Measurements of high-frequency Atmospheric Turbulence and its Impact on the Boundary Layer of Wind Turbine Blades

To gain insight into the differences between onshore and offshore atmospheric turbulence, pressure fluctuations were measured for offshore wind under different environmental conditions. A durable piezo-electric sensor was used to sample turbulent pressure data at 50 kHz. Offshore measurements were performed at 100 m height on Germany’s FINO3 offshore platform in the German Bight together with additional meteorological data provided by Deutscher Wetterdienst (DWD). The statistical evaluation revealed that the stability state in the atmospheric boundary has a large impact on turbulent fluctuations. Therefore, we used higher statistical properties (described by so-called shape factors) to the stability state. Data was classified to be either within the unstable, neutral or stable stratification. We found that in case of stable stratification, the shape factor is mostly close to zero, indicating that a thermally stable environment produces closer-to Gaussian distributions. Non-Gaussian distributions were found in unstable and neutral boundary layer states and an occurrence probability was estimated. Possible impact on laminar-turbulent transition on the blade is discussed with application of so-called laminar airfoils on wind turbine blades. Use of a cut-off frequency to separate load and aerodynamic turbulence is proposed.


Introduction
Wind-energy was very successful during the last decades [1] to reach for a nearly stable annual investment corresponding to 50 GW rated power word-wide.This was in connection and in parallel to an impressive development in Wind Turbine Aerodynamics [2].
Due to this high number of annual installations, site assessment for wind farms has become more and more important and sophisticated even under offshore conditions.Tailored wind turbine design becomes state-of-the-art.In most cases turbulence is treated in context of loads, and frequency ranges higher than a few Hertz are generally considered to be of no importance.However, this high frequency turbulence plays a significant role in laminar-to-turbulent transition inside the boundary layer of blades for airplanes [3,4] and wind turbines [5,6].Due to the much higher drag of turbulent parts thereon, this may give rise to much less efficiency of wind turbines (in terms of c P ) as desired and a proper choice of airfoils is crucial.
Particularly, in this paper, these high-frequency turbulent statistics are studied with respect to higher order statistical moments in some detail.The shape factor according to [7] -giving estimates of the extent to which turbulent fluctuations diverge from Gaussian behavior -is of special interest.
Unlike to earlier investigations, the Non-Gaussianity of turbulent pressure fluctuations could not be linked to one of the more popular atmospheric parameters like Reynolds number based on Taylor's micro-scale [8], wind speed or other common parameter.Therefore, we propose to characterize our findings according to the stability of the atmospheric boundary layer in terms of Richardson's number.We have organized the paper as follows: Firstly, the measurement set-up is described together with an indication of the locations at which they were performed.Then we describe our procedure used for data processing.After that we present and discuss our findings and finally draw some conclusions.

Measurements
Our first set of high-resolution measurements (during the years 2009 until 2011) were performed using piezoelectric pressure sensors from PCB Piezotronics (fig.2) that was connected to an imc Meßsysteme GmbH CS-1208 data logger.The diameter of the sensing element was 12 mm.The minimal pressure resolution was 0.13 Pa, and the possible temporal resolution ranged from 2.5 Hz to 80,000 Hz.In [10] a correction method is proposed to increase the spacial resolution up to extension as large as three times the Taylor's length λ T .As in our case we have values for λ T ranging from 30 to 70 mm [8] we can be sure about the sensor's full resolution of 0.3 msec in time domain.
In our measurements the pressure data was sampled at 50 kHz with a total duration of 100 seconds.Wind speed and temperature were sampled at 1 Hz temporal resolution.
The piezoelectric pressure sensor was calibrated against a hot wire anemometer in a wind tunnel at University of Oldenburg.The turbulent wind speed from the hot wire anemometer and the turbulent pressure variations showed the same statistical properties up to 3 kHz [11].
Onshore measurements were conducted at the Kaiser-Wilhelm-Koog test site of Germanischer Lloyd/Garrad Hassan (see fig. 1).A lattice tower of 60 m height provided booms for mounting the pressure sensor and other measurement equipment.The pressure sensor was mounted at 55 m height.Wind speed and wind direction were recorded at 55 m height by calibrated cup anemometers and wind vanes, respectively.The temperature was recorded at 53 m height by a resistor-type thermometer.FEZ Kiel's platform FINO3 was the location for the offshore measurements.About 80 km west of the island of Sylt (see fig. 1) the platform was constructed close to no operational wind farms like DanTysk and Sandbank 24.The tower is a lattice tower type with booms of sufficient length for undisturbed measurements.Two pressure sensors (fig.3) were mounted at about 100 m height above mean sea level for parallel operation.Data acquisition equipment for meteorological signals was similar to the equipment used onshore.Wind speed and wind direction were available at 100 m height, temperature at 95 m height above mean sea level.

