Army Research Laboratory 

Aberdeen Proving Ground, MD 21005-5066 

ARL-TR-2390 February 2001 

A Chemically Specific 

Burning Rate Predictor Model for 

Energetic Materials 

Martin S. Miller and William R. Anderson 

Weapons and Materials Research Directorate, ARL 

Approved for public release; distribution is unlimited. 
Abstract 

. 

The application of complex networks of elementary chemical reactions to the gas phase of 

burning energetic materials has increased markedly over the last decade. The exquisite 

complexity of these gas-phase reaction networks, coupled with available high-rigor treatments 

of transport, is not matched by an equivalent level of sophistication in descriptions of the 

condensed-phase and interfacial phenomena. Owing to the vastly more complicated, many-body 

nature of the condensed phase, this condition is not likely to be relieved soon. In response to 

these difficulties, a new semi-empirical approach to burning-rate calculation has been developed 

and applied to frozen ozone, cyclotrimethylenetrinitramine (RDX), and nitroglycerine. The new 

approach hypothesizes asingle overall reaction linking the unreacted material to the net products 

of condensed-phase decomposition and characterizes their rate of formation according to an 

empirically derived pyrolysis law. These condensed-phase products become the reactants for the 

gas phase, which are treated in full elementary-reaction detail. Using this new semi-empirical 

model, a methodology for computing the relative effects of several additives on the burning rate 

of nitroglycerine is developed and demonstrated. Hopefully this approach will enable more rapid 

progress in modeling multi-ingredient propellants than did previous approaches attempting to 

model the condensed-phase processes in detail. 

ii 
Table of Contents 

1. 

2. 

3. 

4. 

5. 

6. 

7. 

8. 

9. 

10. 

List of Figures ........................................................................................................... 

List of Tables ........................................................................................................... 

Introduction .............................................................................................................. 

Conceptual Framework.. ......................................................................................... 

Mathematical Framework ....................................................................................... 

Example: Frozen Ozone ......................................................................................... 

Example: RDX ........................................................................................................ 

Example: Nitroglycerine ........................................................................................ 

Effect of Chemical Additives on the Burning Rate.. ......................... . ................... 

V 

vii 

1 

3 

5 

12 

13 

18 

27 

Speculations on Practical Burning-Rate Modifiers .............................................. 

Conclusions ............................................................................................................... 

References ........ .I ....................................................................................................... 

Appendix: Reaction Mechanism (DBll) for Nitroglycerine.. ............................. 

3 1 

32 

35 

41 

Distribution List.. ..................................................................................................... 5 1 

Report Documentation Page ................................................................................... 53 

. . . 

111 
h”IEN’TTONALLY LEFT BLANK. 
List of Figures 

Fieure Page 

b 1. 

2. 

3. 

4. 

5. 

6. 

7. 

8. 

9. 

10. 

11. 

12. 

Demonsuation of the Universality of the Pyrolysis Law for Double-Base 

Pro+lants Based on the Work of Zenin [28] . . . . . . . . . . ..~..*.1~...f.*....*..................**.~.~... 

Quality of Fit of a Pyrolysis Law to an Evaporative Regression Mechanism 

Calculated From a First Principles Treatment of Frozen Ozone D&lag&on [21] . . 

Pyrolysis IAW for RDX Derived From Zenin’s [28] Experimental Data . . . . . . . . . . . . . . . . . 

Comparison of the Burning Rates for Frozen Ozone Computed by the New Model 

Developed in This Report and the Previously Published First-Principles Model . . . . . 

Linear Least-Squares Fit of the Speci%Heat Data of Shoemaker et al. [30] and 

Miller [31] for Solid RDX Over a Range of Initial Temperatures . *....~..~..I...*.***.*..*~ 

Comparison of Burning Rates for RDX Computed by the New Model to Those 

Computed by That of Liau [ 151 and to Experimental Data .**.*....*.**..***........*****....... 

Temperature Profiles for RDX at 1 atm and 293 K, as Computed by the New 

Model, Compared With That of Liau [ 15 ]. . . . ..~~~..~~....~.*.~~.~.~.~..~..~~.~..~~*.......~~~~..~~~~.. 

Species Pro&s for RDX at 1 atm and 293 K, as Computed by the Present Model 

(Solid Lines), Compared With That of Liau [ 151 .. . . . . . . . ..*..*.~.f...~..**........**...~*~~........ 

Mechanism for Condensed-Phase Decomposition of NG Proposed by Levy [39] . . . 

Computed NG Burning Rates at 298 K for Different Decomposition Paths Using 

a New Semi-Empirical Model Compared With Experimentally Measured Rates of 

Andreev [40,41] and Andreev et aL [42] . . . . . . ..f...f.................. . ..*f.......**...***............ 

IdentiEcation of Dominant Chemical Pathways for NG at 10 atm and 298 K Using 

the MSM4 Product Set ..f..**~.~~...~~...~...~......f*...**.*...*..*..*. . ..~~~.ff.~~.~~..~~~..........~~.....~.~~ 

The Effect of Two Additives, NH3 and N2, on the Flame Structure of NG at 

10 atm and 298 K Using Levy’s [39] Decomposition Product Set . ..***......*..*.......... 

10 

11 

11 

13 

14 

15 

16 

17 

21 

22 

23 

28 

V 
INTENTIONALLY LERBLANK. 

Vi 
List of Tables 

Table N 

1. Liquid-Phase Reactions in Deflagrating RDX Adopted by Various Models . . . . . . . . . . . . 4 

2. Values of Condensed-Phase Parameters Used in RDX Calculations . . . . . . . . . . . . . . . . . . . . . . . 14 

3. Values of Condensed-Phase Parameters Used in NG Calculations . . . . . . . . ..*........*.*.... 19 

4. NG Condensed-Phase Decomposition Paths Considered l****.......~~~~~..........*.......~.~.. 19 

5. Relative Sensitivity Coefkients of the Temperature Gradient at the Surface to the 

Most Sensitive Reactions (in Rank Order) for NG, With MSM4 Product Set at 

10 atm and 298-K Initial Temperature . ..~~*....t..l.....***..*.......~.* . . ..~...~~~~.....~....~~...~*.~.~ 26 

6. Effect of Different Chemical Additives on the Burning Rate of NG at 10 atm and 

298 K Assuming the Levy [39] Decomposition Product Set . ..*~*~..f..*~..f..*..**.....~..... 30 

7. Effect of Different Chemical Additives on the Burning Rate of NG at 10 atm and 

298 K Assuming the MSM4 Decomposition Product Set .. ..~.*.~.~f...*.....**.*........~..~~.. 30 

Vii 
INTENTIONALLY LEFTBLANK. 

. . . 

Vlll 
1. Introduction 

The last 10 years have seen an important paradigm shift in the modeling of energetic material 

combustion. Models using chemically nonspecific reaction formalisms have given way to models 

that promise to explain the detailed chemical nature of combustion through their explicit elementaryreaction mechanisms. The seminal prototypes for the chemically nonspecific models were 

developed during wwll by Parr and Crawford [l] and Rice and Ginell[2]. Typically these models 

considered agasification reaction at the surface of the condensed phase and a single overall reaction 

in the gas phase; burning rates were computed by imposing the energy and species conservation 

equations in each phase and at the burning surface. ‘A conceptual review of many of these models 

was given by Miller [3], and a review of their application to composite propellants was provided by 

Ramohti [4]* These early models elucidate the interplay ‘between the chemical and physical 

phenomena that produce the observed patterns of burning rate dependence on pressure and initial 

temperature and provided guidance in the choice of some physical features of composite-propellant 

formulation, such as oxidizer particle size. By their nature, however, these models cannot give 

guidance for chemical formulation and the effects of chemical additives on performance. This role 

had to await the development of chemically specific descriptions of the combustion. Models with 

explicit chemical mechanisms now dominate new development activities and are the subject of this 

article. We will confine ourselves in this report to steady-state combustion, although some recent 

work [5, 61 has addressed the role of elementary reactions in ignition. 

The transition from overall reactions to detailed elementary reactions in the modeling of 

energetic material combustion did not occur suddenly and, in fact, is not yet complete. Thus far, the 

use of elementary reactions has been limited to the gas phase; our fundamental understanding of the 

condensed phase. processes is not allowing more sophistication at present. In the interim, 

condensed phase reactions have been treated as one or more overall reactions. Reaction mechanisms 

for the gas phase were East developed apart from any attempt to compute the burning rate. As early 

as 1965, Sotter [7] assembled amechanism consisting of 12 species reacting by 17 reversible 

reactions to describe the secondary reaction zone of double-base propellants. He numerically 

integrated this mechanism, neglecting transport processes, and found order-of-magnitude agreement 

1 
with experimentally determined induction times for the visible flame. In the 

early-to-mid 198Os, Errnolin et al. (81 worked out elementary-reaction mechanisms for ammonium 

perchlorate and cyclotrimethylenetrinitramine (RDX) [9], guided by mass spectrometric 

measurements in the flames of these condensed systems. 

Attempts to compute the burning rate of an energetic material using realistic chemistry probably 

began with the Guirao and Williams’ [lo] treatment of ammonium perchlorate in 197 1 e Though the 

chemical mechanism consisted of 14 species and 10 irreversible reactions, a small problem by 

today’s standards, computational tools at that time did not permit the simultaneous solution of the 

kinetics and transport. A simplified simultaneousolution of kinetics and transport for a larger 

mechanism of 19 species and 60 reversible reactions was reported by Hatch [ 1 l] in 1986 for 

nitroglycerine. A significant advance in the computational tools available for work of this type 

occurred in 1985 with the publication and availability of the PREMIX code [ 121, a user-friendly, 

well-documented, one-dimensional (-D), premixed, laminar flame code. This code and its later 

improvements provide a high level of rigor to the description of gas-phase transport, allowing for 

such subtle effects as thermal difhrsion and multicomponent transport to be conveniently treated. 

Moreover, the description of thermodynamic functions, transport parameters, reactions, and reaction 

rates in this code is also very general, allowing a wide scope of kinetic representations and 

convenient updating. Melius [ 131 was the first to utilize the PREMIX code in a calculation of 

energetic-material burning rate, addressing the case of RDX, In the United States, as a result of 

several Office of Naval Research and U.S. Army Research Office workshops starting in about 1987, 

a concerted effort was directed at understanding the physics and chemistry of RDX as a prototypical 

system. This focus resulted in a number of further refmements of RDX modeling [14-173. 

Extensions of these general methods have been made to include cyclotetramethylenetetranitramine 

(HMX) [18, 191 and glycidyl azide polymer (GAP) [20]. In order to study the physical aspects of 

three-phase combustion, Miller [21] described adetailed chemical model applied to the combustion 

of frozen ozone as a prototypical energetic material for which very reliable kinetic and 

thermophysical data exist. 
This report focuses on models that compute the burning rate based on &tailed elementary 

reaction mechanisms in the gas phase. However, it is worth mentioning a few models that are 

chemically specific to some degree and utilize overall reactions to dcscril~ the gas phase. An early 

example of this type of m&l comes from BenReuven et al. [22] and BenRcuven [23]. Their model 

treated the combustion of RDX using one overall reaction in the liquid phase, evaporation as the 

surface-gasification mechanism, and two overall reactions in the gas phase. Another example was 

advanced by Bizot and Be&stead [24], who considered double-base propellant combustion using 

three overall reactions in the con&nsed phase and two overall reactions in the gas phase. A recent 

model attempting to simplify the very complex chemistry involved in double-base propellants is that 

by Song and Yang 1251. Like the Bizot and Beckstead model, Song and Yang lump species into 

categories such as al&hy&s and oxidizers. Yet another approach in this vein was taken by Li and 

Williams [26], who argued for the dissociation of HONO as the rate limiting step in the primary 

gas-phase mechanism of RDX and then applied an asymptotic analysis to compute the burning rate 

based on this one reaction. The relative simplicity of these models is appealing, but it will take time 

to determine the extent to which generality and even understanding is sacrificed. 

