Kinetic Description of Multiscale Phenomena

The Annual Kinetic FRG Meeting
September 21-25, 2009

CSIC Building (#406), Seminar Room 4122.

A Quadrature-Based Moment Method for Gas-Particle Flows

Dr. Alberto Passalacqua

Iowa State University

Abstract:  Gas-particle flows are involved in various industrial applications in the energy, oil and gas fields, like coal gasification, production of light hydrocarbons by fluid catalytic cracking, catalytic combustion and different treatments aiming to reduce or eliminate pollutants. In addition, gas-particle flows take part to interesting natural phenomena, like volcanic eruptions, and their understanding is important also for the air transport industry, to prevent phenomena like the brown-out, which might happen when helicopters land on a sandy soil. The particulate phase of a gas-particle flows is described with an analogy to a granular gas, by finding an approximate solution of the kinetic equation in the velocity-based number density function. In the recent past, many works were published in the literature on mathematical modeling of gas-particle flows using hydrodynamic models (Enwald et al., 1996), where Navier-Stokes type equations are solved to describe the particle phase as a continuum, computing its stress tensor using moment closures from the kinetic theory (Gidaspow, 1994; Peirano and Leckner, 1998). These closures, however, are obtained assuming that the flow is dominated by collisions and nearly at equilibrium, which corresponds to consider a particle-phase Knudsen number close to zero, leading to inconsistencies and erroneous or missing predictions of physical phenomena when these models are applied to dilute fluid-particle flows, where rarefaction effects are not negligible. Recently Desjardin et al. (2008) showed that two-fluid models are unable to correctly capture particle trajectory crossing, seriously compromising their ability of correctly describing any velocity moment for finite, non-zero, Stokes numbers, and clarified that the particle segregation captured by two-fluid models for finite Knudsen numbers is artificially high due to their mathematical formulation. Fox (2008) developed a third-order quadrature-based moment method for dilute gas-particle flows, which has been successfully coupled to a fluid solver to compute dilute and moderately dilute gas-particle flows in Passalacqua et al., who validated it against Lagrangian and two-fluid simulations. An example of gas-particle flow in a vertical channel, at different particle concentrations (from 0.1% to 4%), and particle Stokes number is presented in this work, showing the predictive capabilities and the robustness of the quadrature-based moment method to predict the behavior of gas-particle flows. In particular, it is shown how the model correctly describes different flow conditions for increasing particle Stokes numbers, properly predicting a steady-state solution at low Stokes numbers, and the development of flow instabilities, which lead to particle segregation at higher Stokes numbers. The role of the particle concentration on the development of the instability is also examined. 1 E-mail: (A. Passalacqua), (R. O. Fox) References Desjardin, O., Fox, R. O., Villedieu, P., 2008. A quadrature-based moment method for dilute fluid-particle flows. Journal of Computational Physics 227, 2524-2539. Enwald, H., Peirano, E., Almstedt, A. E., 1996. Eulerian two-phase flow theory applied to fluidization. International Journal of Multiphase Flow 22, 21-66. Fox, R. O., 2008. A quadrature-based third-order moment method for dilute gas-particle flows. Journal of Computational Physics 227, 6313-6350. Gidaspow, D., 1994. Multiphase Flow and Fluidization. Academic Press. A. Passalacqua, R. Garg, S. Subramaniam, R. O. Fox, A fully coupled quadrature-based moment method for dilute to moderately dilute fluid-particle flows, Submitted to Chemical Engineering Science. Peirano, E., Leckner, B., 1998. Fundamentals of turbulent gas-solid flows applied to circulating fluidized bed combustion. Progress in Energy and Combustion Science 24, 259- 296. Simonin, O., 1991. Prediction of the dispersed phase turbulence in particle-laden jets. In: 4th International Symposium on Gas-Solid Flows. Vol. 121. ASME-FED, pp. 197 - 206