On the collision rate of small particles in isotropic turbulence. II. Finite inertia case

摘要

Numerical experiments have been performed to study the geometric collision rate of heavy particles with finite inertia. The turbulent flow was generated by direct numerical integration of the full Navier-Stokes equations. The collision kernel peaked at a particle response time between the Kolmogorov and the large-eddy turnover times, implying that both the large-scale and small-scale fluid motions contribute, although in very different manners, to the collision rate. Both numerical results for frozen turbulent fields and a stochastic theory show that the collision kernel approaches the kinetic theory of Abrahamson [Chem. Eng. Sci. 30, 1371 (1975)] only at very large tau(p)/T-e, where tau(p) is the particle response time and T-e is the flow integral time scale. Our results agree with those of Sundaram and Collins [J. Fluid Mech. 335, 75 (1997)] for an evolving flow. A rapid increase of the collision kernel with the particle response time was observed for small tau(p)/tau(k), where tau(k) is the flow Kolmogorov time scale. A small inertia of tau(p)/tau(k) = 0.5 can lead to an order of magnitude increase in the collision kernel relative to the zero-inertia particles. A scaling law for the collision kernel at small tau(p)/tau(k) was proposed and confirmed numerically by varying the particle size, inertial response time, and Bow Reynolds number. A leading-order theory for small tau(p)/tau(k) was developed, showing that the enhanced collision is mainly a result of the nonuniform particle concentration that results from the interaction of heavy particles with local flow microstructures. (C) 1998 American Institute of Physics. [References: 21]