Vortex-induced vibrations on wind turbine blades are a complex phenomenon not predictable by standard engineering models. For this reason, higher-fidelity computational fluid dynamics (CFD) methods are needed. However, the term CFD covers a broad range of fidelities, and this study investigates which choices have to be made when wanting to capture the vortex-induced vibration (VIV) phenomenon to a satisfying degree. The method studied is the so-called forced-motion (FM) approach, where the structural motion is imposed on the CFD blade surface through mode shape assumptions rather than fully coupled two-way fluid–structure interaction. In the study, two independent CFD solvers, EllipSys3D and Ansys CFX, are used and five different turbulence models of varying fidelities are tested. Varying flow scenarios are studied with low to high inclination angles, which determine the component of the flow in the spanwise direction. In all scenarios, the cross-sectional component of the flow is close to perpendicular to the chord of the blade. It is found that the low-inclination-angle and high-inclination-angle scenarios, despite having a difference equivalent to up to only a 30

It is found that a good consistency is seen using different variations of the higher-fidelity hybrid RANS–large eddy simulation (LES) turbulence models, like improved delayed detached eddy simulation (IDDES), stress-blended eddy simulation (SBES) and

This study shows that extensive care and consideration are needed when modeling 3D VIVs using CFD, as the flow phenomena, and thereby solver requirements, rapidly change for different scenarios.

Vortex-induced vibrations (VIVs) on wind turbine blades are a phenomenon gaining relevance as wind turbines become larger and more flexible. When the turbine is not in operation, for instance due to grid loss, maintenance or storm conditions or during erection, the blades can experience wind from various directions, which can result in large angles of attack that are close to perpendicular to the chord. In this range of wind directions, deep stall with a high degree of vortex shedding can occur, meaning that a risk of lock-in between structural modes and shedding frequencies increases.

As VIVs are directly depending on vortex shedding frequency and phase between the corresponding loads and motion velocity, engineering models struggle to compute the phenomenon. It becomes especially problematic as the blade shape, by twist and chord length, changes over the blade span, making a simple Strouhal relationship analysis difficult. For this reason, high-fidelity methods such as computational fluid dynamics (CFD) are needed. Examples of this are the works of

Definition of inclination and pitch angles. Reproduced from

The positions of the VIV branches depend on the blade shape, structural properties and flow velocity. As shown in

In a recent study,

The forced-motion method is not a new concept and has been used extensively, especially on cylinder VIVs

In the present study, the approach of forced-motion (FM) CFD analysis of VIVs is studied further in various aspects. The influence of modeling schemes, turbulence models, grids and more is studied using two well-established CFD solvers: one used and developed by the Technical University of Denmark (DTU), EllipSys3D

The study shows that the chosen modeling approach has large effects on the computed power input for cases with low to medium inclination angles, where uncorrelated natural shedding occurs. For cases with high inclination angles, the sensitivity is found to be much lower, as the defined blade motion controls the flow pattern more in this region.

As two different codes are used, various combinations of grid methods, convective schemes, turbulence models and much more can be studied. The setups of the two solvers are based on the experiences, common practices and computational resources of the users (DTU uses EllipSys3D; SGRE uses Ansys CFX), albeit with a desire of being able to capture the same physics. Common in all simulations is the use of forced-motion CFD simulations as described below in Sect.

In order to undertake high-fidelity modeling of VIVs without using a structural coupling framework, the forced-motion (FM) method is used. Here, it is assumed that the structural response of the blade seen during VIVs can be simplified to being purely the structural modes. This assumption works well when the mode shapes and natural frequencies are not altered significantly by the surrounding flow, which is the case for the current study with low-speed airflow. In these simulations, the first edgewise mode has been chosen, as this is the mode being provoked by the investigated flow scenarios when using fully coupled FSI simulations

The aeroelastic model of the IEA 10 MW wind turbine is publicly available from

First edgewise mode shape of the blade from HAWCStab2 along with the polynomial fit used in forced-motion simulations. The effect of the torsional component, which was less than 0.5

For the specific study, some assumptions are made to enable the FM approach. Firstly, as mentioned, it is assumed that the first structural edgewise mode shape is the only motion present. This means that no contribution from static loads or buffeting loads is included in the motion. This assumption aligns well with what was found in previous studies using fully coupled FSI

