Correction scheme for point-particle models applied to a nonlinear drag law in simulations of particle-fluid interaction

Regularization of the Lagrangian point force approximation for deterministic discrete particle simulations

“…The relative errors for the terminal settling velocities with respect to the reference solution amount to +0.8% for ∆ = 0.5, +3% for ∆ = 1 and −2.5% for ∆ = 2. These orders of magnitude are close to those reported by Zuzio et al (2016); Ireland and Desjardins (2017); Horwitz and Mani (2018).…”

“…In addition to performance considerations, the accuracy of the present method should also be assessed on test cases of intermediate complexity such as homogeneous isotropic turbulence laden with particles. Changes in both particle and turbulence dynamics were reported in the literature for this test case, for instance regarding the rate of energy dissipation Esmaily and Horwitz (2018), particle settling velocities Ireland and Desjardins (2017) and particle preferential concentration Horwitz and Mani (2018) when including corrections to recover the undisturbed fluid velocity at the particle position. It would be interesting to confirm some of these observations using the present approach.…”

“…The current section examines the elementary test case of a particle settling under gravity. Despite its simplicity, this test case clearly demonstrates the convergence issues inherent to the Lagrangian point-force approximation in presence of two way-coupling Gualtieri et al (2015); Zuzio et al (2016); Ireland and Desjardins (2017); Horwitz and Mani (2018). All forces except drag and gravity are neglected so that particle dynamics are governed by the following equations:…”

“…In particular, errors with respect to the theoretical solution amount to only 0.6 % for Re p = 10 and 1.11% for Re p = 50 for ∆ = 1. Moreover, Horwitz and Mani (2018) also simulated the settling problem under gravity at Re p = 10 with nondimensional parameter values similar to those of table 2Summary of numerical and physical parameters for the particle settling under gravity at finite Reynolds number. The particle Reynolds numbers are based on their respective terminal settling velocity.table.caption.12 and their error levels are comparable to the present ones.…”

Exact regularised point particle (ERPP) method for particle-laden wall-bounded flows in the two-way coupling regime

“…Unfortunately, in two-way coupled simulations, the unperturbed flow is unavailable unless specific techniques are exploited to remove the particle self-disturbance (see e.g. Horwitz & Mani (2016, 2018), Capecelatro & Desjardins (2013), Akiki, Jackson & Balachandar (2017) and Ireland & Desjardins (2017) where several methods are proposed to circumvent this problem). These considerations pose challenging issues from the theoretical point of view and call for more accurate modelling of the particle–fluid interaction.…”