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3D NUMERICAL STUDY OF WALL EFFECTS ON VORTEX SHEDDING IN
SUBMARINE PIPELINES
Israel Marino Navas
Armando Blanco
Boris Bossio
Euro Casanova
Departamento de Mecánica, UniversidadSimón Bolívar, Caracas, Venezuela.
Abstract.Nowadays, worldwide energy requirements continue to rise. Annual human population
growth rate has become a good motivation for scientists around the world on finding new ways
for reducing energy requirements by trying to optimize energy generation, transportation and
consumption. Consequently, the human race has seen the need to search all possible energy
sources among which are the oil and gas, usually found offshore. Drilling rigs and production
transport systems are needed to move oil and gas extracted from offshore reservoirs to land
facilities, where those hydrocarbons usually go through several processes in order to be ready to
be used as chemical energy sources in cities and industries.
Submarine pipelines are considered one of the most effective and cost-efficient means of
transportation for moving oil and gas from offshore reservoirs to land. Frequently, long
distances should be covered, since several offshore reservoirs are located far from coastlines.
Submarine pipelines are subject to experience both mechanical and chemical stress conditions.
Specifically, inner and outer flows induce those pipelines to vibrate, jeopardizing their useful
lifespan due to the material fatigue.
Although many advances have been made in the numerical simulation of the flow around
submarine pipelines, most of the studies have considered simplifications such as modeling flow
around a two-dimensional structure.
This paper aims to make three dimensional (3D) simulations for studying the effect of marine
floor (i.e. wall effect) on the frequency of detachment of von Kármán’s vortexes that develop
downstream the pipeline. The numerical simulations were performed using the commercial
software CFX ™ which has been previously validated in cases involving two dimensional
(2D)studies. This paper presents a comparison among numerical predictions on vortex-shedding
frequencies between 3D and 2D models. Both models are subjected to laminar flow regimes with
Reynolds numbers 100 and 300, four different pipeline-seabed distances i.e. 7.5D, 2D, 0.75D
and 0.25D, D being the pipe diameter, and in the case of the 3D model, two different pipe
lengths (100 and 150 m). Numerical results show that the lift coefficient and the Strouhal number
increase as the pipeline approaches the seabed. Additionally, it is shown that vortex shedding
behavior depends on the considered section along the pipeline for the 3D model, this feature
been ignored by the 2D model. Finally, it was found that in the case where the pipe is subjected
to gravity loads perpendicular to free flow conditions (i.e. wall effects not considered), the Root
Mean Square (RMS) lift coefficient value is not zero. This finding shows that when the
deformation of the pipe by gravity is considered, flow asymmetry induced by the actual 3D
pipeline profile gives origin to a pressure gradient, which indicates that the pipe is constantly
loaded in cross-flow direction, thus altering its equilibrium position.
It is concluded that the two-dimensional simplification made for this phenomenon could be
inaccurate depending on the flow parameters and pipe configuration.
Keywords: Submarine pipelines, Vortex-shedding, Lift coefficient, Strouhal number.
Resumen.Actualmente, los requerimientos de energía a nivel mundial siguen aumentando. La tasa
de crecimiento poblacional se ha convertido en una motivación para los científicos alrededor
del mundo para encontrar nuevas formas dereducir los requerimientos energéticos al intentar
optimizar la generación, transporte y consumo de la energía.Debido a esto, el hombre se ha
visto en la necesidad de buscar todas las fuentes posibles de energía entre las cuales se
encuentran los hidrocarburos como el petróleo y gas, sustancias que usualmente son
encontrados costa afuera. Para mover el petróleo y el gas extraídos costa afuera hasta tierra
firme son necesarios diversos sistemas de transporte, ya que es generalmente en tierra firme
donde son procesados para ser utilizados como fuente de energía química en ciudades e
industrias.
Las tuberías submarinas destacanentre los medios de transporte más efectivos para trasladar el
petróleo y el gas desde los yacimientos costa afuera hasta tierra firme. Frecuentemente, estas
reservas de gas y petróleo se encuentran muy alejadas de la costa, razón por la cual las tuberías
deben cubrir un largo trayecto. Estas tuberías submarinas están expuestas a condiciones
mecánicas y químicas críticas; específicamente, los flujos internos y externos inducen
vibraciones mecánicas en la tubería, comprometiendo así la vida útil de la estructura debido a
la fatiga de los materiales que la componen.
A pesar que se han hecho grandes avances en las simulaciones numéricas en los estudios de
flujo de fluidos alrededor de las tuberías submarinas, la mayoría de los estudios han
considerado simplificaciones tales como el modelaje del flujo alrededor de estructuras
bidimensionales.
