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On leading edge erosion at turbine blades due to heavy rain and the application oferosion safe mode control to extend life

Hasager, Charlotte Bay; Bech, Jakob Ilsted; Bak, Christian

Publication date:2019

Document VersionPublisher's PDF, also known as Version of record

Link back to DTU Orbit

Citation (APA):Hasager, C. B. (Author), Bech, J. I. (Author), & Bak, C. (Author). (2019). On leading edge erosion at turbineblades due to heavy rain and the application of erosion safe mode control to extend life. Sound/Visualproduction (digital), DTU Wind Energy.

https://orbit.dtu.dk/en/publications/9857c172-7f5b-499d-9b44-df3c4f81c96a

DTU Wind Energy1 May 2019

On leading edge erosion at turbine blades due to heavy rain and the application of erosion safe mode control to extend life

Charlotte Hasager, Jakob I. Bech, Christian Bak

DTU Wind Energy, Risø Campus, Roskilde, Denmark


Motivation

3

Unforeseen repair cost at several offshore wind farms motivated the research project


Working hypothesis

4

DTU Wind Energy1 May 2019 5


Simulated power curves for the Vestas V52 for different leading edge roughness levels

6

0

100

200

300

400

500

600

700

800

900

3 5 7 9 11 13

Elec

trica

l pow

er [k

W]

Wind speed [m/s]

Clean 20% of full LER 40% of full LER

60% of full LER 80% of full LER Full LER Bech et al. 2018, WES

LER is leading edge roughness. Roughness levels increase for eroded blade.


Rain erosion test example

7

Bech et al. 2018, WES


Rain erosion test data plotted as a Wöhler curve

8


D is drop sizevt is blade speed

Impacts per unit area to failure as function of the kinetic energy for each impact


Wöhler curves for droplet diameters of 1.5, 2.0 and 2.5 mm

9

RET is Rain Erosion Test


Chart1

8482.958466798653717705.29829112022400.6281089541889.973478598

15776.2337339841311525171.3736145729201.43609224258234.350217781

22991.9209664129156842218.1054812884456.03688359130012.12101288

29931.739630815882794888.78433411522665.3873032168631.6428695075

36293.958480914345546766.0824866837642.09645898537755.3425040132

42518.243046999825980743.423959477807.01597552321536.3669223848

15303303.4049858281440.20419990512685.4552187458

9275775.76060499170589.0653208037689.0220964936

5768605.31957721106089.346602224781.8031518786

3671621.605053467524.10946347373043.5383928878

2386572.112701643891.00346254011978.3149337626

1581280.169014929081.02923188591310.7796559659

1066233.9031465619608.9092325427883.83939553

730607.46558360313436.4658964307605.6266442527

508107.2406483549344.5056782271421.1882543912

358244.9935300286588.4169884416296.9620808331

255814.534367654704.6374814916212.0538117912

184843.0497631373399.4141195241153.2230112815

135041.0379183842483.5145903684111.9403434587

99677.99669585461833.15948210182.6266545148

74288.1916494421366.220303823361.5801375371

55868.82050545881027.473077893846.3116623836

42375.4003342113779.318099334535.1264840728

32399.5139656211595.853430148426.8571152674

24960.1636735365459.037723767220.690371886

RET results

1.5 mm

2.0 mm

2.5 mm

Impacts/area to removed coating [cm-2]

Local rotor speed [m/s]

131.2

60

60

60

122

65

65

65

118.5333333333

70

70

70

115.7333333333

75

75

75

112.2666666667

80

80

80

109.6

85

85

85

90

90

90

95

95

95

100

100

100

105

105

105

110

110

110

115

115

115

120

120

120

125

125

125

130

130

130

135

135

135

140

140

140

145

145

145

150

150

150

155

155

155

160

160

160

165

165

165

170

170

170

175

175

175

180

180

180

life model polytech data

POLYTEC results

vo [m/s]140Regn intensitet32.5mm/hdroplet volume0.0000000042

vi [m/s]110droplet speed6m/sdroplet size2mm2

r0-ri [m]0.225mass0.0000041888kg0.0000031416

omega [rad/s]13310002

rpm1273TidRegnmængdeslid [mm]hastighedcinetic energyHits/m2/sfailure atfailure atpower function failurefailure atacc impact energy3

rotor diam2.1[hrs][min][sec][J]hits/m2hits/cm2hits/m2hits/2 mm circle[J/cm2]

0.530.01800.016.3661310.0360517444471288.5E+078.5E+038.58E+072.7E+023.1E+02

1.060.03600.032.51351220.0311729767438231.6E+081.6E+04168259557.5512565.0E+024.9E+02

1.590.05400.048.81611190.0294265677425782.3E+082.3E+04219739821.3262087.2E+026.8E+02

2.0120.07200.065.01821160.0280527562415723.0E+083.0E+04274186721.400559.4E+028.4E+02

2.5150.09000.081.32081120.0263973463403273.6E+083.6E+04363370031.3363811.1E+039.6E+02

3.0180.010800.097.52281100.0251582091393694.3E+084.3E+04453968838.8522371.3E+031.1E+03

c=17.872

32.510010m=4.63

percent of timehours pr yearrain intensityrain ratefall speeddroplet sizedroplet sizerain relative volume1 droplet volumedroplets/m3densitymassblade tip speedcinetic energyhits/m2/shits/m2/hrhits/cm2/shits/cm2/hrpower function impacts to failurehours to failuremm to failurefraction of life spent pr yearfraction of life spent pr yearreduced production

[hrs/year][mm/hr]m/sm/s[mm]m[-][m3][kg/m3]kg[m/s][m-2*hr-1][cm-2s-1][cm-2hr-1][m-2][hrs][%]

0.021.752200.000005555662.50.00250.00000092590.000000008211310000.000008181270.00.020044015679222.85E+070.792237938928521.30E+094.56E+019120.0383.840.0000888889

0.18.76100.0000027778620.0020.0000004630.000000004211110000.000004188880.00.013404128788423.18E+070.884194128331838.38E+092.63E+0226320.0333.330.0001111111

187.650.000001388961.50.00150.00000023150.000000001813110000.000001767190.00.0071569408117894.24E+071.178925504442441.53E+113.61E+03180290.0242.430

3262.820.0000005556610.0010.00000009260.000000000517710000.000000523690.00.002120575159155.73E+071.591549430957304.27E+137.46E+0514914210.0000.040

543810.000000277860.50.00050.00000004630.000000000170710000.000000065490.00.0002650719636622.29E+086.3661977237229186.49E+172.83E+0928301978260.0000.000

20.002100080.00.0134041287sum fraction0.0969.637

rpmm/sD rotorlifetime years:10.37710.377

SWP 2.3-1061690.4778684234108

633.9292006588108

Jakob Ilsted Bech:antaget

Jakob Ilsted Bech:antaget

Jakob Ilsted Bech:cinetic energy with diameter

life model polytech data

kinetic energy [J]

impacts/m2

rain impact fatigue

impact fatigue V-N

d[mm]cmrho [kg/m3]d[mm]cmrho [kg/m3]d[mm]cmrho [kg/m3]

0.00151.79E+01-4.6310000.0021.79E+01-4.6310000.00251.79E+01-4.631000

1.5 mm2.0 mm2.5 mm

vNvNvN

m-2cm-2m-2cm-2m-2cm-2

606.54E+12653717705.298291601.20E+1112022400.6281089605.42E+09541889.973478598

653.12E+12311525171.373614655.73E+105729201.43609224652.58E+09258234.350217781

701.57E+12156842218.105481702.88E+102884456.03688359701.30E+09130012.12101288

758.28E+1182794888.7843341751.52E+101522665.38730321756.86E+0868631.6428695075

804.55E+1145546766.0824866808.38E+09837642.096458985803.78E+0837755.3425040132

852.60E+1125980743.423959854.78E+09477807.015975523852.15E+0821536.3669223848

901.53E+1115303303.4049858902.81E+09281440.204199905901.27E+0812685.4552187458

959.28E+109275775.76060499951.71E+09170589.065320803957.69E+077689.0220964936

1005.77E+105768605.319577211001.06E+09106089.346602221004.78E+074781.8031518786

1053.67E+103671621.60505341056.75E+0867524.10946347371053.04E+073043.5383928878

1102.39E+102386572.11270161104.39E+0843891.00346254011101.98E+071978.3149337626

1151.58E+101581280.16901491152.91E+0829081.02923188591151.31E+071310.7796559659

1201.07E+101066233.903146561201.96E+0819608.90923254271208.84E+06883.83939553

1257.31E+09730607.4655836031251.34E+0813436.46589643071256.06E+06605.6266442527

1305.08E+09508107.2406483541309.34E+079344.50567822711304.21E+06421.1882543912

1353.58E+09358244.9935300281356.59E+076588.41698844161352.97E+06296.9620808331

1402.56E+09255814.534367651404.70E+074704.63748149161402.12E+06212.0538117912

1451.85E+09184843.0497631371453.40E+073399.41411952411451.53E+06153.2230112815

1501.35E+09135041.0379183841502.48E+072483.51459036841501.12E+06111.9403434587

1559.97E+0899677.99669585461551.83E+071833.1594821011558.26E+0582.6266545148

1607.43E+0874288.1916494421601.37E+071366.22030382331606.16E+0561.5801375371

1655.59E+0855868.82050545881651.03E+071027.47307789381654.63E+0546.3116623836

1704.24E+0842375.40033421131707.79E+06779.31809933451703.51E+0535.1264840728

1753.24E+0832399.51396562111755.96E+06595.85343014841752.69E+0526.8571152674

1802.50E+0824960.16367353651804.59E+06459.03772376721802.07E+0520.690371886

N_Ei=18∗(1/12 ρπ)^(-4.63) 〖v_t〗^(-9.26) D^(-13.89)

