A conformal mapping technique to correlate the rotating flow around a wing section of vertical axis wind turbine and an equivalent linear flow around a static wing

Akimoto, Hiromichi; Hara, Yutaka; Kawamura, Takafumi; Takuju, Nakamura; Lee, Yeon-Seung

doi:10.1088/1748-9326/8/4/044040

Cited by 8 publications

(7 citation statements)

References 12 publications

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“…It is known that relative streamlines are curved when seen by a blade undergoing circular motion, and this adds the virtual camber and virtual incident angle to the blade (Migliore et al, 1980;Furukawa et al, 1990;Islam et al, 2007;Akimoto et al, 2013). Figure 3 shows the relations between blade sections in curvilinear flow and blade sections in equivalent parallel flow, where corresponding blade sections are related by conformal mapping (Furukawa et al, 1990;Akimoto et al, 2013). Coordinate in Fig.…”

Section: Conformal Mapping and Blade Sectionmentioning

confidence: 99%

“…Thus, the concave-out configuration may harness more energy than the concave-in configuration. In addition, because flow curvature effects necessitate consideration of the virtual camber (Migliore et al, 1980;Furukawa et al, 1990;Akimoto et al, 2013), it is difficult to determine which airfoil is best for small-scale wind turbines. Of course, in the case of a large chord-to-radius ratio (c/R), the concave-in configuration may be preferable because of canceling out the virtual camber (Islam et al, 2007).…”

Section: Introductionmentioning

confidence: 99%

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Comparison between symmetrical and cambered blade sections for small-scale wind turbines with low center of gravity

Hara

Sumi

Wakimoto

et al. 2014

JFST

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Low-center-of-gravity wind turbines (LCGWTs) characterized by tapered blades whose chord length c increases nonlinearly from the top (where c = 0.11 m) to the bottom (where c = 0.17 m) of each blade. Further, turbines featuring these blades do not need any arms, or even a center pole in the rotor. Two experimental LCGWTs (diameter: 0.4 m; height: 0.25 m) with symmetrical blades (NACA 0018) and cambered blades were built. A dead band, which is a band of tip speed ratio (TSR) where the rotor has negative torque at TSR lower than that where the maximum power-coefficient condition is achieved, was observed when symmetrical blades were subjected to low wind speed. In contrast, no dead band was observed for the cambered blades. Under high wind speeds and over a wide range of TSR values, performance of the LCGWTs was better with cambered blades than with symmetrical blades. Computational fluid dynamics (CFD) analysis of 2-dimensional rotors whose blade sections corresponded to the blade sections at the equatorial planes of both types of LCGWTs showed the same tendency. Performance predictions by the blade element momentum (BEM) method using aerodynamic data on the NACA 0018 blades showed some agreement with the CFD analysis. For the cambered blade rotor, Wilson and Walker's empirical correction of the thrust coefficient, a correction that is typically used in simulations of horizontal axis wind turbines, brought the BEM prediction closer to the CFD prediction than Glauert's correction did. However, the agreement between the BEM prediction with Wilson and Walker's correction and the CFD prediction of the cambered blade rotor was thought to be just a coincidence due to large difference on the torque variations between BEM and CFD. At least, the Wilson and Walker's correction predicts larger torque than the Glauert's correction at high TSR region. : Wind power, Vertical axis wind turbine, Low center of gravity, Cambered blade, Flow curvature, Conformal mapping, Blade element momentum method, Computational fluid dynamics Comparison between symmetrical and cambered blade sections for small-scale wind turbines with low center of gravity

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Section: Conformal Mapping and Blade Sectionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Comparison between symmetrical and cambered blade sections for small-scale wind turbines with low center of gravity

Hara

Sumi

Wakimoto

et al. 2014

JFST

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“…theoretical curves to the experimental data was assumed to indirectly include flow curvature effects (Migliore et al, 1980) in addition to generator efficiency. However, in the present paper, the theoretical curves are directly modified in relation to the virtual incidence (angle of attack) using conformal mapping (Furukawa et al, 1990;Akimoto et al, 2013). After modification, the upstream velocity is multiplied by a factor independent of the tip speed ratio, as the parameter of fitting.…”

