Diagrams comparing the model using shed vortices from schooling fish with the arrangement of VAWTs used in the current study. The range of b is chosen to avoid overlapping turbines. 2a is the downstream distance between two vortices of the same line and 2c is the distance between two adjacent fish. U∞ refers to the free-stream speed.

Most wind farms consist of horizontal axis wind turbines (HAWTs), due to the high power coefficient (mechanical power output divided by the power of the free-stream air through the turbine cross-sectional area) of an isolated turbine. However, when in close proximity to neighboring turbines, HAWTs suffer from a reduced power coefficient.

When a HAWT extracts energy from the free stream, the speed of the flow behind the turbine is reduced. A well-known aerodynamic result is that the maximum amount of power a rotor can extract is proportional to the cube of the free-stream speed. Horizontal axis wind turbines downstream of other HAWTs have a reduced incoming flow speed and thus are capable of extracting significantly less power than that of a spatially-isolated turbine. Theoretical analysis, computational simulations, and experimental results indicate that decreasing the downstream spacing of a row of multiple HAWTs from ten rotor-diameters to five rotor-diameters can decrease the power generated by roughly 40%. Consequently, most modern HAWT wind farms space turbines five to ten rotor-diameters downstream and three or more rotor-diameters laterally.

An alternative paradigm for wind energy extraction is found in vertical axis wind turbine (VAWT) designs. Studies have shown that a single spatially-isolated VAWT has a significantly lower power coefficient and costs approximately a third more than a HAWT with comparable power output. Some sources indicate that the typical spacing constraints on HAWT wind farms do not apply. Furthermore, a recent U.S. patent suggests that aerodynamic interactions between a pair of counter-rotating VAWTs contribute to a higher power coefficient per turbine. Previous work suggests an increase of up to 4% in the average turbine power coefficient of an array of VAWTs, due to steam-tube contraction (induced higher flow speeds around neighboring VAWTs). In contrast, a separate study shows no change or a mild reduction in power coefficient for a pair of closely-spaced VAWTs. However, neither of these studies considered the possibility of alternating the directions of rotation of neighboring VAWTs.

Calculated CAP for the fish-schooling VAWT-array model is shown. Array-spacing parameters, a and b (as shown in the first figure) are normalized by the turbine diameter, D. The black dashed line corresponds to typical parameters of schooling fish.

A potential flow model of inter-VAWT interactions is developed to investigate the effect of changes in VAWT spatial arrangement on the array performance coefficient, which compares the expected average power coefficient of turbines in an array to a spatially-isolated turbine. A geometric arrangement based on the configuration of shed vortices in the wake of schooling fish is shown to significantly increase the array performance coefficient based upon an array of 16x16 wind turbines.

The experimental data used to create a potential flow model describes the flow field around a spatially-isolated VAWT. This single-VAWT model consisted of three parameters: free-stream speed, vortex strength, and dipole strength. A model for an array of VAWTs, based on the single-VAWT model, is developed and an empirical wake is introduced to calculate the expected power output of the array. To evaluate the potential benefits of a particular array configuration, an array performance coefficient, CAP , is defined to compare the average power output of an array configuration to that of a spatially-isolated VAWT. Configurations inspired by the arrangement of shed vortices in the wake of schooling fish are used for interrogating CAP values with varied geometric parameters. Results show the possibility of CAP values up to 1.4, for the 16x16 VAWT array, when not restricted to parameters corresponding to actual schools of fish. The leading mechanism for this increase is stream-tube contraction and concomitant flow acceleration between counter-rotating turbines in close proximity. However, values of CAP are approximately or less than equal to configurations following the schooling of fish regardless of array dimensions considered. These configurations significantly reduced the land use for VAWT wind farms, resulting in array power density increases of over one order of magnitude compared to operational HAWT wind farms.

Although the current model does not explicitly allow for complicated flow behavior, such as vortex shedding, turbulence, and three-dimensional effects, the current vortex and dipole model yield a flow field sufficient for assessing the performance of VAWTs. Furthermore, the field data is only from a small segment of time (one hour for the particular visit reported) and does not fully describe the variety of conditions in which VAWTs can produce power. It is of interest to conduct further measurements on a broad range of full-scale VAWT designs and over different operating conditions in order to refine the single-VAWT model. Similar measurements and considerations are required to refine the model for arrays of full-scale VAWTs. Including these effects may potentially impact the results in terms of expected power output and array power density.

This work was done by Robert W. Whittlesey, Sebastian Liska, and John O. Dabiri of the California Institute of Technology.

This Brief includes a Technical Support Package (TSP).
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Fish schooling as a basis for vertical axis wind turbine farm design

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