N_Ei=c∗(1/12 〖ρπD〗^3 v_t^2 )^(-m)

impact fatigue (4)

d[mm]cmrho [kg/m3]d[mm]cmrho [kg/m3]d[mm]cmrho [kg/m3]

0.00151.79E+01-4.6310000.0021.79E+01-4.6310000.00251.79E+01-4.631000

1.5 mm2.0 mm2.5 mm

vNvNvN

m-2cm-2m-2cm-2m-2cm-2

606.54E+12653717705.298291601.20E+1112022400.6281089605.42E+09541889.973478598

653.12E+12311525171.373614655.73E+105729201.43609224652.58E+09258234.350217781

701.57E+12156842218.105481702.88E+102884456.03688359701.30E+09130012.12101288

758.28E+1182794888.7843341751.52E+101522665.38730321756.86E+0868631.6428695075

804.55E+1145546766.0824866808.38E+09837642.096458985803.78E+0837755.3425040132

852.60E+1125980743.423959854.78E+09477807.015975523852.15E+0821536.3669223848

901.53E+1115303303.4049858902.81E+09281440.204199905901.27E+0812685.4552187458

959.28E+109275775.76060499951.71E+09170589.065320803957.69E+077689.0220964936

1005.77E+105768605.319577211001.06E+09106089.346602221004.78E+074781.8031518786

1053.67E+103671621.60505341056.75E+0867524.10946347371053.04E+073043.5383928878

1102.39E+102386572.11270161104.39E+0843891.00346254011101.98E+071978.3149337626

1151.58E+101581280.16901491152.91E+0829081.02923188591151.31E+071310.7796559659

1201.07E+101066233.903146561201.96E+0819608.90923254271208.84E+06883.83939553

1257.31E+09730607.4655836031251.34E+0813436.46589643071256.06E+06605.6266442527

1305.08E+09508107.2406483541309.34E+079344.50567822711304.21E+06421.1882543912

1353.58E+09358244.9935300281356.59E+076588.41698844161352.97E+06296.9620808331

1402.56E+09255814.534367651404.70E+074704.63748149161402.12E+06212.0538117912

1451.85E+09184843.0497631371453.40E+073399.41411952411451.53E+06153.2230112815

1501.35E+09135041.0379183841502.48E+072483.51459036841501.12E+06111.9403434587

1559.97E+0899677.99669585461551.83E+071833.1594821011558.26E+0582.6266545148

1607.43E+0874288.1916494421601.37E+071366.22030382331606.16E+0561.5801375371

1655.59E+0855868.82050545881651.03E+071027.47307789381654.63E+0546.3116623836

1704.24E+0842375.40033421131707.79E+06779.31809933451703.51E+0535.1264840728

1753.24E+0832399.51396562111755.96E+06595.85343014841752.69E+0526.8571152674

1802.50E+0824960.16367353651804.59E+06459.03772376721802.07E+0520.690371886

N_Ei=18∗(1/12 ρπ)^(-4.63) 〖v_t〗^(-9.26) D^(-13.89)

N_Ei=c∗(1/12 〖ρπD〗^3 v_t^2 )^(-m)

fig 3

0.53.1976750428

13.1337340646

1.53.0711935499

23.0100201659

2.52.9501814358

32.8916457161

2.8343821727

2.7783607596

2.7235521965

2.6699279482

2.6174602045

2.5661218598

2.5158864946

2.4667283564

2.4186223417

2.3715439788

2.3254694103

2.2803753765

2.2362392

2.1930387691

2.1507525235

2.1093594389

2.0688390133

2.0291712524

1.9903366566

1.9523162079

1.9150913566

1.8786440095

1.8429565175

1.8080116642

1.773792654

1.7402831016

1.707467021

1.675328815

1.6438532653

1.6130255221

1.5828310953

1.5532558443

1.5242859697

1.4959080039

1.4681088029

1.4408755377

1.4141956865

1.3880570262

1.3624476257

1.3373558376

1.3127702911

1.2886798854

1.2650737823

1.2419413998

1.2192724054

1.1970567102

1.1752844621

1.1539460405

1.1330320499

1.1125333147

1.0924408733

1.072745973

1.0534400646

1.0345147975

1.0159620146

0.9977737475

0.979942212

0.9624598031

0.9453190911

0.9285128169

0.912033888

0.8958753741

0.8800305035

0.864492659

0.849255374

0.8343123292

0.8196573485

0.805284396

0.7911875721

0.7773611107

0.7637993755

0.7504968573

0.7374481705

0.7246480503

0.71209135

0.6997730378

0.6876881942

0.6758320095

0.6641997808

0.6527869097

0.6415888997

0.6306013539

0.6198199726

0.6092405508

0.5988589762

0.588671227

0.5786733694

0.5688615561

0.5592320238

0.5497810915

0.5405051585

0.5314007022

0.5224642769

0.5136925114

0.5050821079

Fit

Time to removed coating [hrs]


131.2

109.6

122

109.816

118.5333333333

110.032

115.7333333333

110.248

112.2666666667

110.464

109.6

110.68

110.896

111.112

111.328

111.544

111.76

111.976

112.192

112.408

112.624

112.84

113.056

113.272

113.488

113.704

113.92

114.136

114.352

114.568

114.784

115

115.216

115.432

115.648

115.864

116.08

116.296

116.512

116.728

116.944

117.16

117.376

117.592

117.808

118.024

118.24

118.456

118.672

118.888

119.104

119.32

119.536

119.752

119.968

120.184

120.4

120.616

120.832

121.048

121.264

121.48

121.696

121.912

122.128

122.344

122.56

122.776

122.992

123.208

123.424

123.64

123.856

124.072

124.288

124.504

124.72

124.936

125.152

125.368

125.584

125.8

126.016

126.232

126.448

126.664

126.88

127.096

127.312

127.528

127.744

127.96

128.176

128.392

128.608

128.824

129.04

129.256

129.472

129.688

129.904

130.12

130.336

130.552

130.768

130.984

131.2

fig 4

8482.95846679845319.8415509923

15776.233733984144422.3298518267

22991.920966412943546.3395651789

29931.739630815842691.2655401948

36293.958480914341856.5221258607

42518.243046999841041.5424632938

40245.7778065734

39468.6968708487

38709.7852065186

37968.5445983355

37244.4924883448

36537.1614216194

35846.098513798

35170.8649394869

34511.0354406237

33866.1978539499

33235.9526567722

32619.9125302371

32017.7019393754

31428.9567292081

30853.3237362397

30290.4604146922

29740.0344768675

29201.7235470486

28675.2148283813

28160.2047821987

27656.3988192795

27163.5110025519

26681.2637607734

26209.3876127455

25747.6209016332

25295.7095389845

24853.4067580594

24420.4728760957

23996.6750651574

23581.7871312228

23175.589301187

22777.8680174694

22388.4157399223

22007.0307547618

21633.5169902413

21267.6838388095

20909.3459855011

20558.3232423197

20214.4403883818

19877.5270156044

19547.4173797216

19223.9502564294

18906.9688024643

18596.3204214298

18291.8566341916

17993.4329536705

17700.9087638707

17414.1472029822

17133.0150504106

16857.3826175856

16587.1236424115

16322.115187225

16062.2375401323

15807.3741196027

15557.4113821997

15312.238733337

15071.7484409499

14835.8355519769

14604.3978115519

14377.3355848089

14154.5517812079

13935.9517812904

13721.4433657812

13510.9366469516

13304.3440021664

13101.5800095362

12902.5613856046

12707.2069249961

12515.4374419592

12327.175713739

12142.3464257146

11960.8761182432

11782.6931351499

11607.7275738105

11435.9112367685

11267.1775848397

11101.4616916491

10938.7001995557

10778.8312769166

10621.7945766462

10467.5311960271

10315.9836377317

10167.0957720132

10020.812800029

9877.0812182574

9735.8487839736

9597.064481748

9460.6784909365

9326.6421541272

9194.9079465149

9065.4294461729

8938.1613051922

8813.0592216609

8690.0799124579

8569.1810868326

Fit


Kinetic energy of impact [J]

