AIAA 2010-6655
46th AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit
25 - 28 July 2010, Nashville, TN
Kinetic Simulation of Hydrogen Combustion in a
Homogeneous Reactor
R.F.B. Gonçalves1, L.F.A. Ferrão2, R.J.Rocha3, F.B.C. Machado4, K. Iha5 and J.A.F.F. Rocco6
Departamento de Química - Instituto Tecnológico de Aeronáutica - CTA,
São José dos Campos – CEP 12228-901 - S.P. – Brasil
The burning simulation of hydrogen was carried on in the reactor model Aurora,
present in the software Chemkin. The MP2 method was utilized on the calculations
and optimization of the geometries and vibrational frequencies of the reactants,
transition states and products of the elementary reactions of H2 combustion
mechanism, for the determination of the Arrhenius parameters. Simulations of H2
combustion were carried out using two sets of experimental data and the set of
calculated data. The analysis of the calculated parameters for each reaction was
made and compared to the experimental ones through burning simulations. A
detailed study of the mechanism was realized for the verification of the importance
of each reaction on the global process. This methodology will allow the insertion of
new reactions in several mechanisms and also the calculation of parameters for
reactions which cannot be determined experimentally.
I.
Introduction
The reduced size and high inflammability are the main causes for the hydrogen gas to be used as
fuel in propulsive systems, as in liquid propellant rocket motors, fuel cells and scramjet systems1.
Besides, hydrogen presents itself as a clean fuel; the combustion produces water as product (H2 + 1/2O2
→ H2O), with a medium enthalpy of -241,826 kJ mol-1 (gaseous phase)2.
Hydrogen combustion mechanism was the first one to be studied and researches are still being
made aiming the increase on the number of elementary reactions for a better approximation of a more
realistic model, determination and standardization of physic-chemical parameters of each species or
addiction of more steps of the reactions presented on the mechanism.
For the several studies and experiments realized for the determination of kinetic and
thermodynamic parameters of elementary reactions, there is great discrepancy between the used methods;
each one encompasses different factors and generates also different errors. Taking into account these
informations, the computational simulation can be used for the determination of several thermodynamic
and kinetic properties, from ab initio calculations, generating standard results (same methodology, same
scale of accuracy and precision). Besides, through theoretical calculations it is also possible to determine
the parameters for reactions which still are not determined experimentally.
The methods of computational simulation can assist the comprehension of phenomenons and
systems of several areas of the scientific knowledge. They enable the development of new models, thus
approaching the theoretical results to the ones found on the real condition that occurs the phenomena.
In computational simulation, the analyzed systems can be controlled with the desired accuracy
and extreme conditions, such as oxidizing atmosphere and high temperatures, may be accessed. These
extreme conditions may not be attainable in laboratories.3
In the last decades, the combustion modeling and energetic material ignition evolved
enormously,4 being applied to several types of explosives, propellants, gas generators or pyrotechnics
formulations.5 This procedure considers effects like the distribution of reactional zones in condensed
phases, radiation of non-linear specters and non-homogeneity of the propellant.6
1
PhD Candidate, Chemistry Department, [email protected]
PhD Candidate, Chemistry Department, [email protected]
3
MSc Candidate, Chemistry Department, [email protected]
4
Professor, Chemistry Department, [email protected]
5
Professor, Chemistry Department, [email protected]
6
Professor, Chemistry Department, [email protected]
2
Copyright © 2010 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.
The computational package known as “Chemkin”7, has as objective the solution of problems
involving detailed kinetic chemistry utilizing complex reactional mechanisms. The software architecture
has informations of specific problems, models of independent problems and packages with some preselected reaction models which take into account equations of mass conservation, energy, chemical
species and, in some cases, movement quantity. On the resolution of a specific problem there is the need
to consider still the identification of the chemical species involved in the process (combustion) and its
properties such as enthalpy (H), entropy (S) and calorific capacity at constant pressure and volume (Cp,
Cv) beyond the reactional mechanisms and the reaction taxes.
