泵站水锤的波追踪计算方法

推导了波追踪法求解水泵-管道系统水锤和断流弥合水锤的方程，讨论了波追踪法和特征线法在理论、求解过程和计算精度上的异同。经计算得到的水泵过渡过程参数和断流弥合处参数的变化规律表明，两种算法的理论本质上是一致的，但波追踪法直接计算压力波（与初始值的水头差值）；不考虑管道摩阻损失时，两者的计算结果完全一致，表明文中提出的针对泵站和断流弥合处的方程和边界条件是正确的；而考虑摩阻时，由于对摩阻项处理方法的差异，导致两者计算结果略有差异，两者相对差值小于0.3%，两种算法具有相同计算精度；计算断流弥合处的瞬变参数变化时，得到的最大值和最小值相同。对于复杂管路或管网系统，波追踪法可直接依据泵站管道的边界条件计算管道内的水力过渡过程，无须采用数值算法，计算效率相较于特征线法提高。

Wave tracing method for calculation of water hammer in pump stations

A wave tracking method (WTM) for hydraulic transients in a pump-pipe system is derived to solve the equations of water hammer and its bridging in the water column separation case; similarities and differences between this method and the Eulerian fixed-grid method of characteristic (MOC) are compared and discussed in theory, solving procedure, and calculation accuracy. Calculations in two study cases show that theories of the two methods are the same fundamentally but WTM directly calculates the pressure wave (plus head differences in the initial value). WTM calculations are completely consistent with MOC when friction loss is not considered, indicating our equations, boundary conditions, and bridging method for the system with column separation are effective and satisfactory. Even in the cases of friction loss considered, a difference less than 0.3% is revealed between the two methods that share virtually the same accuracy. This slight difference is caused by the treatment of the friction loss term. And both share the same max and min values of transient parameters for water column separating and bridging. For a large-scale pipeline or pipe network system, WTM can directly calculate its hydraulic transients from the boundary conditions, with no need of the numerical algorithms as adopted by MOC, thus enjoying a higher computational efficiency.