4 gas turbine cycles for aircraft propulsion

Gas turbine cycles for aircraft propulsion

• In shaft power cycles, power is in form of generated power. In air craft cycles, whole power is in the form of thrust.

• Propulsion units include turbojets, turbofans and turboprops

• In turbojets and turbofans, the whole thrust is generated in propelling nozzles. In turboprops, most of the thrust is produced by a propeller with only a small contribution from exhaust nozzle.



• Turbojet

The turbine is designed to produce just enough power to drive the compressor. The gas leaving the turbine at high pressure and temperature is expanded to atmospheric pressure in a propelling nozzle to produce high velocity jet. The propelling nozzle refers to the component in which the working fluid is expanded to give a high velocity jet.


• Turbojet

Gas turbine parts

Gas turbine parts

Compressor and turbine of a Gas turbine


• Turbojet

Turbojet

Turbojet Operation

Temperature and pressure distributions

Thrust

Turbofan

• Turbofan

Part of the air delivered by an LP compressor or fan bypasses the core of the engine (HP compressor, combustion and turbines) to form an annular propulsive jet or cooler air surrounding the hot jet. This results in a jet of lower mean velocity resulting in better propulsive efficiency and reduced noise.

Turbofan

Flow in a turbofan

Turbofan Thrust

Turboprop

• Turboprop

For lower speed, a combination of propeller and exhaust jet provides the best propulsive efficiency. It has two stage compressor and ‘can-type’ combustion chamber. Turboprops are also designed with a free turbine driving the propeller or propeller plus LP compressor (called free-turbine turboprop).

Turboprop

Flow in a turboprop

Turboprop

Comparison

Performance Criteria• The net momentum thrust is due

to the rate of change of momentum

)( ajj PPA

• Thus, the total thrust is

)(.

aj CCmF

• Ca is the velocity of air at inlet relative to engine

• Cj Velocity of air at exit relative to engine.

• The net pressure thrust is

)()(.

ajjaj PPACCmF

The propulsion efficiency

• Propulsive efficiency is a measure of the effectiveness with which the propulsive dust is being used for propelling the aircraft but it is not the efficiency of energy conversion.

)/(1

2

]2/)()([(m

)(m

2/)(m jet, theof K.E. FC

FC power), (or thrustenergy propulsive

2.

.

.

2.

a

a

aj

ajaja

aja

aj

p

CC

CCCCC

CCC

CCunused

useful

]2/)[(m

K.E.in Change

power

22.

aj

a

p

CC

FC

Thrust


• Energy conversion efficiency

netf

aj

e

Q

CC

useful

.

22.

m

2/)(m

suppliedenrgy of Rate

propulsionfor K.E.

• Overall efficiency

netf

aja

netf

a

epo

Q

CCC

Q

FC

workuseful

.

.

.

m

2/)(m

m

suppliedenergy


• Specific fuel combustion: fuel consumption per unit thrust, i.e. kg/h N = 0.12 net

ao Qsfc

C 1

• Specific thrust, Fs

sa

aff

s

F

f

mF

mm

F

m

ThrustF

/

/air of rate flow Mass

Thermodynamics of air craft engines

• Diffuser: Velocity decreases in diffuser while pressure increases

• Nozzle: Velocity increases in nozzle while pressure decreases

]2

11[)]/

2

11[

)]1

(2/1[

1 ,2/

22

21

21

MTRTCT

TR

CTTT

RcbutcCTTT

aaaa

aaaoao

ppaaoao

Thermodynamics of air craft engines• Isentropic efficiency of a diffuser

ao

aoi TT

TT

1

1

'

1'

11

a

o

a

o

T

T

P

P

1' /)(1

aaoa TTTT

1' /)(11

aao TTT

1' )/)(11

aaoi TTT1

2

]2

1[

ap

ai Tc

C

21

1ai M

Thermodynamics of air craft enginesThe rest of the components ( compressor, turbine combustion chamber) are treated before.

The ram efficiency isaoa

aor PP

PP

1

Propelling nozzle

Propelling nozzle is the component in which the working fluid is expanded to give a high velocity jet.

Nozzle Efficiency

'5

5

4

4

TT

TT

o

oj

for adiabatic flow 45 oo TT


losses.friction todue PBut 45 oo PP

)/

11)((

'5

5

4

44 TTTTT

o

ojo

1

5 )/(

11[

4

4

PP

T

o

oj

for unchoked nozzle (Mj<1); P5=Pa

For choked nozzle ( Max. rate is reached) M=1, P5=Pc

45 oo TT

To check if it is choked or not


22

55 2

11

2154

ssp

soo MTc

c

T

T

T

T

for choked condition M=1

2

1)1(

2

11 24

c

o

T

TBut isentropic efficiency is

''

4

'

'

)1(1

)(1

44

4

4

4

co

cj

o

c

coj

oc

co

coj

TT

T

T

T

TTTTorTT

TT


11'

)1(1444

o

cj

o

c

o

c

T

T

T

T

P

P

Pc is calculated as

substituting for

14

c

o

T

T

1

)1

21(

11

4

jo

c

P

P1

1

111

j


(unchoked)PcPa if as PP

)( chokedPPPP csca

To calculate A5 of nozzle

55

.

