Filtered models for reacting gas-particle flows
  Using the kinetic-theory-based two-fluid models as a starting point, we develop filtered two-fluid models for a gas-particle flow in the presence of an isothermal, first-order, solid-catalyzed reaction of a gaseous species. As a consequence of the filtering procedure, terms describing the filtered reaction rate and filtered reactant dispersion need to be constituted in order to close the filtered species balance equation. In this work, a constitutive relation for filtered reaction rate is developed by performing fine-grid, two-fluid model simulations of an isothermal, solid-catalyzed, first-order reaction in a periodic domain. It is observed that the cluster-scale effectiveness factor, defined as the ratio between the reaction rate observed in a fine-grid simulation to that observed in a coarse-grid simulation, can be substantially smaller than unity, and it manifests an inverted bell shape dependence on filtered particle volume fraction in all simulation cases. Moreover, the magnitude of the deviation in the cluster-scale effectiveness factor from unity is a strong function of the meso-scale Thiele modulus and dimensionless filter size. Thus coarse-grid simulations of a reacting gas-particle flow will overestimate the reaction rate if the cluster-scale effectiveness factor is not accounted for. 
William Holloway, Sankaran Sundaresan
cond-mat.other physics.flu-dyn