Airfoil Shape Optimization Using a Nonuniform Rational B-Splines Parametrization Under Thickness Constraint

Results for 2-D airfoil shape optimization in transonic regime are presented. Airfoil shapes are represented by nonuniform rational B-splines with appropriate regularity properties. A Navier-Stokes flow solver is used to compute the flow field and to obtain aerodynamic coefficients. A design of experiment is conducted to select the most sensitive design variables among the nonuniform rational B-splines parameters to reduce their number in the final optimization process. Single-point and multipoint formulations of the optimization problem are proposed and compared. The nonuniform rational B-splines parameterization guarantees smooth optimized airfoils. The multipoint optimization formulation combined with the nonuniform rational B-splines parameterization leads to airfoils with good performance over a specified Mach range.