Transonic Turboprop Noise Prediction Using a Rotating Permeable-Surface FW-H Formulation in the Time Domain

This work investigates the robustness of a transonic FW–H formulation for rotating permeable surfaces, developed to enable stable acoustic integration when the permeable surface moves at sonic conditions relative to the observer. The method, based on the desingularized Formulations 1-DS and 1A-DS by Casalino, is assessed through comparison with classical FW–H approaches. Results show that the de-singularized formulation provides consistent far-field noise predictions, preserving high-frequency content by enabling the use of integration surfaces tightly fitted to the blade geometry. By comparison, the solid formulation underestimates acoustic levels due to the absence of quadrupole contributions, while the classical permeable formulation attenuates high-frequency content as a result of numerical dissipation when the integration surface is located away from the source region. A practical guideline is also provided for selecting the time-step ratio σ between the FW–H and CFD time steps, whose value controls the balance between signal smoothing and maximum resolved frequency. Overall, the proposed formulation offers a robust and efficient approach for aeroacoustic predictions in transonic propeller applications.