Inverse design problem for optimizing cascades

Purpose - To optimize the shape of a cascade where velocity (or pressure) distribution is optimally given. Design/methodology/approach - The semi-inverse method suggested by Ji-Huan He is applied to establishment of a variational theory for the discussed inverse problem. The boundary conditions on unknown shape are converted into the natural boundary conditions of the obtained variational functional. Findings - Ji-Huan He's semi-inverse method is a powerful tool to the search for the variational formulation for the discussed problem. The derivation procedure is very simple and convenient; the finite element method based on the variational theory with moving boundary provides a very effective and robust numerical approach to the inverse problem. Research limitations/implications - The design method is limited to frictionless flow. Practical implications - The numerical method based on variational principle with moving boundary can be readily extended to other cases with moving surfaces or free boundaries. Originality/value - The suggested numerical method can satisfy the demand of various cascade designs, where the velocity (or pressure) distribution can be optimally given from different aspects of engineering requirement: aerodynamics, strength, manufacture, etc.