(1) Background. Bubbly flows are used in a wide variety of applications and require accurate modeling. In this paper, three modeling approaches are investigated using the geometrically simple configuration of a gas bubble strongly oscillating in a bubbly medium. (2) Method of approach. A coupled Eulerian-Lagrangian, a multicomponent compressible, and an analytical approach are compared for different void fractions. (3) Results. While the homogeneous mixture models (analytical and multicomponent) compare well with each other, the Eulerian-Lagrangian model captures additional features and inhomogeneities. The discrete bubbles appear to introduce localized perturbations in the void fraction and the pressure distributions not captured by homogeneous mixture models. (4) Conclusions. The bubbly mixture impedes the growth and collapse of the primary bubble while wavy patterns in the velocity, pressure, and void fraction fields propagate in space and time.

References

References
1.
Crowe
,
C. T.
,
Troutt
,
T. R.
, and
Chung
,
J. N.
, 1996, “
Numerical Models for Two-Phase Turbulent Flows
,”
Annu. Rev. Fluid Mech.
,
28
, pp.
11
43
.
2.
Balachandar
,
S.
, and
Eaton
,
J. K.
, 2010, “
Turbulent Dispersed Multiphase Flow
,”
Annu. Rev. Fluid Mech.
,
42
, pp.
111
133
.
3.
Elghobashi
,
S. E.
, 1994, “
On Predicting Particle-Laden Turbulent Flows
,”
Appl. Sci. Res.
,
52
, pp.
309
.
4.
Apte
,
S. V.
,
Mahesh
,
K.
, and
Lundgren
,
T.
, 2008, “
Accounting for Finite-Size Effect in Disperse Two-Phase Flow
,”
Int. J. Multiphase Flow
,
34
(
3
), pp.
260
271
.
5.
Spelt
,
P. D. M
, and
A. Biesheivel
,
A.
, 1997, “
On the Motion of Gas Bubbles in Homogeneous Isotropic Turbulence
,”
J. Fluid Mech.
,
336
, pp.
221
244
.
6.
Druzhinin
,
O. A.
, and
Elghobashi
,
S. E.
, 1998, “
Direct Numerical Simulations of Bubble-Laden Turbulent Flows Using the Two-Fluid Formulation
,”
Phys. Fluids
,
10
, pp.
685
.
7.
Bunner
,
B.
, and
Tryggvason
,
G.
, 2003, “
Effect of Bubble Deformation on the Stability and Properties of Bubbly Flows
,”
J. Fluid Mech.
,
495
, pp.
77
118
.
8.
Esmaeeli
,
A.
, and
Tryggvason
,
G.
, 1998, “
Direct Numerical Simulations of Bubbly Flows. Part 1. Low Reynolds Number Array
,”
J. Fluid Mech.
,
377
, pp.
313
345
.
9.
Brennen
,
C. E.
,
Cavitation and Bubble Dynamics
(
Oxford University Press
,
New York
, 1995).
10.
Van Wijngaarden
,
L.
, 1964, “
On the Collective Collapse of a Large Number of Gas Bubbles in Water
,” Proceedings 11th International Congress of Applied Mechanics,
Springer
,
Berlin
, pp. 854–861.
11.
Prosperetti
,
A.
,
Sundaresan
,
S.
,
Pannala
,
S.
, and
Zhang
,
D. Z.
, “
Segregated Methods for Two-Fluid Models
,” in
Computational Methods for Multiphase Flow
(
Cambridge University Press
,
New York
, 2007), pp.
320
385
.
12.
Chorin
,
A. J.
, 1967, “
A Numerical Method for Solving Incompressible Viscous Flow Problems
,”
J. Comput. Phys.
,
2
, pp.
12
26
.
13.
Roe
,
P. L.
, 1981, “
Approximate Riemann Solvers, Parameter Vectors, and Difference Schemes
,”
J. Comput. Phys.
,
43
, pp.
357
372
.
14.
Van Leer
,
B.
,
Thomas
,
J. L.
,
Roe
,
P. L.
, and
Newsome
,
R. W.
, 1987, “A Comparison of Numerical Flux Formulas for the Euler and Navier-Stokes Equation,” AIAA Paper No. 87-1104-CP.
15.
Chahine
,
G. L.
Hsiao
,
C.-T.
,
Choi
,
J.-K.
, and
Wu
,
X.
, 2008, “
Bubble Augmented Waterjet Propulsion: Two-Phase Model Development and Experimental Validation
,”
27th Symposium on Naval Hydrodynamics
,
Seoul, Korea
, Oct. 5–10.
16.
Hsiao
,
C.-T.
