Fractal-like actuator disc theory for optimal energy extraction
Fractal-like actuator disc theory for optimal energy extraction
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DOI：
10.1017/jfm.2021.766
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发表时间：
2021-11-25
影响因子：
3.7
通讯作者：
Willden, R. H. J.
中科院分区：
文献类型：
--
作者：
Dehtyriov, D.;Schnabl, A. M.;Willden, R. H. J.
从理论上研究了利用相长干涉即局部阻塞的器件的功率提取极限。该设备是使用致动器盘理论建模，在该理论中，我们允许该设备被分割成阵列，然后这些到子阵列的任意次数，以便构建一个n级多尺度设备，其中原始设备经历n - 1细分。这个问题的另一种物理解释是一个平面的涡轮阵列系统，其中涡轮组在最小的n尺度上均匀排列，然后这些组在下一个最小的n -1尺度上相对于彼此均匀间隔，这种模式在所有后续的更大尺度上重复。Nishino & Willden的尺度分离思想（J. Fluid.机甲师，第708卷，2012年b，pp. 596-606），其假设子阵列内的混合比该子阵列周围的旁路流的混合发生得更快，使得在n尺度装置中，混合以该顺序从内部尺度到最外部尺度发生。我们调查的任意级别的多尺度设备的行为，并确定的安排，致动器盘（第n级设备），最大化的功率系数（提取的功率比不受干扰的动能通量通过净盘正面面积）。我们发现，这种最佳安排是接近分形，分形安排给出了类似的结果。随着设备放置在一个无限宽的通道，即零全球堵塞，我们发现，最佳的功率系数趋于统一的设备规模的数量趋于无穷大，一个27/16的增加超过Lanchester-贝兹限制0.593。对于有限宽度通道中的器件，即非零全局阻塞，可以在最大功率系数进一步提升的情况下进行类似的观察。我们讨论了这种能量提取过程的流体力学，并研究了推力和尾流速度系数的尺度分布。数值演示的性能提升，由于多尺度动力学也提供了。我们表明，旁路流再混合和随之而来的能量损失增加设备的功率系数高于单个设备的限制，因此，虽然功率系数可以增加，这是在能量提取的整体效率的代价，减少尾流尺度再混合损失必然上升。对于多尺度装置在有限的整体堵塞两个效果的作用，以增加可提取的功率;整体流向压力梯度与有限的堵塞，和尾流压力恢复与旁路规模的再混合。
The limit of power extraction by a device which makes use of constructive interference, i.e. local blockage, is investigated theoretically. The device is modelled using actuator disc theory in which we allow the device to be split into arrays and these then into sub-arrays an arbitrary number of times so as to construct an n-level multi-scale device in which the original device undergoes n - 1 sub-divisions. The alternative physical interpretation of the problem is a planar system of arrayed turbines in which groups of turbines are homogeneously arrayed at the smallest nth scale, and then these groups are homogeneously spaced relative to each other at the next smallest n - 1th scale, with this pattern repeating at all subsequent larger scales. The scale-separation idea of Nishino & Willden (J. Fluid. Mech., vol. 708, 2012b, pp. 596-606) is employed, which assumes mixing within a sub-array occurs faster than mixing of the by-pass flow around that sub-array, so that in the n-scale device mixing occurs from the inner scale to the outermost scale in that order. We investigate the behaviour of an arbitrary level multi-scale device, and determine the arrangement of actuator discs (nth level devices) which maximises the power coefficient (ratio of power extracted to undisturbed kinetic energy flux through the net disc frontal area). We find that this optimal arrangement is close to fractal, and fractal arrangements give similar results. With the device placed in an infinitely wide channel, i.e. zero global blockage, we find that the optimum power coefficient tends to unity as the number of device scales tends to infinity, a 27/16 increase over the Lanchester-Betz limit of 0.593. For devices in finite width channels, i.e. non-zero global blockage, similar observations can be made with further uplift in the maximum power coefficient. We discuss the fluid mechanics of this energy extraction process and examine the scale distribution of thrust and wake velocity coefficients. Numerical demonstration of performance uplift due to multi-scale dynamics is also provided. We demonstrate that bypass flow remixing and ensuing energy losses increase the device power coefficient above the limits for single devices, so that although the power coefficient can be made to increase, this is at the expense of the overall efficiency of energy extraction which decreases as wake-scale remixing losses necessarily rise. For multi-scale devices in finite overall blockage two effects act to increase extractable power; an overall streamwise pressure gradient associated with finite blockage, and wake pressure recoveries associated with bypass-scale remixing.