二阶非牛顿流体蠕流精确解  

Exact Solutions of Creeping Flow on a Non-Newtonian Second-grade Fluid

作　　者：张道祥[1,2] 冯素晓[1] 

机构地区：[1]上海大学上海市应用数学和力学研究所,上海200072 [2]安徽师范大学数学与计算机科学学院,芜湖241000

出　　处：《力学季刊》2008年第3期418-423,共6页Chinese Quarterly of Mechanics

基　　金：国家自然科学基金项目(10472063);安徽师范大学青年科学基金(2007xqn60)

摘　　要：二阶流体是工业界常见的非牛顿流体,因为其本构关系简单而被广泛采用和研究。逆方法预先假定流场满足某类特定的物理的或几何的特性,从而求出流体运动方程的精确解。本文通过假定平面定常二阶非牛顿流体的涡量场与受到扰动的流函数相等这一特定形式,采用求解非线性微分方程常用的逆方法,推导并获得了平面二阶蠕流流场的精确解,由此容易进一步获得流场的压力。所获得的精确解包含了Poiseuille,简单Couette平行流动以及两相向流体的相互作用等流动。这些精确解为实验,数值以及渐进解的检验提供了借鉴和参考。The second-grade fluid is a common non-Newtonian fluid in the industrial world. It is widely used and investigated because of its simple construction relations. Inverse methods is a powerful tool in solving and obtaining exact solutions for non-Newtonian fluids by asssuming certain physical or geomet-rical properties of the flow field. By the hypothesis turbed by a stream, the exact solutions of the plane tained, thus the pressure field can be obtained. The that the vorticity equals to the streamfunction persecond grade creeping motion were inferred and obobtained solutions conclude common Poiseuille flow, Simple Couette flow and the interaction of two opposing flows. Exact solutions are analytical solutions and can be served as accuracy checks for experimental, numerical and asymptotic methods.

关 键 词：非牛顿流体 二阶流体 蠕流 逆方法 

分 类 号：O357[理学—流体力学] O302[理学—力学]