Spherical Bubble Dynamics in a Bubbly Medium - Dynaflow, Inc.

2012 Intl. Conf. on Numerical Methods in Multiphase Flows
State College, PA, 12-14 June 2012
Spherical Bubble Dynamics in a Bubbly Medium
Jingsen Ma, Sowmitra Singh, Chao-Tsung Hsiao, Jin-Keun Choi, Tiffany Fourmeau and
Georges Chahine
DYNAFLOW, INC.
10621-J Iron Bridge Road, Jessup, MD 20794
Email: jingsen@dynaflow-inc.com
Tel: (301)604-3688
ABSTRACT
For applications involving large bubble
volume changes such as in cavitating flows or for
shock and pressure wave propagation in a bubbly
medium, the dynamics, relative motions,
deformations, and interaction of bubbles with the
surrounding medium are essential and require
accurate modeling. In this presentation, a twoway
coupled Euler-Lagrange model is considered
for a geometrically simple but numerically
challenging configuration: A large spherical
bubble (primary bubble) oscillating in a bubbly
mixture of dispersed bubbles of much smaller
sizes. The model treats the two-phase medium
using a continuum model while the bubbles are
considered in a Lagrangian fashion. For the
primary bubble, the large amplitude motion
dynamics is fully resolved by using a moving
grid interface tracking scheme. For each of the
smaller bubbles, dynamics is modeled by
utilizing a Surface Averaged Pressure (SAP)
modified R-P Keller Herring equation, and the
motion is tracked in a Lagrangian fashion. In
addition, the flow field is simulated by directly
solving the Navier-Stokes equations in an
Eulerian fashion. The two-way coupling between
the Eulerian fluid model and the Lagrangian
discrete bubble model is realized through the
modification to the local density field of the
mixture due to the volume change and motion of
the dispersed bubbles.
The effect of the presence of the dispersed
bubbles on the primary bubble dynamics, on the
propagation of pressure waves in the medium,
and on the distribution in space and time of the
void fraction are investigated for various mixture
properties, such as mean void fraction and bubble
size and distribution.
Primary Bubble
(Moving Grid Method)
Dispersed Bubble
(SAP Model)
Figure 1. Illustration of the problem of the dynamics of a
primary spherical bubble in bubbly medium.

Figure 2. Variation of the primary bubble radius for different
initial void fractions obtained by the Euler-Lagrange model.
The numerical simulations are compared to
Gilmore bubble dynamics equation for the
primary bubble. In the Gilmore analytical model
the bubbly mixture surrounding the primary
bubble is assumed to be a homogenous medium
and an equation of state to describe the bubbly
mixture accounting for changes in the medium
properties in space and time. A comparison
between the numerical and analytical models
reveals the fine differences that arise from
accounting for the dynamics of the discrete
bubbles. Overall, both models show that the
surrounding bubbly medium absorbs the energy
radiated from the primary bubble thereby
damping the bubble oscillations and resulting in
important reduction in both its maximum radius
and its period. These effects become more
significant when the nominal void fraction of the
mixture increases (Figure 2). Experimental
observations conducted in parallel using spark
generated bubbles in bubbly media are found to
be in good qualitative agreement with the
results.
ACKNOWLEDGMNETS
This work was conducted at DYNAFLOW,
INC. (www.dynaflow-inc.com) and was supported
by the Department of Energy under Phase II
SBIR Program No. DE-FG02-07ER84839 and by
the Office of Naval Research under contract No.
N00014-08-C-0448 monitored by Dr. Ki-Han
Kim.