Esta investigación se en estudiar el efecto del lecho marino (efectos de pared) en la frecuencia
de desprendimiento de vórtices de von Kármán que se desarrollan aguas abajo de la tubería,
con un planteamiento tridimensional.Las simulaciones numéricas fueron realizadas utilizando el
software comercial CFX ™, el cual ha sido previamente validado en estudios bi-dimensionales.
Este trabajo presenta una comparación entre la frecuencia de desprendimiento de vórtices en
modelos 3D y 2D. Ambos modelos fueron estudiados en régimen laminar con números de
Reynolds iguales a 100 y 300, cuatro holgurasentre el cilindro y la pared: 7.5D, 2D, 0.75D y
0.25D-donde D representa el diámetro de la tubería- y en el caso del modelo 3D, dos longitudes
de tubería (100 y 150 m). Los resultados muestran que el coeficiente de sustentación y el número
de Strouhal aumentan a medida que la tubería se aproxima al lecho marino. Adicionalmente, se
muestra que el comportamiento tridimensional del desprendimiento de vórtices no es tomado en
cuenta cuando se realiza la simplificación 2D. Finalmente, se observó que en el caso donde la
tubería es deformada por efecto de la gravedad y no se consideran los efectos a pared, el valor
RMS (“Root Mean Square”) del coeficiente de sustentación no se anula. Este hallazgo muestra
que cuando la tubería es deformada por efecto de la gravedad, la asimetría del flujo inducida
por el perfil 3D de la tubería, da origen a un gradiente de presiones tal, que resulta en una
carga perenne en la estructura en la dirección perpendicular al flujo, alterando así su posición
de equilibrio estático.
Se concluye que la simplificación bi-dimensional hecha para este fenómeno puede ser poco
precisa dependiendo de los parámetros del flujo y de la configuración de la tubería.
Palabras Clave:Tuberías submarinas, Desprendimiento de vórtices, Coeficiente de sustentación,
Número de Strouhal.
1. INTRODUCTION
Vortex shedding is a phenomenon that has been highly studied since the early 1900s, both
analytically and experimentally. Nowadays, this topic is taken into account at the design stage of
many engineering applications, such as heat exchangers, nuclear reactors and even in the
climatological field. When studying vortex shedding, the fluid–structure interaction is analyzed,
and it has been found that this phenomenon potentially may compromise the mechanical
integrity of the structure and could cause it to fail, as the case of the Tacoma Narrows bridge,
which collapsed by high vibration amplitudes caused by the wind, in 1940.
Vortex-Induced Vibration (VIV) in submarine pipelines is a case of special interest because
these structures are mechanically affected by external and internal flows. Submarine pipelines
are frequently used in the oil industry for transporting oil and gas from offshore facilities to land.
Those pipelines are supported at the bottom of the sea which has, in some areas, an irregular
topology. For this reason, the supports of the pipes are, sometimes, separated by very long
distances (i.e. around 80-100m), being this support condition the most harmful one, as it
potentially allows the structure to vibrate excessively due to external flow.
The submarine pipelines are frequently modeled as circular cylinders. It is widely known
that the detachment of the vortices occurs when the Reynolds number (Re) value, based on the
cylinder diameter (D), is greater than 40 [1]. Beyond this regime, different flow patterns and
characteristics of the wake downstream of the cylinder are present. If a plane is inserted near the
cylinder, the phenomenon of vortex shedding is affected in structure, stability and frequency of
detachment. This fact has been shown through numerous experimental works (e.g. Taneda, 1965
[2];Göktun, 1975 [3];Bearman&Zdravkovich, 1978 [4];Angriliet al, 1984 [5]). However, none of
these studies takes into account the deformation of the cylinder due to gravity and the effect of
the difference of the gap (G) between the cylinder and the wall in the vortex shedding.
In the simulation field, several studies have been conducted on this phenomenon (e.g. Lei et
al, 2000 [6];Dettner&Peric, 2006 [7];Rajaniet al, 2009 [8]; Medina, 2010 [9]; and Rodríguez,
2012 [1[10]]) recreating accurately and precisely the vortex shedding effect on the
structure,using different codes and methods. Specifically, using CFXTM
, both Medina and
Rodríguez validated their models for analyzing vortex shedding effect on structures, in cases
where the structure was close to a wall, considering laminar flows. However, the cited numerical
analyzes have been simplified modeling a 2D domain. The present study focuses on whether this
simplification is valid for those cases where the ratio G/D is variable along a 3D structure, as is
the case of submarine pipelines which are deformed by the effect of gravity.
