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Research Papers: Flows in Complex Systems

Physical Mechanism of Interblade Vortex Development at Deep Part Load Operation of a Francis Turbine

[+] Author and Article Information
Keita Yamamoto

Laboratory for Hydraulic Machines,
EPFL Avenue de Cour 33 bis,
Lausanne 1007, Switzerland
e-mail: keita.yamamoto@epfl.ch

Andres Müller

Laboratory for Hydraulic Machines,
EPFL Avenue de Cour 33 bis,
Lausanne 1007, Switzerland
e-mail: andres.mueller@epfl.ch

Arthur Favrel

Laboratory for Hydraulic Machines,
EPFL Avenue de Cour 33 bis,
Lausanne 1007, Switzerland
e-mail: arthur.favrel@epfl.ch

François Avellan

Professor
Laboratory for Hydraulic Machines,
EPFL Avenue de Cour 33 bis,
Lausanne 1007, Switzerland
e-mail: francois.avellan@epfl.ch

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received January 24, 2019; final manuscript received May 31, 2019; published online July 12, 2019. Assoc. Editor: Kwang-Yong Kim.

J. Fluids Eng 141(11), 111113 (Jul 12, 2019) (10 pages) Paper No: FE-19-1053; doi: 10.1115/1.4043989 History: Received January 24, 2019; Revised May 31, 2019

For seamless integration of growing electricity production from intermittent renewable energy sources, Francis turbines are under increasing demand to extend their operating range. This requires Francis turbines to operate under off-design conditions, where various types of cavitation are induced. At deep part load condition, an interblade cavitation vortex observed in a runner blade channel is a typical cavitation phenomenon causing pressure fluctuations and erosion, which prevent a reliable operation of Francis turbines at deep part load. The underlying mechanisms of its development are, however, yet to be understood. In an objective of revealing its developing mechanisms, the present study is aimed at investigating flow structures inside runner blade channels by comparison of three different operating conditions at deep part load using numerical simulation results. After demonstrating interblade vortex structures are successfully simulated by performed computations, it is shown that flow inside the runner at deep part load operation is characterized by a remarkable development of recirculating flow on the hub near the runner outlet. This recirculating flow is concluded to be closely associated with interblade vortex development. The skin-friction analyses applied to the hub identify the flow separation caused by a nonuniform distribution of flow, which describes the underlying physical mechanism of interblade vortex development. Investigations are further extended to include a quantitative evaluation of the specific energy loss induced by interblade vortex development. The integration of energy flux defined by rothalpy evidences the energy loss due to the presence of strong interblade vortex structures.

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Figures

Grahic Jump Location
Fig. 5

Comparison of simulated structures of instantaneous interblade vortex (iso surface of Q* = 3.0 × 104) and cavitation (iso-surface of vapor volume fraction 10%) with the visualization result ((a) and (b)), and the time-averaged vortex structure together with the mean vortex lines (c) [29]

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Fig. 6

Comparison of the time-averaged interblade vortex structure highlighted by the iso-surface of the nondimensional Q-criterion Q* = 3.0 × 104 (white surface) and the time-averaged cavitation structure (iso-surface of vapor volume fraction 10%) for OP#1 (a), OP#2 (b), and OP#3 (c)

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Fig. 4

Comparison of the nondimensional pressure distribution at the midspan plane for three different meshes at OP#1 by steady-state simulations: (a) coarse mesh (mesh #1), (b) fine mesh (mesh #2), (c) extra fine mesh (mesh #3), and (d) comparison of the pressure along the line inside the blade channel (see dotted line)

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Fig. 3

Schematics of the computational domain for numerical simulations

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Fig. 2

Velocity triangle at the runner inlet calculated by the discharge velocity CQ for OP#1 (a), OP#2 (b), and OP#3 (c)

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Fig. 1

Visualization of the interblade cavitation vortex from the downstream of the runner (a) and visualization using the instrumented guide vane (b) [23]

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Fig. 7

Comparison of the vortex circulation Γ for the interblade vortex region in the single blade channel at each spanwise location for OP#1, OP#2, and OP#3

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Fig. 8

Schematics of the meridional coordinate (a) and the location of constant spanwise planes in the three-dimensional view (b)

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Fig. 9

Comparison of the velocity contour by the time-averaged nondimensional meridional velocity Cm* together with the flow vector at the spanwise plane s* = 0.99 for OP#1 (a), OP#2 (b), and OP#3 (c)

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Fig. 10

Comparison of the velocity contour by the time-averaged nondimensional meridional velocity Cm* on the meridional plane for OP#1 (a), OP#2 (b), and OP#3 (c). The velocity is averaged in the circumferential direction from the suction side to the pressure side of the blade in the single blade channel.

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Fig. 11

Flow distribution highlighted by the velocity parallel to the blade camber line and flow streamlines at three spanwise locations s* = 0.99 (a), 0.50 (b), and 0.10 (c) for OP#1. Amplitude and direction of the velocity parallel to the blade camber line are given by the vector at six different streamwise locations at each spanwise plane. Streamlines starting from the blade channel inlet are highlighted.

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Fig. 12

The distribution of skin-friction lines on the hub atOP#1 (F: focus and S: saddle). The skin-friction lines are written by the time-averaged wall shear stress over four runner revolutions.

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Fig. 13

Variation of nondimensional pressure along the selected streamline (a) and flow separation line together with the positive pressure gradient region (b). The pressure contour is shown together in dashed line.

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Fig. 14

Flow structure highlighted by streamlines starting from the blade channel inlet near the hub for OP#1

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Fig. 15

Distribution of the nondimensional specific rothalpy I* on the meridional plane at OP#1 (a), OP#2 (b), and OP#3 (c)

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Fig. 16

Evolution of the energy loss factor e (a) and the derivative ∂e/∂m* over the nondimensional streamwise location m*

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