Turbulence multiphase

CFD models for turbulent multiphase reacting flows do not solve the laminar two-fluid balances (Eqs. 164 and 165) directly. First, Reynolds averaging is applied to eliminate the large-scale turbulent fluctuations. Using Eq. (164) as an example, we can apply Reynolds averaging to find (with pg constant)... 

The fluxes of mass, momentum, and energy of phase k transported in a laminar or turbulent multiphase flow can be expressed in terms of the local gradients and the transport coefficients. In a gas-solid multiphase flow, the transport coefficients of the gas phase may be reasonably represented by those in a single-phase flow although certain modifications... 

Development of Generic Flow Models Select suitable framework. Develop model equations (turbulence, multiphase reactive flows)... 

Turbulence is the most complicated kind of fluid motion. There have been several different attempts to understand turbulence and different approaches taken to develop predictive models for turbulent flows. In this chapter, a brief description of some of the concepts relevant to understand turbulence, and a brief overview of different modeling approaches to simulating turbulent flow processes is given. Turbulence models based on time-averaged Navier-Stokes equations, which are the most relevant for chemical reactor engineers, at least for the foreseeable future, are then discussed in detail. The scope of discussion is restricted to single-phase turbulent flows (of Newtonian fluids) without chemical reactions. Modeling of turbulent multiphase flows and turbulent reactive flows are discussed in Chapters 4 and 5 respectively. 

For multiphase flow processes, turbulent effects will be much larger. Even operability will be controlled by the generated turbulence in some cases. For dispersed fluid-fluid flows (as in gas-liquid or liquid-liquid reactors), the local sizes of dispersed phase particles and local transport rates will be controlled by the turbulence energy dissipation rates and turbulence kinetic energy. The modeling of turbulent multiphase flows is discussed in the next chapter. 

Most attempts at modeling complex, turbulent multiphase flows rely on the practices followed for single-phase flows, with some ad hoc modifications to account... 

The recent progress in experimental techniques and applications of DNS and LES for turbulent multiphase flows may lead to new insights necessary to develop better computational models to simulate dispersed multiphase flows with wide particle size distribution in turbulent regimes. Until then, the simulations of such complex turbulent multiphase flow processes have to be accompanied by careful validation (to assess errors due to modeling) and error estimation (due to numerical issues) exercise. Applications of these models to simulate multiphase stirred reactors, bubble column reactors and fluidized bed reactors, are discussed in Part IV of this book. 

A reactor engineer frequently encounters turbulent, multiphase and reactive flows, which are more complex than those discussed in the previous chapter. In this chapter, modifications or special techniques/algorithms required to extend the finite volume method to handle such complexities are discussed. In addition, some of the practical issues involved in carrying out numerical simulations of complex flow models are also discussed. 

Sha WT, Slattery JC (1980) Local Volume-Time Averaged Equations of Motion for Dispersed, Turbulent, Multiphase Flows. NUREG/CR-1491, ANL-80-51... 

Balachandar, S. 2009 A scaling analysis for point-particle approaches to turbulent multiphase flows. International Journal of Multiphase Flow 35, 801-810. 

Fox, R. O. 2007 Introduction and fundamentals of modeling approaches for polydisperse multiphase flows, in Computational Models for Turbulent Multiphase Reacting Flows, Vienna Springer, pp. 1 0. 

Equations 6.3 and 6.4 assume that at equal Re and Sc the value of Shp should be the same irrespective of the type and size of the contacting device/reactor. However, the definitions of Re and Shp pose a formidable problem. The linear dimension term in Re and Shp and the velocity term in Re need to be defined with relevance to the type of system/reactor. Most of the investigators used simple definitions for the velocity term. For instance, in bubble columns, the superficial gas velocity was used, whereas for stirred vessels the tip speed (NxD) was used. The discussion presented in Chapter 5 clearly indicates that these simplified definitions cannot form the basis of convective mass transfer in a highly turbulent multiphase reactor. The hnear dimension to be used in Shp and Re is similarly elusive, particularly in the case of... 

When the flow is highly turbulent multiphase, there are only two practical design options ... 

Turbulent Multiphase Flows with Heat and Mass Transfer... 

Many industrial processes are stiU designed on the basis of the assumptions of plug flow and steady-state uniform two-phase flow. For this chapter, much evidence has been collected with respect to the abundant occurrence of transient mesoscale coherent structures, strands, or clusters in various turbulent multiphase flows, at least at scales and under conditions relevant to industrial processes. This evidence is from a variety of sources experimental observations in academic laboratories, results from hydrodynamic stability analyses, and computational simulation studies (both of the LES and the DNS type). Unfortunately, this evidence comprises many indecisive and even contradictory reports about the drivers behind these structures, clusters, and strands, and about their dependence on density ratio, particle size, volume fractions, operating conditions, and so on. 

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