The dynamic inflow effect describes the unsteady aerodynamic response to fast changes in rotor loading due to the inertia of the wake. Fast changes in turbine loading due to pitch actuation or rotor speed transients lead to load overshoots. The phenomenon is suspected to be also relevant for gust situations; however, this was never shown, and thus the actual load response is also unknown. The paper's objectives are to prove and explain the dynamic inflow effect due to gusts, and compare and subsequently improve a typical dynamic inflow engineering model to the measurements. An active grid is used to impress a 1.8 m diameter model turbine with rotor uniform gusts of the wind tunnel flow. The influence attributed to the dynamic inflow effect is isolated from the comparison of two experimental cases. Firstly, dynamic measurements of loads and radially resolved axial velocities in the rotor plane during a gust situation are performed. Secondly, corresponding quantities are linearly interpolated for the gust wind speed from lookup tables with steady operational points. Furthermore, simulations with a typical blade element momentum code and a higher-fidelity free-vortex wake model are performed. Both the experiment and higher-fidelity model show a dynamic inflow effect due to gusts in the loads and axial velocities. An amplification of induced velocities causes reduced load amplitudes. Consequently, fatigue loading would be lower. This amplification originates from wake inertia. It is influenced by the coherent gust pushed through the rotor like a turbulent box. The wake is superimposed on that coherent gust box, and thus the inertia of the wake and consequently also the flow in the rotor plane is affected. Contemporary dynamic inflow models inherently assume a constant wind velocity. They filter the induced velocity and thus cannot predict the observed amplification of the induced velocity. The commonly used Øye engineering model predicts increased gust load amplitudes and thus higher fatigue loads. With an extra filter term on the quasi-steady wind velocity, the qualitative behaviour observed experimentally and numerically can be caught. In conclusion, these new experimental findings on dynamic inflow due to gusts and improvements to the Øye model enable improvements in wind turbine design by less conservative fatigue loads.

The dynamic inflow phenomenon is an unsteady aerodynamic effect relevant for helicopters

Aeroservoelastic simulations are used to obtain relevant turbine loads in the design and certification process of wind turbines. The aerodynamic part of these simulations is based on the blade element momentum (BEM) theory that gives the aerodynamic forces acting on the rotor blade segments. BEM, however, is inherently based on steady-flow assumptions, and engineering models are needed to catch dynamic phenomena, like the dynamic inflow effect.
Widely used examples are the ECN model

In addition to the need of engineering models for dynamic inflow effects, blade element momentum (BEM) theory is based on the assumption of axial and uniform inflow. Free-vortex wake methods (FVWMs) on the other hand model dynamic inflow effects and also non-uniform inflow intrinsically.

Within two historic EU projects on dynamic inflow

Until now, there is no conclusive information on the relevance or even existence of dynamic inflow effects due to gusts. Consequently, it is also not known if current engineering models can model this expected effect.

The objective of this work is to experimentally prove and quantify the dynamic inflow effect due to gusts and to investigate the behaviour in engineering models. The work continues and builds on the methods of the radially resolved induction factor measurements of a pitch step experiment in

Within this study various methods are combined, and a short overview of the methods is given as a guideline. Firstly the experimental setup is introduced (Sect.

The experiments were performed in the large wind tunnel of ForWind – University of Oldenburg. The Göttingen-type wind tunnel has an outlet section of 3 m by 3 m. The wind tunnel was operated in an open-jet test section configuration with a test section length of 30 m (maximum wind velocity of 32 m s

An active grid is attached to the wind tunnel nozzle to manipulate the flow

The Model Wind Turbine Oldenburg with a diameter (

A 2D laser Doppler anemometer (LDA) by TSI Inc., with a beam expander with a focus length of 2.1 m, is used. The optical measurement device is placed well outside of the wind flow. It is mounted on a motor-driven three-directional traverse with 1.5 m travel distance in each direction (see Fig.

Undisturbed mean wind field of the sine

In this research the active grid is controlled by an overall constant blockage approach, where the inner square part (

The wind fields are quantified based on LDA measurements at 15 positions 0.7

These measurements are synchronised with the grid movement. For each wind field, a spatial mean wind velocity is defined by firstly binning all time series of the positions up to 0.9

The level of uniformity over the swept area is assessed based on the Pearson correlation coefficient, as a measure of correlation of the wind velocity at single positions to the mean wind signal. It is calculated for the separately binned and averaged different positions in comparison to the spatial mean wind signal. These values are plotted colour coded at the measurement positions alongside relevant turbine dimensions in Fig.

