Detonation is a supersonic mode of combustion that is modeled by a system of conservation laws of compressible fluid mechanics coupled with the equations describing thermodynamic and chemical properties of the fluid. Mathematically, these governing equations admit steady-state travelling-wave solutions consisting of a leading shock wave followed by a reaction zone. However, such solutions are often unstable to perturbations and rarely observed in laboratory experiments.
The goal of this work is to study the stability of travelling-wave solutions of detonation models by the following novel approach. We linearize the governing equations about a base travelling-wave solution and solve the resultant linearized problem using high-order numerical methods. The results of these computations are postprocessed using dynamic mode decomposition to extract growth rates and frequencies of the perturbations and predict stability of travelling-wave solutions to infinitesimal perturbations.
We apply this approach to two models based on the reactive Euler equations for perfect gases. For the first model with a one-step reaction mechanism, we find agreement of our results with the results of normal-mode analysis. For the second model with a two-step mechanism, we find that both types of admissible travelling-wave solutions exhibit the same stability spectra.
Then we investigate the Fickett’s detonation analogue coupled with a particular reaction-rate expression. In addition to the linear stability analysis of this model, we demonstrate that it exhibits rich nonlinear dynamics with multiple bifurcations and chaotic behavior.
| Identifer | oai:union.ndltd.org:kaust.edu.sa/oai:repository.kaust.edu.sa:10754/628016 |
| Date | 03 June 2018 |
| Creators | Kabanov, Dmitry |
| Contributors | Kasimov, Aslan R., Tzavaras, Athanasios, Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division, Ketcheson, David I., Samtaney, Ravi, Rosales, Rodolfo Rubén |
| Source Sets | King Abdullah University of Science and Technology |
| Language | English |
| Detected Language | English |
| Type | Dissertation |
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