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The role of global curvature on the structure and propagation of weakly unstable cylindrical detonations

  • Wenhu Han (a1), Wenjun Kong (a1) (a2), Yang Gao (a3) and Chung K. Law (a3) (a4)

Abstract

The role of the global curvature on the structure and propagation of cylindrical detonations is studied allowing and without allowing the development of cellular structures through two-dimensional (2-D) and 1-D simulations, respectively. It is shown that as the detonation transitions from being overdriven to the Chapman–Jouguet (CJ) state, its structure evolves from no cell, to growing cells and then to diverging cells. Furthermore, the increased dimension of the average structure of the cellular cylindrical detonation, coupled with the curved transverse wave, leads to bulk un-reacted pockets as the cells grow, and consequently lower average propagation velocities as compared to those associated with smooth fronts. As the global detonation front expands and its curvature decreases, the extent of the un-reacted pockets diminishes and the average velocity of the cellular cylindrical detonation eventually degenerates to that of the smooth fronts. Consequently, the presence of cellular instability renders detonation more difficult to initiate for weakly unstable detonations.

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Corresponding author

Email addresses for correspondence: wjkong@iet.cn, cklaw@princeton.edu

References

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Alpert, R. L. & Toong, T. Y. 1972 Periodicity in exothermic hypersonic flows about blunt projectiles. Acta Astron. 17, 539560.
Arienti, M. & Shepherd, J. E. 2005 The role of diffusion at shear layer in irregular detonations. In The Fourth Joint Meeting of the US Sections of the Combustion Institute, Philadelphia, PA, March, vol. 182, pp. 2023.
Asahara, M., Tsuboi, N. & Hayashi, A. K. 2010 Two-dimensional simulation on propagation mechanism of H2/O2 cylindrical detonation with a detailed reaction model: influence of initial energy and propagation. Combust. Sci. Technol. 182, 18841900.
Balsara, D. S. & Shu, C. W. 2000 Monotonicity preserving weighted essentially non-oscillatory schemes with increasingly high order of accuracy. J. Comput. Phys. 160, 405452.
Bourlioux, A. & Majda, A. J. 1992 Theoretical and numerical structure for unstable two-dimensional detonations. Combust. Flame 90, 211229.
Clavin, P. & Denet, B. 2002 On the direct initiation of gaseous detonations by an energy source. Phys. Rev. Lett. 88, 044502.
Clavin, P. & Williams, F. A. 2012 Analytical studies of the dynamics of gaseous detonations. Phil. Trans. R. Soc. Lond. A 370, 597624.
Deledicque, V. & Papalexandris, M. V. 2006 Computational study of three-dimensional gaseous detonation structures. Combust. Flame 144, 821837.
Eckett, C. A., Quirk, J. J. & Shepherd, J. E. 2000 The role of unsteadiness in direct initiation of gaseous detonations. J. Fluid Mech. 421, 147183.
Faria, L. & Kasimov, A. R. 2015 Qualitative modeling of the dynamics of detonations with losses. Proc. Combust. Inst. 35, 20152023.
Gamezo, V. N., Desbordes, D. & Oran, E. S. 1999 Formation and evolution of two-dimensional cellular detonations. Combust. Flame 116, 154165.
Han, W., Gao, Y. & Law, C. K. 2015 Coupled pulsating and cellular structure in the propagation of globally planar detonations in free space. Phys. Fluids 27, 106101.
