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    Numerical Computation of Detonation Stability

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    Type
    Dissertation
    Authors
    Kabanov, Dmitry cc
    Advisors
    Kasimov, Aslan R. cc
    Tzavaras, Athanasios cc
    Committee members
    Ketcheson, David I. cc
    Samtaney, Ravi cc
    Rosales, Rodolfo Rubén
    Program
    Applied Mathematics and Computational Science
    KAUST Department
    Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
    Date
    2018-06-03
    Permanent link to this record
    http://hdl.handle.net/10754/628016
    
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    Abstract
    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-F4I7F
    DOI
    10.25781/KAUST-F4I7F
    ae974a485f413a2113503eed53cd6c53
    10.25781/KAUST-F4I7F
    Scopus Count
    Collections
    Applied Mathematics and Computational Science Program; Dissertations; Dissertations; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

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