Quantification of Energy Transformation Processes Between Acoustic and Hydrodynamic Modes in Non-Compact Thermoacoustic Systems via a Helmholtz-Hodge Decomposition Approach
Quantification of Energy Transformation Processes Between Acoustic and Hydrodynamic Modes in Non-Compact Thermoacoustic Systems via a Helmholtz-Hodge Decomposition Approach
复制标题
通过亥姆霍兹-霍奇分解方法量化非紧凑热声系统中声学和流体动力模式之间的能量转换过程
DOI：
10.1115/gt2019-90240
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发表时间：
2019
期刊：
影响因子：
--
通讯作者：
T. Sattelmayer
中科院分区：
文献类型：
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作者：
T. Hofmeister;T. Hummel;B. Schuermans;T. Sattelmayer
线性化欧拉方程（LEE）的解由声学型、熵型和涡旋型摄动组成。后者的激励可以由声学转化为旋转能量引起，而旋转能量来源于声学与平均流动剪切层之间的相互作用。这被称为声诱导涡脱落，代表了本研究感兴趣的现象。在热声学领域，利用LEE进行的数值特征频率模拟已成为确定与旋涡脱落相关的声阻尼率以完成燃气轮机燃烧室热声稳定性分析的焦点。然而，目前还没有根本的调查存在，这就建立了考虑这些LEE阻尼率的合法性。这个问题的产生是由于在LEE本征解中，由旋涡脱落引起的旋涡扰动的隐式存在，而旋涡脱落紧邻声学扰动。总之，相应的阻尼率不能代表纯声阻尼率，这是热声稳定性分析所必需的。这项工作的主要目的包括澄清，通过直接执行LEE特征频率模拟获得的阻尼率是否可以用于热声稳定性评估，尽管它们的特征解被进一步的干扰类型“污染”，即本研究中的涡状干扰。因此，将Helmholtz-Hodge分解方法应用于LEE特征模态振型，从而可以显式地访问声学和涡旋扰动场。这些用于通过适当的能量项的评估从LEE特征解中提取明确的纯声学阻尼率。最后将得到的阻尼率与相应的原始LEE阻尼率和实验对应的阻尼率进行比较。
Solutions of the Linearized Euler Equations (LEE) are composed of acoustic, entropy and vortical perturbation types. The excitation of the latter can be provoked by a transformation of acoustic into rotational energy, which originates from the interaction between acoustics and a mean flow shear-layer. This is known as acoustically induced vortex shedding and represents the phenomenon of interest in this study. In the field of thermoacoustics, numerical eigenfrequency simulations with the LEE have moved into focus to determine the acoustic damping rates associated with vortex shedding to complete thermoacoustic stability analyses of gas turbine combustors. However, there is yet no fundamental investigation existent, which establishes the legitimation to consider these LEE damping rates for this purpose. This question arises due to the implicit presence of vortical disturbances caused by vortex shedding next to the acoustic ones in LEE eigensolutions. In conclusion, the corresponding damping rates are not expected to represent the pure acoustic damping rates, which are exclusively required for a thermoacoustic stability analysis. The main objective of this work comprises the clarification, whether damping rates obtained by straightforwardly performed LEE eigenfrequency simulations can be used for a thermoacoustic stability assessment, although their eigen-solutions are “polluted” by further disturbance types, i.e. the vortical one in this study. Therefore, a Helmholtz-Hodge decomposition approach is applied to LEE eigenmode shapes, which allows to explicitly access acoustic and vortical disturbance fields. These are used to extract the unambiguous, pure acoustic damping rates from LEE eigensolutions via evaluations of appropriate energy terms. The resulting damping rates are finally compared to the corresponding, original LEE damping rates and their experimental counterparts.