Three-dimensional bubble dynamics in rotating flow under an accelerating field such as a centrifugal one is studied in this work. We employ the lattice Boltzmann method in two phase flows to simulate bubble dynamics for different Bond and Morton numbers of 0.1, 1, 10, and 100 and 0.001, 0.01, 0.1, 1, 10, and 100, respectively. Another dimensionless number named as dimensionless force, F*, which is the ratio of buoyancy force to centripetal force is defined to explain the dynamics of the bubbles. In this work, we consider 5×107F*5. The results show that bubbles in rotating flows have different kinds of motions such as spinning, rotating, and translating. Based on the ratios of the forces (dimensionless numbers) acting on the bubble, four different classes of bubble dynamics can be distinguished: (1) stationary spinal bubbles at the center of the rotating flow, (2) spinal bubbles with axial motion at the center of the rotating flow, (3) bubbles with upward spiral motion at an approximate constant radius close to the center of the rotating flow, and (4) bubbles with dominant upward motion.

1.
X.
Shen
and
B.
Deng
, “
Development of interfacial area concentration correlations for small and large bubbles in gas-liquid two-phase flows
,”
Int. J. Multiphase Flow
87
,
136
155
(
2016
).
2.
A. M.
Zhang
and
Y. L.
Liu
, “
Improved three-dimensional bubble dynamics model based on boundary element method
,”
J. Comput. Phys.
294
,
208
223
(
2015
).
3.
M.
Jingsen
,
G. L.
Chahine
, and
C. T.
Hsiao
, “
Spherical bubble dynamics in a bubbly medium using an Euler-Lagrange model
,”
Chem. Eng. Sci.
128
,
64
81
(
2015
).
4.
G. B.
Wallis
,
One-Dimensional Two-Phase Flow
(
MacGraw-Hill
,
New York
,
1969
).
5.
M.
Ishii
,
Thermo-Fluid Dynamic Theory of Two-Phase Flow
(
Eyrolles Paris
,
France
,
1975
).
6.
D.
Obreschkow
,
M.
Bruderer
, and
M.
Farhat
, “
Analytical approximations for the collapse of an empty spherical bubble
,”
Phys. Rev. E
85
,
066303
(
2012
).
7.
P.
Amore
and
F. M.
Fernandez
, “
Mathematical analysis of recent analytical approximations to the collapse of any empty spherical bubble
,”
J. Chem. Phys.
138
,
084511
(
2013
).
8.
A. R.
Klotz
, “
Bubble dynamics in n-dimensions
,”
Phys. Fluids
25
,
082109
(
2013
).
9.
N. A.
Kudryashov
and
D. I.
Sinelshchikov
, “
Analytical solutions of the Rayleigh equation for empty and gas-filled bubble
,”
J. Phys. A: Math. Theor.
47
,
405202
(
2014
).
10.
N. A.
Kudryashov
and
D. I.
Sinelshchikov
, “
Analytical solutions for problems of bubble dynamics
,”
Phys. Lett. A
379
,
798
802
(
2015
).
11.
H.
Alehossein
and
Z.
Qin
, “
Numerical analysis of Rayleigh-Plesset equation for cavitating water jets
,”
Int. J. Numer. Methods Eng.
72
,
780
807
(
2007
).
12.
S. A.
Wilkerson
, “
A boundary integral approach to three-dimensional under water explosion bubble dynamics
,” Ph.D. thesis,
The Johns Hopkins University
,
1990
.
13.
J. P.
Best
and
A.
Kucera
, “
A numerical investigation of non-spherical rebounding bubbles
,”
J. Fluid Mech.
245
,
137
154
(
1992
).
14.
Y. L.
Zhang
,
K. S.
Yeo
,
B. C.
Khoo
, and
C.
Wang
, “
3D jet impact and toroidal bubbles
,”
J. Comput. Phys.
166
,
336
360
(
2001
).
15.
Q. X.
Wang
and
J. R.
Blake
, “
Non-spherical bubble dynamics in a compressible liquid. Part 1. Traveling acoustic wave
,”
J. Fluid Mech.
659
,
191
224
(
2010
).
16.
A.
Pearson
,
E.
Cox
,
J. R.
Blake
, and
S. R.
Otto
, “
Bubble interactions near a free surface
,”
Eng. Anal. Boundary Elem.
28
,
295
313
(
2004
).
