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

稳定的、一维的、涉及高度激活反应的预混火焰（或“爆燃波”）可以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，并且根据它们所经过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定常和非平面传播的一些突出问题。这些由非线性偏微分方程的耦合系统控制，即反应性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寻找，以确定显著或可区分的极限，以及（ii）数值方法。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，并且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非定常和非平面传播的一些突出问题。特别是，(i)应确定自由传播的低速火焰可以熄灭或发展成高速爆震波的情况，以及（ii）应阐明决定这些事件发生的不同方式的机制。这适用于各种不同情况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.