基于变分理论的压力管道内水体弹性模型研究

Study on elastic model of water flow in pressurized pipeline based on variation theory

在水电站水机电系统振动特性和稳定性研究中,需要采用不同阶数的弹性模型来描述不同长度的压力管道内水体的动态特性,常用的刚性模型或不易解耦的低阶弹性模型在应用上存在一定的局限性。基于泛函变分理论和Ritz-Galerkin近似,从水力振动的基本方程出发,推导出适合于水电站稳定性分析和输水系统振动特性研究、并易于解耦的压力管道内水体弹性模型,该模型以压力管道内水体的各阶振荡流量为状态变量,能较准确反映相应的各阶振荡特性。

In the study of vibration and stability of the hydraulic-mechanical-electrical system, the elastic model with different order is needed to describe the hydraulic characteristic of water flow in pressurized pipeline with different length, while the stiff model or traditional elastic models with lower order is difficult to be deeoupled and limited in application. Based on the variation theory and Ritz-Galerkin approximation a linear elastic model of water flow in pressurized pipeline, which is easy to be decoupled and applied in vibration and stability study, is deduced. Furthermore, the vibration modes of water flow in pressurized pipeline are presented with corresponding ordinary differential equations by means of decoupling.