wear characteristics of dense fine particles solid-liquid two … · 2020. 12. 7. · to...

Research ArticleWear Characteristics of Dense Fine Particles Solid-LiquidTwo-Phase Fluid Centrifugal Pump with Open Impellers

YanpingWang 1 ChuanfengHan1 Ye Zhou 2 Zhe Lin 1 JianfengMa3 Xiaojun Li 1

and Wei Zhang1

1Faculty of Mechanical Engineering and Automation Zhejiang Sci-Tech University Hangzhou Zhejiang 310018 China2China Institute of Water Resources and Hydropower Research Beijing 100038 China3ZheJiang Fuchunjiang Hydropower Equipment Company Ltd Hangzhou Zhejiang 311501 China

Correspondence should be addressed to Zhe Lin linzhe0122zstueducn

Received 7 December 2020 Revised 11 January 2021 Accepted 29 March 2021 Published 7 April 2021

Academic Editor Ling Zhou lingzhouujseducn

Copyright copy 2021 YanpingWang et al+is is an open access article distributed under the Creative CommonsAttribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

+e demand for a centrifugal pump with open impellers for conveying dense fine particles in solid-liquid two-phase flow hasincreased significantly in actual engineering +e wear of dense fine particles on the centrifugal pump is also exceedinglyprominent which affects the engineering efficiency and economic benefits +e two-phase flow in the open centrifugal pump isthree-dimensional and unsteady the movement of high-volume concentration particles in the centrifugal pump and its mutualinfluence on the two-phase flow which results in the calculation of wear are very intricate To study the wear characteristics of thecentrifugal pump with open impeller with high-volume concentration particles more accurately numerical simulation andexperimental comparison are carried out for the impeller wear of dense fine particles transported by the centrifugal pump withopen impellers Considering the relationship between particles and walls we used the Fluent 180 built-in rebound function andwear model+e RNG k-εmodel and the DDPMmodel were adopted in the numerical simulation and the numerical solution forcentrifugal pump wear was performed under flow rate (96m3middothminus1 128m3middothminus1 16m3middothminus1 and 192m3middothminus1) different particle sizes(0048mm 0106mm 015mm 027mm and 0425mm) and different particle volume concentrations (10 15 20 25 and30) respectively By comparing the serious wear positions of the impeller the experimental results correspond well with thenumerical simulation which can be used to predict and study the wear characteristics of the impeller +e results show that themost serious area of blade wear is themiddle part of the pressure surface followed by themiddle part of the upper part of the blade+e wear of the impeller is greatly affected by relevant parameters such as pump flow rate particle diameter and particle volumeconcentration +ese results can provide some basis for the wear-resistant design of dense fine particle impeller

1 Introduction

+ere are complex flow problems in multiphase fluidtransportation [1ndash4] +e solid-liquid two-phase centrifugalpump is an important piece of equipment for the hydraulictransportation of solid particles In the process of conveyingparticles due to the collision between the particles and thecomponents in the pump (such as impeller and volute) thecomponents in the pump are worn out [5] +e presence ofparticles will destroy the original flow field and the pro-tective layer of the wall resulting in performance degra-dation and wear damage [6ndash10] which further leads tofrequent replacement or maintenance and the

corresponding conveying system needs to be stopped thusleading to the significant increase of the conveying costs+eresearch of Wilson et al [11] showed that the shutdown costof a large mine is about 1times 105 $hour +erefore the in-ternal wear of centrifugal pumps is one of the importantstudy directions of solid-liquid two-phase flow centrifugalpumps

+ere are many influencing factors for the wall wearproblem of solid-liquid two-phase flow +e scholars havedone a lot of research on the characteristics of solid-liquidtwo-phase flow Gandhi et al [12] studied the influence ofparticle diameter changes on wear and obtained the cor-relation between the wear and particle size Ben-Ami et al

HindawiShock and VibrationVolume 2021 Article ID 6635630 13 pageshttpsdoiorg10115520216635630

[13] established a wear model by studying the impact angleof particles and the wear law of surface materials on the wall+e volume concentration and sharpness of particles are alsoimportant factors for wall wear +e study of Nan et al [14]showed that the flow rate affects the speed of the particlesand then affects the wear performance Within a certainrange the sharpness of the particles has a greater impact onthe wall wear performance Regarding the effect of particlevolume concentration on the wear of solid-liquid two-phaseflow the study of Lai et al [15] showed that the change ofvolume concentration will affect the position of impellerwear Zhangrsquos simulation and analysis of two-phase flowshowed that the abrasion on the pressure side of the impellerof a centrifugal pump is higher than other parts whenconveying high-volume concentration particles [16]Adamczyk et al [17] used the combination of DDPM andEuler-Euler to calculate the flow of circulating particles inthe fluidized bed and compared with the experiment ob-tained a particle motion model suitable for the fluidized bedOu et al [18] used the DDPM and KTGFmodels to carry outthe corresponding numerical simulations on the wear of theelbow pipe under high-volume concentration coal con-veying +e results showed that for the movement of par-ticles under the resistance of centrifugal force and secondaryflow when they pass the elbow partial reunion occurs andthe larger particles are susceptible to impact the curved backwhich has a more obvious impact on erosion and wear Jainet al [19] studied the influence of different particle prop-erties on the flow characteristics of fluidized beds throughradioactive particle tracking technology and DDPM and theresults showed that DDPM can effectively predict the av-erage particle velocity

To make better use of solid-liquid two-phase centrifugalpumpwear simulation to predict its experimental results therelationship between particles and the wall (including wallrebound function and wall wear function) should be con-sidered Many scholars have proposed wall rebound func-tions that are more in line with the experiment according todifferent research directions Sommerfeld and Huber [20]obtained the parameters of the wall rebound model (such asthe coefficient of restitution and friction coefficient) basedon the experimental data +e modified wall reboundfunction can predict the experiment well Forder et al [21]proposed the corresponding wear models through experi-ments and proposed a corresponding particle reboundmodel in combination with particle angles and wall materialsto better study the wear mechanism of control valves Basedon the wear data of flat specimens in water or airflow and 90degstandard elbows in airflow ECRC [5] obtained a newerosion equation and combined CFD with simulating andpredicting the experiment +e wear rate and experimentalresults are in good consistency Regarding the wear in theprocess of conveying solid particles in a fluidized bed Bitter[22 23] proposed a wall wear function based on themovement properties of the particles the hardness of thematerial and the elastic parameters and explained the wearphenomenon of the fluidized bed in the experiment Bystudying the wear characteristics of the particle shape ve-locity shooting angle and different material properties on

the wall surface Neilson and Gilchrist [24] proposed thecorresponding wear function to explain the wear phe-nomenon in the experiment By studying particle propertiesand wall material properties (hardness and load relaxation)Oka [25 26] proposed wear functions for different materialsHuang [27] established a wear function including particlecollision speed angle and particle size and wall materialproperties for the particle-wall wear characteristics duringthe jet process which were in good agreement with the wearexperiment of Finn [28] Regarding the wear caused by theinhalation of solid particles by the turbine G amp T [29]proposed related particle rebound model and wall wearmodels based on the hydrodynamic resistance of the solidparticles the particlersquos rebound on the wall and the wallwear which were used to predict the relevant parts of theturbine wear location etc However the calculation of thethree-dimensional nonconstant value of wear of centrifugalpumps that transport high-volume concentration solid-liquid two-phase flow is still very small In this work topredict the overall wear performance of the centrifugalpump with open impeller under the condition of the high-volume concentration of solid-liquid two-phase flow themethod of three-dimensional indeterminate constant valueanalysis and the DDPMmodel are used and the influence ofrelevant parameters (flow rate particle diameter and vol-ume concentration) on the wear characteristics of centrif-ugal pump flow components is studied +e results of thisstudy are helpful to develop high-volume concentrationsolid-liquid two-phase flow centrifugal pumps such asapplying hard material [30] to wear-prone areas avoidingunnecessary downtime and reducing operating costs

2 Mathematical Model

To predict the wear performance of the centrifugal pumpthe numerical calculation includes the following conditionsbasic assumptions the establishment of solid-liquid two-phase flow control equation the analysis of particle forcesand the selection of particle-wall collision function and wearfunction

21 Basic Assumption +e solid-liquid two-phase flow in-side the model pump is extremely complicated To simplifythe calculation and improve the accuracy of the numericalsimulation results the following assumptions are adopted

