Formulation of high-precision CFD method on non-orthogonal meshes with rigorous mechanical balance at gas-liquid interface

Ito, Kei; Kunugi, Tomoaki*; Ohshima, Hiroyuki

We are developing a high-accuracy gas-liquid two-phase flow simulation method to achieve direct simulations for the gas entrainment (GE) phenomena. Since the GE phenomena is highly affected by local flow path geometries, non-orthogonal meshes are employed to achieve accurate modeling of the geometries. In addition, we are focusing on mechanical balance conditions at gas-liquid interfaces because unphysical behaviors are often induced due to mechanical unbalances. 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. Finally, the new formulations are verified by calculating a stationary gas-bubble in liquid. As a result, the present method succeeds in eliminating completely unphysical phenomena.