Method of moments for gas-solid flows: application to the riser

The method of moments developed for granular flow by Strumendo and Canu (2002) has been extended to fully developed dilute gas-particle flow by coupling the balances for the solid phase to the mass and momentum balances for the gas phase. In addition to collisional dissipation of random kinetic energy, a dissipation due to the drag has been introduced. Boundary conditions for the moments have also been derived. A simulation for steady developed flow without any fitted parameters was compared to the experimental measurements for flow in a riser. The model predicted the observed anisotropy of the measured normal granular stresses. The solid volume fraction and the velocities agreed with data of Tartan and Gidaspow (2004). The shear stresses (per unit density) have the theoretically expected radial distributions. They increase nearly linearly near the tube center, reach a maximum closer to the wall and drop to a small value at the wall. The model, however, has under-predicted the normal stress in the direction of flow, probably due to excessive dissipation of random kinetic energy by the gas to particle drag