Modelling and solutions to the linear stability of a detonation wave in the kinetic frame

Abstract

The analysis of linear stability of a steady detonation wave is formulated for the first time at the kinetic level in the frame of the Boltzmann equation extended to reacting gases. Within this context and for a reversible reaction, the stability problem is carried out, in agreement with most classical papers on gas detonation, through a normal mode approach for the one-dimensional disturbances of the steady wave solution, and an acoustic radiation condition at the final equilibrium as closure condition. The proposed modelling leads to an initial value problem, constituted by the linearized reactive Euler equations in the perturbed shock frame with related Rankine-Hugoniot conditions, which can be solved by means of a proper numerical technique. An application is provided for an elementary bimolecular reaction.

Keywords:

• Boltzmann equation
• chemical reactions
• detonation solution
• linear stability

AMS Subject Classification::

• 35B35
• 76P05
• 80A32
• 82C40
• 76P05

Acknowledgements

The authors are grateful to Prof. R. Monaco for his precious help in the numerical simulations. The paper is partially supported by INDAM-GNFM and CMAT-FCT Minho University.