2. Conceptual Framework 

As previously stated,bur primary interest here is in that class of models which sttive to describe 

the gas-phase reactions as true elementary reactions, the rate cc&?cients for which arc determined 

from independent kinetics experiments, reaction-rate theory, or therm&emical estimation methods. 

This restriction narrOws the number of models to only four [ 14,16,17,21]. In this report, we will 

describe a fifth approach. In developing this new approach, we will apply it to RDX. It will be 

helpful, therefore, to review some of the details of the other RDX models [ 14,16,17] (i.e., those in 

our restricted subset of model types). 

All three models [ 14,16,17] defer to the experimental work of Brill et al. [27] for a description 

of the condensed-phase reactions in RDX. Brill et al. [27] found that RDX decomposes by two 

competing channels, Rl and R2 (see Table 1). Unfortunately, his experiment was unable to 

distinguish between several possible R2 paths, R2a, R2b, and R2c. Both Prasad et al. [16] 

3 
Table 1. Liquid-Phase Reactions in Deflagrating RDX Adopted by Various Models 

Reaction 

Number Reaction 

Heat of 

Reaction 

at 570 K” Model 

Rl RDX+3CH20+3N20 

(kcal/mole) 

-47 All [14,16,17] 

R2a RDX+3HzCN+3N@ 179 P&S [16], 

D&B [ 171 

R2b RDX+3HCN+3HONO 19 - 

RDX+3HCN+3NOz+3H 257 - 

RDX+3HCN+3/2NO+3/2N~+3j2Hz0 34 L&Y [14] 

’ This is the completed surface temperature at 1 atin. 

and Davidson and Beckstead [17] elected to use R2a for the second path. Liau and Yang [14] 

suggested and used in their model another interpretation of Brill’s measurements, R2d. The table 

shows that the degree of endothermicity among the different R2 paths varies dramatically. Unless 

condensed-phase reactions are unimportant to the deflagration of RDX, one would expect such 

differences to have a significant effect on the computed burning rate. Because the three, models 

being considered differ in many details other than the condensed-phase reactions just discussed and 

the burning rates computed by each of the models agree quite well with experimental burning rates, 

it is impossible to see theeffects of the different liquid-phase reactions in isolation. Nonetheless, it

may be significant that the amounts of RDX decomposition reported to occur in the condensed phase 

vary among these models from 40% [ 161 to 25% [ 171 to a “limited” amount [ 141. 

Even though the computational power now exists to treat condensed-phase reactions, our current 

knowledge of these reactions (even at the level of overall descriptions, let alone an elementatyreaction description) is very limited. This uncertainty is not confined simply to the rate c&Ticients, 

but extends to the very identities of both the reactants and products involved in these reactions. We 

believe that these difficulties will not soon be resolved, and it is with this prospect in mind that we 

propose the following new and more practical approach. 

i 

4 
A key difficulty with chemically specific models is dete rmining the identity and information 

rates of mole fractions of chemical species which fmt emerge from the condensed phase into the gas 

phase. We wiU show that given this knowledge and a reaction mechanism for the gas phase, the 

burning rate can be computed. One additional requirement is an expression relating the burning rate 

to the surface temperature; this will be discussed in this report. Though there is speculation required 

in identifying the chemical species emerging from the condensed phase, it is much reduced from 

having to speculate on the reactions occurring in the condensed phase and the rate coefficients of 

those reactions. Techniques to measure or calculate those condensed-phase processes are not likely 

to be realized soon; thus, the semi-empirical approach described here can be thought of as a 

practical, interim strategy pending the development of definitive tools for investigating the 

condensed phase. With these enabling simplifications, the model can be readily adapted to many 

worthwhile purposes, including experimental testing of gas-phase reaction mechanisms, computing 

the burning rate of multi-ingredient propellant formulations, and predicting the effect of chemical 

additives on the burning rate. 

3. Mathematical Framework 

We consider the 1 -D, steady-state deflagration of a condensed substance, which is oriented in a 

coordinate system moving with the linear regression velocity such that the umzacted material at an 

initial temperature of To extends to x = - -, the regressing surface is always at x = 0 with 

temperature T,, and the fmal gaseous combustion products at temperature Tf are found at x = + m. 

The mass conservation equation can be integrated simply to give 

rit = pu= p*r, (1) 

where rit is the mass burning rate or mass flux, p and u are the mass density and mixture mass 

velocity at any point in the interval, respectively, ps is the mass density of the unreacted material at 

its initial temperature, and P is the linear regression rate of the surface. The continuity equation for 

each chemical species iis 

5 
(2) 

Here Yi is the mass fraction of the ith species, Vi is the diffusion velocity of the ith species, @ is the 

molar production rate by reactions of the ith species per unit volume, and Wi is the molecular weight 

of the ith species. Finally, the equation of energy conservation for this system is 

(3) 

where h. is the mixture thermal conductivity, FP is ‘the mixture specific heat, cpi is the specific heat 

of the ith speck, hi is the enthalpy of the ith species, and N is the total number of species being 

considered. 

These equations are to be solved in the condensed and gas phases and their solutions matched 

through appropriate boundary conditions at the surface. In the condensed phase, the energy 

boundary conditions are 

T = TX at x = 0, 

and the species boundary conditions are 

Yi = Yi- at x = -00 

‘i =Yi4atx=-0. 

(4) 

(5) 

In the gas phase, the energy-equation boundary conditions are 

6 
T =T,atx=+O 

dT -=Oatx=i-=, 

dx (6) 

and the gas-phase boundary condition on each species is 

Yi =Y;&atx=+O 

dY. A=Oatx=f=. 

dx (7) 

At the surface between these two regions, the continuity of species and energy flux is guaranteed by 

the following two boundary conditions. Continuity of species flux at the surface is expressed by 

litYi” + p,Y,“Vi” = rizYi” + PlYi’ov,~ ) (8) 

where the superscripts -0 and +0 and subscripts c and g refer to the condensed and gas sides of the 

surface, respectively. Continuity of the energy flux across the surface boundary is expressed by 

These general equations are the starting point for our simplifications. In the gas phase, these 

conservation equations are solved numerically using the PREMIX [ 121 code as a subroutine; thus, 

the gas phase is treated with full rigor in our model. In the condensed phase, we assume that 

(1) there are no in-depth chemical reactions, and (2) molecular diffusion is negligible. With these 

assumptions, the energy equation in the condensed phase reduces to 
$(A$) - ti$$Y$,) = 0.. 

Integrating this equation from x = --~3 to x = -0 results in 

Substituting equation 11 and equation 8 into equation 9 yields 

(10) 

Equation 12 is the form of the energy-flux boundary condition used in the model developed in 

this report. Notice that one does not need to know the enthalpies of the species on the condensed 

phase side of the surface at T,, only their mass fractions there. This is important since heats of 

desorption of the nascent gas-phase species may be difficult to estimate. We are unaware of 

previously published material on this form of the energy-flux boundary condition, perhaps because 

of the novelty of the present context of a single overall condensed-phase reaction being coupled to a 

full elementary-reaction description of the gas phase. This equation enables our treatment. Notice 

also that neither the thermal conductivity, the mass density, nor the specific heat of the condensed 

phase at temperatures near the surface are required; the values of all these quantities are very 

uncertain. Only the specific heat and mass density of the unreacted material over the range of initial 

temperatures are required, at least for purposes of computing the burning rate. Of course, if the 

temperature profile through the condensed phase is needed, then a further integration using values 

for these parameters over the full condensed-phase temperature range will be required. 
In order to compute a burning rate, the following information must be suppliech the enthalpy and 

mass density of the unreacted energetic material over the range of initial tern-s, a set of 

products (species and mole fractions) of the condensed-phase dcomposition, arate of appearance of

these decomposition products as a function of surface temperature, and an elementary reaction 

mechanism through which these decomposition products react in the gas phase. The condensedphase decomposition prc&cts become the initial or nascent gas-phase reactants. 

As pointed out in our conceptual framework discussion, the identities of the condensed-phase 

reaction products are not known completely, even for the relatively well-studied case of RDX. For 

most other energetic materials, the situation is worse still. The only clear constraint we have in 

constructing this species set is elemental balance. Therefore, from the universe of possible product 

sets (i.e., those leading to a balanced overall reaction), plausible products must be selected b&on 

either experimental knowledge of these product identities and concentrations (if available) or 

theoretical consideration of likely reaction paths. In general, multiplicity of such plausible product 

sets may occur. In this case, that which best reproduces the experimental burning rate should be 

chosen. Or, an average of the product sets can be taken based on the assumption of equal apriori 

probabilities of occurrence. In any case, the decomposition set chosen can be improved as new 

experimental data or theoretical insights become available. 

The final type of information required to compute a burning rate is the rate of appearance of the 

condensed-phase decomposition products. For this, we appeal to the very old notion of an 

Arrhenius-like expression [2] relating the burning rate to the surface temperature, such as 

Such an expression has often been termed a ‘byrolysis law” in the propellant-combustion lip. 

There are other forms of this expression in use [28,29], but the above form preserves the dominant 

functionality without additional (probably uncertain) data. In fact, Zenin [28] prefers equation 13 to 

represent his experimental determination of surface temperatures vs. burning rates for a range of 

double-base propellants. Zenin found that this form provides a universal representation for 

9 
double-base propellants of different ingredient proportions (see Figure 1). It is this universality for a 

given class of propellants that impels us to adopt it here as a formalism for the rate of appearance of 

the condensed-phase decomposition products. In the case of double-base propellants, the 

mechanism for surface regression is likely to be reactive in nature because of the polymeric character 

of the nitrocellulose molecules. Figure 2 shows that the pyrolysis law in equation 13 also proves 

appropriate to a purely evaporative surface regression mechanism. Here, the surface temperature for 

the three-phase deflagration of frozen ozone was computed based on nonequilibrium evaporation 

driven by heat feedback from gas-phase reactions [21]. The steady deflagration of RDX is also 

believed to be predominately the result of evaporation [ 141. Figure 3 shows a best-fit pyrolysis law 

(in the least-squares sense) for RDX using the surface-temperature and burning-rate data of Zenin 

[28]. Again the fit is quite reasonable. 

10 

1 

0.1 

I I I 

- fenin Pyrolysis Law 

I e Zenin D&a- a 

1.0 1.2 1.4 1.6 1.8 2.0 2.2 

1 O3 x 1 /T&K) 

Figure 1. Demonstration of the Universality of the Pyrolysis Law for Double-Base Propellants 

Based on the Work of Zenin [28]. 

10 
‘f\l .: m = 2.341~10~ exp(-1720.1Q 

t L 

0 First-Principles Model 

- Least-Squares Fit 

1 

I 

i 

4 5 6 7 

103x1/Ts(K) 

. . . 

Figure 2. Quality of Fit of a Pyrolysis Law to an Evaporative Regression Mechanism 

Calculated From a First Principles Treatment of Frozen Ozone Deflagration [21]. 

IO 

,,-,, . ..*. .y . Zen in RDX Data 

.,. 

- Least-Squares Fit 

,. , 

1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 

lo3 x l/T,(K) 

Figure 3. Pyrolysis Law for RDX Derived From Zenin’s [28] Experimental Data. 

