Important Length Scales in Dense Gas-Particle Flows

There is a long history of studies on application of dimensional analysis to develop scaling relations that can be employed for scale-up and scale-down of gas-particle fluidized beds. It is now well established that two-fluid models (TFM), with constitutive models for the stresses deduced from the kinetic theory of granular materials, are able to capture the formation inhomogeneous structures over a wide range of time and length scales. As resolving all these structures in simulations of industrial scale devices is impractical, filtered models that average over small-scale structures are currently being developed. This has brought to the surface the issue of relevant length scales in gas-particle flows.

In this talk, we will review the various length scales that naturally enter in gas-particle fluidized beds and discuss how an understanding of these scales is being used to construct simplified filtered models. A dimensional analysis of these filtered models then suggests a simple set of dimensionless groups that are important to capture the dynamics of such devices when simulated on coarse computational grids. Finally, we present simulation results, using both a TFM and an Euler-Langrange model, which support our choice of dimensionless parameters.