Accurate calculation of Stokes drag for point-particle tracking in two-way coupled flows

TL;DR

This paper introduces a correction method for accurately calculating Stokes drag in two-way coupled particle-laden flows, significantly reducing errors caused by disturbed fluid velocities near particles.

Contribution

The authors develop a novel correction scheme to estimate undisturbed fluid velocity, improving Stokes drag calculations in two-way coupled simulations.

Findings

Correction reduces velocity error by an order of magnitude.

Method improves accuracy of particle settling velocity predictions.

Validation performed for particle settling in quiescent fluid.

Abstract

In this work, we propose and test a method for calculating Stokes drag applicable to particle-laden fluid flows where two-way momentum coupling is important. In the point-particle formulation, particle dynamics are coupled to fluid dynamics via a source term that appears in the respective momentum equations. When the particle Reynolds number is small and the particle diameter is smaller than the fluid scales, it is common to approximate the momentum coupling source term as the Stokes drag. The Stokes drag force depends on the difference between the undisturbed fluid velocity evaluated at the particle location, and the particle velocity. However, owing to two-way coupling, the fluid velocity is modified in the neighborhood of a particle, relative to its undisturbed value. This causes the computed Stokes drag force to be underestimated in two-way coupled point-particle simulations. We develop estimates for the drag force error as function of the particle size relative to the grid size. We then develop a correction method that estimates the undisturbed fluid velocity from the computed disturbed velocity field. The correction scheme is tested for a particle settling in an otherwise quiescent fluid and is found to reduce the error in computed settling velocity by an order of magnitude compared with common interpolation schemes.