Thermoacoustic instabilities, caused by the feedback between unsteady heat release and acoustic pressure perturbations, are characterised by large-amplitude pressure oscillations. These oscillations, if uncontrolled, pose a threat to the integrity of combustion systems. One strategy to mitigate them is by installing cavity-backed perforated plates with bias flow into the combustion chamber. In this study, we consider a generic combustor configuration: a one-dimentional tube (with open and/or closed ends) containing a compact heat source and a heat exchanger tube row. The idea is to use the heat exchanger tube row as a device (analogously to a cavity-backed perforated plate) to manipulate the downstream end condition. We simulate the row of heat exchanger tubes by a slit-plate with bias flow. We derive the characteristic equation for the complex eigenfrequencies of this set-up. From the growth rates (imaginary parts of the eigenfrequencies), we construct stability maps for various system parameter combinations. The results, obtained for the first two modes of the system, show that by varying the cavity length or the bias flow velocity through the slits, we can stabilise a previously unstable combustion system.

中文翻译：

---

温度不均匀的燃烧室中热交换器的被动不稳定性控制

由不稳定的放热和声压扰动之间的反馈引起的热声不稳定性的特征在于大幅度的压力振荡。如果不加以控制，这些振荡会对燃烧系统的完整性造成威胁。减轻它们的一种策略是通过将带有偏流的背衬孔板安装到燃烧室中。在这项研究中，我们考虑了一种通用的燃烧器配置：一个包含紧凑型热源和换热器管排的一维管（具有开放和/或封闭端）。这个想法是使用热交换器管排作为一种设备（类似于背腔的多孔板）来操纵下游端的情况。我们用带有偏流的狭缝板模拟了换热管的排。我们推导了该设置的复杂特征频率的特征方程。从增长率（本征频率的虚部），我们为各种系统参数组合构造了稳定性图。从系统的前两种模式获得的结果表明，通过改变腔体长度或通过狭缝的偏流速度，我们可以稳定先前不稳定的燃烧系统。