Improved convection cooling in steady channel flows
Improved convection cooling in steady channel flows
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改善稳定通道流中的对流冷却
DOI：
10.1103/physrevfluids.2.104501
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发表时间：
2017
期刊：
影响因子：
--
通讯作者：
S. Alben
中科院分区：
文献类型：
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作者：
S. Alben
我们发现，在固定的粘性耗散率（熵= $Pe^2$）的约束下，稳定的通道流动对于从固定温度壁上传递热量是局部最优的，也就是泵送流体通过通道所需的功率。从抛物流开始，以净通量为延续参数，得到净通量最大时的唯一最优解。通过减小流量，我们最终得到了在通道壁面厚度为$\sim Pe^{-2/5}$的边界层内的熵集中，在边界层外以$\sim Pe^{4/5}$的速度均匀流动的最优流动。我们使用单向流近似的物理参数和解耦近似的数学参数来解释缩放。在单向近似下，当通道长高比为$L$时，边界层厚度尺度为$L^{3/5}$，外流速度尺度为$L^{-1/5}$。在空气中二维泊泽维尔流的湍流过渡附近的雷诺数处，我们发现与泊泽维尔流相比，传热增加了60%。
We find steady channel flows that are locally optimal for transferring heat from fixed-temperature walls, under the constraint of a fixed rate of viscous dissipation (enstrophy = $Pe^2$), also the power needed to pump the fluid through the channel. We generate the optima with net flux as a continuation parameter, starting from parabolic (Poiseuille) flow, the unique optimum at maximum net flux. Decreasing the flux, we eventually reach optimal flows that concentrate the enstrophy in boundary layers of thickness $\sim Pe^{-2/5}$ at the channel walls, and have a uniform flow with speed $\sim Pe^{4/5}$ outside the boundary layers. We explain the scalings using physical arguments with a unidirectional flow approximation, and mathematical arguments using a decoupled approximation. We also show that with channels of aspect ratio (length/height) $L$, the boundary layer thickness scales as $L^{3/5}$ and the outer flow speed scales as $L^{-1/5}$ in the unidirectional approximation. At the Reynolds numbers near the turbulent transition for 2D Poiseuille flow in air, we find a 60\% increase in heat transferred over that of Poiseuille flow.