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Page 1: Aerospace Computing Lab - Homeaero-comlab.stanford.edu/jxyao/aiaa00_reno.pdf · 2019. 6. 23. · -4/ '(k e ( * ) '(k < ! " $# &% ')(¯

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Page 2: Aerospace Computing Lab - Homeaero-comlab.stanford.edu/jxyao/aiaa00_reno.pdf · 2019. 6. 23. · -4/ '(k e ( * ) '(k < ! " $# &% ')(¯

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Hobson-II Cascade, pressure contour

axial distance

Isen

trop

icM

ach

num

ber

-0.0005 0 0.0005 0.001 0.00150.4

0.5

0.6

0.7

0.8

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Laminar Flow Over a Flat Plate Boundary Layerprogram tflo 5 stage schemeRe = 34489 Mach = 0.30 Grid: 129x9x65Calculated Drag Cf: 0.007210Drag Due to Blasius: 0.007151

(a) Skin Friction Along the Plate

1 2 3 4 5log(Rex)

-3-2

.5-2

-1.5

-1lo

g(1/

2*C

f)

Blasius

Cf

(b) Boundary Layer Thickness Growth Along the Plate

1 2 3 4 5log(Rex)

11.

52

2.5

3lo

g(R

eδ)

δ1 Blasius

δ2 Blasius

δ1 calculated

δ2 calculated

(c) Velocity Distribution in Boundary Layer

0 1 2 3 4 5η = y√Re/√x

00.

20.

40.

60.

81

U/U

Blasius

10%

20%

30%

40%

50%

60%

70%

81%

90%

(d) Vertical Velocity Distribution in Boundary Layer

0 1 2 3 4 5η = y√Re/√x

00.

20.

40.

60.

81

V/U

∞√R

ex

Blasius

10%

20%

30%

40%

50%

60%

70%

81%

90%

(e) Viscous Stress Profile in the Boundary Layer

0 1 2 3 4 5η = y√Re/√x

00.

10.

20.

30.

41/

2*C

f√R

ex

Blasius

10%

20%

30%

39%

49%

59%

69%

79%

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−0.05 0� 0.05� 0.1 0.15� 0.2 0.25 Axial Distance (m)¡

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Computed Total Pressure from Inlet to Exit, Aachen 1.5 Turbine

TFLOAPNASA−V5

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Total Pressure (bar) at Inlet

Fra

ctio

nof

Spa

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1.45 1.46 1.47 1.48 1.49 1.5 1.51 1.52 1.53 1.54 1.55 1.560

0.1

0.2

0.3

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0.6

0.7

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TFLO3DFLOWAPNASA-V5

Total Temperature (K) at Inlet

Fra

ctio

nof

Spa

n

305 305.5 306 306.5 307 307.5 308 308.5 309

0.1

0.2

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Total Pressure (bar), 8.8mm after the trailing edge of vane-1

Fra

ctio

nof

Spa

n

1.44 1.46 1.48 1.5 1.52 1.540

0.1

0.2

0.3

0.4

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0.6

0.7

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TFLODataAPNASA-V53DFLOW

Total Temperature (K), 8.8mm after the trailing edge of vane-1

Fra

ctio

nof

Spa

n

302 303 304 305 306 307 308 309 3100

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

TFLODataAPNASA-V53DFLOW

Absolute Flow Angle (tan-1(Vθ/Vx)), 8.8mm after the trailing edge of vane-1

Fra

ctio

nof

Spa

n

-80 -75 -70 -65 -60

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

TFLODataAPNASA-V53DFLOW

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152734152189151645151100150556150011149467148922148378147833147289146744146200145655145111Measured Absolute Total Pressure Contours

8.8 mm after the first vane trailing edge

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Absolute Total Pressure (bar), 8.8mm after the blade trailing edge

