Abstract
By means of three-dimensional direct numerical simulations, we investigate the influence of the regular roughness of heated and cooled plates on the mean heat transport in a cylindrical Rayleigh–Benard convection cell of aspect ratio one. The roughness is introduced by a set of isothermal obstacles, which are attached to the plates and have a form of concentric rings of the same width. The considered Prandtl number $Pr$ equals 1, the Rayleigh number $Ra$ varies from $10^{6}$ to $10^{8}$ , the number of rings on each plate is 1, 2, 4, 8 or 10, the height of the rings is varied from 1.5 % to 49 % of the cylinder height and the gap between the rings is varied from 1.5 % to 18.8 % of the cell diameter. Totally, 135 different cases are analysed. Direct numerical simulations show that with small $Ra$ and wide roughness rings, a small reduction of the mean heat transport (the Nusselt number $Nu$ ) is possible, but, in most cases, the presence of the heated and cooled obstacles generally leads to an increase of $Nu$ , compared to the case of classical Rayleigh–Benard convection with smooth plates. When the rings are very tall and the gaps between them are sufficiently wide, the effective mean heat flux can be several times larger than in the smooth case. For a fixed geometry of the obstacles, the scaling exponent in the $Nu$ versus $Ra$ scaling first increases with growing $Ra$ up to approximately 0.5, but then smoothly decreases back towards the exponent in the no-obstacle case.
Highlights
A process of turbulent thermal convection, which occurs widely in nature, is usually studied in a Rayleigh–Bénard configuration, where a fluid layer is confined between two isothermal horizontal surfaces, a lower warmer one and an upper colder one
Roughness of the heated and cooled plates or the presence of heated and cooled obstacles, which are attached to the corresponding plates, can influence significantly the mean heat and momentum transport in the system, which are represented by the Nusselt number Nu and Reynolds number Re, respectively
Direct numerical simulations of thermal convection in a cylinder of aspect ratio 1, with rough heated and cooled plates or with the ring-shaped obstacles that are attached at the plates, as described in the previous section, have been conducted for 135 different configurations of the ring-shaped obstacles and different numbers of the obstacles, for Pr = 1 and Ra from 106 to 108
Summary
A process of turbulent thermal convection, which occurs widely in nature, is usually studied in a Rayleigh–Bénard configuration, where a fluid layer is confined between two isothermal horizontal surfaces, a lower warmer one and an upper colder one. This was obtained in two-dimensional DNS by Shishkina & Wagner (2011), as well as in the two- and three-dimensional simulations by Zhang et al (2018) and large-eddy simulations by Foroozani et al (2019), for small-height roughness and relatively small Rayleigh numbers In this case the fluid stagnates in the gaps between the roughness elements and this leads in general to thicker thermal boundary layers and smaller overall heat transport in the system, compared to the case of smooth plates. The last section summarises the results and gives a brief outlook
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