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Evolution of detonation formation initiated by a spatially distributed, transient energy source

Published online by Cambridge University Press:  04 August 2016

Jonathan D. Regele ,
David R. Kassoy ,
Mohamad Aslani  and
Oleg V. Vasilyev
Jonathan D. Regele*
Affiliation:
Department of Aerospace Engineering, Iowa State University, Ames, IA 50011, USA
David R. Kassoy
Affiliation:
Department of Mechanical Engineering, University of Colorado, Boulder, CO 80309, USA
Mohamad Aslani
Affiliation:
Department of Aerospace Engineering, Iowa State University, Ames, IA 50011, USA
Oleg V. Vasilyev
Affiliation:
Department of Mechanical Engineering, University of Colorado, Boulder, CO 80309, USA
*
†Email address for correspondence: [email protected]
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Abstract

Detonations usually form through either direct initiation or deflagration-to-detonation transition (DDT). In this work, a detonation initiation process is introduced that shows attributes from each of these two processes. Energy is deposited into a finite volume of fluid in an amount of time that is similar to the acoustic time scale of the heated fluid volume. Two-dimensional simulations of the reactive Euler equations are used to solve for the evolving detonation initiation process. The results show behaviour similar to both direct initiation and DDT. Localized reaction transients are shown to be intimately related to the appearance of a detonation. Thermomechanical concepts are used to provide physical interpretations of the computational results in terms of the interaction between compressibility phenomena on the acoustic time scale and localized, spatially resolved, chemical energy addition on a heat-addition time scale.

JFM classification

Reacting Flows: Combustion Compressible Flows: Compressible Flows Compressible Flows: Detonation waves
Type
Papers
Information
Journal of Fluid Mechanics , Volume 802 , 10 September 2016 , pp. 305 - 332
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Copyright
© 2016 Cambridge University Press 