0.0360517444

0.0251582091

0.0311729767

0.0252671444

0.0294265677

0.0253760798

0.0280527562

0.0254850151

0.0263973463

0.0255939505

0.0251582091

0.0257028858

0.0258118212

0.0259207565

0.0260296919

0.0261386273

0.0262475626

0.026356498

0.0264654333

0.0265743687

0.026683304

0.0267922394

0.0269011747

0.0270101101

0.0271190454

0.0272279808

0.0273369161

0.0274458515

0.0275547869

0.0276637222

0.0277726576

0.0278815929

0.0279905283

0.0280994636

0.028208399

0.0283173343

0.0284262697

0.028535205

0.0286441404

0.0287530757

0.0288620111

0.0289709464

0.0290798818

0.0291888172

0.0292977525

0.0294066879

0.0295156232

0.0296245586

0.0297334939

0.0298424293

0.0299513646

0.0300603

0.0301692353

0.0302781707

0.030387106

0.0304960414

0.0306049768

0.0307139121

0.0308228475

0.0309317828

0.0310407182

0.0311496535

0.0312585889

0.0313675242

0.0314764596

0.0315853949

0.0316943303

0.0318032656

0.031912201

0.0320211363

0.0321300717

0.0322390071

0.0323479424

0.0324568778

0.0325658131

0.0326747485

0.0327836838

0.0328926192

0.0330015545

0.0331104899

0.0332194252

0.0333283606

0.0334372959

0.0335462313

0.0336551667

0.033764102

0.0338730374

0.0339819727

0.0340909081

0.0341998434

0.0343087788

0.0344177141

0.0345266495

0.0346355848

0.0347445202

0.0348534555

0.0349623909

0.0350713262

0.0351802616

0.035289197

0.0353981323

0.0355070677

0.035616003

0.0357249384

0.0358338737

0.0359428091

0.0360517444

fig.5 v-N

8482.958466798653717705.29829112022400.6281089541889.973478598

15776.2337339841311525171.3736145729201.43609224258234.350217781

22991.9209664129156842218.1054812884456.03688359130012.12101288

29931.739630815882794888.78433411522665.3873032168631.6428695075

36293.958480914345546766.0824866837642.09645898537755.3425040132

42518.243046999825980743.423959477807.01597552321536.3669223848

15303303.4049858281440.20419990512685.4552187458

9275775.76060499170589.0653208037689.0220964936

5768605.31957721106089.346602224781.8031518786

3671621.605053467524.10946347373043.5383928878

2386572.112701643891.00346254011978.3149337626

1581280.169014929081.02923188591310.7796559659

1066233.9031465619608.9092325427883.83939553

730607.46558360313436.4658964307605.6266442527

508107.2406483549344.5056782271421.1882543912

358244.9935300286588.4169884416296.9620808331

255814.534367654704.6374814916212.0538117912

184843.0497631373399.4141195241153.2230112815

135041.0379183842483.5145903684111.9403434587

99677.99669585461833.15948210182.6266545148

74288.1916494421366.220303823361.5801375371

55868.82050545881027.473077893846.3116623836

42375.4003342113779.318099334535.1264840728

32399.5139656211595.853430148426.8571152674

24960.1636735365459.037723767220.690371886

RET results

1.5 mm

2.0 mm

2.5 mm



131.2

60

60

60

122

65

65

65

118.5333333333

70

70

70

115.7333333333

75

75

75

112.2666666667

80

80

80

109.6

85

85

85

90

90

90

95

95

95

100

100

100

105

105

105

110

110

110

115

115

115

120

120

120

125

125

125

130

130

130

135

135

135

140

140

140

145

145

145

150

150

150

155

155

155

160

160

160

165

165

165

170

170

170

175

175

175

180

180

180

ASTM E739 stat (time;speed)

SN PointsXYX^2Y^2X*YN6XYHATXXconfiYavgY1Y2SN-lineLower confUpper ConfSUMMARY OUTPUT

131.2000.52.118-0.3014.4860.091-0.6375616132SUMX12.4322.118-0.29662.03980.07190.50480.43300.57673.20109.63109.64109.6

122.0001.02.0860.0004.3530.0000SUMY1.0512.0860.02732.04070.07070.49610.42540.56683.13109.83109.84109.8Regression Statistics

118.5331.52.0740.1764.3010.0310.3651851843SUMXX25.7622.0740.15572.04150.06960.48730.41770.55693.07110.03110.04110.0Multiple R0.8824404681

115.7332.02.0630.3014.2580.0910.6211628918SUMYY0.5982.0630.26222.04240.06840.47860.41010.54703.01110.23110.24110.2R Square0.7787011797

112.2672.52.0500.3984.2040.1580.8158768323SUMXY2.1382.0500.39772.04320.06730.46980.40250.53712.95110.53110.53110.5Adjusted R Square0.7510388271

109.6003.02.0400.4774.1610.2280.973236971SAKX0.00390163422.0400.50482.04410.06620.46110.39490.52732.89110.72110.73110.7Standard Error4.8757093885

SAKY (SAKtotal)0.410.00021.43142.04490.06510.45250.38730.51762.83110.92110.93110.9Observations10

SAPXY-0.04002714510.00021.43142.04580.06400.44380.37970.50782.78111.12111.13111.1

XMEAN2.07194233460.00021.43142.04660.06300.43510.37210.49812.72111.32111.33111.3ANOVA

YMEAN0.1750.00021.43142.04740.06200.42650.36450.48852.67111.52111.53111.5dfSSMSFSignificance F

A1-10.2590717384-10.2591-0.09750.00021.43142.04830.06090.41790.35690.47882.62111.82111.83111.8Regression1669.2021766792669.202176679228.15021529980.0007234162

A021.4312700207474631489600000.01.361E-2200.00021.43142.04910.06000.40930.34930.46922.57112.02112.03112.0Residual8190.180336328223.772542041

R20.992(X=2.700.207.474.631.490.000.000Y^-010)0.00021.43142.05000.05900.40070.34170.45972.52112.22112.23112.2Total9859.3825130074

T-VALUE2.7760.00021.43142.05080.05800.39210.33410.45022.47112.42112.43112.4

F-VALUE6.9400.00021.43142.05160.05710.38360.32640.44072.42112.62112.63112.6CoefficientsStandard Errort StatP-valueLower 95%Upper 95%Lower 95.0%Upper 95.0%

CONFIA11.3058064549-8.9532652835-11.56487819330.00021.43142.05250.05620.37500.31880.43132.37112.82112.83112.8Intercept86.9588264452.934840697429.62982846830.000000001880.191067284193.726585605980.191067284193.7265856059

CONFIA00.033298637321.39821.4650.00021.43142.05330.05540.36650.31120.42192.33113.12113.13113.1X Variable 1-0.00039353120.0000741717-5.30567764760.0007234162-0.0005645715-0.0002224908-0.0005645715-0.0002224908

Xmin109.60.00021.43142.05410.05450.35800.30350.41252.28113.32113.33113.3

Xmax131.22.05490.05370.34950.29580.40322.24113.52113.53113.5

Variansanalysetabel2.05580.05290.34100.28810.39402.19113.72113.72113.7

SAKfS2F2.05660.05210.33260.28040.38472.15113.92113.92113.9RESIDUAL OUTPUT

Regress0.410641353110.411475.802.05740.05140.32420.27270.37562.11114.12114.12114.1

Residual0.00340.0012.05820.05070.31570.26500.36642.07114.42114.42114.4ObservationPredicted YResidualsStandard Residuals

Total0.41452.05910.05010.30730.25730.35742.03114.62114.62114.6164.96200857310.47441169590.1032033599

2.05990.04940.29890.24950.34841.99114.82114.82114.8284.73537537568.12243379941.7669515023

2.06070.04880.29060.24170.33941.95115.02115.02115.0372.3989604863-3.7728515527-0.8207448511

2.06150.04830.28220.23390.33051.92115.22115.22115.2483.96798960833.53894129330.7698600923

N =2.700E+21*S^-10.262.06230.04780.27380.22610.32161.88115.42115.42115.4580.2495136516-3.0746271321-0.6688533467

2.06310.04730.26550.21820.31281.84115.62115.62115.6678.1834750473-4.5407034997-0.987783104

2.06390.04680.25720.21040.30401.81115.92115.92115.9758.2920488965.53846357531.2048354935

NTVALUEFVALUE95%2.06480.04640.24890.20250.29531.77116.12116.12116.1876.1768596485-1.6616650429-0.3614780516

112.706199.52.06560.04610.24060.19460.28671.74116.32116.32116.3966.37832722771.08067647120.2350899941

24.303192.06640.04570.23240.18660.27811.71116.52116.52116.51071.750027599-5.7050796076-1.2410810888

33.1829.552.06720.04550.22410.17860.26961.68116.72116.72116.7111.8219740758-0.0235723844-2.1105589334

42.77646.942.06800.04520.21590.17060.26111.64116.91116.92116.9121.74184586680.00519802610.465406478

