Predicting the Frequency of Combustion Instability Using the Measured Reflection Coefficient through Acoustic Excitation

In this study, the reflection coefficient (RC) and the flame transfer function (FTF) were measured by applying acoustic excitation to a duct-type model combustor and were used to predict the frequency of the combustion instability (CI). The RC is a value that varies with the excitation frequency and the geometry of the combustor as well as other factors. Therefore, in this study, an experimentally measured RC was used to improve the accuracy of prediction in the cases of 25% and 75% hydrogen in a mixture of hydrogen and methane as a fuel. When the measured RCs were used, an unstable condition was correctly predicted, which had not been predicted when the RCs had been assumed to be a certain value. The reason why the CI occurred at a specific frequency was also examined by comparing the peak of the FTF with the resonance frequency, which was calculated using Helmholtz's resonator analysis and a resonance frequency equation. As the CI occurred owing to the interaction between the perturbation in the rate of heat release and that in the pressure, the CI was frequent when the peak of the FTF was close to the resonance frequency such that constructive interference could occur.