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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