While discussing with Xavier Guisnel from VPLP during a marine session at the NUMECA User Meeting, the idea of revising the hydrofoil simulation standards appeared to be a necessity. He mentioned that “the desired lift force should be an input and not just an output of the simulation”. But as CFD software developers, we know that if an input is not a boundary condition but a target value, the code should dynamically and automatically adapt to respect this value. For our case, the hydrofoil position should then be adapted to find a dynamic equilibrium position and reach the desired lift force. Internal debates started and the solution appeared quickly: the quasi-static approach, dedicated to hydrofoil, was born.
At a given frequency, the flow solver adapts the rake and the yaw of the hydrofoil and checks the targeted lift and side forces. With this iterative process, the subsequent predictions of the solver progressively determine the dynamic equilibrium position: angles are quickly stabilized and target forces rapidly reached (1.5s of physical time for convergence in this case).
Figure: side and lift forces convergence
Figure: rake and yaw angles convergence
Also, in terms of meshing, big improvements have been made. Hydrofoils play an important role in the biggest sailing races in the world, like the America’s cup, the Vendee Globe or the Volvo Ocean Race. These teams' designers are constantly challenging us to deliver not only the most accurate data for the hydrofoils, but to do it in a limited time as well. Lots of brainstorming led to the creation of impressive meshes that combine the best of two universes in the CFD world: structured and unstructured meshing. Why is it interesting?
The geometry of hydrofoils is usually not aligned with Cartesian axis. As a consequence, unstructured mesh generators produce non-orthogonal cells close to and on solid surfaces. The idea of combining structured and unstructured meshing, is to keep working with an unstructured mesh, but to initialize the mesh with a structured one first. To do this, we create a kind of a “sock” around the foil and “fill it” with a structured block covering the whole domain created by this sock.
|Figure: sock around the foil
||Figure: Initial structure mesh
We then continue with mesh refinements and viscous layers insertion to make the mesh as representative of the geometry as possible. The mesh quality all along the solid surfaces is just perfect.
Figure: Mesh section of the solid surface of the hydrofoil
As we created a dedicated domain around the hydrofoil, this domain has its own mesh and own degrees of freedom in terms of motion as well. No need for mesh deformation, no need to limit motions amplitudes, thanks to the overset approach connecting this domain with the background mesh: 260k cells are used for the background mesh and 4.9M cells for the hydrofoil mesh.
Figure: Side view of the background and hydrofoil meshes
Figure: Front views of the meshes (blue: background mesh, red: hydrofoil overlapping mesh)
Now your next question could be: Will the free surface be correctly captured? We cannot see any dedicated refinement for it. Also, is the overset interpolation always optimal? For both questions, the answer is YES, thanks to the “adaptive grid refinement”.
Two criteria are combined during the simulation:
1) “free surface capturing” and
2) “overset mesh continuity”.
Together they create the best mesh we can hope for this kind of simulation. The free surface is dynamically refined and since we know that the wake created by a hydrofoil is quite important in amplitude, it is good to see that only the necessary cells are created. This drastically limits CPU time! As a matter of fact, only 700k cells have been created during this simulation.
Figure: Side view of the dynamically adapted mesh during the simulation
Concerning the overset, the dedicated adaptive grid refinement criterion adds cells at the interpolation location to make sure that it stays optimal: a volume ratio of 1 between the background and overlapping meshes is respected as much as possible.
And that’s not all! In real life conditions, its structure can deform sufficiently to influence its performances, even if this deformation will stay relatively small and linear. This is totally in line with the hypothesis of a modal approach for a fluid/structure interaction: this method only requires the mode shapes from the structure computed beforehand and the interaction can be fully solved inside the CFD solver only. As such, no need for heavy and fully coupled fluid/structure solvers dynamic communication. The additional CPU cost here is only about 20%, yet it can bring an important impact on the design decision! In this case for instance the yaw angle changed from 2.53 to 3.40deg and the drag from 8.741 to 8.935N.
Figure: Yaw angle convergence comparing a modal “Modal_QS_UR” and non modal simulation “Motion_QS”
The take-home message for this new big step in terms of CFD simulation for hydrofoils is the following:
- Using a structured initial mesh for the hydrofoil domain leads to a very high quality mesh on the surface of the foil, but also at the overset interpolation.
- The new quasi-static approach dedicated to hydrofoils converges nicely and quickly according to the prescribed target forces.
- The adaptive grid refinement approach simplifies the meshing process and ensures optimum free surface capturing and overset interpolation.