Multi-objective optimization of airfoil geometry for aerodynamic efficiency and noise reduction using bezier parametrization

Abstract

This thesis addresses the growing need for airfoils that combine strong aerodynamic performance with reduced acoustic emissions—an increasingly critical requirement in applications such as UAVs, wind turbines, and urban air mobility. Traditional optimisation methods often focus exclusively on lift and drag, neglecting the implications of noise generation. To fill this gap, a multi-objective optimisation framework is developed that simultaneously targets aerodynamic efficiency and low-noise operation. The NACA0015 airfoil is adopted as the baseline reference, and Bézier curves are employed for geometry parametrisation, offering smooth shape manipulation with a manageable number of design parameters. The optimisation process follows a two-stage strategy. First, Sobol low-discrepancy sequences are used to explore the high-dimensional design space and capture global parameter trends. Subsequently, the NSGA-II genetic algorithm is applied to refine candidate designs under multiple objectives. While the initial acoustic evaluations relied on far-field Sound Pressure Level (SPL) predictions using the NAFNoise solver, these results were found to be inconsistent and could not be validated against experimental benchmarks. To overcome this limitation, a new parameter—Sound Averaged Parameter (SAP)—was introduced as a statistically robust and numerically stable aeroacoustic objective. SAP cannot be measured directly in experiments, but its definition derives from the SPL spectrum, allowing indirect benchmarking through experimental SPL data of the NACA0015 airfoil. This provided confidence in SAP as a relative acoustic metric suitable for optimisation. The final optimisation framework combined four objectives—maximising lift, minimising drag, improving lift-to-drag ratio, and minimising SAP—while enforcing additional stability-based constraints to filter out oscillatory and statistically unreliable designs. Across NSGA-II and Dakota optimisation runs, over 600 candidate designs were evaluated, of which a subset met both aerodynamic and acoustic criteria in a stable manner. Results demonstrate that the SAP-based optimisation successfully identified Pareto-optimal designs that balance aerodynamic efficiency with reduced acoustic impact. Unlike the SPL-based framework, which produced misleading outcomes, the SAP-based method yielded consistent and interpretable trade-offs. These findings highlight the value of integrating robust acoustic metrics into aerodynamic design, offering an effective methodology for the early-stage development of low-noise, high-performance blades and propellers.