research article sediment and cavitation erosion studies through dam...

Research ArticleSediment and Cavitation Erosion Studies through Dam Tunnels

Muhammad Abid1 Jamal Saeed2 and Hafiz Abdul Wajid34

1 Interdisciplinary Research Center COMSATS Institute of Information Technology Wah Cantonment 47040 Pakistan2School of Mechanical and Manufacturing Engineering NUST Islamabad 44000 Pakistan3Department of Mathematics COMSATS Institute of Information Technology Lahore 54000 Pakistan4Department of Electrical Engineering Islamic University of Madinah Madinah 20012 Saudi Arabia

Correspondence should be addressed to Muhammad Abid drabidciitwahedupk

Received 6 November 2015 Accepted 21 February 2016

Academic Editor Sheng-Rui Jian

Copyright copy 2016 Muhammad Abid et al This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

This paper presents results of sediment and cavitation erosion through Tunnel 2 and Tunnel 3 of Tarbela Dam in Pakistan Mainbend and main branch of Tunnel 2 and outlet 1 and outlet 3 of Tunnel 3 are concluded to be critical for cavitation and sedimenterosion Studies are also performed for increased sediments flow rate concluding 5 kgsec as the critical value for sudden increasein erosion rate density Erosion rate is concluded to be the function of sediment flow rate and head condition Particulate masspresently observed is reasonably low hence presently not affecting the velocity and the flow field

1 Introduction

In recent studies it is highlighted that sediments are graduallyaccumulated in Tarbela Dam reservoir resulting in grad-ual decrease in reservoir water storage capacity increasedload on embankment wall and damage to tunnels andturbines [1ndash3] Among the tunnels of Tarbela Dam Tunnel2 and Tunnel 3 are observed to be the most critical [34] their parameters are given in Table 1 Tunnel 3 is abigger tunnel with horizontal inlet at the reservoir bedand intake of 241564m3sec whereas Tunnel 2 has verticalinlet and intake of 97863m3sec Both tunnels are usedfor irrigation and power generation purposes Abid et alin [4ndash7] have highlighted erosion of the walls of tunnelswith present sediment flow rate through them As sedimentaccumulation is increased the number of sediments particlesalso changes through the tunnels hence their effect on thetunnels life needs to be investigated Reynolds Stress Model(RSM) due to its advantage of performing well in highlychaotic and swirling flows and uneven geometries is used topredict flow separation [8] Continuity and modified NavierStokes equation [1ndash3] shows Reynoldsrsquo Stress 120590 which is aflow property and is taken as zero in nonturbulent flows

The constant and coefficients in the RSM used are given inTable 2 Hence

120597120588

120597119905

+ nabla sdot (120588119880119888) = 0

120597 (120588119880119888)

120597119905

+ nabla sdot (120588119880119888otimes 119880119888) = 119861 + nabla sdot (minus120588119906

1015840otimes 1199061015840) + 120590

(1)

where

120590 =

119901

120588

119868 +

120583

120588

[nabla119880119888+ (nabla119880

119888)119879] (2)

Lagrangian particle tracking is used as particles experience anumber of forceswhile passing through the domain includingbuoyancy lift drag and weight However buoyancy forparticles having high density is neglected as this force isnegligible The drag force thus experienced by a particle iscalculated using carrier velocity 119880

119888and particle velocity 119880

119901

as per relation in

119889119880119901

119889119909

= 119865119863(119880119888minus 119880119901) (3)

Hindawi Publishing CorporationJournal of EngineeringVolume 2016 Article ID 8645789 7 pageshttpdxdoiorg10115520168645789

2 Journal of Engineering

Table 1 Tunnels parameters

Parameters Tunnel 2 Tunnel 3Length (m) 84651 90741Inlet Elevation (m) 373 36043Outlet Elevation (m) 33711 34046Inlet Diameter (m) 1096 4887Outlet Branches Diameter (m) 487 732Average Volume Flow Rate of Water (m3sec) 97863 241564Average Available Head (m) 95091 91815Power Generation Capacity (MW) 1050 1728

