**Published at : ** 28 Jan 2019

**IJtech :** IJtech
Vol 10, No 1 (2019)

**DOI :** https://doi.org/10.14716/ijtech.v10i1.1744

Soesanto, Q.M.B., Widiyanto, P., Susatyo, A., Yazid, E., 2019. Cascade Optimization of an Axial-Flow Hydraulic Turbine Type Propeller by a Genetic Algorithm.

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Qidun Maulana Binu Soesanto | Research Centre for Electrical Power and Mechatronics (P2 Telimek), Indonesian Institute of Sciences (LIPI), Komplek LIPI, Jl. Cisitu No. 21/154D, Bandung 40135, Indonesia |

Puji Widiyanto | Research Centre for Electrical Power and Mechatronics (P2 Telimek), Indonesian Institute of Sciences (LIPI), Komplek LIPI, Jl. Cisitu No. 21/154D, Bandung 40135, Indonesia |

Anjar Susatyo | Research Centre for Electrical Power and Mechatronics (P2 Telimek), Indonesian Institute of Sciences (LIPI), Komplek LIPI, Jl. Cisitu No. 21/154D, Bandung 40135, Indonesia |

Edwar Yazid |

Abstract

This study proposes the use of the genetic algorithm (GA) method in hydraulic turbine optimization for renewable energy applications. The algorithm is used to optimize the performance of a two-dimensional hydrofoil cascade for an axial-flow hydraulic turbine. The potential flow around the cascade is analyzed using the surface vorticity panel method, with a modified coupling coefficient to deal with the turbine cascade. Each section of the guide vane and runner blade hydrofoil cascade is optimized to satisfy the shock-free criterion, which is the fluid dynamic ideal to achieve minimum profile losses. Comparison is also made between the direct and random switching methods for the GA crossover operator. The optimization results show that the random switching method outperforms the performance of the direct switching method in terms of the resulting solutions, as well as in terms of the computational time required to reach convergence. As an alternative to experimental trials, the performance of both turbine designs are predicted and analyzed using the three-dimensional computational fluid dynamics (CFD) approach under several operating conditions. The simulation results show that the optimized design, which is obtained by applying the shock-free criterion using the GA, successfully improves the performance of the initial turbine design.

Axial-flow hydraulic turbine; Computational fluid dynamics; Genetic algorithm; Shock-free criterion

Introduction

Hydrodynamic performance analysis is important for optimizing the hydraulic performance of axial-flow hydraulic turbines. The common method is by analyzing the fluid-dynamic behavior around the hydrofoil using a two-dimensional cascade, which is an infinite array of hydrofoils on a two-dimensional (x,y) plane. Several research studies have been conducted to optimize axial-flow hydraulic performance by minimizing hydrofoil losses using certain criteria, such as the minimum suction pressure coefficient (da Cruz et al., 2008; Sutikno & Adam, 2011) and the shock-free inflow criterion, as in the work of Muis et al. (2015, 2016). In addition, the performance of the optimized design needs to be predicted based on real conditions, before prototyping takes place. The three-dimensional computational fluid dynamics (CFD) approach based on the finite volume method is an efficient fluid dynamic tool to predict the performance of turbomachinery, such as hydraulic turbines. This approach allows the prediction of certain flow parameters in complex flow phenomena, which are difficult to obtain experimentally, such as the velocity and pressure contours at any location in the computational domain.

This
research aims to optimize the performance of an axial-flow hydraulic turbine
using the genetic algorithm (GA) method, which is an evolutionary optimization
algorithm based on natural selection. The algorithm is used to find the optimal
design variables to achieve the shock-free criterion (Lewis, 1996).

During the optimization process, the potential flow around the
two-dimensional cascade is analyzed using the surface vorticity panel method
(Lewis, 1991). The performance of the initial and optimized turbine designs is
predicted using the three-dimensional CFD approach, which has previously been
used by several researchers (Drtina & Sallaberger, 1999; Prasad, 2012;
Ramos et al., 2013; Schleicher et al., 2015; Riglin et al., 2016; Kim et al., 2017; Kinsey & Dumas, 2017) to
predict the performance and flow behavior of hydraulic turbines. Subsequently,
the performance of both turbine designs is compared and analyzed.

