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

在世纪上半叶，剑桥学派和哥廷根学派就粘性/摩擦在机翼升力产生中的作用进行了激烈的争论;前一学派认为粘性是必要的，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，它断言理想流体是没有力的;它们不能举起飞机。这一世纪之久的争论由于最近的一个结果而重新活跃起来，该结果断言流场的发展使总曲率最小化;即使流体是非粘性的，机翼上的最小曲率流也是升力的。这个最小曲率原理可以追溯到世纪的赫兹，它是非常通用的;它适用于流体以及其他机械系统。例如，根据广义相对论，行星在时空世界中以最小曲率的方式绕太阳运行。这项由跨学科科学与工程（RAISE）跨学科资助的跨学科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，氦II低于2K）在低于临界速度时表现得像一种理想流体，下面的可检验假设将被研究：飞机能在超临界流体中飞行吗？ 上述假设将通过建立一个超流体风洞进行测试，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。 这一研究将导致一个新的理论，从第一性原理在物理学中的电梯相对于经典的理论。此外，这项研究将纠正世纪来关于升力产生的粘性性质的公认的智慧。因此，这项研究将解决300岁的达朗贝尔悖论表明，达朗贝尔的零力的解决方案只是众多可能的解决方案之一欧拉方程。在许多情况下，大自然选择了提升解决方案。这项研究将显示非定常升力机制的物理特性，目前仅归因于粘性效应。最终，这项研究将导致一个新的理解的作用，粘度在流体力学。这个项目是由NSF ENG/CBET流体动力学，ENG/CMMI动力学，控制和系统诊断，和MPS/DMR凝聚态物理程序资助。这个奖项反映了NSF的法定使命，并已被认为是值得的支持，通过评估使用基金会的智力价值和更广泛的影响审查标准。

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.