Heat transfer and plume statistics in turbulent thermal convection with sparse fractal roughness

Abstract

Rough-surface Rayleigh-Bénard convection is investigated using direct numerical simulations in two-dimensional convection cells with aspect ratio Γ=2. Three types of fractal roughness elements, which are marked as n1, n2 and n3, are constructed based on the Koch curve and sparsely mounted on both the plates, where n denotes the level of the roughness. The considered Rayleigh numbers Ra range from 10⁷ to 10¹¹ with Prandtl number Pr =1. Two regimes are identified for cases n1, n2. In Regime I, the scaling exponents β in the effective Nusselt number Nu vs Ra scaling Nu ∼ Ra^β reach up to about 0.4. However, when Ra is larger than a critical value Ra_c, the flow enters Regime II, with β saturating back to a value close to the smooth-wall case (0.3). Ra_c is found to increase with increasing n, and for case n3, only Regime I is identified in the studied Ra range. The extension of Regime I in case n3 is due to the fact that at high Ra, the smallest roughness elements can play a role to disrupt the thermal boundary layers. The thermal dissipation rate is studied and it is found that the increased β in Regime I is related with enhanced thermal dissipation rate in the bulk. An interesting finding is that no clear convection roll structures can be identified for the rough cases, which is different from the smooth case where well-organized convection rolls can be found. This difference is further quantified by the detailed analysis of the plume statistics, and it is found that the horizontal profiles of plume density and velocity are relatively flattened due to the absence of clear convection rolls.