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http://hdl.handle.net/10985/21858
A New Sensor to Characterize Flow Separation on a Hydrofoil
BOT, Patrick; VOISIN, Dimitri; SOULIER, Antoine; ASTOLFI, Jacques-André
The performance of lifting bodies such as hydrofoils is determined by the flow state and particular attention should be paid to flow separation, as this greatly affects the generated lift and drag. Sailors are used to look at telltales (woolies) to trim their sails or steer their yacht. A French company developed an electronic telltale for sails based on a strain gauge activated by a silicon strand, with the appropriate signal processing to deliver the same information as a classical wool-made telltale, basically attached or separated flow. This new sensor proved useful when woolies are not visible or to deliver a signal to feed a control system, such as the autopilot for example. It was also applied to wind turbines to control the blade pitch. Mer Agit\'ee is now developing an equivalent hydrodynamic e-Telltale to be used on hydrofoils and rudders to help trimming and controlling. The present work presents the investigation of a foil section fitted with this new sensor in a water tunnel, combining force and PIV measurements with the sensor signal, on a wide range of angle of attack. Results show that the hydro e-Telltale enables detecting the flow separation and anticipate stall, and possibly allows for detecting the boundary layer transition to turbulence. In many cases of fluid flow over a lifting body, it is interesting to get some real-time feedback from the flow in order to help optimizing performance and controlling the system. The feedback from this new sensor could be used in a closed-loop controlling system, for example feeding a reduced-order model of the flow around the foil.
Fri, 01 Jan 2021 00:00:00 GMThttp://hdl.handle.net/10985/218582021-01-01T00:00:00ZBOT, PatrickVOISIN, DimitriSOULIER, AntoineASTOLFI, Jacques-AndréThe performance of lifting bodies such as hydrofoils is determined by the flow state and particular attention should be paid to flow separation, as this greatly affects the generated lift and drag. Sailors are used to look at telltales (woolies) to trim their sails or steer their yacht. A French company developed an electronic telltale for sails based on a strain gauge activated by a silicon strand, with the appropriate signal processing to deliver the same information as a classical wool-made telltale, basically attached or separated flow. This new sensor proved useful when woolies are not visible or to deliver a signal to feed a control system, such as the autopilot for example. It was also applied to wind turbines to control the blade pitch. Mer Agit\'ee is now developing an equivalent hydrodynamic e-Telltale to be used on hydrofoils and rudders to help trimming and controlling. The present work presents the investigation of a foil section fitted with this new sensor in a water tunnel, combining force and PIV measurements with the sensor signal, on a wide range of angle of attack. Results show that the hydro e-Telltale enables detecting the flow separation and anticipate stall, and possibly allows for detecting the boundary layer transition to turbulence. In many cases of fluid flow over a lifting body, it is interesting to get some real-time feedback from the flow in order to help optimizing performance and controlling the system. The feedback from this new sensor could be used in a closed-loop controlling system, for example feeding a reduced-order model of the flow around the foil.Flexible hydrofoil optimization for the 35th America's cup with constrained ego method
http://hdl.handle.net/10985/15089
Flexible hydrofoil optimization for the 35th America's cup with constrained ego method
SACHER, Matthieu; DURAND, Mathieu; BERRINI, Elisa; HAUVILLE, Frédéric; DUVIGNEAU, Régis; LE MAITRE, Olivier; ASTOLFI, Jacques-André
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.
