Mach reflection of a ZND detonation wave

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• 作者：J. Li (1)
  J. Ning (1)
  J. H. S. Lee (2)
  
  1. State Key Laboratory of Explosion Science and Technology ; Beijing Institute of Technology ; Beijing ; 100081 ; China
  2. Department of Mechanical Engineering ; McGill University ; Montreal ; QC ; H3A 2K6 ; Canada
  
• 关键词：ZND detonation wave ; Mach reflection ; Characteristic length scale ; Asymptotic self ; similarity
• 刊名：Shock Waves
• 出版年：2015
• 出版时间：May 2015
• 年：2015
• 卷：25
• 期：3
• 页码：293-304
• 全文大小：1,195 KB
• 参考文献：1. Gvozdeva, LG, Predvoditeleva, OA (1969) Triple configurations of detonation waves in gases. Combust. Explo. Shock. 5: pp. 451-461
  2. Ong, R.S.: On the interaction of a Chapman鈥揓ouguet detonation wave with a wedge. PhD. Thesis, University of Michigan, Ann Arbor (1955)
  3. Guo, C, Zhang, D, Xie, W (2001) The Mach reflection of a detonation based on soot track measurements. Combust. Flame 127: pp. 2051-2058 CrossRef
  4. Li, H, Ben-Dor, G, Gr枚nig, H (1997) Analytical study on the oblique reflection of detonation waves. AIAA J. 35: pp. 1712-1720 CrossRef
  5. Meltzer, J., Shepherd, J.E., Akbar, R., Sabet, A.: Mach reflection of detonation waves. In: Kuhl et al. (eds.) AIAA Progress in Astronautics and Aeronautics, pp. 78鈥?4. AIAA, New York (1993)
  6. Yu, Q., Gr枚nig, H.: Numerical simulation on the reflection of detonation waves. In: Proceedings of the 20th International Symposium on Shock Waves, pp. 1143鈥?148. Pasadena, USA (1995)
  7. Edwards, DH, Walker, JR, Nettleton, MA (1984) On the propagation of detonation waves along wedges. Archivum Combustionis 4: pp. 197-209
  8. Ohyagi, S, Obara, T, Nakata, F, Hoshi, S (2000) A numerical simulation of reflection processes of a detonation wave on a wedge. Shock Waves 10: pp. 185-190 CrossRef
  9. Gavrilenko, TP, Nikolaev, YA, Tpchiyan, MR (1980) Supercompressed detonation waves. Combust. Explos. Shock. 15: pp. 659-692 CrossRef
  10. Thomas, GO, Williams, RL (2002) Detonation interaction with wedges and bends. Shock Waves 11: pp. 481-492 CrossRef
  11. Ben-Dor, G (2007) Shock Wave Reflection Phenomena. Springer, New York
  12. Hornung, H (1986) Regular and Mach reflection of shock waves. Annu. Rev. Fluid Mech. 18: pp. 33-58 CrossRef
  13. Neumann, J (1963) Collected Works. Pergamon, New York
  14. Vysk, ND, Smirnov, NN (1986) Mach reflection in a detonating gas with a stem in the form of a shock wave. Mosc. Univ. Mech. Bull. 41: pp. 1-8
  15. Akbar, R.: Mach reflection of gaseous detonation. Ph.D. Thesis, Rensselaer Polytechnic Institute, Troy (1997)
  16. Ben-Dor, G, Dewey, JM, Takayama, K (1987) The reflection of a plane shock over a double wedge. J. Fluid Mech. 176: pp. 483-520 CrossRef
  17. Ben-Dor, G, Dewey, JM, McMillin, DJ, Takayama, K (1988) Experimental investigation of the asymptotically approached Mach reflection over the second surface in a double wedge reflection. Exp. Fluids 6: pp. 429-434 CrossRef
  18. Takayama, K, Ben-Dor, G (1988) Application of streak camera photography for the study of shock wave reflections over a double wedge. Exp. Fluids 6: pp. 11-15 CrossRef
  19. Lau-Chapdelaine, SS-M, Radulescu, MI (2013) Non-uniqueness of solutions in asymptotically self-similar shock reflections. Shock Waves 23: pp. 595-602 CrossRef
  20. Sandeman, J., Leitch, A., Hornung, H.: The influence of relaxation on transition to Mach reflection in pseudosteady flow. Shock tubes and waves. In: Proceedings of the 12th International Symposium, pp. 298鈥?07. Jerusalem (1979)
  21. Hornung, HG, Oertel, H, Sandeman, RJ (1979) Transition to Mach reflexion of shock waves in steady and pseudosteady flow with and without relaxation. J. Fluid Mech. 90: pp. 541-560 CrossRef
  22. Shepherd, J.E., Schultz, E., Akbar, R.: Detonation diffraction. In: Proceedings of the 22th International Symposium on Shock Waves, pp. 18鈥?3. Imperial College, London (1999)
  23. Mach, P, Radulescu, MI (2011) Mach reflection bifurcations as a mechanism of cell multiplication in gaseous detonations. Proc. Combust. Inst. 33: pp. 2279-2285 CrossRef
  24. Radulescu, M.I., Papi, A., Quirk, J.J., Mach, P., Maxwell, B.M.: The origin of shock bifurcations in cellular detonations. In: 22nd International Colloquium on the Dynamics of Explosions and Reactive Systems. Minsk, Belarus (2009)
  25. Ziegler, JL, Deiterding, R, Shepherd, JE, Pullin, DI (2011) An adaptive high-order hybrid scheme for compressive, viscous flows with detailed chemistry. J. Comput. Phys. 230: pp. 7598-7630 CrossRef
  26. Trotsyuk, AV (1999) Numerical study of the reflection of detonation waves from a wedge. Combust. Explos. Shock. 35: pp. 690-697 CrossRef
  27. Ng, H.D., Radulescu, M.I., Higgins, A.J., Nikiforakis, N., Lee, J.H.S.: Numerical investigation of the instability for one-dimensional Chapman鈥揓ouguet detonations with chain-branching kinetics. Combust. Theor. Model. 9(3), 385鈥?01 (2005)
  28. Fickett, W, Davis, WC (1979) Detonation. University of California Press, Berkeley
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• 刊物类别：Physics and Astronomy
• 刊物主题：Physics
  Mechanics, Fluids and Thermodynamics
  Fluids
  Thermodynamics
  Acoustics
  Condensed Matter
  Solid State Physics and Spectroscopy
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1432-2153

文摘

The Mach reflection of a ZND detonation wave on a wedge is investigated numerically. A two-step chain-branching reaction model is used giving a thermally neutral induction zone followed by a chemical reaction zone for the detonation wave. The presence of a finite reaction zone thickness renders the Mach reflection process non-self-similar. The variation of the height of the Mach stem with distance of propagation does not correspond to a straight curve from the wedge apex as governed by self-similar three-shock theory. However, the present results indicate that in the near field around the wedge apex, and in the far field where the reaction zone thickness is small compared to the distance of travel of the Mach stem, the behavior appears to be self-similar. This corresponds to the so-called frozen and equilibrium limit pointed out by Hornung and Sanderman for strong discontinuity shock waves and by Shepherd et al. for cellular detonations. The critical wedge angle for the transition from regular to Mach reflection is found to correspond to the value determined by self-similar three-shock theory, but not by reactive three-shock theory for a discontinuous detonation front.