On the Use of the Porous FWHE for Rotating Blades Noise Prediction

This paper proposes the use of integral formulations for application of permeable Ffowcs Williams and Hawkings Equation (P-FWHE) to the prediction of tonal/broadband noise in the near field generated by rotating devices: a marine propeller in open water and a horizontal-axis wind turbine in a homogeneous onset flow. The integral formulations solving the P-FWHE are extensions of the Farassat 1A formulation, which require flow velocity and pressure distribution upon a fictitious surface in arbitrary motion surrounding the sources of noise. The effects of placement, extension and kinematics of this porous surface on the predicted noise are examined, in order to determine the most numerically effective configuration. For both rotating devices, cylindrical fixed and co-rotating permeable surfaces are considered, with inclusion of the outflow disk to account for the acoustics contribution from downstream closure crossed by the rotor wake structure. Literature works highlight that the outflow disk is typically neglected in such kind of applications, in that source of numerical troubles: one of the objective of this paper is their understanding and the proposal of possible solutions. The hydro/aero-dynamic inputs to the acoustic formulations are based on numerical integrations of the Navier Stokes Equation combined with suitable closure models: in particular, a steady RANS approach with the Spalart and Allamaras model is used for the wind turbine simulation, whereas a Detached Eddy Simulation (DES) closure model is used for the propeller.