Sun, 01 Jan 2017 00:00:00 GMThttp://hdl.handle.net/10985/150892017-01-01T00:00:00ZSACHER, MatthieuDURAND, MathieuBERRINI, ElisaHAUVILLE, FrédéricDUVIGNEAU, RégisLE MAITRE, OlivierASTOLFI, Jacques-AndréThis 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.Verification and validation for the cavitating flow around a NACA0015 hydrofoil
http://hdl.handle.net/10985/21837
Verification and validation for the cavitating flow around a NACA0015 hydrofoil
PERALI, Paolo; HAUVILLE, Frédéric; LEROYER, Alban; ASTOLFI, Jacques-André; VISONNEAU, Michel
When cavitation occurs around hydrofoils it is the cause of noise radiation, vibration and erosion. Consequently numerical cavitation models have been developped and tested over the last decades (Schnerr and Sauer [1]). However, recent works show that numerical predictions for cavitating flow might be very sensitive to the spatial resolution of the mesh and require dicretization errors estimations (Negrato et al. [2], Asnaghi et al. [3]). The experimental and numerical approches joined in this work are the first step of the validation of the ISIS-CFD code for cavitating flows with fluid-structure interaction. Although, only results for a rigid profile in cavitating conditions are presented in this work. The test case is a NACA0015 profile in the cavitation tunnel located at the french Naval Academy Research Institute. On the numerical side, the ISIS-CFD code is used to solve the unsteady Reynolds Averaged Navier Stokes Equations (uRANSE). The two phases mixture dynamics are solved thanks to an interface capturing method and the Sauer cavitation model. The test case is first adressed using a two-dimensional computational domain. A set of unstructured grids is generated using Hexpress to perform a grids and time steps convergence study and obtain uncertainty estimations for both wetted and cavitating flow conditions. Then, the same study is done for an extended three-dimensional geometry taking into account the lateral walls of the tunnel and the convergent section located upstream of the test section. Influences of the turbulence quantities at the inflow and the cavitation model parameters are also assessed. The numerical results are compared with experimental effort measurements, high-speed camera signals and PIV acquisitions provided by Lelong [4]. From the verification and validation analysis a three dimensional grid and a set of computational parameters are chosen for future calculations with fluid-structure interaction and cavitation.
Tue, 01 Jan 2019 00:00:00 GMThttp://hdl.handle.net/10985/218372019-01-01T00:00:00ZPERALI, PaoloHAUVILLE, FrédéricLEROYER, AlbanASTOLFI, Jacques-AndréVISONNEAU, MichelWhen cavitation occurs around hydrofoils it is the cause of noise radiation, vibration and erosion. Consequently numerical cavitation models have been developped and tested over the last decades (Schnerr and Sauer [1]). However, recent works show that numerical predictions for cavitating flow might be very sensitive to the spatial resolution of the mesh and require dicretization errors estimations (Negrato et al. [2], Asnaghi et al. [3]). The experimental and numerical approches joined in this work are the first step of the validation of the ISIS-CFD code for cavitating flows with fluid-structure interaction. Although, only results for a rigid profile in cavitating conditions are presented in this work. The test case is a NACA0015 profile in the cavitation tunnel located at the french Naval Academy Research Institute. On the numerical side, the ISIS-CFD code is used to solve the unsteady Reynolds Averaged Navier Stokes Equations (uRANSE). The two phases mixture dynamics are solved thanks to an interface capturing method and the Sauer cavitation model. The test case is first adressed using a two-dimensional computational domain. A set of unstructured grids is generated using Hexpress to perform a grids and time steps convergence study and obtain uncertainty estimations for both wetted and cavitating flow conditions. Then, the same study is done for an extended three-dimensional geometry taking into account the lateral walls of the tunnel and the convergent section located upstream of the test section. Influences of the turbulence quantities at the inflow and the cavitation model parameters are also assessed. The numerical results are compared with experimental effort measurements, high-speed camera signals and PIV acquisitions provided by Lelong [4]. From the verification and validation analysis a three dimensional grid and a set of computational parameters are chosen for future calculations with fluid-structure interaction and cavitation.Vortex Induced Vibration Analysis of a Cantilevered Hydrofoil by Laser Vibrometry and TR-PIV
http://hdl.handle.net/10985/21859
Vortex Induced Vibration Analysis of a Cantilevered Hydrofoil by Laser Vibrometry and TR-PIV
ASTOLFI, Jacques-André; BOT, Patrick; LEROY, Laure
The structural response of a steel cantilevered hydrofoil is analyzed through an experiment carried out in a hydrodynamic tunnel for Reynolds numbers ranging from 2 105 to 8:25 105. The hydrofoil is set at a 17 angle to the flow direction, in order to maximize the hydrodynamic forcing issued from the vortex shedding, thus enhancing fluid structure interactions. The structural response is measured through the vibration velocity using a laser Doppler vibrometer. The flow dynamics are analyzed through Time Resolved-Particle Image Velocimetry (TR-PIV) and Proper Orthogonal Decomposition. An interaction between the vortex shedding phenomenon and the modal response of the structure is observed. A decrease of the modal frequencies occurs
for Reynolds numbers above 4 105. The modal frequencies are found to decrease towards the vortex shedding frequency as the velocity increases resulting in resonance flow velocities much lower than the ones predicted in a non coupling hypothesis. The experimental results presented in this paper will help to develop fluid-structure interaction models and simulations in naval
applications.
