Angle design of stator-rotor blades for VLH axial flow turbine using surrogate-based optimization

Document Type : Article


1 Sustainable Infrastructure Research and Department of Mechanical Engineering, Faculty of Engineering, Khon Kaen University, Khon Kaen, 40002, Thailand

2 Department of Mechatronics Engineering, Faculty of Engineering, Rajamangala University of Technology Isan, Khon Kaen Campus, Khon Kaen, 40000, Thailand

3 Department of Mechanical Engineering, Faculty of Engineering, Ubon Ratchathani University, Ubon Ratchathani, 34190, Thailand


This paper demonstrates design of a Very Low Head axial flow turbine using surrogate-based optimization. The design variables were blade angles between guide vanes and runner blades, whereas the objective function was turbine efficiency. A Latin Hypercube Sampling method was initially used to design the experiment with thirty sampling points, and a Large Eddy Simulation was modeled to analyze the flow for all sampling points. A correlation between design variables and the turbine efficiency was then evaluated using the surrogate models while the optimal design variables were identified. Also, several optimizers were used to tackle the proposed problem and their performances were investigated. The optimal design of blade angles \mathbit{\beta}_\mathbf{1}-\mathbit{\beta}_\mathbf{8} being 10o, 20o, 30o, 40o, 25o, 45o, 55o and 65o respectively, increased the turbine efficiency up to 89.87 %. The approach of using surrogate modeling was proved to be very effective and simple for optimizing a design of blade angles of stator-rotor and it can be applied for designing any other new blades.


