Abstract: Direct numerical simulations have been performed for turbulent heat transfer in thermal convection and shear flow between parallel permeable walls, on which the transpiration velocity is assumed to be proportional to the local pressure fluctuations (Jimenez et al. 2001 J. Fluid Mech. 442, 89-117). Turbulent heat transfer has been found to be substantially enhanced by the appearance of large-scale turbulence structures (large-scale thermal plumes in convection or large-scale spanwise rolls in shear flow) arising from the wall permeability. At high Rayleigh numbers or high Reynolds numbers we have achieved the ultimate heat transfer represented by a wall heat flux being independent of thermal conductivity, although the heat transfer on the wall is dominated by thermal conduction. The key to the achievement of the ultimate heat transfer is interpreted in terms of significant heat transfer enhancement by large-scale intense turbulence with the length scale of the order of the wall distance and with the velocity scale comparable to the buoyancy-induced terminal velocity in convection or the bulk-mean velocity in shear flow without flow separation from the permeable walls.
Reference: K. Kawano, S. Motoki, M. Shimizu & G. Kawahara 2021 J. Fluid Mech. 914, A13