Tối ưu hóa hình dạng của ống dẫn thủy lực dạng toroidal của tuabin nước

S. G. Cherny, D. V. Chirkov, V. N. Lapin, V. A. Skorospelov, and S. V. Sharov, Numerical Modeling of Flows in Hydraulic Machinery (Nauka, Novosibirsk, 2006) [in Russian]. A. E. Lyutov, D. V. Chirkov, V. A. Skorospelov, P. A. Turuk, and S. G. Cherny, “Coupled multipoint shape optimization of runner and draft tube of hydraulic turbines,” J. Fluids Eng. 137 (11), article ID 111302 (2015). A. Y. Avdyushenko, S. G. Cherny, D. V. Chirkov, V. A. Skorospelov, and P. A. Turuk, “Numerical simulation of transient processes in hydroturbines,” Thermophys. Aeromech. 20 (5), 577–593 (2013). Yu. S. Volkov and V. L. Miroshnichenko, “Development of a mathematical model of a universal characteristic of Francis turbine,” Sib. Zh. Ind. Mat. 1 (1), 77–88 (1998). Yu. S. Volkov, V. L. Miroshnichenko, and A. E. Salienko, “Mathematical modeling of a universal characteristic of a Kaplan turbine,” Mash. Obuchenie Anal. Dannykh 1 (10), 1439–1450 (2014). D. V. Bannikov, D. V. Yesipov, S. G. Cherny, and D. V. Chirkov, “Optimization design of hydroturbine rotors according to the efficiency-strength criteria,” Thermophys. Aeromech. 17 (4), 613–620 (2010). D. V. Chirkov, S. G. Cherny, P. K. Shcherbakov, V. A. Skorospelov, and P. A. Turuk, “Numerical investigation of the air injection effect on the cavitating flow in Francis hydro turbine,” Thermophys. Aeromech. 24 (5), 691–703 (2017). V. V. Bogdanov, W. V. Karsten, V. L. Miroshnichenko, and Yu. S. Volkov, “Application of splines for determining the velocity characteristic of a medium from a vertical seismic survey,” Cent. Eur. J. Math. 11 (4), 779–786 (2013). Yu. E. Anikonov, V. V. Bogdanov, E. Yu. Derevtsov, and Yu. S. Volkov, “On the determination of the velocity and elastic parameters of the focal zone medium from the earthquake hodographs,” Sib. Zh. Ind. Mat. 24 (4), 5–24 (2021) [J. Appl. Ind. Math. 24 (4), 5–24 (2021)]. D. V. Chirkov, A. S. Ankudinova, A. E. Kryukov, S. G. Cherny, and V. A. Skorospelov, “Multi-objective shape optimization of a hydraulic turbine runner using efficiency, strength and weight criteria,” Struct. Multdisciplinary Optim. 58 (2), 627–640 (2018). Y. Enomoto, S. Kurosawa, and H. Kawajiri, “Design optimization of a high specific speed Francis turbine runner,” in Proc. 26 IAHR Symp. Hydraul. Mach. Syst. 2012. IOP Conf. Ser. Earth Environ. Sci. 15, article ID 032010. E. Flores, L. Bornard, L. Tomas, J. Liu, and M. Couston, “Design of large Francis turbine using optimal methods,” in Proc. 26 IAHR Symp. Hydraul. Mach. Syst. 2012. IOP Conf. Ser. Earth Environ. Sci. 15, article ID 022023. L. Puente, M. Reggio, and F. Guibault, “Automatic shape optimization of a hydraulic turbine draft tube,” in Proc. Int. Conf. CFD2003 (Vancouver, 2003). B. Marjavaara, T. Lundström, T. Goel, Y. Mack, and W. Shyy, “Hydraulic turbine diffuser shape optimization by multiple surrogate model approximations of Pareto fronts,” J. Fluids Eng. 129 (9), 1228–1240 (2007). S. Alligne, C. Nicolet, Y. Tsujimoto, and F. Avellan, “Cavitation surge modelling in Francis turbine draft tube,” J. Hydraul. Res. 52 (3), 399–411 (2014). D. Jo\( \breve {s} \)t and A. Lipej, “Numerical prediction of non-cavitating and cavitating vortex rope in a Francis turbine draft tube,” J. Mech. Eng. 57, 445–456 (2011). S. Kurosawa and K. Nakamura, “Design optimization of a high specific speed Francis turbine using multi-objective genetic algorithm,” Int. J. Fluid Mach. Syst. 2 (2), 102–109 (2009). V. A. Skorospelov and P. A. Turuk, “Geometric support in the optimization problem for the surface of the hydroturbine draft tube based on numerical simulation of the flow,” Sib. Zh. Ind. Mat. 20 (4), 55–60 (2017) [J. Appl. Ind. Math. 11 (4), 594–599 (2017)]. S. A. Coons, Surfaces for computer aided design of space forms, Rep. MAC-TR-41. Project MAC, M.I.T. (1967). I. D. Faux and M. J. Platt, Computational Geometry for Design and Manufacture (Ellis Horwood, 1980; Mir, Moscow, 1982). R. Orso, E. Benini, M. Minozzo, R. Bergamin, and A. Magrini, “Two-objective optimization of a Kaplan turbine draft tube using a response surface methodology,” Energies 13 (18), article ID 4899 (2020). V. A. Skorospelov and P. A. Turuk, “Generation of a multiparameter family surfaces of the Kaplan turbine runner blade prior to shape optimization,” Sib. Zh. Ind. Mat. 19 (3), 85–89 (2016) [J.Appl. Ind. Math. 10 (3), 453–457 (2016)]. V. A. Skorospelov and P. A. Turuk, “Geometric support of numerical simulation of flow in the region of the hydroturbine spiral case,” Sib. Zh. Ind. Mat. 21 (2), 93–100 (2018) [J. Appl. Ind. Math. 12 (2), 355–361 (2018)].