52.57065.792.06880.04500.20760.16260.25271.61117.21117.22117.2

62.44695.142.06960.04490.19940.15460.24431.58117.41117.42117.4

72.36464.742.07040.04480.19120.14650.23601.55117.61117.62117.6

82.3064.462.07120.04470.18310.13840.22781.52117.81117.82117.8

92.26224.262.07200.04470.17490.13020.21961.50118.01118.02118.0

102.22814.12.07280.04470.16680.12210.21151.47118.21118.22118.2

112.2013.982.07360.04480.15860.11390.20341.44118.51118.52118.5

122.17882.892.07430.04490.15050.10560.19541.41118.71118.72118.7

132.16043.812.07510.04500.14240.09740.18741.39118.91118.92118.9

142.14483.742.07590.04520.13430.08910.17951.36119.11119.12119.1

152.13153.682.07670.04550.12620.08080.17171.34119.31119.31119.3

162.11993.632.07750.04570.11820.07250.16391.31119.51119.51119.5

172.10983.592.07830.04600.11010.06410.15621.29119.81119.81119.8

182.10093.552.07910.04640.10210.05570.14851.27120.01120.01120.0

192.0933.522.07980.04680.09410.04730.14091.24120.21120.21120.2

202.0863.492.08060.04720.08610.03890.13331.22120.41120.41120.4

212.07963.472.08140.04770.07810.03050.12581.20120.61120.61120.6

222.07393.442.08220.04820.07010.02200.11831.18120.81120.81120.8

232.0693.422.08300.04870.06220.01350.11091.15121.01121.01121.0

242.0643.42.08370.04920.05420.00500.10351.13121.31121.31121.3

252.063.392.08450.04980.0463-0.00350.09611.11121.51121.51121.5

262.0563.372.08530.05040.0384-0.01200.08881.09121.71121.71121.7

272.0523.352.08600.05110.0305-0.02060.08161.07121.91121.91121.9

282.0483.342.08680.05170.0226-0.02910.07431.05122.11122.11122.1

292.0453.332.08760.05240.0147-0.03770.06721.03122.31122.31122.3

302.0423.322.08830.05310.0069-0.04630.06001.02122.61122.61122.6

312.0213.232.08910.0539-0.0010-0.05480.05291.00122.81122.81122.8

402.0213.232.08990.0546-0.0088-0.06340.04580.98123.01123.01123.0

4123.152.09060.0554-0.0166-0.07200.03880.96123.21123.21123.2

6023.152.09140.0562-0.0244-0.08060.03180.95123.41123.41123.4

611.983.072.09220.0570-0.0322-0.08920.02480.93123.61123.61123.6

1201.983.072.09290.0579-0.0400-0.09780.01790.91123.91123.91123.9

1211.9632.09370.0587-0.0478-0.10650.01100.90124.11124.11124.1

2.09440.0596-0.0555-0.11510.00410.88124.31124.31124.3

2.09520.0605-0.0632-0.1237-0.00280.86124.51124.51124.5

2.09590.0614-0.0710-0.1323-0.00960.85124.71124.71124.7

2.09670.0623-0.0787-0.1409-0.01640.83124.91124.91124.9

2.09740.0632-0.0864-0.1496-0.02320.82125.21125.21125.2

2.09820.0641-0.0941-0.1582-0.02990.81125.41125.41125.4

2.09890.0651-0.1017-0.1668-0.03670.79125.61125.61125.6

2.09970.0660-0.1094-0.1754-0.04340.78125.81125.81125.8

2.10040.0670-0.1170-0.1840-0.05000.76126.01126.01126.0

2.10120.0680-0.1247-0.1926-0.05670.75126.21126.21126.2

2.10190.0690-0.1323-0.2012-0.06330.74126.41126.41126.4

2.10270.0699-0.1399-0.2098-0.06990.72126.71126.71126.7

2.10340.0709-0.1475-0.2184-0.07650.71126.91126.91126.9

2.10410.0720-0.1550-0.2270-0.08310.70127.11127.11127.1

2.10490.0730-0.1626-0.2356-0.08960.69127.31127.31127.3

2.10560.0740-0.1702-0.2442-0.09620.68127.51127.51127.5

2.10630.0750-0.1777-0.2527-0.10270.66127.71127.71127.7

2.10710.0761-0.1852-0.2613-0.10920.65128.01128.01128.0

2.10780.0771-0.1927-0.2699-0.11560.64128.21128.21128.2

2.10850.0782-0.2002-0.2784-0.12210.63128.41128.41128.4

2.10930.0792-0.2077-0.2869-0.12850.62128.61128.61128.6

2.11000.0803-0.2152-0.2955-0.13490.61128.81128.81128.8

2.11070.0813-0.2227-0.3040-0.14130.60129.00129.01129.0

2.11150.0824-0.2301-0.3125-0.14770.59129.30129.31129.3

2.11220.0835-0.2376-0.3210-0.15410.58129.50129.51129.5

2.11290.0845-0.2450-0.3295-0.16050.57129.70129.71129.7

2.11360.0856-0.2524-0.3380-0.16680.56129.90129.91129.9

2.11430.0867-0.2598-0.3465-0.17310.55130.10130.11130.1

2.11510.0878-0.2672-0.3550-0.17940.54130.30130.31130.3

2.11580.0889-0.2746-0.3634-0.18570.53130.60130.61130.6

2.11650.0900-0.2819-0.3719-0.19200.52130.80130.81130.8

2.11720.0911-0.2893-0.3803-0.19820.51131.00131.01131.0

2.11790.0921-0.2966-0.3888-0.20450.51131.20131.21131.2

ASTM E739 stat (impacts;energy)


0.0368483.0-1.4433.9292.08215.433-5.6691834105SUMX-9.210-1.4433.9329-1.59930.07194.65634.58444.728245319.840.0384070.0534770.0

0.03115776.2-1.5064.1982.26917.623-6.3231238203SUMY26.153-1.5064.2253-1.59740.07064.64764.57704.718244422.330.0377580.0522640.0Regression Statistics

0.02922991.9-1.5314.3622.34519.023-6.6787074357SUMXX14.154-1.5314.3412-1.59560.06934.63904.56964.708343546.340.0371200.0510850.0Multiple R0.8824404681

0.02829931.7-1.5524.4762.40920.036-6.9470662987SUMYY114.332-1.5524.4373-1.59370.06814.63034.56224.698442691.270.0364950.0499390.0R Square0.7787011797

0.02636294.0-1.5784.5602.49120.792-7.1974236821SUMXY-40.218-1.5784.5596-1.59190.06694.62184.55494.688641856.520.0358820.0488260.0Adjusted R Square0.7510388271

0.02542518.2-1.5994.6292.55821.424-7.4025743521SAKX0.0156065368-1.5994.6563-1.59000.06574.61324.54754.678941041.540.0352800.0477430.0Standard Error4.8757093885

SAKY (SAKtotal)0.340.000-2.7478-1.58820.06454.60474.54024.669240245.780.0346900.0466920.0Observations10

SAPXY-0.07225102180.000-2.7478-1.58640.06344.59634.53294.659639468.700.0341100.0456700.0

XMEAN-1.53505671730.000-2.7478-1.58450.06234.58784.52564.650138709.790.0335400.0446760.0ANOVA

YMEAN4.3590.000-2.7478-1.58270.06124.57944.51834.640637968.540.0329810.0437100.0dfSSMSFSignificance F

A1-4.6295358692-4.6295-0.21600.000-2.7478-1.58090.06014.57114.51104.631137244.490.0324320.0427710.0Regression1669.2021766792669.202176679228.15021529980.0007234162

A0-2.7480.05.262E+120.000-2.7478-1.57910.05904.56274.50374.621836537.160.0318930.0418580.0Residual8190.180336328223.772542041

R20.990(X=00Y^-005)0.000-2.7478-1.57730.05804.55444.49644.612535846.100.0313620.0409710.0Total9859.3825130074

T-VALUE2.7760.000-2.7478-1.57550.05704.54624.48914.603235170.860.0308420.0401080.0

F-VALUE6.9400.000-2.7478-1.57380.05614.53804.48194.594134511.040.0303300.0392690.0CoefficientsStandard Errort StatP-valueLower 95%Upper 95%Lower 95.0%Upper 95.0%

CONFIA10.6529032275-3.9766326417-5.28243909670.000-2.7478-1.57200.05524.52984.47464.584933866.200.0298260.0384530.0Intercept86.9588264452.934840697429.62982846830.000000001880.191067284193.726585605980.191067284193.7265856059

CONFIA00.0332986373-2.781-2.7150.000-2.7478-1.57020.05434.52164.46734.575933235.950.0293310.0376600.0X Variable 1-0.00039353120.0000741717-5.30567764760.0007234162-0.0005645715-0.0002224908-0.0005645715-0.0002224908

Xmin0.02515820910.000-2.7478-1.56850.05344.51354.46014.566932619.910.0288440.0368890.0

Xmax0.0360517444-1.56670.05264.50544.45284.558032017.700.0283660.0361400.0

Variansanalysetabel-1.56500.05184.49734.44554.549131428.960.0278950.0354110.0

SAKfS2F-1.56330.05114.48934.43824.540430853.320.0274310.0347020.0RESIDUAL OUTPUT

Regress0.334488697110.334387.56-1.56150.05034.48134.43104.531630290.460.0269750.0340130.0

Residual0.00340.001-1.55980.04974.47334.42374.523029740.030.0265260.0333430.0ObservationPredicted YResidualsStandard Residuals

Total0.3385-1.55810.04904.46544.41644.514429201.720.0260840.0326920.0164.96200857310.47441169590.1032033599

-1.55640.04844.45754.40914.505928675.210.0256490.0320580.0284.73537537568.12243379941.7669515023

-1.55470.04794.44964.40184.497528160.200.0252210.0314420.0372.3989604863-3.7728515527-0.8207448511

-1.55300.04744.44184.39444.489227656.400.0247990.0308430.0483.96798960833.53894129330.7698600923

N =1.787E-03*S^-4.63-1.55130.04694.43404.38714.480927163.510.0243830.0302610.0580.2495136516-3.0746271321-0.6688533467

-1.54960.04654.42624.37974.472726681.260.0239740.0296940.0678.1834750473-4.5407034997-0.987783104

-1.54790.04614.41854.37244.464526209.390.0235710.0291440.0758.2920488965.53846357531.2048354935

NTVALUEFVALUE95%-1.54630.04584.41074.36504.456525747.620.0231730.0286080.0876.1768596485-1.6616650429-0.3614780516

112.706199.5-1.54460.04554.40304.35764.448525295.710.0227820.0280870.0966.37832722771.08067647120.2350899941

24.30319-1.54300.04524.39544.35024.440624853.410.0223960.0275810.01071.750027599-5.7050796076-1.2410810888

33.1829.55-1.54130.04504.38784.34274.432824420.470.0220160.0270880.0111.8219740758-0.0235723844-2.1105589334

42.77646.94-1.53970.04494.38024.33534.425023996.680.0216410.0266080.0121.74184586680.00519802610.465406478

