Comparison Between Grad’s and Quadrature-Based Methods of Moments for the Numerical Simulation of Unsteady Particle-Laden Flows

Abstract

We present here a new method of moments for the numerical simulation of particle-laden flows. The closure needed in Eulerian methods relies on writing the kinetic descriptor, the velocity destribution function, as a sum of delta-functions instead of the one-delta-function or close-to-Maxwellian assumption in existing methods. The closure velocity distribution function parameters are computed from the transported moments using a quadrature method. Simulation results are compared to those of a close-to-Maxwellian-based Eulerian method and those of a reference Lagrangian simulation, considering only transport and drag of particles in a Taylor-Green fluid flow. For a particular Stokes number of 1 the velocity distribution function is far from equilibrium and particle trajectory crossing is an important feature. We find that the quadrature-based method performs better than the close-to-equilibrium-based method, giving moment profiles closer to those of the Lagrangian reference simulation. However significant differences still remain between quadrature-based and Lagrangian methods results.

A second‐order moment method applied to gas–solid risers

“…53,54 Lostec et al 55 compared the results using the quadrature methods and the Grad's method in a particle laden flow. 53,54 Lostec et al 55 compared the results using the quadrature methods and the Grad's method in a particle laden flow.…”

“…Moments profiles can be obtained from simulations by means of Lagrangian simulation, Grad's method and quadrature-based method. 53,54 Lostec et al 55 compared the results using the quadrature methods and the Grad's method in a particle laden flow. Here, we will consider flow behavior of particles predicted using the SOM model and KTGF, and compare to quadrature-based method simulation results by Passalacqua et al 18 in a periodic vertical channel.…”