Engines en1 v1

8/10/2019 Engines en1 v1

1/54


2/54

0. 0.543330 -4.--01,5-

C*ose &r/&t 0.3 0.2-,55342 1,1.13521-,30.22124-14-4 1,2

1 2

t 21.502-0-1- m/s

1t 31.-20 m/s

a 333.4-5441 m/s

r 140.-513535

61t 0.5,44--04, transoni( speed

*ub radius 0.132-4,-1 mmean radius 0.20-41200, m

02 1.5,55 bar

T02 330.,04303 K

T2 31.020131 K

2 1.3--,54- bar

densti)2 1.51214125 kg/m3

A2 0.154305,5 m2

7lade8*eig*t8e9it 0.1140051 m&t8e9it 0.2,,,14,05 m

&r8e9it 0.142140 m

0.1

umber of stage design

Temperature rise t*roug* fan 42.,04302 K

mean blade speed 211.12-0303 m/s

71 54.,0-24401, deg

1 25.-,1 m/s


3/54

tan b1 ; tanb2

Ca 150 m/s

1,2 &$

&t 0.2-,55342 0.2-,55342

&m 0.20-41200, 0.20-41200,

&r 0.132-4,-1 0.132-4,-1

roperties 1st 2nd stage

01 1.01

t !m/s# 21.502-0-1- 21.502-0-1-02

m !m/s# 211.12-0303 211.12-0303---

r !m/s# 140.-513535 140.-51353551

T!K# 2 30.4

work done fa(tor 0. 0.3

dT !K# 21.4 20.4

delta w*irl +elo(i) dCw !m/s# 103.4,511, 104.41,5-44-13

Cw1 !m/s# 0 11.1221---Cw2 !m/s# 103.4,511, 115.54,3,34

tan71;tan72 2.303221 1.-051502

tan71"tan72 1.44304,5 0.,,1104,5

71 !deg# 54.,0-24401, 53.12-141

72 !deg# 35.54-202251 32.5054545,4

a1 !deg# 0 4.243502-1

a2 !deg# 34.-21051, 3-.,0-351,,5

a3!deg# 4.243502-1 0

71"72 !deg# 1.0,0041-,5 20.,24250355

2/1 !de


4/54


5/54


6/54

C=6&>$$=& ???

0

211.12-

0

32.

0.5

25

140.004

",.,,4352133.340,

1.-051

0.333,,

55.44355

2-.4101

"2.54322

41.,350

2.0333,

0.,351

0.-4-31

1.2545

1 5212


7/54

Known

T*rust 13000

Cruise speed 21.44444444 m/s

&ange 355 km

&ate of (limb 124., m/min

Ceiling 13-1, m

@eig*t!empt)# 4004 kg

ma9 takeoff -200 kg

@ing span 15. m

engt* 14. m@ing area 31. m2

T)pi(al passenger people $eparate (old and *ot

fan dri+en b) turbin

umber of spools 2

=+erall pressure rat 1

7) pass ratio 1. 11.,1203225

an pressure ratio 1.55

Turbine inlet Temp 1235 K Area of intake 0.104-,an'(omp'turb pol) 0. &ad intake 0.24,233 m

:sen eff of noBBle 0.5

me(*ani(al eff 0.

Combus press loss 1.5 bar

Total air mass flow 35 kg/s --.1,1-1--

o 1 bar

T0 2 K

gamma'(omp 1.4000-

gamma' e9p 1.333 55

Cpa 1.005 densit) 1

Cpg 1.14 densit) 2

(ompression e9pansion ,-,


8/54

$pe(ifi( T*rust 352.12 s/kg

densit) 1.1520-44 Total t*urst 1235.21-

A 0.0,,341442 Total t*urst 2-23.1 lb

0.14-0-05 35.212

f/a 0.015 oBBle

mf 0.12,3113 kg/s Area 0.11

mf ,5.30-21003 kg/*r &adius 0.1-121

$C 0.00004232 kg/s

$C 0.1530050- kg/*

Total T*rust 12352.1-

$pe(ifi( T*rust 352.12 s/kgf/a t*eor) 0.015

f/a a(tual 0.015152

mf 0.12,3 kg/s

mf ,5.30-2 kg/*r

$C 0.15301 kg/*


9/54

noBBles are used

e and (ompressor b)


