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高雷诺数流动的基本控制方程体系和扩散跑物化Navier-Stokes方程组的意义和用途
引用本文:高智.高雷诺数流动的基本控制方程体系和扩散跑物化Navier-Stokes方程组的意义和用途[J].力学进展,2005,35(3):427-438.
作者姓名:高智
作者单位:中科院力学所LHD实验室
摘    要:在计算机发达的时代, 高雷诺($Re$)数绕流计算中有无必要使用简化NS方 程组, 本文讨论这个问题. 主要内容如下: (1) 高$Re$数绕流包含3种基本流动: 所有方向对流占优流动、所有方向对流扩散竞争流动和部 分方向对流占优部分方向对流扩散竞争流动(简称干扰剪切流动), 3个基本流动的特征彼 此不同且在流场中所占领域大小彼此相差悬殊, NS方程区域很小, 它们的最简单控制方程组Euler、Navier-Stokes (NS)和扩散抛物化(DP) NS方程组的数 学性质彼此不同, 因此利用Euler-DPNS-NS方程组体系分析计算高$Re$数绕流流动就是一 个合乎逻辑的选择, 该法与利用单一NS方程组的常用方法可以彼此检验和补充. (2) 流体之间以及流体与外界的动量、能量和质量交换, 流态从层流到湍流的演化主要发生在干 扰剪切流动中, 干扰剪切流及其最简单控制方程------DPNS方程组具有基础意义; DPNS方程组 笔者在1967年已提出. (3) 诸简化NS方程组: DPNS、抛物化(P)NS、薄层(TL)NS、黏性层(VL)NS方程组的发展、 相互关系, 它们的历史贡献和今后的用途; 它们的数学性质均为扩散抛物型, 但它们包含的 黏性项彼此有所不同; 从流体力学角度来看, 它们中只有DPNS方程组能够准确描述干扰剪 切流动. 提出把诸简化NS方程组统一为DPNS方程组的建议. (4)干扰剪切流------DPNS方程组 与无干扰剪切流------边界层方程组之间的关系以及进一步研究干扰 剪切流的意义.

关 键 词:流体力学  高$Re$数流动  干扰剪切流动  Navier-Stokes(NS)方程组  扩散抛物化NS(DPNS)方程组
收稿时间:06 13 2005 12:00AM
修稿时间:2005-06-132005-07-13

SIGNIFICANCE AND USE OF BASIC EQUATION SYSTEM GOVERNING HIGH REYNOLDS (Re) NUMBER FLOWS AND DIFFUSION-PARABOLIZED NAVIER-STOKES (DPNS) EQUATIONS
GAO Zhi.SIGNIFICANCE AND USE OF BASIC EQUATION SYSTEM GOVERNING HIGH REYNOLDS (Re) NUMBER FLOWS AND DIFFUSION-PARABOLIZED NAVIER-STOKES (DPNS) EQUATIONS[J].Advances in Mechanics,2005,35(3):427-438.
Authors:GAO Zhi
Abstract:In the times of the rapid development of computer art, one wonders whether it is necessary or not to consider simplified Navier-Stokes (NS) equations in numerical simulations of high Reynolds number flows over bodies. This problem is examined in this paper. (1) Any high Re number flow over bodies consists of three basic flows: the flow with convection-dominant in all spatial directions, the flow with convection-diffusion competition in all directions and the flow with convection-dominant in part directions and convection-diffusion competition in part directions, which is called the interacting shear flow; the features of the three basic flows are different; their simplest conservation equations, i.e. the Euler equations, Navier-Stokes (NS) equations and diffusion parabolized(DP) NS equations, have different mathematical characteristics; there is a great disparity in domains of the three basic flows and the domains of NS equations are very small. Therefore, adopting Euler-DPNS-NS equation system to analyze and compute high Re number flows over bodies is a logical approach. There exists a mutual examined-complemented relationship of this approach with the usual one of adopting only NS equations. Both the momentum-, energy- and mass- exchanges between fluid and fluid, fluid and environment (such as solid wall) and flow evolution from laminar to turbulence take place mainly in the interacting shear flows, which and its simplest conservation equations-DPNS equations are fundamental. The interacting shear flow is exactly a flow with an approximate main-stream direction. The DPNS equations were presented by the author in 19672,15]. (2) There are several simplified NS equations similar to DPNS equations, such as parabolized (P)NS 3,22], thin-layer (TL)NS3,23] and viscous-layer (VL)NS equations6,24] . As to these simplified NS equations, their development, historical contribution to computational fluid dynamics, mathematical characteristics, applications and mutual relations are discussed. (3) The relationship between the interacting shear flows-DPNS equations and non-interacting shear flows-boundary layer equations is also examined. The necessity of studying further the interacting shear flows and DPNS equations are emphasized.
Keywords:fluid mechanics  high Reynolds (Re) number flows  interacting shear flows  Navier-Stokes (NS) equations  diffusion-parabolized (DP) NS equations
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