2/12/20 Chemical/Nuclear Propulsion Space System Design, MAE 342, Princeton University Robert Stengel • Thermal rockets • Performance parameters • Propellants and propellant storage Copyright 2016 by Robert Stengel. All rights reserved. For educational use only. http://www.princeton.edu/~stengel/MAE342.html 1 1 Chemical (Thermal) Rockets • Liquid/Gas Propellant –Monopropellant • Cold gas • Catalytic decomposition –Bipropellant • Separate oxidizer and fuel • Hypergolic (spontaneous) • Solid Propellant ignition –Mixed oxidizer and fuel • External ignition –External ignition • Storage –Burn to completion – Ambient temperature and pressure • Hybrid Propellant – Cryogenic –Liquid oxidizer, solid fuel – Pressurized tank –Throttlable –Throttlable –Start/stop cycling –Start/stop cycling 2 2 1 2/12/20 Cold Gas Thruster (used with inert gas) Moog Divert/Attitude Thruster and Valve 3 3 Monopropellant Hydrazine Thruster Aerojet Rocketdyne • Catalytic decomposition produces thrust • Reliable • Low performance • Toxic 4 4 2 2/12/20 Bi-Propellant Rocket Motor Thrust / Motor Weight ~ 70:1 5 5 Hypergolic, Storable Liquid- Propellant Thruster Titan 2 • Spontaneous combustion • Reliable • Corrosive, toxic 6 6 3 2/12/20 Pressure-Fed and Turbopump Engine Cycles Pressure-Fed Gas-Generator Rocket Rocket Cycle Cycle, with Nozzle Cooling 7 7 Staged Combustion Engine Cycles Staged Combustion Full-Flow Staged Rocket Cycle Combustion Rocket Cycle 8 8 4 2/12/20 German V-2 Rocket Motor, Fuel Injectors, and Turbopump 9 9 Combustion Chamber Injectors 10 10 5 2/12/20 11 11 12 12 6 2/12/20 Origins of the F-1 • Air Force legacy (1955) • Design undertaken before vehicle or mission were identified • Big engine, big problems • 16:1 nozzle expansion • 6.67 MN thrust • F-1 turbopumps • Oxygen: 24,811 gal/min • RP-1: 15,741 gal/min • F-1 injector • Combustion instability • Significant theoretical work by Luigi Crocco and David Harrje, Princeton 13 13 14 14 7 2/12/20 USSR RD-107/8 Rocket Motors RD-107 RD-108 4 combustion chambers, 2 verniers 4 combustion chambers, 4 verniers R-7 Base 4-RD-107, 1-RD-108 15 15 (used on Atlas V) 16 16 8 2/12/20 Special Shuttle Main Engine (RS-25) 17 17 SpaceX Merlin Family Merlin 1A Merlin 1C Merlin 1D (ablative nozzle) (vacuum nozzle) (throttlable) Roll control from turbine exhaust 18 18 9 2/12/20 Blue Origin BE-4 • LOX/Liquefied natural gas • United Launch Alliance has chosen as motor for the Vulcan launch vehicle • Thrust = 2.5 MN (550,000 lb) 19 19 RD-181 and RD-191 RD-181 RD-191 to be used on Orbital- to be used on NPO ATK Antares Energomash Angara 20 20 10 2/12/20 Solid-Fuel Rocket Motor 21 21 22 22 11 2/12/20 Solid-Fuel Rocket Motor Thrust is proportional to burning area Rocket grain patterns affect thrust profile Propellant chamber must sustain high pressure and temperature Environmentally unfriendly exhaust gas 23 23 Hybrid-Fuel Rocket Motor • SpaceShipOne motor – Nitrous oxide – Hydroxy-terminated polybutadiene (HTPB) • Issues – Hard start – Blow back – Complete mixing of oxidizer and fuel toward completion of burn 24 24 12 2/12/20 Rocket Thrust Thrust = m! propellantVexhaust + Aexit ( pexit − pambient ) ≡ m! ceff Thrust c = = Effective exhaust