Numerical investigation on the control of multi-mode thermoacoustic instabilities by utilizing an embedded-necked Helmholtz resonator in a premixed swirl combustor

Lean premixed combustion is key to low-emission gas turbines and aero-engines, but its strong coupling between heat release and acoustics makes the system susceptible to self-excited thermoacoustic instabilities across various operating conditions. Helmholtz resonators are widely used to suppress multi-mode thermoacoustic instabilities but require further study. Compared with conventional designs, embedded-neck Helmholtz resonators offer a more compact solution. This study investigates the control of multi-mode thermoacoustic instabilities using parallel embedded-neck Helmholtz resonators in a premixed swirl combustor. Experiments reveal self-excited oscillations at 110 and 300 Hz under different equivalence ratio, which are accurately predicted by a three-dimensional Helmholtz solver coupled with a flame describing function. Using this validated numerical framework, the control of multi-mode thermoacoustic instabilities by parallel embedded-neck Helmholtz resonators is then systematically investigated. Acoustic and thermoacoustic simulations demonstrate that the parallel resonator achieves a broader effective bandwidth than a single resonator, enabling simultaneous suppression of both instability modes. The results further show that optimal placement of resonators at acoustic pressure antinodes is crucial for effective stabilization. Under optimal conditions, the growth rate of the dominant mode is reduced from 78.1 to −37.3 rad/s, leading to system stabilization. Furthermore, for first-order oscillations, the growth rate is significantly reduced from 1.45 to −10.36 rad/s, but only when the resonator is placed in the plenum at the pressure antinode. It is concluded that optimal control of thermoacoustic oscillations requires selecting Helmholtz resonators with eigenfrequencies tuned to the target oscillations and positioning them in regions of high acoustic pressure amplitude.