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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