52.57065.79-1.53800.04484.37264.32784.417323581.790.0212720.0261420.0

62.44695.14-1.53640.04474.36504.32034.409723175.590.0209090.0256880.0

72.36464.74-1.53480.04474.35754.31284.402222777.870.0205510.0252460.0

82.3064.46-1.53320.04474.35004.30534.394722388.420.0201980.0248160.0

92.26224.26-1.53160.04484.34264.29784.387322007.030.0198510.0243980.0

102.22814.1-1.52990.04494.33514.29024.380021633.520.0195080.0239900.0

112.2013.98-1.52830.04514.32774.28274.372821267.680.0191710.0235930.0

122.17882.89-1.52680.04534.32034.27514.365620909.350.0188400.0232070.0

132.16043.81-1.52520.04554.31304.26754.358520558.320.0185130.0228300.0

142.14483.74-1.52360.04584.30574.25994.351520214.440.0181910.0224630.0

152.13153.68-1.52200.04614.29844.25224.344519877.530.0178750.0221050.0

162.11993.63-1.52040.04654.29114.24464.337619547.420.0175630.0217560.0

172.10983.59-1.51890.04694.28384.23704.330719223.950.0172570.0214150.0

182.10093.55-1.51730.04734.27664.22934.323918906.970.0169560.0210830.0

192.0933.52-1.51580.04784.26944.22174.317218596.320.0166590.0207590.0

202.0863.49-1.51420.04834.26234.21404.310518291.860.0163680.0204420.0

212.07963.47-1.51270.04884.25514.20634.303917993.430.0160810.0201330.0

222.07393.44-1.51110.04944.24804.19864.297417700.910.0157990.0198310.0

232.0693.42-1.50960.04994.24094.19104.290817414.150.0155220.0195360.0

242.0643.4-1.50810.05064.23384.18334.284417133.020.0152500.0192480.0

252.063.39-1.50650.05124.22684.17564.278016857.380.0149830.0189660.0

262.0563.37-1.50500.05194.21984.16794.271616587.120.0147200.0186910.0

272.0523.35-1.50350.05254.21284.16024.265316322.120.0144620.0184210.0

282.0483.34-1.50200.05324.20584.15264.259016062.240.0142090.0181570.0

292.0453.33-1.50050.05404.19894.14494.252815807.370.0139600.0178990.0

302.0423.32-1.49900.05474.19194.13724.246615557.410.0137160.0176460.0

312.0213.23-1.49750.05554.18504.12964.240515312.240.0134760.0173990.0

402.0213.23-1.49600.05634.17824.12194.234415071.750.0132410.0171560.0

4123.15-1.49460.05714.17134.11434.228414835.840.0130090.0169190.0

6023.15-1.49310.05794.16454.10664.222414604.400.0127830.0166860.0

611.983.07-1.49160.05874.15774.09904.216414377.340.0125600.0164580.0

1201.983.07-1.49020.05954.15094.09144.210414154.550.0123410.0162340.0

1211.963-1.48870.06044.14414.08384.204513935.950.0121270.0160150.0

-1.48720.06134.13744.07614.198713721.440.0119160.0158000.0

-1.48580.06214.13074.06864.192813510.940.0117100.0155890.0

-1.48430.06304.12404.06104.187013304.340.0115070.0153820.0

-1.48290.06394.11734.05344.181213101.580.0113090.0151790.0

-1.48150.06484.11074.04594.175512902.560.0111140.0149790.0

-1.48000.06574.10414.03834.169812707.210.0109220.0147840.0

-1.47860.06674.09744.03084.164112515.440.0107350.0145910.0

-1.47720.06764.09094.02334.158412327.180.0105510.0144030.0

-1.47580.06854.08434.01584.152812142.350.0103700.0142170.0

-1.47440.06954.07784.00834.147211960.880.0101930.0140350.0

-1.47290.07044.07124.00084.141711782.690.0100190.0138570.0

-1.47150.07144.06473.99344.136111607.730.098490.0136810.0

-1.47010.07234.05833.98594.130611435.910.096820.0135080.0

-1.46880.07334.05183.97854.125111267.180.095180.0133380.0

-1.46740.07434.04543.97114.119611101.460.093570.0131720.0

-1.46600.07524.03903.96374.114210938.700.091990.0130080.0

-1.46460.07624.03263.95644.108810778.830.090440.0128460.0

-1.46320.07724.02623.94904.103410621.790.088920.0126880.0

-1.46180.07824.01983.94174.098010467.530.087430.0125320.0

-1.46050.07924.01353.93444.092710315.980.085970.0123780.0

-1.45910.08014.00723.92714.087310167.100.084540.0122280.0

-1.45780.08114.00093.91984.082010020.810.083130.0120790.0

-1.45640.08213.99463.91254.07689877.080.081750.0119330.0

-1.45500.08313.98843.90524.07159735.850.080400.0117900.0

-1.45370.08413.98213.89804.06639597.060.079070.0116480.0

-1.45240.08513.97593.89084.06109460.680.077770.0115090.0

-1.45100.08613.96973.88364.05589326.640.076490.0113720.0

-1.44970.08713.96353.87644.05079194.910.075240.0112380.0

-1.44840.08813.95743.86934.04559065.430.074000.0111050.0

-1.44700.08913.95123.86214.04048938.160.072800.0109740.0

-1.44570.09013.94513.85504.03538813.060.071610.0108460.0

-1.44440.09113.93903.84794.03028690.080.070450.0107190.0

-1.44310.09213.93293.84084.02518569.180.069310.0105950.0

fig accu. energ.

305.82545066671140.1660489024

491.79216666671122.4254241385

676.57331829631105.0353869471

839.66779417281087.9875483775

958.06419061731071.2737548677

1069.6828481054.8860806755

1038.816820583

1023.0584828653

1007.6037825111

992.4456346858

977.5771484275

962.9916205667

948.6825298608

934.643531335

920.8684508213

907.3512796881

894.0861697535

881.0674283738

868.2895137025

855.7470301108

843.4347237659

831.3474783592

819.4803109801

807.8283681286

796.386921863

785.1513660757

774.1172128948

763.2800892042

752.6357332798

742.1799915369

731.9088153841

721.8182581804

711.9044722924

702.1637062462

692.5923019723

683.1866921392

673.9433975727

664.8590247583

655.9302634229

647.1538841935

638.5267363303

630.0457455314

621.7079118063

613.5103074163

605.4500748792

597.524425036

589.7306351775

582.0660472292

574.5280659917

567.1141574349

559.821847045

552.6487182213

545.5924107218

538.6506191562

531.8210915236

525.1016277946

518.4900785361

511.9843435765

505.5823707109

499.2821544449

493.0817347748

486.9791960047

480.9726655972

475.0603130585

469.2403488555

463.5110233648

457.8706258517

452.3174834784

446.8499603418

441.4664565374

436.1654072513

430.9452818768

425.8045831573

420.741846352

415.7556384267

410.844557266

406.0072309079

401.2423168008

396.5485010793

391.9244978615

387.3690485654

382.8809212438

378.4589099379

374.1018340481

369.8085377224

365.5778892613

361.4087805387

357.3001264389

353.2508643077

349.25995342

345.3263744596

341.4491290147

337.6272390858

333.8597466066

330.1457129784

326.484218616

322.8743625054

319.3152617745

315.8060512727

312.345883164

308.9339265284

Fit

accumulated imapct energy [J/cm-2]

kinetic energy of impact [J]

0.0360517444

0.0251582091

0.0311729767

0.0252671444

0.0294265677

0.0253760798

0.0280527562

0.0254850151

0.0263973463

0.0255939505

0.0251582091

0.0257028858

0.0258118212

0.0259207565

0.0260296919

0.0261386273

0.0262475626

0.026356498

0.0264654333

0.0265743687

0.026683304

0.0267922394

0.0269011747

0.0270101101

0.0271190454

0.0272279808

0.0273369161

0.0274458515

0.0275547869

0.0276637222

0.0277726576

0.0278815929

0.0279905283

0.0280994636

0.028208399

0.0283173343

0.0284262697

0.028535205

0.0286441404

0.0287530757

0.0288620111

0.0289709464

0.0290798818

0.0291888172

0.0292977525

0.0294066879

0.0295156232

0.0296245586

0.0297334939

0.0298424293

0.0299513646

0.0300603

0.0301692353

0.0302781707

0.030387106

0.0304960414

0.0306049768

0.0307139121

0.0308228475

0.0309317828

0.0310407182

0.0311496535

0.0312585889

0.0313675242

0.0314764596

0.0315853949

0.0316943303

0.0318032656

0.031912201

0.0320211363

0.0321300717

0.0322390071

0.0323479424

0.0324568778

0.0325658131

0.0326747485

0.0327836838

0.0328926192

0.0330015545

0.0331104899

0.0332194252

0.0333283606

0.0334372959

0.0335462313

0.0336551667

0.033764102

0.0338730374

0.0339819727

0.0340909081

0.0341998434

0.0343087788

0.0344177141

0.0345266495

0.0346355848

0.0347445202

0.0348534555

0.0349623909

0.0350713262

0.0351802616

0.035289197

0.0353981323

0.0355070677

0.035616003

0.0357249384

0.0358338737

0.0359428091

0.0360517444

fig

8482.95846679845319.8415510438

15776.233733984144501.1526968153

22991.920966412943698.8185343382

29931.739630815842912.4812025937

36293.958480914342141.791349927

42518.243046999841386.4079156283

40645.9979175265

39920.2362454331

39208.8054602438

38511.3955985505

37827.7039825948

37157.4350354031

36500.30010096

35856.0172692686

35224.3112061582

34604.9129876992

33997.5599390947

33401.9954779185

32817.9689615728

32245.2355388469

31683.5560054579

31132.6966634576

30592.4291843988

30062.5304761508

29542.7825532595

29032.9724107552

28532.891901306

28042.3376156244

27561.1107660335

27089.0170731068

26625.8666552894

26171.4739214239

25725.6574660917

25288.2399676985

24859.0480892212

24437.9123815443

24024.6671893146

23619.150559242

23221.2041507809

22830.673149124

22447.4061804437

22071.2552293262

21702.0755583252

21339.7256295896

20984.0670285

20634.9643892635

20292.2853224091

19955.9003441363

19625.6828074617

19301.5088351196

18983.2572541652

18670.8095322343

18364.0497154179

18062.8643677042

17767.1425119486

17476.7755723285

17191.6573182442

16911.683809627

16636.7533436157

16366.766402567

16101.6256033615

15841.2356479738

15585.5032752697

15334.3372140009

15087.6481369642

14845.3486162936

14607.3530798571

14373.5777687276

14143.9406957002

13918.3616048281

13696.7619319522

13479.0647661941

13265.1948123926

13055.0783544548

12848.6432196003

12645.8187434752

12446.535736111

12250.7264487102

12058.3245412343

11869.2650507738

11683.4843606817

11500.9201704496

11321.5114663065

11145.1984925241

10971.922723408

10801.626835959

10634.2546831866

10469.751268058

10308.0627180672

10149.1362604075

9992.9201977326

9839.3638844908

9688.4177038201

9540.0330449854

9394.1622813496

9250.7587488613

9109.7767250473

8971.1714084978

8834.8988988316

8700.9161771285

8569.1810868186

Fit

impacts to erosion [cm-2]

local rotor speed [m/s]