Conclusion

Numerical optimization of an axial flow hydraulic
turbine using
two-dimensional cascade analysis
has been performed. The GA was found to be an efficient optimizer to satisfy
the shock-free criterion in the two-dimensional hydrofoil cascade for the axial-flow
hydraulic turbine.
However, the switching method used for the
crossover operator of the algorithm should be carefully noted. From the optimization results, the crossover
operator with the random distribution switching method resulted in more robust
solutions compared to the direct method because of its diversity. By applying
this method, the cost function value in each guide vane cascade section is less than E-09, while the
runner blade has an
average value of E-14. Furthermore, the performance of both turbine designs was predicted using the
three-dimensional CFD approach. The simulation results show that the optimized
turbine design improves the hydraulic performance of the initial turbine design
by 4.29% under nominal operating conditions. Moreover, the hydraulic performance of
the optimized
turbine design also outperforms the performance of the initial turbine design under various operating conditions,
ranging from 450 to 550 rpm. Therefore, it can be concluded that the GA as an optimizer used to achieve the shock-free criterion in
two-dimensional cascades has successfully improved the hydraulic performance of
the initial turbine design.

Acknowledgement

The Authors would like to thank to Research Centre for Electrical Power and Mechatronics – Indonesian Institute of Sciences (P2 Telimek – LIPI) for supporting this project.

Supplementary Material

Filename | Description |
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R2-ME-1744-20180919140719.png | Figure 1 Shock-free inflow condition |

R2-ME-1744-20180919140812.png | Figure 2 The geometry of four-digit NACA airfoil |

R2-ME-1744-20180919140945.png | Figure 3 Each hydrofoil section of of axial-flow hydraulic turbine (a)guide vane |

R2-ME-1744-20180919141011.png | Figure 3 Each hydrofoil section of of axial-flow hydraulic turbine (b)runner blade |

R2-ME-1744-20180919142116.png | Figure 3 Each hydrofoil section of of axial-flow hydraulic turbine (c)initial design of axial-flow hydraulic turbine |

R2-ME-1744-20180919142251.png | Figure 4 (a-c) Surface vorticity panel model in two-dimensional cascade |

R2-ME-1744-20180919142332.png | Figure 5 The GA flowchart used for two-dimensional cascade optimization by using shock-free criterion |

R2-ME-1744-20180919142430.png | Figure 6 Computational domain of axial-flow hydraulic turbine |

R2-ME-1744-20180919142602.png | Figure 7a Grid independent results of initial turbine design |

R2-ME-1744-20180919142630.png | Figure 7b Grid independent results of optimized turbine design |

R2-ME-1744-20180919143132.png | Figure 8a The performance comparison between direct and random switching methods for crossover operator at section one of guide vane’s cascade |

R2-ME-1744-20180919143156.png | Figure 8b The performance comparison between direct and random switching methods for crossover operator at section two of guide vane’s cascade |

R2-ME-1744-20180919143220.png | Figure 8c The performance comparison between direct and random switching methods for crossover operator at section three of guide vane’s cascade |

R2-ME-1744-20180919143413.png | Figure 8d The performance comparison between direct and random switching methods for crossover operator at section four of guide vane’s cascade |

R2-ME-1744-20180919143558.png | Figure 8e The performance comparison between direct and random switching methods for crossover operator at section five of guide vane’s cascade |

R2-ME-1744-20180919144514.png | Figure 9a The performance of GA optimizing the stagger angle at each section of runner blade’s cascades |

R2-ME-1744-20180919144642.png | Figuref 9(b) A detailed look of the first ten iterations of cost function evolution while optimizing the stagger angle at each section of runner blade’s cascades |

R2-ME-1744-20180919144715.png | Figure 10 Convergence history during the iteration of conservation equations |

R2-ME-1744-20180919144809.png | Figure 11a Velocity contour of initial turbine passages at meridional plane |

R2-ME-1744-20180919144831.png | Figure 11b Velocity contour of optimized turbine passages at meridional plane |

R2-ME-1744-20180919144907.png | Figure 12a Pressure contour of initial turbine design |

R2-ME-1744-20180919144933.png | Figure 12 Pressure contour of optimized turbine design |

R2-ME-1744-20180919145019.png | Figure 13a Blade-to-blade view of pressure contour at 0.5 spanwise location of initial turbine design |

R2-ME-1744-20180919145041.png | Figure 13b Blade-to-blade view of pressure contour at 0.5 spanwise location of optimized turbine design |

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