A Survey of the Quasi-3D Modeling of Wind Turbine Icing

Abstract

Wind turbine icing has been the subject of intensive research over the past two decades, primarily focusing on applying computational fluid dynamics (CFD) to 2D airfoil simulations for parametric analysis. As a result of blades’ airfoils deformation caused by icing, wind turbines experience a considerable decrease in aerodynamic performance resulting in a substantial loss of productivity. Due to the phenomenon’s complexity and high computational costs, a fully 3D simulation of the entire iced-up rotating turbine becomes infeasible, especially when dealing with several scenarios under various operating and weather conditions. The Quasi-3D steady-state simulation is a practical alternative method to assess power loss resulting from ice accretion on wind turbine blades. To some extent, this approach has been employed in several published studies showing a capability to estimate performance degradation throughout the generation of power curves for both clean and iced wind turbines. In this paper, applying the Quasi-3D simulation method on wind turbine icing was subject to a survey and in-depth analysis based on a comprehensive literature review. The review examines the results of the vast majority of recently published studies that have addressed this approach, summarizing the findings and bringing together research in this area to conclude with clear facts and details that enhance research on the estimation of wind turbine annual power production loss due to icing.

1. Introduction

The transition to renewable energy is globally accelerating to satisfy rising energy consumption and mitigate climate change. Over the past decades, investment in clean energy technologies has gradually increased, and it needs to triple by 2030, according to the IEA world energy outlook [1]. Wind energy is an important form of renewables that is increasingly employed in conjunction with other energy resources to meet the rapidly expanding energy demand. Due to the increasing rotor size and technology optimization, wind turbine efficiency is expected to experience further growth to be widely recognized as one of the most efficient technologies for electrical energy production from a renewable source. Consequently, wind power generation has grown rapidly to become an essential part of the energy market and research worldwide [2]. However, wind energy is mainly dependent on the site of its implementation.

In Nordic countries, the wind potential is very high during winter. In the winter, wind turbines generate more power and are thus able to service a more significant demand owing to increased heating needs. Countries with a strong wind potential and severe climates want to expand the use of renewables [3]. Wind turbine technology must adapt to severe climatic circumstances characterized by frequent low-temperature episodes, particularly icing, in these locations.

Wind turbine icing is defined as the accumulation of atmospheric ice, primarily on rotor blades, during specific meteorological conditions at ambient temperatures below the water freezing point. In certain weather conditions, clouds or supercooled fog can emerge at lower altitudes with a severe temperature inversion leading to ice accretion over wind turbine blades that can last for days or even weeks [4]. In addition to operational, maintenance, and life cycle penalties, the ultimate impact of icing is the reduction in the energy efficiency of wind turbine power generation. Even a small ice deposit on the leading edge of blades’ airfoils has significant consequences on its aerodynamic performance leading to losses in energy production [5]. Therefore, Ice Protection Systems (IPS) and ice detectors became essential equipment to reduce icing effects in wind farms. Nevertheless, little evidence of their effectiveness, adequacy, relevance, or performance optimization has been published, whereas different systems may be more effective for different configurations [6]. Optimizing the performance of wind turbines under icing conditions presents several technical and operational challenges. These challenges depend highly on the site-specific circumstances, the technology employed for ice detection, the nature of the production losses, and the method used to analyze and estimate these losses. To satisfy the demands of the expanding wind industry in northern climates, developing a system capable of detecting ice based on meteorological conditions and evaluating the consequent energy loss is essential to guide wind turbine operators toward optimal operating and de-icing strategies.

Wind turbine icing research relies more on numerical models than experimental approaches to analyze icing consequences and enhance the efficiency of the IPS. Computer simulation may assist in predicting and analyzing wind turbine blades iced airfoils, consequently determining the aerodynamic drop due to icing and the energy required for de-icing under specified weather conditions. In addition, simulation is a robust, less costly method of compliance than experimental testing. With exact and dependable codes, it may be feasible to limit the dependence on costly wind tunnel experiments [7,8].

