Turbulent Rayleigh-Bénard Convection With Fractal-Multiscale Roughness

Rough-surface turbulent thermal convection exist widely in nature and in many industrial processes.Rough-surface Rayleigh-Benard(RB)convection is investigated using direct numerical simulations in two-dimensional convection cells with aspect ratio?=2.Three types of fractal-multiscale roughness elements,which are marked as nl,n2 and n3,are constructed based on the Koch curve and mounted on both the plates.Here,n denotes the level of the roughness.The main research content includes the following two parts:1.The effect of fractal-multiscale roughness on RB convection when Prandtl num-ber Pr=1 is studied.The considered Rayleigh number Ra range from 107 to 1011.Two regimes are identified for case n1 and case n2.In Regime I,the scaling exponents? in the effective Nusselt number(Nu)vs Ra scaling Nu?Ra? reach up to about 0.4.However,when Ra is larger than a critical value Rat,the flow enters Regime II,with? saturating back to a value close to the smooth-wall case(0.3).Rat 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 Reynolds number(Re)and Ra num-ber satisfy the relationship Re-Ra?.the scaling exponents ? is insensitive to wall roughness.In addition,it is found that the increased? 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.2.The effect of Pr number on rough RB convection is studied.The wall roughness is fixed to case n3,and the control parameters are within the range of 107?Ra?1010 and 0.1?Pr<60.At Ra=107 and Ra?3 × 107,the characteristics similar to zonal flow are found when the Pr is moderate,so that the fluid near the roughness elements and the bulk are fully mixed,resulting in a sharp increase in the Nu and Re.When Ra? × 107,the power-law scaling of Nu(Ra,Pr)and Re(Ra,Pr)are Nu-Ra0.417Pr0.083 and Re-Ra0.610 Pr0.835,respec-tively,indicating that increasing Pr can enhance heat transfer and weaken mo-mentum transport.In addition,As the Pr increases,the overall temperature and velocity fluctuations weaken,the thickness of the temperature boundary layer de-creases,the roughness elements become more effective,and the thickness of the velocity boundary layer increases.Besides,there is a strong correlation among the instantaneous temperature field,thermal and kinetic dissipation rates field.Thermal and kinetic dissipation are mainly concentrated near the roughness el-ements.The probability density function distribution of ?? is divided into three parts:bulk flow,plume area/mixed layer,and conductive sublayer.As the Pr number decreases,the thermal dissipation of the bulk and conductive sublayer gradually increases,which is not conducive to the generation of plumes.As the Pr increases,the intermittent nature of kinetic dissipation increases.