Forced response of transverse reacting jet in vitiated crossflow to harmonic velocity disturbances

The orthogonally oriented injector configuration typically used in axial fuel staging-capable gas turbine combustors is known to produce complicated thermoacoustic interactions between two distinct reaction zones. Despite the fundamental importance of transfer functions of transverse reacting jets in vitiated crossflow, however, their distinctive properties remain unknown, and associated low-order modeling combined with two different flame transfer functions remains entirely undemonstrated. From detailed measurements of transfer functions of lean-premixed primary and secondary flames in response to harmonic velocity disturbances, here we show that the transfer function of a transverse reacting jet in high-temperature crossflow is described as having relatively larger gain without undulating patterns, near-linear slow decay in magnitude with respect to the forcing frequency, and remarkably shorter duration response time. By leveraging a reduced-order modeling approach to account for the finite time delay between the two distinct transfer functions and by validating the calculation results against velocity and pressure measurement data, we demonstrate that self-induced instabilities in an axial fuel-staged system can be simultaneously driven by the dynamics of primary and secondary flames, and that the triggering of second-stage-induced instability is characteristically connected to higher-order acoustic modes. Such non-axisymmetric intra-combustor interactions generate a cascade of spectral peaks, including the first and third longitudinal modes and their respective higher harmonics, and additional peaks at the sum and difference of two individual frequencies. While the primary flame's dynamics are capable of selectively exciting the first mode, the secondary jet flame exhibits more complicated modal dynamics, manifested as the L3 mode-coupled jet merging-related flame surface annihilation and the L1 mode-coupled lateral movements of the transverse jet column.