Group Title: 7th International Conference on Multiphase Flow - ICMF 2010 Proceedings
Title: P1.29 - Comparison between 2-D CFD and 1-D code for Wave Growth Simulations
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 Material Information
Title: P1.29 - Comparison between 2-D CFD and 1-D code for Wave Growth Simulations Computational Techniques for Multiphase Flows
Series Title: 7th International Conference on Multiphase Flow - ICMF 2010 Proceedings
Physical Description: Conference Papers
Creator: Kalogerakos, S.
Gourma, M.
Thompson, C.P.
Publisher: International Conference on Multiphase Flow (ICMF)
Publication Date: June 4, 2010
 Subjects
Subject: 2D CFD
wave growth
multiphase flow
VOF
 Notes
Abstract: Limitations in the predictive capability of one-dimensional simulations of pipeline multiphase flow have led to a recent increase in the use of three-dimensional commercial CFD codes in the oil industry. On the other hand, issues arise in 3D simulations when setting initial conditions and with simulation time lengths, especially when long pipelines are involved. An alternative is to use a two-dimensional CFD code with some modifications. In this paper various methods are discussed that allow swift simulations of pipeline two-phase flow with 2D code. Moreover results from 2D commercial code simulations are compared with results obtained with in-house developed 1D code EMAPS (Omgba-Essama 2004). Comparisons include analysis of the wave growth problem, and measurements of the wave rate of growth (Valluri et al 2008). Recommendations are given in cases where 2D CFD can be used with no particular disadvantage compared with 3D CFD, and with comparable running times to 1D code. Specific cases involving simulations where slug flow is observed (Ujang et al 2008) are also discussed.
General Note: The International Conference on Multiphase Flow (ICMF) first was held in Tsukuba, Japan in 1991 and the second ICMF took place in Kyoto, Japan in 1995. During this conference, it was decided to establish an International Governing Board which oversees the major aspects of the conference and makes decisions about future conference locations. Due to the great importance of the field, it was furthermore decided to hold the conference every three years successively in Asia including Australia, Europe including Africa, Russia and the Near East and America. Hence, ICMF 1998 was held in Lyon, France, ICMF 2001 in New Orleans, USA, ICMF 2004 in Yokohama, Japan, and ICMF 2007 in Leipzig, Germany. ICMF-2010 is devoted to all aspects of Multiphase Flow. Researchers from all over the world gathered in order to introduce their recent advances in the field and thereby promote the exchange of new ideas, results and techniques. The conference is a key event in Multiphase Flow and supports the advancement of science in this very important field. The major research topics relevant for the conference are as follows: Bio-Fluid Dynamics; Boiling; Bubbly Flows; Cavitation; Colloidal and Suspension Dynamics; Collision, Agglomeration and Breakup; Computational Techniques for Multiphase Flows; Droplet Flows; Environmental and Geophysical Flows; Experimental Methods for Multiphase Flows; Fluidized and Circulating Fluidized Beds; Fluid Structure Interactions; Granular Media; Industrial Applications; Instabilities; Interfacial Flows; Micro and Nano-Scale Multiphase Flows; Microgravity in Two-Phase Flow; Multiphase Flows with Heat and Mass Transfer; Non-Newtonian Multiphase Flows; Particle-Laden Flows; Particle, Bubble and Drop Dynamics; Reactive Multiphase Flows
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Bibliographic ID: UF00102023
Volume ID: VID00443
Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
Resource Identifier: P129-Kalogerakos-ICMF2010.pdf

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7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 -June 4, 2010


Comparison between 2-D CFD and 1-D code for Wave Growth Simulations


S. Kalogerakos*, M. Gourma* and C. P. Thompson*

Department of Applied Mathematics and Computing, Cranfield University, Cranfield, Beds. MK43 OAL, UK
s.kalogerakos@cranfield.ac.uk
Keywords: 2D CFD, wave growth, multiphase flow, VOF




Abstract

Limitations in the predictive capability of one-dimensional simulations of pipeline multiphase flow have led to
a recent increase in the use of three-dimensional commercial CFD codes in the oil industry. On the other hand,
issues arise in 3D simulations when setting initial conditions and with simulation time lengths, especially when long
pipelines are involved. An alternative is to use a two-dimensional CFD code with some modifications. In this paper
various methods are discussed that allow swift simulations of pipeline two-phase flow with 2D code. Moreover
results from 2D commercial code simulations are compared with results obtained with in-house developed 1D code
EMAPS (Omgba-Essama 2004). Comparisons include analysis of the wave growth problem, and measurements of
the wave rate of growth (Valluri et al 2008). Recommendations are given in cases where 2D CFD can be used with
no particular disadvantage compared with 3D CFD, and with comparable running times to 1D code. Specific cases
involving simulations where slug flow is observed (Ujang et al 2008) are also discussed.


