Hydrofoils have unleashed the speed of sailing boats since the last two America’s Cups and are exclusively designed with CFD. The French company VPLP Design is at the cutting edge of hydrofoil concept and has worked with Alex Thomson Racing and Charal Sailing Team on the last generation of IMOCAs, to design efficient sailing boats that are literally flying over the oceans. Among all their objectives, VPLP has to identify the correct position of the hydrofoils in terms of angles and draughts for a required lift force. This objective traditionally required running 6 to 8 simulations per speed, until FINE™/Marine offered VPLP a new, innovative approach that reduced this workflow to one single simulation, while taking into account more physics.

 

Being able to find the best position of a hydrofoil in a single computation implies that the target lift force should become an input of the simulation. The CFD code should automatically find a dynamic equilibrium position and reach the desired lift force at the same time. A new feature has been developed in FINE™/Marine to reach this objective and is now available as a quasi-static approach dedicated to hydrofoils: the flow solver adapts the hydrofoil rake and yaw angles at a given frequency according to the targeted lift. The subsequent predictions of the solver progressively and rapidly determine the dynamic equilibrium: stabilization is usually reached in about 1 to 2s of physical time.

 

This methodology requires both:

a) freedom in terms of hydrofoil motion which is made possible with the overset technique of FINE™/Marine,

b) a high-quality volumic mesh for accuracy and robustness.

 

The proposed approach is to start NUMECA’s full hex unstructured grid generator OMNIS™/Hexpress from an initial curved block that follows the shape of the hydrofoil (see figure 2). This ensures a high-quality mesh at the hydrofoil surfaces but also at the domain boundaries.

 

FIGURE 1: 3D representation of the wake of the hydrofoil

FIGURE 2: Curved domain around the foil

Mesh refinements and viscous layers are then performed with OMNIS™/Hexpress. Figures 3 and 4 illustrate the nice alignment of cells on the surfaces.

 

Furthermore, to ensure an ideal interpolation, the adaptive grid refinement technique dynamically refines the cells only where strictly necessary: at the free surface location during the simulation and at the overlapping grid boundaries. The total mesh size is thus reduced by 800k cells compared to an equivalent static mesh where the refinements should have been estimated.

 

FIGURE 5: Front view of the meshes (blue: background, red:  hydrofoil overlapping)

FIGURE 6: Side view of the dynamic free surface refinements

 

The importance of fluid-structure interaction

Because the hydrofoils are the only part of the sailing boat touching the water during their flight, they are exposed to high-pressure forces and their structure can deform sufficiently to influence their performance, even if this deformation will stay relatively small and linear. Hence, a modal approach can be used which only requires the mode shapes from the structure computed beforehand. The complete interaction can then be fully solved inside FINE™/Marine without interaction with an FEA code. Because the motion of the foil is relatively steady, a new and faster approach can be also used to solve the structure deformation: a quasi-static approach for deformation, as it is done for the motions. The additional CPU cost is only about 20%, yet it can bring an important impact on the design decision. In this case, for instance, the bending and torsional stiffness influence the dynamic equilibrium position, and therefore the flow field around the hydrofoil. The yaw angle changed from 2.53 to 3.40deg (see figure 7) and the drag from 8.741 to 8.935N.

 

FIGURE 7: Yaw angle convergence comparing a modal "Modal_QS_UR" and non modal "Motion_QS" simulation

FIGURE 8: Deformation of the structure during the  FINE™/Marine simulation with the modal approach

 

VPLP managed to reduce the simulation time of their design process by a factor of 8 while assessing more physics than before. With NUMECA's software dedicated to marine hydrodynamics they are able to study a large number of variants of their hydrofoils with a reliable, fast and robust process. As a next step, the power of NUMECA’s FINE™/Design3D optimization solutions with coarse DoE, uncertainty quantification, and advanced surrogate modeling will allow optimizing the next generation of hydrofoils under real-world conditions.