Abstract

The paper studies one-way and two-way coupling interactions between the liquid turbulence and bubbles' presence in bubbly jets. One-way coupling focuses on jet with low void fraction in which the bubbles have no significant effect on the hydrodynamic liquid fields in comparison to the single-phase jet. It sets out to model the interfacial momentum transfer identifying the turbulent contribution and its effect on the bubbles' dynamics and phase distribution. Two-way coupling considers jets with high void fractions where the liquid turbulence is altered by the bubbles which in turn influence the interfacial momentum transfers. This paper aims to improve the two-fluid model closures by implementing in computational fluid dynamics code a three-equation turbulence model and new interfacial momentum transfer closures. A benchmark of turbulence models combined with different interfacial exchange modeling is achieved to highlight the strong couplings between the interfacial forces, the phase distribution and the hydrodynamic fields of both phases.

References

1.
Lance
,
M.
,
Marié
,
J. L.
, and
Bataille
,
J.
,
1991
, “
Homogeneous Turbulence in Bubbly Flows
,”
ASME J. Fluids Eng.
,
113
(
2
), pp.
295
300
.10.1115/1.2909495
2.
Lopez de Bertodano
,
M.
,
Lahey
,
R. T.
, and
Jones
,
O. C.
,
1994
, “
Development of a K-ɛ Model for Bubbly Two-Phase Flow
,”
ASME J. Fluids Eng.
,
116
(
1
), pp.
128
134
.10.1115/1.2910220
3.
Sato
,
Y.
,
Sadatomi
,
M.
, and
Sekoguchi
,
K.
,
1981
, “
Momentum and Heat Transfer in Two-Phase Bubble Flow—I. Theory
,”
Int. J. Multiphase Flow
,
7
(
2
), pp.
167
177
.10.1016/0301-9322(81)90003-3
4.
Serizawa
,
A.
, and
Kataoka
,
I.
,
1990
, “
Turbulence Suppression in Bubbly Two-Phase Flow
,”
Nucl. Eng. Des.
,
122
(
1–3
), pp.
1
16
.10.1016/0029-5493(90)90193-2
5.
Coste
,
P.
, and
Laviéville
,
J.
,
2015
, “
A Turbulence Model for Large Interfaces in High Reynolds Two-Phase CFD
,”
Nucl. Eng. Des.
,
284
, pp.
162
175
.10.1016/j.nucengdes.2014.12.004
6.
Hosokawa
,
S.
,
Hayashi
,
K.
, and
Tomiyama
,
A.
,
2014
, “
Void Distribution and Bubble Motion in Bubbly Flows in a 4 × 4 Rod Bundle. Part I: Experiments
,”
J. Nucl. Sci. Technol.
,
51
(
2
), pp.
220
230
.10.1080/00223131.2013.862189
7.
Lopez de Bertodano
,
M.
,
Lahey
,
R. T.
, and
Jones
,
O. C.
,
1994
, “
Turbulent Bubbly Two-Phase Flow Data in a Triangular Duct
,”
Nucl. Eng. Des.
,
146
(
1–3
), pp.
43
52
.10.1016/0029-5493(94)90319-0
8.
Lopez de Bertodano
,
M.
,
Lahey
,
R. T.
, and
Jones
,
O. C.
,
1994
, “
Phase Distribution in Bubbly Two-Phase Flow in Vertical Ducts
,”
Int. J. Multiphase Flow
,
20
(
5
), pp.
805
818
.10.1016/0301-9322(94)90095-7
9.
Chahed
,
J.
,
Roig
,
V.
, and
Masbernat
,
L.
,
2003
, “
Eulerian–Eulerian Two-Fluid Model for Turbulent Gas–Liquid Bubbly Flows
,”
Int. J. Multiph. Flow
,
29
(
1
), pp.
23
49
.10.1016/S0301-9322(02)00123-4
10.
Colin
,
C.
,
Fabre
,
J.
, and
Kamp
,
A.
,
2012
, “
Turbulent Bubbly Flow in Pipe Under Gravity and Microgravity Conditions
,”
J. Fluid Mech.
,
711
, pp.
469
515
.10.1017/jfm.2012.401
11.
Rezig
,
M.
,
Bellakhal
,
G.
, and
Chahed
,
J.
,
2017
, “
Phase Distribution in Dispersed Liquid-Liquid Flow in Vertical Pipe: Mean and Turbulent Contributions of Interfacial Force
,”
AIChE J.
