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

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