Direct calculation of wave implosion for detonation initiation

AIAA Journal

Volumn 43, Issue 10, 2005, Pages 2157-2169

  Wang, Bao ^a,b,c   He, Hao ^a,b,c   Yu, S T John ^a,b,c  

^a OHIO STATE UNIVERSITY   (United States)

^b Mechanical Engineering Department   (United States)

^c AIAA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

DETONATION; HYDROGEN; MIXTURES; NAVIER STOKES EQUATIONS; OXYGEN;

DETONATION INITIATION; SOLUTION ELEMENT METHOD; WAVE IMPLOSION;

SHOCK WAVES;

EID: 27144459644     PISSN: 00011452     EISSN: None     Source Type: Journal    
DOI: 10.2514/1.11887     Document Type: Article

References (53)

1. Murray, S., Zhang, D., and Gerrard, K., "The Role of Energy Distribution on the Transmission of Detonation," International Colloquium on Control of Detonation Processes, Office of Naval Research, July 2000.
2. Jackson, S., Grunthaner, M., and Shepherd, J., "Wave Implosion as an Initiation Mechanism for Pulse Detonation Engines," AIAA Paper 2003-4820, July 2003.
3. Jackson, S., and Shepherd, J., "Initiation Systems for Pulse Detonation Engines," AIAA Paper 2002-3627, July 2002.
4. Guderley, G., "Kugelige and Zylindrische Verdichtungsstosse in der Nake des Kugelmittelpunktes Lzw der Zylinderachse," Luftfahrtforschung, Vol. 19, No. 9, 1942, pp. 302-312.
5. Taylor, G. I., "The Formation of a Blast Wave by a Very Intense Explosion, I. Theoretical Discussion," Proceedings of the Physical Society, Section A, Vol. 201, No. 1065, 1950, pp. 159-174.
6. Taylor, G. I., "The Dynamics of the Combustion Products Behind Plane and Spherical Detonation Fronts in Explosives," Proceedings of the Royal Society of London, Vol. 200, No. 1061, 1950, pp. 235-247.
7. Sedov, L. I., Similarity and Dimensional Methods in Mechanics, Cleaver Hume, London, 1959, Chaps. 4 and 5.
8. Sharma, V. D., and Radha, C. H., "Similarity Solutions for Converging Shocks in a Relaxing Gas," International Journal of Engineering Science, Vol. 33, No. 4, 1995, pp. 535-553.
9. Toque, N., "Self-Similar Implosion of a Continuous Stratified Medium." Shock Waves, Vol. 11, No. 3, 2001, pp. 157-165.
10. van Dyke, M., and Guttmann, A., "The Converging Shock Wave from a Spherical or Cylindrical Piston," Journal of Fluid Mechanics, Vol. 120, 1982, pp. 451-462.
11. Boyer, D. W., "An Experimental Study of the Explosion Generated by a Pressurized Sphere," Journal of Fluid Mechanics, Vol. 9, 1960, pp. 401-429.
12. Friedman, M. P., "A Simplified Analysis of Spherical and Cylindrical Blast Waves," Journal of Fluid Mechanics. Vol. 11, 1961, pp. 1-15.
13. Glass, I. I., and Sislian, J. P., Non-Stationary Flows and Shock Waves, Oxford Science Publications, Oxford, 1994, Chap. 12.
14. Baker, W. E., Explosions in Air, Wilfred Baker Engineering, San Antonio, TX, 1973, Chap. 7.
15. Schwendeman, D. W., and Whitham, G. B., "On Converging Shock Waves," Proceedings of the Physical Society. Section A, Vol. 413, No. 1845, 1987, pp. 297-311.
16. Brode, H. L., "Numerical Solution of Spherical Blast Waves," Journal of Applied Physics, Vol. 26, June 1955, pp. 766-775.
17. Brode, H. L., "Blast Wave from a Spherical Charge," Physics of Fluids, Vol. 2, No. 2, 1959, pp. 217-229.
