Flexible hydrofoil optimization for the 35th America's Cup with constrained EGO method

Abstract

This paper investigates the use of constrained surrogate models to solve the multi-design optimization problem of a flexible hydrofoil. The surrogate-based optimization (EGO) substitutes the complex objective function of the problem by an easily evaluable model, constructed from a limited number of computations at carefully selected design points. Associated with ad-hoc statistical strategies to propose optimum candidates within the estimated feasible domain, EGO enables the resolution of complex optimization problems. In this work, we rely on Gaussian processes (GP) to model the objective function and adopt a probabilistic classification method to treat non-explicit inequality constraints and non-explicit representation of the feasible domain. This procedure is applied to the design of the shape and the elastic characteristics of a hydrofoil equipped with deformable elements providing flexibility to the trailing edge. The optimization concerns the minimization of the hydrofoil drag while ensuring a non-cavitating flow, at selected sailing conditions (boat speed and lifting force). The drag value and cavitation criterion are determined by solving a two-dimensional nonlinear fluid-structure interaction problem, based on a static vortex lattice method with viscous boundary layer equations, for the flow, and a nonlinear elasticity solver for the deformations of the elastic components of the foil. We compare the optimized flexible hydrofoil with a rigid foil geometrically optimized for the same sailing conditions. This comparison highlights the hydrodynamical advantages brought by the flexibility: a reduction of the drag over a large range of boat speeds, less susceptibility to cavitation and a smaller angle of attack tuning range.

Lift-to-Drag Ratio of the Application of Hydrofoil With Variation Mounted Position on High-Speed Patrol Vessel

“…Another study also showed that the position of the foil in the vertical direction also had an effect on hydrodynamic performance [22]. The optimum position of hydrofoil was when it was fully submerged at an angle of 36 degrees at the speed 30 knots [23]. There are still very few researchers investigating the effect of the hydrofoil position in the horizontal direction.…”

Morphing Structures, Applications of

“…Other research in morphing hydrofoils can be found in the works from Garg et al (2015) and Sacher et al (2018) in which computational fluid dynamics and structural analysis methods have been used together for coupled hydrodynamicstructural solutions. In other research, a passive trailing edge morphing hydrofoil for sailing applications has been proposed to extend the range of efficiency.…”

A classification approach to efficient global optimization in presence of non-computable domains

“…The objective of the optimization is to minimize the hydrofoil drag force at selected conditions (forward speed and lifting force) while ensuring non-cavitating flows. The complete description of the optimization problem and the hydrodynamical analysis of the optimized hydrofoil are not provided in this paper, which focuses on the method; interested readers can refer to [42]. The original optimization problem proposed in [42] involved 11 design variables describing the shape and elastic characteristics of the foil flexible trailing edge, as schematically illustrated in Figure 11.…”

“…The complete description of the optimization problem and the hydrodynamical analysis of the optimized hydrofoil are not provided in this paper, which focuses on the method; interested readers can refer to [42]. The original optimization problem proposed in [42] involved 11 design variables describing the shape and elastic characteristics of the foil flexible trailing edge, as schematically illustrated in Figure 11. In the present work, the number of design variables is reduced to 5 in order to maintain reasonable computational times and to allow As mentioned before, the optimization concerns the minimization, for 4 conditions, of the hydrofoil drag coefficients C Di=1,...,4 .…”