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.

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. [

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.

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.

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.

Mitigating check valve slamming and subsequentwater hammer events for PPFS using MOC

The method of characteristic(MOC) was adopted to analyze the check valve-induced water hammer behaviors for a Parallel Pumps Feedwater System(PPFS) during the alternate startup process.The motion of check valve disc was simulated using inertial valve model.Transient parameters including the pressure oscillation,local flow velocity and slamming of the check valve disc etc.have been obtained.The results showed that severe slamming between the valve disc and valve seat occurred during the alternate startup of parallel pumps.The induced maximum pressure vibration amplitude is up to 5.0 MPa.The scheme of appending a damping torque to slow down the check valve closing speed was also performed to mitigate of water hammer.It has been numerically approved to be an effective approach.

Numerical Simulation for Two-Phase Water Hammer Flows in Pipe by Quasi-Two-Dimensional Model

The features of a quasi-two-dimensional( quasi-2D) model for simulating two-phase water hammer flows with vaporous cavity in a pipe are investigated. The quasi-2D model with discrete vaporous cavity in the pipe is proposed in this paper. This model uses the quasi-2D model for pure liquid zone and one-dimensional( 1D) discrete vapor cavity model for vaporous cavity zone. The quasi-2D model solves two-dimensional equations for both axial and radial velocities and 1D equations for both pressure head and discharge by the method of characteristics. The 1D discrete vapor cavity model is used to simulate the vaporous cavity occurred when the pressure in the local pipe is lower than the vapor pressure of the liquid. The proposed model is used to simulate two-phase water flows caused by the rapid downstream valve closure in a reservoir-pipe-valve system.The results obtained by the proposed model are compared with those by the corresponding 1D model and the experimental ones provided by the literature,respectively. The comparison shows that the maximum pressure heads simulated by the proposed model are more accurate than those by the corresponding 1D model.

Water hammer in coarse grained solid liquid flows in hydraulic hoisting for ocean mining

The particles of polymetallic nodules in hydraulic hoisting flows that are used for mining in deep sea are rather coarse, therefore their flow velocity is smaller than that of the surrounding water. The characteristics of solid liquid flows such as their density, concentration, elastic modulus and resistance were discussed. The wave propagation speed and the continuity and momentum equations of water hammer in coarse grained solid liquid flows were theoretically derived, and a water hammer model for such flows was developed.

Encapsulated Water Hammer: Theoretical/Experimental Study

Water hammer phenomenon involves the transformation of kinetic energy in pressure energy, this transformation occurs as the fluid conditions change inside the pipe in quite a short time. Industry requires to affront frequent flow interruptions in pipe systems due to the closing of valves or stopping of pumping equipment. This phenomenon can initiate serious damages like destruction of the pipe system involving leakage of the working fluid to the environment. If the system operates in a fragile environment, as in cold regions, concern about the consequences of leakage increases due to the variation of physical properties of fluid as well as the pipe material as a function of the temperature. Water hammer effects can be controlled focusing efforts on reducing the pressure increment that takes place once the phenomenon is presented. Some methods try to reduce the time of closure or the rate of change before the closure using special valves, others install additional elements to absorb the pressure surge and dissipate energy, others install relief valves to release the pressure, and others try to split the problem is smaller sections by installing check valves with dashpot or non-return valves. Splitting the pipeline into shorter sections is often used to help preventing the pipeline length of water falling back after a pump stops. In this paper the numerical results of maximum and minimum pressure values at both ends of a closed section are compared to experimental data. The numerical results follow the experimental trends.

基于Bently-Hammer软件的长距离输水管道水锤防护模拟

基于Bently-Hammer软件对某实际工程中长距离输水系统进行建模,通过实际运行中的不同工况,模拟突发事件在管道与水泵间产生的水锤影响,同时针对系统内突发事件增加液压气动罐、缓闭止回阀等水锤消除措施加以改进,为实际工程提供有效抑制水锤破坏的技术保障。

基于Bentley Hammer的长距离有压管道输水工程的水锤防护研究

【目的】在长距离有压管道输水工程中,因管道内部水流条件复杂而容易产生水锤现象,不仅会影响水流正常输送,还可能导致管道破裂。因此,有必要进行长距离有压管道输水工程的水锤防护研究。【方法】基于台前县城乡供水一体化南水北调配套工程,通过Bentley Hammer软件,在最不利工况下分别建立三种数值模拟模型:无防护措施、加装复合式高速进排气阀水锤防护、气囊式空气罐和复合式高速进排气阀,进行联合水锤防护,对以上三种情况进行水力过渡过程数值模拟分析,研究复合式高速进排气阀与气囊式空气罐联合防护时的水锤防护效果以及气囊式空气罐的防护能力与预设压力和罐体体积之间的关系。【结果】结果表明:复合式高速进排气阀和气囊式空气罐可以很好地消除管道内水锤带来的危害,气囊式空气罐防护能力随着罐体体积和预设压力的增大而增强,罐体体积对其防护能力影响更显著。【结论】选择合理的罐体体积和预设压力可以使水锺防护发挥最好的防护效果,最大化输水工程的经济性。

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.