Optimization design of the draft tube for a low-head Francis turbine

The paper presents a method developed by the authors for designing the draft tube of a low-head Francis turbine. The methodology is based on the law of cross-sectional area distribution along the tube, which significantly improved the efficiency of the optimization process. The design procedure was automated using MATLAB. Optimization was performed in stages using response surface methodology, preliminarily verified on a test case. The results demonstrated an increase in turbine efficiency, including under partial load conditions, along with enhanced cavitation performance of the flow path.
EDN: BYMHAT, https://elibrary/bymhat

References

[1] Soucek J., Nowak P. Optimization of elbow draft tubes for variable speed propeller turbine. Water, 2024, vol. 16, no. 10, art. 1457, doi: https://doi.org/10.3390/w16101457

[2] Semenova A.V., Chirkov D.V., Skorospelov V.A. et al. Optimization design of the elbow draft tube of the hydraulic turbine. IOP Conf. Ser.: Earth Environ. Sci., 2022, vol. 1079, art. 012048, doi: https://doi.org/10.1088/1755-1315/1079/1/012028

[3] Mosonyi E. Water power development. Vol. 1. Low-head power plants. Akad?miai Kiad?, 1987. 880 p.

[4] Kumar S., Cervantes M.J., Gandhi B.K. Flow field analysis of francis turbine draft tube using POD at design and part load operating conditions. JAFM, 2024, vol. 17, no. 4, pp. 770–784, doi: https://doi.org/10.47176/jafm.17.4.2274

[5] Kovalev N.N. Gidroturbiny [Hydroturbines.]. Liningrad, Mashinostroenie Publ., 1971. 584 p. (In Russ.).

[6] Barlit V.V. Gidravlicheskie turbiny [Hydraulic turbines]. Kiev, Vishcha shkola Publ., 1977. 359 p. (In Russ.).

[7] Busyrev A.I., Topazh G.I. Vybor osnovnykh parametrov i elementov protochnoy chasti reaktivnykh gidroturbin [Selection of the main parameters and elements of the flow path of jet hydraulic turbines]. Sankt-Peterburg, Izd-vo Politekh. un-ta Publ., 2007. 122 p. (In Russ.).

[8] Herland I. Design optimization of Francis turbine draft tube. Proc. CRHT X, 2020, vol. 5. URL: https://ttl.ku.edu.np/wp-content/uploads/2020/08/CRHTX-05-Ingelin.pdf

[9] Skorospelov V.A., Turuk P.A. Optimization of the shape of a toroidal hydroturbine draft tube. Sibirskiy zhurnal industrialnoy matematiki, 2022, vol. 25, no. 1, pp. 121–130, doi: https://doi.org/10.33048/SIBJIM.2022.25.109 (in Russ.). (Eng. version: J. Appl. Ind. Math., 2022, vol. 16, no. 1, pp. 148–155, doi: https://doi.org/10.1134/S1990478922010148)

[10] Omran M., Zharkovskiy A.A., Shchur V.A. [Selection of a mathematical model for calculating the flow in the flow path of a radial-axial hydraulic turbine]. Sovremennye tekhnologii i ekonomika v energetike. Mat. Mezhd. nauch.-prakt. konf. [Modern technologies and economics in energy. Proc. Int. Sci.-Pract. Conf.]. Sankt-Peterburg, Politekh-Press Publ., 2022, s. 207–209. (In Russ.).

[11] Zharkovskiy A.A., Shchur V.A., Omran M. et al. Automation of the design of impellers of francis turbines. Izvestiya MGTU MAMI, 2021, vol. 15, no. 4, pp. 18–26. (In Russ.).

[12] Omran M., Zharkovskiy A.A., Shchur V.A. et al. Technique for designing and optimization of the francis turbine blade system. Omskiy nauchnyy vestnik. Ser. Aviatsionno-raketnoe i energeticheskoe mashinostroenie [Omsk Scientific Bulletin. Ser. Aviation-Rocket and Power Engineering], 2023, vol. 7, no. 1, pp. 47–54, doi: https://doi.org/10.25206/2588-0373-2023-7-1-47-54 (in Russ.).

[13] Sokolova M.A., Semenova A.V. [The design of the kaplan turbine runner using the method of the cavitation characteristic prediction]. Gidravlicheskie mashiny, gidropnevmoprivody i gidropnevmoavtomatika. Sovremennoe sostoyanie i perspektivy razvitiya [Hydraulic Machines, Hydraulic-Pneumatic Drives and Hydraulic-Pneumatic Automation. Current State and Development Prospects]. Sankt-Peterburg, 2018, doi: https://doi.org/10.18720/SPBPU/2/id18-35 (in Russ.).

[14] Lebede N., Diallo C. A comparative study of optimization techniques on the Rosenbrock function. OJOp, 2024, vol. 13, no. 3, pp. 51–63, doi: https://doi.org/10.4236/ojop.2024.133004