Inverse Design of Axial Compressor Cascade Blades in Inviscid Subsonic Flow Using Upgraded Elastic Surface Method

The aim of inverse design problems is achieving a geometry corresponding to the wall target pressure distribution. One of the newest inverse design methods, was Elastic Surface Algorithm (ESA) in which the airfoil wall was modeled as a flexible curved beam and the difference between target and current pressure distributions in each iteration was the deformation factor of the airfoil wall. The first version of ESA used for the inverse design of sharp leading edge blade of axial flow compressors, is subject to oscillation, instability and divergence due to high pressure gradients on the blade leading edge. Therefore, it cannot be used for a sharp leading edge blade. The purpose of this research is to develop ESA for axial-flow compressor cascade with sharp leading edge blades. The main basis of this Improvement is paying attention to the deflection curve of the beam, which is continuous and differentiable in all points. The physical property of Timoshenko’s beam in large deformations is used in the upgraded version without applying any geometric filtration to eliminate the fractures of the intermediate profiles. In order to increase the displacement of the beam at each iteration, an optimal relationship between the beam characteristics including the elasticity modulus, the thickness and width of the beam is used. Finally, the upgraded version has been validated in a few cases for subsonic inviscid flow regime. The results indicate the robustness, flexibility and high convergence rate of the upgraded ESA in the design of axial-flow compressor blades.