SCALING PROPERTIES OF VELOCITY STATISTICS OF HEAVY PARTICLES IN TURBULENCE

Droplets, aerosol and other impurities in turbulent flows are typical examples of finite-size particles with a mass density much larger than the carrier fluid, that can not be modeled as point tracers. The knowledge of the statistics of velocity differences between pairs of heavy inertial particles sus- pended in an incompressible turbulent flow is relevant both in the dissipative and in the inertial range of scales. As for the former, it rules the efficiency of collisions between heavy particles in turbulence. While in the latter case, it is important for the statistics of relative dispersion of pairs of particles. We present results obtained from high-resolution direct numerical simulations of incompressible, homogeneous and isotropic turbulence, up to a Taylor scale based Reynolds number Re? ? 400 (with 20483 grid points) and with millions of heavy particles with different inertia [1]. In our set-up, particles assumed to be spherical and rigid, simply move by viscous forces, such as the Stokes drag. The velocity statistics is found to be extremely intermittent. At very small scales, when particles are separated by distances within the dissipative subrange, we found that the competition between regions with quiet regular velocity distributions and regions where very close particles have very different velocities leads to a quasi bi-fractal behaviour of the particle velocity structure functions (moments of particles velocity differences). This points to the existence of quasi-singularities in the statistics of heavy particles velocity. In the limit of small inertia, the particle dynamics approaches that of tracers and consequently the velocity difference over a scale R is essentially coincident with the fluid longitudinal increment over a separation r = R. Conversely, when the inertia becomes very large, particles move ballistically in the flow with uncorrelated velocities and the momnets of velocity differences become independent of the scale R. For intermediate values of the Stokes number, one observes a non-trivial behavior as a function of the scale and of the Stokes number St = ?/??. Here, ? is the particle response time to the fluid, and ?? is the Kolmogorov time scale of the flow. For particles separated by inertial-range distances, we show that the velocity-difference statistics can be characterized in terms of a local roughness exponent, which is a function of the scale-dependent particle Stokes number only, defined as St(r) = ??1/3/r2/3 in terms of the local eddy turnover time.