RAISE: On D'Alembert's Paradox: Can airplanes fly in superfluid?

在20世纪上半叶，剑桥学派和哥廷根学派之间就粘度/摩擦在机翼产生升力中的作用进行了激烈的辩论；前一派认为粘度是必要的，而后者认为理想（非粘性）流体产生升力没有任何矛盾。这场争论深深植根于流体物理学中有300年历史的悖论：达朗贝尔悖论（d 'Alembert paradox），它断言理想流体是无力的；他们抬不起飞机。这个长达一个世纪的争论由于最近的一个结果而重新焕发活力，该结果断言流场的演变是为了最小化总曲率；即使流体是非粘性的，最小曲率流过机翼也会产生升力。最小曲率原理可以追溯到19世纪的赫兹，它是非常普遍的；它既适用于流体系统，也适用于其他机械系统。例如，根据广义相对论，一颗行星在时空世界中以曲率最小的方式绕太阳运行。这项由跨学科科学与工程（RAISE）跨学科资助的研究的目标是测试以下假设：理想的流动能产生升力吗？由于超流体（例如，低于2K的氦II）在低于临界速度时表现得像理想流体，因此将研究以下可测试的假设：飞机能在超流体中飞行吗？上述假设将通过创建一个超流体风洞来验证，该风洞允许超流体流过不同形状的小机翼，并测量由此产生的升力及其时间演变。这项研究将从物理学的第一性原理出发，产生一种与经典理论相对立的新的升力理论。此外，这项研究将纠正一个多世纪以来流行的关于升力产生的粘性本质的公认智慧。因此，这项研究将通过表明达朗贝尔的零力解只是欧拉方程众多可能解中的一种，来解决300年之久的达朗贝尔悖论。在许多情况下，大自然选择了一种提升的解决方案。该研究将揭示目前仅归因于粘性效应的非定常升力机制的物理特性。最终，这项研究将导致对粘度在流体力学中的作用有一个新的认识。该项目由美国国家科学基金会（NSF）的流体动力学、CMMI动力学、控制和系统诊断以及MPS/DMR凝聚态物理项目资助。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

During the first half of the 20th century, there was a serious debate between the Cambridge and Gottingen schools about the role of viscosity/friction in generating lift over a wing; the former school asserts that viscosity is necessary, and the latter does not see any contradiction in generating lift by an ideal (non-viscous) fluid. This debate is deeply rooted in the 300-year-old paradox in fluid physics: d’Alembert paradox, which asserts that ideal fluids are forceless; they cannot lift an airplane. This century-old debate is rejuvenated due to a recent result which asserts that the flow field evolves to minimize total curvature; and a minimum-curvature flow over a wing is lifting even if the fluid is non-viscous. This principle of least curvature, which dates back to Hertz in the 19th century, is quite generic; it is applicable to fluids as well as other mechanical systems. For example, according to general relativity, a planet orbits the sun in the least curvature way over the space-time world. The goal of this Research Advanced by Interdisciplinary Science and Engineering (RAISE) cross-disciplinary grant between engineering and physics is to test the following hypothesis: Can an ideal flow generate lift? Since a superfluid (e.g., Helium II below 2K) behaves like an ideal fluid below a critical velocity, the following testable hypothesis will be investigated instead: Can airplanes fly in superfluid? The above hypothesis will be tested by creating a superfluid wind tunnel allowing a superfluid to flow over small wings of different shapes and measuring the resulting lift force and its time evolution. This research will lead to a new theory of lift from first principles in physics in contrast to the classical theory. Moreover, this research will correct the accepted wisdom that prevailed over a century about the viscous nature of lift generation. Hence, this study will resolve the 300-year-old d’Alembert paradox by showing that d’Alembert’s zero-force solution was only one of many possible solutions of Euler’s equation. And in numerous cases, Nature selects a lifting solution. This research will show the physics of the unsteady lifting mechanism, which is currently solely attributed to viscous effects. Ultimately, this research will lead to a new understanding of the role of viscosity in fluid mechanics.This project was funded by the NSF ENG/CBET Fluid Dynamics, ENG/CMMI Dynamics, Control and Systems Diagnostics, and MPS/DMR Condensed Matter Physics programs.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.