Lect-8 - NPTELnptel.ac.in/courses/101101002/downloads/Lect-08.pdfhigh pressure and temperature – Combustion chamber: fuel is added here, combustion results in high temperature and

1

Lect-8

Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay2

Lect-8

In this lecture...

• Cycle components and component performance– Intake– Compressor/fan– Combustion chamber– Turbine– Nozzle


Lect-8

Cycle components

• Jet engine cycle has several salient components– Air intake/diffuser: decelerates air and

delivers it to the compressor– Fan: present in turbofan engines, drives the

bypass mass flow– Compressor: compresses ingested air to

high pressure and temperature– Combustion chamber: fuel is added here,

combustion results in high temperature and pressure at turbine inlet


Lect-8

Cycle components

– Turbine: Combustion products are expanded through the turbine, generates shaft power to drive the compressor

– Nozzle: Turbine exhaust is further expanded through the nozzle, generates thrust

– Afterburner: used in afterburning turbojets, function similar to combustion chamber


Lect-8

Air intake performance• Inlet losses arise due to wall friction and

shock waves (in a supersonic inlet).• These result in a reduction in total

pressure.• The flow is usually adiabatic as it flows

through the intake.• Performance of intakes are characterised

using total pressure ratio and isentropic efficiency.


Lect-8

Air intake performance

s

T

a

P1

P0a

V02/2cp

1

2s

Pa

2

P02P2

0a 02V2

2/2cp02s

Actual and ideal intake processes


Lect-8

Air intake performance• Isentropic efficiency, ηd, of the diffuser is

• This efficiency can be related to the total pressure ratio (πd) and Mach number

aa

as

aa

asd TT

TThhhh

−−

≅−−

=0

02

0

02η

[ ] 2

/)1(2

2/)1(

12

11

M

M d

d −

−

−+

=

−

γ

πγ

η

γγ


Lect-8

Air intake performance

• During cycle analysis, the value of isentropic efficiency is often calculated based on the Mach number.

• The isentropic efficiency drops drastically as Mach number increases.

• This is because of the presence of shocks and the resultant total pressure losses.

• There are empirical correlations available for estimating the diffuser efficiency as a function of Mach number.


Lect-8

Compressor/fan performance

• Compressors are to a high degree of approximation, adiabatic.

• Compressor performance is evaluated using the isentropic efficiency, ηc

0203

0203

ratio pressuregiven for n compressio of work Actualratio pressuregiven for n compressio of work Ideal

hhhh

ww s

c

ci

C

−−

==

=η


Lect-8


s

T

03s

P02

P0303

02T02

T03s

T03

Actual and ideal compression processes


Lect-8


( )( )

( )( )

11

11/

1/1/

/1

/10203

0203

0203

0203

0203

0203

0203

−−

=

−−

=−−

=

−−

≅−−

=

−

−

C

C

C

s

ssC

PPTTTT

TTTT

hhhh

τπ

τ

η

γγ

γγ

• The isentropic efficiency is thus a function of the total pressure ratio and the total temperature ratio.


Lect-8


• Besides isentropic efficiency, there are other efficiency definitions, stage efficiency and polytropic efficiency that are used in assessing the performance of multistage compressors.

• Stage efficiency will be discussed in detail during the lectures on compressors.

• The three efficiency terms can be related to one another.


Lect-8

Compressor/fan performance• The polytropic efficiency, ηpoly, is defined as

00

00

00

00

0

0

0

0

0

0

/)1(00

0

0

0

0

//1

//

1 Therefore, constant.

gives,relation isentropic the,compressor idealan For

change pressure aldifferenti afor n compressio of work Actualchange pressure aldifferenti afor n compressio of work Ideal

TdTPdP

γγ

TdTTdT

dTdT

PdP

γγ

TdT

PT

dTdT

dhdh

dwdw

iiipoly

ii

ii

iii

poly

−===

−=

×=

===

=

−

η

η

γγ


Lect-8


( )( ) ( )( )

.efficiencypolytropicconstant a assuming ratio pressure with the

efficiency isentropic therelatesequation above The1

11

1,

03, and 02 statesbetween gIntegratin

1 equation, above theRewriting

)/()1(

/1/1

)/()1(C

0

0

0

0

−−

=−

−=

=

−=

−

−−

−

poly

poly

C

C

C

CC

C

poly

or

PdP

γγ

TdT

γηγ

γγγγ

γηγ

ππ

τπη

πτ

η


Lect-8

Combustion chamber performance

• In a combustion chamber (or burner), there are two possibilities of losses, incomplete combustion and total pressure losses.

