of the pressure

penstock and beginning of turbine is a turbine valve for Pelton and Francis

turbines) flows into spiral casing, stay vanes and guide vanes, where pressure

energy from the penstock is transferred into tangential velocity. At the

entrance to the runner (at the exit from guide vanes) the radial velocity is

comparably low to conform to the countinuity equation.

49

Fig. 16: Enthalpy and stagnation enthalpy decrease in runner, diffusor and

volute casing of centrifugal turbine.

The high tangential velocity is in the runner reduced to approximately zero

tangential velocity. Thus, at the exit from the Francis runner, the only velocity

that the water posess, is axial velocity. This is required to empty the runner

and allow influx of new water and to satisfy the continuity equation. Such

situation is however only present in the best efficiency point. Away from this

point, exiting flow posesses various amounts of tangentional velocity, thus

lowering the efficiency.

Fig. 17: Runners of Francis turbines. Left runner is for high heads and right

runner for low heads. Runner for high heads have longer blades to

efficiently convert the available tangential velocity into shaft

torque. They also have more runner blades to guide the flow better.

Runners for low heads usually have high blades for high volume

flow rate.

Francis turbines, which have high heads, feature high tangential velocities at

the entrance to the runner. Such Francis runners have a large number of long

50

blades to be able to efficiently transform all available tangential water velocity

into mechanical shaft torque.

After the runner, the fluid flows in the difussor or draft tube for water turbines.

In the draft tube, water velocity is further reduced. We may apply Bernoulli

equation for the lower reservoir (end of draft tube) and exit from the runner

(beginning of the draft tube). The reduction of velocity in the draft tube causes

pressure reduction at the low pressure side of the runner. Thus, reaction type

water turbines are able to fully make use of the water energy. This is however

not the case for impulse turbines like Pelton turbine.

5.2.3 Enthalpy and pressure rise in axial compressor Enthalpy rise in axial compressor follows similar principles as in the

centrifugal compressor. The main difference is that the exit radius is

approximately the same as the entrance radius. In the axial compressor fluid

flows in axial direction and at the exit from the compressor also in axial

direction. Cross section of multi stage axial compressor with cover open is

shown in Fig. below.

Fig. 18: Siemens axial compressor with 11 stages for industrial use. First stages are larger and last smaller stagess because of the compression of air. In all stages, runner blades are followed by stator blades.

At the entrance to the runner the fluid flow is in axial direction.

In the runner, the static enthalpy, total enthalpy and pressure gradually rise,

similar to the case in radial compressor. Here the increase is in general

smaller than in radial compressor, however it depends also much on the

rotational speed. Flow channel cross section gently decrease due to the

compression of fluid in the runner and also later in the diffusor.

51

At the exit from the runner, the flow enters the diffusor. Here flow has

substantial amount of the tangential kinetic energy, while axial kinetic energy

is such as required to satisfy continuity equation.

In the diffusor (stator), the tangential kinetic energy is transferred to pressure

rise. Here no work is done to the fluid, but enthalpy is increased, while

stagnation enthalpy stays the same. Also, static pressure is increased, total

pressure does not increase.

Axial compressors do not require spiral casings.

Fig. 19: Enthalpy and stagnation enthalpy rise in runner, diffusor and volute casing of four stages axial compressor. Only two stages are shown on the right, but the process continues. The inlet guide vane produces a weak tangential flow at the entrance to the first runner stage.

5.2.4 Enthalpy and pressure reduction in axial turbine In an axial turbine, water at high pressure (for instance bulb turbine) or gas at

high pressure and temperature (gas or steam turbine) flows onto stationary

vanes and rotating runner blades. In water turbines, stationary blades are

called wicked gates and in gas turbines nozzles. The axial steam turbine is

shown in Fig. below. In the water bulb turbine, the water flows through the

pressure channel onto the wicket gate.

In the following we will follow the flow in a water bulb turbine.

52

Fig. 20: Axial steam turbine Siemens SST 800 for an output range of up to

250 MW, n = 3000 /min. Consecutive stages are larger, because

steam expands (pressure after each stage is reduced). First stages

have shrouded rotors. All stages are attached to the same shaft and

rotate at the same rotational speed.

In the wicket gate, the water gets tangential direction of the flow. The more

head (pressure) the water turbine must recover, the wicked gate blades turn

the flow in the tangential direction. Such turbines, intended to recover higher

heads, also have longer wicked gate blades and higher number of blades. In

the axial direction, the flow does not accelerate or decelerate much inside

wicked gate. The stagnation enthalpy here does not change, but enthalpy and

pressure descrease because of increase of velocity in tangential direction.

The flow then enters the runner (rotor for water turbines is called runner).

Inside the runner the energy transfer is performed. The energy of the fluid is

transferred trough the runner blades to the shaft and to electric generator.

Here head, static and stagnation enthalpy decrease. The rotation of the fluid in

the form of tangential velocity is in the optimum operating point fully

removed and at the exit from runner the fluid does not have any tangential

velocity. Axial velocity of the flow does not change in the runner. In water

turbines the cross section of the flow channel does not expand when enthalpy

and pressure decrease, while this is not the case with gas and steam turbines.

53

Fig. 21: Enthalpy and stagnation enthalpy changes in wicket gate and

runner of bulb water turbine.

Situation is similar in gas and steam turbines. In steam turbines, stator blades

are usually called nozzles. The temperature and pressure decrease, therefore

the flow channel cross section gradually increase.

5.3 Torque on the blades of the turbine machine runner The turbomachinery runner of centrifugal compressor is schematically shown

in Fig. below. Using the enclosing of the blade (greyed part) the control

volume approach is applied. Both upper and lower surfaces are axisymmetric

and we say that in our idealized approach no mass, momentum or energy

transfer takes place there (I- inner surface and O-outer surface).

The inlet velocity axial component ca and tangential component ct form a

vector of velocity c1.

The inlet and outlet surfaces are away from the runner. The reason of doing so

is to ensure that all variables are indeed axissymetric and uniform along the

runner. Other variables are also indicated on the Fig. below (index 1

corresponds to inlet and index 2 to outlet).

54

Fig. 22: Energy and momentum transfer in turbomachinery compressor

runner.

The energy transfer takes place through shaft work, which is due to

axisymetricity in the form of torque M. Input shaft power is transmitted to the

control volume as torque on the blade element enclosed within the control

volume. The runner blade exerts a tangential force Ft on the fluid. The runner

blade force then increases for this particular compressor the fluid angular

momentum. The ct2 is due to the action of the runner larger then ct1. The flow

passage in Fig. above acts like a diffusor and thus changes static and

stagnation properties of the flow across the runner.

55

Because of our previous assumption that in our idealized approach no mass,

momentum or energy transfer takes place across lower and upper control

volume surfaces. What is transmitted is the shaft torque through the blade

being submerged in the control volume. We therefore perform integration at

the inlet and outlet only (rings A and D). The continuity equation is

∬ 𝜌1𝑐1𝑟𝑖𝑛𝑔 𝐴

𝑑𝑆1 = ∬ 𝜌2𝑐2𝑟𝑖𝑛𝑔 𝐷

𝑑𝑆2 (51)

The angular momentum equation may be written based on previous equation.

The surface forces in the tangential direction on the control surfaces I and O

are very small and can be neglected. As we mentioned before in Eq. above,

surface and volume forces in the control volume drive the fluid in the turbine

machine. Volume forces like gravity do not contribute to the net torque.

Surface forces however contribute to the net torque. Surface forces are

composed of those perpendicular to the surface (pressure) and parallel with

the surface (shear). This translates equation, written for the control volume to

∬𝑟𝐹𝐵𝑑𝐴

𝑆

= ∬ (𝑟2𝑐𝑢2)

𝑟𝑖𝑛𝑔 𝐷

(𝜌2𝑐2𝑑𝑆2)

− ∬ (𝑟1𝑐𝑢1)

𝑟𝑖𝑛𝑔 𝐴

(𝜌1𝑐1𝑑𝑆1)

(52)

As before here blade force 𝐹𝐵 is force per unit area. The thickness of the

stream integration layer is assumed very small. We can therefore use the

assumption of uniform entry and exit velocity and thus the above equation

reduces to

𝑑𝑀 = 𝑟𝐹𝐵𝑑𝐴 = 𝑑�̇�(𝑟2𝑐𝑢2 − 𝑟1𝑐𝑢1) (53)

The differential torque 𝑑𝑀 on the left side of equation above 𝐹𝐵 is a surface

force per unit area, exerted by blades. The integration is sum of all moments of

all forces acting in the control volume, being in total to the shaft torque. �̇� is

the mass flow through the control volume. Right hand side of equation above

represents the change of angular momentum of the flow. In such a way we

have linked the shaft torque with the change of angular momentum of the

56

flow. If we multiply the above equation with angular frequency, we get shaft

power

−𝑑𝑃𝑠ℎ𝑎𝑓𝑡 = 𝜔(𝑑�̇�)(𝑟2𝑐𝑢2 − 𝑟1𝑐𝑢1) (54)

We are not concerned a lot with the sign of the shaft power. Usually the power

is positive, when the power is done by the fluid (turbines) and negative when

the power is given to the fluid (fans, compressors, pumps).

5.4 Euler equation for turbine machinery We may integrate the above equation and we get the Euler equation of turbine

machinery

−𝑃𝑠ℎ𝑎𝑓𝑡 = �̇�𝜔(𝑟2𝑐𝑢2 − 𝑟1𝑐𝑢1) . (55)

The above Euler equation is valid only for a two dimensional strip shown in

the Figure above. The equation above is valid for the cases, when the velocities

𝑐𝑢1 and 𝑐𝑢2 are constant across the entire inlet and outlet cross sections. This

is however usually not the case and we use averaged values or perform the

integration of the equation above.

For the axial turbine machine, both radii 𝑟1 and 𝑟2 are equal and the equation

above becomes

−𝑃𝑠ℎ𝑎𝑓𝑡 = �̇�𝑐(𝑐𝑢2 − 𝑐𝑢1) (56)

In the above equation we have used a known relation 𝑐 = 𝜔𝑟. For a fan,

compressor or pump the exit tangential velocity 𝑐𝑢2 is higher than inlet

velocity 𝑐𝑢1. In this way the axial turbine machine (fan, compressor or pump)

gives power to the fluid. The situation is reversed for an axial turbine, here

exit tangential velocity 𝑐𝑢2 is lower than inlet velocity 𝑐𝑢1.

Same logic applies also for radial turbines, fans, compressors and pumps. For a

centrifugal machine we have

−𝑃𝑠ℎ𝑎𝑓𝑡 = �̇�(𝑢2𝑐𝑢2 − 𝑢1𝑐𝑢1) (57)

𝑢1 and 𝑢2 are exit and inlet blade velocities. For a centrifugal machine 𝑢2>𝑢1,

therefore for the same change of tangential velocities 𝑐𝑢1 and 𝑐𝑢2 the

centrifugal machine has higher input and output shaft power. This results in

higher head or pressure drop or rise. Also, higher blade velocities result in

higher input and output shaft power. The change in angular momentum or

tangential velocity are directly proportional to the shaft power.

The energy equation, applied to the control volume from Figure above is

57

�̇� = 𝑃𝑠ℎ𝑎𝑓𝑡 + 𝑃𝑠ℎ𝑒𝑎𝑟 + �̇�(ℎ02 − ℎ01) (58)

If we consider that not heat is transferred through machine walls (adiabatic

process) and that 𝑃𝑠ℎ𝑒𝑎𝑟 = 0 we get

−𝑃𝑠ℎ𝑎𝑓𝑡 = �̇�(ℎ02 − ℎ01) (59)

This equation is valid for viscous, compressible flows and includes all losses

associated with viscous flow. Shear stresses due to shear forces of shear layers

in radial direction are neglected. If upper and lower control surfaces are

exactly the same as upper and lower walls of the turbine machine, where

velocity is zero 𝑐 = 0, the above equation is valid for all flows.

The shaft power input in fan, pump and compressor is directly related to the

change of total enthalpy of the fluid. Again, for the fan, compressor or pump,

ℎ02 > ℎ01, therefore shaft power is negative. The situation is refersed for a

turbine mode of operation. Equation above (for angular momentum) and

equation above (for energy), relate 𝑃𝑠ℎ𝑎𝑓𝑡 to the flow and thermodynamic

properties. Both give for general turbine machine handling liquids and

compressible fluids

−𝑃𝑠ℎ𝑎𝑓𝑡

�̇�= (ℎ02 − ℎ01) = (𝑢2𝑐𝑢2 − 𝑢1𝑐𝑢1) (60)

for a liquid (pump, water turbine)or low pressure air handling (fan) turbine

machine we write

−𝑃𝑠ℎ𝑎𝑓𝑡

�̇�=1

𝜌(𝑝02 − 𝑝01) = 𝑔(ℎ2 − ℎ1) (61)

Here h is head or height of delivered fluid in the units of height. Again, it is

evident, that stagnation pressure or enthalpy rise or drop in a turbine machine

is directly related to the change of tangential velocity and blade velocity. This

Euler equation is the most basic equation of turbine machinery.

In the following we will discuss the flow properties in radial and axial

compressors. We will consider idealized situation and will therefore make few

assumptions that:

- blades are very thin,

- runner has infinite number of blades

- blades ideally guide the flow,

- no shadow of velocity exists behind the blade,

58

- the turbine machine operates at the nomila operating point of highest

efficiency (BEP, best efficiency point),

- no gap losses are present,

- the flow in the entire turbine machine is frictionless,

- etc.

5.5 Radial flow compressors and pumps Radial flow compressors and pumps are used in applications, where high

pressure is required. Radial compressors are simple, reliable, cheap and

therefore often preferred choice of compressors. On the other side, the radial

compressors have a rather high cross section area and are suited for aircraft

applications only for low to moderate power. Radial flow compressors are

widely used in industrial, automotive, rocket, air conditioning, irrigation

systems, power generation sytems, and other applications. Pressure ratios of

over 10 may be achieved in single stages, while rotational speed over 10000

rpm are usual, up to almost 200000 rpm in some applications.

Radial pumps are the most used type of pumps for industrial applications.

In centrifugal turbine machines, on the fluid in the runner act centrifugal,

Coriolis and tangential forces. These forces are the consequence of rotation

and change of radius of the element of the fluid, while rotation of the runner is

responsible for them.

In radial turbine machines fluid enter the machine in axial direction and exits

in radial direction. However, in much of radial runner designs, the flow

changes direction from axial to radial even before it enters the runner. Such

radial turbine machines have axial entrance to the turbine machine, but radial

entrance to the runner. Exit from both runner and turbine machine is radial.

5.5.1 Triangles of velocity in radial compressors and pumps To explore the principle of operation of radial turbine machinery, we must

consider Euler equation first (Eq. above). The Euler equation governs

enthalpy, pressure and temperature rise in the turbine machines.

Velocity triangles are shown in Fig. below for a radial turbine.

59

Fig. 23: Triangles of velocity in radial turbine in best efficiency point

Velocity triangles are shown in Fig. below for a radial compressor.

60

Fig. 24: Triangles of velocity in radial compressor in best efficiency point

In fully axial machine, 𝑢1 = 𝑢2 and the flow enters and exits the turbine

machine at the same radius. The total enthalpy rise is achieved in the runner

stage, when the fluid is accelerated in tangential direction and fluid's

tangential momentum increases. In addition to this, the centrifugal

compressor achieves part of the total enthalpy rise from centrifugal and

Coriolis forces due to change of radius. This offers radial compressors

additional increase of total enthalpy or pressure rise in comparison with axial

compressors, resulting in a widespread use of these machines.

The increased total enthalpy and pressure rise has also adverse effects. Among

them are formation of adverse pressure gradient, flow instabilities, flow

separation and secondary flow. Due to this and the need to turn the flow

direction in the case of multistage design, centrifugal compressors have in

general lower efficiency than axial compressors.

The flow in radial compressor is shown in the Fig. above. The figure above

considers two cases, one with the axial entrance to the runner and flow

inducer and the other with radial entrance to the runner. The role of the

61

inducer is to turn the flow from axial to radial direction. The inducer helps to

decrease flow separation near the leading edge, increase efficiency and

decrease noise. We will consider the case, when the flow after leaving the

inducer continues in purely radial direction. If the flow is in radial and axial

direction, such machines are called diagonal compressors.

At the exit from the runner, the flow has large velocity components in radial

and tangentional direction. The component in radial direction contributes to

the volume flow rate, while the component in the tangentional direction must

be slowed down to gain enthalpy and pressure rise. For this case, the flow is

diffused or slowed down. This is performed in radial direction in radial

diffusor or in axial diffusor, in both cases the flow must be slowed down

slowly to prevent flow separation and generation of turbulent vortices that

decrease efficiency of diffusors. Axial diffusors often start with a scroll or

spiral casing, extending into a pipe or axial diffusor within the piping.

In radial compressors the cross section of runner passages increases with

radius. This may lead to compressibility problems. To mitigate this, flow

channel cross section is decreased such that runner's thickness is smaller at

the exit (distance between both shrouds).

In many instances, especially for small pumps and compressors, diffusor or

scroll are omitted. In such case, the runner discharges directly in the volute. In

such case, stall and surge margins are greatly reduced, but the flow is not well

guided and much of the pressure rise (due to stagnation pressure loss) is lost

due to turbulent dissipation. However, pressure rise in the runner is not lost.

In the following we will examine the flow in the radial compressor. The flow

enters the inducer in position 1. The relative flow to the runner is described

by the vector �⃗⃗⃗�1 in the relative rotating coordinate system of the blade. The

relative velocity �⃗⃗⃗�1 is directed in the same direction as the blade leading edge

to prevent losses at the entrance to the runner. However, the blade rotates

with tangential velocity �⃗⃗�1 and the absolute velocity of the flow at the

entrance to the runner is according to the equation of the velocity triangle

equal to 𝑐1. The product 𝑢1𝑐𝑢1 is angular momentum that the flow has at the

entrance to the runner.

With purely radial entrance as shown in Fig. above, the product 𝑢1𝑐𝑢1 equals

zero. We do a very serious simplification here regarding how the flow

accelerates just before it enters the runner. Basically we allow that the flow

accelerated just before it enters the runner. This is not the case for instance

with the compressors with inlet guide vanes, which direct the flow to the

runner or with for instance Francis water turbines, which have a guide vane at

the entrance to the runner.

62

The runner of the centrifugal compressor accelerates the flow in the tangential

direction. In radial direction the flow can not be accelerated, because this

would violate the continuity equation. By giving the flow a component of

velocity in tangential direction, the runer increases the angular momentum of

the flow and gives energy to the fluid.

At the exit from the runner at position 2, the radius has increased to 𝑟2. The

velocity exits the runner at relative velocity vector of the flow in the relative

rotating coordinate system �⃗⃗⃗�2. The flow wants to continue the flow in the

direction of the blade, however in the relative coordinate system of the blade.

For the observer in the stationary coordinate system, the flow has a velocity

𝑐2, as it is the sum of velocities �⃗⃗⃗�2 and �⃗⃗�2.

The flow then enters the diffuser or volute. For a vaneless radial difussor or

volute, the position 2 is the final position, which needs discussion. But if the

compressor is equipped with a vaned diffusor, the vanes leading edges at

position 3 should be oriented in the direction of exit velocity 𝑐2 in absolute

coordinate system. The flow thus enters the vaned diffusor at such angle, that

no losses appear due to transition from the runner to the vaned difussor. The

diffusor directs the flow in the desired direction and increases pressure to use

all available velocity of the stagnation pressure.

5.5.2 Second form of Euler equation The Fig. below shows velocity triangles at the exit from the centrifugal runner.

The flow direction corresponds to fans, compressors and pumps. We want to

write second form of Euler equation without terms 𝑐𝑢1 and 𝑐𝑢2.

Fig. 25: Velocity triangle at the exit from the centrifugal runner, used to

write second form of Euler equation

The Euler equation can be re-written using the cosinus theorem (law of

cosines), written for the case of Fig. above

𝑤22 = 𝑐2

2 + 𝑢22 − 2𝑢2𝑐2 cos(𝛼2) = 𝑐2

2 + 𝑢22 − 2𝑢2𝑐𝑢2 (62)

With the use of Equation above, we get for the entrance

63

𝑢1𝑐𝑢1 =1

2(𝑐12 + 𝑢1

2 −𝑤12) (63)

and for the exit

𝑢2𝑐𝑢2 =1

2(𝑐22 + 𝑢2

2 −𝑤22) (64)

and Euler equation can be rewritten in a so called first form of Euler equation

as

−𝑃𝑠ℎ𝑎𝑓𝑡

�̇�= (ℎ02 − ℎ01) = (𝑢2𝑐𝑢2 − 𝑢1𝑐𝑢1)

=1

2[(𝑐2

2 − 𝑐12) + (𝑢2

2 − 𝑢12) − (𝑤2

2 − 𝑤12)]

(65)

This form of Euler equation provides additional understanding of energy

transfer in the turbine machinery. We will consider the case of radial

compressor:

- The first term (𝑐22 − 𝑐1

2) corersponds to the increase (Eck, Ventilatoren,

2003) of kinetic energy. The pressure available from this term is at the exit

from the runner not readily available. According to the Bernoulli equation

can this velocity be slowed down and transferred to the pressure in

diffusors, spiral casings etc.

- The second term (𝑢22 − 𝑢1

2) corresponds to the increase of static pressure

(Eck, Ventilatoren, 2003) in the runner. It is important to stress this very

much, this is the most important term in the entire Euler equation, because

there are no losses connected with this term. This term is not available

with axial turbine machines (inlet and outlet radii being the same),

meaning that radial turbine machines are able to achieve higher pressure

increase then axial turbine machines.

