Acoustic Formulations for Aeronautical and Naval Rotorcraft Noise Prediction Based on the Ffowcs Williams and Hawkings Equation

Noise requirements will be key design drivers in the development of the new generations of propeller-driven aircraft, helicopters and ships. Therefore aeroacoustics and hydroacoustics become increasingly important scientific branches since accurate acoustic predictions are an essential tool for the required Design for Reduced Noise Generation. Generally speaking, the prediction of aerodynamically and hydrodynamically generated noise can be considered as an aerodynamic/hydrodynamic analysis followed by an acoustic one. The present thesis focuses on the development of acoustic formulations based on the Ffocws Williams and Hawkings equation (FWHE), to describe the structure of the noise field induced by propeller driven aeronautical and naval craft, both in the unbounded space and in the presence of scattering bodies, like a fuselage or hull. The reason why the FWHE is at the basis of the developed acoustic formulations is its proven capabiity of providing physically consistent aeroacoustic predictions. Literature shows that, in the aeronautical context, the FWHE is a very efficient aeroacoustic tool allowing the prediction of the fluctuating pressure field induced by rotors and propellers, both for subsonic and transonic flight conditions. The present thesis focuses on the development of acoustic formulations based on the Ffocws Williams and Hawkings equation (FWHE), to describe the structure of the noise field induced by propeller driven aeronautical and naval craft, both in the unbounded space and in the presence of scattering bodies, like a fuselage or hull. The reason why the FWHE is at the basis of the developed acoustic formulations is its proven capability of providing physically consistent aeroacoustic predictions. Literature shows that, in the aeronautical context, the FWHE is a very efficient aeroacoustic tool allowing the prediction of the fluctuating pressure field induced by rotors and propellers, both for subsonic and transonic flight conditions. Although the modelling of noise generation and propagation in the naval context is as complicated as in aeronautics, most of the hydroacoustics analysis of non-cavitating and cavitating propellers is based on the unsteady Bernoulli equation. For this thesis, therefore, it was decided to first apply the FWHE for the prediction of noise generated by naval propellers in unbounded space. A comparison between the FWH-based and the Bernoulli-based approach has been carried out using potential flow assumptions. A novel formulation based on the porous form of the FWHE has been developed to predict the sound radiated by a cavitating propeller subjected to non-uniform inflow. The comparison has been performed both theoretically and numerically. A non-cavitating naval propeller, subjected to a uniform onset flow, has been analyzed. Observing that typical naval operating conditions are such that non-linear terms may be coherently neglected in both formulations, no hydrodynamic input concerning the flow-field around the propeller is required. The Laplace equation for the velocity potential has been solved through a boundary integral formulation and a zero-order boundary integral method (BEM) has been applied as discretization strategy. Using the velocity potential and pressure field on the propeller surface, numerical hydroacoustics investigations showed that the assumed shape of the potential wake has a large influence on the pressure disturbance evaluated by means of the Bernoulli equation. The results obtained with the FWHE, however, are not affected by the assumed wake because here the wake contributes to the noise field only through its indirect effects on the loading noise term. The introduction of free wake modelling resolves the discrepancies in the hydroacoustics results from a th