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Flame Propagation and Growth to Detonation in Multiphase Flows

  • J. W. Nunziato
  • M. R. Baer
Conference paper
Part of the The IMA Volumes in Mathematics and Its Applications book series (IMA, volume 12)

Abstract

In this paper, we present a two-phase flow theory for the combustion of gas-permeable, reactive granular materials. In particular, we focus on the fundamental physical-chemical processes associated with the transition from deflagration to detonation in granular explosives and propellants. A numerical strategy, based on the method of fractional steps and flux-corrected transport (FCT), is discussed with the view toward multidimensional computations. Comparison of our results with experimental data for the explosive CP suggests that a thermodynamically consistent theory can describe the acceleration of the flame front in three (of the four) major flow regimes commonly observed; convective burning, compressive deflagration, and detonation.

Keywords

Initial Density Flame Front Combustion Wave Flame Propagation Flame Spread 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    K. K. Andreev, “The Problem of the Mechanism of the Transition from Burning to Detonation in Explosives,” J. Phys. Chem., 17, 533, (1944).Google Scholar
  2. 2.
    N. Griffiths, and J. M. Groocock, “Burning to Detonation of Solid Explosives,” J. Chem. Soc. London, 814 4154 (1960).Google Scholar
  3. 3.
    D. Price, and R. R. Bernecker, “Effect of Wax on the Deflagration to Detonation Transition of Porous Explosives,” Behavior of Dense Media Under High Dynamic Pressure, Commissariat a l’Energie Atomique, Paris, 149 (1978).Google Scholar
  4. 4.
    H. W. Sandusky, “Compressive Ignition and Burning in Porous Beds of Energetic Materials,” Proc. 1983 JANNAF Propulsion System Hazards Meeting, Los Alamos, 249 (1983).Google Scholar
  5. 5.
    M. R. Baer, R. J. Gross, J. W. Nunziato, and E. A. Igel, “An Experimental and Theoretical Study of Deflagration-to-Detonation Transition (DDT) in the Granular Explosive, CP,” Combustion and Flame, 65, 15 (1986).CrossRefGoogle Scholar
  6. 6.
    J. W. Nunziato, “Initiation and Growth-to-Detonation in Reactive Mixtures,” Shock Waves in Condensed Matter—1983 (J. R. Asay, R. A. Graham, G. K. Straub, eds.), Elsevier, New York, 581 (1984).Google Scholar
  7. 7.
    M. R. Baer and J. W. Nunziato, “A ‘Hot-Spot’ Initiation Model for Energetic Granular Materials,” to be published (1987).Google Scholar
  8. 8.
    A. W. Campbell, “Deflagration-to-Detonation Transition in Granular HMX,” Proc. 1980 JANNAF Propulsion System Hazards Meeting, Los Alamos, 105 (1980).Google Scholar
  9. 9.
    C. Truesdell, Rational Thermodynamics, McGraw-Hill, New York (1984).zbMATHGoogle Scholar
  10. 10.
    S. L. Passman, J. W. Nunziato, and E. K. Walsh, “A Theory of Multiphase Mixtures,” Rational Thermodynamics (C. Truesdell, ed.), Springer-Verlag, New York; (1984).Google Scholar
  11. 11.
    M. Ishii, Thermo-Fluid Dynamic Theory of Two-Phase Flow, Eyrolles, Paris (1975).zbMATHGoogle Scholar
  12. 12.
    D. A. Drew and L. A. Segel, “Averaged Equations for Two-Phase Flows,” Studies App. Math., 1, 205 (1971).Google Scholar
  13. 13.
    M. W. Beckstead, N. L. Peterson, D. T. Pilcher, B. D. Hopkins, and H. Krier, “Convec-tive Combustion Modeling Applied to Deflagration-to-Detonation Transition of HMX,” Combustion and Flame, 30, 231 (1977).CrossRefGoogle Scholar
  14. 14.
    P. B. Butler, M. F. Lembeck, and H. Krier, “Modeling of Shock Development and Transition to Detonation Initiated by Burning in Porous Propellant Beds,” Combustion and Flame, 46, 75 (1982).CrossRefGoogle Scholar
  15. 15.
    K. K. Kuo, and M. Summerfield, “High Speed Combustion of Mobile Granular Solid Propellants: Wave Structure and the Equivalent Rankine-Hugoniot Relation,” Fifteenth Symposium (International) on Combustion, 515 (1974).Google Scholar
  16. 16.
    D. E. Kooker and R. D. Anderson, “A Mechanism for the Burning Rate of High Density, Porous Energetic Materials,” Seventh Symposium (International) on Detonation, 198 (1981).Google Scholar
  17. 17.
