Reconstruction of the reflection coefficient downstream of a flame from dual siso flame response measurements

This study introduces an innovative approach to assess the thermoacoustic characteristics of components downstream of a flame, employing two sets of distinct Single-Input-Single-Output (SISO) acoustic measurements. Conventional direct assessments of downstream reflection coefficients face challenges due to the need for measurements in the high-temperature downstream region and complexities arising from heat inflow from the flame. To address these challenges, we leverage the widely adopted dispersion relation format from the theory of radio-frequency circuits. In the current methodology, the flame transfer function (TF) technique, as a well-established tool in thermoacoustics, is used. The second method utilizes a standard impedance tube test based on a one-port acoustic reflection test, conducted on the upstream/cold side with a flame present. To demonstrate the effectiveness of our approach, we applied the method to a ducted premixed burner-stabilized Bunsen-type flame. The straightforward reconstruction of downstream reflection coefficients revealed strong sensitivity to noise and uncertainty, particularly in higher frequencies, necessitating specialized data treatment. To mitigate this sensitivity, we conducted multiple tests with slight changes in operating conditions, creating a dataset expected to yield nearly identical downstream reflection coefficients. We then formulated an over-determined system of linear equations, employing the least-squares method to minimize errors and sensitivity. This work showcases a significant reduction in sensitivity through the use of multiple tests and data treatment techniques. The reconstructed downstream acoustics were employed to construct the reflection coefficient measured at upstream side of active subsystem and flame TF at a thermal power close to that corresponding to the reconstructed downstream acoustics, demonstrating substantial improvements in accuracy and reliability.