- The third term includes relative velocity change. In the turbine machines

runner the flow is decelerated because of cross section increase and

therefore 𝑤2 < 𝑤1. This corresponds according to Bernoulli equation if we

assume flow without losses to static pressure increase of 𝜌

2(𝑤1

2 −𝑤22).

We can write the above Equation with enthalpies instead of stagnation

enthalpies and we get

64

(ℎ2 − ℎ1) =1

2[(𝑢2

2 − 𝑢12) − (𝑤2

2 −𝑤12)] (66)

As above, the part of the enthalpy (or pressure or temperature) rise is due to

change of radius (centrifugal effect, first term on the right) and part due to

change of relative velocity (reduction of velocity, second term on the right). In

comparison with radial compressors, axial compressors do not have the

centrifugal term

The Euler equation can be written for the case of compressor with radial inlet

as (we assume purely radial inlet without any tangential velocity or pre-swirl)

−𝑃𝑠ℎ𝑎𝑓𝑡

�̇�= 𝑢2𝑐𝑢2 (67)

This is because we assume that in the perpendicular velocity triangle at the

inlet the projection of velocity is 𝑐𝑢1 = 0. The first form of Euler equation

reads now

−𝑃𝑠ℎ𝑎𝑓𝑡

�̇�=1

2[𝑐22 + 𝑢2

2 −𝑤22] (68)

5.5.3 Reactivity For the characterisation of fans, compressors and pumps, it is important to

discuss, how high is the pressure immediately after the runner and how much

pressure can be gained from the transformation of velocity to pressure. The

answer is again provided in Eq. above. The last two terms ∆𝑝 =𝜌

2((𝑢2

2 − 𝑢12) −

(𝑤22 −𝑤1

2)) set the static pressure after the runner, also called gap presure. As

discussed above, the first term 𝜌

2(𝑐22 − 𝑐1

2) can be transformed to pressure if

the fluid flow velocity is decreased. Because transformation of velocity into

pressure is always related to significant losses, we want to minimise this term.

This means that we want to maximise the term R, which we call reactivity

𝑅 =∆𝑝𝑠𝑡𝑎𝑡∆𝑝𝑡𝑜𝑡𝑎𝑙

=∆𝑝

∆𝑝0 (69)

Reactivity R is therefore the ratio of pressure increase in the runner versus

total pressure increase.

65

We can further relate static pressure increase with reactivity in the followng

discussion. Static pressure increase is (we do not consider total velocity for

the static pressure increase):

∆𝑝

𝜌=1

2[(𝑢2

2 − 𝑢12) − (𝑤2

2 −𝑤12)] (70)

If we assume, that 𝑐𝑢1 = 0 (radial entrance to the radial runner), then the inlet

velocity triangle is rectangular

𝑤12 − 𝑢1

2 = 𝑐12 (71)

and

∆𝑝

𝜌=1

2[𝑢22 −𝑤2

2 + 𝑐12] (72)

we get the equation for reactivity

𝑅 =∆𝑝𝑠𝑡𝑎𝑡∆𝑝𝑡𝑜𝑡𝑎𝑙

=𝑢22 −𝑤2

2 + 𝑐12

2𝑢2𝑐𝑢2 . (73)

We make further simplification now and we assume that actual velocity may

be replaced by meridional velocity 𝑐1 = 𝑐1𝑚 = 𝑐2𝑚. It is true for axial turbine

machinery, but only approximate for a radial machine, in everyday's design of

radial fans however this is a valid assumption We get therefore

𝑅 =𝑢22 −𝑤2

2 + 𝑐2𝑚2

2𝑢2𝑐𝑢2=𝑢22 − (𝑢2 − 𝑐𝑢2)

2

2𝑢2𝑐𝑢2 (74)

We have used in the above equation

𝑤22 − 𝑐2𝑚

2 = (𝑢2 − 𝑐𝑢2)2

(75)

The equation above transforms to

𝑅 =−𝑐𝑢2

2 + 2𝑢2 𝑐𝑢22𝑢2𝑐𝑢2

= 1 −1

2

𝑐𝑢2𝑢2

(76)

We compare runners with the same circumferential speeds, that at the same

radius and same thickness deliver the same volume flow rate. Therefore, the

velocity 𝑐2𝑚 is constant. For different blade angles at the exit 𝛽2 from the

66

runner different velocity triangles are formed according to the Figure below.

For the presentation purposes we include the dimensionless pressure ratio

𝜓𝑡ℎ

𝜓𝑡ℎ =∆𝑝𝑡ℎ𝜌2𝑢22= 2

𝑐𝑢2𝑢2

(77)

and in the Figure below we include both pressure ration 𝜓𝑡ℎ and static

pressure ratio 𝜓𝑠𝑡𝑎𝑡 𝑡ℎ over the velocity triangles.

The absolute value of static pressure ratio may be found from the product

below

𝜓𝑠𝑡𝑎𝑡 𝑡ℎ = 𝜓𝑡ℎ ∙ 𝑅 = 2(𝑐𝑢2𝑢2)

(

1−

(𝑐𝑢2𝑢2)

2

)

= 2(

𝑐𝑢2𝑢2) − (

𝑐𝑢2𝑢2)

2

= 2(𝑐𝑢2𝑢2) − (

𝑐𝑢2𝑢2)

2

(78)

𝜓𝑠𝑡𝑎𝑡 𝑡ℎ is parabola, that crosses the abscissa at 𝑐𝑢2 = 0 and 𝑐𝑢2 = 2𝑢2. The

highest value is achieved at 𝑐𝑢2 = 𝑢2 with the value 1. At the blade angle 90 °,

that is with radial blades, one half of the total pressure is static and the other

half is provided in the form of kinetic energy. At 𝑐𝑢2 = 2𝑢2 is static pressure is

0 and the total pressure the highest, thus offering the highest possible total

pressure, if the velocity can be transformed later in the static pressure. In this

case 𝑐𝑢2 = 2𝑢2 the runner has produced only kinetic energy. Such runners are

known as impulse runners (Slo.: Ger.: Gleichdruckräder). The runners, in

which pressure in the runner increases, are called reactive runners

(Überdruckräder). The most fans in everydays life use the reaction principle of

operation.

67

Fig. 26: Kinetic and static pressure for different blade angles

The flow conditions from the above picture can be achieved by:

- forward curved blades,

- radial blades and

- backward curved blades.

Figure below shows the above forms of blades. The inlet angle is for all types

in the Figure below the same, because the same inlet angle is required for a

selected volume flow rate and rotational frequency. Fans in everydays use all

three forms of curvature of blades.

The reactivity is a very important parameter of turbine machinery design.

Nevertheless reactivity is related to the internal operation of a turbine

machine, that is for the operator not important, with other words, it is an

internal matter of turbine machine developer. For the operator of a turbine

machine, the reactivity is of little interest, because he is only concerned about

overall performance of a turbine machine.

68

What is however important for the end user in relation to reactivits, is related

to the cross section area of outlet. Some fans and pumps deliver very high

volume flow rates. If such machines deliver the flow at very high velocities, it

is difficicult for a user to use very large cross sections, allowing for gradual

decrease of velocity.

We may consider a fan that sucks air from an infinite space and releases it in

the pipe or channel of selected cross section. In this case, the after the fan

measured stagnation pressure is the total pressure difference and the

5.5.4 Radial runner characteristics The pressure characteristics in relation to for the operation of a turbine

machine. The Fig. below shows the effect of backward, radial and forward

curved blades. By using the geometric relation we want to link the velocity

projection on tangential velocity 𝑐𝑢2, velocity in meridional direction 𝑐𝑚2 (to

be later related to volume flow rate) and blade angle 𝛽2 using equation

𝑐𝑚2

𝑢2 − 𝑐𝑢2= tan𝛽2 (79)

from the above equation follows

𝑐𝑢2 = 𝑢2 −𝑐𝑚2tan𝛽2

(80)

text

∆𝑝0𝜌= 𝑢2𝑐𝑢2 = 𝑢2 (𝑢2 − 𝑐𝑚2

1

tan𝛽2) (81)

By using the continuity equation for the volume flow rate, the meridional

velocity, being the same as radial velocity for purely radial machines, is at

constant rotational frequency proportional to volume flow rate

𝑐𝑚2 =�̇�

𝜋𝐷2𝑏 . (82)

For the pressure we get from first form of Euler equation for the case of radial

inlet 𝑢1𝑐𝑢1 = 0

∆𝑝0𝜌= 𝑢2𝑐𝑢2 = 𝑢2 (𝑢2 −

�̇�

𝜋𝐷2𝑏∙

1

tan(𝛽2)) (83)

69

With the increase of angle of relative velocity 𝛽2 at constant tangential velocity

𝑢2 the absolute 𝑐2 and relative 𝑤2 velocity of the flow are increased. This

changes theoretical characteristics of the turbine machine according to the

modified Euler equation

∆𝑝0𝜌= 𝑢2

2 (1 −�̇�

𝜋𝐷2𝑏𝑢2cot(𝛽2)) = 𝑢2

2 − 𝑢2𝑘2�̇� (84)

The relation ∆𝑝0

𝜌= 𝑓(�̇�) results in a straight line with the slope related to the

blade angle 𝛽2:

- with the forvard curved blades the total pressure increases with the

volume flow rate,

- with radial blades the total pressure remains constant and

- with backward curved blades the total pressure decreases with the

volume flow rate.

The relation is shown in Fig. below.

70

Fig. 27: Radial flow compressor and it's velocity triangles

5.5.5 Radial runner power and torque We can write the above equation in terms of power instead of specific power,

enthalpy or pressure

𝑃 = ∆𝑝0 ∙ �̇� (85)

here ∆𝑝0 is total or stagnation pressure rise across the centrifugal

compressor. The theoretical power of the centrifugal turbine machine is

𝑃 = 𝜌�̇� (𝑢22 − �̇� ∙

𝑢2𝜋𝐷2𝑏2 tan(𝛽2)

) . (86)

The equation above results in the required power consumed by the centrifugal

compressor according to the type of blades. The power of the centrifugal

compressor according to the type of blades is shown in the Figure above. The

power:

- increases as a parabola with volume flow rate for forward curved blades

(above the line of radial blades),

- increases a line with flow rate for radial blades and

- inreases as a parabola with volume flow rate for backward curved blades

(below the line of radial blades).

71

Because of equation 𝑀 = 𝑃 ∙ 𝜔 the torque characteristics features same

behavior as pressure curves.

5.5.6 Radial runner static pressure In the section above we have discussed static and total pressure increase in

relation to the runner blades angle. We have set constant flow rate and

meridional velocity.

Now we want to derive the equation for the variation of static pressure with

regard to the volume flow rate. Static pressure increase is of high importance

as dynamic pressure is difficult to transform to pressure without turbulent

losses.

For this, we revert to second form of Euler Equation above

∆𝑝

𝜌=1

2[𝑢22 −𝑤2

2 + 𝑐12] (87)

and assume 𝑐1 = 𝑐2𝑚

∆𝑝

𝜌=1

2[𝑢22 −𝑤2

2 + 𝑐𝑚22 ] (88)

and also

𝑐𝑚2 = 𝑤2 sin𝛽2 (89)

to get

∆𝑝

𝜌=1

2(𝑢2

2 − 𝑐𝑚22 (

1

tan2 𝛽2)) =

1

2(𝑢2

2 −�̇�2

𝜋2𝑑22𝑏22 tan2 𝛽2

) . (90)

The function ∆𝑝

𝜌= 𝑓(�̇�) is a parabola. Because of the function tan2 𝛽2 there are

no difefrencies between forward and backward curved blades. For radial

blades with 𝛽2 = 90 ° the ∆𝑝

𝜌 is equal

1

2𝑢22. At zero flow rate the static pressure

is one half of total pressure.

5.5.7 Radial runner real pressure characteristics The power consumption and pressure or enthalpy rise in the Figure above is

only theoretical. The combined result of most important sources of losses

mentioned effects is shown in the Figure below with regard to the theoretical

pressure characteristics:

72

- A: Losses occur because flow does not follow exactly the runner blades

curvature and angle. This is a consequence of finite number of blades.

Irerspectible of the blade angle 𝛽2 the projetion 𝑐𝑢2 will be smaller,

reducing the teoretically achiavable pressure rise of the runner. One can

not necessarily consider this as a loss of energy, because the energy is not

provided by the runner

- B: Losses because of friction in the runner, these are proportional to the

square of velocity (∝ 𝑐2)

- C: Impact losses (Slo.: udarne izgube) from the impact of the flow to the

blades at an non-ideal angle. At the volume flow rate, higher that the

nominal (optimal) the triangles of velocity change and relative velicity

angles β are not in the direction of the blade (higher or lower). The

consequences are impact of the flow to the blades walls, increase of

stagnation pressure, vortices, separation of the boundary layer etc. Impact

losses are present in the runner and alsi in the stator

- D: Volumetric losses (also called gap losses, Spaltverluste) are a

consequence of fluid flow past the runner between the wall and the runner

in the direction of the pressure gradient, for pumps and fans the volume

flow rate decreases and operating point also decreases.

In addition pressure or enthalpy decrease from theoretical considerations is a

consequence of:

- change of direction at the inlet to the radial runner from axial into radial

direction (∝ 𝑐2),

- friction losses in guide vanes, spiral casing and diffusor (∝ 𝑐2),

- non ideal inflow (impact losses) to the guide vane or difussor, etc.

73

Fig. 28: Influence of finite number of blades, friction and non ideal inflow in the runner, guide vane or difussor

5.6 Axial flow ventilators, fans, compresors and pumps Like a centrifugal turbine machinery, also axial turbine machinery got it's

name from the prevailing direction of the flow. In the axial turbine machinery,

the flow direction is in the axis of rotation. For this, the axial turbine machine

consists of a hub, on which blades are attached. Ideally, all fluid elements

receive same specific energy, regardless where on the radius they are.

Often the axial turbine machinery is enclosed in a duct. Implementation of

axial turbine machine in such cases is simple, as such machine forms only a

part of the duct.

Axial turbine machines are widely used for ventilation, propulsion and power

generation. For ventilation, they are used whenever low pressure increase and

large volume flow rates are required. The axial compressors are the preferred

choice for aviation applications, because they have lower frontal cross section

and lower drag. Also, they are better from the viewpoint of flow

characteristics. Real fluid effects in centrifugal compressors are much more

pronounced. On the other hand, the advantage of centrifugal compressor is it's

simplicity. This is sometimes preffered for industrial applications, where

reliability is more important than high efficiency. Axial water turbines are

widely used for water power generation for low heads and wind turbines are

used as a source of green energy.

74

Installation in ducts also dictates the use of a stator, because vortices in the

duct are in a large part converted into heat. The stator directs the flow in the

axial direction and by the same time enabling increase in pressure.

For the purpose of presentation, we often cut the blades of both runner and

stator and represent them in a plane as a runner and stator cascade (see

Figure above). A cascade is an infinite series of runner and stator blades. The

cascade is set for a selected radius, as angles of runner and stator blades

change with radius. Flow through cascades has been in the past researched a

lot.

In the figure below we write triangles of velocity at the inlet and trailing edge

of blades of axial cascade. To write triangles of velocity, we follow similar

principles as for centrifugal machines.

Fans in everydays use always have only a single stage, while compressors may

have several stages. A stage is comprised of a runner (rotating part) and stator

(stationary part).

The purpose of inlet guide vane is to direct the flow smoothly onto the runner.

The axial runner is sensitive to changes of incidence angle, thus use of inlet

guide vane may help. Inlet guide vanes also may prevent ingestion of debris

and break large turbulent structures, present in the atmosphere.

Fig. 29: Axial flow compressor and it's velocity triangles.

The triangles of velocity of a axial turbine cascade are shown in Fig. below.

75

Fig. 30: Axial flow turbine and it's velocity triangles

5.6.1 Euler equation for axial turbine machinery The Euler equation is in the simplest form and without considering the

predznak

𝑃𝑠ℎ𝑎𝑓𝑡 = �̇�(𝑢2𝑐𝑢2 − 𝑢1𝑐𝑢1) . (91)

For axial turbine machinery, we assume that flow enters and exits the runner

at the same radius, the tangential velocity therefore does not change. The

radial velocity we assume is 0. Therefore 𝑢1 = 𝑢2 = 𝑢 and Euler equation,

written for the pressure is

∆𝑝

𝜌= 𝑢(𝑐𝑢2 − 𝑐𝑢1) . (92)

For the axial inlet the 𝑐𝑢1 = 0 and Euler equation simplifies to

∆𝑝

𝜌= 𝑢𝑐𝑢2 . (93)

For axial fans and compressors we usualy consider four main cases:

- stator, followed by the runner,

- runner, folowed by the stator,

- stator followed by runner and another stator,

- stator, followed by a runner in a configuration, where both receive the

flow at an angle.

In the first case (stator, followed by the runner) the stator increases velocity of

the flow and creates a vortice before the runner. At the exit from the runner

76

the flow has only the axial velocity and no tangential velocity. This case looks

promising because velocity in the stator increases and losses in the stator are

low. However the losses in the runner are high and such configuration is not

very common. The pressure increase for this first case is

∆𝑝

𝜌= 𝑢𝑐𝑢1 . (94)

In the second case the runner gives rotation to the fluid and the stator

downstream of the runner directs the flow in the axial direction. This is the

most common case of axial turbine machinery. The pressure increase for this

second case is

∆𝑝

𝜌= 𝑢𝑐𝑢2 . (95)

In the third case the stator is provided in front and after the runner. The inlet

and exit velocities to and from the runner are mirrored. The absolute inlet

velocity and exit velocities are the same. This means that the runner produces

only static pressure. The pressure increase for this third case is

∆𝑝

𝜌= 2𝑢𝑐𝑢1 = 2𝑢𝑐𝑢2 . (96)

In the fourth case the stator is followed by a runner. In this case the relative

and absolute velocities have the same amplitude. They are directed in

mirrored directions. That means that both the stator and runner receive flow

at an angle. This means, that velocities are lower than in the above three cases.

This case is often applied when velocities in the flow channels are high and

friction losses and compressibility losses high. Due to non-axial inlet this case

is used in designs with several stages.

77

6 Similarity theory and dimensional analysis of turbine machinery

Similitude is a concept applicable to the testing of engineering models. A

model is said to have similitude with the real application if the two share

geometric similarity, kinematic similarity and dynamic similarity. Similarity

and similitude are interchangeable in this context. With the similarity theory,

students may gain a deep and for their future work in industry very useful

understanding of the operation of turbomachinery. Similarity theory is a

formal process where a group of variables that describe the selected physical

phenomena, is reduced or changed to a smaller number of dimensionless

groups of variables.

In practice, we often use terms model and prototype. For the hydraulic

machines, the model is a water turbine, which is being developed at the

institute, and the prototype is called the water turbine, which is installed in

the power plant. The prototype may alo be called application.

For conversion from model to prototype it it is necessary to provide hydraulic

similarity. Hydraulic similarity is guaranteed if the turbomachinery:

- has similar geometric dimensions (this similarity is also called geometric

similarity)

- both turbine machines have equal ratios of different forces acting

between the fluid and the components of the turbine machine (this similar

is called dynamic similarity) and

- both turbine machines have equal ratios of velocity components in each

of the corresponding points of the model and of the prototype (this

similarity is called kinematic similarity or similarity of movement, this also

means that the dimensional similarity is necessary for the existance of the

kinematic similarity), this also means that both machines have the same

velocity triangles.

Theory of similarity turbomachinery has several major areas of application:

- to predict the performance of prototype turbine machine from experiments

carried out on a model turbine machine, that is for changed size of the

turbine machine,

78

- to determinine the most suitable type of turbine machine based on

maximum efficiency, pressure, flow rate and rotational speed, and

- to predict the performance of turbomachinery for changed rotational speed

or fluid density density.

Similar turbomachines are two turbomachines, which differ only in size. This

means that the ratio of all local dimensions between the two turbine machines

is the same. For two similar turbine machines, all angles of the turbine blades

in respective points are the same. Also, fluid flow in both similar turboine

machines is directed in the same direction.

In this chapter we will focus on hydraulic machinery. For research and

application of hydraulic machinery (pumps and turbines), engineers use the

similarity theory with great success for decades. Basic principles of similarity

theory are well known for more than a century

There are several methods to select the dimensionless variables. Based on

logical considerations and using Bernoulli's equation dimensionless variables

n, d and and their exponents can be determined for flow, pressure and

hydraulic power (see also Table below). In the following we will first use a

simple approach (subsection 4.1) of selection of dimensionless numbers,

while later will in subsection 4.2 make a more fundamental approach. Both

will lead to the same selection of dimensionless numbers.

6.1 Simple approach to of selection of dimensionless numbers For rotational speed of the turbine machine we may make the following

engineering considerations:

- the volume flow rate is proportional to the rotational speed of the turbine

machine (for instance: for 2 x increase of rotational speed, the volume of

pumped fluid is 2 x larger, hence n �̇�),

- to establish a dependence between rotational speed and pressure, we

should first consider Bernouli equation, in the Bernoulli equation, pressure

is proportional to square of velocity, while velocity is proportional to

angular speed (according to equation of rotational speed, 𝑣 = 𝜔𝑟, hence n2

p),

- if we gain limit our simple approach to hydraulic machines, turbine

machine power is a product of volume flow rate and pressure, hence n3 P,

For dimension (size, diameter) we may make the following considerations:

- the volume of the element of turbine machine is proportional to third

power of dimension (for instance: for 2 x increase of characteristic

dimesion, the volume of pumped fluid is 8 x larger, hence d3 �̇�),

79

- to establish a dependence between dimension and pressure, we again use

Bernoulli equation, pressure is proportional to square of velocity, while

velocity is proportional to angular speed (according to equation of

rotational speed, 𝑣 = 𝜔𝑟 𝜔𝑑, hence d2 p).

