Mathematical Sciences: Nonlinear Dyamics in Combustion

9301635研究人员贝利斯对燃烧中复杂的空间和时间模式的发展进行了数值研究。这些模式与狭窄的反应区相关联，在狭窄的空间区域中，因变量发生快速变化。解是用自适应伪谱方法得到的，在计算过程中引入了坐标变换，以更好地分辨反应区和相关的模式。他考虑了蜂窝火焰中调制行波的形成，不同类型调制行波之间的转变以及调制行波与混沌模式之间的转变，一步反应和多反应机制，气体的热膨胀对模式的形成和演化的作用，以及凝聚相无气燃烧中空间和时间模式的形成。他还进一步发展了数值方法，以解决存在多个快速变化区域的问题。已经观察到，许多可燃混合物不一定以单一形式燃烧。相反，涟漪和其他图案可能会沿着火焰发生。这种模式的形成被认为是从层流燃烧(燃烧以规则的、可预测的方式发生)向湍流燃烧(燃烧以不稳定的、看似随机的方式发生)过渡的重要阶段。对过渡过程的了解是控制过渡过程以实现更有效燃烧的基本前提。在许多情况下，这些模式不能用分析方法来预测，并且实验远不如无反应流动的先进。在该项目中，研究人员研究了燃烧中花纹的形成和向湍流的转变问题。该项目使用超级计算机计算来研究这些模式的形成以及它们背后的物理机制。这项研究既与气体燃烧有关，也与化石燃料的燃烧有关，也与固体直接燃烧的无气体燃烧有关。最后一种工艺用于材料的合成，特别是先进陶瓷和金属合金的合成。

9301635 Bayliss The investigator numerically studies the development of complex spatial and temporal patterns in combustion. These patterns are associated with narrow reaction zones in which rapid changes in the dependent variables occur across narrow spatial regions. The solutions are obtained using an adaptive pseudo-spectral method in which coordinate transformations are introduced during the course of the computation to better resolve the reaction zone and the associated patterns. He considers the formation of modulated traveling waves (MTWs) in cellular flames, transitions between different types of MTWs and transitions between MTWs and chaotic patterns, one-step and multiple reaction mechanisms, the role of thermal expansion of the gas on the formation and evolution of the patterns, and the formation of spatial and temporal patterns in condensed phase gasless combustion. He also further develops the numerical method to account for problems where there are multiple regions of rapid variation. It has been observed that many combustible mixtures do not necessarily burn in a unifrom pattern. Rather, ripples and other patterns can occur along the flame. The formation of such patterns is believed to be an important stage in the transition from laminar combustion (in which the burning occurs in a regular, predictable manner) to turbulent combustion (in which the burning occurs in an erratic, seemingly random fashion). An understanding of the transition process is an essential prerequisite to control of the transition process to lead to more efficient burning. In many instances these patterns can not be predicted by analytic means and experiments are much less advanced than for nonreacting flows. In the project, the investigator studies the problem of the formation of patterns and the transition to turbulence in combustion. The project uses supercomputer computations to study the formation of these patterns and the physical mechanisms underly ing them. The study relates both to gaseous combustion, i.e., the burning of fossil fuels, and gasless combustion, in which a solid burns directly. The last process is employed in the synthesis of materials, in particular of advanced ceramics and metallic alloys.