Asymptotic Solutions of Two Fundamental Problems in Gaseous Detonations

References

• Bychkov, V., A. Petchenko, V. Akkerman, and L. Erikson. 2005. Theory and modeling of accelerating flames in tubes. Phys. Rev. E 72:046307. doi:10.1103/PhysRevE.72.046307.
   Web of Science ®Google Scholar
• Clanet, C., and G. Searby. 1996. On the tulip flame phenomenon. Combust. Flame 105:225–38. doi:10.1016/0010-2180(95)00195-6.
   Web of Science ®Google Scholar
• Clavin, P., and B. Denet. 2018. Decay of plane detonation waves to the self-propagating Chapman-Jouguet regime. J. Fluid Mech 845:175–202.
   Web of Science ®Google Scholar
• Clavin, P., and B. Denet. 2020. Analytical study of the direct initiation of gaseous detonations for small heat release. J. Fluid. Mech 897:A30. doi:10.1017/jfm.2020.359.
   Web of Science ®Google Scholar
• Clavin, P., and L. He. 1996. Stability and nonlinear dynamics of one-dimensional overdriven detonations in gases. J Fluid Mech 306:353–78. doi:10.1017/S0022112096001334.
   Web of Science ®Google Scholar
• Clavin, P., R. Hernández-Sánchez, and B. Denet. 2021. Asymptotic analysis analysis of the critical dynamics of spherical gaseous detonations. J. Fluid Mech 915:A122. doi:10.1017/jfm.2021.196.
   Web of Science ®Google Scholar
• Clavin, P., P. Pelcé, and L. He. 1990. One-dimensional vibratory instability of planar flames propagating in tubes. J. Fluid Mech 216:299–322. doi:10.1017/S0022112090000441.
   Web of Science ®Google Scholar
• Clavin, P., and G. Searby. 2016. Combustion waves and fronts in flows. Cambridge: Cambridge University Press.
   Google Scholar
• Clavin, P., and H. Tofaili. 2021. A one dimensional model for deflagration to detonation transition on the tip of elongated flames in tubes. Combust. Flame 232:111522. doi:10.1016/j.combustflame.2021.111522.
   Web of Science ®Google Scholar
• Clavin, P., and F. Williams. 2002. Dynamics of planar gaseous detonations near Chapman-Jouguet conditions for small heat release. Combust. Theor. Model 6:127–39. doi:10.1088/1364-7830/6/1/307.
   Web of Science ®Google Scholar
• Clavin, P., and F. Williams. 2009. Multidimensional stability analysis of gaseous detonations near Chapman-Jouguet conditions for small heat release. J. Fluid Mech 624:125–50. doi:10.1017/S0022112008005387.
   Web of Science ®Google Scholar
• Deshaies, B., and G. Joulin. 1989. Flame-speed sensitivity to temperature change and the deflagration-to-detonation transition. Combust. Flame 77:202–12. doi:10.1016/0010-2180(89)90037-0.
   Web of Science ®Google Scholar
• Eckett, C., J. Quirk, and J. Shepherd. 2000. The role of unsteadiness in direct initiation of gaseous detonations. J. Fluid Mech 421:147–83. doi:10.1017/S0022112000001555.
   Web of Science ®Google Scholar
• Goddard, J., and K. Seshadri, edited by. 2018. Collected works of Professor Paul Libby, Volumes 1-2 (1949-2018). San Diego: University of California.
   Google Scholar
• Gordon, P., L. Kagan, and G. Sivashinsky. 2020. Parametric transition from deflagration to detonation revisited: Planar Geometry. Combust. Flame 211:465–76. doi:10.1016/j.combustflame.2019.10.011.
   Web of Science ®Google Scholar
• He, L., and P. Clavin. 1994. On the direct initiation of gaseous detonations by an energy source. J Fluid Mech 277:227–48. doi:10.1017/S0022112094002740.
   Web of Science ®Google Scholar
• Ivanov, M., A. Kiverin, and M. Liberman. 2011. Hydrogen-oxygen flame acceleration and transition to detonation with a detailed chemical reaction model. Phys. Rev. E 83:O56313. doi:10.1103/PhysRevE.83.056313.
   Web of Science ®Google Scholar
• Kagan, L., and G. Sivashinsky. 2017. Parametric transition from deflagration to detonation: Runaway of fast flames. Proc. Combust. Inst 36:2709–15. doi:10.1016/j.proci.2016.09.026.
