Flow organization and heat transfer in two-dimensional tilted convection with aspect ratio 0.5

Thermal convection in a two-dimensional tilted cell with aspect ratio (Gamma = width/height) 0.5 is studied using direct numerical simulations. The considered tilt angle beta ranges from 0 degrees to 90 degrees. The Prandtl number Pr dependence is first studied in the range of 0.01 <= Pr <= 100 for a fixed Rayleigh number Ra = 10(7). The Ra dependence is also investigated in the range of 10(6) <= Ra <= 10(9) for a fixed Pr = 0.71. Different flow states are identified over the beta-Pr parameter space. It is found that the flow tends to organize in stable vertically-stacked double-roll state (DRS) for small Pr and small beta, while this DRS becomes unstable and flow reversals happen with the increase of beta. This finding complements our previous study of flow reversals in tilted cells with Gamma = 1 and 2 [Wang et al., J. Fluid Mech. 849, 355-372 (2018)]. For relatively larger Pr, the flow gives way to a stable triple-roll state or an unstable triple-roll state for small beta. Moreover, multiple states in the turbulent regime are found for Ra >= 10(8), between which the flow can or cannot switch. In the latter case, the Nu are different for the two states with the same number of convection rolls, but different orientations. It is found that the Nu(beta)/Nu(0) and Re(beta)/Re(0) dependence is strongly influenced by a combination of Ra and Pr. In the present system, we interestingly find that the earlier conclusion that Nu decreases with increasing beta close to beta = 90 degrees for Gamma = 1 does not hold for the present Gamma = 0.5 case with small Pr. Published under license by AIP Publishing.