- if we again limit the simple approach to hydraulic machines, turbine

machine power is a product of volume flow rate and pressure, hence d5 P,

For density, we make the following considerations:

- volume flow rate is not dependent on the density, the compressor runner

delivers the same volume for a single rotation, the mass flow rate however

increases with density

- pressure is linearly dependent on density, this can be seen from Bernoulli

equation, for instance ∆𝑝

𝜌𝛼𝑐2

The equations can be rewritten so that the specific speed v is dimensionless or

has a dimension (min-1), includes the gravitational acceleration g, etc. In this

way, we get the equation for the pressure coefficient (slo.: tlačno število) and

the discharge coefficient (slo.: pretočno število) which are non-dimensional

variables for volume flow rate and pressure. Pressure coefficient can be

written with the gravitational acceleration or withoutn it. If one uses

representation without gravitational acceleration, pressure number is not

dimensionless number and therefore has an unit. However, such a format is

useful only when comparing two similar turbine machines with each other.

Discharge coefficient (Equation below) can be written in two different ways

𝜑 =�̇�

𝑛 𝑑3 , 𝜑 =

�̇�

𝑛60 𝜋2

4 𝑑3

. (97)

We prefer the first version in the Equation above according to [IEC 00193].

Similarly, we can write the equation below for the pressure coefficient. Such

representation is dimensionless variable of the pressure. Pressure coefficient

can be written in three different ways

𝜓 =𝐻

𝑛2 𝑑2 , 𝜓 =

𝑔 𝐻

𝑛2 𝑑2 , 𝜓 =

𝑔 𝐻

(𝑛60)

2 𝜋2

2 𝑑2

. (98)

We may also call this coefficient a energy coefficient according to [IEC 00193].

Later in the chapter x.y. we will also provide an equation for the power

coefficient. From the above equations and follows (compare with the list of

engineering considerations above):

- the flow rate is proportional to rotational speed,

80

- the pressure is proportional to the square of the rotational speed,

- the hydraulic turbine power is proportional to the third power of the

rotational speed (hydraulic turbine power is equal to the product of pressure

and volume flow rate)

- the turbine flow rate is proportional to the third power of the diameter of

the turbine machine,

- the turbine pressure is proportional to the square of the diameter of the

turbine machine,

- the turbine power is proportional to the fifth power of the diameter of the

turbine machine (such exponentation is rare in the field of mechanical

engineering).

The above findings are sumarized in Table below.

Table xyz: Similarity theory in turbine machinery, exponents of variables n, d

and for flow rate, pressure and hydraulic power

variable flow rate pressure hydraulic power n n n2 n3 d d3 d2 d5

1 Dynamic and kinematic similarity conditions can not always be satisfied, but it

is possible to come close to these requirements. The greater the departure

from the application's operating conditions, the more difficult achieving

similarity is. The kinematic similarity and dynamic similarity for both model

and protype can not be satisfied because efficiency of two similar

turbomachines is not the same. We use use empirical equations for correcting

efficiency when going from a model to the prototype or vice versa. In the

development of a water turbine, the efficiency of the actual prototype is

always higher than the efficiency of the model. The difference in efficiency is

mainly the result of a relatively thin boundary layer on a prototype compared

to boundary layer on the model.

The ratios of different forces acting between the fluid and the components of

the turbine are determined by the various similarity numbers (in parentheses

are forces, characteristic for each similarity number):

- Reynolds number (inertia / viscosity),

- Euler's number (pressure / inertia),

- Thoma number (net positive suction head / specific hydraulic energy),

- Froude number (inertia / gravity) and

- Weber number (inertia / surface tension).

81

There are a lot of different models how the conversion of efficiency from the

model to the prototype is estimated. Among these are empirical models, based

on the measurement and the theoretical models. Frequently used is the model

represented in equation (16) [IEC 60193, 1999]

∆𝜂 = (1 − 𝜂m) 𝑉 (1 − (𝑅𝑒m𝑅𝑒p

)

𝛼

) . (99)

Equation (above) is an empirical equation for the conversion of efficiency

from a motel to a prototype, which was derived for radial water turbines

(among them most important Francis turbines). In equation (above) is Δη

difference between the efficiency of the model and prototype. ηm is the

efficiency of the model. 𝑉 is a share of losses, which can be estimated by the

theory of similarity of turbine machinery, 𝑅𝑒m is Reynolds number of the

model, 𝑅𝑒p is the Reynolds number of a prototype and α is empirical exponent.

To estimate losses, which can be estimated by the theory of similarity in

turbine machinery, 𝑉 is estimated to approximately 0.7 [Kjølle 2001] and the

coefficient α estimated to approximately 0.16 [Kjølle 2001]. It is usually

impossible to provide test conditions, which would satisfy all the different

similarity numbers at a time. Therefore, usually the geometric similarity is

satisfied and similarity number that has the greatest impact is considered for

conversion. For hydrauclic turbine machinery the similarity number with the

greatest impacti is the Reynolds number.

6.2 Use of dimensionless numbers Two similar turbine machines, may operate in similar operating points and

have in it same pressure and discharge coefficients.

If we compare two similar turbine machines, we denote them as model and

prototype: 1 or m (model) and 2 or p (prototip). We can also denote with for

instance index 1 water turbine, rotating at rotational frequency n = 10 Hz and

with index 2 the same water turbine, rotating at rotational frequency

n = 11 Hz. In the case of comparison of both model and prototype we have

𝜑m =�̇�m

𝑛m 𝑑m3 = 𝜑p =

�̇�p

𝑛p 𝑑p3 (100)

and

𝜓m =𝑔 𝐻m

𝑛m2 𝑑m

2 = 𝜓p =𝑔 𝐻p

𝑛p2 𝑑p

2 . (101)

82

Models in Kolektor Turboinštitut have all outside diameter 𝑑m = 350 mm,

while prototypes have diameters up to 𝑑p = 8 m. Since water turbines can not

be tested at any diameter or diameter of the prototype, they are tested at a

selected diameter in the institute. The dimensions of the model determine the

diameter of the measuring station in which the model runner is installed, as

the measuring station can not be changed for each measured model

separately. Then the characteristics are converted to the diameter of the

prototype.

If the characteristics of a model water turbine are measured in dimensionless

form (this means that, for example, the discharge number φ and the pressure

number ψ are on the x and y axes), the characteristic for the model and the

prototype is the same. Also, for a dimensionless diagram, the hill diagram is

the same for the model and for the prototype.

Pressure and discharge coefficients are useful for comparing the operating

point of a turbine engine operating at two different speeds. The same turbine

machine is similar to itself, which is why it is applied to the theory of

similarity. We can write it down

𝜑1 = 𝜑2 , �̇�1𝑛1=�̇�2𝑛2

(102)

and

𝜓1 = 𝜓2 , 𝐻1

𝑛12 =

𝐻2

𝑛22 . (103)

In equations above, because d1 = d2, d can be deleted. In Equation (102) we

also delete gravitational acceleration g.

Pressure and discharge coefficients are also useful for comparing the

operating point of similar turbine machines operating at the same speeds. For

a flow number, we can write down

𝜑1 = 𝜑2 , �̇�1

𝑑13 =

�̇�2

𝑑23 . (104)

In the equation (102) n was deleted, because n1 = n2. For the pressure

coefficient we write

𝜓1 = 𝜓2 , 𝐻1

𝑑12 =

𝐻2

𝑑22 . (105)

83

If the turbine machine changes both the size and the rotational speed at the

same time, and if the turbine machines are similar, the Equations below can be

written for operation in similar operating points

𝜑1 = 𝜑2 , �̇�1

𝑛1 𝑑13 =

�̇�2

𝑛2 𝑑23 (106)

and

𝜓1 = 𝜓2 , 𝐻1

𝑛12 𝑑1

2 =𝐻2

𝑛22 𝑑2

2 . (107)

6.3 Fundamental approach to selection of dimensionless numbers We assume that we have the following variables and assume the next function

among variables

𝑓(𝜌, 𝑑, 𝑛, �̇�, 𝐻, 𝜇, 𝑃, 𝐾) = 0 . (108)

In the above equation (108) ρ is fluid density, d diameter, n rotational speed,

�̇� volume flow rate, H height, μ dynamic viscosity of water, P power in K bulk

modulus. In total we have in equation 108 in our case 8 variables.

Buckingham π theorem of dimensional analysis tells us [Buckingham, 1914],

that if we have 3 basic dimensions (mass, length, time), then we can set (8 -

3 = 5) exactly 5 non-dimensional numbers.

We therefore select ρ, d in n as the variables, that include 3 basic dimensions,

and combine them with the rest of 5 variables �̇�, 𝐻, 𝜇, 𝑃, 𝐾. Although we have

currently chosen and selected the specified variables, this is not the only

possible choice of variables, but it is beneficial because in this way we derive

the pressure and discharge coefficients, as we wrote at the beginning of the

chapter. Therefore, we can write down the following findings.

(a) If ρ, d and n is combined with μ, we write 𝜋1 = 𝜇𝑎𝜌𝑏𝑑𝑐𝑛𝑑. This has a

solution 𝜋1 =𝜌 𝑛 𝑑2

𝜇, being Reynolds number.

(b) If ρ, d and n is combined with K, we write 𝜋2 = 𝐾𝑎𝜌𝑏𝑑𝑐𝑛𝑑. This has a

solution 𝜋2 =𝜌 𝑛2 𝑑2

𝐾, being Mach number, the ratio of the peripheral velocity

and velocity of the sound, taking into account the relationship 𝑐sound = √𝐾

𝜌 .

84

(c) If ρ, d and n is combined with P, we write 𝜋3 = 𝑃𝑎𝜌𝑏𝑑𝑐𝑛𝑑. This has a

solution 𝜋3 =𝑃

𝜌 𝑛3 𝑑5= 𝜆, being power coefficient.

(č) If we combine ρ, d and n with �̇�, we write 𝜋4 = �̇�𝑎𝜌𝑏𝑑𝑐𝑛𝑑. This has a

solution 𝜋4 =�̇�

𝑛 𝑑3= 𝜑, being discharge coefficient.

(d) Če ρ, d in n kombiniramo s H, we write 𝜋5 = 𝐻𝑎𝜌𝑏𝑑𝑐𝑛𝑑. This has a solution

𝜋5 =𝐻

𝑛2 𝑑2= 𝜓, being pressure coefficient.

In this way, we also reduced the number of variables, on which the individual

dimensionless number depends. For example,

𝜑 = 𝑓′(𝑅𝑒,𝑀, 𝜆, 𝜓) (109)

and

𝜓 = 𝑓′′(𝑅𝑒,𝑀, 𝜆, 𝜑) . (110)

In a similar way it is also possible to derive a dimensionless number specific

speed of ns, which is used to classify water turbines on Pelton, Francis, Kaplan

and tubular turbines.

85

7 Water turbines

Production of electricity in hydroelectric power plants is the most commonly

used form of renewable energy. In 2010, it accounted for around 21 % of

global electricity production or 3000 TW h [Dixon and Hall, 2010]. The annual

increase in production in hydro power plants in recent years stands at around

3 %.

Fig. 31. Production of electric energy in hydro power plants in five largest producing countries [International Energy Statistics, 2015]

Electricity is worldwide produced in hydroelectric power plants in 150

countries; the Asia-Pacific region in 2010 generated 32 % of its electricity

from hydropower. Figure above shows the production of electricity from

hydropower plants in the five major producing countries in last 30 years.

China is the largest producer of over 800 TW h in 2012, which represents

around 17% of Chinese domestic electricity consumption [International

Energy Statistics, 2015]. The greatest potential for growth in the production of

86

electricity from hydroelectric power plants is in China, Latin America and

Africa.

The cost of electricity production in hydroelectric power plants is relatively

low, thereby hydropower is cost-effective source of renewable energy. The

average cost of electricity in large hydro power plants ranges from 3 cents to 5

cents per kilowatt hour. Hydropower is also a flexible source of electricity

production, since the electric power production can be during energy

production rapidly increased or decreased, whereby the water power plant

operation is changed. However, damming of the stream flow which is required

for dammed hydroelectric power plants, may disrupt the water flow of the

stream and can alter the local ecosystem. In some cases, construction of dams

and reservoirs include displacement of the population. When the hydro power

plant is built, it produces no direct waste and has a greatly reduced production

of the greenhouse gas carbon dioxide CO2 compared to fossil fuel power

plants.

Slovenia produced from hydropower approximately 1/3 of all energy

produced [HSE in obnovljivi viri energije v Sloveniji, 2010]. In 2014, which

was very rich with precipitation, the production of electricity in hydroelectric

power plants amounted to approximately 40% in Slovenia produced

electricity.

The largest producers of water turbines in the world are Andritz, Voith hydro,

Alstom power, General Electric, Mitsubishi, Hitachi, Wasserkraft Volk, Stellba,

ČKD, Hydrolink, Turab, Ossberger, FARAB, Gilkes, itd. Largest hydro power

plants in the world are shown in the Table below.

Table 1: List of largest hydro power plants in the world, all runners are of Francis type name state flow installed

power

/ MW

yearly

production

/ (TW h)

Three Gorges China Jangce 22500 98,1

Itaipu Paraguai and

Brasil

Parana 14000 98,3

Xiluodu China Jinsha 13860 57,1

Guri Venezuela Caroni 10200 53

Tucurui Brasil Tocantins 8370 41

Grand Coulee USA Columbia 6809 20

Xiangjiaba China Jinsha 6448 30,7

87

The biggest hydro power plant in Europe is Volgogradskaya, Russia with

2500 MW. The largest hydroelectric power plants in Slovenia are indicated in

the table below.

Table 2: The largest hydroelectric power plants in Slovenia

name flow installed

power

/ MW

yearly

production

/(GW h)

type of

water

turbine

Avče

(pumped

storage)

Soča 185 in turbine

regime

426 Francis

Zlatoličje Drava 126 577 Kaplan

Formin Drava 116 548 Kaplan

The most powerfull in Slovenia produced water turbine has installed power

375 MW, produced by Litostroj Power, installed in China.

7.1 Water turbine classification In the following we will overview different types of turbines: Pelton, Francis, Kaplan, tube/bulb and other kinds of turbines. Water turbines we classify with regard to the type of the turbine:

- Pelton, - Francis, - Kaplan, - tube/bulb and other turbines.

Hydroelectric power plants are classified by their operation : - run-of-the-river (slo. pretočne), - dammed/accumulation (slo. zajezne/akumulacijske), - pumped-storage (slo. črpalno-zajezne)

Fig. below shows run-of-the-river and accumulation water power plant HPP

Krško and HPP Moste.

88

Fig. 32: Run-of-the-river and accumulation hydro power plants; left: run-of-the-river HPP Krško [source: www.hse.si] right: accumulation HPP Moste [source: SEL d.o.o.]

7.2 Criteria for water turbine classification with respect to the specific speed (ns) Different kinds of turbines are used for different flow rates and heads. V učbeniku bomo za količino (predvsem) pretečene vode uporabljali skupni izraz pretok, čeprav se praviloma ta pretok nanaša na prostorninski tok vode. Besedo pretok na področju vodnih turbinskih strojev uporabljamo tudi zato, ker se ujema s splošno uporabljenimi izrazi, kot so npr. pretočni stroj, pretočno število, pretočna turbina itd. Specific speed ns is a dimensional and also dimensionless parameter used to evaluate the speed of turbine machines (Fig. below). Historically, the specific speed was defined as the rotational speed with which the water turbine should rotate to develop power of one horsepower while using head of 1 m and volume flow rate 1 m3/s. Later, this definition was later updated, but in different ways. With the aid of variable ns (specific speed) the turbines can be roughly classified into three different groups: Pelton, Francis and Kaplan turbines, with the order on appearance based on proportional increase of the specific speed. Pelton turbines cover the area of large heads and low volumetric flow rates, Francis turbines the area of medium heads and flow rates, and Kaplan turbines the area of low heads and large flow rates. The turbine's rotational frequency n, volumetric flow rate �̇� available head H

(height differenc between the upper and lower water level) are project

parameters, which allow the selection of the turbine type. Since there are

several different definitons of ns, let us provide the definition after [IEC 60193,

1999]

89

𝑛s =𝑛 √�̇�

𝐸34⁄=

𝑛 √�̇�

(𝑔 𝐻)34⁄ . (111)

In the Equation above ns is specific speed, E specific hydraulic energy of the machine, n rotational frequency, �̇� volumetric flow rate and H head (the height difference of water levels). The values of �̇�, H and n used for calculation should be the ones defining the point of maximum turbine efficiency (i.e. the expected most common values of these parameters). In accordance to the upper definition ns is a dimensionless parameter. Despite the standard ISO 60193 [IEC 60193, 1999], which requires the operating point of maximum efficiency to be used for calculation of ns, some manufacturers use the point of nominal or maximum power instead. Some definitions of the specific speed omit the gravitational acceleration since

it is practically constant anywhere on Earth. In this case, the definition is not

dimensionless and the calculated values vary depending on the units used.

The problem occurs with American and UK manufacturers, which use imperial

units such as gallons and feet. Also used is a similar form of equation above, in

Slovenia (Turboinštitut, Litostroj) the equation below is used, where the

rotational frequency must be input in / (min-1), while the head and the flow

rate are given in SI units (the operating point with the maximum effciency is

taken) [Krivchenko, 1993]

𝑛s =3.652 𝑛 √�̇�

(𝐻)34⁄

, 𝑛s =576 √𝜑

(𝜓)34⁄ . (112)

Specific speed ns of a turbine sets the turbine's shape in a way so that it is

independent of the turbine's size. is the flow number and the pressure

number. The unit at the left side of the equation above is [1/min], while the

right side is without a unit.

The specific speed parameter also alows that the turbine is resized with

respect to the base design with known properties. The specific speed is also

the main criterion for suitability of a particular installation location with the

turbine type.

According to Equation above, the cassification of turbines is as follows

(Turboinštitut, Litostroj) approximately:

- below ns = 70, Pelton turbines are used,

- from ns = 70 to ns = 350, Francis turbines are used,

- from ns = 350 to ns = 600, Kaplan turbines are used,

- above ns =600, bulb turbines are used

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The Figure below shows selection of turbine runners for different specific

speeds ns. The Figure below shows also different shapes of Francis runners,

that corresponds to indicates specific speeds ns.

Fig. 33: Selection of water turbines for different flow volume rates and heads depending on specific speed ns [adapted according to Krivchenko, 1993]

7.3 Pelton turbine Historically, Pelton turbines (Figure below) have evolved from water wheels.

A Pelton turbine (also known as the Pelton wheel) is an impulse (slo.

enakotlačna/impulzna) turbine with tangential water flow to the turbine

blades. The term impulse turbine means that the pressure in the turbine

casing is equal to the ambient pressure. Installation is vertical or horizontal.

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Fig. 34: Pelton turbine; left: Pelton turbine with open turbine casing [source: http://www.hydrolink.cz]; right: nozzle of the Pelton turbine with needle [source: http://www.canyonhydro.com]

A traditional Pelton turbine design is such that the rotor rotates with one half

of the velocity of the water jet. Water exits the rotor blades (also known as

buckets) with a very low velocity, so that the energy conversion efficiency is

maximized. In practice, the water jet velocity is always slightly higher so that

the water is removed from the rotor area. The peak of efficiency is narrower

as with Francis or Kaplan turbines [Dixon and Hall, 2010].

Pelton turbines are suitable for installation when the flow rate is low and the

head is large, i.e. from 50 m to 2000 m. For the operation of Pelton turbines, it

is not advised that the water level changes significantly. The reason for this is

that the speed of the water flow from the nozzle depends on the pressure or

the head of water. The rotational frequency of the runner is synchronous with

the electrical network, and the rotation speed of the runner is expected to be

only slightly larger than the velocity of the water jet.

Elements of Pelton turbines are shown in Figure below. At the end of the

penstock is turbine valve, later water flows into the distributor (slo.: razdelilni

cevovod). Water is ejected from the nozzles or injectors (Figure below) (slo.:

šoba). In the nozzle, the pressure energy is converted into velocity energy.

The water jet is directed tangentially onto the blades. Upon impact of the jet,

kinetic energy is transferred to the blade. For design it is important that the jet

is deflected back from the blade, but does not hit the next blade. The runner is

spinning, which is why the central part of blades is partly cut out (see Figure

below), forming a splitter (divider) structure which separates the buckets in

two symmetrical compartments. The larger the number of nozzles, the more

blades are exposed to the water jet simultaneously, resulting in larger power

of the Pelton turbine.

Turbine operation is regulated by moving the needle in the nozzle. The needle,

which is usually bulb shaped, is moved by the rod to which it is attached. The

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system can also include a deflector, which prevents pressure surges in case of

the rapid closing of the water flow through the turbine (e.g. due to emergency

shutdown). The deflector deflects the water jet for so long that the spear

completely closes the nozzle. There is a quantity regulation, meaning that the

quantity (flow rate) of water is changed. Such regulation is efficient starting

from very low turbine loads upwards (i.e. from 1/4 of the nominal load). For

this reason, Pelton turbines are used when the flow rate of water changes

significantly.

The blades can be manufactured as a single part together with the turbine disk

(blisk = blade + disk). This solution has been commonly used in recent years,

as nowadays rotors are mostly manufactured by CNC machines.

To close the water flow on the supplying pressure pipeline (penstock), a valve

is used, just like with other turbine types, mostly Francis water turbines.

