Effect Of Unsteady Friction And Valve Closing Law On Water Hammer

Water hammer phenomenon,which is one of the important factors in operation of water transportation system and caused by valve closed suddenly,has a great influence on pipeline and even cause pipeline system burst damage.Hence,the research on the rules of water hammer pressure transmission and prevention measures in the safe operation of water transportation system is one of the major problems.Recently,with the development of technologies such as sensors and liquid rocket engine,people begin to get the variation and optimization aimed to enhance the operation reliability of the engine.It is known that the process of water hammer is complex physical,which is affected by many factors,such as valve type,closed form and pipe material.Therefore,it is of great significance to study the effect of various factors in the water hammer in order to control of water hammer precisely.Now,It is studied by two aspects of unsteady friction and valve closing law.In this dissertation,based on the equation of motion and continuity is established using the characteristic method traditional water hammer calculation model.In the view of improving the calculation accuracy,the different accuracy model of dealing with the friction is discussed;The different corresponding to the characteristic line equation of the complex boundary conditions is introduced;The model is verified,and the results show that it can count the main parameters of water hammer such as maximum and minimum stress value.In order to study the accurately water hammer pressure,it is necessary to introduce a more accurate unsteady friction model to simulate transient flow.In this study,two different unsteady wall friction models are used.For the first one,the unsteady wall friction model developed by Brunone is employed and method of characteristic is used to solve the governing equations numerically.While,another way of introducing unsteady wall friction is to use boundary layer theory,then an analytical solution for water hammer pressure can be obtained by using Laplace transform method;Two models are verified and compared with the experimental results.The results show that not only the maximum value of pressure but also the rate of attenuation and phase changes can be well captured by the two models developed.By using different value of k,it is found that the effects of coefficients in unsteady friction model on water hammer pressure variation are considerable.After obtaining accurately pipeline water hammer pressure,to make the hydraulic transients can be run in accordance with the specified manner,it should be controlled and optimized.The piecewise model is verified by the mature method of characteristic.And the results indicate that it is correct and widely used.Then it is summarized the relationship between the valve closing time and the maximum pressure value and proposed a series of reasonable closing time of the valve under four flow characteristics.Derivative of analytical solution can obtain the extreme value and corresponding speed of value when the pipe end's pressure is minimum,to achieve the purpose of the active control water hammer transient process.