IDEAS home Printed from https://ideas.repec.org/a/gam/jeners/v16y2023i23p7736-d1286455.html

Universal Form of Radial Hydraulic Machinery Four-Quadrant Equations for Calculation of Transient Processes

Author

Listed:
  • Zdravko Giljen

    (Department for Hydraulic Machinery and Energy Systems, Faculty of Mechanical Engineering, University of Belgrade, Kraljice Marije 16, 11120 Belgrade, Serbia)

  • Miloš Nedeljković

    (Department for Hydraulic Machinery and Energy Systems, Faculty of Mechanical Engineering, University of Belgrade, Kraljice Marije 16, 11120 Belgrade, Serbia)

Abstract

Suter curves for the Wh and Wm characteristics and four-quadrant (4Q) diagrams of 11 radial pump–turbine models with different specific speeds ( nq = 24.34, 24.8, 27, 28.6, 38, 41.6, 41.9, 43.83, 50, 56, and 64.04) are presented for the first time in this paper, as well as Suter curves for two pump models ( nq = 25 and 41.8) previously published in the literature. All of these curves were analyzed to establish a certain universal law of behavior, depending on the specific speed. To determine such a law, a fitting procedure using regression and spline methods was carried out. This paper provides details of a research plan and structures (including data collection for four-quadrant diagrams for pump–turbine and pump models under different specific speeds nq ), a procedure for re-calculating four-quadrant diagrams of the models as Suter curves for the Wh and Wm characteristics, definitions of the optimal points for pump and turbine operating modes in pump–turbine models under different specific speeds, and the development of numerical models in MATLAB to obtain a universal equation for the Wh and Wm characteristics. The scientific contribution of this paper is that it is the first to publish original mathematical curves using universal equations for the Wh and Wm characteristics of radial pumps and pump–turbines. The applicability of the equations is demonstrated by considering a pumping station in which two radial pumps were installed, for which the calculation of transient processes was performed using a numerical model developed in MATLAB by the authors. The transition process results are compared for two cases: first, when input data in the numerical model are used with the values of the Suter curves for the Wh and Wm characteristics obtained by re-calculating the four-quadrant operating characteristics ( Q 11 , n 11 , M 11 ) at a given specific speed, and second, when the values of the Suter curves for the Wh and Wm characteristics are obtained from the universal equations.

