Study On The Numerical Simulation Model Of Water Hammer In Four-way Pipe With TVD Scheme

In view of the rapid development of the national economy and the realistic need of the water resources shortage in China,using pipe network to supply water has become an important way to solve the contradiction between water supply and demand now.Pipe network system is facing some security issues in different transient flow conditions,water hammer phenomenon is one of the important factors need to be considered during the pipe network system planning design and operation management.In recent years,water industry researchers are keen to use a variety of numerical schemes to explore the transient flow problems in simple pipeline,most of them focus on the prediction of catching water pressure peak and use the traditional quasi-constant friction hypothetical water hammer equation.Although this approach can be a conservative estimate of instantaneous water hammer pressure,it is obviously powerless to capture of the decay process accurately,and can easily lead to a waste of resources.In this paper,the necessity and feasibility of numerical simulation of water hammer process with TVD scheme are studied in depth,expanding the research field of water hammer simulation with TVD scheme.At the same time,the influence of unsteady friction term processing on the water hammer simulation accuracy is analyzed,developing new ideas for the follow-up research.The main contents include the following aspects:1.We applied Sweby's TVD scheme to the water hammer model of pipe network in Wei Chuang's study,simulating the extreme value of water pressure and the attenuation process at the end of the main pipe as well as branch pipe.Comparing with the Characteristic Method,Lax-Friedrichs scheme,Lax-Wendroff scheme,MacCormack scheme and experimental data,the results indicated that TVD scheme can capture the peak of the water pressure with the highest accuracy,the relative error can meet the project needs and the simulated water hammer decay process was in good agreement with the measured value.For the capture of maximum water hammer pressure,the Characteristic Method was second only to the effect of TVD scheme,the first-order LF scheme simulation had a lowest accuracy;the process of water hammer simulation with the four schemes had a considerably slow attenuation,not match the actual situation.This proves the feasibility and superiority of TVD scheme to simulate the water hammer process.2.The influence of the valve closing characteristic on the water hammer process was analyzed quantitatively.The TVD scheme was used to simulate the change of water hammer pressure at four different valve closing modes.Analysis results showed that:when the closing time was constant and in terms of the maximum water hammer pressure and the attenuation speed,the two-stage straight-line closing mode and the deceleration curve closing mode were equivalent,and the straight-line closing mode and the acceleration curve closure produced larger water hammer pressure and were accompanied by violent and prolonged fluctuation process.And then we studied the impact of the combination of valve closing modes on water hammer process,and found that in four-way pipe,the combination of two valves straight off at the same time generated the smallest water hammer pressure and the fastest attenuation,no intense irregular water hammer oscillation regardless of the main pipe or branch.The two valves instantaneous closure simultaneously generated the maximum pressure and attenuated quite slowly,and the water hammer wave was extremely intense.3.Based on hydraulic system planning and monitoring and the need for improving water hammer simulation accuracy in the study on inverse problem of transient flow,the unsteady friction was introduced into the basic differential equations of water hammer,and the water hammer strictly conservative equation considering the IAB empirical friction model was deduced for the first time,applied to the model test and engineering example-the Alashan hydropower station.The results were compared with the experimental data,the conventional TVD scheme and the Characteristic Method considering the unsteady friction.The results showed that:The TVD scheme with unsteady friction model could capture the entire attenuation and distortion process of water hammer wave peak pressure in each cycle with higher accuracy,and the deviation of numerical simulation had no increasing trend over time.Wherein the capture error of each cycle peak pressure was less than 3% and phase shift was no more than 0.5 radian.In view of the error of time-consuming between the model and traditional model is not obvious,the model has a good potential in engineering application as well as value in research.