Interfacial Pressure Coefficient for Ellipsoids and Its Effect on the Two Fluid Model Eigenvalues

Abstract

Analytical expressions for interfacial pressure coefficients are obtained based on the geometry of the bubbles occurring in twophase flows. It is known that the shape of the bubbles affects the virtual mass and interfacial pressure coefficients, which in turn determines the cutoff void fraction for the wellposedness of twofluid model (TFM). The coefficient used in the interfacial pressure difference correlation is derived assuming potential flow around a perfect sphere. In reality, the bubbles seen in twophase flows get deformed, and hence, it is required to estimate the coefficients for nonspherical geometries. Oblate and prolate ellipsoids are considered, and their respective coefficients are determined. It is seen that the wellposedness limit of the TFM is determined by the combination of virtual mass and interfacial pressure coefficient used. The effect of flow separation on the coefficient values is also analyzed.