Particle-gas interactions in two-fluid models of gas-solid flows
Modelling gas-solid two-phase flows using a two-fluid approach has two main difficulties: formulating constitutive laws for the particulate stresses and modelling the gas turbulence modulation. Due to the complex nature of the gas-particle interactions, there is no universal model covering every flow regime. In this thesis, three flow regimes with distinctive characteristics are studied, i.e. the very dense regime where the solid volume fraction, v2>5%, the dense flow regime where 5%≥1%, and the relatively dilute regime where 1%≥v2>0.1%. In the very dense flow regime, where the interstitial gas is normally neglected, the gas flow is assumed laminar and causes a viscous energy dissipation in the particulate phase. Numerical results for granular materials flowing down an inclined chute show that the interstitial gas may have a considerable effect in these flows. In the dense regime, where the inter-particle collisions are very important, a fluctuational energy transfer rate between the two phases is postulated, similar to that in a dilute Stokes flow. Consequently, the numerical solutions relax the restriction of elastic inter-particle collisions and show good agreement with experimental measurements. In the above two regimes, the kinetic theory of dry granular flow is adopted for the particulate stresses because the inter-particle collisions dominate the flows. The interstitial gas influence on the constitutive flow behaviour of the particulate phase is considered in the relatively dilute flow regime also, and a k-equation with a prescribed turbulent length scale is first used to address the gas turbulence modulation. Numerical results show that the gas turbulence has a significant effect on the microscopic flow behaviour of the particulate phase. The k-equation of Crowe & Gillandt (1998) has the best performance in predicting the experimentally observed phenomena. Finally, the influence of the particles on the k-Ε model coefficients are studied and the turbulent motion is considered to be restricted by the particles, thereby reducing the turbulent length scale directly. The simulation results indicate that these coefficients should be modified in order to incorporate the effect of particles.