As the paper deals with a multitude of cases and setups, the following subsection gives an overview and summarizes the particular characteristics of the setups.

As, according to , wind turbines are exposed to yaw misalignment from 2 up to 10 % of their operating time, these load cases play an important role in wind energy. Therefore, three different cases concerning the inflow direction are taken into account in the present paper. CaseBASE corresponds to the turbine with no yaw misalignment. In CaseYAW15, the turbine is rotated by -15∘ (clockwise) around the vertical axis of the rotor plane. Usually a turbine is rotated around the tower. However, as the model wind turbine is placed in a wind tunnel, a rotation around the tower would lead to different clearance distances of the blades to the wall for one revolution. Therefore, the turbine is rotated around the z axis of the rotor in order to achieve a constant distance between blade tip and wind tunnel walls over a whole revolution. CaseYAW30 is rotated by -30∘. In all simulations uniform inflow is considered. The experimental results have the affix “Exp”, the ones of QBlade “QBlade” and the FLOWer results “FLOWer”. The far field case of FLOWer has the addition “-FF”. Table  gives an overview of the different cases.

Figure  shows the surfaces of CaseBASEFLOWer and CaseYAW30FLOWer. There, the unusual position of the nozzle, which will be explained in Sect. , and the uncommon yaw movement become obvious.

The experimental setup consists of the wind tunnel and the model wind turbine, which will be described in the following sections. The blades of the model wind turbine are described in detail in an additional section, as they deliver the data for the comparison with the numerical solutions.

The next two parts describe the numerical methods of QBlade and give some information about the numerical setup.

In the following, general information about FLOWer is given. Moreover, information about the numerical FLOWer setup is provided.

In the experiment, the three red dots in Fig. a at x=-0.43 d, x=0.5 d and x=1.05 d indicate where hot-wire measurements are conducted. A semiautomatic traverse with four cross-wire probes with a measurement frequency of fs=25kHz and a cutoff frequency of fcut=10kHz is used. Each of the 608 measurement positions, Fig. b, in each cross section is measured for Ts=16s. This time is assumed to be long enough for good statistics for the current setting as the measured integral timescale is ≤0.023s, which is considerably smaller than the acquisition time of 16s. With the inflow velocity of 6.5ms-1 as convective velocity, an integral length of 0.023s⋅6.5ms-1=0.15m is calculated based on Taylor's hypothesis. Offset correction among the probes was realized by repeating 19 measurement points along a vertical line with all four probes. For each measurement position, the mean value of all four measurements was calculated and used as reference. Subsequently, the offset of each probe was calculated. This offset was averaged over all measurement points. Thereby, the offset for each probe was calculated, which was then applied to all measurements in post-processing. The calibration of the probes was performed with the help of a nearby pitot probe at different wind tunnel velocities.

The error of the hot-wire measurements is the sum of the calibration setup error (pitot tube, pressure sensor) and the hot-wire anemometry hardware. The latter was calculated by measuring multiple points in each test case with all probes and the largest deviation is defined as the error. In the present case it amounts to 3.3%, which corresponds to 0.33ms-1 in reference to the maximum calibrated velocity. This is in good agreement with error estimations given in literature; see . The total error, including calibration setup, is calculated to be 4.4%, corresponding to 0.44ms-1.

Only the simulation including wind tunnel walls has been taken into account for the comparison of the velocity planes. In this setup, at each point of the numerical grid, data were extracted for the planes and averaged over five revolutions. In order to evaluate the differences between measurement and simulation, the results of the simulation are interpolated to a grid with the same grid points as the measurement points and the results are subtracted.

The AoA is the angle between the velocity, as seen by the blade (on-blade velocity), and the airfoil chord. Generally, deriving an AoA in rotating domain is somewhat difficult, as the AoA is a two-dimensional value. Moreover, the blade deflects the streamtraces due to its induction and therefore changes the value of the AoA.

