Type
DissertationAuthors
Kabanov, Dmitry
Advisors
Kasimov, Aslan R.
Tzavaras, Athanasios

Committee members
Ketcheson, David I.
Samtaney, Ravi

Rosales, Rodolfo Rubén
Date
2018-06-03Permanent link to this record
http://hdl.handle.net/10754/628016
Metadata
Show full item recordAbstract
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.Citation
Kabanov, D. (2018). Numerical Computation of Detonation Stability. KAUST Research Repository. https://doi.org/10.25781/KAUST-F4I7Fae974a485f413a2113503eed53cd6c53
10.25781/KAUST-F4I7F