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High specific speed Francis turbine for small hydro purposes - Design methodology based on solving the inverse problem in fluid mechanics and the cavitation test experience

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  • Krzemianowski, Zbigniew
  • Steller, Janusz

Abstract

The paper is a result of a research and development project aimed at developing a series of types of high specific speed (90 < nsQ < 100) Francis turbines. The inverse flow analysis approach based on the hodograph theory has been employed in order to develop the blading geometry of quality high enough to minimize the subsequent CFD based optimization process. The three-dimensional turbine blades are developed on meridional stream surfaces determined using the VLM methodology. The mass and momentum conservation equations are written in a curvilinear coordinate system, which is adjusted to the streamlines by means of the Christoffel symbols. The solution is found using the method of characteristics. The developed geometry is optimized by means of the genetic algorithm implemented in CFD software. Model tests were conducted in the Institute of Fluid-Flow Machinery of the Polish Academy of Sciences. Satisfactory coincidence between design assumptions, the CFD based performance assessments and those based on the model test results attained, shows reliability of the methodology adopted. Critical cavitation numbers as established according to different criteria have been applied to plot the sigma permissible isolines on top of the efficiency hill diagram. Physical interpretation of some irregularities in diagnostic characteristics is provided.

Suggested Citation

  • Krzemianowski, Zbigniew & Steller, Janusz, 2021. "High specific speed Francis turbine for small hydro purposes - Design methodology based on solving the inverse problem in fluid mechanics and the cavitation test experience," Renewable Energy, Elsevier, vol. 169(C), pages 1210-1228.
    • Handle: RePEc:eee:renene:v:169:y:2021:i:c:p:1210-1228
    DOI: 10.1016/j.renene.2021.01.095
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    References listed on IDEAS

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    1. Iliev, Igor & Trivedi, Chirag & Dahlhaug, Ole Gunnar, 2019. "Variable-speed operation of Francis turbines: A review of the perspectives and challenges," Renewable and Sustainable Energy Reviews, Elsevier, vol. 103(C), pages 109-121.
    2. Chirag Trivedi & Igor Iliev & Ole Gunnar Dahlhaug, 2020. "Numerical Study of a Francis Turbine over Wide Operating Range: Some Practical Aspects of Verification," Sustainability, MDPI, vol. 12(10), pages 1-10, May.
    3. Trivedi, Chirag & Cervantes, Michel J., 2017. "Fluid-structure interactions in Francis turbines: A perspective review," Renewable and Sustainable Energy Reviews, Elsevier, vol. 68(P1), pages 87-101.
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    Citations

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    Cited by:

    1. Paweł Tomczyk & Krzysztof Mastalerek & Mirosław Wiatkowski & Alban Kuriqi & Jakub Jurasz, 2023. "Assessment of a Francis Micro Hydro Turbine Performance Installed in a Wastewater Treatment Plant," Energies, MDPI, vol. 16(20), pages 1-19, October.
    2. Du, Jiyun & Ge, Zhan & Wu, Hao & Shi, Xudong & Yuan, Fangyang & Yu, Wei & Wang, Dongxiang & Yang, Xinjun, 2022. "Study on the effects of runner geometric parameters on the performance of micro Francis turbines used in water supply system of high-rise buildings," Energy, Elsevier, vol. 256(C).
    3. Wen-Tao Su & Wei Zhao & Maxime Binama & Yue Zhao & Jian-Ying Huang & Xue-Ren Chen, 2022. "Experimental Francis Turbine Cavitation Performances of a Hydro-Energy Plant," Sustainability, MDPI, vol. 14(6), pages 1-20, March.
    4. Krzemianowski, Zbigniew & Steller, Janusz & Janicki, Waldemar & Góralczyk, Adam, 2025. "Cavitation and runaway experimental research of a very high specific speed low-head model Francis turbine – A case study with emphasis on flow analysis in the draft tube," Energy, Elsevier, vol. 337(C).
    5. Damian Liszka & Zbigniew Krzemianowski & Tomasz Węgiel & Dariusz Borkowski & Andrzej Polniak & Konrad Wawrzykowski & Artur Cebula, 2022. "Alternative Solutions for Small Hydropower Plants," Energies, MDPI, vol. 15(4), pages 1-31, February.
    6. Zhou, Ling & Hang, Jianwei & Bai, Ling & Krzemianowski, Zbigniew & El-Emam, Mahmoud A. & Yasser, Eman & Agarwal, Ramesh, 2022. "Application of entropy production theory for energy losses and other investigation in pumps and turbines: A review," Applied Energy, Elsevier, vol. 318(C).
    7. Roh, Min-Su & Shahzer, Mohammad Abu & Kim, Jin-Hyuk, 2025. "Numerical formulation of relationship between optimized runner blade angle and specific speed in a francis turbine," Renewable Energy, Elsevier, vol. 238(C).
    8. Kumar, Prashant & Singal, S.K. & Gohil, Pankaj P., 2024. "A technical review on combined effect of cavitation and silt erosion on Francis turbine," Renewable and Sustainable Energy Reviews, Elsevier, vol. 190(PB).
    9. Krzemianowski, Zbigniew & Przybyliński, Tomasz & Karwacki, Jarosław & Tomaszewski, Adam, 2025. "Experimental research of a high specific speed low-head model Francis turbine – A case study with emphasis on flow visualisation under runner using PIV method and energy production analysis," Energy, Elsevier, vol. 334(C).

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