Examination of appropriate formulations for velocity and pressure calculation methods at interfacial region on collocated physical variables' distribution

Abstract

Authors are developing a high-precision simulation method for gas-liquid two-phase flows on an unstructured grid as a part of numerical studies on gas entrainment phenomena in a sodium-cooled fast reactor. In this study, unphysical behaviors of velocity or pressure distributions near gas-liquid interface induced by inappropriate formulations of momentum advection or velocity-pressure coupling are discussed and appropriate formulations are derived considering proper balance condition of physical quantities. By using these new algorithms, the unphysical behaviors disappeared and numerical simulations could be conducted stably. As a validation of developed simulation method, one air bubble rising in static water was simulated under several conditions dominated by Morton and Eotvos numbers. As a result, simulated bubble shapes well coincided with experimentally observed shapes in each condition. In addition, similar bubble shapes and velocity distributions with results of simulations on the structured grid were obtained on the unstructured grid. These results show that our simulation method can achieve high-precision two-phase flow simulations on both the structured and the unstructured grids.