1. Yang, W., Wu, Y., and Liu, S. "An optimization method on runner blades in bulb turbine based on CFD analysis", Sci. China Technol. Sci., 54(2), pp. 338-344 (2011).
2. Patel, V.A., Jain, S.V., Motwani, K.H., et al. "Numerical optimization of guide vanes and reducer in pump running in turbine mode", Procedia Eng., 51, pp. 797-802 (2013).
3. Ge, X., Feng, Y., Zhou, Y., et al. "Optimization study of shaft tubular turbine in a bidirectional tidal power station", Adv. Mech. Eng., 2013, pp. 1-9 (2013).
4. Amano, R.S. and Abbas, A. "Optimization of intake and draft tubes of a Kaplan micro hydro-turbine", in 15th International Energy Conversion Engineering Conference, Atlanta, GA (2017).
5. Ameen, A., Ibrahim, Z., Othman, F., et al. "Water flow stabilization using submerged weir for draft-tube reaction hydraulic turbine", Sci. Iran., 27(1), pp. 159-176 (2020).
6. Chakrabarty, S., Sarkar, B.K., and Maity, S. "CFD analysis of the hydraulic turbine draft tube to improve system efficiency", MATEC Web Conf., 40 (2016).
7. Mulu, B.G., Cervantes, M.J., Devals, C., et al. "Simulation-based investigation of unsteady  flow in near-hub region of a Kaplan turbine with experimental comparison", Eng. Appl. Comput. Fluid Mech., 9(1), pp. 139-156 (2015).
8. Wang, W., Zhang, L., Yan, Y., et al. "Large-eddy simulation of turbulent flow considering in flow wakes in a Francis turbine blade passage", J. Hydrodyn. Ser B, 19(2), pp. 201-209 (2007).
9. Sutikno, P. and Adam, I.K. "Design, simulation and experimental of the very low head turbine with minimum pressure and free vortex criterions", Int. J. Mech. Mech. Eng., 11(1), pp. 9-16 (2011).
10. Cheng, Y., Lien, F.S., Yee, E., et al. "A comparison of large Eddy simulations with a standard k-ε" Reynoldsaveraged Navier-Stokes model for the prediction of a fully developed turbulent flow over a matrix of cubes", J. Wind Eng. Ind. Aerodyn., 91(11), pp. 1301-1328 (2003).
11. Su, W.T., Li, F.C., Li, X.B., et al. "Assessment of Les performance in simulating complex 3D  flows in turbomachines", Eng. Appl. Comput. Fluid Mech., 6(3), pp.356-365 (2012).
12. Gupta, M.K. and Subbarao, P.M.V. "Development of a semi-analytical model to select a suitable airfoil section for blades of horizontal axis hydrokinetic turbine", Energy Rep., 6, pp. 32-37 (2020).
13. Langroudi, A.T., Afifi, F.Z., Nobari, A.H., et al. "Modeling and numerical investigation on multi-objective design improvement of a novel cross-flow lift-based turbine for in-pipe hydro energy harvesting applications", Energy Convers. Manag., 203, pp. 1-15 (2020).
14. Tingting, Y. and Yuan, Z. "Finite element analysis of stress, deformation and modal of head cover in axial-flow hydro-turbine", J. Drain. Irrig. Mach. Eng., 38(1), pp. 39-44 (2020).
15. Kolekar, N. and Banerjee, A. "A coupled hydrostructural design optimization for hydrokinetic turbines", J. Renew. Sustain. Energy, 5, pp. 1-22 (2013).
16. Mastrogiannakis, I. and Vosniakos, G.C. "Exploring structural design of the Francis hydro-turbine blades using composite materials", Facta Univ. Ser. Mech. Eng., 18(1), pp. 43-55 (2020).
17. Bahrami, S., Tribes, C., Fellenberg, S., et al. "Multi- fidelity design optimization of Francis turbine runner blades", IOP Conf. Ser. Earth Environ. Sci., 22, pp. 1-10 (2014).
18. Mohammadi, M., Riasi, A., and Rezghi, A. "Design and performance optimization of a very low head turbine with high pitch angle based on two-dimensional optimization", J. Braz. Soc. Mech. Sci. Eng., 42(9), pp. 1-18 (2020).
19. Lyutov, A.E., Chirkov, D.V., Skorospelov, V.A., et al. "Coupled multipoint shape optimization of runner and draft tube of hydraulic turbines", J. Fluids Eng., 137(11), pp. 1-11 (2015).
20. Lazari, A. and Cattanei, A. "Design of off-statistics axial-flow fans by means of vortex law optimization", J. Therm. Sci., 23(6), pp. 505-515 (2014).
21. Juraeva, M., Ryu, K.J., and Song, D.J. "Optimum design of a saw-tooth-shaped dental air-turbine using design of experiment", Int. J. Precis. Eng. Manuf., 15(2), pp. 227-234 (2014).
22. Halder, P., Rhee, S.H. and Samad, A. "Numerical optimization of Wells turbine for wave energy extraction", Int. J. Nav. Archit. Ocean Eng., 9, pp. 11-24 (2017).
23. Chen, N., Zhang, H., Huang, W., et al. "Study on aerodynamic design optimization of turbomachinery blades", J. Therm. Sci., 14(4), pp. 298-304 (2005).