The EllipSys3D CFD solver

In this study, simulations are based on unsteady Reynolds-averaged Navier–Stokes (URANS)

For the URANS simulations the quadratic upstream interpolation for convective kinematics (QUICK) convective scheme is used, while for IDDES a combination of QUICK (in the RANS region) and fourth-order central difference (in the LES region) is used as described by

Various grids have been tested in the present study. All surface grids are based on the DTU in-house Parametric Geometry Library (PGL) tool

Surface grid and volume mesh hyperbolically grown from the surface for EllipSys3D. Only every second line is shown for clarity.

The grid deformation procedure in the EllipSys3D simulations is based on an explicit algebraic algorithm, transferring the deformation of the surface grid into the volume grid by a blending approach that exploits the block-structured nature of the computational grid.

The deformed grid is computed by enforcing the Cartesian translation and deformation of the surface grid points along the grid lines normal to the surface. To avoid generating highly non-orthogonal grids at the surface, the normal grid lines are rotated according to the present surface-normal direction. Using blending functions in the direction normal to the surface, it is assured that the grid translation and rotation are only enforced in the proximity of the surface of the geometry. This ensures that the original grid quality is conserved at the surface while preserving the original grid far away from the surface. In between the surface proximity region and the far-field region, a blending region is present where the grid quality risks deterioration in the case of large deformations if the blending is not adequately tuned. Typically, the surface deflections are enforced far away from the surface, while the rotations are limited to a region close to the surface. The blending is based on hyperbolic tangent functions, using the normalized curve length along the grid lines normal to the surface. The procedure can easily be tuned for specific cases by calibrating the blending function constants for a severe static deformation using a steady-state computation. The blending function for translatoric deformations is

The Ansys CFX library

In this study, the simulations are based on URANS with a

For

For the CFX grid, a combination of structured and unstructured grids is used to keep more control near the blade while exploiting the unstructured expansion of the grid further away. The different meshes are generated using Pointwise v22.2, allowing the control of the structured mesh. The first cell size normal to the surface is set to

To take into account the motion of the selected mode shape, the mesh is deformed periodically at the mode frequency. The mesh deformation is computed only during the initialization step as the displacement is imposed. This deformation is computed by diffusing the displacement registered on the blade boundary to the neighboring mesh cells. To prevent any cell from folding over, a mesh stiffness is defined. This stiffness is set to increase near the blade boundaries at a cubic rate and after a distance to the blade boundary of 1 m. The obtained mesh displacement at a given time step is depicted in Fig.

The main difference between the two used CFD codes is their discretization methods, with EllipSys3D being a structured solver, while CFX uses unstructured grids. Both of these have pros and cons; the unstructured-grid approach is more flexible in terms of grid manufacturing but often results in a slower performance. In this work, the grid close to the surface was chosen as structured for the CFX solver as well to avoid too rapid a dissipation of the shed vortices, which is found when using an unstructured approach. Further from the surface, the unstructured grid rapidly expands, limiting the cell count, i.e., ensuring faster computations. For the structured grid in EllipSys3D, an expansion of cells also happens when moving far from the surface. The number of cells used also varies between the two setups based on grid sensitivity studies; see more in Sect.

Domain shapes differ between the two, being spherical for EllipSys3D and square for the CFX setup. This should have no impact, as boundary conditions are far from the considered blade.

The turbulence models implemented in the two solvers differ but should have similar capabilities of capturing the vortex shedding with varying degrees of accuracy from URANS

Finally, the blade surface shows discrepancies at the tip. As the meshing methodology differs between the two setups, the tip cap surface used in CFX is flat, while it is rounded in EllipSys3D. This introduces an 8 cm difference corresponding to less than

Discrepancies of the blade surface at the tip between the two setups: EllipSys3D (rounded tip) and CFX (flat tip).

In this paper, aerodynamic power will be defined as positive when injecting power into the structural system and negative when damping the structural response. When calculating aerodynamic power, the mean power over

When considering the risk of VIVs, it is important to realize that the total power

As with the aerodynamic power injected into the structure for a given amplitude, the corresponding power dissipated by structural damping can be found and compared to the aerodynamic power to assess whether the operating point is stable or not.

