processes
Article Influence of Eccentricity on Hydrodynamic Characteristics of Nuclear Reactor Coolant Pump under Different Cavitation Conditions
Yuanyuan Zhao, Bin Lin, Xiuli Wang * , Rongsheng Zhu and Qiang Fu
National Research Center of Pumps, Jiangsu University, Zhenjiang 212013, China; [email protected] (Y.Z.); [email protected] (B.L.); [email protected] (R.Z.); [email protected] (Q.F.) * Correspondence: [email protected]
Received: 12 November 2019; Accepted: 7 January 2020; Published: 10 January 2020
Abstract: In order to study the influence of eccentricity on hydrodynamic characteristics of nuclear reactor coolant pump under different cavitation conditions, five different schemes were obtained by analyzing and optimizing the existing structural schemes. Based on the RNG k-ε model (Renormalization Group with k-epsilon turbulence models) and two-fluid two-phase flow model, the unsteady numerical analysis and test verification of different designed schemes are carried out by using the flow field software ANSYS CFX. The results of research show that different eccentricities will affect the nuclear reactor coolant pump’s head under different cavitation conditions, and the corresponding head in the scheme with the eccentricity of 5mm under the fracture cavitation condition is lower than that of the other schemes. When the impeller rotates at a certain angle from the initial position under critical and severe cavitation conditions, the radial force acting on the rotor system will fluctuate greatly. Under the condition of fracture cavitation, the radial force changed periodically and the resultant force value is small. Compared to the original scheme, the peak value of radial force is 6◦ clockwise after eccentricity of the impeller appeared. With the aggravation of cavitation condition, the axial force value of impeller decreases, but the corresponding amplitude of the impeller increases. Under critical and severe cavitation conditions, the maximum axial force amplitude of the nuclear reactor coolant pump appears in the two times blade frequency, and in the broken cavitation condition, the maximum axial force amplitude appears at the shaft frequency. When the eccentricity is 20 mm, the axial force fluctuates most under critical and severe cavitation conditions, and when the eccentricity is 10 mm, the corresponding axial force is smaller than that of the original scheme. When the eccentricity is 5 mm, the axial force on the impeller is the smallest, but the amplitude is the largest under the condition of fracture cavitation.
Keywords: nuclear reactor coolant pump; eccentricity; cavitation; radial force; axial force
1. Introduction Despite the disastrous nuclear accident that occurred in Fukushima in 2011, nuclear energy, as a vital part of world energy, will not be affected in the future development [1]. However, the shadow of nuclear accidents cannot be ignored. The risk research of nuclear power plants has become one of the most important topics in this field [2]. As one of the core equipment of nuclear power plant, the nuclear reactor coolant pump and its ability to operate safely and steadily for a long time plays a vital role in the safe and stable operation of the whole nuclear power plant [3]. Small break loss of coolant accident (SBLOCA), a commonly analyzed accident condition, will lead to a sharp decrease in environmental pressure, resulting in cavitation in the impeller of the nuclear reactor coolant pump [4,5]. Cavitation will cause the energy exchange of liquid to be interfered and
Processes 2020, 8, 98; doi:10.3390/pr8010098 www.mdpi.com/journal/processes Processes 2020, 8, 98 2 of 15 destroyed, causing a series of problems such as a change in pump operation characteristics, vibration, and noise [6]. Finally, it will affect the capacity of the pump to convey coolant [7]. Scholars have studied the flow characteristics and radial forces of pumps under cavitation conditions. Lu Pengbo et al. used the speed coefficient method to design the impeller and guide blade of the nuclear reactor coolant pump and obtained the law of the influence of the nuclear reactor coolant pump structure on cavitation [8]. Zhang Yu et al. used numerical simulation methods to obtain the critical pressure and critical temperature of cavitation of the nuclear reactor coolant pump by steady state calculation [9]. Wang Yiming et al. carried out numerical calculations of cavitation in a mixed flow nuclear reactor coolant pump, and the cavitation performance of the nuclear reactor coolant pump was improved through numerical prediction [10]. Wang Xiuli et al. used ANSYS CFX software to conduct simulate analysis on the hydrodynamic characteristics of the nuclear reactor coolant pump in cavitation transition process and got the fluctuation rule of pressure and head in the pump [11]. Shi Weidong et al. carried out unsteady numerical calculations on the non-overload sewage pump, and the effect of centrifugal pump clearance on pressure fluctuation and radial force was studied [12]. Wang Peng et al. studied the influence of eccentricity on the internal flow of the nuclear reactor coolant pump and obtained the influence rule of eccentricity on radial force under single phase working conditions [13]. Meng L et al. studied the effect of interaction between impeller and volute on the cavitation behavior of centrifugal pumps [14]. Ran Tao et al. studied the cavitation performance of pump turbines under pump mode [15]. Qiang Fu et al. studied the flow characteristics of the inner impeller channel of a nuclear centrifugal pump under the condition of steady and transient cavitation condition [16]. However, the cavitation evolution of the nuclear reactor coolant pump impeller in different cavitation and the radial force and axial force variation on the impeller are seldom studied, especially the effect of the eccentric distance of the impeller on the nuclear reactor coolant pump in different cavitation states [17]. Lu Y. et al. studied the third and fourth generation reactor coolant pumps, main including gas-liquid two-phase flow and the transient characteristics of pump under extreme operating conditions, and finding in different gas fraction conditions, the homogeneous distribution of gas phase component in the fluid area was mainly related to the operating condition of pump, and when the volume flow rate deviates from the designed operating point, the fluid medium’s gas phase and liquid phase will separate to some extent [18–20]. In order to further study the effect of eccentricity on the cavitation of the nuclear reactor coolant pump and the radial force and axial force of the impeller under different cavitation conditions, this paper will adopt the eccentricity principle described in the literature and use the flow field analysis software ANSYS CFX to simulate the internal flow field of the nuclear reactor coolant pump in three different cavitation states. The cavitation characteristic, radial force and axial force of different eccentric nuclear reactor coolant pumps are analyzed. The obtained results can provide reference for the design of new nuclear main pumps.