Table 2 Constant and coefficients used in RS Model

Anisotropic Diffusion Constant 119862120583

009Turbulent Schmidt Number 120590

119896100

Reynoldsrsquo Stress Coefficients

1198621199041

1801198621199042

0601198621120576

1441198622120576

192

The drag force per unit mass 119865119863of the particle is calculated

using (4) where 119862119863is the Drag Coefficient and is taken as

044 for the two-way coupling considered

119865119863=

1

120591119901

119862119863

Re119901

24

(4)

Particlersquos response time to change in flow and particlesReynoldsrsquo number are calculated using (5) and (6) respec-tively These equations are given as follows

120591119901=

1205881199011198892

119901

18120583

(5)

Re119901=

119889119901(119880 minus 119880

119901)

]

(6)

where 119880 is the carrier phase velocity while 119880119901is the particle

velocity and ] is the carrier phase dynamic viscosityFinnie erosion model given in (7) is used in conjunction

with Lagrangian particle tracking in ANSYS CFX [8 9]Water passing through the tunnels carries sediment particlesand in the regions where there is discontinuity in the direc-tion of flow or turbulence particles disassociate themselvesfrom the water and follow a path dictated by its inertiabecause of high Stokes number [10] In these regions particlesstrike the walls of the tunnels resulting in erosion Erosiondue to sediment particles is a function of impact velocity andimpact angle of the particles The exponent 119899 in the Finnieerosion model is taken as 2 and 119896 is taken as 1 Two-waycoupling or multiphase flow conditions are considered as theeffect of increased number of sediment particles for erosionis studied [10] Hence

119864 = 119896 sdot 119881119899

119901sdot 119891 (120574) (7)

Table 3 Variables used in Rayleigh-Plessetrsquos cavitation model

119875119904

4240 Pa119865cond 001119865vap 50120588119903

1000119903nuc 5e minus 4119877119891

025119877119861

1 120583m

where 119891(120574) = (13)cos2(120574) when tan(120574) gt 13 and 119891(120574) =sin(120574) minus 3sin2(120574) when tan(120574) lt 13

Cavitation is a phenomenon that results from a pressuredrop of the liquid phase below saturation pressure of theliquid under the conditions Based on the tunnels geometry Sbend and outlet branches sharp bends pressure drop of wateris expected along these locations Therefore erosion due tocavitation phenomenon is studied Rayleigh-Plessetrsquos modelgiven in (8) is used to govern the water vapors formation andcondensation [11] and different variables used in the modelare summarized in Table 3 Therefore

119877119861

1198892119877119861

1198891199052+ 15 (

119889119877119861

119889119905

)

2

+

2120590

120588119891119877119861

=

119901V minus 119901

120588119891

(8)

where 119877119861is nucleation radius of the bubble 119901V is vapor

pressure p is reference pressure and 120588119891is the fluid density

2 Modeling Meshing andBoundary Conditions

Both tunnels are modeled in Pro-Engineer software [12](Figure 1) and mesh is generated in ANSYS ICEM CFD[8] In order to capture erosion along inner walls a highernumber of elements with prism elements are added in finiteelement model of Abid et al [3ndash7] (Figure 2) Table 4 showsresults of mesh sensitivity analysis including number and sizeof elements computational time and other variables [13]Table 5 shows general CFD parameters used in ANSYSCFXTable 6 shows boundary conditions initialization conditionand hypothetical sediment flow rate in the tunnels to studythe effect of increased number of particles on erosion ratedensity during winter average and summer seasons that islow medium and high water heads To save computationaltime and resource velocities have been initialized to getconverged solution sooner Particle injection is considereduniform based on the geometry of the tunnels

3 Results and Discussion

The velocity of water at different critical locations of Tunnel2 and Tunnel 3 for different head condition and sedimentsflow rate is summarized in Tables 7 and 8 respectively Nochange in velocity of the water with variation in sedimentsflow rate is observed and is concluded due to small particulatemass hence no effect on the flow field Along different tunnelsections different velocities are recorded Maximum and

Journal of Engineering 3

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

Figure 1 Modeling of Tunnel 2 (a) main bend (b) main branch (c) outlets Tunnel 3 (d) S bend and (e) outlets

(a) (b) (c)

(d) (e) (f)

Figure 2 Meshing Tunnel 2 (andashc) and Tunnel 3 (dndashf)

minimum velocity are observed at maximum and minimumwater heads respectively It is also concluded that any changein water velocity results in change in sediment velocity

