analysis of thrust equation for ideal turbo jet engine p m v subbarao professor mechanical...

Analysis of Thrust Equation for Ideal Turbo Jet Engine

P M V Subbarao

Professor

Mechanical Engineering Department

Understanding the Features of A True Flying Machine Muscles

….

Ideal Turbo Jet Cycle

T0

1,2

3

4

5,6

s

p0

s

1,2

34

5,6

Ideal Turbo Jet Cycle

Thrust

acjetairT VVfmF 1

pTVStation ac &,:1

fppfV jet &, 030

pTVStation ac &,:1

002002 &, ppTTVci

0,0030,003 & prpTT comppcompp

0,0040,004 & prpTT comppcc

cc

p

comppcc

TcVH

f

00

,00

..

Thrust

Isentropic Expansion in an Active Turbine

0,0,0,00405 TTT turbpccturbp

0,0,005 prrp comppturbp

turbppturbine TcfmW ,004 11

Theory of Jet Propulsion : Jet Enough Work

The power input to the compressor = The power output of the turbine

turbinecompressor WW

turbppcomppp TcfmTcm ,004,00 111

turbpcompp TfT ,004,00 111

0,004 TT cc

0,0,0,00 111 TfT ccturbpcompp

ccturbpcompp f ,0,0,0 111

cc

comppturbp f ,0

,0,0 1

11

cc

comppturbp f ,0

,0,0 1

11

cc

comppccpturbine

fTcfmW

,0

,00,0 1

111

05041 TTcfmW pturbine

Isentropic Expansion in a Passive Turbine(Nozzle)

Thermodynamic SSSF model for Nozzle

0605 11 hfmhfm

06050605 & ppTT

2

26

605

VTcTc pp

605

26

2TTc

Vp

1

0505

1

05

6056

p

pT

p

pTT

Limit of Utilization: Open Cycle Engine: Just to Ambient Pressure!!!

04,00504,005 & prpTT turbpturbp

1

04,004,06

pr

pTT

turbpturbp

1

04

1

,004,06

1

p

p

rTT

turbpturbp

1

04046

p

pTT

0,00304 prpp compp

1

0,0046

pr

pTT

compp

1

0,0

046

1

p

p

r

TT

compp

1

0,0

046

p

pTT

compp

1

0,0

,006

p

pTT

compp

cc

605

26

2TTc

Vp

Maximum Obtainable Jet Kinetic Energy:

compp

ccTT,0

,06

04,0

,005 1

11 T

fT

cc

compp

04,005 TT turbp

00

04

,0

,005 1

11 T

T

T

fT

cc

compp

0,0,0

,005 1

11 T

fT cc

cc

compp

cc

p

comppcc

TcVH

f

00

,00

..

62 05

26 TTcV

p

compp

ccTT,0

,06

0,0,0

,005 1

11 T

fT cc

cc

compp

62 05

26 TTcV

p

compp

cccc

cc

comppp TT

fc

V

,0

,00,0

,0

,02

6

1

11

2

cc

p

comppcc

TcVH

f

00

,00

..

compp

cccc

cc

ccp

comppcc

comppp TT

TcVH

cV

,0

,00,0

,0

00

,00

,02

6

..1

11

2

compp

cccc

cc

comppp T

T

fTc

V

,0

,00,0

,0

,02

6

1

11

2

Generation of Thrust : The Capacity

acjetT VVfmF 1

ac

compp

cccc

cc

compppT V

T

T

fTcfmF

,0

,00,0

,0

,0

1

1121

compp

cccc

cc

compppjet T

T

fTcV

,0

,00,0

,0

,0

1

112

Specific Thrust S

acjet VVfS 1

ac

compp

cccc

cc

comppp V

T

T

fTcfS

,0

,00,0

,0

,0

1

1121

Propulsive Power or Thrust Power:

acjetacacTp VVfmVVFP 1

Thrust Specific Fuel Consumption TSFC

acjetacjet

fuel

T

fuel

VVf

f

VVfm

m

F

mTSFC

11

ac

compp

cccc

cc

comppp V

TT

fTcf

fTSFC

,0

,00,0

,0

,0

1

1121

Aviation Appreciation

Propulsion Efficiency

Jet theofPower Kinetic Available

PowerThrustpropulsion

2212 acjet

acTpropulsion

VVfm

VF

22)1(

2

1

acjet

acacjetpropulsion

VVfm

VVVfm

22)1(

12

acjet

acacjetpropulsion VVf

VVVf

compp

cccc

cc

compppjet T

T

fTcV

,0

,00,0

,0

,0

1

112

Thermodynamic Appreciation

Thermodynamic Efficiency

InputPower Thermal

Jet theofPower Kinetic Availablethermal

..

12

22

VHm

VVfm

fuel

acjet

thermal

..

121 22

VHf

VVf acjet

thermal

22)1(

12

acjet

acacjetpropulsion VVf

VVVf

thermalpropulsionoveral

..

121 22

VHf

VVf acjet

thermal

22)1(

12

acjet

acacjetpropulsion VVf

VVVf

thermalpropulsionoveral

..

121 22

VHf

VVf acjet

thermal

Jet engine Performance Parameters

ac

compp

cccc

cc

comppp V

TT

fTcf

fTSFC

,0

,00,0

,0

,0

1

1121

ac

compp

cccc

cc

comppp V

T

T

fTcfS

,0

,00,0

,0

,0

1

1121