velocity eff m! m! ≡ Mass flow rate of on-board propellant 25 25 Specific Impulse Thrust ceff m / s Isp = = , Units = 2 = seconds m! go go m / s go ≡ Gravitational acceleration at earth's surface • go is a normalizing factor for the definition • Chemical rocket specific impulse (vacuum) – Solid propellants: < 295 s – Liquid propellants: < 510 s • Space Shuttle Specific Impulses –Solid boosters: 242-269 s –Main engines: 455 s –OMS: 313 s –RCS: 260-280 s 26 26 13 2/12/20 Specific Impulse Specific impulse is a product of characteristic velocity, c*, and rocket thrust coefficient, CF Thrust ceff Isp = = m! go go = CF c* go V = exhaust when C = 1, p = p g F e ambient o • Characteristic velocity is related to – combustion chamber performance – propellant characteristics • Thrust coefficient is related to – nozzle shape – exit/ambient pressure differential 27 27 The Rocket Equation Ideal velocity increment of a rocket stage, Konstantin ΔVI (gravity and aerodynamic effects Tsiolkovsky neglected) dm dV Thrust m! c Ispgo = = eff = − dt dt m m m Vf m f dm m f dV = −Ispgo = −Ispgo ln m ∫ ∫ m mi Vi mi ⎛ mi ⎞ (Vf −Vi ) ≡ ΔVI = Ispgo ln⎜ ⎟ ≡ Ispgo ln µ ⎝ m f ⎠ 28 28 14 2/12/20 Volumetric Specific Impulse Specific impulse ⎛ m final + mpropellant ⎞ ⎛ mpropellant ⎞ ΔVI = Ispgo ln µ = Ispgo ln⎜ ⎟ = Ispgo ln⎜1+ ⎟ ⎝ m final ⎠ ⎝ m final ⎠ ⎛ Densitypropellant •Volumepropellant ⎞ = Ispgo ln⎜1+ ⎟ ⎝ m final ⎠ ⎛ ρ propellant •Volpropellant ⎞ Volpropellant ≈ goIsp ⎜ ⎟ = go (Ispρ propellant ) ⎝ m final ⎠ m final Volumetric specific impulse I VI I spvol ! sp = spρ propellant 29 29 Volumetric Specific Impulse • For fixed volume and final mass, increasing volumetric specific impulse increases ideal velocity increment Density, VIsp, s (g/cc), VIsp, s (g/cc), g/cc Isp, s, SL SL Isp, s, vac vac LOX/Kerosene 1.3 265 345 304 395 LOX/LH2 (Saturn V) 0.28 360 101 424 119 LOX/LH2 (Shuttle) 0.28 390 109 455 127 Shuttle Solid Booster 1.35 242 327 262 354 •Saturn V Specific Impulses, vacuum (sea level) –1st Stage, 5 F-1 LOX-Kerosene Engines: 304 s (265 s) –2nd Stage, 5 J-2 LOX-LH2 Engines: 424 s (~360 s) –3rd Stage, 1 J-2 LOX-LH2 Engine: 424 s (~360 s) 30 30 15 2/12/20 Typical Values of Chemical SSME Rocket Specific Impulse • Chamber pressure = 7 MPa (low by modern standards) • Expansion to exit pressure = 0.1 MPa Liquid-Fuel Rockets VIsp, kg- Solid-Propellant Rockets VIsp, kg- Monopropellant Isp, s s/m^3 x 10^3 Hydrogen Peroxide 165 238 Double-Base Isp, s s/m^3 x 10^3 Hydrazine 199 201 AFU 196 297 Nitromethane 255 290 ATN 235 376 JPN 250 405 Bipropellant VIsp, kg- Composite Fuel Oxidizer Isp, s s/m^3 x 10^3 JPL 540A 231 383 Kerosene Oxygen 301 307 TRX-H609 245 431 Flourine 320 394 PBAN (SSV) 260 461 Red Fuming Nitric Acid 268 369 Hybrid-Fuel Rocket Hydrogen Oxygen 390 109 Fuel Oxidizer Isp, s Flourine 410 189 Nitrogen HTPB N2O 250 UDMH Tetroxide 286 339 31 31 Exhaust Velocity vs. Thrust Acceleration 32 32 16 2/12/20 Rocket Characteristic Velocity, c* γ +1 1 R T ⎛ 2 ⎞ 2(γ −1) c* = o c , where Γ = γ Γ M ⎝⎜ γ +1⎠⎟ 3 2 2 Ro = universal gas constant = 8.3×10 kg m s °K Tc = chamber temperature, °K M = exhaust gas mean molecular weight γ = ratio of specific heats (~1.2-1.4) 33 33 Rocket