径向边界驱动下蠕流问题的仿真  

Calculation and Simulation of Creeping Flow in Wedge Cavities Driven by Radial Boundary Walls

作　　者：王艳[1] 邓子辰[1] 高小科[1] 

机构地区：[1]西北工业大学力学与土木建筑学院,陕西西安710072

出　　处：《计算机仿真》2011年第1期396-399,共4页Computer Simulation

基　　金：国家自然科学基金(10902089);西北工业大学基础研究基金(JC200812)资助项目

摘　　要：在流体力学优化算法的研究中,环扇形域是各种旋转设备的典型横截面,针对环扇形空腔内蠕流的研究问题,传统的求解方法是在拉格朗日体下求解拉普拉斯方程、泊松方程或双调和方程,使得高阶微分方程求解困难,同时难以满足混合边界条件问题。在辛体系下,针对侧边为非齐次流速条件的扇形域内蠕流问题提出了辛算法。以仿真径向r方向为时间系,由流速和其对偶向量组成全状态变量,将控制方程写成辛对偶形式,在辛空间下变量应用分离变量法及辛本征向量展开法,求解出对应于齐次方程和齐次边界条件的本征值和本征解,并求解出非齐次边界条件对应的特解。证明上述算法不仅将微分方程降阶,而且边界条件的处理也比较简单易行。计算结果验证了辛方法解决此类问题的有效性。The creeping flow in a wedge shaped geometry is commonly encountered in a revolving mechanical device. The traditional solution is to solve the laplace equation, the possion equation or the biharmanic equation in ,the Lagrange system, which will lead to the difficulities of solving the high order partial differential equations and treating the mixing .boundary conditions The symplectic analytical method is introduced for, solvhag problem of the creeping flow in wedge cavities driven bythe radial boundary walls. Simulating radial coordinate r as time dual variables of velocities are found and the Hamiltonian.function is achieved by the Legendre transformation. Taking veloeities and dual variables as the basic variables, the Hamiltonian formulation can be introduced into creeping flow probiems and a direct method is put forward. The solutiona the problem are composed of a general solution and a particular solution. In the ymplectw space the solution be solved via the method of separanon of variables and＇ expansion of eigenfiunctions, whilst the particular solution can be obtained by solwng the homogeneous, equatmn and the non-homogeneous boundary conditions. Numerical results show that the symplectie method is effec tive for creeping flow problems in the wedge cavities.

关 键 词：环扇形域 径向边界驱动 蠕流 辛本征解 

分 类 号：O357.1[理学—流体力学]