Closing the water flow from the upper reservoir on the penstock, allows for a

relative quick shutdown of the turbine (load rejection) and also for turbine

maintenance or service.

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Fig. 35: Pelton water turbine schematics, here Pelton turbine with vertical axis and 6 nozzles is shown, 1: valve, 2: water distributor, 3: nozzle, 4: deflector, 5: runner, 6: shaft, 7: outflow, 8: lower water level, 9: generator, 10: turbine cover, 11: tailrace tunnel

Fig. 36: Runners of Pelton water turbines; left: old runner of Pelton turbine of PHHP Walchensee, Germany [vir: https://en.wikipedia.org]; right: runner details [z dovoljenjem: Andino d.o.o.]

Pelton turbines can have one nozzle, but they may have more, up to 6 [Kjølle,

2001]. Pelton turbines with horizontal axis have up to two shafts, Pelton water

turbines with vertical axis have 4-6 nozzles, if there is a need for greater

volume flow rate. The reason for this is the fact that with the horizontal axis,

with more than two nozzles water can not leave the space around the runner

soon enough.

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7.4 Francis water turbines A Francis turbine is a back-pressure/reactive (slo. nadtlačna) turbine of a

radial - axial design. It is used for medium flow rates and heads. Francis

turbine is shown in Figure below, while cross section of flow field for PHPP

Avče is shown in Figure below. Francis turbines have single regulation,

meaning that only guide (stay) vanes have an adjustable position for the

purpose of regulation, while the rotor blades are fixed. Francis turbines are

reactive turbines. This means that the water in the spiral casing and the guide

vanes increases it's circumferential velocity. Water with a large

circumferential velocity component then passes through the runner blades,

wherein the water circumferential velocity is reduced. In this way, the water

transfer energy and the angular momentum to the runner and a generator, as

it was described by the equation (above).

In some rare cases, Francis turbines have the rotational frequency control.

Such turbines are mostly pump storage water turbines. This means that the

rotational frequency can be varied, usually by a few % of the nominal

rotational frequency. In Slovenia, the only power plant with such regulation is

HE Avče (regulation of nominal rotational frequency from -2% to +4%).

Francis turbines are used for heads from 20 to 500 m. Typical diameters are

from 1 m to 10 m. Almost all Francis turbines are installed so that the axis of

rotation is vertical. In general, Francis water turbines are of horizontal or

vertical type, depending on the orientation of axis. Smaller Francis water

turbines have horizontal axis. They are easier to maintain, because the axial

bearings are only lightly loaded in comparison with vertical arrangement,

which also means that the cooling of the bearings is performed more easily.

Francis turbines have very high efficiency, often more than 95 % [Dixon and

Hall, 2010]. For these reasons, Francis turbines are the most commonly used

turbine type among the water turbines.

The main components of a Francis turbine are: (1) spiral casing, (2) fixed inlet

stay vanes, (3) guide vanes, (4) runner, (5) draft tube, (6) shaft, (7) bearings,

etc. The water turbines usually also include a generator, but correctly in this

case the whole system is called hydroaggregate. Most of these components are

also used in Kaplan turbines. In the following part of this chapter, individual

parts of a Francisos turbine will be discussed. Later (in chapter below) other

parts necessary for safe and reliable operation of hydroelectric power plants

will also be described.

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Fig. 37: Schematics of Francis water turbine

The spiral casing is installed around the turbine stay and guide vanes and

connected to it through by an entire length of perimeter. At the inlet, the spiral

casing is connected to the penstock or closing valve. Through the perimeter,

water flows onto the stay vanes and guide vanes and then in the turbine. The

spiral casing is designed so that the fluid velocity is constant in all transversal

segments of the aperture. For this reason, the diameter of the spiral casing is

gradually reduced away from the inlet. Water flows through the opening in the

stay vanes, guide vanes and continues later through the runner. Francis

turbines have spiral casings with circular cross-section of welded steel and

mostly molded in the concrete.

The water guiding part consists of stay vanes and guide vanes. The guide

vanes have a double function of converting the water pressure to

circumferential kinetic energy and directing the flow onto the turbine blades.

The guide vanes are usually distributed in two rows as fixed stay vanes and

adjustable guide vanes in the second row. Stay vanes are not adjustable, they

roughly guide water to the guide vanes and increase the strength of the

turbine (strength of the spiral casing) such that the high pressure in the

turbine casing can not to open the entire turbine. The guide vanes are

adjustable with their rotation. Guide vanes are rotated (moved) around a pivot

pin of the blade, which is also an integral part of the guide vane itself. By

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closing the flow of water on the runner of Francis water turbines, the volume

flow rate is increased or reduced and thus the turbine power is regulated. The

guide vanes are connected to a guide ring, which allows for all the vanes to be

rotated at the same time and by the same angle. The guide vanes and the rings

are rotated by hydraulic or servo motor propulsion. The guide vanes also

allow to fully stop the water flow onto the turbine rotor (during normal or

forced shutdown, maintenance etc.). The water supply to the runner can not

be completely shut off with the guide vanes due to gap, acting above and

below the guide vanes. Resulting volume flow rate through the gaps is too

small to allow for even a slow rotation of the Francis water turbine runner.

Fig. 38: PHPP Avče, cross section of flow tract, with water intake system and tailrace channel. From the figure the submergence of the turbine may be seen, implemented to prevent cavitation.

The gap is necessary for the rotation of the guide vanes. The water flow is shut

of with guide vanes for normal shutdown or emergency shutdown. During

repairs, dates are used to shut of the flow through the turbine.

The runner (note that the terms stator and rotor are usually used for the fixed

and moving part of a generator, while for the rotating part of the turbine we

use the term runner) rotates and converts the energy of water to the

mechanical energy of the shaft rotation. The rotor is mechanically linked to

the shaft, which is attached to the generator at the other end. The Francis

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runner has fixed blades, meaning that the Francis water turbine has single

regulation (regulation is only possible by rotation of guide vanes).

Fig. 39: Francis turbine runners, Left: Francis turbine runner, Three Gorges HPP, China [source: https://en.wikipedia.org]; right: PSHPP Avče runner - measurement of cavitation erosion with measurement hand, view of the runner from suction side [source: SENG d.o.o.]

The draft tube is the element installed below the runner with a function of

slowing the water flow and leading the water towards the tailrace tunnel (in

pumped storage power plants, the inlet-outlet tailrace tunnel). For the Francis

water turbine to convert all of the available water flow energy (according to

the Bernoulli equation water flow contains the energy according to the

pressure, kinetic and potential component), the water flow should slow down

in the draft tube and exit the Francis turbines with almost no kinetic energy.

The function of the draft tube is therefore to enable that all available pressure

energy is converted into useful work. The kinetic energy of the flow, which

leaves the water draft tube, is lost energy, but a well-made and properly sized

draft tube can reduce such losses to a minimum. In the case of Pelton turbines

this is not so, with Pelton water turbines some pressure is always lost. Pelton

runner must always be installed at some height above the lower water

reservoir. The installation height of Pelton runner above the lower water is

needed to enable the water from Pelton turbines to drain the turbine casing

and this presure is lost with Pelton turbines.

The other elements of hydroelectric power plants will be presented in chapter

below. At this point, let us mention only the shaft, generator and bearings. The

shaft is an element, linking the rotor to the generator. The bearings hold the

runner, the shaft and the generator in a horizontal and vertical direction and

enable rotation with minimal frictional losses. Normally, a turbine has at least

one thrust bearing (slo.: nosilni ležaj) (supports the turbine in the vertical

direction) and at least one guide bearing (slo.: vodilni ležaj).

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Fig. 40: HPP Bratsk, Russsia, 18x250 MW, the largest hydro power plant, where a Slovenian company performed acceptance tests, Kolektor Turboinštitut d.o.o. Left: transportation of the runner, [source: http://www.hydroworld.com]. Right: machinery hall of HPP Bratsk [source: Kolektor Turboinštitut d.o.o.].

Apart from electricity production, a Francis water turbine can also be used for

pumped storage power plants. In this case, we use the term pump storage

hydro power plant (PSHPP), pump storage turbine, pumping hydro power

plant or even pump turbine. The pump storage water turbine PSHPP Avče,

Slovenija, is shown in Figure below. In the pumping mode of operation the

turbine acts as a pump, pumping the water from the lower reservoir to the

upper reservoir. In the pumping mode, when a sufficient amount of cheap

electric energy is available, nuclear power plants operate in base load mode

(slo:. pasovno obratovanje), the generator operates as an electric motor. This

is mostly in the night time, when nuclear power plants produce most of the

electricity and the demand is low. By accumulating water, the lower and upper

accumulation serve as large sources of storing the unneeded electric energy.

This is one of several methods to temporarily store the surplus of electric

power for later use.

All water turbine runners, but especially the Francis pump storage turbine

runners, must be sufficiently submerged (slo.: potopitev). Therefore, for all

water turbines, the runner is installed at the lowest part of the flow tract.

Submergion in the case of pump storage turbine Avče is shown in Figure

above. High submergion must be provided for the runner to operate without

the occurrence of cavitation, in particular, this problem is pronounced during

the pumping mode of operation. Cavitation is a physical phenomenon in which

the water vapor bubbles occur when the surrounding pressure is lower than

the evaporation pressure of water. Cavitation can cause damage to the

mechanical parts with the cavitation erosion or through the increased

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vibrations of the water turbine machine. When the cavitation bubbles implode

near the surface of the runner, this may cause erosion of the surfaces of the

runner. Cavitation often also increases the vibrations of water turbine, which

leads to increased wear of mechanical parts.

Fig. 41: Building of PHPP Avče, lowering of the runner in the machinery hall shaft [source: SENG d.o.o.]

To prevent cavitation, the runner must be installed low enough below the

surface of the lower reservoir. With sufficient submersion of the turbine

during the operation of the water turbine machine, high enough energy is

achieved on the suction side of the runner. In Chapter below (cavitation in

water turbines) we will later write numbers NPSE and NPSH, which are called

the net positive suction energy and the net positive suction head. NPSE and

NPSH are the sum of two contributions from pressure and velocity

components. If the numbers NPSE and NPSH on the suction side and therefore

the submergence of the water turbine runner are large enough, the cavitation

is avoided. By submergence of the turbine high enough pressure on the

suction side of the runner is provided and the cavitation is prevented.

Cavitation does not occur in all operating points of Francis turbines. By

selecting the operating point, the operator can influence the occurrence of

cavitation, if the electricity market situation and the needs of the transmission

electricity grid permit so. For the prevention of adverse effects of cavitation

erosion and vibreations, in addition to the submergence of the Francis

turbines, appropriate measures for cavitation occurence mitigation are

applied. These are the control the Francis turbines with inverter (if provided)

and blowing of air through the hollow shaft to the suction cone is performed.

7.5 Kaplan water turbines A Kaplan turbine (Figure below) is a reaction water turbine with adjustable

rotor blades. It is a turbine with double regulation, as the angles of both guide

vanes and runner blades can be adjusted. Historically speaking the Kaplan

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turbine is the evolution of the Francis turbine for watercourses with low

heads and high flow rates. Kaplan turbines are normally used for heads

between 10 m and 50 m and for power of up to 200 MW. The nominal

efficiency exceeds 92 %, but can be lower in the case of very low heads and

small flow rates.

The inflow of water is carried out in the same way as with Francis turbines, i.e.

through the pressure pipeline (penstock) into the spiral casing (Kaplan

turbines because of the large size in most cases lack the turbine valve),

through the fixed stay vanes and adjustable guide vanes. Kaplan turbines for

high heads have spiral casing manufactured from steel, while those for low

heads have simplified spiral case made of concrete (Figure below). After the

stay and guide vanes, the water turns downwards, before reaching the rotor.

This means bouth the inflow and outflow to/from the runner are axial, while

the turbine as a whole has radial inflow and axial outflow (Figures below). The

runner blades have adjustable angles. Blade angle adjustment is performed

hydraulically, with hydraulic oil flowing through the center of the shaft. The

inflow of oil into the shaft is on the upper side above the generator cover. The

sealing of the oil system in the shaft must be well made to prevent oil leakages

into the river. Similarly to Francis turbines, the water exits the rotor into the

suction tube to the outlet.

The double regulation allows the operation of Kaplan turbines in a wide range

of operating points.

A special version of the Kaplan turbine is the propeller turbine, which has a

similar design, but with fixed runner blades. Propeller turbines have single

regulation with guide vanes, like Francis turbines. Due to the simpler design

and a higher rotational frequency, propeller turbines are used to replace older

Francis turbines installed in power plants with lower heads (up to

approximately 10 m). A larger rotational frequancy allows for a smaller,

lighter and cheaper generator. Higher rotational speed allows for lower

number of poles of the generator. Usually with small agregates of propeller

turbines, where water level changes are small, a multiplying gear mechanism

is used, further raising the rotation frequency of the generator shaft. An

example of such propeller turbine with multiplying gear in Slovenia is SHPP

Planina, where the muliplication ratio is 10x.

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Fig. 42: Schematics of Kaplan turbine; 1: spiral casing, 2: stay vanes, 3: guide vanes, 4: runner, 5: draft tube, 6: shaft, 7: flange separating turbine shaft and generator shaft, 8: guide vane ring, 9: hydraulic motor for rotation of guide vane ring, 10: guide/thrust bearing combination

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Fig. 43: Kaplan turbine; left: spiral casing of Kaplan turbine during annual servicing check, HPP Solkan; in the middle: view of the runner from the spiral casing, HE Solkan; right: old runner of HPP Plave I, seen are pivot pins of runner blades [source: SENG d.o.o.]

0

Fig. 44: Flow field of Kaplan turbine, example of HE Solkan

7.6 Tubular turbines The term tubular (slo.: cevna turbina) turbines denotes a group of several

turbine subtypes: bulb turbine (slo.: cevna turbina s hruško), pit turbine (slo.:

cevna turbina v jašku), S turbine and Saxo turbine. Tubular turbines are a

proper solution when the head is lower than 30 m and have in the recent

years almost completely replaced the low-head Kaplan turbines. Tube

turbines can operate reversibly in e.g. tidal power plants.

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Some sources and authors treat tube turbines as a variation of Kaplan

turbines, while the others consider them as an independent water turbine

type. In this textbook we will consider tubular turbines as a separyte type of

water turbines.

The cross-section of flow filed of the bulb tubular turbine is shown in Figure

below. Tubular turbines are appropriate choice of the water turbine where

there are no large fluctuations of the net head and discharge, and they are

often used as aggregates of biological minimum. Such aggregates exploit the

biological minimum of water discharge through a riverbed, while the majority

of the flow is diverted through the derivation channel or tunnel, that is away

from the riverbed. Another application of such aggregates is the biological

minimum discharge into the fish hatchery (slo.: ribje drstišče). In Slovenia, for

example. such hydro power plant is SHPP Vrhovo.

Fig. 45: Bulb turbine - cross section of flow field of the bulb turbine

Among the tubular turbines, we will describe more in details bulb turbine,

others will be only briefly discussed. Tubular turbines have in comparison

with Kaplan turbines two most important advantages:

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- because it is not required that the flow inside the tubular turbine to make

a turn, is the efficiency slightly higher in comparison with Kaplan turbines

and

- lower manufacturing and construction costs due to compact size of

tubular turbines, because deep digging and construction of deep pits is not

required (flow channel is horizontal), and because of suitability for very

low heads it is also not reqzured to have large flooding area because of

damming and upper reservoir.

Main drawbacks of tubular turbines are:

- in the bulb space is limited, therefore equipment in bulbs is of small size

and may be therefore less durable, life span shorter and servicing more

challenging and difficult and

- smaller tubular turbines must use multiplying gear mechanism to

increase rotational frequency of the generator shaft in relation to turbine

shaft.

7.6.1 Bulb turbine A tubular turbine with a bulb (slo.: cevna turbina s hruško) is an axial turbine

with a horizontal shaft and axial water inlet onto the runner. A tubular turbine

with a bulb is shown in Fig. below. It is equipped with a flat conical draft tube.

Bub turbines allow for a large flow rate and consequently large power even

for low heads. A direct drive generator is installed in the watertight bulb,

which is attached to the turbine's inlet stay vanes. The bulbous shape of the

generator casing gives the name to this particular turbine type.

Fig. 46: A tubular turbine with a bulb, [source: http://alstomenergy.gepower.com]

The difference between a Kaplan and a bulb turbine is in the inflow of water

onto the turbine. Kaplan tubines have a radial inflow of water, while the inflow

in bulb turbines is axial. Both types of turbines have an axial outflow. Due to

such installation the water flow direction does not change significantly,

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allowing for a good efficiency and compact size. The compact installation size

considerably lowers the costs of construcion works and allows for a flexible

installation.

The rotor of a bulb turbines has blades with adjustable angle, meaning that the

turbine regulation is double (regulation of guide vanes and turbine blades),

similar to the Kaplan turbine.

Bulb turbines in comparison with Kaplan and Francis turbines lack the spiral

casing and have a draft tube significantly different in shape from draft tubes of

Kaplan and Francis turbines.

7.6.2 Pit turbine Tubular pit turbine (slo. cevna turbina v jašku) design is similar to bulb

turbines, with a notable difference that the generator is installed in the shaft

within the flow tract. Tubular pit turbine is shown in Figure below. In the case

of smaller power plamts it is impossible to have the generator enclosed in a

watertight bulb within the flow, because the space is limited. The generator is

usually connected to the turbine shaft through a multiplying gear mechanism,

which is installed in the turbine shaft and enables generator rotation with a

sufficiently high frequency despite the slow turbine rotation. This way, the

costs of manufacturing the generator are reduced, making possible that even

power plants with very low heads can operate profitably. A design with direct

transmission of torque between the turbine and the generator is also possible.

Fig. 47: Tubular pit turbine [source: http://turab.com]

7.6.3 Tubular turbine S Tubular S turbine is a variation of the bulb turbine. Tubular S turbine is shown

in Figure below. This type of turbine has a horizontal axis and axial inflow of

water onto the runner. It is equiped with an S-shaped draft tube with one or

two bends. The shaft runs through the bend of the draft tube out of flow tract.

The generator is located outside of the flow tract. This turbine type is suitable

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for smaller hydroelectric plants with up to 10 MW power, which do not allow

for installation of the generator in a watertight bulb within the flow.

Fig. 48: Tubular S turbine, generator is located outside of flow tract of the water turbine, [source: http://www.cchpe.net]

7.6.4 Axial turbine with a vertical shaft – Saxo turbine Tubular Saxo turbine is a variation of the bulb turbine (Figure below). In

recent years a tubular Saxo turbine design has been successfuly implemented

by Litostroj in Canada. This is a vertical axial turbine, which in its upper part

between the inlet and the runner is similar to a tube turbine with an inlet bend

and a semi-axial stay and guide vanes. In the lower part between the rotor and

the end of the draft tube, it is similar to conventional Kaplan turbines. The

water flows onto the rotor in the axial direction. The generator is installed

above the turbine, with the shaft running trough the inlet bend. The suction

tube can either be straight or with a bend. Saxo turbines can cover the

complete operating range of bulb and Kaplan turbines.

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Fig. 49: Schematics of tubular Saxo turbine [source: Litostroj]

7.7 Other type of water turbines Other types of water turbines will be mentioned below. We will separate them

according to reaction and impulse type of operation.

Reaction types of water turbines are: Deriaz turbine, Tyson turbine and Gorlov

turbine. Deriaz turbines have adjustable runner blades, water flow in the

runner is diagonal (Figure below). Deriaz turbine is similar to Kaplan turbine,

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only that runner blades are inclined, what is useful for higher heads from 20 to

100 m. Tyson turbine does not need the casing, it is put directly in the flowing

water of the watercourse. It is composed of propeller, attached to the raft. The

runner drives the generator, usualy on the raft, connected to the runner with

the belt. Tyson turbine is pulled in the middle of the watercourse, where the

water flow speed is the highest. Gorlov turbine is water turbine, developed

from Darriusove turbine, only that it has bent blades (Figure below). Water

flow acts on the blades of Gorlov turbine with the torque, causing the turbine

to spin. The fluid flow direction is perpendicular to the rotating shaft of the

turbine.

Fig. 50: Runner of Deriaz turbine [source: http://dic.academic.ru]

Impulse water turbines are: water wheel, Turgo turbine, Banki turbine (also

called cross-flow turbine), Jonval turbine in Arhimed screw turbine. Water

wheel is an old turbine machine, which in the past used to drive mills and

water sawmills, but was also used for irrigation and drainage (Figure below).

The water whell was first mentioned BC, the usage has spread from ancient

Greece to Roman empire to other parts of the world.

109

Fig. 51. Other types of water turbines. Left: Gorlov turbine, [source: https://en.wikipedia.org/wiki/Gorlov_helical_turbine]. Right: Turgo turbine, [source: www.dtlhydro.com].

Turgo turbine is similar to Pelton turbine, only that it has only a half of the

runner. The runner is therefore more easily to manufacture (Figure below).

Water flows to the turbine from the side, while the turbine enables higher

discharges as the Pelton turbine. Turgo turbine operates in the range og

heads, where Pelton and Francis turbine overlap. Banki turbine is interesting,

because it is the only turbine, through which the water flows twice. Jonval

turbine is similar to water wheel with the difference, that water flows to the

turbine from the top. Arhimed screw was traditionally used for water

pumping, while today it is mostly used for wastewater pumping in wastewater

treatment plants. in the other direction Arhimed wheel works as a turbine.

Archimed screw water turbine is fish friendly turbine (Figure below).