In the experiment the AoA and the on-blade velocity are measured by three-hole probes located at 65 and 85%R. The derivation of the sectionwise values, referenced to the quarter-chord point of each section, is detailed by and will be explained here shortly. Generally, this measurement method is advantageous, as no static tunnel reference pressure is needed and short tubing, as the pressure sensors are located in the blade, mitigates possible delay effects. The three-hole probes measure the αprobe and Urel,probe in reference to the probe position upstream of the wing. These values are derived by calibration of the pressure differences among tubes to the flow angle and velocity. However, when mounted on the wing, the results are affected by the induction of the blade and therefore need to be translated into the sectional AoA α and the relative velocity Urel. In this project a procedure based on two-dimensional flow assumption on the wing, Fig. , was employed.

Herein, αprobe is first rotated into the local coordinate system, which is based on the local chord, to derive αprobe,section. Subsequently, a look-up table is used, which was derived with viscous XFOIL calculations. This table correlates the measurement at the probes' head upstream of the wing to the actual local section AoA α. Thereby, the induction effect is accounted for and α and Urel are found. The analysis showed that the dependency of the local flow angle at the probe to the actual AoA is almost a first-order function in the linear region of the lift polar (the AoA range in which the lift has a nearly constant slope). The approximated equation (Eq. ) gives information about the order of conversion for this 2-D approach. α=0.58∘⋅αprobe-0.64∘ The data set was created by analyzing polars from α=-30 to 30∘ in steps of 0.5∘. Steps in between are interpolated. This procedure requires two-dimensional flow over the blade, which is assumed to be appropriate in this case, in comparison to quantitative tuft flow analysis , which indicated few three-dimensional effects on the surface flow.

In order to estimate the measurement error of the three-hole probes, data sets from calibrations of the probe alone and of measurements of the probe installed in a 2-D-wing setup were analyzed. The data sets include variation in AoA from -30 to 30∘ and the variation in the free-stream velocity. From this analysis, which also includes the error of the induction correction and sensor uncertainties, the maximal absolute error for AoA was estimated to be 0.8∘ (considering only the attached flow regime) and for the on-blade velocity it was estimated to be 0.4ms-1.

In QBlade, the AoAs are evaluated at the quarter chord position of the airfoils at the lifting line (the bound vorticity) of the rotor blades. The AoA is calculated from the part of the absolute velocity vector that lies inside the respective airfoils cross-sectional plane – which corresponds to the on-blade velocity. The absolute velocity vector itself is a superposition of the inflow, relative, wake-induced and self-induced velocity vectors.

Different methods to derive the effective sectional AoA from 3-D CFD-predicted flow fields are compared and evaluated by . Details of the methods are described in that paper. The two methods, which are most suitable for the present case, are used for the AoA extraction shown in this paper. The RAV method uses two planes, one upstream and one downstream of the rotor (see Fig. ). In these planes, the average velocities are calculated and afterwards the velocity components are used to determine the velocity in the rotor plane without the induction of the blade. The method is based on the method of , who determined airfoil characteristics from 3-D CFD rotor computations. It was successfully applied by to investigate unsteady 3-D effects on trailing edge flaps, and by for CFD analysis of a two-bladed multi-megawatt turbine. In the line averaging method (LineAve or CircAve), the AoA is determined by averaging the velocity over a closed line around each blade cut (see Fig. ). For both approaches, the results are averaged over five revolutions.

In the present paper, the flapwise (out of plane) moment (My) and the edgewise (in plane) moment (Mx) are investigated.

Due to problems with the full-bridge strain-gauge setup in the experiment, strong fluctuations are visible in the raw data and heavy filtering was necessary. Therefore, the bending moments cannot yet be considered a valid basis for quantitative comparisons and code validation purposes.

In the LLFVW method of QBlade the blade bending moments are evaluated by summing up the elemental blade forces, obtained from an integration of the normal and tangential forces along the blade span that are obtained via the stored airfoil coefficients.

In the CFD simulation, the bending moments in the blade root result from the pressure and friction on the blade surface. For each surface cell the forces are computed and multiplied with the corresponding radius. Then they are averaged over five revolutions.

The velocity planes, which are taken into account in the present study, are placed 0.43 d upstream and 0.5 d downstream of the rotor plane (see Fig. ). The plane 1.05 d downstream of the rotor plane (see Fig. ) is neglected in the present study, as the evaluation would not have brought further benefit for the paper. Moreover, at this location, the influence of the nozzle is already present, which influences the wake development on top of the wind tunnel walls.

