Project 3, CEA Exercise
• This Programing Assignment is due on Beginning of Final Exam Period
-- 11:30 AM MDT, Wednesday May 3.
• We are going to build a chemistry table for an AP-composite rocket
Propellant, and investigate the effects due to increasing metallization
of the grain.
• Look at important effects on flame temperature, molecular weights, and
C* (infinitely expanded nozzle)
MAE 5450 - Propulsion Systems
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Download and Build CEA Code
• Down Load the CEAGUI from the NASA Glenn Research center Web site
- Recommend you use the windows GIU as it seems to be bug free …
- Linix code has a bunch of compile errors that need to be fixed
- Special Setup Procedure for MAC User ..
http://www.neng.usu.edu/classes/mae/6530/propulsion_systems/section7/ceagui_FAQ_g77MacPC.pdf
• See … http://www.grc.nasa.gov/WWW/CEAWeb/ceaRequestForm.htm
1)Update your comuter’s Java Runtime Environment, Reboot Computer
• Java SE Runtime Environment 8 Downloads
Works for most of you
MAE 5450 - Propulsion Systems
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Download and Build CEA Code (2)
• FCEA2.exe … built code for PC processor
• Download all three(3) .zip files and save into the installation directory
• Extract (unzip) the CEAgui JAR file (CEAgui-jar.zip)
• Extract (unzip)the CEA+ Fortran Package (CEA+Fortran.zip) for CEA files
• Extract (unzip) the CEAexec Package (CEAexec-win.zip)
• You must have the 6! Unzipped files installed in the installation directory
à 1) CEAgui.jar, 2) thermo.lib, 3) trans.lib, 4) b1b2b3.exe, 5) syntax.exe, and 6) FCEA2.exe in the installation
directory.)
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Download and Build CEA Code (3)
• Directory Structure
JAVA GUI Interface
Command Line (DOS) Interface
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Project Background
Need at
Least 15%
minimum
total HTPB
binder by mass
for “cake” to
stick together
M HTPB
0.150 ≤
M Al + M APSystems
+ M HTPB )
MAE 5450(- Propulsion
Adiabatic Flame Temperature of AP/HTPB/Al
Composite Propellant as function of Mass
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Project Background (2)
• Investigate Mixture effects
O/F
Plot T0,g ,C* for both Chamber & Throat vs O/F for increasing aluminization levels
• Using equilibrium properties at Throat, plot data for various mixture ratios
and determine optimal operating mixture ratio (based on C*) .. Assume T0 is
constant through out motoe
• Based on flow properties from nozzle throat …
Update AMW L-700 model for “Best case” Formulation Properties
MAE 5450 - Propulsion Systems
Assume that St. Roberts burn /erosive burn/Bates
Grain parameters are same as previously used
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Project Overview
•
Set up input file to run as “Rocket” Problem with a combustion pressure
of 3000 kPa (30 bars)
• Look AP Composite propellant with Mixture ratio of AP/HTPB/AL
• Run code in “equilibrium”, with “infinite” combustor contraction ratio
• Use results for molecular weight(Mw), ratio of specific heats (g), and
combustion temperature to calculate and C*
1) Based on Chamber, g, Mw.etc.
2) Based on Throat (*), g, Mw. etc.
…. Assume that T0chamber = T0*
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Project Overview
(2)
• Apply what we learn to AMW-L700 Motor Analysis
.. Look at both Cylindrical Port with both erosive burn and Bates grain ..
Compare original and “improved” propellant” formulation (be sure to reevaluate the propellant density based on formulation) Using new g, Rg,
Mw, T0 ….......
Compare time history plots of
chamber pressure
thrust
regression rate
Calculate and compare …
total impulse .. effective Isp’s
… assume that Saint Robert’s burn parameters (a, n} and the erosion
parameters (k, Mcrit) remain unchanged for new propellant
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Project Overview
(3)
• Using equilibrium combustor properties from CEA
• Based on Equilibrium flow “Frozen” at nozzle throat …
Compare to project 2 solution including erosive burn model for cylindrical grain
and /Bates grain model
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Equilibrium Properties at
Chamber and Throat (example)
CHAMBER THROAT
P0/Pstatic
P, BAR
T, K
RHO, KG/CU M
H, KJ/KG
U, KJ/KG
G, KJ/KG
S, KJ/(KG)(K)
1.0000
31.000
2925.58
3.65500
0.00000
-848.15
-26683.
