Coarse-grained numerical simulation for compressible fluid–particle two-phase flows

Compressible fluid–particle two-phase flows broadly exist in engineering problems, and the Eulerian–Lagrangian method is a popular branch of simulation studies. Usually, the coarse-grained strategy is adopted to reduce computational costs, and the coarse-grained criterion becomes critical for maintaining accuracy. In this study, a coarse-grained criterion was proposed for simulating compressible particulate two-phase flows by considering similarity invariants and regime transition behaviors. Based on our developed computation framework, in which the particle phase is solved using the discrete element method, a series of benchmark cases, including shock impacting granular column, shock impacting granular layer, and shock impacting granular ring cases, were considered to investigate the validity of the proposed criterion. It was proven that the stiffness coefficient should be scaled to the parcel size to maintain the invariance of the spreading velocity of the particle stress wave and the restitution coefficient should be reduced to help recover the internal energy dissipation inside the parcels. Furthermore, to describe more accurately the regime transition behaviors, which are common phenomena in compressible particulate two-phase flows, an adaptive interpolation operator was introduced to adjust the influencing range of the Lagrangian parcels dynamically.