Numerical Optimization of flapping foil kinematics using high-order spectral difference method

A high-order spectral difference (SD ) scheme based cost-effective optimization approach is proposed to optimize the kinematics of flapping airfoils for maximum propulsive efficiency. Specifically, a gradient-based opti1nization algorithm is coupled with a high-order SD Navier-Stokes solver to search for the optimal kinematics of a series of NACA. 4-digit airfoils undergoing combined plunge and pitch 1notion on a coarse mesh. Then the high-order SD solver is used to capture the detailed vortex structures associated with the optimal kinemnatics of the flapping flight on a fine mesh. The proposed nu1nerical optimization framework is used to study the efiects of airfoil thickness, Reynolds number, and pitching pivot location for optimal cruise flight. The flow physics behind optimal airfoil oscillation is explained by examining the corresponding flow fields, aerodynamic forces and the variation of effective angle of attack.