Section: Resultsmentioning

confidence: 99%

“…Fitting curves to experimental data using the theoretical model shown in previous papers (Hara et al, 2014c(Hara et al, , 2014d are replaced with new fitting curves modified by virtual incidence based on flow curvature effects (Migliore et al, 1980;Furukawa et al, 1990;Akimoto et al, 2013). Variations in the vorticity field around circular blades, relating to differences in the tip speed ratio, are described in detail using results of CFD analysis.…”

Section: Introductionmentioning

confidence: 99%

Experiment and numerical simulation of an aluminum circular-blade butterfly wind turbine

Hara

Shiozaki

Nishiono

et al. 2016

JFST

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To reduce costs involved in manufacturing small wind turbines, an aluminum circular-blade butterfly wind turbine (ACBBWT) has been developed, in which four blades of the turbine were extruded and bent to shape then attached directly to a rotating flange. The ACBBWT is a vertical axis wind turbine (VAWT) and the rotor diameter of the prototype is 2.06 m. Experiments to obtain the output performance were conducted outdoors using an axial blower; however, the data obtained were rather scattered due to the effects of natural wind. Therefore, performance curves in the high wind speed range are predicted by fitting theoretical curves based on the Blade Element Momentum (BEM) theory, in which modification of virtual incidence due to flow curvature effects is included. Three-dimensional computational fluid dynamics (CFD) analysis of a circular-blade wind turbine model (dia. 2 m) with a shape almost identical to that of the experimental rotor is performed. The results assuming an energy-conversion efficiency of 0.8 agree well with the experimental results at 7 m/s. CFD analysis shows that tip vortices are shed from the top and bottom parts of a circular blade, as with straight-blade VAWTs. However, vorticity in the circular-blade case is lower than that in the straight-blade case, and the cross-section of each tip vortex shed from circular blades appears to be in the shape of a deformed ellipse. In cases of small tip speed ratios, vortex shedding caused by the dynamic stall phenomena is observed around the equator plane in both the downstream and upstream regions, and the vortex shed in the downstream region by a circular blade forms a looped shape. Since distributions of surface pressure and skin friction obtained by 3D-CFD have a similar pattern in both the upstream and downstream regions, which is related to vortex shedding, it is considered that the vortex in the upstream region is likely to also have a looped shape.

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“…Secondly, during rotation of the rotor the virtual camber of the airfoil occurs at the zero angle of attack caused by curved flow around the rotor blade. This means that the symmetrical airfoil of the vertical-axis wind turbine behaves as a cambered airfoil (Akimoto et al, 2013). Moreover, in the case of the airfoil oscillating around the zero average angle of attack, C L cannot be equal to zero because of the momentum and the inertia of the fluid (Laneville and Vittecoq, 1986).…”

Section: Unsteady Airfoil Characteristics Of the Wind Turbine Bladementioning

confidence: 99%

Steady and unsteady analysis of NACA 0018 airfoil in vertical-axis wind turbine

Rogowski

Hansen

Maroński

2018

jtam

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Numerical results are presented for aerodynamic unsteady and steady airfoil characteristics of the NACA 0018 airfoil of a two-dimensional vertical-axis wind turbine. A geometrical model of the Darrieus-type wind turbine and the rotor operating parameters used for numerical simulation are taken from the literature. Airfoil characteristics are investigated using the same mesh distribution around the airfoil edges and two turbulence models: the RNG k-ε and the SST Transition. Computed results for the SST Transition model are in good agreement with the experiment, especially for static airfoil characteristics.

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A conformal mapping technique to correlate the rotating flow around a wing section of vertical axis wind turbine and an equivalent linear flow around a static wing

Cited by 8 publications

References 12 publications

Comparison between symmetrical and cambered blade sections for small-scale wind turbines with low center of gravity

Comparison between symmetrical and cambered blade sections for small-scale wind turbines with low center of gravity

Experiment and numerical simulation of an aluminum circular-blade butterfly wind turbine

Steady and unsteady analysis of NACA 0018 airfoil in vertical-axis wind turbine

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