Multiphase Reactive Flow

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

There are a few other non-PDF approaches to simulating reactive flow processes (for example, the linear eddy model of Kerstein, 1991 and the conditional moment closure model of Bilger, 1993). These approaches are not discussed here as most of the engineering simulations of reactive flow processes can be achieved by the approaches discussed earlier. The discussion so far has been restricted to single-phase turbulent reactive flow processes. We now briefly consider modeling multiphase reactive flow processes. 

In general, multiphase reactive flow processes are classified into three types according to the location of the reaction zone ... 

Surface reactions options for rate controlling steps/UD Multiphase reactive flows mass transfer/reactions in all phases ... 

In this section the population balance modeling approach established by Randolph [95], Randolph and Larson [96], Himmelblau and Bischoff [35], and Ramkrishna [93, 94] is outlined. The population balance model is considered a concept for describing the evolution of populations of countable entities like bubble, drops and particles. In particular, in multiphase reactive flow the dispersed phase is treated as a population of particles distributed not only in physical space (i.e., in the ambient continuous phase) but also in an abstract property space [37, 95]. In the terminology of Hulburt and Katz [37], one refers to the spatial coordinates as external coordinates and the property coordinates as internal coordinates. The joint space of internal and external coordinates is referred to as the particle phase space. In this case the quantity of basic interest is a density function like the average number of particles per unit volume of the particle state space. The population balance may thus be considered an equation for the number density and regarded as a number balance for particles of a particular state. 

In this chapter several numerical methods frequently employed in reactor engineering are introduced. To simulate the important phenomena determining single- and multiphase reactive flows, mathematical equations with different characteristics have to be solved. The relevant equations considered are the governing equations of single phase fluid mechanics, the multi-fluid model equations for multiphase flows, and the population balance equation. 

The high resolution lattice Boltzmann scheme, for example, is currently popular in the CFD research community performing LES and direct numerical simulations due to the simple implementation and high accuracy obtained, but this method is still under development and yet not suitable for multiphase reactive flows. The numerical scheme is constructed from and solves a kinetic theory representation of the actual flow. A good review can be found in Chen and Doolen [27]. 

A proper convergence criterion is important, from both the accuracy and efficiency points of view, because it is deciding when to stop the iterative process. Research codes are generally iterating until the machine accuracy is reached, whereas the commercial codes are less accurate as efficiency is commonly desired by the customers. In commercial CFD codes, a convergence criterion defined by the reduction of the normalized residual, as calculated from the initial guess variable values, by a factor of 10 is frequently considered sufficient by contract research- and salespersons. However, for complex multiphase reactive flows this approach may easily lead to unphysical solutions. 

For most multiphase reactive flow problems, it is not possible to analyze all the operators in the complete solution method simultaneously. Instead the different operators of the method are analyzed separately one by one. The working hypothesis is that if the operators do not possess the desired properties solely, neither will the complete method. Unfortunately, the reverse is not necessarily true. In practical calculation we can only use a finite grid resolution, and the numerical results will only be physically realistic when the discretization schemes have certain fundamental properties. The usual numerical terminology employed in the CFD literature is outlined in this section [141, 202, 49]. 

In multiphase reactive flows, the interfacial transfer fluxes of momentum, heat and species mass are of great importance. These interfacial transfer fluxes are generally modeled as a product of the interfacial area concentration and a mean interfacial flux. It is normally assumed that the mean interfacial fluxes are, in turn, given as the product of the difference in the phase values of the primitive variables (driving force) multiplied by the transfer (proportionality) coefficients. Mathematically, a generic flux Ifc can be expressed on the form ... 

Jakobsen, H. A., Chemical Reactor Modeling. Multiphase Reactive Flows, Springer-Verlag, Berlin, 2008. 

Jakobsen HA. Chemical reactor modeling multiphase reactive flows. Berlin/Heidelberg Springer 2008. 

A statistical description of multiphase flow might be developed based on an analogy to the Boltzmann theory of gases [11, 39, 60,63, 66, 91, 125,135]. The fundamental variable is the particle distribution function with an appropriate choice of internal coordinates relevant for the particular problem in question. Most of the multiphase flow modeling work performed so far has focused on isothermal, non-reactive mono-disperse mixtures. However, in chemical reactor engineering the industrial interest lies in multiphase reactive flow systems that include poly-dispersed mixtures of multiple particle types, with their associated effects of mixing, segregation and heat and mass transfer. 

In part I most of the fundamental theory of single phase reactive flows is presented. In part II most of the fundamental theory of multiphase reactive flows is presented. In both parts a few numerical model simulation application examples are given to elucidate the link between theory and applications. In part III the chemical reactor equipment to be modeled are described. Several engineering models are introduced and discussed. A survey of the frequently used numerical methods, algorithms, and schemes is provided. A few practical engineering applications of the modeling tools are presented and discussed. The working principles of several experimental techniques employed in order to get data for model validation are outlined. 

Xie, N., Battaglia, F., Fox, R.O. Simulations of multiphase reactive flows in fluidized beds using in situ adaptive tabulation. Combust. Theory Model. 8, 195-209 (2004)... 

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