Abstract
Numerical simulations of gas-liquid two-phase flows are frequently employed by a lot of researchers to evaluate complicated two-phase flow phenomena. In fact, we also have studied the applicability of the numerical simulation to GE (gas entrainment) phenomena on gas-liquid interfaces. In our study, we are developing a high-accuracy gas-liquid two-phase flow simulation method to achieve direct simulations for the GE phenomena. Since the GE phenomena is highly affected by local flow path geometries near occurrence regions of the GE phenomena, non-orthogonal meshes are employed in our study to achieve accurate modeling of the flow path geometries. In addition, we are focusing on mechanical balance conditions at gas-liquid interfaces because it is well-known that unphysical behaviors can be induced easily by mechanical unbalances at gas-liquid interfaces. In this paper, appropriate formulations satisfying rigorous mechanical balances between surface tension and pressure are derived on non-orthogonal meshes. In the formulations, a surface tension potential is introduced based on the Laplace equation as a consistent form with a formulation of a pressure jump condition at gas-liquid interface. In addition, for numerical simulations of stratified flows, a gravitational potential is also introduced to formulate a discontinuity of a pressure gradient at gas-liquid interface. Finally, the new formulations are verified by calculating a stationary gas-bubble in liquid. As a result, the present method succeeds in eliminating perfectly unphysical phenomena (spurious velocities) induced by inappropriate formulations. The present method also gives a physically appropriate simulation result near stratified gas-liquid interface where conventional methods (without the appropriate formulations) fail to eliminate occurrences of unphysical phenomena.
