Influence of spatial arrangements of roughness elements on turbulent Rayleigh-Bénard convection

Abstract

Turbulent Rayleigh-Bénard convection in a square cavity with rough horizontal walls is investigated at a fixed Prandtl number Pr = 0.7 over the Rayleigh number range of 106 ≤ Ra ≤ 109. We have proposed five models with rough elements of the same height but different spatial distributions to evaluate their influences on the heat transport and flow structures of the system. It is found that the flow reversal can be promoted at a Rayleigh number around 107. In all the rough models, the heat transfer is impeded at a low Ra and enhanced at a Rayleigh number beyond a critical value. Interestingly, the heat transfer and flow structure can be clustered by the sparsity of the rough element distribution. Different scaling exponents for heat transfer are identified for sparsely distributed rough models and compactly distributed models. On the other hand, the spatial distribution of rough elements has little effect on the scaling of the Reynolds number.