Nomenclature

Roman symbols
g gravitational constant (ms 1)
j complex part
k wavelength (m)
p pressure (Nm 2)
u velocity (m/s)
Greek symbols
aL Liquid volume fraction
ac Gas volume fraction
S viscosity (kg/(sm))
p density (kg/(ms2))
w frequency (1/s))



Introduction

Commercial software Ansys FLUENT is a well-known
CFD software solution that is being used by various
companies and in this paper use of FLUENT was aimed
at simulations of two-phase flow in horizontal circular
pipes of constant diameter. On the other hand, the one-
dimensional software called EMAPS (Eulerian Multi-
phase Adaptive Pipeline Solver) was written in Cranfield
University and is based on Fortran F90.
Validation of FLUENT results was initially carried


out by investigating the wavegrowth problem, which
consists in introducing a perturbation at the inlet and
analysing its propagation and wave growth rate. In this
case, a full 8m long sine wave was introduced in a 30m
long horizontal pipe with constant diameter of 78mm,
at 15m from the inlet and constant superficial velocities
for liquid 0.4 m/s and gas 2.0m/s (water and air) were
imposed; these conditions were implemented by writing
custom user code (UDFs) in C++ for FLUENT. Initial
conditions are shown in Fig. 1.


Figure 1: Initial sine wave introduced in the 30m pipe.


I Xt '-








7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 -June 4, 2010


Simulations were carried out using both viscous
model k-epsilon and Reynolds stress model. There was
an issue with the fact that a further perturbation appears
to stem from the inlet (in the FLUENT simulation) and
then propagates along the channel, quickly neutralising
the sine wave. In the EMAPS one-dimensional code on
the other hand, the sine-wave is propagating but keeps
its general sine shape well beyond 10 seconds.
It was thus decided to attempt to counteract the forma-
tion of the perturbation at the inlet by first carrying out
a steady state simulation in FLUENT, and then applying
the sine-wave to the steady state solution and starting
the transient simulation from that point. Gas was set to
be incompressible, in line with EMAPS settings. The
steady-state simulation converged, and the gas and liq-
uid velocity profiles are given in Fig. 2.


0.99

0.94


S0.9

0 .84

079

074


Figure 3: Wavegrowth as
different cells.


10 15 20
Time(s)


calculated by


Figure 2: Velocity profile after steady state simulation
of wavegrowth.

A transient simulation was then started from the
steady state simulation result, and graphs of the wave
growth at different times are shown in Fig. 6 and Fig. 7
(contours of volume fraction). Using Matlab, it was pos-
sible to estimate the rate of growth. The rate of growth in
EMAPS simulation was estimated to be 0.31 with resid-
ual 0.013, while in FLUENT 2D simulation it was esti-
mated to be 0.34 with residual 0.089. These values were
estimated from the slope of log(max liquid holdup) vs
log(time). As shown in Fig. 4, the time after which the
wave starts to grow is around Is and is different com-
pared to EMAPS (around 11s, as shown in Fig. 3), but
the wavegrowth rate is similar as it only concerns the
rate of growth rather than its position.
It was observed that mesh refinement is essential:
with coarse grid, wavegrowth rate was 0.137 with 0.064
residual. In table 1 are the details of the meshes used.
A recent research carried out by Valluri et al (2008)
using research code TRIOMPH in Imperial College,
London concentrated on the wave growth problem us-


Wavegrowth of sine wave, incompressible flow FLUENT 2D
0076

0074

0 072

0 07

0 068 +

0 066

0 064

0 062 +

006
0 2 3 4 5 6 7
Time (s)

Figure 4: Wavegrowth as simulated using incompress-
ible FLUENT 2D



Table 1: Comparison of meshes used for wavegrowth in
FLUEND 2D
Max face area Cells Faces Nodes

