The decomposition and combustion characteristics of GAP have been studied by several authors. There are, however,significant differences in the results. An initial attempt at modeling GAP with detailed chemistry is made in an effort to sortthrough the various pieces of experimental data and identify what further experiments are necessary to clarify ourunderstanding. A new type of sensitivity analysis is used to identify how the production of particular species in thecondensed phase decomposition of GAP affects the combustion characteristics. Once the level of uncertainty in model inputsis reduced by further experimental studies, this sensitivity analysis can be used as a guide in modifying combustioncharacteristics by changing propellant chemistry. (Author)
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AIAA-97-0592A MECHANISM AND MODEL FOR GAP COMBUSTION*
Jeffrey E. Davidson and Merrill W. BecksteadBrighatn Young University350 CB.Provo.UT 84606
ABSTRACTThe decomposition and combustion characteristics of GAP have been studied by several authors. There
are, however, significant differences in the results. An initial attempt at modeling GAP with detailed chemistry ismade in an effort to sort through the various pieces of experimental data and identify what further experiments arenecessary to clarify our understanding. A new type of sensitivity analysis is used to identify how the production ofparticular species in the condensed phase decomposition of GAP affects the combustion characteristics. Once thelevel of uncertainty in model inputs is reduced by further experimental studies, this sensitivity analysis can be usedas a guide in modifying combustion characteristics by changing propellant chemistry.
INTRODUCTIONGAP (glycidyl azide polymer) is an energetic
material of interest in the rocket industry because of itshigh burn rate (-1 cm/sec at 40 atmospheres) andrelatively low pressure exponent (-0.5). As seen in thechemical formula (C3H5ON3)n, GAP is very deficientin the oxygen needed for complete combustion. RDXand HMX have received a lot of attention in recentyears and the agreement between experimental dataand model calculations is very reasonable.1'2 To ourknowledge, this is the first attempt to model GAPusing detailed chemistry. There are quite a fewdifferences between GAP and the nitramines. RDX andHMX are crystalline whereas GAP is a polymer. Thecalculated adiabatic flame temperatures at oneatmosphere are about 2925 K for the nitramines and1387 K for GAP. According to the modeling of RDXand HMX, evaporation appears to be the dominatemeans of converting the nitramines from condensed togas phase, where most of the decomposition occurs.Evaporation is not likely to be significant for GAP andcondensed phase decomposition appears to dominatethe combustion characteristics.
This paper describes our initial efforts atputting together the pieces of the GAP combustionpuzzle. Not all the pieces fit together because ofdifferences in experiments, experimental error, andinterpretation of results. It is hoped that in attemptingto develop a model of GAP, we will identify whichexperiments are needed to clarify our understandingand hence improve modeling efforts.
The outline of the paper will be as follows.First, the pieces of the puzzle (experimental data) thatwe have from the literature will be summarized. Wewill then incorporate these pieces of the puzzle into amodel and identify what pieces still appear to bemissing.
BACKGROUND
Thermo-Physical propertiesBeing a polymer, the thermo-physical
properties of GAP can vary with the degree andmethod of cross-linking and curing. The monomerconsists of CsHsNsO. In the literature the quotedthermo-physical properties of polymer vary fromauthor to author. Some of the values found are show inTable 1. Cured GAP is typically approximately 85%GAP, 12% hexamethylene diisocynate (HMDI) and 3%trimethylopropane (TMP)3. However, various cross-linking agents can be used at varying content. Thechemical formula for cured GAP is approximatelyC3.3Hs.6OuN2.63'4. Kubota3 and Frankel7 provide theheat of formation of GAP though the value given byKubota appears to pertain to the monomer and that ofFranke) to the polymer. Lengelle4 lists values for cp andX but introduces these values with, "The physico-thermal characteristics of GAP thought to berepresentative are:" (italics added) implying that thesevalues probably do not have an empirical basis.Likewise, Kubota5 did not provide a source for hisvalue for cp. From this brief literature search, it appearsthat the thermo-physical properties of GAP needfurther investigation and definition.
This work was funded by the Air Force Office of Scientific Research under contract AFOSR F496209-93-1-0430. Their support is much appreciated.