,
Lu
,
X.
, and
Chahine
,
G. L.
, 2010, “
Three-Dimensional Modeling of the Dynamics of Therapeutic Ultrasound Contrast Agents
,”
Ultrasound in Medicine and Biology
,
36
(
12
), pp.
2065
2079
.
17.
G. L.
,
Chahine
, 2009, “
Numerical Simulation of Bubble Flow Interactions
,”
Journal of Hydrodynamics
,
21
(
3
), pp
316
332
.
18.
Hsiao
,
C.-T.
,
Chahine
,
G. L.
, and
Liu
,
H.-L.
, 2003, “
Scaling Effects on Prediction of Cavitation Inception in a Line Vortex Flow
,”
J. Fluid Eng.
,
125
, pp.
53
60
.
19.
Plesset
,
M. S.
, and
Prosperetti
,
A.
, 1977, “
Bubble Dynamics and Cavitation
,”
Annu. Rev. Fluid Mech.
,
9
, pp.
145
185
.
20.
Johnson
,
V. E.
, and
Hsieh
,
T.
, 1966, “
The Influence of the Trajectories of Gas Nuclei on Cavitation Inception
,” Sixth Symposium on Naval Hydrodynamics, pp.
163
179
.
21.
Haberman
,
W. L.
, and
Morton
,
R. K.
, 1953, “
An Experimental Investigation of the Drag and Shape of Air Bubbles Rising in Various Liquids
,” Report No. 802, DTMB.
22.
Wardlaw
,
A.
, Jr.
, and
Luton
J. A.
, 2000, “
Fluid-Structure Interaction for Close-in Explosions
,”
Shock Vib.
,
7
, pp.
265
275
.
23.
Wardlaw
,
A.
, Jr.
,
Luton
,
J. A.
Renzi
,
J. J.
, and
Kiddy
,
K.
, “
Fluid-Structure Coupling Methodology for Undersea Weapons
,” in
Fluid Structure Interaction II
(
WIT Press
, Boston, 2003), pp.
251
263
.
24.
Gilmore
,
F. R.
, 1952, “
The Growth and Collapse of a Spherical Bubble in a Viscous Compressible Liquid
,” California Institute of Technology, Hydro. Lab. Report No. 26-4.
25.
Dymond
,
J. H.
, and
Malhotra
,
R.
, 1988,
“The Tait Equation: 100 Years On,”
Int. J. Thermophys.
,
9
(
6
), pp.
941
951
.
26.
Morch
,
K. A.
, 1981, “
Cavity Cluster Dynamics and Cavitation Erosion
,”
Proc. ASME. Cavitation and Polyphase Flow Forum
, pp.
1
10
.
27.
Chahine
, G. L., 1983, “
Cloud Cavitation: Theory
,”
Proc. 14th Symposium on Naval Hydrodynamics
,
Ann Arbor, Michigan, National Academy Press
,
Washington, D.C.
, pp.
165
194
.
28.
Chahine
,
G. L.
, and
Liu
,
H.-L.
, 1985, “
A Singular Perturbation Theory of the Growth of a Bubble Cluster in a Superheated Liquid
,”
J. Fluid Mech.
,
156
, pp.
257
279
.
29.
Jayaprakash
,
A.
Singh
,
S.
, and
Chahine
,
G. L.
, 2010, “
Bubble Dynamics in a Two-Phase Bubbly Mixture
,” ASME 2010 International Mechanical Engineering Congress & Exposition, Vancouver, British Columbia, Nov. 10–12, Paper No. IMECE2010-40509.
30.
Hsiao
,
C.-T.
, and
Chahine
,
G. L.
, 2001, “
Numerical Simulation of Bubble Dynamics in a Vortex Flow Using Navier-Stokes Computations and Moving Chimera Grid Scheme
,” Fourth International Symposium on Cavitation, California Institute of Technology, Pasadena, CA, June 20–
23
.
31.
Hodges
,
B. R.
,
Street
,
R. L.
, and
Zang
,
Y.
, 1996, “
A Method for Simulation of Viscous, Nonlinear, Free-Surface Flows
,” 20th Symposium on Naval Hydrodynamics, pp.
791
809
.
32.
Hsiao
,
C.-T.
, 1996, “Numerical study of the Tip Vortex Flow over a Finite-Span Hydrofoil,” Ph.D. thesis, Department of Mechanical Engineering, The Pennsylvania State University, PA.
33.
Rayleigh
,
L.
, 1917, “
On the Pressure Developed in a Liquid During the Collapse of a Spherical Cavity
,”
Phil. Mag.
34
,
94
98
.
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