2. Theoretical Analysis and Scheme Design At present, the ideal structure of the volute of the nuclear reactor coolant pump is mainly the symmetrical annular volute. The structure has the following three advantages: (1) it is easy to manufacture; (2) high bearing capacity of the annular structure; (3) the radial force of the rotor system is uniform. However, in practical application, the existence of the outlet pipe not only destroys the original internal flow rule of volute, produces larger vibration force and causes the vibration and noise in the unit, but also causes the asymmetrical distribution of pressure in the volute and produces larger radial force, which affects the operation life of the pump unit. Therefore, it is necessary to optimize the design of annular volute on the basis of original structural design to ensure the smoothness of internal flow and balance to eliminate radial force. This paper mainly uses the eccentricity produced by the center line of the impeller and the central line of the annular volute to eliminate the adverse effects of the outlet pipe on the annular volute. Processes 2020, 8, x FOR PEER REVIEW 3 of 15 Processes 2020, 8, 98 3 of 15
From Figure 1, it can be seen that the fluid at the junction between the outlet pipe of the annular voluteFrom and Figurethe volute1, it canhas beno seen pressure that theon fluidthe pump at the case, junction and betweenthe pressure the outletof the pipefluid of on the the annular pump shellvolute corresponding and the volute to hasthe noposition pressure of the on outlet the pump pipe case,(the S3 and region the pressure in Figure of 1) the is fluidthe main on the factor pump of theshell radial corresponding force. Using to thethe positionhydraulic of design the outlet method pipe (the of the S3 regioncentral inline Figure of the1) isannular the main volute factor and of thethe centerradial force.line of Using the impeller the hydraulic (the downward design method eccentri of thec delta central of linethe ofimpeller the annular center volute line), and the thepressure center fromline of the the eccentricity impeller (the (S1, downward S2 region in eccentric Figure 1) delta is used of theto balance impeller the center pressure line), at the the pressure relative fromposition the ofeccentricity the outlet (S1,(the S2S3 regionregion inin FigureFigure1 1).) is The used pressure to balance at the the rest pressure of the atannular the relative volute position is offset ofin thethe radialoutlet (thedirection. S3 region For inthe Figure pressure1). The formed pressure at attw theo restpositions of the of annular S1, S2, volute the ishorizontal o ffset in thedirection radial counteractsdirection. For each the other, pressure and formed the direction at two of positions the synt ofhetic S1, pressure S2, the horizontal is vertically direction upward counteracts to balance each the pressureother, and at the the direction S3. of the synthetic pressure is vertically upward to balance the pressure at the S3.
Figure 1. The optimized compensation scheme. Figure 1. The optimized compensation scheme.
The areas S1, S2 and S3 are used to approximate the representation of the pressure. As such, to balanceThe outareas the S radial1, S2 and force, S3 are we used just have to approximate to make the the relation representation among them of tothe meet pressure. Equation As such, (1): to balance out the radial force, we just have to make the relation among them to meet Equation (1): 0.9S3 ≤ S1 ++ S2 ≤1.1S3 (1) 0.9 S 3 ≤ S 1 S 2 ≤ 1.1S 3 (1) InIn order order to to ensure ensure the the eccentricity eccentricity schemes schemes are are conducted conducted when when the the impeller, impeller, guide guide blade, blade, water water chamber,chamber, andand thethe layoutlayout of of the the outlet outlet section section are ar invariable,e invariable, move move the pumpthe pump casing casing to the to pump the pump outlet outletsection section for a distancefor a distance e (The e eccentricity(The eccentricity is defined is defined as the as dithefference difference between between the centerlinethe centerline of the of theimpeller impeller and and the centerlinethe centerline of the of volute.the volute. As shown As shown in e in in Figure e in Figure2. unit: 2. mm),unit: mm), and the and impeller, the impeller, guide guideblade andblade inlet and section inlet section remain remain at the originalat the original position. position. The eccentricity The eccentricity scheme scheme of the nuclearof the nuclear reactor reactorcoolant coolant pump ispump shown is inshown Figure in3 .Figure The influence 3. The infl of eccentricityuence of eccentricity on the head, on the radial head, force, radial and force, axial andforce axial of the force nuclear of the reactor nuclear coolant reactor pump coolant in pump cavitation in cavitation under five under schemes five sc ofhemes eccentricity of eccentricity e = 0 mm, e =e 0= mm,5 mm, e = e 5= mm,10 mm, e = 10 e = mm,15 mm, e = 15 and mm, e = and20 mme = 20 is studied.mm is studied.
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Processes 2020, 8, x FOR PEER REVIEW 5 of 15 Figure 2. The eccentricity scheme of the nuclear reactor coolant pump. Figure 2. The eccentricity scheme of the nuclear reactor coolant pump.
3. Numerical Simulation
3.1. Computing Model and Grid Partition The object of this study is the AP1000 nuclear reactor coolant pump with a vertical single stage single suction mixed flow pump. The conveying medium is clean water. In order to ensure the accuracy and reliability of the numerical simulation, the size of the prototype pump is reduced and tested. The main parameters of the prototype pump are shown in Table 1, and the main parameters of the model pump after conversion are shown in Table 2. The rotor is a cantilever structure, and a radial guide blade is arranged outside the impeller to make the fluid uniformly enter the annular volute.
Table 1. Parameters of the prototype pump.
Designed Q (m3/h) Designed Head H (m) Rotational Speed n (r/min) Specific Speed ns 17,886 111.3 1480 351.4 FigureFigure 3. 3.3D3D modeling modeling and and grid grid of of the the water water body of thethe nuclearnuclear reactor reactor coolant coolant pump. pump. 3. Numerical Simulation PRO/E software is usedTable to 2. generate Parameters the of 3D the calculation model pump area after model. conversion. The main water body of the whole3.1.Designed Computing pump areQ Model (m in3 /h)turn and entrance,Designed Grid Partition impeller, Head H (m)guide Rotational blade, pumping Speed chamber, n (r/min) and Specific outlet section.Speed n Thes hexahedral114.2 structure meshing of the3.83 overflowing parts of the nuclear 1480 reactor coolant pump 351.4 is carried out byThe ICEM object CFD. of this The study 3D modeling is the AP1000 and grid nuclear of the reactor water body coolant of pumpthe nucl withear reactor a vertical coolant single pump stage aresingle shown suction in Figure mixed flow3. pump. The conveying medium is clean water. In order to ensure the accuracy and reliabilityIn order to of ensure the numerical that the structural simulation, grids the of size all ofparts the of prototype the above pump partition is reduced meet the and needs tested. of computation,The main parameters the grid independence of the prototype of the pump model are shownis tested. in In Table this1 paper,, and the there main are parameters five schemes, of thebut threemodel schemes pump after of different conversion density are shownand grid in size Table are2. Theused rotor for the is agrid cantilever division structure, of the water and aparts radial of theguide nuclear blade isreactor arranged coolant outside pump, theimpeller and three to makegroups the of fluid calculation uniformly schemes enter the are annular obtained. volute. The number of grids are 1.26 million, 2.60 million, and 4.31 million, respectively. The head from the three sets of calculations is shown in Figure 4. It can be seen from the Figure 4 that when the number of schemes 1 grid is adopted, the calculation head of the pump is 106.17 m, and the calculation head is 110.41 m when scheme 2 is adopted, and the calculation value of the head of scheme 3 is 110.63 m. It can be seen that when the number of water grids exceeds 2.60 million, the change of the head of the pump at the rated operating point will be less than 0.5%, and the number of excess grids will occupy a large number of computer resources, which requires a higher configuration computer and takes a long time to ensure accuracy and economic efficiency. Thus, the grids are more suitable to approximate 2.60 million, and the structural grid of scheme 2 is adopted in this paper.
111
110
109
108 Head/m 107
106 1.01.52.02.53.03.54.04.5 million
Figure 4. The head for each scheme.
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Table 1. Parameters of the prototype pump.
