arXiv 1908.028962019-08-20physics.flu-dynmath.FAmath.OC

二维壁到壁最佳传输

Wall-to-wall optimal transport in two dimensions

Andre N. Souza, Ian Tobasco, Charles R. Doering

发表信息：: J. Fluid Mech. 889 (2020) A34
DOI：: 10.1017/jfm.2020.42

摘要：

梯度上升法是用来计算两个等温无滑移平行壁面之间的热传递最大化的不可压缩流动。通过与应变均方根率成比例的Péclet数$\text{Pe}$来参数化速度场的大小，该方案被应用于计算优化扩散传热的对流增强的二维流动，即，努塞尔数$\text{Nu}$到$\text{Pe} \approx 10^5$。所得到的传输表现出从线性区域中的$\text{Pe} < 10$的$\text{Nu}-1 \sim \text{Pe}^{2}$到$\text{Pe} > 10^3$的$\text{Nu} \sim \text{Pe}^{0.54}$的缩放变化。最优场被观察到是近似可分离的，即，壁平行坐标和壁法线坐标的函数的乘积。分析采用可分离的Anastomic产生一个条件上限$\lesssim \text{Pe}^{6/11} = \text{Pe}^{0.\overline{54}}$为$\text{Pe} \rightarrow \infty$类似于计算实现的缩放。浮力驱动的瑞利-贝纳德对流的传热的影响进行了讨论。

英文摘要：

Gradient ascent methods are developed to compute incompressible flows that maximize heat transport between two isothermal no-slip parallel walls. Parameterizing the magnitude of velocity fields by a Péclet number $\text{Pe}$ proportional to their root-mean-square rate-of-strain, the schemes are applied to compute two-dimensional flows optimizing convective enhancement of diffusive heat transfer, i.e., the Nusselt number $\text{Nu}$ up to $\text{Pe} \approx 10^5$. The resulting transport exhibits a change of scaling from $\text{Nu}-1 \sim \text{Pe}^{2}$ for $\text{Pe} < 10$ in the linear regime to $\text{Nu} \sim \text{Pe}^{0.54}$ for $\text{Pe} > 10^3$. Optimal fields are observed to be approximately separable, i.e., products of functions of the wall-parallel and wall-normal coordinates. Analysis employing a separable ansatz yields a conditional upper bound $\lesssim \text{Pe}^{6/11} = \text{Pe}^{0.\overline{54}}$ as $\text{Pe} \rightarrow \infty$ similar to the computationally achieved scaling. Implications for heat transfer in buoyancy-driven Rayleigh-Bénard convection are discussed.

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