Aerodynamic shape design of rotor airfoils undergoing unsteady motion

A new design method is suggested that can handle the dynamic response of an airfoil subjected to unsteady motion and flow conditions. A new objective function and constraints are defined to represent the overall characteristics of the rotor airfoil over a single cycle. A weighting function is also introduced to enable a designer to determine the specific azimuthal location at which the performance is improved intensively. A numerical analysis code that can handle the oscillatory pitching motion of an airfoil and the inflow Mach number variation is developed. The analyses during the design process are limited to the cases without dynamic stall because the numerical analysis code cannot predict the dynamic stall phenomena with sufficient accuracy. Response surface methodology is exclusively employed to construct and optimize the response surface models of the objective functions and constraints. The advantages of the method are demonstrated by a comprehensive comparison with a static three-point design method. The dynamic method can yield a better airfoil for the following reasons: 1) The static performance is not always proportional to the dynamic performance. 2) The moment constraint used in the static three-point design is too tight to allow enough variation of the design variables. 3) The objective function of the static three-point design may be implicitly overweighted at a certain design point so that the overall aerodynamic performance is miscalculated, unlike in the present method. The variations of the aerodynamic performance with weighting functions are also discussed.