Re: Water Hammer Analysis Parmakian Pdf 19
Major Rowley
A new fast and efficient marching algorithm is introduced to solve the basic quasilinear, hyperbolic partial differential equations describing unsteady, flow in conduits by the method of characteristics. The details of the marching method are presented with an illustration of the waterhammer problem in a simple piping system both for friction and frictionless cases. It is shown that for the same accuracy the new marching method requires fewer computational steps, less computer memory and time.
Create citation alert 1755-1315/1079/1/012003 Abstract Water hammer shortens hydraulic passage lifespan and may cause sudden failure. The primary goal is to use a hierarchical approach to assess the main parameters associated with water hammer. This will help investigate their influence and assist in decision making. Analytical calculation results and a numerical model are compared against experimental data. Our investigations examine water hammer overpressure loading induced by transient regimes. We used data from experimental campaigns carried out within the Hydro-Québec fleet that cover different types of hydraulic turbines and hydraulic passage configurations as experimental dataset. Guide vane closing rate was the main parameter controlled during the overpressure experiments and a general trend was identified for overpressure. This empirical trend is compared to model estimates in order to validate the hypothesis taken into account for calculations. An in-depth understanding of the water hammer phenomenon helps to select the appropriate theoretical model and recommend the optimal operating parameters to extend lifetime and to avoid catastrophic failures. Our study case suggests that available experimental data can be used along with gradually increasing analysis complexity to identify the optimal methodology for a given configuration.
Water hammer analysis is a fundamental work of pipeline systemsdesign process for water distribution networks. The main characteristics formine drainage system are the limited space and high cost of equipment andpipeline changing. In order to solve the protection problem of valve-closingwater hammer for mine drainage system, a water hammer protection method formine drainage system based on velocity adjustment of HCV (Hydraulic ControlValve) is proposed in this paper. The mathematic model of water hammerfluctuations is established based on the characteristic line method. Then,boundary conditions of water hammer controlling for mine drainage system aredetermined and its simplex model is established. The optimization adjustmentstrategy is solved from the mathematic model of multistage valve-closing.Taking a mine drainage system as an example, compared results betweensimulations and experiments show that the proposed method and the optimizedvalve-closing strategy are effective.
Mine drainage system is an important part in the safety productionof coal mine [1]. Due to the limited space and the high cost of equipmentchanging, water hammer is a common phenomenon in mine drainage system and itsharm is inestimable [2, 3]. The minor injuries of water hammer can causesevere shock or even pipes breaking, and the major injuries can causeequipment damaging, pumping station flooding, or even injuries to undergroundstaff. There are several traditional water hammer protection methods such asinstalling vacuum valves, exhaust valve, and pressure tank. However, whenthese water hammer protection methods are used to mine drainage system, theoriginal piping arrangement has to be changed because additional equipment isneeded. It is unenforceable to do this in this limited mine space and thecost is too high. In this situation, controlling the time and velocity ofvalve-closing is an effective means to protect water hammer in mine drainagesystem. A water hammer is easily to be formed in pipeline if thevalve-closing is fast. On the contrary, the capability of pumps isinefficient if the valve-closing is too slow because pumps in mine drainagesystem are centrifugal. This inefficient operation has damage for pumps,because power provided by pumps is converted into heat. Therefore, it isimportant for us to research the critical valve-closing velocity forHydraulic Control Valve (HCV). Researches of theoretical system andengineering applications for water hammer protection of pipeline fluiddelivery areas are increasingly improved [4-6]. But it is still a difficultproblem in mine drainage system because of the limited mine space [7, 8].
At present, the theories and methods of water hammer and itsprotection means become more and more mature. In summary, researches aboutthis problem are mainly in three aspects: hydraulic transient modeling, thecalculation, and protection methods of water hammer.
