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，剑桥学派和哥廷根学派之间就粘度/摩擦力在机翼上产生升力的作用进行了一场激烈的争论；前者认为粘度是必要的，而后者则认为没有任何必要。理想（非粘性）流体产生升力的矛盾这一争论深深植根于流体物理学中已有 300 年历史的悖论：达朗贝尔悖论，该悖论声称理想流体是由于最近的一项研究结果表明，即使流体是非流动的，机翼上的最小曲率流也会升力，这一长达一个世纪的争论重新焕发活力。这种最小曲率原理可以追溯到 19 世纪的赫兹，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。跨学科科学与工程（RAISE）工程和物理学之间的跨学科资助的这项高级研究的目标是测试以下假设：理想流能否产生升力。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，因此将研究以下可检验的假设：飞机可以在超流体中飞行吗？超流体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，与经典理论相反，这项研究将根据物理学第一原理得出新的升力理论。将纠正一个多世纪以来关于升力产生的粘性性质的公认观点。因此，这项研究将通过证明达朗贝尔的零力解决方案只是其中之一来解决已有 300 年历史的达朗贝尔悖论。在许多情况下，《自然》杂志选择了欧拉方程的一种升力解，该研究将展示目前仅归因于粘性效应的非定常升力机制的物理原理。粘度在流体力学中的作用。该项目由 NSF ENG/CBET 流体动力学、ENG/CMMI 动力学、控制和系统诊断以及 MPS/DMR 凝聚态物理资助该奖项反映了 NSF 的法定使命，并通过使用基金会的智力价值和更广泛的影响审查标准进行评估，被认为值得支持。