Numerical investigation and modeling of reacting gas-solid flows in the presence of clusters

This work presents a volume-filtered formulation for describing chemically reacting flows in the presence of solid catalytic particles. The equations are discretized in a Eulerian-Lagrangian framework and applied to flows of isothermal, heterogeneously reacting chemical species in fully developed three-dimensional risers. The aim of this study is to identify and quantify the influence of particle clusters on heterogenous reactions. The Archimedes number, Ar, is varied from 500 to 12,500, and the Damkohler number, Da, from 0.1 to 10. To assess the multiphase dynamic effects on the chemistry, conversion times from the three-dimensional simulations are compared to a zero dimensional model that solves for the temporal evolution of the species mass fraction and ignores all spatial variations. The conversion process associated with the three-dimensional simulations is shown to be significantly longer compared to the zero dimensional solution, with an increasing effect for larger values of Da. The discrepancies can be fully attributed to the presence of clusters, which are accounted for in the zero order equations by an additional term that contains the covariance between species mass fraction and particle volume fraction fluctuations, which needs to be modeled. To this purpose, contributions to the fluctuating chemical source term are evaluated from the three-dimensional data and discussed, and a presumed shape probability distribution function (PDF) approach is investigated. This PDF approach models the fluctuating chemical source term by a product of a beta distribution for the species mass fraction and a lognormal distribution for the particle concentration, and yields a mean species solution that agrees very well with the three-dimensional results for the range of Ar and Da considered in this study. (C) 2014 Elsevier Ltd. All rights reserved.