Propagation of Fronts in Porous Media Combustion

本研究项目主要是对多孔介质中锋面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，揭示了多孔介质燃烧中的一些新效应和新机制，如低速(亚音速)爆轰、燃烧到爆轰的转变以及各种类型的不稳定性。本文研究了多孔介质中的燃烧模型，该模型由温度、贫化反应物浓度和压力的三个退化抛物线方程组成。该项目调查了燃烧锋面的长期行为、它们的稳定性以及传播速度的界限。稳定性将通过数值和分析工具的组合来探索。该项目还研究了所谓的高激活能极限，以及从缓慢传播的爆燃到爆轰的转变。预混气体燃烧是在点火前完全混合的气态反应物的燃烧。预混燃烧最显著的特点是它能够假定一个自持的反应锋面以亚音速或超音速以明确的速度传播。燃烧锋构成了一个真正令人着迷的动力系统，表现出令人惊叹的丰富的各种现象，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)，混沌的自运动和类分形增长，以及各种滞后转变。当前的项目是关于多孔介质中燃烧前沿动力学的数学分析，包括对传播速度、其极限、稳定性以及从爆燃到爆轰燃烧的转变的评估。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.