Damkohler numbers parallel

In order to implement the PDF equations into a LES context, a filtered version of the PDF equation is required, usually denoted as filtered density function (FDF). Although the LES filtering operation implies that SGS modeling has to be taken into account in order to capture micromixing effects, the reaction term remains closed in the FDF formulation. Van Vliet et al. (2001) showed that the sensitivity to the Damkohler number of the yield of competitive parallel reactions in isotropic homogeneous turbulence is qualitatively well predicted by FDF/LES. They applied the method for calculating the selectivity for a set of competing reactions in a tubular reactor at Re = 4,000. 

A simplified mathematical description of this three-zone model proved [332], however, that the quantity of material converted in the dispersion zone could be ignored, if the original concentration ratio of A and B was less than 0.1 and the action of micro- and macro-mixing is described by the Damkohler number Da = fczCBo/s and n = 27twD/ qs) (where w is the flow rate D is the dispersion coefficient q is the liquid throughput and s [s ] is the shrinkage rate of the volume element). The model was evaluated with competitive reactions in series and parallel reactions, and was found to be adequately applicable. 

The parallel-pore model provides an in-depth description of the void volume fraction and tortuosity factor Tor based on averages over the distribution in size and orientation, respectively, of catalytic pores that are modeled as straight cylinders. These catalyst-dependent strncture factors provide the final tools that are required to calculate the effective intrapellet diffusion coefficients for reactants and prodncts, as well as intrapellet Damkohler numbers. The following conditions are invoked ... 

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