The dynamic inflow effect denotes the unsteady aerodynamic response to fast changes in rotor loading due to a gradual adaption of the wake. This does lead to load overshoots. The objective of the paper was to increase the understanding of that effect based on pitch step experiments on a 1.8 m diameter model wind turbine, which are performed in the large open jet wind tunnel of ForWind – University of Oldenburg. The flow in the rotor plane is measured with a 2D laser Doppler anemometer, and the dynamic wake induction factor transients in axial and tangential direction are extracted. Further, integral load measurements with strain gauges and hot-wire measurements in the near and close far wake are performed. The results show a clear gradual decay of the axial induction factors after a pitch step, giving the first direct experimental evidence of dynamic inflow due to pitch steps. Two engineering models are fitted to the induction factor transients to further investigate the relevant time constants of the dynamic inflow process. The radial dependency of the axial induction time constants as well as the dependency on the pitch direction is discussed. It is confirmed that the nature of the dynamic inflow decay is better described by two rather than only one time constant. The dynamic changes in wake radius are connected to the radial dependency of the axial induction transients. In conclusion, the comparative discussion of inductions, wake deployment and loads facilitate an improved physical understanding of the dynamic inflow process for wind turbines. Furthermore, these measurements provide a new detailed validation case for dynamic inflow models and other types of simulations.

Dynamic inflow describes the unsteady response of loads to fast changes in rotor loading, e.g. due to fast pitching of the rotor blades or gusts. This unsteady aerodynamic effect leads to load overshoots due to the inertia of the global flow field, as the axial wake induction in the rotor plane cannot change instantaneously but only gradually to a new equilibrium flow field.

In addition to the direct impact on the dynamic loading,

First extensive studies in the 1990s within the Joule I and II projects on the development of dynamic inflow models for wind turbines are described in

Later

Within the Model EXperiment In controlled COnditions (MEXICO) framework, pitch steps are performed on a 4.5 m diameter model wind turbine, featuring pressure distribution measurements at five radial stations, as well as in high- and mid-fidelity simulations

The objective of this paper is to get deeper insights into the dynamic inflow effect for wind turbines due to pitch steps. The main novelty in this work is the dynamic induction measurement. The radial dependency and differences between the pitch directions are investigated using time constant analysis. Furthermore, the behaviour of the flow in the near and close far wake and integral loads are used to compare the differences between the pitch directions. These different measurements are contemplated together to allow for new insights into the dynamic inflow effect, test presumptions and validate findings of prior work.

In Sect.

In this subsection, all relevant information on the experiment is introduced, consisting of the setup, experimental matrix, wake induction derivation from measurements, ensemble averaging approach and correction models.

The experiments were performed in the large wind tunnel at ForWind – University of Oldenburg. It is a Göttingen-type wind tunnel that can be operated in an open jet or a closed test section configuration. The test section length measures 30 m, and the rectangular wind tunnel nozzle dimensions of 3 m by 3 m, as shown in Fig.

The utilised Model Wind Turbine Oldenburg has a diameter of 1.8 m (MoWiTO 1.8). The machine is an aerodynamically scaled version of the NREL 5 MW generic turbine (see

The MoWiTO 1.8 nacelle is shown in Fig.

The setup of the MoWiTO 1.8 in the wind tunnel is sketched in Fig.

Integral loads of flapwise blade root bending moment (

Hot-wire measurements in the near wake (up to 1

In the rotor plane, laser Doppler anemometer (LDA) measurements are performed with a 2D system by TSI Inc. A beam expander with a focus length of 2.1 m is used to not disturb the flow. Both lasers have a maximum power of 1 W. The LDA probe is mounted on a three-axis traverse system and can be driven by 1.5 m in each direction by motor. Measurement points are in the rotor plane at hub height. They are positioned radially (negative

Sketch of the setup in the wind tunnel. View from

The turbine is operated at a rotational speed of 480 rpm and wind velocity of 6.1 m s

The rotor blades are collectively pitched by 5.9

The representative encoder reading of one pitch motor is plotted in Fig.

Pitch motor encoder signal for a pitch step to high load followed by a step to low load with additional zoomed-in views of the actual pitch steps.