9.1209
1.7428
17.787
2744.19
2.2555 0
-454.46
-1243.08
9 -25484.0
9.1209
MW, (1/n)
(dLV/dLP)t
(dLV/dLT)p
Cp, KJ/(KG)(K)
GAMMAs
SON VEL,M/SEC
MACH NUMBER
28.680
-1.01044
1.2400
3.1727
1.1495
987.4
0.000
28.932
-1.00776
1.1912
2.9098
1.1526
953.4
1.000
MAE 5450 - Propulsion Systems
Assume P0, T0 constant
throughout motor
Calculate C* based on local
g (throat), Mw (throat) , T0 (chamber)
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Chamber Pressure Ballistic Equation
Show that when “shifting equilibrium” from chamber to throat
and then properties frozen at throat is used … the chamber
pressure equation for solid motor must be modified as …
Rg = Ru/Mw
*
*,
Mw* -> properties at throat
Rg -> based on molecular weight at chamber conditions, Mw
P0, T0 Chamber stagnation Pressure, temperature
Use modified chamber pressure ballistic
equation in your follow-on analysis
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Characteristic Velocity, C*
• The characteristic velocity is a figure
of thermo-chemical merit for a particular
propellant and may be considered to be
Indicative of the combustion efficiency.
*
*
*
*
*
• Lower Molecular Weight Propellants Produce Higher C*
• For this calculation based value on g, M at the nozzle throat …
w
MAE 5450 - Propulsion Systems
*
Mass Fraction Relationships
Relate O F to (%)NH ClO
4
4
⎧
⎪
M NH ClO
⎪
4
4
⎪
O/ F≡
⎪
⎪
M HTPB + M AL
⎪
⎪
⎪
→⎪
⎨
⎪
⎪
⎛
⎞⎟
M NH ClO
⎪
⎜⎜
⎪
4
4
⎟⎟
%
≡
100%×
⎪
(
)
⎜
⎪
NH 4ClO4
⎜⎜⎝ M NH ClO + M HTPB + M AL ⎟⎟⎠
⎪
4
4
⎪
⎪
⎩
⎫
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎬
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎭
⎛
⎞⎟
⎜⎜
⎛
⎞⎟
⎟⎟
⎜
⎟⎟
⎜⎜
⎛
⎞⎟
⎜⎜
⎟⎟
M NH ClO
1
1
⎜⎜
⎟⎟ = 100%×⎛⎜ O / F ⎞⎟⎟
4
4
⎟
⎜
⎟
⎜
→ (%)NH ClO = 100%×⎜
⎟⎟ = 100%×⎜⎜
⎟⎟ = 100%×⎜
⎜⎜
⎜⎜⎝ M NH ClO + M HTPB + M AL ⎟⎠
⎜⎜
4
4
M HTPB + M AL ⎟⎟
1 ⎟⎟⎟
O / F +1⎟⎟⎠
⎝
⎜
4
4
⎟⎟
⎜⎜1+
⎟⎟
⎜⎜⎝1+
⎠
O
/
F
M NH ClO ⎟⎠
⎜⎝
4
4
(%)NH ClO
4
Inverse → O / F =
1−
4
100%
(%)NH ClO
4
4
100%
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Mass Fraction Relationships (2)
…i.e. Mass Constraint Rsolid on terms of O/F and fal
Rsolid ≡
M NH ClO + M AL
4
4
M NH ClO + M HTPB + M AL
4
4
M AL
f Al ≡
M HTPB + M AL
→ Rsolid =
M NH ClO = (O / F ) ⋅( M HTPB + M AL )
4
Rsolid
M AL
+1
M NH ClO
4
4
M AL
+1
(O / F )⋅( M HTPB + M AL )
M AL + M HTPB
M AL + M HTPB
+1
+1
M NH ClO
(O / F )⋅( M HTPB + M AL )
4
4
=
M AL
+1
(O / F )⋅( M HTPB + M AL )
1
+1
(O / F )
4
M AL
M AL
+1
+ (O / F )
f Al + (O / F )
(O / F )⋅( M HTPB + M AL ) (O / F ) ( M HTPB + M AL )
=
⋅
=
=
1
(O / F )
(O / F ) +1
(O / F ) +1
+1
(O / F )
Rsolid − f Al
Inverse → (O / F ) =
1− Rsolid
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Mass Fraction Relationships (3)
…Summary
(%)NH ClO
4
4
(O / F ) =
Rsolid ≡
⎛
⎞⎟
M NH ClO
⎜⎜
4
4
⎟⎟
= 100%×⎜
⎜⎜⎝ M NH ClO + M HTPB + M AL ⎟⎟⎠
4
4
Mass Constraint
M NH ClO
4
4
( M HTPB + M AL )
M NH ClO + M AL
4
4
M NH ClO + M HTPB + M AL
4
4
→
(O / F ) + f Al
Rsolid =
(O / F ) +1
(O / F ) =
Rsolid − f Al
1− Rsolid
M AL
f Al ≡
M HTPB + M AL
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Mass Fraction Relationships (4)
…i.e. Mass Constraint on terms of O/F and fal
⎛
⎞⎟
M Al + M AP
⎜⎜
⎟⎟ −
⎜⎜⎝ M
+ M Al + M AP ⎟⎠
HTPB
O / FMax =
⎛
M Al + M AP
⎜
1−⎜⎜
⎜⎝ M
+M +M
HTPB
Required ....
