The space-time structure of sound produced by stacked rotors in hover using Vold-Kalman filters and proper orthogonal decomposition

Proper orthogonal decomposition and the Vold-Kalman order tracking filter are combined to evaluate the most energetic components of the sound field produced by a coaxial, co-rotating rotor in hover. The study leverages the database generated by Tinney and Valdez (2020; AIAA J. vol. 58, no. 4) comprising an array of eight stationary microphones oriented to capture the acoustic near-field below the rotor disk plane where ground observers are expected to reside and where concerns over community annoyance are greatest. Changes to rotor conditions focus primarily on rotor speed and index angle (angular separation between the upper and lower rotors), as this has the greatest effect on the sound field produced by stacked rotors by way of the constructive and destructive interference of the sound generated, separately, by the upper and lower rotors. Proper orthogonal decomposition is performed using a kernel constructed from auto and cross-spectral densities of the spatially coherent sound field. The eigenvectors demonstrate the spatial extent of the sound field for discrete frequencies corresponding to the first few blade pass frequency harmonics. In order to improve the clarity and accuracy of the low-order reconstructions, a second generation, Vold-Kalman multi-order tracking filter is employed to isolate discrete frequencies. Relative to conventional spectral filtering methods, the Vold-Kalman filter is performed in the time-domain and is shown to accurately isolate discrete tones while preserving changes to the phase of the signal. Findings from this analysis reveal the effect of index angle on the spatial make-up of the coherent sound field produced by hovering stacked rotors.