Abstract
PurposeTo optimize the shape of a cascade where velocity (or pressure) distribution is optimally given.Design/methodology/approachThe 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.FindingsJi‐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/implicationsThe design method is limited to frictionless flow.Practical implicationsThe numerical method based on variational principle with moving boundary can be readily extended to other cases with moving surfaces or free boundaries.Originality/valueThe 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.
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