3 Designed Q (m /h) Designed Head H (m) Rotational Speed n (r/min) Specific Speed ns 17,886 111.3 1480 351.4
Table 2. Parameters of the model pump after conversion.
3 Designed Q (m /h) Designed Head H (m) Rotational Speed n (r/min) Specific Speed ns 114.2 3.83 1480 351.4 Figure 3. 3D modeling and grid of the water body of the nuclear reactor coolant pump.
PRO/EPRO/E software software is is used used to to generate generate the the 3D 3D calculation calculation area area model. model. The The main main water water body body of the of wholethe whole pump pump are in are turn in turn entrance, entrance, impeller, impeller, guide guide blade, blade, pumping pumping chamber, chamber, and outlet and outlet section. section. The hexahedralThe hexahedral structure structure meshing meshing of the ofoverflowing the overflowing parts of parts the nuclear of the nuclear reactor reactorcoolant coolantpump is pump carried is outcarried by ICEM out by CFD. ICEM The CFD. 3D Themodeling 3D modeling and grid and of gridthe water of the body water of body the nucl of theear nuclear reactor reactorcoolant coolant pump arepump shown are shownin Figure in Figure3. 3. In order to ensure that the structural grids of all parts of the above partitionpartition meet the needs of computation, the grid independence of the model is tested. In In this this paper, paper, there there are five five schemes, but three schemes of different different density and grid size are used for the grid division of the water parts of the nuclearnuclear reactorreactor coolant coolant pump, pump, and and three three groups grou ofps calculation of calculation schemes schemes are obtained. are obtained. The number The numberof grids of are grids 1.26 are million, 1.26 million, 2.60 million, 2.60 million, and 4.31 and million, 4.31 million, respectively. respectively. The head The from head the from three the sets three of setscalculations of calculations is shown is inshown Figure in4 .Figure It can be4. It seen can from be seen the Figurefrom the4 that Figure when 4 thethat number when the of schemesnumber 1of schemesgrid is adopted, 1 grid is the adopted, calculation the calculation head of the head pump of the is 106.17 pump m, is 106.17 and the m, calculation and the calculation head is 110.41 head mis when110.41 scheme m when 2 isscheme adopted, 2 is andadopted, the calculation and the calculation value of the value head of of the scheme head 3 of is scheme 110.63 m. 3 is It 110.63 can be m. seen It canthat be when seen the that number when the of water number grids of exceedswater grids 2.60 ex million,ceeds 2.60 the changemillion, of the the change head ofof the the pump head of at the pumprated operating at the rated point operating will be lesspoint than will 0.5%, be less and than the number0.5%, and of the excess number grids of will excess occupy grids a large will numberoccupy aof large computer number resources, of computer which resources, requires a higherwhich configurationrequires a higher computer configuration and takes computer a long time and to takes ensure a longaccuracy time and to economicensure accuracy efficiency. and Thus, economic the grids ef areficiency. more suitableThus, the to approximate grids are more 2.60 million,suitable and to approximatethe structural 2.60 grid million, of scheme and 2 the is adopted structural in thisgrid paper.of scheme 2 is adopted in this paper.
111
110
109
108 Head/m 107
106 1.01.52.02.53.03.54.04.5 million Figure 4. The head for each scheme. Figure 4. The head for each scheme.
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3.2. Numerical Calculation Me Methodthod and Boundary Condition The steady state calculation of cavitation is carried out through ANSYS CFX software, and the total inlet pressure correspondingcorresponding to thethe criticalcritical cavitation,cavitation, severe cavitation and fracture cavitation of the nuclear reactor coolant pump is carried out. The impeller, as a rotating part, adopts a rotating coordinate system, and the definitiondefinition domain is setset asas RotatingRotating domain.domain. The rotation speed of the impeller isis set set as as 1480 1480 r/min. r/min. There There are are three three main main interfaces interfaces to be setto be in thisset paper,in thisnamely paper, thenamely interface the ofinterface inlet section-impeller, of inlet section-impeller, impeller-guide impeller-guide vane, and guide vane, vane-volute, and guide vane-volute, which are set which as the are Frozen set as Rotor. the TheFrozen steady-state Rotor. The calculation steady-state results calculation of the three results cavitation of the conditionsthree cavitation are taken conditions as theinitial are taken conditions as the ofinitial the unsteadyconditions state of the calculation, unsteady state and thecalculation, RNG k-ε andturbulence the RNG model k-ε turbulence and two fluidmodel two and phase two fluid flow modeltwo phase are usedflow tomodel calculate are used the results. to calculate The interface the results. in the The unsteady interface state in the calculation unsteady is state setto calculation Transient Rotor-Statoris set to Transient mode, Rotor-Stator and in the simulation, mode, and the in rotation the simulation, time of the the impeller rotation is time 60/1480 of the= 0.0405 impeller s, and is 60/1480 = 0.0405 s, and the time step of the unsteady numerical simulation3 is 3.378 × 10−3 s (the time the time step of the unsteady numerical simulation is 3.378 10− s (the time of impeller’s turning of impeller’s turning over 3°), and the total time is 0.24324 s. × over 3◦), and the total time is 0.24324 s. The inletinlet conditioncondition is is the the total total pressure pressure inlet, inlet, and and the the outlet outlet condition condition is the is giventhe given outlet outlet mass mass flow. Theflow. flow The rate flow of rate the modelof the ismodel calculated is calculated by controlling by controlling the outlet the boundary outlet boundary conditions. conditions. The standard The wallstandard function wall isfunction used in is the used near in wall the near surface. wall The surface. wall The boundary wall boundary condition condition is adiabatic is adiabatic and non-slip and −6 wall;non-slip the averagewall; the diameter average ofdiameter the bubble of the is setbubble to 2 is10 set6 tom, 2 the× 10 volume m, the fraction volume of fraction water at of the water inlet at is × − setthe toinlet 1, andis set the to volume1, and the fraction volume of thefraction bubble of isthe set bubble to 0. is set to 0.
4. Calculation Results and Analysis Figure5 5is is the the testing testing site site and and the performancethe performance curve curve compared compared between between the experimental the experimental results andresults the and simulation the simulation results. Itresults. is shown It is by shown the diagram by the diagram that the maximum that the maximum efficiency efficiency point of the point pump of appearsthe pump at appears the design at the point. design After point. 1.2 Qn, After H 1.2 and Qn,η begin H and to η fall begin sharply to fall with sharply the increase with the of increase flow, and of theflow, cavitation and the cavitation may have may developed have developed to a considerable to a considerable extent at this extent time. at this time.
Figure 5. Cont.