18. Flores, J., and Holt, M., "Grimm's Method Applied to Underwater Explosions," Journal of Computational Physics, Vol. 44, No. 2, 1981, pp. 377-387.
19. Glimm, J., "Solutions in the Large For Nonlinear Hyperbolic Systems of Equations," Communications on Pure and Applied Mathematics, Vol. 18, No. 4, 1965, pp. 697-715.
20. Charrier, P., and Tessieras, B., "A Front-Tracking Method Applied to Hyperbolic Systems of Nonlinear Conservation Laws," SIAM Journal on Numerical Analysis, Vol. 23, No. 2, 1986, pp. 461-472.
21. Devore, C. R., and Oran, E. S., "The Stability of Imploding Detonations in the Geometrical Shock Dynamics (CCW) Model," Physics of Fluids A, Vol. 4, No. 4, 1992, pp. 835-844.
22. Oran, E. S., and DeVore, C. R., "The Stability of Imploding Detonations: Results of Numerical Simulations," Physics of Fluids. Vol. 6, No. 1, 1996, pp. 369-380.
23. Boris, J. P., and Book, D. L., "Flux-Corrected Transport I. SHASTA, A Fluid Transport Algorithm That Works," Journal of Computational Physics, Vol. 11, No. 1, 1973, pp. 38-69.
24. Book, D. L., Boris, J. P., and Hain, K., "Flux-Corrected Transport II. Generalizations of the Method," Journal of Computational Physics, Vol. 18, No. 3, 1975, pp. 248-283.
25. Payne, R. B., "A Numerical Method for a Converging Cylindrical Shock," Journal of Fluid Mechanics, Vol. 2, 1956, pp. 185-200.
26. Lax, P. D., "Weak Solutions of Nonlinear Hyperbolic Equations and Their Numerical Computation." Communication on Pure and Applied Mathematics, Vol. 7, No. 1-2, 1954, pp. 159-193.
27. Falcovitz, J., and Birman, A., "A Singularities Tracking Conservation Laws Scheme for Compressible Duct Flows," Journal of Computational Physics, Vol. 115, No. 2, 1994, pp. 431-439.
28. Ben-Artzi, M., and Falvovitz, J., "A Second-Order Godunov-Type Scheme for Compressible Fluid Dynamics," Journal of Computational Physics, Vol. 55, No. 1, 1984, pp. 1-32.
29. Sod, G. A., "A Numerical Study of a Converging Cylindrical Shock," Journal of Fluid Mechanics, Vol. 83, 1977, pp. 785-794.
30. He, L. T., "Theoretical Determination of the Critical Conditions for the Direct Initiation of Detonations in Hydrogen-Oxygen Mixtures," Combustion and Flame, Vol. 104, No. 4, 1996, pp. 401-418.
31. Menikoff, R., Lackner, K. S., and Bukiet, B. G., "Modeling Flows with Curved Detonation Waves," Combustion and Flame, Vol. 104, No. 3, 1996, pp. 219-240.
32. Yu, S. T., and Chang, S. C., "Treatments of Stiff Source Terms in Conservation Laws by the Method of Space-Time Conservation Element and Solution Element," AIAA Paper 97-0435, Jan. 1997.
33. 2/Ar Mixtures by the CESE Method," AIAA Paper 2004-0793, Jan. 2004.
34. Yu, S. T., and Chang, S. C., "Applications of the Space-Time Conservation Element and Solution Element Method to Unsteady Chemically Reactive Flows," AIAA Paper 97-2099, June 1997.
35. Im, K.-S., Kim, C.-K., Yu, S. T., Chang, S. C., and Jorgenson, P. C. E., "Application of the CESE Method to Detonation with Realistic Finite-Rate Chemistry," AIAA Paper 2002-1020, Jan. 2002.
36. Park, S.-J., Yu, S. T., Lai, M.-C., Chang, S. C., and Jorgenson, P. C. E., "Direct Calculations of Stable and Unstable ZND Detonations by the Space-Time Conservation Element and Solution Element Method," AIAA Paper 99-0491, Jan. 1999.
