Characterizing energy growth during combustion instabilities: Singularvalues or eigenvalues?
Characterizing energy growth during combustion instabilities: Singularvalues or eigenvalues?
复制标题
表征燃烧不稳定期间的能量增长：奇异值还是特征值？
DOI：
10.1016/j.proci.2008.05.035
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发表时间：
2009
期刊：
影响因子：
--
通讯作者：
R. Sujith
中科院分区：
文献类型：
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作者：
S. Nagaraja;Kushal S. Kedia;R. Sujith
热声系统中的非正态性近年来受到广泛关注。研究表明，在非正态但经典线性稳定的系统中，小扰动在最终衰减之前会有显著的瞬态能量增长。这种增长发生在没有非线性效应的情况下。这种现象可以用控制线性算子的非正态性或系统特征向量的非正交性来解释。在本文中，我们研究了一般燃烧室的瞬态能量增长的各个方面，用流行的n -τ模型近似地描述了局部热释放。采用伽辽金技术简化了局部热源存在时管道内的控制声学方程，并给出了相应的边界条件。利用奇异值分解（SVD）计算瞬态能量增长。用奇异值分解作为工具来获得最大可能的能量放大和放大所需的最佳初始条件。讨论了无能量增长的充分必要条件。进行了参数分析，以突出系统参数对最大瞬态增长率的影响，并获得热声系统的稳定区域。
Non-normality in thermoacoustic systems has received attention recently. It has been shown that in a non-normal but classically linearly stable system, there can be significant transient energy growth of small perturbations before their eventual decay. This growth occurs in the absence of non-linear effects. This phenomenon can be explained by the non-normality of the governing linear operator or the non-orthogonality of the eigenvectors of the system. In this paper, we study various aspects of this transient energy growth for a general combustor, with localized heat release approximated by the popular n–τ model. Galerkin technique is used to simplify the governing acoustic equations in a duct in the presence of a localized heat source with appropriate boundary conditions. Singularvalue decomposition (SVD) is used to compute the transient energy growth. SVD is used as a tool to obtain the maximum possible energy amplification and the optimal initial conditions required for this amplification. The necessary and sufficient conditions for no energy growth are discussed. A parametric analysis is performed to highlight the effect of system parameters on the maximum transient growth rate and to obtain regions of stability of the thermoacoustic system.