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DeTurris - Aero 540

Kyutech SEIC Q2 2019

Rocket Propulsion

Taught by: Dr. Dianne DeTurris 20 Years Experience Teaching Rocket Propulsion

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DeTurris - Aero 540

Textbook: Rocket Propulsion Elements by Sutton and Biblarz

7th, 8th or 9th edition we will not cover the entire book, only some sections

•  Chapter 1 Classification •  Chapter 2 Fundamental Equations

•  Chapter 3 Nozzles, Ideal Rocket •  Chapter 4 Flight Performance

•  Chapter 5 Chemical Analysis of Propellants

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DeTurris - Aero 540

Sutton and Biblarz; Rocket Propulsion Elements

•  Chapter 6 Liquid Propellant Rockets - Basics •  Chapter 7 Liquid Propellants •  Chapter 8 Thrust Chambers •  Chapter 9 Liquid Rocket Combustion •  Chapter 10 Turbopumps •  Chapter 11 Engine Systems and Integration

•  Chapter 12 Solid Rocket Basics •  Chapter 13 Solid Propellants •  Chapter 14 Combustion of Solid Propellants and Stability •  Chapter 15 Solid Motor Components and Design •  Chapter 17 Electric Propulsion

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DeTurris - Aero 540

Chapter 1: Rocket Definitions

•  Airbreathing (Jet) Propulsion vs. Rocket Propulsion –  Airbreathing (jet) pulls in air as oxidizer –  Rocket propulsion carries oxidizer onboard the rocket

•  Rocket Propulsion can be: –  Chemical, electric, nuclear and solar

Ø  Chemical includes solid, liquid, and hybrid rockets

•  Rocket Motor vs. Rocket Engine –  Rocket motor: solid propellant (No moving parts) –  Rocket engine: liquid propellant rockets (Moving parts)

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DeTurris - Aero 540

Rocket Principles

•  Momentum exchange between rocket and exhaust gases (Newton’s 3rd Law)

– First create expanding gases: Propellants react in a small volume; fast expansion and fast temperature rise

– Next create momentum: Nozzle turns internal energy of gases into kinetic energy

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DeTurris - Aero 540

Rocket Nomenclature

Propellant Reaction:

Gases w/ Potential Energy (Pressure and Temperature)

Nozzle

* = t

1 = c 2 = e

( )dtmVdThrust =

Combustion Chamber

3 = a

Exit

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DeTurris - Aero 540

Chapter 2: Performance Definitions

Use Conservation of Mass and Momentum together to get an equation for thrust in terms of exhaust momentum and pressure difference across the nozzle exit:

apepevF

!

xCV

Static Thrust Equation

F = mve + pe − pa( )Ae

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DeTurris - Aero 540

Rocket Performance: Total and Specific Impulse Total Impulse: Force integrated over the burn time

FtIdtFIt

t =⇒⋅= ∫0

!!

Specific Impulse: Total impulse per unit weight of propellant (in seconds)

Isp =

F ⋅dt

0

t

∫g0 m ⋅dt∫

⇒ Isp =Fmg0

⎥⎦

⎤⎢⎣

⎡ ⋅⎥⎦

⎤⎢⎣

⎡ ⋅=

secor

secftslugmkgIt

!

[ ]2

2sec sec sec

secspkg mI

kg m⎡ ⎤⋅

= =⎢ ⎥⎣ ⎦

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DeTurris - Aero 540

Rocket Performance: Effective Exhaust Velocity

Recall that static thrust equation has two components: Momentum and Pressure Effective Exhaust Velocity:

F = mve + pe − pa( )Ae

mFgIc s!

=≡ 0

…the effective exhaust velocity includes the exit velocity of the exhaust gases and the pressure component of thrust

c = ve + pe − pa( ) Aem

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DeTurris - Aero 540

Rocket Performance: c* and SPC

Specific Propellant Consumption (SPC):

SPC ≡ Isp−1 =mg0F

( ) ⎥⎦

⎤⎢⎣

⎡=

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

⇒−

−

sec1

secsecor sec

2m

N

kg

lb

lbUnits

thrustf

fuelm

Characteristic Exhaust Velocity:

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1

12

*−+

⎥⎦

⎤⎢⎣

⎡+

====kk

F

tc

F

osp

kk

kRTCc

mAP

CgI

c! m/sec or ft/sec

Useful for ducted propulsion systems

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DeTurris - Aero 540

Rocket Combustion and Internal Efficiencies

Combustion Efficiency :

Internal Efficiency :

effectiveness of converting available engine power into kinetic power

%9994propellantunit per reaction ofheat idealpropellantunit per reaction ofheat actual

−≈

ideal

real

R

Rc QQ

=η

cRidealQmcmη

η!

!2

21

int =

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DeTurris - Aero 540

Rocket Propulsive Efficiency

Propulsive Efficiency:

how much of the exhaust energy actually propels vehicle

( )22 uccumcummp

−+=

!!

!η

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DeTurris - Aero 540

Energy Balance - Efficiencies

100% 99% 97% 40-70%

0-50% Available energy for propulsion

Chemical energy in propellant

Energy available in combustion chamber

Total energy of exhaust jet

Kinetic energy of exhaust jet

cη

intη

pη

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DeTurris - Aero 540

Chapter 3: Ideal Rocket Performance

•  Homogeneous propellant

•  Negligible condensed phase products

•  Perfect gas

•  Adiabatic across walls

•  Steady, 1-D flow

•  Uniform flow across nozzle

•  Chemical equilibrium

•  No friction or boundary layer effects

•  No shocks in nozzle, isentropic expansion Idea

l Roc

ket A

ssum

ptio

ns

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DeTurris - Aero 540

Analyze rocket as ideal and then adjust for real case, which includes efficiencies

Background thermodynamics equations useful to ideal rockets ...

P=ρRT P0=ρ0RT0

P = static pressure ρ = density R = gas constant T = static temperature P0= stagnation pressure ρ0 = stagnation density T0 = stagnation temperature

Start with ideal gas law:

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DeTurris - Aero 540

Use Definition of Speed of Sound and Compressible Flow Equations

RTa γ=20

00

TT

PP

=ρρ

12100

211

−−

⎟⎠

⎞⎜⎝

⎛ −+=⎟

⎠

⎞⎜⎝

⎛=γγ

γγ

γ MTT

PP

22

0

211

21 M

RTCRV

TT

P

−+=+=γ

γγ

Ideal gas law and definition of speed of sound

Compressible flow

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DeTurris - Aero 540

Use Energy Equation to Derive Exit Velocity

0 22 1

22

2

21

10 ≈+=+= VVhVhh

( ) ⎟⎟⎠

⎞⎜⎜⎝

⎛−=−≅

0

20202 122

TTTChhV P

1−=γγRCP

⎟⎟⎠

⎞⎜⎜⎝

⎛−

−=

0

202 1

12

TTRTV

γγ

2

2

00VTCTCh PP +==

Exit velocity