Fra

ctio

nof

Spa

n

1.25 1.26 1.27 1.28 1.29 1.3 1.31 1.32 1.33 1.34 1.350

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

TFLODataAPNASA-V53DFLOW

Absolute Total Temperature(K), 8.8mm after the blade trailing edge

Fra

ctio

nof

Spa

n

290 291 292 293 294 295 296 297 2980

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

TFLODataAPNASA-V53DFLOW

Absolute Flow Angle (Tan-1(Vθ/Vx)), 8.8mm after the blade trailing edge

Fra

ctio

nof

Spa

n

-60 -50 -40 -30 -20 -10 0 100

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

TFLODataAPNASA-V53DFLOW

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�9ÜÕÖ@ÛfÑgÔÛ�Ó;Ý âúÖ<ÔàÖ<å,ßàÑTÞ)øcøgô Þ(,?Ö<Ô�Þ?Ò?Ö<ð4ßàá?ß�Þ?ø í Ô�Ö<è�èîÓ;ÔàÖ5û_ßàá?ß�Þ)øßàÖ<Ý í Ö<Ô�Þ)ßàÓÕÔ�Ö?û�Þ)ò;èàá?øcÓ_ß�Öhõ;á�öñÞ?åÕÒ?øcÖ?û�Þ)å*ð�Þ)ò;èàá?øcÓ_ßàÖ¢3Þ?ÛÜåýÓÕÝ@ò0ÖfÔ Þ?ÔàÖ\Û�á?Ý í Þ?ÔàÖ�ð�Ñcå�Ð"ÑcÒ?ÓÕÔ�Ö<è9Ø?Ø Þ)å;ð�Ø&�3�hÚýÑcÝCÑgøTÞ)ÔÛ�á5å;Û�øcÓ;èàÑgá5å;è ð_ÔÞ�ö å�âúá?Ô ß�ÜÕÖ@ÛfÞ5èîÖ�á?âþß�ÜÕÖ�6;Ôèîß ,�Þ)åÕÖuÞ?å;ðòÕøTÞ?ð_Ö�Û<Þ)å ò*ÖuÞ?ÔàÔ�ÑI,?Ö<ð4Þ�ßçÜÕÖ<ÔàÖ�� Ð�� � í Ô�á_ð_Ó;ÛfÖ<è èàÑcÝ ÑcøTÞ)Ô Ô�Ö<èàÓÕøgß�è ßàá�� ãE�l�]Ú/�çì)uy�uÞ?å;ð���\Ð�� ��~ ßàÜ;á?ÓÕÒ5Ü4ß�ÜÕÖ�ð_ÑpoYÖfÔ�Öfå*Û�Ö<èëß�Öfå;ð4ßàáCò0ÖzèàøcÑgÒ5Ü5ß�øgôøTÞ)Ô�Ò?ÖfÔ"âúá5ÔhßàÜÕÖçèàÖ<Ûfá?å;ð�,�Þ)åÕÖ��� Ð�� � èàÜÕá�öçèBÛ�øcá5èàÖ Þ)Ò?Ô�ÖfÖfìÝCÖfå,ß�ö Ñ'ß�Üùß�ÜÕÖ�Ö�ü í Ö<ÔàÑcÝCÖfå,ß�Þ?ø ðÕÞ�ßÞ3Ö�è í Ö<ÛfÑcÞ?øgøcô�Ñgå ßàÜ;Öè í Þ)åýö ÑTèîÖ�ð_ÑcÔàÖ�Û%ß�Ñgá5å��

Absolute Total Pressure (bar), 8.8mm after the second vane trailing edge

Fra

ctio

nof

Spa

n

1.24 1.25 1.26 1.27 1.28 1.29 1.3 1.31 1.32 1.33 1.340

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

TFLODataAPNASA-V53DFLOW

Absolute Total Temperature (K), 8.8mm after the second vane trailing edge

Fra

ctio

nof

Spa

n

290 291 292 293 294 295 296 297 2980

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

TFLODataAPNASA-V53DFLOW

Ð"ÑgÒ5ÓÕÔ�Ö Ø?ØÕÙçã Ô�Ö<ð_ÑTÛ%ß�Ö<ð Û�ÑcÔÛ�ÓÕÝ âúÖfÔ�Öfå,ß�ÑcÞ?øgøcô�Þ(,5ÖfÔÞ)Ò5Ö<ðFßàá?ìß�Þ?ø í Ô�Ö<è�èîÓÕÔ�Ö Þ)å;ð÷ßàá?ß�Þ)ø ß�ÖfÝ í ÖfÔÞ�ßàÓ;ÔàÖ Þ�ß Þ èîß�Þ�ß�Ñgá5å�!� �)ÝCÝ ð_á�ö å;èîßàÔ�Ö<Þ?Ý á?âÕßàÜ;Ö ß�Ô�Þ?ÑgøcÑgå;ÒçÖ<ð_Ò5Ö á?âÕßàÜÕÖ9èàÖ<Û�á5å;ð,�Þ)åÕÖ