11 
4. Example: Frozen Ozone 

Our fmt example of the application of this new model is that of the self-sustained deflagtzion of 

frozen ozone. Using the pyrolysis law previously determined from a fast-principles model [21] to 

test for consistency, the burning rate is computed by the new model and compared with the burning 

rate computed by the first-principles model. Such a test is not as trivial as it might seem. The 

calculational details involving the evaporative surface-regression mechanism of the first-principles 

model is considerably more complicated than that involved in the new model. However, the 

evaporation process is characterized by an energy barrier (heat of vaporization), and the assumption 

of local thermodynamic equilibrium introduces a Boltzmann factor this suggests that the process 

may be controlled by an Arrhenius-like term. On the other hand, the evaporation-mechanism 

equations [21] do not lead to such a simple expression, though an Arrhenius-like dependence on 

temperature evidently does have an implicit relevance given the excellent fit of the pyrolysis law 

observed in Figure 2. 

Since any condensed-phase ractions in liquid ozone are too slow to influence the deflagration 

rate, the mechanism of surface regression is the following: evaporation driven by heat, released in 

gas-phase reactions, and conducted back to the surface. In this situation, the nascent gas-phase 

species is evaporated ozone (i.e., Yz = 1). Coupling this with the fitted pyrolysis law just clcscribed 

and the reaction mechanism consisting of three reversible reactions [21], we have computed the 

frozen ozone burning rate by our new model. It will be compared to the rate computed by the fnstprinciples model [21]. Figure 4 shows that the agreement is excellent. The first-principles model in 

this case includes thermal diffusion and multicomponentransport, and the numerical grid spacing is 

fme enough that the burning rates are computed to an accuracy within a few tenths of a percent. 

Also, the central differencing option was selected. Thus, the success both of the pyrolysis law and 

the new model is based on a high level of computational rigor. The dominant chemical steps 

occurring in the gas phase for the ozone case are thoroughly discussed in Miller [21). 

12 
0 First-Principles Model 

+ Present Model 

0.1 L / # LIIII 

1 10 

Pressure ( atm ) 

Figure 4. Comparison of the Burning Rates for Frozen Ozone Computed by the New Model 

Developed in This Report and the Previously Published First-Principles Model [21]. 

5. Example: RDX 

As previously discussed, the condensed-phase decomposition paths for RDX are uncertain. 

Evaporation was determined to be the overwhelmingly dominant mechanism by Melius [13], Liau 

and Yang [ 143, and Liau [ 151, and at least predominant by Davidson and Beckstead [171 and FVasad 

et al. [ 16). We therefore examine the consequences ofassuming in our model that the surfaceregression mechanism is purely evaporative. Thus, by analogy to the ozone case above, vapor-phase 

RDX is assumed to he the sole species emerging from the surface; mathematically.this is expressed 

as Y& = 1. The pyrolysis law is obtained by a linearized least-squares fit to the experimental data 

of Zenin [ZS] and is illustrated in Figure 3. 

The enthalpy of the solid at the initial temperature is determined as follows: the specific heat of 

solid RDX is obtained by a least-squares fit of a linear temperature function to the data of 

13 
Shoemaker et al [30] and Miller [3 11. The fit is shown in Figure 5 and its parameters are in Table 2. 

This functional form of the specific heat is integrated over temperature to determine the enthalpy of 

solid RDX using the value of the heat of formation at 298 K to obtain the integration constant. This 

treatment differs from that of Liau and Yang [ 141 and Liau [15], in that their model assumes a 

constant value of specik heat. 

240 260 280 300 320 340 360 380 400-420 

Temperature (K) 

Figure 5. Linear Least-Squares Fit of the Specific-Heat Data of Shoemaker et al. [30] and 

Miller [31] for Solid RDX Over a Range of Initial Temperatures. 

Table 2. Value of Condensed-Phase Parameters Used in RDX Calculations 

[ Value 

As = 6.134 x 10’ g/cm*+ 

ES = 18,539 Cal/m01 

ps = 1.66 G/CM3 

Wmx = 222.118 g/mol 

AHF = 14,590 ca.l/mol 

Description 

Exponential prefactor in pyrolysis law 

(see text) 

Activation energy in Pyrolysis law 

(see text) 

Mass density of pressed solid used in 

experiments [28] 

RDX molecular weight 

RTDX heat of formation at 298 K 

CP solid =0.03604 + (7.105 x ~o-~)T cal/g-K Specific heat of solid RDX over temperature 

range 260 K (see text) 

14 
The reaction mechanism (Yet&s second model [ 16]), thermodynamic data, and transport data 

for this case is taken from the work of Liau [ 151. The burning rate (Figure 6), temperature 

(Figure 7), and species profiles (Figure 8) computed by the present model at an initial temperature of 

293 K agrees very closely to that computed by the Liau modeL (Dr. Y.-C. Liau kindly made his 

code available to us. All calculations in this article attributed to the Liau model [15] were made 

using the code version dated 13 February 1997.) We emphasize that the gas-phase reaction 

mechanisms, species thermodynamics, and transport parameters in both models are identical; only 

the treatment of the condensed phase and surface-gas&a&I mechanism are Merent. The model 

burning rates shown iu Figure 6 also compare favorably with the experimental data of Miller [32], 

Zenin [28],Ulas et al. [33], Homan et al [34], and Atwood et al. [35]. 

10 

A 

E 

5 

- 1 

g! 

2 

F _ 

F 

‘i 

m 

b 0.1 

E .1 

J 

0.01 f 

I 

0 Miller Experimental Data 

0 Zenln Experimental Data ,. ,, 

P Ulas, et al. Experimental Data 

A Home et al. Expe~men~l Dam ,,,,,, ,,_,,,_,,........ _ ..,..... 

0 Atwood, et al. Experimental Data 

- - Llau & Yang Model 

1 10 

Pressure ( atm ) 

Figure 6. Comparison of Burning Rates for RDX Computed by the New Model to Those 

Computed by That of Liau [15] and to Experimental Data. (See Teti for 

Experimental Data Referenccs) 

15 
I500 

0 

0 500 1000 1500 2000 

Distance from Surface (microns) 

Figure 7. Temperature Profiles for RDX at 1 atm and 293 K, as Computed by the New 

Model, Compared With That of Liau [lS]. 

In the RDX case, we have sought to minimize nongermane computational differences between 

the new semi-empirical model and that of Liau and Yang [14]. Their cl-mice of the 

windward differencing option, numerical grid options, and suppression of the thermal difFusion and 

multicomponentransport options in PREMIX were selected for our calculations as well 

The dominant reaction paths for RDX flames have been discussed previously [13], andwhile the 

reaction mechanism has been expanded and refined since that study, we believe that the conclusions 

have not changed significantly. Hence, no new dominant-path analysis for RDX is given here. 

However, a brief explanation is now given for the slight rise in temperature above the adiabatic 

equilibrium value late in the flame zone, as shown in Figure 7. This behavior is surprising compared 

to 02/fuel combustion in which the temperature rise is monotonic; however, it is quite typical of 

flames oxidized by NzO and NOz. In 02 flames, there is typically an overshoot of H, 0, and OH 

concentrations late in the flame zone, above their eventual equilibrium values. In hydrocarbon/@ 

flames, this overshoot is caused by the following radical chain-branching reactions: 

16 
0.20 

c 

0 -cI 0 

g 0.15 

a, 

8 

0.10 

0.05 

0 500 1000 

, 

._--- cc-- 

,---- 

: *--Lj : 

; ! 

1500 2000 

Distance from Surface (microns) 

Figure 8. Species Profiles for RDX at 1 atm aid 293 K, as Computed by the Present Model 

(Solid Lines), Compared With That of Liau [15] (Dashed Lines). 

17 
and 

H+&+OH+O 

As this excess of radicals recombine in the burnt-gas region, heat is released and the terncontinues to rise to the adiabatic equilibrium value. For NzO- and NOZ-oxidized flames, these 

chain branching reactions are absent. Towards the end of the flame zone, the radical concentrations 

are usually somewhat below their eventual equilibrium values. To reach the final equilibrium 

concentrations of radicals, stable species slowly decompose in the burnt gas region, absorbing heat 

in the process, and lowering the final temperature to the equilibrium value. For the case in 

Figure 7, our calculations show that H, 0, and OH concentrations rise by factors of 2 to 5 between 

800 and 2,ooO p.m. Over this same region, the temperature drops by about 100 K. A similar result 

was observed in computations for a low-pressure HfizO/Ar flame [36]. 

6. Example: Nitroglycerine 

Relatively little information is available on the thermal decomposition pathways of 

nitroglycerine (NG). We examine it here in the context of the new semi-empirical burning rate 

model because it represents a case of intermediate chemical complexity, it continues to play an 

important iole in gun propellants, and it is a substance for which experimental burning rate data 

exists. Vital also is the fact that we could assemble agas-phase reaction mechanism with relatively 

few changes from that previously developed for the dark zone of nitrate-ester and &amine 

propellants [37,38]. This was accomplished by adding only one additional species, C&O, and its 

associated reactions. The resulting mechanism (labeled DE31 1 here) is given in the Appendix and 

consists of 35 species and 178 reversible reactions. Other parameters are given in Table 3. 

For the pyrolysis law, we simply use the universal double-base law determined by Zenin [28] 

and shown in Figure 1. Double-base propellants, of course, consist primarily of different propordons 

of NG and nimellulose. Though NG is therefore one limiting case of a double-base propellant, 

there is not necessarily reason to suppose the double-base pyrolysis law to be applicable to NG 

18 
Table 3. Values of Condensed-Phase Parameters Used in NG Calculations 

Value 

As = 1.8 x lo3 g/cm2-s 

I ES = 9935 cal/mole 

ps = 1.59 g/cm3 

WNG = 227.087 g/mole 

~&JpK=- 88,600 cal/mole 

CT = 0.2975 d/g-K 

Description 

Exponential prefactor in pyrolysis law 

Activation energy in pyrolysis law 

Mass density of liquid NG 

NG molecular weight 

NG heat of formation at 298 K 

Specific heat of liquid NG 

solely on this account. However, both NG and nitrocellulose are nitrate esters whose likely first step 

in decomposition is an N& scission; if this were a rate limiting step, then the decomposition rates 

for NG and nitrocellulose might be expected to be similar. This argument may, in fact, be the 

underlying reason for the apparent universality of the double-base pyrolysis law. In any case, we 

will have to let the results be the ultimate justification for this assumption. 

A major source of ambiguity in applying the new m&l to NG is the identification and 

quantification of the condensed-phase decomposition products, which are the nascent gas-phase 

species. As suggested previously, this is a situation in which a number of possibilities (consistent 

with a balanced reaction) must be examined and, ideally, arbitrated by broad theoretical reasoning. 

Again, the results must be the ultimate justification for this choice. We have examined the use of 

three sets of condensed-phase decomposition products for the NG case. The first is motivated by the 

only other elementary reaction treatment of NG of which we are aware. Hatch [ 1 l] assumed, 

without attempting justification, that NG decomposed by the path, as indicated in Table 4. 

