H. Takahira, THERMAL EFFECTS OF INTERNAL GAS ON THE OSCILLATIONS OF A CLUSTER OF BUBBLES, JSME international journal. Series B, fluids and thermal engineering, 40(2), 1997, pp. 230-239
The governing equations of a cluster of bubbles are derived by taking
account of the thermal effects of the internal gas and the three-dimen
sional translational motion and deformation of each bubble. The equati
ons are applied to the nonlinear oscillations of multiple interacting
bubbles. The frequency response curves are obtained for two typical ar
rangements of bubbles with the same radii, The present results are com
pared with the results of polytropic analysis in which the thermal eff
ects are evaluated using the effective polytropic index and the effect
ive viscosity. It is shown that the heat transfer inside the bubble is
important in investigating the nonlinear bubble oscillations. The pol
ytropic relation for the internal gas does not hold when the nonlinear
ity of the radial oscillation becomes strong. Both radial and surface
oscillations are affected by the translational motion of each bubble.
It is also shown that the subharmonic oscillation of interacting bubbl
es occurs more easily than that of an isolated bubble due to the bubbl
e-bubble interaction.