Wake development and interactions within an array of large wind turbines Frauke Pascheke and Philip E. Hancock, EnFlo, University of Surrey, Guildford, GU2 7XH, UK

e-mail: f.pascheke@surrey.ac.uk, p.hancock@surrey.ac.uk Abstract This paper presents first test results from wind tunnel studies of mean and turbulent wake characteristics within an array of large wind turbines. Up to now, a single rotating speed controlled 1:300 scale model of a 5MW-rated machine with a rotor diameter of 126m and a hub height of 90m is tested in a realistic model off-shore atmospheric boundary layer. The blade design is based on blade-element theory for low Reynolds number blade aerodynamics to comply with modelling requirements. Preliminary tests in a low-turbulence flow at a tip speed ratio of TSR=6 yielded a thrust coefficient of CT=0.52 which is within 5% of the predicted value of the theoretical design case with a lift coefficient of CL= 0.6 (but a larger blade chord to mimic a higher CL). Velocity measurements in the modelled off-shore boundary layer at several downstream positions suggest a transition from near to far wake at a downstream distance of approximately 4 rotor diameters D. At a downstream distance of 10D turbulence intensities in the wake of the single model turbine are still approximately twice as large as in the undisturbed boundary layer. Along with the high turbulence levels a velocity deficit of about 25% is found. Time averaged flow fields and lateral profiles of the vertical velocity clearly illustrate the characteristic swirl generated by the blade rotation, which persists until about a downstream distance of 7D. 1 Introduction The investigation of wake development and wake interactions within an array of large wind turbines is a key objective in the EnFlo Wind tunnel laboratory contribution to the SUPERGEN V - Wind Energy Technologies project. Extracting energy from the wind, the turbine wake is generally characterised by reduced wind speeds and increased levels of turbulence. Within a wind farm array, the effects of several wakes interact. Thus, the turbines produce less energy and stand greater structural loads than single turbines placed in the free stream. Current prediction models need improving for these large machines. Two primary mechanisms determine the decrease of momentum deficit in the wake of a wind turbine: mechanical turbulence generated by the turbine itself, which is controlled by the turbine design and performance and usually is of a relatively high frequency and small scale, and the turbulence level in the ambient atmospheric boundary layer (ABL) flow. With the latter being controlled by terrain roughness, topography, stratification, etc., the characteristic length scales as well as spectral characteristics of these two interacting mechanisms are quite different. 2 Experimental set-up and planned case studies Wake characteristics, development and interactions are being studied in the large EnFlo atmospheric boundary layer wind tunnel (shown in Figure 1) for a 5MW machine with a rotor diameter of 126m and a hub height of 90m. The wind tunnel working section is L x W x H: 22m x 3.5m x 1.5m. A model scale of 1:300 has been chosen to ensure sufficient spatial resolution for the wake measurements. Allowing for reasonable spacing of 6-8 rotor diameters D, up to five rotating, speed controlled scale model wind turbines will be arranged successively in Figure 1: EnFlo atmospheric boundary layer wind tunnel.

the test section. Wake interactions of two parallel turbines with a lateral spacing of 3-4 D will also be studied.

The planned case studies comprise off-shore ABLs for neutral and non-neutral conditions as well as a rural neutrally stratified ABL over different terrain. Wake measurements are made using LDA, including phase-locked measurements to separate ordered motion from ABL and blade generated turbulence. The blade design is based on blade-element theory for low Reynolds number blade aerodynamics (no camber; twist at root: 50.6°; pitch: 2°). The blades are made from thin layers of fibre glass and resin using a custom made former and mounted on a brushed micro motor. The braking voltage speed control is coupled to the signal of a micro-Hall sensor fitted on the micro motor. The Hall sensor signal is furthermore used to phase-lock the measurements.

Figure 2: Scale model turbine.

3 Boundary layer properties (off-shore case) Up to now, initial wind tunnel experiments were conducted in a neutrally stratified off-shore model boundary layer with characteristic mean and turbulent properties at the appropriate scale. Near neutral atmospheric boundary layers usually develop for strong wind conditions and thus are an important case to consider for wind energy applications. In the absence of thermal stratification, atmospheric turbulence in the surface boundary layer is mainly generated mechanically by the given surface roughness. The mean wind speed U depends on the height above ground z and also on the given surface roughness. Across the complete depth of the boundary layer, the vertical profile of the wind speed can be approximated by the power law:

( )!

""

#

$

%%

&

'=

ref

refz

zUzU (1)

where α is the profile exponent, which depends on the underlying terrain. The fitted profile parameter α = 0.108 ± 0.005 (using the reference velocity in zref = 330m) is in good agreement with recommended values for very smooth terrain (i.e. ice, snow, water surface), which are typically in the range of 0.08 ≤ α alpha ≤ 0.12. The left plot in Figure 3 shows vertical profiles of the wind speed in mean wind direction at several locations along the wind tunnel test section and the best fit of the overall average profile to Equation 1 (log-log scale). Note, the X locations in the legend are given as mm distance to the wind tunnel entrance, Z coordinates have been scaled to full scale using the model scale factor 300. As can be seen from the left plot in Figure 3, the exponential function yields a better description of the velocity profile in the upper part of the boundary layer. In the lowest 10-15% of the boundary layer, the velocity increase with height is better described by the logarithmic law for flow near rough walls:

( ) !!"