37. Zhang, Z. C., Yu, S. T., and Chang, S. C., "A Space-time Conservation Element and Solution Element Method for Solving the Two- and Three-Dimensional Unsteady Euler Equations Using Quadrilateral and Hexahedral Meshes," Journal of Computational Physics, Vol. 175, No. 1, 2002. pp. 168-199.
38. Chang, S. C., "The Method of Space-time Conservation Element and Solution Element - A New Approach for Solving the Navier-Stokes and Euler Equations," Journal of Computational Physics, Vol. 119, No. 2, 1995, pp. 295-324.
39. Chang, S. C., Wang, X. Y., and Chow, C. Y., "The Space-Time Conservation Element and Solution Element Method: a New High-Resolution and Genuinely Multidimensional Paradigm for Solving Conservation Laws," Journal of Computational Physics, Vol. 156, No. 1, 1999, pp. 89-136.
40. Chang, S. C., Wang, X. Y., and To, W. M., "Application of the Space-Time Conservation Element and Solution Element Method to One-Dimensional Convection-Diffusion Problems," Journal of Computational Physics, Vol. 165, No. 1, 2000, pp. 189-215.
41. Chang, S. C., "Courant Number Insensitive CE/SE Schemes," AIAA Paper 2002-3890, July 2002.
42. Oran, E. S., Young, T. R., Boris, J. P., and Cohen, A., "Weak and Strong Ignition, I, Numerical Simulations of Shock Tube Experiments," Combustion and Flame, Vol. 48, No. 2, 1982, pp. 135-148.
43. Dryer, F. L., "The Phenomenology of Modeling Combustion Chemistry, Section: 5.1: One- and Two-Step Global Mechanisms," Fossil Fuel Combustion - A Source Book, edited by W. Bartok and A. F. Sarofim, Wiley-Interscience, New York, 1991, Chap. 5.
44. McBride, B. J., and Gordon, S., "Computer Program for Calculation of Complex Chemical Equilibrium Compositions and Applications," NASA Reference Publication 1311, June 1996.
45. Toro, E. F., Riemann Solvers and Numerical Methods for Fluid Dynamics, 2nd ed., Springer, London, 1999, pp. 582-585
46. Lu, T., Law, C. K., and Ju, Y., "Some Aspects of Chemical Kinetics in Chapman-Jouguet Detonation: Induction Length Analysis," Journal of Propulsion and Power, Vol. 19, No. 5, 2003, pp. 901-907.
47. Harten, A., Osher, S. J., Engquist, B. E., and Chakravarthy, S. R., "Some Results on Uniformly High-Order Accurate Essentially Non-Oscillatory Schemes," Journal of Applied Numerical Mathematics, Vol. 2, No. 3-5, 1986, pp. 347-377.
48. Hwang, P., Fedkiw, R. P., Merriman, B., Aslam, T. D., Karagozian, A. R., and Osher, S. J., "Numerical Resolution of Pulsating Detonation Waves," Combustion Theory Modeling, Vol. 4, No. 3, 2000, pp. 217-240.
49. Butler, D. S., "Converging Spherical and Cylindrical Shocks," Armament Research and Development Establishment, Ministry of Supply, Rept. 54/54, Fort Halstead, Kent, England, U.K., June 1954.
50. Stanyukovich, K. P., Unsteady Motion of Continuous Media, Pergamon, Oxford, 1960, p. 524, Chap. 5.
51. de Neef, T., and Nechtman, C., "Numerical Study of the Flow Due to a Cylindrical Implosion," Computational Physics, Vol. 6, No. 2, 1978, pp. 185-202.
52. Takayama, K., Onodera. O., and Hoshiaawa, Y., "Experiments on the Stability of Converging Cylindrical Shock Waves," Theoretical and Applied Mechanics, Vol. 32, No. 1, 1984, pp. 117-127.
53. Kleine, H., "Time Resoled Shadowgraphs of Focusing Cylindrical Shock Waves," Study Treatise at Stosswellenlabor, RWTH Aachen, Aachen, Germany, 1985.