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Chemical/Nuclear PropulsionSpace 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

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Chemical (Thermal) Rockets

• Liquid/Gas Propellant–Monopropellant

• Cold gas• Catalytic decomposition

–Bipropellant• Separate oxidizer and fuel• Hypergolic (spontaneous)

ignition• External ignition• Storage

– Ambient temperature and pressure

– Cryogenic– Pressurized tank

–Throttlable–Start/stop cycling

• Solid Propellant–Mixed oxidizer and fuel–External ignition–Burn to completion

• Hybrid Propellant–Liquid oxidizer, solid fuel–Throttlable–Start/stop cycling

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Cold Gas Thruster(used with inert gas)

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Moog Divert/Attitude Thruster and Valve

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Monopropellant Hydrazine Thruster

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• Catalytic decomposition produces thrust

• Reliable• Low performance• Toxic

Aerojet Rocketdyne

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

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Hypergolic, Storable Liquid-Propellant Thruster

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• Spontaneous combustion

• Reliable• Corrosive, toxic

Titan 2

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Pressure-Fed and TurbopumpEngine Cycles

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Gas-Generator Rocket Cycle, with Nozzle Cooling

Pressure-Fed Rocket Cycle

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Staged Combustion Engine Cycles

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Staged Combustion Rocket Cycle

Full-Flow Staged 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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• 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

Origins of the F-1

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USSR RD-107/8 Rocket MotorsRD-107

4 combustion chambers, 2 verniersRD-108

4 combustion chambers, 4 verniers

R-7 Base4-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

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Merlin 1C (vacuum nozzle)

Merlin 1D (throttlable)

Merlin 1A (ablative nozzle)

Roll control from turbine exhaust

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• LOX/Liquefied natural gas

• United Launch Alliance has chosen as motor for the Vulcan launch vehicle

• Thrust = 2.5 MN (550,000 lb)

Blue Origin BE-4

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RD-181 and RD-191RD-181 RD-191

to be used on Orbital-ATK Antares

to be used on NPO Energomash Angara

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Solid-Fuel Rocket Motor

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Solid-Fuel Rocket Motor

Thrust is proportional to burning areaRocket grain patterns affect thrust profile

Propellant chamber must sustain high pressure and temperatureEnvironmentally 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 = !mpropellantVexhaust + Aexit pexit − pambient( ) ≡ !m ceff

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ceff =Thrust!m

= Effective exhaust velocity

!m ≡Mass flow rate of on-board propellant

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Specific Impulse

• go is a normalizing factor for the definition• Chemical rocket specific impulse (vacuum)

– Solid propellants: < 295 s– Liquid propellants: < 510 s

Isp =Thrust!m go

=ceffgo

, Units = m / sm / s2 = seconds

go ≡ Gravitational acceleration at earth's surface

• Space Shuttle Specific Impulses–Solid boosters: 242-269 s–Main engines: 455 s–OMS: 313 s–RCS: 260-280 s

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Specific Impulse

Isp =Thrust!m go

=ceffgo

= CF c* go

= Vexhaustgo

when CF = 1, pe = pambient

Specific impulse is a product of characteristic velocity, c*, and rocket

thrust coefficient, CF

• Characteristic velocity is related to– combustion chamber performance– propellant characteristics

• Thrust coefficient is related to– nozzle shape– exit/ambient pressure differential

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The Rocket EquationIdeal velocity increment of a rocket stage, ΔVI (gravity and aerodynamic effects

neglected)

dVdt

= Thrustm

=!m ceffm

= −dm

dt Ispgom

Konstantin Tsiolkovsky

dVVi

Vf

∫ = −Ispgo dmm

mi

mf

∫ = −Ispgo lnm mi

mf

Vf −Vi( ) ≡ ΔVI = Ispgo lnmi

mf

⎛

⎝⎜⎞

⎠⎟≡ Ispgo ln µ

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Volumetric Specific Impulse

ΔVI = Ispgo lnµ = Ispgo lnmfinal +mpropellant

m final

⎛

⎝⎜⎞

⎠⎟= Ispgo ln 1+

mpropellant

m final

⎛

⎝⎜⎞

⎠⎟

= Ispgo ln 1+Densitypropellant •Volumepropellant

m final

⎛

⎝⎜⎞

⎠⎟

≈ goIspρ propellant •Volpropellant

m final

⎛

⎝⎜⎞

⎠⎟= go Ispρ propellant( )Volpropellantm final

Specific impulse

Volumetric specific impulse

Ispvol !VIsp = Ispρ propellant29

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Volumetric Specific Impulse

• For fixed volume and final mass, increasing volumetric specific impulse increases ideal velocity increment