Absolute Flow Angle (Tan-1(Vθ/Vx)), 8.8mm after the second vane trailing edge

Fra

ctio

nof

Spa

n

-80 -76 -72 -68 -640

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

TFLODataAPNASA-V53DFLOW

Absolute Mach Number

Fra

ctio

nof

Spa

n

0.3 0.4 0.5 0.6 0.70

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

TFLODataAPNASA-V53DFLOW

Ð"ÑgÒ5ÓÕÔ�Ö�Ø��ÕÙ ã ÔàÖ�ð_ÑcÛ�ßàÖ�ðFÛfÑgÔÛ�ÓÕÝ âúÖ<ÔàÖ<å5ß�ÑcÞ?øgøcô4Þ(,5ÖfÔÞ)Ò?Ö�ðDÞ)òÕìèàá?øcÓ_ßàÖ õ;á�ö Þ)åÕÒ5øgÖ Þ?å;ðóÞ)ò;èàá?øcÓ_ß�ÖZ¢3Þ?ÛÜóåýÓÕÝ@ò0ÖfÔDÞ)ß4Þèîß�Þ�ß�Ñgá5å��!� �)ÝCÝ ð_á�ö å*è�ß�ÔàÖ�Þ)Ý á?â]ß�ÜÕÖ ß�Ô�Þ?ÑgøcÑgå;Ò�Ö<ð_Ò5Ö á)âßàÜ;ÖuèîÖ�Û�á?å*ðm,�Þ)å;Ö®HG°¯�±DP�L�²f[O³�^_P�Xk´mN-µcK/\(¶�·�9ÜÕÖ ÑcåÕÑgßàÑTÞ)ø,ð_Ö�,5Öføcá í ÝCÖfå,ßþÞ?å;ðy,�Þ)øcÑcð;Þ�ßàÑcá?åzá?â,ß�ÜÕÖ Ò5ÖfåÕÖ<Ô�Þ?øßàÓ;Ôàò0á?Ý�Þ?ÛÜ;ÑgåÕÖ<Ôàôóõ*á�ö èîá5øs,5ÖfÔZ� Ð�� � Ü*Þ?è�ò*Ö<Öfå Û�á5Ý ìí øcÖ�ß�Ö<ð��k�9ÜÕÖ4Ô�Ö<èàÓÕøgß@ÑTè Þ",?ÖfÔè�Þ�ßàÑcøcÖ í Ôàá5Ò?ÔÞ)Ý ßàÜ;Þ)ß ÛfÞ?åÜ;Þ?å;ð_øcÖñÞùÔ�Þ?åÕÒ?ÖKá)â@Ò5ÖfåÕÖ<Ô�Þ?ø û Ý ÓÕø'ß�Ñ í øgÖêòÕøTÞ?ð_Öfì�Ô�á�ö>Ò?Öfìá?ÝCÖfßàÔ�ÑgÖ�è Ñcå4ò0á)ß�Ü�èîßàÖ�Þ?ð_ô�Þ)å*ðDÓÕå;èîßàÖ�Þ?ð_ôCõ*á�öGÞ)å;ðDßàÜ;Þ)ßÛfÞ?å�ò*Ö�Ô�ÓÕå�á?å Ö<Ñ'ß�ÜÕÖfÔ èîÑcÝ í øcÖ4öäá?Ô§+ýèîß�Þ)ßàÑcá?å;èuá?Ô@øTÞ)Ô�Ò?Öfìè�ÛfÞ)øcÖ í Þ)ÔÞ)øcøgÖ<ø\Ûfá?Ý í Ó_ß�ÖfÔè ð_Ö í Öfå;ðÕÑgåÕÒóá5åGßàÜ;ÖêèàÑIrfÖñá)âßàÜ;Ö�ßàÖ�è�ß]Û<Þ?èàÖzÑgå$�,ÓÕÖ�è�ß�Ñgá5å��.�]Ö�ßÞ)ÑcøgÖ�ðZ,�Þ?øgÑTðÕÞ)ßàÑcá?å á)âhßàÜ;Öèàá)â+ß�ö9Þ)Ô�ÖFÜ;Þ5èCò*Ö<Öfå í Ô�Ö<èàÖfå,ßàÖ�ðóÞ)å;ðEÛ�á5å5ß�ÑgåýÓÕÖ�è ßàáêß�ÜÕÑcèðÕÞ)ßàÖ��¸�9ÜÕÖ Ô�Ö<èàÓÕø'ßè�èîÜ;á�ö ßàÜ;Þ)ßz� Ð�� � ÑTè�Þ)òÕøcÖ�ßàáêá?òÕìß�Þ?ÑgåCÔ�Ö<èàÓÕøgß�èhß�Ü;Þ�ßëÞ?ÔàÖ�,5ÖfÔ�ô èàÑgÝCÑcøcÞ?Ôhßàá�ß�ÜÕá5èàÖ9âúÔàá5Ý á?ßàÜÕÖ<Ôèîß�Þ�ß�Ö�ì�á)â+ì�ßàÜÕÖfì�Þ?ÔîßuèàÑgÝ ÓÕøTÞ�ßàÑcá?å�ÛfáýðÕÖ<èuÓ*èîÖ�ðêÑgå�ò0á)ß�Ü�Ò?á:,,ìÖfÔ�åÕÝCÖfå,ß�øTÞ)ò0á?ÔÞ�ßàá5ÔàÑcÖ<è Þ)å*ðùÑcå;ð_Ó;èîßàÔ�ô��¹� øgø á)â ß�ÜÕÖ ò;Þ)ìèàÑcÛ3ÖføcÖfÝCÖfå,ß�è�á?â�� Ð�� � d èîßàÖ�Þ?ð_ô,ì7è�ßÞ�ß�ÖKÞ)å*ð�ÓÕå;èîßàÖ�Þ?ð_ô

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