For the LDA measurements, 100 pitch steps were performed for each radial position and pitch direction at a typical sampling frequency of 600 Hz. This sampling frequency is just an order of magnitude estimate, since it depends on many parameters, especially the seeding of tiny oil droplets in the wind tunnel and thus varies constantly. Load measurements are taken during the LDA measurements. Therefore, load signals for 900 pitch steps are available. The hot-wire measurements have been performed separately. A wake rake consisting of four hot wires was used to measure at the described 56 positions in the wake. Thus, the experiment, consisting of 25 pitch steps, had to be performed

The wake induction is derived from the LDA measurements by a method introduced by

In Fig.

Two constraints defined the line of LDA measurements. The first is the height range of the LDA probe head, which is from tower bottom to hub height. The second is to minimise the influence of the tower on the blade nearest to the tower for the measurements in the bisectrix of two blades. This led to a measurement line at the 3 o'clock position. The tower does disturb the axial symmetry, however, based on an estimation of the tower effect with a dipole model as in

To obtain the values in the bisectrix, the LDA system is synchronised with the MoWiTO data acquisition system. Measurements at the constant high load are plotted for one position of the axial and tangential probe over the azimuth angle

In Fig.

Based on these measured axial and tangential velocities, the undisturbed inflow velocity

The method was validated based on particle image velocimetry (PIV) measurements and CFD calculations of the MEXICO rotor by

Ensemble averages are used for the LDA data, hot-wire and strain gauge measurements. The data of many repetitions are aligned, triggered by the pitch command. An average value at each time step is constructed out of this data, for the time span

The induction factors have no fixed sampling frequency, as, firstly, the underlying LDA measurements are non-equidistant and, secondly, only values within the bisectrix of two blades are considered. To construct a single ensemble average out of this data, the 100 repetitions per LDA position are sorted to one signal, and a smoothing approach based on local regression and a weighted least squares and first-order polynomial model is used. For the local regression, 1 % of the data (length of the total dataset is 4.5 s) are used, whereas outliers get weight penalties and are not considered for more than 6 standard deviations. This filter is implemented as “rlowess” within MATLAB 2019b. These smoothed ensembled LDA-based data are resampled to 1 kHz, reducing the original non-equidistant data points by a factor of about 3. The sorted data points along the smoothed resampled signal and 95 % CI for the axial rotor plane (rp) velocity at 0.7

Steady corrections are applied to the thrust and torque signals. For the torque, the mechanical torque is measured at the torque meter. To obtain the aerodynamic rotor torque, the friction in the bearings and the slip ring was calibrated by running the drivetrain without blades with the motor, used as a generator in operation; thus, the friction was measured with the torque meter. A linear function of the angular rotor speed was obtained and the respective value added to the signal.

The rotor thrust is derived from the tower bottom bending moment in fore–aft direction. The strain gauge was calibrated using defined forces in the thrust direction applied to the nacelle at the height of the rotor axis. The tower and nacelle drag was experimentally calibrated with the turbine without blades and was subtracted from the signal. The free stream velocity (

Dynamic corrections were considered for the torque and thrust signal.
Directly after the pitch step, the torque control cannot keep the rotor speed completely steady, so there was a minor deviation of a maximum of 2 % of the rotor speed. Equation (

After the pitch step, there is an oscillation of the tower, which is seen in the tower bottom bending moment. The eigenfrequency of the tower and the damping constant of the oscillation is estimated iteratively and thus the measurement signal is corrected to obtain the aerodynamic thrust. The signals without the dynamic correction will also be shown in the results section as a reference (see Fig.

The decay process after the pitch step is investigated in terms of time constant analysis. Firstly, a one-component time constant model (1c), like that used by

In Fig.

Secondly, a model with two time constants (2c) similar to

These time constants can be used for comparison and tuning of the time constants in the dynamic inflow engineering models of Øye (see

Additionally to the strain-gauge-measured integral turbine loads, these loads are also reconstructed based on the induction measurements. The angle of attack values along the rotor blade are already derived from the experiment through Eq. (

The influence of unsteady airfoil aerodynamics (uA) on the blade level, namely the Theodorsen effect, is not contained in the axial wake induction and therefore has to be additionally considered in the reconstruction. The implementation given in detail in

Here the measurement results are described. In Sect.

