Propagation of Shock Waves in Dilute Bubbly Liquids : 2nd Report, Effect of Internal Phenomena of the Bubble

Abstract

Propagation of shock waves in dilute bubbly liquids is investigated numerically taking into account internal phenomena of the bubbles. In this numerical analysis, the conservation equations for mass, momentum and energy inside each bubbles in the bubbly liquids are solved directly, in order to precisely estimate the effects of internal processes on wave phenonema. Numerical results under several conditions reveal that the radial motion of bubbles, which is affected by internal phenomena, such as thermal conduction through the bubble wall, has a significant influence on the time evolution of the propagation velocity of the shock wave and the relaxation structure behind the wave. The nondimensional thermal diffusivity, D, defined in eq. (13), is one of the most effective parameters to be correlated with the wave propagation process. As the initial bubble radius becomes larger or the pressure ratio becomes smaller, the time required for developing shock waves to steady-state conditions increases and the first maximum of the pressure profile in steady-state conditions becomes lower.