Direct numerical simulation of particle-laden turbulent channel flows with two- and four-way coupling effects: budgets of Reynolds stress and streamwise enstrophy

The budgets of the Reynolds stress and streamwise enstrophy are evaluated through direct numerical simulations for the turbulent particle-laden flow in a vertical channel with momentum exchange between the two phases. The influence of the dispersed particles on the budgets is examined through a comparison of the particle-free and the particle-laden cases at the same Reynolds number of Re-b = 5600 based on the bulk fluid velocity and the distance between the channel walls. Results are obtained for particle ensembles with four response times in simulations with and without streamwise gravity and inter-particle collisions at average mass (volume) fractions of 0.2 (2.7. x. 10(-5)) and 0.5 (6.8. x. 10(-5)). The particle feedback force on the flow of the carrier phase is modeled by a point-force approximation (PSIC-method). It is shown that all the terms in the budgets of the Reynolds stress components are decreased in the presence of particles. The level of reduction depends on the particle response time and it is higher under the effects of gravity and inter-particle collisions. A considerable reduction in all the terms of the streamwise enstrophy budget is also observed. In particular, all production mechanisms, and mainly vortex stretching, are inhibited in the particulate flows and thus the production of streamwise vorticity is significantly damped. A further insight into the direct particle effects on the fluid turbulence is provided by analyzing in detail the fluid-fluid, fluid-particle and particle-particle correlations, and the spectra of the fluid-particle energy exchange rate. The present results indicate that the turbulence production, dissipation and pressure-strain term are generally large quantities, but their summation is relatively small and comparable to the fluid-particle direct energy exchange rate. Consequently, the particle contribution can potentially increase or decrease the fluctuating fluid velocities and eventually control the direction of fluid turbulence modification.