,
63
(
9
), pp.
4214
4223
.10.1002/aic.15736
12.
Rahmani
,
M. A.
,
Jamel
,
C.
,
Ghazi
,
B.
, and
Line
,
A.
,
2011
, “
Gas Dispersion in Air-Lift Reactors: Contribution of the Turbulent Part of the Added Mass Force
,”
AIChE J.
,
57
(
12
), pp.
3315
3330
.10.1002/aic.12539
13.
Aouadi
,
A.
,
Bellakhal
,
G.
, and
Chahed
,
J.
,
2019
, “
Effect of the Turbulent Contribution of the Interfacial Momentum Transfer on the Bubbles Dynamics and Void Fraction Distribution in Vertical Bubbly Jets
,”
Int. J. Multiphase Flow
,
114
, pp.
82
97
.
14.
Chahed
,
J.
,
Aouadi
,
A.
,
Rezig
,
M.
, and
Bellakhal
,
G.
,
2016
, “
The Phenomenon of Bubbles Negative Relative Velocity in Vertical Bubbly Jets
,”
ASME J. Fluids Eng.
,
138
(
12
), p.
121301
.10.1115/1.4033842
15.
Chahed
,
J.
,
Bellakhel
,
G.
, and
Kanfoudi
,
H.
,
2017
, “
Bubbles' Slip Velocity Reduction in the Near Wall Region of Turbulent Bubbly Pipe Flows Under Different Gravity Conditions
,”
Chem. Eng. Res. Des.
,
119
, pp.
231
244
.10.1016/j.cherd.2017.01.015
16.
Chahed
,
J.
, and
Masbernat
,
L.
,
2020
, “
Modeling Interfacial Interactions and Turbulence in the Near-Wall Region of a Vertical Bubbly Boundary Layer
,”
ASME J. Fluids Eng.
,
142
(
6
), p.
061405
.10.1115/1.4045994
17.
Alekseenko
,
S. V.
,
Dulin
,
V. M.
,
Markovich
,
D. M.
, and
Pervunin
,
K. S.
,
2015
, “
Experimental Investigation of Turbulence Modi Fi Cation in Bubbly Axisymmetric Jets
,” J. Eng. Thermophys, 24(2), pp.
101
112
.
18.
Sun
,
T. Y.
, and
Faeth
,
G. M.
,
1986
, “
Structure of Turbulent Bubbly Jets-II. Phase Property Profiles
,”
Int. J. Multiphase Flow
,
12
(
1
), pp.
115
126
.10.1016/0301-9322(86)90007-8
19.
Sun
,
T. Y.
, and
Faeth
,
G. M.
,
1986
, “
Structure of Turbulent Bubbly Jets-I. Methods and Centerline Properties
,”
Int. J. Multiphase Flow
,
12
(
1
), pp.
99
114
.10.1016/0301-9322(86)90006-6
20.
Young
,
M. A.
,
Carbonell
,
R. G.
, and
Ollis
,
D. F.
,
1991
, “
Airlift Bioreactors: Analysis of Local Two-Phase Hydrodynamics
,”
AIChE J.
,
37
(
3
), pp.
403
428
.10.1002/aic.690370311
21.
Simiano
,
M.
,
Lakehal
,
D.
,
Lance
,
M.
, and
Yadigaroglu
,
G.
,
2009
, “
Turbulent Transport Mechanisms in Oscillating Bubble Plumes
,”
J. Fluid Mech.
,
633
, pp.
191
231
.10.1017/S0022112009006971
22.
Ayed
,
H.
,
Chahed
,
J.
, and
Roig
,
V.
,
2007
, “
Hydrodynamics and Mass Transfer in a Turbulent Buoyant Bubbly Shear Layer
,”
AIChE J.
,
53
(
11
), pp.
2742
2753
.10.1002/aic.11290
23.
Hamad
,
F. A.
,
Khan
,
M. K.
, and
Bruun
,
H. H.
,
2013
, “
Experimental Study of Kerosene-Water Two-Phase Flow in a Vertical Pipe Using Hot-Film and Dual Optical Probes
,”
Can. J. Chem. Eng.
,
91
(
7
), pp.
1296
1311
.10.1002/cjce.21743
24.
Hosokawa
,
S.
, and
Tomiyama
,
A.
