The measurements were performed in the atmospheric wind tunnel at the University of Gävle. The wind tunnel facility is a closed loop tunnel with a total length of 28 m and a maximum velocity in the test section of 22 m/s. The contraction ratio is 3:1 and the tunnel is driven by a 45 kW fan placed in the return circuit. The tunnel is equipped with guiding vanes and honeycombs to improve the flow quality. The size of the measurement section is 11 × 3 × 1.5 m³ (length × width × height).

A right-handed coordinate system for the setup is used, which has its origin at the centre of the model at hub height, with as the streamwise coordinate (positive downstream), as the vertical coordinate (positive upwards) and as the spanwise coordinate. The mean streamwise velocity is denoted by and its root-mean-square value of the fluctuations with. The corresponding notation for the vertical component is and. The velocity is scaled with the velocity at hub height, , which is here taken as the mean value over the whole rotor disc. In order to comply with standard boundary layer theory, the inlet profiles are shown with a different vertical coordinate, where the origin is set at the wind tunnel floor. The free-stream velocity is denoted by.

A three bladed turbine model with a hub height of and a sweep area diameter of was used. The turbine blades were designed using an in-house blade element momentum (BEM) code, using the Glauert optimization [15] [16] . The airfoil profile was an SD7003 and the design opti- mization was made for a tip speed ratio. The tip speed ratio is defined as the speed of the blade tip divided by the hub velocity:

Here, is the angular velocity, making the speed of the blade tip. The blades were manufactured of aluminium which was then painted black to mini- mize reflections from the PIV laser. The total twist was 31˚ and the chord length varied from 31 mm close to the hub to 15 mm close to the blade tip. The pitch angle at the tip was set to 3.3˚. The chord Reynolds number (based on chord length and relative velocity) varied from 15,000 close to the hub to 26,000 close to the tip, with an average of 22,000. The blockage ratio (swept area of the rotor divided by the cross-sectional area of the wind tunnel) was 0.9%, which is far below the suggested upper limit of 10% to avoid effects on the wake expansion due to tunnel wall interference [17] . Therefore, no blockage correction methods were applied to compensate for the presence of the wind tunnel walls.

The nacelle consisted of a small electricity generator, which was connected to a known resistance and a variable number of diodes through a Wheatstone bridge. The current through the circuit was calculated by measuring the voltage over the resistance. By applying different loads (i.e. different number of diodes in the electrical circuit), the rotational frequency of the model could be varied from 800 to 4200 rpm, corresponding to a change in tip speed ratio from 1.6 to 8.3, with a fixed free-stream velocity. To avoid taking the electrical losses in the generator into account, the power output, , was calculated as the rotational torque, , multiplied by the angular velocity,. The generator had a torque, , versus current, , relationship of the form, where and are calibration constants. The rotational frequency was measured with a laser emitter and receiver. The laser was aligned so that each passage of a blade blocked the laser, thus causing a pulse signal from the receiver. The thrust force was measured by placing the model on a VETEK load cell.

Hot-film measurements were performed with a single component probe of wire diameter. It was calibrated against a known differential pressure by measuring 15 points and then fitting the points to a polynomial curve. A standard temperature correction was applied, since the tunnel did not have any temperature control at the time.

A Particle Image Velocimetry (PIV) system consisting of a HI Sense Mk II camera (1344 × 1024 pixels) and a laser was used. The physical size of each image was 100 × 77 mm². For the evaluation, an adaptive correlation scheme was used, with 50% overlap and an interrogation area of 32 × 32 pixels. The sampling frequency was 6.1 Hz. Measurements were made in the region and at three different spanwise positions: and, corresponding to the centreline, middle of the wake and edge of the wake. Here, corresponds to the radius of the rotor sweep area. A sketch of the setup, coordinate system and the measured planes are shown in Figure 1.

Two cases with different inlet boundary conditions were compared. The first case had a naturally developing boundary layer along the test section. In this case, both the mean velocity and the turbulence intensity had an almost uniform

distribution across the rotor disc (except for the lowest part). This case is here denoted “naturally developing boundary layer (NBL) inflow”, and will be abbreviated the “NBL case”. For the second case, a thicker boundary layer was created by adding triangular spires in the beginning of the test section, followed by several meters of roughness elements. This was done in order to mimic the atmospheric boundary layer (ABL), and this case will therefore be denoted the “atmospheric boundary layer inflow”, abbreviated as the “ABL case”. In this case, the rotor was subjected to an inflow with strong shear and higher turbulence levels as compared to the NBL case. A picture of the wind tunnel test section with the spires and roughness elements can be seen in Figure 2. For the NBL case, the test section was empty (except for the turbine model), giving rise to a significantly thinner boundary layer compared to the ABL case. The velocity at hub height was 6.0 m/s in the NBL case and 4.2 m/s in the ABL case. The corresponding streamwise turbulence intensities () were 1.3% and 15%, respectively. Both the hub velocities and the turbulence intensities are taken as the mean values over the whole rotor disc.

