hydrodynamics of ocean pipelineshydrodynamics of ocean pipelines 145 assembling of the model. the...

HYDRODYNAMICS OF OCEAN PIPELINES

著者 "YOSHIHARA Susumu, TOYODA Shozo, VENKATARAMANAKatta, AIKO Yorikazu"

journal orpublication title

鹿児島大学工学部研究報告

volume 35page range 143-153別言語のタイトル海底パイプラインの動力学URL http://hdl.handle.net/10232/12423


著者 YOSHIHARA Susumu, TOYODA Shozo, VENKATARAMANAKatta, AIKO Yorikazu

journal orpublication title

鹿児島大学工学部研究報告

volume 35page range 143-153別言語のタイトル海底パイプラインの動力学URL http://hdl.handle.net/10232/00002229


Susumu YOSHIHARA, Shozo TOYODA,

Katta VENKATARAMANA and Yorikazu AIKO

(Received May 31, 1993)

Abstract

This paper describes the preliminary experimental studies on the current forces acting on

cylindrical models in a steady flow, corresponding to the cases of similar but rigid and large dia

meter pipelines in real seas. The models were placed in a circulating water channel horizontally

and normal to the direction of current flow. The strains in the models were recorded using the

strain guages from which fluid forces in the horizontal and vertical direction were obtained. The

drag coefficient, the lift coefficient and the Straul number were also calculated and are shown

againt the Reynolds number.

1. Introduction

Marine pipelines are used for various purposes such as for transporting offshore products to

onshore terminals, for carrying cables, for discharging waste in deep waters, as under-water pas

sageways and so on. Therefore their behaviour under environmental forces has attracted wide in

terest. Bokain and Geoola (1987) studied the behaviour of an elastically mounted circular cylinder

having vibrations restricted to a plane normal to the incident flow and concluded that the flexible

cylinder may undergo either vortex-resonance, a galloping, or a combination of both. Fredsoe and

Hansen (1987) investigated the lift forces acting on pipes with or without a small gap between thepipe and the sea bed and showed that the theoretical expressions can be used to predict the lift

forces satisfactorily. Shankar et al (1987) determined experimentally the wave force coeffcients formarine pipelines. Verley et al (1988) suggested a new hydrodynamic force model, called the wake

model, for the prediction of fluid forces on seabed pipelines and showed that their model overcomes

the deficiencies of the conventional Morison equation. Two effects included explicitly in the new

force model, related to the wake behind the pipeline and the time dependence of the force coffi-

cients, were supported by measurements. Chiew (1991) studied the changes in the flow pattern

around horizontal circular cylinders immersed in shallow open-channel flows with different gap

openings between the cylinder and the bed. He observed that the low flow depth causes backup of

the upstream flow depth due to choking of the flow. This phenomenon causes the occurrence of a

weir-flow condition at the cylinder, where a large drawdown forms. The net result is the increase

in the drag force. Changes to both the drag and the lift forces on the cylinder for varying flow

depth and gap size combinations were measured and the reasons for these changes were discuss

ed.

Most of the above studies deal with the pipelines located on the sea bed or near the sea bed

where the emphasis has been placed on scour effects. But in some situations pipelines may be far

above the sea bed. This paper investigates the fluid forces on such pipelines placed well-above the

144 S. YOSHIHARA, S. TOYODA, VENKATARAMANA K. and Y. AIKO

sea bed but well-below the free surface. The study also examines the variations in the fluid force as

the position of the cylinders normal to the flow change.

2. Experimental setup

Experiments were carried out in the circulating water channel of the Faculty of Fisheries ofKagoshima University. The measuring section of this channel is 6m in length, 2m in width and lmin depth with a maximum water velocity of 2 m/sec.

