A procedure to propagate longitudinal transient gusts through a flow
field by using the resolved-gust approach is implemented in the URANS solver
THETA. Both the gust strike of a

The origins of applying computational
fluid dynamics (CFD) to wind turbine rotors date back to the 1990s when

In the past years, growing computer power has enabled the geometry-resolved
simulation of wind turbines including the sites with CFD. Studies have been performed for example by

The challenges of correctly predicting uncertainty of the fluctuating wind
loads is a research field on its own. For example,

The aerodynamic interferences between the unsteady wind conditions and wind
turbines are of major importance for the prediction of fatigue loads and the
annual power production. Therefore, it is part of the certification
computation for each wind turbine. Nevertheless, the detailed investigation
of isolated effects of the 50-year extreme operating gust (EOG) on the flow
of a wind turbine using high-fidelity methods like CFD is rare even though the
blade loads resulting from the extreme load cases are dimensioning load
cases. In the case of vertical axis wind turbines,

Even though the literature on gust simulations on wind turbines is not extensive, some
research has been conducted in the field of aerospace science.

In the so-called field approach,

The simulation of unsteady inflow conditions of wind turbines in CFD implies
several challenges. The simulation of a wind turbine including the tower is,
itself, an instationary problem which needs the computation of several
rotations to obtain a periodic solution. Superposed by sheared inflow
profiles and instationary (stochastic) inflow conditions, periodicity can
never be gained because the same flow state never occurs twice. Moreover, a
computation in which the rotor motion is adapted to the actual rotor forces
using a strong coupling approach as proposed by

The validation of the resolved-gust approach in the DLR URANS solver THETA

DLR's flow solver THETA is a finite-volume method which solves the incompressible Navier–Stokes (NS) equation on unstructured grids. The grids can contain a mix of tetrahedrons, prisms, pyramids, and hexagons. The transport equations are formulated on dual cells, which are constructed around each point of the primary grid. Therefore, the method is cell centred with respect to the dual grid. The transport equations are solved sequentially and implicitly. The Poisson equation, which links velocity and pressure, is solved by either the Semi-implicit Method for Pressure-Linked Equations (SIMPLE) algorithm for stationary problems or the projection method for unsteady simulations. With the projection method the momentum equations are first solved with an approximated pressure field. The pressure field is then corrected with a Poisson equation to fulfil continuity. Pressure stabilization is used to avoid spurious oscillations caused by the collocated variable arrangement.

The technique of overlapping grids (Chimera) is used to couple fixed and
moving grid blocks. The method was developed by

Implicit time-discretization schemes of first order (implicit Euler) or
second order (Crank–Nicolson; backward differentiating formula, BDF) are implemented. The temporal schemes are
global time stepping schemes. A variety of schemes from first order upwind up
to second order linear or quadratic upwind or a central scheme and a low
dissipation, low dispersion scheme

The THETA code provides a user interface for setting complex initial and boundary conditions using the related C functions. This guarantees a high flexibility on the definition of boundary conditions and a straightforward modelling of very specific test cases. For example, the functions enable the prescription of gusts at the inflow boundary condition, which are then propagated through the flow field. Moreover, all physical models are separated from the basis code. Therefore, new physical models can be implemented without modification of the base code.

For turbulence modelling the commonly used Spalart–Allmaras,

Computational grid set-up;

The comprehensive rotor code FAST

In the present case, most parameters remained on the default of NREL's
v8.16.00a for both FAST and the NREL 5 MW wind turbine. Few
parameters had to be adjusted. As it is, the variable-speed control has
been turned off to ensure a constant rotational speed as in the URANS
computation. The blade stiffness has been increased to the order of

The NREL 5 MW turbine

Due to the narrow gap between rotor and nacelle a valid Chimera overlap region could not be achieved in that region. Thus the nacelle of the NREL 5 MW turbine is neglected while the tower is accounted for. This approach leads to an error in the flow prediction behind the rotor hub but is supposed to have no impact on the blade loads.

The gust simulation is based on the rated wind speed

The computational grid consists of three parts. The first part contains the three
rotor blades, stubs, and the rotor hub. On the blade surface, a structured
grid with

The second part of the grid has the shape of a disc and contains the entire
rotor. The disc measures

The Chimera parent grid has the dimensions of

The 54 prism layers, used to resolve the boundary layer of the viscous floor,
have a total height of

In the Chimera parent grid, the edge length of the cells continuously grows
from very small in the rotor tower and wake region to rather large close to
the far-field boundaries. The entire Chimera parent grid contains
approximately

In Fig.

The procedure of applying the gust to the flow field starts by computing the
flow field around the wind turbine until the flow field and the global rotor
loads have become periodic. For the NREL 5 MW turbine in the given set-up 9
revolutions are required. Then, the inflow velocity on the inflow boundary is
modified according to the velocity change described in
Sect.

The restrictions to ensure a loss-free transport of the gust velocity on the
resolved-gust approach named by

a fine grid upstream of the geometry in question

a fine time step.

To analyse the resolved-gust approach in the incompressible URANS solver THETA, the inflow velocity profile is shear free and the gust velocity remains independent of the height above ground.

