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Research Papers: Flows in Complex Systems

Experimental Evidence of Hydroacoustic Pressure Waves in a Francis Turbine Elbow Draft Tube for Low Discharge Conditions

[+] Author and Article Information
Jorge Arpe, François Avellan

Laboratory for Hydraulic Machines, EPFL, Ecole Polytechnique Fédérale de Lausanne, 33 bis, Avenue de Cour, CH-1007 Lausanne, Switzerland

Christophe Nicolet1

Laboratory for Hydraulic Machines, EPFL, Ecole Polytechnique Fédérale de Lausanne, 33 bis, Avenue de Cour, CH-1007 Lausanne, Switzerlandchristophe.nicolet@epfl.ch

1

Corresponding author.

J. Fluids Eng 131(8), 081102 (Jul 08, 2009) (9 pages) doi:10.1115/1.3155944 History: Received May 13, 2008; Revised April 15, 2009; Published July 08, 2009

The complex three-dimensional unsteady flow developing in the draft tube of a Francis turbine is responsible for pressure fluctuations, which could prevent the whole hydropower plant from operating safely. Indeed, the Francis draft tube is subjected to inlet swirling flow, divergent cross section, and the change of flow direction. As a result, in low discharge off-design operating conditions, a cavitation helical vortex, so-called the vortex rope develops in the draft tube and induces pressure fluctuations in the range of 0.2–0.4 times the runner frequency. This paper presents the extensive unsteady wall pressure measurements performed in the elbow draft tube of a high specific speed Francis turbine scale model at low discharge and at usual plant value of the Thoma cavitation number. The investigation is undertaken for operating conditions corresponding to low discharge, i.e., 0.65–0.85 times the design discharge, which exhibits pressure fluctuations at surprisingly high frequency value, between 2 and 4 times the runner rotation frequency. The pressure fluctuation measurements performed with 104 pressure transducers distributed on the draft tube wall, make apparent in the whole draft tube a fundamental frequency value at 2.5 times the runner frequency. Moreover, the modulations between this frequency with the vortex rope precession frequency are pointed out. The phase shift analysis performed for 2.5 times the runner frequency enables the identification of a pressure wave propagation phenomenon and indicates the location of the corresponding pressure fluctuation excitation source in the elbow; hydroacoustic waves propagate from this source both upstream and downstream the draft tube.

Copyright © 2009 by American Society of Mechanical Engineers
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Figures

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Figure 1

Gaseous vortex core development for two different values of the Thoma cavitation number for the same low discharge operating condition

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Figure 2

CAD model of the Francis turbine scale model

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Figure 3

Locations of the 292 pressure taps along the walls of the elbow draft tube (left), and mounting of the pressure transducer at the draft tube wall (right)

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Figure 4

The investigated low discharge operating point marked in the scale model efficiency hill chart

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Figure 5

Influence of σ on the pressure fluctuations amplitude spectrum; each curve is offset by the corresponding σ value

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Figure 6

Influence of σ on the frequency and the amplitude of pressure fluctuations related to the vortex rope precession and the high frequency phenomenon, HFP

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Figure 7

Time history records of pressure fluctuations for the first five sections in the draft tube

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Figure 8

Evolution of pressure fluctuations amplitude spectra for four paths along the draft tube

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Figure 9

Amplitude spectra of experimental pressure fluctuations measured at S1.75, and the corresponding amplitude spectra of the two signals modulation derived from Eq. 3)

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Figure 10

Analysis at 2.5fn frequency in the section S1.75 at the cone

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Figure 11

Phase shift angular distribution in the section S1.75 for the frequencies fc, fc−fv, and fc+fv

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Figure 12

Phase shift angular distribution in the section S1.75 for the frequency fv

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Figure 13

Amplitude, coherence, and phase spectra of the pressure fluctuations evidencing the 2.5fn pressure wave propagation along path 1

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Figure 14

Unfolded representation in 2D of the phase shift in the cone and the elbow of the draft tube (top) and 3D corresponding representation (bottom) at 2.5fn frequency

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Figure 15

Space distribution of the phase speed along the four paths defined in Fig. 8

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