(1) +e continuous phase (water) is an incompressiblefluid and the physical properties of each phase areconstant

(2) +e particles are spherical glass beads with uniformparticle size regardless of the change in particleshape

(3) +e influence of temperature on the two-phase flowfield is not considered

(4) +e collision between the particles and the wall is anelastic collision

(5) +e liquid phase and the solid phase adopt two-waycoupling and so on

2 Shock and Vibration

22 Solid-Liquid Two-Phase Governing Equation +e two-phase flow in the solid-liquid two-phase centrifugal pump isa turbulent flow Considering the mixed movement andinteraction of liquid and particles and the high-volumeconcentration of solid particles (Cge 10) the Euler-Lagrange equation is used in this article to describe the liquidand solid phases in continuousmedia Based on the principleof mass exchange and momentum conservation of incom-pressible two-phase flow a basic solid-liquid two-phase

governing equation which is adopted by the Fluent 180theory guide is established

z

ztαipi( 1113857 + nabla middot αipiui( 1113857 1113944

n

j1_mji minus _mij1113872 1113873 (1)

+e momentum equation that is adopted by the Fluent180 theory guide is as follows

z

ztαiρiui( 1113857 + nabla middot αiρiuiui( 1113857 minusαinablap + nabla middot αiμi nablaui + u

Ti1113872 11138731113960 1113961 + αiρig + 1113944 F

+ 11139442

j1kji uj minus ui1113872 1113873 + _mjiuij minus _mijuji

⎡⎢⎢⎣ ⎤⎥⎥⎦ + KDS us + uj1113872 1113873 + SDE

(2)

1113944 F FV + FS + FL (3)

where i 1 2 indicates the liquid and solid phase ρi is thedensity of i phase n is the number of phases p is the mixed-phase pressure αi is the volume fraction of i phase vi is therelative velocity of i phase _mij( _mji) indicates the masstransfer from i phase to j phase μi is the viscosity of i phaseuij(uji) represent the phase velocity of i(j) phase and j(i)

phase if _mij gt 0 (the mass of the i phase is transferred to the jphase) then uij ui and if _mij lt 0 (the mass of the j phase istransferred to the i phase) then uij uj (the same if _mji gt 0then uji uj if _mji lt 0 then uji ui) SDE represents theexplicit part of the momentum exchange phase (provided byDPM) us represents the average velocity of discrete phaseparticles KDS represents the momentum exchange coeffi-cient between the average phases of particles kji kij theexchange coefficient between phases

FV represents the virtual mass force which acceleratesthe fluid surrounding the particles When the particledensity is greater than the fluid density this force cannot beignored +e corresponding equation is as follows

FV Cvmρρp

upnablau minusup

dt1113874 1113875 (4)

In the formula when the particles are spherical thevirtual quality coefficient Cvm is 05 [31] up dxdt urepresents fluid velocity up represents particle velocity andρp represents particle density

FS represents the Saffman force which means that whenthe flow field has a large velocity gradient (such as near thewall) the velocity of the particle surface is different that isthe pressure on the surface is different which results in adifference between the particle and the fluid For the force atthe vertical velocity the corresponding governing equationis as follows

FS 162d2p

μρ1

radicu minus up1113872 1113873

zu

zx

1113868111386811138681113868111386811138681113868

1113868111386811138681113868111386811138681113868

1113971

(5)

Regarding the Saffman force under high Reynolds theliterature [32] proposed the following amendments

CS

1 minus 03314α051113872 1113873exp minus

Rep

101113888 1113889 + 03114α05

Rep le 401113872 1113873

00524 α times Rep1113872 111387305

Rep ge 401113872 1113873

⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(6)

α dp middot|zuzY|

u minus up

11138681113868111386811138681113868

11138681113868111386811138681113868 (7)

Rep ρdp u minus up

11138681113868111386811138681113868

11138681113868111386811138681113868

μ (8)

where Rep is the particle instantaneous Reynolds number

Shock and Vibration 3

FL represents the lift force of the particle in the liquidand the lift force of the secondary phase i in the main phase jcan be expressed as follows

FL minusClρjαi uj minus ui1113872 1113873 times nabla times uj1113872 1113873 (9)

In the above formula Cl represents the lift coefficientand its value is 0 for spherical particles [31] ρj represents thedensity of the main phase αi represents the volume con-centration of the secondary phase uj represents the velocityof the main phase ui represents the velocity of the secondaryphase

23 Solid Phase Control Model +e mixture movementand interaction of liquid and particles make the move-ment of particles complex and difficult to predict Sincethis study is about the wear of high-volume concentra-tion particles on the pump the Lagrange method is usedto describe the particle movement +e particle trajectoryequation in the Lagrange method can be written asfollows

dup

dt

u minus up

τr

+g ρp minus ρ1113872 1113873

ρp

+ FV + FS (10)

where up dxdt u represents fluid velocity up representsparticle velocity ρp represents particle density ρ representsliquid density (u minus up)τr represents the resistance per unitparticle mass and τr represents particle relaxation time andcan be written as follows

τr ρpd

2p

18μ24

CdRep (11)

In the formula dp represents particle diameter μ rep-resents fluid viscosity Cd represents the resistance coeffi-cient and Cd can be expressed by the following formula

Cd α1 +α2Rep

+α3Re

2p (12)

In the above formula α1 α2 and α3 are constantsprovided by Morsi and Alexander [33]

24 Selection of Particle-Wall Rebound Function and WearFunction Many scholars [5 16ndash25] put forward particle-wall rebound functions and wear functions that are moresuitable for their experiments according to different ex-perimental conditions and explain the wear phenomenonunder different conditions According to its theoreticalanalysis it is concluded that they are more suitable for wearunder low-volume concentration conditions (Clt 10) Forthe high-volume concentration in this article that is thenumber of particles is too large and to save the corre-sponding computing resources the Fluent 180 built-inparticle-wall rebound model and wear model are used Forspecific models refer to literature which is adopted byFluent 180 theory guide

3 Numerical Simulation Method

31 Pump Model and Mesh Generation +e 1PN4-3KWsingle-stage centrifugal pump with open impeller is selectedas the calculation and experimental model +e basic designparameters are shown in Table 1 To reduce the influence ofthe liquid in and out of the centrifugal pump on the inside ofthe centrifugal pump a 02m pipe is added upstream of theimpeller (4 times the diameter of the impeller inlet) A 012mpipe is added at the outlet of the volute (4 times the diameterof the impeller outlet) NX120 software is used to build thecorresponding model in Figure 1(a) and the computationalgrid uses ICEM to build a grid for the computational do-main +e overall grid of the model is 4120245 the numberof nodes is 757118 and the corresponding calculation do-main and grid are shown in Figure 1(b)

32 Model Verification To verify the model the numericalsimulation and experimental results of the external char-acteristics of the model pump are compared +e results areshown in Figure 2 +e curve error of the numerical sim-ulation results and experimental results in the figure is lessthan 8 Considering the influence of factors such as valvesand processing in the actual process the external charac-teristic error of the model can be considered reasonable

33 Calculation Model and Boundary Conditions Accordingto experience the inlet of the centrifugal pump is set as aspeed inlet and the outlet is a pressure outlet +e velocitiesat the inlet and outlet of the continuous phase and thediscrete phase are uniform and the initial velocity of thediscrete phase is equal to that of the continuous phase In thecalculation domain the speed of the impeller remainsconstant and the inlet pipe outlet pipes and volute remainstationary +e discrete phase and continuous phase adoptbidirectional coupling DDPMmodel and turbulence modelRNG k minus ε are used to calculate the wear of discrete phase ona centrifugal pump

4 Results and Discussion

Numerical simulation is performed with the design con-ditions of the centrifugal pump with an open impeller (referto Table 1) and the particle density of 2450 kgm3+e effectsof flow rate and particle properties (particle size and volumeconcentration) on the wear characteristics of the centrifugalpump with open impeller are studied respectively and thewear law of the whole centrifugal pump is predicted and theexperimental results are compared (Table 2 is the numericalsimulation working condition) +e average wear rate andmaximum wear rate of different parts of the centrifugalpump are calculated and compared +e pressure surface inthis article is divided into the main working part of the bladenamely the main pressure surface and the secondarypressure surface on the back blade +e suction surface isdivided into the main working part of the blade namely themain suction surface and the secondary suction surface onthe back blade +e graph shown in this article is a wear


