论文标题
关于prandtl编号在热源和水槽驱动的对流中的作用
On the role of the Prandtl number in convection driven by heat sources and sinks
论文作者
论文摘要
我们报告了由内部热源和水槽组合驱动的湍流对流的数值研究。以最近的实验实现为动机（Lepot等人，2018年），我们着重于冷却均匀的情况，而内部加热位于底部边界附近，大约是域高度的十分之一。我们获得了缩放法律$ nu \ sim ra^γpr^χ$，用于传热，这是由nusselt Numbernume $ nu $衡量的，该$ nu $表示为瑞利数字$ ra $和prandtl number $ $ pr $的函数。在确认了对$ ra $的依赖性的实验值$γ\约1/2 $之后，我们确定了$ pr $的几个依赖性。对于无应力的底部表面，在[0.003，10] $中的$ pr \范围内，我们观察到指数$χ\ \ \ \ \ 1/2 $，与Spiegel的混合长度理论一致。对于无滑动表面，我们观察到从$χ\ \ \ pr \ leq 0.04 $到$χ\ \ $ \ \ 1/6 $的过渡，对于$ pr \ geq 0.04 $，与Bouillaut等人的缩放预测一致。后一个缩放机制源于与无滑动底部边界相邻的停滞层中的热量积累，我们通过比较扩散和对流热通量的局部贡献来表征。
We report on a numerical study of turbulent convection driven by a combination of internal heat sources and sinks. Motivated by a recent experimental realisation (Lepot et al. 2018), we focus on the situation where the cooling is uniform, while the internal heating is localised near the bottom boundary, over approximately one tenth of the domain height. We obtain scaling laws $Nu \sim Ra^γPr^χ$ for the heat transfer as measured by the Nusselt number $Nu$ expressed as a function of the Rayleigh number $Ra$ and the Prandtl number $Pr$. After confirming the experimental value $γ\approx 1/2$ for the dependence on $Ra$, we identify several regimes of dependence on $Pr$. For a stress-free bottom surface and within a range as broad as $Pr \in [0.003, 10]$, we observe the exponent $χ\approx 1/2$, in agreement with Spiegel's mixing length theory. For a no-slip bottom surface we observe a transition from $χ\approx 1/2$ for $Pr \leq 0.04$ to $χ\approx 1/6$ for $Pr \geq 0.04$, in agreement with scaling predictions by Bouillaut et al. The latter scaling regime stems from heat accumulation in the stagnant layer adjacent to a no-slip bottom boundary, which we characterise by comparing the local contributions of diffusive and convective thermal fluxes.