Comparison with measurements from Laser Cantilever Anemometer
Usually, high frequency turbulence is measured with so-called hot-wire anemometers [12,13] with diameters down to a few micro-meters only.These small sensor extensions guarantee for high spacial and temporal resolution (if properly corrected for the length of the wire [10])but the lifetime is restricted to few hours only.Therefore newly developed devices from University of Oldenburg, Germany, so-called Laser-Cantilever Anemometers (LCA) or special versions thereof, Atmospheric Laser-Cantilever Anemometers (ALCA) were used somewhat later [14][15][16][17].Energy spectra agreed if √ p was compared with v [11].Unfortunately the design of the active sensor (30 µm X 35 µm X 9 µm in size) initially was spoiled with a resonance at about 1 kHz so that it had to be re-designed [18].

Analysis
Our recorded data sets were put into wind speed classes of 6 m/s, 12 m/s and 16 m/s.Measurements were triggered manually if wind conditions were regarded suitable.The bin sizes for each class are ±2 m/s, for offshore class 10 m/s the upper bound was 11 m/s and for offshore class 12 m/s the lower bound was -1 m/s.For each measurement the statistical characteristics were analyzed with respect to power-spectral density, increment distributions, shape factor, structure functions, autocorrelation and Taylor's microscale. 1 We now explain our methods in more detail.
Increments of measured quantities are defined as usual: where u is the velocity, p the pressure, t the time and ∆t a fixed time delay.The increments also eliminate the mean value of the time series and thus stochastic fluctuations remain for a specific time scale ∆t.These increments are our basic statistical quantities for more sophisticated analysis like structure functions or the so-called shape parameter.[7] suggested that the distribution of increments may be described as an superposition of two distributions, one of them being lognormal.The shape factor then may be regarded as a measure of the level of intermittency.In Beck's approach from [20] the shape parameter can be calculated by 2nd and 4th order moments of the distribution: 1 It may be interesting to note that Taylor's microscale may have a complementary interpretation in terms of a Markov-Einstein coherence length [19].To us, this one seems to be much more physical than a somewhat vague interpretation in terms of an average turbulent vortex size where s 2 u is the shape factor for the velocity and s 2 p for the pressure, respectively.The brackets x define the mean value of a quantity x.Further properties are given in [20].A value of s 2 → 0 indicates a normal distribution.
It is well-known at least since the work of [21] that turbulent velocities and pressure obey different scaling laws ∼ k −5/3 and ∼ k −7/5 , respectively, although seemingly related by p ∼ v 2 according to Bernoulli's law.Direct comparison of hot-wire with piezo-electric pressure senor data show comparable power-density spectra up to 4 kHz (see [11],unpublished), however.Theoretical as well as experimental investigations of [22] are still incomplete, so that there is no clear answer so far about how s 2 u and s 2 p are related to each other exactly.When heat transfer occurs, such as in the atmospheric boundary layer if the sea is warmer than the air (autumn), thermal stratification becomes more important.Simple static stability of the boundary layer may be used to characterize levels of turbulence.As was shown by [23], turbulence intensity differs remarkably for stable and unstable flow when used to describe fatigue loads of wind turbines.
A simple characterization of a stratified boundary layer exposed to heat transfer was introduced by [24] as belonging to a class consisting of stable, neutral or unstable states.Different calculation methods are used to distinguish these states ( [24]) depending on what is known as input.In our case a Richardson's number approach was used.This one is defined as: where g is the acceleration of gravity, T is the mean absolute temperature, z is the height normal to the surface and ∂v/∂z is the mean velocity gradient.The z-direction is assumed to be vertical.A potential temperature θ is defined as where p is the pressure and p 0 = 1000 hPa the reference pressure, R = 289 J kg K is the specific gas constant and c p = 1005 J kg K is the specific heat capacity of air.In equation (3) the quantity g T ∂θ/∂z describes the forces introduced by heat transfer in the boundary layer.The term (∂v/∂z) 2 represents the momentum forces in the boundary layer.Now let us consider two points in the boundary layer at height z 1 and z 2 where z 1 < z 2 and ∆z = z 2 − z 1 .Ri from (3) can thus be rewritten with the differences between the two locations as We assume always positive velocity gradients so that only the convective part of Eq.. ( 5) remains.Three typical situations then may be distinguished: The surface is colder than the fluid and the gradient becomes ∂θ/∂z > 0 and therefore Ri > 0. Heat is transported by conduction only, and a convection flow does not occur.In this case the stratification is strong, and turbulence gets damped.The boundary condition is STABLE for Ri > 0.
The temperature gradient is zero and therefore Ri = 0.There is no temperature gradient and therefore no conduction nor convection.This condition is called NEUTRAL.
The surface is warmer than the fluid and the gradient becomes ∂θ/∂z < 0 and therefore Ri < 0. Heat is transported by conduction and by convection from the surface to the fluid.The convection results in a vertical, upward component of the flow that interacts with the horizontal velocity component.This leads to production of turbulence in the boundary layer and therefore is called UNSTABLE.From our measurements we obtained the necessary values for p, T air at 100 m height, wind speed v air and wind direction as well as the sensor signal of the piezoelectric microphone.Assuming the air to be a perfect gas, the density ρ can be calculated by the perfect gas law.
For the derivatives ∂θ/∂z and ∂v/∂z, the temperature and wind speed at a second height must be known.Unfortunately, these data were not available during most of our measurements.Therefore, these gradients had to be approximated in a different way.
Ground temperature T gnd was estimated using data from the Deutscher Wetterdienst (DWD).For the onshore measurements, the ground temperature at a nearby location was available at hourly samples.The temperature of the sea for the offshore measurements was interpolated from the measurement stations at the island of Helgoland and at List on the island of Sylt.
The sign of Ri mostly depends on the temperature gradient, so the velocity gradient can be regarded as of lower importance.Therefore, as a rough estimate v gnd ≈ 0 was used for our calculation of the velocity gradient.This effects mostly the absolute value of Ri but not the heat transfer conditions in the atmospheric boundary layer.
With this procedure estimates for Ri were possible.Identification of stable or unstable states was simple.However, the neutral state requires a value of exactly Ri = 0 which is difficult to attain precisely within our set of approximations.To indicate a nearly neutral state, a bandwidth of |Ri| < 0.02 was used instead.

