Heat Transfer in drop laden turbulence

We study the heat transfer by large deformable drops transported in a turbulent channel flow. We use direct numerical simulation (DNS) of turbulence, combined with a Phase Field Method for the interface description, at fixed shear Reynolds and Weber numbers. In an effort to evaluate the influence of microscopic flow properties, like momentum/thermal diffusivity, on the macroscopic flow properties, like mean temperature or heat transfer rates, we consider four values of the Prandtl number: Pr = 1, 2, 4 and 8. Drops are initially warmer than the turbulent carrier fluid, and release heat at different rates, depending on the value of Pr, but also on their size and on their own dynamics (topology, breakage, drop-drop interaction). Computing the time behavior of the drops and carrier fluid average temperatures, we show that an increase of Pr slows down the heat transfer process. We explain our results by developing a simplified phenomenological model. In particular, we show that the time behavior of the drops average temperature is self similar, and perfectly collapses upon rescaling by t/Pr^2/3. Accordingly, the heat transfer coefficient H scales as H ∼ Pr^-2/3 (resp. Nu ∼ Pr^1/3) at the beginning of the simulation, and tends to H ∼ Pr^-1/2 (resp. Nu ∼ Pr^1/2) at later times. Finally, we focus on the temperature distribution inside the drops, and we observe that an increase of Pr reduces the mixing of temperature inside the drop and leads to an uneven spatial temperature distribution.