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TRANSCRIPT
Jet Propulsion
Lecture-12
Ujjwal K Saha, Ph. D.Department of Mechanical Engineering
Indian Institute of Technology Guwahati
Prepared underQIP-CD Cell Project
Diffuser : (a)-(2)Combustor: (2)-(4)Nozzle : (4)-(6)No Turbomachines
D CC N
(a) (1) (2) (3) (4) (5) (6)
D= DiffuserCC= Combustion chamberN= Nozzle
Fuel inletRamjet Engine
Characteristics:
Can not produce static thrust
Incapable of steady operation at M < 1
Diffuser
Operated from A/c in flight
Initial velocity by launching rockets
Supersonic
Subsonic
Conversion of KE to PE (transformation by Ram effect)
High flight speeds render increase in pressure rise.Supersonic diffusion is caused through a system of shocks.
Diffuser must be designed very efficiently. Supersonic diffuser at a given M does not
perform well at other Mach Number, unless the geometry is variable.
Beyond M = 6, combustion is inefficient and incomplete because of very high temperature of entry air, and this gives improper expansion in the nozzle.
M= 0.2 to 0.3 at combustor inlet.
Flame holders (a shielding device to maintain the flame at high velocity streams) is necessary.
Combustor Temperature = 3000 K.
Scramjet:Combustion takes place in supersonic stream.Injection of fuel into supersonic stream, mixing
& burning in a millisecond. Conventional Fuel does not ignite quickly.Gaseous Hydrogen is suitable .
Schematic of Scramjet
National AeroSpace Plane (NASP) Research Vehicle, X-30.
(0a)(02)
(a)
(b)
Pa
p02(04)(06)
T
S
ProcessesCompression (of air) from (a) to (02)Combustion (constant pressure heat addition)Expansion (of combn products) from (04) to (6)
Analysis (Ideal case)
Compression and Expansion Processes are Reversible and adiabatic
Ramjet
Thrust
( )a f j a aF m m C m C= + −
( )1a j am f C C⎡ ⎤= + −⎣ ⎦
Isentropic
Constant Pressure Heat addition
6oa op p∴ =
Stagnation pressure is constant throughout.
Compn
Expann
Ignoring variation of R, γ throughout/ 1
2
/ 126
6
112
112
oaa
a
oj
p Mp
p Mp
γ γ
γ γ
γ
γ
−
−
−⎛ ⎞= +⎜ ⎟⎝ ⎠
−⎛ ⎞= +⎜ ⎟⎝ ⎠
whereMa= Flight Mach No.Mj= Exit Mach No.
(3)
(2)
6( )j a ap p p p= =With We have, j a
jj a
a
jj a
a
M M
aC C
a
TC C
T
=
∴ =
= (4)or,
04
0
j a
j aa
M M
TC CT
=
=
Also for
(5)Now,
( ) 04 02a f a f fm m h m h m Q+ − =
( ) 04 021a f fm f h h m Q⎡ ⎤+ − =⎣ ⎦
( ) 04 021 ff h h fQ+ − =
( )04 0
04
0 0
/ 1a
f
p a a
T Tf Q T
C T T
−∴ =
−(6)
1/0 0a a
a a
T pT p
γ γ−⎛ ⎞
= ⎜ ⎟⎝ ⎠
1/06 06
6 6
T pT p
γ γ−⎛ ⎞
= ⎜ ⎟⎝ ⎠
0 06
6
0 06
6
a
a
a
a
p pp pT TT T
=
=
∴ =
∵
6 06 04
0 0a a a
T T TT T T
= =or,
and
( ) ( )1 1 1jj a a
a a
CF f C C C fm C
⎡ ⎤= + − = + −⎢ ⎥
⎣ ⎦
( ) 04
01 1a
a
TM RT fT
γ⎡ ⎤
= + −⎢ ⎥⎢ ⎥⎣ ⎦
(7)
04 04 0420 0
1. . 112
a
a a a a a
T T T TT T T T Mγ= =
−+
Now,
1/ 2204 04
0
112 a
a a
T T MT T
γ −−⎛ ⎞∴ = +⎜ ⎟⎝ ⎠
From (1),
( )1/ 2
204 11 1 12a a
a a
TF M RT f Mm T
γγ−⎡ ⎤−⎛ ⎞⎢ ⎥∴ = + + −⎜ ⎟
⎝ ⎠⎢ ⎥⎣ ⎦(8)
/f a
a
m fm fTSFCF F F m
= = =and
Actual Case: Irreversibility's
Diffuser: shocks and wall friction
Nozzle: friction and heat transfer
(0a)
(02)
p02(04)
p04
pb(b)
pa
(a)
T
S
Aerodynamic losses
02
0d
a
pp
π =
04
02c
pp
π =
06
04n
pp
π =
Overall stagnation Pressure Ratio
06overall
0d c n
a
pp
π π π π= =
Actual exhaust pressure may not be equal to( )6 or jp p ap
We have, / 1206
1/2 06
112
112
jj
jj
p Mp
pMp
γ γ
γ γ
γ
γ
−
−
−⎛ ⎞= +⎜ ⎟⎝ ⎠
⎛ ⎞−+ = ⎜ ⎟⎜ ⎟
⎝ ⎠1/
2 06
1/06 0
0
1/1/0 06
0
2 11
2 . . 11
2 . 11
jj
a a
a j a
a a
a a j
pMp
p p pp p p
p p pp p p
γ γ
γ γ
γ γγ γ
γ
γ
γ
−
−
−−
⎡ ⎤⎛ ⎞⎢ ⎥= −⎜ ⎟⎜ ⎟⎢ ⎥− ⎝ ⎠⎢ ⎥⎣ ⎦⎡ ⎤⎛ ⎞⎢ ⎥= −⎜ ⎟⎜ ⎟⎢ ⎥− ⎝ ⎠⎢ ⎥⎣ ⎦⎡ ⎤⎛ ⎞⎛ ⎞⎢ ⎥= −⎜ ⎟⎜ ⎟ ⎜ ⎟⎢ ⎥− ⎝ ⎠ ⎝ ⎠⎢ ⎥⎣ ⎦
Or,
1/2 22 11 1
1 2a
j a d c nj
pM Mp
γ γγ π π π
γ
−⎡ ⎤⎛ ⎞−⎛ ⎞⎢ ⎥= + −⎜ ⎟⎜ ⎟⎜ ⎟⎢ ⎥− ⎝ ⎠⎝ ⎠⎢ ⎥⎣ ⎦(9)
Again,
0404
.