(1) Hydraulic Transient Modeling. For the research on hydraulictransient, from the mathematical derivation of the 18th century to thegraphical analysis of the mid-20th century and to the current computerdigital simulation, scholars have already made a lot of research results. Themajor achievements are getting the relationship between multiphase andmulticomponent transient flow equations, water hammer equations, and thecontrol equations, such as Joukowsky equation [9]. Based on the transientflow simulation theory, Colombo et al. [10] proposed an aqueducts faultdetection technology, Lee et al. [11] proposed the pipe network leak anddeterioration over time detection technology by the time domain reflectometry(TDR), Arbon et al. [12] proposed pipeline corrosion and blockage detectiontechnology, Gong et al. [13] proposed a detection technology for pipefriction, wall thickness, velocity, position, and the length of the pipes,and Ferrante et al. [14] presented a leak detection method with couplingwavelet analysis and a Lagrangian model techniques. Meniconi et al. [15]presented a pipe system diagnosis method with the small amplitude sharppressure waves.
(i) Arithmetic Method. Before the 1930s, the hydraulic transientcalculation of water hammer used Allievi equations mostly [16]. Allieviequations can be called Arithmetic method which is used to solve the problemsof water hammer that with simple boundary conditions and its workload is verylarge.
(ii) Graphic Method. Graphic method is developed in 1930s to1960s. Bergeron, Parmakian, and so forth [17] are committed to develop thismethod. Boundary conditions and the process of water hammer fluctuation areexpressed through coordinate graphics of H and V according to this method.Due to the graphics, it is simple and intuitive for the hydraulic transientcalculation of water hammer. However, the accuracy is not high because thismethod is restricted by calculating means and assumptions.
(iii) Numerical Method. From 1960s, some numerical methodsappeared that can be aided by computers, such as Characteristic (MOC) [18],Wave Characteristic Method (WCM) [19], Implicit Method [20, 21], and FiniteElement Method (FEM) [22,23]. The WCM can solve water hammer problems ofcomplex piping systems and boundary conditions. It is the most common methodbecause of the high accuracy and computing. The Implicit Method dividespipeline into several segments and solves equations of the entire pipelinesystem simultaneously in each segment. The advantage of Implicit Method canbe described in a way that a longer segment is selected and the number ofcalculations is reduced. However, there is more time needed for calculationin large and complex pipeline network system [24]. FEM with flexibility isused in pipe network system which have complex boundary conditions. However,it has a limitation in solving hydraulic transient problems.
(3) Water Hammer Protection. Prevention and controlling means forwater hammer are researched with the development of their theory andcalculation. Wylie [25-27] has researched several protective devices forwater hammer, such as air valves, check valves, pressure tank, and surgetank. Lee [28] and Stephenson [29] discussed the performances of air valvesin water hammer protection. However, these researches have not given aquantitative calculation for the problem of water hammer protection.
This paper proposed a water hammer protection method based onvelocity adjustment of HCV to deal with the problem of valve-closing waterhammer in mine drainage system. The mathematic model of water hammerfluctuations is founded based on MOC according to the hydraulic transient.Then, boundary conditions of water hammer controlling for mine drainagesystem are determined and the simplex model is established. Finally, theoptimization adjustment strategy is solved with simulation and experiment.
The remainder of this paper is organized as follows. Section 2provides the mathematic model of the propagation and superposition model forwater hammer fluctuations. Section 3 provides an optimization method todetermine the adjustment strategy for HCV. Section 4 presents a case study.Concluding remarks are offered in the last section of this paper.
The second-order partial differential equations about H(x, t) andV(x, t) are obtainedthrough thepartial derivative and are taken for variablesx and t in (3). Therefore, the momentum equations for water hammer wave inpipeline drainage system are expressed as
2.2. Propagation and Superposition Model of Water Hammer WaveBased on Characteristic Line Method. Pumps and valves are the generatingsources of water hammer wave in hydraulic transition process of pipelinefluid delivery system. These two kinds of water hammer wave start at the sametime and propagation directions are superimposed. The superposition leads tostrengthening of fluctuations for water hammer. In order to control the waterhammer pressure effectively, the superposition effects of water hammer waveneed to be weakened as much as possible.
The integral operation and differential conversion are introducedto (9). The discrete characteristic equations of water hammer are obtained asfollows. Equation (10) and the characteristic line grid are shown in Figure1:
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