Abstract

Large-scale turbulent flow features in liquid (water) and gas (air) phases in the film region of two-phase slug flow are identified by using proper orthogonal decomposition (POD) of the vorticity fields. Linear combination of POD vorticity modes is used for the qualitative visualization of coherent structures. The vorticity fields are computed from the instantaneous two-dimensional velocity fields measured using a combined particle image velocimetry and laser-induced fluorescence technique (PIV-LIF). Vorticity modes are calculated and compared with the curl of POD velocity mode. POD analysis revealed the presence of dominant vortical structures embedded in both liquid and the gas phases. It is also observed that the gas phase revealed more eddies than the liquid phase. The proportion of enstrophy is higher in the gas phase as first POD vorticity mode contained 7.5% of the total enstrophy, while for the liquid phase; the first mode captured 6.8%. Linear combination of vorticity modes provided effective qualitative information of the coherent structures in both phases. POD-vorticity modes when compared with POD-velocity modes revealed few similarities among the pair of identified vortical structures. Based on the results, it is concluded that POD vorticity revealed hidden flow features of both phases of slug flow, which eventually provides in-depth and comprehensive description of this complex slug flow phenomenon.

References

1.
Kabiri-Samani
,
A. R.
, and
Borghei
,
S. M.
,
2010
, “
Pressure Loss in a Horizontal Two-Phase Slug Flow
,”
ASME J. Fluids Eng.
,
132
(
7
), p.
071304
.10.1115/1.4001969
2.
Goharzadeh
,
A.
,
Rodgers
,
P.
, and
Wang
,
L.
,
2013
, “
Experimental Characterization of Slug Flow on Solid Particle Transport in a 1 Deg Upward Inclined Pipeline
,”
ASME J. Fluids Eng.
,
135
(
8
), p.
081304
.10.1115/1.4024272
3.
SchüMann
,
H.
,
Tutkun
,
M.
,
Yang
,
Z.
, and
Nydal
,
O. J.
,
2016
, “
Experimental Study of Dispersed Oil-Water Flow in a Horizontal Pipe With Enhanced Inlet Mixing, Part 1: Flow Patterns, Phase Distributions and Pressure Gradients
,”
J. Pet. Sci. Eng.
,
145
, pp.
742
752
.10.1016/j.petrol.2016.06.005
4.
Santana
,
A. L. B.
,
Marcelino Neto
,
M. A.
, and
Morales
,
R. E. M.
,
2020
, “
Pressure Drop of Horizontal Air–Water Slug Flow in Different Configurations of Corrugated Pipes
,”
ASME J. Fluids Eng.
,
142
(
11
), p.
111401
.10.1115/1.4047676
5.
Kvernvold
,
O.
,
Vindøy
,
V.
,
Søntvedt
,
T.
,
Saasen
,
A.
, and
Selmer-Olsen
,
S.
,
1984
, “
Velocity Distribution in Horizontal Slug Flow
,”
Int. J. Multiphase Flow
,
10
(
4
), pp.
441
457
.10.1016/0301-9322(84)90055-7
6.
Kline
,
S. J.
,
Reynolds
,
W. C.
,
Schraub
,
F. A.
, and
Runstadle
,
P. W.
,
1967
, “
The Structure of Turbulent Boundary Layers
,”
J. Fluid Mech.
,
30
(
4
), pp.
741
773
.10.1017/S0022112067001740
7.
Brown
,
G. L.
, and
Roshko
,
A.
,
1974
, “
On Density Effects and Large Structure in Turbulent Mixing Layers
,”
J. Fluid Mech.
,
64
(
4
), pp.
775
816
.10.1017/S002211207400190X
8.
Robinson
,
S. K.
,
1991
, “
Coherent Structures in the Turbulent Boundary Layer
,”
Ann. Rev. Fluid Mech.
,
23
(
1
), pp.
601
639
.10.1146/annurev.fl.23.010191.003125
9.
Panton
,
R. L.
,
2001
, “
Overview of the Self-Sustaining Mechanisms of Wall Turbulence
,”
Prog. Aerosp. Sci.
,
37
(
4
), pp.
341
383
.10.1016/S0376-0421(01)00009-4
10.
Head
,
M. R.
, and
Bandyopadhyay
,
P.
,
1981
, “
New Aspect of Turbulent Boundary Layer Structure
,”
J. Fluid Mech.
,
107
(
1
), pp.
297
338
.10.1017/S0022112081001791
11.