Fig. 52: Other types of water turbines; left: water wheel; right: Arhimed screw turbine [source: https://en.wikipedia.org]

110

8 Other elements of hydro power plants

In this chapter we will present main elements of hydro power plants. The

main groups of elements are water intake system, equipment in machinery

hall and other systems.

8.1 Water intake system Water intake system (slo.: vtočni sistem) consists of the upper accumulation,

dams and trash racks.

8.1.1 Dams Dams (slo.: jezovi) are structures which hold the water for different purposes,

including electricity production. There are several types of dams: concrete,

gravity, arch, pillar, embankment or a combination thereof.

Arch dam of HPP Moste and dam of HPP Medvode of combined pillar -

embankment dam are shown in Figure below.

Fig. 53: Hydro power plant dams; left: concrete arch dam of HPP Moste is

the highest dam in Slovenia; right: dam building of HPP Medvode

of of combined pillar - embankment type, behind is Zbiljsko lake

[source: SEL d.o.o.].

Embankment dams (also known as rock-fill dams) are constructed by piling of

rock material around the central waterproof wall, which nowadays is usually

made of concrete. These are used in cases when a wide valley must be

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dammed. Bulk dams are gravitational and are held in place by their own

weight.

To dam deep and narrow gorges, a concrete dam is needed as only the

concrete structure is strong enough to withstand the pressure of water. The

highest concrete dams exceed 300 m in height. The dam cross-section is

usually triangular. Construction of large concrete walls is complicated and

slow, as the structure must be cooled during construction. Concrete dams are

gravitational (held in place by it's own weight), arched (curved in the shape of

an arch and leaning on the sides to the valley banks which holds them in place;

used for damming high and narrow gorges) or pillar (the pillars have deep and

strong foundations which are supported by the ground), or a combination of

differen types.

Apart from the main dam structure, the surrounding supporting area must

also me strenghtened. For example, the dam of HE Medvode (60 m high,

highest in Slovenia) is located in an area where the river Sava created rapids

in dolomite, which is mostly cracked an full of cavities. To assure good

foundations, the ground was stabilized by an injection curtain. The unfilded

width of the curtain is 190 m and extends until the imperviuos base made of

shale and sandstone, which lies in the depth between 27 m and 45 m.

Dams posses risks for accidents for humans and environment. Accidents due

to dams of hydro power plants are very uncommon. The worst accident which

happened due to ignoring the possibility of such landslide happened at Vajont

dam near Longarone, Italy. A part of the nearby hill collapsed into the

accumulation lake Vajont, causing a 200 m high tsunami wave. Nowadays,

larger dams usually have an equipment for detection of landsliding.

8.1.2 Teeth and trash racks The inlet from dams to the power plant channel or tunnel can be designed in

different ways, located separately or as a part of the dam or the dam building.

Different elements are used at the inlet: teeth, trash racks etc. (Figure below).

The teeth (slo.: zobje) reject large floating or sinking debris. Due to the tooth,

the inlet channel is located a few meters below water level and above the

bottom, which reduces the possibility that larger pieces of wood would enter

the power plant. The debris collecting at the tooth must be cleaned with a

cleaning machine.

Trash racks (slo.: rešetke) hold the dirt (tree leaves, branches, stones, sand,

gravel etc.) from travelling through the turbine and damaging it. A sample of

the trash rack for a small hydrop power plant is shown in Figure below. Some

trash racks have a differential pressure meter. If the differential pressure is

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too high, the rack must be cleaned with the cleaning machines. On large water

power plants trash racks are usually not visible.

Fig. 54: Teeth and trash racks of water hydro power plants; left: the tooth

of HPP Medvode and the trash rack, the tooth holds the debris

while the rack is not visible (under the metal guardrail in the

lower left part of the image). Due to the tooth, the inlet channel is

located about 3 m below the water level and above the bottom,

which reduces the possibility that larger pieces of wood would

enter the power plant. In the middle and right: the intake-outlet

system at the pumped storage power plant Avče during

construction and operation. The teeth are vertical and installed in

a way wich prevents larger pices of floating wood from being

sucked into the power plant, [source: SEL d.o.o. in SENG d.o.o.].

Fig. 55: An example of a trash rack on a small hydro power plant, which

at the same time acts as a spilway in the case of flooding [source:

http://www.tps.si].

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8.2 Water supply system The water supply system (Figure below) from the upper accumulation to the

turbine consists of supply (head race) channels, head race tunnels, sand trap,

gates, surge tanks, penstocks (pressure pipelines) and closing elements

(valves). The water supply system is a continuation of the inlet system and can

be very large/long if the damming is far away from the powerhouse. In run-of-

the-river/accumulation power plants the water supply system is short and

incorporated in the dam structure.

8.2.1 Headrace channels and tunnels Headrace channels and tunnels (slo.: dovodni kanali in dovodni tuneli) supply

the water to the penstock (slo.: tlačni cevovod), because in most cases the dam

is not located directly above the powerhouse, but some distance away from it.

The channels are open and are usually desiged as excavated asphalt structures

with low inclination. The channels are made by drilling or blasting the rock

and then covered with concrete. Near the end of the head race channel/tunnel

there is usually a sand trap (slo.: peskolov), an expanded section where flow

velocity is reduced and the particles heavier than water settle on the floor.

Near the end of the head race channel or head race tunnel there is a surge tank

(slo.: vodostan).

Fig. 56: Headrace channels and tunnels for water supply to the water

turbine; left: headrace channel HPP Obernach, Germany; in the

middle: inside penstock of PSHPP Avče [source SENG d.o.o.]; right,

concrete headrace tunnel of HPP Hubelj [source SENG d.o.o.]

8.2.2 Surge tank The surge tank task (also surge tank, slo.: vodostan) is to reduce pressure and

mass flow fluctuations in the penstock and head race tunnel caused by

changes in load, to within acceptable limits. Surge tanks of PSHPP Walchensee

(Germany) and HPP Završnica are shown in Figure below. A surge tank is an

expanded part of the head race tunnel. When pressure and mass fluctuations

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occur, water spills from the penstock into the surge tank, where the water

level is momentarily increased. The surge tank prevents the pressure wave

from propagating into the head race channel/tunnel, thus preventing damage

and spilling.

Fig. 57: Surge tank; left: surge tank of PSHPP Walchensee in Germany;

right: surge tank of HPP Završnica

Behind the surge tank there is usually a gate chamber, which ends the

relatively flat part of the water supply system. Inside the chamber a gate is

installed for the purpose of closing the channel when the penstock must be

drained for inspection and maintenance, without the need of draining the

head race channel. Behind the gate chamber, the penstock begins.

The schematics of surge tanks of HPP Doblar II and Plave II are shown in

section xyz. The surge tank may be built as a simple surge tank, which is just a

horizontal cilinder, or may have in addition an upper and lower surge tank

chambers, a choke and acess tunnel. Upper and lower surge tank chambers

increase useful volume of the surge tank, while they also enable choking of

water flow energy during inflow and outflow from the surge tank. During

opening of turbine valve, when the water in penstock is stationary, the

penstock is gradially filled from water from surge tank and lower surge tank

chamber. Lower surge tank chamber may be built to suppkly water in the

penstock, but when long enough, it may also serve to provide choking and

replace the choking element.

The choking element mitigates fluctuations of water discharge into and out of

the surge tank. It is built as a constriction. The acess tunnel is used for

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inspections, service and air venting of the surge tank and both surge tank

chambers.

8.2.3 Penstock Penstock (slo.: tlačni cevovod) is a pressure pipeline linking the gate chamber

and the power plant. It ends with a ball valve, in case the power plant has one.

The ball valve is usually used for high heads, while for low heads butterfly

valves are more common. Penstocks of PSHPP Walchensee (Germany) and

HPP Hubelj are shown in the Figure below.

Fig. 58: Pressure penstock leads water form upper accumulation to the

water turbine; left: pressure penstock HPP Wachensee, Germany;

in the middle: pressure penstock HPP Hubelj; right: pressure

penstock HPP Hubelj, joint and dilatation [source: SENG d.o.o.]

Longer penstocks have steel walls capable of sustaining high water pressure

within it. Apart from the static pressure, a penstock must also withstand the

additional pressure caused by quick shutdown of the power plant. If the

penstock is vertical, it is named a shaft (slo.: jašek). Penstocks are usually

mounted on pods, which can be fixed or sliding. Due to the (thermal)

expansion penstocks include expansion joints, where two pipes slide one

inside another. Penstock of HPP Solkan with kaplan turbine is shown in

Figure xyz, located between trash rack (4) and turbine (8). Short penstocks

(e.g. in run-of-the-river power plants) are often made of concrete.

8.2.4 Bypass valve or pressure regulator Bypass valve or pressure regulator (slo.: razbremenilni ali varnostni ventil) is

a valve used with some Francis turbines with a large head (Figure below). It is

installed at the turbine inlet and intended to divert some water from the

penstock past and downstream of the turbine. In an event of quick

(emergency) turbine shutdown the rate of bypass valve opening is determined

by the rate of guide vane closing, and reduces pressure loads in the penstock

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due to formation of a pressure wave. The typical time of bypass valve opening

is a few seconds in an emergency shutdown event.

Larger power plants are usually without bypass valve.

8.2.5 Ball valve or butterfly valve in and bypass pipeline A ball valve or butterfly valve (slo.: predturbinski ventil) is and element of

water supply system, used for closing the penstock in a hydro power plant. It

is installed just before the turbine's spiral casing inlet.

The ball valve always closes when the power plant is shut down, and its

closing is slow. Ball valves are hydraulically operated, but also have a weight

for emergency closing in an event of a more serious malfunction of the power

plant and its auxilliary systems. In the case of the emergency shutwown, the

ball valve starts to close together with the stator (guide vanes), to prevent the

turbine from accelerating to excessively high rotational frequencies (i.e.

runaway conditions). Ball valves of PSHPP Avče and HPP Hubelj are shown in

Figure below.

Fig. 59: Turbine valve and bypass for the valve. Left: turbine valve on HPP

Avče. Bypass is bright pipe above the turbine valve. Right: turbine

valve and bypass on HPP Hubelj, again bypass is horizontal pipe

above the turbine valve. A relief valve is also visible left form the

turbine valve [source: SENG].

When the ball valve is closed, the water may be pumped out of the water

turbine for inspection or service.

To open the ball valve, pressure across it must first be equalized. For this

purpose, a bypass (slo.: obvod) is opened before opening the guide vanes,

which results in equalization of pressure before and after the valve.

Ball and butterfly valves are used. From the viewpoint of efficiency ball valves

are better (no obstacle to the water flow), but they are more expensive. Ball

valves are used for pressuresabove approximately 4∙105 Pa.

Run-of-the-river power plants lack the ball valve and its bypass.

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8.2.6 Gates The purpose of the gate (slo.: zapornica) is to close the water flow onto the

turbine. Gates are not used for closing the water flow during normal shutdown

events in everyday's operation, but for longer shutdowns like for inspection

and overhaul In the case of a run-of-a-river power plant, the gate is lowered in

the opening with a crane, usually in multiple parts. Such gates are named

segment gates. In the case of a dammed power plant, the gate is usually

installed at the end of the head race channel/tunnel behind the surge tank,

while another gate is located at the end of the tailrace tunnel. Location of gates

in the system of hydro power plant is shown in Figures below (check all

Figures in the textbook), while location within the spilway is shown in Figure

below below (check all Figures in the textbook). If gates are located inside the

hill, they are arranged in a room that we call gate chamber.

Fig. 60: Installed gates at the outflow from the turbine in HPP Dubrava,

Croatia.

Turbine inlet gates, together with turbine outlet gates, enable the draining of

the turbine compartment. A case of installation of turbine inlet gares for run-

of-the-river power plant HPP Medvode is shown in Figure below.

Apart from gates in turbine fields, the run of the river power plants also have

the gates on the spillways (slo.: prelivno polje).

For repair and inspection of gates are in some cases used temprary gates

called xyz (slo.: zagatnice). Xyz are installed in front of the gate and do not

allow water to reach gates. Later, water between xyz and gates are pumped

out and inspection or repair is performed.

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Fig. 61: Gates of turbine inlet on HPP Medvode; left: gates storage; right:

location where gates are installed in the turbine flow tract

[source: SEL d.o.o.]

8.3 Powerhouse equipment Powerhouse is the facility where the turbines are installed. It can be a part of

the dam structure, or in a separate building. For instance,the powerhouse of

the pumped storage power plant Avče (Figure below) is 80 m deep, to assure

sufficient suction head of the pump-turbine unit. In the following part of this

chapter, the equipment installed in powerhouses will be presented.

Fig. 62: Powerhouse of the hydro power plant. Left: the powerhouse of the

pumped storage power plant Avče, view from the generator

casing upwards, yellow pipes contain power lines from the

generator to the transformer. Grey pipes are for power lines

leading down to the generator excitation. Three black pipes are

for water drainage (water flowing up) and cooling of the

generator (water going up and down) [source: SENG d.o.o.].

Right: the powerhouse of HE Dubrava, Croatia, the turbine is

installed in the hole below the elevator on the left side of the

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image.

8.3.1 Spiral casing Spiral casing, spiral or scroll casing (slo.: spiralno ohišje, spirala) is an element

for supplying the water to the inlet guide vanes and adjustable guide vanes. It

is designed so that the wate outlet velocity is constant along its perimeter.

This is why the cross-section of the spiral casing is gradually reduced along

the perimeter as the water is gradually directed through the stator and onto

the runner. Francis and Pelton turbines have spiral casing, while Pelton and

tubular turbines do not have the spiral casing. In the case of Pelton turbines, a

water flow distributor is used instead of spiral casing.

In spiral casings of some turbines, pressure measurement outlets are installed

to measure the flow rate by the Winter-Kennedy method. The method is based

on measurements of the pressure difference on two locations in the spiral

casing, which rises proportionally with the flow rate. The method is usually

calibrated during acceptance tests, when the flow rate is measured by and

array of vane anemometers.

In the majority of the larger power plants, the spiral casing is poured in

concrete. In smaller power plants such as SHPP Hubelj, it is usually visible.

8.3.2 Stay vanes and guide vanes Stay vanes or stayring vanes (slo.: predvodilne lopatice) The inlet guide vanes

direct the flow from the spiral casing towards the turbine and have a fixed

position (Figure below). With their direction they direct the water flow at the

most suitable angle to guide vanes (slo.: vodilne lopate). Stay vanes have an

important function of providing mechanical strenght as they link the upper

and the lower part of the inner side of the spiral casing.

Fig. 63: Stay vanes and guide vanes of water turbines; left: stay vanes and

guide vanes of HPP Solkan (Kaplan turbine) [z dovoljenjem: SENG

d.o.o.]; right: guide vanes of tubular bulb turbine HPP Dubrava,

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Croatia

Outside of the flow tract, the guide vanes are connected by a guide vane ring

or guide vane wheel (slo.: vodilni obroč), which moves all the vanes

simultaneously and is steered by a hydraulic arm. Guide vane ring is shown in

Figure below. Guide vane ring is moved by a hydraulic arm. In some cases, the

guide vanes are soft mounted and equipped with micro switches. The

microswitches detect if a particular vane did not close completely during the

shutdown procedure (e.g. due to jamming by a tree branch). In this case, the

operator can reopen and close the guide vanes, possibly removing the jammed

objects to be washed away by the water flow. If required, this procedure must

be performed several times. If not sucessfull, in a very unusual event, turbine

flow tract must be emptied and the part removed.

Fig. 64: Guide vane ring; left: guide vane ring on bulb tubular turbine HPP

Dubrava, Croatia; right: guide vane ring on Kaplan turbine HPP

Solkan, visible is the hydraulic arm for guide vane ring rotation,

and the soft mounting of the vanes with micro switches [source:

SENG d.o.o.]

8.3.3 Turbine runner, turbine cover, anti-lifting plate and system for air blowing Turbine runners (slo.: gonilnik) can be of different types (Pelton, Francis,

Kaplan etc.) The shaft can be horizontal or vertical, the latter design more

suitable for higher power ratings.

Turbine cover (slo.: turbinski pokrov) of the runner is (Figure below) a thick

steel plate installed above the rotor. Large thickness is required because the

turbine casing is exposed to high pressures., for instance on PSHPP Avče

approximately 30 cm. Within the turbine casing, the sealing system is also

installed (slo.: tesnilka), which serves the purpose to prevent water flowing

from the flow tract around the runner around the shaft into the powerhouse.

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The air blowing system has several different functions:

- It allows starting up large pumped storage power plants (Figure below) in

the pumping regime. To avoid excessive startup current, the compressors

starts pumping in air, forcedly blown in the turbine compartment, which is

only blown out when the turbine reaches the desired rotational frequency. In

this case, the air is blown from the side.

- It dampens the pressure pulsations in operation of Francis turbines at partial

loads, when a cavitation vortex appears in the draft tube (Figure below). The

vortex swings around with approximately 1/3 of the rotational frequency of

the runner and causes large pressure, torque and electric power fluctuations

as well as bearing vibrations. Introduction of air (compressible medium) into

water reduces the rigidity of the mixture. The valve is located on the top of

hollow shaft, above the generator cover. When the valve is opened, air flows

from machinery room through the hollow shaft through the runner into the

draft tube (Figure below). The pressure in the draft tube is lower than in the

machinery room.

- it dampens the water hammer effect during an emergency shutdown event.

The valve lets the air from the machine room into the suction part of the flow

tract (draft tube), reducing the pressure fluctuations in the penstock In this

case the air enters the flow tract from the runner.

Fig. 65: Water turbines runners; left: runner of Kaplan turbine, view from

below from suction tube (HPP Doblar I); in the middle: lowering

of the runner, holes in the runner are visible, used for air blowing,

PSHPP Avče; right: turbine cover PSHPP Avče [source: SENG

d.o.o.]

Turbine cover with Kaplan turbines includes also anti lifting plate (slo.:

protidvižna plošča). Anti lifting plate is usually made from copper. During

emergency shutdowns, with Kaplan turbines due to pressure, acting on the

runner at eleveted rotational frequencies, lifting force higher than the rotating

parts of the entire water turbine. We can sy, that the turbine runner "glisira"

at elevated rotational frequency.

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Suport bearing , holding the turbine in place during normal operation, does

not prevent lifting of the turbine, this role is taken over by the anti lifting plate.

During normal operation the lifting plate is not used, because it is not required

due to low lifting force. Anti lifting plate is composed of several parts, such

that it can be replaced during service.

Francis turbines do not need anti lifting plate.

8.3.4 Shaft Shaft (slo.: gred) connects the runner with the generator (Figure below). The

shaft is usually made of two or three parts and as such, it can be divided to the

turbine shaft (attached to the turbine's runner) and the generator shaft

(attached to the generator's rotor).

Older turbines have, for instance HPP Doblar I aor HPP Plave I have three very

long shafts. In the past this was commonly used for the case of emergency of

water breaking into machinery room. With such arrangement of very long

shafts, water could only fill water turbine, but not generator and other electric

equipment. Such turbines have beside turbine and generator shaft also

intermediate shaft.

Fig. 66: Shafts of water turbines; left: Turbine shaft (PSHPP Avče). On the

upper part is a flange, which is a connection between turbine and

generator shaft. Right: turbine ane generator shaft of HPP Solkan

[source: SENG d.o.o.].

8.3.5 Ležaji Ležaji (angl. bearings) on water turbines are rolling contact bearings (slo.:

kotalni) on smaller turbines and sliding contact bearings on large turbines.

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Bearings on small turbines are rolling bearings, for instance ball or cylinder

bearings. Each power plant has at least one turbine bearing and one generator

bearing. The guide bearings hold the turbine in place in the radial direction

and the support bearings support it in the axial direction.

The bearings are made of segments with oil up to about the half of the

segment height. The function of oil is both cooling and lubrication of bearings.

The red-colored blocking elements in the image below (from HPP Solkan)

have a function of stabilizing the position of each bearing segment in the axial

direction. Besides, there is also a steel reinforcement in the radial direction

(shown in dark color between the brighter blocking elements) which also

serves for setting the air gap, adjustable by a screw on the outer side of the

bearing, In the image below, the holes in the axial direction on the bearing

segment No. 1 are used or disassembling the segment. The segment No. 2 has

another hole in the center, where the bearing temperature probe is installed

(for monitoring and protection purposes). Also visible from the below image

are different bearing materials. Adjacent to the shaft there is a thin layer of

white metal, which protects the shaft in the case of surface contact. Only the

white metal is damaged because it is softer and has a lower melting point,

meaning that the segment can be easily repaired. Away from the shaft (Figure

below), without the requirement to lift the entire turbine.

Fig. 67: Turbine guide bearing during inspection; left: parts of turbine

guide bearing of HPP Solkan; right: Details of turbine bearing of

HPP Solkan. In dark color a reinforcement is shown to fix the

bearing in the axial direction. Picture was taken with open

bearing cover [source: SENG d.o.o.].

During operation an oil film is formed in the gap between the shaft and the

bearing, and is able to sustain itself without forced lubrication. On larger and

more modern turbines, the bearings are equipped with an oil lubrication

pump for initial lubrication. This lubrication pump (Figure below) assures

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sufficent bearing lubrication, while the turbine is stationary or starting to spin.

The lubrication pump is of a great value for the support bearing, which lifts

the turbine and enables smooth start. If the lubrication pump is in operation,

the turbine can be rotated by hand if there is no water in the flow tract. When

the turbine reaches the normal operating conditions, the lubrication pump

stops. Older turbines without the system for initial lubrication are subject to

greater wear during starts.

The lubrication oil is cooled in a water-cooled oil cooler, which is usually

installed near the bearing (Figure below).