Considering the size of the water channel available for the measurements, it was decided to

use hollow cylindrical pipes made of poly-vinyl chloride(p.v.c) as experimental models. Two types ofmodels were considered for the study. First type was a single pipe(Model 1) and the second typeconsisted of two pipes held together side-by-side(Model 2). Figure 1 shows the experimental set upfor Model 1. Experiments were carried out for two cases of Model 1 i.e., diameter =7.5cm , 20cm.

In the case of Model 2, the diameter of each of the two pipes was fixed as 7.5cm , but experiments

were conducted for different inclinations of the model with respect to the flow direction i.e., the

angle 6 between the flow direction and the line joining the axis of the two pipes was varied. Ex

periments were carried out for 6 = 0°, 15°, 30°, -15° and -30°.

The central portion of the pipe was cut and a measuring section, as described below, was in

serted tightly into the pipe and then the pipe was attached rigidly to steel frames and lowered into

the water channel.

When same loads are applied at points of distance from the center of a simply supported beam,

the bending moment is equal between those points. Using this principle, two circular plates were

inserted at the center between the outer pipe and the measuring section. These plates transfer the

fluid loading from the outer pipe to measuring section. Four strain gauges were attached at the

two mutually perpendicular positions on the measuring section. Thus it was made possible to mea

sure the horiozontal and vertical components of fluid forces on the pipes.

Figure 2 is the photo of the measuring section with strain gauges attached. Figure 3 shows the

operation of inserting the circular plates on each side of the measuring section. Figure 4 shows the

l.fito

Figure 1 Experimental setup

HYDRODYNAMICS OF OCEAN PIPELINES 145

assembling of the model. The measuring section is being tightly inserted into the pipe. Figure 5

shows the assembled model. It is being lowered into the water channel in Figure 6. Figure 7 is a

snapshot of the model set in the water channel.

Figure 2 Photo of measuring section withstrain gauges

Figure 4 Assembling of the model

Figure 6 Lowering the model into waterchannel

Figure 3 Inserting circular plates between theouter pipe and the measuring section

Figure 5 Photo of an assembled model

Figure 7 Snapshot of the model set in thewater channel


3. Results

The experiments were conducted for current velocities ranging from 0.1m /sec to 2 m /sec at

0.1m /sec intervals. The strain data was recoded for about 40 seconds under flow conditions for

each value of the current velocity. The recorded data was digitized using analog-digital converter

and the time step was 0.2 sec. Figure 8 shows the examples of time histories of the strain data in

the horizontal direction for a 24-second duration. The curves are shown for current velocities of

0.5m /sec, 1.0m /sec and 2.0m /sec respectively. The variation from the mean values are given.

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24


As the current velocity increases the strain also becomes larger and more chaotic, as expected. Fi

gure 9 shows the example of time histories of the strain data in the vertical direction. The variation

in the strain for low current velocities is relatively periodic and the period may be dependent upon

the eddy shedding frequency. When the flow velocities are higher, the flow is turbulent and the

variation in the strain becomes random and chaotic.

The relationship between the strains and the forces inducing them were deduced from a sim

ple static calibration test Then, from the mean values of the fluid-induced strains, fluid forces were

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calculated. Figure 10 shows the fluid forces for the case of Model 1. The mean values of the hori

zontal component of the fluid forces i.e„ the drag force and the vertical component of the fluidforces Le., the lift force are plotted against current velocities. Note that each value of the fluid force

was deduced from the average value of the strain data for the 40-second duration. The results are

shown for two cases of Model 1 i.e„ pipe diameter of 7.5cm and 20cm . As expected, drag forces in

crease generally nonlinearly with the current velocity and also with the increase in pipe diameter.

The variation in the drag force is relatively straightforword, but lift force changes more randomlyas current velocities increase for the 20cm pipe indicating complex flow patterns and high of turbu

lence around the pipe. Figure 11 shows the fluid forces for Model 2. Four sets of force data i.e., cor

responding to the horizontal(drag) and vertical(lift) forces on the pipes on the upstream side as

well an on the downstream side are plotted against current velocities. The results are given for

different angles of incidence 6 i.e., different angles between the flow direction and the line joining

the center-line of two pipes. The drag forces generally increase with the increase in the angles of

incidence because it offers more resistance to fluid flow. Also forces on the upstream pipe are larger than those on the downstream pipe.

