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Numerical simulations on propane/oxygen detonation in a narrow channel using a detailed chemical mechanism: formation and detailed structure of irregular cells

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Abstract

Numerical simulations of two-dimensional inviscid detonations for a stoichiometric propane/oxygen gas mixture are performed using a detailed chemical reaction model. The UC San Diego model which includes 57 chemical species and 268 elementary reactions is mainly used in the present study. It is shown that a grid size of 3 µm can capture important features such as the unburned gas pocket behind the detonation when compared to larger grid sizes. The effects of channel width show that the detonation propagates with the CJ (Chapman–Jouguet) velocity for all cases and for more than 100 times the channel width of 4.5 mm. Increasing the channel width results in an irregular detonation cell structure. A transverse detonation forms with cross-hatching marks on the maximum pressure history. The irregular detonation cell structure forms because both the reduced activation energy and the stability parameter have a value of approximately 10; however, the maximum thermicity in the detonation is one. The free radicals C3H7 and H2O2 play an important role in the propane oxidation under the high temperature in the detonation. The maximum concentration exists at a temperature of 2000–3000 K. The fifth-order WCNS (weighted compact nonlinear scheme) scheme can resolve the contact surface and complicated flow structure behind the detonation front compared to the second-order MUSCL (Monotonic Upstream-centered Scheme for Conservation Laws).

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References

  1. HSE. RR718 – Buncefield Explosion Mechanisms Phase 1 (Volumes 1 and 2). https://www.hse.gov.uk/research/rrhtm/rr718.htm. Accessed 27 Nov 2019

  2. Citizens' Nuclear Information Center: Hamaoka Nuclear Power Reactor1. NUKE INFO TOKYO (2002)

  3. Austin, J.M., Printgen, F., Shepherd, J.E.: Reaction zones in highly unstable detonations. Proc. Combust. Inst. 30, 1849–1857 (2005). https://doi.org/10.1016/j.proci.2004.08.157

    Article  Google Scholar 

  4. Ng, H., Higgins, A., Kiyanda, C., Radulescu, M., Lee, J.H.S., Bates, K., Nikiforakis, N.: Nonlinear dynamics and chaos analysis of one-dimensional pulsating detonations. Combust. Theory Model. 9, 159–170 (2005). https://doi.org/10.1016/j.fuel.2008.07.029

    Article  MathSciNet  MATH  Google Scholar 

  5. Gamezo, V.N., Desbordes, D., Oran, E.S.: Formation and evolution of two-dimensional cellular detonations. Combust. Flame 116, 154–165 (1999). https://doi.org/10.1016/S0010-2180(98)00031-5

    Article  Google Scholar 

  6. Mazaheri, K., Mahmoudi, Y., Radulescu, M.I.: Diffusion and hydrodynamic instabilities in gaseous detonations. Combust. Flame 159, 2138–2154 (2012). https://doi.org/10.1016/j.combustflame.2012.01.024

    Article  Google Scholar 

  7. Radulescu, M.I.: A detonation paradox: why inviscid detonation simulations predict the incorrect trend for the role of instability in gaseous cellular detonation? Combust. Flame 195, 151–162 (2018). https://doi.org/10.1016/j.combustflame.2018.05.002

    Article  Google Scholar 

  8. Taylor, B.D, Gamezo, V.N., Oran, E.S.: The influence of chemical kinetics on the structure of hydrogen-air detonations. 50th Aerospace Sciences Meeting, Nashville, TN, AIAA Paper 2012-0979 (2012). https://doi.org/10.2514/6.2012-979

  9. Dounia, O., Vermorel, O., Misdariis, A., Poinsot, T.: Influence of kinetics on DDT simulations. Combust. Flame 200, 1–14 (2019). https://doi.org/10.1016/j.combustflame.2018.11.009

    Article  Google Scholar 

  10. Araki, T., Yoshida, K., Morii, Y., Tsuboi, N., Hayashi, A.K.: Numerical analyses on ethylene/oxygen detonation with multistep chemical reaction mechanisms: grid resolution and chemical reaction model. Combust. Sci. Technol. 188, 346–369 (2016). https://doi.org/10.1080/00102202.2015.1106484