Structural damping is estimated using modal analysis. For single-degree-of-freedom systems, the energy

Given

To obtain the power dissipation, the energy needs to be divided by the period

An equivalent single-degree-of-freedom system for a given mode can be constructed using modal analysis; thus, the stiffness and damping are replaced by modal stiffness and modal damping for a given mode to compute the energy dissipated when the structure moves by a unit amplitude with a certain mode shape.

With eigenmatrix

Using the method above and HAWCStab2

Various grid configurations have been tested in the present study using varying turbulence models. In the higher-fidelity turbulence models (SAS, SBES and IDDES), the resolved length scale in the LES region depends on the grid cell size itself, meaning that large changes in the grid can lead to large changes in the resulting flow. Two separate grid studies were conducted: first, the EllipSys3D solver using the IDDES turbulence models with different inclination angles and largely varying grid resolutions. The grid setups tested are defined in Table

Note that for the sake of visibility, the figure has the number of cells spanwise on the

Physically, it makes sense that lower-inclination cases are more sensitive to the grid and turbulence model than higher-inclination cases, as the amount of chaotic natural shedding in low-inclination cases is quite high. For higher inclinations, there seems to be much more shedding that is correlated with the motion of the blade, meaning that larger, more ordered vortices are resolved. For the flow case of

This finding indicates that the previously found VIV risk mapping from

Grid refinement cases for the EllipSys3D setup.

Grid refinement cases for the CFX setup. The total number of cells is given for the structured part of the mesh.

Total aerodynamic power per cycle,

Total aerodynamic power per cycle,

Secondly, a grid study using various turbulence models was conducted using the CFX setup and the turbulence models URANS, SAS and SBES for the inclination angle of

As seen, the behavior of the higher-fidelity models, SAS, SBES and IDDES, is very similar, and a large dependency on the grid setups is found. The URANS case, however, does not see this dependency but appears to overshoot the aerodynamic power injection for all grids considered.

Accumulated power in time along with spanwise distribution of average aerodynamic power injection for various time steps in the CFD solvers for flow case P100I50. For EllipSys3D the baseline mesh and IDDES were used. For CFX the baseline mesh and SBES were used.

The sensitivity to time step size for the EllipSys3D simulations was studied for the flow case P100I50 with a 1 m amplitude. The baseline time step was set to

Spanwise distribution of aerodynamic power for flow case P100I50.

For the CFX setup, a similar sensitivity study is performed. The baseline time step is less strict, reaching

Vorticity fields resulting from the turbulence models used along with isosurfaces of

Vorticity fields resulting from the turbulence models used along with isosurfaces of

The high-inclination case has flow coming with an inclination angle

The low-inclination case has flow coming with an inclination angle

Zoomed-in view of the outer part of the blade for URANS (DTU setup), IDDES and SAS turbulence;

These small-scale vortices result in negative accumulated power along the span. The spanwise power distribution is therefore also much less in agreement between the lower- and higher-fidelity turbulence models than in the high-inclination case. The lower-fidelity URANS turbulence models predict high spanwise correlation, resulting in a high power injection between 1560 and 2000 W. The higher-fidelity models, however, predict the situation to be positively damped with an accumulated power of

It is important to note that for IDDES, SBES and SAS, this flow case resulted in a positive power injection for lower grid resolution – presented in Figs.

Spanwise distribution of aerodynamic power for flow case P100I30.

Effective power,

Figures

Using both CFD setups, sweeps of amplitudes of up to 2 m were conducted using the various turbulence models. URANS and IDDES simulations were conducted using the EllipSys3D setup, while SBES and SAS simulations were performed on the CFX setup. By these sweeps an approximation of the vibration level can be given, using the structural damping of the considered blade. As presented in Sect.

