Constitutive equations for granular flow with uniform mean shear and spin fields

TL;DR

This study uses numerical simulations to derive constitutive equations for two-dimensional granular flows with uniform shear and spin fields, comparing results with kinetic theory and Kanatani's theory, revealing limitations and areas of agreement.

Contribution

It introduces a micropolar fluid model-based analysis of granular flow simulations, extending kinetic theory applicability and critically evaluating Kanatani's theory.

Findings

Kinetic theory estimates agree at low area fractions (ν=0.1)

Renormalization extends kinetic theory fit up to ν=0.7

Kanatani's dissipation function does not match simulation results at higher densities

Abstract

Numerical simulations of two-dimensional granular flows under uniform shear and external body torque were performed in order to extract the constitutive equations for the system. The outcome of the numerical simulations is analyzed on the basis of the micropolar fluid model. Uniform mean shear field and mean spin field, which is not subordinate to the vorticity field, are realized in the simulations. The estimates of stresses based on kinetic theory by Lun [Lun, J. Fluid Mech., 1991, 233, 539] are in good agreement with the simulation results for a low area fraction $\nu=0.1$ but the agreement becomes weaker as the area fraction gets higher. However, the estimates in the kinetic theory can be fitted to the simulation results up to $\nu=0.7$ by renormalizing the coefficient of roughness. For a relatively dense granular flow ($\nu=0.8$), the simulation results are also compared with Kanatani's theory [Kanatani, Int. J. Eng. Sci., 1979, 17, 419]. It is found that the dissipation function and its decomposition into the constitutive equations in Kanatani's theory are not consistent with the simulation results.