Optimal and off-design operations of acoustic dampers using perforated plates backed by a cavity

The frequency of thermo-acoustic instabilities may vary during operation of combustors, a feature that must be included in the design of robust acoustic dampers tuned to damp specific unstable modes. This problem is tackled here by using perforated plates traversed by a bias flow and backed by a resonant cavity in the absence of grazing flow. A methodology is proposed to find the optimal dimensionless products maximizing absorption in two limit regimes. In these two asymptotic regimes, the optimal bias flow velocity is only controlled by the plate porosity while the size of the back cavity fixes the peak absorption frequency. The present analysis also includes effects of the plate thickness. A Helmholtz resonance and a narrow absorption peak in the frequency space characterize the first absorption regime reached at high Strouhal numbers. Conversely, the second absorption regime reached at low Strouhal numbers operates with a quarter-wave resonance type. This regime requires larger cavity depths but offers a wider absorption bandwidth around the peak absorption frequency. In both cases, total absorption is achieved at the nominal conditions identified. The way the absorption coefficient is reduced when variations of the bias flow velocity around the optimal value are considered is then investigated. Theoretical predictions are validated by measurements in the two nominal regimes identified and at off-design operation. The expressions derived in this study can be used to improve the design of robust acoustic dampers.