Ice accretion on wind turbine blades causes both a change in the shape of its sections and an increase in surface roughness. These lead to degraded aerodynamic performances and lower power output. Here, a high-fidelity multi-step method is presented and applied to simulate a 3 h rime icing event on the National Renewable Energy Laboratory 5 MW wind turbine blade. Five sections belonging to the outer half of the blade were considered. Independent time steps were applied to each blade section to obtain detailed ice shapes. The roughness effect on airfoil performance was included in computational fluid dynamics simulations using an equivalent sand-grain approach. The aerodynamic coefficients of the iced sections were computed considering two different roughness heights and extensions along the blade surface. The power curve before and after the icing event was computed according to the Design Load Case 1.1 of the International Electrotechnical Commission. In the icing event under analysis, the decrease in power output strongly depended on wind speed and, in fact, tip speed ratio. Regarding the different roughness heights and extensions along the blade, power losses were qualitatively similar but significantly different in magnitude despite the well-developed ice shapes. It was found that extended roughness regions in the chordwise direction of the blade can become as detrimental as the ice shape itself.

Arguably, wind energy will lead the energy transition in Europe. In 2022, it produced 15 % of the total generated electricity

Texas region electricity generation by wind energy in February 2021. Winter storms occurred between 10 and 20 February. Source: US Energy Information Administration, Hourly Electric Grid Monitor, available at

Indeed, ice may affect wind turbines in several ways. The first visible effect is the blade aerodynamics degradation, reducing the wind turbine power output. Instrumentation and controller errors may follow. As more ice is accreted, the structural behaviour changes as well, and the fatigue life of the structure can be affected. Ice shedding may also be a severe threat, endangering equipment and people nearby and causing significant load imbalances on the rotor. In many cases, a shutdown may become unavoidable.
For these reasons, wind turbines operating in cold regions must be equipped with an ice protection system (IPS). Electro-thermal IPSs provide a possible solution. These devices are energy-consuming, especially if run in anti-icing mode

The problem of ice accretion on wind turbines has been long studied but is still of great interest. In 2002, the International Energy Agency (IEA) established a cooperation group of international experts, Task 19, to study wind energy in cold climates. The working group has been running ever since. A recent report by the Task 19 group reviewed the technologies available for wind turbines operating in cold climates

Depending on atmospheric conditions, different types of ice can form. Their standard classification is

When ice is formed on an airfoil, two main factors alter its performance: the ice shape and the increase in surface roughness. While the former can be assessed numerically, the latter needs to be estimated either experimentally or using empirical correlations. During ice accretion, the roughness height evolves in a complex way with both space and time

Several numerical studies on power losses due to ice accretion are available in the literature. An exhaustive review was carried out by

One of the first efforts to study ice accretion numerically on a wind turbine was carried out by

In 2013,

Finally,

These results do not show a clear trend in power losses. At 11 m s

A study by

In view of the above, the aim of this work is to (1) perform a high-fidelity ice accretion simulation on the NREL 5 MW wind turbine blade, (2) compute the aerodynamic performances of the iced blade sections as a function of roughness, and (3) assess the effect of icing in operating conditions. The icing event was long enough for streamlined, protruded ice shapes to form and the effects of ice shapes and roughness to be combined. The work was carried out using both open-source software and in-house codes. We presented a preliminary work in this context in

The paper is structured as follows. The methodology is presented in Sect.

The NREL 5 MW reference wind turbine was analysed in this work. The blade structural and aerodynamic designs are based on the Dutch Offshore Wind Energy Converter (DOWEC) project

The aero-servo-elastic response of the wind turbine was modelled with OpenFAST (

Airfoils composing the wind turbine blade.

The first step involved reproducing these experimental data with a CFD solver, SU2

The second step was the simulation of the icing event. The atmospheric conditions of the icing event on the wind turbine are reported in Table

Atmospheric conditions during the icing event studied.

The third step was the computation of the aerodynamic coefficients of the iced sections with SU2. Roughness was modelled using an equivalent sand-grain approach. Two values of

The

The final step was the computation of the power curve of the wind turbine before and after the icing event with OpenFAST. Both steady and turbulent winds were considered. Atmospheric turbulence was modelled as defined by the IEC for the Design Load Case (DLC) 1.1 of a Category B wind turbine

Two main factors change the performance of an iced airfoil: the modification of the airfoil shape and the increase in surface roughness. While the former is computed numerically, the latter is usually estimated with empirical correlations. During ice accretion, the roughness height evolves in a complex way with both time and space

Depending on the value of

Although the use of the relation for

However, these relations do not include the effect of time on

The SU2 code solves RANS equations using an edge-based finite volume discretisation in space on general unstructured grids. The convective and viscous fluxes are then evaluated at the midpoint of an edge. An upwind flux difference splitting (FDS) numerical scheme was chosen to solve the convective fluxes in the incompressible solver. Second-order accuracy of the numerical method was obtained by applying a monotonic upstream-centered scheme for conservation laws (MUSCL) for flux reconstruction. The gradients of the variables at each node were reconstructed using the Green–Gauss theorem. During reconstruction, gradients were limited using the slope limiter by