17.
A.
Dadvand
,
B. C.
Khoo
,
M. T.
Shervani-Tabarc
, and
S.
Khalilpourazarya
, “
Boundary element analysis of the droplet dynamics induced by spark-generated bubble
,”
Eng. Anal. Boundary Elem.
36
,
1595
1603
(
2012
).
18.
C.
Wang
and
B. C.
Khoo
, “
An indirect boundary element method for three-dimensional explosion bubbles
,”
J. Comput. Phys.
194
,
451
480
(
2004
).
19.
R.
Clift
,
J. R.
Grace
, and
M.
Weber
,
Bubbles, Drops, and Particles
(
Academic Press
,
New York
,
1978
).
20.
L.
Chen
,
S. V.
Garimella
,
J.
Reizes
, and
E.
Leonard
, “
The development of a bubble rising in a viscous liquid
,”
J. Fluid Mech.
387
,
61
96
(
1999
).
21.
A.
Tomiyama
,
G. P.
Celata
,
S.
Hosokawa
, and
S.
Yoshida
, “
Terminal velocity of single bubble in surface tension force dominant regime
,”
Int. J. Multiphase Flow
28
,
1497
1519
(
2002
).
22.
M. V. S.
Annaland
,
N. G.
Deen
, and
J. A. M.
Kuipers
, “
Numerical simulation of gas bubbles behavior using a three-dimensional volume of fluid method
,”
Chem. Eng. Sci.
60
,
2999
3011
(
2005
).
23.
M. V. S.
Annaland
,
W.
Dijkhuizen
,
N. G.
Deen
, and
J. A. M.
Kuipers
, “
Numerical simulation of behavior of gas bubbles using a 3-D front-tracking method
,”
AIChE J.
52
,
99
110
(
2006
).
24.
T.
Bonometti
and
J.
Magnaudet
, “
Transition from spherical cap to toroidal bubbles
,”
Phys. Fluids
18
,
052102
(
2006
).
25.
A.
Smolianski
,
H.
Haario
, and
P.
Luuka
, “
Numerical study of dynamics of single bubbles and bubble swarms
,”
Appl. Math. Modell.
32
,
641
659
(
2008
).
26.
J.
Hua
,
J. F.
Stene
, and
P.
Lin
, “
Numerical simulation of 3-D bubbles rising in viscous liquids using front tracking method
,”
J. Comput. Phys.
227
,
3358
3382
(
2008
).
27.
C. W.
Hirt
and
B. D.
Nichols
, “
Volume of fluid (VOF) method for the dynamics of free boundaries
,”
J. Comput. Phys.
39
,
201
225
(
1981
).
28.
E.
Klaseboer
,
R.
Manica
,
D. Y. C.
Chan
, and
B. C.
Khoo
, “
BEM simulation of potential flow with viscous effects as applied to a rising bubble
,”
Eng. Anal. Boundary Elem.
35
,
489
494
(
2011
).
29.
X.
Wang
,
B.
Klaasen
,
J.
Degrève
,
A.
Mahulkar
,
G.
Heynderickx
,
M. F.
Reyniers
,
B.
Blanpain
, and
F.
Verhaeghe
, “
Volume-of-fluid simulations of bubble dynamics in a vertical Hele-Shaw cell
,”
Phys. Fluids
28
,
053304
(
2016
).
30.
A.
Sussman
,
P.
Smereka
, and
S.
Osher
, “
A level set approach for computing solutions to incompressible two-phase flow
,”
J. Comput. Phys.
114
,
146
159
(
1994
).
31.
L.
Bu
and
J.
Zhao
, “
Numerical simulation of the water bubble rising in a liquid column using the combination of level set and moving mesh methods in the collocated grids
,”
Int. J. Therm. Sci.
59
,
1
8
(
2012
).
32.
I.
Chakraborty
,
G.
Bisws
, and
P. S.
Goshdastidar
, “
A coupled level-set and volume of fluid for the buoyant rise of gas bubbles in liquids
,”
Int. J. Heat Mass Transfer
58
,
240
259
(
2013
).
33.
M.
Taeibi-Rahni
and
E.
Loth
, “
Forces on a large cylindrical bubble in an unsteady rotational flow
,”
AIChE J.
42
,
638
648
(
1996
).
34.
E.
Loth
,
M.
Taeibi-Rahni
, and
G.
