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

RAISE：关于达朗贝尔悖论：飞机能在超流体中飞行吗？

• 批准号: 2332556
• 负责人: Haithem Taha
• 金额: $ 100万
• 依托单位: University of California-Irvine
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2023
• 资助国家: 美国
• 起止时间: 2023-08-01 至 2026-07-31
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2332556&HistoricalAwards=false
• 关键词: RAISE; Alembert; Paradox; airplanes; fly

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.

在20世纪上半叶，剑桥和哥廷根学校之间就粘度/摩擦在翼上产生升降机中的作用进行了严重的辩论。前学校断言，粘度是必要的，而后者则没有任何矛盾的矛盾，从而产生理想的（无粘性）流体。这场辩论深深植根于300年历史的流体物理学：D'Alembert Paradox中，该悖论断言理想的流体是无效的。他们无法抬起飞机。由于最近的结果断言流场演变以最大程度地减少总曲率，因此这场世纪历史的辩论恢复活力。即使流体是非粘性的，在机翼上的最小阳离子流也可以提升。这一曲率最小的原则可以追溯到19世纪的赫兹，这是相当通用的。它适用于烟道以及其他机械系统。例如，根据一般相对论，一个行星在整个时空世界中以最小的曲率方式绕太阳旋转。这项研究的目的是跨学科科学与工程（加薪）工程和物理学之间的跨学科赠款是测试以下假设：理想的流程可以产生升力吗？由于超氟（例如2K以下的氦II）的行为就像临界速度以下的理想流体一样，因此将研究以下可检验的假设：可以在超级流体中流动飞机吗？上述假设将通过创建超流体风洞来测试，从而使超氟可以在不同形状的小翅膀上流动并测量所得的升力力及其时间演变。这项研究将导致与古典理论相比之下，从物理学的第一原理中提出了一种新的提升理论。此外，这项研究将纠正一个世纪以来关于升力发电的粘性本质的公认智慧。因此，这项研究将通过表明D'Alembert的零力量解决方案只是Euler方程的众多解决方案之一，从而解决了300年历史的D'Anembert悖论。在许多情况下，大自然选择了提升解决方案。这项研究将显示不稳定的举重机制的物理学，目前仅归因于粘性效应。最终，这项研究将导致对粘度在流体力学中的作用的新理解。该项目由NSF Eng/CBET流体动力学，ENG/CMMI动态，控制和系统诊断，MPS/DMR凝结物理学计划的资料均通过审查良好的依据，这是通过评估良好的支持。