24. Castilho, L., Camacho, R.G.R., and Silva, E.R. "Optimized design of linear cascades for turbomachinery applications", J. Braz. Soc. Mech. Sci. Eng., 38, pp. 813-825 (2016).
25. Wang, W., Pei, J., Yuan, S., et al. "Application of different surrogate models on the optimization of centrifugal pump", J. Mech. Sci. Technol., 30(2), pp. 567-574 (2016).
26. Lu, H., Li, Q., and Pan, T. "Optimization strategy for an axial-flow compressor using a region-segmentation combining surrogate model", J. Aerosp. Eng., 31(5), (2018).
27. Giorgetti, S., Coppitters, D., Contino, F., et al. "Surrogate-assisted modeling and robust optimization of a micro gas turbine plant with carbon capture", in Turbomachinery Technical Conference and Exposition, Arizona, USA (2019).
28. Liu, L., Zhu, B., Bai, L., et al. "Parametric design of an ultrahigh-head pump-turbine runner based on multiobjective optimization", Energies, 10, pp. 1-16 (2017).
29. Round, G.F., Incompressible Flow Turbomachines, Oxford, UK: Elsevier (2004).
30. Altimemy, M., Attiya, B., Daskiran, C., et al. "Mitigation of flow-induced pressure fluctuations in a Francis turbine operating at the design and partial load regimes-LES simulations", Int. J. Heat Fluid Flow, 79, pp. 1-11 (2019).
31. Ramos, H.M., Simao, M., and Borga, A. "Experiments and CFD analyses for a new reaction microhydro propeller with five blades", J. Energy Eng., 139(2), pp. 109-117 (2013).
32. Gholami, A., Bonakdari, H., Akhtari, A.A., et al. "A combination of computational fluid dynamics, artificial neural network and support vectors machines model to predict  flow variables in curved channel", Sci. Iran., 26(2), pp. 726-741 (2019).
33. Hosseini, F.M.M., Ebadi, T., Eslami, A., et al. "Investigation into geotechnical properties of clayey soils contaminated with gasoil using Response Surface Methodology (RSM)", Sci. Iran., 26(3), pp. 1122-1134 (2019).
34. Kurtulus, E., Yildiz, A.R., Sait, S.M., et al. "A novel hybrid Harris hawks-simulated annealing algorithm and RBF-based metamodel for design optimization of highway guardrails", Mater. Test., 62(3), pp. 251-260 (2020).
35. Wansaseub, K., Sleesongsom, S., Panagant, N., et al. "Surrogate-assisted reliability optimisation of an aircraft wing with static and dynamic aeroelastic constraints", Int. J. Aeronaut. Space Sci., 21, pp. 723-732 (2020).
36. Reza, Z. "Dissipation and eddy mixing associated with  flow past an underwater turbine", Master Thesis, Florida Atlantic university, USA (2010).
37. Ferro, L.M.C., Gato, L.M.C., and Falcao, A.F.O. "Design of the rotor blades of a mini hydraulic bulbturbine", Renew. Energy, 36(9), pp. 2395-2403 (2011).
38. Pholdee, N. "Performance enhancement of volutionary optimisation using hybridsation concepts", PhD Thesis, Khon Kaen University, Thailand (2013).
39. Singh, P. and Nestmann, F. "Experimental investigation of the in fluence of blade height and blade number on the performance of low head axial  flow turbines", Renew. Energy, 36, pp. 272-281 (2011).
40. McKay, M.D., Beckman, R.J., and Conover, W.J. "A comparison of three methods for selecting values of input variables in the analysis of output from a computer code", Technometrics, 21(2), pp. 239-245 (1979).
41. Kim, J.H., Choi, J.H., and Kim, K.Y. "Surrogate modeling for optimization of a centrifugal compressor impeller", Int. J. Fluid Mach. Syst., 3(1), pp. 29-38 (2010).
42. Karaboga, D. and Basturk, B. "On the performance of artificial bee colony (ABC) algorithm", Appl. Soft Comput., 8(1), pp. 687-697 (2008).
43. Socha, K. and Dorigo, M. "Ant colony optimization for continuous domains", Eur. J. Oper. Res., 185(3), pp. 1155-1173 (2008).
44. Storn, R. and Price, K. "Differential evolution - a simple and efficient heuristic for global optimization over continuous spaces", J. Glob. Optim., 11(4), pp. 341-359 (1997).
45. Merchaoui, M., Sakly, A., and Mimouni, M.F. "Particle swarm optimisation with adaptive mutation strategy for photovoltaic solar cell/module parameter extraction", Energy Convers. Manag., 175, pp. 151-163 (2018).
46. Mirjalili, S., Mirjalili, S.M., and Lewis, A. "Grey wolf optimizer", Adv. Eng. Softw., 69, pp. 46-61 (2014).
47. Mirjalili, S. "Moth- flame optimization algorithm: A novel nature-inspired heuristic paradigm", Knowl.- Based Syst., 89, pp. 228-249 (2015).