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Table 1: Thermo-physical properties of GAP
Chemical FormulaChemical Structure
Heat of Formation (kcal/g)Density (g/cc)Thermal Conductivity(cal/cm-s-K)Heat Capacity (cal/g-K)Melting Temperature (K)
C3.3H5.60UN2.64 1 C3H5ON3fi 1
H — •OCHCH2
CH2N3
——— OCH2CH20 ——
n
Cj.sHs.sOj. 12 ,̂63
CH2CHO- -H
CH2N3-In 7
1
— -OCHCH2
CH2N3n 6
+0.287 (experimental), +0.2293
1.307, 1.284, 1.276
3.5e-044
0.454, 0.38455
Unknown? Yuan et al, report seeing a molten layer on burning GAP. Noother mention is made in the literature.
Decomposition studiesThere have been several studies on the
decomposition of GAP. The work of three groups(Flanagan, et al.9, Haas and Eliahu10, and Brill,Chen,11 and Oyumi12) will be discussed here. Theirindividual experiments will first be introduced andthen their results compared.
Flanagan, et al. measured the concentrationsof H2, Nz, NO, CO, CH4, C02, N2O, H20, CH2CH2,CH2O, HCN and CH3CH3 using a gas chromatographfor pressures ranging from 6.8 to 68 atmospheres. Theypyrolized the polymer at 1073 K under a high heatingrate-. This temperature is about 300 degrees above thesurface temperatures for self-deflagrating GAPreported by Kubota.5 They were able to measurequantitatively the concentrations of the species listedabove but their elemental balances are not closed. Theycan only account for 58% of the carbon yet have toomuch oxygen (136%) and too much nitrogen (121%).Their results indicate that the decomposition productconcentrations are fairly insensitive to pressure.
Brill and Chen11 have used fastthermolysis/hi IK to study the decomposition of GAPat 1 atmosphere. This method involves using a verythin sample painted onto a metal tip. The tip iselectrically heated and the concentrations of the IR-active species are measured. Because of the inability todetect non-IR active species like N2 and H2, theirreported species concentrations are not absolute butrelative. In an earlier work, Brill and Oyumi11 heated athin sample of GAP spread between two KBr platesunder low and high heating rates. Measurements weretaken between 1 and 1000 psi. Like Flanagan, theirresults also show that concentrations of decompositionproducts are fairly insensitive to pressure.
Haas, et a/.,10 studied GAP decomposition atextremely low pressures (10~2 torr) under laser-assisted
combustion conditions. Gaseous species (N2, CO,C2H4, HCN, CHt, and C2H2) were measured by gaschromatography and mass spectrometry. In addition togaseous species, they also observed that approximately37% of the original GAP was converted to a powderwhose composition is approximately C9H]3N3O2. Theyestimate error bounds on their reported speciesconcentrations to be 25 to 30%.
The mole fractions taken from each of the fourstudies are shown in Figure 1. Because theconcentrations reported by Brill, et al. are relative, thedata from each group is scaled by dividing by thereported mole fraction of CO (See Figure 2). Thoughthe experimental conditions differ greatly from onegroup to another some general observations can bemade. There appears to be better agreement betweenthe results of Haas and Flanagan. Brill reportssignificant concentrations of NH3 and CH20 but theother groups do not. Likewise Brill reports higherconcentrations of HCN but no C2Ht.
Kubota makes the statement, "The resultsshowed that 24% solidified carbon was formed on theburning surface."5 It is unclear how he reached thisconclusion. Lengelle reports a carbon residue on theburning surface of GAP interfering with thermocouplemeasurements.4 Likewise, Yuan8 observedcarbonaceous residues on the burning surface. TheNASA-Lewis equilibrium program13 predictsapproximately 29 mole percent graphite in the finalproducts but Flanagan14 did not see solid carbon andsuggested that we run the equilibrium program againpreventing the formation of solid carbon. It should benoted that Flanagan only accounted for 58% of thecarbon in his elemental mass balances.9 Whensuppressing solid carbon formation, the equilibriumcode predicted concentrations of benzene andnapthlene (~2 mole percent for each) in the finalflame. (See Figure 3) Haas, et al.w reference Mishra15,et al., as observing benzene, pyrole and furan. Benzeneand similar molecules are precursors to soot formation,
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but whether soot, solid carbon and/or aromaticmolecules are formed at all is not clear. This questionneeds to be answered because 24% Csoiid or 2 molepercent benzene is very significant on a mass basis.
