Numerical Investigation on Pressure Pulsation Characteristics and Radial … · 2019. 9. 19. · ResearchArticle Numerical Investigation on Pressure Pulsation Characteristics and

Research ArticleNumerical Investigation on Pressure Pulsation Characteristicsand Radial Force of a Deep-Sea Electric Lifting Pump atOff-Design Conditions

Yajuan Kang ,1,2,3 Shaojun Liu ,2,3,4 Weisheng Zou ,5 and Xiaozhou Hu 1,3

1College of Mechanical and Electrical Engineering, Central South University, Changsha 410083, China2Shenzhen Research Institute of Central South University, Shenzhen 518000, China3National Key Laboratory of Deep Sea Mineral Researches Development and Utilization Technology, 410083 Changsha, China4Shenzhen Far East Mineral Exploitation Research Institute Co. Ltd., Shenzhen 518000, China5College of Mechanical and Vehicle Engineering, Hunan University, Changsha 410082, China

Correspondence should be addressed to Shaojun Liu; [email protected] and Xiaozhou Hu; [email protected]

Received 30 April 2019; Revised 9 August 2019; Accepted 27 August 2019; Published 22 September 2019

Academic Editor: Stefano Manzoni

Copyright © 2019 Yajuan Kang et al. 0is is an open access article distributed under the Creative Commons Attribution License,which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

To predict the vibrational conditions, the generation mechanism, and action law of pressure pulsation and radial force, acomputational fluid dynamics (CFD) study of a deep-sea electric lifting pump operating under different off-design conditions wasperformed. 0e time-domain and frequency-domain response of the pressure pulsation at different monitoring points and theradial force of impeller distribution were obtained. Differences in pressure pulsation characteristics between the first stage andsecond stage were observed. 0e variation law and influential factors of the radial force under different flow rates were discussed.0e present investigation shows that the flow field caused by rotor-stator interaction is not uniform, resulting in uneven pressuredistribution and pressure pulsation, the combined effects of which produce fluctuating radial forces. Parameters obtained viasimulations including head, efficiency, and power, which can reflect the hydraulic performance of the pump, agree well withexperimental results; thus, the accuracy of the simulation model and the calculation method was verified. 0is study provides abasis for improving the structure and reliability of an electric lifting pump.

1. Introduction

0e deep sea contains rich mineral resources such as poly-metallic nodules, cobalt-rich nodules, and hydrothermalsulfides. [1]. With the depletion of terrestrial mineral re-sources, the development and utilization of seabed mineralresources has become a hot topic in the international com-munity [2, 3]. 0e electric lifting pump is a key piece ofequipment for deep-sea mining systems and is used to liftmineral resources from the seabed to the mining vessel on thesea surface; it is known as the “heart” of the lifting system [4].China’s self-developed electric lifting pump is a multistagecentrifugal pump, themain overcurrent components of whichare the impeller and diffuser. Because of the special opera-tional environment and requirements, a conventionalpumpdesign method cannot meet the design requirements of an

electric lifting pump. 0erefore, the electric lifting pumpdesigned in China adopts an increased flow rate method towiden the flow channel of the impeller such that large particlenodules can smoothly pass through [5]. However, because ofthe use of the increased flow rate method, the design flowpoint of the pump deviates from the rated flow point; thus, thepump operates under an off-design condition. When thepump deviates from the design condition, the fluid flowdistribution in the impeller is not as uniform as that underdesign conditions, which leads to pump dynamic instability,and the force acting on the impeller becomes more complex.In addition, the relative movement between the rotatingimpeller and stationary diffuser, and the circular motion ofthe medium flow in the diffuser, during off-design conditionsmay cause the pressure to rapidly fluctuate with time, resultingin pressure pulsation [6]. Pressure pulsation may cause radial

HindawiShock and VibrationVolume 2019, Article ID 4707039, 16 pageshttps://doi.org/10.1155/2019/4707039

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force fluctuation, which will induce vibration and lead tobearing and seal fatigue [7].0e pumpoutlet pressure pulsationmay also cause lifting pipeline resonance, thus seriously af-fecting the deep-sea mining safety. 0erefore, the study of thepressure fluctuation and radial force in the flow field of anelectric lifting pump can not only grasp the characteristics ofpressure fluctuation and radial force but also effectively preventfailure of the pump caused by the pressure fluctuation andradial force.

0e study of the pressure pulsation characteristics andradial force in the centrifugal pump mainly includes twomethods: tests and numerical calculations. Because of the highcost, it is difficult to use experimental means to monitorpressure pulsation and radial force in the pump (particularly onrotating blades). In contrast, with the development of CFDtechnology, calculation of the flow field inside hydraulic me-chanicals has now developed into a full three-dimensional (3D)viscous and unsteady stage, and quite in-depth research resultshave been obtained. Gonzáles et al. [8] numerically studied thepressure fluctuation characteristics of centrifugal pumps andvalidated the feasibility of numerical simulation via experi-ments. Guo and Okamoto [9], Li et al. [10], Feng et al. [11],Zhou et al. [12], Dupont et al. [13], and Shi and Tsukamoto [14]studied pressure pulsation and radial force in a centrifugalpump.0e results showed that pressure pulsations were causedby rotor-stator interaction. Yao [15], Anish et al. [16], andJaatinen et al. [17] investigated the influence of the diffuser onthe flow field in the pump and found that the internal flow fieldof the centrifugal pump was mainly affected by rotor-statorinteraction. Yuan and Ni [18] studied the clocking effect onpressure fluctuation in a centrifugal pump under off-designconditions and concluded that the effect of diffuser clocking onthe pressure pulsation intensity in a centrifugal pumpwasmoreobvious. Solis et al. [19] studied the flow characteristics in therotating impeller region and concluded that the pressurefluctuation frequency was exactly the blade frequency underdifferent flow rates. Esch et al. [20] performed numericalcalculations to predict the radial force of a centrifugal pumpwith different impeller outer diameters and compared thecalculation results to the experimental results, and they showedgood agreement. Barrio et al. [21] studied the radial forcedistribution of a centrifugal pump impeller using theoretical,numerical, and experimental methods and concluded that theradial force under a nondesign condition was greater than thatunder a design condition. Gonzalez et al. [22] studied the radialforce characteristics of an impeller under different tongue gapconditions and found that the change in the gap at the tonguehad a great influence on the radial force. Yang et al. [23] studiedthe radial force of a centrifugal pump and found that the radialforce distribution of the impeller is not uniform, and the phasechange of the impeller is unstable.

