Abstract
In a hydraulic turbine, the search of a better energy exchange with the fluid has led to designs of runner blade of geometrical shapes so complex that they are considered as free-form surfaces. Since such blade characteristics are unable to be expressed by analytic functions, its complete and realistic geometrical reconstruction requires an excessive quantity of design parameters. This study proposes a coherent and robust full 3D blade numerical reconstruction methodology in which the geometrical definition of the blade is independent of its design parameters. A quantitative and qualitative fit evaluation shows that the blade surface reconstruction needs an important quantity of discrete data along the spanwise and streamwise direction to achieve a continuous and smooth definition. The results infer that the shape characteristics of damaged and worn blades without an original CAD model could be recovered, making this methodology attractive for industrial and optimization applications.
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Abbreviations
- TFI :
-
Transfinite interpolation
- PS :
-
Pressure side
- SS :
-
Suction side
- CS:
-
Camber surface
- TD:
-
Thickness distribution
- MCL:
-
Mean camber line
- RSME:
-
Root square mean error
- CAD:
-
Computer aided desing
- CFD:
-
Computational fluid dynamics
- CSM:
-
Computational structural mechanics
- CAE:
-
Computational aided engineering
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Acknowledgments
The authors gratefully acknowledge to the CONACYT México, to the Coordinación de la Investigación Científica of the Universidad Michoacana de San Nicolás de Hidalgo and to Aulas CIMNE, Morelia by the financial and technical support to accomplish this project.
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Giovanni Delgado completed his bachelor’s degree in Mechanical Engineering at the Universidad Michoacana in México. He obtained a Master of Science in Mechanical Engineering at Universidad Michoacana in Mexico. He is candidate for a Doctor of Science in Mechanical Engineering at Universidad Michoacana in México and Professor of the Faculty of Mechanical Engineering at the same university. His areas of interest are turbomachinery, thermofluids and numerical simulation.
Sergio Galván is a Professor and researcher of the Mechanical Engineering Faculty, Universidad Michoacana, México. He received his Ph.D in Mechanical Engineering from L’École Polytechnique de Montréal. As mechanical engineer, in different hydropower stations from Comisión Federal de Electricidad, he was responsible of the maintenance, repairing and operation of the hydraulic turbines. His main research interest includes computational design optimization applied to hydraulic turbines.
Francisco Domínguez-Mota completed a B.Sc. in Physics and Mathematics at the Universidad Michoacana in México. He obtained a Master degree in Applied Mathematics from the Center of Research in Mathematics in Guanajuato, Mexico, and a Ph.D in Mathematics at the Universidad Nacional Autónoma de México. He is a member of the National System of Researchers (SNI) in México, and is a researcher in Applied Mathematics at the Universidad Michoacana. His areas of research include numerical solution of differential equations and applications in engineering, numerical generation of structured grids and applications of optimization in large scale problems.
J. C. García is a doctor of the Centro de Ingeniería y Ciencias Aplicadas, Universidad Autónoma del Estado de Morelos, Morelos, México. He received his Ph.D in Engineering and Applied Science from Universidad Autónoma del Estado de Morelos. His research interests include turbomachinery and mechanical vibrations.
Esteban Valencia is a Professor of the Mechanical Engineering Department at the Escuela Politécnica Nacional de Quito, Ecuador. He received his Ph.D. in Mechanical Engineering from Cranfield University, United Kingdom. His areas of interest are turbomachinery, propulsion and fluids mechanics.
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Delgado, G., Galván, S., Dominguez-Mota, F. et al. Reconstruction methodology of a Francis runner blade using numerical tools. J Mech Sci Technol 34, 1237–1247 (2020). https://doi.org/10.1007/s12206-020-0222-4
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DOI: https://doi.org/10.1007/s12206-020-0222-4