Shock-generated ignition. Newtonian asymptotics for the induction domain between a contact surface and shock

SIAM Journal on Applied Mathematics

Volumn 61, Issue 2, 2000, Pages 701-729

  Parkins, C J ^a  

^a UNIVERSITY OF CAMBRIDGE   (United Kingdom)

Author keywords

Contact surface; Detonation; High activation energy asymptotics; Hot spot; Newtonian asymptotics; Thermal runaway

Indexed keywords

ACTIVATION ENERGY; IGNITION; POSITION MEASUREMENT; SHOCK WAVES; THERMAL EFFECTS;

NEWTONIAN ASYMPTOTICS;

DETONATION;

EID: 0343371456     PISSN: 00361399     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036139997331562     Document Type: Article

References (22)

1. P. A. BLYTHE AND D. G. CRIGHTON, Shock-generated ignition: The induction zone, Proc. Roy. Soc. London Ser. A, 426 (1989), pp. 189-209.
2. A. W. CAMPBELL, W. C. DAVIES, AND J. R. TRAVIS, Shock initiation of detonation in liquid explosives, Phys. Fluids, 4 (1961), pp. 498-510.
3. J. F. CLARKE AND R. S. CANT, Nonsteady gasdynamic effects in the induction domain behind a strong shock wave, Prog. Astronaut. Aeronaut., 95 (1985), pp. 142-163.
4. P. A. BLYTHE, C. J. PARKINS, AND D. G. CRIGHTON, Shock-Generated Ignition: The Singularity Path, in preparation.
5. J. W. DOLD, A. K. KAPILA, AND M. SHORT, Theoretical description of direct initiation of detonation, in Dynamic Structure of Detonation in Gaseous and Dispersed Media, A. A. Borissov, ed., Kluwer Academic Publishers, Norwell, MA, 1991, pp. 109-141.
6. J. W. DOLD AND A. K. KAPILA, Asymptotic Analysis of Detonation Initiation for One-Step Chemistry: I-Emergence of a Weak Detonation, in preparation.
7. J. W. DOLD AND A. K. KAPILA, Asymptotic Analysis of Detonation Initiation for One-Step Chemistry: II-From a Weak Structure to ZND, in preparation.
8. J. W. DOLD. J. F. CLARKE, AND M. SHORT, Steady and unsteady aspects of detonation initiation, in Combustion and High-Speed Flows, J. D. Buckmaster, T. L. Jackson, and A. Kumar, eds., Kluwer Academic Publishers, Norwell, MA, 1994, pp. 493-512.
9. A. FRIEDMAN AND M. A. HERRERO, A nonlinear nonlocal wave equation arising in combustion theory, Nonlinear Anal., 14 (1990) pp. 93-106.
10. T. L. JACKSON AND A. K. KAPILA, Shock-induced thermal runaway, SIAM J. Appl. Math., 45 (1985), pp. 130-137.
11. K. KAILASANTH AND E. S. ORAN, Ignition of flamelets behind incident shock waves, and the transition to detonation, Combust. Sci. Tech., 63 (1989), pp. 345-362.
12. A. J. MAJDA AND V. ROYTBURD, Numerical modeling of the initiation of reacting shock-waves, in Computational Fluid Dynamics and Reacting Gas Flows, B. Enquist, et al. eds., IMA Vol. Math. Appl. 12, Springer-Verlag, New York, 1988, pp. 195-217.
13. J. W. MEYER AND A. K. OPPENHEIM, On the shock-induced ignition of explosive gases, in 13th Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1971, pp. 1153-1164.
14. C. J. PARKINS, Newtonian Asymptotics for Detonation Initiation, Ph.D. thesis, University of Cambridge, Cambridge, UK, 1998.
15. C. J. PARKINS. P. A. BLYTHE, AND D. G. CRIGHTON, Hot Spot Ignition: The Newtonian Limit, Proc. Roy. Soc. London Ser. A., to appear.
16. M. SHORT, Initiation of Detonation for Thermally-Sensitive One-Step Chemistry, Ph.D. thesis, University of Bristol, Bristol, UK, 1992.
17. M. SHORT AND J. W. DOLD, Unsteady gasdynamic evolution of an induction domain between a contact surface and a shock wave. I: Thermal runaway, SIAM J. Appl. Math., 56 (1996), pp. 1295-1316.
18. M. SHORT, On the critical conditions for the initiation of a detonation in a nonuniformly perturbed reactive fluid, SIAM J. Appl. Math., 57 (1997), pp. 1242-1280.
19. G. SINGH AND J. F. CLARKE, Transient phenomena in the initiation of a mechanically driven detonation, Proc. Roy. Soc. London Ser. A, 438 (1992), pp. 23-46.
20. N. N. SMIRNOV AND M. V. TYURNIKOV, Experimental investigation of deflagration to detonation transition in hydrocarbon-air mixtures, Combustion and Flame, 100 (1995), pp. 661-668.
21. S. TAKI AND T. FUJIWARA, One-dimensional nonsteady processes accompanied by the establishment of self-sustained detonation, in 13th Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1971, pp. 1119-1129.
22. P. A. URTIEW AND A. K. OPPENHEIM, Detonative ignition induced by shock merging, in 11th Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1966, pp. 665-760.