Mathematical Sciences: Nonlinear Dyamics in Combustion

[301635]研究者用数值方法研究燃烧过程中复杂时空模式的发展。这些模式与狭窄的反应区有关，其中因变量的快速变化发生在狭窄的空间区域。采用自适应伪谱法求解，在计算过程中引入坐标变换以更好地解析反应区和相关模式。他考虑了蜂窝火焰中调制行波（MTWs）的形成，不同类型MTWs之间的转换以及MTWs与混沌模式之间的转换，一步反应机制和多重反应机制，气体热膨胀对模式形成和演化的作用，以及凝聚相无气燃烧中时空模式的形成。他还进一步发展了数值方法来解释存在多个快速变化区域的问题。据观察，许多可燃混合物并不一定以统一的模式燃烧。相反，沿着火焰会出现波纹和其他图案。这种模式的形成被认为是从层流燃烧（燃烧以一种规则的、可预测的方式发生）到湍流燃烧（燃烧以一种不稳定的、看似随机的方式发生）过渡的一个重要阶段。了解过渡过程是控制过渡过程以提高燃烧效率的必要前提。在许多情况下，这些模式不能用分析方法预测，实验也远不如非反应流先进。在该项目中，研究者研究了燃烧中模式的形成和向湍流过渡的问题。该项目使用超级计算机计算来研究这些图案的形成及其背后的物理机制。这项研究既涉及气体燃烧，即燃烧化石燃料，也涉及固体直接燃烧的无气体燃烧。最后一种方法用于合成材料，特别是高级陶瓷和金属合金。

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.