Results
The computation of the shape parameter was straightforward, and the results are shown in figure 4. The scale for the shape factor is shown on the left.Colors indicate locations, and symbols represent velocity classes.Time series with s 2 p < 2 were grayed out and will not be considered further in the following analysis.For purposes of comparison, shape factors from a particular velocity measurement ( [12], Ū=7.6 m/s, u =1.36 m/s) was included (black line) as well.
The general behavior of both shape parameter functions for velocity and pressure is similar, whereas absolute values differ significantly.This behavior was also observed in [17].Surprisingly, most of the pressure measurements resulted in s 2 p close to zero.Note the differences between the measurements of velocity and pressure concerning sampling rates and length of the time series.
In fig. 4 offshore curves were distinguished with numbers in brackets.They were all recorded on the same day with a short delay only: Pressure time series were recorded for a period of 100 s.For the first data set (1) s 2 p is high.But then the pressure data resulted in s 2 p ≈ 0 until the values increased eight minutes later at (2).The time series (2), ( 3) and ( 4) were consecutive, so it can be said that the shape parameter for the turbulent pressure fluctuations did not remain constant in time for this interval.When all time series from 8:44 to 8:57 were concentrated into one and evaluated according to a common s 2 p , a curve similar to the curve for velocity fluctuations was obtained.This was already presented in [8].
We now try to relate these different statistical behavior to the atmospheric boundary layer state.With our estimation of the Richardson number a stability state was determined.Selected data from all our 119 measured data sets are shown in table 1. Measurements with s 2 p > 0 are marked with a star in the last column.
As can be seen from table 1, high s 2 p (s 2 p > 0) behavior corresponds to unstable to neutral ABL conditions −0.13 ≤ Ri ≤ 0.01.However, a significant correlation with the Richardson number was not found.

