On the weak turbulent motions of an isothermal dry granular dense flow with incompressible grains: part I. Equilibrium turbulent closure models

The weak turbulent motions of a dry granular dense flow and the influence of the turbulent fluctuations caused by the minor short-term elastic/inelastic instantaneous collisions and the major long-term enduring frictional contacts among the grains on the mean flow characteristics are investigated. To this end, the conventional Reynolds-averaging process is applied to obtain the balance equations for the mean primitive fields associated with turbulent closure models. The thermodynamic analysis, based on the Mueller–Liu entropy principle, is carried out to derive the equilibrium formulations of the closure models. It shows that the effect of the turbulent fluctuations on the mean flow characteristics as well as the turbulent kinetic energy and dissipation can be taken into account by the granular coldness: a phenomenological measure of the fluctuating kinetic energy intensity. The implementation of the complete thermodynamically consistent turbulent closure models and the simulation of a gravity-driven stationary flow down an inclined moving plane compared with the experimental outcomes are provided in Part II of the present study.