Modeling pseudo-turbulence for shock-induced flow through particle suspensions

Shock waves interacting with a suspension of particles in the compressible flow regime give rise to complex microscale phenomena – primarily, drag and particle-induced velocity fluctuations termed pseudo-turbulent kinetic energy (PTKE). Particle-resolved simulations of a planar shock interacting with a dense suspension of particles are performed to quantify the budget of PTKE. We propose a two-equation model compatible with coarse-grained simulation techniques such as Euler-Lagrange and Euler-Euler methods in which PTKE and its dissipation are transported. Comparisons are made against existing algebraic models from the literature.