Two-Fluid RANS-RSTM-PDF Model for Turbulent Particulate Flows

Abstract

A novel three-dimensional (3D) model based on Reynolds turbulence stress model (RSTM) closure of equations of carrier and particulate phases was elaborated for channel turbulent flows. The essence of the model is the direct calculation of normal and shear components of the Reynolds stresses for the particulate phase similar to the carrier fluid. The model is based on the Eulerian approach, which is applied for the 3D RANS modeling of the carrier flow and the particulate phase and the statistical probability dense function (PDF) approach focusing on the mathematical description of the second moments of the particulate phase.The obtained numerical results have been verified and validated by comparison with experimental data obtained on turbulent dispersion of solid particles ejected from point source for turbulent uniform linear shear flow. Two cases of spatial orientation of shear of the flow mean velocity were examined: in the direction of gravity and in the direction perpendicular to gravity. Numerical data on turbulent dispersion of particles and spatial displacement of the maximum value of the concentration distribution show satisfactory agreement with experimental results.

Eulerian–Eulerian RSTM-PDF Modeling of Turbulent Particulate Flow

“…The numerical simulation results were validated with the experimental data coming from [20]. The testing facility was similar to the one reported by Philips et al [43] and allowed for observing the shear-particulate flow with flat plates with a variable pitch.…”

“…Three types of flow structures were examined: the conventional flow or typical channel flow, grid-generated turbulence flow, and shear flow directed towards the gravitation direction [20,21]. The plots present the following:…”

“…For comparison purposes, the plots have a shear flow along the y-direction. The numerical results were borrowed from [20]. The simulation model used a Cartesian coordinate system, where x is the streamwise coordinate, y is the transverse coordinate, and z is the bottom-normal (azimuthal) coordinate; u, v, and w are the associated velocity components, respectively.…”

“…The mesh is defined for each particle-velocity variation and all process mechanisms of particle-turbulence and particle-particle interactions. The transport equations are written in terms of various velocity correlations, which may consider either the fluid turbulence augmentation or attenuation caused by the presence of the particles [10,11,[20][21][22]. Zaichik [7] introduced a new PDF approach and they used Boussinesq approximation for the particulate motion equations and algebraic expressions for particle-phase turbulent viscosity and diffusion coefficients.…”