Turbulent thermal convection over rough plates with varying roughness geometries

Abstract: We present a systematic investigation of the effects of roughness geometry on turbulent Rayleigh-B\'enard convection (RBC) over rough plates with pyramid-shaped and periodically distributed roughness elements. Using a parameter $\lambda$ defined as the height of a roughness element over its base width, the heat transport, the flow dynamics and local temperatures are measured for the Rayleigh number range $7.50\times 10^{7} \leq Ra\leq 1.31\times 10^{11}$, and the Prandtl number $Pr$ from 3.57 to 23.34 at four values of $\lambda$. It is found that the heat transport scaling, i.e. $Nu\sim Ra^{\alpha}$ where $Nu$ is the Nusselt number, may be classified into three regimes. In Regime I, the system is in a dynamically smooth state. The heat transport scaling is the same as that in a smooth cell. In Regimes II and III, the heat transport enhances. When $\lambda$ is increased from 0.5 to 4.0, $\alpha$ increases from 0.36 to 0.59 in Regime II, and it increases from 0.30 to 0.50 in Regime III. The experiment demonstrates the heat transport scaling in turbulent RBC can be manipulated using $\lambda$. Previous studies suggest that the transition from Regime I to Regime II, occurs when the thermal boundary layer (BL) thickness becomes smaller than the roughness height $h$. Direct measurements of the viscous BL in the present study suggest that the transition from Regime II to Regime III is likely a result of the viscous BL thickness becoming smaller $h$. The scaling exponent of the Reynolds number $Re$ vs. $Ra$ changes from 0.471 to 0.551 when $\lambda$ is increased from 0.5 to 4.0. It is also found that increasing $\lambda$ increases the clustering of thermal plumes which effectively increases the plumes lifetime that are ultimately responsible for the enhanced heat transport.