Turbulent flow closure types

A variety of statistical models are available for predictions of multiphase turbulent flows [85]. A large number of the application oriented investigations are based on the Eulerian description utilizing turbulence closures for both the dispersed and the carrier phases. The closure schemes for the carrier phase are mostly limited to Boussinesq type approximations in conjunction with modified forms of the conventional k-e model [87]. The models for the dispersed phase are typically via the Hinze-Tchen algebraic relation [88] which relates the eddy viscosity of the dispersed phase to that of the carrier phase. While the simplicity of this model has promoted its use, its nonuniversality has been widely recognized [88]. 

The two-equation turbulence closure with the prescribed parameters given above is called the standard k-e model. With these parameters the model is able to predict several types of turbulent flow, in particular the flows used to... 

Pinho, F.T. (2003) A GNF framework for turbulence flow models of drag reducing fluids and proposal for a x—e type closure. J. Non-Newtonian Fluid Mech., 114, 149-184. 

As discussed in the present chapter, the closure of the chemical source term lies at the heart of models for turbulent reacting flows. Thus, the material on chemical source term closures presented in Chapter 5 will be of interest to all readers. In Chapter 5, attention is given to closures that can be used in conjunction with standard CFD-based turbulence models (e.g., presumed PDF methods). For many readers, these types of closures will be sufficient to model many of the turbulent-reacting-flow problems that they confront in real applications. Moreover, these closures have the advantage of being particularly simple to incorporate into existing CFD codes. 

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. 

There are three types of closure models in CFD simulation of gas—hquid flow in bubble columns, i.e., drag force, bubble-induced turbulence, and kernel functions of bubble breakup and coalescence. We will show how we utilize the EMMS approach to derive new models and integrate them into CFD simulation. 

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