jj
j
jj j j j
CM
RT
TC M RT M R T
T
γ
γ γ
=
∴ = =
0404
204
1./
1/ 12
jj
j j j
M RTT T
C M RT M
γ
γγ
=
−⎛ ⎞= +⎜ ⎟⎝ ⎠
(10)
( ) ( )
( )( )
1
a f j a a j j a
j j aj a
a a
F m m C m C A p p
A p pF f C Cm m
= + − + −
−⎡ ⎤∴ = + − +⎣ ⎦
Actual Thrust
(12)
( )04 0
04
0 0
/ 1a
B f
p a a
T Tf Q T
C T Tη
−∴ =
−(11)
where ηB = combustion efficiency
Ramjets - Basic Operating Features
• Air decelerated in intake (diffuser) and pressure rises due to ram effect.
• Known as ram pressure and significant at supersonic speeds.
• A ramjet therefore needs neither a compressor nor a turbine, simplifying the design and reducing the cost.
• Greatest disadvantage is that it has to be accelerated up to typically M > 2.0 before it produces any useful thrust.
• Also complicated supersonic intake required to avoid shock losses - could be nose, side or ventral mounted.
Ramjets (Front Intake) for GW
• Jet velocity: 900-2400m/s
• Complex intake
• No static thrust (has to be boosted up to speed)
• Mechanically simple, reliable cheap & tolerant of high temperatures.
Sea Dart
Ideal ramjet thrust and fuel consumption
Ideal ramjet thrust and efficiencies
T-s diagram showing aerodynamic losses
Ramjet thrust and fuel consumption
Ramjet thrust and efficiencies
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
Jet Characteristics of Propulsion Systems
SummarySummary
oo Ramjet Ramjet oo Concept of Scramjet Concept of Scramjet oo Ideal Cycle Analysis Ideal Cycle Analysis oo Actual Cycle AnalysisActual Cycle Analysisoo Estimation of Thrust etc.Estimation of Thrust etc.
28
References & Web Resources1. Hill, P.G., and Peterson, C.R., (1992), Mechanics and Thermodynamics of Propulsion,
Addison Wesley.2. Saravanamuttoo, H.I.H, Rogers, G.F.C, and. Cohen, H, (2001), Gas Turbine Theory,
Pearson Education.3. Oates, G.C., (1988), Aerothermodynamics of Gas Turbine and Rocket Propulsion, AIAA,
New York.4. Mattingly, J.D., (1996), Elements of Gas Turbine Propulsion, McGraw Hill.5. Cumpsty, N.A., (2000), Jet Propulsion, Cambridge University Press.6. Bathie, W.W., (1996), Fundamentals of Gas Turbines, John Wiley.7. Treager, I.E., (1997), Aircraft Gas Turbine Engine Technology, Tata McGraw Hill. 1. http://www.soton.ac.uk/~genesis2. http://www.howstuffworks.co3. http://www.pwc.ca/4. http://rolls-royce.com5. http://www.ge.com/aircraftengines/6. http://www.ae.gatech.edu7. http://www.ueet.nasa.gov/Engines101.html8. http://www.aero.hq.nasa.gov/edu/index.html9. http://home.swipnet.se/~w65189/transport_aircraft10. http://howthingswork.virginia.edu/11. http://www2.janes.com/WW/www_results.jsp12. http://www.allison.com/13. http://wings.ucdavis.edu/Book/Propulsion14. http://www.grc.nasa.gov15. http://www.hq.nasa.gov/office/pao/History16. http://membres.lycos.fr/bailliez/aerospace/engine17. http://people.bath.ac.uk/en2jyhs/types.htm18. http://roger.ecn.purdue.edu/~propulsi/propulsion/rockets