Theoretical and experimental investigation on the linear growth rate of the thermo-acoustic combustion instability

A systematic measurement of the linear growth rate and frequency of the oscillation at the onset of thermo-acoustic combustion instability is reported and compared with the results of theoretical approaches. To do so, a specialized setup with a passive control device has been developed. The setup allows quick switching between the stable and unstable operation of the system by switching the upstream boundary condition of the burner/flame from the almost anechoic termination to the closed end. The measurements have been done for a burner with premixed burner-stabilized Bunsen-type flames. When the rate of growth is slow, which means that the time of the linear growth of the oscillation is larger than the switching time, (about 0.01 seconds), the growth rate and the instability onset frequency can be measured accurately. This paper endeavors to make a comparison between the theoretical results of modeling strategies and experimental findings. Two modeling strategies are tested. Within the first approach, one has to measure the frequency response of the combustion appliance from two sides at the one cross-section area, 1) the burner including the flame and downstream sides of the burner/flame as an acoustically active element; 2) reflection coefficient of the upstream side of the burner/flame. Then by applying a system identification procedure, (thermo)-acoustic responses in the complex domain can be obtained. Finally, complex eigen frequency can be calculated by solving the corresponding dispersion equation. The alternative approach was proposed by Kopitz and Polifke in 2008 and allows estimating both the frequency of oscillation and the growth rate from a polar plot of the system’s characteristic equation in the frequency domain. Both methods are tested and compared with experimental findings. The comparison between experimental and modeling results shows that the unstable frequencies can be predicted accurately by both tested modeling strategies. The prediction of the instabilities growth rates is closer to the measured one when the modeling in the Complex (Laplace) domain is used. However, the frequency domain analysis provides less accurate, but still reasonable estimates of the growth rates