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References

Austin, J. M., Pintgen, F. & Shepherd, J. E. 2005 Reaction zones in highly unstable detonations. Proc. Combust. Inst. 30 (2), 1849–1857.Google Scholar
Clarke, J. F. 1985 The mathematics of combustion. In Frontiers in Applied Mathematics (ed. Buckmaster, J. D.), p. 260. Society for Industrial and Applied Mathematics.Google Scholar
Clarke, J. F., Kassoy, D. R., Meharzi, N. E., Riley, N. & Vasantha, R. 1990 On the evolution of plane detonations. Proc. R. Soc. Lond. A 429, 259–283.Google Scholar
Clarke, J. F., Kassoy, D. R. & Riley, N. 1986 On the direct initiation of a plane detonation wave. Proc. R. Soc. Lond. A 408, 129–148.Google Scholar
Deiterding, R. 2009 A parallel adaptive method for simulating shock-induced combustion with detailed chemical kinetics in complex domains. Comput. Struct. 87 (11–12), 769–783.Google Scholar
Dorofeev, S. B. 2011 Flame acceleration and explosion safety applications. Proc. Combust. Inst. 33 (2), 2161–2175.Google Scholar
Eckett, C. A., Quirk, J. J. & Shepherd, J. E. 2000 The role of unsteadiness in direct initiation of gaseous detonations. J. Fluid Mech. 421, 147–183.Google Scholar
Fryxell, B., Olson, K., Ricker, P., Timmes, F. X., Zingale, M., Lamb, D. Q., Macneice, P., Rosner, R., Truran, J. W. & Tufo, H. 2000 FLASH: An adaptive mesh hydrodynamics code for modeling astrophysical thermonuclear flashes. Astrophys. J. Suppl Ser. 131, 273–334.CrossRefGoogle Scholar
Gamezo, V. N., Desbordes, D. & Oran, E. S. 1999 Formation and evolution of two-dimensional cellular detonations. Combust. Flame 116 (1–2), 154–165.Google Scholar
Gamezo, V. N., Khokhlov, A. M. & Oran, E. S. 2001 The influence of shock bifurcations on shock-flame interactions and DDT. Combust. Flame 126 (4), 1810–1826.Google Scholar
Gamezo, V. N., Ogawa, T. & Oran, E. S. 2008 Flame acceleration and DDT in channels with obstacles: effect of obstacle spacing. Combust. Flame 155 (1–2), 302–315.Google Scholar
Ivanov, M., Kiverin, A. & Liberman, M. 2011 Hydrogen-oxygen flame acceleration and transition to detonation in channels with no-slip walls for a detailed chemical reaction model. Phys. Rev. E 83 (5), 1–16.Google Scholar
Kassoy, D. R. 2010 The response of a compressible gas to extremely rapid transient, spatially resolved energy addition: an asymptotic formulation. J. Engng Maths 68 (3–4), 249–262.Google Scholar
Kassoy, D. R. 2014a Mechanical disturbances arising from thermal power deposition in a gas. AIAA J. 52 (10), 2328–2335.Google Scholar
Kassoy, D. R. 2014b Non-diffusive ignition of a gaseous reactive mixture following time-resolved, spatially distributed energy deposition. Combust. Theor. Model. 18 (1), 1–16.CrossRefGoogle Scholar
Kassoy, D. R. 2016 The Zeldovich spontaneous reaction wave propagation concept in the fast/modest heating limits. J. Fluid Mech. 791, 439–463.CrossRefGoogle Scholar
Kassoy, D. R., Kuehn, J. A., Nabity, M. W. & Clarke, J. F. 2008 Detonation initiation on the microsecond time scale: DDTs. Combust. Theor. Model. 12 (6), 1009–1047.Google Scholar
Kessler, D. A., Gamezo, V. N. & Oran, E. S. 2010 Simulations of flame acceleration and deflagration-to-detonation transitions in methane-air systems. Combust. Flame 157 (11), 2063–2077.Google Scholar
Kevlahan, N. K. R. & Vasilyev, O. V. 2005 An adaptive wavelet collocation method for fluid-structure interaction at high Reynolds numbers. SIAM J. Sci. Comput. 26 (6), 1894–1915.Google Scholar
Khokhlov, A., Oran, E. & Thomas, G. 1999 Numerical simulation of deflagration-to-detonation transition: the role of shock-flame interactions in turbulent flames. Combust. Flame 117 (1–2), 323–339.Google Scholar
Khokhlov, A. M. & Oran, E. S. 1999 Numerical simulation of detonation initiation in a flame brush: the role of hot spots. Combust. Flame 119 (4), 400–416.Google Scholar
Kiyanda, C. B. & Higgins, A. J. 2013 Photographic investigation into the mechanism of combustion in irregular detonation waves. Shock Waves 23 (2), 115–130.Google Scholar
Kurtz, M. D. & Regele, J. D. 2014a Acoustic timescale characterisation of a one-dimensional model hot spot. Combust. Theor. Model. 18 (4–5), 532–551.Google Scholar
