Current fast aeroelastic wind turbine codes suitable for certification lack an induction model for standstill conditions. A trailed vorticity model previously used as an addition to a blade element momentum theory based aerodynamic model in normal operation has been extended to allow computing the induced velocities in standstill. The model is validated against analytical results for an elliptical wing in constant inflow and against standstill measurements from the NREL/NASA Phase VI unsteady experiment. The extended model obtains good results in the case of the elliptical wing but underpredicts the steady loading for the Phase VI blade in attached flow. The prediction of the dynamic force coefficient loops from the Phase VI experiment is improved by the trailed vorticity modeling in both attached flow and stall in most cases. The exception is the tangential force coefficient in stall, where the codes and measurements deviate and no clear improvement is visible. This article also contains aeroelastic simulations of the DTU 10 MW reference turbine in standstill at turbulent inflow with a fixed and idling rotor. The influence of the trailed vorticity modeling on the extreme flapwise blade root bending moment is found to be small.

State-of-the-art aeroelastic wind turbine codes that are suitable for
simulating the many time series needed for certification typically use an
aerodynamics model based on blade element momentum (BEM) theory. These BEM-based models can be extended by tip loss corrections and so-called dynamic
inflow models that take the wake inertia into account. With this extension,
they are suitable for predicting the varying induced velocities in an unsteady
aeroelastic simulation. In addition to the dynamic induced velocities, there
are also dynamic effects due to shed vorticity and dynamic stall, which occur
on faster timescales than the dynamic inflow and are typically taken into
account by 2-D unsteady airfoil aerodynamics models, in this work the one
described in

Thus, both the larger-scale wake effects and the smaller-scale unsteady airfoil aerodynamics are taken into account if the turbine is in operation. In standstill, however, BEM theory cannot be used because the basic assumption in BEM, i.e., that the rotor can be approximated by a disc, is violated. Therefore, the induced velocities due to the vortices trailed from the blades are not modeled, which results in both a wrong steady-state load distribution and missing dynamics.

Wind turbine blades are twisted to ensure a reasonable angle of attack distribution along the blade in operation. In standstill, on the other hand, the blade twist leads to large load variations along the blade and thus strong trailed vorticity that is not modeled in the aeroelastic codes used for wind turbine certification. Further, the inflow turbulence, which in normal operation only affects a part of the relative flow velocity at the airfoils (the other part being due to rotor rotation), causes very large dynamic variations in the angle of attack (AOA) along the blade in standstill. In idling conditions a yaw error, as well as nacelle tilt and wind inclination, is directly translated into AOA variations as the blades rotate slowly.

In this work, a trailed vorticity model, which was originally designed for
normal operation and implemented as part of a BEM-based model in the aeroelastic code HAWC2,

The near-wake model (NWM) for trailed vorticity was originally developed for
use in helicopter aerodynamics. It was assumed in the original model that the
trailed vorticity stays in the rotor plane. The induced velocity at a blade
section due to a trailed vortex element decreases as that vortex element
moves away from the blade. This decreasing induction is approximated by
exponential functions. This approximation makes it possible to use an
indicial function algorithm to avoid the time-consuming numerical integration
of vortex arcs based on the Biot–Savart law. The model has since been
modified to enable the computation of the induction due to trailed helical
vortex arcs

A sketch of the near-wake geometry is shown in Fig.

Sketch of the geometry in the near wake. The vortex arc

In order to enable the computation of standstill cases, a new definition of the
angle

The new definition of

If the downwind convection velocity increases, the paths of the trailed
vorticity change from circular (at zero convection speed) over helical (at
moderate convection speed) to straight (at standstill). This influences both
the steady-state value of the induction from trailed vorticity and the
dynamic behavior. Both of these can be modeled by changing the parameter

As described in

To ensure that the model can be used for straight vortices in standstill
conditions and helical vortices in normal operation, a new

For positive values of

For negative values of

Optimal and approximated values for

Approximation of

The 2-D unsteady airfoil aerodynamics model in HAWC2 consists of both an
attached flow model for the 2-D shed vorticity effects and a dynamic stall
model to predict unsteady flow separation, as described in

The trailed vortex strength

The case of an elliptical wing with a 10 m span has been used previously to
test the NWM

Figure

Results for an elliptical wing.