Steady-state problems are solved with a pseudo-time-step technique, in which the solution is marched in time until the time derivative term vanishes and a steady-state solution is reached. An adaptive Courant–Friedrichs–Lewy (CFL) method was used for convergence acceleration in pseudo-time. Convergence was reached when the root mean square of the residual in the entire domain was reduced by at least 3 orders of magnitude for all variables, and the normalised relative difference between two consecutive iterations of lift and drag coefficients, averaged over 100 iterations, was smaller than 10

Each airfoil was simulated approximately between the positive and negative stall angle with a step of 2

Roughness was included in CFD simulations by applying the Boeing extension for the SA turbulence model. The rough-wall model was developed by Spalart

An unstructured hybrid mesh was used to discretise the domain. It was generated using the code uhMesh

Fine grid (NACA 64

During the icing event, we assumed that the presence of roughness due to ice in the stagnation point region caused the transition to a fully turbulent flow. Thus, flow transition was neglected from the beginning of the icing event. This modelling hypothesis was necessary since no roughness-induced transition model is currently available in SU2. The fully turbulent hypothesis may affect two results, i.e. the ice accretion simulations and the aerodynamic coefficients of the iced airfoils.

Regarding flow transition on the iced airfoil, it is interesting to analyse the results of the rough-flat-plate experiment by

Regarding ice accretion simulations,

The problem of ice accretion is clearly unsteady. As ice grows on the surface, the shape of the airfoil changes, modifying the flow field, the droplet trajectories, and the ice shape as well. During this process, two timescales can be identified. One is related to the growth of ice, and the other is related to the modification of the flow field due to ice growth. The former is, in general, much larger than the latter. For this reason, a quasi-steady, multi-step approach must be adopted. The total accretion time is divided into smaller intervals. In each sub-interval, the flow field and droplets' trajectory are kept constant, and an ice accretion step is performed. The interaction between the gas and the liquid (droplet) phase can be taken into account by using an Eulerian two-fluid model

Each of these tasks was performed by different software. Once more, SU2 was used for the computation of the flow field. The Lagrangian particle tracking PoliDrop was used to compute the trajectories of the water droplets and the resulting collection efficiency

In PoliDrop, we used an iterative method to compute the collection efficiency up to an arbitrary precision. The seeding region was updated at each iteration by adding new particles where needed. A uniform seeding front was initialised as a linear grid with equally spaced elements. At the first iteration, the parcels not hitting the airfoil were identified and removed so that the seeding front was reduced in size. The first two parcels flying just above and below the object were not removed so that the impingement limits were refined as well. Then, at each iteration, elements were incrementally split, evolving the current cloud front and computing the collection efficiency

Blade discretisation and sections chosen for ice accretion.

It is clear that the choice of the number of time steps in a multi-step ice accretion simulation and the accuracy of the Lagrangian particle tracking are crucial to obtain an accurate solution efficiently. A proper combination of these parameters is required. These were chosen by comparing the numerical solution with three experimental test cases by

Once a satisfactory set-up for icing simulations was found, the icing event on the full blade was simulated. Icing was monitored on five independent sections, as shown in Fig.

The quasi-steady approximation was applied independently to each section, using different time steps according to the local ice accretion rate. The specific time steps used for each section are presented in Sect.

Due to the high uncertainty in roughness height estimation, two values for

It will be shown in Sect.

To quantify the effect of this modelling choice on airfoil performance and power losses, besides using two different roughness heights, we also considered two regions to which roughness was applied. In the first case, it was applied to the ice shape only. This case is denoted in the text by adding the subscript

Definition of the

To validate the set-up of the CFD solver, the aerodynamic coefficients of the clean airfoils of the blade were computed and compared with experimental data. The aerodynamic coefficients of DU airfoils were measured by Ruud van Rooij of the Delft University of Technology at a Reynolds number of

Roughness heights

Aerodynamic coefficients of the NA18 airfoil.

Aerodynamic coefficients of the DU21 airfoil.

Aerodynamic coefficients of the DU25 airfoil.

Aerodynamic coefficients of the DU30 airfoil.

Aerodynamic coefficients of the DU35 airfoil.

Aerodynamic coefficients of the DU40 airfoil.

First, we analyse the results for fully turbulent flows. All fully turbulent simulations showed satisfactory grid convergence for almost every aerodynamic coefficient computed. The estimate of the discretisation error was computed with the GCI method

When the algebraic BC transition model was included in the system of equations, the aerodynamic coefficients were accurately predicted for all airfoils for attached flows, regardless of their relative thickness. The absolute value of the maximum lift coefficient increased, at both positive and negative stall. This led to more accurate predictions of positive stall for

The Boeing extension for the SA model was then tested to compare the numerical results with the law of the wall for rough surfaces. The relation is presented in Eq. (

Law of the wall using Boeing extension for the SA turbulence model. NA18 airfoil,

Two different approaches were tested for ice accretion. These were almost equivalent in overall computational time. In the first one, the collection efficiency

Test conditions of AERTS test cases.