Erosion rate density is observed to be increased withincrease in sediment flow rate For high head condition thechange can be easily attributed to the increase in velocitiesat all critical locations of both tunnels Figures 3 and 4show changes in erosion rate for Tunnel 2 and Tunnel 3respectively with change in sediment flow rate at differenthead conditions As velocity does not change at any locationunder the same head condition for different sediments flowrate the minor variation in erosion rate density is concludeddue to the slight variation in impact angle For both tunnels

until 5 kgsec sediment flow rate almost zero erosion ratedensity is observed which however started increasing rapidlyafter this and became prominent at the sediment flow rate of50 kgsec This concludes that the sediment flow rate shouldbe carefully measured to avoid any catastrophic failure of thetunnels Main branch of Tunnel 2 and outlet 3 of Tunnel 3are concluded to be critical for sediment erosion Results forsediment erosion density rate for Tunnel 2 and Tunnel 3 aresummarized in Tables 9 and 10 respectively

It is observed from water and sediment flow throughthe tunnels that pressure at the inside of the bends or sharpcorners drops below saturation pressure resulting in watervapors formation Analyses were performed for the various


Table 4 Mesh sensitivity analysis

Equations Mesh size1 2 3 5

U-Momentum Bulk 106E minus 04 142E minus 04 166E minus 04 246E minus 04V-Momentum Bulk 556E minus 05 535E minus 05 446E minus 05 349E minus 05W-Momentum Bulk 762E minus 05 799E minus 05 568E minus 05 805E minus 05Mass of Water 119E minus 05 172E minus 05 187E minus 05 247E minus 05uu-RS 512E minus 04 447E minus 04 912E minus 04 100E minus 03vv-RS 616E minus 04 406E minus 04 519E minus 04 416E minus 04ww-RS 103E minus 03 498E minus 04 498E minus 04 467E minus 04uv-RS 994E minus 05 543E minus 05 196E minus 04 249E minus 04uw-RS 190E minus 04 254E minus 04 191E minus 04 204E minus 04vw-RS 271E minus 04 119E minus 04 600E minus 05 625E minus 05E-Dissipation K 171E minus 04 120E minus 04 942E minus 05 488E minus 05Computational time (sec) 4310 1900 1104 1623

Table 5 Various constants and coefficients used in simulation

Parameter Detail Tunnel 2 Tunnel 3Erosion Finnie Model 119896 = 1 119899 = 2 119896 = 1 119899 = 2Particles injection Uniform injection Two-way coupled Two-way coupledRestitution Coefficient Perpendicular and parallel 09 and 1 respectively 09 and 1 respectivelyDrag Coefficient Schiller and Neumann Correlation 044 for Re

119889gt 1000 044 for Re

119889gt 1000

Particle Integration Tracking distance and time 1200m 300 sec 1200m 300 sec

Table 6 Boundary conditions initialization condition and sediment flow rates at different heads

Type Head Tunnel 2 Tunnel 3

Boundary conditions Pressure (kPa)High 132353 129076

Medium 95091 91815Low 57830 54553

Initial conditions Velocity (msec)High 1155 205

Medium 1033 170Low 757 131

Sediment flow rates at different heads (kgsec) 5 times 10minus5 5 times 10minus4 5 times 10minus3 5 times 10minus2 5 times 10minus1 5 and 50

Table 7 Velocity at different locations of Tunnel 2 under different head and varying sediment flow rates

Head Sediment flow rate (kgsec) Main bend Main branch Out1 Out2 Out3 Out4 Out5 Out6

High 000005 414 548 387 170 204 329 437 30250 414 548 387 170 204 329 437 302

Low 000005 310 410 290 128 153 246 328 22650 310 410 290 128 153 246 328 226


Head Sediment flow rate (kgsec) S1 S2 Out1 Out2 Out3 Out4

Medium 000005 304 250 225 199 209 26550 304 250 225 199 209 265

Low 000005 224 184 166 147 155 19550 224 184 166 147 155 195


Table 9 Erosion rate density (kgmsdotsec) in Tunnel 2 under various head conditions and at fixed sediment flow rate of 50 kgsec

