Potential flow of viscous fluids

粘性流体的势流

• 批准号: 0908561
• 负责人: Ellen Longmire
• 金额: $ 26.09万
• 依托单位: University of Minnesota-Twin Cities
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2009
• 资助国家: 美国
• 起止时间: 2009-07-01 至 2013-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0908561&HistoricalAwards=false
• 关键词: Potential; flow; viscous; fluids

This award is funded under the American Recovery and Reinvestment Act of 2009 (Public Law 111-5).This project carries out mathematical and numerical studies of potential flows of viscous and viscoelastic fluids. The Helmholtz decomposition divides the velocity into a rotational part and an irrotational part. In general, the rotational and irrotational velocities are both required and they are tightly coupled at the boundary, especially when the no-slip condition is applied. The project's goal is to develop a framework for the analysis of both components in the Helmholtz decomposition. Previous NSF supported studies of this topic by the principal investigator's group showed that the common opinion that potential flows are irrotational motions of inviscid fluids in general is not correct: it is neither necessary nor useful to put the viscosity to zero. There are essentially two irrotational theories: viscous potential flow and the dissipation method. Viscous potential flow works best for gas-liquid flows where the viscous normal stress is computed from the irrotational component. The dissipation method (introduced by Stokes in 1851) is based on the self-equilibration of viscous stresses for irrotational flow which do not give rise to forces in the equations: they do work and give rise to energy and dissipation. Unfortunately, predicting which of these two irrotational theories will give the better result is not known a priori but is one of the main goals of this study. Viscous potential flow can be used to study a variety of physical phenomena, including cavitation, capillary breakup and rupture, Rayleigh-Taylor and Kelvin-Helmholtz instabilities (drop and jet breakup), phase change problems involving heat and mass transfer (nuclear reactors), the viscous decay of capillary-gravity waves, waves and rupture of moving thin films, Hele-Shaw flows (oil recovery), etc. It is important to recognize that the theory of potential flows of viscous fluids is a viable topic with a rich physical content.

该奖项由 2009 年美国复苏和再投资法案（公法 111-5）资助。该项目对粘性和粘弹性流体的潜在流动进行数学和数值研究。亥姆霍兹分解将速度分为旋转部分和无旋转部分。一般来说，旋转速度和非旋转速度都是必需的，并且它们在边界处紧密耦合，特别是在应用无滑移条件时。该项目的目标是开发一个框架来分析亥姆霍兹分解中的两个组成部分。先前由主要研究人员小组进行的 NSF 支持的该主题的研究表明，认为势流通常是无粘性流体的无旋运动的普遍观点是不正确的：将粘度设置为零既没有必要也没有用。无旋理论本质上有两种：粘性势流和耗散法。粘性势流最适合气液流，其中粘性法向应力是根据无旋分量计算的。耗散法（由斯托克斯于 1851 年提出）基于无旋流粘性应力的自平衡，在方程中不会产生力：它们做功并产生能量和耗散。不幸的是，预测这两种无旋理论中哪一种会给出更好的结果尚不清楚，但这是本研究的主要目标之一。粘性势流可用于研究多种物理现象，包括空化、毛细管破裂和破裂、瑞利-泰勒和开尔文-亥姆霍兹不稳定性（液滴和射流破裂）、涉及传热和传质的相变问题（核反应堆）、毛细管重力波的粘性衰变、移动薄膜的波和破裂、赫勒-肖流（采油）等，具有重要意义 认识到粘性流体势流理论是一个可行的主题，具有丰富的物理内容。