Evaluation of the thermo-acoustic instability frequency and growth rate via input reflection coefficient measurement for central heating equipment

Abstract

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, Rup, and ii) burner with flame completed by the downstream part of the appliance, Rin. 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 Rin measurements.