Head Main bend Main branch Out1 Out2 Out3 Out4 Out5 Out6High 45 324 269 34 49 52 62 107Medium 28 237 198 30 38 34 60 62Low 17 130 98 15 17 20 27 40


Head S1 S2 Out1 Out2 Out3 Out4High 28 23 16 23 60 11Medium 20 13 11 15 42 7Low 12 10 7 8 24 2

Eros

ion

rate

den

sity 335E + 02

285E + 02

235E + 02

185E + 02

135E + 02

850E + 01

350E + 01

minus150E + 01

Sediment flow rate (kgsec)

50

0E

minus0

5

50

0E

minus0

4

50

0E

minus0

3

50

0E

minus0

2

50

0E

minus0

1 5

50

BMHBMM

BML

(kg

mmiddotse

c)

Figure 3 Erosion rate density atmain branch for all head conditionsand different sediment flow rate in Tunnel 2 (BM main branch Hhigh head M medium head L low head)

head conditions that is high medium and low A significantpressure drop is observed at themain bendmain branch andoutlet branches in Tunnel 2 and S bend and outlet branchesin Tunnel 3 The volume fraction of water vapors is on thehigher side at the critical locations of the tunnels highlightingthe notion that these locations are prone to erosion and isconcluded due to the cavitation effect Cavitation erosionis therefore further superposed on the sediments erosionalready observed The presence of water vapors will bringthese locations under a greater threat The maximum watervapor volume fraction gradient maximum volume fractionof water vapors and Euler or cavitation numbers at differentheads are summarized in Tables 11 and 12 for Tunnel 2and Tunnel 3 respectively It is concluded that the sharperbends have greater tendency of water vapors formation dueto greater pressure drop at these locations Critical locationsare also identified based on the Euler or cavitation numbercalculated at these locations Atmospheric pressure is takento be the reference pressure For Euler number less than 1 theregion is termed ldquocriticalrdquo Cavitation erosion is shown along


50

0E

minus0

5

50

0E

minus0

4

50

0E

minus0

3

50

0E

minus0

2

50

0E

minus0

1 5

50

Out3HOut3M

Out3L

Eros

ion

rate

den

sity

(kg

mmiddotse

c)

600E + 01

500E + 01

400E + 01

300E + 01

200E + 01

100E + 01

000E + 00

minus100E + 01

Figure 4 Erosion rate density at outlet 3 for all head conditions anddifferent sediment flow rate in Tunnel 3 (Out outlet H high headM medium head L low head)

different locations for Tunnel 2 and Tunnel 3 in Figures 5 and6 respectively Main bend of Tunnel 2 and outlet 1 of Tunnel3 are concluded to be critical for cavitation erosion

4 Conclusion

Flow profile is observed to be not affected by the increasein sediment flow rate through the tunnels because of smallparticulate mass and negligible particle-to-particle interac-tion The tracks followed by particles remained unchangedand any rise in erosion rate density is concluded as a directconsequence of head and sediment flow rate Main branch ofTunnel 2 and outlet 3 of Tunnel 3 are concluded to be criticalfor sediment erosion

Keeping in view the expected increased sediment flowrate in the tunnels due to sediment delta movement towardsmain embankment wall for both tunnels until 5 kgsecsediment flow rate almost zero erosion rate density isobserved which however started increasing rapidly after thisand became prominent at the sediment flow rate of 50 kgsec


Table 11 Volume fraction of water vapors and volume fraction gradient in Tunnel 2 under various head conditions

Head Main bend Main branch Outlet branchesOut1simOut6

Max water vapor volumefraction gradient (mminus1)

Max volume fraction ofwater vapors

Volume fraction of water vapors and volume fraction gradientHigh 075 098 098 1729 0980Medium 073 097 097 1792 0977Low 072 096 096 1764 0967

Euler or cavitation numbersHigh 009 024 013 mdash mdashMedium 043 111 063 mdash mdashLow 041 123 036 mdash mdash

Table 12 Volume fraction of water vapors volume fraction gradient and Euler or cavitation numbers in Tunnel 3 under various headconditions

Head S1 S2 Out1 Out2 Out3 Out4 Max water vapor volumefraction gradient (mminus1)

Max volume fraction ofwater vapor

Volume fraction of water vapors and volume fraction gradientHigh 095 095 048 082 082 097 1746 0971Medium 086 095 091 073 076 095 1916 0958Low 087 072 067 045 057 074 1416 0906

