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TECHNICAL PAPERS

Analysis of the Swirling Flow Downstream a Francis Turbine Runner

[+] Author and Article Information
Romeo Susan-Resiga

Hydraulic Machinery Department, “Politehnica”  University of Timişoara, Bvd. Mihai Viteazu 1, RO-300222, Timişoara, Romaniaresiga@mh.mec.utt.ro

Gabriel Dan Ciocan

Ecole Polytechnique Fédérale de Lausanne, Laboratory for Hydraulic Machines, Av. de Cour 33Bis, CH-1007, Lausanne, SwitzerlandGabrielDan.Ciocan@epfl.ch

Ioan Anton

 “Politehnica” University of Timişoara, Hydraulic Machinery Department, Bvd. Mihai Viteazu 1, RO-300222, Timişoara, Romania

François Avellan

École Polytechnique Fédérale de Lausanne, Laboratory for Hydraulic Machines, Av. de Cour 33Bis, CH-1007, Lausanne, Switzerlandfrancois.avellan@epfl.ch

J. Fluids Eng 128(1), 177-189 (Jul 31, 2005) (13 pages) doi:10.1115/1.2137341 History: Received July 09, 2004; Revised July 31, 2005

An experimental and theoretical investigation of the flow at the outlet of a Francis turbine runner is carried out in order to elucidate the causes of a sudden drop in the draft tube pressure recovery coefficient at a discharge near the best efficiency operating point. Laser Doppler anemometry velocity measurements were performed for both axial and circumferential velocity components at the runner outlet. A suitable analytical representation of the swirling flow has been developed taking the discharge coefficient as independent variable. It is found that the investigated mean swirling flow can be accurately represented as a superposition of three distinct vortices. An eigenvalue analysis of the linearized equation for steady, axisymmetric, and inviscid swirling flow reveals that the swirl reaches a critical state precisely (within 1.3%) at the discharge where the sudden variation in draft tube pressure recovery is observed. This is very useful for turbine design and optimization, where a suitable runner geometry should avoid such critical swirl configuration within the normal operating range.

Copyright © 2006 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Efficiency break off obtained by increasing the discharge and keeping the specific energy constant. Model test of a Francis turbine with specific speed 0.56.

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Figure 2

Sketch of the Francis turbine model and LDA setup for the flow survey section at runner outlet-draft tube inlet

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Figure 3

Pressure recovery isolines (thick lines) for the draft tube investigated in the FLINDT project. The turbine operating points (discharge coefficient-specific energy coefficient) are shown with filled circles.

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Figure 4

Reynolds number influence on the dimensionless velocity profiles at operating point with discharge coefficient 0.368 and energy coefficient 1.18

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Figure 5

Specific energy coefficient influence on the dimensionless velocity profiles at operating points with discharge coefficient 0.368

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Figure 6

Circumferential velocity profile for Rankine and Burgers vortex models, respectively

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Figure 7

Axial velocity profiles computed with 6—solid lines and 6—dashed lines, respectively, for several values of the dimensionless parameter a≡ΩR∕U0

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Figure 8

Relative flow angle computed from the experimental data for axial and circumferential velocity components on the survey section. The solid curve is a least squares fit considering a rigid body rotation for the circumferential velocity and a constant axial velocity.

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Figure 9

Axial and circumferential velocity profiles at discharge φ=0.340

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Figure 10

Axial and circumferential velocity profiles at discharge φ=0.360

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Figure 11

Axial and circumferential velocity profiles at discharge φ=0.368

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Figure 12

Axial and circumferential velocity profiles at discharge φ=0.380

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Figure 13

Axial and circumferential velocity profiles at discharge φ=0.390

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Figure 14

Axial and circumferential velocity profiles at discharge φ=0.410

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Figure 15

Characteristic angular velocities Ω0, Ω1, and Ω2 versus discharge coefficient φ

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Figure 16

Characteristic axial velocities U0, U1, and U2 versus discharge coefficient φ

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Figure 17

Vortex core radii R1 and R2 versus discharge coefficient φ

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Figure 18

Synoptic view of the model for swirling flow downstream of a Francis turbine runner

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Figure 19

Relative flow angle on streamtubes

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Figure 20

The swirlnumber S from 23 versus the discharge coefficient φ

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Figure 21

The first four eigenvalues and the pressure recovery coefficient function of the discharge coefficient

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Figure 22

Eigenmodes corresponding to the largest (positive) eigenvalue for subcritical swirling flows

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Figure 23

First two eigenmodes for subcritical swirling flow at φ=0.348

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