Fri, 01 May 2020 00:00:00 GMThttp://hdl.handle.net/10985/218592020-05-01T00:00:00ZASTOLFI, Jacques-AndréBOT, PatrickLEROY, LaureThe structural response of a steel cantilevered hydrofoil is analyzed through an experiment carried out in a hydrodynamic tunnel for Reynolds numbers ranging from 2 105 to 8:25 105. The hydrofoil is set at a 17 angle to the flow direction, in order to maximize the hydrodynamic forcing issued from the vortex shedding, thus enhancing fluid structure interactions. The structural response is measured through the vibration velocity using a laser Doppler vibrometer. The flow dynamics are analyzed through Time Resolved-Particle Image Velocimetry (TR-PIV) and Proper Orthogonal Decomposition. An interaction between the vortex shedding phenomenon and the modal response of the structure is observed. A decrease of the modal frequencies occurs
for Reynolds numbers above 4 105. The modal frequencies are found to decrease towards the vortex shedding frequency as the velocity increases resulting in resonance flow velocities much lower than the ones predicted in a non coupling hypothesis. The experimental results presented in this paper will help to develop fluid-structure interaction models and simulations in naval
applications.Cycloidal Dynamic Propulsion or Positioning System For a Ship
http://hdl.handle.net/10985/21898
Cycloidal Dynamic Propulsion or Positioning System For a Ship
DAMAY, Thomas; HAUVILLE, Frédéric; ASTOLFI, Jacques-André
A cycloidal dynamic propulsion or positioning system for a ship in water that exhibits a direction of flow, including a frame, a rotor mounted to be movable in rotation on the frame about a main axis at right angles to the flow, including a plurality of arms extending radially with respect to the main axis, a main motor equipped with a rotary coder and driving the rotor in rotation, for each arms, a blade mounted to be movable in rotation on the arm about a secondary axis parallel to the main, for each blades,a secondary motor equipped with a rotary coder and driving the blade in rotation, for at least one blade, a load sensor able to evaluate the loads exerted on the blade, and a control unit connected to each coder, strain sensor and motor and controlling the rotation of each motor in terms of angle and speed.