10/54


11/54

Compressor design

known

Compressure pressure ratio 1.55 4.15

Air mass flow 35 kg/s

Turbine inlet Temp 1235 K

Cpa 1.005

amma 1.4

amma/!amma"1# 3.5

$teps%

1" &otational speed' annulus dimensions

2" number of stages' assumed effi(ien()

3" air angles for ea(* stage' mean radius

4" +ariation of air angles from root to tip

5" (ompressabilit) effe(ts

," (ompresssor blading

-" (*e(k on effi(ien()

" off design performan(e" rig testing

Assumption

t 20 m/s

Ca 150 m/s

*ub"tip ratio 0.4"0.,

T01 2 K

01 1.01 bar !n"1#/n 0.31-5

fan eff 0.

Cal(ulated

C1 150 m/s


12/54

0. 0.543330 -4.--01,5-

C*ose &r/&t 0.3 0.2-,55342 1,1.13521-,3

0.22124-14-4 1,2

1 2

t 21.502-0-1- m/s

1t 31.-20 m/s

a 333.4-5441 m/s

r 140.-513535

61t 0.5,44--04, transoni( speed

*ub radius 0.132-4,-1 mmean radius 0.20-41200, m

02 1.5,55 bar

T02 330.,04303 K

T2 31.020131 K

2 1.3--,54- bar

densti)2 1.51214125 kg/m3

A2 0.154305,5 m2

7lade8*eig*t8e9it 0.1140051 m&t8e9it 0.2,,,14,05 m

&r8e9it 0.142140 m

0.1


Temperature rise t*roug* fan 42.,04302 K

mean blade speed 211.12-0303 m/s

71 54.,0-24401, deg

1 25.-,1 m/s


13/54


14/54

a2t 2-.4-511333 2.3113545

E=& &==T 0.-5400-,-2 0.-1,-03032

C3 150.41234303 150.14--23124

T3 2.1443412 31.53-33,1

3 1.112-32253, 1.3-324,124

dens3 1.300415-122 1.5010,21

A3 0.1-4201- 0.15535---25

* 0.13-,-31- 0.1120-,55

entr)

&t $TAT

&r $TAT&t &=T 0.2-,55342 0.2,,,14,05

&r &=T 0.132-4,-1 0.142140

>9it

&t $TAT 0.3453125 0.32,223203

&r $TAT 0.20--1-434 0.20-015,30

&t &=T 0.2-,40,,2 0.2,,212455

&r &=T 0.20-5,4-2 0.20-21-415-t rot 21.34-45, 2-1.504-313

r rot 211.2-- 210.21,3334

Cw2t -.0022,-2 0.05043-041

Cw2r 103.-1250, 104.04--332-31

Cw1t 0 .,5553102

Cw1r 0 15.5-5140021

widt* 0.0452-3 0.03-35,5 0.05,2

0.0114-315 0.0033-1, 0.02140-

0.10-03,


15/54


16/54


17/54

0.11401

C=6&>$$=& ???

120.51-

211.12-

0

32.

0.5

25

140.004

",.,,4352133.340,

1.-051

0.333,,

55.44355

2-.4101

"2.54322

41.,350

2.0333,

0.,351

0.-4-31

1.2545

1 5212


18/54


19/54

30 m/s

mass flow 12.0,- kg/s

inlet radius 0.1223 m

inlet *ub 0.100,

:nlet area 0.01001 m2

outlet radius *ub 0.114112outlet radius Tip 0.15114, 0.03-034

=utlet area 0.030,1 m2

0.0

rimrar) (ombustor +olume 0.01 0.01

(omb

densit) 1 .2----- kg/m3

densit) 2 4.,551,5 kg/m4

a+erage densit) ,.,,4-1 kg/m5

Area 0.05--4 m2

*ub radius middle 0.114112 m

tip radius middle 0.1--21 m 0.0,30

engt* 0.0,-5 m

2.5"3F=E


20/54

Compressor design

knownCompressure pressure ratio 11.,1 4.15

Air mass flow 12.0,,551-2 kg/s

Turbine inlet Temp 1235 K

Cpa 1.005

amma 1.4

amma/!amma"1# 3.5

$teps%

1" &otational speed' annulus dimensions

2" number of stages' assumed effi(ien()