He, L. 1996 Theoretical determination of the critical conditions for the direct initiation of detonations in hydrogen-oxygen mixtures. Combust. Flame 104, 401418.
He, L. & Clavin, P. 1994 On the direct initiation of gaseous detonations by an energy source. J. Fluid Mech. 277, 227248.
Henrick, A. K., Aslam, T. D. & Powers, J. M. 2006 Simulations of pulsating one-dimensional detonations with true fifth order accuracy. J. Comput. Phys. 213, 311329.
Jiang, G. S. & Shu, C. W. 1996 Efficient implementation of weighted ENO schemes. J. Comput. Phys. 126, 202228.
Jiang, Z. L., Han, G. L., Wang, C. & Zhang, F. 2009 Self-organized generation of transverse waves in diverging cylindrical detonations. Combust. Flame 156, 16531661.
Kasimov, A. R. & Stewart, D. S. 2005 Asymptotic theory of evolution and failure of self-sustained detonations. J. Fluid Mech. 525, 161192.
Kessler, D. A., Gamezo, V. N. & Oran, E. S. 2011 Multilevel detonation cell structures in methane-air mixtures. Proc. Combust. Inst. 33, 22112218.
Law, C. K. 2006 Combustion Physics. Cambridge University Press.
Lee, J. H. S. 2008 The Detonation Phenomenon. Cambridge University Press.
Lee, J. H., Knystautas, R., Guirao, C., Bekesy, A. & Sabbagh, S. 1972 On the instability of H2-Cl2 gaseous detonations. Combust. Flame 18, 321325.
Lee, H. I. & Stewart, D. S. 1990 Calculation of linear detonation instability: one-dimensional instability of plane detonation. J. Fluid Mech. 216, 103132.
Mahmoudi, Y. & Mazaheri, K. 2011 High resolution numerical simulation of the structure of 2-D gaseous detonations. Proc. Combust. Inst. 33, 21872194.
Mahmoudi, Y. & Mazaheri, K. 2012 Triple point collision and hot spots in detonations with regular structure. Combust. Sci. Technol. 184, 11351151.
Mahmoudi, Y. & Mazaheri, K. 2015 High resolution numerical simulation of triple point collision and origin of unburned gas pockets in turbulent detonations. Acta Astron. 115, 4051.
Mahmoudi, Y., Mazaheri, K. & Parvar, S. 2013 Hydrodynamic instabilities and transverse waves in propagation mechanism of gaseous detonations. Acta Astron. 91, 263282.
Mazaheri, K., Mahmoudi, Y. & Radulescu, M. I. 2012 Diffusion and hydrodynamic instabilities in gaseous detonations. Combust. Flame 159, 21382154.
McVey, J. B. & Toong, T. Y. 1971 Mechanism of instabilities of exothermic hypersonic blunt-body flows. Combust. Sci. Technol. 3, 6376.
Ng, H. D., Higgins, A. J., Kiyanda, C. B., Radulescu, M. I., Lee, J. H. S., Bates, K. R. & Nikiforakis, N. 2005 Nonlinear dynamics and chaos analysis of one-dimensional pulsating detonations. Combust. Theor. Model. 9, 159170.
Ng, H. D., Kiyanda, C. B., Morgan, G. H. & Nikiforakis, N. 2015 The influence of high-frequency instabilities on the direct initiation of two dimensional gaseous detonations. In 25th International Colloquium on the Dynamics of Explosions and Reactive Systems, August 2C7, Leeds, UK.
Ng, H. D. & Lee, J. H. S. 2003 Direct initiation of detonation with a multi-step reaction scheme. J. Fluid Mech. 476, 179211.
Ng, H. D., Radulescu, M. I., Higgins, A. J., Nikiforakis, N. & Lee, J. H. S. 2005 Numerical investigation of the instability for one-dimensional Chapman–Jouguet detonations with chain-branching kinetics. Combust. Theor. Model. 9, 385401.
Oran, E. S., Weber, J. R., Stefaniw, E. I., Lefebvre, M. H. & Anderson, J. D. 1998 A numerical study of a two-dimensional H2-O2-Ar detonation using a detailed chemical reaction model. Combust. Flame 113, 147163.
