Viscosity influence on heat transfer in drop-laden turbulence

This work numerically investigates the effect of viscosity differences on the heat transfer in a drop-laden turbulent channel flow, where warm drops are dispersed in a cold carrier fluid. This problem is studied by coupling direct numerical simulation (DNS) of turbulence with a phase field method (PFM) for the interface description. We consider warm water drops in cold oil and warm oil drops in cold water. The oil viscosity is four times larger than the water viscosity, while density and thermal diffusivity are equal in the two fluids. Thus, in the first case we set a viscosity ratio (drops over carrier viscosity) of μ_r=1/4 and a Prandtl number (momentum over thermal diffusivity) of Pr=4 in the water carrier phase, which determines a local Prandtl of Pr=16 in the oil drops. Similarly, in the second case we set μ_r=4 and Pr=16 in the oil carrier phase, giving Pr=4 in the water drops. To maintain a constant Péclet number in the systems, a shear Reynolds of Re_τ=600 and Re_τ=150 are imposed in the water and oil carrier phases, respectively. It is observed that the average temperature of each fluid shows an almost coincident evolution in time in the two cases. Since the thermal diffusivity is constant, this result can be attributed to the impact of viscosity on the convective heat transport. Indeed, in the more viscous oil phase the heat transfer is slowed down, while in the less viscous water phase the heat transfer is accelerated. These effects balance each other in the two cases, which therefore result in having an equal heat transfer rate.