3" air angles for ea(* stage' mean radius

4" +ariation of air angles from root to tip

5" (ompressabilit) effe(ts

," (ompresssor blading

-" (*e(k on effi(ien()

" off design performan(e

" rig testing

Assumption &eason

t 350 m/s re+iousl) s*own t*at t*is will lead to a((ept

Ca 150 m/s 6odest' no :Gs' no w*irl +elo(it) at entran(

*ub"tip ratio 0.4"0.,

T01 32. K

01 1.4-254002, bar o loss in intake

!n"1#/n 0.31-5

isen eff 0.

Cal(ulated


21/54

*ub radius 0.0--3450415 m

mean radius 0.11,01-5,22 m

02 1-.0,1-323 bar T02 -1.34-02- K

T2 -0-.153,042 K

2 1,.11--53-04 bar

densti)2 -.-315,5-5 kg/m3

A2 0.01001332 m2 e9it annulus area

7lade8*eig*t8e9it 0.013434,-, m

&t8e9it 0.12232, m

&r8e9it 0.100524 m


Temperature rise t*roug* (om 3.54-02- K

mean blade speed 2,2.425543204 m/s

Ca1Ca2Ca

71 ,0.2411,421 deg

1 302.2-002121 m/s

de


22/54

T!K# 32. 351.5, 3-,.0, 400.0, 423.0, 445.0,

work done fa(tor 0. 0.3 0. 0.3 0.3 0.3

dT !K# 21.-, 24.5 24 23 22 22

delta w*irl +elo(i) dCw !m/s# 5.03403200-- 100. 104.4452 10,.123 101.50 101.50

Cw1 !m/s# ",.,,43521455 2.2325 -.01- -.15125 0.452- 0.452-

Cw2 !m/s# -.3,,-,21 12.1-21 13.4354 14.2-43 11.,-3 11.,-3

tan71 ; Tan72 2.,1531 2.44305 1.-4504 1.-4504 1.-4504 1.-4504

tan71 " Tan73 1.1-5-455 0.,-252 0.,,301 0.-0-4- 0.,-,-2- 0.,-,-2-

71 !deg# ,2.-2035323 5-.3541 50.-2,22 50.542 50.50042 50.50042

1 32.0,5544555

2 0

72 !deg# 50.210000,,1 41.,1,4 2-.--134 2-.51 2.20, 2.20,

a1 !deg# "2.543220402 10.,-04 2-.--134 2-.51 2.20, 2.20,

a2 !deg# 2-.554-131 40.-332 50.-2,22 50.542 50.50042 50.50042

a3!deg# 10.,-03-1-0- 2-.--134 2-.51 2.20, 2.20, 2.20,

71"72 !deg# 11.-1034,,2 15.-342 22.54 23.3343 22.212 22.212

2/1 !de


23/54

&t &=T 0.1521553- 0.1413- 0.14,21 0.1434 0.141- 0.13-34

&r &=T 0.0---3,5 0.02 0.05-54 0.01, 0.00335 0.02301

t rot 344.1,-3-1213 33-.3402 330.04 325.3-4 320.51 31,.0-12

r rot 10.,3-0-25, 1-.510 13.-0- 1.4-2- 204.3323 20.--

Cw2t 5.-5,40,444 ,0.,5-- ,2.15,02 ,3.20-04 ,4.1,53- ,5.0,2

Cw2r 113.243514,4 10.,01 10,.02-4 103.102 100.,50 .50,,3