Table 4. NG Condensed-Phase Decomposition Paths Considered 

Overall NG Decomposition Path Reaction Path Label 

NG (C&N309) II 3 NO2 + 2 CJit20 + HCO Hatch [ 111 

NGO2N~+HONO+2CH~O+CO Levy [39] 

NGlJ3HONO+2HCO+CO MSM4 

19 
We have not found a way to rationalize this path theoreticalIy, but deem it worthwhile to 

consider it anyway based on its previous use. A second path, given in Table 4, was hypothesized by 

J. B. Levy [39] based on theoretical considerations. The steps in NG decomposition proposed by 

Levy are illustrated in Figure 9. A third set (MSM4) of decomposition products is also given in 

Table 4 and is used to compute burning rates. No thcorctical justification based on a detailed 

sequence of paths is offered for this set, but it does lead to good agreement with experimental rates 

(as will be shown). One of our aims in considering a number of condensed-phase reaction paths is to 

gauge the sensitivity of the computed burning rate to the choice of path. 

Figure 10 shows the results of the burning rate calculations using each of the above sets of 

condensed-phase decomposition products at,an initial temperature of 298 K. The Qure also shows 

experimental burning rates measured by Andreev [40,413 and Andreev et al. [42]. The MSM4 

decomposition product set leads to very good agreement with the experimental burning rates over a 

wide range of pressure. It is also of interest to note that the burning rate can vary by as much as an 

order of magnitude among the possible decomposition product sets that we have considered. This 

finding could be considerably important to tailoring the propellant burning rate for specific purposes 

if a way could be found to actively influence the decomposition pathways in the condensed phase. 

In ail of the calculations presented here involving NG (including those of the next section), the 

windward, differencing option and suppression of the thermal diffusion and multicomponent 

transport options were selected. The numerical grid options were such that the burning rates 

presented are numerically accurate to about 2% or better. 

Since this is the most extensive, detailed chemical modeling of NG combustion ever perfarmed, 

a detailed analysis of the gas phase flame for one condition is presented. The case chosen is for pure 

NG at 10 atm at an initial temperature of 298 K, with the assumed MSM4 product set 

(3HONO+2HCO+CO). This is the product set which yields the best agreement between predicted 

burning rates and experiment (see Figure 10). Pathway diagrams, shown in Figure 11, have been 

constructed for this case using a postprocessor code, PREAD, written at ARL for the PREMIX c&. 

To obtain these diagrams, the rates were first integrated over distance from the propellant surface to 

20 
CH20N02 

I 

CHONOP 

CHO 

I 

CHO 

I 

CH20N02 

co 

0 verall: 

+ NO2 

CH20N02 

CHO 

CHO 

I 

CH20N0g 

co 

- I 

CHPONOz 

+ NO2 

CO + NO2 + CHiO 

+ NO2 + CHzO 

+ HONO 

NG -> 2 NO2 + HONO + 2 CHpO + CO 

Figure 9. Mechanism for Condensed-Phase Decomposition of NG Proposed by Levy [39]. 

0.030 cm. This region, which we term the primary reaction zone, includes all of the near surface 

flame up to the leading edge of the dark zone, as determined by plateaus in temperature and key 

species (e.g. NO and concentration profiles [not shown]). Using the integrated rates gives a concise 

global picture of the chemistry in this region. The flame is quite structured in this region, however, 

having five separate peaks in the heat-release profile. A complete discussion of this structure is 

outside the scope of report, but some remarks about the structure are contained in the following 

discussion- The chemistry of the dark zone of NG, the region of low gradients in species 

concentration and temperature between the primary flame and the secondary tlarne (visible flame), is 

similar to that for double-base propellants. That case has been discussed elsewhere [37,3X]. 

21 
+ Calculation with Levy .Products 

I iii0, 

Pressure (MPa) 

Figure 10. Computed NG Burning Rates at 298 K for Different Decomposition Paths Using a 

New Semi-Empirical Model Compared With Experimentally Measured Rates of 

Andreev [40,41] and Andreev et al. [42]. 

22 
(a) Carbon-Chemistry Dominant Pathways. 

+OH (205) q 

+H (18) A 

+HCO (3 

+H (137) 

L +HNO (28) 

+HCO (26) 

-co (19) 

HONO _ ~ ,NO 

A 

.- 

+HCO ( 

‘+NOz (28) 

r +HCO (22) 

HNO 

(b) Nitrogen-Chemistry Dominant Pathways. 

Figure 11. Identification of Dominant Chemical Pathways for NG at 10 at-m and 298 K Using 

the MSM4 Product Set. Numbers in Parentheses Are the Relative Rates of Each 

Reaction Value of 100 in Relative Units, Which Equals 8.817 x low3 moYcm’-s. 

Line Thickness Is Proportional to the Total, Relative, and Integrated Rates for 

Each Path. 

23 
The conversion of HCO to other species is very rapid, which is not surprising considering its 

radical nature. This conversion takes place very close to the surface, occurring within the first 

0.001 cm. As shown in Figure 1 la, most of the HCO is converted to CO by unimolecular 

decomposition or by reaction with NO, H, or NOz. However, a portion of the HCO is temporarily 

converted to CH20, primarily by reacting with I-lNO. The CH20, being much less reactive than 

HCO, survives further into the primary flame. Later in the primary reaction zone, the CHZO is 

converted back into HCO by reacting with OH and H; the HCO formed in this way never builds to 

an appreciable concentration, but is instead converted to CO or CO2 first stage products. 

The nitrogen chemistry is considered in Figure 1,l b. As with HCO, the conversion of HONO to 

other species begins rapidly near the surface because of its direct reaction with a portion of the HCO, 

which forms NO2 and CH20. However, only a small portion of the available HONO reacts prior to 

the depletion of the HCO. Instead, most of the HONO conversion is delayed, occurring mainly 

between 0.001 and 0.015 cm. A portion of the HONO is converted directly to NO via unimolecular 

decomposition. However, much of it is first converted to NO2 via reaction with OH, H, or HCO. 

Curiously, the conversion of NO2 to NO takes place mainly after the burnout of the HONO. 

Ordinarily, in combustion involving NO2 as a major species, it is found that NO2 converting to NO 

by reacting with H atoms is so fast that it occurs at a very early point, and it controls the radical pool 

concentrations: But here, the HONO+M = NO+OH+M reaction is the major radical source, the 

HONO concentration in the region is large, and the HONO+OH rate constant is also large. This 

leads to HONO+M=NO+OH+M and HONO+OH = HzO+N02 as the major nitrogen pathways close 

to the surface, rather than NOz+H = NOtOH. The NO2 formed early in the flame from HONO 

reacts higher in the flame after the HONO is gone. NO? is converted to NO primarily by an H atom 

reaction, but there are also important contributions from HNO, HCO and CO reactions. NO, the 

only nitrogenous species surviving into the dark zone, may be viewed as the nitrogenous ‘>roduct” 

of the first stage combustion- The concentration of HNO is small, except very close to the surface. 

It appears that although their concentrations are small, HNO and NO play important roles in a 

catalytic cycle for the near-surface HCO conversion. 

24 
. 

More information concerning the importance of the various reactions to the predicted burning 

rate may be obtained from a sensitivity analysis. The sensitivity coefficient of the temperature at a 

given spatial grid point to a particular reaction rate is defined as 

si (14) 

where Ai is the A-factor of the ith reaction, T is the temperature at the point of interest, and T,,, is the 

maximum temperature observed in the entire solution. The second grid point in the solution is 

chosen as the point of interest because this-one has special significance. The burning rate is strongly 

controlled by the amount of heat feedback from the gas-phase reactions to the propellant. The heat 

feedback rate is in turn primarily controlled by the temperature gradient at the propellant surface. 

Thus, the magnitude of rate constants for reactions that have a high temperature sensitivity at the 

second grid point in the solution must have a strong influence on the computed burning rate. In fact, 

to a good approximation, the sensitivity coefficient of the heat feedback is. proportional to the 

sensitivity c&frcient of the second grid point. Table 5 shows the fmt-order temperature 

sensitivities for the second gas-phase grid point of the solution (and the heat feedback) for reactions 

with relative values above three. For the coefficient of the second grid point, a relative value of 100 

equals an absolute value of 7.769 x 10q4. A positive temperature sensitivity c&fi&nt indicates that 

an increase in the rate coefficient of the reaction will result in an increase in temperature at point 

two; such an increase is expected to increase the burning rate. Note that the largest sensitivity is for 

HCO+M = H+CO+M. This is not surprising since the reaction not only converts HCO to a fmal 

product, but produces the highly reactive H atom. Sensitivities of most of the other reactions can 

also be rationalized by their effects on the radical pool or formation of fmal products with release of 

heat. The only one whose high, positive sensitivity has been difficult to rationalize is the secondone 

on the list, H2+N& = HONO+H. This reaction is reversed throughout the entire calculational 

domain (e.g., Figure 1 lb). Its reversal is not surprising since HONO is initially in the MSM4 

tiomposition product set. Ordinarily, since this reversed reaction converts a highly reactive H 

atom to comparatively unreactive species, one would expect the corresponding sensitivity would be 

negative. It seems likely that the explanation for the positive sensitivity is the formation of Na, 

25 
Table 5. Relative Sensitivity Coefficients of the Temperature Gradient at the Surface to the 

Most Sensitive Reactions (in Rank Order) for NG, With MSM4 Product Set at 

10 atm and 298-K Initial Temperature. Positive Values Indicate Reactions That 

Increase the Temperature Gradient When the Rate Coefficient for the Reaction Is 

Increased. 

Reaction Number (see,, Appendix) I Relative Sensitivity Coefficient 

33 HCO+M=+H+CO+M 100 

139 Hz+NOz*HONO+H 46.2 

4 NO+OH+M*HONO+M 29.4 

34 H+HCO*Hz+CO - 26.4 

178 HCO+N~~H+C&+NO 23.6 

175 HCO+HNO*CH20+N0 21.3 

177 HCO+NOz+CO+HONO -21.3 

176 C&O + NOZ * HCO + HONO 19.6 

128 H+HNO*Hz+NO - 15.9 

147 HCO+NO--HNO+CO -4.97 

157 H+CHzO*HCO+H2 -3.94 

fd N@+H-fNO+OH 3.17 

which in turn leads to NO and HNO formation close to the surface. The NO and HNO take part in a 

catalytic cycle for rapid HCO conversion to CO and C&O in this region (see Figure 11, both parts). 

This conversion occurs vja reactions between HCO+NO = HNW andHmHN0 = C&O+NO, 

which release considerable heat near the surface. 

Rate constants of most of the highly sensitive reactions shown in Table 5 are well established. 

Three exceptions are R175 (HCO+HNO=CH~O+NO), R178 (HCO+N~=H+C@+NO), and R177 

(HCO+N@ = CO+HONO). The rate constant expression for R175 has especially large errs limits. 

The estimate is attributed to Tsang and Herron [43 3, who obtained it based on comparison to similat 

reactions. Rate constant expressions for R177 and R178 were obtained from Lin et al. [44]. The 

expressions were computed based upon ab initio and TST-RRKM theory. This approach should 

yield reasonable estimates, but experimentation is desirable. 

26 
7. Effect of Chemical Additives on the Burning Rate 

It has always been hoped that theoretical modeling might some day contribute to a solution for 

the problem of the effects of chemical additives on the burning rate of propellants. However, only 

with the relatively recent advent of chemically specific modeling with elementary reactions was 

there any real prospect for realizing these hopes. In this section we demonstrate that theoretical 

guidance useful to the propellant formulator, namely the effect of additives on the burning rate, is 

becoming feasible. 