Figure 3 shows the inlet profiles, measured with hot-film and PIV. The profiles are measured at the position of the turbine, but in absence of the turbine itself. The PIV data have been high-pass filtered using a cut-off frequency based on the longest length scale, which locally can affect the boundary layer, i.e. the sum of the height and width of the cross section of the tunnel (1.5 + 3.0 = 4.5 m) and the velocity at, which was. This gave a cut-off fre- quency of. For the ABL case, a power law fit has been added over the rotor disc location, according to the following equation:

where is the mean streamwise velocity at height above the tunnel floor and is the velocity at hub height,. In atmospheric boundary layer theory, is normally considered to be around, and in cases of extreme shear up to. For the current data, the fit gave, making this a fairly sheared profile across the rotor disc. For both cases, a log law fit was made closest to the floor according to:

where is the friction velocity, is the von Kármán constant and is the surface roughness length. The friction velocity is defined as, where is the skin friction and is the air density. A least squares log law fit gave and (NBL case) and and (ABL case). For comparison, the friction velocity was found to be between 0.06 and 0.11 m/s in a field experiment with [18] . for the present experiment was and, for the NBL and ABL cases, respectively. For a very smooth surface (ice or mud), is generally set to 0.01 mm [19] . The free-stream velocity, the hub velocity, the displacement thickness, the momentum thickness and the shape factor for both cases are summarized in Table 1. Included is also an estimation of the shear across the rotor disc, , i.e. the change in mean velocity over the turbine disc location.

The inlet streamwise turbulence intensities for the two cases are shown in

Figure 4. Note that Figure 3 and Figure 4 are shown with the origin at the wind tunnel floor (the vertical coordinate is therefore denoted) and that is scaled by the hub height. In the rest of the paper, the results are shown with the origin at hub height of the model and the vertical coordinate scaled with the rotor radius.

The power and thrust coefficients are defined as:

where is the power output from the turbine, is the total thrust force and is the sweep area of the rotor,. The measured power and thrust coefficients are plotted in Figure 5. All the following velocity measurements were performed at a tip speed ratio of 5, corresponding to the tip speed ratio the blades were optimized for. This gave and for the NBL case and and for the ABL case. These values were expected, since small-scale model turbines usually perform somewhat worse than full scale ones, with a lower maximum power output and a higher thrust. Due to the small-scale in the wind tunnel, the optimal tip speed ratio is also often lower than for full scale turbines. It can be seen in Figure 5 that the power output in the NBL case is slightly higher than in the case with ABL inflow, while the thrust coefficients remains approximately the same. It is not clear whether the difference is due to the shear layer and/or increased turbulence or if it is a Reynolds number effect. The Reynolds numbers based on hub velocity and rotor diameter were for the NBL case and for the ABL case. A previous study by [9] showed a clear Reynolds number dependence in a similar range: an increase in Reynolds number from to resulted in

an increase in with 12%. Included in Figure 5 is also computations using the BEM method. By looking at the BEM results for the NBL and ABL cases, it can be seen that this method predicts an increasing, but an almost constant, when increasing the Reynolds number, suggesting that the differences between the NBL and ABL cases are a Reynolds number effect. For both cases, the BEM computations predict a higher power output and a lower thrust as compared to the measurements. The discrepancies is due to the lack of measured airfoil data (lift and drag) for these low Reynolds numbers. The BEM computa- tions do however show the same trend as the measurements, for both and.

In order to validate the PIV measurements, a few profiles were also measured with hot-film. An overall good agreement was found. In Figure 6, a comparison between hot-film measurements and PIV measurements is shown for the ABL case. The left column is the mean streamwise velocity and the right column is the corresponding turbulence intensity. The positions are downstream at three spanwise positions:, and. The reason for the larger discrepancy between hot-film and PIV in the mean velocity profiles at is most likely due to the fact that the wake deficit has a very sharp peak at, due to the wake from the nacelle, which was already known from previous measurements [9] . A very small spanwise shift from the location of the maximum velocity deficit would therefore result in a larger velocity. From [9] , the sharp peak in velocity deficit can be estimated to over a spanwise distance. By only looking at the hot-film measurements, it can be seen that the peak in is moving towards the centreline as we move further out in the spanwise direction. It suggests that the turbine is producing a

lot of turbulence on the edge of the rotor disc on the upper half side, but not on the lower half, which has also been seen in previous studies [4] [6] .

Vertical profiles of mean streamwise () and vertical () velocity in the wake are shown in Figures 7-9. The profiles correspond to the wake centerline

location (Figure 7), (Figure 8) and (Figure 9), res- pectively. Each figure shows a comparison between the NBL and the ABL cases for three different downstream positions:, and. Already

this close to the turbine, the ABL case shows a faster recovery of the wake with smoother profiles. This result is not surprising and is due to the higher inlet turbulence levels in the ABL case, which enhances the mixing and transport of momentum. For the vertical component, it can be seen that at and, the NBL and ABL cases are similar, while a larger difference can be seen at. The largest values of are seen at, where it reaches above 10% of the hub velocity. The measurements are taken at the negative spanwise side where a positive vertical component can be expected, assuming that the wake is rotating in the opposite direction as the rotor. Note, the rotor is rotating clockwise when looking in the streamwise direction.

