非稳定流输送管道的耦合振动

Coupled Vibration of Piping System Conveying Unsteady Flow

以Timoshenko梁模型为基础,通过连续方程和动量方程建立了非稳定流输送管道的耦合振动非线性偏微分方程组,这些偏微分方程通过管壁-液体接触面的力平衡、法向速度协调方程以及流体质量守恒和动量守恒而完全耦合。耦合包括管道与液体之间的摩擦耦合、系统轴向振动与横向振动之间的耦合、管道径向与轴向的Poisson耦合。以该模型为基础分别得到了一次简化模型和用于预测输液管道流固互动现象的扩展水锤4-方程模型。分别采用一次简化模型和4-方程模型对一实验进行仿真,并与实验结果进行了比较,表明一次简化模型的仿真结果比4-方程模型更能反映耦合的影响。

A set of coupled nonlinear partial differential equations of motion for the piping system conveying unsteady flowing fluid were developed through the continuity and momentum equations of unsteady flow based on Timoshenko beam theory. The partial differential equations were fully coupled through the equilibriums of contact forces, the normal compatibility of velocity at the fluld-pipe interface,and the conservation of mass and momentum of the transient fluid. The coupling included friction coupling of pipe wall to fluid, coupling of axial to transverse vibration, Poisson coupling of radial to axial vibration. A slightly-simple model was derived based on present model,and the four- equation model of extension water- hammer applied to predict the phenomenon of fluid- structure interaction（FSI） of piping conveying fluid was derived by further simplification of the present model. Comparisons between simulations and results of a test from literature show that the slightly-simple model reflects the coupling influence better than the four-equation model.