Set-valued solutions for non-ideal detonation

Roman Semenko, Luiz Faria, Aslan R. Kasimov, B. S. Ermolaev

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


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.
Original languageEnglish (US)
Pages (from-to)141-160
Number of pages20
JournalShock Waves
Issue number2
StatePublished - Dec 11 2015

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledgements: The research reported in this publication was supported by the King Abdullah University of Science and Technology (KAUST).


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