Cw1t "4.2,4102 "5.0535 "5.1214- "5.1,112 "5.25105 "5.313

Cw1r ".,52213 ".-,02 ".535- ".3212-1 ".11,011 ".15,

widt* 0.0224020-1 0.01,23 0.01-0, 0.0150,2 0.013443 0.0120,,

0.005,00521 0.0040, 0.0042,5 0.003-,, 0.0033,1 0.00301-

rotor 9 0.0224020-1

stator 9 0.02002,0 0.02452 0.021325 0.012 0.01,03 0.01503

dor m 0.5

Eor r 0.1,1

& 0.--1-,


24/54

ble stresses

e' donGt want to in(rease 6a rel to blade


25/54


26/54

4,-.0, 4.0, 511.0, 533.0, 555.0, 5--.0, 5.0, ,21.0, ,43.0,

0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3

22 22 22 22 22 22 22 22 22

101.50 101.50 101.50 101.50 101.50 101.50 101.50 101.50 101.50

0.452- 0.452- 0.452- 0.452- 0.452- 0.452- 0.452- 0.452- 0.452-

11.,-3 11.,-3 11.,-3 11.,-3 11.,-3 11.,-3 11.,-3 11.,-3 11.,-3

1.-4504 1.-4504 1.-4504 1.-4504 1.-4504 1.-4504 1.-4504 1.-4504 1.-4504

0.,-,-2- 0.,-,-2- 0.,-,-2- 0.,-,-2- 0.,-,-2- 0.,-,-2- 0.,-,-2- 0.,-,-2- 0.,-,-2-

50.50042 50.50042 50.50042 50.50042 50.50042 50.50042 50.50042 50.50042 50.50042

2.20, 2.20, 2.20, 2.20, 2.20, 2.20, 2.20, 2.20, 2.20,

2.20, 2.20, 2.20, 2.20, 2.20, 2.20, 2.20, 2.20, 2.20,

50.50042 50.50042 50.50042 50.50042 50.50042 50.50042 50.50042 50.50042 50.50042

2.20, 2.20, 2.20, 2.20, 2.20, 2.20, 2.20, 2.20, 2.20,

22.212 22.212 22.212 22.212 22.212 22.212 22.212 22.212 22.212

0.-21- 0.-21- 0.-21- 0.-21- 0.-21- 0.-21- 0.-21- 0.-21- 0.-21-

0.-21- 0.-21- 0.-21- 0.-21- 0.-21- 0.-21- 0.-21- 0.-21- 0.-21-

1.15,405 1.1401- 1.14225 1.13,153 1.13051 1.125331 1.12054 1.11,101 1.111-

5.111, 5.-3-, ,.-05, -.,230, .,104 .,15- 10.,-1- 12.12, 13.4-034.0, 511.0, 533.0, 555.0, 5--.0, 5.0, ,21.0, ,43.0, ,,5.0,

0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5

53.1-105 53.-4313 54.30003 54.422- 55.3-032 55.4,4 5,.35, 5,.-3 5-.34,,

50.50042 50.50042 50.50042 50.50042 50.50042 50.50042 50.50042 50.50042 50.50042

,5.144 ,4.0--4 ,4.,143, ,4.31451 ,4.00- ,3.,4, ,3.3-411 ,3.04,3 ,2.-10534.,5,03 3,.1,1- 3-.5-42 3.0,,- 40.1,,5, 41.3,20- 42.43- 43.535 44.,10

