Mathematical Sciences: Nonlinear Dyamics in Combustion

数学科学：燃烧中的非线性动力学

• 批准号: 9301635
• 负责人: Alvin Bayliss
• 金额: $ 6.78万
• 依托单位: Northwestern University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1994
• 资助国家: 美国
• 起止时间: 1994-07-15 至 1998-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9301635&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Nonlinear; Dyamics; Combustion

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.

9301635 Bayliss研究者在数值上研究了燃烧中复杂的时空模式的发展。 这些模式与狭窄的反应区域有关，在狭窄的空间区域之间发生因变量的快速变化。 使用自适应伪谱法获得了溶液，其中在计算过程中引入了坐标转换，以更好地解决反应区和相关模式。 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. 他还进一步开发了数值方法，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会以纯模式燃烧。 相反，涟漪和其他模式可以沿火焰发生。 人们认为，这种模式的形成是从层流燃烧的过渡（以常规，可预测的方式发生燃烧）到湍流燃烧的重要阶段（其中以不稳定的，看似随机的方式发生燃烧）。 对过渡过程的理解是控制过渡过程以导致更有效燃烧的基本先决条件。 在许多情况下，这些模式无法通过分析手段来预测，实验比非反射流的先进得多。 在项目中，研究人员研究了形成模式的问题以及燃烧中湍流的过渡。 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的物理机制。 该研究均与气态燃烧有关，即化石燃料的燃烧和无气燃烧，其中固体直接燃烧。 最后一个过程用于材料的合成，特别是高级陶瓷和金属合金。