Date of Award


Degree Name

MS in Aerospace Engineering


Aerospace Engineering


David D. Marshall


The engineering problem of airfoil design has been of great theoretical interest for almost a century and has led to hundreds of papers written and dozens of methods developed over the years. This interest stems from the practical implications of airfoil design. Airfoil selection significantly influences the application's aerodynamic performance. Tailoring an airfoil profile to its specific application can have great performance advantages. This includes considerations of the lift and drag characteristics, pitching moment, volume for fuel and structure, maximum lift coefficient, stall characteristics, as well as off-design performance.

A common way to think about airfoil design is optimization, the process of taking an airfoil and modifying it to improve its performance. The classic design goal is to minimize drag subject to required lift and thickness values to meet aerodynamic and structural constraints. This is typically an expensive operation depending on the selected optimization technique because several flow solutions are often required in order to obtain an updated airfoil profile. The optimizer requires gradients of the design space for a gradient-based optimizer, fitness values of the members of the population for a genetic algorithm, etc.

An alternative approach is to specify some desired performance and find the airfoil profile that achieves this performance. This is known as inverse airfoil design. Inverse design is more computationally efficient than direct optimization because changes in the geometry can be related to the required change in performance, thus requiring fewer flow solutions to obtain an updated profile. The desired performance for an inverse design method is specified as a pressure or velocity distribution over the airfoil at given flight conditions. The improved efficiency of inverse design comes at a cost. Designing a target pressure distribution is no trivial matter and has severe implications on the end performance. There is also no guarantee a specified pressure or velocity distribution can be achieved. However, if an obtainable pressure or velocity distribution can be created that reflects design goals and meets design constraints, inverse design becomes an attractive option over direct optimization.

Many of the available inverse design methods are only valid for incompressible flow. Of those that are valid for compressible flow, many require modifications to the method if shocks are present in the flow. The convergence of the methods are also greatly slowed by the presence of shocks. This paper discusses a series of novel inverse design methods that do not depend on the freestream Mach number. They can be applied to design cases with and without shocks while not requiring modifications to the methods. Shocks also do not have a significant impact on the convergence of the methods. Airfoils are represented with parametric equations from the CST method to control shape changes and relate them to the required changes in the pressure or velocity distribution. To display the power of the methods, design cases are presented in the subsonic and transonic regimes. A circulation control design case is also presented using one of the methods to further show the robustness of the method.