Several studies conjugate the CFD flow and icing simulations with the Blade Element Momentum Theory (BEMT) to generate power curves for iced wind turbines. Some of these approaches were implemented using in-flight icing codes. In contrast, others were special-purpose codes, and most were established methodologies using commercial computer-aided engineering (CAE) software. A survey of these attempts is presented in this paper as progress is achieved on each covered subject. It is also noteworthy to indicate that almost all the published wind turbine icing research consulted in the literature addressed the icing problem for horizontal-axis wind turbines (HAWTs). On the other hand, little research has examined icing on the vertical axis wind turbines (VAWTs). Typically, the geometry of the blades of a common HAWT comprises segments of various forms. This particular geometry requires exclusively three-dimensional modeling of the sophisticated biphasic phenomenon.

However, icing affects more than just the blades; it affects the whole wind turbine with different 3D effects, such as airflow in the radial direction [9]. Furthermore, blade rotation affects ice formation with additional phenomena, such as ice shedding. Therefore, a full three-dimensional simulation of the entire turbine during rotation is considered necessary to capture the flow’s transition and the 3D effects. Furthermore, even a simulation of the entire wind park should incorporate the influence of the aerodynamic wake downstream to assess production under certain icing conditions [10].

Given the difficulties of fully 3D simulation, especially for multiple operation scenarios, the Quasi-3D simulation is a practical alternative approach examined in several published studies to estimate power production loss due to wind turbine icing. First, the method considers 2D-CFD simulations for airfoils from chosen blade sections to estimate their aerodynamic performance for both clean and iced cases. Then, the BEMT is applied through the extrapolation of the airfoils’ aerodynamic performance to generate power curves for the entire rotor.

This review study investigates recent advancements in wind turbine icing modeling and simulation. It offers guidelines on the theory and application of the Quasi-3D simulation approach to generate the power curve in clean and iced cases, along with a strategy and recommendation to assess production loss under various icing conditions. The paper comprises two main sections. The first is dedicated to highlighting the Quasi-3D simulation approach theory and application. It presents the BEMT along with the codes used in its applications. In addition, CFD is presented in light of simulation concerns associated with iced airfoils. Theoretical concepts have been addressed according to their relevance to the presented simulation approach. Section 3 is devoted to reviewing, discussing, and summarizing the academic research conducted on the above-addressed subjects. Finally, a comparison matrix on the reviewed research is presented to conclude with a synthesis to provide the reader with state-of-the-art recommendations using simulation approaches for estimating wind turbine power loss due to icing.

2. Quasi-3D Modeling Approach

The literature review showed that the Quasi-3D analysis provides acceptable results for wind turbines’ power curve generation comparable to the full turbine 3D simulation at significantly lower computational costs [11,12]. The proposed approach calculates the power coefficient through the extrapolation of aerodynamic coefficients from two-dimensional airfoils for selected sections of wind turbine blades. The method uses a combination of CAE tools, including CFD analysis software and a wind turbine multibody dynamic analysis simulation tool.

2.1. Blade-Element-Momentum Theory

The Blade Element Momentum Theory (BEMT) is a model that combines the blade element theory (BET) [13] and the momentum theory (MT) [14]. It is generally applied during wind turbine design to assess turbines’ aerodynamic performance and power curves [15,16]. In addition, BEMT can be employed in icing-induced power loss estimating since it performs the latter calculations for clean and iced wind turbine cases [16]. Its procedure is based on dividing the blade into several segments, as seen in Figure 1. Several assumptions apply. First, there are no aerodynamic interactions between sections. Second, we neglect the velocity component in the spanwise direction and the three-dimensional effects. Finally, each section’s lift and drag characteristics, using a corresponding angle of attack and an incident resultant velocity on the cross-sectional plane, determine the forces acting on the blades [13,14,15].

The thrust (normal force $T_N$) and torque (tangential force $T_Q$) acting on the annular section of the rotor are a function of the axial ($a$) and tangential ($a^{\prime }$) induction factors can be described by equations from the MT [13].

$$d{T}_N=\rho V_a{}^{2}4a\left(1-a\right)\pi rdr$$

(1)

$$d{T}_Q=4a^{\prime }\left(1-a\right)\rho V_a\omega \pi r^{3}dr$$

(2)

where, $V_a$ is the air velocity and $\omega$ the rotational speed of the rotor.

