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Research Papers: Fundamental Issues and Canonical Flows

# Flow Kinematics in Variable-Height Rotating Cylinder Arrays

[+] 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 January 28, 2016; final manuscript received May 12, 2016; published online July 15, 2016. Assoc. Editor: Mark F. Tachie.

J. Fluids Eng 138(11), 111203 (Jul 15, 2016) (11 pages) Paper No: FE-16-1062; doi: 10.1115/1.4033676 History: Received January 28, 2016; Revised May 12, 2016

## Abstract

Experimental data are presented for large arrays of rotating, variable-height cylinders in order to study the dependence of the three-dimensional mean flows on the height heterogeneity of the array. Elements in the examined arrays were spatially arranged in the same staggered paired configuration, and the heights of each element pair varied up to $±$37.5% from the mean height (kept constant across all arrays), such that the arrays were vertically structured. Four vertical structuring configurations were examined at a nominal Reynolds number (based on freestream velocity and cylinder diameter) of 600 and nominal tip-speed ratios of 0, 2, and 4. It was found that the vertical structuring of the array could significantly alter the mean flow patterns. Most notably, a net vertical flow into the array from above was observed, which was augmented by the arrays' vertical structuring, showing a 75% increase from the lowest to highest vertical flows (as evaluated at the maximum element height, at a single rotation rate). This vertical flow into the arrays is of particular interest as it represents an additional mechanism by which high streamwise momentum can be transported from above the array down into the array. An evaluation of the streamwise momentum resource within the array indicates up to a 56% increase in the incoming streamwise velocity to the elements (from the lowest to highest ranking arrays, at a single rotation rate). These arrays of rotating cylinders may provide insight into the flow kinematics of arrays of vertical axis wind turbines (VAWTs). In a physical VAWT array, an increase in incoming streamwise flow velocity to a turbine corresponds to a (cubic) increase in the power output of the turbine. Thus, these results suggest a promising approach to increasing the power output of a VAWT array.

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## Figures

Fig. 1

Schematics of the spatial, rotational, and height configurations of the arrays (within the region of interest). Each symbol indicates the position of an element. The color of the symbol indicates the rotational direction as viewed from above: black is clockwise and gray is counterclockwise. The symbol indicates the height of the element: ◁ indicates a short element, ○ indicates an average element, and indicates a tall element. The red (light gray) lines indicate the transverse locations and streamwise extents of the vertical data sheets taken in each array. The blue (dark gray) box indicates the position and extent of the horizontal data sheets taken.

Fig. 2

Experimental setup illustrations. Left: close-up sketch showing element mounting to gears and plate structure holding gears in place. Right: photo of full array in the flume. Figure adapted from Ref. [10].

Fig. 3

Comparison of Cuin (normalized to maximum measured value) across arrays and rotation rates. Light gray indicates α = 0, medium gray indicates α = 2, and dark gray indicates α = 4.

Fig. 4

Comparison of streamwise momentum flux terms for α = 2. Solid line: 〈u¯〉〈w¯〉, dashed line: 〈u′w′¯〉, and dotted line: 〈u¯̃w¯̃〉. Note that on this scale, for the sawtooth, wedge, and random arrays, the tallest elements are at height 1, the average elements are at height 0.73, and the short elements are at height 0.45, as indicated by the grid lines. While these latter two heights have no meaning for the uniform array, the grid lines have been retained for easier comparison between arrays.

Fig. 5

Time-averaged transverse flows and streamlines in the three horizontal data planes for the (a) sawtooth and (b) wedge arrays, α = 2. Here, as in Fig. 1, the symbol indicates the height of the element: ◁ indicates a short element, ○ indicates an average element, and indicates a tall element. The color of the symbol indicates the rotational direction as viewed from above (if the element intersects the given data sheet; if the element is below the height of the data sheet, the symbol is left white): black indicates clockwise rotation and gray indicates counterclockwise rotation. Note that the missing data along the rows of elements are due to shadowing of the laser sheet.

Fig. 6

Comparison between quantified meander of flow in the array and the performance of the array (for α = 2 data). The symbol indicates the height of the data sheet: ◁ indicates that the data sheet was at or below z = 5D, ○ indicates that the data sheet was at or below 8D, and indicates that the data sheet was at or below 11D. Multiple symbols come from the different arrays. The solid line is the linear best fit: R2 = 0.86.

Fig. 7

Time-averaged vertical flow and streamlines for a selection of the vertical data sheets taken in each array, α = 2. Solid black rectangles indicate that the sheet intersects with a clockwise rotating cylinder. Rectangle outlines indicate the locations of the rows which the laser sheet does not intersect, with the height of the element closest to the laser sheet being indicated. Please note that due to line of sight blocking by other elements along the rows, data were not able to be collected between elements in a row. Interpolation was used to fill these regions of missing data, and features “within” the outlined cylinders may be artifacts of the interpolation.

Fig. 8

Comparison of the flow angle behind each cylinder pair with the local tip-speed ratio (α = 2 data). The symbol indicates the height of the element pair: ◁ indicates a short element pair, ○ indicates an average element pair, and indicates a tall element pair. The solid line indicates the linear best fit: R2 = 0.93.

Fig. 9

Illustrations of vertical flow prediction based on vertical structuring of array: top panel—sawtooth array, y=−1D and bottom panel—wedge array, y = −3D

Fig. 10

Comparison of model predicted vertical flow and measured vertical flow at the maximum height of the array (α = 2 data). The symbol indicates the array: indicates the sawtooth array, ○ indicates the wedge array, △ indicates the random array, and ◇ indicates the uniform height array. The solid line indicates the linear best fit: R2 = 0.99.

Fig. 11

Time–space averaged stress fraction (a) and duration fraction (b) of u′w′ events in quadrant 1 (–⋅), quadrant 2 (–), quadrant 3 (⋅⋅), and quadrant 4 (– –). Hole size = 0 for each of the four arrays.

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