2.20, 2.20, 2.20, 2.20, 2.20, 2.20, 2.20, 2.20, 2.20,

5.,5 5.3451 5.045 5.3-3-- 5-.435- 5-.2 5,.-31 5,.1,32, 55.5-035

3 331415 3 2,2-52 3 1,5 3 1335-2 3 0-2-4 3 014222 2 5- 2 03,23 2 5131


27/54

0.13-1, 0.13,21 0.134,21 0.13310 0.131,,4 0.13021 0.124- 0.12-,5- 0.12,405

0.0411 0.051- 0.0-414 0.02- 0.1003-1 0.101-55 0.1030 0.1043- 0.105,3

311.5- 30.11, 304.50, 301.025 2-.1- 24.,-- 21.,-2 2.-545 25.215

212.32 21,.-325 220.345 223.-,, 22-.0332 230.1,34 233.1-1 23,.0,, 23.2,

,5.2,23 ,,.-4-, ,-.535, ,.30-54 ,.05,32 ,.-5 -0.51142 -1.223, -1.255

,.,033 4.214 3.33,3- 1.03- 0.5,-, .354- .11 -.102- ,.0-,43

"5.3,31 "5.45, "5.532,,5 "5.,0-,0 "5.,4,11 "5.-,3-5 "5.4513 "5.251 ",.014,

".-314,- ".55111 ".3-053 ".211,1 ".052135 "-.504 "-.-50,25 "-.,012 "-.4-0

0.010- 0.00, 0.004 0.00211 0.00-532 0.00,32 0.00,4 0.00525 0.0055

0.002-22 0.0024,- 0.00224, 0.002053 0.0013 0.001-33 0.001, 0.00141 0.0013-5

0.013,0 0.01233, 0.01123 0.0102,4 0.00415 0.00,,5 0.00- 0.00-40, 0.00,-5


28/54


29/54


30/54

,,5.0, ,-.0, -0.0,

0.3 0.3 0.3

22 22 22.01 401.2- 3.54

101.50 101.50 101.5,-

0.452- 0.452- 0.41444

11.,-3 11.,-3 12.0111

1.-4504 1.-4504 1.-4504

0.,-,-2- 0.,-,-2- 0.,--311

50.50042 50.50042 50.50-1

2.20, 2.20, 2.155

2.20, 2.20, 2.155

50.50042 50.50042 50.50-1

2.20, 2.20, 2.155

22.212 22.212 22.311,

0.-21- 0.-21- 0.-21,0-

0.-21- 0.-21- 0.-21,0-

1.1013- 1.104551 1.10125 1.10122 13.5,4

14.454- 1,.5003 1.1004 (*e(k 0,-.0, -0.0, -31.0- 3.344334

0.5 0.5 0.5 1.1

5-.1342 5.2,554 5.-0,42

50.50042 50.50042 50.50-1

,2.3,-1 ,2.01,,4 ,1.,5-145.,05- 4,.553 4-.4,1,

2.20, 2.20, 2.155

54.55- 54.33001 53.,0-3

2 004- 2 -5213- 2 -0502


31/54

0.12515 0.1233 0.1222,

0.10,5 0.10042 0.1020

23.1,1 20.4,5 2--.25

241.,3 244.353 24-.02,

-2.,305 -3.32-4 -4.025-4

5.035- 4.1545 3.25521

",.103,1 ",.15021 ",.2135

"-.3344, "-.210,25 "-.0-11

0.00511 0.004--4 0.0044,3 0.14251

0.0012 0.00114 0.00111, 0.04,0,3

engt* 0.230314

0.00,3 0.005, 0.0055- 0.230314


32/54

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045 0.05

0

0.02

0.04

0.0,

0.0

0.1

0.12

0.14

0.1,

rr

&otor8t

&otor8r

$tator8t

$tator8r


33/54

0 0.1 0.2 0.3 0.4 0.5 0., 0.- 0. 0. 1

"10

0

10

20

30

40

50

,0

-0

0

angles_stage1

a1

a2

b1

b2

r/rm

degrees


34/54

0 0.1 0.2 0.3 0.4 0.5 0., 0.- 0. 0. 1

"10

0

10

20

30

40

50

,0

-0

angles_stage17

a1

a2

b1

b2

r/rm

degrees


35/54

0. 1 1.2 1.4 1., 1. 2 2.2

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

fan size

&t

&r


36/54

Cpg 1.14 kI/kgK

gamma 1.333

g/!g"1# 4

isen effi(ien() 0.

Assumption

Jn 0.05 Con+ergant noBBles are emplo)ed' t*e) are op

s 0.