⎞⎟
⎟⎟
⎟
AP ⎠
(0.85)− f Al
=
1−(0.85)
M Al + M AP
≤ 0.85
M HTPB + M Al + M AP
M Al
f Al =
M HTPB + M Al
MAE 5450 - Propulsion Systems
Al
f Al
M Al
f Al
=
M HTPB 1− f Al
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Mass Fraction Relationships (3)
…e.g. look at à fAl = 0.2 @ O/F = 5
M AL
f Al
0.2
=
=
= 0.25
M HTPB
f Al −1 0.8
→
Required → Rsolid
⎛
⎞⎟
M NH ClO
⎜⎜
4
4
⎟⎟ < 0.85
=⎜
⎜⎜⎝ M NH ClO + M HTPB + M AL ⎟⎟⎠
4
4
Too High of Al Fraction!
(O / F ) + f Al (5) + 0.2 5.2
Rsolid =
=
=
= 0.86667 > 85% ..... NO GOOD! .. Must Lower O/F or f Al
(O / F ) +1 (5) +1 6
… look at à fAl = 0.15 @ O/F = 4.5
M AL
f Al
0.15
=
=
= 0.1765
M HTPB
f Al −1 0.85
→
Required → Rsolid
⎛
⎞⎟
M NH ClO
⎜⎜
4
4
⎟⎟ < 0.85
=⎜
⎜⎜⎝ M NH ClO + M HTPB + M AL ⎟⎟⎠
4
4
(O / F ) + f Al (4.5) + 0.15
Rsolid =
=
= 0.8455 < 85% ..... Just BARELY!
(O / F ) +1
(4.5) +1
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AP Composite Propellant
Key Physical Properties
• AP chemical formula, NH4 Cl O4
ρ NH 4ClO4 = 1.950
Ammonium perchlorate crystals decompose
before melting
g
cm 3
M w NH ClO = 117.49 kg/kg−mol
4
Fine white powder used
as propellant oxidizer
4
MAE 5450 - Propulsion Systems
When AP is mixed with a fuel (like a Al
powder) or polymeric binder (like HTPB) it
can generate considerable het release and
allows self-sustained combustion once lit 18
AP Composite Propellant -- Key
Physical Properties
• Powdered Elemental Al, micron-scale
(molecular weight)
ΔH f0 = 0 KJ /mol
kg / kg − mol
Al Powder acts both as a fuel
and combustion catalyst
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Key Physical Properties, cont’d (2)
• HTPB -- (ARCO R-45TM, polymerization ~ 50)
•
Full Chemical Formula
OH -
- OH
• Butadiene C4H6, with n-50 degree of polymerization with hydroxyl termination
(hydroxyl makes polymerized rubber more hydrophobic)
(C4H6)50 OH2 à Molecular Weight ~ 2766 kg/kg-mol
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Key Physical Properties (3)
• “Reduced” Chemical Formula w Broken
Polymer Bonds
(C4 H6 )⋅(OH )
C4H6 (butadiene gas)
O2
H2
TARs
0.4
0.04
• Main “fuel” for
combustion reaction
Molecular Weight ~ 54.68 kg/kg-mol
ρ HTPB = 0.930
g
cm 3
ΔH f ~ 23.99 KJ / g−mol = 23.99×103 KJ /kg−mol
0
• Enthalpy of Formation Accounts for Energy Required to
Break Polymer Chains
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Key Physical Properties (4)
• HTPB Properties
not listed in CEA
tables
• Insert HTPB
Properties
Here (Not in CEA
tables)
• CEA calculates
mass properties
based on entered
chemical formula
MAE 5450 - Propulsion Systems
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Key Physical Properties (5)
• Other Important Physical Properties
Need to calculate your propellant density for
“best mixture”
ρ HTPB = 0.930
g
cm 3
ρ NH 4ClO4 = 1.950
g
cm 3
ρ Al Powder = 2700 kg
m3
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Key Physical Properties (6)
• Other Important Physical Properties
ρ HTPB = 0.930
g
cm 3
ρ NH 4ClO4 = 1.950
g
cm 3
ρ Al Powder = 2700 kg
m3
ρ propellant =
1
⎛%
⎞⎟ ⎛
⎜⎜ NH4ClO4 ⎟ ⎜ % Al ⎞⎟ ⎛⎜ % HTPB ⎞⎟
⎟⎟ ⎜
⎟⎟
⎜ 100% ⎟⎟ ⎜⎜
⎜
⎟⎠ ⎝100% ⎟⎠ ⎝ 100% ⎟⎠
⎜⎝
+
+
ρ propellant
ρ NH ClO
ρ HTPB
4
MAE 5450 - Propulsion Systems
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CEA Input File ….. Example < file >.inp
problem
o/f=1,1.5,2,2.5,3,3.5,4,4.5,5,5.5,6,6.5,7.,7.5,8,9,
rocket equilibrium frozen nfz=1 tcest,k=3000
p,bar=30,
react
oxid=NH4CLO4(I) wt=100 t,k=298
fuel=AL(cr) wt=25 t,k=298
fuel=HTPB wt=75 t,k=298
h,kj/mol=23.99 C 4 H 6 O 0.04 H 0.04
output
plot p t rho m cp gam end
Setup file by default written to < file > input when
Code is saved using > “save as”
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