A time step of 15 min was used when

PoliMIce simulations of three AERTS test cases. Each column represents the same test case. The three test cases have the same atmospheric conditions and only differ in total ice accretion time (left: 30 min; centre: 60 min; right: 90 min). In each row the same numerical set-up is used for the multi-step ice accretion (top:

Comparison between PoliMIce simulations, LEWICE simulations, and experiments of AERTS test cases.

Moreover, a noticeable reduction in the elapsed real time for the entire 90 min simulation was found (approx. 13 %). For these reasons, the approach consisting of a high number of time steps with lower accuracy for

The set-up with

The local boundary conditions computed at the beginning of the icing event are reported in Table

Local boundary conditions of the five sections under analysis.

There was no need to update the boundary conditions during ice accretion. For instance, the AoA of Section B increased by 0.35

Non-dimensional comparison of the ice shapes on Sections A–E.

Multi-step ice accretion on Section B. The grid for the computation of the aerodynamic coefficients is superimposed onto the computed ice shape, highlighting the removal of highly concave regions. The region within the red box is enlarged in Fig.

Detail of the computational grid on the final ice shape of Section B, showing the orthogonality of the grid. The region corresponds to the red box shown in Fig.

The ice shapes on Sections A, B, and C (i.e. NA18 sections) were very similar. Their main difference was the length of the horn, which decreased towards the root of the blade. Some small secondary protrusions were formed on the main ice shape. These are due to some small oscillations of the collection efficiency, which eventually got amplified step after step because the geometry was not smoothed unless strictly required by the grid generator. Section E was almost unaltered. On this section, 0.42 kg m

The aerodynamic coefficients of the iced sections were then computed in the four cases defined in Sect.

Aerodynamic coefficients of Section A.

Aerodynamic coefficients of Section B.

Aerodynamic coefficients of Section C.

Results of the CFD simulations are shown in Figs.

Aerodynamic coefficients of Section D.

Aerodynamic coefficients of Section E.

Lift-to-drag ratio of Section B considering different cases. Lines represent airfoil efficiency in various cases. Shaded areas represent different contributions to loss in efficiency, providing a qualitative superposition of effects.

Aerodynamic penalties on Sections A–E at

We start considering the

We now consider the two cases of extended roughness:

In the previous section, it was shown that the differences between

The

Then, the power curves were computed with a steady inflow. They are shown in Fig.

Next, the power curves were computed with the turbulent inflow prescribed by the IEC in DLC 1.1. They are shown in Fig.

Power curve with a steady inflow.

Power losses with a steady inflow.

Power curve with a turbulent inflow.

Power losses with a turbulent inflow.

As visible from Figs.

Weibull-averaged power loss computed for the current study and compared with other authors.

From these results, it is clear that the research on numerical simulations of icing on wind turbines should focus on water impingement limits and roughness height. Regarding the impingement limits, better results may be obtained by considering unsteady ice accretion simulations. However, the detail required for time discretisation is unknown. This is not sufficient since it is not possible to obtain reliable results by using the classical empirical correlations for

In this paper, we conducted a detailed numerical simulation of ice accretion on the NREL 5 MW wind turbine blade using the BEM approach. To increase the precision in the computation of ice shapes, we proposed to use independent time steps during a multi-step ice accretion simulation. Moreover, we showed that it is possible to reduce the computational time required for ice accretion simulations by increasing the error in the collection efficiency and adding a very small ice thickness during each step.

Then, we analysed the effect of roughness on the aerodynamic performances of the iced sections. Due to the uncertainty of these parameters, we considered two roughness heights and two roughness extensions on each section. We computed the aerodynamic coefficients for each case, and we assessed whether the aerodynamic penalty was due to ice, roughness, or both. It was shown that roughness can significantly affect the aerodynamics of an iced section, even when a complex ice shape is present, as long as

Finally, we computed the power curves for the low-roughness (

This high variability in the prediction of power losses suggests two main areas of research for future work. The first one should be focused on the correct detection of the impingement limits of water droplets in the highly unsteady environment in which wind turbines work. The second one should be focused on the characterisation of roughness distribution and height on real wind turbine blades.

Data are available upon request from the corresponding author.

FC contributed to the idea of the method, to the execution of the simulations, and to the writing of the paper. AG contributed to the idea of the method and to the writing of the paper.

The contact author has declared that neither 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.

The authors would like to acknowledge Valentina Motta from GE Renewable Energy for the support provided during the early stage of this research.

This paper was edited by Jens Nørkær Sørensen and reviewed by three anonymous referees.