0e aforementioned works on pressure fluctuation andradial force of a centrifugal pump mostly focused on thesingle-stage centrifugal pump or one stage of the multistagecentrifugal pump. Research regarding interference phe-nomenon between the rotating impeller and static diffuserin the multistage centrifugal pump is not sufficiently com-prehensive, and the influence from stage to stage is not con-sidered, which leads to an insufficient understanding of the

internal flow characteristics of the pump as a whole. In ad-dition, up to now, there have been limited research studiesregarding deep-sea electric lifting pumps, particularly researchon the pressure pulsation characteristics and radial force undernondesign conditions and the characteristics of the interactionbetween the stages.

In this study, the 3D unsteady flow field of a two-stageelectric lifting pump was calculated. After being verified byhydraulic performance tests, the CFD model was utilized topredict pressure pulsation and radial force of the multistageelectric lifting pump. 0e pressure pulsation during the firststage and second stage was compared, and the variation lawand influential factors of the radial force under different flowconditions were discussed. 0e present work can provide atheoretical basis for further study of transient characteristicsand structural optimization of a deep-sea electric lifting pump.

2. Numerical Method

2.1. CalculationModels. A two-stage electric lifting pump wasselected as the calculationmodel. According to the requirementof a 1000m pilot marine test system developed by the ChinaOcean Mineral Resources R&D Association (COMRA), therated flow rate of the electric lifting pump is 420m3/h, thedensity of the nodule is 2000 kg/m3, and the maximum particlesize of nodules is 20mm. To allow the coarse particles tosmoothly pass through the electric lifting pump, the increasedflow rate method was applied to design the pump, which canwiden the flow channel; however, this method can cause theflow design point to be at the rated operating point. 0e ro-tating speed n was 1450 rpm, the design flow rate Q was800m3/h, and the single-stage head H was 40m. 0e overallstructure of the two-stage lifting motor pump is shown inFigure 1. A two-dimensional (2D) illustration of the electriclifting pump stage is shown in Figure 2. 0e specification andmain geometric parameters are shown in Table 1.

2.2. Simulation Domain andMesh Generation. 3D modelingof a two-stage electric lifting pump was performed usingPro/E. To avoid the influence of the inlet vortex zone on theflow field and flow rate, a section of the inlet pipe was addedat the impeller inlet; considering the influence of the outletboundary condition on the diffuser outlet and convergence,a section of the outlet pipe was added at the diffuser outlet.0e simulation domain is shown in Figure 3.

0e mesh of the intake pipe, impellers, diffusers, anddischarge pipe was generated using the commercial softwareANSYS 18.0 module ICEM. To facilitate discrete equationconvergence and more accurately solve the pressure gradient,meshes for all the components were created using hexahedralcells as shown in Figure 4. To improve the fitness of the grid,the mesh was locally refined in the near-wall area. Tomeet therequirements of the shear stress transport (SST) k-ω turbu-lence model, the Y+ value was maintained near 1.0 in ac-cordance with the suggestion in the literature, and goodnumerical resolution was ensured in the boundary layer [24].A grid independence verification for a two-stage electriclifting pump simulation was performed considering the six

2 Shock and Vibration

levels of grid refinement as listed in Table 2. To improve thecalculation efficiency without reducing the calculation pre-cision, the head of the rated flow point at less than 1% wasused as the indicator of grid independence verification[25, 26]. As shown in Table 2, fluctuations in the head aresmall when the number of grids is greater than 5.2 million.Considering the configuration and calculation time of thecomputer, the grid numbers for the different componentswere as follows: impeller, 1,012,468; diffuser, 1,365,458; andinlet and outlet, 261,217.

2.3. Monitoring Points. To analyze the pressure pulsationcharacteristics, different monitoring points were set on thepressure side and suction side of the adjacent flow channelsof the first stage impeller blades, respectively, as shown inFigure 5(a). Figure 5(b) shows the monitoring points on thediffuser blades, from which it can be seen that monitoringpoints D11, D12, D13, D14, and D15 are set along the flowdirection. Similarly, the monitoring points were set to thesame position inside the second stage marked with the lowercorner “2.”

2.4. Governing Equations. 0e Reynolds-averaged Navier–Stokes equations were applied for the calculation of the flowfield inside the electrical lifting pump as follows [27]:

(1) Continuity equation:

z(ρ)zt

+z ρui(

zxi� 0. (1)

(2) Momentum equation:

zρizt

+z ρiuj

zxj� −

zP

zxi+

z

zxjμ

zui

zxj+

zuj

zxi

+ μtzui

zxj+

zuj

zxi −

23

ρk + μtzui

zxj δij + Fi,

(2)

where μ is the dynamic viscosity, Fi is the source item, k is theturbulent kinetic energy, and μt is the turbulent viscosity.

D4 = D6

D3 = D5

D2D1

D7

D8

Impellerinlet

Diffuseroutlet

Bladepressure side

Bladesuction side

β2

β1

β3

β4

Diffuser

Impeller

Figure 2: 2D illustration of the electric lifting pump stage.