According to BET, the lift and drag forces are, respectively, perpendicular and parallel to a relative wind speed ($V_{rel}$). This relative wind speed is the sum of the wind velocity vector at the rotor ($V_a\left(1-a\right)$), and the wind velocity vector due to the rotation of the blade ($\omega r\left(1+a^{\prime }\right)$) [13,14]. The relationships between angles, forces, and velocities in one section of a blade are described by Equations (3) to (5) (see Figure 2).

$$\varphi ={\tan }^{-1}\left[\frac{1-a}{\left(1+a\right){\lambda }_r}\right]$$

(3)

$$\alpha =\varphi -{\theta }_P$$

(4)

$$V_{rel}=\frac{V_a\left(1-a\right)}{\sin \varphi }$$

(5)

where $a$ is the axial induction factor, ${\lambda }_r=\omega r/V_a$ is the local speed ratio, $\alpha$ is the angle of attack, $\varphi$ is the angle relative to the wind, and ${\theta }_P$ is the pitch angle.

Based on BET, the thrust and torque acting on the annular rotor section are presented in Equations (6) and (7).

$$d{T}_N=\frac{1}{2}B\rho V_{rel}^2\left(C_l\cos \varphi +C_d\sin \varphi \right)cdr$$

(6)

$$d{T}_Q=\frac{1}{2}B\rho V_{rel}^2\left(C_l\sin \varphi -C_d\cos \varphi \right)crdr$$

(7)

where $B$ is the number of blades and $c$ is the airfoil chord.

As known from the BEMT, a change of momentum of the air passing over the swiping area is due to the blade element force. Thus, the flows passing through contiguous disks do not interact between them. However, this state is only applicable if the axial flow induction aspect is uniform and does not change radially, as shown by Burton et al. [14].

Using 2D airfoil characteristics, the axial and tangential flow induction factors $a$ and $a^{\prime }$ can be estimated iteratively [12] by using Equations (8) and (9) [13,14]:

$$\frac{a}{1-a}=\frac{{\sigma }_r C_x}{4{\sin }^2\varphi }$$

(8)

$$\frac{a^{\prime }}{1-a}=\frac{{\sigma }_r C_y}{{\lambda }_r{\sin }^2\varphi }$$

(9)

where $C_x=C_l\cos \varphi +C_d\sin \varphi$, $C_y=C_l\sin \varphi -C_d\cos \varphi$, $C_l$ is the lift coefficient, $C_d$ is the drag coefficient and ${\sigma }_r$ is the chord solidity, defined as the total blade chord length ($c$) at a given radius ($r$) divided by the circumferential length at that radius:

$${\sigma }_r=\frac{B}{2\pi }\frac{c}{r}$$

(10)

An iterative approach that entails initializing a and a′ to zero, assuming $C_d=0,$ is necessary to discover the performance characteristics of a rotor, i.e., how the power coefficient fluctuates over a broad range of tip speed ratios. Because drag in connected flows is brought on by skin friction and has no bearing on the pressure drop over the rotor, drag is not included in the computation of the flow induction factors [14]. The calculation of $\varphi$, $C_l$, and $C_d$ follows the identification of the induction factors, and this procedure is repeated until convergence is attained [13,14]. Equations (4) and (9) can be used to determine the torque using the final results for $a$, $a^{\prime }$, $\varphi$, $C_l$, and $C_d$ [14]:

$$dQ=4a^{\prime }\left(1-a\right)\rho V_a\omega \pi r^{3}dr-\frac{1}{2}B\rho V_{rel}^2\left(C_l\sin \varphi -C_d\cos \varphi \right)crdr$$

(11)

Finally, each annulus’ contribution to power is integrated to give [13]:

$$P={\int }_r^R\omega dQ$$

(12)

Additionally, the power coefficient is given by [13]:

$$C_P=\frac{P}{P_{wind}}=\frac{{\int }_r^R\omega dQ}{\frac{1}{2}\rho \pi R^2{V}_a{}^3}$$

(13)

The power coefficient C_p of the wind turbine depends on the radius $r$, pitch angle $\beta$, angle of incidence $\alpha$, upstream wind speed $V$, and rotational speed $\omega$ of the airfoils of the considered sections of the blade in addition to the number of blades $B.$ The relative velocity $V_r$, which serves as an input parameter for the CFD calculations, can replace all of the previously mentioned parameters of the velocities triangle of airfoils.