As a first demonstration of the effects of additives on propellant flames, we took the converged 

values of burning rate (0.394 cm/s) and surface temperature (628 K), obtained in a calculation ofNG 

at 10 atm using the Levy decomposition product set and the DBl 1 reaction mechanism, as our 

starting conditions for a series of steady premixed flames with several different additives. A 10% 

mole fraction of NH3 was then added to the Levy product set (reducing the original product mole 

fractions proportionately). The flame structure was then computed and compared to the pure NG 

case-the result is shown in Figure 12. The two-stage flame structure is known to occur because of 

the reduction of HONO and NO2 to NO in the primary reaction zone (next to the surface) and the 

subsequent, slower reduction of NO to Nz in the secondary reaction zone (at the end of the dark 

zone). The secondary reaction zone is also known as the secondary flame or the visible flame. In 

that figure, the secondary gas flame for the pure NG case stands off from the surface by about a 

centimeter. (Notice that the distance scale is logarithmic.) This is typical of the dark zone length of 

double-base propellants. When the NH3 is added, the dark zone collapses by about a factor of five. 

Also, the heat feedback increases by 3 1%. Normally, when the heat feedback increases, one 

can expect the burning rate to increase as well. The effect NH3 has on the dark zone length may 

explain why M30 (29O/, nitrocellulose, 22% nitroglycerine, 47% nitroguanidine, 2% stabilizer) burns 

with no apparent dark zone, unlike any other gun propellant. A major ingredient in M30 is 

nitroguanidine, which may be expected to supply NH, upon decomposition. The chemical rationale 

for this effect will be discussed later in this report. A case with 10% N2 added is shown in Figure 12 

for comparison. The N; has its expected diluent effect, lowering the heat feedback by 28%, but has 

27 
No Additive 

10% NH, Additive 

10% N, Additive 

0.0001 0.001 0.01 0.1 1 

Distance from Surface (cm) 

Figure 12. The Effect of Two Additives, NH3 and Na, on the Flame Structure of NG at 10 atm 

and 298 K Using Levy’s [39] Decomposition Product Set. Surface Temperature 

and Mass Flux Are Fixed at 628 K and 0.626 g/cm*-s, Respectively, for All Cases. 

relatively little effect on the dark zone length. Liau [ 151 performed a similar study of the effect of 

various additives on the dark zone of RDX. 

A more systematic approach is needed to compare the effects of one additive to another in a 

quantitative sense. Adopting the propellant formulation strategy of using enough additive to bring 

the mixture to a zero oxygen balance affords a rational method of determining the amount of each 

additive appropriate for comparison purposes. The oxygen balance is defined as that amount of 

oxygen one must add or subtract to have all oxygen appear in either Hz0 or COz. NG has a positive 

balance of 3.5% (i.e., it has an oxygen surplus). Thus, we compute that one third of a mole ofNH3 

must be added to effect a neutral oxygen balance for each mole of NG. For comparison, we examine 

two other potential additives, CH20 and HZ. We are, of course, limited here to those fuel molecules 

that are already in our reaction mechanism. 

28 
c 

Additional assumptions arc required in order to model the effects of condensed-phase mixtures 

of ingredients. The mass density of the mixture is computed by the methodof additivcpartialmolar 

volumes, such as 

Pmk = wadg 

I 

Cxivi 9 

i 

il5) 

where W,, is the average molecular weight, Xi is the mole fraction of ingredient i, and Vi is the 

molar volume of ingredient i. This quantity is important in calculating the linear burning rate from 

the mass burning rate. Secondly, we assume that the starting mixture enthalpy is given by the 

weighted sum of the ingredient enthalpies. This.is a reasonable approximation to make, but it 

ignores any enthalpy of mixing or solution contributions; there is also some ambiguity as to what 

state is best to use for the additive enthalpy. Finally, we must, of course, assume that the pyrolysis 

law is unchanged as a result of these additives. This assumption is reasonable in view of the small 

amount of each additive. 

The results of the additive computations are given in Table 6 for the Levy decomposition product 

set and Table 7 for the MSM4 decomposition product set. The enthalpies of all of the additives in 

Table 6 and Table 7 at 298 K are taken as that for the gas phase. It should be noted that this 

assumption could have important consequences for the computed burning rate. For example, if the 

enthalpy for NH3 liquid at 298 K is used, the linear burning rate increases by only 12%. This smaller 

increase reflects the additional energy requirement of the heat of vaporization. Clearly, the 

calculation of the unreacted mixture enthalpy may require a more sophisticated theoretical treatment 

In interpreting the small percentage differences shown in these tables, bear in mind that the 

numerical accuracy of these calculations is no worse than 2%; thus, some of the smaller effects 

found may not be sign&ant. 

Through sensitivity and rate analysis, we were able to identify the chemical mechanism for the 

burning-rate enhancement of NG by NH5 Essentially, NH2 reduces NO to fmal product N2 by the 

following two most important paths, 

29 
Table 6. Effect of Different Chemical Additives on the Burning Rate of NG at 10 atm and 

298 K Assuming the Levy [39] Decomposition Product Set 

Additive Weight % Linear Burning Rate Mass Burning Rate Heat Feedback 

(“h increase) (% increase) (% increase) 

NH3 2.4 19 15 19 

CH20 3.2 1 -1 -5 

HZ 0.44 1 -8 -6 

Table 7. Effect of Different Chemical Additives on the Burning Rate of NG at 10 atm and 

298 K Assuming the MSM4 Decomposition Product Set 

Additive Weight % Linear Burning Rate Mass Burning Rate Heat Feedback 

(% increase) (% increase) (% increase) 

NH3 2.4 16 12 14 

CR20 3.2 7 5 2 

H2 0.44 2 -7 -6 

NH2+NO+ NNH+OH 

+ N2 +HzO. 

The NNH thus formed rapidly decomposes to N2 + H. The reaction therefore leads to chain 

branching, which may be important to the burning rate enhancement, in addition to the increased NO 

conversion rate to Nz. The NH2 is formed from NH3, predominately by the following reaction: 

NH3+OH-,NHIz+H20. 

This mechanism reinforces our speculation that M30 forms no dark zone due to the presence of an 

amino group on the nitroguanidine. 

30 
8. Speculations on Practical Burning-Rate Modifiers 

The mechanism of NH3 action invites a further discussion of the M30 case. With 

NI&modified NG, we found both a collapse in the dark-zone length and a significant boost in the 

burning rate. M30 has no dark zone, consistent with our NI&modified NG case, but it burns no 

faster than a single-base propellant and slower than a double-base propellant, a fact which appears to 

be inconsistent with our model calculation. This apparent inconsistency might be explained as 

follows. It is likely that the large percentage of nitroguanidine (NQ) present in M30 is responsible 

for the lack of burning-rate enhancement since it acts .to lower the flame temperature of the 

propellant. Hence, the cooling effect might outweigh the rate acceleration effect for such major 

proportions of NQ. We would expecthat if a small amount of NQ, say 2-5%, was added to either a 

single or double-base propellant, then the burning rate would be increased and the dark-zone length 

diminished. Of course, some of the benefit of the NH2 from NQ could be hindered by the energy 

required to either break down its parent molecule or to get it into the gas phase, as could be seen in 

our model calculation’s sensitivity to the NH3 starting enthalpy state. Nonetheless, here is a 

concrete, theoretically inspired idea that could easily be tested. Thus, though the model needs to be 

further refined and expanded, it can already provide insights of potential worth to the propellant 

formulator. 

The propellant formulator may find it expediento tailor decreases in the burning rate as well as 

increases. For example,..it has been found [45] that for layered propellants, at least a three-to-one 

ratio in the rates of the two layer materials must be attained in order to achieve desired performance 

enhancements. We have conducted preliminary calculations [463 showing HNCO as an additive that 

both decreases the heat feedback (and therefore presumably the burning rate) and decreases the 

visible flame standoff. As NH2 proved to be the active molecule in increasing the heat feedback 

resulting from the addition of NH3 to NG, NCO. appears to be the active molecule for the HNCO 

additive. One factor leading to the reduced heat feedback may be that the radical NC0 combines 

with NO and NO2 near the surface to form relatively stable molecules such as N2, N20, CO, and 

COZ, thereby diminishing the rate of radical growth. Reduction in the visible flame standoff (dark 

zone length) may be due to the tmimolecular decomposition in the dark zone of the NzO which is 

31 
formed in the near surface region via the NC0 reactions. This decomposition, NzO 4 N2 f 0, 

increases the radical growth rate in the dark zone, causing acceleration of the reactions leading to the 

visible flame. In fact, a decrease in the visible flame standoff may be a desirable effect in that it 

might reduce gun ignition delays, delays attributable to the slowness of the reactions leading to the 

substantial heat release of the visible flame [473. Of course, to realize the benefits of these 

provocative ideas, much work is yet to be done both in searching for suitable active molecules and in 

finding practical substances that can release these active molecules. Now, the way is clear for a new 

and productive partnership between the theoreticians and the formulation chemists. 

9. Conclusions 

Models of energetic material combustion have increased enormously in their sophistication and 

complexity in recent years. Treatments of the gas phase involving dozens of species and hundreds of 

elementary reactions are now common. On the other hand, chemically specific descriptions of the 

condensed phase have not kept pace, largely because of the lack of definitive exp’eriments and theory 

relating to the reaction paths there. All existing treatments of the condensed phase consider several 

overall reactions at most, and even these suffer from uncertainties in the identities and concentrations 

of the reactants and products. In the face of these intractabilities, we have developed a new semiempirical model, one which requires as input a single overall reaction representing the conversion of 

unreacted energetic material to the nascent gas-phase species and a pyrolysis law expressing the 

relationship of surface temperature to burning rate. This approach, where the pyrolysis law is 

universal over some class of materials, makes the most sense; the existence of such a relation has 

been previously verified for double-base propellants. We have demonstrated that the simplest form 

of the pyrolysis law also well describes surface regression due to evaporative and reactive 

mechanisms. The capability of this model in describing the burning rate as a function of pressure 

and even species profiles (where available) was illustrated for frozen ozone, RDX, and 

nitroglycerine. 

Key uncertainties in applying this model to energetic materials include the identity and 

concentrations of the products of the condensed-phase decomposition. By examining a number of 

32 
possible product sets, we found that the computed burning rate could vary by as much as an order of 

magnitude among these sets. This finding suggests that it might be possible to influence the burning 

rate of a material by stimulating decomposition along normally less favored paths. 

One of the long-held hopes for chemically specific combustion modeling is the capability to 

compute the effects of chemical additives on the burning rate, in order to rationalize the performance 

tailoring of propellants. We believe that progress is rapidly being made towards fi.Jfilling that 

promise. As a demonstration of this budding capability, we determined the relative effect of three 

additives on the burning rate of nitroglycerine where the amounts of each additive were computed to 

achieve a neutral oxygen balance for each mixture. 

33 
34 
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Calculations and Mechanism Definition for Reactions in an Ammonium Perchlorate Flame.” 

Fiziku Goreniya i Vzryva,’ vol. 18, pp. 61-70, 1982. 

9. Ermolin, N. E., 0. P. Korobinichev, L. V. Kuibida, and V. M. Fomin. ‘Study of the Kinetics 

and Mechanism of Chemical Reactions in Hexogen Flames.” Fizikra Goreniya i Vzryvu, 

vol. 22, pp. 544-553, 1986. 

10. Guirao, C., and F. A. Williams. “A Model for Ammonium Perchlorate Deflagration Between 

20 and 100 atm.” AIAA Journal, vol. 9, pp. 134S-1356,197l. 