Figure a shows the velocity in x direction for the measurement and Fig. b for the FLOWer wind tunnel simulation 0.43 d upstream of the rotor plane. The measuring points are shown as black dots. The dimensions of the wind tunnel, as well as the model wind turbine, are illustrated by dashed lines. Moreover, an isoline with the undisturbed inflow velocity of 6.5ms-1 is shown. The view direction in this picture, and in all following figures of the velocity planes, is from downstream to upstream.

The turbine blockage effect can be observed in both figures. However, the velocity distribution in the simulation is smoother and axisymmetric, leading to a clearly defined blockage, whereas it is more frayed in the experiment. Due to the location of the settling chamber after a corner, see Fig. , the measured x velocity on the left side differs slightly from the velocity on the right side. Additionally, a difference at the bottom and upper position is apparent. Due to construction reasons, the mounting of the aforementioned filter mat (see Sect. ) leaves a small gap at the ceiling of the wind tunnel; a small velocity overshoot is present at the top of the inflow test section. In the simulation, a slightly higher velocity can be seen in the corners of the wind tunnel.

In the experiment, multiple causes of possible measurement errors, such as temperature compensation or induction of the traversing system, are analyzed and ruled out. Therefore, the horizontal inequalities seem to result from the design of the wind tunnel. More information about the hot-wire measurements and possible reasons for the inequality of the flow field can be found in .

Table  gives an overview of some mean parameters characterizing the velocity plane 0.43 d upstream of the rotor plane. In the experiment, the averaging was carried out over the measuring time, in the simulation over five revolutions.

The mean velocities in the streamwise direction are slightly smaller than the desired velocity, both for measurement and simulation. However, as the differences are <0.5% in the simulation and ≈1% in the measurement, the reference velocity can still be considered to be 6.5ms-1 As uniform inflow was used in the present simulation, the standard deviation and turbulence intensity are negligible. The turbulence intensity of the measurement corresponds to the value of the wind tunnel, which was already mentioned in Sect. . The unsteady inflow in the experiment and the uniform inflow in the simulation lead to a discrepancy in the setups. The influence of the turbulence on the results will be discussed later in this document and reviewed in future investigations.

In Fig. , the relative difference between simulation and measurement with regard to the mean inflow velocity of 6.5ms-1 is shown.

The differences between both velocity planes are small as the average deviation amounts to ≈3%. Except for a small area at the bottom of the wind tunnel (around z=0.5m and between -1m<y<0m), the difference is lower than ±10% of the desired inflow velocity, which corresponds to ±0.65ms-1.

Figure  shows the velocity in x direction 0.5 d downstream of the rotor plane, for the measurement (top) and for the simulation (bottom). Again, the measuring points are indicated by black dots, the dimensions of the wind tunnel and the model wind turbine by dashed lines. An isoline with the mean velocity of 6.5ms-1 is shown, too.

Some aspects, as already seen upstream of the rotor (Fig. ), are apparent downstream of the rotor, too, for example the higher velocity over the ceiling in the measurement or the smoother, axisymmetric streamwise velocity in the simulation. In Fig. 10a, b the wake of the rotor, indicated by lower velocity, can be seen clearly. Around the rotor, as a result of limited space due to the wind tunnel walls, higher velocities are achieved. Again, in the experiment, the velocity at the upper part of the wind tunnel is slightly higher than at the bottom.

This missing turbulence in the simulated wind tunnel is the reason why the border of the rotor wake is almost a perfect circle in the lower picture, whereas it is more smeared in the measurement. The decay of the tip vortices has not yet started so shortly behind the rotor plane. As the simulation has a finer resolution, the velocity distribution is smoother there. In the simulation, there is a stronger velocity deficit in the wake of the nacelle. This can have several reasons. In the simulation, the missing inflow turbulence might have a small effect on the stability of the wake, but it is certainly not the main reason for the deviation; see . In the experiment, the boundary layer of the nacelle is not tripped, whereas a fully turbulent approach is used in the simulation. These differences concerning the boundary layer of the nacelle might lead to a different recovery of the wake of the nacelle. Due to the flow separation on the nacelle, the flow in the wake of the nacelle is highly unsteady and the main flow direction is not clearly defined (angles larger than ±60∘ occur in the simulation), whereby proper working conditions of the x-wire probe are no longer guaranteed. Therefore, the measured x component of the velocity is influenced by the y and z components, which could also lead to deviations between measurement and simulation.