Equation 1
4540
351 30last 20
1510-50
HHaas, EliahuS Welner
• Flanagan, Woolery &Kistner
P Oyumi & Brill
E3Chen& Brill
l.inOo
2OI O
o o5 9
Figure 1: Reported Mole Fractions for GAP Decomposition
• Flanagan, Woolery &Kistner
QOyumi & Brill
Observed Species
Figure 2: Comparison of Species from Decomposition Studies
Figure 3: Calculated GAP Equilibrium Products (at 40atmospheres)*
Despite the variance in the studies, there is ageneral consensus on the first decomposition step—thebreaking off of N2 from the azide to form themtrene11'10-5'16'17:
3CHCH2
CH2N3
3CHCH2
CH2N
Kubota5 says that H2 is released with the N2 in theexothermic step (164 kcal/mole). Ranagan9 gives theheat release as -80 kcal/mole. The activation energyfor the above reaction is generally considered to beapproximately 41 kcal/mole.4'5'16'17
Further decomposition of the nitrene is lessunderstood. Dhar and Singh18 say the next step is therelease of H2 (Kubota5 included this in the first step)with a heat of-reaction of 140 to 170 kcal/mole. Kubotasays that the nitrene decomposition produces H2, Csoiidand other gaseous products.19 Brill and Chen11 believethat the nitrene decomposes via two paths. Thedominant step leads to the formation of HCN while thelesser step involves the migration of H to form NH3.None of the other researchers report detecting NH^.Haas, et al.,w also propose two similar decompositionpaths for the nitrene:
CH;— -OCHICH2N
N migration
Equation 2
HCH2
CHNH
>• HCN+ HCO +polymer
' :CH2 + NCO + polymern
The first path mainly leads to HCN, CO and methaneand the second path leads to ethylene, acetylene andCO. They note that the second path could also produceNH3 though it was not observed in their experiments.
The condensed phase reactions of GAP appearto be very complex and poorly understood. Speciesevolving from the surface could range from solidgraphite to naphthalene and from stable species like N2to reactive species like CH2 and monatomic nitrogen.10
At the level of our current understanding, a globaldecomposition mechanism for GAP is probably all thatis justifiable in a numerical model.
Combustion CharacteristicsGAP has some interesting combustion
characteristics, but again there is considerabledisagreement in the literature. For example thepressure exponent of GAP has been reported to be0.2819,0.443,0.524, 0.638, and 0.692.20 Reportedtemperature sensitivities* range from 0.00221 to 0.013
(1/K). These large variations in combustioncharacteristics can likely be attributed to variations in
f Calculated by Nasa-Lewis Equilibriumprogram 13
: Defined as ap=d(ln(rb))/d(Tinit) at constantpressure.
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the preparation process of the GAP. For example,Ranagan, et al, noted that the temperature sensitivityof GAP is very much a function of which curing agentis used.21 To make reliable comparisons betweenexperiment and models it is necessary to know thechemical composition, heat of formation and heatcapacity of the GAP that was used in the experiment.Unfortunately, this information is not included inmost of the publications. The reported combustioncharacteristics will be plotted later in the paper forcomparison with model results.
MODELING
Model DescriptionThe steady-state, one-dimensional, three-
phase model that has been successfully applied toRDX,1 HMX22 and AP23 has been used to study thedeflagration of GAP. The details of the model havebeen described elsewhere (see ref. 22). The modelbreaks the combustion process into three regions: 1)the solid non-reacting region, 2) the two-phasedecomposition region and 3) the gas flame region.Region 1 involves only the integration of the energyequation without any source terms. Region 2 iscalculated as a system of initial boundary valueproblems. The energy and species equations areintegrated in x until all the condensed material hasdisappeared. The resulting temperature and speciesmass fluxes serve as boundary conditions for region 3.Region 3 is calculated using a modified version ofPREMEX.24 The burn rate of the system is determinedby balancing the heat flux between region 2 and region3.
