On the Wave Dispersion Relevant to the Virtual Mass Terms in the Two-Phase Two-Fluid Model

Abstract

Interfacial pressure jump terms are introduced in the momentum equations of the two-fluid two-phase flow while at the same time we keep the conventional virtual mass force as a nonobjective formulation. The pressure discontinuity across a thin interface due to the surface tension is compactly represented by a function of the fluid bulk moduli. The governing equations with the interfacial pressure jump terms produced a hyperbolic equation system having real eigenvalues for the bubbly flow, regardless of whether the virtual mass terms are added or not. The mixture sound speed for the two-phase flow evaluated using the combined interfacial pressure jump and conventional virtual mass terms has shown increasing dispersion of the small-amplitude waves when the virtual mass coefficient is larger. When the virtual mass terms are added to account for the accelerating flow, care should be exercised therefore not to introduce nonphysical wave dispersion.