A New Reduced-Order Model for the Thermal Damping Effect on Radial Motion of a Bubble (2nd Report, Validation of the Model by Numerical Simulation)

Abstract

In this second report, the reduced-order model for a thermal damping effect on a radial motion of a spherical bubble, which is proposed in the first report, is numerically validated. In the present model, temperature gradient at the bubble wall is approximated by using an average bubble temperature and a thermal penetration length inside the bubble based on a linear theory (Prosperetti, 1991).Initially, the numerical method to introduce the present model for the pressure equation is explained. Then, the forced and free oscillations of the bubble are numerically solved in the cases that the nonlinearity of the bubble motion is strong. The result of the present model shows good agreement with the full model, in which the temperature profile inside the bubble is fully solved.