Analysis of the temperature fluctuations in particle-laden isotropic turbulence in the two-way coupling regime.

We perform direct numerical simulation of incompressible, statistically steady and isotropic turbulent flows laden with point-like particles. The fluid temperature is two-way coupled with the particle temperature and the effect of the particle inertia on the temperature statistics is investigated. Balances of the dissipation of the temperature fluctuations are derived and the amplitude of the temperature fluctuations is predicted by exploiting the Obukhov-Corrsin relation. The results show that the particles affect the temperature fluctuation and dissipation in different, non trivial ways, depending on the particle mass and heat capacity. The effect of the inertial particles on the distribution of the temperature fluctuations across the scales of the flow is characterized by means of two-particle and two-point statistics. While the fluid temperature distribution scales in a self-similar way in a wide range of particle inertia, the particle temperature statistics show a marked multifractal behavior due to the particle non-local dynamics. The interaction between the particle non-local dynamics and the ramp-cliff structure of the fluid temperature field is characterized by computing the heat flux due to the particle motion across the fluid temperature fronts.