Thermal convection in a tilted rectangular box

Abstract

Thermal convection in a tilted three-dimensional rectangular box has been systematically investigated by direct numerical simulation. The Rayleigh number Ra varies from 107 to 109, the Prandtl number Pr is set to 0.7, and the tilted angle β ranges from 0° to 90°. The effects of tilting on large-scale circulation (LSC), Nusselt number (Nu), Reynolds number (Re), and boundary layers (BLs) and the Ra-dependency are investigated. For large β exceeding certain values, say 45°, the stable temperature stratification forms in the bulk, resulting in low Re and Nu. It is found that the tilting leads to a distinct trend for Nu and Re: Nu first increases to some extent for small β, then nearly stays unchanged for moderate β, and finally decreases for large β, while Re initially increases for small β and then directly declines with increasing β. Based on the analysis of flow structures, with increasing β, it is found that the volume of the high-velocity tube (HVT) initially increases for 107 ≤ Ra ≤ 108 but decreases for Ra = 109, which is responsible for the variation in Nu at small β. The probability density functions of instantaneous convective heat transport within the HVT show higher probabilities for large values when β increases, implying that LSC tends to be more coherent and causing different tilting behaviors between Nu and Re. Finally, we find that, except for β = 90°, the normalized profiles of viscous and thermal BLs tend to have universal profiles, deviating from the BL of the Prandtl–Blasius–Pohlhausen (PBP) type to some extent regardless of β. Only the thermal BL for β = 90° is found to be in good agreement with the classic PBP laminar BL profile.