131.2

109.6

122

109.816

118.5333333333

110.032

115.7333333333

110.248

112.2666666667

110.464

109.6

110.68

110.896

111.112

111.328

111.544

111.76

111.976

112.192

112.408

112.624

112.84

113.056

113.272

113.488

113.704

113.92

114.136

114.352

114.568

114.784

115

115.216

115.432

115.648

115.864

116.08

116.296

116.512

116.728

116.944

117.16

117.376

117.592

117.808

118.024

118.24

118.456

118.672

118.888

119.104

119.32

119.536

119.752

119.968

120.184

120.4

120.616

120.832

121.048

121.264

121.48

121.696

121.912

122.128

122.344

122.56

122.776

122.992

123.208

123.424

123.64

123.856

124.072

124.288

124.504

124.72

124.936

125.152

125.368

125.584

125.8

126.016

126.232

126.448

126.664

126.88

127.096

127.312

127.528

127.744

127.96

128.176

128.392

128.608

128.824

129.04

129.256

129.472

129.688

129.904

130.12

130.336

130.552

130.768

130.984

131.2

ASTM E739 stat (impacts;acc en)


0.036305.8-1.4432.4852.0826.178-3.5867216599SUMX-9.210-1.4432.4899-1.59930.07193.05702.98513.12881140.170.09660.013450.0

0.031491.8-1.5062.6922.2697.246-4.0544199354SUMY16.942-1.5062.7191-1.59740.07063.05022.97963.12081122.430.09540.013210.0Regression Statistics

0.029676.6-1.5312.8302.3458.011-4.33394905SUMXX14.154-1.5312.8099-1.59560.06933.04342.97403.11271105.040.09420.012960.0Multiple R0.8824404681

0.028839.7-1.5522.9242.4098.550-4.5382863655SUMYY48.049-1.5522.8853-1.59370.06813.03662.96853.10471087.990.09300.012730.0R Square0.7787011797

0.026958.1-1.5782.9812.4918.889-4.7059517004SUMXY-26.064-1.5782.9812-1.59190.06693.02992.96303.09681071.270.09180.012500.0Adjusted R Square0.7510388271

0.0251069.7-1.5993.0292.5589.176-4.8447490003SAKX0.0156065368-1.5993.0570-1.59000.06573.02322.95753.08891054.890.09070.012270.0Standard Error4.8757093885

SAKY (SAKtotal)0.210.000-2.7478-1.58820.06453.01652.95203.08111038.820.08950.012050.0Observations10

SAPXY-0.0566444850.000-2.7478-1.58640.06343.00992.94653.07331023.060.08840.011840.0

XMEAN-1.53505671730.000-2.7478-1.58450.06233.00332.94103.06551007.600.08730.011630.0ANOVA

YMEAN2.8240.000-2.7478-1.58270.06122.99672.93563.0579992.450.08620.011430.0dfSSMSFSignificance F

A1-3.6295358692-3.6295-0.27550.000-2.7478-1.58090.06012.99022.93013.0502977.580.08510.011230.0Regression1669.2021766792669.202176679228.15021529980.0007234162

A0-2.7480.09.404E+090.000-2.7478-1.57910.05902.98362.92463.0427962.990.08410.011030.0Residual8190.180336328223.772542041

R20.983(X=00Y^-004)0.000-2.7478-1.57730.05802.97712.91913.0352948.680.08300.010840.0Total9859.3825130074

T-VALUE2.7760.000-2.7478-1.57550.05702.97062.91363.0277934.640.08200.010660.0

F-VALUE6.9400.000-2.7478-1.57380.05612.96422.90813.0203920.870.08090.010480.0CoefficientsStandard Errort StatP-valueLower 95%Upper 95%Lower 95.0%Upper 95.0%

CONFIA10.6529032275-2.9766326417-4.28243909670.000-2.7478-1.57200.05522.95782.90263.0129907.350.07990.010300.0Intercept86.9588264452.934840697429.62982846830.000000001880.191067284193.726585605980.191067284193.7265856059

CONFIA00.0332986373-2.781-2.7150.000-2.7478-1.57020.05432.95142.89713.0057894.090.07890.010130.0X Variable 1-0.00039353120.0000741717-5.30567764760.0007234162-0.0005645715-0.0002224908-0.0005645715-0.0002224908

Xmin0.02515820910.000-2.7478-1.56850.05342.94502.89162.9984881.070.07790.09960.0

Xmax0.0360517444-1.56670.05262.93872.88612.9913868.290.07690.09800.0

Variansanalysetabel-1.56500.05182.93232.88052.9842855.750.07600.09640.0

SAKfS2F-1.56330.05112.92612.87502.9771843.430.07500.09490.0RESIDUAL OUTPUT

Regress0.205593190210.206238.21-1.56150.05032.91982.86942.9701831.350.07400.09340.0

Residual0.00340.001-1.55980.04972.91352.86392.9632819.480.07310.09190.0ObservationPredicted YResidualsStandard Residuals

Total0.2095-1.55810.04902.90732.85832.9563807.830.07220.09040.0164.96200857310.47441169590.1032033599

-1.55640.04842.90112.85272.9496796.390.07120.08900.0284.73537537568.12243379941.7669515023

-1.55470.04792.89502.84712.9428785.150.07030.08770.0372.3989604863-3.7728515527-0.8207448511

-1.55300.04742.88882.84142.9362774.120.06940.08630.0483.96798960833.53894129330.7698600923

N =1.787E-03*S^-3.63-1.55130.04692.88272.83582.9296763.280.06850.08500.0580.2495136516-3.0746271321-0.6688533467

-1.54960.04652.87662.83012.9231752.640.06760.08380.0678.1834750473-4.5407034997-0.987783104

-1.54790.04612.87052.82442.9166742.180.06670.08250.0758.2920488965.53846357531.2048354935

NTVALUEFVALUE95%-1.54630.04582.86452.81872.9102731.910.06590.08130.0876.1768596485-1.6616650429-0.3614780516

112.706199.5-1.54460.04552.85842.81302.9039721.820.06500.08010.0966.37832722771.08067647120.2350899941

24.30319-1.54300.04522.85242.80722.8976711.900.06420.07900.01071.750027599-5.7050796076-1.2410810888

33.1829.55-1.54130.04502.84642.80142.8915702.160.06330.07790.0111.8219740758-0.0235723844-2.1105589334

42.77646.94-1.53970.04492.84052.79562.8853692.590.06250.07680.0121.74184586680.00519802610.465406478