The software Gaussian8, of molecular electronic structure simulation has as objective the
approximated calculation of the Schrödinger equation solutions for molecular systems, from molecular
quantum chemistry methods. This software, allows wave functions calculations of molecular systems
utilizing several approximated methods, like the ones known as semi-empirical and the ones known as ab
initio, or first principles methods.
The objectives of the present work are the simulation of the hydrogen/oxygen system
combustion with two sets of experimental parameters and with a calculated one by quantum chemistry
methods and the detailed analysis of the mechanism.
II.
Methodology
The burning simulation of hydrogen was carried on in the reactor model Aurora, as it is codified
in the software Chemkin. This reactor simulates the combustion of gases (fuel and oxidizer)
homogeneously dispersed through all the volume of the chamber. In this model, the simulation is directed
to verify the chemical species variation and the variation on the combustion chamber volume, from the
moment of ignition to the exit of the chamber.
Two sets of experimental results for the mechanism were acquired, one in the structure of the
software Chemkin, version 3.71 and the other on the literature.9 The elementary reactions along with their
Arrhenius parameters may be observed on Table 1. It is possible to observe the variation on the kinetic
parameters, especially on the rate constants of the reactions, i.e. different experimental methodologies
were used in order to determine these data. Burning simulations were carried out with both of the
experimental data sets; the conditions of the combustion chamber were the same for both experiments, in
order to assure a comparison based only in the Arrhenius parameters.
In order to standardize the data of the reactions, a methodology of calculation of the parameters
is being developed by quantum chemical methods. Initially, the molecules of five of the reactions that
compose the combustion mechanism were submitted to electronic structure calculations using the MP2
molecular quantum chemistry method and the Dunning conjunct of base functions10 aug-cc-pVTZ. For
these calculations was used the software Gaussian 03. These data were compared with the experimental
sets by the kinetic simulation. Several simulations were made, using the calculated data and mixing these
with the experimental sets, in order to observe any change in the behavior of the system.
A detailed study of the mechanism was also realized by removing the reactions (one at a time)
and simulating the combustion. This method makes possible the observation of the importance and
contribution of each reaction to the process.
Table 1: H2 combustion mechanism and its respective kinetic parameters, according to the Arrhenius
equation (k=A.Tb.exp(Ea/RT)).
III.
Results and Discussion
Fig. 1 shows the comparison between the burning simulations of the system H2/O2 with the
different sets of parameters. The difference in the mole fractions of the main species is significant when
comparing the results of the simulations with experimental sets (Fig. 1 “a” and “b”); the results obtained
with the “experimental 1” data set seems better than with the other experimental set, because of a higher
quantity of product (H2O) is produced and lower quantities of fuel and intermediates remain on the exit of
the chamber, at 0,4 µs.
Mole Fraction
Mole Fraction
a
b
Time (s)
Mole Fraction
Time (s)
c
Time (s)
Figure 1: H2 burning simulation with the data sets a) Experimental 1, b) Experimental 2 and c)
Calculated
The result shown in Fig. 1 “c” demonstrates the non-convergence of the process. In this case
there are two possibilities: the calculated data do not present good acuity or the five reactions only are not
sufficient for the process simulation. To verify the possibilities, new simulations with just the five
reactions and each set of experimental data were made. These simulations also did not converge,
presenting the same combustion behavior as Fig. 1 c. Therefore, the five utilized reactions are not enough
to determine the combustion behavior of the system.
To investigate also the acuity of the calculated parameters, a substitution of the experimental
parameters of the reactions with the theoretical ones was made, one by one, as observed on Fig. 2.
b
Mole Fraction
Mole Fraction
a
Time (s)
Time (s)
d
Mole Fraction
Mole Fraction
c
Time (s)
Time (s)
Figure 2: Simulation of H2 burning with the “experimental 2” data set and MP2 parameter for the
a) reaction 3, b) reaction 4, c) reaction 11 e d) reaction 12.