The corresponding profiles of streamwise () and vertical () turbulence intensity are shown in Figures 10-12. In the streamwise component (left co- lumns of the figures), it can be seen that the turbine in general produces kinetic energy in the NBL case: the values of are in general higher after the tur- bine than at the inlet. In the ABL case on the other hand, the turbulence levels in the wake are of the same order as at the inlet, about 15% of. Apparently, the turbine does not generate additional turbulence in this case. The tip vortices can clearly be seen as a peak in the turbulence levels in some of the positions for the NBL case, but not in the ABL case. This is particularly clear around

at (Figure 11) and around at (Figure 12(a)). It is possible that the higher inlet turbulence levels in the ABL case make the tip vortices break down faster, which would explain why they are not detectable in these images.

Large differences between the two cases can be seen in the vertical component of the turbulence intensity (right columns of Figures 10-12). The increased turbulence and shear of the ABL case changes the completely in the NBL case. The tip vortices are visible as sharp peaks in at and, but not in the ABL case. The mean vertical component at the inlet was below 0.5% of the streamwise velocity, in both the NBL and the ABL cases. The vertical component of the turbulence intensity was 3% and 12% at the inlet, in the NBL and ABL cases, respectively. In the NBL case, the values of in the wake is around 5% in average, meaning that the turbine increases as compared to the inlet. For the ABL case, remains in average about the same as at the inlet, about 12% in average, even though the distribution is changing. is here varying between 8% - 17%.

The clear peaks in turbulence intensity displayed in Figure 11(a) and Figure 11(b) correspond to the tip vortices. Instantaneous velocity images of streamwise and vertical velocity are shown at this location in Figure 13(a) and Figure 13(b), respectively. The tip vortices can be seen as adjacent regions of high and low speed. The result, based on both images, is a counter-clockwise rotation of the vortices. This is shown more clearly in Figure 14, where the local mean velocity has been subtracted from each point in Figure 13(a), in order to suppress the influence of the boundary layer. The arrows correspond to the vector sum of and, which shows the actual additional rota- tion caused by the vortices.

In order to study the vortex statistics of this flow case, an in-house developed vortex detection program was used, which is described in [20] [21] . Vortices are

here detected by using the approach suggested by [22] , which is based on iden- tifying closed or spiral streamline patterns by looking at the complex eigenvalues of the 2D velocity gradient tensor:

A vortex is then defined as a region where the imaginary eigenvalues are positive and greater than a predefined threshold value. The vortex strength is here defined as the maximum imaginary eigenvalue () within the identified region, and the position of is defined as the vortex centre. The circulation is calculated according to:

where is a circle with origin at the vortex centre. By performing this inte- gration, stepping outwards from the vortex centre until the maximum circula- tion is reached, each vortex can be identified and approximated by a circle. The diameter of this circle will in the following be used as a measure of the vortex size.

Figure 15 shows the 5% strongest vortices for each -position. The (+)-signs denote vortices which have positive circulation and counter-clockwise rotation, while the (’)-signs show vortices with negative circulation and clock- wise rotation. The spanwise position is at, where the tip vortices could be seen clearly (see Figure 13 and Figure 14). For the NBL case, the strongest vortices are located in a smaller vertical region and most of them are in the same (counter-clockwise) direction. These are apparently the tip vortices, which are not as visible in the ABL case, where the vortices show a larger spread in -direction and also a more even distribution of rotational direction. This is in accordance with the results from the turbulence intensity profiles shown in Figure 11, which showed signs of the tip vortices for the NBL case, but not for the ABL case. It should also be noted that the 5% strongest vortices shown here are much stronger in the NBL case; the strongest 5% corresponds to for the most upstream position (). For the ABL case, the 5%-threshold is. Figure 15 is assembled from three different PIV images (i.e. three different downstream positions), which is the explanation for the gaps without vortices seen most clearly for the NBL case at and 2.1.

Figure 16 shows the 5% largest vortices for the NBL (upper figure) and ABL (lower figure) cases. It can again be seen that the vortices in the NBL case are spread over a smaller vertical distance and are to a larger extent in the same direction. The probability density function (PDF) of the vortex size for all

detected vortices is shown in Figure 17(a) and Figure 17(b), for the NBL and ABL cases, respectively. The figure shows one function for every downstream image (three different downstream regions, corresponding to the three different PIV images that were taken).

For the NBL case, the vortices are decreasing in size with downstream dis- tance. In contrary, for the ABL case, the vortices have about the same size for all positions. The vortex diameter corresponding to the highest peak in the PDF for the NBL case is decreasing from about 0.10 to approximately 0.077, while it remains around 0.083 for all three positions in the ABL case. A possible ex- plaination is that different types of vortices are detected in the two cases. For the NBL case, mainly large, strong tip vortices are detected, which apparently de- crease in size as they are convected downstream. In the ABL case, the vortices are smaller (at least far upstream), weaker, appear in both directions and are spread over a larger vertical distance. These vortices do not decrease in size in the same way as the tip vortices.