Boundary Integral Formulations for the Aeroacoustics of Deformable Bodies

The rapid expansion of the aviation industry and the advent of Urban Air Mobility (UAM) dictate stringent noise reduction targets for next-generation aircraft. To meet these goals, breakthrough designs such as Distributed-Propulsion (DP) systems and highly flexible, morphing airframes are being actively explored. However, these configurations introduce complex aeroacoustic phenomena heavily influenced by structural deformations and installation scattering effects. Consequently, there is a critical need for fast, efficient prediction tools capable of explicitly accounting for the acoustic impact of arbitrarily moving and deforming surfaces during preliminary design phases. This thesis presents the development and validation of a unified boundary integral formulation (BIF) to solve the arbitrarily-forced acoustic wave equation in fluid domains bounded by deforming surfaces. The framework is highly versatile, describing the perturbation field in terms of either acoustic pressure—via the Lighthill and Ffowcs Williams and Hawkings equations—or velocity potential. It is rigorously derived in two fully equivalent reference systems: a fluid frame of reference (FFR) and a moving frame of reference (MFR). The approach effectively handles both solid and fictitious porous surfaces, the latter serving as interfaces for coupling with aerodynamic solvers to efficiently propagate noise to the far-field. A zeroth-order Boundary Element Method (BEM) is employed for the numerical application of the formulations, providing the necessary spatial and temporal discretization. For acoustic radiation, the methodology is validated against several canonical test cases. A significant original contribution is the derivation of a novel exact analytical solution for the noise radiated by a solid sphere undergoing large-amplitude, high-frequency pulsations, which benchmarks the BEM solver in extreme kinematic conditions. In a realistic application, the formulation simulates the noise emitted by a BO-105 helicopter rotor in forward flight. Comparisons with HELINOISE experimental data demonstrate the solver's accuracy; specifically, the deformable-boundary formulation provides predictions slightly closer to experimental results than the rigid-boundary assumption. Further analysis on a more flexible rotor configuration reveals that the influence of dynamic deformations on the acoustic signature and directivity becomes markedly more pronounced. Furthermore, the formulation is extended to solve acoustic scattering from deforming bodies. The study reveals that kinematic nonlinearities inherent to dynamic boundary deformation generate a multi-harmonic scattered spectrum even with a mono-harmonic incident wave. This is validated for a pulsating spherical scatterer against both existing literature for small amplitudes and a new exact analytical linear solution developed within this thesis for large-amplitude vibrations. Finally, a fully nonlinear scattering formulation is introduced to include fluid nonlinearities generated by the deformation-induced flow field, solved via an innovative "velocity-potential cascade" iterative algorithm. In conclusion, this research establishes a unified and computationally efficient boundary-integral framework for predicting wave-propagation phenomena from arbitrarily deforming structures, applicable to both radiation and scattering problems involving solid or porous surfaces. By accurately capturing complex deformation and scattering effects, the proposed methodology represents a versatile predictive tool to support the aeroacoustic design of innovative aircraft configurations from the earliest conceptual phases.