Analytical Implementation and Prediction of Hydraulic Characteristics for a Francis Turbine Runner Operated at BEP

Yu Chen, Jianxu Zhou, Bryan Karney, Qiang Guo and Jian Zhang
Additional contact information
Yu Chen: School of Mechanical Engineering, Nanjing Institute of Technology, Nanjing 211167, China
Jianxu Zhou: College of Water Conservancy and Hydropower Engineering, Hohai University, Nanjing 210098, China
Bryan Karney: Department of Civil Engineering, University of Toronto, Toronto, ON M5S 1A4, Canada
Qiang Guo: College of Water Conservancy and Hydropower Engineering, Hohai University, Nanjing 210098, China
Jian Zhang: College of Water Conservancy and Hydropower Engineering, Hohai University, Nanjing 210098, China

Sustainability, 2022, vol. 14, issue 4, 1-19

Abstract: The extensive investigation and profound understanding of the hydraulic characteristics of the Francis turbine are crucial to ensure a safe and stable hydraulic system. Especially, predicting the runner’s hydraulic efficiency with high fidelity is mandatory at the early stage of a new hydropower project. For these purposes, the current technologies mainly include experimentation and CFD simulation. Both methods generally have the demerits of a long period, massive investment and high requirements for supercomputers. In this work, an analytical solution is therefore introduced in order to predict the internal flow field and working performance of the runner while the Francis turbine operates at the best efficiency point (BEP). This approach, based on differential-geometry theory and the kinematics of ideal fluid, discretizes the blade channel by several spatial streamlines. Then, the dynamic parameters of these streamlines are determined in a curved-surface coordinate system, including velocity components, flow angles, Eulerian energy and pressure differences across the blade. Additionally, velocity components are converted from the spatial-velocity triangle to the Cartesian coordinate system, and the absolute-velocity vectors as well as the streamlines are subsequently derived. A validation of this approach is then presented. The analytical solution of hydraulic efficiency shows good agreement with the experimental value and simulation result. Additionally, the distributions of pressure differences over the blade, velocity and Eulerian energy are well predicted with respect to the CFD results. Finally, the discrepancy and distribution of the dynamic parameters are discussed.

Keywords: analytical solution; mathematic analysis; Francis turbine; hydraulic characteristics; efficiency prediction; BEP (search for similar items in EconPapers)
JEL-codes: O13 Q Q0 Q2 Q3 Q5 Q56 (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2071-1050/14/4/1965/pdf (application/pdf)
https://www.mdpi.com/2071-1050/14/4/1965/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jsusta:v:14:y:2022:i:4:p:1965-:d:745400

Access Statistics for this article

Sustainability is currently edited by Ms. Alexandra Wu

More articles in Sustainability from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().