1 2 3 4 5 6 7

Figure 1: Overall structure of the two-stage electric lifting pump. 1, inlet flange; 2, motor; 3, motor cylinder body; 4, impeller; 5, diffuser;6, pump cylinder body; 7, outlet flange.

Shock and Vibration 3

2.5. Boundary Condition and Solution Method. �e inletboundary was set as the total pressure with the referencepressure 1 atm, and the turbulent density of the inlet was setto 5%; the outlet was set as the mass �ow. �e impeller wascalculated in a rotating coordinate system in a multi-coordinate system, and the remainder of the �ow passageswas calculated in a stationary coordinate system. �e SSTk-ω turbulence model combines the merits of the k-ωturbulence model and the k-ε turbulence model in theboundary layer calculations and has good calculation

accuracy, as suggested by Ofuchi. �us, it was chosen as thecalculation model in this work [28, 29]. In the unsteadycalculation, the dynamic and static components were cou-pled using a transient rotor-stator method and the steadycalculation results were taken as the initial conditions for theunsteady calculation.�e governing equations were spatiallydiscretized based on the nite volume method. �e timediscretization adopts the second-order full implicit scheme.�e unsteady time step was set to 4.597×10− 4 s, corre-sponding to the changed angle of 4° of the impeller rotation.For accuracy analysis, 10 cycles were calculated, and the dataof the last cycle were analyzed. �e convergence criterionwas set to 10− 5.

3. Experimental Verification

To verify the calculation accuracy, the head, power, andeciency of the two-stage electric lifting pump underdierent �ow rates were numerically predicted and com-pared to the corresponding experimental results. Completehydraulic performance experiments were carried out on atest bench for the two-stage electric lifting pump, as shown inFigure 6. �e test device, conditions, methods, and data wereall in accordance with the requirements of the acceptance testfor hydraulic performance of a rotary power pump GB/T3216-2016 [30].

�e test device was mainly composed of an electric liftingpump, test pipelines, and a stabilization pipe. �e test in-strument was composed of an electromagnetic �ow meter, apressure transmitter, and a hydraulic mechanical compre-hensive tester. A change in the working point was realized by

Table 1: Main specications and geometric parameters.

Description Parameter ValueRated �ow rate Qr (m3/h) 420Design �ow rate Qd (m3/h) 800Stage S 2Total head H (m) 80Single-stage head Hs (m) 40Rotating speed n (rpm) 1450Specic speed ns 157Length of the two-stage electric lifting pump L (mm) 5739

Impeller

Inlet inlet diameter D1 (mm) 85Outlet inlet diameter D2 (mm) 390Inlet outlet diameter D3 (mm) 240Outlet outlet diameter D4 (mm) 408

Inlet blade angle β1 29°Outlet blade angle β2 21°

Outlet blade width b2 (mm) 75Blade number Z1 3

Diuser

Inlet inlet diameter D5 (mm) 390Outlet inlet diameter D6 (mm) 85Inlet outlet diameter D7 (mm) 550Outlet outlet diameter D8 (mm) 240

Inlet blade angle β3 12°Outlet blade angle β4 85°Vane number Z2 4

Several dimensions are shown in Figure 2.

Inlet:total pressure (Pref = 1atm)

Outlet:specified flow rate

Discharge pipe

Diffusers

Intake pipe

Impellers

�e second stage

�e first stage

ω

Figure 3: Generic representation of the simulation domain.


adjusting the opening of the regulating valve in the outletpipeline. �e pump was tested at a speed of 1450 rpm.

Figure 7 shows a comparison between the numericalresults and experimental results at dierent �ow rates. �esimulation values were consistent with the overall trends of

the experimental values. Specically, the head of the pumpobtained via the numerical simulations was slightly higherthan that via the experiments, and the relative error (relativeerror is the ratio of the dierence between the simulatedvalue and the experimental value to the experimental value)

(a) (b) (c)

Figure 4: Computational grids used for the electric lifting pump: (a) impeller, (b) diuser, and (c) two-stage model.

S11P11

P12

P13

P14

P15

S12

S13S14 S15

(a)

D15

21°

21°

21°

21°

D14

D13

D12

D11

(b)

Figure 5: Monitoring point positions inside the (a) impeller and (b) diuser.

Table 2: Grid independence analysis (Q� 420m3/h; n� 1450 rpm).

Grid Impeller Diuser Inlet andoutlet Total (two stages)Head(m)

1 388455 504336 324512 2110094 87.142 562764 788689 432589 3135495 88.483 863458 1097513 467894 4389836 89.574 1012468 1365458 522434 5278286 89.755 1413368 1545079 625603 6542497 89.816 1732435 1887846 651450 7892012 89.89


was no greater than 4.5%, while the design �ow point was3.1%; however, the simulated eciency at a small �ow pointwas slightly larger than the experimental value, and therelative error was no greater than 10%, while the design �owpoint was 2.9%. �erefore, it can be concluded that thenumerical method and model can accurately predict thehydraulic performance characteristics of the electric liftingpump. �eir correctness can be veried and provide aguarantee for further investigations regarding pressure�uctuation and impeller radial force.

4. Results

4.1. Pressure Pulsation. In real industrial applications, be-cause the impeller is rotating at a high speed and the diuseris stationary, a so-called rotor-stator interaction phenom-enon occurs, which is the main reason for the pressurepulsation in the pump. For the rated �ow rate, the staticpressure distribution at z� 170mm (this section is theposition of the impeller outlet and the diuser inlet) withdierent time steps is shown in Figure 8. It is shown thatbecause of the interaction between the rotor and stator, asthe impeller blade is near the diuser blade, the staticpressure in the edge of impeller blade and the correspondingpassage signicantly increases, resulting in an uneven staticpressure distribution. �e combined action of these �uc-tuating pressures produces the �uctuating radial force of the�uid. �erefore, to study the �uid radial force inside thepump, the pressure pulsation inside the pump needs to beanalyzed.

