Large-scale structures of turbulent Rayleigh–Bénard convection in a slim-box

Abstract

We report a numerical study of the large-scale structure of turbulent Rayleigh–Bénard convection (RBC) in a slim-box using direct numerical simulations. The simulations are performed in a rectangular cell of 1/6 depth-to-width ratio with the Rayleigh number from Ra=1×107 to 5×109 and Prandtl number equal to 0.7. It turns out that the large-scale circulation is driven by the jet flows, which consist of thermal plume clusters emitted from the conducting plate. The oblique impinging jet presents similar behavior for Ra. Moreover, the Reynolds number defined by the jet speed is approximated as a power law Rem∼Ra0.50. The oblique jet impinges onto the horizontal plate and develops into a wall jet. The similar flow patterns over the plate indicate the coherent motion of the wall jet. The wall jet presents a three-layer structure including the viscous sublayer, the mixing layer, and the bulk. The velocity in each layer has its characteristic parameters. We analyzed the turbulent kinetic energy and dissipation and obtained the scaling laws of the horizontal and vertical velocity fluctuations and the heights of their peaks. The thermal boundary layer and the heat transfer on the plate are investigated. The self-similarity of the thermal boundary layer solution is verified by boundary layer theory. Further analysis reveals that the Nusselt number on the conducting plate is possessed by an exponential law of the horizontal location, Nux=Num exp (−x̃), where Num is the maximum Nusselt number on the plate and x̃ is the normalized horizontal distance to the stagnation point. We derived a power law of the maximum heat transfer on the plate by scaling analysis, Num∼Ra0.2925, in agreement with the simulations. All results indicate that both the oblique impinging jet and the wall jet characterize the near-wall flow and the global heat transfer of turbulent RBC at moderate Rayleigh numbers.