Abstract
Heat transfer of natural convection in inclined cavities is one of the hot research topics in nonlinear non-equilibrium systems. In this paper, direct numerical simulations of natural convection in an inclined square cavity are carried out by using a high-accuracy numerical method. The effects of the different trends of inclination angle in a range of 0°–180° on the nonlinear evolution of flow field, heat transfer efficiency, and bifurcation are investigated. The Rayleigh number varies in a range from 10<sup>3</sup> to 10<sup>6</sup>. The results show that the heat transfer efficiency characterized by Nusselt number is highly dependent on the Rayleigh number, Prandtl number, and the inclination angle. When the Rayleigh number is high, the Nusselt number will have a small jump near the inclination angle in a range of 80°–100°. The evolution of the flow field and temperature field are more complicated at high Rayleigh number. There are one to three vortices of different intensities in the cavity. At low Rayleigh number and inclination angle of the cavity being close to 90°, the flow state is composed mainly of heat conduction state. In addition, it is found that there exist two stable branches of solutions in a range of Rayleigh number (4949, 314721) when the inclination angle is in the interval of (70°, 110°).
Highlights
Variation of Nusselt number with inclination angle near the upper bound of bifurcation interval: (a) Ra = 314720 ; (b) Ra = 314721
此外, 腔体水平放置时, 相同 Rayleigh 数下不同流体介质的对流传热效率不同, 且流体 的 Prandtl 数越大则传热越强, 例如流体介质为水 时的传热效率大于流体介质为空气时的情况
Summary
当腔体倾角介于 70◦—110◦ 之间时, 在 Rayleigh 数 Ra ∈ (4949, 314721)内存在解的两条稳定分支. 最 近, Wang 等 [25−29] 直接数值模拟研究了不同参数 对二维腔体内热对流演变过程的影响, 其中 Rayleigh 数的范围为 107 ⩽ Ra ⩽ 1010 ; 高 宽 比 为 0.5 — 128 , Prandtl 数 为 0.01 ⩽ P r ⩽ 100 , 腔 体 倾 斜角度的范围为 0◦—90◦ . Ra 和 P r 分别为 Rayleigh 数和 Prandtl 数, 定 义为: gγ∆T H3 ν 结果表明, 在高 Rayleigh 数 下, 本文所取网格尺寸与精细网格下特征参数 (流 函数 ψ 和 Nusselt 数 N u 等) 的最大相对误差均小
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