水力旋流器流场动力学模型的李群分析法  

The Lie Group Analytical Method for Dynamic Model of Flow Field in Hydrocyclone

作　　者：郑明亮 冯鲜[1] 李文霞[1] ZHENG Mingliang;FENG Xian;LI Wenxia(School of Electrical and Mechanical Engineering,Taihu Univereity of Wuxi,Wuxi 214064.China)

机构地区：[1]无锡太湖学院机电工程学院

出　　处：《重庆理工大学学报（自然科学）》2020年第1期156-160,共5页Journal of Chongqing University of Technology：Natural Science

基　　金：国家自然科学基金面上项目(21676031);江苏省高等学校自然科学基金(18KJB460027)

摘　　要：对于水介质旋流器内部单相液体湍流动力学模型,从Navier-Stokes方程组出发,得出了柱坐标形式的速度和压力场控制方程模型。应用李群分析方法,推导出系统常微分方程的允许无穷小对称性和首次积分,更重要的是给出了详细的解析表达式和性质讨论。研究发现旋流器湍流切向速度随半径减小而增大,呈自由涡流特征,同一截面处压力随半径增大而变大。研究结果为考虑边界和初始条件的湍流精确解析解提供了有效途径,也为湍流模型各种数值算法提供了验证。For a single-phase liquid turbulent dynamic model in a water medium cyclone, the governing equations of velocity and pressure fields with cylindrical coordinates are obtained from the Navier-Stokes equations. The Lie group analysis method is applied to derive the allowable infinitesimal symmetry and the first integral of the system’s ordinary differential equations, and more importantly,their detailed analytical expressions and properties are given. It is found that the clipping velocity of the turbulent flow increases with the decrease of radius, which shows the characteristics of free vortex flow, and the pressure increases with the radius increasing at the same section. The content of this paper provides an effective way to obtain the exact analytical solution of turbulence while considering boundary and initial conditions, and it also provides a verification for various numerical algorithms of turbulence models.

关 键 词：旋流器 NAVIER-STOKES方程组 对称性 首次积分 切向速度 

分 类 号：O316[理学—一般力学与力学基础] TD928[理学—力学]