Suggested Citation

  • Zdravko Giljen & Miloš Nedeljković, 2023. "Universal Form of Radial Hydraulic Machinery Four-Quadrant Equations for Calculation of Transient Processes," Energies, MDPI, vol. 16(23), pages 1-27, November.
    • Handle: RePEc:gam:jeners:v:16:y:2023:i:23:p:7736-:d:1286455
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/1996-1073/16/23/7736/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/1996-1073/16/23/7736/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Wang, Wenjie & Guo, Hailong & Zhang, Chenying & Shen, Jiawei & Pei, Ji & Yuan, Shouqi, 2023. "Transient characteristics of PAT in micro pumped hydro energy storage during abnormal shutdown process," Renewable Energy, Elsevier, vol. 209(C), pages 401-412.
    2. Huang, Si & Qiu, Guangqi & Su, Xianghui & Chen, Junrong & Zou, Wenlang, 2017. "Performance prediction of a centrifugal pump as turbine using rotor-volute matching principle," Renewable Energy, Elsevier, vol. 108(C), pages 64-71.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Zhang, Xiaowen & Tang, Fangping & Pavesi, Giorgio & Hu, Chongyang & Song, Xijie, 2024. "Influence of gate cutoff effect on flow mode conversion and energy dissipation during power-off of prototype tubular pump system," Energy, Elsevier, vol. 308(C).
    2. Gad, Mona & Gao, Bo & Ni, Dan & Zhang, Ning, 2025. "Numerical investigation of the wake structure and flow energy loss in the pump as a turbine with splitter blades," Renewable Energy, Elsevier, vol. 252(C).
    3. Lin, Tong & Zhu, Zuchao & Li, Xiaojun & Li, Jian & Lin, Yanpi, 2021. "Theoretical, experimental, and numerical methods to predict the best efficiency point of centrifugal pump as turbine," Renewable Energy, Elsevier, vol. 168(C), pages 31-44.
    4. Pei, Yingju & Liu, Qingyou & Wang, Chuan & Wang, Guorong, 2021. "Energy efficiency prediction model and energy characteristics of subsea disc pump based on velocity slip and similarity theory," Energy, Elsevier, vol. 229(C).
    5. Rossi, Mosè & Nigro, Alessandra & Renzi, Massimiliano, 2019. "Experimental and numerical assessment of a methodology for performance prediction of Pumps-as-Turbines (PaTs) operating in off-design conditions," Applied Energy, Elsevier, vol. 248(C), pages 555-566.
    6. Renzi, Massimiliano & Nigro, Alessandra & Rossi, Mosè, 2020. "A methodology to forecast the main non-dimensional performance parameters of pumps-as-turbines (PaTs) operating at Best Efficiency Point (BEP)," Renewable Energy, Elsevier, vol. 160(C), pages 16-25.
    7. Chen, Xiaoping & Zhang, Zhiguo & Huang, Jianmin & Zhou, Xiaojie & Zhu, Zuchao, 2024. "Numerical investigation on energy change field in a centrifugal pump as turbine under different flow rates," Renewable Energy, Elsevier, vol. 230(C).
    8. Shojaeefard, Mohammad Hassan & Saremian, Salman, 2023. "Studying the impact of impeller geometrical parameters on the high-efficiency working range of pump as turbine (PAT) installed in the water distribution network," Renewable Energy, Elsevier, vol. 216(C).
    9. Ghorani, Mohammad Mahdi & Sotoude Haghighi, Mohammad Hadi & Maleki, Ali & Riasi, Alireza, 2020. "A numerical study on mechanisms of energy dissipation in a pump as turbine (PAT) using entropy generation theory," Renewable Energy, Elsevier, vol. 162(C), pages 1036-1053.
    10. Crespo Chacón, Miguel & Rodríguez Díaz, Juan Antonio & García Morillo, Jorge & McNabola, Aonghus, 2020. "Hydropower energy recovery in irrigation networks: Validation of a methodology for flow prediction and pump as turbine selection," Renewable Energy, Elsevier, vol. 147(P1), pages 1728-1738.
    11. Binama, Maxime & Su, Wen-Tao & Cai, Wei-Hua & Li, Xiao-Bin & Muhirwa, Alexis & Li, Biao & Bisengimana, Emmanuel, 2019. "Blade trailing edge position influencing pump as turbine (PAT) pressure field under part-load conditions," Renewable Energy, Elsevier, vol. 136(C), pages 33-47.
    12. Zhang, Chenying & Wang, Wenjie & Pavesi, Giorgio & Yuan, Shouqi & Pei, Ji, 2024. "Research on the mechanism of severe unsteadiness of PAT braking condition during the power failure," Renewable Energy, Elsevier, vol. 232(C).
    13. Abdulbasit Nasir & Edessa Dribssa & Misrak Girma & Habtamu Bayera Madessa, 2023. "Selection and Performance Prediction of a Pump as a Turbine for Power Generation Applications," Energies, MDPI, vol. 16(13), pages 1-16, June.
    14. Yu-Liang Zhang & Jin-Fu Li & You-Qu Zheng, 2023. "Effect of valve opening on starting performance of pump as turbine," PLOS ONE, Public Library of Science, vol. 18(11), pages 1-26, November.
    15. Tahani, Mojtaba & Kandi, Ali & Moghimi, Mahdi & Houreh, Shahram Derakhshan, 2020. "Rotational speed variation assessment of centrifugal pump-as-turbine as an energy utilization device under water distribution network condition," Energy, Elsevier, vol. 213(C).
    16. Shojaeefard, Mohammad Hassan & Saremian, Salman, 2022. "Effects of impeller geometry modification on performance of pump as turbine in the urban water distribution network," Energy, Elsevier, vol. 255(C).
    17. Saremian, Salman & Shojaeefard, Mohammad Hassan, 2025. "Study on the impact of volute geometric modification on the performance of centrifugal pump as turbine," Renewable Energy, Elsevier, vol. 253(C).
    18. Telikani, Akbar & Rossi, Mosé & Khajehali, Naghmeh & Renzi, Massimiliano, 2023. "Pumps-as-Turbines’ (PaTs) performance prediction improvement using evolutionary artificial neural networks," Applied Energy, Elsevier, vol. 330(PA).
    19. Yu, Wenjin & Zhou, Peijian & Miao, Zhouqian & Zhao, Haoru & Mou, Jiegang & Zhou, Wenqiang, 2024. "Energy performance prediction of pump as turbine (PAT) based on PIWOA-BP neural network," Renewable Energy, Elsevier, vol. 222(C).
    20. Rossi, Mosè & Comodi, Gabriele & Piacente, Nicola & Renzi, Massimiliano, 2020. "Energy recovery in oil refineries by means of a Hydraulic Power Recovery Turbine (HPRT) handling viscous liquids," Applied Energy, Elsevier, vol. 270(C).

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jeners:v:16:y:2023:i:23:p:7736-:d:1286455. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager The email address of this maintainer does not seem to be valid anymore. Please ask MDPI Indexing Manager to update the entry or send us the correct address (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.