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

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.

Inertial particle velocity and distribution in vertical turbulent channel flow: A numerical and experimental comparison

“…On the other hand, point-particle DNS has well known limitations in accounting for two-way coupling between particles and fluid flows, which motivated a number of recent efforts [18,19]. However, at the considered concentrations and particle Reynolds numbers, it is not obvious how the classical mechanisms by which particles would affect the turbulence (particle wakes, mass loading, enhanced dissipation, see Balachandar and Eaton [2]) may account for the observed discrepancies.…”

A correction scheme for two-way coupled point-particle simulations on anisotropic grids

“…In total 19 cases are simulated with results shown in Table 2. To provide a reference, errors are also reported for the simulations run with no correction as well as with the correction proposed in [10] using trilinear interpolation.…”

“…The present correction method is the best at reducing this part of the error, providing a much Table 2: The error in the simulated velocity of a single particle settling under gravity on an isotropic grid. The effect of the grid size Λ (i) , particle Reynolds number Re p , and the Stokes number S t are shown on the error in the settling velocity e , error in the drift velocity e ⊥ , and the overall error e. The present correction scheme is compared with the case with no correction and H&M, which is the correction proposed in [10]. e is not reported for uncorrected cases since it is almost identical to e .…”

Experimental study of inertial particles clustering and settling in homogeneous turbulence

“…Moreover, modeling the backreaction of the dispersed phase by point-particle methods present technical issues associated with the application of the point-wise forcing on the fluid computational grid (Balachandar 2009;Eaton 2009;Gualtieri et al 2013). To overcome these shortcomings, advanced methods have recently been proposed (Gualtieri et al 2015;Horwitz & Mani 2016;Ireland & Desjardins 2017) whose merits need to be fully appreciated in future comparisons with well-controlled experiments. Setting up the turbulent flow in two-way coupled simulations is also a critical issue: forcing steady-state homogeneous turbulence in either Fourier or physical space leads to artificial energy transfers hardly discernible from the actual interphase dynamics (Lucci et al 2010).…”