Thu, 03 Mar 2022 00:00:00 GMThttp://hdl.handle.net/10985/218982022-03-03T00:00:00ZDAMAY, ThomasHAUVILLE, FrédéricASTOLFI, Jacques-AndréA cycloidal dynamic propulsion or positioning system for a ship in water that exhibits a direction of flow, including a frame, a rotor mounted to be movable in rotation on the frame about a main axis at right angles to the flow, including a plurality of arms extending radially with respect to the main axis, a main motor equipped with a rotary coder and driving the rotor in rotation, for each arms, a blade mounted to be movable in rotation on the arm about a secondary axis parallel to the main, for each blades,a secondary motor equipped with a rotary coder and driving the blade in rotation, for at least one blade, a load sensor able to evaluate the loads exerted on the blade, and a control unit connected to each coder, strain sensor and motor and controlling the rotation of each motor in terms of angle and speed.Système de propulsion ou de positionnement dynamique cycloidal pour un navire
http://hdl.handle.net/10985/21915
Système de propulsion ou de positionnement dynamique cycloidal pour un navire
DAMAY, Thomas; HAUVILLE, Frédéric; ASTOLFI, Jacques-André
L'invention concerne un système de propulsion ou de positionnement dynamique cycloïdal pour un navire baignant dans une eau présentant une direction d'écoulement et comportant un châssis, un rotor montè mobile en rotation sur le châssis autour d'un axe principal perpendiculaire à la direction d'écoulement, et comportant une pluralité de bras s'étendant radialement par rapport à l'axe principal, un moteur principal équipé d'un codeur rotatif et entraînant ledit rotor en rotation, pour chaque bras, une pale montée mobile en rotation sur le bras autour d'un axe secondaire parallèle à l'axe principal, pour chaque pale, un moteur secondaire équipé d'un codeur rotatif et entraînant ladite pale en rotation, pour au moins une pale, un capteur d'effort agencé de manière à pouvoir évaluer les efforts qui s'exercent sur la pale, et une unité de contrôle connectée à chaque codeur rotatif, au capteur à jauge de contrainte et à chaque moteur et commandant la rotation en angle et en vitesse de chaque moteur.
Tue, 01 Jan 2019 00:00:00 GMThttp://hdl.handle.net/10985/219152019-01-01T00:00:00ZDAMAY, ThomasHAUVILLE, FrédéricASTOLFI, Jacques-AndréL'invention concerne un système de propulsion ou de positionnement dynamique cycloïdal pour un navire baignant dans une eau présentant une direction d'écoulement et comportant un châssis, un rotor montè mobile en rotation sur le châssis autour d'un axe principal perpendiculaire à la direction d'écoulement, et comportant une pluralité de bras s'étendant radialement par rapport à l'axe principal, un moteur principal équipé d'un codeur rotatif et entraînant ledit rotor en rotation, pour chaque bras, une pale montée mobile en rotation sur le bras autour d'un axe secondaire parallèle à l'axe principal, pour chaque pale, un moteur secondaire équipé d'un codeur rotatif et entraînant ladite pale en rotation, pour au moins une pale, un capteur d'effort agencé de manière à pouvoir évaluer les efforts qui s'exercent sur la pale, et une unité de contrôle connectée à chaque codeur rotatif, au capteur à jauge de contrainte et à chaque moteur et commandant la rotation en angle et en vitesse de chaque moteur.A classification approach to efficient global optimization in presence of non-computable domains
http://hdl.handle.net/10985/15139
A classification approach to efficient global optimization in presence of non-computable domains
SACHER, Matthieu; DUVIGNEAU, Régis; LE MAÎTRE, Olivier; DURAND, Mathieu; BERRINI, Elisa; HAUVILLE, Frédéric; ASTOLFI, Jacques-André
Gaussian-Process based optimization methods have become very popular in recent years for the global optimization of complex systems with high computational costs. These methods rely on the sequential construction of a statistical surrogate model, using a training set of computed objective function values, which is refined according to a prescribed infilling strategy. However, this sequential optimization procedure can stop prematurely if the objective function cannot be computed at a proposed point. Such a situation can occur when the search space encompasses design points corresponding to an unphysical configuration, an ill-posed problem, or a non-computable problem due to the limitation of numerical solvers. To avoid such a premature stop in the optimization procedure, we propose to use a classification model to learn non-computable areas and to adapt the infilling strategy accordingly. Specifically, the proposed method splits the training set into two subsets composed of computable and non-computable points. A surrogate model for the objective function is built using the training set of computable points, only, whereas a probabilistic classification model is built using the union of the computable and non-computable training sets. The classifier is then incorporated in the surrogate-based optimization procedure to avoid proposing new points in the non-computable domain while improving the classification uncertainty if needed. The method has the advantage to automatically adapt both the surrogate of the objective function and the classifier during the iterative optimization process. Therefore, non-computable areas do not need to be a priori known. The proposed method is applied to several analytical problems presenting different types of difficulty, and to the optimization of a fully nonlinear fluid-structure interaction system. The latter problem concerns the drag minimization of a flexible hydrofoil with cavitation constraints. The efficiency of the proposed method compared favorably to a reference evolutionary algorithm, except for situations where the feasible domain is a small portion of the design space.