Kaftori
,
D.
,
Hetsroni
,
G.
, and
Banerjee
,
S.
,
1994
, “
Funnel-Shaped Vortical Structures in Wall Turbulence
,”
Phys. Fluids
,
6
(
9
), pp.
3035
3050
.10.1063/1.868129
12.
ZHOU
,
J.
,
Adrian
,
R. J.
,
Balachandar
,
S.
, and
Kendall
,
T. M.
,
1999
, “
Kendall, M. Mechanisms for Generating Coherent Packets of Hairpin Vortices in Channel Flow
,”
J. Fluid Mech.
,
387
, pp.
353
396
.10.1017/S002211209900467X
13.
Adrian
,
R. J.
,
Christensen
,
K. T.
, and
Liu
,
Z.-C.
,
2000
, “
Analysis and Interpretation of Instantaneous Turbulent Velocity Fields
,”
Exp. Fluids.
,
29
(
3
), pp.
275
290
.10.1007/s003489900087
14.
Adrian
,
R. J.
,
2007
, “
Hairpin Vortex Organization in Wall Turbulence
,”
Phys. Fluids
,
19
(
4
), p.
041301
.10.1063/1.2717527
15.
Kevlahan
,
N. K.-R.
,
Hunt
,
J.
, and
Vassilicos
,
J.
,
1994
, “
A Comparison of Different Analytical Techniques for Identifying Structures in Turbulence
,”
Appl. Sci. Res.
,
53
(
3–4
), pp.
339
355
.10.1007/BF00849109
16.
Bonnet
,
J. P.
,
Delville
,
J.
,
Glauser
,
M. N.
,
Antonia
,
R. A.
,
Bisset
,
D. K.
,
Cole
,
D. R.
,
Fiedler
,
H. E.
,
Garem
,
J. H.
,
Hilberg
,
D.
,
Jeong
,
J.
,
Kevlahan
,
N. K. R.
,
Ukeiley
,
L. S.
, and
Vincendeau
,
E.
,
1998
, “
Collaborating Testing of Eddy Structure Identification Methods on Free Turbulent Shear Flows
,”
Exp. Fluids
,
25
(
3
), pp.
197
225
.10.1007/s003480050224
17.
Liu
,
Z.-C.
,
Adrian
,
R. J.
, and
Hanratty
,
R. J.
,
2001
, “
Large-Scale Modes of Turbulent Channel Flow: Transport and Structure
,”
J. Fluid Mech.
,
448
, pp.
53
80
.10.1017/S0022112001005808
18.
Wu
,
Y.
, and
Christensen
,
K. T.
,
2010
, “
Spatial Structure of a Turbulent Boundary Layer With Irregular Surface Roughness
,”
J. Fluid Mech.
,
655
, pp.
380
418
.10.1017/S0022112010000960
19.
Baltzer
,
J. R.
, and
Adrian
,
R. J.
,
2011
, “
Structure, Scaling, and Synthesis of Proper Orthogonal Decomposition Modes of Inhomogeneous Turbulence
,”
Phys Fluids
,
23
(
1
), p.
015107
.10.1063/1.3540663
20.
Hellström
,
L. H. O.
,
Ganapathisubramani
,
B.
, and
Smits
,
A. J.
,
2016
, “
Coherent Structures in Transitional Pipe Flow
,”
Phys. Rev. Fluids
,
1
, p.
024403
.10.1103/PhysRevFluids.1.024403
21.
Hellström
,
L. H. O.
, and
Smits
,
A. J.
,
2017
, “
Structure Identification in Pipe Flow Using Proper Orthogonal Decomposition
,”
Philos. Trans. R. Soc. A
,
375
(
2089
), p.
20160086
.10.1098/rsta.2016.0086
22.
Muralidhar
,
S. D.
,
Podvin
,
B.
,
Mathelin
,
L.
, and
Fraigneau
,
Y.
,
2019
, “
Spatio-Temporal Proper Orthogonal Decomposition of Turbulent Channel Flow
,”
J. Fluid Mech.
,
864
pp.
614
639
.10.1017/jfm.2019.48
23.
Pinilla
,
J. A.
,
Guerrero
,
E.
,
Pineda
,
H.
,
Posada
,
R.
,
Pereyra
,
D.
, and
Ratkovich
,
N.
,
2019
, “
CFD Modeling and Validation for Two-Phase Medium Viscosity Oil-Air Flow in Horizontal Pipes
,”
Chem. Eng. Commun.
