Mathematical Sciences: The Modulation of Flames of Various Types in a Premixed Reactive Atmosphere

9403798稳定的一维预混火焰(或“爆燃波”)，涉及高度活跃的反应，可根据其传播马赫数进行分类，不同马赫数的火焰具有不同的数学结构。然而，在实践中，大多数火焰在空间上是狭窄的，并根据它们传播的当地环境不断地调整它们的速度和形状。该项目的目的是澄清有关不同类型火焰的非稳定和非平面传播的一些悬而未决的问题。它们是由一个耦合的非线性偏微分方程组，即。反应性的Navier-Stokes方程，其近似解将通过(I)系统地使用渐近和摄动方法来识别显著或显著的极限，以及(Ii)数值方法来寻求。稳定的一维火焰可以根据其传播速度进行分类，不同速度的火焰具有不同的数学结构。然而，在实践中，大多数火焰在空间上是狭窄的，并根据它们所经过的环境不断地调整它们的速度和形状。该项目的目的是解决有关不同类型火焰的不稳定和非平面传播的一些悬而未决的问题。具体而言，(1)应建立可扑灭自由传播的低速火焰或发展成高速爆震波的环境，以及(2)应澄清决定这些事件发生的不同方式的机制。这可应用于各种不同环境下燃烧现象的控制和安全。

9403798 Booty Steady, one-dimensional, premixed flames (or "deflagration waves") involving reactions that are highly activated can be categorized by their propagation Mach number, with flames of different Mach number having a different mathematical structure. In practice, however, most flames are spatially narrow and continually adjust both their speed and shape in accordance with the local environment through which they travel. The aim of the project is to clarify some of the outstanding issues regarding the unsteady and nonplanar propagation of different types of flames. These are governed by a coupled system of nonlinear partial differential equations, viz. the reactive Navier-Stokes equations, of which approximate solutions will be sought by (i) the systematic use of asymptotic and perturbation methods, for identifying significant or distinguished limits, and (ii) numerical methods. Steady, one-dimensional flames can be categorized by their propagation speed, with flames of different speed having a different mathematical structure. In practice, however, most flames are spatially narrow and continually adjust both their speed and shape in accordance with the environment through which they travel. The aim of the project is to address some of the outstanding issues regarding the unsteady and nonplanar propagation of different types of flame. In particular, (i) circumstances should be established under which a freely propagating, low-speed flame can either be extinguished or develop into a high-speed detonation wave, and (ii) the mechanism determining the different ways in which these events can occur should be clarified. This has applications to the control and safety of combustion phenomena in various different contexts.