Airfoil shape design using the Navier-Stokes equations

Abstract

This chapter describes a design method for an airfoil shape. The flow field is dominated by the Navier‑Stokes equations. An objective function is defined. The airfoil shape is optimized by varying the design variables, such that the objective function is minimized. The sequential quadratic programming procedure is used for the optimization. The procedure iterates solving a quadratic programming subproblem. Each iteration requires the gradient of the objective function with respect to the design variables. The gradient is calculated by using the implicit function theorem. The calculation costs only as much CPU time as one flow simulation. Hence, the CPU time for the design decreases greatly. A preliminary numerical test is shown for a compressor cascade.