,
2004
, “
Turbulence Modification in Gas-Liquid and Solid-Liquid Dispersed Two-Phase Pipe Flows
,”
Int. J. Heat Fluid Flow
,
25
(
3
), pp.
489
498
.10.1016/j.ijheatfluidflow.2004.02.001
25.
Hu
,
B.
,
Matar
,
O. K.
,
Hewitt
,
G. F.
, and
Angeli
,
P.
,
2007
, “
Mean and Turbulent Fluctuating Velocities in Oil-Water Vertical Dispersed Flows
,”
Chem. Eng. Sci.
,
62
(
4
), pp.
1199
1214
.10.1016/j.ces.2006.10.008
26.
Legendre
,
D.
,
Colin
,
C.
,
Fabre
,
J.
, and
Magnaudet
,
J.
,
1999
, “
Influence of Gravity Upon the Bubble Distribution in a Turbulent Pipe Flow: Comparison Between Numerical Simulations and Experimental Data
,”
J. Chim. Phys. Physico-Chim. Biol.
,
96
(
6
), pp.
951
957
.10.1051/jcp:1999181
27.
Serizawa
,
A.
,
Kataoka
,
I.
, and
Michiyoshi
,
I.
,
1975
, “
Turbulence Structure of Air-Water Bubbly Flow—III. Transport Properties
,”
Int. J. Multiphase Flow
,
2
(
3
), pp.
247
259
.10.1016/0301-9322(75)90013-0
28.
Roig
,
V.
,
Suzanne
,
C.
, and
Masbernat
,
L.
,
1998
, “
Experimental Investigation of a Turbulent Bubbly Mixing Layer
,”
Int. J. Multiphase Flow
,
24
(
1
), pp.
35
54
.10.1016/S0301-9322(97)00046-3
29.
Serizawa
,
A.
,
Kataoka
,
I.
, and
Michiyoshi
,
I.
,
1992
, “
Experimental Data Set No. 24: Phase Distribution in Bubbly Flow
,”
Multiphase Sci. Technol.
,
6
(
1–4
), pp.
257
301
.10.1615/MultScienTechn.v6.i1-4.180
30.
Lance
,
M.
, and
Bataille
,
J.
,
1991
, “
Turbulence in the Liquid Phase of a Uniform Bubbly Air-Water Flow
,”
J. Fluid Mech.
,
222
(
1
), pp.
95
118
.
31.
Shawkat
,
M. E.
,
Ching
,
C. Y.
, and
Shoukri
,
M.
,
2008
, “
Bubble and Liquid Turbulence Characteristics of Bubbly Flow in a Large Diameter Vertical Pipe
,”
Int. J. Multiphase Flow
,
34
(
8
), pp.
767
785
.10.1016/j.ijmultiphaseflow.2008.01.007
32.
Seo
,
H.
, and
Kim
,
K. C.
,
2021
, “
Experimental Study on Flow and Turbulence Characteristics of Bubbly Jet With Low Void Fraction
,”
Int. J. Multiphase Flow
,
142
, p.
103738
.10.1016/j.ijmultiphaseflow.2021.103738
33.
Parthasarathy
,
R.
, and
Faeth
,
G.
,
1987
, “
Structure of Particle-Laden Water Jets in Still Water
,”
Int. J. Multiphase flow
,
13
(
5
), pp.
699
716
.10.1016/0301-9322(87)90046-2
34.
Modarress
,
D.
,
Wuerer
,
J.
, and
Elghobashi
,
S.
,
1984
, “
An Experimental Study of a Turbulent Round Two-Phase Jet
,”
Chem. Eng. Commun.
,
28
(
4–6
), pp.
341
354
.10.1080/00986448408940142
35.
Sun
,
T. Y.
,
1985
, “
A Theoretical and Experimental Study of Noncondensible Turbulent Bubbly Jets
,” Ph.D. thesis, Pennsylvania State University, University Park.
36.
Kataoka
,
I.
, and
Serizawa
,
A.
,
1989
, “
Basic Equations of Turbulence in Gas-Liquid Two-Phase Flow
,”
Int. J. Multiphase Flow
,
15
(
5
), pp.
843
855
.10.1016/0301-9322(89)90045-1
37.
Lee
,
S. L.
,
Lahey
,
R. T.
, and
Jones
,
O. C.
,
1989
, “
The Prediction of Two-Phase Turbulence and Phase Distribution Phenomena Using a K-ε Model
,”
Jpn. J. Multiphase Flow
,
3
(
4
), pp.
