层流和紊流流态下对输流管道运动方程的修正  

Equation of motion for vibrating pipes with laminar and turbulent flow profiles

作　　者：郭长青[1,2] 张楚汉[1] 

机构地区：[1]清华大学水利水电工程系,水沙科学与水利水电工程国家再点实验室,北京100084 [2]南华大学数理学院,衡阳421001

出　　处：《清华大学学报（自然科学版）》2011年第6期760-763,共4页Journal of Tsinghua University(Science and Technology)

基　　金：国家自然科学基金资助项目(50375070)

摘　　要：为了考虑实际流体流速非均匀分布对输流管道振动和稳定性的影响,对目前广泛采用的基于理想流体模型的输流管道运动方程进行了修正。对圆管层流,由抛物线分布律得到的离心力项流态修正系数为1.333;对圆管紊流,由指数律和对数律得到基本一致的结果:流态修正系数随Reynolds数的增大而减小,在Re=103—105范围内,流态修正系数为1.018—1.053。与理想流体情况相比,层流和紊流流态下管道的临界流速均有所下降。发散失稳临界流速降低比率分别为13.4%和0.9%—2.5%。流态对颤振失稳临界流速的影响更大,层流下的降低比率可达36%。通过引入等效流速和等效质量2个新概念,可将不同流态下的输流管道问题用理想流体流动下的运动方程进行求解。Non-uniform flow velocity distributions occur in real fluids in fluid-conveying pipes.The widely used equation of motion for fluid-conveying pipes,based on ideal flow was modified to account for non-ideal effects.For laminar flow in a circular pipe,the parabolic profile gives a flow profile modification factor for the centrifugal force term of 1.333.For turbulent flow in a circular pipe,both the exponential and logarithmic velocity profiles give similar results with the modification factors decreasing with increasing Reynolds number and lying in 1.018—1.053 for Re=103—105.The critical flow velocities for divergence in these cases were found to be 13.4%,0.9%—2.5% lower than for ideal fluid flow,while those for flutter are even lower,36% for the laminar flow profile.An equivalent flow velocity and an equivalent mass were developed for vibrating pipe flow problems with different flow profiles for solutions using the equation of motion for ideal fluid flow.

关 键 词：关键词:流固耦合 层流 紊流 输流管道 运动方程 临界流速 

分 类 号：O353.1[理学—流体力学]