The H2 burning simulation with the “experimental 2” data set and MP2 data for the Reaction 1
did not converge, presenting a behavior similar to the one showed before. This behavior demonstrates the
need of refinement of the calculated parameter for this reaction, possibly with other method or base.
The parameters of the other reactions also need certain refinement, since they modified the
system behavior (more notable on the substitution of the Reaction 4 parameters), although not preventing
the results convergence.
Since that just the data calculated by quantum chemistry methods for the Reaction 1 resulted on
the non-convergence of the system, new simulations were made with the “experimental 1 and 2” data set,
with the addition of MP2 parameters for the reactions 3, 4, 11 and 12. The results can be observed on Fig.
3.
Mole Fraction
Mole Fraction
Time (s)
Time (s)
Mole Fraction
Figure 3: Simulation of H2 burning with the “experimental 1 and 2” data sets with addition of the
MP2 parameters for the reactions 3, 4, 11 and 12, respectively.
Again there are observed small modifications on the curves behavior. This result is very
satisfactory, since it is possible the development of the calculations through more precise methods.
Therefore, it is proven the possibility of utilization of reactional parameters determined only by quantum
calculations.
The next step of the study was the analysis of the reactions that are really important for the
description of the hydrogen combustion. Therefore, from the “experimental 2” data set, several
simulations were made, being that in each one, one of the reactions of the mechanism was removed. Figs.
4 to 7 show the results of this study.
Time (s)
Mole Fraction
Mole Fraction
Figure 4: Simulation of H2 burning with the “experimental 2” data set, with the removal of
Reaction 2.
Time (s)
Time (s)
Figure 5: Simulation of H2 burning with the “experimental 2” data set, with the removal of
Reactions 3 and 4, respectively.
Mole Fraction
Time (s)
Mole Fraction
Figure 6: Simulation of H2 burning with the “experimental 2” data set, with the removal of
Reaction 9.
Time (s)
Figure 7: Simulation of H2 burning with the “experimental 2” data set, with the removal of
Reaction 10.
On the absence of Reaction 1, the simulation doesn’t converge. Probably this reaction is the
initiator of the combustion mechanism, so the first step of the process.
Without Reaction 2, the simulation presented just the variation of the molar fraction of four
different species; therefore the Reaction 2 is also part of the initiation process of the mechanism, together
with Reaction 1. These two reactions are responsible for the supplying of elementary hydrogen,
elementary oxygen and hydroxyl for the continuity of the process.
The behavior of the system on the absence of the Reactions 3 and 10 was unexpected; after the
ignition, there was a period of stability and after began the burning process. Possibly these two reactions
are responsible for the increase on the gases burning velocity, i.e. must act as catalysts for the process.
Reaction 9 is responsible for the HO2 molecule synthesis (one of the mechanism intermediates)
and in its absence, the formation of hydrogen peroxide is also impossible.
With the withdrawal of Reaction 11 to 18, there were not great variations on the observed
behavior. This behavior was in a certain way expected, because the priority analysis of the study until
now is on the main mechanism species. The withdrawal of these reactions modifies totally the behavior of
the intermediates of the mechanism, which have reduced molar fractions. The analysis of the
intermediates is one of the next steps of this methodology of study of energetic materials.
IV.
Conclusions
The determination of the Arrhenius parameters to some of the reactions present in the
hydrogen/oxygen combustion mechanism was made through quantum chemistry methods. Simulations of
H2 combustion were carried out using two sets of experimental data and the set of calculated data. The
analysis of the calculated parameters for each reaction was made and compared to the experimental ones
through burning simulations. A detailed study of the mechanism was realized for the verification of the
importance of each reaction on the global process. This methodology in development will allow the
insertion of new reactions in several mechanisms and also the calculation of parameters for reactions
which cannot be determined experimentally.
V.
Acknowledgements
The authors thank Molygrafit Lubrificantes Especiais, CAPES and CNPq for the financial
support.