Correlation coefficients within the local stream-tube radius are very high for both wind fields and for the sine variation for all measured positions, as expected based on the investigation by

Cross-correlation between the mean velocity 0.7

Aerodynamic rotor torque, thrust and flapwise blade root bending moments are obtained based on strain gauge measurements.

Additionally to the two wind fields, a staircase variation with 12 steps with a length of 25 s each and velocity range from 4.6 to 9.0 m s

The staircase wind field is characterised at five horizontal positions between 0.1 and 0.9

Experimental test cases including number of measurement positions of the LDA and repetitions.

pos.

The method by

In Fig.

The axial and tangential wake induction factors are defined by Eqs. (

The measurements of

The dynamic and quasi-steady case during a gust is compared for different load and rotor flow signals. The difference between both cases results from the dynamic inflow effect. The dynamic measurement is denoted as the dynamic case. The quasi-steady case is the respective signal during the same gust without dynamic effects. They are interpolated from lookup tables based on the instantaneous gust wind speed. These lookup tables are based on a quasi-steady characterisation experiment. The processing of both the dynamic and quasi-steady signals is introduced in this subsection.

Ensemble averages are calculated for each of the loads from the various repetitions of the two dynamic cases. For the sine gust the ensemble average of the flapwise blade root bending moment (

The LDA-based induction measurement data for the sine variation are processed with a similar approach. The data points within the threshold in the bisectrix of the single repetitions are synchronised with the wind field and combined to one single signal. As the rotational frequency of 8 Hz of the rotor is a multiple of the frequency of the sine at 1 Hz, there are 24 data point clusters for this three-bladed turbine over one sine period (in Sect.

Corrections are applied to the torque and thrust signals based on the strain gauge measurements. To obtain the aerodynamic rotor torque, the measurement signal is corrected for two effects. Firstly, the friction in the main shaft bearings and slip ring is added to the measured torque. This correction increases the torque by 3 % at the mean velocity of the wind fields. Secondly, there is an inertial effect of the rotor due to slight changes in the rotor speed up to

The thrust is derived from the tower bottom bending moment in fore–aft direction. The measurement is corrected for the influence of tower and nacelle drag. This drag was estimated based on a quadratic fit to a measurement of the tower bottom bending moment at various wind speeds with the turbine without installed blades.

Quasi-steady turbine loads and rotor flow are obtained based on linear interpolation from non-dimensional lookup tables for a range of TSR and dimensionalised again. These lookup tables are based on a detailed characterisation of the turbine with the staircase wind protocol. The uncommon blade root bending moment coefficient

Turbine characteristics for construction of the quasi-steady case. Relevant TSR range for the sine and stochastic wind variation is TSR 5.6 to 9.5 and 5.4 to 9.8, respectively.

The axial (see Eq.

Distributions of

The solid lines represent the highest, lowest and middle operational TSR configurations for the needed range of the sine case within the staircase characterisation. The error bars indicate the quadratic error of the inflow uncertainty and the 95 % CI of the induction measurement for the inductions and the propagated error for the angle of attack. Another high-TSR state is extrapolated and shown in dashed lines. This extrapolation, however, is only minor. At the highest TSR operational point in the characterisation, the rotor speed dropped due to the chosen controller settings. This led to a lower TSR value than needed for the construction of the quasi-steady signals. For the load characterisation, additional characterisations at higher rotor speed were recorded. Therefore, the highest recorded TSR in the characterisations of loads and inductions differs.

The trends for the axial and tangential induction and angle of attack are as expected. The axial induction factor (Fig.

The tangential induction factor (Fig.

The angle of attack (Fig.

The quasi-steady turbine loads and inductions, lacking the dynamic inflow effects, are obtained for the dynamic wind field by interpolation from this characterisation. The reference wind speed of the gust at the rotor plane position is used for the construction. This reference speed is the mean of the measured 15 positions in front of the turbine, and a time delay was obtained based on minimising the root mean square error in the cross-correlation of the mean wind to the mean velocity of the three reference wind measurements in the rotor plane.

In BEM simulations, engineering models are needed to catch the dynamic inflow effect. By filtering the induced velocity, the inertia of the wake is considered, leading to a load overshoot for a sudden change in rotor load, e.g. by a fast pitch step.

The dynamic inflow effect due to a pitch step should be described by two time constants

A gust can also lead to fast changes in

In the following are the formulations of the Øye dynamic inflow model and a suggested improvement to the model.

