Multi-scale Simulation of the Interaction of a Shock Wave and a Cloud of Particles

A multi-scale method is proposed in which resolved mesoscale simulations of the interaction of a normal moving shock with a rectangular cloud of particles yield a parametric representation of the drag due to these particles. This establishes a link between the meso- and macroscale through metamodels, which provide closure terms for a macroscale model. The latter is used to simulate a process-scale problem via an Eulerian-Lagrangian approach, assuming a point-particle representation of the particle phase. Results obtained using a traditional cloud-in-cell method with first-order particle-to-grid weighing are compared to those of the novel “SPARSE” algorithm which represents the entire particle cloud with a single macro-particle and approximates the actual cloud shape with a bivariate Gaussian distribution for the purpose of weighing the particle momentum and energy contribution to the carrier flow onto the Eulerian fluid grid. The resulting multi-scale approach has the potential to improve the accuracy and efficiency of shocked particle-laden flow simulations and enable simulation of realistic scales.