An overview of some mean parameters characterizing the velocity plane 0.5 d downstream of the rotor plane are given in Table .

Again, the mean velocity almost corresponds to the desired reference velocity, as the differences between the actual velocity and 6.5ms-1 are <0.5% for both measurement and simulation. Due to the closed wind tunnel and the mass continuity, bigger differences would not have been physical. As the tip and root vortices, as well as the separation behind the nacelle, lead to velocity fluctuations, the standard deviation, as well as the turbulence intensity, increase compared to the plane upstream from the rotor; see Table . Through the superposition of the vortices created by the turbine and the inflow turbulence, the values for the measurement are still larger. As the present wind tunnel is a circuit wind tunnel, effects like pumping might occur. And due to the long measurement time of the hot-wire probes, these fluctuations might also be included in the values shown in Table .

Figure  shows the relative difference between simulation and measurement with regard to the mean inflow velocity of 6.5ms-1.

It can be seen that in the wake of the nacelle and in the area of the tip vortices, the differences between simulation and measurement are higher than 10%. In the remaining part, the difference is smaller. The mean deviation amounts to ≈7%, which is considerably higher than the value for the plane upstream of the turbine. The reason for the high value is primarily the area in the wake of the nacelle, where differences >50% occur. If a circular area with a radius r<0.56m and its origin at the center of the rotor is neglected in the averaging, the mean deviation reduces to <6% as the mean deviation in this area itself amounts to about 31%. Thereby it has to be kept in mind that due to the large flow angles in the wake of the nacelle, the measured values in this area have to be treated with caution.

All things considered, the accordance between experiment and simulation is acceptable, as the differences are, except for some parts in the outer region of the rotor and in the wake of the nacelle, smaller than ±0.65ms-1.

Hereinafter, the on-blade velocity, meaning the velocity seen by the blade section at a distinct radial position, for CaseBASE for the experiment, QBlade and FLOWer (both methods RAV and CircAve) are displayed at two different rotor locations (65 and 85%R) over the azimuth (Fig. ). A radius of 0%R corresponds to the rotor center, whereas an azimuth of 0∘ corresponds to the top position of the first blade.

At 65%R, the simulations overestimate the velocity; at 85%R there is a better accordance between the simulation results and the experiment. The difference caused by the different inflow turbulence is even less pronounced at the on-blade velocity compared to the velocity planes, as the rotational velocity has a much higher influence than the inflow velocity. Therefore, the fluctuations in the measurements are not so distinct and the differences between measurement and simulation caused by the inflow turbulence are small. For their cases with and without free-stream turbulence, also experienced only small differences in the drag coefficient, which depends on the AoA and consequently also on the on-blade velocity. The higher fluctuations in the experiment at the outer radial position might be a result of a vibration of the mounting of the probe. The averaged standard deviation for the measured velocity amounts to σon-blade(65%R)=0.11ms-1 and σon-blade(85%R)=0.08ms-1.

In order to better assess the quantitative differences among the curves, Table  gives an overview of the relative differences between the experiment and the different simulation results of the averaged on-blade velocity (Δv‾=vSim‾-vExp‾) for CaseBASE at both probe positions.

The reference velocity in each case is the undisturbed velocity at the probe position, which was calculated with vRef=vinflow2+(ω⋅R)2 and amounts to vRef(65%R)=19.49ms-1 and vRef(85%R)=24.90ms-1.

For both radial positions, all simulations match fairly well to each other, as the differences from the experiment are relatively similar. However, all simulations overestimate the experimental results. For the FLOWer simulations, both methods (RAV and CircAve) show almost the same results (Δv‾FLOWer-RAV and Δv‾FLOWer-CircAve≈4% at 65%R and Δv‾FLOWer-RAV and Δv‾FLOWer-CircAve<2% at 85%R), whereby the CircAve method seems to fit better to the experimental results. In the outer part of the blade, where the probes are located, the on-blade velocity is dominated by the tangential velocity. Consequently, both FLOWer setups (wind tunnel and far field), show almost the same results, too. But due to the wind tunnel walls, the inflow velocity in the rotor plane is slightly higher than in the far field case, which can be seen in the marginally higher curves for the wind tunnel case.

