Acoustic Response of a Helmholtz Resonator Exposed to Hot-Gas Penetration and High Amplitude Oscillations

Helmholtz resonators are often used in the gas turbine industry for the damping of thermoacoustic instabilities. To prevent thermal destruction, these devices are usually cooled by a purging flow. Since the acoustic velocity inside the neck of the resonator becomes very high already at moderate pressure oscillation levels, hot-gas penetration cannot always be fully avoided. This study extends a well-known nonlinear impedance model to include the influence of hot-gas intrusion into the Helmholtz resonator neck. A time dependent but spatially averaged density function of the volume flow in the neck is developed. The steady component of this density function is implemented into the nonlinear impedance model to account for the effect of hot-gas intrusion. The proposed model predicts a significant shift in the resonance frequency of the damper towards higher frequencies depending on the amplitude of the acoustic velocity in the neck and the temperature of the penetrating hot gas. Subsequently, the model is verified by the experimental investigation of two resonance frequencies (86 Hz and 128 Hz) for two hot gas temperatures (1470 K and 570 K) and various pressure oscillation amplitudes. The multi-microphone-method, in combination with a microphone flush-mounted in the resonator volume, is used to determine the impedance of the Helmholtz damper. Additionally, a movable ultra-thin thermocouple was used to determine the degree of hot-gas penetration and the change of the mean temperature at various axial positions in the neck. A very good agreement between the model and the experimental data is obtained for all levels of pressure amplitudes and of hot-gas penetration depths. The mean air temperatures in the neck were accurately predicted, too.