Fig. 68: Cooling system and system for initial bearing lubrication; left:

heat exchanger oil/water on HPP Medvode [source: SEL d.o.o.];

right: high pressure pump for initial bearing lubrication of HPP

Solkan, left turbine shaft [source: SENG d.o.o.]

Smaller hydro power plants have simpler bearings, such as HE Hubelj pictured

below. Even smaller turbines have rolling bearings, which are easier for

maintenance in comparison with sliding contact bearings.

Fig. 69: The bearings on small HPP are simple, in the case of HPP Hubelj

are of sliding contact type. Also visible is the flywheel (slo.:

vztrajnik), which is used when the powerplant runs in island

mode of operation (slo.: otočno obratovanje) separated from the

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remaining electricicty producers in the electric network [source:

SENG d.o.o.].

8.3.6 Shaft seal Shaft seal (slo.: tesnilka gredi) is an element of water turbines, which prevents

the water to flow from the region of high pressure of the flow tract into the

powerhouse, except in for this envisaged places. The shaft seal is susceptible

to the dirt from the watercourse from the turbine tract. It is therefore required

to prevent the dirty water to flow into the seal. To do so, a cleaned sealing

water is therefore pumped into the turbine tract near the sealing. This clean

sealing water later flows through the seal and later into the drainage.

System of the sealing water must be well designed. This includes filtering of

water form the river, maintaining of pressure and volume flow rate from the

turbine tract into the seal , because it is important to prevent the dirty water

to enter the seal even, when the turbine is not in operation. When the turbine

is not in operation, a small volume flow rate of clean water through the seal is

required. The filtered wate helps to cool the bearing.

For sealing a system of sealing ropes (slo.: tesnilna vrvica) and slip rings (slo.:

drsni obroč) is used. Sealing ropes are usually of specially woven type with

rectangular cross section. To protect the shaft, in the region of sealing, a

special steel jacket is mounted on the shaft. This steel jacket can be replaced.

Sometimes also labyrint seals are used or for very low head also cuffs (slo.:

manšete).

A pneumostop is also often used wuith seals. A pmneumostop is a rubber

element of trapeze cross section, featuring a groove on the outside. This

rubber element is then on the outside non moving part of the seal mounted

near the sealing. When the turbine is not in operation, the pressure is applient

to the inside of a pneumostop. Then the turbine is not in operation, the

pneumostop rubber touches the shaft and prevents entrance of water. The

seal for good operation requires shaft rotation. Pneumostop is only used,

when the shaft does not rotate, during daily shutdowns and also during

mainetnance and servicing of the turbine.

8.3.7 Creep detector Creep detector (slo.: zaznavalo premikanja). Creep detector is shown in Figure

below. Creep detector usually works on the principle of inductive detection of

pulses.

Creep detection device can be a part of the rotational frequency measurement

system or a standalone instrument. If the turbine is rotating very slowly even

when the guide vanes are closed, this usually means that one or more vanes

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are leaking (due to dirt, branches etc.), being stuck betwwen the guide vanes.

When the system senses a slow rotation, auxiliary systems (bearing pumps

etc.) are turned on to prevent damage of the moving parts. In such case, must

the operator of the turbine several times open and close the guide vanes, that

the blocing branch is flushed away. In very rare cases, when the foreign object

can not be flushed away, turbine mist be closed, water pumped out and the

object removed manually.

Some water turbines have installed one more protection device to prevent

rotation with too high rotational frequency. The protection is composed of tho

pins located on the shaft, which at the rotational speed of around 120% of

nomoinal rotational frequency, move out of their original place and press the

switch (in Figure below in the front of the creep detector). The switch starts

the emergency shutdown procedure.

Fig. 70. Creep detector in HPP Solkan, located in rectangular casing, in

the front is mechanical systems with pins, protecting from

increase of rotational frequency of the turbine [source: SENG

d.o.o.].

8.3.8 Governing of the angle of guide vanes and runner blades The governor (slo.: sistem krmiljenja) is the system of regulation of the angle

of guide vanes and in the case of Kaplana and turbular turbine also runner

blades. Old governor of SHPP Hubelj and governor of HPP Solkan are shown in

Figure below.

The governor in the phase of startup of the turbine , when the turbine is not

synchronised with the electric grid (the electric grid does not brake the

turbine yet), takes care of the proper rotational frequency of the turbine. The

governor sets proper angle o guide vanes and runner blades.

When the turbine is synchronized with the electric grid and producing

electricity, also must regulate the angle og guide vanes and runner blades. This

is done so, that at momentary net head the required power of the turbine is

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achieved at the minimum required volume flow rate of water through the

turbine, that is with optimal setting of angles of guide vanes and runner

blades.

Fig. 71: Goeverning of angle of guide vanes and runner blades; left: old

hydraulic governor on SHPP Hubelj (not in use anymore); right:

hydraulic aggregate with mechanical governor of rotational

speed of HPP Solkan [source: SENG d.o.o.]

Several types of governors exist, from purely mechanic types, over

electrohydrauliy types to electronic and digitaly types. Governors are

connected to hydraulic aggregate, which if required performs changes of

angles of guide vanes and runner blades.

Very long time ago hydro power plants were operated manually and there

were no governors. Now, electronic or digital governors are used (Figure

below), that perform governing tasks more accurate than older governors.

This relates to less mechanical stresses to turbine during synchronisation to

electric grid.

Hydraulic aggregate is connected with pressurized reservoir of oil, which is

only partially filled with oil, rest being air. The air is pressurized at the same

pressure as hydraulic oil and has several functions. It prevents frequent turn

on of the hydraulic pump. At the same time it damps sudden pressure

fluctuations in the oil system. In the case of failure of the hydraulic aggregate

the compressed air contains enough energy to perform most important task to

turn the turbine off, close the guide vanes and open the turbine blades.

Hydraulic aggregate of HPP Medvode is shown in Figure below.

The quality of oil in the hydraulic system is yearly checked for presence of

metals. For instance, presence of copper indicates a copepr seal with heavy

wear and possible leakage of hydraulic oil.

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Fig. 72: Regulation of HPP Medvode; left: digital turbine governor; right:

the governor controls also the hydraulic aggregate for regulation

of guide vanes and rotor blades of Kaplan turbine [source: SEL

d.o.o.]

8.3.9 Inverter Few powerplants are equipped with an inverter (in Slovenia, only the pumped

storage power plant Avče, Figure below). The inverter allows rotational

frequency variation in a certain range, for example from -4 % to +6 % of the

nominal rotational frequency, called also varspeed. This allows to reach a

better efficiency and more flexibility for adjusting the operation to current

conditions in the electroenergetic system and to the available quantity of

water.

In PSHPP Avče the motor /generator is a DFIM doubly fed induction machine

(slo.: dvojno napajan asinhronski stroj) with variable rotational frequency.

The benefit of variable rotational frequency is mainly better efficiency. The

required power and available head can be adapted such that the efficiency of

the system is as high as possible. Benefits are also short response time,

synchronisation and poer regulation in the pump mode of operation.

Excitation system is specific to PSHPP Avče and enables varspeed operation

(Figure below). It is composed of three level VSI Voltage Source Inverter (slo.:

trinivojski inverterski pretvorniški sistem), composed of rectifier/inverter,

connected into direct current circuit. Main excitation system elements are

thyristors, being among the most advanced versions of power converters.

Excitation system sets voltage, frequency and slip to the generator rotor.

The turbine can operate in wide interval of operating points. In the pump

mode of operation the PSHPP Avče regulates the water volume flow rate

solely by changing it's rotational frequency, without using guide vanes.

regulation with guide vanes is possible, but efficiency is low.

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Fig. 73: Excitation system og PSHPP Avče; left in the container are control

part, cooling part and power part, right is excitation transformer

[source: SENG d.o.o.].

8.3.10 Brakes Brakes (slo.: zavore) are mechanical elements used to stop the turbine when it

rotates very slowly. Before that point, the turbine is braked hydraulically by

closing the guide vanes, or also adjusting the rotor blade angle in the case of

Kaplan turbines. When the turbine stops, the brakes are released. After that,

the turbine must remain still, which is monitored by the creep detection

system. If the runner starts to rotate by itsef from the standstill, this is usually

due to the dirt jammed in the guide vanes, which prevents full closing. The

turbine must not rotate when not in operation, as such rotation can damage it.

The brakes are not intended to be used for permanent braking.

Brakes are usual mechanical with pneumatic excitation, driven by low

pressure compressor.

8.3.11 Generator and its electric equipment The generator is a device where mechanical energy from the shaft is

converted to electric energy. A generator consist of a rotor winding and a

stator winding. Generators of HPP Doblar II and HPP Solkan are shown in

Figure below. All the electric generators in powerplants operate on the

principle of electric induction, where voltage is generated as a wire passes the

magnetic field lines. In smaller generators, the magnetic field is produced by

permanent magnets, while in bigger units electromagnets, which require

additional source of current for excitation, are more common. Generators can

be of synchronous or asynchronous type.

In modern synchronous AC generators, the excitation current is produced

from a separated external source. Since the excitation current is much lower

than the current in the induced winding the excitation circuit is usually

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installed to the rotor of the generator because the slip rings are not suitable

for conducting very large currents. The excitation current represent an

important part of plant's own use of energy (slo.: lastna raba energije).

Most of generators is induced by DC current. With DC current excited

generator can only operate sinchronous with the electric grid, which in

Europe has frequency 50,0 Hz. Rotational speed of the generator and the

entire poer plant is therefore set by the number of poles of generator staror

winding and rotor winding. The only water power plant in Slovenia (and first

of such type in Europe), which used AC current for excitation, is PSHPP Avče. A

part of electric energy is taken from the electric grid and is fed over the

excitation systen to the rotor of the generator. In PSHPP Avče this enables

varspeed operation, as explained in the subsection above. Varspeed operation

is useful in pumping mode of operation, where regulation is performed weth

changes of rotational frequency instead of with the guide vanes. Excitation

system is composed of control, cooling and power electropnics parts. For the

purpose of cooling, water is filtered and demineralised to avoid electrical

short circuiting.

generator is very heavy and big, therefore in the case of large power plants it

can not be transported in one piece. In PSHPP AVče stator and rotor each

weigh more than 200 t. Generators are therefore assembled in water power

plants and rotors must be therefore balanced before first use. This is

performed at very low rotational frequency at first with measurement dial

indicators, later with measurement of vibrations at various inreasing

rotational frequencies for instance 25%, 50% etc. and with adding the mass on

required places of the generator rotor.

In large water power plants the generator is installed in generator casing or

barrel, filled with gas and equiped with systems for gas conditioning and fire

protection.

Generator is with supports or brackets (slo.: kovinske podpore) connected to

walls, supporting the generator bearing. The largest loads of supports are

during startup and shutdown, when temperature variations and resulting

stresses are the highest.

Other electric equipment includes the switchyard, distribution switchard,

transformers, generator breakers or fuses, diesel power unit, batteries etc.

The diesel power unit (Figure below) is constantly heated to be always

prepared for startup, when a backup power source is required for the plant's

own energy consumption. The own consumption of the power plant includes

the electric energy requirad for running the plant's systems, inclusing those

running when the plant is out of operation. These are mostly the drainage

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pumps, pumps for the needs of seal of the turbine shaft, for cooling of main

transformer and for excitation system.

Fig. 74: Generators in water power plants; left: powerhouse and

generator cover of HPP Doblar II; in the middle: rotor of the

generator HPP Solkan during servicing; right: stator of the

generator HPP Solkan during servicing [source: SENG d.o.o.].

When not in operation, water power plant uses electric energy for auxiliary

systems from the electric grid. When this is not possible, a diesel generator is

used. Fpor instance, amount of water needed during operation of PSHPP Avče

is around 300 l/s, and while in not in operation it is 11 l/h.

Fig. 75. Diesel aggregate in HPP Medvode [source: SEL d.o.o.].

8.4 Other systems in the powerplant The other systems include spilways, the drainage system, different cooling

systems, the system for oil supply and cleaning etc. The drainage pumps

operate constantly, as water usually slowly breaks into the power plant

building. The drainage pumps are a large source of the plant's own

consumption and must also operate when the power plant is offline and not

producing electricity.

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8.4.1 Spillways and spillway gates Spillways (slo.: prelivna polja) release water form watercourse, when upper

resorvoir is full and volume flow rate of the river is too large, to be entirely

directed through turbine fields. This is the case at high water and flooding.

The spilway of HPP Solkan is shown in Figure below. The case, when the main

spilway gate is open, is shown in the figure below in the middle.

Gates (slo.: zapornice) of spilways are of two types, they may be attached to

the sides of spilways or to the crown of of the dam. Gates, attached to the sides

of spilways are for instance gredne, tablaste, segmentne, valjčne in kavljaste

gates. Gates, attached to the dam's crown are for instance sektorske,

preklopne ali krožne gates.

In addition gates may be distinguished regarding operation to main or

auxiliary gates. Main gates enable operation , when the spilway is active.

Auxiliary gates are used dureing revisiona and servicing of main gates and the

spilway.

Auxiliary gates are similar in ooperation to the gates of the flow field.

Depending on the type of water power plant, a spilway may have two auxiliary

gates, one above and one below the main gate. Auxiliary segment gates are for

instance put into place with a crane and are used, when water around the

main gate must be drained.

Main gates are from one or several segments. A sample of the main table gate

of HPP Medvode is shown in Fig below (right). For instance, main table gate

closes the flow through the spilway, when the flow rate of the river is low and

all water flows through turbines.

In the case of increased flow rate, when the turbines cannot take all the

waterthe table gate first drops (low flow rate across the gate), then rises (high

flow rate under the gate) or is fully removed (the whole spillway is closed).

The problem with flooding waters is that the river flow carries large branches

or even trees which can become stuck in the spillway, greatly reducing the

flow rate.

Fully open spillways in run-of-the-river power plants should not represent

any resistance to the flow of the watercourse. The watercourse should flow

through the open spilways full unrestricted, meaning that there should be no

head lost on the spilways. This means, that in such case the head of turbine

fields is almost zero and turbines on run-of-the-river power plants can not

operate. With derivation power plants like HPP Doblar and HPP Plave

operation during floods is possible. With derivation power plants the height

(slo.: kota) of the upper water is almost the same as during normal operation,

while height of lower water may be higher than usual.

133

Fig. 76. Cross section of the spilway of HPP Solkan.

Fig. 77: Spilways on run-of-the-river water power plants, left: HPP

Solkan with two spilways and three turbine fileds [source: SENG

d.o.o.]; in the middle: flow fields of HPP Solkan during floods in

year 2012 [source: SENG d.o.o.]; right: table gate of hook type on

the spilway of HPP Medvode [source: SEL d.o.o.]

The water from turbine or spillways flows into the lower accumulation, where

some power plants have floating gates. These are hollow gates lowered by the

crane into the water of the lower accumulation, then they float to the place of

installation, where they are are filled with water and being sunk as a result.

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Floating gates are used for the maintenance of the outflow facility

downstream of the power plant or under the waterfall (slo.: podslapje) etc..

Water power plants, that must alwas release some water to maintain a

biological minimum of watre flow rate, may not close all gates. They therefor

do not have gats on all spilways and turbine fields. Beside this, revisions and

servicing are only performed on one turbine field at a time.

8.4.2 Sump pumps Sump or drainage pumps (slo.: drenažne črpalke) pump water from the

machinery hall. Because turbines are usually mounted very low to achieve

proper turbine submersion, water is ingressed in the machinery hall. This

water is inside the machinery hall collected in channels into the sump, located

in the lowest part of the water power plant. In th esump pump, sump pumps

are located. They are operated from time to time to prevent flooding of the

machinery hall.

In the cases, when machinery hall is large and deep, walls of the machinery

hall have side pressure relief caverns, from where the water is also pumped

out. This is the case of PSHPP Avče.

Sump pumps are also used to pump water from the turbine flow tract. For

such case, a bypass is built, linking flow trach and sump pumps. Water first

flows by gravity from turbine flow tract to the sump, from where sump pumps

pum the water out of the power plant. By doing so, inspections and servicing

of turbine flow tract are possible. Similar case is for gates of the spilway, if

they are located near the sump.

8.4.3 Fish passages Fish passages (slo.: ribji prehodi oz. ribje steze) are technical mitigation

measures to reduce negative impact of water power plants and dams on

fishes. The selected type of fish passage is selected (passage, elevator, side

channel, etc.) and conducted in the way, that suits fish species present in the

watercourse.

The construction of hydroelectric power plants is associated with a series of

interventions in waterourse. One of the most negative effects of the

destruction of habitats and disruption of migratory routes of fish on the

spawning grounds and pasišča. The first notes on the installation of fish

passages date back to the 17th century, their number has significantly

increased until about 1850, with the building of the first hydroelectric plants.

Previously, the dams were used for agricultural purposes. The first

documented fish passes were built in the years 1852-1854 on stream

Ballisodare Ireland [Kolman et al, 2010].

135

Reservoirs affect river hydrology and seasonal variability of flow. Due

removed riparian vegetation are subjected to heating embankment, resulting

in higher water temperatures and lower oxygen content, which are fish stress

factors. On the other hand colder water negatively affects the reproduction,

increased by a relatively large number of specimens and adult fish [Kolman et

al, 2010]. At the site of release of warmer water in the stream with normal

cold water some fish may die. Such a change affects reproduction and food

production for the rest of the fish population.

Dams can also become a focus of a variety of diseases. In anaerobic processes

at the bottom of the riverbed methane is formed, which can cause fish kills

[Kolman et al, 2010].

The reasons for the migration of river fish species are in search of various

habitats, allowing for the survival of fish species. Many mature freshwater fish

migrate upstream to spawning grounds or in the stream itself or in its

tributaries, young fish are migrating downstream with the flow [Kolman et al,

2010]. Under the dams fish species collect due to greater opportunities for

pillaging even during seasonal migration. It has been shown that after setting

the dam, the number of species and population size is very quickly reduced,

leaving only those species that in the new circumstances can survive [Kolman

et al, 2010].

The dam is often an impenetrable barrier that can completely alter the natural

flow regime and thus prevent permanent migratory of fish species such as the

transition between different mountainous and downstream habitats.

An important building block of fish passages is an input and the ability to

attract fish to migration [Kolman et al, 2010]. Also crucial is the flow rate of

the watercourse during fish migration and behavior patterns of different

species of fish. The plan for fish passage includes mechanical and hydraulic

solutions to discourage fish going into the turbine flow tract for example with

grids, and guidance into the fish passage. All power plants do not have have

fish passages, in such cases it is necessary to migrat juvenile fish by other

means.

The issue of fish passage is mostly mentioned only in large hydroelectric

plants, while on small hydropower plants and small streams the problem is

too often forgotten.

Example of fish passes in water power plant is shown in Figures below. Fish

Bowling is usually carried out in such a way that the drop in head is divided

into several segments, or small pools, through which water flows. In each pool

regions of high and low velocity of water are present. Regions of low water

velocity allow the young and weak fishes to rest.

136

In Slovenia HPP Mavčiče and HPP Vrhovo have an artificial spawning as

compensation for interrupted migration of fish species, however only artificial

spawning in Mavčiče is in operation [Kolman et al, 2010]. On the river Drava

more fish passages were built, but many have been abandoned in the past

because of dysfunction.

Fig. 78: Fish passage of HPP Krško; left: upstream connection with

Sava river, right: fish migrate into the fish passage only at a

certain height, it is therefore required to make several

entrances height wise. All entrances are then merged in a

single fish passage. In the case of HPP Krško two entrances

were built [Source: Hidroelektrarne na Spodnji Savi, d.o.o.].

In Slovenia, the most modern fish pasage was built on HPP Blanca, where on

the side of the plant enough space for the fish passage was present. Some

water power plants in Slovenia do not have fish passages, for example. HPP

Solkan and HPP Moste. In the case of HPP Solkan local fishing association

(family) cares for transportation of fish upstream and downstream.

Fig. 79: Fish passage of HPP Krško, individual basins contain regions of

relatively calm water, allowing the fishes to rest [Source:

Hidroelektrarne na Spodnji Savi, d.o.o.].

137

138

9 Manufacture of runners of water turbines

Manufacture of runners of water turbines differs according to the type and

size of the runner. In this chapter we will consider manufacture of runners,

while we will not discuss manufacture of other mechanical equipment of

water turbines.

Usually for the manufacture of runners of water turbines two types of

materials are used. In the first group are usual stainless steels like X6 CrNi 18-

10. In the other group are harder steels, often used are for instance

X5 CrNi 18-10 or X3 CrNiMo 13-4. Selection of material depends on the type of

runner and experience of the manufacturer. Austenitic stailess steels belong to

the first group, they are used for the manufacture of simple and small runners

up to the diameter approximately 500 mm. Using this material, manufacture is

relatively easy, for instance before welding preheating is not required. Also

not required is the tempering. Because steel is not magnetic, for the control of

quality of the material the method of magnetoflux is not used. Welding of the

large Francis runner is shown in Figure below.

Fig. 80: Welding of large Francis runner [source: https://www.ewm-group.com]

Steels in the second group are not stainless steels, however they have better

cavitation resistance properties, they are much more resistant to cavitation

erosion damage. For instance material X3 CrNiMo 13-4 is hard, difficult to

treat, availability is difficult and requires special treatment during welding

and manufacture. For manufacture of runners from such materials a preheting

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is required for instance runner must be preheated (with heaters to

approximately 100 °C) and annealing must be performed for reduce inner

stresses in the material. Using the mentioned material after welding, grinding,

glowing etc. runner's geometrical shape is altered, therefore additional

turning is required before installation.