In Fig.

For the high load case, the axial induction has values between 0.25 near the root (0.25

The tangential induction for both cases is high near the root and decreases with radius with a high rate in the beginning and then more gentle. Due to the larger rotor torque, the high load case shows higher values.

The angle of attack distribution for the high load and low load cases shows angles of attack of 4 to 6

The observed difference between the two angle of attack distributions is smaller than the pitch step value of 5.9

These maximum and minimum dynamic angles of attack are shown as dotted lines in Fig.

The axial induction factor transients are shown in Fig.

The fits of the one-time-constant (1c) and two-time-constant (2c) models are also shown in the plots. The fits start from the instance the pitch step is terminated at

Axial wake induction factor over time for pitch step to high load and low load for the four radii 0.3, 0.5, 0.7 and 0.9

The fitted time constant

In Fig.

One-time-constant model fit of

Two-time-constant model fit to the axial wake induction factor, derived from the rotor plane LDA measurements with the ratio

To overcome this limitation, the ratio

The fitted

Values of

The fitting accuracy of the applied models is determined based on the root mean square error (RMSE) in the fitting range

Root mean square error (RMSE) between measured axial wake induction factor and the three fitted models, 1c-fit and 2c-fit with

For both step directions, there is no difference in RMSE for the root near stations up to 0.3

The tangential wake induction factors over time for both pitch directions are presented for the four radii 0.3, 0.5, 0.7 and 0.9

Tangential wake induction factor over time for pitch step to high load and low load for the four radii 0.3, 0.5, 0.7 and 0.9

In contrast to the axial induction, the tangential induction shows an overshooting behaviour. The exponential fit starts around

The fitted

One-time-constant model fit of

For the step to high load, only two radii at the root and two radii near the tip fulfil this requirement, whereas for the step to low load only the tip most radius at 0.95

The influence of the small, allowed shift in the start of the fit is also investigated. For a strict starting point of the fit at

In the following the hub height hot-wire measurements downstream of the turbine in the near and close far wake up to 2

Top view on velocity contour in the horizontal plane at hub height of the wake at the four different timestamps 0, 0.4, 0.8 and 1.2 s after the pitch steps to high and to low load, normalised by the free stream velocity. The turbine dimensions are indicated in correct scale in the plots as a reference, with the

The first contours at

The contours for the following timestamps show the transition to the new steady state. These transitions seem at first glance different for the two pitch directions. For both pitch directions at

To further interpret this measurement, normalised velocity contours are presented to the new equilibrium steady state in Fig.

Top view on velocity contour in the horizontal plane at hub height of the difference to the new steady wake equilibrium at the four different timestamps 0, 0.4, 0.8 and 1.2 s after the pitch steps to high and to low load, normalised by the free stream velocity. The turbine dimensions are indicated in correct scale in the plots as a reference, with the

Therefore, a value of 0.5 means that the wake has to adapt by 0.5

Next, the deployment of the axial wake velocity as a response to the load steps is analysed. Six of the hot-wire signals used to make the contour plot are plotted over time for the step to high load for the radii of 0.2, 0.6 and 1

Ensemble averages of the axial wake velocity measured by hot wires for the three radii of 0.2, 0.6 and 1

For the radius at 0.6

In the next step, the wake front velocity is analysed to measure how fast the transition point (the wake front) between the old wake and the new wake convects. This wake front can be thought of as being similar to a weather front. We define the wake front velocity by the time this characteristic wake front needs to travel from one considered downstream position to the next. So exemplarily in Fig.

In Fig.

Velocity of the wake front for both pitch directions, normalised by the free wind velocity. For orientation, also the theoretical normalised wind velocity in the rotor plane (

Thus between every two considered downstream distances a mean velocity with which the wake front moved can be calculated. Between the two nearest distances to the rotor, 0.5 and 0.75

Next, the integral loads are compared as shown in Fig.