335
368
.10.3811/jjmf.3.335
38.
Magolan
,
B.
,
Lubchenko
,
N.
, and
Baglietto
,
E.
,
2019
, “
A Quantitative and Generalized Assessment of Bubble-Induced Turbulence Models for Gas-Liquid Systems
,”
Chem. Eng. Sci. X
,
2
, p.
100009
.10.1016/j.cesx.2019.100009
39.
Morel
,
C.
,
1995
, “
An Order of Magnitude Analysis of the Two-Phase K-ε Model
,”
Int. J. Fluid Mech. Res.
,
22
(
3–4
), pp.
21
44
.10.1615/InterJFluidMechRes.v22.i3-4.30
40.
Troshko
,
A. A.
, and
Hassan
,
Y. A.
,
2001
, “
A Two-Equation Turbulence Model of Turbulent Bubbly Flows
,”
Int. J. Multiphase Flow
,
27
(
11
), pp.
1965
2000
.10.1016/S0301-9322(01)00043-X
41.
Guan
,
X.
,
Li
,
Z.
,
Wang
,
L.
,
Li
,
X.
, and
Cheng
,
Y.
,
2015
, “
A Dual-Scale Turbulence Model for Gas-Liquid Bubbly Flows
,”
Chin. J. Chem. Eng.
,
23
(
11
), pp.
1737
1745
.10.1016/j.cjche.2015.09.003
42.
Bellakhal
,
G.
,
Chaibina
,
F.
, and
Chahed
,
J.
,
2020
, “
Assessment of Turbulence Models for Bubbly Flows: Toward a Five-Equation Turbulence Model
,”
Chem. Eng. Sci.
,
220
, pp.
115
425
.
43.
Sarkar
,
D.
, and
Savory
,
E.
,
2021
, “
Numerical Modeling of Freestream Turbulence Decay Using Different Commercial Computational Fluid Dynamics Codes
,”
ASME J. Fluids Eng.
,
143
(
4
), p.
041503
.10.1115/1.4049679
44.
Bellakhal
,
G.
,
Chahed
,
J.
, and
Masbernat
,
L.
,
2004
, “
Analysis of the Turbulence Statistics and Anisotropy in Homogeneous Shear Bubbly Flow Using a Turbulent Viscosity Model
,”
J. Turbul.
,
5
, pp.
37
41
.
45.
Lahey
,
R. T.
,
1992
, “
The Prediction of Phase Distribution and Separation Phenomena Using Two-Fluid Models
,”
Boiling Heat Transfer
,
Elsevier
, New York, pp.
85
122
.
46.
Lance
,
M.
, and
Lopez de Bertodano
,
M.
,
1994
, “
Phase Distribution Phenomena and Wall Effects in Bubbly Two-Phase Flows
,”
Multiph. Sci. Technol.
,
8
(
1–4
), pp.
69
123
.10.1615/MultScienTechn.v8.i1-4.30
47.
Simonin
,
O.
, and
Viollet
,
P.
,
1989
, “
Numerical Study on Phase Dispersion Mechanisms in Turbulent Bubbly Flows
,” Proc. International Conference on Mechanics of two-phase Flows, June 12–15, Taipei, Taiwan.
48.
Wang
,
D. M.
, and
Issa
,
R. I.
, and Gosman, A. D., 1994, “Numerical Prediction of Dispersed Bubbly Flow in a Sudden Enlargement,” Proceedings of ASME FEDSM’05, 9th International Symposium on Gas-Liquid Two-phase Flows, Houston, TX, June 19–23.
49.
Politano
,
M. S.
,
Carrica
,
P. M.
, and
Converti
,
J.
,
2003
, “
A Model for Turbulent Polydisperse Two-Phase Flow in Vertical Channels
,”
Int. J. Multiphase Flow
,
29
(
7
), pp.
1153
1182
.10.1016/S0301-9322(03)00065-X
50.
Rzehak
,
R.
, and
Krepper
,
E.
,
2013
, “
CFD Modeling of Bubble-Induced Turbulence
,”
Int. J. Multiphase Flow
,
55
, pp.
138
155
.10.1016/j.ijmultiphaseflow.2013.04.007
51.
Lopez De Bertodano
,
M.
,
Lee
,
S.-J.
