Effect of the volume fraction gradient on the phase interaction force model for disperse two-phase flows

Wang, Min; Zhang, Duan Z.; Balachandar, S.

doi:10.1103/physrevfluids.9.104301

Title: Effect of the volume fraction gradient on the phase interaction force model for disperse two-phase flows

Journal Article · 01 October 2024 · Physical Review Fluids (Online)

DOI: https://doi.org/10.1103/physrevfluids.9.104301 · OSTI ID:2472576

^[1];

^[2]

Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
Univ. of Florida, Gainesville, FL (United States)

In this work, the effects of the particle volume fraction gradient on fluid-particle interactions are studied. The phase interaction force is decomposed into three terms. For the first term, namely the symmetrized force density, we present theoretical reasoning and numerical evidence to assume that it is independent of the particle volume fraction gradient. The second term is the particle volume fraction gradient times a newly introduced diffusion stress. The third term is the divergence of the particle-fluid-particle (PFP) stress. If this assumption of independence of the particle volume fraction gradient for the first term can be verified, to the first order of the ratio of the mean distance between particles to the macroscopic lengthscale, all three terms can be studied and modeled in flows with uniform particle distributions. Models thus obtained are applicable to statistically inhomogeneous flows, with the second and third terms accounting for statistical inhomogeneity. To verify this assumption, numerical simulations of flows passing fixed arrays of particles are performed. Both uniform and nonuniform particle volume fractions are studied and compared for disperse multiphase flows with the particle Reynolds numbers ranging from 1 to 100, and particle volume fraction ranging from 1% to 26% in statistically steady states. It is found that the symmetrized force (first) term can be well approximated by the drag force obtained from studies of uniform flows. The diffusion stress is positive along the flow direction and negative in the directions perpendicular to the flow. In the case of moving particles, this stress could potentially cause particle aggregation in the flow direction and dispersion in the directions perpendicular to the flow. Finally, the diffusion stress is only important when there is a volume fraction gradient, while the PFP stress can be important in inhomogeneous flows with either nonuniform particle concentrations or nonuniform average relative velocities between the phases.

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Research Organization:: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)

Sponsoring Organization:: USDOE National Nuclear Security Administration (NNSA); US Department of the Navy, Office of Naval Research (ONR)

Grant/Contract Number:: 89233218CNA000001; NA0002378

OSTI ID:: 2472576

Report Number(s):: LA-UR--24-25806

Journal Information:: Physical Review Fluids (Online), Journal Name: Physical Review Fluids (Online) Journal Issue: 10 Vol. 9; ISSN 2469-990X

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

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Title: Effect of the volume fraction gradient on the phase interaction force model for disperse two-phase flows

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