(riti(al pressure ratio 1.515,5

=+erallTemp drop 34,.33-3

mass flow 11.1, kg/s

:nlet temp 1235 K

3 stages

ressure ratio 01/03 4.31-,225

:nlet pressure 1,.5

ressure reLuired 3.2154-,ressure : got 3.2154-,

3,0 &e+/s fi9ed b) t*e (ompressor' t*e design

300 m/s e9perien(e w*i(* stressing diffi(ulti

M 2.45150,


37/54

T1 1223.021 T02"T2 -5.0-5111-3

1 15.14,3 T02T01 1235

densit)1 4.530-3 T2 115.10242-

A1 0.015430- T2"T2G 3.-544-555*1 0.0151, T2G 115,.155-,132,

&r/&t1 1.15000, 01/2 1.301-433

satisfa(tD1 )es 2 12.,-30,03,

satisfa(tD2 no 01/( 1.515,5041,

(*o(kedD no

densit)2 3.0,32

A2 0.0154321-

A2n !t*roa 0.010433,43*2 0.01252,03-1

&r/&t2 1.0124-2

satisfa(tD1 )es

satisfa(tD2 no

* 0.0204-,

7lade *eig*t/widt* 3 needs to be (*anged w*en t*e blade stresses

widt* 0.00,42 0.25 is rat*er low' be(ause we want to redu(e

$pa(e b/w stator and rotor blades 0.001-3-3 suall) b/w 0.2 and 0.5

2(*o(ked ,,,.14415

T( .11302



M 2.45150,

N 0.

a3 12 deg tr) to a+oid negati+e +alues at t*e r

tan a3 0.21255,,

tanb3 1 4,255,,


38/54

A1 0.014,,5 01/2 1.4322-4-,34

*1 0.01-5 2 -.0-4-22022

&r/&t1 1.14524- 01/( 1.515,5041,

satisfa(tD1 )es (*o(kedD nosatisfa(tD2 no densit)2 2.3003-2

A2 0.0131121

A2n !t*roa 0.010145113

*2 0.0232,355

&r/&t2 1.1231-5531

satisfa(tD1 )es

satisfa(tD2 no

* 0.025-1-7lade *eig*t/widt* 3 needs to be (*anged w*en t*e blade stresses

widt* 0.005-23 0.25 is rat*er low' be(ause we want to redu(e

$pa(e b/w stator and rotor blades 0.0021431 suall) b/w 0.2 and 0.5



M 2.45150,

N 0.

a3 2 deg tr) to a+oid negati+e +alues at t*e r

tan a3 0.531-04

tanb3 1.-1-04

E=& 0.,0-

73 ,0.,,3 degtan b2 0.0500- stage pressure ratio

tan a2 1.3000-

b2 3.3--02

a2 52 ,224--


39/54

A2n !t*roa 0.01,3-40,

*2 0.0323,-11-3

&r/&t2 1.2--52211

satisfa(tD1 )essatisfa(tD2 )es

* 0.03,5542

7lade *eig*t/widt* 3 needs to be (*anged w*en t*e blade stresses

widt* 0.01214- 0.25 is rat*er low' be(ause we want to redu(e

$pa(e b/w stator and rotor blades 0.00304,2 suall) b/w 0.2 and 0.5


40/54

erating wit* a pressure ratio !p01/p2# less t*an (rit pressure ratio

no of stages 3

$tage Temp drop 115.445 K

1 115.445

2 115.445

3 115.445

of t*e (ompressor is more (riti(al t*an turbine be(ause of de(elerating flow

es will be se+ere.


41/54

3 .-3-0 E=& 0.525,-

densit)3 3.0,0-5 73 ,.44,4- deg

A3 0.02430 b2 22.4,221 deg

*3 0.021, a2 ,-.4352 deg03 10.1325 a1 0 deg

63 0.230343

T3O 105.54

3 35.01,

32/2F(p ,4.5,35

&r/&t2 1.24-104

satisfa(tD1 )essatisfa(tD2 )es

Jr 0.34531

JrPJn )es

are being e+aluated

*e a9ial lengt* and weig*t of t*e turbine. ibrational stresses indu(ed in rotor blades as t*e) pass t*roug* wa


es will be se+ere.

ot' t*erefore aim for a E=& of abo+e 0.4


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63 0.3224

T3O ,-.34,2

3 425.21232/2F(p -.-5023

&r/&t2 1.23-53

satisfa(tD1 )es

satisfa(tD2 )es

Jr 0.10,053

JrPJn )es

are being e+aluated



es will be se+ere.

