Particle laden turbulent flows find applications in many industrial processes such as energy conversion, air pollution control, pneumatic conveying of solids, fluidized bed reactors etc. In these types of flows, there are strong coupling between the turbulent fluctuations in the fluid velocity fields, and the fluctuating velocities of the particles. It was also found that even at a very low solid volume fraction particle-particle and particle-wall interactions play important role in determining the dynamics of dispersed phase (Goswami and Kumaran, 2011). It is diffucult to directly scale-up the dynamic properties obtained from the small geometry to the scale of industrial importance. Therefore modeling such flows are inevitable besides the predictions through direct numerical simulation (DNS), which can only be used for small system size.
A fluctuating-force model has been developed (Goswami and Kumaran, 2011) to predict the effect of the turbulent fluid velocity fluctuations on the particle phase in a turbulent gas-solid suspension in the limit of high Stokes number. In the model, turbulent velocity fluctuation is considered to be an anisotropic Gaussian white noise. The noise amplitude is determined from the time correlations of the spatially varying inhomogeneous fluid velocity fluctuations computed using Direct Numerical Simulations (DNS). From the direct numerical simulation (DNS), we obtain the velocity space diffusion coefficient for the turbulent phase. This velocity space diffusion coefficient is embedded in the particle equation of motion to simulate the dynamical behaviour of the particle phase. In the present work particle-particle and particle-wall collision have been considered to be inelastic. Surface roughness of the particles and walls also have been included in the collision model. Using such a model particle concetration distribution accross the channel has been predicted. The distibutions and the moments of the linear and angular velocities have been investigated and compared with the DNS results.
P. S. Goswami and V. Kumaran, J. Fluid Mech. 687, 1 (2011).