Analysis of the Leakage Behavior of Francis Turbines and Its Impact on the Hydraulic Efficiency—A Validation of an Analytical Model Based on Computational Fluid Dynamics Results

Jürgen Schiffer; Helmut Benigni; Helmut Jaberg

doi:10.1115/1.4034865

Journal of Fluids Engineering | Volume 139 | Issue 2 | research-article

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Research Papers: Flows in Complex Systems

Analysis of the Leakage Behavior of Francis Turbines and Its Impact on the Hydraulic Efficiency—A Validation of an Analytical Model Based on Computational Fluid Dynamics Results

Jürgen Schiffer, Helmut Benigni and Helmut Jaberg

[+] Author and Article Information

Jürgen Schiffer

Institute of Hydraulic Fluid Machinery,
Graz University of Technology,
Kopernikusgasse 24/IV,
Graz 8010, Austria
e-mail: juergen.schiffer@tugraz.at

Helmut Benigni

Institute of Hydraulic Fluid Machinery,
Graz University of Technology,
Kopernikusgasse 24/IV,
Graz 8010, Austria
e-mail: helmut.benigni@tugraz.at

Helmut Jaberg

Institute of Hydraulic Fluid Machinery,
Graz University of Technology,
Kopernikusgasse 24/IV,
Graz 8010, Austria
e-mail: helmut.jaberg@tugraz.at

¹Corresponding author.

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received December 17, 2015; final manuscript received September 2, 2016; published online December 7, 2016. Assoc. Editor: Bart van Esch.

J. Fluids Eng 139(2), 021106 (Dec 07, 2016) (11 pages) Paper No: FE-15-1931; doi: 10.1115/1.4034865 History: Received December 17, 2015; Revised September 02, 2016

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Abstract

The present contribution addresses the analysis of the leakage behavior of a small hydro Francis turbine using an analytical approach, which was validated based on the results of computational fluid dynamics (CFD). For a custom-designed Francis turbine with a specific speed of n_q = 41.9 rpm, the flow chambers resulting from the labyrinth geometry were added to a traditional full CFD model of the turbine and numerical simulations were performed for several operation points ranging from part load (Q_min = 0.5 × Q_opt) to over load (Q_max = 1.3 × Q_opt). Consequently, the single losses occurring in the runner seals on crown and band side as well as the pressure distribution within the runner side spaces could be evaluated and compared to the results gained with an analytical approach, which was originally developed to calculate the leakage flow of centrifugal pumps. The comparison of the pressure distribution achieved with the numerical simulation and the analytical calculation shows that both approaches match well if the angular velocity of the fluid ω_Fluid trapped in the runner side spaces is calculated in an appropriate way. Furthermore, the achieved results demonstrate that the use of the analytical model enables the calculation of the disk friction and leakage losses with sufficient accuracy. This paper contributes to the improvement of the performance prediction of Francis turbines based on combined numerical and analytical calculations.

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Fig. 1

View into the spiral case and distributor

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Fig. 2

Meshes around the labyrinth region of the runner

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Fig. 3

Mesh detail—runner seal on crown side

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Fig. 4

Mesh detail—runner seal on band side

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Fig. 5

Turbine model view from the top

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Fig. 6

Visualization of the runner mesh with the corresponding labyrinth seals on crown and band side

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Fig. 7

Convergence history for the BEP

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Fig. 8

Hydraulic turbine efficiency η_IEC and loss analysis based on (Eq. (4)) for various operation points at a constant turbine head of H = 125 m

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Fig. 9

Loss analysis based on (Eq. (4)) at the BEP for different mesh qualities

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Fig. 10

Francis runner with contour plot showing rotation factor k_ro as the ratio of “ω_Fluid/ω_Runner” and three-dimensional streamlines within the runner side space on crown side

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Fig. 11

Rotation factor k_rot calculated for the seal region on crown side

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Fig. 12

Pressure distribution in the seal region on crown side based on a numerical and analytical approach

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Fig. 13

Pressure distribution in the seal region on band side based on a numerical and analytical approach

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Fig. 14

Overview of the analytical and numerical results for disk friction (referring to BEP)

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Fig. 15

Overview of the analytical and numerical results for leakage (referring to BEP)

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Schiffer J, Benigni H, Jaberg H. Analysis of the Leakage Behavior of Francis Turbines and Its Impact on the Hydraulic Efficiency—A Validation of an Analytical Model Based on Computational Fluid Dynamics Results. ASME. J. Fluids Eng. 2016;139(2):021106-021106-11. doi:10.1115/1.4034865.

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Analysis of the Leakage Behavior of Francis Turbines and Its Impact on the Hydraulic Efficiency—A Validation of an Analytical Model Based on Computational Fluid Dynamics Results

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