On the role of roughness valleys in turbulent Rayleigh-Bénard convection

Three-dimensional direct numerical simulations are used to characterize turbulent buoy-ant convection in a box-shaped Rayleigh Bénard cavity with a rough bottom plate madeof a series of square based blocks separated by valleys. The cavity is filled with water, andthe Rayleigh number varies over five decades up to 10 10 . As mentioned in the literature,three successive heat transfer regimes are identified: from inactive roughness (I) to aregime (III) where the heat transfer increase is larger than the one expected from theonly roughness induced surface increase. The heat transfers of the transitional regime IIare particularly intense. After validation against experimental and numerical data fromliterature, we highlight the role of the inner fluid trapped within valleys. It is shown thatthe heat transfer through the fluid interface between the cavity bulk and the inner fluidis strongly related to the overall heat transfer at the rough plate, with an exponent ofthe heat transfer scaling law close to 1/2 in the regime II. We found that this regimeis active when the thermal boundary layer is thinner than the roughness height and, atthe same time, the kinetic boundary layer is larger. As compared to regimes I and III,regime II is characterized by larger temperature fluctuations, especially near the roughplate, and a larger friction coefficient. A fluctuating rough layer overlaying both blocksand valleys appears in the regime III, in addition to the classical boundary layers formedalong the plate topography.