Water hammer protection for diversion systems in front of pumps in long-distance water supply projects

For a water supply system with long-distance diversion pipelines, in addition to the water hammer problems that occur beyond pumps, the safety of the water diversion pipeline in front of pumps also deserves attention. In this study, a water hammer protection scheme combined with an overflow surge tank and a regulating valve was developed. A mathematical model of the overflow surge tank was developed, and an analytical formula for the height of the overflow surge tank was derived. Furthermore, a practical water supply project was used to evaluate the feasibility of the combined protection scheme and analyze the sensitivity of valve regulation rules. The results showed that the combined protection scheme effectively reduced the height of the surge tank, lessened the difficulties related to construction, and reduced the necessary financial investment for the project. The two-stage closing rule articulated as fast first and then slow could minimize the overflow volume of the surge tank when the power failure occurred, while the two-stage opening rule articulated as slow first and then fast could be more conducive to the safety of the water supply system when the pump started up.

Analytical study on water hammer pressure in pressurized conduits with a throttled surge chamber for slow closure

This paper presents an analytical investigation of water hammer in a hydraulic pressurized pipe system with a throttled surge chamber located at the junction between a tunnel and a penstock, and a valve positioned at the downstream end of the penstock. Analytical formulas of maximum water hammer pressures at the downstream end of the tunnel and the valve were derived for a system subjected to linear and slow valve closure. The analytical results were then compared with numerical ones obtained using the method of characteristics. There is agreement between them. The formulas can be applied to estimating water hammer pressure at the valve and transmission of water hammer pressure through the surge chamber at the junction for a hydraulic pipe system with a surge chamber.

Analysis on Shock Wave Speed of Water Hammer of Lifting Pipes for Deep-Sea Mining

Water hammer occurs whenever the fluid velocity in vertical lifting pipe systems for deep-sea mining suddenly changes. In this work, the shock wave was proven to play an important role in changing pressures and periods, and mathematical and numerical modeling technology was presented for simulated transient pressure in the abnormal pump operation. As volume concentrations were taken into account of shock wave speed, the experiment results about the pressure-time history, discharge-time history and period for the lifting pipe system showed that： as its concentrations rose up, the maximum transient pressure went down, so did its discharges; when its volume concentrations increased gradually, the period numbers of pressure decay were getting less and less, and the corresponding shock wave speed decreased. These results have highly coincided with simulation results. The conclusions are important to design lifting transporting system to prevent water hammer in order to avoid potentially devastating consequences, such as damage to components and equipment and risks to personnel.

Water hammer prediction and control:the Green's function method

By Green＇s function method we show that the water hammer （WH） can be analytically predicted for both laminar and turbulent flows （for the latter, with an eddy vis- cosity depending solely on the space coordinates）, and thus its hazardous effect can be rationally controlled and mini- mized. To this end, we generalize a laminar water hammer equation of Wang et al. （J. Hydrodynamics, B2, 51, 1995） to include arbitrary initial condition and variable viscosity, and obtain its solution by Green＇s function method. The pre- dicted characteristic WH behaviors by the solutions are in excellent agreement with both direct numerical simulation of the original governing equations and, by adjusting the eddy viscosity coefficient, experimentally measured turbulent flow data. Optimal WH control principle is thereby constructed and demonstrated.

Study on the Technology of Supplying Water Safely by Long-Distance Pipeline

The extensively built long-distance water transmission pipelines have become the main water sources for urban areas. To ensure the reliability and safety of the water supply, from the viewpoint of overall management, it would be necessary to establish a system of information management for the pipeline. The monitoring, calculating and analyzing functions of the system serve to give controlling instructions and safe operating rules to the automatic equipment and technician, making sure the resistance coefficient distribution along the pipeline is reasonable; the hydraulic state transition is smooth when operating conditions change or water supply accidents occur, avoiding the damage of water hammer. This paper covered the composition structures of the information management system of long-distance water transmission pipelines and the functions of the subsystems, and finally elaborated on the approaches and steps of building a mathematics model for the analysis of dynamic hydraulic status.

