Visualization by PIV of dynamic stall on a vertical axis wind turbine
Abstract
The aerodynamic behavior of a vertical axis wind turbine (VAWT) is analyzed by means of 2D particle image velocimetry (PIV), focusing on the development of dynamic stall at different tip speed ratios. The VAWT has an unsteady aerodynamic behavior due to the variation with the azimuth angle θ of the blade’s sections’ angle of attack, perceived velocity and Reynolds number. The phenomenon of dynamic stall is then an inherent effect of the operation of a VAWT at low tip speed ratios, impacting both loads and power. The present work is driven by the need to understand this phenomenon, by visualizing and quantifying it, and to create a database for model validation. The experimental method uses PIV to visualize the development of the flow over the suction side of the airfoil for two different reference Reynolds numbers and three tip speed ratios in the operational regime of a small urban wind turbine. The fieldofview of the experiment covers the entire rotation of the blade and almost the entire rotor area. The analysis describes the evolution of the flow around the airfoil and in the rotor area, with special focus on the leading edge separation vortex and trailing edge shed vorticity development. The method also allows the quantification of the flow, both the velocity field and the vorticity/circulation (only the results of the vorticity/circulation distribution are presented), in terms of the phase locked average and the random component.
Keywords
Vortex Vorticity Particle Image Velocimetry Vortical Structure Suction SideList of symbols
 c
airfoil/blade chord (m)
 D
rotor diameter (m)
 F_{N}
normal force (N)
 F_{T}
tangential force (N)
 k
reduced frequency
 R
rotor radius (m)
 Re
Reynolds number Re = cλU _{∞}/ν
 Re_{D}
Reynolds number (rotor scale) Re = DU _{∞}/ν
 U_{∞}
unperturbed velocity (m/s)
 U_{eff}
effective velocity perceived by blade (m/s)
 U_{local}
local flow velocity (m/s)
 V_{res}
Effective velocity perceived by blade (induction neglected) (m/s)
 WS
PIV processing interrogation window size (pixels)
 α
angle of attack
 λ
tip speed ratio ΩR/U _{∞}
 θ
azimuth angle
 ω
perturbation frequency (rad/s)
 Ω
rotation frequency/vorticity (rad/s)
 Γ
circulation (m^{2}/s)
 μ_{Γ}
average value of circulation (m^{2}/s)
 ν
kinematic viscosity
 σ_{Γ}
standard deviation of circulation (m^{2}/s)
1 Introduction
The increasing awareness of the need for environmentally sustainable housing and cities has driven the development of wind energy conversion systems for the built environment. One of the results of the development of solutions for the built environment is the reappearance of vertical axis wind turbines (VAWTs). Extensive research on VAWTs was conducted until the end of the 1980s (especially in North America), when, due to the increasing success of the application of horizontal axis wind turbines (HAWTs) in Europe, it was discontinued. Yet, in the built environment, VAWTs present several advantages over the more common HAWTs, namely: low sound emission (a consequence of its operation at lower tip speed ratios), better esthetics due to its threedimensionality (more suitable for integration in some architectural projects, since it follows the concept of volume of the building), its insensitivity to yaw and its increased performance in skew (see Mertens et al. 2003; Simão Ferreira et al. 2006).
Previous experimental work on dynamic stall effects on VAWTs focused mainly on performance measurements (see Laneville and Vittecoq 1986) or using flow visualization techniques (see Brochier et al. 1986). Fujisawa and Shibuya (2001, 1999) developed a first attempt at flow field measurements of a Darrieus using particle image velocimetry (PIV) at Reynolds numbers Re _{ D } = 3,000 and Re = 1,000 (water flow). The significantly lower Reynolds number as compared with fullscale wind energy applications results in a different development of the shedding of vorticity, with larger vortex pairs being shed than at higher Reynolds. The improvement of PIV techniques during the last years allows a revisit of this phenomenon with higher spatial resolution, acquiring not only a better qualitative but also quantitative description of the flow.
The level of unsteadiness is determined by the reduced frequency k, defined as k = ωc/2U _{eff}, where ω is the angular frequency of the unsteadiness, c is the blade’s chord and U _{eff} is the velocity of the blade. In this experiment, due to the variation of U _{eff} with rotation angle, k was defined for a VAWT as k = ωc/(2λU _{∞}) = ωc/(2ωR) = c/(2R), where λ is the tip speed ratio and R is the radius of the turbine. For this experimental work k = 0.125, placing the conditions in the unsteady aerodynamics region.
Experimental data is needed to gain a better knowledge of the VAWT dynamic stall process, and also to obtain an experimental database that can be used to validate the flow field calculated with numerical models; such validation is not possible with force or pressure data alone.
2 Experimental apparatus and procedure
2.1 Wind tunnel facility
The lowspeed lowturbulence wind tunnel (LTT) of the Faculty of Aerospace Engineering of Delft University of Technology (TU Delft) has an octagonal test section that is 1.80 m wide, 1.25 m high and 2.60 m long. This tunnel has a contraction ratio of 17.6, resulting in a maximum test section velocity of 100 m/s and a low turbulence intensity ranging from 0.015% at 10 m/s to 0.07% at 75 m/s.
2.2 The rotor
The rotor model is an HDarrieus vertical axis wind turbine ^{1} initially built for the investigation of pitchable VAWTs in ground effect (Coene 1983). The model is redesigned for the PIV experimental work, allowing a better access to the field of view (FOV), adding phase locking control and decreasing laser reflections. The large aspect ratio of the blade (AR = 20) and a symmetry disk at each blade tip helps to achieve 2D flow conditions at the midsection.
Range of flow and rotor parameters for all experimental runs
Ω (rad/s)  λ  U_{∞} (m/s)  Re  Re _{max}  Re _{min} 