Mon, 01 Jan 2018 00:00:00 GMThttp://hdl.handle.net/10985/151392018-01-01T00:00:00ZSACHER, MatthieuDUVIGNEAU, RégisLE MAÎTRE, OlivierDURAND, MathieuBERRINI, ElisaHAUVILLE, FrédéricASTOLFI, Jacques-AndréGaussian-Process based optimization methods have become very popular in recent years for the global optimization of complex systems with high computational costs. These methods rely on the sequential construction of a statistical surrogate model, using a training set of computed objective function values, which is refined according to a prescribed infilling strategy. However, this sequential optimization procedure can stop prematurely if the objective function cannot be computed at a proposed point. Such a situation can occur when the search space encompasses design points corresponding to an unphysical configuration, an ill-posed problem, or a non-computable problem due to the limitation of numerical solvers. To avoid such a premature stop in the optimization procedure, we propose to use a classification model to learn non-computable areas and to adapt the infilling strategy accordingly. Specifically, the proposed method splits the training set into two subsets composed of computable and non-computable points. A surrogate model for the objective function is built using the training set of computable points, only, whereas a probabilistic classification model is built using the union of the computable and non-computable training sets. The classifier is then incorporated in the surrogate-based optimization procedure to avoid proposing new points in the non-computable domain while improving the classification uncertainty if needed. The method has the advantage to automatically adapt both the surrogate of the objective function and the classifier during the iterative optimization process. Therefore, non-computable areas do not need to be a priori known. The proposed method is applied to several analytical problems presenting different types of difficulty, and to the optimization of a fully nonlinear fluid-structure interaction system. The latter problem concerns the drag minimization of a flexible hydrofoil with cavitation constraints. The efficiency of the proposed method compared favorably to a reference evolutionary algorithm, except for situations where the feasible domain is a small portion of the design space.Development of an Experimental Blade-controlled Cycloidal Propeller
http://hdl.handle.net/10985/21835
Development of an Experimental Blade-controlled Cycloidal Propeller
FASSE, Guillaume; HAUVILLE, Frédéric; GERMAIN, Grégory; ASTOLFI, Jacques-André; BECKER, Florent
As an interesting naval propulsion system, this paper presents the development of an experimental cycloidal propeller. Cross-flow propellers are characterized by the rotation of several blades around a vertical axis associated with a movement of each blade around its axis (blade pitching). Two kinematic modes depending on the advance coefficient Lambda are distinguished: cycloidal mode for low ship speeds (Lambda < 1) and trochoidal mode for high speeds (Lambda > 1). The final goal is to establish pitch laws, for each of those two modes, dealing with a target optimization (thrust maximizing for example). For this purpose, an experimental thruster designed at the IRENav can perform more or less complicated pitch laws thanks to three servo motor controlling each blade independently. Kinematics of cycloid propellers is first outlined, and pitch laws are defined by a quasi-static approach. Then Ifremer facilities of Boulogne-sur-Mer are presented. The experimental thruster is also described as its current blade-control system. Finally, improvements on the electronic command have proceeded through the development of a Digital Twins and a test bench.