Table 1 Design parameters of the centrifugal pump

Flow (m3h) Head (m) Rotating speed (rmin) Inlet diameter (mm) Outlet diameter (mm) Number of blades16 13 1450 50 25 5

(a) (b)

Figure 1 Centrifugal pump model and grid (a) Centrifugal pump model (b) centrifugal pump grid

17

16

15

14

13

12

11

10

9

8

7

0 2 4 6 8 10 12 14 16 18 20

05

04

03

02

01

00

η (

)

Simulation headExperiment head

Simulation efficiencyExperiment efficiency

Q (m3lowasthndash1)

H (m

)

Figure 2 Verification of external characteristics of centrifugal pump


cloud graph with time t 05 s and the time when the wearrate (including the average wear rate and the maximumwearrate) is calculated is t 02 s

41 Influence of Flow Rate on Centrifugal Pump WearUnder the premise of volume concentration C 20 andparticle size d 0106mm the influence of flow rate on thewear of the centrifugal pump with open impellers is studiedFor cases 1ndash4 listed in Table 2 the flow rates includeQ 96m3middothminus1 128m3middothminus1 16m3middothminus1 and 192m3middothminus1 whichcorrespond to the wear cloud diagram of different parts inFigures 3ndash6 +e change of flow rate drives the change ofparticle velocity and effects of movement of high-volumeconcentration particle Hence the wear position of differentparts of the centrifugal pumpwith an open impeller is changed

Figure 3 shows that the increase of flow rate changes thewear position and wear amount of the whole impeller Fig-ures 4 and 5 reveal the wear cloud diagram of the pressuresurface and suction surface of the blade +e increase of flowrate makes the wear of the pressure surface gradually increaseand the wear location is concentrated in the middle of thepressure surface moreover the wear location of the suctionsurface moves from the foremost to the middle Figure 6indicates the effect of flow rate on the wear of the volute +eincrease in flow rate makes the wear position of the volutechange but the main wear area is around the volute dia-phragm +e change of flow rate makes the movement of thesolid-liquid two-phase flow at the volute tongue change +ewear area near the volute tongue shows an expanding trend asa whole the wear area of the volute tongue under designconditions is relatively small compared to others Figure 7shows the relationship between the wear rate and flow rate ofdifferent parts of the solid-liquid two-phase centrifugal pump+e main trend of the average rate of wall wear is increased+emaximumwear rate of themain suction surface decreasesfirst and then increases with the increase of the flow rate themaximum wear rate of volute increases decreases and thenincreases and the others keep increasing

+e wear rate of the main parts of the centrifugal pumpwith open impeller (such as the main pressure surface themain suction surface and the volute) increases with theincrease of the flow the maximum wear rate of the mainsuction surface first increases and then decreases +esmallest value is under the design flow rate and the value ofthe maximum wear rate is the smallest indicating that themaximum wear rate of the suction surface has a certainimprovement under the design conditions

42 gte Influence of Particle Size on Centrifugal PumpWearBased on the design flowQ 16m3middothminus1 and the high-volumeconcentration C 20 the effect of particle size on the wear

of the centrifugal pump with an open impeller is studied Forcases 5ndash9 listed in Table 2 the particle sizes included 0048mm 0106mm 015mm 027mm and 0425mmcorresponding to the wear clouds in Figures 8ndash11 +echange of particle size makes the particle more constrainedby gravity and its own momentum changes +at is thechange of particle size makes the wear position of differentparts of centrifugal pump with open impellers change

+e particle size has a great influence on the wearposition of the impeller (see Figure 8) +e larger theparticle size the more severe the wear of the front end ofthe impeller Figures 9 and 10 show the influence of theparticle size on the wear of the pressure surface andsuction surface respectively +e increase of particle sizecauses the wear position of the pressure surface to movefrom the front end to the middle and the wear of the frontend of the suction surface is worse +e wear position ofthe pressure surface moves downward with the increase ofgravity (ie the increase in particle size) +e main wear ofthe front end of the suction surface becomes more seriousDifferent from the impeller the increase of the particle sizefirst increases the wear range around the volute tongue andthen decreases to a certain extent +e average wear rate ofthe volute and the secondary suction surface decreaseswith the increase of the particle size and in the otherposition the average wear rate increases (Figure 12(a))+e increase of the particle size reduces its followabilitywhich reduces the collision probability of particles withthe wall of the volute so its average wear rate graduallydecreases +e increase in particle size makes the maxi-mum wear rate of the volute wall increase gradually +emaximum wear rate of the secondary suction surfacedecreases with the increase of the particle size and thewear rate of the volute and suction surface is the largestamong all parts (Figure 12(b)) It is because that the in-crease of particle size reduces the probability of particlescolliding with the secondary suction surface Hence boththe average wear rate and the maximum wear rate of thesecondary suction surface decrease

43 gte Influence of Particle Volume Concentration onCentrifugal Pump Wear Under the premise of design flowQ 16m3middothminus1 and particle size d 0106mm the influenceof volume concentration on the wear of the centrifugalpump with open impeller is studied For cases 10ndash14 listed inTable 2 the volume concentration includes C 10 1520 25 and 30 and the corresponding wear clouds arein Figures 13ndash16 +e probability of particles hitting thecentrifugal pump changes with the change of particle vol-ume concentration which has a great effect on the wear rateand wear location of the wall

Table 2 Detailed operation conditions

Parameter Cases 1ndash4 Cases 5ndash9 Cases 10ndash14Flow rate(m3middothminus1) 96 128 16 192 16 16Particle volume concentration () 20 20 10 15 20 25 30Particle diameter (mm) 0106 0048 0106 015 027 0425 0106


1E ndash 07 27E ndash 07 44E ndash 07 61E ndash 07 78E ndash 07 95E ndash 07 112E ndash 06 129E ndash 06 146E ndash 06 163E ndash 06 18E ndash 06

DPM erosion(kgm2)

(a) (b) (c) (d)

Figure 3 Impeller wear clouds at different flow rates (a) Q 96m3middothminus1 (b) Q 128m3middothminus1 (c) Q 16m3middothminus1 and (d) Q 192m3middothminus1


DPM erosion(kgm2)

(a) (b) (c) (d)

Figure 4 Pressure surface wear clouds at different flow rates (a) Q 96m3middothminus1 (b) Q 128m3middothminus1 (c) Q 16m3middothminus1 and(d) Q 192m3middothminus1


DPM erosion(kgm2)

(a) (b) (c) (d)

Figure 5 Suction surface wear clouds at different flow rates (a) Q 96m3middothminus1 (b) Q 128m3middothminus1 (c) Q 16m3middothminus1 and(d) Q 192m3middothminus1


DPM erosion(kgm2)

(a) (b) (c) (d)

Figure 6 Volute wear clouds at different flow rates (a) Q 96m3middothminus1 (b) Q 128m3middothminus1 (c) Q 16m3middothminus1 and (d) Q 192m3middothminus1


With the increase in particle volume concentration thewear of the impeller gradually increases (as shown in Fig-ure 13) +e area of the pressure surface wear spreads to theentire pressure surface and the amount of wear increasesrelated to the particle size volume concentration increases(Figure 14) When the volume concentration is lower(Clt 10) the wear area of the suction surface is mainlyconcentrated in the front end and when the volume

concentration is higher (Cge 20) it is mainly concentratedin the middle (Figure 15)

In Figure 16 with the increase in volume concentrationthe main wear area of the volute extends from the tongue tothe surrounding +e average wear rate of the secondarysuction surface decreases and the other parts increases +eaverage wear rate of the main pressure surface shows anupward trend with the increase of the particle volume

40 x 10ndash6

35 x 10ndash6

30 x 10ndash6

25 x 10ndash6

20 x 10ndash6

15 x 10ndash6

10 x 10ndash6

50 x 10ndash7

00

Aver

age e

rosio

n ra

te (k

gmiddotm

ndash2middotsndash1

)

ImpellerMain pressure surfaceMain suction surface

Subordinate pressuresurfaceSubordinate suctionsurfaceVolute

06Q 08Q Q 12QFlow rate (Q = 16m3middothndash1)

(a)

14 x 10ndash3

12 x 10ndash3

10 x 10ndash3

80 x 10ndash4

60 x 10ndash4

40 x 10ndash4

20 x 10ndash4

00

Max

imum

eros

ion

rate

(kgmiddot

mndash2

middotsndash1)




