This paper presents an adjoint optimization technique and its application to the design of a transonic turbine cascade. Capable of a quick and exact sensitivity analysis and using little computational resources, the adjoint method has been a focus of research in aerodynamic shape design optimization. The goal of this work is to extend the adjoint method into turbomachinery design applications for viscous and compressible flow, and to further improve the aerodynamic performance. In the work, the minimization of the entropy generation rate with the mass flow rate constraint was considered as the cost function of the optimization, and was applied in the direct design process. The adjoint boundary conditions of the corresponding cost function were derived in detail, using the nonslip boundary condition on the blade wall, while the flow viscous effect on the cascade inlet and outlet was neglected. Numerical techniques used in Computational Fluid Dynamics (CFD) were employed to solve the adjoint linear partial difference equations. With the solved adjoint variables, the final expression of the cost function gradient with respect to the design variables was formulated. Combined with quasi-Newton algorithm, an aerodynamic design approach based on the adjoint method for turbine blades was presented, which was independent of the Navier–Stokes solver being used. Finally, to validate the present optimization algorithm, the aerodynamic design cases of a transonic turbine blade with and without mass flow rate restriction were performed and analyzed.
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e-mail: zpfeng@mail.xjtu.edu.cn
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July 2011
Research Papers
2D Viscous Aerodynamic Shape Design Optimization for Turbine Blades Based on Adjoint Method
Haitao Li,
Haitao Li
Institute of Turbomachinery,
Xi’an Jiaotong University
, Xi’an 710049, P.R.China
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Liming Song,
Liming Song
Institute of Turbomachinery,
Xi’an Jiaotong University
, Xi’an 710049, P.R.China
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Yingchen Li,
Yingchen Li
Institute of Turbomachinery,
Xi’an Jiaotong University
, Xi’an 710049, P.R.China
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Zhenping Feng
Zhenping Feng
Institute of Turbomachinery,
e-mail: zpfeng@mail.xjtu.edu.cn
Xi’an Jiaotong University
, Xi’an 710049, P.R.China
Search for other works by this author on:
Haitao Li
Institute of Turbomachinery,
Xi’an Jiaotong University
, Xi’an 710049, P.R.China
Liming Song
Institute of Turbomachinery,
Xi’an Jiaotong University
, Xi’an 710049, P.R.China
Yingchen Li
Institute of Turbomachinery,
Xi’an Jiaotong University
, Xi’an 710049, P.R.China
Zhenping Feng
Institute of Turbomachinery,
Xi’an Jiaotong University
, Xi’an 710049, P.R.Chinae-mail: zpfeng@mail.xjtu.edu.cn
J. Turbomach. Jul 2011, 133(3): 031014 (8 pages)
Published Online: November 16, 2010
Article history
Received:
August 21, 2009
Revised:
November 5, 2009
Online:
November 16, 2010
Published:
November 16, 2010
Citation
Li, H., Song, L., Li, Y., and Feng, Z. (November 16, 2010). "2D Viscous Aerodynamic Shape Design Optimization for Turbine Blades Based on Adjoint Method." ASME. J. Turbomach. July 2011; 133(3): 031014. https://doi.org/10.1115/1.4001234
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