(163h) A Kinetic Model for a Non-Isothermal Granular Gas with Bi-Disperse Particles

A seventh-order quadrature-based moment method for the solution of the complete Boltzmann equation (Fox, 2008), with the complete Boltzmann collision integral, is applied to the simulation of a bi-disperse granular mixture.

Two different test cases are considered: an isolated granular mixture of spherical, inelastic spheres, which cools down due to collisions, and a binary granular mixture between two Maxwellian stationary walls at different temperatures.

In the homogeneous case, particles accommodate an homogeneous cooling state, where the temperature ratio of the two species becomes constant, with different granular temperatures for each species. The temperature ratio is studied as a function of mass ratio, size ration, density, and mixture composition. Particles with restitution coefficient equal to 0.95 and 0.8 are considered, and results are compared with molecular dynamics predictions (Dahl et al., 2002).

A mixture characterized by a volume fraction ratio equal to 4, a particle diameter and density ratios of 2, with restitution coefficient equal to 0.9 is considered for the non-homogeneous simulation of a binary mixture between two non-isothermal walls, with a temperature ratio between the walls equal to 10 and a wall distance to particle diameter ratio equal to 15.4. Results for the species granular temperature profiles and for the concentrations are provided and compared with molecular dynamics data of Galvin et al. (2005).

In both applications, the quadrature-based method provides results for the available moments (e.g. number density, mean velocity, stress tensor, energy flux, etc.) in quantitative agreement with the molecular dynamics data.

References

Dahl, S. R., C. M. Hrenya, V. Garzo, and J. W. Dufty. 2002. Kinetic temperatures for a granular mixture. Physical Review E 66, no. 4, 041301.

Fox, R.O. 2008. Higher-order quadrature-based moment methods for kinetic equations. Journal of Computational Physics (submitted).

Galvin, J. E., S. R. Dahl, e C. M. Hrenya. 2005. On the role of non-equipartition in the dynamics of rapidly flowing granular mixtures. Journal of Fluid Mechanics 528, 207-232.