(b)

Figure 7 Comparison of wear rate of different parts at different flow rates (a) Average wear rate (b) maximum wear rate


DPM erosion(kgm2)

(a) (b) (c) (d) (e)

Figure 8 Impeller surface wear clouds at different particle sizes (a) d 0048mm (b) d 0106mm (c) d 015mm (d) d 027mm and(e) d 0425mm


DPM erosion(kgm2)

(a) (b) (c) (d) (e)

Figure 9 Pressure surface wear clouds at different particle sizes (a) d 0048mm (b) d 0106mm (c) d 015mm (d) d 027mm and(e) d 0425mm



DPM erosion(kgm2)

(a) (b) (c) (d) (e)

Figure 10 Suction surface wear clouds with different particle sizes (a) d 0048mm (b) d 0106mm (c) d 015mm (d) d 027mmand (e) d 0425mm


DPM erosion(kgm2)

(a) (b) (c) (d) (e)

Figure 11 Volute wear clouds with different particle sizes (a) d 0048mm (b) d 0106mm (c) d 015mm (d) d 027mm and(e) d 0425mm

50 x 10ndash6

40 x 10ndash6

30 x 10ndash6

20 x 10ndash6

10 x 10ndash6

00

Aver

age e

rosio

n ra

te (k

gmiddotm

ndash2middotsndash1

)

000 005 010 015 020 025 030 035 040 045Diameter (mm)



(a)

14 x 10ndash3

12 x 10ndash3

10 x 10ndash3

80 x 10ndash4

60 x 10ndash4

40 x 10ndash4

20 x 10ndash4

00

Max

imum

eros

ion

rate

(kgmiddot

mndash2

middotsndash1)

000 005 010 015 020 025 030 035 040 045Diameter (mm)



18 x 10ndash3

16 x 10ndash3

(b)

Figure 12 Comparison of wear rates of different parts at different particle sizes (a) Average wear rate (b) maximum wear rate



DPM erosion(kgm2)

(a) (b) (c) (d) (e)

Figure 13 Impeller wear clouds at different particle volume concentrations (a) C 10 (b) C 15 (c) C 20 (d) C 25 and(e) C 30


DPM erosion(kgm2)

(a) (b) (c) (d) (e)

Figure 14 Pressure surface wear clouds at different particle volume concentrations (a) C 10 (b) C 15 (c) C 20 (d) C 25 and(e) C 30


DPM erosion(kgm2)

(a) (b) (c) (d) (e)

Figure 15 Suction surface wear clouds at different particle volume concentrations (a) C 10 (b) C 15 (c) C 20 (d) C 25 and(e) C 30


DPM erosion(kgm2)

(a) (b) (c) (d) (e)

Figure 16 Volute wear clouds at different particle volume concentrations (a) C 10 (b) C 15 (c) C 20 (d) C 25 and (e)C 30


concentration and maintains the maximum average rate of allparts +e average wear rate of the secondary suction surfaceis varying from 20 to 25 in all parts which is the largest inFigure 17(a) +e increase of particle volume concentrationcauses the maximum wear rate of the main suction surface to

first decrease and then increase the secondary suction surfacemaintains a consistent downward trend and the other partsmaintain an upward trend (Figure 17(b))

+e increase of volume concentration makes the mainwear area of the pressure surface extend from the front end

50 x 10ndash6

40 x 10ndash6

30 x 10ndash6

20 x 10ndash6

10 x 10ndash6

Aver

age e

rosio

n ra

te (k

gmiddotm

ndash2middotsndash1

)

10 15 20 25 30Concentration ()



(a)

30 x 10ndash3

25 x 10ndash3

20 x 10ndash3

15 x 10ndash3

10 x 10ndash3

50 x 10ndash4

Max

imum

eros

ion

rate

(kgmiddot

mndash2

middotsndash1)




(b)

Figure 17 Comparison of wear rates of different parts at different particle volume concentrations (a) Average wear rate (b) maximumwearrate

(a) (b)

(c)

Figure 18Wear numerical simulation and experimental comparison of the impeller (a) Impeller before experiment (b) experimental wearof impeller (c) experimental wear of pressure surface


to the tail +e average wear rate and maximum wear rate ofthe main pressure surface increase and the average wear rateof the secondary pressure surface increases but the maxi-mum wear rate of the secondary pressure surface decreasesfirst and then increases with the increase of volume con-centration+e average wear rate and maximumwear rate ofthe main suction surface increase +e particles with high-volume concentration will aggregate as the volume con-centration increases more particles are located in the flowchannel of the impeller which makes the average wear andmaximum wear of the secondary suction surface show adownward trend +e degree of wear around the volutetongue increases with the increase of particle volume con-centration the average wear rate gradually increases and themaximum wear rate first decreases and then increases

44 Centrifugal Pump Wear Test Comparison Figure 18(a)is the painted impeller before the impeller wear testFigures 18(b) and 18(c) are the wear test results of a cen-trifugal pump with the open impeller at the condition ofvolume concentration C 20 particle diameterd 0106mm and flow rate Q 16m3middothminus1 and centrifugalpump running 48 hours It can be seen intuitively that themain wear positions of the impeller appear in the middle ofthe blade and the front end of the blade By comparing thewear map of the impeller experiment (Figures 18(b) and18(c)) with the wear cloud map in the simulation(Figures 3(c) and 4(c)) it is found that the wear position ofthe impeller appears at the middle and the leading edge ofthe blade which is almost similar to that of the numericalsimulation When using this type of centrifugal pump toconvey high-volume concentration particles the wear re-sistance of the middle part of the impeller blade and theleading edge of the blade should be considered

5 Conclusion

+e wear of the centrifugal pumps with open impellers thatconvey high-volume concentrations of particles is mainlycaused by particle movement In this study the three-di-mensional unsteady and two-phase coupling Euler-Lagrangemethod is used to simulate the wear of the centrifugal pumpwith an open impeller +rough the analysis of the wearcloud diagram it is concluded that when the centrifugalpump delivers high-volume concentration solid-liquid two-phase flow the main wear part appears on the pressuresurface of the impeller Compared with other parts theaverage wear rate of the main pressure surface is the largest+e second is the part of the volute tongue According to thenumerical simulation of the change of the wear cloud imageof the volute tongue it is concluded that the two-phase flowis extremely active around it and the probability of particlescolliding with the surrounding wall is greatly increasedwhich increases the wear rate Parameters such as flow rateparticle size and particle volume concentration mainly havea significant impact on the wear of the leading edge themiddle of the blade and the volute tongue of the centrifugalpump with an open impeller

Data Availability

All data included in this study are available upon request bycontact with the corresponding author

Conflicts of Interest

+e authors declare no conflicts of interest

Acknowledgments

+e authors acknowledge the financial support of NationalNatural Science of China and the Key Research and De-velopment Program of Zhejiang Province +e work wassupported by NSFC (Grant no 51676174) and Key Researchand Development Program of Zhejiang Province (Grant no2020C1027)

References

[1] T Lin Z Zhu X Li J Li and Y Lin ldquo+eoretical experi-mental and numerical methods to predict the best efficiencypoint of centrifugal pump as turbinerdquo Renewable Energyvol 168 no 5 pp 31ndash44 2021

[2] Y Yang L Zhou W Shi Z He Y Han and Y Xiao ldquoIn-terstage difference of pressure pulsation in a three-stageelectrical submersible pumprdquo Journal of Petroleum Scienceand Engineering vol 196 Article ID 107653 2021

[3] X Li T Shen P Li X Guo and Z Zhu ldquoExtended com-pressible thermal cavitation model for the numerical simu-lation of cryogenic cavitating flowrdquo International Journal ofHydrogen Energy vol 45 no 16 pp 10104ndash10118 2020

[4] L Zhou C Han L Bai W Li M A El-Emam and W ShildquoCFD-DEM bidirectional coupling simulation and experi-mental investigation of particle ejections and energy con-version in a spouted bedrdquo Energy vol 211 no 15 p 1186722020

[5] Y Zhang E P Reuterfors B S McLaury S A Shirazi andE F Rybicki ldquoComparison of computed and measuredparticle velocities and erosion in water and air flowsrdquo Wearvol 263 no 1ndash6 pp 330ndash338 2007

