Research And Application Of Wave Tracing Method To Calculate Water Hammer In Pumping Station

Pumping station engineering is widely used in the fields of cross-basin water transfer,urban water supply,and agricultural irrigation.The frequent occurrence of hydraulic transitions during the operation of pumping stations is the main threat to the safety of pumping stations and the stable operation of water pipelines.Carrying out accurate simulation and prediction of the hydraulic transition process,and taking effective protective measures to avoid or minimize the adverse effects of water hammer are of great significance to the safety application of pumping station engineering.This paper establishes a mathematical model of wave tracing method applied to water hammer calculation in pumping stations,analyzes the similarities and differences between wave tracing method(WTM)and the Eulerian fixed-grid method of characteristic(MOC)in calculating water hammer,and verifies the accuracy of this model with field experimental data.The main results are as follows:First of all,based on the theory of wave tracing method,the application model of wave tracing method on various boundary conditions is established,and the wave tracing method is derived to solve the water hammer equation of the pump-pipe system,and the Suter algorithm and the wave tracing equation are combined to solve the pump Boundary conditions,in addition,through the law that the pressure inside the cavity is strong and small when the cutoff cavity is generated and the water hammer wave needs to propagate in the continuum medium,the equation of the cut-off to bridge the water hammer is derived.Secondly,the wave tracking method(WTM)of hydraulic transients and the Eulerian fixed-grid method of characteristic(MOC)to solve the equations of water hammer and water column separation to bridge water hammer in the pump-pipe system.The similarities and differences between WTM and the MOC are discussed in theory,solving procedure and calculation accuracy.The calculating results of two cases show that the theories of the two algorithms are the same in fundamental,but the wave tracking method directly calculates the pressure wave(the head difference with the initial value);The calculating results of WTM are completely consistent with the MOC results when friction loss is not considered;However,when considering the friction,the relative difference between the results of two algorithms is less than 0.3%,which can be considered two methods possess the same calculating accuracy.The slight difference is caused by the treatment of the friction loss term.The maximum and minimum values of the water column separating and bridging transient history calculated by WTM and MOC are the same.Compared with MOC,WTM calculate the hydraulic transition process in the pipeline based on the boundary conditions directly,without using numerical algorithms.The calculating efficiency of WTM is higher than MOC,especially for complex pipeline or pipe networks.Finally,the wave tracing method(WTM)is used to simulate and calculate the accidental pumping water hammer,the normal pumping water hammer,and the start water hammer of the Nanwuniu secondary pumping station to study the flow and pressure changes in the pipeline.The change trend of the various parameters calculated by the wave tracking method is consistent with the experimental results,and the calculation has high accuracy,which verifies the accuracy of the calculation model in this paper,and lays the foundation for the wave tracking method to be applied to the water hammer calculation of pumping stations.