55 / CmAACm ss

ccccs RTCCmAFor where/ nozzle, choked .

Thermodynamics of air craft enginesExampleSimple turbojet cycle

)2

11( 2

1MTT ao

84.0/ RTaCM a

sfc, Required

m/s 270

%4 ;99.0

95.0 ;90.0 ,1200T ;8

98.0 ;93.0 ,87.0 ,7.255

bm

jto3

bic

a

a

C

PcompressorofP

Kr

KT


Kc

CTT

p

aao 292

2

2

1

1.54(1.132)

7.255*1000*005.1*2

270*93.01

21

3.5

221

ap

a

a

o

Tc

C

p

P

barrPP oo 67.612

)(K 1200

5.564]1(1

1[

3

1

12

givenT

KrTT

o

cc

oo


CpgTTCTTww

barP

PPP

moopoocTm

D

boo

a /)( ;

4.6)1(

1234

2

23

accoao

jco

o

oot

Oo

o

PPnozzlechokingPPPP

PP

barP

TTpp

KT

g

g

; //

194.11

111/1/

327.2

33.1,)/1(1

1/

959

44

1

4

1

34

`

4

34

4


84.0,0.1,/8.560

287 ,/ 515.0

914.1,215.1)/(

01.822)1

2(

. & ),(1

2

2

11

21

,1 ;, ;5

5

3

5

22

5

5

4

4

4

4

45

MMsmRTMCC

RmkgRT

P

P

Pbar

PP

PPP

KTT

workmechlossheatnoTTTT

MTc

C

T

T

PPPMchokingPPState

ccc

c

ccs

c

o

co

oc

oc

oocs

ssp

s

c

o

acsac


kgsmCmACAm

CCNotes

ss

as

/00346.0/1/

)270560( :

2555

.

0178.0/ 0174.0 :

5.635 ,5.564

2.525)()( ; .

/ 00346.0/1/

232

2555

b

ooo

ass

ass

ss

fthffchart

TTT

ppm

ACCFthrustsp

kgsmcmACAm


snkgsfc

C

m

FC

NkgF

fsfc

net

a

netf

a

s

/185.01000*43000

1

)3600

122.0(

2701

/122.03600


Example:2: Turbofan AnalysisOverall pressure ratio given

25.1

9.0,19

34

1

3

oob

scstsfo

o

PPP

P

P

.0

/115

99.0

95.0

3

a

a

m

n

h

c

C

skgm

m

mB

sea level Pa =1 bar

Ta=288 K


State 1 is sea level since Ca=0.0Required: sfc, Fs

75.17,1300:

734)1

()/(/

19)/:

1,4.1,7.337)/(/

65.1:

344

32323

113

21212

1

1

2

2

4

3

1

2

booo

ooooo

ooo

on

n

oooo

oo

oo

PpPKTS

KTn

nPPTT

barpPPS

KTPPTT

barPP

PPS


333.1,11

:5

tn

nS

barPT

TPP

KT

TTCmTTCm

o

n

n

o

o

oo

o

ooPhoophm

mHPTc

ag

415.4,/

7.949

))(()(

5

4

5

45

5

2354

1


barPT

T

P

P

CTTBCTT

TTCmTTCm

S

o

n

n

o

o

o

o

PgmooPoO

OOPghmoOPa

LPTmf

a

A

78.1

7.773/))(1(

)()(

:

6

5

6

5

6

1256

6512

1

6

check for choking of both nozzles ( hot and cold)


workmech. no and

,,1147 );(2

2.6755.98

333.1,5.98)(1

,// ;

78.1/ ;914.11

111:

6772

7

7

1

7

1

:7

7

6

6

66

6/6

/6

6

adiabatic

TTcTTcC

KTT

P

PTTT

unchokedPPpppPcompare

PPP

PS

unchokedPP

chokingPP

ooPoP

o

o

aono

cacoao

aonc

o

ca

ca


C7= 476 m/s

1/ 2.508 a7 :Notes 77 MsmRT

for cold nozzle ( do same)

barPPunchokedPorPP

P

P

P

P

Pbut

P

P

acac

o

a

o

a

o

Nc

o

1 ;,

65.1 ;4.1 ,965.111

1

8

1

22

22

note: Nozzles are independent of each other regarding choking.


smCcTTcC

KTP

PTTT

aa PoP

o

aoNo

/293 ;1007),(2

9.2941

882

8

8

1

8

2

2

22

Notes: a8=344.2; M8<1

016.0)734 ,566)(

//13.339115/39000 ;39000

25300 ;13700

/25.861

;/75.281

34/3

87

thooo

stotal

cchh

ca

h

FKTKTf

skgNFNF

NCmFNCmF

skgB

amBmskg

B

mm


NhkgF

msfc

hkgmfmassumedffact

total

f

fuelhfbth

./0425.0

/16563600 ); 0.1(/.

Documents

4 gas turbine cycles for aircraft propulsion