11. Hatch, R. L. ‘%hemicaI Kinetics Combustion Model of the NG/Binder System.” Pruceebgs 

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35 
12. Kee, R. J., J. F. Grcar, M. D. Smooke, and 5. A. Miller. “‘A Fortran Program for Modeling 

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13. Melius, C. F. “Thermochemical Modeling: II. Application to Ignition and Combustion of 

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14. Liau, Y. -C., and V. Yang. ‘Analysis of RDX Monopropellant Combustion With Two-Phase 

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15. Liau, Y. -C. “A Comprehensive Analysis of RDX Propellant Combustion and Ignition With 

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16. Prasad, K., R. A. Yetter, and M. D. Smooke. “‘An Eigenvalue Method for Computing the 

Burning Rates of RDX Propellants.” Combustion Science and Technology, vol. 124, pp. 35-82, 

1997. 

17. Davidson, J. E., and M. W. Beckstead. “Improvements to Steady-State Combustion Modeling 

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1997. 

18. Davidson, J. E., and M. W. Beckstead. “A Three-Phase Model of HMX Combustion-” 

Proceedings of the 26th Symposium (International) on Combustion, The Combustion Institute, 

Pittsburgh, PA, pp. 1989-l 996,1996. 

19. Prasad, K., R. A. Yetter, and M. D. Smooke. “An Eigenvalue Method for Computing the 

Burning Rate of HMX Propellants.” Combustion and Flame, vol. 115, pp. 406-416, 1998. 

20. Davidson, J. E., and M. W. Beckstead. ‘A Mechanism and Model for GAP Combustion.” 

Proceedings of the 33rd JANNAF Combustion Meeting, CPIA Publication 653, vol. II, 

pp. 91-100,1996. 

21. Miller, M. S. “Three-Phase Combustion Modelling: Frozen Ozone, a Prototype System.” 

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Detonation Chemistry of Energetic Materials, edited by T. B. Brill, T. P. Russell, W. C. Tao, 

and R. B. Wardle, Materials Research Society, Pittsburgh, PA, pp- 169-l 80, 1996. 

22. BenReuven, M., L. H. Caveny, R. J. Vichnevetsky, and M. Sumrnerfreld. “‘Flame Zone and 

Sub-Surface Reaction Model for Deflagrating RDX.” Proceedings of the 16th Symposium 

(International) on Combustion, The Combustion Institute, Pittsburgh, PA, pp. 1223-1233,1977. 

36 
23. BenReuven, M. “Nitramine Monopro@lant Deflagration and Non-Steady, Reacting Rocket 

Chamber Flows.” Ph.D dissertation, Department of Mechanical and Aerospace Engineering, 

Princeton University, Princeton, NJ, January 1980. 

24. Bizot, A., and M. W. Beckstead “A Model for Double Base Ropellant Combustion.” 

Proceedings of the 22nd Symposium (International) on Combustion, The Combustion Institute, 

Pittsburgh, PA, pp. 1827-1834,1989. 

25. Song, H., and D. Yang. ‘%lc&l for predicting the Burning Rate of Double Base Propellants 

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Karlsruhe, Federal Republic of Germany, pp. 84-l-84-12,24-27 June 1997. 

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Power, vol. 12, pp. 302-309, 1996. 

27. Brill, T. B., H. Arisawa, P. J. Brush, P. E. Gongwer, and G. K. Williams. “Surface Chemisuy 

of Burning Explosives and Propellants.” Journal of Physical Chemistry, vol. 99, 

pp. 13&l-1392,1995. 

28. Zenin, A. ‘HMX and RDX: Combustion Mechanism and Influence on Modern Double-Base 

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29. Ward, M. J., S. F. Son, and M. Q. Brewster. “Steady Deflagration of HMX With Simple 

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30. Shmmaker, R. L., J.-A. Stark, and R. E. Taylor. ‘Theimophysical Properties of Pro@lants.” 

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32. Miller, M. S. U.S. Army Research Latwrratory, Aberdeen Proving Ground, MD, unpublished 

data. 

33. UIas, A., Y. C. Lu, K. K. Kuo, and T. Freyman. ‘Measurement of Temperahue and NO and 

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of the 32nd JANNAF Combustion Meeting, CPIA Publication 631, vol. I, pp. 46149,1995. 

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Meeting, Tucson, AZ, 1998, in press. 

37 
35. Atwood, A., P. 0. Curran, C. F. Price, and J. Wiknich. “Burning Rate, Radiant Ignition, and 

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vol. 94, pp. 407+25,1993. 

37. Anderson, W. R., N. Ilincic, N. E. Meagher, K. Seshadri, and J. A. Vanderhoff. “‘Detailed and 

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Combustion Subcommittee Meeting and 1995 Propulsion Systems Hazards Subcommittee 

Meeting, CPIA Publication 638, vol. I, pp. 197-114, 1995. 

38. Ilincic, N., W. R. Anderson, K. Seshadri, and N. Meagher. “Simplified Chemical-Kinetic 

Mechanisms for Characterizing the Structure of the Dark Zones of Double-Base and Nitramine 

Propellants.” Proceedings of the 26th Symposium (International) on Combustion, The 

Combustion Institute, Pittsburgh, PA, pp. 1997-2006, 1996. 

39. Levy, J. B. Personal communication with E. Freedman. U.S. Army Research Laboratory, 

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41. Andreev, K. K. “Thermal Decomposition and Combustion of Explosives.” Gosenergoizdat,, 

Moscow-Leningrad, 1957. 

42. Andreev, K. K., A. P. Glazkova, and I. A. Tereshkin. “&Investigation of Pressure, Temperature, 

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Physics Institute, MOSCOW, 1959-l 960. 

43. Tsang, W., and J. T. Herron. “Chemical-Kinetic Data Base for Propellant Combustion I 

Reactions Involving NO, N02, HNO, HNO2, HCN, and N20.” Journal of Physica and 

Chemical Reference Data, vol. 20, pp. 6Ow63,199l. 

44. Lin, C. Y., 8. T. Wang, M. C. Lin, and C. F. Melius. “A Shock Tube Study of the CHzO + NO2 

Reaction at High Temperatures.” International Journal of Chemical Kinetics, vol. 22, 

pp. 455-482,1990. 

45. Robbins, F. W., and D. A. Worrell. “Fastcore Layered Propellant Study.” Proceedings of the 

29th JANNAF Combustion Meeting, CPIA Publication 593, vol. 1, pp. 91-98, 1992. 

38 
46. Miller, M. S., and W. R. Anderson. “Detailed Combustion Modeling as an Aid to Propellant 

Formulation: Two New Strategies.” U.S. Army Research Laboratory Memorandum Report, 

1999, in press. 

47. Kooker, D. E., S. L. Howard, and L. -M. Chang. “Flamespreading in Granular Solid Propellant: 

Initial Results.” Proceedings of the 30th JANNAF Combustion Meeting, CPIAPublication 606, 

~01s I, pp. 241-258,1993. 

39 
40 
Appendix: 

Reaction Mechanism (DBll) for Nitroglycerine 

41 
INI-ENTIONALLYWTKAIW. 

. 

42 
CHEMKIN INTERPRETER OUTPUT: CHEMKIN-II Version 3.6 Apr. 1994 

DOUBLE PRECTSION 

-_-_-_f___---f-f____ 

ELEMENTS ATOMIC 

CONSIDERED WEIGHT 

_--_______----I----_ 

1. H 1.00797 

2. c 12.0112 

3. 0 15.9994 

4. N 14.0067 

-__--_t----_---_____l_____l_____________-------- 

SPECIES 

CONSIDERED 

--_-_---__-_-_ 

1. H 

2. HZ 

3. 02 

4. H20 

5. co2 

6. CO 

7. N2 

8. NO2 

9. N20 

10. NO 

11. HONO 

12. OH 

13. 0 

14. HO2 

15. H202 

16. CH20 

17. CH30 

18. CH2 OH 

19. CH30H 

20. CH 

21. c 

22. HCO 

23. NH3 

24. NH2 

25. NH 

26. N 

27. N-NH 

28. HNO 

29. HOC0 

30. Em-No 

31. N2H2 

32. N2H3 

33. NZH4 

34. NO3 

35. NC0 

C 

PH 

HA 

AR 

S G MOLECULAR TEMPERATURE 

E E WEIGHT LOW HIGH 

ELEMENT COUNT 

H C 0 N 

__*--f_--*_-----___*_ 

GO 1.00797 

G 0 2.01594 

G 0 31.99880 

G 0 18.01534 

G 0 44.00995 

G 0 28.01055 

G 0 28.01340 

G 0 46.00550 

G 0 44.01280 

G 0 iO.00610 

G 0 47.01347 

GO 17.00737 

G 0 15.99940 

G 0 33.00677 

G 0 34.01474 

+ G 0 30.02649 

GO 31.03446 

G 0 31.03446 

G 0 32.04243 

G 0 13.01912 

GO 12.01115 

G 0 29.01852 

G 0 17.03061 

GO 16.02264 

G 0 15.01467 

G 0 14.00670 

G 0 29.02137 

G 0 31.01407 

G 0 45.01792 

G 0 45.02077 

G 0 30.02934 

G 0 31.03731 

G 0 32.04528 

G 0 62.00490 

GO 42.01725 

------------------------------------------ 

300.0 5000.0 1 0 0 0 

300.0 5000.0 2 0 0 0 

300.0 5000.0 0 0 2 0 

300.0 5000.0 2 0 1 0 

300.0 5000.0 0 1 2 0 

300.0 5000.0 0 1 1 0 

300.0 5000.0 0 0 0 2 

300.0 5000.0 0 0 2 1 

300.0 5000.0 0 012' 

200.0 6000.0 0 0 1 1 

300.0 5000.0 1 0 2 1 

300.0 5000.0 1 0 1 0 

300.0 5000.0 0 0 1 0 

300.0 5000.0 1 0 2 0 

300.0 5000.0 2 0 2 0 

200.0 6000.0 2 1 1 0 

300.0 3000.0 3 110 

250.0 4000.0 3 1 1 0 

300.0 5000.0 4 1 1 0 

300.0 5000.0 1 1 0 0 

300.0 5000.0 010 0 

300.0 5000.0 1 1 1 0 

300.0 5000.0 3 0 0 1 

200.0 6000.0 2 0 0 1 

200.0 6000.0 1 0 0 1 

300.0 5000.0 0 0 0 1 

250.0 4000.0 1 0 0 2 

200.0 6000.0 1 0 1 1 

300.0 4000.0 1 1 2 0 

300.0 5000.0 1 0 1 2 

300.0 5000.0 2 0 0 2 

300.0 5000.0 3 0 0 2 

300.0 5000.0 4 0 0 2 

300.0 5000.0 0 0 3 1 

200.0 6000.0 0 111 
(k = A T**b exp(-E/RT)) 

REACTIONS CONSIDERED A b 

1. N02(+M)=NO+O(+M) 7.6003+18 -1.27 

Low pressure limit: 0.247003+29 -O-337003+01 0.748003+05 

T&H VALUES 0.95000E+OO -O.lOOOOE-03 

N20 Enhanced by 1.500E+OO 

H20 Enhanced by 4.400E+OO 

N2 Enhanced by 1.000E+00 

co2 Enhanced by 2.300E+OO 

2. N20(+M)=N2+O(+M) .' 1.2603+12 0.00 

Low pressure limit: O-597003+15 0.00000E400 O-566403+05 

N20 Enhanced by 5.000E+OO 

H20 Enhanced by 7.500E+OO 

N2 Enhanced by 1.000E+00 

co2 Enhanced by 3.200E+OO 

02 Enhanced by 8.200E-01 

3. H+NO(+M)=HNO(+M) 1.520E+15 -0.41 

Low pressure limit: 0.40000E+21 -0.175003+01 0.00000E+00 

N20 Enhanced by 5.000E+OO 

H20 Enhanced by S.OOOE+OO 

N2 Enhanced by l.OOOE+OO 

co2 Enhanced by 1.300E+OO 

4. NO+OH(+M)=HONO(+M) 1.9883+12 -0.05 

Low pressure limit: 0.508003+24 -0.25100E+Ol -0.676003+02 

T&H VALUE 0.62000E+OO 

5. 

