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Research Papers: Fundamental Issues and Canonical Flows

A Kinematic Description of the Key Flow Characteristics in an Array of Finite-Height Rotating Cylinders

[+] Author and Article Information
Anna E. Craig

Department of Mechanical Engineering,
Stanford University,
Stanford, CA 94035
e-mail: craig0a@stanford.edu

John O. Dabiri

Professor
Department of Civil and
Environmental Engineering;
Department of Mechanical Engineering,
Stanford University,
Stanford, CA 94035

Jeffrey R. Koseff

Professor
Department of Civil and
Environmental Engineering,
Stanford University,
Stanford, CA 94035

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received September 4, 2015; final manuscript received December 25, 2015; published online April 22, 2016. Assoc. Editor: Daniel Maynes.

J. Fluids Eng 138(7), 070906 (Apr 22, 2016) (16 pages) Paper No: FE-15-1630; doi: 10.1115/1.4032600 History: Received September 04, 2015; Revised December 25, 2015

Experimental data are presented for large arrays of rotating, finite-height cylinders to study the dependence of the three-dimensional (3D) mean flows on the geometric and rotational configurations of the array. Two geometric configurations, each with two rotational configurations, were examined at a nominal Reynolds number of 600 and nominal tip-speed ratios of 0, 2, and 4. It was found that the rotation of the cylinders drives the formation of streamwise and transverse flow patterns between cylinders and that net time–space averaged transverse and vertical flows exist within the developed flow region of the array. This net vertical mean flow provides an additional mechanism for the exchange of momentum between the flow within the array and the flow above it, independent from the turbulent exchange mechanisms which are also observed to increase by almost a factor of three in a rotating array. As an array of rotating cylinders may provide insight into the flow kinematics of an array of vertical axis wind turbines (VAWTs), this planform momentum flux (both mean and turbulent) is of particular interest, as it has the potential to increase the energy resource available to turbines far downstream of the leading edge of the array. In the present study, the streamwise momentum flux into the array could be increased for the rotating-element arrays by up to a factor of 5.7 compared to the stationary-element arrays, while the streamwise flow frontally averaged over the elements could be increased by up to a factor of four in the rotating-element arrays compared to stationary-element arrays.

Copyright © 2016 by ASME
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Figures

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Fig. 1

Experimental setup illustrations. (a) Close-up sketch showing element mounting to gears and plate structure holding gears in place. (b) Photo of full array in the flume.

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Fig. 2

Schematic showing planform views of array configurations. Black circles indicate clockwise rotating elements, gray circles indicate counterclockwise rotating elements, as viewed from above.

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Fig. 3

Time-partial-space averaged streamwise (left group) and vertical (right group) flow profiles for each array at third (solid line) and fourth (dashed line) measurement positions. Light gray (red online) indicates α = 0 and dark gray (blue online) indicates α = 4. Uncertainties are shown by shaded region surrounding each line.

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Fig. 4

Time-full-space averaged vertical flow profiles at the fourth measurement location of the arrays, spatial average taken over central unit cell. Dotted line (red online) indicates the staggered RI array, dashed line (green online) indicates the staggered RII array, dashed -dotted (blue online) line indicates the pair doublet array, and solid line (black) indicates the paired reverse doublet array.

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Fig. 5

Sketch of proposed “typical” mean flow patterns surrounding a stationary cylinder pair, deep within array. A and a are indications of the continuation of flow patterns from one unit cell in the array to the next.

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Fig. 6

Sketch of proposed typical mean flow patterns surrounding a paired doublet-rotating cylinder pair, deep within array

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Fig. 7

Sketch of proposed typical mean flow patterns surrounding a paired reverse doublet-rotating cylinder pair, deep within array. A and a and B and b are indications of the continuation of flow patterns from one unit cell in the array to the next.

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Fig. 8

Sketch of proposed typical mean flow patterns surrounding a subset of cylinders, deep within the staggered RI array

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Fig. 9

Sketch of proposed typical mean flow patterns surrounding a subset of cylinders, deep within the staggered RII array. Cylinders A and B may be treated as a doublet-type rotating pair; cylinders B and C may be treated as a reverse-type rotating pair.

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Fig. 10

Normalized spatial power spectral density of u′. Spectra taken over transverse (left group) or vertical (right group) lines of data just behind elements at 176D and ensemble averaged over each data realization. Light gray (red online) indicates a stationary array, dark gray (blue online) indicates a rotating array (α = 4); the black line is − 5/3 slope for reference. Thickness of lines indicates uncertainties.

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Fig. 11

Normalized temporal power spectral density of v′ (left group) and w′ (right group). Spectra taken at each point in small region within an element wake and spatially averaged. Light gray (red online) indicates a stationary array, dark gray (blue online) indicates a rotating array (α = 4). Thickness of lines indicates uncertainties.

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Fig. 12

Spatially averaged duration fraction (left) and stress fraction (right) of u′w′ events in quadrant 1 (–⋅), quadrant 2 (–), quadrant 3 (⋅⋅) and quadrant 4 (– –). (Hole size = 0). α = 0 in light gray (red online), α = 4 in dark gray (blue online).

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Fig. 13

Comparison of streamwise momentum fluxes: from mean flow, 〈w¯〉〈u¯〉, (solid line); from Reynolds stresses, 〈u′w′¯〉, (dashed line); and from dispersive stresses, 〈u¯̃w¯̃〉, (dotted line). Stationary array shown in light gray (red online), rotating array shown in dark gray (blue online).

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Fig. 14

The depth averaged mean incoming streamwise flow, 〈u3¯|in, plotted against the depth-time-space averaged vertical flow. Medium gray (red online) indicates staggered RI array, light gray (green online) indicates staggered RII array, dark gray (blue online) indicates paired doublet array, and black indicates paired reverse doublet array. Circles indicate α = 0, squares indicate α = 2, and triangles indicate α = 4.

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Fig. 15

(a) u¯ and (b) v¯ and w¯ in the paired geometry array for α = 0. The synthesized sketch of flow patterns given in Fig. 5 is included at the top for convenient comparison. Black lines in the first panels mark locations of intersection with perpendicular sheets. In the horizontal sheets, (top row) open circles indicate the locations of the (stationary) cylinders. In the vertical sheets, dark gray rectangles indicate the data sheet intersected a (stationary) cylinder, while open rectangles indicate the locations of the cylinder rows, but the data sheet did not intersect a cylinder.

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Fig. 16

(a) u¯ and (b) v¯ and w¯ in the paired doublet array for α = 4. The synthesized sketch of flow patterns given in Fig. 6 is included at the top for convenient comparison. Black lines in the first panels mark locations of intersection with perpendicular sheets. Black circles and rectangles indicate data sheet intersection with a clockwise rotating cylinder, gray circles and squares indicate data sheet intersection with a counterclockwise rotating cylinder, and open rectangles indicate the locations of the cylinder rows, but the data sheet did not intersect a cylinder.

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Fig. 17

(a) u¯ and (b) v¯ and w¯ in the paired reverse doublet array for α = 4. The synthesized sketch of flow patterns given in Fig. 7 is included at the top for convenient comparison. For additional information, please see caption of Fig. 16.

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Fig. 18

(a) u¯ and (b) v¯ and w¯ in the staggered RI array for α = 4. The synthesized sketch of flow patterns given in Fig. 8 is included at the top for convenient comparison. For additional information, please see caption of Fig. 16.

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Fig. 19

(a) u¯ and (b) v¯ and w¯ in the staggered RII array for α = 4. The synthesized sketch of flow patterns given in Fig. 9 is included at the top for convenient comparison. For additional information, please see caption of Fig. 16.

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