A variational theory of lift
A variational theory of lift
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DOI：
10.1017/jfm.2022.348
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发表时间：
2021-04
影响因子：
3.7
通讯作者：
Cody Gonzalez;Haithem E. Taha
中科院分区：
文献类型：
--
作者：
Cody Gonzalez;Haithem E. Taha
在本文中，我们恢复了分析力学中一个特殊的，不太常见的变分原理（赫兹最小曲率原理），以建立一个新的理想流体动力学欧拉方程的变分模拟。新的变分公式与基于汉密尔顿最小作用量原理的公式有根本的不同。利用这个新的变分公式，我们推广了二维物体上流动的百年问题；我们开发了一个变分闭包条件，与库塔条件不同，它是从第一性原理推导出来的。所开发的变分原理减少到经典的库塔-茹科夫斯基条件在锐边翼型的特殊情况下，这挑战了公认的智慧关于库塔条件是粘滞效应的表现。相反，我们发现它代表动量守恒。此外，所发展的变分原理首次提供了不适用库塔条件的无锐边光滑形状上升力的理论模型。我们讨论了这种与当前理论的根本分歧如何解释超流体计算研究和实验中的差异。
Abstract In this paper we revive a special, less-common, variational principle in analytical mechanics (Hertz’ principle of least curvature) to develop a novel variational analogue of Euler's equations for the dynamics of an ideal fluid. The new variational formulation is fundamentally different from those formulations based on Hamilton's principle of least action. Using this new variational formulation, we generalize the century-old problem of the flow over a two-dimensional body; we developed a variational closure condition that is, unlike the Kutta condition, derived from first principles. The developed variational principle reduces to the classical Kutta–Zhukovsky condition in the special case of a sharp-edged airfoil, which challenges the accepted wisdom about the Kutta condition being a manifestation of viscous effects. Rather, we found that it represents conservation of momentum. Moreover, the developed variational principle provides, for the first time, a theoretical model for lift over smooth shapes without sharp edges where the Kutta condition is not applicable. We discuss how this fundamental divergence from current theory can explain discrepancies in computational studies and experiments with superfluids.