With increasing radius, the difference between the wind tunnel and the far field case decreases, as the rotational part of the velocity becomes more and more dominant. The QBlade results are closest to the measured data, which is surprising, as the wind tunnel walls are not taken into account in the LLFVW simulations. Due to the lack of walls, they have a better accordance with the FLOWer far field results than with the ones including the walls. The influence of the tower blockage around an azimuth of 180∘ can be seen at both radial positions as a small increase before the tower passage and a small drop afterwards. The increase in the inflow velocity is due to the displacement effect of the tower. Directly upstream of the tower, the velocity is reduced until it has recovered shortly afterwards. Except for this drop, the velocity is almost constant over the whole revolution.

Figure  shows the velocity over the azimuth under yaw = -15∘. As the wind tunnel walls should not be neglected in the present setup, a far field case under yawed conditions for FLOWer was not simulated.

Under 15∘ yaw misalignment, the averaged standard deviation for the measured velocity is the same as for CaseBASE (σon-blade(65%R)=0.11ms-1 and σon-blade(85%R)=0.08ms-1). Table  gives an overview of the relative differences between the experiment and the different simulation results of the averaged on-blade velocity for CaseYAW15 at both probe positions.

At 65%R, the experimental and QBlade results are almost identical (Δv‾QBlade≈1%), whereas FLOWer predicts a slightly higher velocity (≈0.5ms-1, which corresponds to Δv‾FLOWer≈3%). At 85%R, there is still a small offset between QBlade and FLOWer, but the measurement lies between the two curves, which can also be seen at the different signs of the differences in Table . Moreover, as already seen for the case with no yaw misalignment, the differences are smaller further outboard. In total, the differences between experiment and simulations are smaller than under straight inflow.

The influence of the tower is covered by the influence of the yaw misalignment, which leads to stronger variations over one revolution. In the upper part of the rotor (azimuth = 270–90∘), the blade advances, while it retreats in the lower part (azimuth = 90–270∘). This leads to a 1p variation in inflow velocity as seen by the blade. Further information and detailed discussions about effects occurring under yaw misalignment, like the 1p variation, are summarized by .

In Fig. , where the velocity over the azimuth under yaw = -30∘ is plotted, the influence of the yaw misalignment is even more pronounced.

Again, the averaged standard deviation for the measured velocity amounts to σon-blade(65%R)=0.11ms-1 and σon-blade(85%R)=0.08ms-1. In Table , the relative differences between experiment and the different simulation results of the averaged on-blade velocity for CaseYAW30 at both probe positions are displayed.

Almost the same characteristics as already mentioned with regard to Fig.  can be found for -30∘ yaw misalignment. However, at 65%R, the FLOWer results have a better agreement with the experiment in the upper part of the rotor (270 to 90∘ azimuth) than in the lower part (90 to 270∘ azimuth). At 85%R the FLOWer curves and the measured curve correspond well (|Δv‾FLOWer|≤0.11%), whereas the QBlade results have a bigger deviation from the experimental results. Overall, the differences between the simulated curves and the measured curves decrease again with increasing yaw misalignment.

As for the on-blade velocity, in the following, the AoA for CaseBASE for the experiment, QBlade and FLOWer (both methods RAV and CircAve) are displayed at two different rotor locations (65 and 85 %) over the azimuth (Fig. ).

The tower blockage effect can be clearly seen at azimuth = 180∘, where the AoA has a drop of approximately 1∘. The influence of the tower is very distinct, due to its relative large diameter, compared to the other components of the turbine. For both, QBlade and FLOWer, the curve is almost constant before and after this drop. The dip in the experiment at an azimuth of approximately 90∘ is a result of the traverse, which was located in the test section upstream of the rotor.

Table  gives an overview of the differences between the experiment and the different simulation results of the averaged AoA (Δα‾=αSim‾-αExp‾) for CaseBASE at both probe positions in order to quantify them. In contrast to the on-blade velocity, no relative values were calculated.