• Combustion efficiency can be defined by carrying out an energy balance across the combustor.

• Two different values of specific heat at constant pressure: one for fluid upstream of the combustor and the other for fluid downstream of the combustor.


Lect-8

Combustion chamber performance

( ) ( )

( )

burner.

theof upstreamair for valueaverage theis andburner

theof downstream gasesfor valueaverage theis Where,

,efficiency Combustion

0304

0330440304

pa

pg

ff

papgf

ff

ppf

ff

fb

b

cc

QmTcmTcmm

QmTcmTcmm

Qmhmhmm

−+=

−+=

−+=η

η


Lect-8

Combustion chamber performance• Total pressure losses arise from two effects:

– viscous losses in the combustion chamber– total pressure loss due to combustion at finite

Mach number

• Combustion efficiency is usually very high in gas turbine engines.

• In real cycle analysis both these parameters are used.

1

loss, pressurechamber Combustion

03

04 <=PP

bπ


Lect-8

Turbine performance• The flow in a turbine is also assumed to be

adiabatic, though in actual engines there could be turbine blade cooling.

• Isentropic efficiency of the turbine is defined in a manner similar to that of the compressor.

γγπτ

η

/)1(0504

0504

11

ratio pressuregiven for n compressio of work Idealratio pressuregiven for n compressio of work Actual

−−−

=−−

==

=

t

t

sti

t

t

hhhh

ww


Lect-8

Turbine performance

s

T

04

P05

P04

0505s

T05T05s

T04

Actual and ideal turbine processes


Lect-8

Turbine performance• The polytropic efficiency, ηpoly, is defined

as

[ ] 00

00

00

00

0

0

0

0

0

0

/)1(00

0

0

0

0

//)1(/

//

1 Therefore, constant.

gives,relation isentropic the turbine,idealan For

change pressure aldifferenti afor work turbineIdealchange pressure aldifferenti afor work turbineActual

PdPTdT

TdTTdT

dTdT

PdP

γγ

TdT

PT

dTdT

dhdh

dwdw

iipoly

ii

ii

iii

poly

γγη

η

γγ

−===

−=

×=

===

=

−


Lect-8

Turbine performance

[ ]

( )( )

( )( )

.efficiencypolytropicconstant a assuming ratio pressure with the

efficiency isentropic therelatesequation above The1

111

1,

05, and 04 statesbetween gIntegratin

/1

/1

/1

)1(/t

γγ

γηγ

η

ηγγ

ππ

ττη

τπ

−

−

−

−−−

=−−

=

=

t

t

t

tt

t

poly

poly

poly

or


Lect-8

Nozzle performance

• The flow in the nozzle is also adiabatic.• However losses in a nozzle could occur due

to incomplete expansion (under or over-expansion).

• Friction may reduce the isentropic efficiency.

• The efficiency is defined by

sn hh

hh

706

706

−−

=η


Lect-8

Nozzle performance

s

h06

P7

P6

7s

Actual and ideal nozzle processes

P06

7


Lect-8

Afterburner performance• Afterburner is thermodynamically similar to

a combustion chamber. • The performance parameters for an

afterburner is thus the combustion efficiency and the total pressure loss.

• In case of engines with afterburning, the corresponding performance parameters for an afterburner needs to be taken into account.


Lect-8

Mechanical efficiency• Mechanical efficiency is sometimes used to

account for the loss or extraction of power on that shaft.

• Mechanical efficiency is defined as

• Mechanical efficiency is less than one due to losses in power that occur from shaft bearings and also power extraction for driving accessories like oil and fuel pumps.

t

Cm W

W

==

turbinefromshaft theenteringpower compressor shaft to theleavingpower η


Lect-8

Typical component efficienciesComponent Figure of merit Type Value

Diffuser πd SubsonicSupersonic

0.95-0.980.85-0.95

Compressor ηC - 0.85-0.90

Burner ηbπb

- 0.96-0.990.90-0.95

Turbine ηt UncooledCooled

0.85-0.920.84-0.90

Afterburner ηabπab

- 0.96-0.990.90-0.95

Nozzle ηn - 0.95-0.98

Mechanical ηm - 0.96-0.99


Lect-8

In this lecture...

• Cycle components and component performance– Intake– Compressor/fan– Combustion chamber– Turbine– Nozzle


Lect-8

In the next lecture...

• Tutorial on ideal cycles and component performance.

Documents

Lect-8 - NPTELnptel.ac.in/courses/101101002/downloads/Lect-08.pdfhigh pressure and temperature – Combustion chamber: fuel is added here, combustion results in high temperature and