Spanwise wall forcing can reduce turbulent heat transfer more than drag

Abstract

Direct numerical simulations are performed of turbulent forced convection in a half channel flow with wall oscillating either as a spanwise plane oscillation or to generate a streamwise travelling wave. The friction Reynolds number is fixed at $Re_{\tau_0} = 590$, but the Prandtl number $Pr$ is varied from 0.71 to 20. For $Pr>1$, the heat transfer is reduced by more than the drag, 40\% compared to 30\% at $Pr=7.5$. This outcome is related to the different responses of the velocity and thermal fields to the Stokes layer. It is shown that the Stokes layer near the wall attenuates the large-scale energy of the turbulent heat-flux and the turbulent shear-stress, but amplifies their small-scale energy. At higher Prandtl numbers, the thinning of the conductive sublayer means that the energetic scales of the turbulent heat-flux move closer to the wall, where they are exposed to a stronger Stokes layer production, increasing the contribution of the small-scale energy amplification. A predictive model is derived for the Reynolds and Prandtl number dependence of the heat-transfer reduction based on the scaling of the thermal statistics. The model agrees well with the computations for Prandtl numbers up to 20.