Shock Waves

pp 1–11 | Cite as

Analysis of mild ignition in a shock tube using a highly resolved 3D-LES and high-order shock-capturing schemes

  • J. T. LipkowiczEmail author
  • I. Wlokas
  • A. M. Kempf
Original Article


A highly resolved three-dimensional large-eddy simulation (LES) is presented for a shock tube containing a stoichiometric hydrogen–oxygen (\(\hbox {H}_2\)/\(\hbox {O}_2\)) mixture, and the results are compared against experimental results. A parametric study is conducted to test the effects of grid resolution, numerical scheme, and initial conditions before the 3D simulations are presented in detail. An approximate Riemann solver and a high-order interpolation scheme are used to solve the conservation equations of the viscous, compressible fluid and to account for turbulence behind the reflected shock. Chemical source terms are calculated by a finite-rate model. Simultaneous results of pseudo-Schlieren, temperature, pressure, and species are presented. The ignition delay time is predicted in agreement with the experiments by the three-dimensional simulations. The mechanism of mild ignition is analysed by Lagrangian tracer particles, tracking temperature histories of material particles. We observed strongly increased temperatures in the core region away from the end wall, explaining the very early occurrence of mild ignition in this case.


Large-eddy simulations (LES) Mild ignition Shock tube Tracer particles Bifurcation 



The authors gratefully acknowledge the financial support by DFG Grant KE 1751/8-1, the computing time on magnitUDE granted by the Center for Computational Sciences and Simulation of the Universität of Duisburg-Essen through DFG INST 20876/209-1 FUGG, INST 20876/243-1 FUGG at the Zentrum für Informations- und Mediendienste, and the computing time on the supercomputer HazelHen (ACID 44116). We also want to thank Elaine Oran for inspiring discussions that improved the paper.


