Consequences of non-normality and nonlinearity in flow / premixed flame / acoustic interactions for combustion instability

在具有非正态本征模的动力系统中，即使所有的模都是线性稳定的，模的相互作用也可以导致大的瞬时增长。在这种情况下，在低幅度扰动存在的情况下，可能会发生亚临界到不稳定的转变，经典的线性稳定性分析成为系统行为的糟糕指标。热声相互作用的非正常性质最近才被发现；到目前为止，对燃烧动力学的可能后果只在非常简单的理想化模型问题的背景下进行了探索。目前的建议旨在研究流动/预混火焰/声学相互作用中的非正规性和非线性，并开发相应的工具，有可能以定量的精度处理应用感兴趣的构型，例如湍流预混旋流火焰。建议从基于可压缩流动公式的“整体”方法开始，开发和验证各种耦合建模策略。整体方法在某种意义上是无模型的，应主要用于生成参考数据，因为它在计算上非常昂贵。耦合方法利用不可压缩模型进行流动/燃烧相互作用和随后的模型简化，效率要高得多。然而，它们的准确性，特别是在非正常影响方面，必须得到验证。这些模拟的结果将被用来开发能够捕获非正常和非线性影响的系统辨识方法。特别令人感兴趣的是火焰的内部动力学(对应于内部自由度)在热声演化中的作用。这涉及到波动能量的适当定义(从数学上讲：选择系统状态向量的“范数”)以及用于识别简化模型的适当模型结构的问题。对于后者，以下几点也很重要：根据渐近分析，流体动力流动/燃烧子模型中出现声学雷诺应力项。在识别火焰模型参数时，必须研究是否以及如何考虑这些项。应用互补的数值和实验工具以及分析方法进行热声稳定性分析，确保了协同效益。

In dynamical systems with non-normal eigenmodes, modal interactions can result in large transient growth even if all modes are linearly stable. Under such circumstances, subcritical transition to instability may occur in the presence of low-amplitude perturbations, and classical linear stability analysis becomes a poor indicator of system behaviour.The non-normal nature of thermo acoustic interactions has been identified only recently; possible consequences for combustion dynamics have until now been explored only in the context of very simple, idealized model problems. The current proposal aims to examine non-normality and nonlinearity in the context of flow / premixed flame / acoustic interactions, and to develop corresponding tools that have the potential to handle with quantitative accuracy also configurations of applied interest, e.g. turbulent premix swirl flames.It is proposed to proceed systematically: Starting from a “monolithic” approach based on a compressible flow formulation, a variety of coupled modelling strategies shall be developed and validated. The monolithic approach, which is in a sense model-free, shall be used primarily to generate reference data, as it is computationally very expensive. Coupled approaches, which make use of an incompressible model for the flow / combustion interaction and subsequent model reduction, are much more efficient. However, their accuracy in particular in regard to non-normal effects, must be validated.Results from these simulations will be used to develop methodologies for system identification that can capture non-normal and nonlinear effects. Of particular interest is the role of the internal dynamics (corresponding to internal degrees of freedom) of the flame in thermo acoustic evolution. This touches the question of the appropriate definition of fluctuation energy (mathematically speaking: the choice of “norm” of the system state vector) as well as the appropriate model structure for identification of reduced models. The following point is also important for the latter: according to asymptotic analysis, acoustic Reynolds stress terms appear in the hydrodynamic flow/combustion sub-model. It has to be investigated, if and how these terms should be considered in the identification of flame model parameters.The application of complementary numerical and experimental tools as well as analytical methods for thermo acoustic stability analysis ensures synergistic benefits.