   Web of Science ®Google Scholar
• Koksharov, A., V. Bykov, L. Kagan, and G. Sivashinsky. 2018. Deflagration-to-detonation transition in an unconfined space. Combust. Flame 195:163–69. doi:10.1016/j.combustflame.2018.03.006.
   Web of Science ®Google Scholar
• Korobeinikov, P. V. 1971. Gas dynamics of explosions. Ann. Rev. Fluid Mech 3:317–46. doi:10.1146/annurev.fl.03.010171.001533.
   Web of Science ®Google Scholar
• Kutnetsov, M., M. Liberman, and I. Matsukov. 2010. Experimental study of the preheated zone formation and deflagration to detonation transition. Combust. Sci. Technol 182:1628–44. doi:10.1080/00102202.2010.497327.
   Web of Science ®Google Scholar
• Landau, L., and E. Lifshitz. 1986. Fluid Mechanics. Pergamon Press.
   Google Scholar
• Lee, J. 2008. The detonation phenomenon. Cambridge: Cambridge University Press.
   Google Scholar
• Levin, V., and V. Chernyi. 1967. Asymptotic laws of behavior of detonation waves. Prikl. Mat. Mekh 31:393–405.
   Google Scholar
• Liberman, M., M. Ivanov, A. Kiverin, M. Kuznetsov, A. Chukalovsky, and T. Rakhimova. 2010. Deflagration-to-detonation transition in highly reactive combustible mixtures. Acta Astronautica 67 (7–8):688–701. doi:10.1016/j.actaastro.2010.05.024.
   Web of Science ®Google Scholar
• Liñan, A., V. Kurdyumov, and A. Sanchez. 2012. Initiation of reactive blast waves by external energy. sources. Comptes Rendus Mécanique 340 (11–12):829–44. doi:10.1016/j.crme.2012.10.033.
   Web of Science ®Google Scholar
• Ponizy, B., A. Claverie, and B. Veyssière. 2014. Tulip flame - the mechanism of flame front inversion. Combustion and Flame 161 (12):3051–62. doi:10.1016/j.combustflame.2014.06.001.
   Web of Science ®Google Scholar
• Sanchez, A., and F. Williams. 2014. Recent advances in understanding of flammability characteristics of hydrogen. Prog. Energy Combust. Sci 41:1–55.
   Web of Science ®Google Scholar
• Sedov, L. 1946. Propagation of strong blast waves. Prikl. Mat. Meckh 10:241–50.
   Google Scholar
• Shchelkin, K., and Y. Troshin. 1965. Gasdynamics of combustion. Baltimore: Mono Book Corp.
   Google Scholar
• Sivashinsky, G. 1977. Nonlinear analysis of hydrodynamic instability in laminar flames. Acta Astronaut. 4:1177–206.
   Web of Science ®Google Scholar
• Taylor, G. I. 1950a. The formation of a blast wave by a very intense explosion. Proc. R. Soc. London A 201:159–74.
   Web of Science ®Google Scholar
• Taylor, G. I. 1950b. The dynamics of combustion products behind plane and spherical detonation fronts. Proc. R. Soc. London A 200:235–47.
   Web of Science ®Google Scholar
• Tofaili, H., G. Lodato, L. Vervisch, and P. Clavin. 2021. One-dimensional dynamics of gaseous detonations revisited. Combust. Flame 232:111535.
   Web of Science ®Google Scholar
• Valiev, D., V. Bychkov, V. Akkerman, and L. Erikson. 2009. Different stages of flame acceleration from slow burning to Chapman-Jouguet deflagration. Phys. Rev. E 80:036317.
   Web of Science ®Google Scholar
• Wu, M., M. Burke, S. Son, and R. Yetter 2007, Flame acceleration and the transition to detonation of stoichiometric ethylene/oxygen in microscale tubes, Proc. Comb. Inst., 31 pp. 2429–36.
   Google Scholar
• Wu, M., and C. Wang 2011, Reaction propagation modes in millimeter-scale tubes for ethylene/oxygen mixtures, Proc. Comb. Inst., 33 pp. 2287–93.
   Google Scholar
• Zeldovich, Y. B. 1942. On the distribution of pressure and velocity in products of detonation blasts, in particular for spherical propagating detonation waves. Zhur. Eksp. Teor. Fiz 12:389–406.
   Google Scholar
• Zeldovich, Y. B. 1980. Regime classification of an exothermic reaction with nonuniform initial conditions. Combust. Flame 39:211–14.
   Web of Science ®Google Scholar
• Zeldovich, Y. B., and D. Frank-Kamenetskii. 1938. A theory of thermal flame propagation. Acta Phys. Chim 9:341–50.
   Google Scholar