Propagation of Fronts in Porous Media Combustion

该研究项目的重点是对多孔介质中波前的传播和稳定性进行数学分析。 该项目的动机是最近的理论进展，揭示了一些新的影响和制度，在多孔介质燃烧，如低速（亚音速）爆震，爆燃到爆震过渡，和各种类型的不稳定性。 本文研究了多孔介质中的燃烧模型，该模型由三个退化的抛物方程组成，分别是温度、缺陷反应物浓度和压力。 该项目研究了燃烧前沿的长期行为、其稳定性和传播速度的界限。 稳定性将通过数值和分析工具相结合来探索。 该项目还研究了所谓的高活化能极限，以及从缓慢传播的爆燃到爆炸的过渡。 预混气体燃烧是指在点火前完全混合的气体反应物的燃烧。 预混燃烧最显著的特点是它能够假定一个自持的反应前沿以一个明确的速度以亚音速或超音速传播。 燃烧锋构成了一个真正迷人的动力学系统，展示了令人惊讶的丰富多样的现象，如可能的传播机制的非唯一性，它们的诞生（点火）和毁灭（灭绝），混沌自运动和分形状增长，以及各种滞后过渡。 目前的项目涉及多孔介质中燃烧前沿动力学的数学分析，包括传播速度、极限、稳定性以及从爆燃到爆轰燃烧的过渡的评估。 研究结果对推进系统的工程设计具有潜在的应用价值。

This research project is focused on mathematical analysis of the propagation and stability of fronts in a porous medium. The project is motivated by recent theoretical advances that revealed a number of new effects and regimes in porous media combustion, such as low-velocity (subsonic) detonation, deflagration to detonation transitions, and various types of instabilities. This work studies a model for combustion in porous media consisting of three degenerate parabolic equations for temperature, concentration of the deficient reactant, and pressure. The project investigates the long-time behavior of the combustion fronts, their stability, and bounds on propagation velocity. Stability will be explored by a combination of numerical and analytical tools. The project also studies the so-called high activation energy limit, as well as the transition from slowly propagating deflagration to detonation. Premixed gas combustion is the combustion of gaseous reactants that are perfectly mixed prior to ignition. The most distinctive feature of premixed combustion is its ability to assume a self-sustained reaction front propagating subsonically or supersonically at a well-defined speed. Combustion fronts constitute a truly fascinating dynamical system, displaying an amazingly rich variety of phenomena, such as non-uniqueness of possible propagation regimes, their birth (ignition) and destruction (extinction), chaotic self-motion and fractal-like growth, and various hysteretic transitions. The current project is concerned with the mathematical analysis of combustion front dynamics in a porous medium, involving evaluation of the propagation velocity, its limits, stability, and the transition from deflagrative to detonative combustion. The results of the work have potential application to engineering design of propulsion systems.