有压管道水击波动过程及优化控制的解析研究

为了实现阀调节对有压管道水击过程的精确控制,获得水击波动过程的解析解很有意义。该文在详细分析水击基本微分方程组及初边值条件的基础上,将波动方程在有限区间内的行波解应用于线性水击波动问题中。通过给定阀门处速度变化规律,引入曲线积分与路径无关条件,得到了阀门关闭过程中管道内无因次水击压强的精确解析解。应用Ritz法求解泛函极值,得到了使管道阀门处峰值压强为最小值时所对应的速度变化及相应的关阀规律。以此构建程序控制,就可最大限度地削减水击压强,以求通过阀门来实施对水击过程的主动控制。

THE ANALYTIC RESEARCH ON THE WAVE PROCESS AND OPTIMAL CONTROL OF WATER HAMMER IN PIPES

To realize the accurate control of water hammer process in pipes by valve stroking, it is important to obtain the analytical solution of the wave process of water hammer. Based on the analysis of the basic differential equations and the initial and boundary conditions of water hammer, traveling wave solution in finite domain is applied to the linear water hammer. Giving the velocity change relationship at the valve and using the theorem of integral curve independent of path, the accurate analytical solution of the dimensionless pressure is obtained in the valve closing process. Through solving extremum of the functionals by Ritz method, the rule of the velocity change and the corresponding rule of valve closing, which minimize the peak pressure of pipes at the valve, can be obtained. By constructing the control program on the valve closing, the water hammer pressure can be reduced effectively, and the active control of water hammer by regulating the valve can be realized.