Numerical study of the linear and non-linear damping in an acoustically forced cold-flow test rig with coupled cavities

Quantifying the oscillation amplitude of thermoacoustic instabilities remains a critical and challenging issue, as it is a complex balance between driving and damping processes. The New Pressurized Coupled Cavities (NPCCs) setup designed for the study of acoustic damping is analyzed in this work. It is a cold-flow test rig mimicking the geometry of a liquid rocket engine and equipped with an acoustic forcing device. The chamber 1T mode triggers a strong non-linear harmonic response, while the 1T1L and 1T2L exhibit weak non-linearities. Disturbance energy budgets are used in large-eddy simulations to characterize the damping phenomena with the 1T2L and 1T1L forcing. The correct global damping of the system is retrieved, and local damping contributions are extracted. Then, a non-linear term representing the energy transfer to the harmonics is derived from non-linear acoustics theory. Combined with a linear model, this model correctly retrieves the limit-cycle of the 1T mode.