Euler-Lagrange modelling of dilute particle-laden flows with arbitrary particle-size to mesh-spacing ratio

Abstract This paper addresses the two-way coupled Euler-Lagrange modelling of dilute particle-laden flows, with arbitrary particle-size to mesh-spacing ratio. Two-way coupled Euler-Lagrange methods classically require particles to be much smaller than the computational mesh cells for them to be accurately tracked. Particles that do not satisfy this requirement can be considered by introducing a source term regularisation operator that typically consists in convoluting the point-wise particle momentum sources with a smooth kernel. Particles that are larger than the mesh cells, however, generate a significant local flow disturbance, which, in turn, results in poor estimates of the fluid forces acting on them. To circumvent this issue, this paper proposes a new framework to recover the local undisturbed velocity at the location of a given particle, that is the local flow velocity from which the disturbance due to the presence of the particle is subtracted. It relies upon the solution of the Stokes flow through a regularised momentum source and is extended to finite Reynolds numbers based on the Oseen flow solution. Owing to the polynomial nature of the regularisation kernel considered in this paper, a correction for the averaged local flow disturbance can be analytically derived, allowing to filter out scales of the flow motion that are smaller than the particle, which should not be taken into account to compute the interaction/drag forces acting on the particle. The proposed correction scheme is applied to the simulation of a particle settling under the influence of gravity, for varying particle-size to mesh-spacing ratios and varying Reynolds numbers. The method is shown to nearly eliminate any impact of the underlying mesh resolution on the modelling of a particle's trajectory. Finally, optimal values for the scale of the regularisation kernel are provided and their impact on the flow is discussed.