Vortex-Induced Vibration of symmetric airfoils used in Vertical-Axis Wind Turbines
Introduction
Vortex-induced vibration (VIV) occurs in bluff bodies when the frequency of vortex shedding off a bluff body locks-in with the structure’s natural frequency. Once the oscillations start, the shedding frequency deviates from that predicted for a fixed bluff body based on the Strouhal law, and matches the frequency of oscillations for a range of reduced velocities (a dimensionless number relating the flow velocity to the structural natural frequency). This range of large-amplitude oscillations is called the lock-in range. VIV has been extensively studied for the model case of a flexibly-mounted cylinder placed in flow (Williamson and Govardhan, 2004, Sarpkaya, 2004), and to some extent for cases of bluff bodies with non-circular cross-sections (Nemes et al., 2012, Zhao et al., 2014, Seyed-Aghazadeh et al., 2017). For bluff bodies with non-circular cross-sections, a non-zero mean lift force acts on the body, which could result in another type of response with a lower frequency compared with the shedding frequency and larger amplitude compared with what is observed in VIV, called galloping. A combined VIV and galloping response is sometimes observed in these cases.
In order for VIV to be observed in a streamlined structure (i.e. an airfoil), the airfoil needs to be placed at relatively large angles of attack such that vortices are shed in the wake of the body. One practical example of an airfoil that is placed at large angles of attack is observed in Vertical Axis Wind Turbines (VAWTs). VAWTs have been considered recently as a viable alternative for floating offshore wind turbines (Sun et al., 2012, Paquette and Barone, 2012), and therefore a deeper understanding of how they behave is of great significance. This need for a deeper understanding of the behavior of airfoils at large angles of attack has led to recent numerical and experimental studies on VIV of airfoils. During extreme weather, installation or maintenance, wind turbines are parked (i.e. they do not rotate). Blades of a parked VAWT then will be exposed to wind that could approach them at any possible angle of attack, from 0°to 360°, thus there is a need for understanding the response of the structure at all of these possible angles of attack.
Skrzypiński et al. (2014a) used CFD results to study both prescribed motion and self-excited oscillations of a DU96-W-180 airfoil at different angles of attack and they concluded that VIV is likely to be observed “at modern wind turbine blades at standstill”. Skrzypiński et al. (2014b) also studied VIV of a DU96-W-180 airfoil placed at an angle of attack of 90°(i.e., when the long axis of the airfoil was perpendicular to the incoming flow) using a numerical technique with forced motion in the chordwise direction. They also studied the case of an elastically-mounted airfoil, free to move in the flapwise, chordwise and torsional directions, and discussed “the possibility of the lock-in phenomenon for airfoils” (Skrzypiński et al., 2014b). Ehrmann et al. (2014), through wind tunnel experiments, studied the influence of sharp trailing/leading edges on the reduction of VIV magnitude using three elastically-mounted airfoils at a fixed angle of attack of 90°. They tested a NACA 0018 airfoil and two modifications of the same airfoil: (i) a “round leading- and trailing-edge”, which started with the round end of the NACA 0018 airfoil to the location of maximum thickness, at which point the thickness of the airfoil remained constant, and was symmetric about the midpoint of the airfoil, and (ii) a “sharp leading- and trailing-edge”, which started with the sharp end of the NACA 0018 airfoil and gradually increased in thickness until reaching the maximum thickness at the midpoint. They observed that the cases with a sharp edge oscillate with a much lower amplitude and concluded that one sharp edge is enough to reduce the VIV magnitude. Zou et al. (2015) developed a double-wake vortex model and validated it using experimental data for a DU96-W-180 airfoil, and CFD results obtained for the same airfoil by Skrzypiński et al. (2014b) for angles of attack in the vicinity of (i.e. ). Using this model, Zou et al. (2015) analyzed the response of a 2D airfoil undergoing imposed sinusoidal edgewise motions and determined that maximum power due to aerodynamic forces occurs when the airfoil is forced to oscillate at the shedding frequency. Besem et al. (2016) used CFD simulations to study the response of a NACA 0012 airfoil placed in flow. They considered the case where the airfoil was forced to oscillate with a prescribed motion and the case where the airfoil was free to oscillate in a free-play region. They observed the lock-in region for both cases with a strong hysteresis effect in the case of self-excited oscillations.