There is a good accordance between the experiment and the FLOWer results despite the fact that the simulated curves lie outside of the measured standard deviation whose average is however small (σα(65%R)=0.10∘ and σα(85%R)=0.14∘). Even so, they are within the range of the maximum absolute error of 0.8∘; compare Sect. . The larger value for the more outboard region mirrors the effect of the vibrating mounting of the probe. Both AoA evaluation methods for the FLOWer solution show almost the same distribution, especially at 85% (|Δα‾FLOWer|≤0.23∘ at 65%R and |Δα‾FLOWer|≤0.03∘ at 85%R). Reasons for the differences can be attributed to the different approach of the methods (RAV is averaging over time and CircAve has a local approach; see ). At 65%, the level of the AoA is approximately 0.5∘ lower than further outboard for the experiment, QBlade and FLOWer.

An offset of >2∘ between the simulation results of QBlade and FLOWer (including wind tunnel walls) is present for both radial positions. This is a result of the neglect of the wind tunnel walls in the QBlade simulation. As the walls impede the expansion of the wake, the velocity in the rotor plane and consequently the AoA are higher for the case including wind tunnel. A comparison between the QBlade results and the FLOWer results under far field conditions verifies this assumption, as both the distributions and the offsets to the measured values, see Table , are almost similar. More information about this phenomenon and the underlying reasons can be found in and . The small kinks at ≈90 and ≈270∘ azimuth in the QBlade results are a result of the usage of the tower model. This model has to be switched on at a certain blade position. In the present simulations this is carried out as soon as the blade position is located below the nacelle, leading to a discontinuity, which is reduced through interpolation. However, as the tower has a relatively large diameter, the kink cannot be completely prevented.

A comparison of the AoA distribution calculated by QBlade and FLOWer over the normalized radius at an azimuth = 0∘ for the wind tunnel and far field cases is shown in Fig. .

Again, the influence of the wind tunnel can be seen in the constant offset between the two FLOWer cases. As already seen in Fig.  and Table , the offset between the RAV and the CircAve results amounts to ≈0.15∘ at 65%R and decreases to ≈0.06∘ at 85%R for both cases (far field and wind tunnel). As already mentioned, the differences are a result of the different approaches of the two methods; see . Between approximately 40 and 90% of the radius, there is a good accordance between the QBlade and the RAV solution of the FLOWer far field case.

Figure  shows the AoA over the azimuth under yaw = -15∘.

The same characteristics as under yaw = 0∘ can also be seen in Fig.  under yaw = -15∘. Again, the influences of the tower blockage and the traverse are clearly visible. Unlike in CaseBASE, the AoA is not constant before and after the drop caused by the tower, due to the yaw misalignment.

In Table , an overview of the differences between experiment and the different simulation results of the averaged AoA for CaseYAW15 at both probe positions is given.

As in CaseBASE, the FLOWer results show a good agreement with the measurements at both radial positions (|Δα‾FLOWer|≤0.18∘ at 65%R and |Δα‾FLOWer|≤0.13∘ at 85%R) and the average of the measured deviation is again small and similar to the values for the CaseBASE (σα(65%R)=0.10∘ and σα(85%R)=0.14∘). Again, the differences of the CFD results including wind tunnel are smaller than the maximal absolute error of 0.8∘. The two different evaluation methods for FLOWer show almost the same results, too. The difference between the two radial positions amounts to approximately 1∘ for all setups. The offset between QBlade and FLOWer is >1.8∘ but smaller than for case CaseBASE and can still be attributed to the influence of the wind tunnel walls. The reduction of the difference between QBlade and FLOWer is a result of the yaw misalignment. Through the rotation of the rotor plane out of the inflow plane, the projected plane becomes smaller, leading to a smaller blockage in the wind tunnel. As the change of the projected area follows the cosine function, the changes in the differences are not linear. As already mentioned, a far field case under yaw misalignment for FLOWer was not simulated. The kinks at ≈90 and ≈270∘ azimuth are still present, but less pronounced.

In Fig.  the AoA distribution over the azimuth for a yaw misalignment of -30∘ can be seen.

The effects of the tower blockage and the traverse are still visible. The effects caused by the yaw misalignment are more pronounced here.

An overview of the differences between experiment and the different simulation results of the averaged AoA for CaseYAW30 at both probe positions is given in Table .

