Hydromechanics of swimming propulsion. Part 2. Some optimum shape problems
Hydromechanics of swimming propulsion. Part 2. Some optimum shape problems
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DOI：
10.1017/s0022112071000685
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发表时间：
1971-04
影响因子：
3.7
通讯作者：
By T. YAO-TSU;U. W.
中科院分区：
文献类型：
--
作者：
By T. YAO-TSU;U. W.
在这一部分中考虑的最佳形状的问题是为那些轮廓的二维柔性板的时间谐波运动，将最小化的能量损失的条件下，固定的推力，也可能在其他等周约束。首先，刚性板的最佳运动是完全确定的，它是必要的第一，以减少原来的奇异二次形式代表的能量损失的一个定期的一个较低的订单，这是然后听话的通常的变分方法。发现了一个有利的折减频率范围，在这个范围内，在规定的条件下，来自前缘吸力的推力贡献尽可能小，在这个范围之外，这种贡献变得如此之大，以致在实践中很难实现而不失速。这个最优解与Lighthill（1970）的最新理论进行了比较;发现这些独立得出的结论实际上是一致的。本理论进一步应用于预测的运动海豚尾巴的大的长宽比，并发现与实验测量结果令人满意的协议。在最佳效率的基础上，对鸟类扑翼飞行中的翅膀运动作了定性的讨论。最佳形状的柔性板进行了分析，为最一般的情况下的无限自由度。结果表明，在一定程度上可以确定的解决方案，但确切的形状并不总是唯一确定的。
The optimum shape problems considered in this part are for those profiles of a two-dimensional flexible plate in time-harmonic motion that will minimize the energy loss under the condition of fixed thrust and possibly also under other isoperimetric constraints. First, the optimum movement of a rigid plate is completely determined; it is necessary first to reduce the original singular quadratic form representing the energy loss to a regular one of a lower order, which is then tractable by usual variational methods. A favourable range of the reduced frequency is found in which the thrust contribution coming from the leading-edge suction is as small as possible under the prescribed conditions, outside of which this contribution becomes so large as to be hard to realize in practice without stalling. This optimum solution is compared with the recent theory of Lighthill (1970); these independently arrived-at conclusions are found to be virtually in agreement. The present theory is further applied to predict the movement of a porpoise tail of large aspect-ratio and is found in satisfactory agreement with the experimental measurements. A qualitative discussion of the wing movement in flapping flight of birds is also given on the basis of optimum efficiency. The optimum shape of a flexible plate is analysed for the most general case of infinite degrees of freedom. It is shown that the solution can be determined to a certain extent, but the exact shape is not always uniquely determinate.