Integral turbine loads based on strain gauges with (SG) and without (SG no corr.) the dynamic corrections (as introduced in Sect.

Firstly, a clear overshooting behaviour of all load signals is apparent. Comparing the strain gauge measurements for

A more detailed comparison of the steady values at high and low loads between the strain-gauge-measured integral loads and the reconstructed loads is plotted in Fig.

The slight overprediction of reconstructed loads for the

Comparison of the steady load levels for high and low loads for the integral turbine loads

Further, the dynamics after the pitch step are compared. The amount of load overshoot, normalised by the difference between the steady values, is given for the load signals for both pitch directions in Fig.

The addition of the uA model reduces the amount of overshoot for all load channels. For

The amount of overshoot is higher for the step to low load, when comparing the amount of overshoot between the two pitch directions per load channel and method. Based on the LDA reconstructed loads, which are not subject to dynamic corrections that might introduce errors, the normalised overshoot for

The fitted values for the one-time-constant model to the integral loads is presented in Fig.

In order to assess the reasons for the differences in load overshoot it is of interest to investigate the theoretical maximum load overshoot when changing from one operational point to the other. This can be estimated based on the steady states of the operational points and the theoretical dynamic maximum and minimum angle of attack distribution, as was introduced in Fig.

Theoretical dynamic overshoot for the step to high and low loads for the integral turbine loads

A clear difference can be seen between the pitch directions for the axial loads

In this section, the results for the inductions, wake flow and loads will be discussed. A focus for comparisons is on publications in connection to the NREL unsteady aerodynamics experiments phase VI (see

Dynamic inflow phenomena on wind turbines were already indirectly shown in experiments based on integral loads for the 2 MW Tjæreborg turbine (see

Pitch steps of the phase VI experiment were performed at 5 m s

Pitch steps in this paper were performed at 6.1 m s

The observed slight radial dependency for the single time constant (see Fig.

For the two time-constant model fits to the axial wake inductions, two variants of time constants, one with a freely fitted weighting ratio

For

The

The only minor differences in fitting error between the two variants with

The overshooting behaviour of the tangential induction is a new finding. The time constants of the one-time-constant model have no clear radial dependency. They are lower for the step to low load and in general, slightly lower than those fitted for the axial induction. The overshoot also is more prominent for the step to low load. This behaviour is of interest for the physical understanding of the dynamic inflow effect, as the overshoot in the torque is directly counteracted by the change in wake rotation. We assume that the shed vortices due to the change in circulation introduce this instant overshoot in tangential induction. For the modelling of the dynamic inflow effect in BEM-based codes, this behaviour is only of secondary interest, as the influence of the tangential induction on the angle of attack is negligible, apart from the blade root.

No relevant influence of the shear layer between the open jet wind tunnel and the surrounding air is seen in the wake snapshots (see Fig.

The velocity snapshots in the wake show differences in wake evolution between the pitch directions. The faster progression of the wake for the pitch step to low load supports the presumption made by

The dynamic widening of the wake after the pitch step to low load, as drawn in Fig.

The overshoot in the velocity in the wake after a sudden change in thrust, as observed here for the radii at 1.0

The quantitative comparison of the wake front velocity (see Fig.

A fast initial wake front velocity is seen between 0.5 and 0.75

In the further course, the wake front velocity slows down for both cases. For the step to low load, it even slows down between 1.25 and 1.75

The general comparison of the load signals obtained from strain gauges and reconstructed from the LDA measurements (see Fig.

For the steady equilibrium, the comparison between the strain gauge measurements and the reconstructed loads (see Fig.

For the flapwise blade root bending moment and the thrust, the load overshoot is much more pronounced for the step to low load than for the step to high load, whereas the trend for the torque is the same but to a smaller extent. The magnitude of the overshoot depends on how much the axial induction has already adapted during the pitch process. As discussed in Sect.

The higher relative overshoot of the torque by a factor of 3 to 4.5 compared to the flapwise blade root bending moment and the rotor thrust can be related to the lag in inflow angle and thus angle of attack behind the quasi-steady value.

The simplified approach to estimate the theoretical maximum overshoot for the load signals based on the steady inductions and the pitch angle change with the BET reconstruction (see Fig.

