AbstractsEngineering

Particle laden turbulent flows find applications in many industrial processes such as energy conversion, air pollution control 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. In order to analyze the stresses and the heat and mass transfer properties in turbulent suspensions, it is necessary to have a good understanding of not just the mean flow of the gas and particles, but also of the fluctuations in the two phases. The coupling is a two-way coupling; the fluid turbulence contributes to the velocity fluctuations in the particles, and conversely, the particle velocity fluctuations generate fluctuations in the fluid. Two-phase flow models capture these interactions only in an indirect way, usually through a ‘particle pressure’ term for the particle phase. In the present work the effect of fluid velocity fluctuations on the dynamics of the particles in a turbulent gas-solid suspension is analyzed in the low Reynolds number and high Stokes number limit, where the particle relaxation time is long compared to the correlation time for the fluid velocity fluctuations. The direct numerical simulation (DNS) is used for solving the Navier-Stokes equations for the fluid, the particles are modeled as hard spheres which undergo elastic collisions. A one-way coupling algorithm is used where the force exerted by the fluid on the particles is incorporated, but not the reverse force exerted by the particles on the fluid. This is because the main focus of our study is to examine the effect of the fluid turbulence on the particle fluctuations, and we are interested in examining whether a Langevin model with random forcing can accurately capture the effect of fluid turbulence on the particle phase. First, the turbulent flow in a plane Couette is analyzed. Though this is a model flow which is not encountered often in applications, it is easier to analyze because the turbulent velocity fluctuations are maximum at the center of the channel, in contrast to the Poiseuille flow, where the velocity fluctuations are maximum at a location between the center and the wall. Also, in a Couette flow, the wall-normal and the spanwise root mean square velocities are nearly a constant in the central region in the channel, and the percentage variation in the stream-wise velocity fluctuations is also less than that in a pressure driven Poiseuille flow. Therefore, it is possible to treat the central region as a region with homogeneous, but anisotropic, fluid velocity fluctuations and with a linear mean velocity variation. The particle mean and root mean square fluctuating velocities, as well as the probability distribution function for the fluid velocity fluctuations and the distribution of acceleration of the particles in the central region of the Couette, which comprises about 20% of the entire channel have been studied. It is found that the distribution of particle velocities is very different from a Gaussian, especially in the…