Research Papers: Flows in Complex Systems

Characteristics and Control of the Draft-Tube Flow in Part-Load Francis Turbine

[+] Author and Article Information
Ri-kui Zhang, Feng Mao

State Key Laboratory for Turbulence and Complex Systems, College of Engineering, Peking University, Beijing 100871, China

Jie-Zhi Wu1

State Key Laboratory for Turbulence and Complex Systems, College of Engineering, Peking University, Beijing 100871, China; University of Tennessee Space Institute, Tullahoma, TN 37388jzwu@mech.pku.edu.cn

Shi-Yi Chen

State Key Laboratory for Turbulence and Complex Systems, College of Engineering, Peking University, Beijing, 100871, China; Department of Mechanical Engineering, Johns Hopkins University, Baltimore, MD 21218

Yu-Lin Wu, Shu-Hong Liu

State Key laboratory of Hydroscience and Engineering, Department of Thermal Engineering, Tsinghua University, Beijing 100084, China


Corresponding author.

J. Fluids Eng 131(2), 021101 (Jan 07, 2009) (13 pages) doi:10.1115/1.3002318 History: Received December 10, 2006; Revised May 15, 2008; Published January 07, 2009

Under part-load conditions, a Francis turbine often suffers from very severe low-frequency and large-amplitude pressure fluctuation, which is caused by the unsteady motion of vortices (known as “vortex ropes”) in the draft tube. This paper first reports our numerical investigation of relevant complex flow phenomena in the entire draft tube, based on the Reynolds-averaged Navier–Stokes (RANS) equations. We then focus on the physical mechanisms underlying these complex and somewhat chaotic flow phenomena of the draft-tube flow under a part-load condition. The flow stability and robustness are our special concern, since they determine what kind of control methodology will be effective for eliminating or alleviating those adverse phenomena. Our main findings about the flow behavior in the three segments of the draft tube, i.e., the cone inlet, the elbow segment, and the outlet segment with three exits, are as follows. (1) In the cone segment, we reconfirmed a previous finding of our research group based on the turbine’s whole-flow RANS computation that the harmful vortex rope is an inevitable consequence of the global instability of the swirling flow. We further identified that this instability is caused crucially by the reversed axial flow at the inlet of the draft tube. (2) In the elbow segment, we found a reversed flow continued from the inlet cone, which evolves to slow and chaotic motion. There is also a fast forward stream driven by a localized favorable axial pressure gradient, which carries the whole mass flux downstream. The forward stream and reversed flow coexist side-by-side in the elbow, with a complex and unstable shear layer in between. (3) In the outlet segment with three exits, the forward stream always goes through a fixed exit, leaving the other two exits with a chaotic and low-speed fluid motion. Based on these findings, we propose a few control principles to suppress the reversed flow and to eliminate the harmful helical vortex ropes. Of the methods we tested numerically, a simple jet injection in the inlet is proven successful.

Copyright © 2009 by American Society of Mechanical Engineers
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Figure 15

Distribution of |u′⋅∇u′¯| in the elbow and outlets

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Figure 16

Time-averaged streamlines and ∂P/∂x contours on three (y,z) planes at x=0.7, 1.1, and 1.5 in the draft tube for Case I. Red lines describe the forward flow, and blue lines indicate the reversed flow initiated at the center of vortex rope (color online).

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Figure 17

Mean-pressure partition along the outlets at a horizontal sectional plane with z=−3.6

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Figure 19

Isosurfaces of Δ(Δ/Δmax=6×10−6) of the controlled flow by jet injection. Starting from the onset of control, the dimensionless times in (a)–(f) are t=0, 3.60, 5.04, 7.92, 12.25, and 32.4, respectively.

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Figure 20

Pressure fluctuations of the controlled flow by jet injection: (a) and (b) are the pressure fluctuations on six check points, whose locations are marked in (c)

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Figure 21

Instantaneous streamlines of the controlled flow in the draft tube at t=32.4

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Figure 14

Variations of kinetic energy (a) and pressure (b) versus time at four points on a sectional plane (Section II in Fig. 1); the locations of the plane and date-extracted points are defined in (c)

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Figure 13

Mass flux partition. Solid, dashed, dashed-dotted, and dashed-dot-dotted lines denote the fluxes through the cone inlet and right, middle, and left outlets, respectively. (a) Case I and (b) Case II.

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Figure 12

Instantaneous streamlines, the −z-velocity contours at the inlet, and the x-velocity contours on a cross section near the exit of the elbow for Case I. Red and blue lines are in the forward and reversed streams, respectively. (a) t=11.52 and (b) t=13.39 (color online).

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Figure 11

AI/CI trajectory lines of the Batchelor vortex on the (a,q) plane for Cases I and II, compared with a WTF simulation result (the dashed-dot-dotted line and the dashed-dotted line are the results under part-load and full-load conditions, respectively). The arrows point to the downstream direction. Thin lines are the AI/CI boundaries for azimuthal modes n=+1, +2, +3 and the bold line is the outermost boundary of the AI zone, taken from Ref. 14.

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Figure 10

Azimuthal and axial velocity profiles of the basic flow and the fitted Batchelor vortex on a cross section (z=−2.0), where the data are made dimensionless by the velocity scale V0∗ defined by Eq. 1 and the cone inlet diameter D∗: (a) Case I and (b) Case II

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Figure 9

Temporal-averaged streamlines and pressure distribution on the meridian plane of the cone: (a) Case I, where S is a saddle point and (b) Case II

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Figure 8

Isosurfaces of Δ(Δ/Δmax=2×10−6) in Case II at (a) t=2.13 and (b) t=2.66. (c) Shows instantaneous streamlines at t=2.13.

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Figure 7

Pressure fluctuations on test points (as shown in Fig. 6) and their amplitude spectra in Case I: (a) pressure fluctuations and (b) power spectra of amplitude

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Figure 6

Vortex rope in Case I by using isosurfaces of Δ (Δ/Δmax=6×10−6, where Δmax is the maximum of Δ in the draft tube): (a) t=11.52 and (b) t=13.39, where P1, P2, and P3 are test points

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Figure 5

Velocity and axial vorticity profiles of the Batchelor vortex. Quantities are nondimensionalized by the global scales D∗ and V0∗. (a) is the azimuthal velocity profile and (b) and (c) are the axial velocity (W) and vorticity (ωz) profiles of Cases I and II, respectively.

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Figure 4

(a) Sole draft-tube Model: (I) draft tube and (II) river; and (b) a part of the cone surface grid

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Figure 3

Vortex breakdown above a delta wing, spiral-type on the left and bubble-type on the right (1)

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Figure 2

Typical vortex ropes in the draft-tube cone of a Francis turbine model (photos taken at Harbin Electric Machinery Co. by Q. D. Cai): (a) spiral-type vortex rope and a (b) bubble-type vortex rope

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Figure 1

A Francis turbine. (I) spiral case; (II) vanes and runner, with (i) stay vanes, (ii) guide vanes, and (iii) runner; (III) draft tube, with (iv) cone, (v) elbow, and (vi) outlet segments. The outlets (a), (b), and (c) will be referred to as the left, middle, and right outlets, respectively.

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Figure 18

Azimuthal (V) and axial (W) velocity profiles at the cone inlet for the water-injection control simulation quantities are nondimensionalized by global scales



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