,
Lahey
,
R. T.
, and
Drew
,
D. A.
,
1990
, “
The Prediction of Two-Phase Turbulence and Phase Distribution Phenomena Using a Reynolds Stress Model
,”
ASME J. Fluids Eng.
,
112
(
1
), pp.
107
113
.10.1115/1.2909357
52.
Mimouni
,
S.
,
Archambeau
,
F.
,
Boucker
,
M.
,
Laviéville
,
J.
, and
Morel
,
C.
,
2009
, “
A Second-Order Turbulence Model Based on a Reynolds Stress Approach for Two-Phase Flow—Part I: Adiabatic Cases
,”
Sci. Technol. Nuclear Installations
,
2009
, pp.
1
14
.10.1155/2009/792395
53.
Rzehak
,
R.
, and
Krepper
,
E.
,
2013
, “
Bubble-Induced Turbulence: Comparison of CFD Models
,”
Nucl. Eng. Des.
,
258
, pp.
57
65
.10.1016/j.nucengdes.2013.02.008
54.
Rzehak
,
R.
, and
Krepper
,
E.
,
2013
, “
Closure Models for Turbulent Bubbly Flows: A CFD Study
,”
Nucl. Eng. Des.
,
265
, pp.
701
711
.10.1016/j.nucengdes.2013.09.003
55.
Ma
,
T.
,
Santarelli
,
C.
,
Ziegenhein
,
T.
,
Lucas
,
D.
, and
Fröhlich
,
J.
,
2017
, “
Direct Numerical Simulation–Based Reynolds-Averaged Closure for Bubble-Induced Turbulence
,”
Phys. Rev. Fluids
,
2
(
3
), p.
034301
.10.1103/PhysRevFluids.2.034301
56.
Chaibina
,
F.
,
Bellakhal
,
G.
, and
Chahed
,
J.
,
2019
, “
First and Second Order Turbulence Closures Applied to Homogeneous Turbulent Bubbly Flows
,”
J. Appl. Fluid Mech.
,
12
(
6
), pp.
1813
1823
.10.29252/jafm.12.06.29756
57.
Ayeb Mrabtini
,
H.
,
Bellakhal
,
G.
, and
Chahed
,
J.
,
2017
, “
Analysis of the Homogeneous Turbulence Structure in Uniformly Sheared Bubbly Flow
,”
Nucl. Eng. Des.
,
320
, pp.
112
122
.10.1016/j.nucengdes.2017.05.012
58.
Tchen
,
C. M.
,
1947
,
Mean Value and Correlation Problems Connected With the Motion of Small Particles Suspended in a Turbulent Fluid
,
Martinus Nijhoff
,
The Hague, The Netherlands
.
59.
Hinze
,
J.
,
1975
,
Turbulence
,
McGraw-Hill
, New York.
60.
ANSYS, I., 2015, “
ANSYS CFX-Solver Manager Users Guide - [PDF Document]
,” SAS IP, Inc, Canonsburg, PA, https://cupdf.com/document/ansys-cfx-solver-manager-users-guide.html
61.
Benzon
,
D.
,
Židonis
,
A.
,
Panagiotopoulos
,
A.
,
Aggidis
,
G. A.
,
Anagnostopoulos
,
J. S.
, and
Papantonis
,
D. E.
,
2015
, “
Impulse Turbine Injector Design Improvement Using Computational Fluid Dynamics
,”
ASME J. Fluids Eng.
,
137
(
4
), p.
041106
.10.1115/1.4029310
62.
Zoppé
,
B.
,
Pellone
,
C.
,
Maitre
,
T.
, and
Leroy
,
P.
,
2006
, “
Flow Analysis Inside a Pelton Turbine Bucket
,”
ASME J. Turbomach.
,
128
(
3
), pp.
500
511
.10.1115/1.2184350
63.
Chen
,
C. J.
, and
Nikitopoulos
,
C. P.
,
1979
, “
On the Near Field Characteristics of Axisymmetric Turbulent Buoyant Jets in a Uniform Environment
,”
Int. J. Heat Mass Transfer
,
22
(
2
), pp.
245
255
.10.1016/0017-9310(79)90148-0
64.
Schiller, L., and Naumann, A.Z.,
1933
, “
Uber Die Grundlegenden Berechnungen Bei Der Schwerkraftaufbereitung
,” Z.
Ver. Deut. Ing.
,
77
(
12
), pp.
318
320
.
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