Article: Esmaily, M; Horwitz, JAK; “A Correction Scheme for Two-Way Coupled Point-Particle Simulations on Anisotropic Grids”, Journal of Computational Physics, 375: 960-982
Abstract: The accuracy of Lagrangian point-particle models for simulation of particle-laden flows may degrade when the particle and fluid momentum equations are two-way coupled. The exchange of force between the fluid and particle changes the velocity of the fluid at the location of the particle, thereby modifying the slip velocity and producing an erroneous prediction of coupling forces between fluid and particle. In this article, we propose a correction scheme to reduce this error and predict the undisturbed fluid velocity accurately. Conceptually, in this method, the computation cell is treated as a solid object immersed in the fluid that is subjected to the two-way coupling force and dragged at a velocity that is identical to the disturbance created by the particle.
The proposed scheme is generic as it can be applied to unstructured grids with arbitrary geometry, particles that have different size and density, and arbitrary interpolation scheme. In its crudest form for isotropic grids, the present correction scheme reduces to dividing the Stokes drag by 1 – 0.75A for A <= 1, where A is the ratio of the particle diameter to the grid size. The accuracy of the proposed scheme is evaluated by comparing the computed settling velocity of an individual and pair of particles under gravity on anisotropic rectilinear grids against analytical solutions. This comparison shows up to two orders of magnitude reduction in error in cases where the particle is up to 5 times larger than the grid that may have an aspect ratio of over 10. Furthermore, a comparison against a particle-resolved simulation of decaying isotropic turbulence demonstrates the excellent accuracy of the proposed scheme. (C) 2018 Elsevier Inc. All rights reserved.
Funding Acknowledgement: United States Department of Energy’s (DoE) National Nuclear Security Administration (NNSA) under the Predictive Science Academic Alliance Program II (PSAAPII) at Stanford University [DE-AC05-00OR22725]; National Science Foundation Graduate Research Fellowship [DGE-114747]
Funding Text: We thank Shankar Subramaniam and Mohammad Mehrabadi for sharing their particle-resolved simulation results and Ali Mani and Shima Alizadeh for fruitful discussions. This work was funded by the United States Department of Energy’s (DoE) National Nuclear Security Administration (NNSA) under the Predictive Science Academic Alliance Program II (PSAAPII) at Stanford University under Contract No. DE-AC05-00OR22725. We acknowledge the use of computational hours on the Certainty cluster at Stanford University, where all these tools have been developed. Jeremy Horwitz would also like to acknowledge support from the National Science Foundation Graduate Research Fellowship under Grant No. DGE-114747. Any opinion, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation.