Interactions between Multiple Unstable Transversal Modes in High-Frequency Thermoacoustic Systems

在过去，与吸气式预混燃烧系统中非紧凑、多维、高频热声振荡有关的线性和非线性动力学研究都是在单模假设下进行的。这意味着只存在一个控制极限环振荡的线性不稳定声学模式，而其他模式被假定为线性稳定且可以忽略不计。然而，这种单一模式的概念是值得怀疑的，特别是在相关燃烧室截止频率以外的高频区域，其中存在多个线性不稳定模式并相互作用。不考虑所有可能的不稳定模式将影响燃烧室的稳定和可靠运行。拟议的项目首次寻求建立对支配由多个不稳定模式组成的高频热声振荡的物理机制的基本理解。为此，一个实验室规模的、涡流稳定的预混燃烧室，其中高频区域的多个横模是线性不稳定的，作为基准系统。具体地说，该项目分为三个主要研究目标：第一个目标是揭示第二种横向模式的线性火焰驱动机理和非线性燃烧室动力学。这包括，除了对基本物理学的理解外，还包括开发适当的数学量化和模拟工具。在物理解释和建模方法方面，应通过第二个目标产生关于多个不稳定横模之间相互作用机制的具体知识。最后，第三个目标是开发和验证可靠的系统识别方法，以提取特别适用于多模式系统的相关热声参数(例如，线性增长率)。

In the past, linear and nonlinear dynamics related to non-compact, multi-dimensional, high-frequency thermoacoustic oscillations in air-breathing, premixed combustion systems have been investigated with a single mode assumption. This implies the existence of only one linearly unstable acoustic mode that governs the limit-cycle oscillations, while further modes are presumed as linearly stable and of negligible relevance. However, this single mode notion is questionable especially in the high-frequency regime beyond the concerned combustion chamber's cut-on frequency, where multiple linearly unstable modes exist and interact. A non-consideration of all possibly unstable modes would compromise a stable and reliable combustor operation. For the first time, the proposed project seeks to establish a fundamental understanding on physical mechanisms that govern high-frequency thermoacoustic oscillations constituted by multiple unstable modes. For this purpose, a lab-scale, swirl-stabilized, premixed combustor in which multiple transversal modes in the high-frequency regime are linearly unstable serves as a benchmark system. Specifically, the proposed project is divided into three main research objectives: The first one aims to unravel linear flame driving mechanisms and nonlinear combustor dynamics of the second transversal mode. This includes, besides understanding of principal physics, the development of appropriate mathematical quantification and simulation tools. Specific knowledge on interaction mechanisms between multiple unstable transversal modes in terms of physical explanations and modeling approaches shall be generated through the second objective. Finally, the third objective seeks to develop and validate reliable system identification methodologies to extract relevant thermoacoustic parameters (e.g. linear growth rates) that are particularly applicable to multi-modal systems.