In annular combustion systems, azimuthal thermoacoustic modes manifest themselves predominantly as travelling or standing waves. Several phenomena can influence the modal behaviour of annular thermoacoustics. To monitor the stability of azimuthal thermoacoustics in industrial installations, a better understanding of the dynamics is required to correctly interpret online measurements. In this work, thermoacoustic eigensolutions of annular combustion systems are investigated, using a low-order analytic model. Heat release fluctuations are considered as a weak source term for a given acoustic eigenmode. The fluctuating heat release is modelled as a linear feedback to the local acoustics, in which the feedback response is a function of the azimuthal coordinate, causing cylindrical symmetry breaking. A bifurcation map is generated as a function of azimuthal mean flow velocity around the annulus. It is shown that a pitchfork bifurcation exists, separating standing wave and travelling wave solutions. Due to the interaction with non-uniform thermoacoustic feedback, an azimuthal flow with a low Mach number can significantly influence the system stability. Close to the bifurcation point, the non-normal nature of the dynamic system can induce a considerable gain of acoustic energy and yield more predictable time traces. These findings address the influence of non-normality, when applying a linear damping rate, acoustic amplitude or entropy-based quantity with the intent to monitor combustion dynamics in an annular combustion system.

中文翻译：

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圆柱对称破坏环形燃烧系统中方位角大流量的分叉研究

在环形燃烧系统中，方位热声模式主要表现为行波或驻波。几种现象会影响环形热声学的模态行为。为了监视工业设备中方位热声的稳定性，需要对动力学有更好的了解，才能正确解释在线测量结果。在这项工作中，使用低阶解析模型研究了环形燃烧系统的热声本征解。对于给定的声学本征模，热释放波动被认为是一个较弱的源项。波动的热量释放被建模为对局部声学的线性反馈，其中反馈响应是方位坐标的函数，从而导致圆柱对称性破坏。分叉图根据圆环周围的方位平均流速生成。结果表明存在干草叉分叉，将驻波解和行波解分开。由于与非均匀热声反馈的相互作用，马赫数低的方位角流会严重影响系统稳定性。接近分叉点，动态系统的非正常性质会引起相当大的声能增益，并产生更可预测的时间轨迹。这些发现解决了非线性的影响，当应用线性阻尼率，声振幅或基于熵的量来监控环形燃烧系统中的燃烧动力学时。分离驻波和行波解。由于与非均匀热声反馈的相互作用，马赫数低的方位角流会严重影响系统稳定性。接近分叉点，动态系统的非正常性质会引起相当大的声能增益，并产生更可预测的时间轨迹。这些发现解决了当应用线性阻尼率，声振幅或基于熵的量以监控环形燃烧系统中的燃烧动态时，非正态性的影响。分离驻波和行波解。由于与非均匀热声反馈的相互作用，马赫数低的方位角流会严重影响系统稳定性。接近分叉点，动态系统的非正常性质会引起相当大的声能增益，并产生更可预测的时间轨迹。这些发现解决了当应用线性阻尼率，声振幅或基于熵的量以监控环形燃烧系统中的燃烧动态时，非正态性的影响。动态系统的非正常性质会引起相当大的声能增益，并产生更可预测的时间轨迹。这些发现解决了当应用线性阻尼率，声振幅或基于熵的量以监控环形燃烧系统中的燃烧动态时，非正态性的影响。动态系统的非正常性质会引起相当大的声能增益，并产生更可预测的时间轨迹。这些发现解决了当应用线性阻尼率，声振幅或基于熵的量以监控环形燃烧系统中的燃烧动态时，非正态性的影响。