  1. 1.
    Mirels, H.: Attenuation in a shock tube due to unsteady-boundary-layer action. NACA-TR-1333, National Advisory Committee for Aeronautics (1957)Google Scholar
  2. 2.
    White, D.R.: Influence of diaphragm opening time on shock-tube flows. J. Fluid Mech. 4(6), 585–599 (1958). CrossRefzbMATHGoogle Scholar
  3. 3.
    Petersen, E.L., Hanson, R.K.: Nonideal effects behind reflected shock waves in a high-pressure shock tube. Shock Waves 10(6), 405–420 (2001). CrossRefGoogle Scholar
  4. 4.
    Meyer, J.W., Oppenheim, A.K.: On the shock-induced ignition of explosive gases. Proc. Combust. Inst. 13(1), 1153–1164 (1971). CrossRefGoogle Scholar
  5. 5.
    Blumenthal, R., Fieweger, K., Komp, K.H., Adomeit, G.: Gas dynamic features of self ignition of non diluted fuel/air mixtures at high pressure. Combust. Sci. Technol. 123(1–6), 1–30 (1997). CrossRefGoogle Scholar
  6. 6.
    Chaos, M., Dryer, F.L.: Chemical-kinetic modeling of ignition delay: Considerations in interpreting shock tube data. Int. J. Chem. Kinet. 42(3), 143–150 (2010). CrossRefGoogle Scholar
  7. 7.
    Mark, H.: The interaction of a reflected shock wave with the boundary layer in a shock tube. NACA-TM-1418, National Advisory Committee for Aeronautics (1958)Google Scholar
  8. 8.
    Strehlow, R.A., Cohen, A.: Limitations of the reflected shock technique for studying fast chemical reactions and its application to the observation of relaxation in nitrogen and oxygen. J. Chem. Phys. 30(1), 257–265 (1959). CrossRefGoogle Scholar
  9. 9.
    Davies, L.: Influence of reflected shock and boundary-layer interaction on shock-tube flows. Phys. Fluids 12(5), I–37 (1969). CrossRefGoogle Scholar
  10. 10.
    Voevodsky, V., Soloukhin, R.: On the mechanism and explosion limits of hydrogen–oxygen chain self-ignition in shock waves. Proc. Combust. Inst. 10(1), 279–283 (1965). CrossRefGoogle Scholar
  11. 11.
    Berets, D.J., Greene, E.F., Kistiakowsky, G.B.: Gaseous detonations. I. Stationary waves in hydrogen–oxygen mixtures\(^1\). J. Am. Chem. Soc. 72(3), 1080–1086 (1950). CrossRefGoogle Scholar
  12. 12.
    Fay, J.A.: Some experiments on the initiation of detonation in \(2{\text{ H }}_2{-}{\text{ O }}_2\) mixtures by uniform shock waves. Proc. Combust. Inst. 4(1), 501–507 (1953). CrossRefGoogle Scholar
  13. 13.
    Steinberg, M., Kaskan, W.: The ignition of combustible mixtures by shock waves. Proc. Combust. Inst. 5(1), 664–672 (1955). CrossRefGoogle Scholar
  14. 14.
    Oran, E., Young, T., Boris, J., Cohen, A.: Weak and strong ignition. I. Numerical simulations of shock tube experiments. Combust. Flame 48, 135–148 (1982). CrossRefGoogle Scholar
  15. 15.
    Oran, E.S., Gamezo, V.N.: Origins of the deflagration-to-detonation transition in gas-phase combustion. Combust. Flame 148(1–2), 4–47 (2007). CrossRefGoogle Scholar
  16. 16.
    Ihme, M., Sun, Y., Deiterding, R.: Detailed simulations of shock-bifurcation and ignition of an argon-diluted hydrogen/oxygen mixture in a shock tube. 51st AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition Grapevine (Dallas/Ft. Worth Region), TX, AIAA Paper 2013-0538 (2013).
  17. 17.
    Grogan, K.P., Ihme, M.: Weak and strong ignition of hydrogen/oxygen mixtures in shock-tube systems. Proc. Combust. Inst. 35(2), 2181–2189 (2015). CrossRefGoogle Scholar
  18. 18.
    Khokhlov, A., Austin, J., Knisely, A.: Development of hot spots and ignition behind reflected shocks in \(2{\text{ H }}_2 + {\text{ O }}_2\). Proceedings of the 25th International Colloquium on the Dynamics of Explosions and Reactive Systems, ICDERS, Leeds, UK, Paper 020 (2015)Google Scholar
  19. 19.
    Dziemińska, E., Hayashi, A.K.: Auto-ignition and DDT driven by shock wave—boundary layer interaction in oxyhydrogen mixture. Int. J. Hydrogen Energy 38(10), 4185–4193 (2013). CrossRefGoogle Scholar
  20. 20.
    Proch, F., Kempf, A.M.: Numerical analysis of the Cambridge stratified flame series using artificial thickened flame LES with tabulated premixed flame chemistry. Combust. Flame 161(10), 2627–2646 (2014). CrossRefGoogle Scholar
  21. 21.
