Impact of Particle Volume Fraction Gradient on Particle-Fluid Phase Interaction Models*

Phase interaction forces are crucial in modeling multiphase flows. Most existing models have been developed based on statistically homogeneous flows, even though most practical flows are inhomogeneous. This study examines the effects of particle volume fraction gradients on fluid-particle interactions through numerical simulations of flows passing through fixed arrays of particles with volume fraction gradients. Both uniform and non-uniform particle volume fractions are analyzed and compared for disperse multiphase flows, with particle Reynolds numbers ranging from 1 to 100 and particle volume fractions ranging from 1% to 26% in statistically steady states.

The findings indicate that as the Reynolds number increases, the effect of the particle concentration gradient becomes significant and should be considered in particle-fluid phase interaction models for practical multiphase flow simulations. Recent work decomposed fluid-particle phase interaction into a particle-mean-field force and the divergence of particle-fluid-particle (PFP) stress for uniform particle-fluid systems. Our studies suggest that for general disperse multiphase flows, the particle-mean-field force can be further divided into a drag force term and a diffusion force term, which is the product of the particle volume fraction gradient and a newly introduced diffusion stress.