Tryggvason
, “
Deformable bubbles in a free shear layer
,”
Int. J. Multiphase Flow
23
,
977
1001
(
1997
).
35.
M.
Rezavand
and
M.
Taeibi-Rahni
, “
Numerical simulation of multiphase flows using SPH projection method
,”
Appl. Math. Eng. Manage. Technol.
3
,
277
287
(
2015
).
36.
M.
Rezavand
,
M.
Meister
,
D.
Winkler
, and
M.
Taeibi-Rahni
, “
A simple ISPH algorithm for two-phase flows with high density ratios
,” in
11th International SPHERIC Workshop
,
Munich
,
2016
.
37.
K.
Szewc
,
J.
Pozorski
, and
J. P.
Minier
, “
Simulations of single bubbles rising through viscous liquids using smoothed particle hydrodynamics
,”
Int. J. Multiphase Flow
50
,
98
105
(
2013
).
38.
M. R.
Swift
,
E.
Orlandini
,
W. R.
Osborn
, and
J. M.
Yeomans
, “
Lattice Boltzmann simulations of liquid-gas and binary fluid systems
,”
Phys. Rev. E
54
,
5041
(
1996
).
39.
N.
Takada
,
M.
Misawa
,
A.
Tomiyama
, and
S.
Fujiwara
, “
Numerical simulation of two- and three-dimensional two-phase fluid motion by lattice Boltzmann method
,”
Comput. Phys. Commun.
129
,
233
246
(
2000
).
40.
X.
Frank
,
D.
Funfschilling
,
N.
Midoux
, and
H. Z.
Li
, “
Bubbles in a viscous liquid: Lattice Boltzmann simulation and experimental validation
,”
J. Fluid Mech.
546
,
113
122
(
2006
).
41.
A.
Xu
,
S.
Succi
, and
B. M.
Boghosian
, “
Lattice BBGKY scheme for two-phase flows: One-dimensional case
,”
Math. Comput. Simul.
72
,
249
252
(
2006
).
42.
H. W.
Zheng
,
C.
Shu
, and
Y. T.
Chew
, “
A lattice Boltzmann model for multiphase flows with large density ratio
,”
J. Comput. Phys.
218
,
353
371
(
2006
).
43.
S.
Mukherjee
and
J.
Abraham
, “
Lattice Boltzmann simulation of two-phase flow with high density ratio in axially symmetric geometry
,”
Phys. Rev. E
75
,
026701
(
2007
).
44.
T.
Inamuro
,
T.
Ogata
,
S.
Tajima
, and
N. A.
Konishi
, “
A lattice Boltzmann method for incompressible two-phase flows with large density differences
,”
J. Comput. Phys.
198
,
628
644
(
2004
).
45.
T.
Inamuro
,
T.
Ogata
, and
F.
Ogino
, “
Lattice Boltzmann simulation of bubble flows
,” in
Lecture Note in Computer Science
(
Springer, Berlin, Heidelberg
,
2003
), pp.
1015
1020
.
46.
K.
Sankaranarayanan
,
X.
Shan
,
I. G.
Kevrekidis
, and
S.
Sundaresan
, “
Bubble flow simulations with lattice Boltzmann method
,”
Chem. Eng. Sci.
54
,
4817
4823
(
1999
).
47.
X.
Shan
and
H.
Chen
, “
Lattice Boltzmann model for simulating flows with multiple phases and components
,”
Phys. Rev. E
47
,
1815
(
1993
).
48.
X.
Shan
and
G.
Doolen
, “
Multicomponent lattice-Boltzmann method for interparticle interaction
,”
J. Stat. Phys.
81
,
379
393
(
1995
).
49.
X.
Shan
and
X.
He
, “
Discretization of the velocity space in the solution of the Boltzmann equation
,”
Phys. Rev. Lett.
80
,
65
(
1998
).
50.
K.
Sankaranarayanan
,
X.
Shan
,
I. G.
Kevrekidis
, and
S.
Sundaresan
, “
Analysis of drag and virtual mass forces in bubbly suspensions using an implicit formulation of the lattice Boltzmann method
,”
J. Fluid Mech.
452
,
61
96
(
2002
).
51.
I. Z.
Kortuglu
and
Ch. L.
Lin
, “
Lattice Boltzmann study of bubble dynamics
,”
Numer. Heat Transfer Part B
50
,
333
351
(
2006
).
