Direct Numerical Simulation of Turbulent Heat Transfer Across a Mobile, Sheared Gas-Liquid Interface

The impact of interfacial dynamics on turbulent heat transfer at a deformable, sheared gas-liquid interface is studied using Direct Numerical Simulation (DNS). The flow system comprises a gas and a liquid phase flowing in opposite directions. The governing equations for the two fluids are alternately solved in separate domains and then coupled at the interface by imposing continuity of velocity and stress. The deformations of the interface fall in the range of capillary waves of waveslope ak=0.01 (wave amplitude a times wavenumber k), and very small phase speed-to-friction velocity ratio, $c/u*.$ The influence of low-to-moderate molecular Prandtl numbers $Pr$ on the transport in the immediate vicinity of the interface is examined for the gas phase, and results are compared to existing wall-bounded flow data. The shear-based Reynolds number $Re*$ is 171 and Prandtl numbers of 1, 5, and 10 were studied. The effects induced by changes in $Pr$ in both wall-bounded flow and over a gas-liquid interface were analyzed by comparing the relevant statistical flow properties, including the budgets for the temperature variance and the turbulent heat fluxes. Overall, $Pr$ was found to affect the results in very much the same way as in most of the available wall flow data. The intensity of the averaged normal heat flux at high Prandtl numbers is found to be slightly greater near the interface than at the wall. Similar to what is observed in wall flows, for $Pr=1$ the turbulent viscosity and diffusivity are found to asymptote with $z+3,$ where $z+$ is the distance to the interface, and with $z+n,$ where n>3 for $Pr=5$ and 10. This implies that the gas phase perceives deformable interfaces as impermeable walls for small amplitude waves with wavelengths much larger than the diffusive sublayers. Moreover, high-frequency fluctuating fields are shown to play a minor role in transferring heat across the interface, with a marked filtering effect of $Pr.$ A new scaling law for the normalized heat transfer coefficient, $K+$ has been derived with the help of the DNS data. This law, which could be used in the range of $Pr=1$ to 10 for similar flow conditions, suggests an approximate $Pr−3/5$ relationship, lying between the $Pr−1/2$ dependence for free surfaces and the $Pr−2/3$ law for immobile interfaces and much higher Prandtl numbers. A close inspection of the transfer rates reveals a strong and consistent relationship between $K+,$ the frequency of sweeps impacting the interface, the interfacial velocity streaks, and the interfacial shear stress.