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This situation will greatlyweaken the effect of accumulator absorbing flow andpressure pulsation.In allusion to this instance, this paper brings a new typewater pump whose outlet chamber is connected to multipleaccumulators with the same bladder volume and differentcharged pressure. The simulation and experiment resultsindicate that the accumulators can hold the best effect of ab-sorbing flow pulsation and pressure pulsation all along whenthe outlet flowrate and pressure of the water pump change.2 Structural representation of water pumpThe structural representation of water pump, which is anaxial piston pump, is shown in Fig. 1. A set of accumula-tors are circle distributed around the outlet chamber. Eachaccumulator’s inlet port intercommunicates with the outletchamber of water pump, and the accumulators absorb theflow pulsation and pressure pulsation during operating.The bladder volume of each accumulator is designed thesame with a view to the structure symmetry of the wa-ter pump, namely VAqk = VAq(k-1) = = VAq1, and eachbladder will be charged with different gas pressure to ab-sorb pressure pulsation well even though water pump ex-ports time varying flowrate and pressure.3 Mathematical model of accumulators absorbingthe flow pulsation and pressure pulsationAccording to the structural representation and workingcharacteristics of the water pump shown in Fig. 1, theprinciple of accumulators working in HWPS is demon-strated in Fig. 2. For accessibility, the following premises are acceptedfor the mathematical model of the accumulators absorbingthe flow pulsation and pressure pulsation [9, 10]:1. The changing of gas state in each accumulator isregarded as adiabatic processpAkVKAk ¼ constant ð1Þ2. The water pressure in an accumulator is equal to thegas pressure in the bladder.3. All accumulators have the same parameters of the inletport.4. The gravity force, compressibility and cavitations ofwater, and the leakage of HWPS can be disregarded.According to Fig. 2 and the hypothesis mentionedabove, equations describing HWPS could be educed asfollowing:3.1 Instantaneous output flowrate of water pumpWithout regard for volume loss caused by leakage andcompressibility of water, the instantaneous output flowrateof the axial piston water pump could be expressed asq ¼ qrnp60zpX zpj¼1sinnp30t þ 2ðj 1Þpzp ð2Þ3.2 Flowrate through nozzleThe viscosity of water is small and the Reynolds number innozzle is large. The flowrate qN through the nozzle can beobtained as follows:qN ¼ CNANffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2ðp pNÞqsð3Þ3.3 Force balance of water in the anterior pipelineof accumulatorsAccording to Newton’s second law, the force balanceequations of water in the anterior pipeline of accumulatorscan be described belowðp pAkÞAA ¼ qAAlAdðqAk=AAÞdtþ AAkklAdAqv2k2vk ¼ qAkAA PqAk ¼ q qN:8> > > <> > > :ð4ÞWhen the actual size of the anterior pipeline isdA = 0.012 m, lA = 0.0059 m, and the pressure differenceof the anterior pipeline takes the maximumDpk = 10 9 106Pa 9 0.8 % = 8 9 104Pa, the vk andRek can be calculated as vk ¼ Cdffiffiffiffiffiffiffi2Dpkqq¼ 0:6ffiffiffiffiffiffiffiffiffiffiffiffiffiffi2 8 1041000q¼7:5 ms 1,Rek ¼ vkdAl ¼ 7:5 0:0121:007 10 6 ¼ 0:9 105\1 105.While this kind of turbulence flow happens in the anteriorpipeline, the resistance coefficient kk along the anteriorpipeline can be calculated by Ref [11] as below. If theShaftSwash platePistonOutlet ChamberAccumulatorValve Inlet portA AAccumulatorOutlet ChamberOutlet portPiston barrelRelief valveView A-AFig. 1 Structure of water pump with accumulatorsAccumulatorsRelief valveWater pumpp, qNozzleqN pjetpAkVAkqAk qA1pA1VA1Fig. 2 Work principle of water pump with accumulators in HWPS pressure pulsation factor dp[0.8 %, the kk calculated byEq. 5 is not applicable.kk ¼ 0:316Re0:25kRek ¼ vkdAl8> > <> > :ð5Þ4 Parameters of accumulatorsAccording to the water pump’s service behavior requiredby HWPS, the working pressure range is fixed at pmin topmax,and N pressure spots are chosen from the range(pmin B pc1\pc2\…\pcN B pmax). At each pressurespot, a corresponding accumulator whose charged pres-sure is related to the pressure spot is designed. In thisway, the pressure pulsation in HWPS can be absorbed allalong when working pressure changes between pmin andpma