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Figure 5. The testing site and comparison between the experimental results and the simulation results. Figure 5. The testing site and comparison between the experimental results and the simulation 4.1. Theresults. Effect of Eccentricity on the Head
4.1. TheThrough Effect of the Eccentricity steady numerical on the Head simulation and analysis to the nuclear reactor coolant pump model, the three inlet total pressure are selected as 140 kPa, 110 kPa, and 100 kPa respectively in this paper. On theThroughFigure basis of 5.the theThe steady three testing groups numerical site and of steady-statecomparison simulation between calculation and an thalysise results, experimental to the the nuclear unsteady results reactor and numerical the coolant simulation simulation pump model,of the cavitationresults. the three ofinlet the total pump pressure is carried are out, selected and the as change140 kPa, curves 110 kPa, of the and three 100 groupskPa respectively of pump headin this at paper.any time On in the Figure basis6 ofare the obtained. three groups In order of steady-state to ensure the calculatio accuracyn ofresults, the calculation the unsteady results, numerical all the 4.1. The Effect of Eccentricity on the Head simulationcurves in Figure of the6 cavitationtake the data of the of thepump last is cycle carried of the out, calculation and the change cycle for curves drawing. of the three groups of pump head at any time in Figure 6 are obtained. In order to ensure the accuracy of the calculation FigureThrough7 is a the vapor steady phase numerical volume fraction simulation diagram and ofan threealysis di tofferent the nuclear inlet blades reactor under coolant eccentric pump e results, all the curves in Figure 6 take the data of the last cycle of the calculation cycle for drawing. =model,0 mm. the The three volume inlet fraction total pressure distribution are selected of vapor as phase 140 kPa, in each 110 kPa, eccentric and 100 scheme kPa isrespectively similar, so in here this wepaper. take onlyOn the as anbasis example. of the three groups of steady-state calculation results, the unsteady e=0mm numerical e=0mm 103.5 e=5mm simulation109To better of illustrate the cavitation the diff oferent the characteristicspump e=5mm is carried between out, and curves the change in Figure curves6a, we of will the divide three groups the five of e=10mm e=10mm curvespump in head Figure at6 anya into time a hierarchical in Figure 6 graph, are e=15mm obtained. as shown In in order Figure to8 .ensure The five the curves accuracy from of top the e=15mm to calculation bottom e=20mm areresults, eccentricity108 all the ecurves= 15 mm, in Figure e = 10 6 mm, take e thee=20mm= 5data mm, of e the= 0 last mm,103.0 cycle and of e =the20 calculation mm in turn. cycle for drawing.
107 e=0mm e=0mm 102.5 103.5 e=5mm 109 e=5mm 106 e=10mm e=10mm e=15mm Head/m Head/m e=15mm 102.0 e=20mm 105108 e=20mm 103.0
101.5 104107 102.5
103106 101.0 Head/m Head/m 0.20 0.21 0.22 0.23 0.24 0.25 102.00.20 0.21 0.22 0.23 0.24 0.25 105 Time/s Time/s 101.5 104 (a) (b)
103 101.0 0.20 0.21 0.22 0.23 0.24 0.25 0.20 0.21 0.22 0.23 0.24 0.25 Time/s Time/s (a) (b)
Figure 6. Cont.
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e=0mm 80 e=5mm Processes 2020, 8, 98 e=10mm 8 of 15 Processes 2020, 8, x FOR PEER REVIEW e=15mm 8 of 15 78 e=20mm
e=0mm 76 80 e=5mm e=10mm e=15mm 74 78 e=20mm Head/m
72 76
70 74 Head/m
68 72 0.20 0.21 0.22 0.23 0.24 0.25 Time/s 70 (c) 68 Figure 6. The change curves0.20 of the head 0.21 ((a 0.22–c) represent 0.23 conditions 0.24 0.25 with inlet total pressure of Time/s 140 kPa, 110 kPa, and 100 kPa respectively). (c) Figure 7 is a vapor phase volume fraction diagram of three different inlet blades under eccentric Figure 6. The change curves of the head ((a–c) represent conditions with inlet total pressure of 140 kPa, e = 0 mm.Figure The 6. volume The change fraction curves distribution of the head of (( avapo–c) representr phase inconditions each eccentric with inlet scheme total pressureis similar, of so 110140 kPa, kPa, and 110 100 kPa, kPa and respectively). 100 kPa respectively). here we take only as an example. Figure 7 is a vapor phase volume fraction diagram of three different inlet blades under eccentric e = 0 mm. The volume fraction distribution of vapor phase in each eccentric scheme is similar, so here we take only as an example.
(a) (b) (c)
Figure 7. The vapor phase volume fraction diagram of three different inlet pressure condition under Figure 7. The vapor phase volume fraction diagram of three different inlet pressure condition eccentric e = 0 mm (a–c) represent conditions with inlet total pressure of 140 kPa, 110 kPa and 100 kPa under eccentric e = 0 mm (a–c) represent conditions with inlet total pressure of 140 kPa, 110 kPa respectively). Processesand 2020 100, 8 kPa, x FOR respectively). PEER REVIEW (a) (b) (c) 9 of 15
ToFigure better 7.illustrate The vapor the phase different108 volume characteristics fraction diagram between of threecurves different in Figure inlet 6a, pressure we will condition divide the 106 e=15mm five curvesunder in eccentric Figure 6a e =into 0 mm a 104hierarchical (a–c) represent graph, conditions as shown with in inlet Figure total 8. pressure The five of curves 140 kPa, from 110 topkPa to and 100 kPa respectively). 0.20 0.21 0.22 0.23 0.24 0.25 bottom are eccentricity e = 15 mm,108 e = 10 mm, e = 5 mm, e = 0 mm, and e = 20 mm in turn. 106 A e=10mm 104 To better illustrate the different0.20 0.21characteristics 0.22 0.23 between 0.24 curves 0.25 in Figure 6a, we will divide the 108 five curves in Figure 6a into106 a hierarchical graph,A as shown in Figure e=5mm 8. The five curves from top to 104 bottom are eccentricity e = 15Head/m mm,0.20 e = 0.21 10 mm, 0.22 e = 5 0.23mm, e 0.24= 0 mm, 0.25 and e = 20 mm in turn. 108 106 A e=0mm 104 0.20 0.21 0.22 0.23 0.24 0.25 108 106 A e=20mm 104 0.20 0.21 0.22 0.23 0.24 0.25 Time/s Figure 8. The hierarchical graph under the inlet total pressure being140 kPa. Figure 8. The hierarchical graph under the inlet total pressure being140 kPa. When the total inlet pressure of the calculation model is 140 kPa, cavitation occurs inside the When the total inlet pressure of the calculation model is 140 kPa, cavitation occurs inside the nuclear reactor coolant pump, and the head of the nuclear reactor coolant pump will fluctuate around nuclear reactor coolant pump, and the head of the nuclear reactor coolant pump will fluctuate around 107 m. As shown in Figure 8, the head of each eccentric schemes decreases by about 3.8% during the cavitation stage in contrast with the stage of conveying single-phase liquid. Through Figure 7, it can be found that the area of the air bubble in the impeller is small, the volume fraction of the gas in the region is low, the effect of the slight cavitation on the normal transport of the coolant is small at the moment, and the critical cavitation stage is defined. In Figure 6b, the difference of head curves is increased under the eccentricity schemes. When the total inlet pressure is 110 kPa, the head is about 102.5 m, which is 8% lower than that in the non-cavitation state. Figure 8 shows that at this stage, the cavitation area of the impeller increases and the volume fraction of gas increases. The blockage of bubbles in some of the impeller channels has obviously affected the transportation of coolant. Comparing the curves in Figure 6b, the head in the scheme of eccentric distance e = 5 mm is higher than that of the original plan. The cavitation state is defined as a severe cavitation. Figure 6c corresponds to the head curve in each eccentric scheme under the total inlet pressure of 100 kPa. At this moment, the pump head is only 75 m, which is reduced by more than 33%. As can be seen from Figure 8, a large number of bubbles are gathered in the impeller channel, which will block the flow of coolant and seriously affect the safe operation of the nuclear reactor coolant pump. From the cavitation performance curve, it can be found that at this time the pump head presents a fracture type descent, so the cavitation condition is defined as fracture cavitation. According to Figure 6c, in the scheme with eccentricity e = 5 mm under fracture cavitation, head was obviously lower than that of the other groups, while the other groups of heads maintained a high consistency.