2. PHYSICAL MODEL
An air-filled structural steel pipe immersed in water is considered here. This submarine
pipeline has deflected due to gravity effects, therefore, there are different gaps G(Z) along its
longitude between it and the seabed. In order to engage in a short description of the VIV in a
cylinder, the reader must keep in mind that when the fluid encounters an object in its path, the
velocity of the fluid particle along the contact surface is zero causing a velocity gradient near the
object forming a boundary layer. In the case of the cylinder, the formed boundary layer would try
to surround it and at some point, the boundary layer will separate from the cylinder's surface, due
to its excessive curvature. This situation will promote the formation of vortexes. Vortexes are not
frequently formed symmetrically from the cylinder's symmetry plane and this is the cause of
different lift forces at the two sides of the cylinder; this originates a resultant global lift force
acting on the cylinder, inducing structure displacements in the transversal direction to the fluid
flow. The generated transversal movement changes the vortexes formation nature in a way that
vibration amplitude is limited, in most cases. At low Reynolds’s number values, current lines are
expected to be symmetrical, as long as predicted by potential flow theory.
Figure 1-Sketch of the deformed pipe near the seabed and being exposed to an external flow
Figure 1shows a submarine pipeline subjected to amarine current. In the figure it is shown
the velocity profile of the marine current approaching the pipe, where Uo is the free flow speed
of the marine current. Downstream, vortexesare detached, which will result in a harmonic
excitation on the pipe in the cross-flow direction. This study focuses on studying the effect of the
gap (G) between the bottom of the pipe and seabed and marine current velocity values on the
frequency of detachment of the vortices, fs. Different marine current velocity values will be
considered through different Reynolds’s number values.
Strouhal’s number is a dimensionless parameter used in problems of oscillatory and
transitory flux, which represents physically the relation between the inertial forces caused by the
flux instability and the inertial forces caused by the change of velocity from a point to another in
the fluid field[1]. Strouhal’s number is defined as:
(1)
Where,
S is the Strouhal’s number.
fs is the vortex shedding frequency
D is the pipe diameter
Uo is the free-stream velocity
It is well known that the vortex shedding frequency fs is the same that the lift force
frequency and two times the drag force frequency [1].
Fluid dynamics was modeled by transient Navier-Stokes equations for Newtonian and
incompressible fluids:
(2)
(3)
Where,
ρis the fluid density.
V is the velocity vector.
g is the body force vector.
p is the pressure.
μis the dynamic viscosity of the fluid.
The energy equation isnot considered because the system is isothermal and there is no mass or
heat transfer involved.
3. NUMERICAL MODEL
ANSYS CFX software is a high-performance, general purpose fluid dynamics program that
has been applied to solve wide-ranging fluid flow problems.This computational fluid dynamics
software was used for solving the problem in question.This program applies the finite volume
method to solve the equations shown previously, using an implicit method which has a second
order accuracy in both time and space.
The considered boundary conditions are shown in the Fig. 2.The set initial conditions were
obtained from a steady-state simulation using both the same domain and boundary
conditions.The“upwind” advection scheme was set for optimizing the computational required
time to get the results.
Figure 2- Boundary conditions used in the domain
The opening condition (definedby pressure value) was used to allow the recirculation of the flow
in the outlet surface and a velocity definition based on the Reynolds number was used in the inlet
condition.
4. CASES OF STUDY
On this paper, the effect of marine floor (i.e. wall effect) on the frequency of detachment of
von Kármán’s vortexes that develop downstream the pipeline is studied. The obtained 3D results
were compared with the ones from the 2D case studied by Medina [9], in which the“wall effect”
in a 2D cylinder under laminar flow was studied. Four different gaps (G) denoted as: G1=0,25D,
G2=0,75D, G3=2D and G4= 7,5D were considered. The last case was defined as “no-borders”
(NB) because the wall effect at this distance is indeed neglected. It is important to bear in mind
that one of the mainfocuses and motivations of this paper is to compare the 2D simplification
results [9] with the present full model (3D) results, hence,the cases of study of this work were the
same that Medina [9]considered. In order to add a 3D parameter, two pipeline length (L)
wasconsidered as well.Figure 3shows a diagram of the cases studiedon this work.
Figure 3-Cases of study
5. RESULTS
A sweeping method was used to build the discrete geometry around the deformed cylinder.
Therewere considered hexahedral elements witha second order form function in order to be able
to achieve better accuracy in the interpolation of the solution between the faces of the cells. The
block around the cylinder had five layers of prismatic elements and a first element size of 0,425
mm. These parameters were validated by Medina [9], whosuccessfully represents the vortex
detachment of a 2D cylinder. For the case of a 3D domain it is necessary to estimate the number
of cells in the longitudinal axis of the pipe to capture with precision the physics of the problem.
