Mel341 3

Introduction to Jet Propulsion

P M V Subbarao

Professor

Mechanical Engineering Department

Strong and Reliable Muscles for the Aircraft……

Global Momentum Analysis

Momentum Equation

pinletpexit

Vac Vjet

∑ =dt

dMF cmsurface

Reynolds Transport Theorem:

inletexitcvcm MM

dt

dM

dt

dM −+=

Newton’s Second Law of Motion

inletexitcv

surface MMdt

dMF −+=∑

For a frictionless flight, pressure forces are only the surface forces…

inletexitcv

ductwallexitexitinletinlet MMdt

dMFApAp −+=−− ∑∑

Steady state steady flow

inletexitductwallexitexitinletinlet MMFApAp −=−− ∑∑

airairjetjetductwallexitexitinletinlet VmVmFApAp −=−− ∑∑

airairjetjetexitexitinletinletductwall VmVmApApF +−−= ∑∑

airairjetjetexitexitinletinletductwall VmVmApApF +−−= ∑∑

Pressure Thrust Momentum Thrust

At design cruising conditions : Pressure thrust is zero.

airairjetjetthrust VmVmF −=

atmexitinlet ppp ==

Generation of Thrust : The Capacity

acairjetjetT VmVmF −=Thrust

( ) acairjetfuelairT VmVmmF −+=

( ){ }acjetairT VVfmF −+= 1

f : Fuel-air ratio

Dynamic Equilibrium : Cruising Vehicle

For a cruising vehicle:

( ){ } Vehicleon 1 dragVVfmF acjetairT =−+=

( ){ }2

12

airac

acdragacjetair

VACVVfm ρ=−+

Drag on Aircraft

Generation of Lift

Drag Coefficient of an Air Craft

Generation of Lift

Drag Coefficient of an Air Craft

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

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

Propulsive Power or Thrust Power:

( ){ }acjetairacacTp VVfmVVFP −+== 1

Specific Thrust S

( ) acjetair

T VVfm

FS −+== 1

Measure of compactness of a jet engine:

Thrust Specific Fuel Consumption TSFC

( ){ } ( ){ }acjetacjetair

fuel

T

fuel

VVf

f

VVfm

m

F

mTSFC

−+=

−+==

11

Measure of fuel economy:

Aviation Appreciation

Propulsion Efficiency

Jet theofPower Kinetic Available

PowerThrustpropulsion =η

( ){ }2212 acjetair

acTpropulsion

VVfm

VF

−+=

η

( ) ( ){ }22)1(

2

1

acjetair

acacjetairpropulsion

VVfm

VVVfm

−+

−+=

η

Jet Characteristics

• Quantities defining a jet are:– cross-sectional area;– composition;– velocity.

jetjetjetjet VAm ρ=

acairjetjetjetT VmVAF −= 2ρ

acairjetjetT VmVmF −=

Of these, only the velocity is a truly characteristic feature and is of considerable quantitative significance.

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

Nozzle : Steady State Steady Flow

First Law :

No heat transfer and no work transfer & No Change in potential energy.

in jet

cv

jetin

cv WgzV

hmgzV

hmQ +

++=

+++

22

22

jetin

Vh

Vh

+=

+

22

22

Combined analysis of conservation of mass and first law

22

+=

+jetjet

jetinin

in A

mh

A

mh

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

22Tc

c

VTc

c

VTc p

p

jetjetp

p

ininp =

+=

+

γγ 1−

=

jet

in

jet

in

p

p

T

T

Isentropic expansion of an ideal and calorically perfect gas.