Experimental measurement methods and theoretical evaluations based on low-order modeling approaches for both the growth rate and frequency at the onset of thermo-acoustic combustion instability are proposed, and their performance is evaluated. The developed techniques are demonstrated through a systematic measurement of the linear growth rate and frequency of evolving oscillations in the laboratory setup and also applied for the thermo-acoustic qualification of an industrial domestic boiler and a heat cell unit (combination of a burner with a heat-exchanger). Generic measurements have been done for a burner deck with premixed surface-stabilized Bunsen-type flames. The industrial domestic boiler and the heat cell unit are equipped with burners of a similar type but differ by their perforation pattern. They have been tested at different conditions and the experimental and theoretical results are compared. Two modeling strategies are tested: 1- in Laplace domain, with estimating a rational function in the complex domain to fit the measured frequency response, 2- exclusively in frequency domain, without estimating a rational function. Both methods include measurement of the frequency response of two reflection coefficients from i) the upstream part of the system, , and ii) burner with flame completed by the downstream part of the appliance, . Within the first approach, a procedure for an analytic continuation of the measured frequency response to the complex domain is applied and complex eigenfrequencies are calculated by solving the corresponding dispersion equation. An alternative approach was proposed by Kopitz and Polifke and allows estimating both the frequency of oscillation and the growth rate from the analysis of the polar plot of the system's characteristic equation in the frequency domain. The comparison shows that the unstable frequencies can be predicted accurately by both tested modeling strategies. This conclusion holds also for the tested industrial applications. The prediction of the instability growth rates is closer to the measured one when the modeling method in the complex domain is used. However, the frequency domain analysis provides less accurate, but still reasonable estimates of the growth rates and frequencies. Moreover, a good overview of thermo-acoustic performance of each industrial boiler/burner at different conditions is obtained via measurements.

中文翻译：

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通过测量中央供暖设备的输入反射系数来评估热声不稳定频率和增长率

提出了基于低阶建模方法的热声燃烧不稳定开始时的增长率和频率的实验测量方法和理论评估，并评估了它们的性能。所开发的技术通过在实验室设置中系统测量线性增长率和不断变化的振荡频率来展示，并且还应用于工业家用锅炉和热室单元（燃烧器与热源的组合）的热声鉴定。 -交换器）。已经对具有预混合表面稳定本生型火焰的燃烧器平台进行了一般测量。工业家用锅炉和热室单元配备有类似类型的燃烧器，但其穿孔图案不同。它们在不同条件下进行了测试，并对实验结果和理论结果进行了比较。测试了两种建模策略：1-在拉普拉斯域中，估计复数域中的有理函数以拟合测量的频率响应，2-仅在频域中，而不估计有理函数。两种方法都包括测量两个反射系数的频率响应，这些反射系数来自 i) 系统的上游部分，和 ii) 带有由设备的下游部分完成的火焰的燃烧器，。在第一种方法中，应用了将测量的频率响应分析延续到复数域的过程，并通过求解相应的色散方程来计算复数特征频率。 Kopitz 和 Polifke 提出了另一种方法，可以通过分析频域中系统特征方程的极坐标图来估计振荡频率和增长率。比较表明，两种测试的建模策略都可以准确预测不稳定频率。这一结论也适用于经过测试的工业应用。使用复杂域建模方法时，不稳定增长率的预测更接近实测值。然而，频域分析提供的增长率和频率的估计不太准确，但仍然合理。此外，通过测量可以获得每个工业锅炉/燃烧器在不同条件下的热声性能的良好概述。