AI 中文总结
本文分析小展弦比三角翼的气动特性，回顾前缘吸力类比与细长体理论，证明后者在展弦比趋于零时可准确预测势升力并用于近似涡升力。
AI 中文摘要
我们考虑一个小展弦比 $A>0$ 的尖缘三角翼，这是一个三维机翼的例子，其气动特性不能仅用势升力来建模。一对附着涡起着重要作用，它们产生涡升力。我们详细回顾了由 Edward Polhamus（NASA 技术说明 D-3767，1966年）提出的前缘吸力类比，该类比表明，通过避免对机翼周围流动涡量的任何直接分析，可以获得对涡升力最准确的描述。我们还描述了由 Jones（NACA 报告第835号，1946年）引入的二维细长体理论，用于近似势升力。我们证明，忽略两个边界上的不可积性问题和椭圆正则性问题，细长体理论足以在 $A\ o 0$ 时准确预测势升力。我们还表明，这种二维近似对于证明前缘吸力类比的建模假设是必要的，因此细长体模型也可用于在 $A\ o 0$ 时近似涡升力。为完整起见，我们提供了必要的机翼理论的额外解释。
英文摘要
We consider a sharp-edge delta wing of small aspect ratio $A>0$, which is an example of a 3D airfoil whose aerodynamic properties cannot be modeled using the potential lift}only. An important role is played by a pair of attached vortices, which generate the vortex lift. We review in detail the leading-edge suction analogy, developed by Edward Polhamus (NASA Technical Note D-3767, 1966), which shows that the most accurate description of the vortex lift can be obtained by avoiding any direct analysis of vorticity of the flow around the wing. We also describe a 2D slender wing theory, which was introduced by Jones (NACA report no. 835, 1946) to approximate the potential lift. We show that, neglecting certain two borderline nonintegrability issues and an elliptic regularity issue, the slender wing theory is sufficient to yield accurate prediction of the potential lift as $A\to 0$. We also show that this 2D approximation is necessary to justify the modelling assumptions of the leading-edge suction analogy, so that the slender wing model can also be used to approximate the vortex lift as $A\to 0$. For completeness, we provide additional explanations of the necessary airfoil theory.
Comments25 pages, 11 figures
