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.

小行星9301635 研究人员数值研究燃烧中复杂的空间和时间模式的发展。 这些模式与狭窄的反应区相关，其中因变量的快速变化发生在狭窄的空间区域。 使用自适应伪谱方法获得的解决方案，其中在计算过程中引入坐标变换，以更好地解决反应区和相关的图案。 他认为调制行波（MTWs）在细胞火焰的形成，不同类型的MTWs之间的过渡和MTWs和混沌模式之间的过渡，一步和多个反应机制，气体的热膨胀对模式的形成和演变的作用，以及在凝聚相无气燃烧的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均匀的模式燃烧。 相反，波纹和其他图案可以沿着火焰沿着发生。 这种模式的形成被认为是从层流燃烧（其中燃烧以规则的、可预测的方式发生）到湍流燃烧（其中燃烧以不稳定的、看似随机的方式发生）的过渡中的重要阶段。 了解过渡过程是控制过渡过程以实现更有效燃烧的必要先决条件。 在许多情况下，这些模式不能预测的分析手段和实验是先进得多的比无反应流。 在该项目中，研究人员研究了燃烧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。 该研究涉及气体燃烧，即，化石燃料的燃烧和固体直接燃烧的无气燃烧。 最后一种工艺用于材料的合成，特别是高级陶瓷和金属合金的合成。