Set-valued solutions for non-ideal detonation
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Author(s)
Semenko, R.
Kasimov, A. R.
Ermolaev, B. S.
Faria, Luiz
Date Issued
December 2015
Journal
Shock Waves
Publisher
Springer Berlin Heidelberg
Citation
Semenko, R., L. M. Faria, A. R. Kasimov, and B. S. Ermolaev. “Set-Valued Solutions for Non-Ideal Detonation.” Shock Waves 26, no. 2 (December 11, 2015): 141–160.
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Author's final manuscript
Abstract
The existence and structure of a steady-state gaseous detonation propagating in a packed bed of solid inert particles are analyzed in the one-dimensional approximation by taking into consideration frictional and heat losses between the gas and the particles. A new formulation of the governing equations is introduced that eliminates the difficulties with numerical integration across the sonic singularity in the reactive Euler equations. With the new algorithm, we find that when the sonic point disappears from the flow, there exists a one-parameter family of solutions parameterized by either pressure or temperature at the end of the reaction zone. These solutions (termed “set-valued” here) correspond to a continuous spectrum of the eigenvalue problem that determines the detonation velocity as a function of a loss factor.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.1007/s00193-015-0610-3
