Flame transfer function spatial distributions and synthesis method in a multi-nozzle model combustor

This study proposes an analytical synthesis method in the complex domain for reconstructing the global flame transfer function (FTF) from local flame transfer functions (LFTFs) within the flame linear response regime of a multi-nozzle combustor. Experiments were conducted on a lean-premixed five-nozzle model combustor using chemiluminescence-based zonal measurement, from which both the gain and phase of the LFTFs were obtained. In comparison with the FTF of a single-nozzle combustor, the convective time delay of the central nozzle and outer nozzle were determined to be 9.3 and 21.0 ms, while the peak frequencies of gain profiles for their respective LFTFs were 80 and 110 Hz. The disparity in peak response frequencies between the central and outer nozzles highlights the spatial non-uniformity induced by flame–flame interactions. The global FTF gain profile exhibits a distinct peak frequency at 90 Hz, and the global flame convective delay is 13.1 ms, which falls between the central nozzle and the outer nozzle delay time. This demonstrates that the global FTF in the multi-nozzle combustor is jointly governed by both central and outer nozzle flames. The synthesized global FTF gain, calculated through the analytical synthesis method, agrees well with experimental results at perturbation frequencies above 100 Hz, and the calculated global flame convective delay time is determined to be 13.97 ms, demonstrating its potential for predicting thermoacoustic behavior in complex combustors.