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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.