A geometric singular perturbation analysis of detonation and deflagration waves
Abstract
The existence of steady plane wave solutions of the Navier-Stokes equations for a reacting gas is analyzed. Under the assumption of an ignition temperature the existence of detonation and deflagration waves close to the corresponding waves of the ZND-model is proved in the limit of small viscosity, heat conductivity, and diffusion. The method is constructive, since the classical solutions of the ZND-model serve as singular solutions in the context of geometric singular perturbation theory. The singular solutions consist of orbits on which the dynamics are slow-driven by chemical reaction and of orbits on which the dynamics are fast-driven by gasdynamic shocks. The approach is geometric and leads to a clear, complete picture of the existence, structure, and asymptotic behavior of detonation and deflagration waves.
- Publication:
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SIAM Journal of Mathematical Analysis
- Pub Date:
- July 1993
- Bibcode:
- 1993SJMA...24..968G
- Keywords:
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- Computational Fluid Dynamics;
- Deflagration;
- Detonation Waves;
- Navier-Stokes Equation;
- Perturbation Theory;
- Reacting Flow;
- Asymptotic Properties;
- Chemical Reactions;
- Conductive Heat Transfer;
- Gas Flow;
- Ignition Temperature;
- Traveling Waves;
- Fluid Mechanics and Heat Transfer