速度边界层剪切定律（英文）  

Shear law of velocity boundary layer

作　　者：李明军[1] 蔡振宇[1] 

机构地区：[1]沈阳师范大学数学与系统科学学院,沈阳110034

出　　处：《沈阳师范大学学报（自然科学版）》2016年第4期419-425,共7页Journal of Shenyang Normal University:Natural Science Edition

基　　金：Supported by National Natural Science Foundation of China(11171281)

摘　　要：自20C初,路德维希·普朗特提出相关理论以来,边界层理论被人们所熟知。然而,边界层方程的解并不能恰当地描述高雷诺数流体。通过普朗特边界层方程的平均值和脉动值推导出带有脉动函数F的广义的Blasius方程,并且通过理论推导和数值模拟建立内边界层的速度剪切定律。前缘处边界厚度δ0=c2/Reu,其中Reu=U∞/ν,当求位移厚度时,c=1.720 8,求动量损失厚度时,c=0.664。此外,速度边界层上的极值定理和数值实验表明速度边界层的牛顿线性剪切定律完全满足于F=0.1和F=0.01,对于非线性剪切定律满足于F=0.001和F→0。这样的机制在传统的边界层理论中从未被讨论过。The theory of boundary layer has been known for many years since 1900＇s due to Ludwig Prandtl＇s contribution.However,solutions to the boundary layer equation does not properly describe high-Reynolds-number flows.In this paper,a generalized Blasius＇s equation with fluctuation function Fis derived by using the Prindtl＇s boundary equation of mean value and fluctuation,and a shear law of velocity in the inner boundary layer is built theoretically and numerically.The boundary thickness of the leading edge point is found to beδ0=c^2/Reu,where Reu =U∞/ν,c= 1.7208 as displacement constant or c= 0.664 as momentum constant,respectively.Moreover,the Limit Value Theorem on the velocity boundary layer and numerical experiments show that the Newtonian linear shear law of velocity boundary layer is perfectly satisfied for F=0.1and F=0.01,and the nonlinear shear law is presented for F=0.001 and F→0.Such a mechanism has never been demonstrated in the classical boundary layer theory.

关 键 词：广义的Blasius方程 波动函数 边界厚度 牛顿线性剪切定律 

分 类 号：O242[理学—计算数学]