Vibration analysis of fluid- structure interaction in water hammer based on transfer matrix method

In consideration of the problem that the effect of conduit structure on water hammer has been ignored in the classical theory,the Poisson coupling between the fluid and the pipeline was studied and a fourteen-equation mathematical model of fluid-structure interaction(FSI)was developed.Then,the transfer matrix method(TMM)was used to calculate the modal frequency,modal shape and frequency response.The results were compared with that in experiment to verify the correctness of the TMM and the results show that the fluid-structure coupling has a greater impact on the modal frequencies than the modal shape.Finally,the influence on the response spectrum of different damping ratios was studied and the results show that the natural frequency under different damping ratios has changed little but there is a big difference for the pressure spectrum.With the decreasing of damping ratio,the damping of the system on frequency spectrum is more and more significant and the dispersion and dissipation is more and more apparent.Therefore the appropriate damping ratio should be selected to minimize the effects of the vibration of the FSI.The results provide references for the theory research of FSI in the transient process.

Attenuating water hammer pressure by means of gas storage tank

The basic equations for computing the volume of gas storage tank were derived from the principles of attenuating water hammer pressure. Verifications using experiments indicate that the proposed equation can provide a fare precision in the predictions. By using the model of solid liquid two phase flow, the gas storage tank, pressure relief valves and slow closure reverse control valves were compared with practical engineering problems, and the functions of gas storage tank in attenuating water hammer pressure were further investigated. [

Flux Vector Splitting Schemes for Water Hammer Flows in Pumping Supply Systems with Air Vessels

To solve water hammer problems in pipeline systems,many numerical simulation approaches have been developed. This paper improves a flux vector splitting( FVS) scheme whose grid is the same as the fixedgrid MOC scheme. The proposed FVS scheme is used to analyze water hammer problems caused by a pump abrupt shutdown in a pumping system with an air vessel. This paper also proposes a pump-valve-vessel model combining a pump-valve model with an air vessel model. The results show that the data obtained by the FVS scheme are similar to the ones obtained by the fixed-grid method of characteristics( MOC). And the results using the pump-valve-vessel model are almost the same as the ones using both the pump-valve model and the air vessel model. Therefore,it is effective that the proposed FVS scheme is used to solve water hammer problems and the pump-valve-vessel model replaces both the pump-valve model and the air vessel model to simulate water hammer flows in the pumping system with the air vessel.

Water Hammer Model of Shock Absorber Throttle Slice

In allusion to easy invalidation of damping valve in vehicle shock absorber caused by the impact from the road surface, the importance of the study of damping valve water hammer pressure is presented. The physical model of damping valve with the circle throttle slice is established. The time for the throttle slice deformation is studied by using the finite software, and the laws that how the structure parameters affect the deformation time are obtained. Combining the theory of water hammer, the water hammer initial and boundary condition of the damping valve is deduced, and the water hammer model of throttle slice is established. The analysis of simulation results indicates that the water hammer pressure amplitude and the amount of water hammer oscillation period can be reduced and the dependability of the valve can be enhanced by modifying the structure parameters and aperture width between slice and valve body.

Analytic study on the optimal control of water hammer waves in pipes

To realize the accurate control of water hammer in pipes by valve stroking, based on basic differential equations of water hammer subjected to initial and boundary conditions, the traveling solution of wave equations in finite region was applied to the linear water hammer problem. With the given velocity function at the valve and the introduction of curve integration independent of integral path, the exact analytic solution of dimensionless water hammer pressure was obtained in the course of valve closing. Based on the definition of eigen wave height, optimal eigen wave height and observation time, the control goal of water hammer pressure and the judgment rule of the optimal eigen wave height were determined, then the optimal velocity function in the calculated example was derived, which can reduce the water hammer pressure maximally. According to this function, a valve closing program was set, and the optimal control of water hammer could be realized.

The Third Invariant Form of Hydrodynamic Equations and Application for Definition of Water Hammer Characteristics in Pipe

There were for a long time two invariant forms of hydrodynamic equations： one was related to coordinate system of references, and the other was versus to measure units of characteristics. These both invariant forms had important roles in the development of theoretical and practical applications of hydro-aerodynamics and related industries. The third invariant form of hydrodynamic equations is one for the dimensions of spaces. For this goal, the hyper quantities （space and physics） are introduced. Then these are created we can easily cover all problems in arbitrary dimensions （3D, 2D, 1D, separate space for liquids or constituent matters）. In particularly, when they are applied to water hammer problem, which is an especially problem, we can receive immediately celerity and pressure of the event.