52.
S.
Ghosh
,
P.
Patil
,
S. C.
Mishra
,
A. P.
Das
, and
P. K.
Das
, “
3-D lattice Boltzmann model for asymmetric Taylor bubble and Taylor drop in inclined channel
,”
Eng. Appl. Comput. Fluid Mech.
6
,
383
394
(
2012
).
53.
M.
Alizadeh
,
S. M.
Seyyedi
,
M.
Taeibi-Rahni
, and
D. D.
Ganji
, “
Three-dimensional numerical simulation of rising bubbles in the presence of cylindrical obstacles, using lattice Boltzmann method
,”
J. Mol. Liq.
236
,
151
161
(
2017
).
54.
F.
Ren
,
B.
Song
, and
B. M.
Sukop
, “
Terminal shape and velocity of a rising bubble by phase-field-based incompressible lattice Boltzmann model
,”
Adv. Water Resour.
97
,
100
109
(
2016
).
55.
A.
Gupta
and
R.
Kumar
, “
Lattice Boltzmann simulation to study multiple bubble dynamics
,”
Int. J. Heat Mass Transfer
51
,
5192
5203
(
2008
).
56.
L. A.
Bower
and
T.
Lee
, “
Numerical simulation of single bubble rising in vertical and inclined square channel using lattice Boltzmann method
,”
Chem. Eng. Sci.
66
,
935
952
(
2011
).
57.
S.
Anwar
, “
Lattice Boltzmann modeling of buoyant rise of single and multiple bubbles
,”
Comput. Fluids
88
,
430
439
(
2013
).
58.
T.
Lee
and
C. L.
Lin
, “
A stable discretization of the lattice Boltzmann equation for simulation of incompressible two-phase flows at high density ratio
,”
J. Comput. Phys.
206
,
16
47
(
2005
).
59.
A.
Fakhari
and
T.
Lee
, “
Multiple-relaxation-time lattice Boltzmann method for immiscible fluids at high Reynolds numbers
,”
Phys. Rev. E
87
,
023304
(
2013
).
60.
R.
Miller
and
L.
Liggieri
,
Bubble and Drop Interfaces
, Progress in Colloid and Interface Science Vol. 2 (
CRC Press, Taylor & Francis Group
,
2011
).
61.
R.
Miller
,
A.
Hofmann
,
R.
Hartmann
,
A.
Halbig
, and
K. H.
Schano
, “
Measuring dynamic surface and interfacial tension
,”
Adv. Mater.
4
,
370
374
(
1992
).
62.
R.
Van Der Walle
, “
Void fraction, bubble velocity and bubble size in two-phase flow
,”
Int. J. Multiphase Flow
11
,
317
345
(
1985
).
63.
M. A. R.
Talaia
, “
Terminal velocity of a bubble rise in a liquid column
,”
World Acad. Sci. Eng. Technol.
28
,
264
268
(
2007
).
64.
M.
Wu
and
M.
Gharib
, “
Experimental studies on the shape and path of small air bubbles rising in clean water
,”
Phys. Fluids
14
,
L49
L51
(
2002
).
65.
N. M. S.
Hassan
,
M. M. K.
Khan
, and
M. G.
Rasul
, “
A study of bubble trajectory and drag coefficient in water and non-Newotonian fluids
,”
WSEAS Trans. Fluid Mech.
3
,
261
270
(
2008
).
66.
K.
Wichterle
,
K.
Smutna
, and
M.
Vecet
, “
Shape and rising velocity of bubbles
,” in
Proceedings of the 36th International Conference of SSCHE, Tatranske Matliare, Slovakia
(
Slovak Society of Chemical Engineering
,
2009
), pp.
1
12
.
67.
J. S.
Ruggles
,
R. G.
Cook
,
P.
Anamalai
, and
R.
Cole
, “
Bubble and drop trajectories in rotating flows
,”
Exp. Therm. Fluid Sci.
1
,
293
301
(
1988
).
68.
R. J.
Hung
,
Y. D.
Tsao
, and
B. B.
Hong
, “
Axisymmetric bubble profile in a slowly rotating helium Dewar under low and microgravity environment
,”
Acta Astronaut.
19
,
411
426
(
1989
).
69.
L.
