The ultimate state of turbulent permeable-channel flow

Abstract

Direct numerical simulations have been performed for heat and momentum transfer in internally heated turbulent shear flow with constant bulk mean velocity and temperature, and, between parallel, isothermal, no-slip and permeable walls. The wall-normal transpiration velocity on the walls is assumed to be proportional to the local pressure fluctuations, i.e. (Jiménez et al., J. Fluid Mech., vol. 442, 2001, pp. 89-117). The temperature is supposed to be a passive scalar, and the Prandtl number is set to unity. Turbulent heat and momentum transfer in permeable-channel flow for the dimensionless permeability parameter has been found to exhibit distinct states depending on the Reynolds number. At, the classical Blasius law of the friction coefficient and its similarity to the Stanton number, are observed, whereas at, the so-called ultimate scaling, and, is found. The ultimate state is attributed to the appearance of large-scale intense spanwise rolls with the length scale of arising from the Kelvin-Helmholtz type of shear-layer instability over the permeable walls. The large-scale rolls can induce large-amplitude velocity fluctuations of as in free shear layers, so that the Taylor dissipation law (or equivalently) holds. In spite of strong turbulence promotion there is no flow separation, and thus large-amplitude temperature fluctuations of can also be induced similarly. As a consequence, the ultimate heat transfer is achieved, i.e. a wall heat flux scales with (or equivalently) independent of thermal diffusivity, although the heat transfer on the walls is dominated by thermal conduction.