In the Øye dynamic inflow model the steady induced velocities are filtered through two first-order differential equations as in Eqs. (

The Øye model is developed for the assumption of constant wind velocity and filters the induced velocity through two first-order differential equations. In

Wake with mixed vorticity as a result of a fast change in thrust (modified from

In Fig.

However, the wake with the old and new vorticity is convected by the local wind velocity, partly wake induced. For the shown case, this local wind velocity in the relevant wake distance is in parts higher than in the rotor plane. The wake is convected faster than in the assumption for the Øye model. This effect is expected to increase the axial velocity as additional air volume is pulled through the rotor by the inertia of the wake. This increases the angle of attack during the step change to lower wind velocity and thus leads to a more gradual change in the turbine load.

To include this effect in the dynamic inflow model, an additional time derivative on the undisturbed wind velocity

Two different kinds of simulations, a BEM and a FVWM based, are used for comparison with the experimental data. For the BEM simulation the dynamic inflow engineering model is disabled to get the steady case. For the FVWM the quasi-steady cases are generated similar to the experiment. A lookup table with relevant quantities is generated based on a staircase wind input, and the quasi-steady case is obtained from linear interpolation by the respective wind field. The same airfoil polars as in Sect.

The first simulation environment is a BEM model programmed in MATLAB and based on

Sine wind field

The second simulation environment is the FVWM model implemented in QBlade

Both model setups were already used in

At first, the integral loads for sine and stochastic wind fields are presented, comparing the quasi-steady experiment and dynamic experiment. Next, the radially resolved axial velocity and induced velocity of the sine gust is investigated. The thrust force is reconstructed based on these induction measurements. Lastly, a comparison of thrust and induced velocity for the sine gust of BEM and FVWM simulations to the experiment is presented.

In Fig.

In the comparison of the quasi-steady case with the experiment case, the three considered load channels show similar behaviour. At the positive gust peak at

Stochastic wind variation

The steady and dynamic curves differ mainly for the range of

Figure

The comparison of the quasi-steady and dynamic

Quasi-steady and dynamic axial velocity and induced velocity for sine wind field at radii 0.4

The second instance is around

For the sine wind field, quasi-steady and dynamic

In Fig.

The steady and dynamic axial velocity shows similar behaviour for the three chosen radii. However, differences are evident at the lower tipping points. For all three radii the dynamic case shows higher

In Fig.

The quasi-steady values show a dip by 0.4 m s

In general the dynamic

At 0.8

In Fig.

Thrust force reconstructed for the quasi-steady experiment and dynamic experiment from

In Fig.

Steady and dynamic thrust

In Fig.

For experiment and FVWM, the behaviour of the dynamic case shows a reduced load amplitude in relation to the respective quasi-steady case, with the main difference at the lower tipping point at

In Fig.

In Fig.

The dynamic

In Appendix

The comparison of the steady and dynamic loads of the sine wind variation (see Fig.

The dynamic and quasi-steady loads differ for a duration of

For the stochastic wind variation (see Fig.

For the observed reduced load peak due to a positive gust, the

The described differences between the steady and dynamic axial velocity (see Fig.

For 0.8

The reconstructed steady thrust (see Fig.

For the reconstructed thrust, qualitatively the same effect as for the direct load measurement at the lower tipping point is seen, leading to a lower load amplitude for the dynamic case. The difference at the lower tipping point between the steady case and the dynamic case here is smaller, with 8 % compared to 20 % for the strain gauge measured load, each normalised by the respective quasi-steady maximum-to-minimum load difference. Considering the 95 % CI, these differences range from

For the steady and dynamic axial velocity, induced velocity, and reconstructed thrust from the rotor flow, a consistent picture to the independent load measurement is given. Therefore, despite the noticeable uncertainty range of these measurements and derived flow quantities, these data give a strong indication of the dynamic inflow effect due to gusts directly in the flow.

The Øye dynamic inflow model was experimentally validated several times, showing accurate predictions for pitch steps, e.g. for integral turbine loads in

The increase in dynamic load within the Øye dynamic inflow model is due to the filtering of the induced velocity. Approaching the lower load tipping point in the sine gust, the lower drop in induced velocity is equivalent to a higher drop of the dynamic axial velocity. This leads to a higher drop of the angle of attack and thus lower load. This general trend of an increase in load amplitude is therefore present for all engineering models that are based on solely filtering the induced velocities (see

The improved Øye dynamic inflow model (see Sect.

