J . Phys. Chem. 1990, 94, 294-295
294
Novel Kinetic Scheme for the Ammonium Perchlorate Gas Phase H. Sahu, T. S. Sheshadri,* and V. K. Jain Department of Aerospace Engineering, Indian Institute of Science, Bangalore 560 012, India (Received: April 21, 1989; In Final Form: July 3, 1989)
A novel gas-phase kinetic scheme for ammonium perchlorate (AP) deflagration involving 22 reactions among 18 species
is developed. The kinetic scheme is based on a study of the effect of initial conditions on the solution of the differential equations of adiabatic constant-pressure combustion kinetics. The existence of condensed-phase reaction products provides alternate pathways for the consumption of NH3and HCIOl produced by gas-phase dissociation of AP. Theoretically obtained temperature-time profiles of the novel scheme do not change when the conventional reaction pathways are included, indicating that the novel scheme is a substantially faster rate process. The new scheme does not involve the species CIO, which has long been considered a critical component of the AP gas phase and which is included in the conventional reaction pathways. The new scheme develops faster overall reaction rates, steeper temperature-time profiles, and in a deflagration model will result in higher heat-transfer rates from gas phase to the condensed phase.
Introduction Theoretical studies of AP monopropellant deflagration require representation of the gas-phase chemical kinetics either in terms of an effective overall reaction or in terms of an elementary reaction scheme. In either case, previous studies have regarded the species CIO as critical to the gas-phase kinetic scheme.'-, In this work a novel kinetic scheme is developed that produces the observed deflagration products and that does not involve any direct reaction between ammonia and any oxide of chlorine. Furthermore, adiabatic constant-pressure temperature-time solution profiles of the novel scheme do not change even when the reaction pathways of the earlier schemes are included. This indicates that the present scheme is the fastest among all the reaction pathways and the one that would actually occur.
AP Gas-Phase Kinetic Scheme The novel gas-phase kinetic scheme for AP deflagration is listed in Table I along with the references from which rate data were obtained. The rate constant of each reaction is of the form k = A P exp(-E/RT), and the table lists values of A , /3, and E for each reaction. The reaction scheme of Table I evolved from a consideration of the effect of initial conditions on the solutions of the system of differential equations representing adiabatic constant-pressure kinetics. These equations are
( I ) Jacobs, P. W. M.; Pearson, G. S. Combust. Flame 1969, 13, 419. (2) Guirao, C.; Williams, F. A. AZAA J. 1971, 9, 1345. (3) Ermolin, N. E.; Korobeinichev, 0. P.; Tereshchenko, A. G.; Fomin, V. M. Fizika Goreniya Vzrvya 1982, 18, 61. (4) Jensen, D. E.; Jones, G. A. Combust. Flame 1978, 32, 1. (5) Seidle, J. P.; Branch, M. C. Combust. Flame 1983, 52, 47. (6) Bodenstein, M.; Padelt, E.; Schumacher, H. J. Z . fhys. Chem. 1929, BS, 209. (7) Steiner, H.; Rideal, E. K. froc. R. SOC.London, A 1939, 173, 503. (8) Gilbert, R.; Jacobs, P. W. M. Combust. Flame 1971, 17, 343. (9) Cheskis, S. G.; Nadtochenko, V. A.; Sarkisov, 0. M. Int. J . Chem. Kinet. 1981, 13, 1041. (10) Zellner, R.; Wagner, G.; Himme, B. J. fhys. Chem. 1980,84,3196. ( I I ) Miller, J. A.; Smooke, M. D.; Green, R. M:; Kee, R. J. Combust. Sci. Technol. 1983, 34, 149. (12) Michel, K. W.; Wagner, H. G. Symp. ( f n t . ) Combust. [froc.]1965, loth, 353. (13) Muzio, L. J.; Arand, J. K.; Teixeira, D. P. Symp. ( f n t . ) Combust. [Proc.] 1916, Ibth, 199. (14) Miller, J. A.; Branch, M. C.; Kee, R. J. Combust. Flame 1981, 43. 81. (15) Baulch, D. L.; Drysdale, D. D.; Horne, D. G.; Lloyd, A. C. Eualuated Kinetic Data for High Temperature Reactions; Butterworths: London, 1972; pp I , 69, 101, 109, 141.
