High Speed Propulsion KTH Rocket Course 28 Ulf.Olsson.Thn @Telia.com
What velocities? Isaac Newton: Law of gravity 1687 g = R g R 2 2 Perigee Apogee V = 2gR 112 m/s to leave earth. Hyperbolic velocity. V = gr Circular velocity 79 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 & 2 = ( Tt 4 / T 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 2 Max TIT,M tip Throttling down T t3 = T cm Main fuel=, π c =1 15 1 5 Design point η = FV m& h V 2 f ( + /2) Ramjet mode (afterburner) 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 % 4 35 3 Precooled + Supersonic fan 25 2 15 Base Supersonic fan 1 5 Ramjet 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 9 v Volvo Aero -id/datum/ 27
η % 4 35 3 25 2 15 1 5 PDE more efficient than ramjet less fuel Ramjet High efficicency Light weight Simple Pulsejet FV η = mh & f 1 2 3 4 5 6 7 Fig. 18.4 Mach
% 4 35 3 PDE has take-off thrust Same max speed: M Fa I a η = = mh h s / & f 25 2 15 1 5 Pulsejet M max T ta 2 = ( 1) γ 1 T where stagnation temp = combustion temp Ramjet 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 (156 K) γ 1 2 γ 1 2 Tt = T 1+ M = T3 1+ M3 2 2 3 156 K Scramjet M >1 if 2 γ + 1 T 3 M 1 =6 3 γ 1 2 T
US scramjet test hardware
The jet speed of a scramjet 3 4 M = M 3 4 Constant Mach in combustor Kinetic efficiencies V3 = V 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 ki kc kn t3
The scramjet performance 3 4 T = T t3 t Jet speed: T V = V η ηη T t 4 j ki kc kn t3 Note max stoich f=.291 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 & = + There is a max flight speed of the scramjet at F=
The maximum Mach number of the scramjet F= at: M max ( 1+ f ) ( f) 2 η hf η γ 1 CT p 1-ηke 1+ b s ke = 1 Kinetic efficiency 65-75% gives max Mach number 1-15. Run fuel rich to reach a higher Mach number:
% The scramjet functions between Mach 6 and Mach 15 35 3 25 η = FV mf & ( h + V /2) 2 Kin effic 9% 2 15 1 8% f = f stoich 5 Fuel rich f = 2f stoich 5 1 15 Mach 2 The efficiency of a Scramjet
Problems with the scramjet p. 549 3 4 Fuel injection shock waves Note: M M T T 3 3 Incomplete combustion High combustor Mach numbers Very sensitive to kinetic efficiencies T V = V η ηη T t 4 j ki kc kn t3
Scramjet powered spaceplane Large intake with variable geometry
T t 4 Small specific thrust surplus F mv & γ 1 2 Tt = T(1 + M) 2 = (1 + f) η T / T 1 ke t 4 t Potentially catastrophic thrust loss at large drag
6 I s / V V =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<M<15 Rocket M>15 2 4 6 8 1 12 14 16 18 Mach
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 Specific impulse for spaceplanes Pulsed ramrocket 5 4 Ramrocket Precooled Turboram I s F = m & p 3 2 Scram 1 Rocket LACE 2 4 6 8 1 12 14 16 18 Mach
Heat protection is a big problem K 2 15 1 5 Al Ti Ceramics Superalloys 1 2 3 4 5 6 7 8 MACH Stagnation temperature and materials
Tsiolkovsky equation with gravity and atmosphere Ordinary Tsiolkovsky: mc m = e V / I s Modified for aero and gravity losses: Konstantin Tsiolkovsky V m m c p dv 1 exp( ) m m I = = η 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=5 kpa α Ozon layer 5 km Stratosphere 1 km Atmospheric pressure: p p sl = e h/ h h =667 m 1 1 p γ p q = ρv = V = M 2 2 RT 2 2 2 2 M = 2q γ pe sl h/ h Flight at constant dynamic pressure q
Rocket q=5 kpa 5 km Stratosphere Ozon layer 2 km Spaceplane and rocket trajectories
6 5 I s / V PDE Effective average specific impulses 4 3 Precooled Turboram 573 V I V dv = η I eff f s 2 1 Ramrocket 548 Scram Rocket 349 2 4 6 8 1 12 14 16 18 Propulsion cycles for spaceplanes Mach
% take-off weight to satellite orbit m m = e c V / I eff 2% Structure winged single stage Turbo/Scram/Rocket Ramrocket Stages 1% Structure rocket Liquid rocket 3 2 Payload % 1 Solid rocket Single stage Effective specific impulse m/s 2 4
A jumbo to space? Yes, but how? I s / V 14 12 Ideal engine η e =1 I s F h V = = ηe( + ) m& V 2 p 1 8 6 PDE 4 2 Turboram Scramjet m / m.4 ( η = η = 1) pl e f 5 1 15 2 25 3 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 3 W/kg. Insect 6 W/kg. Gripen 25 W/kg. Ariane 2 W/kg. Man 3 W/kg.