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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

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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

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Cold Gas Thruster (used with inert gas)

Moog Divert/Attitude Thruster and Valve 3

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Monopropellant Hydrazine Thruster

Aerojet Rocketdyne

• Catalytic decomposition produces thrust • Reliable • Low performance

• Toxic 4

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Bi-Propellant Rocket Motor Thrust / Motor Weight ~ 70:1

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Hypergolic, Storable Liquid- Propellant Thruster

Titan 2

• Spontaneous combustion • Reliable • Corrosive, toxic 6

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Pressure-Fed and Turbopump Engine Cycles

Pressure-Fed Gas-Generator Rocket Rocket Cycle Cycle, with Nozzle Cooling

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Staged Combustion Engine Cycles

Staged Combustion Full-Flow Staged Rocket Cycle Combustion Rocket Cycle

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German V-2 Rocket Motor, Fuel Injectors, and Turbopump

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Combustion Chamber Injectors

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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

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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

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(used on Atlas V)

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Special Shuttle Main Engine (RS-25)

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SpaceX Merlin Family Merlin 1A Merlin 1C Merlin 1D (ablative nozzle) (vacuum nozzle) (throttlable)

Roll control from turbine exhaust 18

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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)

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RD-181 and RD-191

RD-181 RD-191

to be used on Orbital- to be used on NPO ATK Antares Energomash Angara 20

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Solid-Fuel Rocket Motor

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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

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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

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Rocket Thrust Thrust = m! V + A p − p ≡ m! c propellant exhaust exit ( exit ambient ) eff Thrust c = = Effective exhaust velocity eff m! m Mass flow rate of on-board propellant ! ≡

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Specific Impulse

Thrust ceff m / s Isp = = , Units = 2 = seconds m! go go m / s g Gravitational acceleration at earth's surface o ≡

• 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

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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

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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

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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

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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

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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

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Exhaust Velocity vs. Thrust Acceleration

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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)

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Rocket Characteristic Velocity, c*

pc At c* = = exhaust velocity if CF = 1 m!

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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

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Thrust Coefficient, CF, vs. Nozzle Expansion Ratio • xx

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Mixture Ratio, r m! m! r = oxidizer ; m! = total ; "leaner" < r < "richer" m! fuel 1+ r fuel • Stoichiometric mixture: complete chemical reaction of propellants • Specific impulse maximized with lean mixture ratio, r (i.e., below stoichiometric maximum)

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Effect of Pressure Ratio on Mass Flow

In choked flow, mass Choked flow flow rate is maximized occurs when γ γ −1 Γ pc At m! = pe ⎛ 2 ⎞ R T ≤ ≈ 0.53 o c p ⎝⎜ γ +1⎠⎟ M c 38

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Combustion Instability

• Complex mix of species, phases, pressures, temperatures, and flows • Cavity resonance

Harrje, NASA SP- 194, 1972

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Combustion Instability

Stable Response to Disturbance

Unstable Response to Disturbance

40 Harrje, NASA SP-194, 1972

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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

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Rocket Nozzles

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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

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Rocket Nozzles

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Linear Spike/Plug Nozzles

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Throttling, Start/Stop Cycling

CECE Demonstrator Pintle Injector

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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

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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

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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

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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

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Project Rover, 1955-1972

NERVA Rocket, Isp ~ 900 sec

NERVA-Powered Mars Mission Kiwi-B4-A Reactor/Rocket

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Liquid/Particle-Core Nuclear Rocket

• Nuclear fuel mixed with working fluid • In principle, could operate above melting point of nuclear fuel

• Isp ~ 1,300 – 1,500 sec • Conceptual • Massive radioactive waste 53

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Open-Cycle Gas Core Nuclear Rocket

• Toroidal circulation of working fluid confines nuclear fuel to center • Fuel does not touch the wall • Conceptual • Massive radioactive waste

• Isp ~ 3,000 – 5,000 sec 54

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Closed-Cycle Gas Core Nuclear Rocket

• “Nuclear light bulb” • Nuclear fuel contained in quartz container

• Isp ~ 1,500 – 2,000 sec • Conceptual

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Nuclear-Pulse (“Explosion”) Rocket - Project Orion

“Physics packages” ejected behind the pusher plate

https://en.wikipedia.org/wiki/Project_Orion_(nuclear_propulsion) 56

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Next Time: Launch Vehicles

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Supplemental Material

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Propellant Tanks Propellant must be kept near the exit duct without bubbles during thrusting

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Ion/Plasma Thrusters

Engine Propellant Required power Specific impulse Thrust kW s mN NSTAR Xenon 2.3 3,300 to 1,700 92 max NEXT[ Xenon 6.9 4,300 236 max HiPEP Xenon 20–50 6,000–9,000 460–670 Hall effect Xenon 25 3,250 950 FEEP Liquid Cesium 6×10−5–0.06 6,000–10,000 0.001–1 VASIMR Argon 200 3,000–12,000 ~5,000 DS4G Xenon 250 19,300 2,500 max

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Variable Specific Impulse Magnetoplasma Rocket (VASIMR)

Required Specific Propellant power impulse Thrust kW s mN Argon 200 3,000–12,000 ~5,000

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DAWN Spacecraft

Engine Propellant Required power Specific impulse Thrust kW s mN NSTAR Xenon 2.3 3,300 to 1,700 92 max 62

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