6. 

7. 

8. 

9. 

10. 

11. 

12. 

13. 

14. 

15. 

16. 

17. 

18. 

19. 

20. 

21. 

22. 

23. 

24. 

25. 

26. 

N20 Enhanced by 5.000E+OO 

H20 Enhanced by 8.300E+OO 

N2 Enhanced by l.OOOE+OO 

co2 Enhanced by 1.500E+00 

NO+M=N+O+M 1.400E+15 

N2 Enhanced by l.OOOE+OO 

H2 Enhanced by 2.200E+OO 

H20 Enhanced by 6.700E+OO 

co2 Enhanced by 3.000E+OO 

N20 Enhanced by 2.200E+OO 

N~+M=N+N+M 3.710E+21 

N20+N=N2+NO l.OOOE+13 

N02+N=N20+0 S.OlOE+12 

N02+N=NO+NO 3.980Et12 

N02+N02=NO+N0+02 l-6303+12 

NOZ+N02=NO+N03 9.6403+09 

N02+N03=NO+N02+02 1.400E+ll 

HNO+NO=N2O+OH 8.5103+12 

HNO+OZ=H02+NO l.OOOE+13 

HNO+N02=HONO+NO 6.000E+11 

HONO+O=OH+N02 1.200E+13 

HONO+OH=H20+N02 1.270E+lO 

HONO+NH2=N02+NH3 l.OOOE+lO 

HNO+O=OH+NO 3.6103+13 

NH+O=NO+H 5.5003+13 

NH+O=N+OH 3.7203+13 

NH+NH=N2+H+H S.lOOE+13 

NH+M=N+H+M 2.6503+14 

NH2+NO=NZO+H2 5.000E+13 

CH+02=HCO+O 3.3003+13 

CH+O=CO+H 5.7003+13 

0.00 148430.0 

1.60 225000.0 

0.00 19870.0 

0.00 0.0 

0.00 0.0 

0.00 26120.0 

0.73 20920 .o 

0.00 3180.0 

0.00 29590 .o 

0.00 25000.0 

0.00 1987.0 

0.00 5961.0 

1.00 135.0 

1.00 0.0 

0.00 0.0 

0.00 0.0 

0.00 0.0 

0.00 0.0 

0.00 75510.0 

0.00 24640.0 

0.00 0.0 

0.00 0.0 

E 

73290.0 

62620.0 

0.0 

-721.0 

44 
27. CH+OH=HCO+H 

28. CH+C02=HCO+CO 

29. CH+H=C+H2 

30. c+o2=co+o 

31. C+OH=CO+H 

32. OH+HCOc=>HZO+CO 

33. HCO+M<=>H+CO+M 

H2 Enhanced by 

H20 Enhanced by 

co Enhanced by 

co2 Enhanced by 

34. H+HCOc=>H2+CO 

35. HCO+O=CO+OH 

36. HCO+O=C02+H 

37. HC0+02<=>H02+CO 

38. CO+O(+M)=C02(tM) 

Low pressure limit: O-135003+25 

T&H VALUE 0.10000E+01 

H20 

H2 

co 

co2 

N20 

39. CO+OH=C02+H 

40. c0+02=c02+0 

43. H02+CO=C02+OH 

42. H2+02=20H 

43. OH+H2=H2O+H 

44. 02+H=O+OH 

45. O+HZ=OH+H 

46. H+02+M=H02+M 

H20 

co2 

H2 

co 

N2 

47. OH+HOZ=H20+02 

48. H+H02=20H 

49. O+H02=02+OH 

50. 20H=O+H20 

51. 2H+M=H2+M 

H2 

H20 

co2 

52. 2H+H2=2H2 

53. 2H+H20=H2+H20 

54. 2H+C02=H2+C02 

55. H+OH+M=H20+M 

H20 

56. H+O+M=OH+M 

H20 

57. O+O+M=02+M 

58. H+H02=H2+02 

59. 2H02=H202+02 

60. H202+M=20H+M 

61. H202+H=H02+H2 

62. H202+OH=H20+H02 

63. NO+H02=N02+OH 

Enhanced by 

Enhanced by 

Enhanced by 

Enhanced by 

Enhanced by 

Enhanced by 

Enhanced by 

Enhanced by 

Enhanced by 

Enhanced by 

Enhanced by 

Enhanced by 

Enhanced by 

Enhanced by 

Enhanced by 

3.000E+13 0.00 

3.4003+12 0.00 

1.500E+14 0.00 

2.000E+13 0.00 

5.000E+13 0.00 

5.000E+13 0.00 

1.8703+17 -1.00 

2.000E+OO 

1.200E+Ol 

1.500E+OO 

2.000E+OO 

7.3403+13 0.00 

3.000E+13 0.00 

3.000E+13 0.00 

7.600E+12 0.00 

1.800E+lO 0.00 

-0.279003+01 0.419003+04 

1.200E+Ol 

2.5OOE+OO 

1.900E+OO 

3.800E+OO 

5.000E+OO 

1.510E+OY 

2.5303+12 

5.8003+13 

1.700E+13 

2.1603+08 

3.5203+16 

5.0603+04 

3.6103+17 

1.860E+01 

4.200E+OO 

2.900E+OO 

2.100E+OO 

1.300E+OO 

7.5003+12 

l-6903+14 

1.400E+13 

6.000E+08 

l.OOOE+l8 

O.OOOE+OO 

O.OOOE+OO 

O.OOOE+OO 

9.2003+16 

6.000E+19 

5.4903+20 

l-6003+22 

5.000E+OO 

6.2003+16 

5.000E+OO 

l-8903+13 

6.6303+13 

1.800Et12 

1.300E+17 

4.8203+13 

l-7503+12 

2.110E+12 

1.30 -758.0 

0.00 47688.0 

0.00 22934.0 

0.00 47780.0 

1.50 3430.0 

-0.70 17070.0 

2.67 6290.0 

-0.72 0.0 

0.00 0.0 

0.00 874.0 

0.00 1073.0 

1.30 0.0 

-1.00 0.0 

-0.60 0.0 

-1.25 0.0 

-2.00 0.0 

-2.00 0.0 

-0.60 0.0 

0.00 -1788.0 

0.00 2126.0 

0.00 0.0 

0.00 45500.0 

0.00 7948.0 

0.00 318.0 

0.00 -479.0 

0.0 

690.0 

0.0 

0.0 

0.0 

0.0 

17000.0 

0.0 

0.0 

0.0 

400.0 

2380.0 

45 
64. 

65. 

66. 

67. 

68. 

69. 

70. 

71. 

72. 

73. 

74. 

75. 

76. 

77. 

78. 

79. 

N02+H=NO+OH 

N02+0=N0+02 

NCOtH=NH+CO 

NCO+O=NO+CO 

NCO+N=N2+CO 

NCO+OH=NO+CO+H 

NCO+M=N+CO+M 

N20 

H20 

N2 

co2 

NCO+NO=NZO+CO 

NCO+NO=C02+N2 

NCO+N02=C02+N20 

NCO+N02=CO+NO+NO 

Iw+o2=HNo+o 

NH+02=NO+OH 

NH+NO=N2O+H 

NH+NO=N2+OH 

N20+H=N2+OH 

Declared duplicate 

80. N20+H=N2+OH 

Declared duplicate 

81. NNH+O=N20+H 

82. NN'H+O=NO+NH 

83. N20+0=N2+02 

84. N20+0=NO+NO 

85. H+KNO=NH+OH 

86. NH+OH=N+HZO 

87. NH+N=NZ+H 

88. N+H2=NH+H 

89. HNO+H=NH2+0 

90. NH2+O=NH+OH 

91. NH2+OH=NH+H20 

92. NH2tH=NH+H2 

93. N-H2+NH=N2H2+H - 

94. NH2+N=N2+H+H 

95. IW2+02=HNO+OH 

96. NH2+NH2=N2H2+H2 

97. NHZ+NH2.+iH+NH3 

98. NH2+NH2=N2H3+H 

99. NH2+NH2+M=N2H4+M 

100. NH2+N02=N2O+H20 

101. NH+N02=N2O+OH 

102. N2H4+H=N2H3+H2 

103. NZH4+OH=N2H3+H20 

104. N2H4+0=N2H3+OH 

105. N2H3=N2H2+H 

106. N2H3+H=N2H2+H2 

107. N2H3+OH=N2H2+H20 

108. N2H3+0=N2H2+OH 

109. N2H2+M=NNH+H+M 

H20 

02 

N2 

H2 

110. N2H2+H=NNH+H2 

111. NZHZ+O=NH2+NO 

1.300E+14 

3.900E+12 

5.4003+13 

4.5203+13 

2.00OE+13 

2.000E+13 

1.1403+23 

Enhanced by 5.000E+OO 

Enhanced by 5.000E+OO 

Enhanced by l.OOOE+OO 

Enhanced by 1.500E+OO 

8.8003+17 

l.l30E+18 

1.9503+13 

1.7703+12 

4.6103+05 

1.2803+06 

3.5003+14 

2.1603+13 

2.5303+10 

reaction... 

2.230E+14 

reaction... 

1.400E+14 

3.3003+14 

3.6543+12 

9.985E+13 

3.000E+14 

5.000E+ll 

3.000E+13 

1.600E+14 

3.5003+15 

6.7503+12 

4.000E+06 

4.000E+13 

1.500E+15 

7.2003+13 

4.5003+12 

5 .OOOE+ll 

5.000E+13 

1.7903+13 

2.9803+47 

2.8403+18 

l.OOOE+13 

1.000E+12 

3.000E+lO 

2.000E+13 

1.200E+l.3 

l.OOOE+12 

3.000E+lO 

2.000E+13 

5.000E+16 

Enhanced by 1.500E+Ol 

Enhanced by 2.000E+OO 

Enhanced by 2.000E+OO 

Enhanced by 2.000E+OO 

5.000E+13 

l.OOOE+13 

0.00 361.0 

0.00 -238.0 

0.00 0.0 

0.00 0.0 

0.00 0.0 

0.00 7500.0 

-1.95 59930 .o 

-1.78 790.0 

-1.78 790.0 

-0.26 -620.0 

-0.26 -620.0 

2.00 6500.0 

1.50 100.0 

-0.46 16.1 

-0.23 0.0 

0.00 4550.0 

6.00 16750.0 

-6.40 477.0 

-0.23 -1013.0 

6.00 15900.0 

d.00 28040.0 

d.00 18000.0 

.d.so 2000.0 

d.00 0.0 

d.00 25140.0 

-6.30 28200.0 

0.00 0.0 

2.00 1000.0 

d-00 3650.0 

-d-50 0.0 

d.00 0.0 

0.00 25000.0 

0.00 0.0 

0.00 10000.0 

-d.35 11320.0 

-d-44 9680.0 

-2.20 0.0 

0.00 0.0 

d-50 2000.0 

6.68 1290.0 

0.00 1000 .o 

0.00 58000.0 

0.50 2000.0 

0.68 1290 - 0 

0.00 1000.0 

0.00 50000.0 

0.00 

0.00 

1000.0 

0.0 

46 
112. N2H2+0=NNH+OH 

113. N2H2+OH=NNH'+H20 

114. N2H2+NH=NNH+NH2 

115. N2H2+NH2=NH3+NNH 

116. NH2+NO=NNH+OH 

117. NH2+NO=N2+H20 

118. NH3+OH=NH2+H20 

119. NH3+H=NH2+H2 

120. NH3+0=NH2+OH 

121. NH3+M=NH2+H+M 

122. NNH+NO=N2+HNO 

123. NNH+H=N2+H2 

124. NNH+OH=N2+H20 

125. NNH+NH2=N2+NH3 

126. NNH+IWf=N2+NH2 

127. HNO+OH=NO+H20 

128. H+HNO=H2+NO 

129. HNO+NH2=NH3+NO 

130. N+NO=N2+0 

131. O+NO=N+OZ 

132. NO+H=N+OH 

133. HNO+HNO=N20+H20 

134. N20+NO=N2+N02 

135. NO+NO+NO=N20+N02 

136. HOCO+M=OH+CO+M 

137. CO+NO2=NO+CO2 

138. CH+N02=HCO+NO 

139. H2+N02=HONO+H 

140. NNH=N2+H 

Declared duplicate reaction... 