ot' t*erefore aim for a E=& of abo+e 0.4

$tage Temp drop K

2 115.4451.,2351-45,


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satisfa(tD1 )es

satisfa(tD2 )es

Jr "0.03205JrPJn no

are being e+aluated



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E=& 0.,0

73 ,0.,,3 deg

b2 3.3--0 deg

a2 52.,224 dega1 2 deg

kes of t*e noBBle blades' and t*e) in(rease s*arpl) wit* de(rease in a9ial spa(e b/w t*e blade rows#


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48/54

&epeating stage design multistage design

work done fa(tor is unne(essar) be(ause of t*e a((elerating flow t*e effe(t of t*e growt* of t*e boundar) l

de(elerating flow wit* an ad+erse pressure gradient.

low psi !temp drop (oeff# and low p*i !flow (oeff# )ield best stage effi(ien(ies.

low psi !temp drop (oeff# and low p*i !flow (oeff# impl) low gas +elo(ities and *en(e redu(ed fri(tion losses

low pis means more stages for a gi+en o+erall turbine output and a low p*i means a larger turbine annulus$in(e weig*t and frontal area are desirable to be low' *ig*er +alues of psi and p*i must be used.

=pt +alues for psi range from 3 to 5' and p*i range from 0. to 1. A low swirl angle !a3 H 20 deg# is desirabl

pipe and propelling noBBle.

mean diameter design is (*osen

Con+ergant"di+ergant noBBles are not used sin(e t*e) tend to be ineffi(ient at pressure ratios ot*er t*an t*

*ig* C2 usuall) impl) *ig* +alues of 2. :f 6a relati+e to t*e mo+ing blades at inlet' 6+2' e9(eeds 0.-5' ad

wa+es in rotor blade passages

gamma 1.333

g/!g"1# 4

Assumption


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tan a3 0.21255-

tanb3 2.21255-

E=& 0.4030,

73 ,5.,-,, degtan b2 0.,0022

tan a2 2.,0022

b2 30.-5,4

a2 ,.,45-

a1 2

&m 0.24-31

$tage 1 stage 2 stage 3Ca1 C1 C3 1,.55 Ca2 150 T03

C12/2(p 12.5-01, C2 41-.12 T3

T1 -,.024 T02"T2 -,.05, 3

1 3.,0, T02T01 .,,2, densit)3

densit)1 1.435,, T2 12.,02 A3

A1 0.045-5, T2"T2G 3.024 *3

*1 0.024-0 T2G 0.- 63

&r/&t1 1.0-501 01/2 1.45-415 T3O

satisfa(tD1 )es 2 2.,22141 3satisfa(tD2 no 01/( 1.515,5 32/2F(p

(*o(kedD no &r/&t2

densit)2 1.124335 satisfa(tD1

A2 0.0,,1-2 satisfa(tD2

A2n !t*roa 0.023-52

*2 0.0122,

&r/&t2 1.0444,

satisfa(tD1 )es Jr satisfa(tD2 no JrPJn

* 0.02-23

7lade *eig*t/widt* 3 needs to be (*anged w*en t*e blade stresses are being e+

widt* 0.000-- 0.25 is rat*er low' be(ause we want to redu(e t*e a9ial len


50/54

a)er along t*e annulus walls is mu(* less t*an w*en t*ere is a

area for a gi+en mass fllow

e be(ause swirl in(reases losses in Iet

design +alue !i.e. at part load#. And partl) be(ause

itional loss ma) be in(urred b) formation of s*o(k


51/54

--.4032

-,5.331

2.120

0.,43

0.0--0

0.041,33

0.2--12

--0.,3,3

3,4.20,5-.--23

1.1514

)es

no

"0.0313 tip leakage loss in rotor blades makes t*is )esno

aluated

t* and weig*t of t*e turbine. ibrational stresses indu(ed in rotor blades as t*e) pass t*roug* wakes of t*e noBBl


52/54


53/54

blades' and t*e) in(rease s*arpl) wit* de(rease in a9ial spa(e b/w t*e blade rows#


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0 0.01 0.02 0.03 0.04 0.05 0.0, 0.0- 0.0 0.0 0.1

0

2

4

,

10

12

2nd stage

a1a2

b1

b2

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