Tackling Combustion Instability in Low-Emission Energy Systems: Mathematical Modelling, Numerical Simulations and Control Algorithms

燃烧不稳定性的特征是燃烧室内压力的大幅波动，这对高性能、低排放能源系统（如燃气轮机）的设计者来说是一个重大挑战。这种不稳定性是由于声学、热释放和传递以及流体力学之间复杂的相互作用而产生的，这些相互作用发生在巨大的时间/长度尺度上。过去，相互作用的各个方面都是孤立地建模的，而且往往是基于经验的。先进的数学技术，匹配渐近展开技术和多尺度方法，提供了一种自洽和系统的方式来处理这种多物理现象的手段。利用这种方法，最近推导出了一种适用于所谓波纹小火焰状态的第一原理火焰-声相互作用理论。理论中的简化体系得到了燃烧不稳定的关键机理，但在计算上要容易得多。在目前提出的项目中，将首先扩展火焰-声相互作用理论，以解释一般外部施加的扰动的影响。一个更一般的渐近理论将在所谓的薄反应区体系中形成。数值算法求解渐近约化系统将发展。原则上，渐近理论和数值方法提供了预测燃烧不稳定开始的有效工具。该方法的保真度将通过精确的直接数值模拟（DNS）来评估。它将应用于与重要实验有关的情况，以预测一些显著的现象，如自持振荡、压力振荡引起的火焰稳定、压力和/或焓波动引起的参数不稳定以及混沌火焰的发生。理论模型将被用于通过调节燃料率来开发有效的主动控制燃烧不稳定性，并且设计的控制器的有效性和鲁棒性将通过使用渐近模型以及反应流的基本方程进行仿真来测试。

Combustion instability is characterized by large-amplitude pressure fluctuations in combustion chambers, and it presents a major challenge for the designer of high-performance, low-emission energy systems such as gas turbines. The instability arises due to complex interactions among acoustics, heat release and transport, and hydrodynamics, which occur over a huge span of time/length scales. In the past, various aspects of the interaction were modelled in isolation, and often on an empirical basis. Advanced mathematical techniques, matched asymptotic expansion technique and multiple-scale methods, provide a means to tackle this multi-physical phenomenon in a self-consistent and systematical manner. By using this approach, a first-principle flame-acoustic interaction theory, valid in the so-called corrugated flamelet regime, has been derived recently. The reduced system in the theory ratains the key mechanisms of combustions instability but is much more tractable computationally. In the present proposed project, the flame-acoustic interaction theory will be extended first to account for the influence of a general externally imposed perturbation. A more general asymptotic theory will be formulated in the so-called thin-reaction-zone regime. Numerical algorithms to solve the asymptotically reduced systems will be developed. The asymptotic theories and numerical methods provide, in principle, an efficient tool for predicting the onset of combustion instability. The fidelity of this approach will be assessed by accurate direct numerical simulations (DNS). It will be applied to the situations pertaining to important experiments in order to predict a number of remarkable phenomena, such as self-sustained oscillations, flame stabilization by pressure oscillations, parametric instability induced by pressure and/or enthalpy fluctuations and onset of chaotic flames. The theoretical models will be employed to develop effective active control of combustion instability by modulating fuel rate, and the effectiveness and robustness of the controllers designed will be tested by simulations using the asymptotic models as well as the fundamental equations for reacting flows.