Kurtz, M. D. & Regele, J. D. 2014b Acoustic timescale characterization of symmetric and asymmetric multidimensional hot spots. Combust. Theor. Model. 18 (6), 711–729.Google Scholar
Laney, C. B. 1998 Computational Gasdynamics. Cambridge University Press.Google Scholar
Lee, J. H. S., Knystautas, R. & Yoshikawa, N. 1978 Photochemical initiation of gaseous detonations. Acta Astron. 5, 971–982.Google Scholar
Maley, L., Bhattacharjee, R., Lau-Chapdelaine, S. M. & Radulescu, M. I. 2015 Influence of hydrodynamic instabilities on the propagation mechanism of fast flames. Proc. Combust. Inst. 35 (2), 2117–2126.Google Scholar
Mazaheri, K., Mahmoudi, Y. & Radulescu, M. I. 2012 Diffusion and hydrodynamic instabilities in gaseous detonations. Combust. Flame 159 (6), 2138–2154.Google Scholar
Oppenheim, A. K., Kuhl, A. L., Lundstrom, E. A. & Kamel, M. M. 1972 A parametric study of self-similar blast waves. J. Fluid Mech. 52 (4), 657–682.Google Scholar
Oppenheim, A. K. & Soloukhin, R. I. 1973 Experiments in gasdynamics of explosions. Annu. Rev. Fluid Mech. 5, 31–58.Google Scholar
Oran, E. S. & Gamezo, V. N. 2007 Origins of the deflagration-to-detonation transition in gas-phase combustion. Combust. Flame 148 (1–2), 4–47.Google Scholar
Oran, E. S. & Khokhlov, A. M. 1999 Deflagrations, hot spots, and the transition to detonation. Phil. Trans. R. Soc. Lond. A 357 (1764), 3539–3551.CrossRefGoogle Scholar
Powers, J. 2006 Review of multiscale modeling of detonation. J. Propul. Power 22 (6), 1217–1229.CrossRefGoogle Scholar
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 (2), 1859–1867.CrossRefGoogle Scholar
Radulescu, M. I. & Maxwell, B. M. 2011 The mechanism of detonation attenuation by a porous medium and its subsequent re-initiation. J. Fluid Mech. 667, 96–134.Google Scholar
Radulescu, M. I., Sharpe, G. J., Law, C. K. & Lee, J. H. S. 2007 The hydrodynamic structure of unstable cellular detonations. J. Fluid Mech. 580, 31–81.Google Scholar
Regele, J. D.2008 Numerical modeling of acoustic timescale detonation initation using the adaptive wavelet-collocation method. PhD thesis, University of Colorado, Boulder.Google Scholar
Regele, J. D., Kassoy, D. R. & Vasilyev, O. V. 2012 Effects of high activation energies on acoustic timescale detonation initiation. Combust. Theor. Model. 16 (4), 650–678.Google Scholar
Regele, J. D. & Vasilyev, O. V. 2009 An adaptive wavelet-collocation method for shock computations. Intl J. Comput. Fluid Dyn. 23 (7), 503–518.Google Scholar
Romick, C. M., Aslam, T. D. & Powers, J. M. 2012 The effect of diffusion on the dynamics of unsteady detonations. J. Fluid Mech. 699, 453–464.Google Scholar
Romick, C. M., Aslam, T. D. & Powers, J. M. 2015 Verified and validated calculation of unsteady dynamics of viscous hydrogen-air detonations. J. Fluid Mech. 769, 154–181.Google Scholar
Roy, G. D., Frolov, S. M., Borisov, A. A. & Netzer, D. W. 2004 Pulse detonation propulsion: challenges, current status, and future perspective. Prog. Energy Combust. Sci. 30 (6), 545–672.Google Scholar
Seitenzahl, I. R., Meakin, C. A., Townsley, D. M., Lamb, D. Q. & Truran, J. W. 2009 Spontaneous initiation of detonations in white dwarf environments: determination of critical sizes. Astrophys. J. 696 (1), 515–527.CrossRefGoogle Scholar
Sileem, A. A., Kassoy, D. R. & Hayashi, A. K. 1991 Thermally initiated detonation through deflagration to detonation transition. Proc. R. Soc. Lond. A 435 (1895), 459–482.Google Scholar
Toro, E. F. 1999 Riemann Solvers and Numerical Methods for Fluid Dynamics, 2nd edn. Springer.Google Scholar
Vasilyev, O. V. & Bowman, C. 2000 Second-generation wavelet collocation method for the solution of partial differential equations. J. Comput. Phys. 165 (2), 660–693.Google Scholar
Zeldovich, Ya. B. 1980 Regime classification of an exothermic reaction with nonuniform initial conditions. Combust. Flame 39 (2), 211–214.CrossRefGoogle Scholar
Zhu, Y. J., Chao, J. & Lee, J. H. S. 2007 An experimental investigation of the propagation mechanism of critical deflagration waves that lead to the onset of detonation. Proc. Combust. Inst. 31, 2455–2462.Google Scholar
Ziegler, J. L., Deiterding, R., Shepherd, J. E. & Pullin, D. I. 2011 An adaptive high-order hybrid scheme for compressive, viscous flows with detailed chemistry. J. Comput. Phys. 230 (20), 7598–7630.Google Scholar