Further, in the overshoot analysis (see Fig.

The 1c model investigation shows a good agreement between the strain-gauge-measurement-derived and reconstruction-based

Structural interactions are assumed to be the main driver for the observed differences in overshoot and also for the differences in the fitted time constants between the strain gauge signals and reconstructed loads with and without the uA model.

The objective of the presented dynamic inflow measurements was to deepen the general physical understanding of the dynamic inflow effect for wind turbines.

Direct experimental evidence of dynamic inflow is given through a very clear delay of induction factors at different radial positions at the rotor plane in response to a pitch angle step. Until now, dynamic inflow effects were only proven indirectly through measurements of turbine loads or flow measurements in the wake. It is affirmed that a two-time-constant model is more suited than a one-time-constant model to describe the behaviour of the axial induction for such a pitch step. The fast time constant of this model, representing the near-wake influence, has a strong radial dependency near the root and a clear, respectively slight, dependency in the middle and tip region for the step to high, respectively low, load. The slow time constant, related to the close far wake, shows a slight decrease towards the outer part for the step to low load and a slight increase for the step to high load. The overshooting behaviour of the tangential induction is a novel finding of this work. It could be explained by the shed vorticity, which results from the circulation change during the pitch step. We expect that the radial dependency of the axial induction time constant is related to the observed dynamic wake expansion for the step to low load. With the wake measurement, it is affirmed that the formation of the mixed wake after the pitch step convects faster for the step to low load, than for the step to high load. We suppose that this is the reason for the lower slow time constants of the axial induction for the step to low load. It is found that the mixed wake after the pitch step initially travels at nearly free stream velocity for both pitch directions. We assume that the dynamic inflow effect in this near wake is governed by the tip vortex due to the fast change in trailed vorticity. These vortices travel at such high velocities. Another finding is that the initial decay of the axial inductions during the pitch step is similar for both pitch directions. Furthermore, the aerodynamic characteristics of the turbine is identified to be the reason for the higher load overshoot for the pitch step to low load.

This comprehensive pitch step measurement set allows for detailed validation of engineering models and simulations for two relevant operational states, as we performed with the induction data in

Further investigations are recommended with high-fidelity models of induction effects, e.g. FVWM or actuator line CFD simulations, to support the interpretation of the data and improvement of models. Further planned steps to extend the understanding of the dynamic inflow process and enhance or develop models on the basis of this experimental setup are the generation of a wider database of pitch steps with varying parameters of inflow velocities, rotor speeds and rotor induction levels but also more realistic inflow conditions, including e.g. non-uniform inflow and gusts. With a wider database it can be tested whether, besides the axial induction, radial position and typical dynamic inflow time scaling factor

The detailed derivation based on the theorem of Biot–Savart is given in

Equation (A11) of

The analytical solution of the axial probe

The uA model as described in detail in

The model consists of two filter functions, Eqs. (

The 1c model fit is applied to the hot-wire signal shown in Fig.

Further, the fitted

Between 0.5 and 1.5

In the actuator disc experiments by

Spanwise evolvement of the axial wake velocity from 0.5 to 2

The preprocessed experimental data along with further documentation are available at

FB designed, performed, processed and analysed the experiment and wrote the article. DO assisted in the experiment, estimated steady corrections and wrote postprocessing scripts for the LDA data. JGS and MK contributed with several fruitful discussions from an early planning stage. MK supervised the work. All co-authors thoroughly reviewed the article.

The contact author has declared that neither they nor their co-authors have any competing interests.

Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

We thank Iván Herráez and Elia Daniele for the discussions on the wake induction measurement method. We further thank Dominik Traphan and Tom Wester for their help with the LDA system. We would also like to thank the two reviewers Luca Greco and Georg Raimund Pirrung for their helpful comments.

This work was partially funded by the Ministry for Science and Culture of Lower Saxony through the funding initiative Niedersächsisches Vorab in the project “ventus efficiens” (reference no. ZN3024).

This paper was edited by Alessandro Bianchini and reviewed by Georg Raimund Pirrung and Luca Greco.