The majority of the existing studies on VIV of an airfoil placed at large angles of attack have been focused on angles of attack close to 90°. An airfoil used in a VAWT, however, experiences all possible angles of attack, from 0°to 360°, when the turbine is parked. Since the airfoils used in VAWTs are symmetric airfoils, a range of 0°to 180°would cover all possible angles of attack that they could experience. In order to obtain an overall view of the airfoil’s behavior at various angles of attack, and specifically to pinpoint the angle of attack at which VIV starts, and how the magnitude of the response and the width of the lock-in range change with varying angles of attack, in this study we have conducted a series of experiments on a symmetric airfoil that is extensively used in the current designs of VAWTs. We have placed a NACA 0021 airfoil within the test-section of a water tunnel at various angles of attack, , covering the full possible range of 0° 180°. We have conducted the tests over a range of reduced velocities of 0.6 (defined as , where U is the flow velocity, is the structure’s natural frequency in otherwise still water, and C is the airfoil’s chord length), corresponding to a range of Reynolds numbers of 600 Re 13,300 (defined as Re /, where and are the density and viscosity of water, respectively).
Section snippets
Experimental setup
The experiments were conducted in a re-circulating water tunnel, with a test section of 1.27 m 0.5 m 0.38 m and a turbulence intensity of less than 1% for up to a flow velocity of U 0.3 m/s. A NACA 0021 airfoil was printed of ABS plastic with a chord of 4.13 cm and a length of 23.9 cm. The airfoil was affixed to a surface-piercing cylindrical extension with a diameter of 12.7 mm and a length of 5.0 cm, such that the entire airfoil length and half of the cylindrical extension were
An overall view of the response
The displacement time histories were measured for all angles of attack over a range of reduced velocities. These time histories were used to obtain the magnitude and frequency of oscillations at each point. Fig. 3 shows dimensionless amplitude of oscillations, (defined as A/C, where A is the amplitude of oscillations, and C is the airfoil’s chord length), of the airfoil crossflow oscillations versus the reduced velocity, , at varying angles of attack, . For angles of attack smaller
The wake and the flow forces
Fig. 5 shows the wake, flow force time history and frequency content for the airfoil placed at 60°and 120°, i.e., and , respectively at . The crossflow force coefficient is found as 2L, where is the flow force measured using the force sensor in the crossflow direction, L is the length of the airfoil, and is a dimensionless time, defined as . In all frequency plots, the frequency is normalized by the natural frequency of the system in
The relevance to VAWT designs
To get a general idea on the range of reduced velocities that are applicable to the existing VAWT designs, we considered two such designs: (i) a Sandia 34-meter VAWT design (Ashwill, 1992, Carne et al., 1989) and (ii) a DeepWind 5 MW VAWT design (Wang et al., 2013, Paulsen et al., 2012).
The blades of the Sandia 34-meter VAWT were designed structurally and aerodynamically to minimize stresses and maximize energy production. The ends of the blade are straight NACA 0021 profiles with a chord of
Conclusions
Flow-induced oscillations of a NACA 0021 airfoil at various angles of attack in the range of 0° 180°are studied experimentally in a re-circulating water tunnel over a range of reduced velocities of , corresponding to a Reynolds number range of 600 Re 13,300. The airfoil is flexibly-mounted and free to oscillate in the crossflow direction only, perpendicular to the incoming flow. For smaller angles of attack ( 55°), no oscillations are observed in the entire reduced
Acknowledgment
This research is supported in part by the National Science Foundation, USA under NSF award number CBET 1437988.
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