Trans RINA, Vol 153, Part B2, Intl J Small Craft Tech, 2011 Jul-Dec


a parameterization of its camber and trim angle on its three main sections (bottom, middle and top sections). This


defines a mono objective and six variables


optimization problem (O1P6). In this first example no FSI loop is implemented yet. The optimization process resolves the three-dimensional Navier-Stokes equations in RANS formulation with the turbulence model


and the CMA-ES


algorithm search for optimal cambers and trim angles in the three sail sections.


The mesh is automatically generated on GAMBIT with sail surface boundary layer resolution of y+=O(300) and a total of 125 000 cells. This is a coarse but sufficient mesh resolution to test the optimization as was shown


during previous tests. The resolution


constraint may be relaxed during optimization because, as noted above, automatic mesh generation has a high repeatability. Another reason is that we just need to rank various sail shapes, not to predict their absolute performance. In fact, as shown in a previous paper, the important point is to be sure that main flow features of the explored rig configurations are qualitatively well predicted [19]. At the end of the process, when the best shape is found, it is always possible to increase the mesh resolution during another RANS simulation for higher absolute accuracy.


During the optimization process, which in this small case has been stopped at 91 RANS simulations, all the sail designs tested are represented in the design space and in the performance space. The history of the optimization process may be followed. As an example, in Figure 10, the aerodynamic performance of all the tested configurations is represented in the (Cl, Cl/Cd) plane. Because the optimization search for maximum lift coefficient, an accumulation of tested design is clearly visible in the maximum lift coefficient region during the end of the optimization. When you see that and you think it is enough, it is time to stop the optimization process.


A subset of designs, the non-dominated designs,


separates the aerodynamic performance plane in two regions (Figure 10). On the left of the Pareto frontier, we see the region of accessible designs and on the right, the region of inaccessible designs (for the given optimization problem). The non-dominated solutions along the Pareto frontier gives the best compromises achievable in


the plane (Cl, Cl/Cd) with the


parameterized sail studied during this optimization problem.


The friction lines (lines tangent to the friction vector on the wall surface) on the leeward side of the sail for selected designs extracted during the optimization are shown on Figure 11. On the two first sail designs, separation zones are clearly identified at the top of the sail for design 1 and in the mid-section on design 2. On the following sail design 3 the flow is more attached


Spalart-Allmaras evolutionary


along nearly all the sail surface with only a very small separation at the top of the sail. Design 4 is the optimal design found at optimal


the end of the optimization. This sail design shows no separated zones. It


maximizes the driving force in the range tested for camber and trim angle (4%<f/c<40%, 5°<<25°). It may be noted that the optimal three-dimensional sail, as opposed to two-dimensional optimal sails, found by the ES optimization, is not far from a separated flow but is not separated.


Given optimization examples in two and now in three- dimensional flows illustrates what can be done on sail design with the computational framework ADONF. It may be used to quantify the influence of mainsail-jib overlapping factor, sail camber position, entry and exit angles, etc, in a simple manner or to find the optimal design based on a given objective function and design constraints.


Figure 10: aerodynamic performances of all the tested sail designs during the optimization process in the plane (lift, lift-to-drag ratio).


Figure 11: selected sail designs before the convergence toward an optimal sail design.


©2011: The Royal Institution of Naval Architects B-111


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