[6] C Sunil S N Singh and V Seshadri ldquoA comparative studyon the performance characteristics of centrifugal and pro-gressive cavity slurry pumps with high volume concentrationfly ash slurriesrdquo Particulate Science and Technology vol 29no 4 pp 378ndash396 2011

[7] B Wu X-L Wang H Liu and H-L Xu ldquoNumerical simu-lation and analysis of solid-liquid two-phase three-dimensionalunsteady flow in centrifugal slurry pumprdquo Journal of CentralSouth University vol 22 no 8 pp 3008ndash3016 2015

[8] B K Gandhi S N Singh and V Seshadri ldquoPerformancecharacteristics of centrifugal slurry pumpsrdquo Journal of FluidsEngineering vol 123 no 2 pp 271ndash280 2001

[9] T Engin and M Gur ldquoComparative evaluation of someexisting correlations to predict head degradation of centrif-ugal slurry pumpsrdquo Journal of Fluids Engineering vol 125no 1 pp 149ndash157 2003

[10] M C Roco P Nair and G R Addie ldquoCasing headloss incentrifugal slurry pumpsrdquo Journal of Fluids Engineeringvol 108 no 4 pp 453ndash464 1986

[11] K C Wilson G R Addie A Sellgren and R Clift PumpSelection and Cost Considerations Springer Boston MAUSA 2006


[12] B K Gandhi and S V Borse ldquoEffects of particle size and sizedistribution on estimating erosion wear of cast iron in sand-water slurriesrdquo Indian Journal of Engineering amp MaterialsSciences vol 9 no 6 pp 480ndash486 2002

[13] Y Ben-Ami A Uzi and A Levy ldquoModelling the particlesimpingement angle to produce maximum erosionrdquo PowderTechnology vol 301 pp 1032ndash1043 2016

[14] L Nan H Arabnejad S A Shirazi et al ldquoExperimental studyof particle size shape and particle flow rate on Erosion ofstainless steelrdquo Powder Technology vol 336 pp 70ndash79 2018

[15] F Lai Y Wang S A EI-Shahat G Li and X Zhu ldquoNu-merical study of solid particle erosion in a centrifugal pumpfor liquid-solid flowrdquo Journal of Fluids Engineering vol 141no 12 Article ID 121302 2019

[16] Y Zhang Y Li B Cui Z Zhu and H Dou ldquoNumericalsimulation and analysis of solid-liquid two-phase flow incentrifugal pumprdquo Chinese Journal of Mechanical Engineer-ing vol 26 no 1 pp 53ndash60 2013

[17] W P Adamczyk A Klimanek R A Białecki G WecelP Kozołub and T Czakiert ldquoComparison of the standardEuler-Euler and hybrid Euler-Lagrange approaches formodeling particle transport in a pilot-scale circulating flu-idized bedrdquo Particuology vol 15 no 4 pp 129ndash137 2014

[18] G Ou K Bie Z Zheng G Shu C Wang and B ChengldquoNumerical simulation on the erosion wear of a multiphaseflow pipelinerdquo gte International Journal of AdvancedManufacturing Technology vol 96 no 5ndash8 pp 1705ndash17132018

[19] V Jain L Kalo D Kumar H J Pant and R K UpadhyayldquoExperimental and numerical investigation of liquid-solidbinary fluidized beds radioactive particle tracking techniqueand dense discrete phase model simulationsrdquo Particuologyvol 33 no 4 pp 112ndash122 2017

[20] M Sommerfeld and N Huber ldquoExperimental analysis andmodelling of particle-wall collisionsrdquo International Journal ofMultiphase Flow vol 25 no 6-7 pp 1457ndash1489 1999

[21] A Forder M +ew D Harrison et al ldquoA numerical in-vestigation of solid particle erosion experienced within oilfieldcontrol valvesrdquo Wear vol 216 no 2 pp 184ndash193 1998

[22] J G A Bitter ldquoA study of erosion phenomena part Irdquo Wearvol 6 no 1 pp 5ndash21 1963

[23] J G A Bitter ldquoA study of erosion phenomenardquoWear vol 6no 3 pp 169ndash190 1963

[24] J H Neilson and A Gilchrist ldquoErosion by a stream of solidparticlesrdquo Wear vol 11 no 2 pp 111ndash122 1968

[25] Y I Oka K Okamura T Yoshida et al ldquoPractical estimationof erosion damage caused by solid particle impactrdquo Wearvol 259 no 1ndash6 pp 95ndash101 2005

[26] Y I Oka and T Yoshida ldquoPractical estimation of erosiondamage caused by solid particle impactrdquo Wear vol 259no 1ndash6 pp 102ndash109 2005

[27] C Huang S Chiovelli P Minev J Luo and K NandakumarldquoA comprehensive phenomenological model for erosion ofmaterials in jet flowrdquo Powder Technology vol 187 no 3pp 273ndash279 2008

[28] I Finnie ldquoErosion of surfaces by solid particlesrdquoWear vol 3no 2 pp 87ndash103 1960

[29] G Grant and W Tabakoff ldquoErosion prediction in turbo-machinery resulting from environmental solid particlesrdquoJournal of Aircraft vol 12 no 5 pp 471ndash478 1975

[30] A V Levy and W Buqian ldquoErosion of hard material coatingsystemsrdquo Wear vol 121 no 3 pp 325ndash346 1988

[31] J S Marshall ldquoDiscrete-element modeling of particulateaerosol flowsrdquo Journal of Computational Physics vol 228no 5 pp 1541ndash1561 2009

[32] R Mei ldquoAn approximate expression for the shear lift force ona spherical particle at finite Reynolds numberrdquo InternationalJournal of Multiphase Flow vol 18 no 1 pp 145ndash147 1992

[33] S A Morsi and A J Alexander ldquoAn investigation of particletrajectories in two-phase flow systemsrdquo Journal of FluidMechanics vol 55 no 2 pp 193ndash208 1972


[13] established a wear model by studying the impact angleof particles and the wear law of surface materials on the wall+e volume concentration and sharpness of particles are alsoimportant factors for wall wear +e study of Nan et al [14]showed that the flow rate affects the speed of the particlesand then affects the wear performance Within a certainrange the sharpness of the particles has a greater impact onthe wall wear performance Regarding the effect of particlevolume concentration on the wear of solid-liquid two-phaseflow the study of Lai et al [15] showed that the change ofvolume concentration will affect the position of impellerwear Zhangrsquos simulation and analysis of two-phase flowshowed that the abrasion on the pressure side of the impellerof a centrifugal pump is higher than other parts whenconveying high-volume concentration particles [16]Adamczyk et al [17] used the combination of DDPM andEuler-Euler to calculate the flow of circulating particles inthe fluidized bed and compared with the experiment ob-tained a particle motion model suitable for the fluidized bedOu et al [18] used the DDPM and KTGFmodels to carry outthe corresponding numerical simulations on the wear of theelbow pipe under high-volume concentration coal con-veying +e results showed that for the movement of par-ticles under the resistance of centrifugal force and secondaryflow when they pass the elbow partial reunion occurs andthe larger particles are susceptible to impact the curved backwhich has a more obvious impact on erosion and wear Jainet al [19] studied the influence of different particle prop-erties on the flow characteristics of fluidized beds throughradioactive particle tracking technology and DDPM and theresults showed that DDPM can effectively predict the av-erage particle velocity

