端部旋转的圆柱形容器内的Stokes流  

Stokes Flow in Cylindrical Containers With Rotating Ends

作　　者：王尕平 刘竟慧 WANG Gaping;LIU Jinghui(School of Civil Engineering,Dalian Jiaotong University,Dalian,Liaoning 116028,P.R.China)

机构地区：[1]大连交通大学土木工程学院,辽宁大连116028

出　　处：《应用数学和力学》2023年第1期52-60,共9页Applied Mathematics and Mechanics

基　　金：国家自然科学基金(11202043)。

摘　　要：该文以端部旋转的圆柱形容器内的Stokes流为研究对象,根据流动的特点,将轴向坐标模拟为时间,则问题归结为Hamilton对偶方程的本征值和本征解问题.利用本征解空间的完备性和本征解之间的共轭辛正交关系,给出了问题解的展开形式,并建立了展开系数的数值求解方法.采用该方法研究了单端旋转、两端以相同或相反角速度旋转时不同外形比(容器的高度与半径之比)时圆柱形容器内流动速度和应力的分布情况,展示了不同边界条件下流场的一些特点.The Stokes flow in cylindrical containers with rotating ends was studied.Based on the characteristics of the flow,the problem was reduced to the eigenvalue and eigensolution problem of Hamiltonian dual equations with the axial coordinate simulated as the time scale.By means of the completeness of the symplectic eigensolution space and the adjoint symplectic orthogonality relationship between the eigensolutions,the expansion of the solution to the problem was obtained,and the numerical method for calculating the expansion coefficients was given.In the cases of one-end rotating,two-end rotating at the same or opposite angular velocity,the velocity and stress distributions of the flow in the cylindrical containers with different aspect ratios(of the length to the radius),were investigated.The velocity and stress distributions,and the characteristics of the flows under different boundary conditions were revealed.

关 键 词：STOKES流 HAMILTON 旋转端部 圆柱形容器 

分 类 号：O357.1[理学—流体力学]