jetenige

1. Introduction to Jet Propulsion
P MV Subbarao
Professor
Mechanical Engineering Department
Strong and Reliable Muscles for the Aircraft……

2. Global Momentum Analysis

3. Momentum Equation
pinlet
pexit
Vac Vjet
∑ =
dt
dM
F cm
surface
Reynolds Transport Theorem:
inletexit
cvcm
MM
dt
dM
dt
dM  −+=
Newton’s Second Law of Motion

4. inletexit
cv
surface MM
dt
dM
F  −+=∑
For a frictionless flight, pressure forces are only the
surface forces…
inletexit
cv
ductwallexitexitinletinlet MM
dt
dM
FApAp  −+=−− ∑∑
Steady state steady flow
inletexitductwallexitexitinletinlet MMFApAp  −=−− ∑∑
airairjetjetductwallexitexitinletinlet VmVmFApAp  −=−− ∑∑
airairjetjetexitexitinletinletductwall VmVmApApF  +−−= ∑∑

5. airairjetjetexitexitinletinletductwall VmVmApApF  +−−= ∑∑
Pressure Thrust Momentum Thrust
At design cruising conditions : Pressure thrust is zero.
airairjetjetthrust VmVmF  −=
atmexitinlet ppp ==

6. Generation of Thrust : The Capacity
acairjetjetT VmVmF  −=
Thrust
( ) acairjetfuelairT VmVmmF  −+=
( ){ }acjetairT VVfmF −+= 1
f : Fuel-air ratio

7. Dynamic Equilibrium : Cruising Vehicle
For a cruising vehicle:
( ){ } Vehicleon1 dragVVfmF acjetairT =−+= 
( ){ }
2
1
2
air
ac
acdragacjetair
V
ACVVfm ρ=−+

8. Drag on Aircraft

9. Generation of Lift

10. Drag Coefficient of an Air Craft

11. Generation of Lift

12. Drag Coefficient of an Air Craft

13. Lift - to - Drag Ratio
Flight article Scenario L/D ratio
Virgin Atlantic
GlobalFlyer
Cruise 37[
Lockheed U-2 Cruise ~28
Rutan Voyager Cruise[4]
27
Albatross 20
Boeing 747 Cruise 17
Common tern 12
Herring gull 10
Concorde M2 Cruise 7.14
Cessna 150 Cruise 7
Concorde Approach 4.35
House sparrow 4

14. Minimum Drag Coefficients
Aircraft Type Aspect Ratio CDmin
RQ-2 Pioneer Single piston-engine UAV 9.39 0.0600
North American Navion Single piston-engine general aviation 6.20 0.0510
Cessna 172/182 Single piston-engine general aviation 7.40 0.0270
Cessna 310 Twin piston-engine general aviation 7.78 0.0270
Marchetti S-211 Single jet-engine military trainer 5.09 0.0205
Cessna T-37 Twin jet-engine military trainer 6.28 0.0200
Beech 99 Twin turboprop commuter 7.56 0.0270
Cessna 620 Four piston-engine transport 8.93 0.0322
Learjet 24 Twin jet-engine business jet 5.03 0.0216
Lockheed Jetstar Four jet-engine business jet 5.33 0.0126
F-104 Starfighter Single jet-engine fighter 2.45 0.0480
F-4 Phantom II Twin jet-engine fighter 2.83 0.0205 (subsonic)
0.0439 (supersonic)
Lightning Twin jet-engine fighter 2.52 0.0200
Convair 880 Four jet-engine airliner 7.20 0.0240
Douglas DC-8 Four jet-engine airliner 7.79 0.0188
Boeing 747 Four jet-engine airliner 6.98 0.0305
X-15 Hypersonic research plane 2.50 0.0950

15. Propulsive Power or Thrust Power:
( ){ }acjetairacacTp VVfmVVFP −+== 1
Specific Thrust S
( ) acjet
air
T
VVf
m
F
S −+== 1

Measure of compactness of a jet engine:

16. Thrust Specific Fuel Consumption TSFC
( ){ } ( ){ }acjetacjetair
fuel
T
fuel
VVf
f
VVfm
m
F
m
TSFC
−+
=
−+
==
11

Measure of fuel economy:

17. Aviation Appreciation
Propulsion Efficiency
JettheofPowerKineticAvailable
PowerThrust
propulsion =η
( ){ }22
1
2
acjet
air
acT
propulsion
VVf
m
VF
−+
=

η
( )( )
{ }22
)1(
2
1
acjet
air
acacjetair
propulsion
VVf
m
VVVfm
−+
−+
=


η

18. Jet Characteristics
• Quantities defining a jet are:
– cross-sectional area;
– composition;
– velocity.
jetjetjetjet VAm ρ=
acairjetjetjetT VmVAF −=
2
ρ
acairjetjetT VmVmF  −=
Of these, only the velocity is a truly characteristic feature and is of
considerable quantitative significance.

19. Jet Characteristics of Practical Propulsion Systems
System Jet Velocity (m/s)
Turbofan 200 - 600
Turbojet (sea-level, static) 350 - 600
Turbojet (Mach 2 at 36000 ft) 900 - 1200
Ramjet (Mach 2 at 36000 ft) 900 - 1200
Ramjet (Mach 4 at 36000 ft) 1800 - 2400
Solid Rocket 1500 – 2600
Liquid Rocket 2000 – 3500

20. Nozzle : Steady State Steady Flow
First Law :
No heat transfer and no work transfer & No Change in potential
energy.
in jet
cv
jetin
cv Wgz
V
hmgz
V
hmQ  +





++=





+++
22
22
jetin
V
h
V
h 





+=





+
22
22

21. Combined analysis of conservation of mass and first law
22








+=






+
jetjet
jet
inin
in
A
m
h
A
m
h
ρρ

A SSSF of gas through variable area duct can interchange the
enthalpy and kinetic energy as per above equation.
Consider gas as an ideal and calorically perfect.
0
22
22
Tc
c
V
Tc
c
V
Tc p
p
jet
jetp
p
in
inp =








+=








+

22. γ
γ 1−








=
jet
in
jet
in
p
p
T
T
Isentropic expansion of an ideal and calorically perfect gas.