Structure of Shock Waves in Bubbly Liquid

Abstract

In this paper, steady and unsteady shock waves in a bubbly liquid are treated numerically. A new system of model equations describing the bubbly flow is applied and the detailed flow structure behind a shock front is investigated in detail. It is proved that the velocity difference between the liquid and the gas phases induced by a stationary shock wave is of order α1/2, wher α is the void fraction of the gas-phase. Radial oscillation of bubbles tends to produce a oscillatory profile of the translational velocity of the bubbles near the wave fronts. Numerical simulation shows that oscillatory behaviour of the mixture pressure is significantly suppressed by the translational motion of bubbles and that the whole shock structure is remarkably affected by the velocity difference between the phases especially in the case of weak shocks. It is confirmed that the stationary shock wave is realized as an asymptotic solution for a shock tube problem with uniform conditions in the low pressure and high pressure chambers.