(70c) Generating Macroscopic Quantities of Particle-Fluid Flows of Coarse Particles By an Averaging Method: Selection of Sample Sizes and Test of Solid Pressure Correlation

Q.F. Hou¹, Z. Y. Zhou¹, J. S. Curtis², and A.B. Yu^1,3

¹ARC Research Hub for Computational Particle Technology, Department of Chemical Engineering, Monash University, Clayton, VIC 3800, Australia

²College of Engineering, University of California, Davis, One Shields Ave, Davis, CA 95616, USA

³Centre for Simulation and Modelling of Particulate Systems, Southeast University - Monash University Joint Research Institute, Suzhou 215123, PR China

Abstract

Macroscopic quantities of particle-fluid flow such as solid density and stress tensor can be obtained from microscopic variables such as particle positions and interaction forces through averaging methods. In using average methods, spatial and temporal sample sizes play an important role. However, how to properly select sample sizes is not clearly understood. Furthermore, the validity of the obtained correlations using the obtained macroscopic quantities has not been well examined. By using the combined approach of computational fluid dynamics and discrete element method, this work is attempted to give answers to these two concerns. First, the effect of spatial and temporal sample sizes on averaged macroscopic quantities is discussed. Guidance for the selection of sample sizes is provided to generate macroscopic quantities which are compatible with continuum mechanics. Then the correlation between solid pressure and solid fraction is established and compared to the correlations available in the literature. It agrees quantitatively with experimental observations and semi-empirical correlations but agrees only qualitatively with kinetic theory predictions. The evidence proves that the averaging method is an effective approach in linking microscopic and macroscopic properties of particle-fluid flows. If the sample sizes are selected properly valid correlations can be formulated for continuum modeling.

Key words: fluidized beds, granular media, particle-fluid flows