In general, several types of manufacturing processes may be used to

manufacture runners of water turbines, they depend on size, type and

complexity of the runner and technical abilities of the manufacturer. Processes

differ to some extent among diffrent manufacturers. Manufacturing processes

include:

- manufacture with CNC machines from one piece,

- manufacture with CNC machines from two pieces and welding of both

halves,

- manufacture with welding of blades on the hub (slo. pesto) and rim (also

shroud, ring, slo. venec).

With kaplan turbines blades and hub are manufactured separately. later

blades are attached to the hub using screws. Pelton turbines are manufactured

in one peace or with welding of blades on the hub of the water turbine.

9.1 Manufacture of Pelton turbine runners Runners of Pelton turbines are manufactured from one piece or with welding

of blades on the hub. pelton turbines are not manufactured from usual

stainless steels like CrNi 18-10. Manufacture of runners of Pelton turbines

with welding is shown in Figure below, while manufacture from one piece is

shown in the Figure below.

Fig. 81: Manufacture of Pelton turbine runner, left: grinding of the runner before welding of blades; right: welding of blades [source: Andino d.o.o.]

The hub of Pelton turbine is manufactured such, that steel casting is turned on

the outer surface. Blades may be manufactured in one piece together with the

140

hub or separately. In the second case blades are later welded to the hub of the

Pelton turbine. In the past, blades were always welded or even bolted to the

hub, because the possibility of manufacture in one piece did not exist. All

pieces, that is hub and all blades, are checked before further manufacture with

the metheod of penetration and magnetic flux leakage.

Fig. 82: Manufacture of Pelton water turbine runners. Left: manufacture of Pelton turbine blades on milling machine, runner is manufactured from one piece; in the middle and right: grinding [source: Siapro d.o.o., www.siapro.eu]

In the case, that blades ale welded to the Pelton turbine hub, all castings are

processed before welding using milling procedure. Welding surface may be at

the blade root, but may also be at some other radius, for instance in the middle

of the blade, as shown in the Figure below.

Fig. 83: Pelton turbine runner with almost all blades welded [source: Andino d.o.o.]

After the welding, all welds are grinded until the requested surface quality is

achieved and suitable radius is achieved. For welding and further processing

the runner is mounted such that a worker welds and grinds blades in the

141

suitable working height. After grinding, welds are checked with penetration,

magnetic flux leakage method and ultrasound, and also with Xrays imaging, if

the buyer requests so. After welding, glowing is required as with Francis

runners to reduce internal strasses. After glowing, Pelton turbine runners are

again turned to achieve required outer dimensions of the runner. After

turning, the runner is polished and balanced and such ready for

preinstallation and installation.

9.2 Manufacture of Francis turbine runners Among all types of water turbine runners, manufacture of Francis turbine

runners is the most difficult. Francis turbine runners may be manufactured

using 3D milling method (small Francis turbine runners) from one piece or

two pieces or with welding of blades between the hub and rim. The blades are

manufactured using bending of the sheet metal (middle size of Francis turbine

runners, Figure below) or with casting (large Francis turbine runners). Hub

and rim are manufactured from castings, forging or sheet metal. All pieces are

checked before further manufacture using penetration and magnetic flux

leakage.

If the runner is manufactured using welding of blades between the hub and

rim, bended or casted blades are processed using 3D milling. Surfaces of

blades are during this phase manufactured such, that later only grinding and

polishing is required, while geometric shape is not changed anymore. Using

CNC milling also welded surfaces are processed.

Fig. 84: Manufacture of Francis water turbine runners; left: manufacture of small runner with milling; right: manufacture of blades using sheet metal bending [source: Andino d.o.o.]

Hub and rim are before insertion of blades set in appropriate position in

relation to each other. Hub and rim are then held together by additional

welded steel supports (Figure below). Steel supports are positioned on the

side of the runner at it's circumference. The hub is usually located on the

142

ground on the montage plateau, while the rim is lifted and supported by the

machine, which enables measurements of oplet of the rim and it's rotation

around it's horizontal axis. By doing so the runner is turned outside down.

When the appropriate positioning of the rim is set and it's oplet is low enough,

the rim is connected with the hub with steel supports and thus fixed. The steel

supports remain attached until the glowing.

Before the blades are welded in position, blades must be inserted in

appropriate positions, inclined at appropriate angles in space and arranged at

appropriate distances among each other. Because blades are after casting or

bending processed using 3D milling, they usually fit well in the space between

the hub and the rim and they fit only at an appropriate angle. In addition,

during turning of hub and rim, marking lines are turned on the rim and hug,

further facilitating insertion of blades in height. The arrangement at

appropriate distances among each other is performed by dividing the

circumference for the set number of blades (Figure below).

Fig. 85: Manufacture of Francis turbine runner, arrangement of hub and the rim in appropriate relative position. They are held in place by steel supports on the side of the runner [source: Andino d.o.o.]

In the next step, blades must be welded in the position between the hub and

the rim. Before welding, for the selected steels, welded parts must be heated

to approximately 100 °C. This is checked by thermocouples, evenly arranged

on welded parts of the runner (Figure below). First, a root of the weld is

welded, while later this is grinded from the other side, because the first weld

was welded such that a gap was present between both welded parts, the blade

and rim or hub. Later, the weld is welded to it's full extent. Also, analysis

samples are welded. Welding of largest runners is performed by certified

companies with certified and highly skilled personnel. After welding, welds

are grinded to the desired surface quality and radii are formed as desired. The

above desribed work is very demanding for the welding personell, especially

143

during summers, in part due to the welding itself, but also because of very

high temperature of the heated runner, poor access etc.

After grinding, quality of welds is chequed for quality with penetration (Figure

below), magnetic flux leakage method or if required by the buyer also with

xrays method.

In the next phase of the manufacture of the runner, glowing is performed. By

doings so, internal material stresses are reduced. Internal matterial stresses

arised in previous steps of manufacture, especially during welding. This is

performed in the oven at appropriate temperature and time. Glowing is

performed according to selected programme, usually a slow increasing of

temperature is required to around 600 °C, temperature is maintained for the

selected period of time, later follows slow decrease of temperature. Test

samples are also glowed.

Fig. 86: Placement of blades among the hub and rim. Blades after casting or bending are machined by 3D milling and fit well between the hub and rim over their entire surface, only they need to be equidistantly placed over the circumference [source: Andino d.o.o.].

After glowing steel supports at the side of the runner are removed. Again

turning is required to give the runner the final outside dimensions. Because

welding inserts addition stresses in the material, the runner's shape is

changed slightls. Because of the, in the first phase of the manufacture of the

runner, the runner is manufactured with few mm larger outside dimensions of

the rim and hub and with slihtly smaller inner dimensions. After welding and

glowing, the runner is turned again and during this final turning the runner

gets it's final outside dimensions (Figure below).

144

Fig. 87: Manufacture of the Francis water turbine runner, welding of blades onto the hub and rim. During welding the runner must be heated to around 100 °C, which is checked by temperature measurements using thermocouples as seen in the left picture [source: Andino d.o.o.].

Fig. 88: Manufacture of Francis water turbine runner, left: grinding [source: Siapro d.o.o., www.siapro.eu]; right: penetration of the runner for evaliation of material and quality of welds [source: Andino d.o.o.]

After final turning the Francis turbine runner is grinded (Figure above),

polished and balanced. Balancing is usually performed statically; only in few

cased dynamic balancing is required.

145

Fig. 89: Turning of the rim and hub of the Francis water turbine on the final outer dimension [source: Siapro d.o.o., www.siapro.eu]

To detect similarity between the model and prototype a standars on

measurements of properties performance of water turbine models provides

information [IEC 60191, 1999] abouts the procedure of checking of similarity.

By cheching of similarity, outlet openings, height of inlet opening, hiw evenly

blades are arranged around the circumference, but also sometimes with the jig

or measurement arm or 3D scanner also shapes of individual blades. Among

mentioned parameters, the outlet opening is the most important. This is the

shortest distance between trailing edge of a blade and surface of the next

blade. This is because this dimension has the most pronounced influence on

the performance and hill diagram, most notably on the maximum volume flow

rate.

Recently, small and medium sized Francis turbines are manufactured from

two halves as shown in the Figure below. In this case, welding surface a single

plane located is in the middle of the runner in vertical dimension and not as

described above between the hub, rim and the blades.

9.3 Manufacture of runners of Kaplan turbines Manufacture of runners of Kaplan turbines is simpler than manufacture of

Francis turbine runners. Blades are manufactured from one piece. The blade is

then bolted to the hub of the turbine runner.

Blades of Kaplan turbines are usually casted. This is because blades of kaplan

turbines are usually very large to enable high volume flow rates. For

manufacture with forging or sheet metal bending Kaplan runner blades are

usually too large and too thick. Kaplan turbine blades are casted together with

it's pivot pin. Later it is check for quality using penetration and magnetic flux

leakage method. Separately also the hub is casted.

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Fig. 90: Manufacture of blades of Kaplan water turbine runners [source: Siapro d.o.o., www.siapro.eu]

After casting of Kaplan turbine runner blades together with the pivot pin

processed using CNC milling method (Figure above). After the milling, blade

surface is grinded. In a similar was also the hub is milled with a CNC machine

and later grinded.

As with Francis turbines, blades must be glowed and checked for defects using

penetration, magnetic flux leakage method or possibly xrays method. After the

manufacture of Kaplan turbine blades are fully manufactured, pivot pins are

attached to the hub during pre assembly and assembly.

9.4 Pre assembly, assembly and installation of water turbines Pre assembly is assembly, performed at the location of the manufacturer of

the water turbine. Figure below shows pre assembly of Kaplan turbine. The

final assembly and installation are performed at the final location of the power

plant.

During the pre assembly the turbine manufacturer checks for matching of

individual elements of water turbine, spiral casing, turbine coverguide vanes,

bearings, runner, shaft, draft tube etc.

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Fig. 91: Pre assembly of Kaplan water turbine [source: Siapro d.o.o., www.siapro.eu]

Transportation of water turbines is often difficult because of large size and

vey high weight of water turbines. If the water turbine is small enough, it is

transportet assembled. In the case that this is not possible, it is transported in

several pieces and partly assembled. With the largest turbines, all large

elements are transported separately, for instance the runner.

Fig. 92: Installation of Kaplan turbine [source: Siapro d.o.o., www.siapro.eu (left) and SEL d.o.o. (in the middle and right)]

During assembly at the location of power plant the pre assembly is repeated

(Figure below). For instance spiral casing is usually within concrete, during

concrete pouring and hardening the spiral casing is deformed slightly. In this

case relevant elements of the flow tract must be turned before installation of

the runner. These are all large elements, where a very small clearance must be

achieved. This is made by a specially adapted turbing machine, which is

lowered in the flow tract of the Francis or Kaplan turbine.

With large and very large Francis turbines with vertical axis individualk

elements of water turbines are consecutively lowered in the water turbine

shaft, first runner with the runner shaft, later turbine casing, bearings,

generator shaft, generator, etc.

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10 The properties of operation of water power plants

This section will present some properties of water turbines, namely the

operating characteristics, hill diagram and operation of pumps/turbines, etc.

For a better understending let us consider two variables which are a part of

the characteristics, namely the specific hydraulic energy and flow rate. Indices

1 and 2 mark the pressure and suction part of the machine, respectively,

where specific hydraulic energy is determined (Figure below).

Fig. 93: Schematic representation of a water turbine. The flow flows in the direction of the arrow for the pump or the turbine. With index 1 we denote pressure side, while with index 2 we denote suction side.

The specific hydraulic energy is a variable which gives the amount of specific

energy that water can transfer to the turbine [IEC 60193, 1999]

𝐸 =𝑝abs1 − 𝑝abs2

�̅�+𝑐12 − 𝑐2

2

2+ �̅� (𝑧1 − 𝑧2) . (113)

149

In above equation, 𝑝abs1 and 𝑝abs2 are the absolute pressures at

measurement planes 1 and 2 and consist of two parts:

- overpressure in the pipeline and

- atmospheric pressure.

𝑐1 and 𝑐2 are corresponding velocities in measurement planes 1 and 2. �̅� g is

the average gravitational acceleration. Difference (𝑧1 − 𝑧2) is the height

geodethic difference between both measurement planes. �̅� is the average

density of water.

Let us try to write the above equation in a simplified form.

For the sake of simplicity or historical reasons, often heights/heads are used

instead of the specific hydraulic energy. Under the assumption that the water

flow velocity difference 𝑐1 and 𝑐2 is insignificant, that the system has two free

surfaces (1 and 2), and that atmospheric pressures 𝑝abs1 in 𝑝abs2 on the free

surface of water are approximately the same, the equation above can be

rewritten as the dependence of the specific energy on the geodetic height

difference 𝐻st the difference between the upper and lower water level:

𝐸 ≈ 𝑔 ̅(𝑧1 − 𝑧2) ≈ 𝑔 𝐻st . (114)

The geodetic height difference between the upper and lower water level in

hydroelectric power plants is called static height difference 𝐻st. The total

pressure difference of a hydro power plan 𝐻b is the gross head, which follows

from 𝐻st and the kinetic energy difference. Therefore, 𝐻b je torej bruto padec,

is the static height difference, reduced by the fraction of energy, represented

by velocity increase from 1 to 2

𝐻b = 𝐻st +𝑐12

2 𝑔−𝑐22

2 𝑔 . (115)

The net head 𝐻n of a hydro power plant is obtained, if the gross head 𝐻b is

subtracted the hydrodinamic losses ∑𝐻izg in the inlet part until the turbine

and the outlet part until the lower accumulation

𝐻n = 𝐻st +𝑐12

2 𝑔−𝑐22

2 𝑔−∑𝐻izg . (116)

The flow rate is the quantity of water, passing through planes 1 in 2. The flow

rate through both planes is assumed to be the same.

In the case of some power plants such as HE Plave and HE Doblar (Figure

below), the upper accumulation is far from the powerhouse of the plant.

Water flows through a long supply tunnel (penstock). In this case, the sum of

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losses is relatively large and the water level in the penstock is not the same on

the inlet and outlet, it is different by the sum of head losses from the equation

above.

Often, instead of the specific hydraulic energy, head or flow rate,

dimensionless variables are used for instance 𝜑 (flow number), 𝜓 (pressure

number) etc. Similarly, the dimensionless power number 𝜆, can be defined, but

many other dimensionless numbers exist as well.

Fig. 94: Flow system of HPP Plave from the dam Ajba to the outflow into watercourse. Due to losses in the penstock, not all gross head is available to the turbine.

10.1 Characteristics and hill diagram of turbines Properties of turbines are presented by characteristic diagrams and hill

diagrams. Depending on the type of regulation, three different types of

turbines exist::

- turbines without regulation,

- turbines with single regulation and

- turbines with double regulation.

In diagrams of characteristics and hill diagrams manufacturers of water

turbines usually provides several regions, these are regions of of allowed

operation, regions of operation with limitations, non allowed region, reference

region for the purpose of acceptance tests and test region.

In the following we will review characteristics and hill digrams and their

regulation.

10.1.1 Characteristics of water turbines In the case of an unregulated tubine (Figure below) power, flow rate and

efficiency are given at a selected rotational frequency. Measurements are

conducted by variation of the specific hydraulic energy and measurement of

other variables.

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For the unregulated turbine, both axis are swithched usually in comparison

with compressors, pumps and fans. With turbine pumps characteristics of

pressure, head or specific hydraulic energy decreases with increasing flow

rate, while with water turbines it is exactly the opposite. With water turbines

the characteristics of pressure, head or specific hydraulic energy rises with the

volume flow rate.

The reason for this in a unregulated turbine (Figure below) is, that an

operator of the turbine can not select the specific hydraulc energy, it is

provided by the heights of upper and lower accumulation and losses related to

the current volume flow rate. The specific hydraulic energy is therefore

independent variable, while volume flow rate or flow number are dependent

variables.

Fig. 95: Characteristics of non-regulated water turbine

A characteristic diagram or shurtly turbine characteristics for single

regulation turbines is shown in the Figure below. The difeference with

unregulated turbine is for a single regulated turbine, that discharge through

the turbine may be regulated even though the operator still can not influence

the geodetic heights of upper na lower accumulation. we therefore with single

and later also double regulated water turbines for the x axis select

independent variable flow number or volume flow rate, while on the y axis we

select specific hydraulic energy, head, pressure number or pressure.

In the case of a single regulated turbine, measurements must be taken in a

sufficient number of operating points for every selected dimensionless specific

energy E, such that the curves of constant efficiency, guide vanes opening and

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power can be drawn. Measurements on the measuring station are conducted

by establishing the selected dimensionless specific energy E. on the

boundaries of the turbine with the aid of an auxiliary pump. Then, the guide

vanes are opened and closed and for each guide vane angle we measure the

flow rate (presented as the flow number on the diagram), power and

efficiency. Measurements are usually performed for a single rotational

frequency. Normally, the range of flow rates in which the turbine can operate

is prescribed.

A diagram in the image below can be used to obtain a chart with a three-

dimensional surface, also known as the hill diagram (slo.: hill diagram). This is

done such that the characteristics are sliced in planes, horizontal to the

volume fklow rate and specific hydraulic energy.

Fig. 96: Characteristics of a single regulated water turbine, for instance Francis turbine

Turbines with double regulation allow in addtion to regulation of guide vanes

angle also variation of the runner blade angle . The characteristics of a

double regulation turbine is presented in the Figure below. In the process of

determining the characteristics, turbine power and efficiency are measured at

different rotor blade angles. This is due to the fact that on model turbines, it is

easier to change the stator opening than the rotor blade angle (in the latter

case, the turbine must be disassembled). To disassemble the model turbine, it

must be emptied of water, remove the draft tube and a runner, with templates

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set the new angle of runner blades, attach the blades at the new angle, mount

the runnaer, draft tube and fill the turbine with water again. Measurements on

the measuring station are conducted by establishing the selected

dimensionless specific energy E on the boundaries of the turbine with the air

of an auxiliary pump. Then, the guide vanes/stator are opened and closed and

for each stguide vane angle we measure the flow rate (presented as the flow

number on the diagram), power and efficiency. Efficiency curves turn out to be

fairly steep at a constant angle of the rotor blade rotation e. Over the peaks

of these partial curves a common curve of constant efficiency is drawn as an

envelope (presented by a dashed line in the Figure below). Measurements are

usually performed for a single rotational frequency.

Fig. 97: Characteristcs of double regulated water turbine, for instance Kaplan turbine. With water turbine with double regulation we must for each measurement point change also angle of runner blades .

10.1.2 Hill diagram Characteristic – capability of a turbine as a hydraulic motor for driving the

generator are obtained by model measurements on test rigs, as presented

above in the previous subsection. Measured are basic characteristics: volume

flow rate �̇�, torque M, efficiency 𝜂, specific hydraulic energy E and power P

From characteristic diagrams (such as the one presented in the above

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subsection), complex turbine characteristics named the hill diagram can be

obtained (slo.: školjčni diagram).

Hill diagram for single regulated turbine (Figure below) and for double

regulated turbine (Figure below) is made such, that curves of partial

efficiencies are cut horizontally with the plane of specific hydraulic energy E

and volume flow rate �̇�.

In the hill diagram there are lines of constant of guide vanes angle , lines of

constant angle of runner blades , lines of constant effieciency 𝜂 (these have

the shape of the hill isohypses, hence the name of the hill diagram) and lines of

constant power.

The following turbine operational limits are evident from the hill diagram:

- maximum allowed flow rate, limited by the emergence of cavitation

[Avellan, 2004], while cavitation is mitigated by slightly smaller opening of

guide vanes,

- maximum power, which is mostly limited by the generator power,

- runaway curve at efficiency = 0,

- maximum allowed specific hydraulic energy as a consequence of

cavitation on the leading edge of runner blades [Avellan, 2004] on the

suction side or the highest possible denivelation of upper and lowest

possible denivelation of lower accumulation,

- lowest possible head or specific hydraulic energy an a consequence of

cavitation on the runner leading edge [Avellan, 2004] on pressure side or

lowest allowed denivelation of the upper accumulation and highest

possible denivelation of the lower accumulation,

- lowest allowed volume flow rate, set by manufacturer of the turbine,

because at very low volume flow rates turbine experiences high vibrations

and related turbine wear, with Francis turbines this is mainly due to the

phenomenon of cavitation vortex in the draft tube and cavitation vortices

in the inter blade space of the runner [Širok et al., 2006].

The fourth and fifth bullet points are limitations as a consequence of the flow

properties on the inlet edge of the runner. This is especiall true for Francis

turbines, because they lack possibility of regulation of angle of runner blades.

This is much less relevant for Kaplan turbines. Limitation because of highest

and lowest allowed denivelation in a limitation of the power plant and not of

the turbine and is valid for both Francis and Pelton turbines.

As stated in the sixth bullet point, with Francis turbines operating at partial

loads and volume flow rates, that is to the left from the point of max.

efficiency, two penomena occur, which influence operation of Francis turbines.

These are occurence of cavitation vortex in the draft tube and occurence of

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cavitation vortexes in inter blade space of the runner. Approximately 90 %

from the nominal volume flow rate of Francis turbine down to the 60 % of the

nominal flow rate, there is a region of marked occurence of cavitation vortex

in the suction tube. This occurence is mitigated by injection of compressed air

into the draft tube through the hollow shaft. The cavitation vortex does not

limit operation of Francis turbines, because Francis turbines can be regulated

down to even much lower volume flow rates. Later at much smaller part loads

and volume flow rates, the remaining angular momentum is too high and

cavitation vortex can not form, therefore the cavitation vortex in the draft tube

dissapears.

In the interval of around 15 to 30 % of nominal flow rate, cavitation vortices in

inter blade space of the runner are poresent. In every, every second or every

third inter blade space from the upper hub wall down the cavitation vortex

winds down into the runner. This limitation is set by every manufacturer for

each produced turbine.

