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[en] Numerical solution of water hammer is presented in this paper. The contribution is focused on water hammer in the area of low pressure, which is completely different than high pressure case. Little volume of air and influence of the pipe are assumed in water, which cause sound speed change due to pressure alterations. Computation is compared with experimental measurement.
[en] Understanding water hammer is very important to the prevention of excessive pressure build-up in pipelines. Many researchers have studied this phenomenon, drawing effective solutions through the time- and frequency-domain approaches. For the purposes of enhancing the advantages of the frequency-domain approach and, thereby, rendering investigations of the dynamic characteristics of pipelines more effective, we propose partial fraction expansion of the transfer function between the unsteady flow source and a given section. We simulate the proposed approach using a vibration element inserted into a simple pipeline, deducing much useful physical information pertaining to pipeline design. We conclude that locating the resonance of the vibration element between the first and second resonances of the pipeline can mitigate the excessive pressure build-up attendant on the occurrence of water hammer. Our method of partial fraction expansion is expected to be useful and effective in analyses of unsteady flows in pipelines
[en] This paper presents “contribution to sample variance plot”, a natural extension of the “contribution to the sample mean plot”, which is a graphical tool for global sensitivity analysis originally proposed by Sinclair. These graphical tools have a great potential to display graphically sensitivity information given a generic input sample and its related model realizations. The contribution to the sample variance can be obtained at no extra computational cost, i.e. from the same points used for deriving the contribution to the sample mean and/or scatter-plots. The proposed approach effectively instructs the analyst on how to achieve a targeted reduction of the variance, by operating on the extremes of the input parameters' ranges. The approach is tested against a known benchmark for sensitivity studies, the Ishigami test function, and a numerical model simulating the behaviour of a water hammer effect in a piping system.
[en] Effects of air vessel on water hammer process in a pumping station with high-head were analyzed by using the characteristics method. The results show that the air vessel volume is the key parameter that determines the protective effect on water hammer pressure. The maximum pressure in the system declines with increasing air vessel volume. For a fixed volume of air vessel, the shape of air vessel and mounting style, such as horizontal or vertical mounting, have little effect on the water hammer. In order to obtain good protection effects, the position of air vessel should be close to the outlet of the pump. Generally, once the volume of air vessel is guaranteed, the water hammer of a entire pipeline is effectively controlled
[en] The steam generators and associated feedwater piping designed by Babcock and Wilcox have been relatively free of waterhammer occurrences. Nevertheless, during startup testing of Duke Power Company's Oconee Nuclear Station in December, 1971, waterhammer did occur in the main feedwater lines which prompted a revision to the startup procedures. The sequence of events which took place prior to and following the waterhammer event is presented
[en] The waterhammer phenomena of check valves is analysed. The solution of differential equation governing the moving of valve plate is derived. The formula of calculating dimensionless number J(t) of valve openning is obtained and the waterhammer pressure wave on the chek valve is calculated by means of characteristic lines. The result showed that the peak value of the only one third of that on the hanging check valve. Increasing limit value of plate angle φ0 and moment of inertia J on the valve plate can result in the decreasing of waterhammer pressure wave peak and can relax vibration of the valve plate. The computational results of waterhammer wave conform to that of the experiment
[en] Improved analytical models have been proposed that can predict the lower and upper limits of the water hammer region for given flow conditions by incorporation of recent advances made in the understanding of phenomena associated with the condensation-induced water hammer into existing methods. Present models are applicable for steam-water counterflow in a long horizontal pipe geometry. Both lower and upper bounds of the water hammer region are expressed in terms of the 'critical inlet water flow rate' as a function of axial position. Water hammer region boundaries predicted by present and typical existing models are compared for particular flow conditions of the water hammer event occurred at San Onofre Unit 1 to assess the applicability of the models examined. The result shows that present models for lower and upper bounds of the water hammer region compare favorably with the best performing existing models
[en] The dynamic fluid-structure interaction (FSI) during hydraulic transient is known to be of special importance for flexible or movable pipeline system. Some kinds of FSI effects can be observed however even for relatively rigidly supported pipeline. Such effects, not anticipated by the classic waterhammer theory, were identified during experiments on waterhammer phenomenon conducted at a laboratory rig in the Szewalski Institute of Fluid-Flow Machinery of the Polish Academy of Sciences in Gdansk (IMP PAN). Additional pressure oscillations of higher frequencies observed during experiments were supposed to be the result of dynamic fluid-structure interaction. The problem of hydraulic transient with FSI effect taken into account has been of IMP PAN interest for some time and the four equation model of the phenomenon was applied and implemented at a computer program. A method of characteristics with time marching procedure and a 'wave method' for solving the resulted finite difference equations were used at the algorithm. Selected measured and computed pressure records during the transient are presented in the paper. The analyses of the results allows to conclude that the additional effects observed at experiments were really produced by FSI effect (Poisson coupling). Some discrepancies between experimental and numerical results exist however and the analysis and attempt to explain the causes of them are proposed as well.