Granular flows, kinetic energy

In most gas-particle flow situations occurring in fluidized bed reactors, a standard k — e turbulence model is used to describe the turbulence in the continuous phase whereas a separate transport equation is formulated for the kinetic energy (or granular temperature) of the particulate phase [122, 42, 41, 165, 84, 52]. Further details on granular flows are given in chap 4. 

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 severe implications of these facts have been partially uncovered in reference [5] as a result of formulating a kinetic theory for granular flow without interaction with the ambient medium. These implications, as well as additional difficulties due to the necessity to calculate the energy supply to the particle fluctuations, make somewhat problematic, at the present state of the art, the formulation of a reliable and sufficiently simple hydrodynamic model even for coarse dispersions. We have succeeded in this respect only at the expense of making certain supplementary assumptions. These assumptions cne ... 

The active layer depth and bed flow properties depend on the coefficient of restitution of the material. The flow properties of interest include granular temperature, which is a measure of kinetic energy in random motion of particles, and dilation. Granular temperature was found to be high at regions of low concentration with high mean velocity. These experiments also characterize the shape of the active layer to... 

In order to solve for the foregoing conservation equations to establish the granular flow field they must be closed by plausible constitutive relations for the stress terms, P, and Pf, the kinetic energy flux, q, and rate of dissipation by inelastic collision, 7, along with suitable boundary conditions. Applying these equations to describe the flow of material in the transverse plane of the rotary kiln will require a true quantification of the actual flow properties, for example velocity, in the various modes of rotary kiln observed and described earlier in Chapter 2. 

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