Theory of Weakly Unstable Multi-Dimensional Detonation

References

• Abouseif , G. E. and Toong , T. Y. ( 1982 ). Theory of unstable one dimensional detonations , Combust. and Flame 45 , 67 – 94 .
   Web of Science ®Google Scholar
• Abouseif , G. E. and Toong , T. Y. ( 1986 ). Theory of unstable two-dimensional detonations: Genesis of the transverse waves , Combust. and Flame 63 , 191 – 207 .
   Google Scholar
• Alpert , R. L. and Toong , T. Y. ( 1972 ). Periodicity in Exothermic Hypersonic Flows about Blunt Projectiles . Astronautica Acta 17 , 539 – 560 .
   Web of Science ®Google Scholar
• Barthel , H.O. ( 1974 ). Predicted spacings in hydrogen-oxygen-argon detonations . Phys. Fluids , 17 , 1547 – 1553 .
   Web of Science ®Google Scholar
• Barthel , H. O. and Strehlow , R. A. ( 1966 ). Phys. Fluids , 9 , 1986 – 1900 .
   Google Scholar
• Behrens , H. , Struth , W. and Wecken , F. ( 1965 ). Tenth Symposium (International) on Combustion . pp. 245 – 252 . The Combustion Institute , Pittsburgh .
   Google Scholar
• Blythe , P. A. and Crighton , D. G. ( 1989 ). Shock generated ignition: the induction zone , Proc. R. Soc. Lond. A 426 , 189 – 209 .
   Google Scholar
• Blythe , P. A. ( 1979 ). Wave propagation and ignition in a combustible mixture . Seventeenth Symposium (Intenational) on Combustion , pp. 909 – 916 . The Combustion Institute , Pittsburgh .
   Google Scholar
• Bourlioux , A. and Majda , A. J. ( 1992 ). Theoretical and numerical structure for unstable two-dimensional detonations . Combust. and Flame 90 , 211 – 229 .
   Web of Science ®Google Scholar
• Bourlioux , A. ( 1991 ). Ph. D. thesis. Princeton University .
   Google Scholar
• Buckmaster , J. D. and Ludford , G. S. S. ( 1986 ). The effect of structure on the instability of detonations I. Role of the induction zone , Twenty-first Symposium (International) on Combustion . pp. 1669 – 1676 . The Combustion Institute , Pittsburgh .
   Google Scholar
• Clark , J. F. ( 1985 ). Fioite Amplitude waves in combustible gases . Buckmaster J.D. The Mathematics of Combustion, SIAM , Phiadelphia , 183 .
   Google Scholar
• Clark , J. F. ( 1989 ). Fast Flames, waves and detonation . Prog. Energy. Combust. Sci. 15 , 241 – 271 .
   Google Scholar
• Clavin , P. , He , L. ( l996a ). Stability and non-linear stability analysis of one-dimensional overdriven detonations . J. Fluid Mechanics . 306 , 353 – 378 .
   Google Scholar
• Clavin , P. and He , L. ( 1996b ). Acoustic effects in the nonlinear oscillations of plane detonations . Physical Review E 53 ( 5 ), 4778 .
   Web of Science ®Google Scholar
• Clavin , P. , He , L. and Williams , F. ( 1997 ). Multidimensional stability analysis of moderately overdriven gaseous detonation , Phys. Fluid. 9 ( 12 ), 3764 – 3785 .
   Web of Science ®Google Scholar
• Denisov , Yu N. and Troshin , Ya. K. ( 1959 ). Dokl. Akad. Nauk SSSR 125 , 110 – 113 .
   Google Scholar
• Doering , W. ( 1943 ). On the detonation process in gases . Ann. Phys. 43 421 – 436 .
   Google Scholar
• D'yakov , S. P. ( 1954 ). The stability of shock waves: Investigation of the problem of the stability of shock wave in arbitrary media, Zh. Eksp . Teor. Fiz. 27 , 288 .
   Google Scholar
• Erpenbeck , J. J. ( 1963 ). Structure and stability of the square-wave detonation . in Ninth Symposium (International) on Combustion . p. 442 – 453 . Academic Press , New York .
   Google Scholar
• Erpenbeck , J. J. ( 1964 ). Stability of idealized one-reaction detonations . Phys. Fluids , 7 ( 5 ), 684 – 696 .
   Web of Science ®Google Scholar
• Erpenbeck , J. J. ( 1966 ). Phys. Fluids , 9 , 1293 – 1306 .
   Web of Science ®Google Scholar
• Erpenbeck , J.J. ( 1969 ). TWelfth Symposium (International) on Combustion , p. 711 – 721 , The Combustion Institute , Pittsburgh , PA .
   Google Scholar
• Fickett , W. ( 1985 ). Stability of the square-wave detonation in a model system . Physica D , 16 , 358 – 370 .
   Google Scholar
• Fickett , W. and Davis , w.C. ( 1979 ). Detonation , University of California press , Berkeley .
   Google Scholar
• He , L. ( 1995 ). Stability analysis of planar gaseous detonations . Europhysics Letters 32 ( 4 ), 325 -– 330 .
