A novel method for bounding the phase fractions at both ends in Eulerian multi-fluid model

Abstract

The study aims to present a convenient but practical method to guarantee the boundedness and conservation of phase fractions in the Eulerian multi-fluid model. The established Eulerian multi-fluid model is based on the finite volume method and implemented in the platform of OpenFOAM-v2012, which is an open-source software. It is completely unnecessary to employ any reconstruction techniques or rewrite the phase continuity equations to maintain the boundedness and conservation of phase fractions in the proposed method. The advection flux of the phase continuity equation is constructed within the coupling procedure of velocity and pressure and explicitly evaluated when solving the phase continuity equation. The upwind interpolation of the phase fraction is carried out before constructing the pressure equation; thus, the advection flux of the phase continuity equation could be corrected by the pressure equation for boundedness and conservation consideration. Those unique treatments only slightly differ from the standard solution procedure, but the boundedness and conservation could be naturally guaranteed. The proposed method is verified by two test cases, including the phase separation and the two-phase upward flow, to demonstrate the boundedness, conservation, and accuracy of the proposed method.