Anatomy and SSSF Analysis of Ideal Turbo Jet Engine

P M V Subbarao

Professor

Mechanical Engineering Department

Features of A True Flying Machine Muscles ….

Anatomy of A Jet Engine

1 2 3 4 5 6

Vac

Vjet

Ideal Turbo Jet Cycle

T

1

3

4

5

p

s

1

34

5

s

2 6 : Jet

6: Jet

2

Anatomy of A Jet Engine : Intake

1 2

1 -- 2s = constantT: Increasingp: Increasing

Vac

Vjet

Inlet : Steady State Stead Flow

Conservation of mass mmm 21

CVCV WgzV

hmgzV

hmQ

2

2

1

2

22

First Law :

222111 VAVA

22

22

2

21

1

Vh

Vh

No heat transfer and no work transfer : A Pure Passive compressor : No Change in potential energy.

Assume gas as an ideal and calorically perfect.

22

22

2

21

1

VTc

VTc pp

p

pp

p c

VTc

c

VTc

22

22

2

21

1

eTemperaturDynamicc

V

p

2

2

Kinetic energy that can produce enthalpy and hence temperature rise and vice versa.

More fundamentally,

• Temperature (Static Temperature) is a measure of microscopic kinetic energy.

• Dynamic Temperature is a measure of macroscopic kinetic energy.

• Define:

• Total Temperature = Static Temperature + Dynamic Temperature

0102

22

2

21

1 22TcTc

c

VTc

c

VTc pp

pp

pp

• A fluid at rest (zero macroscopic kinetic energy) can convert its internal energy or enthalpy into kinetic energy, provided:

• It is above absolute zero pressure and temperature.

• A moving fluid (finite macroscopic kinetic energy) can convert its kinetic energy into internal energy or enthalpy.

• Maximum possible conversion corresponds to fluid coming to rest.

p

pp

p c

VTc

c

VTc

22

22

2

21

1 222111 VAVAwith

Measure of An Action Measure of Hardware

Measure of benefits at zero running cost Measure of capital cost

An Inlet of A Jet engine is a passive compressor, i.e. zero running cost

Measure of Compression

p

pp

p c

VTc

c

VTc

22

22

2

21

1

An ideal intake device is an isentropic compressor with zero power input.

1

1

2

1

2

T

T

p

p

At design condition: 1

22

T

T

p

p

Maximum Possible Compression

0102

22

2

21

1 22TcTc

c

VTc

c

VTc pp

pp

pp

An inlet device with zero exit velocity will produce maximum compression.

1

1

02

1

02

T

T

p

p

At design condition:

10202

T

T

p

p 10101

T

T

p

p 100

T

T

p

p

Control Volumes Can never Afford to Generate Maximum Compression

Total Pressure and Total Temperature are just reference measures…..

Anatomy of A Jet Engine : Compressor

2 3 2 -- 3s = constantT : increasingp : increasing

Vac

Vjet

Compressor : Steady State Stead Flow Process

CVCV WgzV

hmgzV

hmQ

3

2

2

2

22

First Law :

Conservation of mass mmm 32 333222 VAVA

No heat transfer, change in potential energies is negligible

3

2

2

2

22

Vh

VhmW compressor

CVWV

hmV

hm

3

2

2

2

22

3

2

2

2

22

VTc

VTcmW ppcompressor

0302 TTcmW pcompressor

0302 hhmW compressor

A compressor of A Jet engine is an active device, i.e. there exist capital and running cost.

If so, why is this?

Do I get more befit than the expenditure?

Does it also compensate extra capital cost too?

Measure of Extra Life Generation

compressorpp WTcmTcm

0203

Isentropic active compression

1

02

03

02

03

T

T

p

p

1

2

02

2

02

T

T

p

p 1

3

03

3

03

T

T

p

p 1

2

3

2

3

T

T

p

p

Anatomy of A Jet Engine: Combustion Chamber

3 4 3 -- 4s : increasingT: increasingp : constant???

Vac

Vjet

3 – 4 : Isobaric Heat addition

CVQ

No work transfer and change in potential energies is negligible

CVCV WgzV

hmgzV

hmQ

3

2

4

2

2

3 22

3

2

4

2

2

3 22

Vhm

VhmQCV

3 – 4 : Ideal Combustor

No work transfer and change in potential energies is negligible & adiabatic combustion

fmfmmmm airfairgas 11

CV

gas

gas

air

airfuelCV WgzV

hmgzV

hmHVmQ

22

22

gas

gas

air

airfuel

Vhm

VhmHVm

22

22

03 041fuel p pm HV mc T m f c T

How much fuel should be added to get High fuel economy?

How to get a compact jet engine ?

0403 )1( TcfTcHVf pp

pc

HVfTTf

0304)1(

Anatomy of A Jet Engine:Turbine

4 54 -- 5s = constantT : decreasingp : decreasing

Vac

Vjet

Turbine : SSSF Process :

No heat transfer. Change in potential energies is negligible

4

5

T

04 051turbineW m f h h

2 2

4 5

1 12 2

CVCVV V

Q m f h gz m f h gz W

CVWV

hfmV

hfm

5

2

4

2

21

21

04 051turbine pW m f c T T

Turbine is to produce just enough power.

turbine compressorW W

04 05 02 031p pm c f T T m c T T

02 03

05 04 1

T TT T

f

The vigor of Jet: 051pmc f T

Anatomy of A Jet Engine : Nozzle

5 65 -- 6s = constantT : DecreasingP: decreasing

Vac

Vjet

Nozzle : Steady State Stead Flow

2 25 6

5 62 2

V Vh h

0

26

6

25

5 22Tc

c

VTc

c

VTc p

pp

pp

Anatomy of An Ideal Jet Engine

1 2 3 4 5 6

1 -- 2s = constantT0 = constantP0 = constant

2 -- 3s = constantT0 = increasingP0 = increasing

3 -- 4s = increasingT0 = increasingP0 = constant

4 -- 5s = constantT0 = decreasingP0 = decreasing

5 -- 6s = constantT0 = constantP0 = constant

Ideal Turbo Jet Cycle

T0

1,2

3

4

5,6

s

p0

s

1,2

34

5,6