75  2  7.5  5 × 10^{4}  7.4 × 10^{4}  2.5 × 10^{4} 
75  3  5.0  5 × 10^{4}  6.6 × 10^{4}  3.3 × 10^{4} 
75  4  3.7  5 × 10^{4}  6.1 × 10^{4}  3.7 × 10^{4} 
105  2  10.5  7 × 10^{4}  1.0 × 10^{5}  3.5 × 10^{4} 
105  3  7.0  7 × 10^{4}  9.2 × 10^{4}  4.6 × 10^{4} 
105  4  5.3  7 × 10^{4}  8.7 × 10^{4}  5.2 × 10^{4} 
2.3 Diagnostic apparatus
The flow is continuously seeded with approximately 1 μm droplets generated by a fog machine. The particle tracers are illuminated by a light sheet introduced vertically into the test section, perpendicular to the blade and located at it’s mid span. The laser light sheet is generated by a Quantec CFR 200 Nd:YAG laser (200 mJ/pulse), and is approximately 2 mm thick at the FOV. A CCD camera of 1,374 × 1,040 pixels is used with a narrowband green filter for daylight interference. The reference FOV is approximately 120 mm × 100 mm; the time interval between exposures is set based to an approximately 8pixel displacement assuming U = 4U _{∞}. Approximately between 30 and 100 samples are acquired per azimuthal position. The images are analyzed with the iterative multigrid window deformation technique (Scarano and Riethmuller 2000) with an integration window size of 31 pixels and overlap factor of 50%.
3 Phase averaging of the velocity field
The analysis of the flow and dynamic stall development is performed assuming the existence of a dominant phase locked average flow field, determined by the azimuthal position of the blade. The instantaneous flow can be regarded as the result of a mean flow, a phase averaged flow and a random fluctuating term, following the traditional triple decomposition. The predominance and asymmetry of the phase averaged flow, and the importance of the vorticity development in terms of rotor induction, imply that the analysis of a time averaged mean flow is irrelevant for physical insight. Thus, the analysis will focus on the phase averaged and random flow components.
Wernert and Favier (1999) presents an analysis on the phase averaging and convergence of the measured average towards the real average for the case of velocity vectors at a given point (in the airfoil’s suction side); from this result it is inferred that an acceptable approximation of the velocity at one point can be obtained with ensembles of a few hundred samples.

it presents a more useful, concise, effective and reproducible parameter for model validation, since it focus on a single integral parameter (in comparison with validation through velocity field),

it decreases the importance of the randomness of the vortical structures’ location/shape, giving more emphasis to the randomness of its magnitude,

a practical estimation can be achieved using less samples (dozens, instead of hundreds),

and it allows for a quantification of the magnitude and distribution of the random component.
The use of circulation as the evaluation parameter is problematic in the regions of the flow where the vortex is very diffused, and a small value of vorticity is spread over an large area. For these regions of the low, larger numbers of samples are then required (in the vicinity of a hundred) to compensate for a relatively larger effect of background noise.
3.1 The tip speed ratio as flow governing parameter
The experimental work covers three tip speed ratios and two Reynolds numbers. However, the results presented will focus mainly on the case of λ = 2, for it presents the clearest effects of dynamic stall. The cases of λ = 3 and λ = 4 will be presented later in this work for comparison with the results discussed for λ = 2.
3.2 Determining the phase average and random component of leading edge vortex
The quantification of the circulation of the vorticity shed at the airfoil surface will focus on the counterrotating vortex separated at the leading edge, when this is clearly away from the airfoil surface. The quantification of the vorticity close to the surface of the blade is compromised by the reflection of the laser from the surface. For λ = 2, the distance between the vorticity generated at the leading edge and the surface is sufficient to minimize the effect of the surface reflection on the measurements postprocessing and allow the quantification of the vorticity magnitude.