Euler or cavitation numbersHigh 086 109 041 039 051 096 mdash mdashMedium 097 112 049 068 080 112 mdash mdashLow 109 138 069 100 188 240 mdash mdash

(a) (b)

(c)

Figure 5 Cavitation erosion (water vapors) at different locations of Tunnel 2


(a) (b)


Hence the possibility of catastrophic failure of the tunnelsdue to increased sediment flow rate cannot be ignored

Cavitation is observed to be threatening at several loca-tions Main bend of Tunnel 2 and outlet 1 of Tunnel 3 areconcluded to be critical for cavitation erosionThe combinedeffect of both erosion due to sediments and cavitation furtherincreases the erosion rate density

Competing Interests

The authors declare that they have no competing interests

References

[1] MHanif Sediment Concentration (ppm) Annual Reservoir Sed-imentation Report Survey and Hydrology Department TarbelaDam Project 2009

[2] M Abid and M U Siddiqi ldquoMultiphase flow simulationsthrough Tarbela Dam Spillways and Tunnelsrdquo Journal of WaterResource and Protection vol 2 no 6 pp 532ndash539 2010

[3] M R Siddiqui Water and sediment flow simulation in tarbeladam reservoir [MS thesis] GIK Institute Topi Pakistan 2010

[4] A A Noon Study of the effect of sediment flows through TarbelaDam Tunnels [MS thesis] GIK Institute Topi Pakistan 2010

[5] M Abid and A A Noon ldquoTurbulent flow simulations throughTarbela Dam Tunnel-2rdquo Journal of Engineering vol 2 no 7 pp205ndash213 2010

[6] M Abid A A Noon and H AWajid ldquoSimulation of turbulentflow through tarbela dam tunnel 3rdquo IIUM Engineering Journalvol 11 no 2 pp 201ndash224 2010

[7] M Abid A A NoonMW Al-Grafi andH AWajid ldquoErosionstudy of Tarbela Dam Tunnel-1rdquo Iranian Journal of Science andTechnology vol 38 no 1 pp 253ndash261 2014

[8] ANSYS NSYS CFX Reference Guide Release 11 ANSYS 2009[9] I Finnie ldquoErosion of surfaces by solid particlesrdquo Wear vol 3

no 2 pp 87ndash103 1960[10] G Brown ldquoUse of CFD to predict and reduce erosion in

industrial slurry piping systemrdquo in Proceedings of the 5th Inter-national Conference on CFD in the Process Industries (CSIROrsquo06) Melbourne Australia December 2006

[11] J Madadnia and I Owen ldquoAccelerated surface erosion bycavitating particulate-laden flowsrdquoWear vol 165 no 1 pp 113ndash116 1993

[12] ProEngineer Wildfire Release 4 Parametric Technology Cor-poration 2009

[13] G Iaccarino ldquoPredictions of a turbulent separated flow usingcommercial CFD codesrdquo Journal of Fluids Engineering vol 123no 4 pp 819ndash828 2001

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Shock and Vibration


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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks



Table 1 Tunnels parameters

Parameters Tunnel 2 Tunnel 3Length (m) 84651 90741Inlet Elevation (m) 373 36043Outlet Elevation (m) 33711 34046Inlet Diameter (m) 1096 4887Outlet Branches Diameter (m) 487 732Average Volume Flow Rate of Water (m3sec) 97863 241564Average Available Head (m) 95091 91815Power Generation Capacity (MW) 1050 1728

Table 2 Constant and coefficients used in RS Model

Anisotropic Diffusion Constant 119862120583

009Turbulent Schmidt Number 120590

119896100

Reynoldsrsquo Stress Coefficients

1198621199041

1801198621199042

0601198621120576

1441198622120576

192

The drag force per unit mass 119865119863of the particle is calculated

using (4) where 119862119863is the Drag Coefficient and is taken as

044 for the two-way coupling considered

119865119863=

1

120591119901

119862119863

Re119901

24

(4)

Particlersquos response time to change in flow and particlesReynoldsrsquo number are calculated using (5) and (6) respec-tively These equations are given as follows

120591119901=

1205881199011198892

119901

18120583

(5)

