Nonequilibrium Reynolds stress for the dispersed phase of solid particles in turbulent flows

Abstract

The nonequilibrium turbulent transport of dispersed-solid phase is investigated theoretically, and confirmed with simple numerical experiments. The nonequilibrium form of the particle Reynolds stress was obtained as a function of Stokes number, St(tau) (=tau(p)/tau), where tau(p) is the particle relaxation time and tau the characteristic time scale of particle-turbulence interaction. The nonequilibrium memory effect could be explicitly expressed as a damped residual contribution of initial particle Reynolds stress. Major interest is given to the region of tausimilar toO(tau(L)), where tau(L) is the integral time scale associated with the Lagrangian autocorrelation of fluctuating velocities of carrier turbulence. In two-dimensional (2D) simple shear flows with stationary homogeneous turbulence, explicit expressions for the equilibrium and nonequilibrium particle Reynolds stress were obtained, and their characteristics were analyzed extensively for a wide range of particle relaxation time and various conditions of mean shearing of the carrier phase. The reliability of theoretical predictions was tested through a comparison with results of stochastic simulation of particle motion. It was shown that the particle inertia and the mean shearing of the carrier phase seriously affect the relaxation time of particle Reynolds stress required to reach its equilibrium state in such a way that the relaxation time to equilibrium increases in proportional to the increase of tau(p) and this trend is augmented by increasing the mean shearing of the carrier phase. Finally, a nonequilibrium constitutive equation for the dispersed phase Reynolds stress was obtained in a form usable in the two-fluid Eulerian approach for two-phase turbulent flows. (C) 2002 American Institute of Physics.