Adjoint-Based Inverse Design of Axial Compressor Airfoils

Abstract

Direct design optimisation methods for turbomachinery blades have consistently gained in popularity over time. This has been accomplished by significant advances in optimisation algorithms, and notably the development of adjoint-based gradient computation, which provides objective sensitivity information at comparatively low computational cost. This enables the use of first-order optimisation methods for more complex design problems. On the other hand, interest in inverse design methods has steadily diminished over time. This is because these methods come with significant disadvantages or weaknesses, such as requiring strong simplification or only being narrowly applicable, e.g. incompressible, potential flow. However, by applying the advances in optimisation techniques to an inverse design strategy, a versatile and effective design tool can be created with functionalities not offered by direct design techniques.

In order to evaluate the feasibility and usefulness of such a method, an adjoint-based inverse design tool for 2D axial compressor blades was developed. The tool requires a baseline geometry and a target pressure or isentropic Mach distribution along the blade wall. It then analyses the flow field around the initial geometry and modifies autonomously the shape to reach closer to the desired target distribution. A discrete adjoint approach is used to compute the gradients of the objective with respect to each of the design variables. The objective and its gradients are used by a the first-order SQP optimisation algorithm to iterate the design until it matches the target distribution as closely as possible.

The newly developed design tool was used in an attempt of improving the performance of the NASA stage 35 stator blade. For comparison, also single- and multi-objective direct design optimisations were performed. It became clear that while significantly cheaper in computational cost and simpler in program complexity, the inverse design method cannot be used to reliably produce improved designs. The value of the resulting design is entirely dependent on the quality of the target distribution. It is up to the designer to create a target which is physically possible and leads to increased performance.

Still, inverse design does provide unique capabilities not offered by direct design. The tool was successfully used to retrieve the blade geometry used in a different work based on published isentropic Mach number distributions. The obtained geometry closely matched the actual geometry used in the source work. This demonstrates the accuracy of the method and the fulfilment of a use case not offered by other design methods.