Dispersion and temperature statistics of inertial particles in isotropic turbulence

The dispersion and temperature distribution of inertial particles are important in many turbulent, multiphase flow problems. In order to understand these better, direct numerical simulations (DNSs) are performed for inertial particles in a fluid with a constant temperature gradient and whose motion is either statistically stationary or decaying, isotropic turbulence. It is found that, for long times, the dispersion of inertial particles is the greatest when the Stokes number, Stη=τp/τη, is of order 1, where τp and τη are, respectively, the particle response time and the flow Kolmogorov time scale. A similar result is found for the long time behavior of the time rate of change of the mean-square particle temperature fluctuations, d⟨Tp′2⟩/dt. To understand the DNS results better, an evolution equation for ⟨Tp′2⟩, along with the short and long time limits, is derived analytically from the thermal energy equation for inertial particles.