#$$%

&= '

0

lnz

zuzU

( (2)

where u* is the friction velocity, κ ≈ 0.41 is the von Kármán’s constant and z0 is the roughness length. The friction velocity relates to the Reynolds shear stress by u*² = τw / ρ, where τw / ρ = <u’w’> near the surface.

Using the spatial averaged measured Reynolds stresses <u’w’> (for heights z ≤ 60m, a mean friction velocity of u* = sqrt <u’w’> 0.101 ± 0.004 m/s was found. The associated fitted mean roughness length takes a value of z0=0.02 ± 0.01 m (compare right plot in Figure 3). Recommended values of the roughness length for smooth terrain are at least an order of magnitude smaller (in the range 0.00005 m ≤ z0 ≤ 0.005 m). Since the EnFlo wind tunnel operates at low windspeeds (≤ 2.5 m/s) a larger z0 is beneficial (even necessary) to maintain fully turbulent flow conditions. However, the main focus for the study is on a proper representation of mean and turbulent flow characteristics at higher elevations (i.e. wind turbine hub height) and not near the surface.

Figure 3: Left: Vertical profiles of mean Wind speed at several locations in the wind tunnel test section in comparison with exponential fit of Equation 1 (log-log scale). Right: Comparison to logarithmic law given by Equation 2 (semi-log scale).

Turbulence intensities of the three velocity components are defined as the ratio of the standard deviation of the velocity component to the mean wind velocity:

)()(

zUzI

i

i

!= , (3)

where i=u, v, w. Figure 4 shows turbulence intensity profiles for all three velocity components at several locations in the test section area indicating the inherent variability. In addition, reference profiles suggested by ESDU [1] for smooth terrain (based on roughness length 0.00005 ≤ z0 ≤ 0.005m are shown for all three velocity components. Despite the larger roughness length of z0=0.02 ± 0.01, derived from the logarithmic fit of the mean velocity profile, the turbulence intensities suggest a ratio of turbulence to mean wind speed appropriate for a smooth terrain boundary layer. As can be seen from Figure 3, the mean profiles of turbulence intensities lie well within the range recommended for smooth terrain. Comparatively higher turbulence intensities are found for the vertical velocity component.

Figure 4: Turbulence intensity profiles for all three velocity components at several locations in the wind tunnel test section.

The spectral energy densities found in a height of 42 m (full scale) agree generally well with Kaimal [2] (all three velocity components) and Kármán [3] (longitudinal velocity component only) as shown in Figures 5 and 6. On closer inspection, a shift of the maximum energy towards higher normalised frequencies is present in the spectra of lateral velocity fluctuations Svv (Figure 5left), which corresponds to somewhat smaller characteristic turbulent structures.

Figure 5: Normalised spectral energy density of the longitudinal velocity component. Comparison with reference surface spectra after (left) Kármán [3] and (right) Simiu and Scanlan [4] and Kaimal [2].

Figure 6: Normalised spectral energy density of the (left) lateral and (right) vertical velocity components. Comparison with reference surface spectra after Kaimal [2].

Integral length scales are shown in Figure 7. The wind tunnel data comprises values taken at three locations along the test section: X=9800, 13800 and 17800 mm, Y=0 mm (centreline).

Counihan’s [5] empirical function Lux (z0=0.005m), which is indicated by the dashed line in the left plot of Figure 7 refers to minimum values for the smooth roughness class. As requested, the majority of the wind tunnel values are near to or larger than the reference and thus agree well with smooth terrain characteristics. The right plot in Figure 7 shows the x-direction length scales for all three velocity components. A somewhat uncharacteristic shape is found for the profile of the lateral length scales. Instead of increasing with height up to approximately a height of 200-250m the length scales remain constant across the depth of the boundary layer. Presumably, this characteristic results from the already suggested diminished lateral turbulence.

Figure 7: Variation of integral length scales with height. Left: Comparison of Lux with field data and empirical relationship after Counihan [5]. Right: Integral length scale profiles of all three velocity components.

4 Initial tests in low turbulence flow Pre-tests in an uniform, low turbulence flow have been conducted to test the model turbine speed control and to compare model turbine performance with the theoretical design case (tip speed ratio TSR=6; design lift coefficient CL=0.6, but larger chord). From wake velocity measurements a thrust coefficient of CT=0.52 was determined which is within about 5% of the predicted value. Figure 8 shows phase-locked velocity traces at two stations near the blade tip (r/R ≈ 1) taken in the uniform, low turbulence flow at a downstream position of 0.5D. The finding of a 180° phase shift coincide with a shed tip vortex. A similar feature is observed near the root. Figure 9 shows phase-locked velocity profiles at hub height at the same downstream position. The different symbols refer to phase-locked rotor

Figure 8: Phase-locked wake measurements at 0.5D downstream (low turbulence flow).

angles which are chosen to be 120° apart. As expected, similar mean velocity profiles are found for the three blades. The comparison between the left and right plot in Figure 9 shows that mirrored profile shapes are found for opposing rotor angles.

