Project3_assignment_2018.pdf

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.)

MAE 5450 - Propulsion Systems

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Download and Build CEA Code (3) • Directory Structure

JAVA GUI Interface

Command Line (DOS) Interface MAE 5450 - Propulsion Systems

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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 5

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. 2) Based on Throat (*), g, Mw. …. 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 MAE 5450 - Propulsion Systems

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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 MAE 5450 - Propulsion Systems

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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 …

*,

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 MAE 5450 - Propulsion Systems

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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

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⎧ ⎪ 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

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M NH ClO + M HTPB + M AL 4

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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

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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

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=

M AL +1 (O / F )⋅( M HTPB + M AL ) 1 +1 (O / F )

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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 MAE 5450 - Propulsion Systems

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Mass Fraction Relationships (3) …Summary

(%)NH ClO 4

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(O / F ) = Rsolid ≡

⎛ ⎞⎟ M NH ClO ⎜⎜ 4 4 ⎟⎟ = 100%×⎜ ⎜⎜⎝ M NH ClO + M HTPB + M AL ⎟⎟⎠ 4 4

Mass Constraint

M NH ClO 4

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( M HTPB + M AL ) M NH ClO + M AL 4

4

M NH ClO + M HTPB + M AL 4

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→

(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 16

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 MAE 5450 - Propulsion Systems

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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

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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 MAE 5450 - Propulsion Systems

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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

MAE 5450 - Propulsion Systems

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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

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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” MAE 5450 - Propulsion Systems

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