There are some significant differences inapplying the combustion model to a polymer ratherthan a crystalline substance. For RDX, HMX, and APregion 2 began at the melt temperature. But for GAPonly one reference to a molten layer on the surface wasfound in the literature but no melting temperature isgiven.8 For GAP, region 2 starts at some temperatureabove the initial temperature and below a temperaturewhere decomposition is occurring at any significantrate. As long as this criteria is observed the choice oftemperature to start region two had insignificant effectson model outputs. Evaporation is another significantdifference in modeling GAP and the nitramines. ForRDX and HMX, evaporation was the dominate path ofconversion of condensed phase material to gas phaseaccording to the model. Being a polymer, evaporationis likely to be insignificant. For the nitramines,evaporation helped determine the boundary betweenregion 2 and region 3 (the surface of the burningpropellant). For GAP, the surface is defined as the
point where 99.999% of the condensed phase materialhas disappeared due to decomposition into gaseousspecies. Because of the linear relationship betweenconcentration of the condensed species and thedecomposition rates, the exact solution is asymptotic to100%. To avoid this problem, we choose a numbervery close to 100%. Finally, most of the chemicalreactions occurring in the combustion of the nitraminesare occurring in region 3 but for GAP much of the heatrelease happens in the two-phase region. Thecondensed-phase decomposition mechanism of RDXand HMX used in the model is very simple. Most of theoriginal propellant was assumed to evaporate with afraction decomposing into 4 relatively stable species(NO2, HCN, N2O and CH2O). For GAP, numerousspecies with a wide range of stability have beendetected coming off of the surface. Many of the majorspecies detected are already near their thermodynamicequilibrium concentrations (N2 and CO). This causestwo problems. The first problem is developing acondensed phase decomposition mechanism thataccurately reproduces the species observed in thedecomposition studies. The second problem involvesthe calculation of the burning rate. Because the gas-phase flame of GAP is so weak and the burn rate ofGAP is so high (about 4.3 times higher thanRDX/HMX at 1 atmosphere§), the gas-phase reactionsare blown away from the surface. Experimentally thisis observed as a weak flame detached from the surface.The model shows that convection carries the gasesaway from the surface before they can react to asignificant degree. This leads to difficulty in numericalconvergence of region 3 and the calculation of the burnrate.
Model InputsIn this attempt at modeling GAP, we choose
to use the propellant properties listed in Table 2.Table 2: Properties used in Modeling
Chemical Composition
Heat CapacityDensityHeat of Formation (@298K)Thermal Conductivity
C33H56OiiN26(GAP10)0.3845 kcal/g K5
1.3g/cm3
0.28 Kcal/g7
3.5E-4 cal/cm-s-K4
The chemical composition was taken from reference 4and multiplied by 10 to simulate the polymer (GAP10).Other values were taken from the sources as referencedin the table. The gas-phase reaction mechanism was
8 Frankel reports that GAP self-extinguishesat 1 atmosphere.7
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developed by assembling the Melius25-Yetter26 gasphase mechanism for RDX, Cohen's27 AP mechanismand the GRI hydrocarbon mechanism.28 Of theresulting mechanism, some species which would not bepresent were eliminated (like RDX, chlorinecontaining species, etc.). The result was a mechanismcontaining 58 species involved in 292 reactions. Thismechanism is probably much more complicated than isnecessary but at this point, our model is not establishedwell enough to reduce the mechanism. Many differentglobal decomposition mechanisms were tried for thecondensed phase. As expected, the predictedTable 3: Proposed Condensed-phase Reaction Mechanisms"
combustion characteristics are largely controlled by thecondensed phase reactions. The various mechanismswere developed by setting the burn rate at 40atmospheres to 1.96 cm/sec (as seen in experiment7)and adjusting the species being produced and the pre-exponential rate constants until the heat fluxes at theinterface between regions two and three matched. Thena series of runs were performed to see how the model'spredictions compare to experimental data at otherinitial temperatures and pressures. Some of themechanisms that were tried are shown in Table 3.Each mechanism has four steps and, for ease of
Figure 4: Comparison of Condensed Phase Decomposition Products
GAP10 is 10 units of polymer backbone structure, GAPR10 is GAP10 minus 8N2. Activation energyunits are kcal/mole. The activation energy for Step 1 was measured by Lengelle, et al.4 Numbers representstoichiometric coefficients. For example, Step 1 in Mech A is GAP10->1GAPR10+8N2.
