DOI: https://doi.org/10.26089/NumMet.v20r326

Numerical simulation of detonation wave propagation using a two-stage kinetics model of chemical reactions in the shock-attached frame

Authors

  • Ya.E. Poroshyna

Keywords:

mathematical modeling
detonation wave
shock-attached frame
two-stage kinetics model

Abstract

For the numerical study of a pulsating detonation wave using a two-stage kinetics model of chemical reactions in the shock-attached frame, a new numerical algorithm is proposed. For the four known modes of detonation wave propagation, the effect of the approximation order of the proposed numerical algorithm, the length of the computational domain, the grid resolution, and the type of the far-field boundary condition on the simulation results is analyzed in the framework of this model. The character of pulsations is compared with the numerical results obtained by a number of other authors.


Published

2019-08-12

Issue

Section

Section 1. Numerical methods and applications

Author Biography

Ya.E. Poroshyna


References

  1. Ya. B. Zel’dovich, “On the Theory of Detonation Propagation in Gaseous Systems,” Zh. Eksp. Teor. Fiz. 10 (5), 542-568 (1940).
  2. J. von Neumann, “Theory of Detonation Waves,” in Collected Works (Pergamon, London, 1963), Vol. 6, pp. 203-218.
  3. W. D{öring, “{Ü}ber den Detonationsvorgang in Gasen [On Detonation Processes in Gases],” Ann. Phys. 43, 421-436 (1943).
  4. J. J. Erpenbeck, “Stability of Steady-State Equilibrium Detonations,” Phys. Fluids 5 (5), 604-614 (1962).
  5. W. Fickett and W. W. Wood, “Flow Calculations for Pulsating One-Dimensional Detonations,” Phys. Fluids 9 (5), 903-916 (1966).
  6. V. P. Korobeinikov, V. A. Levin, V. V. Markov, and G. G. Chernyi, “Propagation of Blast Waves in a Combustible Gas,” Acta Astronaut. 17 (5-6), 529-537 (1972).
  7. L. I. Sedov, V. P. Korobeinikov, and V. V. Markov, “The Theory of Blast Wave Propagation,” Tr. Mat. Inst. im. V.A. Steklova, Akad. Nauk SSSR 175, 178-216 (1986) [Proc. Steklov Inst. Math. 175, 187-228 (1988)].
  8. M. Short and G. J. Sharpe, “Pulsating Instability of Detonations with a Two-Step Chain-Branching Reaction Model: Theory and Numerics,” Combust. Theory Modelling 7 (2), 401-416 (2003).
  9. J. B. McVey and T. Y. Toong, “Mechanism of Instabilities of Exothermic Hypersonic Blunt-Body Flows,” Combust. Sci. Technol. 3 (2), 63-76 (1971).
  10. W. Fickett and W. C. Davis, Detonation: Theory and Experiment (University of California Press, Berkeley, 1979).
  11. H. D. Ng, M. I. Radulescu, A. J. Higgins, et al., “Numerical Investigation of the Instability for One-Dimensional Chapman-Jouguet Detonations with Chain-Branching Kinetics,” Combust. Theory Modelling 9 (3), 385-401 (2005).
  12. C. Leung, M. I. Radulescu, and G. J. Sharpe, “Characteristics Analysis of the One-Dimensional Pulsating Dynamics of Chain-Branching Detonations,” Phys. Fluids 22 (2010).
    doi 10.1063/1.3520188
  13. A. R. Kasimov and D. S. Stewart, “On the Dynamics of Self-Sustained One-Dimensional Detonations: A Numerical Study in the Shock-Attached Frame,” Phys. Fluids 16 (10), 3566-3578 (2004).
  14. A. S. Kholodov, “Construction of Difference Schemes with Positive Approximation for Hyperbolic Equations,” Zh. Vychisl. Mat. Mat. Fiz. 18 (6), 1476-1492 (1978) [USSR Comput. Math. Math. Phys. 18 (6), 116-132 (1978)].
  15. A. I. Lopato and P. S. Utkin, “Detailed Simulation of the Pulsating Detonation Wave in the Shock-Attached Frame,” Zh. Vychisl. Mat. Mat. Fiz. 56 (5), 856-868 (2016) [Comput. Math. Math. Phys. 56 (5), 841-853 (2016)].
  16. A. I. Lopato and P. S. Utkin, “Toward Second-Order Algorithm for the Pulsating Detonation Wave Modeling in the Shock-Attached Frame,” Combust. Sci. Technol. 188 (11-12), 1844-1856 (2016).
  17. A. I. Lopato and P. S. Utkin, “Two Approaches to the Mathematical Modeling of Detonation Waves,” Mat. Model. 28 (2), 133-145 (2016) [Math. Models Comput. Simul. 8 (5), 585-594 (2016)].
  18. Y. Daimon and A. Matsuo, “Unsteady Features on One-Dimensional Hydrogen-Air Detonations,” Phys. Fluids 19 (2007).
    doi 10.1063/1.2801478
  19. M. Short and D. Wang, “On the Dynamics of Pulsating Detonations,” Combust. Theory Modelling 5 (3), 343-352 (2001).