Time Development of a Sample Time-Series
Therefore, for the measurement of Oct. 19, 2010 time variation of the shape factor was investigated in more detail.It is presented in table 2.
The measurement started at 8:44 a.m. when s 2 p was high and the turbulence intensity from cup anemometers was low.In the following 7 minutes time series were found to have s 2 p ≈ 0, mean velocity and potential temperature of air remaining constant.Only turbulence intensity was increasing from about 4 to about 8 %.
At 8:54 a.m. the shape factor began to rise (see also curve (2) of fig.4).Promptly, the turbulence intensity dropped more than 5.5 percentage points and also the potential temperature of the air decreased by 0.4 K with rising shape factor.
Our interpretation is summarized as follows: The Boundary Layer corresponding to time interval from 8:45 to 8:49 was stratified and turbulent pressure fluctuations were distributed in a Gaussian way.At 8:50 a.m. a cluster of warm air rose up from warmer sea-surface to higher (and colder) regions (θ air ≈ const., v W fluctuating).This may have led to a stronger vertical shear thereby disturbing the (Gaussian) turbulent structures.formulate the hypothesis that the probability Φ 0 is correct.And we also state the alternative hypothesis that the actual probability is indeed lower than Φ 0 , and the real probability for the occurrence of high-s 2 p events is Φ 1 ≈ 0.06.The 42 onshore measurements were used as the set of random samples, and the hypothesis would be rejected when less than four high-s 2 p -events occur.These assumptions lead to a probability of 6 %, where Φ 0 = 1/6 would be assumed to be true, despite the fact it was wrong.Also, the probability Φ 0 might be rejected despite it was true with a probability of 24 %.
It could be concluded that onshore the probability for high-s 2 p events was about 16 % with a confidence level of 94 %.

Impact on Boundary Layer Transition on a Wind Turbine Blade
In the preceeding sections we have described that small-scale turbulence below Taylor's length-scale of less than 50 mm strongly shows non-Gaussian behavior.We now describe shortly how this may be related to turbulent-laminar transition on wind turbine blades.It has to be noted, that much more detailed investigations have been performed in the upper atmosphere for small aircrafts [3,4].Corresponding field experiments on wind turbines were reported in [5,25].From these, it can be concluded that despite high, integral turbulence intensity of more that 10 %, the energy content suitable for receptivity of TS-waves is even smaller than in a wind-tunnel environment.More evidence for a possible low-frequency cut-off for aerodynamic important turbulence can be given by a simple argument to estimate an upper frequency f for a boundary layer (BL) responding to an oscillating outer flow: Stokes [26], pp 191 ff, shows that an outer flow (oscillating with frequency ω) is damped out by viscosity according to U = u 0 • e −ky • cos(ωt − ky) with k = √ ω/2ν, ν being the kinematical viscosity and U the main flow in x-direction and y being perpendicular to x.Now, if we introduce a Stokes boundary layer thickness by δ S = 2π/k we reach for f = 4πν/δ 2 ≈ 200 Hz in our case.Here, we have set δ S to an approximate value of 1 mm, a typical value for laminar boundary layers on airfoils at Reynolds numbers of several million.Therefore this high-frequency, non-Gaussian regime plays an important role in triggering TS-type of BL instability on the path to fully developed turbulence.

Conclusions
High-frequency -above 100 Hz -resolved measurements of pressure fluctuations for different average wind-velocities under on-and offshore conditions were investigated with respect to higher order statistical properties and were related to atmospheric boundary layer stability.It was found that up to 4 kHz pressure and velocity fluctuations obeys the same power spectrum and further, that out of 119 time series in total some show high shape factors occurring with total probability of about 10 %, independent of Taylor-length based Reynolds-number.64 % out of all high shape-factor events were recorded during unstable thermal stratifications and the level of occurrence seems to be almost doubled when compared to the on-shore case.If a continuous sequence of time series is investigated, strong variations of the shape factor are sometimes observed even during short periods of about half an hour.
As we argue for a separation of time-scales to distinguish between in-stationary and turbulent flow at about 100 Hz, it now becomes clear that a severe reduction of turbulence intensity takes place and explains why usage of laminar airfoils (NACA 63-215 for example) is meaningful.

Figure 4 .
Figure 4. Shape parameters for all collected measurements.Colors represent locations: Offshore, Onshore with wind coming from land or sea side.Symbols represent the velocity classes for the wind speed.Measurements with max(s 2 p ) < 2 are in grey.For reasons of comparison Taylor's and Kolmogorov's time scales are given by 5 msec and 0.05 msec, resp.Sensor's resolution goes down to approximately 0.3 msec only.

Table 1 .
Summary of selected ABL stability cases.Potential temperatures θ, wind speeds v W and turbulence intensities Ti from cup anemometers, Ri numbers and estimated ABL state

Table 2 .
Development of Time-Series on Oct 19.Potential temperatures θ, wind speeds v W and turbulence intensities Ti from cup anemometers, Ri numbers and estimated ABL state