4.2. The effect of Eccentricity on the Radial Force of the Impeller Figure 9 is the polar diagram of the resultant of radial force distribution on the impeller under different conditions of critical cavitation, severe cavitation and fracture cavitation.
Radial Force / N Radial Force / N 0 e=0mm 0 e=0mm 15,000 15,000 330 30 e=5mm 330 30 e=5mm e=10mm 10,000 e=10mm 10,000 300 60 e=15mm 300 60 e=15mm 5,000 e=20mm 5,000 e=20mm
0 270 90 0 270 90
5,000 5,000
240 120 240 120 10,000 10,000
15,000 210 150 15,000 210 150 180 180
(a) The critical cavitation (b) The severe cavitation
Processes 2020, 8, x FOR PEER REVIEW 9 of 15
108 106 e=15mm 104 0.20 0.21 0.22 0.23 0.24 0.25 108 106 A e=10mm 104 0.20 0.21 0.22 0.23 0.24 0.25 108 106 A e=5mm 104 Head/m 0.20 0.21 0.22 0.23 0.24 0.25 108 106 A e=0mm 104 0.20 0.21 0.22 0.23 0.24 0.25 108 106 A e=20mm 104 0.20 0.21 0.22 0.23 0.24 0.25 Time/s Figure 8. The hierarchical graph under the inlet total pressure being140 kPa.
ProcessesWhen2020 ,the8, 98 total inlet pressure of the calculation model is 140 kPa, cavitation occurs inside9 ofthe 15 nuclear reactor coolant pump, and the head of the nuclear reactor coolant pump will fluctuate around107 m. As107 shown m. As inshown Figure in8, Figure the head 8, ofthe each head eccentric of each schemes eccentric decreases schemes bydecreases about 3.8% by about during 3.8% the duringcavitation the stage cavitation in contrast stage with in contrast the stage with of conveying the stage single-phaseof conveying liquid. single- Throughphase liquid. Figure Through7, it can Figurebe found 7, it that can thebe found area of that the the air bubblearea of the in the air impellerbubble in is the small, impeller the volume is small, fraction the volume of the fraction gas in theof theregion gas isin low,the region the eff isect low, of the the slight effect cavitationof the slight on cavitation the normal on transport the normal of transport the coolant of isthe small coolant at the is smallmoment, at the and moment, the critical and cavitationthe critical stage cavitation is defined. stage is defined. InIn Figure Figure 66b,b, thethe di differencefference of of head head curves curves is is increased increased under under the the eccentricity eccentricity schemes. schemes. When When the thetotal total inlet inlet pressure pressure is 110 is kPa, 110 the kPa, head the is abouthead 102.5is about m, which102.5 ism 8%, which lower is than 8% that lower in the than non-cavitation that in the nonstate.-cavitation Figure8 showsstate. Figure that at 8 this show stage,s that the at cavitation this stage, area the ofcavitation the impeller area increases of the impeller and the increases volume andfraction the volume of gas increases.fraction of The gas blockageincreases. of The bubbles blockage in some of bubbles of the in impeller some of channels the impeller has obviouslychannels hasaffected obviously the transportation affected the transportation of coolant. Comparing of coolant. the Comparing curves in Figurethe curves6b, the in headFigure in 6 theb, the scheme head ofin theeccentric scheme distance of eccentric e = 5 distance mm is higher e = 5 m thanm is that higher of the than original that of plan. the original The cavitation plan. The state cavitation is defined state as a iseveres defined cavitation. as a severe cavitation. FigureFigure 66cc correspondscorresponds toto thethe head head curve curve in in each each eccentric eccentric scheme scheme under under the the total total inlet inlet pressure pressure of of100 10 kPa.0 kPa. At At this this moment, moment, the the pump pump head head is is only only 75 75 m, m, which which is is reduced reduced by bymore more thanthan 33%.33%. As can can bebe seen seen from from Figure Figure 88,, aa largelarge numbernumber ofof bubblesbubbles areare gatheredgathered inin thethe impellerimpeller channel,channel, whichwhich willwill blockblock the the flow flow of of coolant coolant and and seriously seriously affect affect the the safe safe operation operation of of the the nuclear nuclear reactor reactor coolant coolant pump. pump. FromFrom the the cavitation cavitation performance performance curve, curve, it itcan can be be found found that that at atthis this time time the the pump pump head head presents presents a fracturea fracture type type descent, descent, so so the the cavitation cavitation condition condition is is defined defined as as fracture fracture cavitation. According According to to FigureFigure 6c,c, inin thethe schemescheme withwith eccentricityeccentricity ee = 55 m mmm under under fracture fracture cavitation, cavitation, head head was was obviously obviously lowerlower than than that that of of the the other other groups, groups, while while t thehe other groups of head headss maintained a high consistency.
4.2.4.2. The The effect effect of of Eccentricity Eccentricity on on the the Radial Radial Force Force of of the the Impeller Impeller FigureFigure 9 isis thethe polarpolar diagramdiagram ofof thethe resultantresultant ofof radialradial forceforce distributiondistribution onon thethe impellerimpeller underunder differentdifferent conditions of critical cavitation, severe cavitation and fracture cavitation.
