HYDRODYNAMICS THEORY AND CALCULATION IN WATER WAVE PUMP DESIGN

216Journal of Hydrodynamics , Ser. B,2005,17(2):216- 221China Ocean Press, Beiing - Printed in ChinaHYDRODYNAMICS THEORY AND CALCULATION IN WATER .WAVEPUMP DESIGNLIU Ying- xueShanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072，ChinaDepartment of Environment and Energy Engineering， Shanghai Institute of Technology， Shanghai200235，China, e-mail:liuyxd@ 126. comTAO Yi, LIU Gao-lianShanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China(Received Feb. 9, 2004)ABSTRACT: This paper introduces the hydrodynamics theo-to the fluid, and simultaneously increase the energyry related to water wave pump. Water wave pump isa new of one part of the inflow. So, this pump can onlytype pump, which uses the particular quality of water wavesupply water discontinuously and the frequentand re-divides the inflow energy to increase the pressure ofpening and closing of the valves is easy to damageone part of the inflow water with the rest water flowing awayfeelye. The reerceh and development of such a pump is of the valves and gives out loud noise and the eficien-importance and significant value and profitable social interest cy is rather low which makes it hard to be widelyin that it can fully utilize the residual energy of natural source used. That is the reason why it is very difficult toin idustrial and civil water circle systems. Through hydrody- see its application by now.namics research and calculation, a series of valid design pa-As is well known, water pump is a kind of flu-rameters were obtained and the predicted results achieved.id machines that can transform electricity and/orKEY WORDS:water wave theory， one-dimensional urother power into mechanical energy and then intosteady flow, water hammer pump, CFDthe potential and momentum energy. Its efficiencydepends not only on the technological performanceof its material, but also on the in- depth understand-1. INTRODUCTIONing of fluid mechanics theory. In recent years, dueIn the middle and end of 18th century, waterto the limited ability of pump researchers and thehammer pumps were produced based on people'spreference of pump manufacturers， the study ounderstanding of fluid mechanics. Water hammerpump in China is only of tracking and copying, andpump is a kind of pumps that can reallocate the en-hardly creative. The researchers are short of crea-ergy through a force produced by an abrupt change.tive spirit to initiate new type pumps and motion toIt divides the energy of the middle- pressure inflowwater into two parts，with the smaller part havinginvestigate the internal flow and performance ofhigher water head and the larger part having lowerpumps. Even worse, the costliness of experimentalwater head. Obviously， this pump can not onlydevices and their operation fee and their limited uschange the energy and then use it, but also enrichage add hardness to the researchers to carry out thethe pump category and make people know more a-internal flow field investigation. It restraints on thebout the mystery of fluid mechanicsI1.2].one hand the development of this field, and on theWater hammer pump does work to water other hand the development of the capability tothrough the opening and closing actions of two中国煤化工! new type pump.valves. The switching on and off of the valves canYHC N M H Gointing the operatingproduce transient compressive and expansive wave principle of both traditional water hammer pumpProject supported by the Shanghai Science and Technology Development Fund Subsidizes(Grant No: 00ZF14023).Biography:LIU Ying- xue (1955-), Male, Ph. D.，Professor217and gas wave supercharger, and initiated a new type seSo，the pressed water in the working compart-hydraulic machine. It proposed a new idea of devel- ment is driven to the air compartment through valveoping the water wave pump. In recent two years，B and then to the discharge pipe. In this way"we did a thorough investigation of the water wave water is lifted up. Subsequently， the pressure inpump and overcame the individual shortcomings of the air compartment drops, and valve B also dropswater hammer pumps and gas wave superchargers. due to its own weight and covers the outlet. Simul-We introduce its fluid mechanics theory and calcula- taneously, valve A is driven to drop by spring forcetion method hereinafter.and lets water to flow out of the working compart-ment. The pumps work in this way