圆外区域Stokes流的速度场研究  

Research on Velocity Solutions of Stokes flow in Exterior Circular Region

作　　者：彭维红[1] 董正筑[1] 曹国华[1] 赵慧明[1] 

机构地区：[1]中国矿业大学理学院,江苏徐州221116

出　　处：《中国矿业大学学报》2008年第3期422-427,共6页Journal of China University of Mining & Technology

基　　金：国家自然科学基金项目(50574089);教育部新世纪优秀人才支持计划项目(NCET-06-0475)

摘　　要：以均质不可压缩低雷诺数牛顿流体为研究对象,根据多连体区域中的速度和应力单值条件,推导出满足圆外区域Stokes方程组的解所具有的复变函数表达式的形式.并将边界上的速度函数展开为罗朗级数,与复速度函数的罗朗级数表达式对比,确定罗朗级数的各系数,再利用傅立叶级数和卷积的几个公式进行计算,求得圆外区域只与边界速度有关的Stokes问题的边界积分公式.最后利用所得边界积分公式研究了内边界有孔口的圆域外部Stokes流的速度分布,其值在无穷远处均趋于零,速度变化趋势与CFD软件数值计算的结果进行对比,两者吻合.Aiming at an incompressible Newton flow at low Reynolds numbers, which is continuous, the analytical functions for the Stokes problem of exterior circular region were deduced under single value conditions of the velocity and stress in multi-connectivity region, which satisfy the complex functions of the Stokes equations＇ solution. Then expand the velocity functions on the boundary for the Stokes problem of exterior circular domain into Laurent series, compare them with Laurent series of the complex velocity functions, and make use of some for- mulas in Fourier series and convolutions, the boundary integral formula can be confirmed related to boundary velocity for outer circle Stokes problem. Finally, the boundary formula is used to study the velocity distributions of stokes flow in Exterior Circular Region with a cavity in its inner boundary, the velocity value are coming to zero in the infinite domain; and it is computed numerically by CFD software, the obtained velocity distributions suggest that they are uniform.

关 键 词：STOKES问题 速度函数 傅立叶级数及卷积 边界积分公式 

分 类 号：O352[理学—流体力学]