(25a) Filtered Models for Reacting Gas-Particle Flows

Particle laden flows are used in a wide variety of industrially relevant processes that span applications ranging from the synthesis of specialty chemicals to the refining of petroleum products. Gas-particle flows exhibit persistent fluctuations in velocity and particle volume fraction that span a range of length and time scales. Flow structures are manifested as a consequence of the instability of the uniformly fluidized state [1], and can be predicted via continuum models that treat the particle and fluid phases as interpenetrating continua [2]. These models commonly take the form of balance equations for mass, momentum, and energy associated with fluctuating motion of particle and fluid phases. While the continuum model framework is capable of predicting these flow structures, the ability to accurately resolve all relevant length scales requires very fine grid resolution (on the order of 10 particle diameters) [3]. Such fine resolution is not affordable when simulating gas-particle flows large devices, and much coarser grid resolution is generally employed.

Recently, filtered models have been developed for the accurate simulation of non-reacting gas-particle flows on coarse numerical grids without neglecting the consequences of fine scale structure [4]. The present study is concerned with the extension of previous work to reacting gas-particle flows.  Coarse-grid simulations of reacting multiphase flows require filtered species and energy balances, in addition to filtered hydrodynamic equations. In the present study we construct filtered balance equations for gaseous reactants participating in catalytic reactions on the solid surface. Such filtered equations call for filtered chemical reaction rates, which should account for modification of the reaction rates brought about by mesoscale inhomogeneous structures.

To this end we have performed highly resolved simulations of gas-particle flow in the presence of a solid catalyzed, irreversible, first order, isothermal, gas phase reaction. Our simulations reveal that the effectiveness factor associated with mesoscale structures decreases systematically with increasing filter size and reaction rate constant. This implies that coarse-grid simulations of reacting multiphase flows will overestimate conversions if proper allowances are not made for the decreased effectiveness factors. A model for the cluster-scale effectiveness factor will be presented, which was constructed by filtering high resolution reacting gas-particle flow simulations.

[1] Sangani A, Koch, DL. Particle pressure and marginal stability limits for a homoge- neous monodisperse gas-fluidized bed: kinetic theory and numerical simulations. J. Fluid. Mech. 1999; 400: 229-263.

[2] Jackson R, The Dynamics of Fluidized Particles. Cambridge University Press: Cambridge, 2000.

[3] Agrawal K, Loezos, PN, Syamlal, M, Sundaresan, S. The role of meso-scale structures in rapid gas-solid flows. J. Fluid. Mech. 2001; 445: 151-185

[4] Igci, Y, Andrews, AT, Sundaresan, S, Pannala, S, O’Brien, T. Filtered two-fluid models for fluidized gas-particle suspensions. AIChE J. 2008; 54: 1431-1448