- Author
- Margolin, L. G.
- Title
- Turbulent Diffusion of Small Particles.
- Coporate
- California Univ., Los Alamos
- Report
- UC-34; LA-7040-T, November 1977, 150 p.
- Keywords
- diffusion | particles
- Abstract
- The diffusion of small, spherical, rigid particles suspended in an incompressible turbulent fluid, but not interacting with each other, is studied. As a stochastic process, the turbulent fluid velocity field is assumed to be homogeneous, isotropic and stationary. The assumptions on the particle force lawa, as is usual in this kind of study, are fairly restrictive. Most of our discussion assumes the stokes regime; and we begin with a particle equation of motion which includes only the effects of Stokes drag and a virtual mass force. for this simple force law we find an exact solution for the particle velocity correlation function, for all times and initial conditions, in terms of a fluid velocity correlation function measured along the motion of the particle. We show that for times larger than a certain time scale, the particle velocity correlation becomes stationary, and agrees with that found by Liu, who used a different method and assumed a stationary particle velocity correlation that the outset. This means that if, as in the model of Tchen, the particle remains in the same neighborhood of fluid for times less than oron the order of the Lagrangian integral scale, so that the intergrals over time of the Lagrangian correlation and correlation of fluid velocities along the motion of the particle coincide, then the long time particle diffusivity in this model is the same as the passive scalar diffusivity. Next, we include Basset and gravitational buoyancy forces on the particle, still in the Stokes regime. We are still able to solve for the exact particle velocity correlation in terms of the correlation of fluid velocities along the motion of the particle, for all times and initial conditions. Under the same conditions as above, the long time particle diffusivity remains the same as the passive scalar fluid diffusivity. Then, we consider the effect of small shears in the fluid velocity, under the additional restrictions of a certain high frequency regime for the turbulence, and that the shears convect past the particle much faster than the growth of the boundary layer. New force terms due to the presence of such shears are calculated and incorporated into the equation of motion. a perturbation solution to this equation is constructed, and the resultant particle velocity correlation function and diffusion coefficient are calculated. To lowest order, the particle diffusivity is found to be unaltered by the presence of small mean flow shears. The last model we treat is one in which particles traverse a turbulent fluid with a large mean velocity. Among other restrictions, we assume linearized form drag. We calculate the diffusion coefficient for such particles and find it to be much smaller than the passive scalar diffusion coefficient, and we find agreement within five percent with the experimental results of Snyder and Lumley.