52.57065.79-1.53800.04482.83452.78982.8793683.190.06160.07570.0

62.44695.14-1.53640.04472.82862.78392.8733673.940.06080.07470.0

72.36464.74-1.53480.04472.82272.77802.8674664.860.06000.07370.0

82.3064.46-1.53320.04472.81692.77212.8616655.930.05920.07270.0

92.26224.26-1.53160.04482.81102.76622.8558647.150.05840.07170.0

102.22814.1-1.52990.04492.80522.76032.8501638.530.05760.07080.0

112.2013.98-1.52830.04512.79942.75432.8444630.050.05680.06990.0

122.17882.89-1.52680.04532.79362.74832.8389621.710.05600.06900.0

132.16043.81-1.52520.04552.78782.74232.8333613.510.05520.06810.0

142.14483.74-1.52360.04582.78212.73632.8279605.450.05450.06730.0

152.13153.68-1.52200.04612.77642.73022.8225597.520.05370.06640.0

162.11993.63-1.52040.04652.77072.72422.8171589.730.05300.06560.0

172.10983.59-1.51890.04692.76502.71812.8119582.070.05230.06480.0

182.10093.55-1.51730.04732.75932.71202.8066574.530.05150.06410.0

192.0933.52-1.51580.04782.75372.70592.8014567.110.05080.06330.0

202.0863.49-1.51420.04832.74802.69982.7963559.820.05010.06260.0

212.07963.47-1.51270.04882.74242.69362.7912552.650.04940.06180.0

222.07393.44-1.51110.04942.73692.68752.7862545.590.04870.06110.0

232.0693.42-1.50960.04992.73132.68142.7812538.650.04800.06040.0

242.0643.4-1.50810.05062.72582.67522.7763531.820.04730.05970.0

252.063.39-1.50650.05122.72022.66912.7714525.100.04670.05910.0

262.0563.37-1.50500.05192.71472.66292.7666518.490.04600.05840.0

272.0523.35-1.50350.05252.70932.65672.7618511.980.04540.05780.0

282.0483.34-1.50200.05322.70382.65062.7570505.580.04470.05720.0

292.0453.33-1.50050.05402.69832.64442.7523499.280.04410.05650.0

302.0423.32-1.49900.05472.69292.63822.7476493.080.04350.05590.0

312.0213.23-1.49750.05552.68752.63202.7430486.980.04290.05530.0

402.0213.23-1.49600.05632.68212.62592.7384480.970.04230.05470.0

4123.15-1.49460.05712.67672.61972.7338475.060.04170.05420.0

6023.15-1.49310.05792.67142.61352.7293469.240.04110.05360.0

611.983.07-1.49160.05872.66612.60742.7248463.510.04050.05310.0

1201.983.07-1.49020.05952.66072.60122.7203457.870.03990.05250.0

1211.963-1.48870.06042.65542.59512.7158452.320.03940.05200.0

-1.48720.06132.65022.58892.7114446.850.03880.05150.0

-1.48580.06212.64492.58282.7070441.470.03830.05090.0

-1.48430.06302.63972.57662.7027436.170.03770.05040.0

-1.48290.06392.63442.57052.6983430.950.03720.04990.0

-1.48150.06482.62922.56442.6940425.800.03670.04940.0

-1.48000.06572.62402.55832.6897420.740.03620.04890.0

-1.47860.06672.61882.55222.6855415.760.03570.04850.0

-1.47720.06762.61372.54612.6813410.840.03520.04800.0

-1.47580.06852.60852.54002.6771406.010.03470.04750.0

-1.47440.06952.60342.53392.6729401.240.03420.04710.0

-1.47290.07042.59832.52792.6687396.550.03370.04660.0

-1.47150.07142.59322.52182.6646391.920.03330.04620.0

-1.47010.07232.58812.51582.6604387.370.03280.04580.0

-1.46880.07332.58312.50982.6564382.880.03230.04530.0

-1.46740.07432.57802.50382.6523378.460.03190.04490.0

-1.46600.07522.57302.49782.6482374.100.03150.04450.0

-1.46460.07622.56802.49182.6442369.810.03100.04410.0

-1.46320.07722.56302.48582.6402365.580.03060.04370.0

-1.46180.07822.55802.47982.6362361.410.03020.04330.0

-1.46050.07922.55302.47392.6322357.300.02980.04290.0

-1.45910.08012.54812.46792.6282353.250.02940.04250.0

-1.45780.08112.54312.46202.6243349.260.02900.04210.0

-1.45640.08212.53822.45612.6204345.330.02860.04170.0

-1.45500.08312.53332.45022.6165341.450.02820.04130.0

-1.45370.08412.52842.44432.6126337.630.02780.04100.0

-1.45240.08512.52362.43842.6087333.860.02740.04060.0

-1.45100.08612.51872.43262.6048330.150.02710.04030.0

-1.44970.08712.51392.42672.6010326.480.02670.03990.0

-1.44840.08812.50902.42092.5972322.870.02640.03960.0

-1.44700.08912.50422.41512.5934319.320.02600.03920.0

-1.44570.09012.49942.40932.5896315.810.02570.03890.0

-1.44440.09112.49462.40352.5858312.350.02530.03850.0

-1.44310.09212.48992.39772.5820308.930.02500.03820.0

ASTM E739 stat (impacts;speed)


131.2008483.02.1183.9294.48615.4338.3204033354SUMX12.4322.1183.93292.03980.07194.65634.58444.728245319.84109.638407109.653477109.6

122.00015776.22.0864.1984.35317.6238.7585455209SUMY26.1532.0864.22532.04070.07074.64844.57774.719144501.15109.837815109.852370109.8Regression Statistics

118.53322991.92.0744.3624.30119.0239.0452114031SUMXX25.7622.0744.34122.04150.06964.64054.57094.710043698.82110.037232110.051289110.0Multiple R0.8824404681

115.73329931.72.0634.4764.25820.0369.2363123663SUMYY114.3322.0634.43732.04240.06844.63264.56424.701042912.48110.236657110.250235110.2R Square0.7787011797

112.26736294.02.0504.5604.20420.7929.3488041277SUMXY54.1512.0504.55962.04320.06734.62474.55744.692042141.79110.536092110.549205110.5Adjusted R Square0.7510388271

109.60042518.22.0404.6294.16121.4249.4414167683SAKX0.00390163422.0404.65632.04410.06624.61694.55074.683141386.41110.735535110.748201110.7Standard Error4.8757093885

SAKY (SAKtotal)0.340.00023.54302.04490.06514.60904.54394.674140646.00110.934987110.947220110.9Observations10

SAPXY-0.03612551090.00023.54302.04580.06404.60124.53724.665239920.24111.134447111.146263111.1

XMEAN2.07194233460.00023.54302.04660.06304.59344.53044.656439208.81111.333915111.345329111.3ANOVA

YMEAN4.3590.00023.54302.04740.06204.58564.52364.647538511.40111.533391111.544417111.5dfSSMSFSignificance F

A1-9.2590717384-9.2591-0.10800.00023.54302.04830.06094.57784.51694.638837827.70111.832875111.843527111.8Regression1669.2021766792669.202176679228.15021529980.0007234162

A023.543349172985649783340000000.01.031E-2180.00023.54302.04910.06004.57004.51014.630037157.44112.032366112.042658112.0Residual8190.180336328223.772542041

R20.990(X=349.172.985.649.783.000.000.000Y^-009)0.00023.54302.05000.05904.56234.50334.621336500.30112.231864112.241811112.2Total9859.3825130074

T-VALUE2.7760.00023.54302.05080.05804.55464.49654.612635856.02112.431370112.440983112.4

F-VALUE6.9400.00023.54302.05160.05714.54684.48974.604035224.31112.630883112.640176112.6CoefficientsStandard Errort StatP-valueLower 95%Upper 95%Lower 95.0%Upper 95.0%

CONFIA11.305806455-7.9532652834-10.56487819340.00023.54302.05250.05624.53914.48294.595434604.91112.830403112.839388112.8Intercept86.9588264452.934840697429.62982846830.000000001880.191067284193.726585605980.191067284193.7265856059

CONFIA00.033298637323.51023.5760.00023.54302.05330.05544.53144.47614.586833997.56113.129929113.138619113.1X Variable 1-0.00039353120.0000741717-5.30567764760.0007234162-0.0005645715-0.0002224908-0.0005645715-0.0002224908

Xmin109.60.00023.54302.05410.05454.52384.46934.578333402.00113.329462113.337869113.3

Xmax131.22.05490.05374.51614.46244.569832817.97113.529001113.537137113.5

Variansanalysetabel2.05580.05294.50854.45564.561432245.24113.728547113.736423113.7

SAKfS2F2.05660.05214.50084.44874.553031683.56113.928099113.935726113.9RESIDUAL OUTPUT

Regress0.334488697110.334387.562.05740.05144.49324.44184.544631132.70114.127657114.135046114.1

Residual0.00340.0012.05820.05074.48564.43494.536330592.43114.427220114.434382114.4ObservationPredicted YResidualsStandard Residuals

Total0.33852.05910.05014.47804.42804.528130062.53114.626790114.633735114.6164.96200857310.47441169590.1032033599

2.05990.04944.47054.42104.519929542.78114.826365114.833104114.8284.73537537568.12243379941.7669515023

2.06070.04884.46294.41414.511729032.97115.025945115.032488115.0372.3989604863-3.7728515527-0.8207448511

2.06150.04834.45534.40714.503628532.89115.225531115.231888115.2483.96798960833.53894129330.7698600923

N =3.492E+23*S^-9.262.06230.04784.44784.40014.495628042.34115.425122115.431302115.4580.2495136516-3.0746271321-0.6688533467

2.06310.04734.44034.39304.487627561.11115.624719115.630730115.6678.1834750473-4.5407034997-0.987783104

2.06390.04684.43284.38604.479627089.02115.924320115.930173115.9758.2920488965.53846357531.2048354935

NTVALUEFVALUE95%2.06480.04644.42534.37894.471726625.87116.123927116.129630116.1876.1768596485-1.6616650429-0.3614780516

112.706199.52.06560.04614.41784.37184.463926171.47116.323538116.329100116.3966.37832722771.08067647120.2350899941

24.303192.06640.04574.41044.36464.456125725.66116.523154116.528583116.51071.750027599-5.7050796076-1.2410810888

33.1829.552.06720.04554.40294.35754.448425288.24116.722775116.728079116.7111.8219740758-0.0235723844-2.1105589334

42.77646.942.06800.04524.39554.35034.440724859.05116.922401116.927587116.9121.74184586680.00519802610.465406478

