Numerical simulation of grid-generated turbulent particulate flow by three-dimensional Reynolds stress

Abstract

A three-dimensional (3D) Reynolds stress turbulence model based on 3D Reynolds-averaged Navier-Stokes equations has been elaborated for grid-generated turbulence in particulate downward flow arranged in the channel domain of the square cross section. The model presented considers both the enhancement and attenuation of turbulence by means of the additional terms of the transport equations of the normal Reynolds stress components. It allows us to carry out calculations covering the long distance of the channel length without using algebraic assumptions for various components of the Reynolds stress. The results obtained show the effects of particles and mesh size of the turbulence generating grids on turbulence modification. In particular, the presence of solid particles at the initial period of turbulence decay results in the pronounced enhancement of turbulence that diminishes appreciably downwards in the area of typical channel turbulent flow. As the results show, the character of modification of all three normal components of the Reynolds stress taking place at the initial period of turbulence decay are uniform almost all over the channel cross sections. The increase in the grid mesh size slows down the rate of the turbulence enhancement which is caused by particles.There are different approaches and numerical models that describe the mutual effect of gas turbulence and particles. The k ε − models, earlier elaborated for turbulent particulate flows, e.g., Elghobashi and Abou-Arab (1983), Pourahmadi and Humphrey (1983), Rizk and Elghobashi (1989), Simonin (1990), Deutsch and Simonin (1991), considered turbulence attenuation only by the additional terms of the equations of the turbulence kinetic energy and its dissipation rate. The results obtained by these models were validated by the experimental data on turbulent particulate free-surface flows (Shraiber et al., 1990).The models by Crowe and Gillandt (1998) and Crowe (2000) considered both the turbulence augmentation and attenuation in pipe particulate flows depending on the flow mass loading and the Stokes number. Later on these models have been expanded for free-surface flows. As opposed to the k ε

Eulerian–Eulerian RSTM-PDF Modeling of Turbulent Particulate Flow

“…The 16 mm mesh size was used to generate the mesh generated turbulence flow. As can be seen in Figure 2, the experimental data and numerical results are in good agreement [21].…”

“…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:…”

“…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.…”