Volume Fraction Effects on the Added Mass Force

The added mass or inviscid unsteady force is a well-known phenomenon in multiphase flow arising from acceleration effects. Modeling of the added mass force is of interest in a multitude of industrial, engineering, and environmental applications. The present work seeks an improved understanding of the added mass force in the incompressible regime by accounting for volume fraction effects. We explore the effects of volume fraction on the added mass force in different triply periodic configurations consisting of volume fractions ranging from 0 to 0.4 using computational tools. This is achieved by impulsively applying a spatially uniform body force to the fluid while holding the particle in place, thereby accelerating the flow in a spatially homogeneous manner. We extract the added mass coefficient by separating the pressure gradient and added mass forces. In the dilute limit, we recover the analytical value of the added mass coefficient of 0.5 and observe substantial deviation from this in the finite volume fraction regime.