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comparison, steps are listed together rather than inmechanisms. The differences in rate constants betweenmechanisms for each step are minor. The species moleflux fractions coming off of the surface for the threemechanisms are compared in Figure 4. The molefractions shown are scaled by the mole fraction of CO.Thus Figure 4 can easily be compared to scaledexperimental values shown in Figure 2. Mechanism Aassumes that much of the carbon goes to Csoud asreported by Kubota.5 Flanagan29 questions theproduction of Csojid. A and B both produce significantamounts of the very reactive species CH2. Because theformation of CE^ requires significant energy (hightemperatures), Litzinger recommended that it bedropped from our decomposition mechanism.30 Finally,both mechanisms A and B produce CNO. In Haas'sproposed mechanism (Equation 1 and Equation 2above) NCO (not CNO) is produced, but according toFlanagan it is unlikely that many nitrogen-oxygenbonds (like in CNO) are being formed in the condensedphase because of the lack of oxygen. In developingmechanism C, the objective was to avoid species likeCNO, CSO]id and CH2- Comparisons with experimentaldata and model predictions using each mechanism aremade below.
COMPARISION WITH EXPERIMENTAL DATABecause of the lack of a definitive mechanism,
mechanisms A, B and C were each optimized to giveapproximately the correct burn rate at 40 atmospheres.There remains enough uncertainty in the condensedphase mechanism that attempting to do furtheroptimization at this point would only force-fit themodel with possibly unrealistic parameters. Thecalculated burn rate as a function of pressure iscompared to experimental data in Figure 5. Theagreement is reasonable for this stage of modeling.
Figure 6: Surface Temperature
_ 1500-5 1400-I 1300-
u 1100'I 1000-| 900-| 800-I 700-
«no .
m _ t l j g j ,_M. —— *( • J*.~ —— *" ——
//'""
// m NasaLewis ———— MechA
0 20 40 60 SO 100
Pressure (aim)
Figure 7: Adiabatic Flame Temperature
Kubota5 measured the surface temperature ofGAP at pressures less than 10 atm (See Figure 6).Mechanism A under-predicts the surface temperatureby about 50 K. All three mechanisms under-predictLengelle's4 value of 800 K at about 40 atm.
Figure 7 shows the adiabatic flametemperature compared to that calculated by the NASA-Lewis equilibrium program.13 Mechanisms A and Bcome much closer to thermal-equilibrium than doesmechanism C. In fact, calculations made using
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0.012
2 o.oi •
0.
S 0.006-Ol
0.
g A
•
• MechAAMechB»MechC
0 20 40 60 80 100 120
Qs (cal/g) (heat released In condensed phase)
Figure 9: Temperature Sensitivity and Q,
mechanism C show only about a 100 K increase abovethe surface temperature. Lengelle* reports a flametemperature as "(?) 1300 K" at -40 atm. This indicatesthat the combustion of GAP may not go to completion.
Kubota5 reports the temperature sensitivity ofGAP to be 0.01. Figure 8 displays a plot of Kubota'svalue against model predictions. Although the modelseach use the same physical properties for GAP, thereare significant differences in op. According to themodel ap is largely determined by the solid heatcapacity, but appears to be also influenced by the heatreleased due to reaction in the condensed phase, Qs(See Figure 9).
Table 4: Sensitivity to Production of Species Analysis (Mechanism C)
SENSITIVITY ANALYSISIn developing the condensed phase
decomposition mechanisms both the species beingproduced and the rate constants were varied to aid inthe numerical convergence of the burn rate at 40 atm.To determine the effect that the production of aparticular specie has on the combustion characteristicswhere S represents each species, one at a time. This, ofcourse, violates the mass and energy balances to asmall degree but provides some useful information. Fora particular specie, this sensitivity analysis indicateswhether its production increases the burn rate ordecreases the burn rate. This analysis also providessimilar information relative to the surface temperature,flame temperature, and other combustioncharacteristics as necessary. This type of sensitivityanalysis will vary with the base mechanism. Thepresence and concentration of other species affects theinfluence a particular species has on thesecharacteristics. Table 4 summarizes these results formechanism C at 40 atm. As calculated by the model, asmall amount of each gaseous specie was generated inone of the decomposition reaction mechanisms. Forexample, starting with mechanism C, reaction 2 wasperturbed to:
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According to the results in Table 4, if thedecomposition of GAP produces species with nitrogen-oxygen bonds the final flame temperature and burnrate are higher. On the other hand, if the solid-phasedecomposition of GAP produces final products likeCOz and H^O, the flame temperature, surfacetemperature and burn rate are lower. Producingradicals like CH, N, NCN and CN tends to increase thesurface temperature. All three mechanisms giveapproximately the same burn rate at 40 atm, but thisanalysis does explain why the calculated adiabaticflame temperatures using mechanisms A and B arehigher than those of mechanism C. Both A and Bproduce CNO in the condensed phase. Though notlisted in Table 4, it ranks as number 12 in increasingthe flame temperature. It does contain a nitrogen-oxygen bond. This analysis can also explain why thesurface temperature of mechanism A is low comparedto both experimental data and the model results usingthe other two mechanisms. The reason appears to bethe high production rate of H2 (See Figure 4). Again itis not listed in the top ten species for decreasing thesurface temperature for mechanism C but is rankednumber eight when the sensitivity calculations are runusing mechanism A. This type of analysis is veryuseful in trying to understand the complexdecomposition of GAP. Currently there is not a welldefined decomposition mechanism but as one evolves,this type of analysis can guide researchers as to whatspecies could be being produced or which species'thermodynamic properties need review. Once most ofthe uncertainty in the model has been resolved byexperiment, this type of analysis could be useful inidentifying ways of modifying the combustion of apropellant by altering its chemistry.
