High Speed Propulsion

KTH Rocket Course 2008

Ulf.Olsson.Thn @Telia.com

V gR= 2

11200 m/sto leave earth.Hyperbolic velocity.

Circular velocity 7900 m/s.Mach 26.

20

0 2

Rg gR

=Isaac Newton:Law of gravity 1687

What velocities?

0V gR=

Perigee Apogee

mV2 /R

mg

The spaceplane would give more flexible space access.(Eugen Sänger and Irene Bredt 1944).

Wings and atmospheric oxygene

The SR71- the highest speed aircraft ever (Mach 3.2)

The limits of the turbojet engine ( )jF m V V= −&

Inletefficiency

Rotationalspeed

Turbineinlettemperature

Chokingturbines

Compressor exit temperatureLimits the pressure ratio

Chokingbypass canal

Staticpressure balance

4 00

2 ( / 1)1 t

F T Tma γ

= −−&

The turbine inlet temperature limits the thrust.

0

5

10

15

20

25

0 1 2 3 4 5 6

Efficiency %

Mach

MaxTIT,Mtip

Designpoint

Throttling down Tt3 = Tcm

Main fuel=0, πc=1

Ramjet mode(afterburner)

Turboramjet

2( / 2)f

FVm h V

η =+&

Close down the turbomachine at high speed

LH2

Supersonic fan for less inlet losses

Precooling for extended turbojet operation

0

5

10

15

20

25

30

35

40

0 1 2 3 4 5 6 7 8Mach

Efficiency %

Precooled +Supersonic fan

Supersonic fan

Base

Ramjet

The principle of a Pulse Detonation Engine (PDE)

Air

Fuel Jet

V1-German WW1 pulsejet

Volvo Aero-id/datum/ 27

p

v

Humphrey (PDE) constant volume combustion

Brayton (ramjet and turbojet)Constant pressure combustion

0

3

4

9

0

5

10

15

20

25

30

35

40

0 1 2 3 4 5 6 7Mach

%ηPDE more efficient than ramjet – less fuel

Ramjet

Pulsejet

f

FVm h

η =&

Fig. 18.4

•High efficicency•Light weight•Simple

0

5

10

15

20

25

30

35

40

0 1 2 3 4 5 6 7Mach

%

Ramjet

0 00/ s

f

Fa I aMm h h

η = =&

PDE has take-off thrust

Pulsejet

max0

2 ( 1)1

taTMTγ

= −−

Same max speed:

where stagnation temp = combustion temp

Fig. 18.4

2 20 0 3 3

1 11 12 2tT T M T Mγ γ− −⎛ ⎞ ⎛ ⎞= + = +⎜ ⎟ ⎜ ⎟

⎝ ⎠ ⎝ ⎠

Increase M3 to keep T3 low to prevent dissociation (1560 K)

0 3

The idea of the scramjet

30

0

2 1 11 2

TMT

γγ

⎡ ⎤+⎛ ⎞⟩ −⎢ ⎥⎜ ⎟− ⎝ ⎠⎣ ⎦Scramjet M3 >1 if =6

1560 K

US scramjet test hardware

44 4 4 4

3 3 3 3 3

t

t

TV M a TV M a T T

= = =

3 0 kiV V η=

3 4

3 4M M=

40

3

tj ki kc kn

t

TV VT

η η η=

The jet speed of a scramjet

0

Kinetic efficiencies

Constant Machin combustor

3 4

( ) 4 31 p t p t bf C T C T fhη+ − =

3 0t tT T=

0

0(1 ) jF f V Vm= + −

&

The scramjet performance

40

3

tj ki kc kn

t

TV VT

η η η=

Note max stoich f=0.0291 for hydrogen

There is a max flight speed of the scramjet at F=0

Heat release:

Jet speed:

Specific thrust:

( )( )

kemax

0 ke

12 11 1- 1

b s

p

fhfMC T f

ηηγ η

⎡ ⎤+= −⎢ ⎥

− +⎢ ⎥⎣ ⎦F=0 at:

Kinetic efficiency 65-75% gives max Mach number 10-15.

