Hostname: page-component-586b7cd67f-dsjbd Total loading time: 0 Render date: 2024-11-23T03:11:11.403Z Has data issue: false hasContentIssue false
  • English
  • Français

The role of multidimensional instabilities in direct initiation of gaseous detonations in free space

Published online by Cambridge University Press:  20 January 2017

Hua Shen  and
Matteo Parsani
Hua Shen*
Affiliation:
King Abdullah University of Science and Technology (KAUST), Extreme Computing Research Center (ECRC), Computer, Electrical and Mathematical Sciences & Engineering (CEMSE), Thuwal, 23955-6900, Kingdom of Saudi Arabia
Matteo Parsani
Affiliation:
King Abdullah University of Science and Technology (KAUST), Extreme Computing Research Center (ECRC), Computer, Electrical and Mathematical Sciences & Engineering (CEMSE), Thuwal, 23955-6900, Kingdom of Saudi Arabia
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

We numerically investigate the direct initiation of detonations driven by the propagation of a blast wave into a unconfined gaseous combustible mixture to study the role played by multidimensional instabilities in direct initiation of stable and unstable detonations. To this end, we first model the dynamics of unsteady propagation of detonation using the one-dimensional compressible Euler equations with a one-step chemical reaction model and cylindrical geometrical source terms. Subsequently, we use two-dimensional compressible Euler equations with just the chemical reaction source term to directly model cylindrical detonations. The one-dimensional results suggest that there are three regimes in the direct initiation for stable detonations, that the critical energy for mildly unstable detonations is not unique, and that highly unstable detonations are not self-sustainable. These phenomena agree well with one-dimensional theories and computations available in the literature. However, our two-dimensional results indicate that one-dimensional approaches are valid only for stable detonations. In mildly and highly unstable detonations, one-dimensional approaches break down because they cannot take the effects and interactions of multidimensional instabilities into account. In fact, instabilities generated in multidimensional settings yield the formation of strong transverse waves that, on one hand, increase the risk of failure of the detonation and, on the other hand, lead to the initiation of local over-driven detonations that enhance the overall self-sustainability of the global process. The competition between these two possible outcomes plays an important role in the direct initiation of detonations.

JFM classification

Reacting Flows: Detonations Reacting Flows: Reacting Flows Compressible Flows: Shock waves
Type
Rapids
Information
Journal of Fluid Mechanics , Volume 813 , 25 February 2017 , R4
Check for updates
Copyright
© 2017 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Chang, S.-C. 1995 The method of space-time conservation element and solution element – a new approach for solving the Navier–Stokes and Euler equations. J. Comput. Phys. 119 (2), 295–324.CrossRefGoogle 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
Erpenbeck, J. J. 1967 Nonlinear theory of unstable one-dimensional detonations. Phys. Fluids 10, 274–288.Google Scholar
Fickett, W. & Davis, W. C. 1979 Detonation. University of California Press.Google Scholar
He, L. T. & Clavin, P. 1994 On the direct initiation of gaseous detonations by an energy source. J. Fluid Mech. 277, 227–248.Google Scholar
He, L. T. & Lee, J. H. S. 1995 The dynamical limit of one-dimensional detonations. Phys. Fluids 7 (5), 1151–1158.Google Scholar
Hwang, P., Fedkiw, R. P., Merriman, B., Aslam, T. D., Karagozian, A. R. & Osher, S. J. 2000 Numerical resolution of pulsating detonation waves. Combust. Sci. Technol. 4 (3), 217–240.Google Scholar
Kassoy, D. R. 2016 The Zel’dovich spontaneous reaction wave propagation concept in the fast/modest heating limits. J. Fluid Mech. 791, 439–463.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
Lee, J. H. S. 1977 Initiation of gaseous detonation. Annu. Rev. Phys. Chem. 28, 75–104.Google Scholar
Lee, J. H. S. 1984 Dynamic parameters of gaseous detonations. Annu. Rev. Fluid Mech. 16, 311–336.Google Scholar
Lee, H. I. & Stewart, D. S. 1990 Calculation of linear detonation instability: one-dimensional instability of plane detonation. J. Fluid Mech. 216, 103–132.Google Scholar
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, 40–51.Google Scholar
Mazaheri, K.1997 Mechanism of the onset of detonation in blast initiation. PhD thesis, McGill University, Montreal, Canada.Google Scholar
Mazaheri, K., Mahmoudi, Y. & Radulescu, M. I. 2012 Diffusion and hydrodynamic instabilities in gaseous detonations. Combust. Flame 159, 2138–2154.Google Scholar
Ng, H. D. & Lee, J. H. S. 2003 Direct initiation of detonation with a multi-step reaction scheme. J. Fluid Mech. 476, 179–211.Google Scholar
Oran, E. S. & Gamezo, V. N. 2007 Origins of the deflagration-to-detonation transition in gas-phase combustion. Combust. Flame 148, 4–47.Google Scholar
Qi, C. K. & Chen, Z. 2016 Effects of temperature perturbation on direct detonation initiation. Proc. Combust. Inst. doi:10.1016/j.proci.2016.06.093.Google Scholar
Radulescu, M. I., Higgins, A. J., Murray, S. B. & Lee, J. H. S. 2003 An experimental investigation of the direct initiation of cylindrical detonations. J. Fluid Mech. 480, 1–24.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., Kassoy, D. R., Aslani, M. & Vasilyev, O. V. 2016 Evolution of detonation formation initiated by a spatially disturbuted, transient energy source. J. Fluid Mech. 802, 305–332.Google Scholar
Shen, H. & Wen, C.-Y. 2016 A characteristic space-time conservation element and solution element method for conservation laws II. Multidimensional extension. J. Comput. Phys. 305, 775–792.CrossRefGoogle Scholar
Shen, H., Wen, C.-Y., Parsani, M. & Shu, C.-W. 2017 Maximum-principle-satisfying space-time conservation element and solution element scheme applied to compressible multifluids. J. Comput. Phys. 330, 668–692.CrossRefGoogle Scholar
Shen, H., Wen, C.-Y. & Zhang, D. L. 2015 A characteristic space-time conservation element and solution element method for conservation laws. J. Comput. Phys. 288, 101–118.Google Scholar
Zel’dovich, Y. B., Kogarko, S. M. & Simonov, N. N. 1956 An experimental investigation of spherical detonation of gases. Sov. Phys. Tech. Phys. 1 (8), 1689–1731.Google Scholar
Zel’dovich, Y. B., Librovich, V. B., Makhviladze, G. M. & Sivashinskil, G. I. 1970 On the onset of detonation in a nonuniformly heated gas. J. Appl. Mech. Tech. Phys. 11 (2), 264–270.Google Scholar