The measured values of the forces in the above figures indicate the complexity of the flow pat

tern around the ocean pipelines which may depend on various factors such as eddies and other

forms of turbulence, relative roughness, body orientation, proximity effects, parameters of the

kinematics of the flow field, etc. It is common practice to represent these uncertainties using hy-

drodynamic coefficients. A coefficient Cd corresponding the drag force Fd and a lift coefficient C/

corresponding to the lift force F{ can be calculated from the normal drag and lift equations:

Fd(or Fd =^-q,(orC/) pAt?

where A is the projected area of the pipe, P is the mass density of water and u is the velocity of

current. Figure 12 shows the values of the drag coefficient Cdplotted against the Reynolds number

Re. The values follow a pattern observed generally for vertical cylinders in unidirectional flows. Fi

gure 13 shows the values of the lift coefficient C/ plotted against the Reynolds number. The values

show large scatter, the general tendency decreasing with the increase in Reynolds number is clear.

Figures 14 and 15 show the values of the drag coefficient Cd and the lift coefficient C/ respec

tively plotted against the Reynolds number Re for Model 2 which consists of two pipes held

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together. The distribution of the values of the coefficients varies with the angle of incidence and the values are

different from those corresponding to Model 1 which consists of a single pipe. When two pipes are held

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there are also interacting effects between these pipes. Therefore the force distribution and hence the values of

the coefficients show different distribution. But the general trend of the values with the Reynolds number is the

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of strains in the vertical direction were analyzed Fast Fourier Transform and frequencies corresponding to

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Reynolds number for Model 1 Le., for the case of single pipe model. The values are relatively constant for the

range of the Reynolds number for small diameter pipe indicating regular shedding. For the large diameter pipe,

the Straul number dips which indicates the approach of critical flow domain.

4. Conclusions

A laboratory study on the hydrodynamic forces on ocean pipelines in steady current flow has

been carried out. It is found that the drag force generally increases with flow velocity as expected.

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The variation of lift force is more complex and is significantly affected by the eddies and other forms of tur

bulence around the models. For Model 2 which consists of two pipes held together, the fluid forces are greater

on the upstream side. The forces are also influenced by the orientation of the pipelines with respect to flow.

The values of the hydrodynamic coefficients and the Straul number are generally similar to the results for ver

tical cylinders in uniform flows.

Acknowledgements

Mr Shoichiro Tamae and Mr Seiichiro Ishizaka, undergraduate students, helped in carrying

out the laboratory experiments.

References

1) Bokain, A. and F. Geoola (1987) :Flow-induced vibrations of marine risers, /. Waterway, Port,Coastal and Ocean Eng., ASCE, 113 (1) ,pp. 22-38.

2) Chiew, Y. (1991) :Flow around horizontal circular cylinder in shallow flows, /. Waterway, Port,Coastal and Ocean Eng., ASCE, 117 (2) ,pp. 120-135.

3) Fredsoe, J. and E.A. Hansen (1987) : Lift forces on pipelines in steady flow, /. Waterway, Port,Coastal and Ocean Eng., ASCE, 113 (2) ,pp. 139-155.

4) Shankar, N.J., H. Cheong and K. Subbiah (1988) :Wave force coefficients for submarine pipelines,/ Waterway, Port, Coastal and Ocean Eng, ASCE, 114 (4) ,pp. 472-486.

5) Verley, R.L., K.F. Lambrakos and K. Reed (1989) : Hydrodynamic forces on sea bed pipelines, /.Waterway, Port, Coastal and Ocean Eng., ASCE, 115 (2) ,pp. 190-204.

hydrodynamics of ocean pipelineshydrodynamics of ocean pipelines 145 assembling of the model. the...

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