1Department of Modern Mechanics, University of Science and Technology of China, Hefei 230027 2Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072
Abstract：Thermal convection in a three-dimensional tilted rectangular cell with aspect ratio 0.5 is studied using direct numerical simulations within both Oberbeck–Boussinesq (OB) approximation and strong non-Oberbeck–Boussinesq (NOB) effects. The considered Rayleigh numbers $Ra$ range from $10^5$ to $10^7$, the working fluid is air at 300 K, and the corresponding Prandtl number $Pr$ is 0.71. Within the OB approximation, it is found that there exist multiple states for $Ra=10^5$ and hysteresis for $Ra=10^6$. For a relatively small tilt angle $\beta$, the large-scale circulation can either orient along one of the vertical diagonal planes (denoted by $M_{\rm d}$ mode) or orient parallel to the front wall (denoted by $M_{\rm p}$ mode). Which of the two modes transports heat more efficiently is not definitive, and it depends on the Rayleigh number $Ra$. For $Ra=10^7$ and $\beta=0^\circ$, the time-averaged flow field contains four rolls in the upper half and lower half of the cell, respectively, $M_{\rm d}$ and $M_{\rm p}$ modes only developing in tilted cells. By investigating NOB effects in tilted convection for fixed $Ra=10^6$, it is found that the NOB effects on the Nusselt number $Nu$, the Reynolds number $Re$ and the central temperature $T_{\rm c}$ for different $\beta$ ranges are different. NOB effects can either increase or decrease $Nu$, $Re$ and $T_{\rm c}$ when $\beta$ is varied.
2017, Vol. 34 
