Spatially resolved response of a transcritical LOX/H₂ coaxial flame to injector-coupled transverse acoustic forcing

High-frequency transverse combustion instabilities remain a critical challenge for liquid rocket engines. The flame response to transverse acoustic forcing is not yet fully understood. Here, the thermoacoustic response of a transcritical LOX/H₂ flame is studied under controlled transverse acoustic forcing. A single-injector configuration extracted from the multi-injector BKD combustor is investigated using a Detached Eddy Simulation framework for forced-response analysis, with the transverse acoustic excitation introduced based on the Helmholtz eigenmode solution. The results demonstrate that the flame response exhibits strong frequency selectivity, governed by the acoustic characteristics of the injector passage. The strongest heat release response occurs when the forcing frequency approaches the longitudinal acoustic resonance of the LOX injector, leading to enhanced flame sensitivity through injector-acoustic coupling. Dynamic Mode Decomposition identifies a convective response pathway, in which reactant and heat release perturbations are transported downstream through coherent structures in the reactive shear layer. Furthermore, a distributed flame describing function analysis reveals that the spatial flame response cannot be fully described by a simple convective time-delay model. With increasing forcing amplitude, the low phase-lag region expands within the primary reaction zone, indicating an increasing contribution from local acoustic modulation. These findings demonstrate that the high-frequency thermoacoustic response of transcritical LOX/H₂ flames is controlled by the combined effects of convectively transported disturbances and pressure-coupled flame modulation, providing new insights into the mechanisms of transverse combustion instabilities in liquid rocket engines.