Direct Numerical Simulation of Fluidization of 1204 Spheres

One goal pursued there is to demonstrate that numerical experiments on fluidization can be processed in log-log plots for straight lines leading to power laws as did Richardson and Zaki 1954 for real experiments. As far as we know, we are the only group of researchers to carry out this program. There is no prior literature, in which power laws are obtained from numerical experiments. On the other hand, there are a number of numerical packages for particles in fluids that might be used in this way. The methods of Stokesian dynamics (see Brady 1993) can be recommended for problems in which inertia is absent. Hofler, Muller, Schwarzer and Wachmann 1999 introduced two approximate Euler-Lagrangian simulation methods for particle in fluids. In one method, the particle surface is discretitized in grid topology; spheres are polygons on flat places between nodes. In the second method, a volume force term is introduced to emulate rigid body motion on the particle surface; this method is similar to the force coupling methods, introduced by Maxey, Patel 1997. Hofler et al 1999 calculated sedimentation of 65,000 spheres but at Reynolds numbers so small that it is essentially Stokes flow. Johnson and Tezduyar 1999 used a fully resolved DNS/ALE method to compute sedimentation of 1,000 spheres at Reynolds numbers not larger than 10. A fully resolved method which is based on matching explicit Stokes flow representations of flow near particles with computations on a grid has been proposed by Ory, Oguz and Prosperetti 2000. The problem of particulates in turbulent flows has been considered by a few authors: Crowe, Chung, Troutt 1996, McLaughlin 1994, Maxey, Patel, Chang, Wang 1997; these approaches use point particle approximations because fully resolved computations in turbulent flow are not presently possible.