•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

Density, g/cc Isp, s, SL

VIsp, s (g/cc), SL Isp, s, vac

VIsp, s (g/cc), vac

LOX/Kerosene 1.3 265 345 304 395

LOX/LH2 (Saturn V) 0.28 360 101 424 119LOX/LH2 (Shuttle) 0.28 390 109 455 127

Shuttle Solid Booster 1.35 242 327 262 354

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Typical Values of Chemical Rocket Specific Impulse • Chamber pressure = 7 MPa (low by

modern standards)• Expansion to exit pressure = 0.1 MPa

Solid-Propellant Rockets

Double-Base Isp, sVIsp, kg-s/m^3 x 10^3

AFU 196 297ATN 235 376JPN 250 405

CompositeJPL 540A 231 383TRX-H609 245 431PBAN (SSV) 260 461

Liquid-Fuel Rockets

Monopropellant Isp, sVIsp, kg-s/m^3 x 10^3

Hydrogen Peroxide 165 238Hydrazine 199 201Nitromethane 255 290

Bipropellant

Fuel Oxidizer Isp, sVIsp, kg-s/m^3 x 10^3

Kerosene Oxygen 301 307Flourine 320 394Red Fuming Nitric Acid 268 369

Hydrogen Oxygen 390 109Flourine 410 189

UDMHNitrogen Tetroxide 286 339

Hybrid-Fuel RocketFuel Oxidizer Isp, sHTPB N2O 250

SSME

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Exhaust Velocity vs. Thrust Acceleration

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Rocket Characteristic Velocity, c*

c*= 1Γ

RoTcM

, where Γ = γ 2γ +1

⎛⎝⎜

⎞⎠⎟

γ +12 γ −1( )

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Ro = universal gas constant = 8.3×103 kg m2 s2 °K

Tc = chamber temperature, °KM = exhaust gas mean molecular weightγ = ratio of specific heats ~1.2-1.4( )

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Rocket Characteristic Velocity, c*

c*= pcAt

!m= exhaust velocity if CF = 1

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Rocket Thrust Coefficient, CF

CF typically 0.5 - 2

CF =ThrustpcAt

= λΓ 2γγ −1

⎛⎝⎜

⎞⎠⎟1− pe

pc

⎛⎝⎜

⎞⎠⎟

γ −1( ) γ⎡

⎣⎢⎢

⎤

⎦⎥⎥+ pe − pambient

pc

⎛⎝⎜

⎞⎠⎟AeAt

Thrust = λ !m ve + Ae pe − pambient( )λ : reduction ratio (function of nozzle shape)

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Thrust Coefficient, CF, vs. Nozzle Expansion Ratio

• xx

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Mixture Ratio, r

• Stoichiometric mixture: complete chemical reaction of propellants

• Specific impulse maximizedwith lean mixture ratio, r (i.e., below stoichiometric maximum)

r =!moxidizer

!mfuel

; !mfuel =!mtotal

1+ r; "leaner"< r < "richer"

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Effect of Pressure Ratio on Mass Flow

!m = Γ pcAtR oTc

M

In choked flow, mass flow rate is maximized

pepc

≤ 2γ +1

⎛⎝⎜

⎞⎠⎟

γ γ −1

≈ 0.53

Choked flow occurs when

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Combustion Instability

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Harrje, NASA SP-194, 1972

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

• Cavity resonance

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Combustion Instability

40Harrje, NASA SP-194, 1972

Stable Response to Disturbance

Unstable Response to Disturbance

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Shock DiamondsWhen pe ≠pa, exhaust flow is over- or underexpanded

Effective exhaust velocity < maximum value

Vikinghttps://www.youtube.com/watch?v=qiMSko4HBe8

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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

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CECE Demonstrator PintleInjector

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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– Hypergolic propellants– Catalytic propellant– Ion/plasma rockets

• Thrusters commanded in pairs to cancel velocity change

Apollo Lunar Module RCS Space Shuttle RCS

• Issues– Specific impulse– Propellant mass– Expendability

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RCS Thruster

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Divert and Attitude Control Thrusters

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https://www.youtube.com/watch?v=W8efpDBvTDE

https://www.youtube.com/watch?v=KBMU6l6GsdM

https://www.youtube.com/watch?v=JURQYH669_g

https://www.youtube.com/watch?v=71qgI6bddM8

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Nuclear Propulsion

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• 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

c*= 1Γ

RoTcM

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Solid-Core Nuclear Rocket

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• 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

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Project Rover, 1955-1972

Kiwi-B4-A Reactor/Rocket

NERVA Rocket, Isp ~ 900 sec

NERVA-Powered Mars Mission

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Liquid/Particle-Core Nuclear Rocket

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• 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

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Open-Cycle Gas Core Nuclear Rocket

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• 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

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Closed-Cycle Gas Core Nuclear Rocket

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• “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

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“Physics packages” ejected behind the pusher plate

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

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Next Time:Launch Vehicles

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Supplemental Material

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Propellant Tanks

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

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Ion/Plasma Thrusters

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Engine Propellant Required power Specific impulse ThrustkW s mN

NSTAR Xenon 2.3 3,300 to 1,700 92 maxNEXT[ Xenon 6.9 4,300 236 maxHiPEP Xenon 20–50 6,000–9,000 460–670

Hall effect Xenon 25 3,250 950FEEP Liquid Cesium 6×10−5–0.06 6,000–10,000 0.001–1

VASIMR Argon 200 3,000–12,000 ~5,000DS4G Xenon 250 19,300 2,500 max

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Variable Specific Impulse Magnetoplasma Rocket (VASIMR)

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PropellantRequired

powerSpecific impulse Thrust

kW s mNArgon 200 3,000–12,000 ~5,000

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DAWN Spacecraft

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Engine Propellant Required power Specific impulse ThrustkW s mN

NSTAR Xenon 2.3 3,300 to 1,700 92 max

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