    Rittler, A., Deng, L., Wlokas, I., Kempf, A.: Large eddy simulations of nanoparticle synthesis from flame spray pyrolysis. Proc. Combust. Inst. 36(1), 1077–1087 (2017). CrossRefGoogle Scholar
  22. 22.
    Rieth, M., Proch, F., Rabaçal, M., Franchetti, B., Marincola, F.C., Kempf, A.: Flamelet LES of a semi-industrial pulverized coal furnace. Combust. Flame 173, 39–56 (2016). CrossRefGoogle Scholar
  23. 23.
    Nguyen, T., Kempf, A.M.: Investigation of numerical effects on the flow and combustion in LES of ICE. Oil Gas Sci. Technol. 72(4), 25 (2017). CrossRefGoogle Scholar
  24. 24.
    Poinsot, T.J., Veynante, D.: Theoretical and Numerical Combustion, 3rd edn. Aquaprint, Bordeaux (2012)Google Scholar
  25. 25.
    Williamson, J.: Low-storage Runge–Kutta schemes. J. Comput. Phys. 35(1), 48–56 (1980). MathSciNetCrossRefzbMATHGoogle Scholar
  26. 26.
    Kitamura, K., Hashimoto, A.: Reduced dissipation AUSM-family fluxes: HR-SLAU2 and HR-AUSM\(^+\)-up for high resolution unsteady flow simulations. Comput. Fluids 126, 41–57 (2016). MathSciNetCrossRefzbMATHGoogle Scholar
  27. 27.
    Suresh, A., Huynh, H.: Accurate monotonicity-preserving schemes with Runge–Kutta time stepping. J. Comput. Phys. 136(1), 83–99 (1997). MathSciNetCrossRefzbMATHGoogle Scholar
  28. 28.
    Nicoud, F., Toda, H.B., Cabrit, O., Bose, S., Lee, J.: Using singular values to build a subgrid-scale model for large eddy simulations. Phys. Fluids 23(8), 085106 (2011). CrossRefGoogle Scholar
  29. 29.
    Goodwin, D.G., Moffat, H.K., Speth, R.L.: Cantera: An Object-oriented Software Toolkit for Chemical Kinetics, Thermodynamics, and Transport Processes. Version 2.4.0 (2017).
  30. 30.
    Bird, R.B., Stewart, W.E., Lightfoot, E.N.: Transport Phenomena. Wiley, New York (1960)Google Scholar
  31. 31.
    Peters, N., Warnatz, J. (eds.): Numerical Methods in Laminar Flame Propagation. Vieweg+Teubner Verlag, Braunschweig (1982). CrossRefGoogle Scholar
  32. 32.
    Kee, R.J., Coltrin, M.E., Glarborg, P.: Chemically Reacting Flow. Wiley, New York (2003). CrossRefGoogle Scholar
  33. 33.
    Cohen, S.D., Hindmarsh, A.C., Dubois, P.F.: CVODE, a stiff/nonstiff ODE solver in C. Comput. Phys. 10(2), 138 (1996). CrossRefGoogle Scholar
  34. 34.
    Hindmarsh, A.C., Brown, P.N., Grant, K.E., Lee, S.L., Serban, R., Shumaker, D.E., Woodward, C.S.: SUNDIALS: Suite of nonlinear and differential/algebraic equation solvers. ACM Trans. Math. Softw. 31(3), 363–396 (2005). MathSciNetCrossRefGoogle Scholar
  35. 35.
    Conaire, M.Ó., Curran, H.J., Simmie, J.M., Pitz, W.J., Westbrook, C.K.: A comprehensive modeling study of hydrogen oxidation. Int. J. Chem. Kinet. 36(11), 603–622 (2004). CrossRefGoogle Scholar
  36. 36.
    Wang, L., Peters, N.: The length-scale distribution function of the distance between extremal points in passive scalar turbulence. J. Fluid Mech. 554(1), 457–475 (2006). CrossRefzbMATHGoogle Scholar
  37. 37.
    Weber, Y.S., Oran, E.S., Boris, J.P., Anderson, J.D.: The numerical simulation of shock bifurcation near the end wall of a shock tube. Phys. Fluids 7(10), 2475–2488 (1995). CrossRefzbMATHGoogle Scholar
  38. 38.
    Matsuo, K., Kawagoe, S., Kage, K.: The interaction of a reflected shock wave with the boundary layer in a shock tube. Bull. JSME 17(110), 1039–1046 (1974). CrossRefGoogle Scholar
  39. 39.
    Lamnaouer, M., Kassab, A., Divo, E., Polley, N., Garza-Urquiza, R., Petersen, E.: A conjugate axisymmetric model of a high-pressure shock-tube facility. Int. J. Numer. Methods Heat Fluid Flow 24(4), 873–890 (2014). CrossRefGoogle Scholar
  40. 40.
    Hanson, R.K., Pang, G.A., Chakraborty, S., Ren, W., Wang, S., Davidson, D.F.: Constrained reaction volume approach for studying chemical kinetics behind reflected shock waves. Combust. Flame 160(9), 1550–1558 (2013). CrossRefGoogle Scholar
  41. 41.
    Fieweger, K., Blumenthal, R., Adomeit, G.: Self-ignition of S.I. engine model fuels: A shock tube investigation at high pressure. Combust. Flame 109(4), 599–619 (1997). CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Fluid Dynamics, IVGUniversity of Duisburg-EssenDuisburgGermany

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