   Google Scholar
• He , L. ( 1996a ). On the instability of two-dimensional overdriven detonations . MAE Technical Report 2935 , Princeton University , August 1996 .
   Google Scholar
• He , L. ( l996b ). Instability analysis of Chapman-Jouguet detonation waves: a square wave model approximation , MAE Technical Report 2086 , Princeton University , August 1996 .
   Google Scholar
• He , L. ( 1999 ). On the instability of two-dimensional square wave detonations . Combustion Theory and Modeling 3 , 297 – 322 .
   Web of Science ®Google Scholar
• He , L. and Clavin , P. ( 1994 ). On the direct initiation of gaseous detonations by an energy source , J. Fluid. Mech. 277 , 227 .
   Web of Science ®Google Scholar
• He , L. and Clavin , P. ( 1995 ). Dynamics of planar detonations . C.R. Acad. Sci. Paris L 320 , Serie II b , p. 635 – 640 .
   Google Scholar
• He , L. and Clavin , P. ( 2000 ). Theory of cellular detonations in gases . Part I. Highly overdriven detonations. Accepted for publication J. Fluid Mechanics.
   Google Scholar
• He , L. and John H. . Lee ( 1995 ). The dynarnical limit of one-dimensional detonations . Physics of Fluids , 7 ( 5 ) 1151 -– 1158 .
   Google Scholar
• He , L. and C.K. Law ( 1999 ). The role of hydrodynamic instability in detonation fronts . MAE technical report N 3013 , Princeton University. Submitted for publication .
   Google Scholar
• Kontorvich , V.M. ( 1957 ). Soviet Phys.IETP 6 , 1179 .
   Google Scholar
• Landau , L. ( 1944 ). Acta Physicochim . 19 , 77 .
   Google Scholar
• Landau , L. and Lifchitz , E. ( 1989 ). Mechanique des Fluids 2nd Edn. MIR .
   Google Scholar
• Lehr , H.F. ( 1972 ). Experiments on Shock-Induced Combustion . Astronautica Acta 17 , 589 – 597 .
   Web of Science ®Google Scholar
• Lee , John H. ( 1984 ). Dynamic parameters of gaseous detonations . Ann. Rev. Fluid Mech. 5 , 31 – 58 .
   Google Scholar
• Joulin , G. and Vidal , P. ( 1996 ). An introduction to the instabilities of flames, shocks and detonations , in "Hydrodynamics and nonlinear instabilities" , Combridge University Press .
   Google Scholar
• Majda , A. and Rosales , R. ( 1983 ). tA theory for spontaneous mach stem formation in reacting shock waves, 1: the basic perturbation analysis . SIAM J. Appl. Math. 43 , 1310 – 1334 .
   Web of Science ®Google Scholar
• Majda , A. and Roytburd , V. ( 1992 ). Low-frequency multidimensional instabilities for reacting shock waves. Studies in Applied Mathematics 87 135 – 174 .
   Google Scholar
• Manzhlei , B. and Subbotin , B.A. Stability of an compressed detonations . Fizika Goreniya I Vzryva 12 ( 6 ), 936 – 819 . 1976 .
   Google Scholar
• Mcvey , J.B. and Toong , T.Y. ( 1971 ). Mechanism of Instabilities of Exothermic Hypersonic Blunt-Body Flows , Combust. Sci. and Technol. 3 , 63 – 76 .
   Web of Science ®Google Scholar
• Oppenheim , A.K. and Soloukhin , R.I. ( 1973 ). Experiments in Gasdynamics of Explosions . Ann. Rev. Fluid Mech. 5 , 31 – 58 .
   Web of Science ®Google Scholar
• Sivashinsky , G.I. ( 1977 ). Nonlinear analysis of hydrodynamic instability in laminar flames - I. Derivation of basic equations . Acta Astronautica 4 , 1177 – 1206 .
   Web of Science ®Google Scholar
• Whitham , G.B. ( 1958 ). On the propagation of shock waves through regions of non-uniform area or flow . J. FluidMech. 4, 337 – 360 .
   Web of Science ®Google Scholar
• Vielle , P. ( 1900 ). Rôle des discontinuhés dans la propagation des phénomènes explosifs . C.R. Acad. Sci. Paris L 131 , 413 – 416. .
   Google Scholar
• Yao , J. and Stewart ( 1996 ). On the dynamics of multi-dimensional detonation . J. Fluid. Mech. 309 , 225 – 275 .
   Web of Science ®Google Scholar
• Von Neumann , J. ( 1942 ). Theory of detonation waves. In John Von Neumann, collected works . Vol. 6 New York Macmillan .
   Google Scholar
• Zaidel , R.M. and Zeldovich , Ya. B. ( 1963 ). One-dimensional instability and attenuation of detonation . Zh. Prikl. Mekh. Tekn. Fiz. 6 , 59 – 65 .
   Google Scholar
• Zeldovich , YA. B. ( 1942 ). On the Ibeory of detonation propagation in gaseous systems. In Selected Works of Yakov Borisvich Zeldovich, Volume I Chemical Physics and Hydrodynamics , J.P. Ostriker , ( G.I. Barenblatt R.A. Sunyaev ) pp. 411 – 451 , Princeton University Press .
   Google Scholar