To analyze the pressure pulsation, the pressure pulsationcoecient Cp was used to measure the magnitude of thepressure pulsation as follows:

Cp �P − P0.5 ρu2

, (3)

where P is the static pressure at the position of the moni-toring point, P is the average pressure of the impeller in onerotation period, ρ is the water density, and u is the peripheralspeed of the impeller outlet.

Shock absorber (26.3m)

No. 2 tower

Water tank(7.65m)

Gate valve (6m)Electric valve (4m)

Back pressurecompensator (0m)

Water bag (–1.4m)

No. 1 working platform (0m)

Pressure gauge (2.4m)Feeder (4.1m)

Control room (4.2m)Electric li�ing pump (7.05m)Bin (7.05m)

Pressure gauge (7.2m)

No. 2 working platform(7.8m)

No. 1 tower

Differential pressuregauge (14–18m)

No. 3 workingplatform (19m)

Flow meter (19.2m)Glass tube (20.2m)

No. 4 workingplatform (22m)

Calibration box(22.2m)

No. 5 workingplatform (26.6m)

Regulated water tank (27.6m)Li�ing pipe outlet (28.6m)

Water pump (0m)

Inverted U-tube

Figure 6: Two-stage electric lifting pump experimental system.

NUM EXPPowerEfficiencyHead

0

20

40

60

80

η (%

)

0

20

40

60

80

100

120

H (m

)

100 200 300 400 500 600 700 800 900 10000Q (m3/h)

0

200

400

600

800

P (k

W)

Figure 7: Characteristic curves of the two-stage electric liftingpump.


Figures 9(a) and 9(b) show that the pressure pulsation ofmonitoring points in the impeller is periodic in the first-stage impeller. When the impeller blade sweeps the diffuserblade, there is a significant pressure fluctuation in the im-peller. Four similar waveforms appear in one cycle, which isequal to the number of diffuser blades. 0e pressure pul-sation from the impeller inlet to the outlet gradually in-creases, and the pressure pulsation excitation is from theimpeller outlet. 0e medium at the impeller outlet has ahigher velocity and exchanges energy with the diffuser inlet,resulting in the largest pressure pulsation amplitude oc-curring at the impeller outlet. Figure 9 shows that themonitoring points P11, S11, P12, and S12 near the impellerinlet have two troughs, indicating that the inlet pressure isnot very stable. Comparing Figures 9(a) and 9(b), it can beseen that the pressure pulsation intensity on the bladepressure side is greater than that on the suction side.

Figure 9(c) shows the pressure pulsation time domain ofthe monitoring points in the diffuser. 0ere are threesimilar pressure waveforms in one cycle, and there are twopeaks at the monitoring point D11 near the diffuser inlet,indicating that the diffuser inlet pressure is unstable mainlybecause the rotating impeller produces axial frequencypulsation on the stationary diffuser, that is, dynamic andstatic coupling between the impeller and diffuser results inpressure pulsation. 0e pressure fluctuations near thediffuser inlet are more severe than those in other positions.0e pressure pulsation amplitude from the inlet to theoutlet of the diffuser gradually decreases, which indicates

that the impeller outlet and diffuser inlet are the mainexcitation source of the pressure pulsation; the pulsationexcitation is continuously attenuated as it moves away fromthe boundary between the impeller and diffuser.

Figure 10 shows the time-domain diagrams of moni-toring points during the second stage. During the secondstage, the flow channel periodically changes as during thefirst stage. 0e amplitude of the pulsation coefficient in theimpeller gradually increases from the impeller inlet to theimpeller outlet, while the diffuser gradually decreases fromthe inlet to the outlet. However, the amplitude of thepressure pulsation coefficient of each monitoring pointduring the second stage is greater than that of the first stage,indicating that the flow channel of the second stage is af-fected not only by its own rotor-stator interaction but also bythe first-stage flow channel in the front; thus, the excitation issuperimposed.

To further analyze the pressure pulsation of the impellerand diffuser, fast Fourier transform was applied to show theunsteady pressure features in the frequency domain.Equation (4) was used to calculate the blade passing fre-quency fib as follows:

fib �n

60× Z, (4)

where n is the speed and Z is the blade number.0e impeller speed is 1450 r/min, the impeller frequency

fi is 24Hz, and the impeller blade frequency fib is 72Hz.Figures 11(a) and 11(b) show that the main frequency of the

Z = 170mm

(a)

t1 t2 t3

Diffuser Diffuser Diffuser

Impeller Impeller Impeller

Pressure4.682e + 0054.317e + 0053.952e + 0053.587e + 0053.223e + 0052.858e + 0052.493e + 0052.129e + 0051.764e + 0051.399e + 0051.035e + 005

(Pa)

(b)

Figure 8: Static pressure distribution at (a) z � 170mm (this section is the position of the impeller outlet and the diffuser inlet) and(b) different time steps.


pulsation signal of the monitoring points in the impeller hasthe same value of 96Hz, that is, 4 times the impeller fre-quency, which is exactly equal to the number of diuserblades. �is phenomenon shows that the pressure pulsationin the impeller is closely related to the frequency of theimpeller and number of diuser blades. Figure 11(c) showsthat the main frequency of the pulsation excitation at themonitoring points in the diuser is 72Hz, which is con-sistent with the impeller blade frequency.

�e pressure pulsation frequency of the internal mon-itoring points of the secondary diuser is one-time fib, whichis similar to the frequency domain distribution of the rst-stage diuser. However, at each monitoring point in thesecondary diuser, the pressure also �uctuated signicantlyat 2 times fib and 3 times fib, as shown in Figure 12(c), mainlybecause the secondary diuser was not only aected by theblade frequency of the secondary impeller but also the rst-

stage �ow passage. Moreover, the rst diuser has a swirling�ow, while the secondary diuser outlet has a free out�ow.�e dierent out�ow conditions of the two-stage vane resultin a certain dierence in the frequency distribution betweenthe diusers during the rst and second stages.