,
206
(
5
), pp.
654
671
.10.1080/00986445.2018.1516646
24.
Guerrero
,
E.
,
Pinilla
,
A.
, and
Ratkovich
,
N.
,
2020
, “
Assessment of Well Trajectory Effect on Slug Flow Parameters Using CFD Tools
,”
Chem. Eng. Commun.
,
207
(
10
), pp.
1390
1402
.10.1080/00986445.2019.1652604
25.
Pineda
,
Pé.
,
Rez
,
H.
,
Kim
,
T.
,
Pereyra
,
E.
, and
Ratkovich
,
N.
,
2018
, “
CFD Modeling of Air and Highly Viscous Liquid Two-Phase Slug Flow in Horizontal Pipes
,”
Chem. Eng. Res. Des.
,
136
, pp.
638
653
.10.1016/j.cherd.2018.06.023
26.
Li
,
J.
,
Zhang
,
T.
,
Sun
,
S.
, and
Yu
,
B.
,
2019
, “
Numerical Investigation of the POD Reduced-Order Model for Fast Predictions of Two-Phase Flows in Porous Media
,”
Int. J. Numer. Method H
,
29
(
11
), pp.
4167
4204
.10.1108/HFF-02-2019-0129
27.
Yi
,
S. J.
,
Kim
,
S. M.
,
Kim
,
H. D.
,
Kim
,
J. W.
, and
Kim
,
K. C.
,
2010
, “
Spatial and Temporal Structures of Turbulent Bubble-Driven Flows in a Rectangular Tank
,”
J. Mech. Sci. Technol.
,
24
(
9
), pp.
1819
1827
.10.1007/s12206-010-0628-5
28.
Pang
,
M.
, and
Wei
,
J.
,
2013
, “
Experimental Investigation on the Turbulence Channel Flow Laden With Small Bubbles by PIV
,”
Chem. Eng. Sci.
,
93
, pp.
302
315
.10.1016/j.ces.2013.02.062
29.
Viggiano
,
B.
,
Tutkun
,
M.
, and
Cal
,
R. L.
,
2019
, “
Hessian-Based Topology of Two-Phase Slug Flow
,”
Int. J. Multiphase Flow
,
119
, pp.
84
94
.10.1016/j.ijmultiphaseflow.2019.07.003
30.
Ali
,
N.
,
Viggiano
,
B.
,
Tutkun
,
M.
, and
Cal
,
R. L.
,
2021
, “
Data-Driven Machine Learning for Accurate Prediction and Statistical Quantification of Two Phase Flow Regimes
,”
J. Petrol. Sci. Eng.
,
202
, p.
108488
.10.1016/j.petrol.2021.108488
31.
Ali
,
N.
,
Viggiano
,
B.
,
Tutkun
,
M.
, and
Cal
,
R. L.
,
2020
, “
Cluster-Based Reduced-Order Descriptions of Two Phase Flows
,”
Chem. Eng. Sci.
,
222
, p.
115660
.10.1016/j.ces.2020.115660
32.
Ali
,
N.
,
Viggiano
,
B.
,
Tutkun
,
M.
, and
Cal
,
R. L.
,
2021
, “
Forecasting the Evolution of Chaotic Dynamics of Two-Phase Slug Flow Regimes
,”
J. Petrol. Sci. Eng.
,
205
, p.
108904
.10.1016/j.petrol.2021.108904
33.
Perry
,
A. E.
, and
Chong
,
M. S.
,
1994
, “
Topology of Flow Patterns in Vortex Motions and Turbulence
,”
Appl. Sci. Res.
,
53
(
3–4
), pp.
357
374
.10.1007/BF00849110
34.
Klewicki
,
J. C.
,
1997
, “
Self-Sustaining Traits of Near-Wall Motions Underlying Boundary Layer Stress Transport
,”
Self-Sustaining Mechanisms of Wall Turbulence
,
R. L.
Panton
, ed.,
Computational Mechanics Publications
,
Southampton, UK
, pp.
135
166
.
35.
Gunes
,
H.
, and
Rist
,
U.
,
2004
, “
Proper Orthogonal Decomposition Reconstruction of a Transitional Boundary Layer With and Without Control
,”
Phys. Fluids
,
16
(
8
), pp.
2763
2784
.10.1063/1.1758151
36.
Hussain
,
F.
,
1986
, “
Coherent Structures and Turbulence
,”
J. Fluid Mech.
,
173
, pp.