At 65%, there is a difference between the measurement and FLOWer results at the downward-moving blade (azimuth = 0–180∘), probably due to the traverse placed in the wind tunnel, whereas there is a good agreement at the upward-moving blade (azimuth = 180–360∘). The average accordance between the experiment and the FLOWer simulations is satisfactory, as the differences are small (|Δα‾FLOWer|≤0.23∘). Further outboard, the curves correspond very well over the whole revolution (|Δα‾FLOWer|≤0.12∘), except for the dip at a 90∘ azimuth. The average of the deviation amounts to σα(65%R)=0.09∘ and σα(85%R)=0.13∘, which can be considered small. The offset between QBlade and FLOWer, due to the missing wind tunnel walls in QBlade, has decreased and amounts now to <1.6∘.

For all three cases (CaseBASE, CaseYAW15 and CaseYAW30) at both radial positions, despite the constant offset from the QBlade results, the amplitude and phase of the AoA of the experiment, QBlade and FLOWer have a good agreement.

In the following, the flapwise bending moments (out of plane, My) for one blade, simulated with QBlade and FLOWer, are compared to each other for all three cases. Figure  shows the curves for CaseBASE (Fig. a), CaseYAW15 (Fig. b) and CaseYAW30 (Fig. c).

As the forces and moments mainly depend on the AoA, the same characteristics (tower shadow, influence of yaw misalignment, etc.) as in Figs. , and can be seen in Fig. , as they cascade down from the AoA to the loads.

In Table , the relative differences among the simulation results of the flapwise bending moment are displayed.

The difference between the two FLOWer results for the baseline case (top figure, ≈20%) represents the influence of the wind tunnel walls. However, this time, the accordance between the QBlade results and the FLOWer wind tunnel case (<9%) is slightly better than between the QBlade case and the FLOWer far field case. This unexpected result might be a result of the choice of the XFOIL polars used for the present QBlade simulations because although the AoAs are similar between QBlade and CaseBASEFLOWer-FF (see Fig.  and Table ), the bending moments differ. Comparisons of the radial moment distribution and of the force coefficient over the azimuth could lead to a better understanding and assessment of the differences.

The amplitude and phase of the 1p frequency, caused by the yaw misalignment, show a good accordance between QBlade and FLOWer for CaseBASE and CaseYAW15. The mean differences under yaw misalignment decrease with increasing yaw angle (<8% under 15∘ yaw misalignment and <3% under 30∘ yaw misalignment), showing the same tendency as the AoA (Tables , and ). Except for the constant offset, the fit between the curves of the QBlade and FLOWer simulations is similar to the one for the on-blade velocity and the AoA. This time, the kinks in the curves at ≈90∘ and especially at ≈270∘ are a bit more pronounced. For all three cases, QBlade predicts, due to the missing wind tunnel walls, smaller values than FLOWer.

The comparison of the edgewise bending moments (in plane, Mx) can be found in Fig. .

The same characteristics of the curves as for the flapwise bending moments (see Fig. ) can be found in the simulated edgewise bending moments.

The relative differences among the different simulation results for the edgewise bending moments are summarized in Table .

The differences between the FLOWer results with and without wind tunnel walls are larger than for the flapwise bending moment (ΔMx‾≈33% compared to ΔMy‾<20%; see Table ). This corresponds to the results of and , who also experienced a stronger influence of the walls on the power than on the thrust. The reason for this phenomenon is attributed to the different sensitivity of the forces to AoA variations. The tangential force, which is the main driver of the in-plane moment, is more prone to changes in the AoA compared to the normal force. Consequently, small differences in the AoA lead to larger deviations in FT than in FN. Other than for My, the QBlade results for Mx are closer to the FLOWer far field results than to the wind tunnel results. The progression of the edgewise bending moment is almost similar between QBlade and FLOWer for all three inflow directions. The mean differences under 15∘ yaw misalignment (≈19%) are slightly smaller than for CaseBASE (≈21%), but the difference under 30∘ yaw misalignment is significantly smaller (<11%) than for the other two cases. Again, the change in the projected area and the blockage in the wind tunnel can be alluded to as reason for this tendency.

To sum up, the progression of the curves fit quite good for both moments, except the kinks caused by the tower shadow model in QBlade. The offset among the results seems to depend on consideration of the wind tunnel walls and the chosen polar set in QBlade. The decreasing differences between QBlade and FLOWer with increasing yaw misalignment are a result of the decreasing projected rotor plane, which influences the blockage in the wind tunnel.