continuouslyOPERATION PRINCIPLE OF WATER and dischargewater periodically.TheoreticallyHAMMER PUMPspeaking，water hammer pump can automaticallyTo explain the idea of water wave pump，we work when valve A starts.first introduce the water hammer pump and its op-What should be mentioned is that only a smallerating principle. Water hammer pump consistsof a part q of the inflow middle pressure water Q can bepressure pipe of 10m- 20m long, a working compart- lifted to a high place of h with a big part becomingment with two valves ( namely the hammer valve A low (or no) pressure water and flowing away. Theand pressure valve B), an air compartment and the quantity of q depends onh。We can see that when hdischarge pipe. It principally works with two ac- gets bigger q gets smaller. In practical situations, htions (see Fig. 1).is much larger thanH，but the hmx (extreme head)depends on the distance between the outlet ofhammer valve A and the water surface H，and onthe inflow quantity Q，and on the friction drag ofWater pipe speakthe valves, and on the height of the pressure in theair compartment (See Fig. 2).Middling pressure waterheadAir room|hHworkronm B3Air room| HFig.1 Water hammer pump to produce energy processwork principiumA workrocm IWhen valve A is opened, water in the working，compartment springs out because there exists a Fig. 2Water hammer pump to raise pressure processpressure difference. The continuous supply of in-working principiumflow water and constant pressure difference can pro-vide a speed to spring out. At this time，the pres-If we only look at the ratio of inflow Q to thesure in the air compartment is evidently higher than high-pressure outflow q，namely the energy effi-that in the working compartment, so valve B is ciency， the working performance of water hammerclosed. But because the water in the working com- pumpsis too low. But if we consider the fact thatpartment is flowing. valve A will be lifted up bythe the inflow water is the water in rivers and in thespringing out water and even become closed. The ecirculated water systems with no energy supplied.water is abruptly stopped, which presses the fluid Fur中国煤化Ind night with no needin the working compartment. The pressure rockets of PMHC N M H Gh-pressure water andso rapidly that it makes the working compartment saves a lot of power source. It is still a good energy-wall be elastically transformed. W ater hammer phe-saving machine. But it has the following shortcom-nomenon happens. Meanwhile， valve B is pressedings: (1) it supplies water intermittently， (2) itto open as the pressure in the compartment increa-produces loud noise, (3) the valves are easily dam-218aged. All of them explain the reason why it cannot1也_4τw_Dw._..2w(2)be used widely and inherently. To refresh this con-ρasD。Dtwventional achievement, we will have to make break-through innovations to it.For the water hammer in the groove, the conti-nuity equation shall be3. HYDRODYNAMICS PRINCIPLE IN WATER 1 Dp +a2 ?w= 0ρIWAVE PUMP DESIGNWe should say that the operating principle ofWhen the groove is horizontal, w, is zero.water wave pumps is based on that of the waterBecause we do not take account of the friction,hammer pumps and that of the gas superchargers.the momentum equation can be simplified as :Employing the operating principle of the super-chargers-1. 10-12],we design the water wave pump in-to several circles with each circle having one middle-Dw+1业(3)DtTρispressure inflow inlet，one high- pressure outlet anda low-pressure outlet. The inlet joints with a high-Replacing pressure p with head h，namely, h =pressure and a low-pressure outlet continuously. Itsp/pg，and subtitling it into Eqs. (1) and (2), weprinciple is as the same as that of the frequentlyget the following equations:switched-on and off valves in water hanmer pumps.In physical plane, water flows through this systemD(4)as shown in Fig. 3. There are 4 stages in all We Dt' g dwill analyze the fluid mechanics principle and designthis pump.Dwah_+g5a=0(5)High pressureMiddling，介waterUsing the characteristics theory， we can obtainpressure waterfrom the above equations2|>Low pressured:d/d.w士a, h=干a/g(6)Fig. 3 Hydrodynamics principiumAt the inlet, we have Bernoulli equation: h=(w2 +u2)/2g = H，wherea is the sonic speed inwater, which depends mainly on the volume per-In the pump body， the groove revolves along centage of air in water. Ordinarily, we can give athe rotor. So， its speed has a tangential compo- speed according to a certain situation.nent. Therefore, we divide the velocityV of the flu-id into the circumferential velocity u and the axialvelocity w.hFor one dimensional unsteady flow， its conti-一hwnuity equation and momentum equation are, respec-hn Ntively,Continuity equation:hsD(om)中国煤化工Dt= D,(pAds) =0(1)MHCNMH G_Momentum equation:Fig.4 Status plane219Table 1 Parametric values when twice reflectionParametric values whenRotating speed 250rpmRotating speed 300rpmUnittwice reflectionWsm = 5.0697m/sWam =6. 