Inverse design problem for optimizing cascades

• Published in: Aircraft Engineering and Aerospace Technology Vol. 78; no. 6; pp. 515 - 521
• Main Author: Wu, Zhao-Chun
• Format: Journal Article
• Language: English
• Published: Bradford Emerald Group Publishing Limited 01.11.2006
• Subjects: Aerodynamics; Boundary conditions; Boundary value problems; Design optimization; Finite element method; Free boundaries; Inverse design; Inverse method; Inverse problems; Mathematical analysis; Methods; Numerical methods; Pressure distribution; Robustness (mathematics); Simulation; Stress concentration; Variational techniques; Velocity; Aerodynamics; Velocity; Variational techniques
• ISSN: 1748-8842; 0002-2667; 1758-4213
• DOI: 10.1108/00022660610707193

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.