Table 1 showsthe mesh sensitivity analysis for the case of the present study were a high
numerical precision was required (i.e.Re=300, L=150 m, G/D=0,25).CL and CD represent the lift
and drag coefficients, respectively and S is the Strouhal’s number
Table 1-Mesh sensitivity study
Number of divisions CL CD S
20 0,4000 0,1755
40 0,0667 0,4190 0,1873
80 0,0714 0,4286 0,2435
These results show that the mesh criterion convergence has not been reached. However in
Simón Bolívar University's facilities there were no computer that had the capacity to perform a
simulation with a partition of 120 cells in the longitudinal direction of the cylinder. Additionally,
80 divisions is also a challenging goal to achieve because the time required for running all the
study cases with this partition would exceeded the available time to write this work, for this
reason a mesh with only 40 division was employed.
The time step used in the present work was determined by means of the Courant number
which was fixed at a value of 1 for a more accurate solution.Theresults shown in this sectionwere
selected at a certain time, where the RMS valuesand amplitudesof the drag and lift forcesdon't
varied significantly.In order to be able to compare these results with the ones obtained by
Medina [9](Re=300),a monitor point was defined at a distance near the pipe (y/D=1, x/D=1) at
the mid plane of the longitudinal direction.This was made to be able to compare the frequency
value of the vortices detachment in a plane of the domain with the 2D simplification. The tables
2 & 3 show the results obtained at a flow regime of Re=100 and tables 4 & 5 show the results
obtained at Re=300.
As expected, the lift coefficient value increases as the cylinder gets closer to the wall. The
wall effect produce an asymmetry in the flow around the pipe, causing a rise in the pressure field
in the cylinder’s bottom, then, the resultant perpendicular force increases as well. Additionally, it
is observed that for all the flux regimes and pipe lengths, the lift force is not equal to zero in the
NB case. This is caused by the flow asymmetry that is formed around the deformed structure.
The catenary form of the pipe produces a higher pressure distribution in the pipe bottom,
resulting in a persistent force that has to be taken into account because it changes the equilibrium
position of the structure.
To discard a possible numerical error on this affirmation, the simulation of a straight
cylinder was done, considering the same flux regime, pipe-length and gap (NB) conditions. The
resultant lift coefficient for this case was 7,5x10-5
which is a negligible value in comparison with
the one obtained in the simulation of the deformed cylinder. Figure 4 shows the streamlines for
these two cases.
Table 2-Results obtained for Re=100, L=100 m
Seabed Gap, G CL CD S
NB 0,5387 0,1660
2D 0,0408 0,6135 0,2080
0,75D 0,0407 0,6510 0,1750
0,25D 0,0701 0,6211 0,1969
Table 3-Results obtained for Re=100, L=150 m
Seabed Gap, G CL CD S
NB 0,8032 0,1625
2D 0,0475 0,8485 0,1618
0,75D 0,0582 0,8990 0,1796
0,25D 0,0665 0,8770 0,1778
Table 4-Results obtained for Re=300, L=100 m
Seabed Gap, G CL CD S S*
NB 0,4205 0,1805 0,1791
2D 0,1257 0,4633 0,1958 0,1998
0,75D 0,1582 0,4866 0,2040 0,2046
0,25D 0,0701 0,4453 0,2028 0,1694
Note: S* correspond to the Strouhal’s number calculated using the oscillation frequency of
the velocity in the monitor point near the pipe in the mid-plane of the structure.
Table 5-Results obtained for Re=300, L=150 m
Seabed Gap, G CL CD S S*
NB 0,3967 0,1800 0,1752
2D 0,0726 0,3711 0,1738 0,1951
0,75D 0,1177 0,4333 0,1870 0,1898
0,25D 0,0655 0,4281 0,1871 0,1812
In the tables 4 and 5 it is shown that the difference between the Strouhal’s number value
measured using the lift force frequency and the one that is calculated using the monitor point
velocity near the cylinder, is very low (i.e. <5%) for most cases. This proves that the deflection
of the pipe causes a three-dimensional behavior in the flow and that the shedding frequency
depends on the entire flow field.
Figure 4- Dimensionless velocity (U/Uo) streamlines around the pipeline.
(a) straight cylinder (b) deformed cylinder.
The results shown in Figs. 5 to 7 suggest that the 2D simplification doesn’t reproduce
accurately the detachment of vortexes in a deform cylinder who is near a plane, because the three
dimensionality of the vortex street it’s not considered in the 2D model. Fig 8 shows this
phenomenon graphically.
