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.

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。

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.

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. [

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.

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.

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.

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.

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.

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.

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.

基于Bentley Hammer的泵站输水系统管道优化前后的水力过渡过程研究

为了研究泵站输水系统管道优化前后事故停泵的水力过渡过程的特性,基于实际工程,运用Bentley Hammer软件,建立泵站输水系统双泵并联机组数学模型,研究两阶段不同关阀方案下管道优化前后对水锤压力、机组转速等最不利水锤参数的影响。结果表明,管道优化后最大水锤压力降低了3.76%~8.85%,最小水锤压力提升了4.89%~8.85%,最大倒转速度提高了1.47%~81.35%;快关时间对最不利水锤参数有显著影响,管道优化后泵站输水系统最不利水锤参数均比优化前提前发生。表明管道优化有效改善了泵站输水系统的水锤特性,提高了泵站输水系统的安全性。

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.

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.

多分水口长距离输水工程停泵水锤防护措施

为了能够有效避免多泵且多分水口输水系统在无防护抽水断电时可能出现较为严重的负水锤带来的危害,建立了全长106.46 km的大型供水工程的数学模型进行系统过渡过程计算,选择空气阀与两阶段液控蝶阀联合防护与单向塔防护2种方案消除其负水锤,在前者远不达理想防护效果后针对后者进行优化.结合工程实际在确定了单向塔的数量、位置以及塔高后,对不同位置单向塔的底面积进行多种方案的对比选取,最终选用塔1#的底面积为28.26 m^(2),塔2#的底面积为176.63 m^(2);为了防止单向塔漏空需要分水口以及供水终端调流阀配合关闭,在确保管道最大压力不超出其承压能力的前提下,创新性地对各分水口调流阀与供水终端调流阀的关闭时间规律进行了效果比较,使输水系统能够更加经济安全地稳定运行,为此类长距离多分水口多泵供水工程的水锤防护提供了优化方向.

水击补气式压力罐及水力瞬变仿真

空气阀常常安装在输水管检修孔侧壁,进气后部分气体就会存留在检修孔上部产生气垫式压力罐的水击防护作用。据此,提出了水击补气式压力罐装置的设计方法,即利用泵站事故断电产生的水击负压现象,通过真空破坏阀或空气阀给压力罐补气,以防止输水管发生液体汽化现象并削减水击最大压力。然后,建立了水击补气式压力罐水力瞬变数值仿真数学模型。最后,以一个实际输水工程为例,计算比较了分别设置空气阀、空气阀调压室及真空破坏阀补气式压力罐时的水击防护效果,结果表明,补气式压力罐水击防护效果最好。

有机玻璃管道直接水锤压力特性试验研究

为了了解黏弹性管道的水锤压力特性,文中通过搭建水库-管道-阀门系统模型,进行了系列关阀水锤试验,针对有机玻璃管道中末端阀门初始开度分别为30%,100%时关阀产生的直接水锤压力变化规律进行了研究,从黏弹性材料的本构关系角度分析了关阀时间对黏弹性材料直接水锤的影响机理,并对2种不同初始开度下阀门附近的流场进行了三维数值模拟.研究结果表明:黏弹性管道中直接水锤压力变化规律与传统的水锤理论不符,直接水锤压力不仅与阀门的关闭时间有关,还与阀门的初始开度有关,满足“阀门关闭越快,直接水锤压力越大”与“阀门初始开度越小,直接水锤压力越大”的规律.