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Part of the book series: Notes on Numerical Fluid Mechanics ((NNFM,volume 24))

Abstract

Shock induced ignition and the subsequent development of reactive-gasdynamic waves in two-dimensional confined ducts are investigated by means of numerical simulations. The inhomo-geneous Euler equations are employed to describe the gasdynamic-chemical interactions. A second order accurate two-step Godunov-type scheme, which directly accounts for the source terms, is proposed. Its performance is demonstrated by solving a test problem, whose exact solution is available. Two examples of flows within L-shaped configurations reveal interesting mechanisms, which support the formation of reactive Mach-stems, and thus trigger the onset of multidimensional detonation waves. A relation of the present idealized model problems to knock damage in internal combustion engines is pointed out.

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References

  1. Pischinger, F., Kollmeier, H.P., Spicher, U., Das Klopfen im OttomotorEin altes Problem aus neuer Sicht, Mitteilungen des Instituts f. Verbrennungskraftmaschinen u. Thermodynamik, TU Graz 49, (1987).

    Google Scholar 

  2. Korobieinikov, V.P., Levin, V.A., Markov, V.V., Citenyi, G.G., Propagation of Blast Waves in a Combustible Gas, Astronautica Acta 17, 529 (1972).

    Google Scholar 

  3. Oran, E.S., Boris, J.P., Young, T., Flanigan, M., Burks, T., Picone, M., Numerical Simulations of Detonations in Methane-Air Mixtures, Proc. of the 18th Symp. on Combustion, The Combustion Institute (1982).

    Google Scholar 

  4. Williams, F.A., Combustion Theory, 2nd Edition, Benjamin/Cummings (1985).

    Google Scholar 

  5. Klein, R., Stoßinduzierte Zündung und der Übergang zur Detonation in engen Spalten, Dissertation, KWTH Aachen (1988).

    Google Scholar 

  6. Peters, N., Numerical and Asymptotic Analysis of Systematically Reduced Reaction Schemes for Hydrocarbon Flames, in: Numerical Simulations of Combustion Phenomena, Lecture Notes in Physics, 241, 90–109, Springer (1985).

    Chapter  Google Scholar 

  7. Peters, N., Systematic Reduction of Flame KineticsPrincipals and Details, 11th ICODERS, Warsaw, August 1987.

    Google Scholar 

  8. Schmidt, F.A.F., Verbrennungskraßmaschinen, 4. Aufl., Springer (1967).

    Google Scholar 

  9. Fickett, W., Davis, W.C., Detonation, University of California Press (1979).

    Google Scholar 

  10. Oran, E.S., Boris, J.P., Detailed Modelling of Combustion SystemsProgr. Energy Comb. Sci. 7, 1–72 (1981).

    Article  Google Scholar 

  11. Strang, G., On the Construction and Comparison of Difference Schemes, SIAM, J. Num. Anal. 5, 506–517 (1968).

    Article  MathSciNet  MATH  Google Scholar 

  12. Einfeldt, B., On Godunov-Type Methods for Gasdynamics, SIAM, J. Num. Anal. 25, No. 2 (1988).

    Article  MathSciNet  Google Scholar 

  13. Harten, A., Lax, P.D., van Leer, B., On Upstream-Diferencing and Godunov-Type Schemes for Hyperbolic Conservation Laws, SIAM Review 25, 35–61 (1983).

    Article  MathSciNet  MATH  Google Scholar 

  14. Roe, P.L., Approximate Riemann-solvers, Parameter Vectors and Difference Schemes, J. Comp. Phys. 43, 357–372 (1981).

    Article  MathSciNet  MATH  Google Scholar 

  15. Einfeldt, B., On Godunov-Type Methods for the Euler Equations with a General Equation of State, Proc. of the 16th Int. Conf. on Shock Tubes and Waves, Ed. H. Grönig, VCH-Verlagsgesellschaft, Weinheim, West-Germany (1988).

    Google Scholar 

  16. Sweby, P.K., High-Resolution Schemes Using Flux Limiters for Hyperbolic Conservation Laws, Siam, J. NUm. Anal. 21, 995–1011 (1984).

    Article  MathSciNet  MATH  Google Scholar 

  17. Münz, CD., Näherungsverfahren höherer Ordnung zur Approximation von Stoßwellen, Berichte 26, 28, Fak. f. Mathem., Universität Karlsruhe (1985).

    Google Scholar 

  18. Colella, P., Glaz, H.M., Efficient Solution Algorithms for the Riemann-Problem for Real Gases, J. Comp. Phys. 59, 264–289 (1985).

    Article  MathSciNet  MATH  Google Scholar 

  19. Klein, R., Shock Initiated Ignition in a L-Shaped Duct: Two Aspects of its Numerical Simulation, to appear in Proc. of the 7th GAMM-Conference on Numerical Methods in Fluid Mechanis, Louvain La Neuve, Belgium (1987).

    Google Scholar 

  20. Roe, P.L., Upwind Differencing Schemes for Hyperbolic Conservation Laws with Source Terms, Eds.: A. Dold, B. Eckmann, Lecture Notes in Mathematics, 1270, Springer (1987).

    Google Scholar 

  21. Woodward, P., Colella, P., The Numerical Simulation of Two-Dimensional Fluid Flow with Strong Shocks, J. Comp. Phys. 54, 115–173 (1984).

    MathSciNet  MATH  Google Scholar 

  22. Clarke, J.F., Toro, E.F., Gas Flows Generated by Solid Propellant Burning, Lecture Notes in Physics 241, Numerical Simulation of Combustion Phenomena (Eds.: R. Glowinsky, B. Larrouturou, R. Temam), Springer (1985).

    Google Scholar 

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© 1989 Friedr. Vieweg & Sohn Verlagsgesellschaft mbH, Braunschweig

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Klein, R. (1989). Detonation Initiation Due to Shock Wave-Boundary Interactions. In: Ballmann, J., Jeltsch, R. (eds) Nonlinear Hyperbolic Equations — Theory, Computation Methods, and Applications. Notes on Numerical Fluid Mechanics, vol 24. Vieweg+Teubner Verlag. https://doi.org/10.1007/978-3-322-87869-4_29

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  • DOI: https://doi.org/10.1007/978-3-322-87869-4_29

  • Publisher Name: Vieweg+Teubner Verlag

  • Print ISBN: 978-3-528-08098-3

  • Online ISBN: 978-3-322-87869-4

  • eBook Packages: Springer Book Archive

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