Radial Force / N Radial Force / N 0 e=0mm 0 e=0mm 15,000 15,000 330 30 e=5mm 330 30 e=5mm e=10mm 10,000 e=10mm 10,000 300 60 e=15mm 300 60 e=15mm 5,000 e=20mm 5,000 e=20mm
0 270 90 0 270 90
5,000 5,000
240 120 240 120 10,000 10,000
15,000 210 150 15,000 210 150 Processes 2020, 8, x FOR PEER REVIEW180 180 10 of 15 (a) The critical cavitation (b) The severe cavitation e=0mm Radial Force / N 0 15,000 330 30 e=5mm e=10mm 10,000 e=15mm 300 60 e=20mm 5,000
0 270 90
5,000
240 120 10,000
15,000 210 150 180
(c) The fracture cavitation Figure 9. The polar diagram of the resultant of radial force distribution on the impeller. Figure 9. The polar diagram of the resultant of radial force distribution on the impeller. The last cycle of each unsteady solution is selected for analysis. Each curve is composed of 120 dataThe points last cycle connected of each by unsteady smooth solution lines. The is valueselected of eachfor analysis. point in Each the curve curve represents is composed the resultantof 120 data points connected by smooth lines. The value of each point in the curve represents the resultant force of the radial force at a certain point in the direction. The matching relationship between the impeller and guide blade is consistent at each 0° curve. Observing the above three pictures, we can see that the radial force direction of the impeller changes 10 times periodically in one cycle. Under the critical cavitation condition, the maximum radial force of the impeller is about 10 kN when rotating between 30°and 150°, and the minimum value is about 4 kN. As the impeller continues to rotate, the maximum radial force increases first and then decreases, reaching a maximum value of 13.7 KN in the 290° direction. In this process, the minimum radial force decreases correspondingly, and the radial force of eccentric scheme 10 mm is about 1 kN. When cavitation develops to severe cavitation, the radial force changes more sharply during the rotation of the impeller. The variability of radial force on the impeller between 90° and 240° is less than that in other directions, and the peak value of the radial force in the adjacent four cycles is close, and the periodic variation of the original radial force of the original scheme eccentricity e = 0 mm is not obvious. The difference between the eccentricity schemes is increased, and the difference is mainly reflected in two aspects: first, the maximum radial force of each scheme appears in different directions; second, the difference of radial force increases in the same direction. Under the severe cavitation condition, the radial force change amplitude of the impeller from the initial position to the 90° and the 240° direction to the 360° direction is obviously increased, reaching the maximum value of 15 kN at the initial position, and values in the other directions are slightly larger than the critical cavitation radial force. The minimum radial force in this direction is obviously less than that from 90° to 240°. When the total inlet pressure is equal to 100 kPa, the nuclear reactor coolant pump is in the state of fracture cavitation. At this point, the influence of eccentricity on the radial force of impeller is weakened. As shown in Figure 9c, the radial force of the impeller shows obvious periodicity during a cycle of rotation, the radial force changes smoothly, and resultant radial force in the range of 0– 150° during impeller rotation slightly greater than 150–360° range. The peak value and valley value of each cycle are basically equal, the radial force peak is about 11 kN, and the valley value is about 5 kN. Comparing Figure 9a with 9b, the minimum radial force decreases as the impeller is rotated to the direction of the radial force that is significantly increased, and the amplitude of the radial force increases. The asymmetric distribution of radial force will aggravate the vibration of the nuclear reactor coolant pump under cavitation condition and threaten the safe operation of the nuclear reactor coolant pump. Moreover, the phenomenon of radial force asymmetry is more prominent in severe cavitation stage. When the internal cavitation of the impeller develops to the fracture cavitation, the radial force asymmetry will be improved. Comparing the three pictures in Figure 9, it is found that the radial force distribution in the fracture cavitation state is better than that in the
Processes 2020, 8, 98 10 of 15 force of the radial force at a certain point in the direction. The matching relationship between the impeller and guide blade is consistent at each 0◦ curve. Observing the above three pictures, we can see that the radial force direction of the impeller changes 10 times periodically in one cycle. Under the critical cavitation condition, the maximum radial force of the impeller is about 10 kN when rotating between 30◦and 150◦, and the minimum value is about 4 kN. As the impeller continues to rotate, the maximum radial force increases first and then decreases, reaching a maximum value of 13.7 KN in the 290◦ direction. In this process, the minimum radial force decreases correspondingly, and the radial force of eccentric scheme 10 mm is about 1 kN. When cavitation develops to severe cavitation, the radial force changes more sharply during the rotation of the impeller. The variability of radial force on the impeller between 90◦ and 240◦ is less than that in other directions, and the peak value of the radial force in the adjacent four cycles is close, and the periodic variation of the original radial force of the original scheme eccentricity e = 0 mm is not obvious. The difference between the eccentricity schemes is increased, and the difference is mainly reflected in two aspects: first, the maximum radial force of each scheme appears in different directions; second, the difference of radial force increases in the same direction. Under the severe cavitation condition, the radial force change amplitude of the impeller from the initial position to the 90◦ and the 240◦ direction to the 360◦ direction is obviously increased, reaching the maximum value of 15 kN at the initial position, and values in the other directions are slightly larger than the critical cavitation radial force. The minimum radial force in this direction is obviously less than that from 90◦ to 240◦. When the total inlet pressure is equal to 100 kPa, the nuclear reactor coolant pump is in the state of fracture cavitation. At this point, the influence of eccentricity on the radial force of impeller is weakened. As shown in Figure9c, the radial force of the impeller shows obvious periodicity during a cycle of rotation, the radial force changes smoothly, and resultant radial force in the range of 0–150◦ during impeller rotation slightly greater than 150–360◦ range. The peak value and valley value of each cycle are basically equal, the radial force peak is about 11 kN, and the valley value is about 5 kN. Comparing Figure9a with b, the minimum radial force decreases as the impeller is rotated to the direction of the radial force that is significantly increased, and the amplitude of the radial force increases. The asymmetric distribution of radial force will aggravate the vibration of the nuclear reactor coolant pump under cavitation condition and threaten the safe operation of the nuclear reactor coolant pump. Moreover, the phenomenon of radial force asymmetry is more prominent in severe cavitation stage. When the internal cavitation of the impeller develops to the fracture cavitation, the radial force asymmetry will be improved. Comparing the three pictures in Figure9, it is found that the radial force distribution in the fracture cavitation state is better than that in the critical and severe cavitation state. Not only is the variation of radial force smaller, but also the maximum radial force is slightly smaller than the critical and severe cavitation. In Figure9c, the position of the radial force peak in each cycle of the eccentricity of 5, 10, 15, and 20 four groups is about 6◦ clockwise relative to the eccentricity of 0, and the position of the valley value is basically consistent. It shows that the eccentric scheme can change the direction of the resultant radial force on the impeller of the pump. In the critical and severe cavitation state, the phenomenon is not obvious because of the cavitation inside the impeller of the pump.
4.3. Influence of Eccentricity on Axial Force of Nuclear Reactor Coolant Pump Impeller Figure 10 is the time-domain diagram of the axial force of a nuclear reactor coolant pump impeller under different eccentricity and different cavitation conditions. In numerical calculation, the +Z axis is pointed from the front cover plate of the impeller to the rear cover plate. The axial force is negative in the figure, indicating that the axial force direction points to the impeller inlet. As shown in Figure 10, with the deepening of cavitation of the nuclear reactor coolant pump, the axial force of the impeller decreases, and the downward trend increases with the increase of cavitation. The average axial force under critical cavitation is 149 kN, which is 4.7% larger than that under severe cavitation. The axial force decreases linearly in the fracture cavitation, and the axial force is 56.4~61.7% of axial force in Processes 2020, 8, x FOR PEER REVIEW 11 of 15 critical and severe cavitation state. Not only is the variation of radial force smaller, but also the maximum radial force is slightly smaller than the critical and severe cavitation. In Figure 9c, the position of the radial force peak in each cycle of the eccentricity of 5, 10, 15, and 20 four groups is about 6° clockwise relative to the eccentricity of 0, and the position of the valley value is basically consistent. It shows that the eccentric scheme can change the direction of the resultant radial force on the impeller of the pump. In the critical and severe cavitation state, the phenomenon is not obvious because of the cavitation inside the impeller of the pump.