An Analysis of the Factors Influencing Cavitation in the Cylinder Liner of a Diesel Engine

Avoiding cavitation inside the water jacket is one of the most important issues regarding the proper design of a diesel engine’s cylinder liner.Using CFD simulations conducted in the frame of a mixture multiphase approach,a moving grid technology and near-wall cavitation model,in the present study the factors and fluid-dynamic patterns that influence cavitation are investigated from both macroscopic and mesoscopic perspectives.Several factors are examined,namely:wall vibration,water jacket width,initial cavitation bubble radius,coolant temperature,and number of bubbles.The results show that reducing the cylinder liner vibration intensity can significantly weaken the cavitation.Similarly,increasing the water jacket width is instrumental in avoiding cavitation.Increasing the coolant temperature reduces the microjet velocity related to bubble collapse,while increasing the number of bubbles produces a much larger water hammer pressure that can cause more damage to the cylinder liner.

The pressure field in the liquid column in the tube-arrest method

We have been using the method of tube-arrest as a means of producing transient single cavitation bubble. In the present paper we seek to comprehend the mechanism of production and inquire into the structure of the ab initio pressure field in the arrested liquid column. The generated pressure wave is shown by combining the theoretical analysis with the experimental observation to be a slightly varied version of water hammer. With relatively clean liquid, the magnitude of the tension peak generating the TSB is likely to reach of several millions Pa. It is also shown that the so generated cavitation bubble originating from the gas-containing bulk liquid is in ‘violent’ motion.

Effects of instantaneous shut-in of high production gas well on fluid flow in tubing

As the classical transient flow model cannot simulate the water hammer effect of gas well, a transient flow mathematical model of multiphase flow gas well is established based on the mechanism of water hammer effect and the theory of multiphase flow. With this model, the transient flow of gas well can be simulated by segmenting the curved part of tubing and calculating numerical solution with the method of characteristic curve. The results show that the higher the opening coefficient of the valve when closed, the larger the peak value of the wellhead pressure, the more gentle the pressure fluctuation, and the less obvious the pressure mutation area will be. On the premise of not exceeding the maximum shut-in pressure of the tubing, adopting large opening coefficient can reduce the impact of the pressure wave. The higher the cross-section liquid holdup, the greater the pressure wave speed, and the shorter the propagation period will be. The larger the liquid holdup, the larger the variation range of pressure, and the greater the pressure will be. In actual production, the production parameters can be adjusted to get the appropriate liquid holdup, control the magnitude and range of fluctuation pressure, and reduce the impact of water hammer effect. When the valve closing time increases, the maximum fluctuating pressure value of the wellhead decreases, the time of pressure peak delays, and the pressure mutation area gradually disappears. The shorter the valve closing time, the faster the pressure wave propagates. Case simulation proves that the transient flow model of gas well can optimize the reasonable valve opening coefficient and valve closing time, reduce the harm of water hammer impact on the wellhead device and tubing, and ensure the integrity of the wellbore.

Experimental study on dynamic pipe fracture in consideration of hydropower plant model

In the case of sudden valve closure, water hammer creates the most powerful pressure and damage to pipeline systems. The best way to protect the pipeline system is to eliminate water hammer. The main reasons for water hammer occurrence are valve closure, high initial velocity, and static pressure. However, it is difficult to eliminate water hammer. Water hammer tends to occur when the valve is being closed. In this study, the pipe fracture caused by static water pressure, gradually increasing pressure, and suddenly increasing pressure were compared experimentally in a breaking PVC test pipe. The quasi-static zone, the dynamic zone, and the transition zone are defined through the results of those experiments, with consideration of the fracture patterns of test pipes and impulses. The maximum pressure results were used to design the pipeline even though it is in the dynamic zone.