    Article  Google Scholar 

  11. Mevel, R., Gallier, S.: Structure of detonation propagating in lean and rich dimethyl ether–oxygen mixtures. Shock Waves 28, 955–966 (2018). https://doi.org/10.1007/s00193-018-0837-x

    Article  Google Scholar 

  12. Combustion Kinetics Laboratory. USC-mech II. https://ignis.usc.edu/Mechanisms/Model%20release.html. Accessed 27 Nov 2019

  13. Gas Research Institute. GRI-mech 3.0. https://combustion.berkeley.edu/gri-mech/version30/text30.html. Accessed 27 Nov 2019

  14. UC San Diego combustion research group. The San Diego Mechanism. https://web.eng.ucsd.edu/mae/groups/combustion/mechanism.html. Accessed 27 Nov 2019

  15. Kee, R.J.: CHEMKIN-II: A FORTRAN chemical kinetics package for the analysis of gas-phase chemical kinetics. Sandia National Laboratories Report (1989)

  16. Luz, A.E.: SENKIN: A FORTRAN program for predicting homogeneous gas phase chemical kinetics with sensitivity analysis. Sandia National Laboratories Report (1988)

  17. Tang, C., Man, X., Wei, L., Pan, L., Huang, Z.: Further study on the ignition delay times of propane-hydrogen-oxygen argon mixtures: effect of equivalence ratio. Combust. Flame 160, 2283–2290 (2013). https://doi.org/10.1016/j.combustflame.2013.05.012

    Article  Google Scholar 

  18. Stull, D.R., Prophet, H.: JANAF Thermochemical Tables, 2nd edn. U.S. Department of Commerce, National Bureau of Standards, Washington (1971)

    Google Scholar 

  19. Kee, R.J., Coltrin, M.E., Glaborg, P.: Chemically Reacting Flow: Theory and Practice. Wiley, Hoboken (2005)

    Google Scholar 

  20. Wada, Y., Liou, M.S.: An accurate and robust flux splitting scheme for shock and contact discontinues. SIAM J. Sci. Comput. 18, 633–657 (1997). https://doi.org/10.1137/S1064827595287626

    Article  MathSciNet  MATH  Google Scholar 

  21. Leer, B.V.: Towards the ultimate conservative difference scheme. V. A second-order sequel to Godunov’s method. J. Comput. Phys. 32, 101–136 (1979). https://doi.org/10.1016/0021-9991(79)90145-1

    Article  MATH  Google Scholar 

  22. Toro, E.F., Spruce, M., Spears, W.: Restoration of the contact surface in the HLL-Riemann solver. Shock Waves 4, 25–34 (1994). https://doi.org/10.1007/BF01414629

    Article  MATH  Google Scholar 

  23. Deng, X.G., Zhang, H.: Developing high-order weighted compact nonlinear schemes. J. Comput. Phys. 165, 22–44 (2000). https://doi.org/10.1006/jcph.2000.6594

    Article  MathSciNet  MATH  Google Scholar 

  24. Zhang, S., Jiang, S., Shu, C.-W.: Development of nonlinear weighted compact schemes with increasingly higher order accuracy. J. Comput. Phys. 227, 7294–7321 (2008). https://doi.org/10.1016/j.jcp.2008.04.012

    Article  MathSciNet  MATH  Google Scholar 

  25. Nonomura, T., Fujii, K.: Robust explicit formulation of weighted compact nonlinear scheme. Comput. Fluids 85, 8–18 (2013). https://doi.org/10.1016/j.compfluid.2012.09.001

    Article  MathSciNet  MATH  Google Scholar 

  26. Nonomura, T., Fujii, K.: Effects of difference scheme type in high-order weighted compact nonlinear schemes. J. Comput. Phys. 228, 3533–3539 (2009). https://doi.org/10.1016/j.jcp.2009.02.018

    Article  MATH  Google Scholar 

  27. Nonomura, T., Iizuka, N., Fujii, K.: Freestream and vortex preservation properties of highorder WENO and WCNS on curvilinear grids. Comput. Fluids 39, 197–214 (2010). https://doi.org/10.1016/j.compfluid.2009.08.005

    Article  MathSciNet  MATH  Google Scholar 

  28. Niibo, T., Morii, Y., Asahara, M., Tsuboi, N., Hayashi, A.K.: Numerical study on direct initiation of cylindrical detonation in H2/O2 mixtures: effect of higher-order schemes on detonation propagation. Combust. Sci. Technol. 188, 2044–2059 (2016). https://doi.org/10.1080/00102202.2016.1215109

