Predicting the Flying shape and forces on Upwind Sails Sriram Shankaran, Antony Jameson   We predict the flying shape and forces on upwind sails in an iterative fashion: The pressure loading obtained from an inviscid flow solution is coupled to a non-linear structural analysis program which computes the deflected shape of the sail. The process is repeated until a converged deflected shape of the sail is obtained. Flow solver The equations governing inviscid incompressible flow are solved using the method of `artificial compressibility' . The resulting equations are discretized on an unstructured tetrahedral mesh and integrated in time. Convergence to steady state is accelerated using multigrid and iterative residual averaging techniques and further reduction in computational time is obtained by the use of parallel computing. The combined use of these techniques enables a flow computation to be performed in roughly 10 minutes using 8 processors of a SGI Origin 2000 and typically requires 50-75 multigrid W-cycles. Structural analysis The pressure loading obtained from the flow solution is transferred to a Finite Element structural package (MSC/NASTRAN), which computes the deflected shape of the sail. Membrane elements with structural properties of dacron are used to model the sail and the static deflected shape of the sail is obtained by solving the steady equations of motion. The tetrahedral mesh is displaced to conform to the deflected shape of the sail and a new pressure loading is computed for the deflected shape. This process is iteratively repeated until the deflected shape of the sail is obtained. Results The computed lift and induced drag for a main sail with elliptic planform compares well with results from lifting surface theories. Simulations have also been performed for a main sail and a head and main sail combination which is representative of the sails used in Americas Cup. Future directions Future efforts will be directed at shape optimization techniques using adjoint methods to maximize the speed of the boat for given characteristics of the hull, keel and appendages by controlling the twist, camber and trim of the sail.
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