Figure 9: Phase-locked wake velocity profiles at hub height at 0.5D downstream (low turbulence flow).

5 Preliminary test results from off-shore ABL In the presence of ambient turbulence, the present speed control is insufficient to keep the desired TSR constant within reasonable limits of ± 2%. Further improvement is needed before ordered motions in the wake can be explored. Figures 10 and 11 show the development of mean and turbulent wake flow characteristics in the realistic model off-shore ABL for a selection of downstream positions. And Figure 12 shows lateral profiles of stream-wise and vertical velocity at hub height for the same selection of downstream positions. Dashed grey lines indicate mean upstream boundary layer conditions. The model results suggest a transition from near to far wake at a downstream distance of approximately 4D. Mean turbulence levels are still significantly increased by a factor of two 10 diameters downstream of the model turbine (left and centre plot in Figure 11), a result which is confirmed by field experiments (Högström et al. [6] and Højstrup [7]). However, the field studies indicated no significant velocity defect at 10D downstream, whereas this study shows a still noticeable velocity deficit of about 25% as can be seen from the left plot in Figure 10.

Figure 10: Vertical profiles of velocity and turbulent fluxes in the wake of a single turbine (off-shore ABL).

Figure 11: Vertical profiles of turbulence intensity and Reynolds stress in the wake of a single turbine (off-shore ABL).

Figure 12: Lateral profiles of stream-wise and vertical velocity in the wake of a single turbine in an off-shore ABL (flow out of paper plane, counter-clockwise rotation).

Time averaged flow fields of the mean and turbulent stream-wise and vertical flow components are shown in Figures 13-17. The mean vertical velocity component in particular illustrate the characteristic swirl generated by the blade rotation, which persists until about a downstream distance of 7D (compare also lateral profile of vertical velocity at hub height shown in Figure 12).

Figure 13: Development of the mean velocity in the wake of a single turbine in an off-shore ABL (flow out of paper plane, counter clockwise blade rotation). Downstream positions from left to right: 2D, 4D, 7D.

Figure 14: Development of the mean vertical velocity in the wake of a single turbine in an off-shore ABL (flow out of paper plane, counter clockwise blade rotation). Downstream positions from left to right: 2D, 4D, 7D.

Figure 15 : Development of the mean longitudinal variance in the wake of a single turbine in an off-shore ABL (flow out of paper plane, counter clockwise blade rotation). Downstream positions from left to right: 2D, 4D, 7D.

Figure 16: Development of the mean lateral variance in the wake of a single turbine in an off-shore ABL (flow out of paper plane, counter clockwise blade rotation). Downstream positions from left to right: 2D, 4D, 7D.

Figure 17: Development of the mean Reynolds stress in the wake of a single turbine in an off-shore ABL (flow out of paper plane, counter clockwise blade rotation). Downstream positions from left to right: 2D, 4D, 7D.

5 Conclusions The performance of a single rotating speed controlled 1:300 scale model of a 5MW-rated machine with a rotor diameter of 126m and a hub height of 90m has been tested in an uniform low turbulence flow to compare the model turbine performance with the theoretical design case which is based on blade-element theory for low Reynolds number blade aerodynamics. So far, good agreement is found. Placed in a carefully modelled off-shore atmospheric boundary layer, preliminary two-dimensional velocity measurements in the turbine wake suggest a transition from near to far wake at a downstream distance of about 4 rotor diameters D. Increased turbulence levels at 10D are in good agreement with results from field measurements. Along with the high turbulence levels a noticeable velocity deficit is still present. The characteristic swirl generated by the blade rotation persists until about a downstream position of 7D as illustrated by time averaged flow fields and lateral profiles of the vertical velocity. The preliminary test results found the basis of further model improvement needed to explore ordered motions in the wake by means of phase-locked measurements. 6 References [1] ESDU. Characteristics of atmospheric turbulence near the ground. Part II: Single point data for strong winds (neutral atmosphere). ESDU 85020. Engineering Sciences Data Unit, London, 1985. [2] Kaimal JC, Wyngaard JC, Coté OR. Spectral characteristics of surface-layer turbulence. Q.J.R. Meteorological Society 1972; 98:536-589. [3] von Kármán T. Progress in the statistical theory of turbulence. Proc. Nat. Acad. Sciences 1948; 34:530-539. [4] Simiu E, Scanlan RH. Wind Effects on Structures – Part A: The Atmosphere. John Wiley & Sons; pp:704. [5] Counihan J. Adiabatic atmospheric boundary layers: A review and analysis of data from the period 1880-1972. Atmospheric Environment 1975; 9:871-905. [6] Högström U, Asimakopoulos DN, Kambezidis H, Helmis CG, Smedman A. A field study of the wake behind a 2MW wind turbine. Atmospheric Environment 1988; 22(4):803-820. [7] Højstrup J. Spectral coherence in wind turbine wakes. Journal of Wind Engineering and Industrial Aerodynamics 1999; 80:137-146.