Granular flow kinetic theory application

It must be noted here that most industrial fluidized bed reactors operate in a turbulent flow regime. Trajectory simulations of individual particles in a turbulent field may become quite complicated and time consuming. Details of models used to account for the influence of turbulence on particle trajectories are discussed in Chapter 4. These complications and constraints on available computational resources may restrict the number of particles considered in DPM simulations. Eulerian-Eulerian approaches based on the kinetic theory of granular flows may be more suitable to model such cases. Application of this approach to simulations of fluidized beds is discussed below. 

In this section the application of multiphase flow theory to model the performance of fluidized bed reactors is outlined. A number of models for fluidized bed reactor flows have been established based on solving the average fundamental continuity, momentum and turbulent kinetic energy equations. The conventional granular flow theory for dense beds has been reviewed in chap 4. However, the majority of the papers published on this topic still focus on pure gas-particle flows, intending to develop closures that are able to predict the important flow phenomena observed analyzing experimental data. Very few attempts have been made to predict the performance of chemical reactive processes using this type of model. 

The outcome of this procedure is, in addition to the previously described kinetic theory of granular flow (KTGF) transport equations with the given flux and source closures, characteristic transport equations for species mass and thermal temperature. It is noted that the use of second order velocity moments or higher moments usually requires some kind of manipulation in order to obtain equations in the desired form. The derivation of the thermal temperature equation for reactive systems is certainly not trivial. The application of this theory to reactive systems is extensively discussed in the following two sections. 

Reddy, K. A. and V. Kumaran. 2007. Applicability of constitutive relations from kinetic theory for dense granular flow. Phys. Rev. E 76, 061305. 

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