CONCLUSIONOur lack of understanding of the combustion
of GAP is significant. To our knowledge, there are fewdefinitive property values for GAP in the literature.Most values reported in the literature appear to havebeen estimated. Several research groups have donesignificant studies on the decomposition of GAP, butthe various groups arrive at very different conclusions.Some report large amounts of solid carbon while otherssay that they did not see any. Some measure significantamounts of NH3 and CH2O while others report smallamounts of GH^O and no NHj. One researcher reportsseeing aromatic molecules. Some of these differenceslikely stem from differences in the preparation of thepolymer and in experimental technique. The method ofpreparation can affect the chemical composition, theheat of formation, and the physical properties, butseveral papers on experimental data leave out these
critical pieces of information. There are also verysignificant differences in the reported bum rate,temperature sensitivity and other combustioncharacteristics in the literature. At this point, there isenough uncertainty in the properties and performanceof GAP that modeling can easily become a curve-fitting exercise. In summary, the following information(in approximate order of importance) needs to beclarified:
• Chemical composition and heat offormation of the GAP being tested.
• Quantitative concentrations of thedecomposition products of GAP(including possibly very reactive species).
• Establish and quantify the presence ofCSoiid, benzene, NH3 etc.
• Burn rate as a function of pressure andinitial temperature.
• The final flame temperature.• The final combustion products of GAP.• Surface Temperature.• Temperature Profile.The purpose of this study has not been to force
the model to fit the data. Rather, we have attempted toindicate what further experimental data are required toeliminate some of the degrees of freedom currently inour model. We have also used a type of sensitivityanalysis of model predictions with respect to theproduction of various species in the decompositionmechanism of GAP to identify possible alternatives tothe reported decomposition products. From thisanalysis, species containing nitrogen-oxygen bondswill increase the final flame temperature and burn ratethough the formation of such bonds appears unlikely inGAP combustion. Once most of the uncertainty in themodel has been resolved by experiment, this type ofanalysis could be useful in identifying ways ofmodifying the combustion of a propellant by alteringits chemistry.
REFERENCES
1 Davidson, J. E., and Beckstead, M. W.,"Improvements to RDX Combustion Modeling," 32nd
2 Prasad, K., Yetter, R., and Smooke, M., "AnEigenvalue Method for Computing the Burning Ratesof RDX Propellants," 32nd JANNAF CombustionMeeting, Huntsville AL, CPIA # 638, Vol. 1, pp 69-84.Oct 23-27, 1995.
3 Kubota, N. and Sonobe, T., "CombustionMechanism of Azide Polymer." Propellants,Explosives, Pyrotechnics Vol. 13 pp. 172-177, (1988)
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4 Lengelle, G., Fourest, B., Godon, J. C., andGuin C., "Condensed Phase Behavior and AblationRate of Fuels for Hybrid Propulsion," 2P"1 JointPropulsion Conference, AIAA 93-2413, June 28-30,1993.
5 Kubota, N. and Sonobe, T., "Combustion ofGAP Propellents," Comb. And Detonation Phenomena,19fh International Annual Conference oflCT,Germany, (1988).
6 Kubota, N. and Sonobe, T., "Burning RateCatalysis of Azide/Nitramine Propellants," 23rd
Symposium (International) on Comnbustion, TheCombustion Institute, pp. 1331,1337 (1990).