Figure 5-Lift coefficient comparison with Medina [9] (Re=300)
Figure 6-Drag coefficient comparison with Medina [9] (Re=300)
Figure 7-Strouhal's number comparison with Medina [9] (Re=300)
Figure 8-Dimensionless velocity (U/Uo) streamlines around the pipeline
(Re=300 and L=100 m). (a) G/D=NB; (b) G/D=2; (c) G/D=0,75; (d) G/D=0,25
Figure 9-Dimensionless velocity (U/Uo) contour plot in the mid-plane of the pipeline
(Re=300 and L=100 m). (a) G/D=NB. (b) G/D=2. (c) G/D=0,75. (d) G/D=0,25
Figure 8illustrates the three-dimensionality of the flow previously mentioned which show
that the vortex street, that is formed downstream of the pipe, has different frequencies of
detachment. This delayin frequency becomesmore evident as the gap between the cylinder and
the seabed reduces, causing a 3D curvature in the vortex street. Fig 8d shows that for the case
where the gap is smaller than 0,3D, the vortex shedding is suppressed. This behavior, also shown
in Fig. 9d,has beenreportedsome authors [1], [2], [3], [6], [9].
6. CONCLUSIONS
A 3D Numerical study of wall effects on vortex shedding in submarine pipelines was
conducted in this work. The effect of marine floor on the frequency of detachment of von
Kármán’s vortexes, that develop downstream the pipeline, was analyzed throughnumerical
results,showing that the lift coefficient and the Strouhal number increase as the pipeline
approaches the seabed. Results, also showed that vortex shedding behavior depended on the
considered section along the pipeline for the 3D model, being this feature ignored by 2D models.
Finally, it was found that in the case where the pipe is subjected to gravity loads perpendicular
toits longitudinal axis, and no wall effect is considered (i.e. NB condition) the RMS lift
coefficient value is not zero. This finding shows that when the deformation of the pipe due to
gravity is considered, flow asymmetry induced by the actual 3D pipeline profile gives origin to a
pressure gradient, which indicates that the pipe is constantly loaded in cross-flow direction, thus
modifying its equilibrium position. As general conclusions, it may be stated that:
For cases were the wall-effect and the deformation of the pipe due to gravity or any body-
force is important, 2D simplification is not recommended.
The three-dimensionality of the deformed pipe causes a variation in the near-wall vortex
shedding frequency in all the pipeline length.
When the deformation of the pipeline is important, it is necessary to take into account the
force in the cross-flow direction which changes the equilibrium position of the structure.
7. REFERENCES
[1]. Blevins, R.,Flow Induced Vibrations. Krieger Publishing Company, 2001.
[2]. Taneda, S., Experimental Investigation of Vortex Streets. Journal of the physical society
of Japan, vol. 20, n. 9, pp 1714-1721, 1965.
[3]. Göktun, S.,The drag and lift characteristics of a cylinder placed near a plane surface.
Msc thesis, Navalpostgraduate school, California, USA, 1975.
[4]. Bearman, P.&Zdravkovich, M., Flow around a circular cylinder near a plane boundary.
Journal of Fluid Mechanics, vol. 89, n. 1, pp. 33-47, 1978.
[5]. Angrilli, F., Bergamaschi, S., &Cossalter, V., Investigation of wall induced
modifications to vortex shedding from a circular cylinder. Journal of Fluids
Engineering, vol. 104, n. 1, pp. 518-522, 1982.
[6]. Lei, C., Cheng, L., Armfield, S., & Kavanagh, K., Vortex shedding suppression for flow
over a circular cylinder near a plane boundary. Ocean engineering, vol 27, pp. 1109-
1127, 2000.
[7]. Dettmer, W., &Peric, D., A computational framework for fluid-rigid body interaction:
Finite element formulation and applications. Computer methods in applied mechanics
and engineering, vol. 195, pp. 1633-1666, 2006.
[8]. Rajani, B., Kandasamy, A., &Majumdar, S., Numerical simulation of laminar flow past
a circular cylinder. Applied mathematical modeling, vol. 33, pp. 1228-1247, 2009.
[9]. Medina, M., Estudio numérico del efecto de paredes en la frecuencia de
desprendimiento de vórtices en tuberías submarinas. Bachelor thesis, Universidad
Simón Bolívar, Caracas, Venezuela, 2010.
[10]. Rodríguez, A., Simulación numérica del flujo alrededor de un cilindro móvil utilizando
ANSYS-CFX. Bachelor thesis, Universidad Simón Bolívar, Caracas, Venezuela, 2012.