水锤激励下黏弹性输流直管轴向振动响应特性

Axial vibration response of the viscoelastic fluid-conveying straight pipe induced by water hammer

针对水箱-管道-阀门系统,基于考虑了管壁黏滞作用的输流直管轴向振动流固耦合四方程模型,利用有限差分法和隐式欧拉法,配合牛顿-拉夫逊方法,研究弹性和黏弹性管道在水锤激励下的轴向耦合振动响应特性,对比分析了泊松耦合和连接耦合对管道振动响应特性的影响,并与前人的数值结果和实验成果对比,吻合良好。结果表明:两种耦合作用对管道轴向振动影响不容忽视;只考虑泊松耦合时,管内脉动压力水头增大明显,振动加快;同时考虑泊松耦合和连接耦合时,振动更加复杂,压力水头响应曲线更加不规则;黏弹性管道与弹性管道轴向振动响应特性差别明显,黏弹性管道脉动压力水头会随时间迅速衰减,且相位较弹性管道延迟,而弹性管道脉动压力水头无衰减趋势。

In this paper, a numerical model based on the finite difference method, the implicit Euler method and the Newton- Raphson method are proposed to study the axial-coupling vibration response of the elastic and viscoelastic pipes caused by water hammer. In the considered system of reservoir-pipeline-valve, the mathematical model of axial vibration in fluid-conveying straight pipes concerning the viscoelasticity effect of pipe-wall is the hyperbolic four-equation model. Meanwhile, considering the Poisson coupling and the junction coupling in the pipeline, the numerical results are in good agreement with other numerical and experimental solutions. It indicated that both of two coupling effects on the axial vibration of the pipeline cannot be ignored. When only Poisson coupling is considered, the fluctuation of pressure head increases obviously and the vibration is accelerated. On the other hand, while the Poisson coupling and the junction coupling are considered simultaneously, vibration become more complex and the response curve of pressure head is more irregular. Moreover, the distinct differences in response characteristics of axial vibration were found between the viscoelastic pipe and the elastic pipe. The pulsating pressure head of viscoelastic pipe will decreases rapidly with time, and the phase is delayed with respect to elastic pipe, while the pressure head of the elastic pipe has no attenuation tendency.