Pseudo-turbulence models for compressible flow through random particle suspensions

A model for the pseudo-turbulent Reynolds stress tensor in compressible flows through monodisperse particle
clouds is developed based on data from particle resolved numerical simulations. This model extends previous
models for the incompressible regime to subsonic bulk Mach numbers. A Lagrangian model for the local
pseudo-turbulent Reynolds stress around a particle, based on the correlation of a local estimate of the Reynolds
stress and the drag force on the particle, is also presented. This model can be employed in Euler–Lagrange
type simulations. Additionally, corresponding models for the pseudo-turbulent transport of turbulence kinetic
energy, the velocity triple-correlation in the volume averaged total energy equation, is also introduced as a
first effort aimed at closing the energy equation.