VI.
References
1
BURTSCHELL, Y., SEROR S., PARISSE, J. D., ZEITOUN, D., Numerical simulation of air/H-2 combustion
processes in a scramjet turbulent flow, Progress in Computational Fluid Dynamics, v. 8, n. 6, p. 320-330, 2008.
2
DEAN, J. A.; Lange’s Handbook of Chemistry. McGraw-Hill, 1999, p. 6.95.
3
VASHISHTA, P.; KALIA, R. K.; NAKANO, A.; J. Phys. Chem, 2006, 110, 3727.
4
BECKSTEAD, M. W. Recent Progress in Modeling Solid Propellant Combustion, 2005.
5
BECKSTEAD, M. W.; PUDUPPAKKAM, K.; THAKRE, P.; YANG, V.; Progress in Energy and Combustion
Science. 2007, 33, 497.
6
ERIKSON, W. W.; BECKSTEAD, M. W. Modeling unsteady monopropellant combustion with full chemical
kinetics. AIAA, 1997.
7
KEE R. J., RUPLEY F. M., MILLER J. A., COLTRIN M. E., GRCAR J. F., MEEKS E., MOFFAT H. K., LUTZ
A. E., DIXON- LEWIS G., SMOOKE M. D., WARNATZ J., EVANS G. H., LARSON R. S., MITCHELL R. E.,
PETZOLD L. R., REYNOLDS W. C., CARACOTSIOS M., STEWART W. E., GLARBORG P., WANG C.,
ADIGUN O., CHEMKIN Collection, Release 3.6, Reaction Design, Inc., San Diego, CA, 2000.
8
FRISCH M. J., TRUCKS G. W., SCHLEGEL H. B., SCUSERIA G. E., ROBB M. A., CHEESEMAN J. R.,
MONTGOMERY J. A., VREVEN JR., T., KUDIN K. N., BURANT J. C., MILLAM J. M., IYENGAR S. S.,
TOMASI J., BARONE V., MENNUCCI B., COSSI M., SCALMANI G., REGA N., PETERSSON G. A.,
NAKATSUJI H., HADA M., EHARA M., TOYOTA K., FUKUDA R., HASEGAWA J., ISHIDA M., NAKAJIMA
T., HONDA Y., KITAO O., NAKAI H., KLENE M., LI X., KNOX J. E., HRATCHIAN H. P., CROSS J. B.,
ADAMO C., JARAMILLO J., GOMPERTS R., STRATMANN R. E., YAZYEV O., AUSTIN A. J., CAMMI R.,
POMELLI C., OCHTERSKI J. W., AYALA P. Y., MOROKUMA K., VOTH G. A., SALVADOR P.,
DANNENBERG J. J., ZAKRZEWSKI V. G., DAPPRICH S., DANIELS A. D., STRAIN M. C., FARKAS O.,
MALICK D. K., RABUCK A. D., RAGHAVACHARI K., FORESMAN J. B., ORTIZ J. V., CUI Q., BABOUL A.
G., CLIFFORD S., CIOSLOWSKI J., STEFANOV B. B., LIU G., LIASHENKO A., PISKORZ P., KOMAROMI I.,
MARTIN R. L., FOX D. J., KEITH T., AL-LAHAM M. A., PENG C. Y., NANAYAKKARA A., CHALLACOMBE
M., GILL P. M. W., JOHNSON B., CHEN W., WONG M. W., GONZALEZ C., e POPLE J. A., Program Gaussian
03, Revision C.02, Gaussian Inc., Wallingford CT, 2004.
9
CONNAIRE, M. O., CURRAN, H J., SIMMIE, J. M., PITZ, W. J. AND WESTBROOK, C.K., A Comprehensive
Modeling Study of Hydrogen Oxidation, International Journal of Chemical Kinetics, 36:603-622, 2004: UCRLJC-152569.
10
DUNNING Jr., T. H.; J. Chem. Phys., v. 90, p. 1007, 1989.