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Research Papers: Flows in Complex Systems

A Reference Pelton Turbine—Three-Dimensional Flow Front Tracking Within a Rotating Pelton Bucket

[+] Author and Article Information
Bjørn W. Solemslie

Waterpower Laboratory,
Department of Energy and Process Engineering,
Norwegian University of Science
and Technology,
Alfred Getz v. 4,
Trondheim 7030, Norway
e-mail: bjorn.w.solemslie@ntnu.no

Ole G. Dahlhaug

Professor
Waterpower Laboratory,
Department of Energy and Process Engineering,
Norwegian University of Science
and Technology,
Alfred Getz v. 4,
Trondheim 7030, Norway
e-mail: ole.g.dahlhaug@ntnu.no

1Corresponding author.

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received December 2, 2016; final manuscript received May 27, 2018; published online June 26, 2018. Assoc. Editor: Elias Balaras.

J. Fluids Eng 140(12), 121104 (Jun 26, 2018) (8 pages) Paper No: FE-16-1792; doi: 10.1115/1.4040444 History: Received December 02, 2016; Revised May 27, 2018

A postprocessing method has been developed to enable the extraction of quantifiable data from images captured from within the rotating frame of reference of a Pelton turbine. The turbine tested was the reference Pelton runner, designed at the Waterpower Laboratory, Norwegian University of Science and Technology (NTNU). The method relies on interpolation to three-dimensional (3D) map the inner hydraulic surface of the bucket. Interpolation has been conducted with two different schemes, i.e., Barycentric triangular and biharmonic spline, where the latter showed significant increase in accuracy. The 3D mapping provides the world coordinates of the pixels within the bucket and enables the tracking of the water front as it propagates through the bucket. The method has been described and the uncertainties have been estimated in the order of 0.4 mm for most of the hydraulic surface. The results follow expected, and previously observed, behavior and show great promise with regard to validation of numerical simulations. Results obtained by the method will be of great interest for the computational fluid dynamics (CFD) community as it can be used as direct validation data for flow propagation found with numerical methods. The method relies heavily on manual input due to the high noise and low contrast of the available images, which causes an increase in both uncertainty and time consumption. Suggestion for reducing uncertainty and time consumption are presented and will be implemented in future publications.

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References

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Figures

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Fig. 1

Hydraulic system and instrumentation

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Fig. 2

The main dimensions of the bucket (a), the view of the camera with areas of interest indicated (b), and the cropped output of the postprocessing including only the hydraulic surface of the bucket (c)

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Fig. 3

Schematic description of Barycentric coordinates (a), and one triangle ofthe mesh with a single contained pixel seen in the image (b) and world coordinate (c)

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Fig. 4

Cause of deviation (einterp) between interpolation and actual geometry, and the definition of the deviation

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Fig. 5

Estimation of the uncertainty caused by the interpolation done with the Barycentric scheme (a) and higher order scheme (b)

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Fig. 6

(a) Difference in mesh lines (black) and grid lines (white) on the inner surface near the lip area causing the lower order interpolation error. (b) Definition of the uncertainty region for tracing uncertainty and illustration of the caused change in world coordinates from pixel (XiYi).

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Fig. 7

Estimation of the uncertainty caused by manual tracing on the interpolation surface found with the Barycentric scheme (a) and higher order scheme (b)

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Fig. 8

Pixel density for Barycentric (a) and higher order (b) interpolation

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Fig. 9

Estimation of the total uncertainty in world coordinates for the Barycentric (a) and higher order (b) interpolation

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Fig. 10

Images with front (black) and impinging jet area (shaded) indicated. Δα defined as in Fig. 11, and all images are captured at nozzle opening (ψ) of 2 mm. Estimated tracing uncertainty multiplied by 2 indicated by bounding bands (white).

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Fig. 11

Definition of the angular position of the bucket (Δα)

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Fig. 12

Water fronts seen in Fig. 10 in world coordinates within the bucket obtained with a higher order interpolation, with uncertainty bands indicated. The uncertainty is based on the total uncertainty estimate shown in Fig. 9(b).

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Fig. 13

Undulating front observed during turbine operation with front indicated with black dashed line

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