    M. R. Baer and J. W. Nunziato, “A Two-Phase Mixture Theory for Deflagration-to-Detonation Transition in Reactive Granular Materials,” Intl. J. Multiphase Flow, 12, 861 (1986).zbMATHCrossRefGoogle Scholar
  18. 18.
    M. R. Baer, R. E. Benner, R. J. Gross, and J. W. Nunziato, “Modeling and Computation of Deflagration-to-Detonation Transition (DDT) in Reactive Granular Materials,” Reacting Flows: Combustion and Chemical Reactors (G. S. S. Ludford, ed.), American Mathematical Society, Providence, Lectures in Applied Mathematics, 24, 479 (1986).Google Scholar
  19. 19.
    M. M. Carroll, and A. Holt, “Static and Dynamic Pore-Collapse for Ductile Porous Materials,” J. App. Phys., 43, 1627 (1972).ADSGoogle Scholar
  20. 20.
    N. N. Yanenko, The Method of Fractional Steps (Trans, by M. Holt) Springer-Verlag, New York (1971).zbMATHGoogle Scholar
  21. 21.
    J. P. Boris and D. L. Book, “Solution of Continuity Equations by the Method of Flux-Corrected Transport,” Methods in Computational Physics, Vol. 16 (J. Kelleen, ed.) Academic Press, New York (1976).Google Scholar
  22. 22.
    W. G. Vincenti and C. H. Kruger, Introduction to Physical Gas Dynamics, J. Wiley, New York (1965).Google Scholar
  23. 23.
    F. A. Williams, Combustion Theory, Addison Wesley, Massachusetts (1965).Google Scholar
  24. 24.
    C. T. Crowe, J. A. Nicholls, and R. B. Morrison, “Drag Coefficients of Inert and Burning Particles Accelerating in Gas Streams,” Ninth Symposium (International) on Combustion, 395 (1963).Google Scholar
  25. 25.
    R. Courant and D. Hilbert, Methods of Mathematical Physics, Vol. II, Interscience, New York (1962).zbMATHGoogle Scholar
  26. 26.
    J. M. Hyman, “A Method of Lines Approach to the Numerical Solution of Conservation Laws,” Rept. LA-VR 79–837, Los Alamos Laboratory (1979).Google Scholar
  27. 27.
    L. F. Shampine and H. A. Watts, “DEPAC — Design of a User Oriented Package of ODE Solvers,” Sandia National Laboratories Rept. SAND79–2374 (1980).Google Scholar
  28. 28.
    R. J. Kee and J. A. Miller, “A Split-Operator, Finite-Difference Solution for Axisymmetric Laminar-Jet Diffusion Flames,” AIAA J. 16, 169 (1978).MathSciNetADSzbMATHCrossRefGoogle Scholar
  29. 29.
    D. L. Book, and M. A. Fry, “Airblast Simulations Using Flux-Corrected Transport Codes,” NRL Memorandum Rept. 5334, Naval Research Lab., 1984.Google Scholar
  30. 30.
    R. J. Gross and M. R. Baer, “A Study of Numerical Solution Methods for Two-Phase Flows,” Sandia National Laboratories Rept. SAND84–1633 (1986).Google Scholar
  31. 31.
    S. A. Sheffield, D. E. Mitchell, and D. B. Hayes, “An Equation of State and Chemical Kinetics for Hexanitrostilbene (HNS) Explosive,” Sixth Symposium (International) on Detonation, 748 (1977).Google Scholar
  32. 32.
    E. Lee, H. C. Hornig, and J. W. Kury, “Adiabatic Expansion of High Explosive Detonation Products,” LNLL VCRL-50422 (1968).CrossRefGoogle Scholar
  33. 33.
    M. Cowperthwaite and W. H. Zwisler, “TIGER: Computer Code Documentation,” Stanford Research Institute Pub. No. Z106, 1974.Google Scholar
  34. 34.
    P. L. Stanton, E. A. Igel, L. M. Lee, J. M. Mohler and G. T. West, “Characterization of the DDT Explosive, CP,” Seventh Symposium (International) on Detonation, 457, 1981.Google Scholar
  35. 35.
    J. Shepherd, and D. Begeal, “Transient Compressible Flow in Porous Materials,” Sandia National Laboratories Rept. SAND83–1788 (1983).Google Scholar
  36. 36.
    F. A. L. Dullien, Porous Media Fluid Transport and Pore Structure, Academic Press (1979).Google Scholar
  37. 37.
    N. I. Gel’Perin and V. G. Ainstein, “Heat Transfer in Fluidized Beds,” Fluidization, Academic Press, New York (1971).Google Scholar
  38. 38.
    M. R. Baer, “Numerical Studies of Dynamic Compaction of Inert and Energetic Granular Materials,” to be published (1987).Google Scholar
  39. 39.
    M. R. Baer and R. J. Gross, “A Two-Dimensional Flux-Corrected Transport Solver for Convectively Dominated Flows,” Sandia National Laboratories Rept. SAND85–0613 (1986).CrossRefGoogle Scholar

Copyright information

© Springer-Verlag New York Inc. 1988

Authors and Affiliations

  • J. W. Nunziato
    • 1
  • M. R. Baer
    • 1
  1. 1.Fluid and Thermal Sciences DepartmentSandia National LaboratoriesAlbuquerqueUSA

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