Abstract
The present work is focused on the numerical simulation of the deflagration to detonation transition. The Euler equations expressed for a time-dependent, compressible, and one-dimensional flow with finite-rate kinetics are solved with adaptive mesh refinement. Because of the problem stiffness, a time-step splitting method is used to couple the conservation equations and the chemical kinetics equations. The calculated length of the deflagration to detonation transition in H2-O2 and CH4-O2 mixtures in a confined domain and the time evolution of detonation are in good agreement with the theoretical values of constant volume explosions and Chapman-Jouguet conditions. The length of the transitional region is compared with experimental findings for a range of initial fuel concentrations, which shows that the model predicts the tendencies qualitatively well but yields significant quantitative deviations.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
REFERENCES
P. A. Bauer, E. K. Dabora, and N. Manson, “Chronology of early research on detonation-wave,” in: A. L. Kuhl, J. C. Leyer, A. A. Borisov, and W. A. Sirignano (eds.), Progress in Astronautics and Aeronautics, Vol. 133: Dynamics of Detonations and Explosions: Detonations, AIAA, Washington (1991), pp. 3–18.
R. G. Schmitt and P. B. Butler, “Detonation properties of gases at elevated initial pressures,” Combust. Sci. Technol., 106, 167–193 (1995).
J. E. Shepherd, “The chemical kinetics of hydrogen-air diluent detonations,” in: J. R. Bowen, J.-C. Leyer, and R. J. Soloukhin (eds.), Progress in Astronautics and Aeronautics, Vol. 106: Dynamics of Explosions, AIAA, Washington (1986), pp. 263–293.
M. A. Nettleton, Gaseous Detonations, Their Nature, Effects and Control, Chapman and Hall (1987).
C. K. Westbrook, “Chemical kinetics of hydrocarbon oxidation in gaseous detonations,” Combust. Flame, 46, 191–210 (1982).
B. M. Dobratz, “LLNL Explosives Handbook, Properties of Chemical Explosives and Explosive Simulants,” Report No. UCRL-52997, Lawrence Livermore National Laboratory, March (1981).
W. Fickett and W. C. Davis, Detonation, The Univ. of California Press (1979).
L. E. Bollinger, M. C. Fong, and R. Edse, “Experimental measurements and theoretical analysis of detonation induction distances,” ARS J., 31, 588–595 (1961).
J. B. Hinkey, T. R. A. Bussing, and L. Kaye, “Shock tube experiments for the development of a hydrogen-fueled pulse detonation engine,” AIAA Paper No. 95-2578 (1995).
K. Kailasanath, E. S. Oran, J. P. Boris, and T. R. Young, “Determination of detonation cell size and the role of transverse waves in two-dimensional detonations,” Combust. Flame, 61, 199–209 (1985).
H. K. Brüls, M. H. Lefebvre, and J. Berghmans, “On derivations from ideal Chapman-Jouguet detonation velocity,” in: Proc. Twenty-Fifth Symp. (Int.) on Combustion, The Combustion Inst., Pittsburgh (1994), pp. 37–44.
N. N. Smirnov and J. J. Panfilov, “Deflagration to detonation transition in combustible gas mixtures,” Combust. Flame, 101, 91–100 (1995).
A. K. Oppenheim, N. Manson, and H. G. G. Wagner, “Recent progress in detonation research,” AIAA J., 1, 2243–2252 (1963).
J. H. S. Lee, “Dynamics parameters of gaseous detonations,” Ann. Rev. Fluid Mech., 16, 311–336 (1984).
H. J. Weber, A. Mack, and P. Roth, “Combustion and pressure wave interaction in enclosed mixture initiated by temperature nonuniformities,” Combust. Flame, 97, 281–295 (1994).
P. A. Bauer, H. N. Presles, and M. Dunard, “Detonation characteristics of gaseous methane-oxyden-nitrogen mixtures at extremely elevated initial pressures,” in: A. L. Kuhl, J. C. Leyer, A. A. Borisov, and W. A. Sirignano (eds.), Progress in Astronautics and Aeronautics, Vol. 133: Dynamics of Detonations and Explosions: Detonations, AIAA, Washington (1991), pp. 56–62.
L. He and P. Calvin, “Critical conditions for detonation initiation in cold gaseous mixtures by nonuniform hot pockets of reactive gases,” in: 24th Symp. on Combustion (1992), pp. 1861–1867.
U. Bielert and M. Sichel, “Numerical simulation of premixed combustion processes in closed tubes,” Combust. Flame, 114, 397 (1998).
J. Warnatz, U. Maas, and R. W. Dibble, Combustion, Springer (1996).
E. S. Oran and J. P. Boris, Numerical Simulation of Reactive Flow, Elsevier, New York (1987).
R. J. Gross and M. R. Baer, “ETBFCT A Solver for One-Dimensional Transport Equations,” Report No. SAND85-1273, Sandia National Laboratories (1985).
R. G. Schmitt, P. B. Butler, and N. French, “Chemkin Real Gas: A Fortran Package for the Analysis of Thermodynamics and Chemical Kinetics in High Pressure Systems,” Report No. UIME-PBB 93-006, University of Iowa (1993).
J. K. Bechtold and C. K. Law, “Extinction of premixed methane-air flames with reduced reaction mechanism,” Combust. Sci. Technol., 100, 371–378 (1994).
G. O. Thomas, M. J. Edwards, and D. H. Edwards, “Studies of detonation quenching by water sprays,” Combust. Sci. Technol., 71, 233–245 (1990).
Author information
Authors and Affiliations
Additional information
__________
Translated from Fizika Goreniya i Vzryva, Vol. 41, No. 2, pp. 108–115, March–April, 2005.
Rights and permissions
About this article
Cite this article
Parra-Santos, M.T., Castro-Ruiz, F. & Méndez-Bueno, C. Numerical simulation of the deflagration to detonation transition. Combust Explos Shock Waves 41, 215–222 (2005). https://doi.org/10.1007/s10573-005-0025-z
Received:
Issue Date:
DOI: https://doi.org/10.1007/s10573-005-0025-z