EFFECT OF INTERFACIAL PRESSURE JUMP AND VIRTUAL MASS TERMS ON SOUND WAVE PROPAGATION IN THE TWO-PHASE FLOW

Virtual mass terms as an interfacial force, taking account of relative acceleration of the bubbles in the liquid phase, have been generally accepted in the two-phase flow models since they conditionally stabilize the numerical scheme. Despite the convincing physical reasoning associated with the bubble flow dynamics, it can be shown that the virtual mass terms unfortunately cause non-physical dispersion in the sound wave propagation. By introducing in the momentum equations new interfacial pressure jump terms based on the surface tension and represented by a function of the fluid bulk moduli, the governing equation system becomes strictly hyperbolic in the present paper with real eigenvalues, regardless of inclusion of the virtual mass terms. It is remarkable that the eigenvalues give realistic speeds of sound when the objective virtual mass terms are reduced more and more until they vanish. On the occasion that the virtual mass terms have to be kept with the interfacial pressure jump terms in the wave-dominant two-phase flow problems, we recommend that the non-physical wave dispersion due to the virtual mass terms should be appropriately controlled.