Analysis of the Presence of Vapor in Residual Heat Removal System in Modes 314 Loss-of-Coolant Accident Conditions Using RELAP5

The Westinghouse Nuclear Safety Advisory Letter NSAL-09-8 investigated the possibility of presence of vapor in RHR （residual heat removal） system in modes 3/4 LOCA （loss-of-coolant accident） conditions. This concerns the Westinghouse standard three-loops plant for which the RHR is the low pressure part of the St （safety injection）. In some cases one or both RHR trains may become inoperable for SI function. As a response to this letter, Westinghouse Electric Belgium is providing RELAP5 analyzes for Westinghouse NSSS （nuclear steam supply system） European plants to assess the thermal hydraulic behavior of the RHR suction piping system for ECCS （emergency core cooling system） initiation events postulated to occur during startup/shutdown operations. Several concerns including condensation induced water hammer and voiding at the RHR pump have been investigated. As a conclusion, the analysis allowed to define the bounding hot leg temperature conditions under which both RHR trains remain safely operable. These bounding conditions are then implemented by the customer in their OPs （operating procedures） to achieve safe operations and successful accident management.

Water hammer in the pump-rising pipeline system with an air chamber

Water hammer following the tripping of pumps can lead to overpressure and negative pressure. Reduction in overpressure and negative pressure may be necessary to avoid failure, to improve the efficiency of operation and to avoid fatigue of system components. The field tests on the water hammer have been conducted on the pump rising pipeline system with an air chamber. The hydraulic transient was simulated using the method of characteristics. Minimizing the least squares problem representing the difference between the measured and predicted transient response in the system performs the calibration of the simulation program. Among the input variables used in the water hammer analysis, the polytropic exponent, the discharge coefficient and the wave speed were calibrated. The computer program developed in this study will be useful in designing the optimum parameters of an air chamber for the real pump pipeline system. The correct selection of air chamber size and the effect of the inner diameter of the orifice to minimize water hammer have been investigated by both field measurements and numerical modeling.

ON BASIC EQUATIONS OF WATER HAMMER

Based on the derivation of the continuity equation of water hammer, the modification coefficient used in the wave speed formula is discussed thoroughly. Mistakes presented in current formulas are analyzed. Finally in this paper a summarizing comment is given on the problem that whether or not the slope term Vsina should be included in the characteristic equations.

THEORETICAL,NUMERICAL AND EXPERIMENTAL STUDY OF WATER HAMMER IN PIPE SYSTEM WITH COLUMN SURGE CHAMBER

A new kind of governing equations for water hammer based on the elasticcolumn theory was proposed and adopted to analyse water hammer phenomenon in the pipe system with avertical column surge chamber and water level fluctuation in the surge chamber during pressuretransient. The wrongness existing in the classical governing equations for water hammer wasanalysed. A typical reservoir-valve pipe system was chosen as an example to verify the new governingequations numerically and experimentally. The finite difference method based on the method ofcharacteristics was used to solve numerically the nonlinear characteristic equations. The temporalevolutions of transient volume flux and head and of water level fluctuation for various surgechamber configurations were worked out, assuming that the air in the surge chamber are compressible.The relevant experiment was conducted to verify the new governing equations and numerical method.The numerical and experimental results show that the new governing equations are valid and theconventional assumption that the pressure head at the base of a surge chamber equals that of thestatic head above it during pressure transient is not always valid. The surge chamber generallyreises the period of transient pressure wave in pipe system, reduces the maximum pressure envelopeand lifts the minimum envelope substantially. The water level fluctuation in the surge chamber wasnumerically and experimentally observed. Increasing the size of the surge chamber and/or decreasingthe initial air pressure in the surge chamber enhance the effectiveness of the surge chamber insuppressing pressure wave.

ANALYSIS OF STATE-CHANGING WATER HAMMER IN A LONG PIPE

Pressure wave propagation along a pipe attached with an activepressure-controlling system at an end was described by an unsteady state-changing motion of thepressure wave fronts, in order to study the interaction among successive waves caused by successivecontrolling spillovers with the consideration of liquid compressibility due to high head. A modelfor water hammer propagation was established by using the continuity, momentum, and energyequations. The influence of the wave interactions on the pressure suppression was analyzed. Testingverifications were conducted with a 2575m length and 776m head penstock in hydro-power station. Thecomputed results are in good agrement with the tested ones.