Carrión
,
M. A.
Herrada
, and
V. N.
Shtern
, “
Topology changes in a water-oil swirling flow
,”
Phys. Fluids
29
,
032109
(
2017
).
70.
M.
Tutar
and
F.
Erdogdu
, “
Numerical simulation of heat transfer and velocity field characteristics of two-phase flow systems in axially rotating horizontal cans
,”
J. Food Eng.
111
,
366
385
(
2012
).
71.
J. A. W.
Elliott
,
C. A.
Ward
, and
D.
Yee
, “
Bubble shapes in rotating two-phase fluid systems: A thermodynamic approach
,”
J. Fluid Mech.
319
,
1
23
(
1996
).
72.
L.
Zhang
,
L.
Chen
, and
X.
Shao
, “
The migration and growth of nuclei in an ideal vortex flow
,”
Phys. Fluids
28
,
123305
(
2016
).
73.
D.
Matsumoto
,
K.
Fukudome
, and
H.
Wada
, “
Two-dimensional fluid dynamics in a sharply bent channel: Laminar flow, separation bubble, and vortex dynamics
,”
Phys. Fluids
28
,
103602
(
2016
).
74.
J.
Zeng
and
G.
Constantinescu
, “
Flow and coherent structures around circular cylinders in shallow water
,”
Phys. Fluids
29
,
066601
(
2017
).
75.
E. A.
Van Nierop
,
S.
Luther
,
J. J.
Bluemink
,
J.
Magnaudet
,
A.
Prosperetti
, and
D.
Lohse
, “
Drag and lift forces on bubbles in a rotating flow
,”
J. Fluid Mech.
571
,
439
454
(
2007
).
76.
M.
Rastello
,
J. L.
Marie
,
N.
Grosjean
, and
M.
Lance
, “
Study of bubble’s equilibrium in a rotating flow
,” in
The 6th International Conference on Multiphase Flow
,
2007
.
77.
M.
Rastello
,
J. L.
Marie
,
N.
Grosjean
, and
M.
Lance
, “
Drag and lift forces on interface-contaminated bubbles spinning in a rotating flow
,”
J. Fluid Mech.
624
,
159
178
(
2009
).
78.
M.
Rastello
,
J. L.
Marie
, and
M.
Lance
, “
Drag and lift forces on clean spherical and ellipsoidal bubbles in a solid body rotating flow
,”
J. Fluid Mech.
682
,
434
459
(
2011
).
79.
P.
Lakshmanan
,
F.
Peters
,
N.
Fries
, and
P.
Ehrhard
, “
Gas bubbles in simulation and experiment
,”
J. Colloid Interface Sci.
354
,
364
372
(
2011
).
80.
H. F.
Bauer
and
J.
Siekmann
, “
Theoretical investigation of gas management in zero gravity space manufacturing
,”
NASA Technical Document 19710002246
,
1969
, pp.
346
350
.
81.
L.
Zhao
and
K. S.
Rezkallah
, “
Gas-liquid flow patterns at microgravity conditions
,”
Int. J. Multiphase Flow
19
,
751
763
(
1993
).
82.
D. C.
Lowe
and
K. S.
Razkallah
, “
Flow regime identification in microgravity two-phase flows using void fraction signals
,”
Int. J. Multiphase Flow
25
,
433
457
(
1999
).
83.
M. C.
Sukop
,
T.
Daniel
, and
J.
Thorne
,
Lattice Boltzmann Modeling: An Introduction to Geoscientists and Engineers
(
Springer
,
2006
).
84.
T.
Lee
and
P. F.
Fischer
, “
Eliminating parasitic currents in the lattice Boltzmann equation method for nonideal gas
,”
Phys. Rev. E
74
,
046709
(
2006
).
85.
X.
He
,
Sh.
Chen
, and
R.
Zhang
, “
A lattice Boltzmann scheme for incompressible multiphase flow and its application in simulation of Rayleigh–Taylor instability
,”
J. Comput. Phys.
152
,
642
663
(
1999
).
86.
J.
Rowlinson
and
B.
Widom
,
Molecular Theory of Capillarity
(
Dover Publications, Inc.
,
New York
,
2002
).
87.
T.
Inamuro
,
T.
Miyahara
, and
F.
Ogino
, “
Lattice Boltzmann simulation of drop deformation and breakup in a simple shear flow
,” in
Computational Fluid Dynamics
(
Springer
,
2000
).
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