Two-way coupled Cloud-In-Cell modeling of non-isothermal particle-laden flows: A Subgrid Particle-Averaged Reynolds Stress-Equivalent (SPARSE) formulation

Abstract

A two-way coupled Cloud-In-Cell (CIC) formulation for particle-laden flows is presented that accounts for cloud size and subgrid-scale stresses using averaging techniques, and for cloud deformation using methods from continuum mechanics. It traces a physical cloud of particles as a point and distributes its influence on the carrier flow via a multivariate Gaussian distribution function. The method extends the one-way coupled SPARSE (Subgrid Particle-Averaged Reynolds Stress-Equivalent) method in Davis et al. (2017) [20] to account for two-way coupling between the fluid and dispersed phases and the effect of subcloud thermal stresses resulting from fluctuations in the velocity and temperature of the physical particles amalgamated in each macro-particle. Two-dimensional benchmark simulations of a Mach 3.5 normal shock impinging on an initially stationary particle cloud show that the two-way coupled SPARSE model predicts the average cloud position and spread more accurately than a two-way coupled, first-order CIC approach, illustrating the importance of accounting for higher-order moments and cloud deformation. Through an appropriate initial division of the particle cloud into subclouds, SPARSE's predictions of the time-averaged horizontal and vertical cloud spread match those of a reference Particle-Source-In-Cell (PSIC) approach to within less than 4% and 1%, respectively, using up to two orders of magnitude fewer computational particles. This makes SPARSE a suitable tool for enabling accurate process-scale simulations of particle-laden flows that are not feasible with current PSIC or CIC methods.