Radial distribution of normal force coefficients at 3.5

In all following comparisons, “HAWC2” refers to HAWC2 standstill
simulations. The BEM model and dynamic inflow model are disabled because the
BEM model is not valid in standstill and the dynamic inflow model simulates
the unsteady behavior of the BEM induction. The 2-D unsteady aerodynamics
model containing shed vorticity and dynamic stall modeling as introduced in
Sect.

In addition to the 2-D unsteady aerodynamics model, the “HAWC2 NW” simulations include the trailed vorticity modeling by the extended near-wake model.

Besides measurements at operation,
the Phase VI experiment also contained measurements in standstill, some of
which have been compared to computational fluid dynamics (CFD) results by

The inflow speed in the cases presented here is 20 m s

A comparison of the radial distribution of the normal force coefficient is
shown in Fig.

The steady-state comparison of the tangential force coefficients in these
cases in Fig.

Radial distribution of tangential force coefficients at
3.5

Two cases of a pitching blade are presented here: case O47010 with a mean
geometric AOA at the 47 % station of 3

Case O47010. Variation about mean

The normal force coefficient variation for the O47010 case is shown in
Fig.

Case O47010. Variation about mean

The

The loops of the tangential force coefficient in the O47320 case are shown in
Fig.

Case O47320;

Case O47320;

Aeroelastic simulations on the DTU 10 MW reference turbine

Distribution of induction, AOA, and loads for the upward-pointing blade. The mean values are shown as solid lines, and the dashed lines indicate the standard deviations; IP indicates in-plane.

Distribution of induction, AOA, and loads for the upward-pointing blade. The mean values are shown as solid lines, and the dashed lines indicate the standard deviations.

The compared codes are HAWC2 with dynamic stall enabled but without induction
model and HAWC2 NW, where both dynamic stall and induction due to the trailed
vorticity are modeled. In order to enable direct comparisons between the
different aerodynamic models a few computations have been performed with a
locked rotor and only a single turbulence seed. The radial distributions of
AOA, induced velocities, and aerodynamic forces on the blade pointing
vertically upward are discussed in Sect.

To evaluate the extreme blade root flapwise bending moments, simulations with
an idling rotor in the wind direction range of

Distribution of induction, AOA, and loads for the upward-pointing blade. The mean values are shown as solid lines, and the dashed lines indicate the standard deviations.

The radial distributions of in-plane induced velocity, AOA, and edgewise and
flapwise aerodynamic forces are shown in Fig.

Maximum flapwise

The flow is stalled along the whole blade at 15

Computations with 36 different turbulence seeds per wind direction and for
each of the two aerodynamic models have been performed to investigate the
influence of the aerodynamic model on the extreme flapwise and edgewise blade
root bending moment. The result of these simulations is shown in
Fig.

The dashed lines represent the mean value of the maximum absolute flapwise
and edgewise blade root bending moment in the 36 simulations. The absolute
maximum of the maxima encountered in the simulations is shown as solid lines.
It can be seen that including the near-wake model in the simulations reduces
the mean maximum value by roughly 0.5 to 1.5 %, depending on the wind
direction. An exception for this reduction is the edgewise moment at
25

The mean values of the mean and standard deviation of the idling speed for
the 36 seeds are shown in Fig.

Mean and standard deviation of the idling rotor speed. The near-wake model slightly reduces mean idling rotor speed as well as its standard deviation, which is consistent with the generally lower flapwise loading predicted by HAWC2 NW.