4.3. Influence of Eccentricity on Axial Force of Nuclear Reactor Coolant Pump Impeller Figure 10 is the time-domain diagram of the axial force of a nuclear reactor coolant pump impeller under different eccentricity and different cavitation conditions. In numerical calculation, the +Z axis is pointed from the front cover plate of the impeller to the rear cover plate. The axial force is negative in the figure, indicating that the axial force direction points to the impeller inlet. As shown in Figure 10, with the deepening of cavitation of the nuclear reactor coolant pump, the axial force of the impeller decreases, and the downward trend increases with the increase of cavitation.
ProcessesThe average2020, 8, 98 axial force under critical cavitation is 149 kN, which is 4.7% larger than that 11 under of 15 severe cavitation. The axial force decreases linearly in the fracture cavitation, and the axial force is 56.4~61.7% of axial force in critical cavitation state. In Figure 10c, the axial force in the eccentricity e = critical5 mm cavitation scheme is state. significantly In Figure smaller 10c, the thanaxial force that ofin the the eccentricity other four e groups,= 5 mm andscheme the is axial significantly force is smallerreduced than by 4 that kN.of the other four groups, and the axial force is reduced by 4 kN.
e=0mm e=0mm e=5mm -141,000 e=5mm e=10mm -148,000 e=10mm e=15mm e=15mm e=20mm -141,500 e=20mm -148,500
N
/ -142,000 -149,000
-142,500 -149,500
Axial Force / N
Axial Force -143,000 -150,000
-143,500 -150,500 0.20 0.21 0.22 0.23 0.24 0.25 0.20 0.21 0.22 0.23 0.24 0.25 Time/s Time/s (a) The critical cavitation (b) The severe cavitation e=0mm e=5mm -82,000 e=10mm e=15mm -84,000 e=20mm
-86,000
-88,000
Axial Force / N -90,000
-92,000
-94,000
0.20 0.21 0.22 0.23 0.24 0.25 Time/s (c) The fracture cavitation
Figure 10. The time-domain diagram of the axial force of a nuclear reactor coolant pump impeller.
InFigure the fracture 10. The cavitation time-domain status, diagram the axial of the force axial in the force two of groups a nuclear of eccentricity reactor coolante = pump5 mm and e = 10impeller. mm is less than that in the original scheme eccentricity e = 0 mm. When the eccentricity e = 15 mm and e = 20 mm, axial forces are basically equal, which are greater than the original scheme In the fracture cavitation status, the axial force in the two groups of eccentricity e = 5 mm and e = eccentricity e = 0 mm. When the impeller is in critical cavitation and severe cavitation stages, the 10 mm is less than that in the original scheme eccentricity e = 0 mm. When the eccentricity e = 15 mm axial force time-domain diagram fluctuates in disorder. Although the axial force changes of each and e = 20 mm, axial forces are basically equal, which are greater than the original scheme group showed a certain periodicity, the periodic characteristics of each group were obviously different. eccentricity e = 0 mm. When the impeller is in critical cavitation and severe cavitation stages, the The difference value between the maximum and the minimum of the axial force in the critical and axial force time-domain diagram fluctuates in disorder. Although the axial force changes of each severe cavitation state when e = 20 mm is the maximum value, and this will lead to the larger group showed a certain periodicity, the periodic characteristics of each group were obviously vibration of the impeller in the axial direction. It is found that the axial force fluctuation when the eccentricity e = 10 mm is smaller than that of the original scheme, and the curve is distributed above the original scheme curve, indicating that the axial force of the impeller is slightly smaller than in the original scheme. Figure 11 is the frequency-domain diagram of the axial force of the impeller in the pump under different eccentricity and different cavitation conditions. Table3 is the frequency and amplitude analysis table of the axial force of the impeller in the pump. In this paper, the impeller speed of the main hydraulic pump model is 1480 r/min and the number of blades is 5. The calculated shaft frequency is 24.67 Hz and the blade frequency is 123.33 Hz. Under the critical cavitation condition, the maximum amplitude of axial force appears at two times of shaft frequency. The maximum amplitude of the five groups of e = 0 mm, e = 5 mm, e = 10 mm, e = 15 mm, and e = 20 mm are 385 N, 306 N, 377 N, 375 N, and 395 N, respectively. There is a larger amplitude at blade frequency and shaft frequency. There is a large amplitude at three times of blade frequency in the four schemes other than e = 15 mm scheme. The vibration is mainly concentrated in the low and medium frequency, and the amplitude decreases after three times of blade frequency. The eccentricity e = 10 mm scheme has the most steady amplitude after two times of blade frequency. The maximum amplitude of the five schemes in the high frequency range is that of the original scheme. Processes 2020, 8, x FOR PEER REVIEW 12 of 15 group showed a certain periodicity, the periodic characteristics of each group were obviously different. The difference value between the maximum and the minimum of the axial force in the critical and severe cavitation state when e = 20 mm is the maximum value, and this will lead to the larger vibration of the impeller in the axial direction. It is found that the axial force fluctuation when the eccentricity e = 10 mm is smaller than that of the original scheme, and the curve is distributed above the original scheme curve, indicating that the axial force of the impeller is slightly smaller than in the original scheme. Figure 11 is the frequency-domain diagram of the axial force of the impeller in the pump under different eccentricity and different cavitation conditions. Table 3 is the frequency and amplitude analysis table of the axial force of the impeller in the pump. In this paper, the impeller speed of the main hydraulic pump model is 1480 r/min and the number of blades is 5. The calculated shaft frequency is 24.67 Hz and the blade frequency is 123.33 Hz. Under the critical cavitation condition, the maximum amplitude of axial force appears at two times of shaft frequency. The maximum amplitude of the five groups of e = 0 mm, e = 5 mm, e = 10 mm, e = 15 mm, and e = 20 mm are 385 N, 306 N, 377 N, 375 N, and 395 N, respectively. There is a larger amplitude at blade frequency and shaft frequency. There is a large amplitude at three times of blade frequency in the four schemes other than e = 15 mm scheme. The vibration is mainly concentrated in the low and medium frequency, and the amplitude decreases after three times of blade frequency. The eccentricity e = 10 mm scheme has the most steady amplitude after two times of blade frequency. The maximum Processes 2020, 8, 98 12 of 15 amplitude of the five schemes in the high frequency range is that of the original scheme.
