论文标题
prandtl编号对湍流剪切热对流的影响
The effect of Prandtl number on turbulent sheared thermal convection
论文作者
论文摘要
在湍流壁剪切的热对流中,有三种不同的流程度,具体取决于热强迫和壁剪切的相对相关性。在本文中,我们报告了此类剪切的雷利 - 贝纳德对流的直接数值模拟的结果,在固定的雷利数字上$ ra = 10^6 $,在范围内将墙上的雷诺数在$ 0 \ leq re_w \ leq re_w \ leq req 4000 $和prandtl $ 0.22 $ 0.22 \ leq pr \ leq pr \ leq 4. 6 $ 4中,以前的工作。 (2020),其中$ pr $保持统一和热力强迫($ ra $)的变化。我们涵盖了广泛的批量理查森数字$ 0.014 \ leq ri \ leq 100 $,并表明prandtl数字强烈影响流量结构的形态和动力学。特别是,在固定的$ ra $和$ re_w $下,高的prandtl数字会导致墙壁上更强大的动量运输,因此产生了更大的墙壁剪切对流量结构的影响,从而增加了$ re_w $对Nusselt号码的效果。此外,我们分析了热和动力学边界层厚度,并将其行为与所得的流动状态相关联。对于最大的剪切速率和$ PR $数字,我们观察到Prandtl-Von Karman日志层的出现,这表明边界层中湍流动力学的开始。最后,我们的结果允许将Grossmann-Lohse理论扩展到Rayleigh-Bénard对流中的热运输理论到剪切的案例,并普遍描述$ NU(RA,PR,RE_W)$。
In turbulent wall sheared thermal convection, there are three different flow regimes, depending on the relative relevance of thermal forcing and wall shear. In this paper we report the results of direct numerical simulations of such sheared Rayleigh-Bénard convection, at fixed Rayleigh number $Ra=10^6$, varying the wall Reynolds number in the range $0 \leq Re_w \leq 4000$ and Prandtl number $0.22 \leq Pr \leq 4.6$, extending our prior work by Blass et al. (2020), where $Pr$ was kept constant at unity and the thermal forcing ($Ra$) varied. We cover a wide span of bulk Richardson numbers $0.014 \leq Ri \leq 100$ and show that the Prandtl number strongly influences the morphology and dynamics of the flow structures. In particular, at fixed $Ra$ and $Re_w$, a high Prandtl number causes stronger momentum transport from the walls and therefore yields a greater impact of the wall shear on the flow structures, resulting in an increased effect of $Re_w$ on the Nusselt number. Furthermore, we analyse the thermal and kinetic boundary layer thicknesses and relate their behaviour to the resulting flow regimes. For the largest shear rates and $Pr$ numbers, we observe the emergence of a Prandtl-von Karman log-layer, signalling the onset of turbulent dynamics in the boundary layer. Finally, our results allow to extend the Grossmann-Lohse theory for heat transport in Rayleigh-Bénard convection to the sheared case, universally describing $Nu(Ra,Pr,Re_w)$.