Tue, 01 Jan 2019 00:00:00 GMThttp://hdl.handle.net/10985/218352019-01-01T00:00:00ZFASSE, GuillaumeHAUVILLE, FrédéricGERMAIN, GrégoryASTOLFI, Jacques-AndréBECKER, FlorentAs an interesting naval propulsion system, this paper presents the development of an experimental cycloidal propeller. Cross-flow propellers are characterized by the rotation of several blades around a vertical axis associated with a movement of each blade around its axis (blade pitching). Two kinematic modes depending on the advance coefficient Lambda are distinguished: cycloidal mode for low ship speeds (Lambda < 1) and trochoidal mode for high speeds (Lambda > 1). The final goal is to establish pitch laws, for each of those two modes, dealing with a target optimization (thrust maximizing for example). For this purpose, an experimental thruster designed at the IRENav can perform more or less complicated pitch laws thanks to three servo motor controlling each blade independently. Kinematics of cycloid propellers is first outlined, and pitch laws are defined by a quasi-static approach. Then Ifremer facilities of Boulogne-sur-Mer are presented. The experimental thruster is also described as its current blade-control system. Finally, improvements on the electronic command have proceeded through the development of a Digital Twins and a test bench.Surrogates and Classification approaches for Efficient Global Optimization (EGO) with Inequality Constraints
http://hdl.handle.net/10985/21860
Surrogates and Classification approaches for Efficient Global Optimization (EGO) with Inequality Constraints
SACHER, Matthieu; DUVIGNEAU, Régis; LE MAITRE, Olivier; DURAND, Mathieu; BERRINI, Elisa; HAUVILLE, Frédéric; ASTOLFI, Jacques-André
In this work, we compare the use of Gaussian Process (GP) models for the constraints [Schonlau 1997] with a classification approach relying on a Least-Squares Support Vector Machine (LS-SVM) [Suykens and Vandewalle 1999]. We propose several adaptations of the classification approach in order to improve the efficiency of the EGO procedure, in particular an extension of the binary LS-SVM classifier to come-up with a probabilistic estimation of the feasible domain. The efficiencies of the GP-models and classification methods are compared in term of computational complexities, distinguishing the construction of the GPmodels
or LS-SVM classifier from the resolution of the optimization problem. The effect of the number of design parameters on the numerical costs is also investigated. The approaches are tested on the optimization of a complex non-linear Fluid-Structure Interaction system modeling a two dimensional flexible hydrofoil. Multi-design variables, defining the unloaded geometry of the
foil and the characteristics of its elastic trailing edge, are used in the minimization of the foil’s drag, under constraints set to ensure minimal lift force and prevent cavitation at selected boat-speeds.
Mon, 01 May 2017 00:00:00 GMThttp://hdl.handle.net/10985/218602017-05-01T00:00:00ZSACHER, MatthieuDUVIGNEAU, RégisLE MAITRE, OlivierDURAND, MathieuBERRINI, ElisaHAUVILLE, FrédéricASTOLFI, Jacques-AndréIn this work, we compare the use of Gaussian Process (GP) models for the constraints [Schonlau 1997] with a classification approach relying on a Least-Squares Support Vector Machine (LS-SVM) [Suykens and Vandewalle 1999]. We propose several adaptations of the classification approach in order to improve the efficiency of the EGO procedure, in particular an extension of the binary LS-SVM classifier to come-up with a probabilistic estimation of the feasible domain. The efficiencies of the GP-models and classification methods are compared in term of computational complexities, distinguishing the construction of the GPmodels
or LS-SVM classifier from the resolution of the optimization problem. The effect of the number of design parameters on the numerical costs is also investigated. The approaches are tested on the optimization of a complex non-linear Fluid-Structure Interaction system modeling a two dimensional flexible hydrofoil. Multi-design variables, defining the unloaded geometry of the
foil and the characteristics of its elastic trailing edge, are used in the minimization of the foil’s drag, under constraints set to ensure minimal lift force and prevent cavitation at selected boat-speeds.