Optimal heat transfer enhancement in plane Couette flow
Optimal heat transfer enhancement in plane Couette flow
复制标题
平面库埃特流中的最佳强化传热
DOI：
10.1017/jfm.2017.779
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发表时间：
2018
影响因子：
3.7
通讯作者：
Masaki Shimizu
中科院分区：
文献类型：
--
作者：
Shingo Motoki;Genta Kawahara;Masaki Shimizu
从理论上探讨了平面库爱特流的最佳强化传热。要优化的矢量场（称为“速度”）是与时间无关的，无发散，温度是根据速度确定的，作为对流扩散方程的解。普朗特数被设置为统一的，一致的边界条件施加在速度和温度场。以壁面热通量（或等效总标量耗散）超过总能量耗散的部分作为目标泛函，采用变分法导出Euler-Lagrange方程，数值求解该方程，得到泛函最大化意义下的最优状态。在低雷诺数下，层流导电场是一种最佳状态。在三维速度场中，除了大尺度的涡卷外，在近壁处还出现了小尺度的准流向涡管。流向涡沿展向倾斜，从而产生与平均切变涡反平行的反气旋涡，产生明显的三维性。缠绕在倾斜反气旋涡流周围的等温线受到平均流的横轴剪切，因此缠绕等温线的间距较窄，因此温度梯度比纯流向（二维）涡流管周围的温度梯度更陡，从而加强标量耗散，从而增加壁面热通量。此外，倾斜的反气旋涡诱导朝向壁的流动以将低温（或高温）流体推到热（或冷）壁上，从而增强壁热通量。优化的三维速度场实现了更高的壁面热通量和更低的能量耗散比平面Couette湍流。
Optimal heat transfer enhancement has been explored theoretically in plane Couette flow. The vector field (referred to as the ‘velocity’) to be optimised is time independent and divergence free, and temperature is determined in terms of the velocity as a solution to an advection-diffusion equation. The Prandtl number is set to unity, and consistent boundary conditions are imposed on the velocity and the temperature fields. The excess of a wall heat flux (or equivalently total scalar dissipation) over total energy dissipation is taken as an objective functional, and by using a variational method the Euler–Lagrange equations are derived, which are solved numerically to obtain the optimal states in the sense of maximisation of the functional. The laminar conductive field is an optimal state at low Reynolds number . In the three-dimensional velocity field there appear smaller-scale hierarchical quasi-streamwise vortex tubes near the walls in addition to the large-scale rolls. The streamwise vortices are tilted in the spanwise direction so that they may produce the anticyclonic vorticity antiparallel to the mean-shear vorticity, bringing about significant three-dimensionality. The isotherms wrapped around the tilted anticyclonic vortices undergo the cross-axial shear of the mean flow, so that the spacing of the wrapped isotherms is narrower and so the temperature gradient is steeper than those around a purely streamwise (two-dimensional) vortex tube, intensifying scalar dissipation and so a wall heat flux. Moreover, the tilted anticyclonic vortices induce the flow towards the wall to push low- (or high-) temperature fluids on the hot (or cold) wall, enhancing a wall heat flux. The optimised three-dimensional velocity fields achieve a much higher wall heat flux and much lower energy dissipation than those of plane Couette turbulence.