The general trend of the induced wind velocity in the improved Øye is similar to the FVWM simulation; however, the amplification of the dynamic signal is more pronounced. In comparison, the experiment also indicates a more pronounced amplification of the induced velocity than the FVWM simulations.

This lower amplification in induced velocity of FVWM is in line with the less prominent dynamic load reduction of the FVWM compared to the experiment and the BEM simulation with the improved Øye dynamic inflow model. Together, the FVWM simulations and the experiment give a first validation of the analytically motivated improvements to the Øye dynamic inflow model.

As expected, the dynamic inflow effect due to gusts is caught by the FVWM modelling approach. The less pronounced effect on the loads is suspected to be connected to the non-perfect wake convection method, which was observed in a pitch step comparison with the same FVWM model in

Given a wider experimental and numerical data basis, the additional term
(

In contrast to our findings,

For the presented experiment, there are nearly 4 times higher values at

Using scaling (see Sect.

We experimentally proved the dynamic inflow effect due to gusts for wind turbines. We tested if the Øye dynamic inflow engineering model is able to predict the effect and proposed an improvement.

Firstly, experiments under reproducible gust conditions and highly resolved measurements of the longitudinal wind field proved a dynamic inflow effect due to gusts. The effect leads to damped load amplitudes and thus reduced fatigue loads. This was observed most clearly for negative gust cases at high thrust coefficients and attributed to high changes in induced velocity. For positive gusts, the effect was less pronounced and only seen for one high-thrust-coefficient configuration.

The dynamic inflow effect is also seen in the measurements of axial flow and induced velocity in the rotor plane. The effect leads to an amplification of the induced velocities. The effect is also seen in FVWM simulations for the loads and induced velocity but with slightly lower amplitudes for the induced velocity than in the experiment. Widely applied engineering models filter the induced velocities, e.g. the Øye model

Now that the effect is known further, pinpointed wind tunnel experiments are needed for the development, tuning and validation of dynamic inflow models for gusts. One focus should be to further reduce uncertainties, especially in the inflow. Furthermore, the typical operation of variable-speed-controlled wind turbine in the free field is more complex than the presented wind tunnel test. Comparisons between FVWM and BEM simulations similar to

Two additional comparisons between the BEM model variants (steady, Øye and improved Øye model) are presented to demonstrate the applicability of the suggested approach for varying gust scenarios. The comparison is based on

The first comparison is designed to qualitatively relate the reaction on a sine gust case with three different frequencies. Therefore, the time period

The qualitative changes for doubling and halving the sine frequency are caught by the improved Øye model as suggested by the FVWM.

In Fig.

For the BEM case the original Øye dynamic inflow model gives a reduction in amplitude through the filtering approach, as is expected. The improved Øye model as well as the dynamic FVWM lead to higher amplitudes, compared to the respective (quasi-)steady cases. In general the behaviour in relation to the respective (quasi-)steady case of the improved Øye model and the FVWM are similar. However, amplitudes for the dynamic FVWM are lower than estimated by the improved Øye model, especially when the induced velocity increases. In parts these differences also reflect the difference in the respective steady signal, which shows higher amplitudes for the BEM model than for the FVWM. Also, in the comparison of a pitch step experiment in

Steady and dynamic induced velocity at 0.6

For a quantitative comparison, the difference between the (quasi-)steady and dynamic induced velocity at each time point is compared in a scatter plot in Fig.

Based on the Pearson correlation coefficient (

Steady and dynamic induced velocity at

Scatter plot with correlation coefficients of the differences in

Time series of the measurements are available at

FB designed, performed, processed, and analysed the experiment and simulations; proposed the model improvements; and wrote the manuscript. LN developed the protocols for the active grid and assisted in the experiment. DO assisted in the experiment and protocol iterations. MH, GS and MK contributed with several fruitful discussions. MK supervised the work. All authors reviewed the manuscript.

The contact author has declared that none of the authors has any competing interests.

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

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). We thank Apostolos Langidis for the help in the wind tunnel experiment; Andreas Rott for the discussions on the model improvement part; and Lars Kröger, Lisa Rademacher and Tom Wester for their help with the LDA. We would also like to thank the two reviewers, Georg Raimund Pirrung and Wei Yu, for their helpful comments and suggestions.

This research has been supported by the Niedersächsisches Ministerium für Wissenschaft und Kultur (grant no. ZN3024).

This paper was edited by Sandrine Aubrun and reviewed by Georg Raimund Pirrung and Wei Yu.