Characteristic Velocity, c* p A c* = c t = exhaust velocity if C = 1 m! F 34 34 17 2/12/20 Rocket Thrust Coefficient, CF (γ −1) γ Thrust ⎛ 2γ ⎞ ⎡ ⎛ p ⎞ ⎤ ⎛ p − p ⎞ A C = = λΓ ⎢1− e ⎥ + e ambient e F p A ⎝⎜ γ −1⎠⎟ ⎝⎜ p ⎠⎟ ⎝⎜ p ⎠⎟ A c t ⎣⎢ c ⎦⎥ c t Thrust = λ m! ve + Ae ( pe − pambient ) λ :reduction ratio (function of nozzle shape) CF typically 0.5 - 2 35 35 Thrust Coefficient, CF, vs. Nozzle Expansion Ratio • xx 36 36 18 2/12/20 Mixture Ratio, r m! oxidizer m! total r = ; m! fuel = ; "leaner" < r < "richer" m! fuel 1+ r • Stoichiometric mixture: complete chemical reaction of propellants • Specific impulse maximized with lean mixture ratio, r (i.e., below stoichiometric maximum) 37 37 Effect of Pressure Ratio on Mass Flow In choked flow, mass Choked flow flow rate is maximized occurs when Γ p A γ γ −1 m! = c t p ⎛ 2 ⎞ e ≤ ≈ 0.53 R oTc ⎜ ⎟ pc ⎝ γ +1⎠ M 38 38 19 2/12/20 Combustion Instability • Complex mix of species, phases, pressures, temperatures, and flows • Cavity resonance Harrje, NASA SP- 194, 1972 39 39 Combustion Instability Stable Response to Disturbance Unstable Response to Disturbance 40 Harrje, NASA SP-194, 1972 40 20 2/12/20 Shock Diamonds When pe ≠pa, exhaust flow is over- or underexpanded Effective exhaust velocity < maximum value Viking https://www.youtube.com/watch?v=qiMSko4HBe8 41 41 Rocket Nozzles 42 42 21 2/12/20 Rocket Nozzles • Expansion ratio, Ae/At, chosen to match exhaust pressure to average ambient pressure – Ariane rockets: Viking V for sea level, Viking IV for high altitude • Rocket nozzle types – DeLaval nozzle – Isentropic expansion nozzle – Spike/plug nozzles – Expansion-deflection nozzle 43 43 Rocket Nozzles 44 44 22 2/12/20 Linear Spike/Plug Nozzles 45 45 Throttling, Start/Stop Cycling CECE Demonstrator Pintle Injector 46 46 23 2/12/20 Reaction Control Thrusters • Direct control of angular rate • Unloading momentum wheels or control-moment gyros • Reaction control thrusters are typically on-off devices using – Cold gas • Issues – Hypergolic propellants – Specific impulse – Catalytic propellant – Propellant mass – Ion/plasma rockets – Expendability • Thrusters commanded in pairs to cancel velocity change Apollo Lunar Module RCS Space Shuttle RCS RCS Thruster 47 47 Divert and Attitude Control Thrusters https://www.youtube.com/watch?v=W8efpDBvTDE https://www.youtube.com/watch?v=71qgI6bddM8 https://www.youtube.com/watch?v=KBMU6l6GsdM https://www.youtube.com/watch?v=JURQYH669_g 48 48 24 2/12/20 Nuclear Propulsion 1 R T c* = o c Γ M • Nuclear reaction produces thermal energy to heat inert working fluid – Solid core – Liquid core – Gaseous core • High propellant temperature leads to high specific impulse • Working fluid chosen for low molecular weight and storability 49 49 Solid-Core Nuclear Rocket • Operating temperature limited by – melting point of reactor materials – cracking of core coating – matching coefficients of expansion • Possible propellants: hydrogen, helium, liquid oxygen, water, ammonia • Isp = 850 – 1,000 sec • T / W ~ 7:1 50 50 25 2/12/20 Project Rover, 1955-1972 NERVA Rocket, Isp ~ 900 sec NERVA-Powered Mars Mission Kiwi-B4-A Reactor/Rocket 51 51 52 52 26 2/12/20 Liquid/Particle-Core Nuclear Rocket • Nuclear