7 Frankel, M. B., Grant, L. R., and Flanagan,J. E., "Historical Development of Glycidyl AzidePolymer," Journal of Propulsion and Power, Vol. 8,No. 3, May-June 1992.
5 Yuan, L.Y., Liu, T. K, and Cheng, S. S.,"The Combustion Characteristics of GAP GumstockPropellants," AIAA 96-3235 Joint PropulsionConference July 1-3, 1996.
9 Flanagan, J., Woolery, D. and Kistner, R.,"Fundamental Studies of Azide Decomposition andCombustion," AFRPL TR-96-094, Dec. 1986.
11 Chen, J. K., and Brill, T, B., "ThermalDecomposition of Energetic Materials 54. Kinetics andNear-Surface Products of Azide Polymers AMMO,BAMO and GAP in Simulated Combustion,"Combustion and Flame Vol 87, pp. 157-168,1991.
12 Oyumi, Y. and Brill, T. B., "ThermalDecomposition of Energetic Materials 12. InfraredSpectral and Rapid Thermolysis Studies of Azide-Containing Monomers and Polymers," Combustionand Flame Vol 65, pp 127-135, 1986.
13 McBride, B. J., Gordon, S., " ComputerProgram for Calculation of Complex ChemicalEquilibrium Compositions and Applications," NASAReference Publication 1311, June 1996.
14 Personal communication with JosephFlanagan, July, 1996.
15 Mishra, I, Juneau, S. P. and Groom, T.,1984 JANNAF Propulsion Meeting, CPIA Publication390, pp. 118-132,1984.
15Farber, M., Harris, S. P. and Srivastave, R.D., "Mass Spectrometric Kinetic Studies on SeveralAzido Polymers," Combustion and Flame, Vol 55, pp.203-311, 1984.
17 Goshgarian, B. B., "The Mechanism ofNitramine and Advanced Propellant Ingredient Initial
18 Dhar, S. S., and Singh, Haridwar,"Burnrate & Catalysis Behaviour of GAP based CMDBPropellants," AIAA 95-2586, Joint PropulsionConference, San Diego CA, Jul. 10-12, 1995.
19 Kubota, N., Sonobe, T., Yamamoto, A., andShimizu, H., "Burning Rate Characteristics of GAPPropellants," J. Propulsion, Vol 6, No. 6 pp. 686-689,Nov.-Dec. 1990.
20 Simmons, R. L., "Unusual CombustionBehavior of Nitramines and Azides," 4th IntemaltionalSymposium on Special Topics on Chemical Propulsion,Stockholm, Sweden May, 1996.
21 Flanagan, Joseph E., Woolery, Dean O.,and Kistner, Richard L., "Combustion Behavior ofAzide Polymers," CPIA 432 Vol. 2,22nd JANNAFCombustion Meeting, Pasadena CA. Oct 7-10, 1985.
22 Davidson, J. E., and Beckstead, M. W., "AThree-Phase Combustion Model of HMX," 26th
International Symposium on Combustion,'" TheCombustion Institute, Naples, Italy, July, 1996.
23 Tanaka, M., and Beckstead, M. W., "AThree Phase Combustion Model of AmmoniumPerchlorate," AIAA 96-2888, 32nd Joint PropulsionConference, Lake Buena Vista, FL., July, 1996.
24 Kee, J. Grcar, J. F., Smooke M. D. andMiller, J. A., "A FORTRAN Program for ModelingSteady Laminar One-Dimensional Premixed Flames,"SANDIA REPORT SAND85-8240»UC-4-l. April1992.
25 Melius, C. F., "Thermochemical Modeling:EL. Application to Ignition and Combustion ofEnergetic Materials," Chemistry and Physics ofEnergetic Materials, (ed. S. N. Bulusu) pp, 51-78,1990.
26 Yetter, R. A., Dryer, F. L., Alien, M. T.,Gatto, J. L., "Development of Gas-Phase ReactionMechanism for Nitramine Combustion," Journal ofPropulsion and Power, Vol. 11, No. 4, pp.683-697,Jul-Aug. 1995.
27 Cohen, N.," A Review of Kinetic Modelsfor the High Temperature Gas Phase Decomposition ofAmmonium Perchlorate," Aerospace Report No.AFT-92(9558)-3, pp. 1-36, 1992.
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