Upgrade and development of elastic surface inverse design method for axial compressor cascade with sharp-edged blades

Abstract

The aim of an inverse design method is to calculate the geometry corresponding to a target pressure distribution along the walls. Elastic Surface Algorithm (ESA), as one of the newest residual-corrective inverse design method, was proposed for external flows in 2014. In this method, the airfoil walls were considered as a flexible elastic beam that deforms due to the difference between the target and current pressure distribution at each shape modification step. Nevertheless, the previous version of ESA is subjected to oscillation, instability, and divergence for a cascade of sharp-edged blades due to the steep pressure gradient at the leading edge. This study upgrades the ESA for the shape design of sharp-edged blades with steep gradients of pressure near the stagnation point. The basis of this upgrade was to use the deflection curve of Timoshenko beam which is continuous and differentiable at all the nodes. The upgraded ESA against the original ESA used only the physical characteristics of Timoshenko beam instead of applying a geometric filtration for the removal of fractures in the intermediate profiles at large deformations. To increase the beam deformation at each shape modification, the upgraded ESA removed the constraint of node displacement along the spine direction, which is normal to the chord line, so that the nodes of Timoshenko beam could freely move based on the large deformation equations. In addition, the optimal values of elastic modulus, thickness, and width of the beam were obtained to increase the convergence rate of the ESA. The upgraded ESA was finally verified for a DCA blade cascade in subsonic and transonic flow regimes under different angles of attack and different initially-guessed geometries. The results showed the upgraded ESA to be a robust, flexible, and fast-converging inverse design method for sharp-edged blades with steep pressure gradients.