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就粘性/摩擦在机翼上方产生升力的作用进行了激烈的辩论；前者认为粘性是必要的，而后者并不认为用理想(非粘性)流体产生升力有任何矛盾。这场辩论深深植根于流体物理学中已有300年历史的悖论：达伦贝尔悖论，该悖论断言理想流体是无力的；它们不能抬起飞机。这一长达百年的争论因最近的一项结果而重新焕发活力，该结果断言，流场的演变使总曲率最小；即使流体是非粘性的，机翼上的最小曲率流动也是抬升的。这一最小曲率原理可以追溯到19世纪的赫兹，它是非常普遍的；它适用于流体和其他机械系统。例如，根据广义相对论，一颗行星在时空世界中以最小的曲率绕太阳运行。这项由跨学科科学与工程(RAISE)授予工程学和物理学之间的跨学科拨款的研究的目标是检验以下假设：理想的流动能产生升力吗？由于超流体(例如，低于2K的氦II)在临界速度以下的行为类似于理想流体，因此将转而研究以下可检验的假设：飞机能否以超速度运行(fly in Superfluid？上述假设将通过创建一个超流体风洞来验证，该风洞允许超流体在不同形状的小机翼上流动，并测量由此产生的升力及其时间演变。这项研究将导致一种与经典理论不同的新的物理学第一原理升力理论。此外，这项研究将纠正一个世纪以来普遍存在的关于Lift生成的粘性本质的公认智慧。因此，这项研究将解决已有300年历史的达朗伯特悖论，证明达朗贝尔的零力解只是欧拉方程的许多可能解之一。在许多情况下，大自然选择了一种提升解决方案。这项研究将展示非定常提升机制的物理原理，目前仅将其归因于粘性效应。最终，这项研究将导致对粘度在流体力学中的作用的新的理解。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凝聚态物理计划资助。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势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.