To make better use of solid-liquid two-phase centrifugalpumpwear simulation to predict its experimental results therelationship between particles and the wall (including wallrebound function and wall wear function) should be con-sidered Many scholars have proposed wall rebound func-tions that are more in line with the experiment according todifferent research directions Sommerfeld and Huber [20]obtained the parameters of the wall rebound model (such asthe coefficient of restitution and friction coefficient) basedon the experimental data +e modified wall reboundfunction can predict the experiment well Forder et al [21]proposed the corresponding wear models through experi-ments and proposed a corresponding particle reboundmodel in combination with particle angles and wall materialsto better study the wear mechanism of control valves Basedon the wear data of flat specimens in water or airflow and 90degstandard elbows in airflow ECRC [5] obtained a newerosion equation and combined CFD with simulating andpredicting the experiment +e wear rate and experimentalresults are in good consistency Regarding the wear in theprocess of conveying solid particles in a fluidized bed Bitter[22 23] proposed a wall wear function based on themovement properties of the particles the hardness of thematerial and the elastic parameters and explained the wearphenomenon of the fluidized bed in the experiment Bystudying the wear characteristics of the particle shape ve-locity shooting angle and different material properties on

the wall surface Neilson and Gilchrist [24] proposed thecorresponding wear function to explain the wear phe-nomenon in the experiment By studying particle propertiesand wall material properties (hardness and load relaxation)Oka [25 26] proposed wear functions for different materialsHuang [27] established a wear function including particlecollision speed angle and particle size and wall materialproperties for the particle-wall wear characteristics duringthe jet process which were in good agreement with the wearexperiment of Finn [28] Regarding the wear caused by theinhalation of solid particles by the turbine G amp T [29]proposed related particle rebound model and wall wearmodels based on the hydrodynamic resistance of the solidparticles the particlersquos rebound on the wall and the wallwear which were used to predict the relevant parts of theturbine wear location etc However the calculation of thethree-dimensional nonconstant value of wear of centrifugalpumps that transport high-volume concentration solid-liquid two-phase flow is still very small In this work topredict the overall wear performance of the centrifugalpump with open impeller under the condition of the high-volume concentration of solid-liquid two-phase flow themethod of three-dimensional indeterminate constant valueanalysis and the DDPMmodel are used and the influence ofrelevant parameters (flow rate particle diameter and vol-ume concentration) on the wear characteristics of centrif-ugal pump flow components is studied +e results of thisstudy are helpful to develop high-volume concentrationsolid-liquid two-phase flow centrifugal pumps such asapplying hard material [30] to wear-prone areas avoidingunnecessary downtime and reducing operating costs

2 Mathematical Model

To predict the wear performance of the centrifugal pumpthe numerical calculation includes the following conditionsbasic assumptions the establishment of solid-liquid two-phase flow control equation the analysis of particle forcesand the selection of particle-wall collision function and wearfunction

21 Basic Assumption +e solid-liquid two-phase flow in-side the model pump is extremely complicated To simplifythe calculation and improve the accuracy of the numericalsimulation results the following assumptions are adopted

(1) +e continuous phase (water) is an incompressiblefluid and the physical properties of each phase areconstant

(2) +e particles are spherical glass beads with uniformparticle size regardless of the change in particleshape

(3) +e influence of temperature on the two-phase flowfield is not considered

(4) +e collision between the particles and the wall is anelastic collision

(5) +e liquid phase and the solid phase adopt two-waycoupling and so on




z


n

j1_mji minus _mij1113872 1113873 (1)


z


Ti1113872 11138731113960 1113961 + αiρig + 1113944 F

+ 11139442


⎡⎢⎢⎣ ⎤⎥⎥⎦ + KDS us + uj1113872 1113873 + SDE

(2)

1113944 F FV + FS + FL (3)




FV Cvmρρp

upnablau minusup

dt1113874 1113875 (4)



FS 162d2p

μρ1


zu

zx

1113868111386811138681113868111386811138681113868

1113868111386811138681113868111386811138681113868

1113971

(5)


CS

1 minus 03314α051113872 1113873exp minus

Rep

101113888 1113889 + 03114α05

Rep le 401113872 1113873

00524 α times Rep1113872 111387305

Rep ge 401113872 1113873

⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(6)

α dp middot|zuzY|

u minus up

11138681113868111386811138681113868

11138681113868111386811138681113868 (7)

Rep ρdp u minus up

11138681113868111386811138681113868

11138681113868111386811138681113868

μ (8)







dup

dt

u minus up

τr

+g ρp minus ρ1113872 1113873

ρp

+ FV + FS (10)


τr ρpd

2p

18μ24

CdRep (11)


Cd α1 +α2Rep

+α3Re

2p (12)












(a) (b)


17

16

15

14

13

12

11

10

9

8

7

0 2 4 6 8 10 12 14 16 18 20

05

04

03

02

01

00

η (

)



Q (m3lowasthndash1)

H (m

)















DPM erosion(kgm2)

(a) (b) (c) (d)



DPM erosion(kgm2)

(a) (b) (c) (d)



DPM erosion(kgm2)

(a) (b) (c) (d)



DPM erosion(kgm2)

(a) (b) (c) (d)






40 x 10ndash6

35 x 10ndash6

30 x 10ndash6

25 x 10ndash6

20 x 10ndash6

15 x 10ndash6

10 x 10ndash6

50 x 10ndash7

00

Aver

age e

rosio

n ra

te (k

gmiddotm

ndash2middotsndash1

)




(a)

14 x 10ndash3

12 x 10ndash3

10 x 10ndash3

80 x 10ndash4

60 x 10ndash4

40 x 10ndash4

20 x 10ndash4

00

Max

imum

eros

ion

rate

(kgmiddot

mndash2

middotsndash1)




(b)



DPM erosion(kgm2)

(a) (b) (c) (d) (e)



DPM erosion(kgm2)

(a) (b) (c) (d) (e)




DPM erosion(kgm2)

(a) (b) (c) (d) (e)



DPM erosion(kgm2)

(a) (b) (c) (d) (e)


50 x 10ndash6

40 x 10ndash6

30 x 10ndash6

20 x 10ndash6

10 x 10ndash6

00

Aver

age e

rosio

n ra

te (k

gmiddotm

ndash2middotsndash1

)

000 005 010 015 020 025 030 035 040 045Diameter (mm)



(a)

14 x 10ndash3

12 x 10ndash3

10 x 10ndash3

80 x 10ndash4

60 x 10ndash4

40 x 10ndash4

20 x 10ndash4

00

Max

imum

eros

ion

rate

(kgmiddot

mndash2

middotsndash1)

000 005 010 015 020 025 030 035 040 045Diameter (mm)



18 x 10ndash3

16 x 10ndash3

(b)




DPM erosion(kgm2)

(a) (b) (c) (d) (e)



DPM erosion(kgm2)

(a) (b) (c) (d) (e)



DPM erosion(kgm2)

(a) (b) (c) (d) (e)



DPM erosion(kgm2)

(a) (b) (c) (d) (e)






50 x 10ndash6

40 x 10ndash6

30 x 10ndash6

20 x 10ndash6

10 x 10ndash6

Aver

age e

rosio

n ra

te (k

gmiddotm

ndash2middotsndash1

)




(a)

30 x 10ndash3

25 x 10ndash3

20 x 10ndash3

15 x 10ndash3

10 x 10ndash3

50 x 10ndash4

Max

imum

eros

ion

rate

(kgmiddot

mndash2

middotsndash1)




(b)


(a) (b)

(c)





5 Conclusion


Data Availability




Acknowledgments


References






































z


n

j1_mji minus _mij1113872 1113873 (1)


z


Ti1113872 11138731113960 1113961 + αiρig + 1113944 F

+ 11139442


⎡⎢⎢⎣ ⎤⎥⎥⎦ + KDS us + uj1113872 1113873 + SDE

(2)

1113944 F FV + FS + FL (3)




FV Cvmρρp

upnablau minusup

dt1113874 1113875 (4)



FS 162d2p

μρ1


zu

zx

1113868111386811138681113868111386811138681113868

1113868111386811138681113868111386811138681113868

1113971

(5)


CS

1 minus 03314α051113872 1113873exp minus

Rep

101113888 1113889 + 03114α05

Rep le 401113872 1113873

00524 α times Rep1113872 111387305

Rep ge 401113872 1113873

⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(6)

α dp middot|zuzY|

u minus up

11138681113868111386811138681113868

11138681113868111386811138681113868 (7)

Rep ρdp u minus up

11138681113868111386811138681113868

11138681113868111386811138681113868

μ (8)







dup

dt

u minus up

τr

+g ρp minus ρ1113872 1113873

ρp

+ FV + FS (10)


τr ρpd

2p

18μ24

CdRep (11)


Cd α1 +α2Rep

+α3Re

2p (12)












(a) (b)


17

16

15

14

13

12

11

10

9

8

7

0 2 4 6 8 10 12 14 16 18 20

05

04

03

02

01

00

η (

)



Q (m3lowasthndash1)

H (m

)















DPM erosion(kgm2)

(a) (b) (c) (d)



DPM erosion(kgm2)

(a) (b) (c) (d)



DPM erosion(kgm2)

(a) (b) (c) (d)



DPM erosion(kgm2)

(a) (b) (c) (d)






40 x 10ndash6

35 x 10ndash6

30 x 10ndash6

25 x 10ndash6

20 x 10ndash6

15 x 10ndash6

10 x 10ndash6

50 x 10ndash7

00

Aver

age e

rosio

n ra

te (k

gmiddotm

ndash2middotsndash1

)