43005m/sInlet pressure headHsmm9. 557379. 35784Outlet relative velocityV2mm/s4.847796.21303Inlet relative velocityWsw4. 624545. 994329.612429.42689Outlet relative speed4.401285. 77561Stationary speedHm180. 144236. 239High- pressure water headHum198. 314254. 024High-pressure outlet0.445160. 435726relative speedDistance between the inlet andD1-6n0. 0117810. 0141372the low pressure outletThe low- pressure outlet width0. 04699240. 0563463Inlet widthD350. 04714360.0565773High- pressure outlet widthD0. 02354880. 028259Low pressure outlet angleO2611. 966514. 3485Inlet angle :O3512. 00514. 4073High- pressure outlet angleO5. 996677.19608Low-pressure outlet dischargem3/h39. 122360. 8043Inlet dischargem'/h .41.131963.2643Highr pressure outlet discharge1. 886942. 21637Average radius inlet :Alfas30. 615025. 0119deflection angleAverage radius inlet32. 97226. 5868Average radius low pressureAlfac34. 2791.27. 4485outlet deflection angleAlfa231. 750825. 7739outlet deflection AngleAverage radius high- pressureAlfa,81.559781. 736中国煤化工CNMH GThen, according to the characteristics theory, the 4TYHW3mpstages in Fig. 3 can be expressed by the 4 points inthe status plane in Fig.4. If we have an Hp , an in-Fromw= um/rm andn= 60w/2π = 60um /2πrm，let velocity W3mp and h3mp，we obtain: .we can solve Eqs. (4) and (5) under the condition220that we set a low pressure outlet head h2mpinflow itself produces a velocity component to drivethe rotor. In the initial products of water wavepump, outer energy is used to overcome the frictionW2m = W3mp一点(h2zmp一h2mp)，of the rotor.him = h2np +“(w2m - wim),5. CONCLUSIONSgIn this study, calculation and design of the wa-ter wave pump are based on fluid mechanics theory.W1m = 0, hsm = h1m+hsmp一h2mp，The pump is the integration and optimization of theworking principle and function of the conventionalwsm=上(h3mp - h2mp)water hammer pumps and gas superchargers anwater turbine pumps. It is not like the supercharg-Then we can get the size and capacity of the inlet ers that needs high pressure power source, and notand the outlet.like the water turbine pump that needs twice energyFirst we set the length L of the pipe and as-exchange and makes the performance rather bad ，sume w to be the relative velocity. From Eq. (3)，and not like the water hammer pump that dependson the switching on and off of the valves and makeswe get，loud noise. It can supply water continuously, workt12 =t23 =Lwith no outer energy, and fully develop and useW2m十anatural water resources and the residual water in in-dustrial and civil piping systems. By properly usingthe wave energy, it reallocates the energy of the in-ls4 =二-W3mp 十aaflow, that is to say，makes one part of the inflowwater have high pressure and the rest low pressure.t41=二，t2=t12十t2s,tz=t23十t34，[t completely disconnects with the conventionalW4maworking principles and ways of pumps. It is an o-riginal，advanced and particular creation.t; = tz4+t，d. = t,um, Q; = t;XnX 6，In this paper, we only discuss about the one-dimensitonal unsteady calculation. We will discussQ=dmX(r,-rn)●W.,i=2,3,4in another paper the radius equilibrium calculationthat needs further research.4. NUMERICAL RESULTSAccording to Ref. [9]，the design of waterwave pumps shall consist of the following twoREFERENCESsteps: (1) one dimensional unsteady flow calcula-tion on average radius (as discussed above)，(2) ra-[1BENSON R. S. The thermodynamics and gas dynamicsdial equilibrium calculation. Here in this paper, wof internal combustion engines[ M]. Oxford: Clarendononly discuss the first step.Press, Vol. I, 1982, 141-215.The body length, outer radius. inter radius. [2] LIu Ga-lian, TAO Yi, 1IU Ying -xue. Variationalgroove height, deflect angle of the impeller, inflowformulation of 1-D unsteady compressible flow in a de-head and low- pressure outlet head are 0.8m, 0. 5m,forming tube[ A]. 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