A computational methodology, which combines a computational fluid dynamics (CFD) technique and a computational structural dynamics (CSD) technique, is employed to design a deformable foil whose kinematics is inspired by the propulsive motion of the fin or the tail of a fish or a cetacean. The unsteady incompressible Navier–Stokes equations are solved using a second-order accurate finite difference method and an immersed-boundary method to effectively impose boundary conditions on complex moving boundaries. A finite element-based structural dynamics solver is employed to compute the deformation of the foil due to interaction with fluid. The integrated CFD–CSD simulation capability is coupled with a surrogate management framework (SMF) for nongradient-based multivariable optimization in order to optimize flapping kinematics and flexibility of the foil. The flapping kinematics is manipulated for a rigid nondeforming foil through the pitching amplitude and the phase angle between heaving and pitching motions. The flexibility is additionally controlled for a flexible deforming foil through the selection of material with a range of Young's modulus. A parametric analysis with respect to pitching amplitude, phase angle, and Young's modulus on propulsion efficiency is presented at Reynolds number of 1100 for the NACA 0012 airfoil.

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