(a)

14 x 10ndash3

12 x 10ndash3

10 x 10ndash3

80 x 10ndash4

60 x 10ndash4

40 x 10ndash4

20 x 10ndash4

00

Max

imum

eros

ion

rate

(kgmiddot

mndash2

middotsndash1)




(b)



DPM erosion(kgm2)

(a) (b) (c) (d) (e)



DPM erosion(kgm2)

(a) (b) (c) (d) (e)




DPM erosion(kgm2)

(a) (b) (c) (d) (e)



DPM erosion(kgm2)

(a) (b) (c) (d) (e)


50 x 10ndash6

40 x 10ndash6

30 x 10ndash6

20 x 10ndash6

10 x 10ndash6

00

Aver

age e

rosio

n ra

te (k

gmiddotm

ndash2middotsndash1

)

000 005 010 015 020 025 030 035 040 045Diameter (mm)



(a)

14 x 10ndash3

12 x 10ndash3

10 x 10ndash3

80 x 10ndash4

60 x 10ndash4

40 x 10ndash4

20 x 10ndash4

00

Max

imum

eros

ion

rate

(kgmiddot

mndash2

middotsndash1)

000 005 010 015 020 025 030 035 040 045Diameter (mm)



18 x 10ndash3

16 x 10ndash3

(b)




DPM erosion(kgm2)

(a) (b) (c) (d) (e)



DPM erosion(kgm2)

(a) (b) (c) (d) (e)



DPM erosion(kgm2)

(a) (b) (c) (d) (e)



DPM erosion(kgm2)

(a) (b) (c) (d) (e)






50 x 10ndash6

40 x 10ndash6

30 x 10ndash6

20 x 10ndash6

10 x 10ndash6

Aver

age e

rosio

n ra

te (k

gmiddotm

ndash2middotsndash1

)




(a)

30 x 10ndash3

25 x 10ndash3

20 x 10ndash3

15 x 10ndash3

10 x 10ndash3

50 x 10ndash4

Max

imum

eros

ion

rate

(kgmiddot

mndash2

middotsndash1)




(b)


(a) (b)

(c)





5 Conclusion


Data Availability




Acknowledgments


References








































dup

dt

u minus up

τr

+g ρp minus ρ1113872 1113873

ρp

+ FV + FS (10)


τr ρpd

2p

18μ24

CdRep (11)


Cd α1 +α2Rep

+α3Re

2p (12)












(a) (b)


17

16

15

14

13

12

11

10

9

8

7

0 2 4 6 8 10 12 14 16 18 20

05

04

03

02

01

00

η (

)



Q (m3lowasthndash1)

H (m

)















DPM erosion(kgm2)

(a) (b) (c) (d)



DPM erosion(kgm2)

(a) (b) (c) (d)



DPM erosion(kgm2)

(a) (b) (c) (d)



DPM erosion(kgm2)

(a) (b) (c) (d)






40 x 10ndash6

35 x 10ndash6

30 x 10ndash6

25 x 10ndash6

20 x 10ndash6

15 x 10ndash6

10 x 10ndash6

50 x 10ndash7

00

Aver

age e

rosio

n ra

te (k

gmiddotm

ndash2middotsndash1

)




(a)

14 x 10ndash3

12 x 10ndash3

10 x 10ndash3

80 x 10ndash4

60 x 10ndash4

40 x 10ndash4

20 x 10ndash4

00

Max

imum

eros

ion

rate

(kgmiddot

mndash2

middotsndash1)




(b)



DPM erosion(kgm2)

(a) (b) (c) (d) (e)



DPM erosion(kgm2)

(a) (b) (c) (d) (e)




DPM erosion(kgm2)

(a) (b) (c) (d) (e)



DPM erosion(kgm2)

(a) (b) (c) (d) (e)


50 x 10ndash6

40 x 10ndash6

30 x 10ndash6

20 x 10ndash6

10 x 10ndash6

00

Aver

age e

rosio

n ra

te (k

gmiddotm

ndash2middotsndash1

)

000 005 010 015 020 025 030 035 040 045Diameter (mm)



(a)

14 x 10ndash3

12 x 10ndash3

10 x 10ndash3

80 x 10ndash4

60 x 10ndash4

40 x 10ndash4

20 x 10ndash4

00

Max

imum

eros

ion

rate

(kgmiddot

mndash2

middotsndash1)

000 005 010 015 020 025 030 035 040 045Diameter (mm)



18 x 10ndash3

16 x 10ndash3

(b)




DPM erosion(kgm2)

(a) (b) (c) (d) (e)



DPM erosion(kgm2)

(a) (b) (c) (d) (e)



DPM erosion(kgm2)

(a) (b) (c) (d) (e)



DPM erosion(kgm2)

(a) (b) (c) (d) (e)






50 x 10ndash6

40 x 10ndash6

30 x 10ndash6

20 x 10ndash6

10 x 10ndash6

Aver

age e

rosio

n ra

te (k

gmiddotm

ndash2middotsndash1

)




(a)

30 x 10ndash3

25 x 10ndash3

20 x 10ndash3

15 x 10ndash3

10 x 10ndash3

50 x 10ndash4

Max

imum

eros

ion

rate

(kgmiddot

mndash2

middotsndash1)




(b)


(a) (b)

(c)





5 Conclusion


Data Availability




Acknowledgments


References






































(a) (b)


17

16

15

14

13

12

11

10

9

8

7

0 2 4 6 8 10 12 14 16 18 20

05

04

03

02

01

00

η (

)



Q (m3lowasthndash1)

H (m

)















DPM erosion(kgm2)

(a) (b) (c) (d)



DPM erosion(kgm2)

(a) (b) (c) (d)



DPM erosion(kgm2)

(a) (b) (c) (d)



DPM erosion(kgm2)

(a) (b) (c) (d)






40 x 10ndash6

35 x 10ndash6

30 x 10ndash6

25 x 10ndash6

20 x 10ndash6

15 x 10ndash6

10 x 10ndash6

50 x 10ndash7

00

Aver

age e

rosio

n ra

te (k

gmiddotm

ndash2middotsndash1

)




(a)

14 x 10ndash3

12 x 10ndash3

10 x 10ndash3

80 x 10ndash4

60 x 10ndash4

40 x 10ndash4

20 x 10ndash4

00

Max

imum

eros

ion

rate

(kgmiddot

mndash2

middotsndash1)




(b)



DPM erosion(kgm2)

(a) (b) (c) (d) (e)



DPM erosion(kgm2)

(a) (b) (c) (d) (e)




DPM erosion(kgm2)

(a) (b) (c) (d) (e)



DPM erosion(kgm2)

(a) (b) (c) (d) (e)


50 x 10ndash6

40 x 10ndash6

30 x 10ndash6

20 x 10ndash6

10 x 10ndash6

00

Aver

age e

rosio

n ra

te (k

gmiddotm

ndash2middotsndash1

)

000 005 010 015 020 025 030 035 040 045Diameter (mm)



(a)

14 x 10ndash3

12 x 10ndash3

10 x 10ndash3

80 x 10ndash4

60 x 10ndash4

40 x 10ndash4

20 x 10ndash4

00

Max

imum

eros

ion

rate

(kgmiddot

mndash2

middotsndash1)

000 005 010 015 020 025 030 035 040 045Diameter (mm)



18 x 10ndash3

16 x 10ndash3

(b)




DPM erosion(kgm2)

(a) (b) (c) (d) (e)



DPM erosion(kgm2)

(a) (b) (c) (d) (e)



DPM erosion(kgm2)

(a) (b) (c) (d) (e)



DPM erosion(kgm2)

(a) (b) (c) (d) (e)






50 x 10ndash6

40 x 10ndash6

30 x 10ndash6

20 x 10ndash6

10 x 10ndash6

Aver

age e

rosio

n ra

te (k

gmiddotm

ndash2middotsndash1

)




(a)

30 x 10ndash3

25 x 10ndash3

20 x 10ndash3

15 x 10ndash3

10 x 10ndash3

50 x 10ndash4

Max

imum

eros

ion

rate

(kgmiddot

mndash2

middotsndash1)




(b)


(a) (b)

(c)





5 Conclusion


Data Availability




Acknowledgments


References
















































DPM erosion(kgm2)

