Potential flow of viscous fluids

该奖项是根据2009年美国复苏和再投资法案(公法111-5)资助的。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不旋转部分。一般情况下，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，用于分析亥姆霍兹分解中的两个组成部分。美国国家科学基金会以前支持的主要研究小组对这一主题的研究表明，通常认为势流是无粘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，也没有用处。无旋理论本质上有两种：粘性势流和耗散法。粘性势流最适合于气液两相流动，其中粘性法向应力是由无旋转分量计算得出的。耗散法(由Stokes在1851年提出)是基于无旋流的粘性应力的自平衡，它不会在方程中产生力：它们确实做功并引起能量和耗散。不幸的是，预测这两种不旋转理论中哪一种会给出更好的结果并不是先验的，但这是这项研究的主要目标之一。粘性势流可以用来研究各种物理现象，包括空化、毛细管破裂和破裂、Rayleigh-Taylor和Kelvin-Helmholtz不稳定性(液滴和射流破裂)、涉及热和质量传递的相变问题(核反应堆)、毛细重力波的粘性衰减、运动薄膜的波和破裂、Hele-Shaw流动(石油回收)等。认识到粘性流体的势流理论是一个具有丰富物理内容的可行课题是很重要的。

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.