(54d) Simulation of Mono- and Bi-Disperse Gas-Particle Riser Flow with Quadrature-Based Moment Methods

Gas-particle flows can be described by a kinetic equation for the particle phase coupled with the Navier-Stokes equations for the fluid phase through a momentum exchange term. The direct solution of the kinetic equation is prohibitive for most applications due to the high dimensionality of the space of independent variables. A viable alternative is represented by moment methods, where moments of the velocity distribution function are transported in space and time. A fully coupled third-order, quadrature-based moment method (Fox, 2008; Passalacqua et al., 2010) was applied in this work to the simulation of mono- (He et al, 2009a) and bi-disperse (Mathiesen et al., 2000) gas-particle flows in the riser of a circulating fluidized bed. Closures for the moment spatial fluxes and the source terms in the moment transport equations are provided by a quadrature-based representation of the particle velocity distribution function. A Bhatnagar-Gross-Krook collision model is used in the mono-disperse case, while the full Boltzmann integral is adopted in the bi-disperse case. The predicted values of mean local phase velocities, RMS velocities, and particle volume fractions are compared with the predictions of Euler-Euler multi-fluid models, with kinetic theory closures for the particle phase, Euler-Lagrange simulations (He at al, 2009a; 2009b), and experimental data from the literature (He at al, 2009a; Mathiesen et al, 2000). The grid-independence of the solution provided by Euler-Euler hydrodynamic models and quadrature-based moment methods is examined to illustrate that QMOM achieves grid-independent solutions, due to its ability of predicting particle-trajectory crossing without incurring in the formation of delta-shocks, and allowing converged statistics to be extracted from the simulation.

References

Fox, R. O. A quadrature-based third-order moment method for dilute gas-particle flows. J. Comput.  Phys. 2008, 227, 6313–6350.

He, Y.; Deen, N.; Van Sint Annaland, M.; Kuipers, J. A. M. Gas-solid turbulent flow in acirculating fluidized bed riser: Experimental and numerical study of monodisperse particle systems. Ind. Eng. Chem. Res. 2009a, 8091 – 8097.

He, Y.; Deen, N.; Van Sint Annaland, M.; Kuipers, J. A. M. Gas-solid turbulent flow in a circulating fluidized bed riser: Numerical study of binary particle systems. Ind. Eng. Chem. Res. 2009b, 8098 – 8108.

Passalacqua, A.; Fox, R. O.; Garg, R.; Subramaniam, S. A fully coupled quadrature-based moment method for dilute to moderately dilute fluid-particle flows. Chem. Engng. Sci. 2010, 65, 2267 – 2283.

Mathiesen, V.; Solberg, T.; Hjertager, B. H. An experimental and computational study of multiphase flow behavior in a circulating fluidized bed. Int. J. Multiphase Flow 2000, 387 – 419.