4.2. Radial Force. �e radial force is primarily attributed tothe unstable pressure distribution at the impeller outletresulting from the nonuniform �ow eld and rotor-statorinteractions.

�e streamline distribution for dierent �ow rates isshown in Figure 13. �e circum�uence and vortices in thetrailing edge of the impeller and diuser can be clearlyobserved under o-design conditions. �e smaller the �owrate, the more turbulent the �ow.�e unsteady �ow eld inthe pump aects the pressure distribution on the solid

S11S12S13

S14S15

–0.008

–0.006

–0.004

–0.002

0.000

0.002

0.004

0.006

0.008

C p

0.42 0.43 0.44 0.45 0.460.41t (s)

(a)

P11P12P13

P14P15

–0.03

–0.02

–0.01

0.00

0.01

0.02

0.03

C p

0.42 0.43 0.44 0.45 0.460.41t (s)

(b)

D11D12D13

D14D15

–0.02

–0.01

0.00

0.01

0.02

C p

0.42 0.43 0.44 0.45 0.460.41t (s)

(c)

Figure 9: Pressure pulsation time-domain diagram of the rst stage: (a) impeller blade suction side, (b) impeller blade pressure side, and(c) diuser.


surface of the impeller which changes over time, as shownin Figure 14.

Because of the relative motion between the high-speedrotating impeller and the static diuser, the pressure distri-bution along the circumferential direction is obviouslyasymmetrical (as shown in the black box area). As the �ow ratedecreases, the pressure distribution is increasingly uneven.From a geometrical perspective, this is because of a mismatchbetween the liquid �ow angle and diuser inlet angle undernondesign conditions, which exacerbates the rotor-stator in-terference between the impeller and the diuser.

Assuming that the area of each grid node is equal andthe static pressure at each grid node is uniformly dis-tributed, the forces acting on each node in all directions canbe solved. �en, the magnitude and direction of the totalforces can be obtained through the force synthesis theorem.�e radial force acting on the impeller can be obtained

according to the following equations in the numericalsimulations [6, 31, 32]:

Fi � Pi2πR2D2N

( ), (5)

Fxi � − FixiR2( ),

Fyi � − FiyiR2( ),

(6)

Fx �∑N

i�1Fxi ,

Fy �∑N

i�1Fyi ,

(7)

S21S22S23

S24S25

–0.015

–0.010

–0.005

0.000

0.005

0.010

C p

0.42 0.43 0.44 0.45 0.460.41t (s)

(a)

P21P22P23

P24P25

–0.04

–0.03

–0.02

–0.01

0.00

0.01

0.02

0.03

C p

0.42 0.43 0.44 0.45 0.460.41t (s)

(b)

D11D12D13

D14D15

–0.03

–0.02

–0.01

0.00

0.01

0.02

0.03

C p

0.42 0.43 0.44 0.45 0.460.41t (s)

(c)

Figure 10: Pressure pulsation time-domain diagram of the second stage: (a) impeller blade suction side, (b) impeller blade pressure side, and(c) diuser.


F ��F2x + F2y√

,

α � arctanFxFx( ),

(8)

whereN is the number of grid nodes on the coupling surface;Pi is the pressure of the i-th grid node; Fi is the pressure of thetiny area of the i-th grid node; Fix and Fiy are the componentsof the pressure of the tiny region of the i-th mesh node in thex-axis and y-axis directions, respectively; Fx and Fy are thecomponents of total radial force F in the x-axis and y-axisdirections, respectively; R2 is the impeller radius; D2 is the�ange outlet diameter; and alpha is the angle between theradial force and x direction.

Figure 15 shows the polar coordinate diagram of theradial force on the impellers of the two-stage electric liftingpump under four dierent �ow rates. �e circumferentialcoordinates represent the angle of the impeller rotationduring a rotating period, while the length of the connectingline from the center of the circle to a point on the curverepresents the radial force at a certain moment. Figure 15shows the radial force decreases with an increase in �ow rate.When Q� 200m3/h, the radial force of the impeller is ap-proximately twice that of the designed �ow condition

because the velocity and pressure distribution of the liquidaround the impeller is more uneven when the pump operatesunder nondesign conditions, thus resulting in a larger radialforce. �e distribution of the radial force under dierent�ow conditions is basically the same and all show a certainperiodicity. �e rotor-stator interference between the im-peller and diuser has a signicant in�uence on the radialforce. When a blade of the impeller passes over the vaneblade, a certain degree of radial force pulsation occurs. �etransient radial force is the most unstable at Q� 200m3/h.�is phenomenon easily causes unstable rotor operation. Atthe rated working point, the radial force is smaller and the�uctuation is more regular than at a �ow rate of 200m3/h.�e transient radial force under design conditions has thestrongest regularity and thus the smallest �uctuation.

For the same �ow rate, the radial force on the secondaryimpeller is greater than that on the rst impeller, and the�uctuation is stronger. �is is because of the uneven dis-tribution of the �ow pattern at the outlet of the rst impeller,which will further deteriorate when it propagates to the nextstage. �erefore, it can be easily inferred that the secondaryimpeller is strongly aected by the interference eect.

Figure 16 shows a radial force vector diagram of theimpeller in a rotating cycle under dierent �ow conditions.

S11S12

S13S14

S15 Monit

oring

point

s

0 200 300 400 500 600100Frequency (Hz)

0

810

1620

2430

3240

Am

plitu

de (P

a)

(a)

100 200 300 400 500 6000Frequency (Hz)

0

2400

4800

7200

9600

12000

Am

plitu

de (P

a)

P15

P14

P13

Mon

itorin

g poin

ts

P12

P11

(b)

D11D12

D13D14

D15 Monit

oring

point

s100 200 300 400 500 6000

Frequency (Hz)

0

2400

4800

7200

9600

12000

Am

plitu

de (P

a)(c)

Figure 11: Pressure pulsation in the frequency domain at monitoring points during the rst stage: (a) impeller blade suction side,(b) impeller blade pressure side, and (c) diuser.