    Article  Google Scholar 

  29. Iida, R., Asahara, M., Hayashi, A.K., Tsuboi, N., Nonomura, T.: Implementation of weighted compact nonlinear scheme for hydrogen/air detonation. Combust. Sci. Technol. 186, 1736–1757 (2014). https://doi.org/10.1080/00102202.2014.935646

    Article  Google Scholar 

  30. Morii, Y., Terashima, H., Koshi, H., Shimizu, T., Shima, E.: ERENA: a fast and robust Jacobian-free integration method for ordinary differential equations of chemical kinetics. J. Comput. Phys. 322, 547–558 (2016). https://doi.org/10.1016/j.jcp.2016.06.022

    Article  MathSciNet  MATH  Google Scholar 

  31. Gottlieb, S., Ketcheson, D.I., Shu, C.W.: High order strong stability preserving time discretizations. J. Comput. Phys. 38, 251–289 (2009). https://doi.org/10.1007/s10915-008-9239-z

    Article  MathSciNet  MATH  Google Scholar 

  32. Kaneshige, M.J: Gaseous detonation initiation and stabilization by hypervelocity projectiles. Ph.D. thesis, California Institute of Technology (1999)

  33. Knystautas, R., Lee, J.H., Guirao, C.M.: The critical tube diameter for detonation failure in hydrocarbon–air mixtures. Combust. Flame 48(1), 63–83 (1982). https://doi.org/10.1016/0010-2180(82)90116-X

    Article  Google Scholar 

  34. Tsuboi, N., Daimon, Y., Hayashi, A.K.: Three-dimensional numerical simulation of detonations in coaxial tubes. Shock Waves 18, 379–392 (2008). https://doi.org/10.1007/s00193-008-0152-z

    Article  MATH  Google Scholar 

  35. Shi, L., Shen, H., Zhang, P., Zhang, D., Wen, C.: Assessment of vibrational non-equilibrium effect on detonation cell size. Combust. Sci. Technol. 189, 841–853 (2016). https://doi.org/10.1080/00102202.2016.1260561

    Article  Google Scholar 

  36. Tsuboi, N., Eto, K., Hayashi, A.K.: Detailed structure of spinning detonation in a circular tube. Combust. Flame 149(1–2), 144–161 (2007). https://doi.org/10.1016/j.combustflame.2006.12.004

    Article  Google Scholar 

  37. Manzhalei, V.I.: Fine structure of the leading front of a gas detonation. Combust. Explos. Shock Waves 13, 402–404 (1977)

    Article  Google Scholar 

  38. Falconer, J.W., Knox, J.H.: The high-temperature oxidation of propane. Proc. R. Soc. A (Math. Phys. Eng. Sci.) 250(1263), 493–513 (1959). https://doi.org/10.1098/rspa.1959.0079

    Article  Google Scholar 

Download references

Acknowledgements

This research used computational resources of the Reedbush-U and Oakbridge-CX provided by the University of Tokyo through the HPCI System Research project (Project ID: hp180119, hp190082). This research was also performed on the Supercomputing System of Kyushu University.

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Authors and Affiliations

  1. Department of Mechanical and Control Engineering, Kyushu Institute of Technology, Kitakyushu, Fukuoka, Japan

    N. Takeshima, K. Ozawa & N. Tsuboi

  2. Department of Mechanical Engineering, Aoyama Gakuin University, Sagamihara, Kanagawa, Japan

    A. K. Hayashi

  3. Institute of Fluid Science, Tohoku University, Sendai, Miyagi, Japan

    Y. Morii

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  1. N. Takeshima
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Correspondence to N. Tsuboi.

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Communicated by G. Ciccarelli.

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This paper is based on work that was presented at the 25th International Colloquium on the Dynamics of Explosions and Reactive Systems, Beijing, China, July 28–August 2, 2019.

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Takeshima, N., Ozawa, K., Tsuboi, N. et al. Numerical simulations on propane/oxygen detonation in a narrow channel using a detailed chemical mechanism: formation and detailed structure of irregular cells. Shock Waves 30, 809–824 (2020). https://doi.org/10.1007/s00193-020-00978-5

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