Coarse Mesh 3.608e-02 186,760 377,626 190,867
Refined Mesh 2.070e-02 336,076 679,504 343,429



ing compressible flow, and thus it was decided to repeat
the previous simulation also using compressible flows
in FLUENT. The graph of maximum liquid heights vs.
time is shown in Fig. 5 and it starts occurring at around
3s, thus marginally closer to EMAPS results as com-
pared with the incompressible flow results. Using Mat-
lab, wavegrowth rate was found to be 0.32 with residual
0.062, thus again a better result. Therefore it appears
that using compressible flow in FLUENT 2D for wave-


): 3
) '


EMAPS with












Wavegrowth of sine wave, compressible flow FLUENT 2D
0078

0076
0074

0072

007

0068

0066

0064

0062
0 5 10 15 20
Time (s)

Figure 5: Wavegrowth as simulated using compressible
FLUENT 2D


Figure 6: Contour of liquid volume fraction using Flu-
ent 2D simulation of wavegrowth after 8.9s


7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 -June 4, 2010


growth analysis does indeed give results that are very
close to the ones obtained in 1D code, even though the
model is different.


Mathematical validation of rate of growth

In order to carry out a validation on the number obtained
in the previous section for the rate of growth, a pertur-
bation analysis of the VOF model was completed. A
perturbation was introduced in the continuity and mo-
mentum equations, and the dispersion frequency w was
eventually calculated, after solving the dispersion equa-
tion D(k, w) = 0. Initially any second order terms were
neglected.

Continuity eqn. : dOtL + dOxLU 0

Momentum eqn. : Otpu + V(pd- u + p)
a0 (0au) + y (, i) + pg+ FP

It was assumed that all time-dependent functions can
be expressed as = , I '. Moreover (Fluent
2006) the source term F can be expressed as:

F= i (1)
(F (Pi + Pj)

where i and j are the two phases, Tij is the surface ten-
sion coefficient, and K, is the curvature at the surface
where the surface tension is calculated. After various
simplifications, the real part and imaginary part of the
dispersion relation are shown below. It is assumed that
the pressure can be expressed as p = ( -1)cvTp = Fp,
where 7 is the ratio of specific heats and cv is the spe-
cific heat coefficient at constant volume. Also Ap =
Pi Pj.
Real Part


D,(k, w) = k2ou(w -
w -aoAp,9 + kuo
kpo

Imaginary Part

Dj(k,w)
uokaouAp + upo(w -
Spow 2 + w(uokaoAp
+ 2(2, ..,, -, .,,-, .., -


Figure 7: Contour of liquid volume fraction using Flu-
ent 2D simulation of wavegrowth after 9.8s


kuo) kaouApg = 0
(2)


kaouAPkF
2 ..) kuo
- 3pokuo)+
aoApF) 0


(3)
This is just a second-order equation of the form ax2 +
bx + c, where the solution is given by -bb2 ac
the previous equation, the terms are:

b2 +,q-I12Ap2+,,.,9 O .12a O
"..,, a5Ap + ,-, -- : ",.,,A 0 an

4ac 8k2 2 2 ?11? ,,',A,) 4k2 opoApF

S\a() 2oa 1/2
b2 -4ac kuopo (1 +c (Ap 2 2ao AP +4 4
A po P 0o 0 Apo }







7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 -June 4, 2010


When using the real part solution for the dispersion
relation as per eqn. 2, and substituting the variables used
for FLUENT simulation of wavegrowth, the number ob-
tained is 0.31, which is remarkably close to the value
0.34/0.32 obtained with the simulation. This would in-
dicate that as a magnitude check the procedure is consis-
tent.


Slug formation and growth

After having shown that the wavegrowth problem can be
simulated in a satisfactory manner using 2D Fluent, thus
resulting in a simulation time that is approximately 10
times smaller compared with 3D Fluent, it was important
to investigate and compare results of simulations that
deal with two-phase flow. In particular transient flows
with initial conditions that are known to produce slugs
of certain frequencies have been chosen for the current
investigation and comparison. Manolis cases (Manolis
1995) have been used in order to compare results with
known experimental data. The values of the initial con-
ditions can be seen in table 2. It is important that the fre-
quency obtained satisfies mesh independence, therefore
for each simulation three different meshes were used,
each with a higher number of cells as shown in table 3.
The mesh refers to a horizontal channel of length 30m
and diameter 78mm. The term cell configuration refers
to number of cells in the y direction and number of cells
in the x direction, so for example 20-3000 refers to 20
cells in the diameter direction and 3000 cells in the pipe
length direction. An example of a graph of liquid holdup
vs. time for case 36 is shown in Fig. 8.


