Les of Gas-particle Turbulent Channel Flow (the Effect of Inter-particle Collision on Structure of Particle Distribution)

Particle dispersion in a fully-developed turbulent flow was studied. Numerical simulations with two-way coupling were performed for downward particle-laden turbulent flows in a vertical channel. Fluid turbulence was calculated by using LES, while the particle motion was treated by Lagrangean approach. In addition, inter-particle collision was taken into consideration. In this work, we focused our attention on the spatial structure of turbulence and particle distribution in the near-wall and the channel center regions. Furthermore, the effect of inter-particle collision on the spatial structure of particle distribution was discussed. It was found that the inter-particle collision affects the particle concentration distribution in the range of the present condition. The spatial structure and scale of clusters obtained by numerical simulation with inter-particle collision agree well with those of the experiments by Fessler et al. (1994) Introduction Interactions between particles and fluid turbulence, which are the turbulence modification in fluid flows and the effect of fluid turbulence on the particle motion, have been physically interesting phenomena in gasparticle flows. In this two decades the turbulence modification has been attracting many researchers attentions, and many studies have been conducted. There are some papers which intend to correlate the experimental data (for example, Gore & Crowe 1989), however the physics of the turbulence modification has not been clarified sufficiently. In these days, some numerical simulations of two-phase turbulent flow have been performed by using the direct simulation techniques of turbulent flow (Squires & Eaton 1990, Elghobashi & Truesdell 1992). Regarding turbulent channel flows, Rouson & Eaton (1994) performed DNS and Wang & Squires (1996) performed LES. Both group showed that heavy particles tend to disperse uniformly and light particles form clusters. The authors have performed LES of particle-laden turbulent channel flow (Tanaka et al. 1997) in the same conditions as the experiments by Kulick et al. (1993). We have compared the numerical results with their experimental ones and pointed out the effect of interparticle collision is very large especially on the statistical properties of particle motion. In this paper, the instantaneous spatial structures of particle distribution and gas turbulence are studied. The correlation between them and the effect of inter-particle collision on the structure are discussed. Also, particle distribution obtained by numerical simulations are compared with the experiment by Fessler et al. (1994). Numerical simulation Particle motion The algorithm of inter-particle collision is a key point in this work, because it greatly affects the computation time. We followed the technique of uncoupling developed by Bird (1976). By using this technique, the calculation of particle motion is split up into two stages. In the first stage, all particles are moved based on equation of motion free from particleparticle interaction. In the second stage, particle-wall and inter-particle collision are calculated. The occurrence of inter-particle collision during the first stage is examined for all particles. If a particle collides with another particle, then the velocities of collision pair are replaced by post-collision ones without changing their position. This technique of uncoupling requires that the time step in calculation must be much smaller than the mean free time, which is discussed later. Particle Motion without Col l i s ion The particle motion for a small rigid sphere in a turbulent flow field is described by a complicated integrodifferential equation (Maxey & Riley, 1983). However, if the density of the particle is substantially larger than the density of the carrier fluid, the equation of particle motion can be simplified. The equation of translational motion used in the simulations is given by,