the shape of the null vorticity contour that defines the location of the vortical structures,

the existence of several smaller vortical structures (darker areas) in the instantaneous results instead of a single large vortical structure as seen in the phase average.
The actual vortical structure shed from the leading edge consists of several connected small vortical structures, varying in magnitude and location in each sample. Although varying, their magnitude and location correspond, in average, to what is observed in the phase locked average, inside its null vorticity contour. Nevertheless, these clockwise vortical structures interact with counterrotating vortical structures generated over the suction side of the blade surface which possess their own randomness (the evolution of this counterclockwise vorticity is discussed later in the paper).
The averaging of the circulation of the vortical structures is a linear process. Therefore, the difference between the magnitude of the phase locked average leading edge vortex and the average magnitude of the instantaneous vorticity is a result of the averaging at the contour limit. It includes both clockwise and counterrotating vortical structures generated at the blade’s surface.
The differences between the values of circulation calculated by both methods indicates the uncertainty related to the low number of samples used. For an infinite number of samples, it is expected that both methods would converge to a single estimate.
Figure 8 also presents a comparison between the standard deviation of the circulation of the instantaneous samples and the standard deviation of the circulation along the contour defined by the phase average vortex. The error bars indicate the uncertainty interval at a 0.95 confidence level.
The results show a lower value of circulation for the phase averaged case than when one calculates the value of circulation for each individual sample; this is a consequence from the averaging inside the contour of counterclockwise vorticity close to the blade’s surface and the definition of the vortex contour, both for the instantaneous samples and the phase averaged flow field. However, the difference is small (approximately 0.05Γ in the worst case) and in scale with the error associated with the postprocessing methodology or experimental uncertainty.
The results for the estimation of the standard deviation of the circulation of the samples do not show any significant deviation between the two methods of estimation. The circulation of phase average is thus an acceptable approximation for the leading edge separated vorticity average magnitude and its randomness. The randomness of the phase locked average is defined as the standard deviation of the circulation of the instantaneous samples following the contour defined by the phase average.
3.3 Uncertainty associated with the experimental procedure
The accuracy of the phase locking is usually an important source of error in similar experiments. From the experimental data it is possible to conclude that any oscillation of the phase locking azimuthal angle of the different samples is imperceptible and much smaller than the uncertainty of the actual value of the phase locking azimuthal angle, estimated at ±0.03°. This oscillation is the result of variations during the rotation of the aerodynamic torque and reaction of the controller for torque at the generator. This low level of uncertainty in the azimuthal position can be considered as negligible.
The bias associated with the angle of attack of the blade (due to uncertainty in the definition of zero position and due to blade bending), was estimated at a maximum of ±0.25°, based on observations at the most upwind position of the rotation.
3.3.1 Wind tunnel blockage
The problem of the influence of the blockage on rotor experiments has been a topic of research for almost a century (see Glauert 1935; Loeffler and Steinhoff 1985; Mikkelsen and Sørensen 2002; Mikkelsen 2003). Still, these models focus on horizontal axis rotors (both propellers and wind turbines), where the rotor is modeled as an actuator disk of constant induction over the entire disk. In the case of a VAWT, the load and induction is not uniform over the rotor area; it usually presents a sinusoidal distribution, with a peak around y = 0 mm. The blockage effect of a VAWT is thus much smaller than what is calculated with the constant induction assumption used by Glauert (1935). To assess the extent of the blockage effect, a 2D Navier–Stokes numerical model is used (see Simão Ferreira et al. 2007) to simulate the case of the rotor in the wind tunnel and compare with the simulation of the same VAWT in open field. The difference in thrust between the two cases is negligible; thus blockage effects are considered to be small.
3.4 Influence of the size of the interrogation window
Another source of uncertainty in the data processing step is an incorrect choice of the interrogation window, the subframe pixel area where the displacement is evaluated. In the current experimental work this is particularly severe due to the large velocity gradient in the separated flow region over the suction side of the airfoil. A too large interrogation window will average the velocity field, while a too small one will not contain enough particles and a good noise to signal ratio.
The standard deviation of the measured circulation does not show any significant difference for the two window sizes because it is mainly determined by the strong vorticity at the core. Once again, the error bars in the measurement points relate to the uncertainty of the estimators at a 0.95 confidence level; they do not represent the experimental error.
4 The influence of Reynolds numbers
5 Variation of shed vorticity with rotation angle

the shed vorticity is confined to a limited portion of the field of view, thus allowing a more focused analysis, both in position and value,

the shed vorticity allows for timeline analysis of the development of the flow and a direct relation between the flow field and the loads in the blade.