�e vector coordinate of a point in the gure represents themagnitude and direction of the radial force at a certainmoment. �e impeller center coordinates are (0, 0). �eradial force distinctly changes both in magnitude and di-rection as the impeller rotates. Under dierent �ow rates, thedistribution of the radial force vectors is similar, a triangle-like distribution. Each lap corresponds to a change period inthe radial force and each peak point represents a rotor-statorinterference between the impeller and the diuser. Becausethe number of impeller blades is 3 and the number ofdiusers is 4, the impeller and the diuser interfere 12 timesduring a cycle of impeller rotation, resulting in 12 peakpoints. �e structure of the impeller and diuser and therotor-stator interference is related to the radial force. �eaction law and induction mechanism of the radial force ofthe unsteady �uid in the pump can be explained as follows:the vectors vary in size and direction, which indicates thatthe radial force acting on the impeller is unstable. When the�ow rate is less than the rated point, the center of the vectorforce distribution deviates from the axis and the impeller iseccentrically subjected to radial force.�erefore, consideringthe pump system stability, it is preferably avoided to operateat less than the rated condition for a long time period.

5. Conclusions

In this study, the pressure pulsation characteristics andradial forces in a two-stage electric lifting pump for deep-seamining were studied. �e numerical simulation method wasrst validated by external characteristic tests, and then thepressure pulsation characteristics at the same positionduring the rst and second stages were analyzed. Finally, theradial force under dierent �ow rates was compared. �emain conclusions are as follows:

First, the time-domain characteristics of the pressurepulsation during the rst and second stages of the pump aresimilar. �e amplitude of the impeller pressure pulsationcoecient gradually increases from the inlet to outlet, whilethe pressure pulsation coecient amplitude in the diusergradually decreases from the inlet to outlet. Energy ex-change between the impeller and diuser results in thelargest pressure pulsation coecient occurring at the im-peller outlet. �e monitoring points on the impeller bladesshow four similar waveforms during one cycle, consistentwith the number of diuser blades. �e monitoring pointson the diuser blades show three similar waveforms duringone cycle, which is consistent with the number of impeller

S21S22

S23S24

S25 Mon

itorin

g poin

ts

100 200 300 400 500 6000

Frequency (Hz)

0

1800

3600

5400

7200

9000

Am

plitu

de (P

a)

(a)

P21P22

P23P24

P25 Mon

itorin

g poin

ts

100 200 300 400 500 6000

Frequency (Hz)

0

3000

6000

9000

12000

15000

Am

plitu

de (P

a)

(b)

D21D22

D23D24

D25 Monit

oring

point

s

100 200 300 400 500 6000

Frequency (Hz)

0

2400

4800

7200

9600

12000

Am

plitu

de (P

a)(c)

Figure 12: Pressure pulsation in the frequency domain at monitoring points during the second stage: (a) impeller blade suction side,(b) impeller blade pressure side, and (c) diuser.


blades. 0erefore, the pressure pulsation period of theimpeller is related to the number of diffuser blades, whilethe pressure pulsation period in the diffuser is related to thenumber of impeller blades.

Second, there was a certain difference in the frequencydomain distribution between the first stage and the secondstage diffuser, which may have been because the secondaryimpeller is not only affected by the secondary impeller but

Q = 420m3/hQ = 200m3/h

Q = 600m3/h Q = 800m3/h

(a)

Q = 200m3/h

Velocitycontour 8

2.51e + 0012.26e + 0012.00e + 0011.75e + 0011.50e + 0011.25e + 0011.00e + 0017.52e + 0005.01e + 0002.51e + 0000.00e + 000

(m s–1)

Impeller

Diffuser

Q = 420m3/h

Velocitycontour 8

2.46e + 0012.22e + 0011.97e + 0011.72e + 0011.48e + 0011.23e + 0019.85e + 0007.39e + 0004.93e + 0002.46e + 0000.00e + 000

(m s–1)

Diffuser

Impeller

Q = 600m3/h

Velocity2.40e + 0012.16e + 0011.92e + 0011.68e + 0011.44e + 0011.20e + 0019.59e + 0007.19e + 0004.79e + 0002.40e + 0000.00e + 000

(m s–1)

Diffuser

Impeller

Velocitycontour 9

2.58e + 0012.32e + 0012.06e + 0011.81e + 0011.55e + 0011.29e + 0011.03e + 0017.74e + 0005.16e + 0002.58e + 0000.00e + 000

(m s–1)Q = 800m3/h

Diffuser

Impeller

(b)

Figure 13: Streamline distribution for different flow rates (a) in the two-stage pump and (b) z� 170mm.


4.69e + 005Pressure

4.33e + 0053.96e + 0053.60e + 0053.23e + 0052.87e + 0052.50e + 0052.14e + 0051.77e + 0051.41e + 0051.04e + 005

(Pa)

Diffuser

Impeller Impeller

Q = 200m3/h Q = 420m3/h

4.69e + 005Pressure

4.33e + 0053.96e + 0053.60e + 0053.23e + 0052.87e + 0052.50e + 0052.14e + 0051.77e + 0051.41e + 0051.04e + 005

(Pa)

Diffuser

ImpellerImpeller

Q = 800m3/hQ = 620m3/h

Figure 14: Static pressure distribution at Z� 170mm for different flow rates.

