Nonlinear Characterization of Acoustic Resonators

Combustion systems like rocket combustion chambers or gas turbines are prone to thermoacoustic instabilities.  Such instabilities occur due to a feedback between the unsteady heat release of the combustion process and the acoustic field within the combustion chamber. The use of acoustic resonators – as shown in Fig. 1 for a rocket thrust chamber – is common practice to increase the stability margins. These resonators dissipate acoustic energy predominantly in small frequency ranges around their eigenfrequencies and, thus, have to be tuned according to the oscillation modes of the combustion chamber. The dissipation mechanisms differ significantly, depending on the  sound pressure level (SPL). At low SPLs, this process is dominated by thermo-viscous dissipation, which is a linear effect, i.e., independent of perturbation amplitude. Increasing the excitation amplitudes additionally leads to flow separation at the edges of the resonator, which converts the irrotational acoustic into a hydrodynamic, rotational motion. The vortices formed remain laminar for moderate excitation levels and turn fully turbulent for yet larger levels. This effect is strongly nonlinear and increases the dissipation considerably.