a description of the development of the flow and quantification of the shed vorticity field for the three different tip speed ratios,

and the quantification of the circulation of the leading edge vortex for the λ = 2 case.
5.1 The λ = 2 case

from θ ≈ 70° to θ ≈ 95°, where there is an almost linear growth of the magnitude of the leading edge vorticity,

from θ ≈ 95° to θ ≈ 138°, where the magnitude continues to grow at a lower rate until it reaches a maximum just before the vortex separates from the airfoil.
The termination of linear increase of magnitude at θ ≈ 95° is coincident with the roll up of the trailing edge vorticity (this is discussed later in this paper).
6 Evolution of counterclockwise vorticity
Figure 15 presents the post trailing edge wake segment at θ = 83°. Two adjacent regions of vorticity can be observed: a clockwise (negative) vorticity originated from the leading edge separated vorticity and a counterclockwise (positive) vorticity generated by the suction side boundary layer, aft of the leading edge separation. As previously seen, the clockwise vorticity will rollup into a large leading edge vortex (Figs. 16, 17); a detail of this process can be seen in the left half of Fig. 16 (θ = 90°), where the leading edge vortex and the extremity of the vorticity convected in the remaining wake (identified as ‘negative vorticity’ in Fig. 15) are presented. As was the case with the clockwise vorticity, the counterclockwise vorticity also rollsup, concentrating at suction side/trailing edge. The flow (second half of Fig. 17, θ = 90°) results in two disconnected wake regions: one over the airfoil, consisting of rolledup vorticity and another of previously shed wake vorticity, containing both negative and positive vorticity. This phenomenon is coincident with the slowing of the increase of the magnitude of the leading edge vorticity at θ ≈ 95° mentioned in the previous section.
7 λ = 3 and λ = 4
The cases for λ = 3 and λ = 4 are succinctly presented for comparison with the λ = 2 case.
The lower angles of attack for λ = 4 result in no large rollup of vorticity or vortex detachment, leading to the development of a continuous wake.
8 Conclusions
The particle image velocity results of the evolution of dynamic stall for a Darrieus VAWT at low tip speed ratios identify 2D phase locked and random components of the flow field. The measurements allow the quantification of both the phase average circulation and the random variation of circulation about that phase average of the clockwise vorticity shed from the leading edge laminar separation. This variation about the phase average is wellrepresented by a normal distribution.
The counterclockwise vorticity generated and shed at the trailing edge is measured, showing the evolution of the shed vorticity, its rollup, release and subsequent interaction with the downwind passage of the blade. The quantification of the circulation of this vorticity is not possible because a large amount of that vorticity is located close to the surface of the airfoil, where reflection of the laser invalidates the measurement.
The results focus on the case λ = 2, for this presents the largest angles of attack and shedding of the largest amounts of vorticity, thus allowing a clearer quantification or the process. However, the cases λ = 3 and λ = 4 are also observed; comparing the three tip speed ratio cases shows that the different development of the flow is not only dependent on the magnitude of angles of attack, but also on how the shed vorticity is transported and continues to interact with the airfoil.
The work also evaluates the phase averaging process and the error associated with it, both in determining the average value of circulation and in determining its randomness. The analysis also shows that the phase average, although reasonably describing magnitude, tends to smooth and present the vorticity in large unique vortices, while the instantaneous samples showed a distribution of several small vortices. These results have implications for the validation of numerical models; although a correct magnitude of shed vorticity may be predicted by the numerical model, its distribution and location of that shed vorticity will result in different flow properties over the surface of the airfoil/blade.
The decision to analyze the vorticity of the flow instead of the actual velocity field is proved useful. The vorticity field is easier to visualize and compare than the velocity field, and it also gives a more direct understanding of the evolution of the flow because it is easier to associate the evolution of lift in the airfoil/blade with the vorticity shed. Also, the phase averaging of the circulation of the vorticity field requires a lower number of samples for a given level of uncertainty than in case the measurement of point velocities.
The results are useful for the validation of the numerical models; they not only give a reasonable description of part of the development of the dynamic stall process, they also present a useful estimate of the strength of the shed vorticity. Yet, the sources of uncertainty of the results must be taken into account in the numerical model validation, specially when using the quantification of the vortex strength.
Although the data has a considerable uncertainty associated, it is currently used by the authors for the validation of CFD models, with promising results to be published. The results are also used for the evaluation of the feasibility of using PIV data for load estimation, which is a follow up of the present work.
Footnotes
 1.
The model as been referred in other work as “cyclogiro”. The difference between the two nomenclatures is due to application, since it is one and the same aerodynamic concept. In this work the model will be referred to as a Darrieus VAWT.
 2.
Blade–vortex Interaction phenomenae still occurs in the downwind portion of the blade rotation.
 3.
The remaining vortical structures outside the contour of the vortex are made invisible to simplify the figure. These structures will be discussed later in this paper.
 4.
The remaining vorticity outside the vortex contour is made invisible for clarity of the figure
Notes
Open Access
This article is distributed under the terms of the Creative Commons Attribution Noncommercial License which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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