52.57065.792.06880.04504.38814.34304.433124437.91117.222031117.227107117.2

62.44695.142.06960.04494.38074.33584.425524024.67117.421666117.426640117.4

72.36464.742.07040.04484.37334.32854.418023619.15117.621306117.626184117.6

82.3064.462.07120.04474.36594.32124.410623221.20117.820950117.825739117.8

92.26224.262.07200.04474.35854.31384.403222830.67118.020599118.025305118.0

102.22814.12.07280.04474.35124.30654.395922447.41118.220252118.224881118.2

112.2013.982.07360.04484.34384.29914.388622071.26118.519909118.524468118.5

122.17882.892.07430.04494.33654.29164.381421702.08118.719571118.724065118.7

132.16043.812.07510.04504.32924.28424.374221339.73118.919238118.923671118.9

142.14483.742.07590.04524.32194.27674.367120984.07119.118909119.123287119.1

152.13153.682.07670.04554.31464.26914.360120634.96119.318584119.322912119.3

162.11993.632.07750.04574.30734.26164.353120292.29119.518264119.522546119.5

172.10983.592.07830.04604.30014.25404.346119955.90119.817949119.822188119.8

182.10093.552.07910.04644.29284.24644.339219625.68120.017637120.021838120.0

192.0933.522.07980.04684.28564.23884.332419301.51120.217331120.221497120.2

202.0863.492.08060.04724.27844.23124.325618983.26120.417028120.421163120.4

212.07963.472.08140.04774.27124.22354.318818670.81120.616730120.620836120.6

222.07393.442.08220.04824.26404.21584.312118364.05120.816437120.820517120.8

232.0693.422.08300.04874.25684.20814.305518062.86121.016148121.020205121.0

242.0643.42.08370.04924.24964.20044.298817767.14121.315863121.319900121.3

252.063.392.08450.04984.24254.19274.292317476.78121.515583121.519601121.5

262.0563.372.08530.05044.23534.18494.285717191.66121.715307121.719308121.7

272.0523.352.08600.05114.22824.17714.279216911.68121.915036121.919022121.9

282.0483.342.08680.05174.22114.16934.272816636.75122.114769122.118741122.1

292.0453.332.08760.05244.21404.16154.266416366.77122.314506122.318466122.3

302.0423.322.08830.05314.20694.15374.260016101.63122.614247122.618197122.6

312.0213.232.08910.05394.19984.14594.253715841.24122.813993122.817933122.8

402.0213.232.08990.05464.19274.13814.247315585.50123.013743123.017675123.0

4123.152.09060.05544.18574.13034.241115334.34123.213498123.217421123.2

6023.152.09140.05624.17864.12244.234815087.65123.413256123.417172123.4

611.983.072.09220.05704.17164.11464.228614845.35123.613019123.616928123.6

1201.983.072.09290.05794.16464.10674.222414607.35123.912785123.916689123.9

1211.9632.09370.05874.15764.09894.216314373.58124.112556124.116454124.1

2.09440.05964.15064.09104.210114143.94124.312331124.316223124.3

2.09520.06054.14364.08314.204013918.36124.512110124.515997124.5

2.09590.06144.13664.07534.198013696.76124.711892124.715775124.7

2.09670.06234.12974.06744.191913479.06124.911679124.915557124.9

2.09740.06324.12274.05954.185913265.19125.211469125.215343125.2

2.09820.06414.11584.05174.179913055.08125.411263125.415132125.4

2.09890.06514.10894.04384.173912848.64125.611061125.614925125.6

2.09970.06604.10194.03594.168012645.82125.810862125.814722125.8

2.10040.06704.09504.02814.162012446.54126.010667126.014522126.0

2.10120.06804.08824.02024.156112250.73126.210476126.214326126.2

2.10190.06904.08134.01234.150212058.32126.410288126.414133126.4

2.10270.06994.07444.00454.144411869.27126.710104126.713943126.7

2.10340.07094.06763.99664.138511683.48126.99923126.913757126.9

2.10410.07204.06073.98884.132711500.92127.19745127.113573127.1

2.10490.07304.05393.98094.126911321.51127.39570127.313393127.3

2.10560.07404.04713.97314.121111145.20127.59399127.513216127.5

2.10630.07504.04033.96534.115310971.92127.79231127.713041127.7

2.10710.07614.03353.95744.109610801.63128.09066128.012869128.0

2.10780.07714.02673.94964.103810634.25128.28904128.212700128.2

2.10850.07824.01993.94184.098110469.75128.48745128.412534128.4

2.10930.07924.01323.93404.092410308.06128.68589128.612370128.6

2.11000.08034.00643.92624.086710149.14128.88436128.812209128.8

2.11070.08133.99973.91844.08109992.92129.08286129.012051129.0

2.11150.08243.99303.91064.07549839.36129.38139129.311895129.3

2.11220.08353.98633.90284.06979688.42129.57994129.511741129.5

2.11290.08453.97953.89504.06419540.03129.77853129.711590129.7

2.11360.08563.97293.88724.05859394.16129.97713129.911441129.9

2.11430.08673.96623.87954.05299250.76130.17577130.111295130.1

2.11510.08783.95953.87174.04739109.78130.37443130.311150130.3

2.11580.08893.95283.86404.04178971.17130.67311130.611008130.6

2.11650.09003.94623.85624.03628834.90130.87182130.810868130.8

2.11720.09113.93963.84854.03068700.92131.07055131.010730131.0

2.11790.09213.93293.84084.02518569.18131.26931131.210595131.2


Extending lifetime

10


Assumptions:

11


Weibull A• 7 m/s• 8 m/s• 9 m/s

Wind turbine Rain climate Wind climate

Vestas V52 850 kW pitch regulated variable speed and modified rotation speed to make it consistent with larger turbines.

The temperate maritime climateof occurences of rain intensity is taken from Jones and Sims, 1978.


Control strategies

12

Apart from a reference case where it is assumed that there is no erosion, six different control strate

on the model for expected lifetime for the blade leading edge:

• Control strategy 1 with expected life time of 1.6 years • Control strategy 2 with expected life time of 10.4 years • Control strategy 3 with expected life time of 24.4 years • Control strategy 4 with expected life time of 53.9 years • Control strategy 5 with expected life time of 106.5 years • Control strategy 6 with expected life time of infinite many years

No reduction (90 m/s)

Reduction ”light” 80 m/s and 70 m/s

Reduction ”severe” 55m/s, 65m/s and 70m/s

Idealized



Life time of the blade leading edge with no reduction of the tip speed. Control strategy 1

Rain intensity

Droplet size

Percent of time

Hours pr year

Blade tip speed

Hours to failure

Fraction of life spent pr year

[mm/hr] [mm] [%] [hrs/year] [m/s] [hrs] [%]

20 2.5 0.02 1.8 90 3.5 51 10 2.0 0.1 8.8 90 79 11 5 1.5 1 88 90 3606 2.4 2 1.0 3 263 90 745710 0.0 1 0.5 5 438 90 2830197826 0.0

Sum of fractions [%]: 64

Expected life [years]: 1.6



Life time of the blade leading edge with reduction of the tip speed to 70m/s and 80m/s.Control strategy 2

Rain intensity

Droplet size

Percent of time

Hours pr year

Blade tip speed

Hours to failure



20 2.5 0.02 1.8 70 46 3.8 10 2.0 0.1 8.8 80 263 3.3 5 1.5 1 88 90 3606 2.4 2 1.0 3 263 90 745710 0.0 1 0.5 5 438 90 2830197826 0.0

Sum of fractions [%]: 9.6

Expected life [years]: 10.4



Life time of the blade leading edge with reduction of the tip speed to 55m/s, 65m/s and 70m/s.Control strategy 5

Rain intensity

Droplet size

Percent of time

Hours pr year

Blade tip speed

Hours to failure



20 2.5 0.02 1.8 55 541 0.3 10 2.0 0.1 8.8 65 2215 0.4 5 1.5 1 88 70 47514 0.2 2 1.0 3 263 90 745710 0.0 1 0.5 5 438 90 2830197826 0.0

Sum of fractions [%]: 0.9

Expected life [years]: 107



AEP relative to AEP with no erosion

16

Weibull A parameter



• Energy price: o 50 €/MWh o 250 €/MWh

• Inspection cost: o 500 €/rotor o 1500 €/rotor

• Repair cost o 10000 €/rotor o 20000 €/rotor

Stand still of 1 day inspected

Stand still of 2 days repaired

Cost of operation and maintenance



Loss of income due to erosion, inspection and repair

18

Weibull A parameter



In what geography is leading edge erosion a challenge?

19


Rainfall erosivity (for soils)

20

Rainfall erosivity for soils is modelled as a function of the kinetic energy of rain, the maximum intensity of rainfall, the cumulative rainfall, the soil properties and the slopes of terrain. The map on rainfall erosivity in Europe at 500 m spatial resolution assessed by European Soil Data Centre (Panagos et al., 2015).

A map for wind turbine blades is in preparation in the EROSION research project.

Rainfall erosivity (for wind turbine blades?)


Conclusions

21

A framework for prediction and a mitigation strategy for leading edge erosion was presented.

The model takes into account the entire value chain: leading edge test data, actual on site precipitation, erosion rate, loss of production due to erosion, operation and maintenance.

The lost energy production due to occasional tip speed reduction is marginal in proportion to the alternative of lost production due to eroded blades.

Thus, the cost – benefit balance of erosion control looks very promising and shows a great potential for reducing the loss of produced energy due to erosion and the cost of operation and maintenance.

To accomplish erosion control there is a need for more knowledge on the correlation between precipitation and erosion for different leading edge structures and materials, and for development of methods and equipment for on-site now casting of precipitation.


Reading:

22


Acknowledgements

23

Support from Innovation Fund Denmark is acknowledged

www.rain-erosion.dk

Slide Number 1Slide Number 2MotivationWorking hypothesisSlide Number 5Simulated power curves for the Vestas V52 for different leading edge roughness levelsRain erosion test exampleRain erosion test data plotted as a Wöhler curve��Wöhler curves for droplet diameters of 1.5, 2.0 and 2.5 mm�Extending lifetimeAssumptions:Control strategiesSlide Number 13Slide Number 14Slide Number 15AEP relative to AEP with no erosionCost of operation and maintenanceLoss of income due to erosion, inspection and repairIn what geography is leading edge erosion a challenge?Rainfall erosivity (for soils)ConclusionsReading:Acknowledgements

on leading edge erosion at turbine blades due to heavy ...dtu wind energy. control strategies. 12....

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