303
356
.10.1017/S0022112086001192
37.
Kostas
,
J.
,
Soria
,
J.
, and
Chong
,
M. S.
,
2005
, “
A Comparison Between Snapshot POD Analysis of PIV Velocity and Vorticity Data
,”
Exp. Fluids
,
38
(
2
), pp.
146
160
.10.1007/s00348-004-0873-4
38.
Liberzon
,
A.
,
Gurka
,
R.
,
Tiselj
,
I.
, and
Hetsroni
,
G.
,
2005
, “
Spatial Characterization of the Numerically Simulated Vorticity Fields of a Flow in a Flume
,”
Theor. Comput. Fluid Dyn.
,
19
(
2
), pp.
115
125
.10.1007/s00162-004-0156-y
39.
Tabib
,
M. V.
, and
Joshi
,
J. B.
,
2008
, “
Analysis of Dominant Structures and Their Flow Dynamics in Chemical Process Equipment Using Snapshot Proper Orthogonal Decomposition Technique
,”
Chem. Eng. Sci.
,
63
(
14
), pp.
3695
3715
.10.1016/j.ces.2008.04.046
40.
Chong
,
M. S.
,
Perry
,
A. E.
, and
Cantwell
,
B. J.
,
1990
, “
A General Classification of Three-Dimensional Flow Fields
,”
Phys. Fluids
,
2
(
5
), pp.
765
777
.10.1063/1.857730
41.
Gurka
,
R.
,
Liberzon
,
A.
, and
Hetsroni
,
G.
,
2006
, “
POD of Vorticity Fields: A Method for Spatial Characterization of Coherent Structures
,”
Int. J. Heat Fluid Flow
,
27
(
3
), pp.
416
423
.10.1016/j.ijheatfluidflow.2006.01.001
42.
Munir
,
S.
,
Siddiqui
,
M. I.
,
Heikal
,
M. R.
,
Sercey
,
G. D.
, and
Aziz
,
A. R. A.
,
2015
, “
Identification of Dominant Structures and Their Flow Dynamics in the Turbulent Two-Phase Flow Using POD Technique
,”
J. Mech. Sci. Technol.
,
29
(
11
), pp.
4701
4710
.10.1007/s12206-015-1017-x
43.
Siddiqui
,
M. I.
,
Munir
,
S.
,
Heikal
,
M. R.
,
Sercey
,
G. D.
,
Aziz
,
A. R. A.
, and
Dass
,
S. C.
,
2016
, “
Simultaneous Velocity Measurements and the Coupling Effect of the Liquid and Gas Phases in Slug Flow Using PIV-LIF Technique
,”
J. Vis.
,
19
(
1
), pp.
103
114
.10.1007/s12650-015-0302-1
44.
Lumley
,
J. L.
,
1967
, “
The Structure of Inhomogeneous Turbulent Flows
,”
Atmospheric Turbulence and Wave Propagation
,
A. M.
Yaglam
,
V. I.
Tatarsky
, eds.,
Nauka
,
Moscow, Russia
, pp.
166
178
.
45.
Sirovich
,
L.
,
1987
, “
Turbulence and the Dynamics of Coherent Structures. Part I: Coherent Structures
,”
Quart. Appl. Math.
,
45
(
3
), pp.
561
571
.10.1090/qam/910462
46.
Czapp
,
M.
,
Muller
,
C.
,
Fern
,
á.
,
Ndez
,
P. A.
, and
Sattelmayer
,
T.
,
2012
, “
High-Speed Stereo and 2D Measurements of Two-Phase Slug Flow in a Horizontal Pipe
,”
Proceedings of the 16th International Symposium on Applications of Laser Techniques to Fluid Mechanics
,
Lisbon, Portugal
, July. 9–12.
47.
O'Halloran
,
S. P.
,
Beck
,
B. T.
,
Hosni
,
M. H.
, and
Eckels
,
S. J.
,
2008
, “
Experimental Measurements and Numerical Simulations of Two-Phase Stratified, Wavy and Slug Flow in a Narrow Rectangular Channel
,”
ASME
Paper No. FEDSM2005-77091.
10.1115/FEDSM2005-77091
48.
Breuer
,
K.
, and
Sirovich
,
L.
,
1991
, “
The Use of the Karhunen-Loéve Procedure for the Calculation of Linear Eigenfunctions
,”
J. Comput. Phys
,
96
(
2
), pp.
277
296
.10.1016/0021-9991(91)90237-F
You do not currently have access to this content.