Table 2: Manolis Cases used for hydrodynamic slug
flow simulation
Case VG (m/s) VL (m/s) RL
22 4.016 0.519 0.670
36 1.548 0.519 0.808
38 2.058 0.498 0.766


where VG is the gas superficial velocity, VL is the
liquid superficial velocity, and RL is the initial liquid
holdup.
As shown in Fig. 9 all three simulations of Mano-
lis cases seem to converge to frequency results that
are within 4% of the experimental results. This agree-
ment gives more support to the possibility of using two-
dimensional Fluent in order to carry out pipe simulations
for two-phases. Extrapolations to more phases and/or
more complicated shapes are not straightforward, and
more tests will have to be carried out in order to confirm
that. In more complicated shapes with less symmetry
compared with a pipe, the approximation of a pipe using


Manolis Case 36 Mesh-60-9000
Liquid Holdup vs Time


Time (s)


Figure 8: Liquid holdup vs. time for Manolis case 36




Table 3: Slug frequencies in FLUENT 2D simulations
of Manolis cases 22, 36, 38
Case Cells 2D Fluent Experimental Manolis
Frequency (Hz) Frequency (Hz)
22 20-3000 0.0255 0.1333
22 40-6000 0.1286 0.1333
22 60-9000 0.1300 0.1333
36 20-3000 0.197 0.2444
36 40-6000 0.236 0.2444
36 60-9000 0.238 0.2444
38 20-3000 0.1467 0.2167
38 40-6000 0.2000 0.2167
38 60-9000 0.2250 0.2167




Mesh Convergence of
Slug Frequencies for Manolis cases
0.2500
0.2000 i---"a'- '
0.1500 Case
0.1000
ShCase 38
0.0500
0.0000
20-3000 40-6000 60-9000
Mesh used


Figure 9: Mesh convergence for slug frequencies calcu-
lated for Manolis cases




a two-dimensional channel will probably not be appro-
priate.







7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 -June 4, 2010


Conclusions

The use of 2D code gave satisfactory results that are
in agreement with EMAPS 1D code and with Manolis
data, and also mesh independence was reached. Vali-
dation tests carried out include analysis of wave growth
and slug development. One of the advantages of this use
is knowing that the friction factors that are widely used
in many 1D codes are not satisfactory in slug regimes,
especially in the front region of a slug. In these regimes
it is difficult experimentally to estimate stresses at the
interface between the liquid film and gas (Hewitt 2009).
In fact in these regions slug superficial velocity is a
quantity that does not enter in any dynamics. As field
discontinuities are important, friction factors cannot be
approximated by continuous functions (Taitel & Duk-
ler 1977). Simulation of transient flows using FLUENT
2D after an initial steady-state simulation, offers also the
possibility of calculating these stresses and these values
can be used to calibrate friction factors in 1D code, and
moreover simulation times are approximately 10 times
smaller compared with FLUENT 3D.

References

FLUENT 6.3 User Guide, Fluent Inc., 2006

Hewitt G. F., Private communication, TMF4 Meeting,
Imperial College of Science, Technology and Medicine,
UK, 2009

Manolis I.G., High Pressure Gas-Liquid Slug Flow,
Ph.D. Thesis, Department of Chemical Engineering
and Chemical Technology, Imperial College of Science,
Technology and Medicine, UK, 1995

Omgba-Essama C., Ph.D. Thesis, Cranfield University,
UK, 2004

Taitel Y. and Dukler A. E., A model for predicting slug
frequency during gas-liquid flow in horizontal and near
horizontal pipes, Int. J. Multiphase Flow, 1977

Ujang P.M., Pan P., Manfield PD., Lawrence C.J., He-
witt G.F., Prediction of the translational velocity of liq-
uid slugs in gas-liquid slug flow using computational
fluid dynamics. Multiphase Science and Technology,
Vol. 20. pp. 25-79, 2008

Valluri P, Spelt PD.M., Lawrence C.J., et al. Numer-
ical simulation of the onset of slug initiation in laminar
horizontal channel flow, INT J MULTIPHASE FLOW,
2008, Vol: 34, Pages: 206 225, ISSN: 0301-9322




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