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Potential order-of-magnitude enhancement of wind farm power density via counter-rotating vertical-axis wind turbine arrays
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10.1063/1.3608170
/content/aip/journal/jrse/3/4/10.1063/1.3608170
http://aip.metastore.ingenta.com/content/aip/journal/jrse/3/4/10.1063/1.3608170

Figures

Image of FIG. 1.
FIG. 1.

VAWT configurations. (A) View of field site toward southwest (approximately upwind). Each turbine is 10 m tall to the top of the rotor blades. Three-turbine array is at left, two-turbine array is in center. Inset at right indicates height of the turbines relative to a 1.9-m tall person. (B) Schematic top view of two-VAWT configurations. Top of panel is due north. Circles indicate 1.2-m turbine diameter, arrows indicate the direction of turbine rotation. Turbine spacing (i.e., 1.65 turbine diameters) is indicated by the length of the single grey lines and is drawn to scale. Red circle, turbine CCW1; blue circle, turbine CW1; and black circles, additional positions of turbine CW1 tested during measurements of wind direction sensitivity. Black arrow at lower left indicates prevailing wind direction in panels (B)-(D) (see Figures 2 and 3 for full distributions of wind speed and direction, respectively). (C) Schematic top view of three-VAWT configurations. Blue circles (i.e., clockwise-rotating turbines) are spaced 1.65 turbine diameters from red turbine (i.e., counter-clockwise-rotating turbine), as indicated by the length of the single grey lines. Black circle, alternate position of upper blue circle at 4 turbine diameters downwind, as indicated by the length of the double grey lines. (D) Schematic top view of six-VAWT configuration. Red and blue circles indicate the positions of six VAWTs during measurements. Length of double grey lines indicates 4 turbine diameter spacing. Grey circles indicate additional turbine positions in a hypothetical larger-scale array.

Image of FIG. 2.
FIG. 2.

Measured daily average wind speed (solid line) and standard deviation turbulence fluctuations (dashed band) over the duration of field tests.

Image of FIG. 3.
FIG. 3.

Histogram of measured wind direction. Angle coordinate is measured in degrees from north. Radial coordinate is the number of hours observed for each wind direction.

Image of FIG. 4.
FIG. 4.

Measurement of two-VAWT configuration with 1.65 turbine diameter separation (see Fig. 1(B)). (A) Plot of normalized power coefficient (radial coordinate) versus incident wind direction (angle coordinate in degrees from north). Inset turbine schematic indicates the position of VAWTs relative to incident wind. Length of grey line indicates 1.65 turbine diameter spacing. Wind directions observed for less than 900 s are omitted (i.e., incident wind from the north). Values of indicate turbine performance equal to that of the isolated turbine. (B) Solid line, plot of normalized power coefficient versus tip speed ratio for all incident wind directions. The tip speed ratio is given by (πDΩ)U −1, where D is the wind turbine rotor diameter, Ω is the turbine rotation rate, and U is the wind speed. Vertical dotted line indicates designed operating tip speed ratio of turbines.

Image of FIG. 5.
FIG. 5.

Normalized power coefficient of turbine CW3 (upper clockwise turbines in Fig. 1(C)) versus turbine tip speed ratio. Prevailing wind direction is indicated by black arrow at lower left of Fig. 1(B). Blue curve, 1.65-diameter downwind spacing from counter-rotating upwind turbine pair (i.e., upper blue circle in Fig. 1(C)); black curve, 4-diameter downwind spacing (i.e., upper black circle in Fig. 1(C)). Values of indicate turbine performance equal to that of the isolated turbine. Vertical dotted line indicates designed operating tip speed ratio of turbines.

Image of FIG. 6.
FIG. 6.

Performance of counter-rotating six-VAWT configuration. (A) Plot of normalized power coefficient versus tip speed ratio for all incident wind directions. Data are normalized by the power coefficient of the farthest upwind turbine (i.e., CW turbine in left column of Fig. 1(D)). Dotted red curve, CCW turbine in left column of Fig. 1(D); dashed red curve, CCW turbine in middle column; solid red curve, CCW turbine in right column; dash-dot red curve, CCW turbine in right column with adjacent CW turbine removed; dashed blue curve, CW turbine in middle column; and solid blue curve, CW turbine in right column. Vertical dotted line indicates designed operating tip speed ratio of turbines. (B) Measured array power density versus planform kinetic energy flux (see text for definition). Data points are labeled according to the measurement date. Closed circles, 24-h average (except 10 September, which is an average from 13:00 to 24:00); open circles, average above cut-in wind speed.

Image of FIG. 7.
FIG. 7.

Turbine rated power and spacing combinations for order-of-magnitude increase in wind farm power density relative to existing HAWT farms. Blue curve, 30 W m−2 wind farm power density. Curve assumes 1.2-m turbine diameter as in the present tests, 30% turbine capacity factor, and 10% power loss due to aerodynamic interactions within the VAWT array. Dashed grey curves correspond to the power densities of existing renewable energy technologies (Ref. 3).

Image of FIG. 8.
FIG. 8.

Planform kinetic energy flux versus the ratio of mean wind speed above the wind farm U r to the unperturbed mean wind speed U (i.e., in the absence of the wind farm). The planform kinetic energy flux is correspondingly reduced with U r replacing U in Eqs. (4) and (5). For mean wind speeds that are greater than approximately 1/3 of the unperturbed wind speed, the planform kinetic energy flux exceeds the performance of current HAWT farms (black dashed line). For U r /U > 0.75, the VAWT farm planform kinetic flux is an order of magnitude greater than the performance of modern HAWT farms.

Image of FIG. 9.
FIG. 9.

Schematic of induced airflow between co-rotating VAWTs (panel (A)) and counter-rotating VAWTs (panel (B)). Co-rotating VAWTs (circles) induce airflow (hollow arrows) in opposite directions, whereas counter-rotating VAWTs (circles) induce airflow (hollow arrows) in the same direction.

Image of FIG. 10.
FIG. 10.

Visual signature of VAWT array. Image taken approximately 1 km from test facility (indicated by white arrow). 10 m height of VAWTs is labeled at right, in addition to approximate 100 m height of a typical large HAWT. Photo credit: R. W. Whittlesey.

Tables

Generic image for table
Table I.

Comparison of VAWT and HAWT power density. The power density is calculated as the turbine rated power divided by the area of the circular footprint swept by the turbine rotor blades when rotated in yaw by 360°.

Generic image for table
Table II.

Field test schedule. See text and Figure 1 for definitions of abbreviations.

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/content/aip/journal/jrse/3/4/10.1063/1.3608170
2011-07-19
2014-04-16
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Potential order-of-magnitude enhancement of wind farm power density via counter-rotating vertical-axis wind turbine arrays
http://aip.metastore.ingenta.com/content/aip/journal/jrse/3/4/10.1063/1.3608170
10.1063/1.3608170
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