Qi, C. & Chen, Z. 2016 Effects of temperature perturbation on direct detonation initiation. Proc. Combust. Inst. (in press).
Radulescu, M. I. & Lee, J. H. S. 2002 The failure mechanism of gaseous detonations: experiments in porous wall tubes. Combust. Flame 131, 2946.
Radulescu, M. I., Sharpe, G. J. & Law, C. K. 2007a Effect of cellular instabilities on the blast initiation of weakly unstable detonations. In 20th International Colloquium on the Dynamics of Explosions and Reactive Systems.
Radulescu, M. I., Sharpe, G. J., Law, C. K. & Lee, J. H. S. 2007b The hydrodynamic structure of unstable cellular detonations. J. Fluid Mech. 580, 3181.
Radulescu, M. I., Sharpe, G. J., Lee, J. H. S., Kiyanda, C. B., Higgins, A. J. & Hanson, R. K. 2005 The ignition mechanism in irregular structure gaseous detonations. Proc. Combust. Inst. 30, 18591867.
Sharpe, G. J. & Falle, S. A. E. G. 2000 Numerical simulations of pulsating detonations: I. Nonlinear stability of steady detonations. Combust. Theor. Model. 4, 557574.
Sharpe, G. J. & Radulescu, M. I. 2011 Statistical analysis of cellular detonation dynamics from numerical simulations: one-step chemistry. Combust. Theor. Model. 15, 619723.
Soloukhin, R. I. 1966 Multiheaded structure of gaseous detonation. Combust. Flame 10, 5158.
Short, M. 2001 A nonlinear evolution equation for pulsating Chapman–Jouguet detonations with chain-branching kinetics. J. Fluid Mech. 430, 381430.
Short, M., Kapila, A. K. & Quirk, J. J. 1999 The chemical-gas dynamic mechanisms of pulsating detonation wave instability. Philos. Trans. R. Soc. Lond. A 357, 36213637.
Short, M. & Stewart, D. S. 1998 Cellular detonation stability. Part 1. A normal-mode linear analysis. J. Fluid Mech. 368, 229262.
Shu, C. W. & Osher, S. 1988 Efficient implementation of essentially non-oscillatory shock-capturing schemes. J. Comput. Phys. 77, 439471.
Sow, A., Chinnayya, A. & Hadjadj, A. 2014 Mean structure of one-dimensional unstable detonations with friction. J. Fluid Mech. 743, 503533.
Vasil’ev, A. A. & Trotsyuk, A. V. 2003 Experimental investigation and numerical simulation of an expanding multifront detonation wave. Combust. Explos. Shock Waves 39, 8090.
Vasil’ev, A. A., Vasiliev, V. A. & Trotsyuk, A. V. 2010 Bifurcation structures in gas detonation. Combust. Explos. Shock Waves 46, 196206.
Wang, C., Shu, C. W., Han, W. & Ning, J. 2013 High resolution WENO simulation of 3D detonation waves. Combust. Flame 160, 447462.
Wang, C., Zhang, X., Shu, C. W. & Ning, J. 2012 Robust high order discontinuous Galerkin schemes for two-dimensional gaseous detonations. J. Comput. Phys. 231, 653665.
Watt, S. D. & Sharpe, G. J. 2003 One-dimensional linear stability of curved detonations. Proc. R. Soc. Lond. A 460, 25512568.
Watt, S. D. & Sharpe, G. J. 2005 Linear and nonlinear dynamics of cylindrically and spherically expanding detonation waves. J. Fluid Mech. 522, 329356.
Yao, J. & Stewart, D. S. 1996 On the dynamics of multi-dimensional detonation. J. Fluid Mech. 309, 225275.
Zhang, X. & Shu, C. W. 2012 Positivity-preserving high order finite difference WENO schemes for compressible Euler equations. J. Comput. Phys. 231, 22452258.
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The role of global curvature on the structure and propagation of weakly unstable cylindrical detonations

  • Wenhu Han (a1), Wenjun Kong (a1) (a2), Yang Gao (a3) and Chung K. Law (a3) (a4)

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