(455g) A Fully Coupled Third-Order Quadrature-Based Moment Method for the Simulation of Gas-Particle Flows
A third-order quadrature-based moment method (Fox, 2008) for simulating poly-disperse fluid-particle flows has been implemented in a computational fluid dynamics code, accounting for the full coupling between the gas and the dispersed phase. The particle phase is described by solving the moments transport equations obtained from kinetic theory, using a kinetic-based finite-volume technique, which is able to predict phenomena that lead to locally discontinuous velocity fields like the particle trajectory crossing. The moment equations are fully coupled with a fluid solver. The partial elimination algorithm (Spalding, 1980) is adopted to ensure a stable numerical solution in strongly coupled flows (Passalacqua et al., 2009). The algorithm has been extended to deal with locally packed zones, where the particle mean free path has to be limited to prevent the particle phase volume fraction from reaching unphysical values and compromising the stability of the numerical procedure.
The robustness of the implementation is tested by simulating a gas-particle flow in a vertical channel, with typical riser-flow particles (density: 1500 km/m3 , particle diameter 80μm and 250μm, corresponding to a Stokes number of 0.061 and 0.61 respectively). The results are compared to the predictions of the classical two-fluid models (Gidaspow, 1994) in both the considered cases, and with Euler-Lagrange simulations (Garg et al, 2009) in the case of Stokes number equal to 0.61.
The fluid and particle velocities, particle-phase volume fraction and granular temperature are observed to reach a steady state in the case of Stokes number 0.061, while the two-fluid model predictions shows unsteady flow structures.
In the case with the higher Stokes number, instabilities are observed that led to the formation of structures and initiate the particle segregation phenomena, inducing the formation of the typical flow structures experimentally observed in risers. The process that causes the development of the instability predicted by the quadrature-based method is confirmed by Euler-Lagrange simulations, while the two-fluid model provides an inconsistent result. The inconsistencies observed in two-fluid models are explained by considering the local particle Knudsen number, which is significantly higher than the limit of 0.1, above which the hydrodynamic model is unable to properly describe the flow properties, even adopting partial slip boundary conditions, and higher order approximation of the Boltzmann equation are required (Bird, 1994).
Bird, G. A. 1994. Molecular Gas Dynamics and the Direct Simulation of Gas Flows. 2° ed. Oxford University Press, USA.
Fox, R.O. 2008. A quadrature-based third-order moment method for dilute gas-particle flows. Journal of Computational Physics 227, no. 12: 6313-6350.
Garg, R., C. Narayanan, and S. Subramaniam. 2009. A numerically convergent Lagrangian-Eulerian simulation method for dispersed two-phase flows. International Journal of Multiphase Flow 35, no. 4: 376-388.
Gidaspow, D. 1994. Multiphase Flow and Fluidization. 1° ed. Academic Press.
Passalacqua, A., R. Garg, S. Subramaniam, and R. O. Fox. 2009. A fully coupled quadrature-based moment method for dilute to moderately dilute fluid-particle flows. Chemical Engineering Science (Submitted).
Spalding, D.B. 1980. Numerical computation of multi-phase fluid flow and heat transfer. In Recent Advances in Numerical Methods in Fluids, Ed. C. Taylor. Pineridge Press.