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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
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/10232/00002229
HYDRODYNAMICS OF OCEAN PIPELINES
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
146 S. YOSHIHARA, S. TOYODA, VENKATARAMANA K. and Y. AIKO
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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Figure 8 Examples of time histories of strain in horizontal direction(Model 1, pipe diameter =7.5cm)
24
HYDRODYNAMICS OF OCEAN PIPELINES 147
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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(Model 1, pipe diameter =7.5cm)
24
148 S. YOSHIHARA, S. TOYODA, VENKATARAMANA K. and Y. AIKO
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
,_ 1 (1)
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HYDRODYNAMICS OF OCEAN PIPELINES 149
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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
together, as in the case of Model 2, the fluid loading on the upstream pipe and the downstream pipe vary and
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
same as for single pipe of Model 1.
For steady flows past pipelines due to a current, the main measure of the frequency of lift forces is the
Straul number S which is a function of the eddy sheddinng frequency. In the present study, the time histories
150 S. YOSHIHARA, S. TOYODA, VENKATARAMANA K. and Y. AIKO
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of strains in the vertical direction were analyzed Fast Fourier Transform and frequencies corresponding to
maximum amplitudes were located. Assuming that these correspond to eddy shedding frequencies at each cur
rent velocity, Straul number was calculated. Figure 16 shows this Straul number plotted as a function of
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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HYDRODYNAMICS OF OCEAN PIPELINES
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S. YOSHIHARA, S. TOYODA, VENKATARAMANA K. and Y. AIKO
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HYDRODYNAMICS OF OCEAN PIPELINES
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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.