Optimal convection cooling flows in general 2D geometries
Optimal convection cooling flows in general 2D geometries
复制标题
一般 2D 几何形状中的最佳对流冷却流
DOI：
10.1017/jfm.2017.35
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发表时间：
2016
影响因子：
3.7
通讯作者：
S. Alben
中科院分区：
文献类型：
--
作者：
S. Alben
我们将一种计算水平层中最佳二维对流冷却流的最新方法推广到各种几何形状，包括与技术应用相关的几何形状。我们将问题写在一对共形坐标中，即纯传导温度及其调和共轭。我们找到了冷却环形域中的圆柱体、嵌入冷表面的热板以及具有热内部和冷外部的通道的最佳流动。在固定动能的约束下，最佳流动在共角坐标系中基本相同。在物理坐标中，它们由尺寸范围从热表面的长度到热表面和冷表面界面处的小截止长度的涡流组成。在固定熵（或固定粘性耗散率）的约束下，方程中出现依赖于几何形状的度量因子。共形坐标在这里很有用，因为它们将问题映射到矩形域，有利于数值求解。在熵预算较小的情况下，最佳流动由与流域大小相同的涡流主导。
We generalize a recent method for computing optimal 2D convection cooling flows in a horizontal layer to a wide range of geometries, including those relevant for technological applications. We write the problem in a conformal pair of coordinates which are the pure conduction temperature and its harmonic conjugate. We find optimal flows for cooling a cylinder in an annular domain, a hot plate embedded in a cold surface, and a channel with a hot interior and cold exterior. With a constraint of fixed kinetic energy, the optimal flows are all essentially the same in the conformal coordinates. In the physical coordinates, they consist of vortices ranging in size from the length of the hot surface to a small cutoff length at the interface of the hot and cold surfaces. With the constraint of fixed enstrophy (or fixed rate of viscous dissipation), a geometry-dependent metric factor appears in the equations. The conformal coordinates are useful here because they map the problems to a rectangular domain, facilitating numerical solutions. With a small enstrophy budget, the optimal flows are dominated by vortices that have the same size as the flow domain.