Article: Capecelatro, J; Desjardins, O; Fox, RO; (2016) “Strongly Coupled Fluid-Particle Flows in Vertical Channels. II. Turbulence Modeling”, Physics of Fluids, 28 (3)
Abstract: In Part I, simulations of strongly coupled fluid-particle flow in a vertical channel were performed with the purpose of understanding, in general, the fundamental physics of wall-bounded multiphase turbulence and, in particular, the roles of the spatially correlated and uncorrelated components of the particle velocity. The exact Reynolds-averaged (RA) equations for high-mass-loading suspensions were presented, and the unclosed terms that are retained in the context of fully developed channel flow were evaluated in an Eulerian-Lagrangian (EL) framework. Here, data from the EL simulations are used to validate a multiphase Reynolds-stress model (RSM) that predicts the wall-normal distribution of the two-phase, one-point turbulence statistics up to second order. It is shown that the anisotropy of the Reynolds stresses both near the wall and far away is a crucial component for predicting the distribution of the RA particle-phase volume fraction. Moreover, the decomposition of the phase-average (PA) particle-phase fluctuating energy into the spatially correlated and uncorrelated components is necessary to account for the boundary conditions at the wall. When these factors are properly accounted for in the RSM, the agreement with the EL turbulence statistics is satisfactory at first order (e.g., PA velocities) but less so at second order (e.g., PA turbulent kinetic energy). Finally, an algebraic stress model for the PA particle-phase pressure tensor and the Reynolds stresses is derived from the RSM using the weak-equilibrium assumption. (C) 2016 AIP Publishing LLC.
Funding Acknowledgement: European Union [246556]; US National Science Foundation [CBET-1437865, CBET-1437903]
Funding Text: The research leading to the results reported in this work has received funding from the European Union Seventh Framework Programme (No. FP7/2007-2013) under Grant Agreement No. 246556, and from the US National Science Foundation under Grant Nos. CBET-1437865 and CBET-1437903.