As seen for the high-inclination case with

A comprehensive study has been conducted, investigating the impacts of various simulation choices for vortex-induced vibrations of wind turbine blades. Common for all studies was the forced-motion CFD approach, where the structural first edgewise mode was imposed as a motion in the CFD simulations, which in earlier work has been shown to be feasible. Two independent CFD methodologies were used: the DTU in-house EllipSys3D solver and the commercial Ansys CFX solver used at Siemens Gamesa. Various grid strategies and turbulence models were tested and compared, showing a high degree of sensitivity for low-inclination flow, meaning spanwise flow closer to perpendicular to the span rather than along the span. It is found that for these inclinations, care is needed regarding the selection of the turbulence model and grid. The observed differences are due to the artificial coherency in the vortex structures created by unsteady RANS models, leading to a high input of aerodynamic power. For coarse grids, the URANS region of the higher-fidelity DES-like turbulence models becomes too big, leading to similar results to those for pure URANS simulations. For finer grids, the higher-fidelity models resolve the more chaotic smaller-scale vortices, which breaks the coherence and power injection. For higher-inclination cases, the sensitivities to the grid and turbulence models are much lower, as the degree of chaotic natural shedding is low compared to the coherent structures, which can be resolved fairly well even using URANS turbulence.

This leads to the main conclusion of the present study: a lot of care needs to be taken when simulating vortex-induced vibrations of wind turbine blades. Various conditions will need separate sensitivity investigations in order to ensure the accuracy of the results. This is important since it is otherwise a risk that computations that are much too heavy are conducted for cases that do not need it. Even worse, the computations that were found to be well resolved for one case may fail to predict the VIVs in other cases.

The topic of VIVs is becoming increasingly relevant with the increasing sizes of wind turbines, and much more research is needed. As a continuation of the current study, an expansion on the parametric space is needed to make final conclusions on turbulence models and grid requirements. This study shows that the necessity of high-fidelity turbulence and fine grids is highly dependent on flow scenario. As of now, no general rule of thumb about how and when to use various models can be justified. This would need a larger mapping of flow cases and rotor designs. However, the tendency seems to be that the need for higher accuracy increases with the degree of natural shedding along the blade, meaning that low inclinations are more difficult to compute correctly.

Even though forced-motion simulations have the possibility of being more efficient than fully coupled FSI simulations, the simulation time needed for broad mappings is still high, especially if various amplitudes or flow velocities are needed. By use of reduced-order modeling, the number of simulations needed could possibly be reduced significantly.

The current study only considers clamped single blades undergoing the first edgewise blade mode vibration. As wind turbines are coupled systems, the coupled rotor modes should likewise be studied. This highly increases the complexity as the modes of a wind turbine are many, and the motion of the individual blades will then depend on the azimuth position.

CFD – computational fluid dynamics

VIV – vortex-induced vibration

FM – forced motion

FSI – fluid–structure interaction

LES – large eddy simulation

IDDES – improved delayed detached eddy simulation

URANS – unsteady Reynolds-averaged Navier–Stokes

SAS – scale-adaptive simulation

SBES – stress-blended eddy simulation

QUICK – quadratic upstream interpolation for convective kinematics

AoA – angle of attack

DTU – Technical University of Denmark

SGRE – Siemens Gamesa Renewable Energy

IEA – International Energy Agency

PGL – Parametric Geometry Library

VCO – vertex-centered orthogonality

SST – shear stress transport

The geometry and the structural model of the considered wind turbine are publicly available at

CG conducted EllipSys3D simulations, did analysis of the results and did the main writing of the paper. FH-M did the majority of the CFX calculations, analysis and methodology implementation in CFX, as well as participating in the redaction and reviewing of the paper. NNS conducted EllipSys3D simulations and took part in the analysis and the reviewing of the paper. GRP conducted HAWCStab2 analysis and damping estimations, supported on analysis of EllipSys3D simulations, and reviewed the paper. Valuable support was provided by PJ, AA and BD regarding the analysis of CFX results, methodology implementation in CFX, and reviewing the paper. All authors contributed to editing the paper.

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 made in the text, published maps, institutional affiliations, or any other geographical representation in this paper. While Copernicus Publications makes every effort to include appropriate place names, the final responsibility lies with the authors.

Computational resources were provided by the DTU Risø cluster Sophia

This research is part of the PRESTIGE project supported by Innovation Fund Denmark (grant no. 9090-00025B).

This paper was edited by Johan Meyers and reviewed by two anonymous referees.