Role of pseudo-turbulent stresses in shocked particle clouds and construction of surrogate models for closure

Macroscale models of shock–particle interactions require closure terms for unresolved solid–fluid momentum and energy transfer. These comprise the effects of mean as well as fluctuating fluid-phase velocity fields in the particle cloud. Mean drag and Reynolds stress equivalent terms (also known as pseudo-turbulent terms) appear in the macroscale equations. Closure laws for the pseudo-turbulent terms are constructed in this work from ensembles of high-fidelity mesoscale simulations. The computations are performed over a wide range of Mach numbers ( M ) and particle volume fractions ( ϕ ) and are used to explicitly compute the pseudo-turbulent stresses from the Favre average of the velocity fluctuations in the flow field. The computed stresses are then used as inputs to a Modified Bayesian Kriging method to generate surrogate models. The surrogates can be used as closure models for the pseudo-turbulent terms in macroscale computations of shock–particle interactions. It is found that the kinetic energy associated with the velocity fluctuations is comparable to that of the mean flow—especially for increasing M and ϕ . This work is a first attempt to quantify and evaluate the effect of velocity fluctuations for problems of shock–particle interactions.