Design methodologies for axial compressor airfoils have undergone significant changes over the past decades. While inverse design methods have played a significant historical role, today they are mostly replaced by direct methods. Inverse methods do impose either the desired pressure or velocity distribution and search for the corresponding blade profile, in contrast to direct methods which modify directly the blade shape to reduce losses. Inverse methods therefore require the designer to know pressure or velocity profiles which provide low losses, and are as such mostly effective only in the hands of an experienced designer.
Inverse methods, however, pose some advantages: through setting velocity profiles which feature good off-design performance, the computational cost for the design of profiles can be significantly reduced compared to direct methods, which require to simulate multiple operating points. Additionally, inverse methods offer a way to adapt blades for experimental testing if the wind tunnel imposes restrictions on e.g. Mach number, allowing for similar boundary layer conditions. Finally, inverse methods can be used to deduce the blade geometry from measured or published velocity distributions.
Within this article, we aim to verify the use of inverse methods by applying more recent optimisation techniques to the inverse problem. Specifically, we test the performance of an inverse method that uses a gradient based technique to solve the inverse problem. The merits of the inverse method are investigated for different use cases. It is found that conventional, direct design methods are preferred for design improvement, although more expensive. The inverse method is, however, well-suited for adapting existing profiles to altered operating conditions, and for reproducing the blade shape based on published data.