Reconstruction of the reflection coefficient downstream of a flame from dual SISO acoustic measurements of flame

The downstream section of the combustion chamber is typically hot, making direct measurement of its acoustic characteristics, such as the reflection coefficient, technically and methodologically challenging. Consequently, reconstructing the acoustic properties of the hot downstream subsystem using measurements from the cold upstream side of the burner is an attractive approach. This study presents the concept, methodology, and experimental evaluation of a reconstruction method based on acoustic network theory using two-port and one-port models. The core process inverts the bilinear relationship between the unknown downstream and measured upstream reflection coefficients via the impedance tube method, requiring the flame transfer matrix obtained from standard measurements. Notably, all acoustic sensors, except the photomultiplier (PMT) for heat release rate fluctuations, are installed on the cold upstream side of the burner. Although theoretically straightforward, applying the reconstruction procedure to experimental data is challenging. We assess its feasibility for reconstructing the downstream reflection coefficient in laboratory combustion systems. Results show that the reconstructed coefficients generally match theoretical predictions across a wide frequency range. However, sensitivity analysis reveals high susceptibility to measurement uncertainties in certain frequency bands, highlighting the need for specialized data processing. Applying Tikhonov regularization effectively mitigates these errors, improving the robustness of the reconstruction.