Inflow velocity with dependence on physical time

The

The time-dependent velocity change of the EOG is modelled following the

As described in Sect.

The agreement among the URANS computations performed with THETA, TAU, and
the reference documentation of the NREL 5 MW wind turbine

Rotor thrust

Rotor torque

Between

If the wind turbine operates in uniform flow conditions, a
3

The impact of the

Gust-induced peak loads on the rotor during the

During the gust,

Table

In both tables it can be seen that a reduction of the wind speed due to
calm or the increase in the wind speed with the same amplitude leads to very
similar absolute changes in rotor thrust and rotor torque. By comparing the
values of Tables

It is also important to note that the rotor loads return to the values of
constant inflow conditions right after the gust ended. This indicates that
there are neither reflections nor numerical oscillations,
which lower the numerical accuracy, in the flow field. In summary, the behaviour of rotor thrust

Averaged rotor loads during the

By considering blade deflections and changes to the rotational speed in future aeroelastic computations, the resulting rotor torque and rotor thrust will change.

Rotor thrust

Rotor position at minimum

Figure

Span-wise distribution of

The maximum velocity

Pressure distribution of the blade at the inboard section,

Pressure distribution of the blade at the midsection,

Pressure distribution of the blade at the outboard section,

To analyse the flow state on the blade during the gust, two instances have
been chosen: after

Gust-induced peak load during the EOG on the rotor in relation to the constant blade load.

In accordance to Fig.

In all three figures the pressure is displayed in the upper half and is normalized with the vector sum of the tip speed and the constant inflow velocity. For a meaningful comparison to constant inflow conditions, it was ensured that the investigated sections result from blades at the same azimuth positions.

A noticeable difference in

The friction coefficients on the blade sections in undisturbed flow are
displayed in Figs.

Conversely to the inboard section, changes in separation at the midsection
appear due to the gust only. In Fig.

The same analysis is performed for the blade that is situated right in front
of the tower or at

Finally, the transport of the tip vortices is investigated. It has to be understood as an indication of whether the velocity transport in the field works as expected but the tip vortex transport has only small meaning for the transient rotor loading during the gust. In addition, the velocity in the field changes gradually because of the infinite speed of sound in the entire flow domain. Thus, the vortices that are shed from the blade at a given wind speed are not transported with their specific gust transport velocity. Contrariwise, all existing vortices experience identical changes in the gust transport velocity. Thus, the geometrical distance between existing vortices remains constant.

Tip vortex transportation in the vertical plane through the rotor centre.

In Fig.

Tip vortex transportation in the main flow direction with dependence on the wake age at three time instances during the gust.

Tip vortex transportation vertical to main flow direction with dependence on the wake age at three time instances during the gust.

The aerodynamic characteristics, rotor thrust, and rotor torque of course depend on the assumption of stiff rotor blades and constant rotational speed. If the rotor had finite mass and inertia or a speed control algorithm had been applied, the rotor loading during the gust would have been reduced significantly. Moreover, the symmetry of the rotor loading decreases as soon as the structure dynamics are taken into account.

The study presented the validation of the
resolved-gust approach that was implemented in the URANS solver THETA. As
a test case, the generic 5 MW wind turbine was computed, operating
under a

the wind speed is constant in height and time (except gust velocity);

the gust velocity is constant in height;

the gust transport velocity is equal to speed of sound which is infinite;

the boundary conditions of the flow domain are chosen to prevent the flow from escaping sideways.

The results represented the effects that are expected during the instationary inflow condition in combination with the given boundary conditions very well. Rotor thrust and rotor torque follow the gust shape very closely. An analysis of the time history of rotor thrust and rotor torque during the gust show an increased rotor loading of about 100 % compared to constant inflow. Pressure distributions and friction force coefficients reveal that the flow on the rotor blades at maximum gust velocity is separated and thus highly instationary. Moreover, the effect of accelerating wind speeds was found in the rotor wake as the distance between the vortices is stretched and compressed according to the changes of the wind speed.

The comparison of the results with the aeroelastic software FAST showed a
very good agreement of rotor thrust and rotor torque during the EOG. Thus, it
is a valid and accurate method to predict wind turbine loads during an EOG.
Nevertheless, a complete validation is not possible at this state as a gust
experiment for a wind turbine is not available. The first mandatory step for
further research on the gust simulation with URANS is to perform a
grid-independence and time-step study with the resolved-gust approach. Based
on these results, a gust transport velocity with other than infinite speed of
sound have to be achieved. This may be realized by adjustments of the
resolved-gust approach, by implementing the field approach of, for example,

NREL 5 MW data are available from NREL reports; no other data are available.

The author declares that she has no conflict of interest.

This article is part of the special issue “Wind Energy Science Conference 2017”. It is a result of the Wind Energy Science Conference 2017, Lyngby, Copenhagen, Denmark, 26–29 June 2017.

The presented work was funded by the Federal Ministry of Economic Affairs and Energy of the Federal Republic of Germany under grant number 0325719. The article processing charges for this open-access publication were covered by a Research Centre of the Helmholtz Association. Edited by: Jens Nørkær Sørensen Reviewed by: Niels N. Sørensen and two anonymous referees