Hot spot ignition: The Newtonian limit

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

Volumn 456, Issue 2004, 2000, Pages 2857-2882

  Parkins, C J ^a   Blythe, P A ^b   Crighton, D G ^a  

^a UNIVERSITY OF CAMBRIDGE   (United Kingdom)

^b Lehigh University   (United States)

Author keywords

Clarke's equation; Ignition; Newtonian limit; Singularity paths

Indexed keywords

EID: 33746463964     PISSN: 13645021     EISSN: None     Source Type: Journal    
DOI: 10.1098/rspa.2000.0644     Document Type: Article

References (26)

1. Blythc, P. A. & Crighton, D. G. 1989 Shock generated ignition: the induction zone. Proc. R. Soc. Land. A 426, 189-209.
2. Blythe, P. A., Parkins, C. J. & Crighton-, D. G. 2001 Singularity structure for shock induced ignition. (In preparation.)
3. Clarke, J. F. 1981 Propagation of gas dynamic disturbances in an explosive atmosphere. Prog. Astronaut. Aeronaut. 76, 383-402.
4. Clarke, J. F. & Cant, R. S. 1985 Nonsteady gasdynamic effects in the induction domain behind a strong shock wave. Prog. Astronaut. Aeronaut. 95, 142-163.
5. Clarke, J. F. & Nikiforakis, N. 1999 Remarks on diffusionless combustion. Phil. Trans. R. Soc. Land. A 357, 3605-3620.
6. Dold, J. W. &: Kapila, A. K. 2001o Asymptotic analysis of detonation initiation for one-step chemistry. I. Emergence of a weak detonation. (In preparation.)
7. Dold, J. W. & Kapila, A. K. 20016 Asymptotic analysis of detonation initiation for one-step chemistry. II. From a weak structure to ZND. (In preparation.)
8. Dold, J. W., Kapila, A. K. & Short, M. 1991 Theoretical description of direct initiation of detonation for one-step chemistry. In Dynamic structure of detonation in gaseous and dispersed media (ed. A. A. Borissov), pp. 109-141. Dordrecht: Kluwer Academic.
9. Dold, J. W., Clarke, J. F. & Short, M. 1995 Steady and unsteady aspects of detonation initiation. In Combustion and high-speed flows (ed. J. D. Buckmaster, T. L. Jackson & A. Kumar), pp. 493-512. Dordrecht: Kluwer Academic.
10. Friedman, A & Herrero, M. A. 1990 A nonlinear local wave equation arising in combustion theory. Nonlinear Analysis Theory Methods Applications 14, 93-106.
11. Gelfand, B. E., Polenov, A. N., Frolov, S. M. & Tsyganov, S. A. 1985 On the onset of detonation in a non-uniformly heated gas mixture. Fizika Goreniya Vzryva 21, 118-123.
12. Jackson, T. L. & Kapila, J. K. 1985 Shock-induced thermal runaway. SIAM J. Appl. Math. 45, 130-137.
13. Jackson, T. L., Kapila, A. K. & Stewart, D. S. 1989 Evolution of a reaction center in an explosive material. SIAM J. Appl. Math. 49, 432-458.
14. Kapila, A. K. & Jackson, T. L. 1986 Dynamics of hot-spot evolution in a reactive compressible flow. In IMA Workshop on CFD in Reacting Flows (ed. M. Luskin, A. Majda & B. Engquist). Springer.
15. Meyer, J. W. & Oppenheim, A. K. 1971 On the shock-induced ignition of explosive gases. In 13th Symp. Int. on Combustion, pp. 1153-1164. Pittsburgh, PA: The Combustion Institute.
16. Nikiforakis, N. & Clarke, J. F. 1996 Quasi-steady structures in the two dimensional initiation of combustion. Proc. R. Soc. Land. A 452, 2023-2042.
17. Parkins, C. J. 1998 Newtonian asymptotics for detonation initiation. PhD thesis, University of Cambridge.
18. Parkins, C. J. 1999 Shock-generated ignition: Newtonian asymptotics for the induction domain between a contact surface and shock. SIAM J. Appl. Math. 61, 701-729.
19. Short, M. 1992 Initiation of detonation for thermally-sensitive one-step chemistry. PhD thesis, University of Bristol.
20. Short, M. 1997 On the critical conditions for the initiation of a detonation in a non-uniformly perturbed reactive fluid. SIAM J. Appl. Math. 57, 1242-1280.
21. Short, M. & Stewart, D. S. 1997 Low-frequency two-dimensional linear instability of plane detonation. J. Fluid Mech. 340, 249-295.
22. Singh, G. & Clarke, J. F. 1992 Transient phenomena in the initiation of a mechanically driven plane detonation. Proc. R. Soc. Land. A 438, 23-46.
23. Urtiew, P. A. & Oppenheim, A. K. 1966 Detonative ignition induced by shock merging. In llth Symp. Int. on Combustion, pp. 665-670. Pittsburgh, PA: The Combustion Institute.
24. Van Dyke, M. 1964 Perturbation methods in fluid mechanics. Academic.
25. Zeldovich, Ya. B. 1980 Regime classification of an exothermic reaction with nonuniform initial conditions. Combustion Flame 39, 211-214.
26. Zeldovich, Ya. B., Librovich, V. B., Makhhviladze, G. M. & Sivashinsky, G. I. 1970 Development of detonation in a non-uniformly preheated gas. Astronautica Acta 15, 313-321.