141. NNH+M=N2+H+M 

Declared duplicate reaction... 

142. KNO+NO+NO=KNNO+N02 

143. HNNO+NO=NNH+N02 

144. HNNO+NO=NZ+HONO 

145. HNNO+Ei=H+N20+M146. HNNO+M=N2+OH+M 

147. HCO+NO=HNO+CO 

148. O+CH20<=>OH+HCO 

149. O+CH20H<=>OH+CH20 

150. O+CH30<=>OH+CH20 

151. O+CH30Hc=>OH+CH20H 

152. O+CH30Hc=>OH+CH30 

153. 02+CH20c=>H02+HCO 

154. H+HCO(+M)<=>CH20(+M) 

2.000E+13 

1.000E+l3 

l.OOOE+13 

1.000E+13 

9.300E+ll 

2.000E+20 

2.040E+06 

5.4203+05 

9.4003+06 

2.2003+16 

2.000E+13 

1.000E+14 

5.000E+13 

S.OOOE+13 

5.000E+13 

1.2953+07 

4.4603+11 

2.000E+13 

3.2703+12 

3.8003+09 

1.700E+14 

3.6303-03 

4.2903+13 

1.070E+lO 

2.1903+23 

9.0403+13 

l.OlOE+14 

3.210E+12 

3.000E+08 

0.00 1000.0 

0.00 1000.0 

0.00 1000.0 

0.00 1000.0 

0.00 0.0 

2.60 924.0 

2.04 566.0 

2.40 9917.0 

1.94 6460.0 

0.00 93470.0 

0.00 0.0 

0.00 0.0 

0.00 0.0 

0.00 0.0 

0.00 0.0 

1.88 -958.0 

0.72 655.0 

0.00 1000.0 

0.30 0.0 

1.00 41375.0 

0.00 48800.0 

3.98 1190.0 

0.00 47130.0 

0.00 26800.0 

1.89 35270.0 

0.00 33780.0 

0.00 0.0 

0.00 28810.0 

0.00 0.0 

l.OOOE+13 0.50 3060.0 

1.700E+ll 

3.2003+12 

2.600E+ll 

2.2003+15 

l.OOOE+X 

7.2303+12 

3.9003+13 

l.OOOE+13 

l.OOOE+13 

3.880E+OS 

1.300E+05 

l.OOOE+14 

l.O90E+12 

0.00 2100.0 

0.00 270.0 

0.00 810.0 

0.00 21600.0 

0.00 25600.0 

0.00 0.0 

0.00 3540.0 

0.00 0.0 

0.00 0.0 

2.50 3100.0 

2.50 5000.0 

0.00 40000.0 

0.48 -260.0 

Low pressure limit: O.l3500E+25 -0.257003+01 O-142503+04 

TROE centering: 0.782403+00 0.271003+03 0.275503+04. 0.65700E+04 

H2 Enhanced by 2.000E+OO 

H20 Enhanced by 6.000E+00 

co Enhanced by 1.500E+OO 

co2 Enhanced by 2.000E+OO 

155. H+CH20(+M)c=>CH20H(+M) 5.400E+ll 0.45 3600.0 

47 
Low pressure limit: 0.127003+33 -0.482003+01 0.653003+04 

TROE centering: O-718703+00 O.l0300E+03 0.129103+04 O-416003+04 

H2 Enhanced by 2.000E+OO 

H20 Enhanced by 6.000E400 

co Enhanced by 1.500E+OO 

co2 Enhanced by 2.000E+OO 

156. H+CH20(+M)<=>CH30(+M) 5.400E+ll 0.45 2600.0 

Low pressure limit: 0.220003+31 -0.48000E+Ol 0.556003+04 

TROE centering: 0.758003+00 0.940003+02 0.155503+04 O-420003+04 

H2 Enhanced by 2.000E+OO 

H20 " Enhanced by 6.000E+00 

co Enhanced by 1.500E+OO 

co2 Enhanced by 2.000E+OO 

157. H+CH20c=>HCO+H2 2.300E+lO 1.05 3275.0 

158. H+CH20H(+M)c=>CH30H(+M) 1.800E+13 0.00 0.0 

Low pressure limit: 0.300003+32 -0.48000E+Ol 0.330003+04 

TROE centering: 0.767903+00 0.338003+03 0.181203+04 0.508103+04 

H2 Enhanced by 2.000E+OO 

H20 Enhanced by 6*000E+00 

co Enhanced by l.SOOE+OO 

co2 Enhanced by 2.000E+OO 

159. H+CH20H<=>H2+CH20 2.000E+13 0.00 0.0 

160. H+CH30(+M)c=>CH30H(+M) 5.000E+13 0.00 0.0 

Low pressure limit: 0.860003+29 -0.40000E+Ol O-302503+04 

TROE centering: O-890203+00 O-144003+03 0.283803+04 0.455693+05 

H2 Enhanced by 2.000E+OO 

H20 Enhanced by 6.000E+00 

co Enhanced by 1.500E+OO 

co2 Enhanced by 2.000E+OO 

161. H+CH30<=>H+CH20H 3.4003+06 1.60 0.0 

162. H+CH30<=>H2+CH20 2.000E+13 0.00 0.0 

163. H+CH30Hc=>CH20H+H2 1.700E+07 2.10 4870.0 

164. H+CH30H<=>CH30+H2 4.2003+06 2.10 4870.0 

165. H2+CO(+M)<=>CH20(+M) 4.3003+07 1.50 79600.0 

Low pressure limit: 0.507003+28 -0.342003+01 O-843503+05 

TROE centering: O-932003+00 O-197003+03 O-154003+04 0.10300E+05 

H2 Enhanced by 2.000E+OO 

H20 Enhanced by 6.000E+00 

co Enhanced by 1.500E+OO 

co2 .~ Enhanced by 2.000E-tOO 

166. OH+CH20<=rHCO+H20 3.4303+09 1.18 -447.0 

167. OH+CH20H<=>H20+CH20 f.OOOE+12 0.00 0.0 

168. OH+CH30<=>H20+CH20 5.000E+12 0.00 0.0 

169. OH+CH30Hc=>CH20H+H20 1.4403+06 2.00 -840.0 

170. OH+CH30H<=>CH30+H20 6.3003+06 2.00 1500.0 

171. H02+CH20c=>HCO+H202 l.OOOE+12 0.00 8000.0 

172. CH+H20c=>H+CH20 1.7133+13 0.00 -755.0 

173. CH20H+02<=>HOZ+CH20 1.800E+13 0.00 900.0 

174. CH30+02c=>H02+CH20 4.2803-13 7.60 -3530.0 

1'75. HCO+HNO=CH20+NO 6 .OOOE+ll 0.00 2000.0 

176. CH20+N02=HCO+HONO 8.0203+02 2.77 13730.0 

177. HCO+N02=CO+HONO 1.2403+23 -3.29 2355.0 

178. HCO+N02=H+C02+NO 8.3903+15 -0.75 1930.0 

4x 
Note: Units for the rate parameters are centimeter, second, and mole, and for E, Cal/mole. For 

reactions followed by three numerical parameters, the rate-coefficient expression is 

k = ATbexp(-ERT). For reactions which appear twice with the phrase “declared duplicate 

reaction . . ..‘I the rate coefficient is computed as the sum of the two three-parameter expressions- For 

reactions involving a generalized collider species, M, collider efficiencies other than 1.0 are 

specified. For reactions involving pressure-dependent rate expressions (those with a collider species 

specified as [+M]), three types of expression are used. If “T&H VALUE” occurs in the output, the 

Tsang and Herron form was used (as described in Tsang and Herron*‘), with constants a~ and ai (if 

the latter is used) appearing, respectively, on the same line. A version of CHEMKIN, modified at 

ARL, was used for this computation. If “TROE centering:” occurs, the TROE form was used with 

the appropriate parameters specified on that line. If neither of these is mentioned, the Lindemann 

form was assumed. Descriptions of the TROE and Lindemann expressions may be found in the 

CHEMKIN manual2 

T Note that the log expressions used in this source are for base 10 (W. Tsang, private communication). 

Tsang, W., and J. T. Herron. “Chemical Kinetic Data Base for Propellant Combustion I Reactions Involving NO, NOZ, 

HIJO, HN02, HCN, and NzO.” Journal ofPhysical and Chemical Refirence Data, vol. 20, p. 609-663, 1991. 

’ Kee, R. J., F. M. Rupley, and J. A. Miller. “Chemkin-II: A Fortran Chemical Kinetics Package for the Analysis of 

Gas-Phase Chemical Kinetics.” Sandia National Laboratories Report SAND89-8009, September 1989. 

49 
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52 
Approved for public release; diseibution is unlimited. 

19. ABsrRAcrfMRdu4m 0oD-m 

The application of complex networks of elementary chemical reactions to the gas phase of burning energetic 

mater& has increased mark@ly over the last decade. The exquisite complexity of these gas-phase reaction networks 

xx~pled with available high-rigor treapnents of msport, is not matched by an equivalent level of sophistication im 

aesaiptions 0f the condensed-phase and interfacial phenomena Owing to the vastly more complicated, many-l@ 

nature of the condensed phase, this condition is not likely to be relieved soon. In response to these difkulties, a neu 

semi-empirical approach to burning-rate calculation has ken developed and applied to frozen ozone 

zyclo&imethyl~tramine (RDX), and nitroglycerine. The new approach hypothesizes a single ovemll nztctiom 

linking the ururzted mat&al to the net products of condensed-phase decomposition and characterizes their rate 01 

formation acEording to an empirically derived pyrolysis law. These condensed-phase products become the reactanti 

for the gas phase, which are treated in full elementary-reaction detail. Using this new semi-empirical mcukl, e 

methodology for computing the relative effects of several additives on the burning rate of nitroglyckne is developec 

and demonstrated. Hopefuuy this approach will enable more rapid pro-s in modeling multi-ingredient propellantr 

than did previous approaches attempting to model the condensed-phase processes in detail. 

14. SuBJEcrTERm 

modeling, energetic mate&Is, propellant, combustion 

16. NUMBER W PAQEB 

49 

16. PRlcE COEIE 

17. SECURllv cusauwAllcN 16. SEUJRlTY ClAsslFlcATlON 19. sEcuRrrY cus6JFlcAnoN 20. UYITATION OF ABSTRACT 

OFREPORT OFTH18PAoE OFAUNCLASSIFIED UNCLASSIFIED UNCLASSIFIED UL 
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54 
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