Abstract
The implementation of hydrofoils is an effective method of improving the speed and efficiency of marine vessels. The lift generated by hydrofoils effectively counters the displacement of a vessel, resulting in a significant reduction in hull drag and improvement in seakeeping characteristics by maintaining altitude above the waves. Recent advances in sensing and controls and composite materials have enabled increased use of foils in ship design. Engineers face significant challenges in the foil design process due to high loading (~50 kPa), a wide range of operational lift coefficients, and the need to avoid flow cavitation, which can lead to an abrupt loss of lift if not properly addressed. In addition, hydrofoils typically operate in the transitional flow regime, requiring the use of numerical approaches which can accurately predict the position of flow transition. To meet this challenge, the design process can be automated using a computational approach based on a shape optimization problem, whereby the design variables represent the sectional geometry of a foil. In this thesis, a robust optimizer based on the method of particle swarms is coupled with the XFOIL flow solver, which has been proven capable of accurately predicting forces on 2D wing sections in viscous flow at transitional Reynolds numbers. The foil geometry is parameterized using PARSEC polynomials, allowing for N=10 degrees of freedom. The cost function is constructed from a weighted combination of drag coefficients computed at three operational conditions: takeoff, cruise, and high speed. Penalty functions are imposed to ensure that the foil remains free of cavitation and set upper and lower thickness bounds to satisfy structural constraints. The optimizer is applied to the redesign of a foil section for an America's Cup AC50 class foiling catamaran. The foil section obtained from the optimizer was found to operate with a 20% reduction in drag over the original section, while satisfying the structural and cavitation requirements. Additional numerical experiments examine the influence of the weighting factors in the objective function and the robustness of optimal designs over a range of loading and Reynolds numbers. The resulting approach represents a robust optimizer for 2D hydrofoil sections that is capable of overnight turnaround times on a laptop computer.