0

30

6090

120

150

180

210

240270

300

330

050100150200250300350400

F(N

)

Q = 200m3/hQ = 420m3/h

Q = 600m3/hQ = 800m3/h

(a)

0

30

6090

120

150

180

210

240270

300

330

050100150200250300350400

F(N

)

Q = 200m3/hQ = 420m3/h

Q = 600m3/hQ = 800m3/h

(b)

Figure 15: Polar coordinate diagrams of radial forces in the (a) primary impeller and (b) secondary impeller.


also aected by the grabbing �ow channel; thus, the signal issuperimposed. Another reason may have been the dierentout�ow conditions of the primary and secondary diusers.

Finally, the radial force was basically caused by theunstable pressure distribution at the impeller outlet. �e�ow asymmetry in the rotating impeller caused by the rotor-stator interference results in an unbalanced radial force. Atthe rated operating point, the radial force periodically�uctuates and the distribution of the vector diagram is alsoregular. When the �ow rate is less than the rated point, theradial force �uctuation is very strong and unstable and thecenter of vector force distribution deviates from the axis.�erefore, considering the pump system stability, it ispreferably avoided to operate at less than the rated conditionfor a long time period. �e radial force acting on the sec-ondary impeller is greater than that on the rst impeller, andthe �uctuation is more intense. It is not accurate to simulatethe force acting on the impeller in a multistage pump usingonly one single-stage model.

Nomenclature

Q: Flow rateQd: Design �ow rateQr: Rated �ow rateH: HeadS: Stagen: Rotating speedη: Hydraulic eciencyD1: Impeller inlet inlet diameterD2: Impeller outlet inlet diameterD3: Impeller inlet outlet diameterD4: Impeller outlet outlet diameterD5: Diuser inlet inlet diameterD6: Diuser outlet inlet diameterD7: Diuser inlet outlet diameter

D8: Diuser outlet outlet diameterb2: Impeller outlet widthβ1: Impeller inlet blade angleΒ2: Impeller outlet blade angleβ3: Diuser inlet blade angleβ4: Diuser outlet blade angleZ1: Impeller blade numberZ2: Diuser blade numberP: PressureCp: Pressure coecientρ: Densityμ: Dynamic viscosityμt: Turbulent viscosityk: Turbulent kinetic energyfi: Impeller frequencyfib: Blade passing frequencyF: Radial forcens: �e specic speed, ns � 3.65n

��Q

√/H0.75.

Data Availability

�e data used to support the ndings of this study are in-cluded in the paper.

Conflicts of Interest

�e authors declare that they have no con�icts of interest.

Acknowledgments

�is work was supported by the National Key Research andDevelopment Project of China (2016YFC0304103), ResearchProject of Shenzhen Science and Technology Innovation(JCYJ20150929102555935), and Shenzhen Major SupportProject (HYZDFC20140801010002).

–300 –200 –100 0 100 200 300 400 500–400

–300

–200

–100

0

100

200

300

400

Fy (N)

F x (N

)

Q = 200m3/hQ = 420m3/h

Q = 600m3/hQ = 800m3/h

(a)

Fy (N)

F x (N

)

Q = 200m3/hQ = 420m3/h

Q = 600m3/hQ = 800m3/h

–300 –200 –100 0 100 200 300 400 500–400

–300

–200

–100

0

100

200

300

400

(b)

Figure 16: Radial force vector diagram in the (a) rst-stage impeller and (b) second-stage impeller.


References

[1] Y. Nishi, “Static analysis of axially moving cables applied formining nodules on the deep sea floor,” Applied Ocean Re-search, vol. 34, pp. 45–51, 2012.

[2] Y. Shirayama, H. Itoh, and T. Fukushima, “Recent de-velopments in environmental impact assessment with regardto mining of deep-sea mineral resources,” Deep-Sea Mining,Springer International Publishing, New York, NY, USA, 2017.

[3] S. Liu, C. Liu, and Y. Dai, “Status and progress on researchesand developments of deep oceanmining equipments,” Journalof Mechanical Engineering, vol. 50, no. 2, pp. 8–18, 2014.

[4] W. S. Zou, Z. H. Li, and A. L. Chen, “Lifting motor pump indeep sea mining,” Journal of Central South University. NaturalScience Edition, vol. 42, no. 2, pp. 221–225, 2010.

[5] Y. Kang, S. Liu, W. Zou, H. Zhao, and X. Hu, “Design andanalysis of an innovative deep-sea lifting motor pump,”Applied Ocean Research, vol. 82, pp. 22–31, 2019.

[6] Z. Z. Sun, Y. M. Zhang, H. P. Xia, and S. S. Chen, “Radial forceand pressure fluctuation analysis of axial flow pump rotorunder different working conditions,” Journal of Irrigation andDrainage, vol. 38, no. 1, pp. 122–128, 2019.

[7] W. Jiang, G. Li, P.-f. Liu, and L. Fu, “Numerical investigationof influence of the clocking effect on the unsteady pressurefluctuations and radial forces in the centrifugal pump withvaned diffuser,” International Communications in Heat andMass Transfer, vol. 71, no. 1, pp. 164–171, 2016.

[8] J. Gonzáles, C. Santolaria, J. L. Parrondo et al., “Unsteadyradial forces on the impeller of a centrifugal pump with radialgap variation,” in Proceedings of the ASME/JSME 2003 4thJoint Fluids Summer Engineering Conference. Volume 1: Fora,Parts A, B, C, and D, vol. 45, pp. 1173–1181, Honolulu, HI,USA, July 2003.

[9] S. Guo and H. Okamoto, “An experimental study on the fluidforces induced by rotor-stator interaction in a centrifugalpump,” Fe International Journal of Rotating Machinery,vol. 9, no. 2, pp. 135–144, 2003.

[10] Y. B. Li, R. N. Li, X. R. Chen, W. G. Zhao, and L. X. Shen,“Numerical investigation of pressure fluctuation for a mixedflow pump impeller and vanes diffuser,” IOP ConferenceSeries: Earth and Environmental Science, vol. 15, no. 3,pp. 692–697, 2012.