Run fuel rich to reach a higher Mach number:

The maximum Mach number of the scramjet

0

5

10

15

20

25

30

35

0 5 10 15 20

%

Mach

Kin effic 90%

80%

The efficiency of a Scramjet

f = fstoich

Fuel rich f = 2fstoich

The scramjet functions between Mach 6 and Mach 15

02

0( / 2)FV

mf h Vη =

+&

Problems with the scramjet

Fuel injection shock waves Incomplete combustion

Very sensitive to kinetic efficiencies

3 0

0 3

M TM T

≈Note:

40

3

tj ki kc kn

t

TV VT

η η η=

3 4

High combustor Mach numbers

p. 549

Scramjet powered spaceplane

Large intake with variable geometry

Potentially catastrophic thrust loss at large drag

4 00

(1 ) / 1ke t tF f T T

mVη= + −

&Small specific thrust surplus

20 0 0

1(1 )2tT T Mγ −

= +

4tT

0

1

2

3

4

5

6

0 2 4 6 8 10 12 14 16 18

Mach

Is / V0

The rocket has a higher specific impulse than the scramjet engine over about Mach 15

V0 =circular velocity

?

What about lowspeed propulsion

Scram 6<M<15Rocket M>15

LH2

Liquid air

LOX

Air

LACE-Liquid Air Combustion Engine

Air/LOXLH2

LH2

LOX

Precooled turboram-rocket

Pulsed ramrocket

Combined engines

Ramrocket

0

1

2

3

4

5

6

0 2 4 6 8 10 12 14 16 18

PrecooledTurboram

Ramrocket

Scram

Rocket

Mach

Is / V0

Pulsed ramrocket

LACE

PrecooledTurboram

Specific impulse for spaceplanes

sp

FIm

=&

2000

1500

1000

500

0 1 2 3 4 6 75 8MACH

K

Al

Ti

Superalloys

Ceramics

Stagnation temperature and materials

Heat protection is a big problem

0 0 0

1 exp( )V

pc

f s

mm dVm m Iη

= − = −∫

Tsiolkovsky equation with gravity and atmosphere

/

0

sV Icm em

−=Ordinary Tsiolkovsky:

Konstantin TsiolkovskyModified for aero and gravity losses:

Flight efficiency

1/(1 sin )fD g gL a a

η α α⎛ ⎞

= + − +⎜ ⎟⎝ ⎠

2VcosgR

2Vm LR+

α

mg

Flight efficiency

Waverider L/D=6(M+2)/M

Conventional L/D=4(M+3)/M

The Lift-to-Drag ratio decreases with speed

Ozon layerStratosphere

50 km

10 km

2 2 21 12 2 2

p pq V V MRT

γρ= = =

Spaceplane trajectory

0/h h

sl

p ep

−= h0 =6670 m

0/

2h h

sl

qMp eγ −=

αq=50 kPa

Atmospheric pressure:

Flight at constant dynamic pressure q

Ozon layer

Stratosphere

50 km

20 km

q=50 kPa

Spaceplane and rocket trajectories

Rocket

0

1

2

3

4

5

6

0 2 4 6 8 10 12 14 16 18

PrecooledTurboram

Ramrocket

Scram

Rocket

Mach

Is / V0

Propulsion cycles for spaceplanes

PDE

00

0

V

eff f s

V dVI Iη

= ∫

Effective average specific impulses

3409

5730

5480

Effective specific impulse m/s

20%

10%

2000 4000

3

2

1

Stages

Liquidrocket

Solid rocketSingle stage

Structure rocket

% take-off weight to satellite orbit

Turbo/Scram/Rocket

RamrocketStructure winged single stage

0 /0

e ffV Icm m e −=

Payload %

0

2

4

6

8

10

12

14

0 5 10 15 20 25 30

Ideal engine ηe=1

PDE

Scramjet

Is / V0

Mach

Turboram

( )2s e

p

F h VIm V

η= = +&

0 e f/ 0.4 ( 1)plm m η η≈ = =

A jumbo to space? Yes, but how?

Limits to airbreathing propulsion

Electricity; Magnetohydrodynamics

The Soviet AJAX system

Magnetohydrodynamic airbreathing vehicle

Ionized boundary layer Virtual nose

Electrical energy

Gripen 2500 W/kg.

Man 3 W/kg.Insect 60 W/kg.

Ariane20000 W/kg.

Most powerful of all engines

Humming bird 300 W/kg.