400 e=15mm 400 e=15mm 200 200 0 0 0 300 600 900 1200 0 300 600 900 1200 400 400 e=10mm e=10mm 200 200 0 0 0 300 600 900 1200 0 300 600 900 1200 400 400 e=5mm 200 e=5mm 200 0 0 0 300 600 900 1200 0 300 600 900 1200 400 e=0mm 400 e=0mm 200 200 0 0 Axial Force Amplitude/N 0 300 600 900 1200 Axial Force Amplitude/N 0 300 600 900 1200 400 e=20mm 400 e=20mm 200 200 0 0 0 300 600 900 1200 0 300 600 900 1200 Frequency/Hz Frequency/Hz (a) The critical cavitation (b) The severe cavitation 2000 e=15mm 1000 0 0 300 600 900 1200 2000 1000 e=10mm 0 2000 0 300 600 900 1200 1000 e=5mm 0 2000 0 300 600 900 1200 1000 e=0mm 0 0 300 600 900 1200
Axial Force Amplitude/N Force Axial 2000 1000 e=20mm 0 0 300 600 900 1200
Frequency/Hz (c) The fracture cavitation
Figure 11. The frequency-domain diagram of the axial force of the impeller in the pump.
Table 3. The frequency and amplitude analysis table of the axial force of the impeller in the pump.
Cavitation e = 0 mm e = 5 mm e = 10 mm e = 15 mm e = 20 mm States The maximum Critical 355 306 377 375 355 amplitudes (N) cavitation Blade frequency (f ) 3 f 3 f 2 f 2 f 3 f The maximum Severe 345 226 398 381 370 amplitudes (N) cavitation Blade frequency (f ) 2 f 2 f 2 f 2 f 1 f The maximum Fracture 1424 1675 1408 1435 1464 amplitudes (N) cavitation Blade frequency (f ) 1 f 1 f 1 f 1 f 1 f Note: f —the blade frequency.
In the severe cavitation condition, the maximum amplitude appears at the blade frequency when e = 20 mm and appears at 2 times the blade frequency in other four schemes. The figures of e = 0 mm, e = 5 mm, e = 10 mm, e = 15 mm, and e = 20 mm show that the maximum amplitudes in each curve Processes 2020, 8, 98 13 of 15 are 345 N, 226 N, 398 N, 381 N, and 270 N in turn. The e = 5 mm curve shows low amplitude vibration at all frequency bands. Compared with the other four groups, at all frequency bands of eccentricity e = 5 mm, there has no obvious steady or high amplitude region. The amplitude of the original scheme was 330 N and 343 N at 4.5 times the blade frequency and 7 times the blade frequency and was almost equal to the maximum amplitude of the two times blade frequency, and the rest of the schemes did not appear the fluctuation of the amplitude which is equal to the maximum amplitude in the high frequency range. Under the condition of fracture cavitation, the maximum amplitude is located at shaft frequency, and the minimum amplitude appears at blade frequency. The amplitude decreases greatly and the vibration is gentle after blade frequency. The maximum amplitudes of each group after 3 times the blade frequency were no more than 150 N, and the vibration was concentrated in the low frequency range. The maximum amplitude of each curve is 1424 N, 1675 N, 1408 N, 1435 N, and 1464 N, respectively. Through the comparison of the axial force frequency-domain diagram under different cavitation conditions, it was shown that the maximum amplitudes of the critical and severe cavitation conditions were basically equal, and the maximum amplitude of the axial force vibration under fracture cavitation is far greater than that in the other two conditions. As for the overall axial force frequency diagram, with the development of cavitation, the amplitude of axial force vibration increases. In the same cavitation state, the difference in frequency-domain between different eccentricity schemes is obvious, and the vibration characteristics of each curve are not consistent in the full frequency range. The same eccentricity scheme also shows different rules under different cavitation states. Taking eccentricity e = 5 mm, e = 10 mm, e = 15 mm as an example, and the vibration in low frequency range of e = 10 mm and e = 15 mm under critical and severe cavitation state is larger than that of e = 5 mm, while the amplitude of the e = 5 mm scheme at the shaft frequency under fracture cavitation is much larger than that of the e = 10 mm and e = 15 mm two groups. Combined Figure 10 with Figure 11, it can be found that when the eccentricity is e = 5 mm, the axial force of the impeller is smaller than the other three schemes. The amplitude of the whole frequency band under critical and severe cavitation state is smaller than that at the shaft frequency of the other groups, except for the amplitude at the shaft frequency in the fracture cavitation stage, which was a larger one.
5. Conclusions In this paper, through the steady and unsteady numerical simulation of the internal flow field of the nuclear reactor coolant pump under three different cavitation states, the change rules of cavitation characteristics, radial force and axial force of the pump under different eccentricity are studied. The following conclusions are drawn:
1. The influence of different eccentricity on the cavitation performance of the nuclear reactor coolant pump is obvious, and the effect is increased with the aggravation of cavitation condition. Under the condition of fracture cavitation, the influence on head is the greatest when the eccentricity is 5 mm. 2. Under the critical and severe cavitation conditions, the radial force of the rotor system varies greatly with the impeller rotation, and the radial force variation of the rotor system under the fracture cavitation condition is more uniform. 3. Under severe cavitation conditions, the difference of eccentricity schemes is most significant in the range of 90 to 240 degrees. Under fracture cavitation condition, when the eccentricity is 5 mm, 10 mm, 15 mm, and 20 mm respectively, the position of the radial force peak is about 6 degrees clockwise as to the 0 mm scheme, and the position of the valley value is basically unchanged. 4. Under critical and severe cavitation conditions, the maximum axial force amplitude of the nuclear reactor coolant pump appears at 2 times of the blade frequency and occurs at shaft frequency under the condition of fracture cavitation. Under the condition of fracture cavitation, the corresponding axial force amplitude is much larger than that in critical and severe cavitation conditions. Processes 2020, 8, 98 14 of 15
5. When the nuclear reactor coolant pump is in the critical and severe cavitation condition, the axial force fluctuates most when the eccentricity is 20 mm, and the axial force amplitude is smaller when the eccentricity is 10 mm, and the axial force is smaller than that in the original scheme. In the fracture cavitation condition, when the eccentricity is 5 mm, the axial force of the rotor system is the least, but the amplitude of the axial force is the largest at the shaft frequency. The obtained results can provide reference for the design of new nuclear main pumps.
Author Contributions: Y.Z.: Experiments and simulations; B.L.: modification of the paper; X.W.: ideas and funding acquisition; R.Z., Q.F.: experimental and simulated data processing. All authors have read and agreed to the published version of the manuscript Funding: National Key Research and Development Project (2018YFB0606105); “Supported by the Open Research Fund of Key Laboratory of ministry (provincial), (Sanxia University)” (2017KJX14); National Natural Science Foundation of China (51379091); National Youth Natural Science Foundation of China (51509112); Key R&D programs of Jiangsu Province of China (BE2016160, BE2017140, BE2018112); Natural Science Foundation of Jiangsu Province of China (BK20171302); Prospective joint research project of Jiangsu Province (BY2016072-02); The China Postdoctoral Science Foundation Funded Project (2019M651734); National Youth Natural Science Foundation of China (51906085) Key R&D programs of Anhui Province of China (201904a05020070); Key R&D programs of Taizhou City (TG201918). Conflicts of Interest: The authors declare no conflict of interest.
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