Re119901=

119889119901(119880 minus 119880

119901)

]

(6)

where 119880 is the carrier phase velocity while 119880119901is the particle

velocity and ] is the carrier phase dynamic viscosityFinnie erosion model given in (7) is used in conjunction

with Lagrangian particle tracking in ANSYS CFX [8 9]Water passing through the tunnels carries sediment particlesand in the regions where there is discontinuity in the direc-tion of flow or turbulence particles disassociate themselvesfrom the water and follow a path dictated by its inertiabecause of high Stokes number [10] In these regions particlesstrike the walls of the tunnels resulting in erosion Erosiondue to sediment particles is a function of impact velocity andimpact angle of the particles The exponent 119899 in the Finnieerosion model is taken as 2 and 119896 is taken as 1 Two-waycoupling or multiphase flow conditions are considered as theeffect of increased number of sediment particles for erosionis studied [10] Hence

119864 = 119896 sdot 119881119899

119901sdot 119891 (120574) (7)

Table 3 Variables used in Rayleigh-Plessetrsquos cavitation model

119875119904

4240 Pa119865cond 001119865vap 50120588119903

1000119903nuc 5e minus 4119877119891

025119877119861

1 120583m

where 119891(120574) = (13)cos2(120574) when tan(120574) gt 13 and 119891(120574) =sin(120574) minus 3sin2(120574) when tan(120574) lt 13

Cavitation is a phenomenon that results from a pressuredrop of the liquid phase below saturation pressure of theliquid under the conditions Based on the tunnels geometry Sbend and outlet branches sharp bends pressure drop of wateris expected along these locations Therefore erosion due tocavitation phenomenon is studied Rayleigh-Plessetrsquos modelgiven in (8) is used to govern the water vapors formation andcondensation [11] and different variables used in the modelare summarized in Table 3 Therefore

119877119861

1198892119877119861

1198891199052+ 15 (

119889119877119861

119889119905

)

2

+

2120590

120588119891119877119861

=

119901V minus 119901

120588119891

(8)

where 119877119861is nucleation radius of the bubble 119901V is vapor

pressure p is reference pressure and 120588119891is the fluid density

2 Modeling Meshing andBoundary Conditions

Both tunnels are modeled in Pro-Engineer software [12](Figure 1) and mesh is generated in ANSYS ICEM CFD[8] In order to capture erosion along inner walls a highernumber of elements with prism elements are added in finiteelement model of Abid et al [3ndash7] (Figure 2) Table 4 showsresults of mesh sensitivity analysis including number and sizeof elements computational time and other variables [13]Table 5 shows general CFD parameters used in ANSYSCFXTable 6 shows boundary conditions initialization conditionand hypothetical sediment flow rate in the tunnels to studythe effect of increased number of particles on erosion ratedensity during winter average and summer seasons that islow medium and high water heads To save computationaltime and resource velocities have been initialized to getconverged solution sooner Particle injection is considereduniform based on the geometry of the tunnels

3 Results and Discussion

The velocity of water at different critical locations of Tunnel2 and Tunnel 3 for different head condition and sedimentsflow rate is summarized in Tables 7 and 8 respectively Nochange in velocity of the water with variation in sedimentsflow rate is observed and is concluded due to small particulatemass hence no effect on the flow field Along different tunnelsections different velocities are recorded Maximum and


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


(a) (b) (c)

(d) (e) (f)












119889gt 1000 044 for Re

119889gt 1000





Medium 95091 91815Low 57830 54553


Medium 1033 170Low 757 131




High 000005 414 548 387 170 204 329 437 30250 414 548 387 170 204 329 437 302

Low 000005 310 410 290 128 153 246 328 22650 310 410 290 128 153 246 328 226



Medium 000005 304 250 225 199 209 26550 304 250 225 199 209 265

Low 000005 224 184 166 147 155 19550 224 184 166 147 155 195






Eros

ion

rate

den

sity 335E + 02

285E + 02

235E + 02

185E + 02

135E + 02

850E + 01

350E + 01

minus150E + 01


50

0E

minus0

5

50

0E

minus0

4

50

0E

minus0

3

50

0E

minus0

2

50

0E

minus0

1 5

50

BMHBMM

BML

(kg

mmiddotse

c)