The load comparison in idling conditions shows that adding the near-wake model might appear to reduce the extreme loading if a small number of turbulence seeds is used. A high number of turbulence seeds, on the other hand, is expected to lead to the same extreme loading independent of trailed vorticity model. Another conclusion is that the maximum extreme loading is much higher than the average extremes of the 10 min time series with different turbulence seeds. A large number of seeds might be necessary to achieve realistic extreme values in an aeroelastic load analysis in standstill conditions.

The near-wake model has been extended to compute the induction due to trailed vorticity in standstill and idling conditions. Due to the twist distribution of a wind turbine blade and the larger effect of turbulence in standstill when compared to operational conditions, strong vortices can be trailed from any position along the span of the blade. In idling conditions yaw errors, tilt angle, and wind inclinations directly translate into AOA variations on the slowly rotating blades. Comparison with the analytical solution of a constant downwash for an elliptical wing shows good agreement with results from the extended near-wake model, with the original model wrongly predicting large radial variations in the downwash.

Comparison with measurements from the NREL/NASA Ames Phase VI experiment in attached flow conditions shows an unexplained offset between the steady-state normal and tangential force coefficients measured and predicted by HAWC2 NW. However, the HAWC2 NW code predicts the effect of the trailed vorticity on the radial load gradients in steady state.

A comparison of the dynamic variation in the force coefficients for a
sinusoidally pitching blade in attached flow shows that HAWC2 NW can predict
dynamic loops that agree much better with the measurements than those
predicted by HAWC2 on the major part of the blade. The agreement is improved
both in terms of

In a steady-state comparison at high mean AOA, where the flow is separated at most of the blade, the near-wake model can predict the root vortex at the inner part of the blade in attached flow. At the rest of the blade, no clear improvement due to the added trailed vorticity modeling is visible. At the tip, which is in deep stall, the predicted normal force coefficient agrees less well with the measurements.

The unsteady comparison at high AOA shows a clear improvement at the inner
part of the blade, which is in attached flow. Also on the outer part the
openings of the

As expected, the aeroelastic computations in standstill with turbulent inflow and a fixed rotor show that the near-wake model reduces the mean blade loading mainly at radial positions in attached flow compared to the standard standstill aerodynamic model without induction. The standard deviations of the force variations are reduced accordingly. Because the relative velocity in standstill is similar at all radial positions of the blade and the chord gets smaller towards the tip, no large tip loss effects have been observed and the main induction is clearly due to the root vortex.

Also computations with idling rotor in a yaw error range of

For a different turbine and more flexible blade design, standstill vibrations in attached flow can be possible. The impact of the trailed vorticity modeling on these vibrations could be addressed in future research.

The damping of vibrations in parked or idling conditions can also be highly dependent on the dynamic stall model parameters. The attached flow parameters used in HAWC2 are based on the analytical solution for the dynamic lift and drag of a flat plate, and the airfoil thickness could be taken into account here. Also the time constants for the flow separation are currently assumed to be independent of the airfoil, as well as identical in positive and negative stall. This assumption is certainly wrong for cambered airfoils, and a better approach could be identified in the future.

Leading-edge separation, which is not part of the current dynamic stall model
implementation, could become very important at extreme yaw errors, where the
AOA is around 180

The measurement data are available by request from NREL using the relevant case numbers found in the article. The aerodynamic computations have been executed with HAWC2. Commercial and research licenses for HAWC2 can be purchased from DTU.

The authors declare that they have no conflict of interest.

This article is part of the special issue “The Science of Making Torque from Wind (TORQUE) 2016”. It is a result of the The Science of Making Torque from Wind (TORQUE 2016) conference, Munich, Germany, 5–7 October 2016.

The work has been conducted within the project “Research and development of optimal wind turbine rotors under offshore wind conditions in China (OffWindChina)”, funded by “Det Strategiske Forskningsråd ved Programkomiteen for Bæredygtig Energi og Miljø”, contract 12-130590. Edited by: Gerard J. W. van Bussel Reviewed by: Xabier Munduate and Vasilis A. Riziotis