Direct numerical simulation of spatially developing turbulent boundary layer for skin friction drag reduction by wall surface-heating or cooling

Abstract

Direct numerical simulation (DNS) of zero-pressure-gradient spatially developing turbulent boundary layer with uniform heating (UH) or cooling (UC) is performed aiming at skin friction drag reduction. The Reynolds number based on the free-stream velocity, U ∞, the 99% boundary layer thickness at the inlet, δ0, and the kinematic viscosity, ν, is set to be 3000 and the Prandtl number is 0.71. The computational domain is set to be 9πδ0×3δ0×πδ0 in the streamwise, wall-normal, and spanwise directions, respectively. A constant temperature is imposed on the wall. The Richardson number Ri for the buoyancy is varied in the range of −0.1⩽Ri⩽0.1. The DNS results show that UC reduces skin friction drag with a maximum drag reduction rate of 65%, while UH enhances it. The trend is similar to that in channel flow studied by Iida and Kasagi in 1997 and Iida et al.in 2002 and that in spatially developing boundary layer flow by Hattori et al. in 2007. Dynamical decomposition of skin friction drag using the identity equation (FIK identity, discussed by Fukagata et al.in 2002) quantitatively shows that drag reduction by UC is due to reduced Reynolds shear stress (RSS), while drag increase by UH is augmentation of RSS. The control efficiency of UC, however, is found to be largely negative; namely, net power saving is not achieved.