Parametric Cycle Analysis of Ideal Turbo Jet Engine

Parametric Cycle Analysis of Ideal Turbo Jet Engine

P M V Subbarao

Professor

Mechanical Engineering Department

Lecture - 8

Selection of Optimal Design Cruising Conditions….

Effect of Flight Mach Number on Compactness

Mac

Spe

cifi

c T

hrus

t kN

.s/k

g

0,cc=4.5

r0p=1

r0p=2

r0p=3

r0p=5

r0p=10

r0p=20r0p=30

Effect of Flight Mach Number on Fuel Air Ratio

Mac

f

r0p

1

235

10

20

30

0,cc=4.5

Effect of Flight Mach Number on Fuel EconomyT

SF

C k

g/ k

N.h

r

Mac

r0p=1

r0p=3

r0p=5

r0p=10r0p=20

r0p=30

r0p=2

0,cc=4.5

Effect of Flight Mach Number on Fuel Air Ratio

Mac

f

r0p

1

235

10

20

30

0,cc=4.5

Effect of Flight Mach Number on Propulsion Efficiency

Mac

propulsion

0,cc=4.5

r0p =2

r0p = 5

r0p = 30

Effect of Flight Mach Number on Thermal Efficiency

Mac

Thermal

r0p

0,cc=4.5

Effect of Flight Mach Number on Overall Efficiency

Mac

O

r0p

0,cc=4.5

Effect of Pressure Ratio on Compactness

rp

Spe

cifi

c T

hrus

t kN

.s/k

gMac=0

Mac=0.5

Mac=1.5

Mac=2.0

Mac=2.5Mac=3.0

Mac=1.0

0,cc=4.5

Effect of Pressure Ratio on Fuel Economy

rp

TS

FC

kg/

kN

.hr

Mac

0,cc=4.5

Effect of Pressure Ratio on Fuel Air Ratio

rp

f

0,cc=4.5

Effect of Pressure Ratio on Propulsive Efficiency

rp

propulsion

0,cc=4.5

Effect of Pressure Ratio on Thermal Efficiency

rp

Thermal

0,cc=4.5

Effect of Pressure Ratio on Overall Efficiency

rp

Overall

0,cc=4.5

Effect of Pressure Ratio on Compactness

rp

Spe

cifi

c T

hrus

t kN

.s/k

gMac=0

Mac=0.5

Mac=1.5

Mac=2.0

Mac=2.5Mac=3.0

Mac=1.0

0,cc=4.5

Turbo Jet with Afterburner

inlet

1 23 4 5 6 7

Elevation of Temperature of the Jet:

After Burner : More Energy at Same Life

, , 06 , 05AB air fuel comb fuel AB p air fuel comb pQ m m m c T m m c T

, , , 06 , 05. .fuel ab air fuel comb fuel AB p air fuel comb pm H V m m m c T m m c T

, , 06 05. . 1 1fuel ab air comb fuel AB p air comb pm H V m f m c T m f c T

, 06 05

,

1 1. . air comb fule AB p air comb p

fuel ab

m f m c T m f c TH V

m

0506 11.. TfTfff

cVH combabcomb

ab

p

0506 11..

TfTffVH

cf combabcomb

pab

, 06 05

,

1 1. . air comb fule AB p air comb p

fuel ab

m f m c T m f c TH V

m

Minimum Jet Temperature

07 06 0, 0abT T T Jet Static Temperature :

Jet Total Temperature :

1

0,7 0

0 , 0

ab

p comp

pT T

p

1 1

77 06 0, 0

05 05ab

p pT T T

p p

Characterization of AB Jet

Maximum obtainable Mach number of Jet

077

27

11

2

TT

M

Performance of Jet

7 11T comb abF m f f V V

Propulsive Power or Thrust Power:

1 1 7 11p T comb abP F V V m f f V V

Specific Thrust S 7 11 comb abS f f V V

Thrust Specific Fuel Consumption TSFC

7 11fuel fuel

T comb ab

m mTSFC

F m f f V V

AB & No ABS

peci

fic T

hrus

t

TS

FC

W/O AB

W AB

W/O AB

W AB

rp = 10

Ideal Afterburning Turbojet Engine Performance : Specific Thrust Vs Compressor Pressure Ratio

Spe

cific

Thr

ust

kN.s

/kg

rp

2.5

3.0

Compressor Pressure Ratio : rp

Spe

cific

Thr

ust

kN.s

/kg

Maircraft

Ideal Turbojet Engine Performance : Specific Thrust Vs Compressor Pressure Ratio

Ideal Afterburning Turbojet Engine Performance : TSFC Vs Compressor Pressure Ratio

rp

TS

FC

kg/

kN

.hr

Effect of Pressure Ratio on Fuel Economy

rp

TS

FC

kg/

kN

.hr

Mac

Constant TIT

rp

f

Ideal Afterburning Turbojet Engine Performance : TSFC Vs Compressor Pressure

Ratio

Ideal Afterburning Turbojet Engine Performance : Efficiencies Vs Compressor Pressure Ratio

rp

Summary of Turbojet Performance

• A high compressor pressure ratio is desirable for subsonic flight for good specific thrust and low fuel consumption.

• A special care must be used in selecting the compressor pressure ratio for the supersonic flight Mach number.

• Rapid drop in specific thrust with pressure ratio at supersonic conditions.

• There exist a pressure ratio for each Mach number of a supersonic flight, that gives maximum specific thrust.

• The fuel air ratio decreases with increasing Mach number and compressor pressure ratio.

• Propulsive efficiency increases with increasing Mach number.

Rapid fall in specific thrust under supersonic conditions is a serious concern.

Optimization of Turbojet Performance

P M V Subbarao

Professor

Mechanical Engineering Department

Better Deal for Compactness & Fuel Economy…

Optimum Compressor Pressure Ratio

• At supersonic flight conditions, a maximum value of Specific thrust is Exhibited at certain compressor pressure ratio.

• The value of pressure ratio to maximize the specific thrust at a given flight Mach number should be found by differentiation of specific thrust equation.

1 jet aircraftS f V V

0 , 0 ,

0 0

( , & )0p comp ac p cc

p p

F r MS

r r

0 , 0,1 ( , & )jet aircraft p comp ac ccS f V V F r M

For Maximum Specific Thrust:

0 , 0 ,

0 0

( , & )0p comp ac p cc

p p

F MS

0 , 0 ,

0 0

1 ( , & )0

jet p comp ac p cc

p p

f V F M

compp

ccacccturbpjet McV

,0

,02,0,0 2

11

1

2

compp

ccacccturbp

jet Mc

V

,0

,02,0,0

2

2

11

1

2

0 0 ,

00

. .cc p comp

ccp

fH V

c T

op

compp

ccacccturbp

op

jet Mf

c

Vf

,0

,02,0,0

2

21

11

121

cc

comppturbop f ,0

,0, 1

11

r0p,opt

Mac

Optimum Compressor Pressure Ratio Vs Mach Number

W/o AB

W AB

Optimal Turbojet Engine PerformanceS

peci

fic T

hrus

t kN

.s/k

g

TS

FC

kg/

kN

.hr

Without After Burner

With After Burner

Mac

Energy Flow in Jet Engine

Long distance travel demands high flight velocity.High flight velocity leads to drop in compactness and fuel economy.A Single Jet is blackmailing the jet engine !!!

Energy input