Cavitation vortex can form also to the right of the max. efficiency point. In this

case the cavitation vortex os of different shape, more flat than left from the

max. efficiency point and is limited to the middle of the draft tube.

The maximum power is specified due to the properties of the generator, which

is only capable of generating power up to the maximum allowed power.

Exceeding the maximum power limit would lead to a generator failure.

The runaway speed is the turbine speed at full flow rate.

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Fig. 98: Hill diagram of water turbine with single regulation (Francis turbine). Shown are lines of constant efficiency and lines of constant guide vanes opening.

The runaway speed (slo.: pobežna vrtilna frekvenca) is the turbine rotational

speed at full flow rate and zero load. In the case of a runaway event the

turbine operation shifts very rapidly along the curve of the constant stator

opening (as set in the moment of losing the generator load) down until the

runaway curve. This means that both dimensional and dimensionless

pressureacross the turbine are singificantly reduced. In the case of Francis

turbines, this means a transition to lower flow rates, while in the case of

Kaplan turbines, the flow rates may even increase, depending on the direction

of constant stator opening curves..

Hill diagrams can be either dimensional or dimensionless (on x axis is flow

number 𝜑 and on y axis pressure number 𝜓) In the case of dimensionless

presentation, some parts of the diagram are either relatively compressed or

expanded with respect to the others, which is why some customers require

turbine manufacturers to provide both types of the hill diagram. Hill diagrams,

available to the public show relative lalues of efficiency, max efficiency is

usualy 1 or 100 %. Manufacturers of tubines do not want to disclose real

efficiencies of their products.

157

Fig. 99: Hill diagram of water turbine with double regulation (Kaplan turbine). In addition to hill diagram of single regulated turbine we mark curves of constant runner blade angles .

With the aid of hill diagrams shown in Figures above, the operator can easily

find and select the regions of optimal operation of water turbine.

10.2 Pump/turbine operation in four quadrants (extended range of operation) Turbines and pumps can operate in four quadrants depending on the specific

nominal speed 𝑛ED and the nominal flow rate �̇�ED (𝑛ED =𝑛 𝐷

√𝐸 in �̇�ED =

�̇�

𝐷2 √𝐸).

The four quadrants are defined with respect to the value (positive or negative)

of flow rate and rotational frequency. In the image below, (a) marks the

oparation at the highest specified power and (c) the operation at the lowest

allowed power. The individual parts (quadrants) are::

- bottom left - pumping quadrant,

- bottom right - braking pumping quadrant,

- top left - braking turbine quadrant,

- top right - turbine quadrant.

Some of the quadrants are further divided, for example the top left quadrant is

divided to the turbine part and turbine dissipative (brake) part with the

runaway curve (zero shaft torque, generator is out of operation /

disconnected from the power grid) separating them. The runaway curve

denotes a region, where the the torque is zero and generator does not brake

the turbine, that means is either malfunctioning or not connected to the

electric grid. Above the runaway curve there is a pure turbine area, where

turbines operate most of the time. In this region the volume flow rate is

positive, rotational frequency positive and torque positive. Below the runaway

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curve is an area of turbine dissipation (brake) with positive flow rate and

rotational frequency, but negative torque. Such operating conditions are rare

thoug possible with some turbines, but only occur in transitional flow regimes.

Such operation regime can not be calle operating point, because the water

turbine operates in such regime only transiently.

During the operation in the turbine regime, the turbine operates on one of the

constant guide vanes opening curves between the vertical lines, which mark

the minimal and maximal allowed power. In the case of emergency shutdown,

the operating point slides along the constant efficiency curve to the runaway

curve (e.g., until the extreme upper-right point in the graph). Then, as the

guide vanes are closing, the operating point moves along the runaway curve to

the center of the coordinate system (zero flow rate and rotational frequency).

Fig. 100: Operation of water turbines in four quadrants. With (a) we denote operation at the highest allowed power and with (b) operation with the smallest allowed power.

159

10 Cavitation in water turbines and pumps

In the discussion about turbine in the introductory sections we did not

distinguish between different fluids. However, water turbine machinery

(pumps and turbines) are faced with a phenomenon of cavitation, which puts

serious limits to water turbine machinery operation.

10.1 Introduction to cavitation Boiling can be characterized as a vaporization of a liquid at constant pressure,

due to increase of a liquid’s temperature (Figure below). Vaporization of a

liquid can also be achived at constant temperature if the pressure drops below

vaporization pressure. Cavitation as a physical phenomenon, related to

boiling, can be characterized as a transition from liquid to vapour phase and

back to homogenious liquid at approximately constant pressure (Figure

below).

Fig. 101: Boiling and cavitation in p-T and p- diagrams.

Cavitation can be usually seen as a crowd of small vapour bubbles, which size

can varies from nanometers to few milimeters in diameter. The energy

collected in a cavitation bubble during the growth phase can be released in the

collapse phase in various forms. Cavitation bubble collapse can cause very

high pressure pulsations – up to several 100 bars and extreme temperatures,

up to 1000°C can occurs in the center of the collapsed bubble. If the bubble

collapse asymmetrical a so called micro jet can be formed, which velocity can

be reached up to several 100 m/s.

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Fig. 102: Cavitation bubbles in a Venturi section

Cavitation probability and intensity is characterised by a cavitation number 𝜎,

it is defined as

𝜎 =

𝑝0 − 𝑝𝑣

𝜌𝑐02

2

. (117)

High values of cavitation number are connected with high risks and low

cavitation numbers with high risks of cavitation. Unfavourable cavitation

effects in turbine machinery are:

- increased noise,

- increased vibrations,

- damages to bearings and sealings,

- cavitation erosion (Figure below),

- reduction in efficiency etc.

Fig. 103: Kavitacijska erozija in kavitacija v gonilnikih Francisovih turbin; levo: kavitacijska erozija v gonilniku Francisove turbine; desno: kavitacija v modelu gonilnika Francisove turbine [Širok in sod., 2006]

By knowing and understanding the phenomenon of cavitation, one can use it

as a tool in various technical processes. Nowadays cavitation is used also for

surface cleaning for surfaces with difficult acess, in wastewater for bacteria

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killing and homogenisation, in medicine for kidney stone crushing, in food

industry for milk homogenization etc.

Types of cavitation according to how they are formed are

- hydrodynamic (caused by flow passing the submerged body),

- acoustic (caused by high intensity pressure waves, traveling through the

liquid),

- laser induced (caused by high intensity laser light, vaporization is caused

by local temperature increase of a liquid – not regular growth mechanism),

etc.

Types of cavitation according to the shape

- attached/steady cavitation (leading edge – pressure or suction side)

- unsteady cavitation cloud shedding

- sheet cavitation,

- root cavitation,

- individual bubble cavitation

- tip vortex cavitation,

- hub vortex cavitation

- supercavitation and

- .

Fig. 104. Different types of cavitation vortices in Francis turbine [source: Kolektor Turboinštitut d.o.o.].

10.2 Relation to the operating point of the turbine machine We will discuss cavitation in Kaplan and Francis turbines. For leading edge

cavitation we will provide an explanation, at what flow rates such cavitation is

formed.

10.2.1 In Kaplan turbine The flow properties in Kaplan turbine runner are shown in the Figure below.

The cavitation is present in several locations:

- (a) Sheet cavitation is caused by local pressure drop due to high velocity

flow

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- (b) Cavitation on the leading edge / suction side is caused by non-optimal

angle of attack

- (c) Cavitation on the leading edge / pressure side is caused by non-

optimal angle of attack

- (d) Cavitation near the root of the runner is caused by local non-optimal

hydrodynamic geometry of the runner

- (e) Cavitation at the tip of the blade is caused by highest circumferential

velocity.

Fig. 105. Triangles of velocities and pressures on blades in Kaplan turbine (PS - pressure side and SS - suction side)

Locations where cavitation is found in Kaplan turbines is shown in Fig. below

163

Fig. 106. Locations of cavitation occurence in Kaplan turbines pretvori v svg

In Kaplan turbines cavitation vortex very rarely occurs. . Vortex occurs when

the turbine operates at very low discharges and low pressures.

10.2.2 In Francis turbine Locations where cavitation is found in Francis turbines is shown in Fig. below:

- (a) cavitation at the trailing edge, due to high velocity flow, which can not

follow the blades,

- (b) cavitation on the suction side at the leading edge, due to non-optimal

angle of attack,

- (c) cavitation on the pressure side at the leading edge, due to non-optimal

angle of attack,

- (d) vortex cavitation between the blades, due to flow separation (low

discharge) and

- (e) cavitating vortex in the draft tube.

Cavitationg vortex in the draft tube is very common in Francis turbines.

164

Fig. 107. Locations of cavitation occurence in Francis turbines

10.2.3 In centrifugal pump The flow properties in centrifugal pump are shown in the Figure below. The

cavitation is present in several locations:

- (a) cavitation on the leading edge on pressure side (�̇� > �̇�𝑜𝑝𝑡),

- (b) cavitation on leading edge on suction side (�̇� < �̇�𝑜𝑝𝑡),

- (c) cavitation by the sealing,

- (d) cavitation on the holes – drilled to reduce axial forces and

- (e) cavitation at the tongue.

165

Fig. 108. Triangles of velocities and pressures on blades in centrifugal pump (PS - pressure side and SS - suction side)

Locations where cavitation is found in centrifugal pumps are shown in Fig.

below.

Fig. 109. Locations of cavitation occurence in centrifugal pumps

10.3 Cavitation and NPSH/NPSE characteristics The pump operates on the intersection of operating characteristics and

resistance characteristics of the system. In addition, producer of pumps

provides in addition also a NPSE characteristics for the pump. Fans don't need

it, because they operate with air. The NPSE characteristics is a NPSH

characteristics, multiplied by gravitationa acceleration 𝑁𝑃𝑆𝐸 = 𝑔 ∙ 𝑁𝑃𝑆𝐻.

NPSE characteristics provides information how much energy is available to

the pump on the suction side. Although E and NPSE have the same unit m2/s2,

166

there is a fundamental difference between the two. The specific hydraulic

energy E represents the change of specific energy of water when pumped from

suction to pressure side and is also according to the Euler equation to

𝑢2𝑐𝑢2 − 𝑢1𝑐𝑢1. The NPSE on the other hand only considers the flow conditions

on one side, that is on the suction side.

10.3.1 In pumps The NPSE characteristics is provided by the manufacturer of the pump and is

measured on the test stand. The measurement of NPSE is performed as shown

in the Figure below. For every operationg point on the NPSE characteristics

(right) an entire σ - η diagram is measured for turbines and an entire σ - H

diagram is measured for pumps. The entire σ - η (or σ - H ) or diagram

corresponds to only one operating point, however different specific energies

and heads are measured on the measuring station such that the vacuum is

achieved in the measuring station using a vacuum pump. The �̇� and E values

are in most of the σ - η (or σ - H ) diagram the same, until (on the left of the

diagram) the efficiency or head falls by 1 %. The cavitation is present for sure

much earlier (at lower vacuum), however the 1 % limit is used for

convenience. The NPSE value, at which the efficiency or head falls by 1 % is

indicated on the NPSE diagram on the right of the Figure below.

The above discussed NPSE value we also denote as required NPSE or NPSEr.

The name required NPSEr is from the requirement (Slo: "NPSE črpalke ali

NPSEč) of the turbine of the pump runner to operate without cavitation. The

NPSEr characteristic almost always increases with volume flow rate, as the

available pressure decreases with increasing volume flow rate (velocity inside

the runner also increases).

However there is another NPSE value to consider, which is provided by the

system, NPSEa or available. The available NPSEa must be for cavitation free

operation always higher than required NPSEr. With other words, the hydraulc

system must be able to provide at the suction side of the turbine machine

higher available energy than required by the machine for cavitation free

operation. The pump is therefore able to operate left from the intersection of

both NPSEa and NPSEr characteristics. Usually at the intersection the cavitation

is already severe and for long term operation it is required to operate at even

lower volume flow rates.

167

Fig. 110: NPSEa and NPSEr characteristics and pressure characteristics of the turbine machine (right). Every single operationg point is derived from a diagram σ - η (or σ - H ) (left).

To estimate the available NPSEa it is the most convenient to consider the case

of usual installation of pumps from the Figure below. According to the Figure

below the pump gets water from the sump and pushes it in the pressure

pipeline, upper open reservoir or pressure reservoir. Per definition the NPSEa

is

𝑁𝑃𝑆𝐸𝑎 =𝑝1𝑎𝑏𝑠 − 𝑝𝑣

𝜌 +𝑐2

2 . (118)

Available NPSEa is the total energy available on the suction side of the turbine

machine, reduced for the contribution of the vapour pressure. This reduction

may be very small for low water temperatures, but when the water

temperature approaches boiling temperature, it may become significant.

Usually it is impossible to measure the absolute pressure at the location of the

inlet to the pump due to vortices and other turbulent flow phenomena near

the runner entrance. We therefore measure absolute pressure somewhere

further upstream in the location indicated as 𝑝0. For both location we write

the Bernouilli equation and assume no flow losses between both locations 0

and 1. The location 0 is H above the location 1

𝑝0𝑎𝑏𝑠𝜌

+𝑐02

2+ 𝑔𝐻 =

𝑝1𝑎𝑏𝑠𝜌 +𝑐12

2 . (119)

168

We want to eliminate 𝑝0𝑎𝑏𝑠 from the Equation above, as we argued that it is

impossible to measure pressure there. By also assuming that velocity in cross

section 0 is negligible due to a large size of the cross section, we get

𝑝1𝑎𝑏𝑠𝜌

=𝑝0𝑎𝑏𝑠𝜌

+ 𝑔𝐻 −𝑐12

2 . (120)

With insertion of Equation above to Equation above we get

𝑁𝑃𝑆𝐸𝑎 =𝑝0𝑎𝑏𝑠 − 𝑝𝑣

𝜌+ 𝑔𝐻. (121)

It is convenient to include losses and we get

𝑁𝑃𝑆𝐸𝑎 =𝑝0𝑎𝑏𝑠 − 𝑝𝑣

𝜌+ 𝑔𝐻 − 𝐸𝐿𝑆 . (122)

The Equation above explains, why available NPSEa decreases with volume flow

rate 𝐸𝐿𝑆𝛼�̇�2𝛼𝑐2. With the increase of volume flow rate less and less energy is

available at the inlet of the pump, hence the pump is more prone to cavitation.

Fig. 111: Situation for the understanding of the available NPSEa

10.3.2 In turbines Figure below shows the installation of the water turbine. In agreement with

Fig. below the plane 2 is located at the end of draft tube and not in location of

the runner, here producer of mechanical equipment guarantees for

specifications to the buyer. The second reason, why plane 2 is located away

from the runner location 𝑧1 = 𝑧ref is, that we are unable to measure pressure

directly at the runner die to high tangential velocity which may influence the

validity of wall pressure measurements. Therefore, we must recalculate the

flow conditions from the plane 2 to the reference level of the runner.

Fo water turbines we modify Equation above for the change of specific

hydraulic energy in the plane 2 and reference level zref. The reference level

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usually corresponds to the middle of the runner and equation for neto positive

specific energy is

𝑁𝑃𝑆𝐸 =𝑝abs2 − 𝑝v

𝜌2+𝑐22

2− 𝑔 (𝑧ref − 𝑧2) . (123)

If pressure measurements in the plane 2 are possible and pressure tappings

are available and accessible, we directly use the above equation. Very often

water turbines have pre-installed pressure tappings enabling such

measurements and acceptance measurements.

Fig. 112: Water levels and heads in the water turbine for estimation of NPSE and NPSH. The case is shown, that does not enable pressure measurements in plane 2 and losses from planes 2 and 2' are not negligible.

If pressure measurement is not possible, we may estimate NPSE from water

levels at the low accumulation. We use equation below, where losses ±𝐸LS

represent losses from plane 2 to the lower accumulation level and sign + is for

turbine mode of operation and sign - for pump mode of operation

170

𝑁𝑃𝑆𝐸 = 𝑔 𝑁𝑃𝑆𝐻

=(𝑝amb2′′ − 𝑝v)

𝜌2+𝑐2′2

2− 𝑔 (𝑧ref − 𝑧2′′) ± 𝐸LS

=(𝑝amb2′′ − 𝑝v)

𝜌2+𝑐2′2

2− 𝑔 𝑍S ± 𝐸LS .

(124)

Water height in plane 2' is lower than stationary water in lower reservoir,

because flow here still has some kinetic energy. Later, when the flow comes to

a standstill and it's kinetic energy is 0, the velocity term becomes zero and

height may be calculyted to stationary lower water level far away from the

turbine outflow. Equation above is modified into equation below and ±𝐸LS

represent losses from plane 2 to the outflow and sign + is used for turbine

mode of operation and - for pump mode of operation.

𝑁𝑃𝑆𝐸 = 𝑔 𝑁𝑃𝑆𝐻 =(𝑝amb2′′ − 𝑝v)

𝜌2− 𝑔 (zref − 𝑧sv) ± 𝐸LS . (125)

𝑧sv in the equation above is the level of water in lower reservoir.

10.4 Prevention of cavitation effects in water turbines From the viewpoint of available head and characteristics it is not necessary for

a water turbine to be installed at the lowest point in the flow path. Installation

at the lowest location is recommended and in fact also required for economic

reasons due to cavitation. Cavitation occurs when the pressure in the liquid

drops below the vapor pressure and cavitation bubbles develop. Cavitation

and cavitation bubbles reduce the efficiency of the plant and damage the

runner. In the case of implosions of cavitation bubbles near a solid surface,

usually on a suction side of the runner, a high pressure is generated that

erodes the material from the surface. The water turbine must operate at

sufficiently large NPSH, that is, a sufficiently large net positive suction height.

An example of the immersion of a water turbine is shown in Figure below,

which show the upper accumulation, the supply tunnel, the pressure line, the

cross-section of the flow field, the engine room and the inlet of the PHE Avče.

The mechanical shaft in the case of the Avče Pumping Station is about 80 m

deep, with the water turbine located on its bottom, approximately 60 m below

the lower water level, that is, the accumulation of Ajba.

In practice, water turbines are installed as high as possible in order to reduce

the civil engineering construction costs, which represent the largest part of

costs in the construction of a hydroelectric power plant. Installation of the

plant as high as possible can still mean that the immersion (the height of the

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installation of the water turbine below the lower water level) should be up to

60 m.

Fig. 113: Horizontal profile of ČHE Avče. Machinery hall is fully on the right and below. The vertical 7 and horizontal penstock 8 were built because of steepnes of the hill at that particular location and possibility of landsline in the case of horizontal penstock.

10.5 Influence of particles in the flow on cavitation in water turbines It is known that the appearance of cavitation bubbles and the resulting

cavitation characteristics can be largely influenced by impurities and nuclei in

the fluid (an invisible proportion of air or bubbles of gas with a radius of less

than 50 μm). The content of the nuclei affects not only the beginning of the

appearance of cavitation, but also the development of a traveling bubble

cavitation. A precise determination of the required minimum values of the

content of nuclei and dissolved gas is not yet possible, as these data are not

available in accessible scientific literature [Dular, 2014]. The influence of

individual parameters such as the type of water turbine machine, specific

hydraulic energy, etc. it is not yet sufficiently explored.

The appearance of the cavitation and the possibility of its observation

depends on the type of cavitation associated with the type of water turbine.

Especially for cavitation tests in the Francis model turbines of medium and

high specific speeds, where cavitation appears at the exit of the runner, it is

important that the water contains sufficient nuclei that can be activated and

grown in areas where the local pressure is equal to or lower than vapour

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pressure. Prototype measurements indicate that there are usually enough

cores in the water to accelerate cavitation in areas of low pressure. On test

sites where we have a closed water circuit, on the other hand, the number of

particles is reduced due to the degassing of water during cavitation tests. As a

result, a small number of cores are activated for each selected σ value (eg. for

σpl), which to some extent reduces the extent of visible cavitation.

Therefore, the quality of water with respect to cavitation nuclei is similar to

the conditions in the prototype, if the content of the nuclei in the flow path of

the model measuring station is sufficient. This ensures the proper

development of cavitation in all areas where the local pressure equals or

decreases below the vapour pressure of the water. An adequate number of

active cavity nuclei in model measurements can be provided by increasing the

head, by introducing nuclei into water, or by using non degassed water. By

increasing the head in the measurements, it is necessary to be careful because

it can lead to distorted results due to the reduced similarity.

10.6 Runner erosion due to solid dispersed particles The erosion of the driver may also result beside due to a cavitation also due to impurities in the water. Impurities or dispersed particles in water damage the runner by abrasion. Abrasion is different around the world, the most problematic are watercourses with a high amount of deposits, among them for instance watercourses in Southeast Asia and some watercourses in the Dolomites in Italy. In order to reduce the erosion of the runner due to abrasion with impurities in water, a number of studies are carried out tregarding hydraulic shaping of blades and material selection, in order to reduce abrasion and also maintain good hydraulic properties of the water turbine.

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References

Dixon, S. L., Hall, C. A., Fluid Mechanics and thermodynamics of turbomachinery,

Elsevier, 2010

Schlichting, H., Boundary layer theory, 7th ed., McGraw-Hill, New York, 1979

Tuma, M., Sekavčnik, M., E, Energetski stroji in naprave, osnove in uporaba,

druga izdaja, Univerza v Ljubljani, 2005

Korpela, S., A., Principles of Turbomachinery, John Wiley & sons, New Jersey,

2011

Lakshminarayana, B., Fluid dynamics and heat transfer of Turbomachinery,

John Wiley & sons, New York, 1996