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-Bénard convection (RBC) over rough plates with pyramid-shaped and periodically distributed roughness elements. Using a parameter λ 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 7.50×10 7 Ra 1.31×10 11 , and the Prandtl number P r from 3.57 to 23.34 at four values of λ (0.5, 1.0, 1.9, and 4.0). It is found that the heat transport scaling, i.e. N u ∼ Ra α where N u is the Nusselt number, may be classified into three regimes in turbulent RBC over rough plates. 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 λ is increased from 0.5 to 4.0, α increases from 0.36 to 0.59 in Regime II, and it increases from 0.30 to 0.50 in Regime III. The experiment thus clearly demonstrates that the heat transport scaling in turbulent RBC can be manipulated using λ in the heat transport enhanced regime. Previous studies suggest that the transition to heat transport enhanced regime, i.e. from Regime I to Regime II, occurs when the thermal boundary layer (BL) thickness becomes smaller than the roughness height. 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 than the roughness height. The scaling exponent of the Reynolds number Re with respect to Ra changes from 0.471 to 0.551 when λ is increased from 0.5 to 4.0, suggesting a change of the dynamics of the large-scale circulation. Interestingly, the transition from Regime II to Regime III in terms of the heat transport scaling is not reflected in the Re-scaling with Ra. It is also found that increasing λ increases the clustering of thermal plumes which effectively increases the plumes lifetime. This leads to a great increase in the probability of observing large temperature fluctuations in the bulk flow, which corresponds to the formation of more coherent plumes or plume clusters that are ultimately responsible for the enhanced heat transport.

Thermal transfer in Rayleigh–Bénard cell with smooth or rough boundaries

“…It may be related to other published works which have reported an increase of the prefactor C caused by enhanced plume emissions, rather than an increase of the exponent a due to a change in the structure of the boundary layer. It seems consistent, in particular, to the recent results of Xie & Xia (2017) in their symmetric rough cell where both plates have pyramid-shaped roughness elements.…”

“…Like Xie & Xia (2017), three regimes can be consistently exhibited: (i) below Ra c , N u r /f GL (Ra r ) are horizontal lines, meaning that the behavior is similar to a smooth plate, and consistent with the GL model within ±20 %. (ii) a regime of increased scaling exponent occurs beyond Ra c , fairly compatible with a = 1/2, and more precisely with Eq.…”

“…Recent experiments from Xie & Xia (2017) also evidence this role of roughness geometry. They have varied the roughness aspect ratio, λ, defined as the height of a single roughness element over its base, and found that the asymptotic scaling law exponents increases with λ.…”

“…That could be caused by the effect of the Prandtl number which is not taken into account in this description. Recent experiments of Xie & Xia (2017) also suggest that the heat transfer efficiency in the case of rough boundaries gets larger when the Prandtl number is increased. They evidence such increase only for larger Prandtl numbers than we do, but the geometry of the cells and roughness significantly differ.…”

Heat transfer in rough-wall turbulent thermal convection in the ultimate regime

“…To trigger the onset of the ultimate regime, i.e. the transition from a laminar-type BL to a turbulent one, various wall-roughness elements have been employed, both in experiments [26][27][28][29][30][31][32][33][34][35] and in numerical simulations [36][37][38][39]. In general, these efforts have led to an enhanced N u versus Ra scaling in some intermediate Ra regime, and in limited Ra regimes even an effective N u versus Ra scaling exponent of 1/2 can be achieved.…”