High Speed Propulsion - KTH

High Speed Propulsion
KTH Rocket Course 2008
Ulf.Olsson.Thn @Telia.com

What velocities?
Isaac Newton:
Law of gravity 1687
g
=
R
g R
2
0
0 2
Perigee
Apogee
V
= 2gR
11200 m/s
to leave earth.
Hyperbolic velocity.
V0
=
gR
Circular velocity 7900 m/s.
Mach 26.
mg
mV 2 /R

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 F = mV & ( −V)
j

The turbine inlet temperature limits the thrust.
F
ma &
0
2
= ( Tt
4 / T0
− 1)
γ − 1
Inlet
efficiency
Turbine
inlet
temperature
Choking
turbines
Static
pressure
balance
Choking
bypass canal
Rotational
speed
Compressor exit temperature
Limits the pressure ratio

Efficiency %
Turboramjet
25
20
Max
TIT,M tip
Throttling down T t3 = T cm
Main fuel=0, π c =1
15
10
5
Design
point
η =
FV
m&
h V
2
f
( + /2)
Ramjet mode
(afterburner)
0
0 1 2 3 4 5 6
Close down the turbomachine at high speed
Mach

Supersonic fan for less inlet losses
LH2
Precooling for extended turbojet operation

Efficiency %
40
35
30
Precooled +
Supersonic fan
25
20
15
Base
Supersonic fan
10
5
Ramjet
0
0 1 2 3 4 5 6 7 8
Mach

Fuel
Jet
Air
The principle of a Pulse Detonation Engine (PDE)

V1-German WW1 pulsejet

p
4
Humphrey (PDE) constant volume combustion
3
Brayton (ramjet and turbojet)
Constant pressure combustion
0
9
v
Volvo Aero
-id/datum/ 27

η
%
40
35
30
25
20
15
10
5
PDE more efficient than ramjet – less fuel
Ramjet
•High efficicency
•Light weight
•Simple
Pulsejet
FV
η =
mh &
f
0
0 1 2 3 4 5 6 7
Fig. 18.4
Mach

%
40
35
30
PDE has take-off thrust
Same max speed:
M Fa I a
η = = mh h
0 s 0
/
0
&
f
25
20
15
10
5
Pulsejet
M
max
T ta
2
= ( − 1)
γ −1
T
where stagnation temp = combustion temp
Ramjet
0
0
0 1 2 3 4 5 6 7
Fig. 18.4
Mach

The idea of the scramjet
Increase M 3 to keep T 3 low to prevent dissociation (1560 K)
⎛ γ −1 2⎞ ⎛ γ −1
2⎞
Tt
= T0⎜1+ M0 ⎟= T3⎜1+
M3
⎟
⎝ 2 ⎠ ⎝ 2 ⎠
0 3
1560 K
Scramjet M >1 if 2 ⎡⎛γ
+ 1⎞T
⎤
3
M
0〉 ⎢⎜
⎟ −1⎥
=6
3 γ −1⎣⎝ 2 ⎠T0
⎦

US scramjet test hardware

The jet speed of a scramjet
0
3
4
M
=
M
3 4
Constant Mach
in combustor
Kinetic efficiencies
V3 = V0 ηki
V4 M4a4 T4
T
= = =
V M a T T
t 4
3 3 3 3 t3
T
V = V η ηη T
t 4
j 0 ki kc kn
t3

The scramjet performance
0
3 4
T
= T
t3 t0
Jet speed:
T
V = V η ηη T
t 4
j 0 ki kc kn
t3
Note max stoich f=0.0291 for hydrogen
Heat release:
Specific thrust:
( ) 4 3
1
p t p t b
+ f C T − C T =η fh
F
(1 f ) V j
V
m &
= + −
0
There is a max flight speed of the scramjet at F=0

The maximum Mach number of the scramjet
F=0 at:
M
max
( 1+
f )
( f)
2 ⎡η
hf η
⎢
γ − 1⎢⎣
CT
p 0
1-ηke
1+
b s ke
= −
⎤
1⎥
⎥⎦
Kinetic efficiency 65-75% gives max Mach number 10-15.
Run fuel rich to reach a higher Mach number:

%
The scramjet functions between Mach 6 and Mach 15
35
30
25
η =
FV
mf & ( h + V /2)
0
2
0
Kin effic 90%
20
15
10
80%
f = f stoich
5
0
Fuel rich f = 2f stoich
0 5 10 15 Mach 20
The efficiency of a Scramjet

Problems with the scramjet
p. 549
3 4
Fuel injection shock waves
Note:
M
M
≈
T
T
3 0
0 3
Incomplete combustion
High combustor Mach numbers
Very sensitive to kinetic efficiencies
T
V = V η ηη T
t 4
j 0 ki kc kn
t3

Scramjet powered spaceplane
Large intake with variable geometry

T t 4
Small specific thrust surplus
F
mV &
0
γ −1
2
Tt
0
= T0(1 + M0)
2
= (1 + f) η T / T −1
ke t 4 t 0
Potentially catastrophic thrust loss at large drag

6
I s / V 0
V 0
=circular velocity
5
The rocket has a higher specific impulse than the
scramjet engine over about Mach 15
4
3
2
What about low
speed propulsion
1
?
Scram 6

Combined engines
Air
Liquid air
LH2
LH2
LOX
LACE-Liquid Air Combustion Engine
LOX
Precooled turboram-rocket
LH2
Air/LOX
Ramrocket
Pulsed ramrocket

6
I s / V 0
Specific impulse for spaceplanes
Pulsed ramrocket
5
4
Ramrocket
Precooled
Turboram
I
s
F
=
m &
p
3
2
Scram
1
0
Rocket
LACE
0 2 4 6 8 10 12 14 16 18
Mach

Heat protection is a big problem
K
2000
1500
1000
500
Al
Ti
Ceramics
Superalloys
0 1 2 3 4 5 6 7 8
MACH
Stagnation temperature and materials

Tsiolkovsky equation with gravity and atmosphere
Ordinary Tsiolkovsky:
mc
m
0
=
e
−V / I s
Modified for aero and gravity losses:
Konstantin Tsiolkovsky
V
m m
c
p dV
1 exp( )
m m I
= − = −∫ η
0 0 0
f
s
Flight efficiency

Flight efficiency
2
V
m
R +
L
α
mg
The Lift-to-Drag ratio decreases with speed
Conventional L/D=4(M+3)/M
Waverider L/D=6(M+2)/M
2
D⎛
V ⎞ g g
η
f
= 1/(1+ ⎜cosα − ⎟ + sin α)
L ⎝ gR ⎠ a a

Spaceplane trajectory
q=50 kPa
α
Ozon layer
50 km
Stratosphere
10 km
Atmospheric pressure:
p
p
sl
=
e
−h/
h
0
h 0 =6670 m
1 1 p γ p
q = ρV = V = M
2 2 RT 2
2 2 2
M
=
2q
γ pe
sl
−h/
h
0
Flight at constant dynamic pressure q

Rocket
q=50 kPa
50 km
Stratosphere
Ozon layer
20 km
Spaceplane and rocket trajectories

6
5
I s / V 0
PDE
Effective average specific impulses
4
3
Precooled
Turboram
5730
V
I
0
V
0
dV
= ∫ η I
eff 0 f s
2
1
Ramrocket
5480
Scram
Rocket
3409
0
0 2 4 6 8 10 12 14 16 18
Propulsion cycles for spaceplanes
Mach

% take-off weight to satellite orbit
m m = e −
c
0
V0 / I eff
20%
Structure winged single stage
Turbo/Scram/Rocket
Ramrocket
Stages
10%
Structure rocket
Liquid
rocket
3
2
Payload %
1
Solid rocket
Single stage
Effective specific impulse m/s
2000 4000

A jumbo to space?
Yes, but how?
I s / V 0
14
12
Ideal engine η e =1
I
s
F h V
= = ηe( + )
m&
V 2
p
10
8
6
PDE
4
2
Turboram
Scramjet
m / m ≈ 0.4 ( η = η = 1)
pl
0 e f
0
0 5 10 15 20 25 30
Limits to airbreathing propulsion
Mach

Electricity; Magnetohydrodynamics
The Soviet AJAX system
Ionized boundary layer
Virtual nose
Electrical energy
Magnetohydrodynamic airbreathing vehicle

Most powerful of all engines
Humming bird 300 W/kg.
Insect 60 W/kg.
Gripen 2500 W/kg.
Ariane
20000 W/kg.
Man 3 W/kg.