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Research Papers: Fundamental Issues and Canonical Flows

Measurement of the Self-Oscillating Vortex Rope Dynamics for Hydroacoustic Stability Analysis

[+] Author and Article Information
Andres Müller

EPFL Laboratory for Hydraulic Machines
Lausanne 1007, Switzerland
e-mail: andres.mueller@epfl.ch

Keita Yamamoto

EPFL Laboratory for Hydraulic Machines
Lausanne 1007, Switzerland
e-mail: keita.yamamoto@epfl.ch

Sébastien Alligné

Power Vision Engineering LLC,
Ecublens 1024, Switzerland

Koichi Yonezawa

Assistant Professor
Graduate School of Engineering Science,
Osaka University,
Toyonaka, Osaka 560-8531, Japan

Yoshinobu Tsujimoto

Professor Emeritus
Mem. ASME
Graduate School of Engineering Science,
Osaka University,
Toyonaka, Osaka 560-8531, Japan

François Avellan

Professor
EPFL Laboratory for Hydraulic Machines,
Lausanne 1007, Switzerland

1Corresponding author.

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received December 2, 2014; final manuscript received October 8, 2015; published online November 4, 2015. Assoc. Editor: Olivier Coutier-Delgosha.

J. Fluids Eng 138(2), 021206 (Nov 04, 2015) (8 pages) Paper No: FE-14-1721; doi: 10.1115/1.4031778 History: Received December 02, 2014; Revised October 08, 2015

Flow instabilities in hydraulic machines often feature oscillating cavitation volumes, which locally introduce compliance and mass flow gain effects. These unsteady characteristics play a crucial role in one-dimensional stability models and can be determined through the definition of transfer functions for the state variables, where the cavitation volume is commonly estimated from the discharge difference between two points located upstream and downstream of the cavity. This approach is demonstrated on a test rig with a microturbine, featuring a self-oscillating vortex rope in its conical draft tube. The fluctuating discharges at the turbine inlet and the draft tube outlet are determined with the pressure–time method using differential pressure transducers. The cavitation volume is then calculated by integrating the corresponding discharge difference over time. In order to validate the results, an alternative volume approximation method is presented, based on the image processing of a high-speed flow visualization. In this procedure, the edges of the vortex rope are detected to calculate the local cross section areas of the cavity. It is shown that the cavitation volumes obtained by the two methods are in good agreement. Thus, the fluctuating part of the cavitation volume oscillation can be accurately estimated by integrating the difference between the volumetric upstream and downstream discharges. Finally, the volume and discharge fluctuations from the pressure–time method are averaged over one mean period of the pressure oscillation. This enables an analysis of the key physical flow parameters’ behavior over one characteristic period of the instability and a discussion of its sustaining mechanisms.

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Figures

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Fig. 1

Closed-loop test configuration for the simulation of a hydraulic powerplant with microturbine and conical diffuser

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Fig. 2

Microturbine runner (top) and volute geometry (bottom)

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Fig. 3

Close view of the draft tube cone with an inlet and outlet diameter of D1¯ = 31mm and cone Dcone = 57 mm. The straight part measures L1 = 50.8 mm and the conical part has a length of L2 = 186 mm with a half-angle of 4 deg.

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Fig. 4

Draft tube flow visualization showing one period T of the vortex rope oscillation: (a) t = 0, (b) t = 0.11 · T, (c) t = 0.22 · T, (d) t = 0.33 · T, (e) t = 0.44 · T, (f) t = 0.55  ·  T, (g) t = 0.66 · T, (h) t = 0.77 · T, (i) t = 0.88 · T, and (j) t = T

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Fig. 5

Amplitude (solid line) and phase angle (dashed line) of the cross-spectral power density between the pressure sensors p3 and p6

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Fig. 6

Control volume in the draft tube containing the volume Vc

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Fig. 7

Draft tube cone in cavitation-free conditions with sections I, II, III, IV, and V for image processing

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Fig. 8

Subtraction of a reference image from a video frame (top) and masked binary conversion (bottom) for the edge detection in sections I, III, and V

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Fig. 9

Pixel value curve along a vertical line for the edge detection in sections II and IV. The dashed horizontal lines represent the locations of the estimated cavity edges according to the local minima of the pixel value curve.

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Fig. 10 Top

low-pass filtered cp from p2 with instant phase (dashed line) and bottom: mean phase average with standard deviation (vertical error bars)

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Fig. 11

Nondimensional volume Vc* estimated from flow visualization (point markers) with low-pass filtered signal (solid line) as a function of the number of runner revolutions

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Fig. 12

Nondimensional vortex rope volume Vc* from flow visualization, wall-pressure coefficient from p2, and nondimensional discharge fluctuations Q̃1∗, and Q̃2∗ as a function of the number of runner revolutions

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Fig. 13

Nondimensional, centered Vc* from flow visualization (point markers) and from discharge measurements (dashed line) as a function of the number of runner revolutions

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Fig. 14

Mean pressure phase-averaged vortex rope volume (top) and discharge fluctuations (bottom) with standard deviations (vertical error bars)

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Fig. 15

Vortex rope volume as a function of the upstream and downstream discharge fluctuations during one mean period of the pressure oscillation

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