[11] J. Feng, F. K. Benra, and H. J. Dohmen, “Numerical in-vestigation on pressure fluctuations for different configura-tions of vaned diffuser pumps,” International Journal ofRotating Machinery, vol. 2007, Article ID 34752, 10 pages,2007.

[12] L. Zhou, W. D. Shi, W. G. Lu, H. Li, and B. Pei, “Analysis onpressure fluctuation of unsteady flow in deep-well centrifugalpump,” Transactions of the Chinese Society of AgriculturalEngineering, vol. 27, no. 10, pp. 44–49, 2011.

[13] P. Dupont, G. Caignaert, G. Bois et al., “Rotor-stator in-teractions in a vane-diffuser radial flow pump,” in Proceedingsof ASME Fluids Engineering Division Summer Meeting,pp. 1087–1094, Houston, TX, USA, October 2005.

[14] F. Shi and H. Tsukamoto, “Numerical study of pressurefluctuations caused by impeller-diffuser interaction in a dif-fuser pump stage,” Journal of Fluids Engineering, vol. 123,no. 3, pp. 466–474, 2001.

[15] Z. Yao, “Experimental investigation of time-frequencycharacteristics of pressure fluctuations in a double-suctioncentrifugal pump,” Journal of Fluids Engineering, vol. 133,no. 10, pp. 1076–1081, 2011.

[16] S. Anish, N. Sitaram, and H. D. Kim, “A numerical study ofthe unsteady interaction effects on diffuser performance in acentrifugal compressor,” Journal of Turbomachinery, vol. 136,no. 1, pp. 253–256, 2013.

[17] A. Jaatinen, A. Grönman, T. Turunen-Saaresti, and J. Backman,“Effect of high negative incidence on the performance of acentrifugal compressor stage with conventional vaned dif-fusers,” Journal of Fermal Science, vol. 20, no. 2, pp. 97–105,2011.

[18] S. Q. Yuan and Y. Y. Ni, “Unsteady turbulent simulation andpressure fluctuation analysis for centrifugal pumps,” ChineseJournal of Mechanical Engineering, vol. 22, no. 1, pp. 1–6, 2009.

[19] M. Solis, F. Bakir, and S. Khelladi, “Pressure fluctuationsreduction in centrifugal pumps: influence of impeller ge-ometry and radial gap,” in Proceedings of the ASME 2009Fluids Engineering Division Summer Meeting. Volume 1:Symposia, Parts A, B and C, pp. 253–265, American Society ofMechanical Engineers (ASME), Vail, CO, USA, August 2009.

[20] B. P. M. van Esch, “Performance and radial loading of amixed-flow pump under non-uniform suction flow,” Journalof Fluids Engineering, vol. 131, no. 5, pp. 36–40, 2009.

[21] R. Barrio, J. Fernández, E. Blanco, and J. Parrondo, “Esti-mation of radial load in centrifugal pumps using computa-tional fluid dynamics,” European Journal of Mechanics-B/Fluids, vol. 30, no. 3, pp. 316–324, 2011.

[22] J. Gonzalez, J. Fernandez, E. Blanco, and C. Santolaria,“Numerical simulation of dynanic effects due to impeller-volute intercaction in a centrifugal pump: pump analysis anddesign,” Journal of Fluids Engineering, vol. 124, no. 2,pp. 348–355, 2002.

[23] M. Yang, S. Min, and F. J. Wang, “Pressure fluctuationcharacteristics of double volute pump and numerical simu-lation of radial force of impeller,” Journal of AgriculturalMachinery, vol. 40, no. 11, pp. 83–88, 2009.

[24] ANSYS, ANSYS Academic Research, Release14.5, HelpSystem,CFX Documentation, ANSYS, Inc., Canonsburg, PA, USA,2002.

[25] M. G. Tan, R. Ding, H. L. Liu, and X. F. Wu, “Study onunsteady radial force characteristics in a dual-channel sewagepump,” Journal of Huazhong University of Science andTechnology, vol. 43, no. 12, pp. 42–47, 2015.

[26] W. D. Cao, G. H. Liu, W. D. Shi, and W. Dangxiong,“Distribution characteristics of unsteady pressure insidemultistage centrifugal pump,” Transactions of the ChineseSociety of Agricultural Engineering, vol. 30, no. 14, pp. 64–70,2014.

[27] X. Zhu, G. Li, W. Jiang, and L. Fu, “Experimental and nu-merical investigation on application of half vane diffusers forcentrifugal pump,” International Communications in Heatand Mass Transfer, vol. 79, pp. 114–127, 2016.

[28] Y. Y. Shi and Y. Z. Huang, “Numerical simulation of externalcharacteristics of axial flow pump and comparative study ofturbulence model,” Equipment Manufacturing Technology, vol. 5,pp. 86–89, 2018.

[29] E. M. Ofuchi, H. Stel, T. Sirino et al., “Numerical investigationof the effect of viscosity in a multistage electric submersiblepump,” Engineering Applications of Computational FluidMechanics, vol. 11, no. 1, pp. 258–272, 2017.

[30] D. G. Duan, Z. M. Wei, X. Q. Jiang et al., “Technical dif-ferences between new and old standards for acceptance test ofhydraulic performance of rotary power pumps,” AgriculturalEngineering, vol. 7, no. 6, pp. 139–141, 2017.

[31] H. W. Iversen, R. E. Rolling, and J. J. Carlson, “Volutepressure distribution Radial force on the impeller and volute


mixing losses of a radial flow centrifugal pump,” Journal ofEngineering for Power, vol. 82, no. 2, pp. 143-144, 1960.

[32] W. Y. Zhao, L. Zhang, and J. Luo, “Radial force numericalanalysis of double suction centrifugal pump,” Irrigation andDrainage Machinery, vol. 27, no. 4, pp. 205–209, 2009.


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