Comparison of kinetic theory predictions with experimental results for a vibrated three-dimensional granular bed

Abstract

The three-dimensional conservation equations relating energy and momentum transfer in a vibrated three-dimensional granular bed have been solved numerically by the finite element method. Two closures based on granular kinetic theory were used: one, the standard Fourier law relating heat flux to temperature gradient and the other, including an additional concentration gradient term. Each prediction of the two-dimensional axisymmetric granular temperature and packing fraction fields was compared against a one-dimensional model and three-dimensional experimental results, acquired using the technique of positron emission particle tracking. Both closures resulted in solutions that were in reasonable agreement with the experimental results, but it was found that differences between the predictions of each of the closures were relatively small in comparison to the anisotropy of the experimentally determined temperature distribution. © 2006 American Institute of Physics.