(a) (b) (c) (d)



DPM erosion(kgm2)

(a) (b) (c) (d)



DPM erosion(kgm2)

(a) (b) (c) (d)



DPM erosion(kgm2)

(a) (b) (c) (d)






40 x 10ndash6

35 x 10ndash6

30 x 10ndash6

25 x 10ndash6

20 x 10ndash6

15 x 10ndash6

10 x 10ndash6

50 x 10ndash7

00

Aver

age e

rosio

n ra

te (k

gmiddotm

ndash2middotsndash1

)




(a)

14 x 10ndash3

12 x 10ndash3

10 x 10ndash3

80 x 10ndash4

60 x 10ndash4

40 x 10ndash4

20 x 10ndash4

00

Max

imum

eros

ion

rate

(kgmiddot

mndash2

middotsndash1)




(b)



DPM erosion(kgm2)

(a) (b) (c) (d) (e)



DPM erosion(kgm2)

(a) (b) (c) (d) (e)




DPM erosion(kgm2)

(a) (b) (c) (d) (e)



DPM erosion(kgm2)

(a) (b) (c) (d) (e)


50 x 10ndash6

40 x 10ndash6

30 x 10ndash6

20 x 10ndash6

10 x 10ndash6

00

Aver

age e

rosio

n ra

te (k

gmiddotm

ndash2middotsndash1

)

000 005 010 015 020 025 030 035 040 045Diameter (mm)



(a)

14 x 10ndash3

12 x 10ndash3

10 x 10ndash3

80 x 10ndash4

60 x 10ndash4

40 x 10ndash4

20 x 10ndash4

00

Max

imum

eros

ion

rate

(kgmiddot

mndash2

middotsndash1)

000 005 010 015 020 025 030 035 040 045Diameter (mm)



18 x 10ndash3

16 x 10ndash3

(b)




DPM erosion(kgm2)

(a) (b) (c) (d) (e)



DPM erosion(kgm2)

(a) (b) (c) (d) (e)



DPM erosion(kgm2)

(a) (b) (c) (d) (e)



DPM erosion(kgm2)

(a) (b) (c) (d) (e)






50 x 10ndash6

40 x 10ndash6

30 x 10ndash6

20 x 10ndash6

10 x 10ndash6

Aver

age e

rosio

n ra

te (k

gmiddotm

ndash2middotsndash1

)




(a)

30 x 10ndash3

25 x 10ndash3

20 x 10ndash3

15 x 10ndash3

10 x 10ndash3

50 x 10ndash4

Max

imum

eros

ion

rate

(kgmiddot

mndash2

middotsndash1)




(b)


(a) (b)

(c)





5 Conclusion


Data Availability




Acknowledgments


References







































40 x 10ndash6

35 x 10ndash6

30 x 10ndash6

25 x 10ndash6

20 x 10ndash6

15 x 10ndash6

10 x 10ndash6

50 x 10ndash7

00

Aver

age e

rosio

n ra

te (k

gmiddotm

ndash2middotsndash1

)




(a)

14 x 10ndash3

12 x 10ndash3

10 x 10ndash3

80 x 10ndash4

60 x 10ndash4

40 x 10ndash4

20 x 10ndash4

00

Max

imum

eros

ion

rate

(kgmiddot

mndash2

middotsndash1)




(b)



DPM erosion(kgm2)

(a) (b) (c) (d) (e)



DPM erosion(kgm2)

(a) (b) (c) (d) (e)




DPM erosion(kgm2)

(a) (b) (c) (d) (e)



DPM erosion(kgm2)

(a) (b) (c) (d) (e)


50 x 10ndash6

40 x 10ndash6

30 x 10ndash6

20 x 10ndash6

10 x 10ndash6

00

Aver

age e

rosio

n ra

te (k

gmiddotm

ndash2middotsndash1

)

000 005 010 015 020 025 030 035 040 045Diameter (mm)



(a)

14 x 10ndash3

12 x 10ndash3

10 x 10ndash3

80 x 10ndash4

60 x 10ndash4

40 x 10ndash4

20 x 10ndash4

00

Max

imum

eros

ion

rate

(kgmiddot

mndash2

middotsndash1)

000 005 010 015 020 025 030 035 040 045Diameter (mm)



18 x 10ndash3

16 x 10ndash3

(b)




DPM erosion(kgm2)

(a) (b) (c) (d) (e)



DPM erosion(kgm2)

(a) (b) (c) (d) (e)



DPM erosion(kgm2)

(a) (b) (c) (d) (e)



DPM erosion(kgm2)

(a) (b) (c) (d) (e)






50 x 10ndash6

40 x 10ndash6

30 x 10ndash6

20 x 10ndash6

10 x 10ndash6

Aver

age e

rosio

n ra

te (k

gmiddotm

ndash2middotsndash1

)




(a)

30 x 10ndash3

25 x 10ndash3

20 x 10ndash3

15 x 10ndash3

10 x 10ndash3

50 x 10ndash4

Max

imum

eros

ion

rate

(kgmiddot

mndash2

middotsndash1)




(b)


(a) (b)

(c)





5 Conclusion


Data Availability




Acknowledgments


References





































DPM erosion(kgm2)

(a) (b) (c) (d) (e)



DPM erosion(kgm2)

(a) (b) (c) (d) (e)


50 x 10ndash6

40 x 10ndash6

30 x 10ndash6

20 x 10ndash6

10 x 10ndash6

00

Aver

age e

rosio

n ra

te (k

gmiddotm

ndash2middotsndash1

)

000 005 010 015 020 025 030 035 040 045Diameter (mm)



(a)

14 x 10ndash3

12 x 10ndash3

10 x 10ndash3

80 x 10ndash4

60 x 10ndash4

40 x 10ndash4

20 x 10ndash4

00

Max

imum

eros

ion

rate

(kgmiddot

mndash2

middotsndash1)

000 005 010 015 020 025 030 035 040 045Diameter (mm)



18 x 10ndash3

16 x 10ndash3

(b)




DPM erosion(kgm2)

(a) (b) (c) (d) (e)



DPM erosion(kgm2)

(a) (b) (c) (d) (e)



DPM erosion(kgm2)

(a) (b) (c) (d) (e)



DPM erosion(kgm2)

(a) (b) (c) (d) (e)






50 x 10ndash6

40 x 10ndash6

30 x 10ndash6

20 x 10ndash6

10 x 10ndash6

Aver

age e

rosio

n ra

te (k

gmiddotm

ndash2middotsndash1

)




(a)

30 x 10ndash3

25 x 10ndash3

20 x 10ndash3

15 x 10ndash3

10 x 10ndash3

50 x 10ndash4

Max

imum

eros

ion

rate

(kgmiddot

mndash2

middotsndash1)




(b)


(a) (b)

(c)





5 Conclusion


Data Availability




Acknowledgments


References





































DPM erosion(kgm2)

(a) (b) (c) (d) (e)



DPM erosion(kgm2)

(a) (b) (c) (d) (e)



DPM erosion(kgm2)

(a) (b) (c) (d) (e)



DPM erosion(kgm2)

(a) (b) (c) (d) (e)






50 x 10ndash6

40 x 10ndash6

30 x 10ndash6

20 x 10ndash6

10 x 10ndash6

Aver

age e

rosio

n ra

te (k

gmiddotm

ndash2middotsndash1

)




(a)

30 x 10ndash3

25 x 10ndash3

20 x 10ndash3

15 x 10ndash3

10 x 10ndash3

50 x 10ndash4

Max

imum

eros

ion

rate

(kgmiddot

mndash2

middotsndash1)




(b)


(a) (b)

(c)





5 Conclusion


Data Availability




Acknowledgments


References







































50 x 10ndash6

40 x 10ndash6

30 x 10ndash6

20 x 10ndash6

10 x 10ndash6

Aver

age e

rosio

n ra

te (k

gmiddotm

ndash2middotsndash1

)




(a)

30 x 10ndash3

25 x 10ndash3

20 x 10ndash3

15 x 10ndash3

10 x 10ndash3

50 x 10ndash4

Max

imum

eros

ion

rate

(kgmiddot

mndash2

middotsndash1)




(b)


(a) (b)

(c)





5 Conclusion


Data Availability




Acknowledgments


References






































5 Conclusion


Data Availability




Acknowledgments


References




































wear characteristics of dense fine particles solid-liquid two … · 2020. 12. 7. · to...

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