0022-3654/90/2094-0294$02.50/0
-2((v;T;
dni)Ahf,}
dT
i = 1, ..., N where T = gas temperature, t = time, Ahfi = molar heat of formation of species i at temperature T, Ci = concentration of species i in moles per volume, and Cpi = molar specific heat of species i at temperature T. The terms ( I / V)(dni/dt) are obtained by using the usual reaction rate expressions in terms of species concentrations, temperature, and rate constants of the elementary reactions of the reaction mechanism. The above constitute a system of ( N 1) first-order differential equations and can be solved for the (N 1) unknowns ( T and C,), as functions of time, provided the initial conditions T(t=O) and C,(t=O), i = 1, ..., N , are known. The choice of adiabatic constant-pressure kinetics is natural, as the deflagration process is also adiabatic and constant pressure. However, when it is desired to obtain a single effective overall reaction from a reaction mechanism, it may be more convenient and computationally simpler to use isothermal constant-pressure kinetics., In any case, the important point is that the evolution of the solutions of the above equations are dependent on the initial conditions, Le., the temperature and species concentrations at the beginning of the gas-phase reactions. In the case of AP deflagration, a large fraction of the AP reacts in the condensed phase producing deflagration products.2 Thus, the gas-phase reaction begins with relatively small quantities of unreacted NH, and HCIO, and relatively large quantities of final deflagration products. Under these conditions the fastest reaction pathways for completing the gas-phase reactions are different from those corresponding to a situation where one starts only with unreacted NH, and HCIO,. As an example, a reaction pathway for oxidizing ammonia such as NH, + N O NH, + HNO, NH2 0 2 H N O OH, HNO OH H,O NO, HNO + HNO HzO NZO
+
+
+ +
---
+ + +
would proceed immediately in the former case due to the large availability of N O and 0,.In the latter case, this pathway would
0 1990 American Chemical Society
Novel Kinetic Scheme for the AP Gas Phase
The Journal of Physical Chemistry, Vol. 94, No. I , I990 295
TABLE I: AP Gas-Phase Reaction Mechanism" no. react ion I CI + CI + M C12 + M 2 C12 + M CI + CI + M 3 H +NO +M HNO + M 4 HNO + M H + NO + M 5 CI2 + H HCI + CI
-+ -+ + + + - + - + + + +
6 7 8 9
CIO, C103 C12 3 0 2 H HCI CI H2 H2 O H H20 H HC104 CI03 O H HNO HNO H20 N20 H N O NH2 NH3 N O HNO OH H20 N O H20 + 0 -+ H2 + 0 2 NH N O - N20 + H NH2 NH2 N2 2H2 NH2 NH2 NH3 N H NH2 + N O --+ N2 + H2O NH2 + 0 2 HNO OH NH, NO NH2 H N O NH3 + 0 NH2 + O H N2O M 2" 0 M OH + OH H2 + 02 +
IO
+ +
11
12 13 14 15 16 17
+ + +
18 19 20 21 22
+ +
+ +
+
+
-+
+
+
4
+
+
+
+ + +
4
" Units of A P are s-I
A
P
7.26 x 1014 4.02 x 1015 1.81 X 10l6 3.0 X l o i 6 8.43 x 1013 1014 7.24 x 1013 5.2 x 1013 6.7 X 10I2 3.95 x 10'2 5.0 x 1013 3.6 x 1013 6.76 x 1013 4.33 x 1014 3.98 x 1013 6.3 X 10l2 7.02 x 1019 4.5 x 10'2 8 X IO" 1.5 x 10'2 1.62 x 1014 1.93 X 10I2
0 0 0 0 0 0 0 0 0 0 0 0 0 -0.5 0 0 -2.46 0 0 0 0 0
ref 4 4 4 5 4 6 7 5 8 9 5 5 10 11 12 5 5 5 13 5 14 15
for unimolecular reactions, cm3 mol-' s-I for bimolecular reactions, and cm6 mol-2 s-I for termolecular reactions.
x IO'
I
I2Ot
t -25
-30
E , kcal/mol -1.78 55.06 -0.596 48.68 1.15 11.93 5.2 6.5 43.3 5 1.o 0 18.4 0 12 10 1.88 25 2.0 6.04 51.6 0.48
-20
-I5
-10
-5
L n Time ( s e c )
Figure 1. Adiabatic, constant-pressure, temperature-time profile. The solid line is for the reaction scheme of Table I. Dots are for the reaction scheme of Table I the conventional reaction scheme from ref 2.
+
not be important until NO and O2have been produced by alternate means. Results and Discussion
The initial conditions needed for the solution of the differential equations ( 1 ) and (2) were generated from the assumption that
about 80% of AP reacts in the condensed phase producing deflagration products in accordance with (1 5) of ref 2. The solution of the differential equations (1) and (2) for the reaction scheme of Table I results in a temperature-time profile as shown by the solid line in Figure 1. If the conventional reaction pathways were either kinetically competitive with the present scheme or faster than the present scheme, their inclusion with the present scheme must bring about changes in the temperature-time profile. To see if they do, elementary reactions of ref 2 not included in the present scheme were added to the present scheme and the differential equations (1) and (2) were solved for the combined scheme. The temperature-time profile for the combined scheme is as shown by the dots in Figure 1. It is clear that the addition of the conventional reaction pathways to the present scheme have absolutely no effect on the evolution of the temperature profile in the gas phase. Thus, the conventional reaction pathways cannot compete with the reaction pathway of Table I for conditions corresponding to the case when large fractions of AP react in the condensed phase. It would thus appear that the reaction scheme presented here is the one that actually occurs in the AP gas phase. Furthermore, for the novel reaction scheme, the average value of dT/dt in the range 0 I t I IO-'s (defined as ((T(t=lO-'s) - T(t=O s))/lO-')) exceeds, by a factor of at least 4,the corresponding value that is obtained by solving (1) and (2) for.the kinetic scheme of ref 2 alone. dT/dt in this time range is directly related to dT/dx in the neighborhood of the propellant surface and thereby determines the heat feedback from the gas phase to the condensed phase. Thus, use of the present scheme will strongly alter the deflagration model results of ref 2. Finally, the solution of (1) and (2) for the novel reaction scheme yields at large times (Le., t = 1 s), a stoichiometry very similar to that of (15) of ref 2. Thus, the novel reaction scheme can also produce the observed deflagration products. Registry No. H3N.HC104, 7790-98-9.
