Transition models from the quenched to ignited states for flows of inertial particles suspended in a simple sheared viscous fluid

Abstract

Abstract A review of existing theories for flows of inertial particles suspended in an unbounded sheared viscous fluid is presented first. A comparison between theoretical predictions and numerical simulation results is made for Stokes numbers from $1$ to $10$ in dilute and dense flows. Both particle agitation and anisotropy coefficients are examined, showing that neither of them is able to give satisfactory results in dense flows. A more precise calculation of collisional contributions to the balance law of the particle stress tensor is presented. Results of the corresponding theory are in very good agreement with numerical simulations both in dilute and dense flows.