50

0E

minus0

5

50

0E

minus0

4

50

0E

minus0

3

50

0E

minus0

2

50

0E

minus0

1 5

50

Out3HOut3M

Out3L

Eros

ion

rate

den

sity

(kg

mmiddotse

c)

600E + 01

500E + 01

400E + 01

300E + 01

200E + 01

100E + 01

000E + 00

minus100E + 01



4 Conclusion















(a) (b)

(c)



(a) (b)




Competing Interests


References
















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










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


(a) (b) (c)

(d) (e) (f)












119889gt 1000 044 for Re

119889gt 1000





Medium 95091 91815Low 57830 54553


Medium 1033 170Low 757 131




High 000005 414 548 387 170 204 329 437 30250 414 548 387 170 204 329 437 302

Low 000005 310 410 290 128 153 246 328 22650 310 410 290 128 153 246 328 226



Medium 000005 304 250 225 199 209 26550 304 250 225 199 209 265

Low 000005 224 184 166 147 155 19550 224 184 166 147 155 195






Eros

ion

rate

den

sity 335E + 02

285E + 02

235E + 02

185E + 02

135E + 02

850E + 01

350E + 01

minus150E + 01


50

0E

minus0

5

50

0E

minus0

4

50

0E

minus0

3

50

0E

minus0

2

50

0E

minus0

1 5

50

BMHBMM

BML

(kg

mmiddotse

c)




50

0E

minus0

5

50

0E

minus0

4

50

0E

minus0

3

50

0E

minus0

2

50

0E

minus0

1 5

50

Out3HOut3M

Out3L

Eros

ion

rate

den

sity

(kg

mmiddotse

c)

600E + 01

500E + 01

400E + 01

300E + 01

200E + 01

100E + 01

000E + 00

minus100E + 01



4 Conclusion















(a) (b)

(c)



(a) (b)




Competing Interests


References
















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation















119889gt 1000 044 for Re

119889gt 1000





Medium 95091 91815Low 57830 54553


Medium 1033 170Low 757 131




High 000005 414 548 387 170 204 329 437 30250 414 548 387 170 204 329 437 302

Low 000005 310 410 290 128 153 246 328 22650 310 410 290 128 153 246 328 226



Medium 000005 304 250 225 199 209 26550 304 250 225 199 209 265

Low 000005 224 184 166 147 155 19550 224 184 166 147 155 195






Eros

ion

rate

den

sity 335E + 02

285E + 02

235E + 02

185E + 02

135E + 02

850E + 01

350E + 01

minus150E + 01


50

0E

minus0

5

50

0E

minus0

4

50

0E

minus0

3

50

0E

minus0

2

50

0E

minus0

1 5

50

BMHBMM

BML

(kg

mmiddotse

c)




50

0E

minus0

5

50

0E

minus0

4

50

0E

minus0

3

50

0E

minus0

2

50

0E

minus0

1 5

50

Out3HOut3M

Out3L

Eros

ion

rate

den

sity

(kg

mmiddotse

c)

600E + 01

500E + 01

400E + 01

300E + 01

200E + 01

100E + 01

000E + 00

minus100E + 01



4 Conclusion















(a) (b)

(c)



(a) (b)




Competing Interests


References
















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation














Eros

ion

rate

den

sity 335E + 02

285E + 02

235E + 02

185E + 02

135E + 02

850E + 01

350E + 01

minus150E + 01


50

0E

minus0

5

50

0E

minus0

4

50

0E

minus0

3

50

0E

minus0

2

50

0E

minus0

1 5

50

BMHBMM

BML

(kg

mmiddotse

c)




50

0E

minus0

5

50

0E

minus0

4

50

0E

minus0

3

50

0E

minus0

2

50

0E

minus0

1 5

50

Out3HOut3M

Out3L

Eros

ion

rate

den

sity

(kg

mmiddotse

c)

600E + 01

500E + 01

400E + 01

300E + 01

200E + 01

100E + 01

000E + 00

minus100E + 01



4 Conclusion















(a) (b)

(c)



(a) (b)




Competing Interests


References
















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation





















(a) (b)

(c)



(a) (b)




Competing Interests


References
















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










(a) (b)




Competing Interests


References
















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









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