Effect of Reynolds Number on Isotropic Turbulent Dispersion

Abstract

The influence of the spatio-temporal structure of isotropic turbulence on the dispersion of fluid and particles with inertia is investigated. The spatial structure is represented by an extended von Kármán energy spectrum model which includes an inertial sub-range and allows evaluation of the effect of the turbulence Reynolds number, Reλ . Dispersion of fluid is analyzed using four different models for the Eulerian temporal auto-correlation function D(τ). The fluid diffusivity, normalized by the integral length scale L11 and the root-mean-square turbulent velocity u0 , depends on Reλ . The parameter cE = T0 u0 /L11 , in which T0 is the Eulerian integral time scale, has commonly been assumed to be constant. It is shown that cE strongly affects the value of the fluid diffusivity. The dispersion of a particle with finite inertia and finite settling velocity is analyzed for a large range of a particle inertia and settling velocity. Particle turbulence intensity and diffusivity are influenced strongly by turbulence structure.