2.1.1. Improved BEMT

From the perspective of Bai and Wang [15], adopting a CFD-BEM mixed approach to analyze wind turbine aerodynamic performance is problematic when considering the accuracy of numerical methodologies. The BEMT is unreliable for predicting the distribution of aerodynamic loads on wind turbine blades, especially in situations involving the separation of the boundary layer on the airfoil suction side [15], a phenomenon that is commonly expected for the iced airfoils. Dynamic stall significantly raises yaw moments and the blade’s cyclic loads [17]. The CFD-BEM approach cannot predict the flow field created by a finite number of blades. It predicts thrust accurately but tends to overestimate the power.

Regarding the analysis of three-dimensional flows, the BEMT method has drawbacks because of the presumptions indicated at the beginning. Therefore, the CFD-BEM approach must increase its accuracy by incorporating the 3D impacts surrounding the blade while estimating the power curve of a wind turbine following an icing event [15]. As a result, some corrections have been developed to increase the BEMT’s predictive accuracy. The 3D effects are typically insignificant on a large segment of a wind turbine blade but are considerable around the tip and the hub region. 3D effects are also significant in modeling the airflow turbulence along the radial direction [18]. Some sections of wind turbine blades may operate at high local angles of attack, resulting in flow separation and turbulent wakes. Several corrections must be considered to model these 3D effects, including Spera’s correction, Du-Selig stall delay model, and Prandtl’s tip loss factor [15,19,20]. These correction models are addressed in the following:

Prandtl’s Tip Loss Factor

As air flows around the blade’s tip from the lower to the upper surface, the lift will be reduced, and consequently, the power near the tip is reduced. This happens because a blade’s suction side has lower pressure than the pressure side. It is more pronounced in turbines that have fewer, larger blades. The correction factor $F$ (see Equation (14)) is presented, primarily affecting the forces derived from momentum theory:

$$F=\left(\frac{2}{\pi }\right){\cos }^{-1}\left[\mathit{exp}\left(-\left\{\frac{\left(B/2\right)\left[1-\left(r/R\right)\right]}{\left(r/R\right)\sin \varphi }\right\}\right)\right]$$

(14)

From Equation (14), the angle of relative wind ($\varphi$), the number of blades ($B$), and the position on the blade ($r/R$) all affect this correction factor F. Close attention must be paid to the angle in the inverse cosine, which must be expressed in radians [19].

Stall Delay Model

Compared to a static airfoil in a wind tunnel, the stall region in revolving blades starts in places with a higher angle of attack. Centrifugal force can lessen the unfavorable pressure gradient that forces an airfoil to stall. The following laminar boundary layer theory can be used to characterize an aerodynamic stall [13] mathematically.

$$C_{l, 3D}=C_l+3{\left(\frac{c}{r}\right)}^2\Delta C_l$$

(15)

$$C_{d, 3D}=C_d+3{\left(\frac{c}{r}\right)}^2\Delta C_d$$

(16)

where, $\Delta C_l$ and $\Delta C_d$ are the variations in lift and drag coefficients found in the unseparated flow, $c/r$ is the local chord length normalized according to the radial direction. The induction factors can be stated as follows when taking into account the impacts of tip loss and stall delay [15]:

$$a=\frac{C_x{\sigma }_r}{4F{\sin }^2\varphi +C_x{\sigma }_r}$$

(17)

$$a^{\prime }=\frac{C_y{\sigma }_r\left(1-a\right)}{4F\lambda {\sin }^2\varphi }$$

(18)

Viterna—Corrigan (VC) Stall Model

This model’s foundation is that HAWTs have a large aspect ratio and a flow field resembling a 2D airfoil. Thus, the lift coefficient before the stall angle of attack has been determined using the lifting line theory. The VC model is used to estimate the lift and drag coefficients for an angle of attack ($\alpha$) larger than the angle of attack in which the maximum coefficient is recorded (${\alpha }_s$), and is expressed as follows when the flow enters the fully formed stall area [15]:

$$C_l=\frac{1}{2}{C}_{d,max}\sin 2\alpha +\frac{K_L{\cos }^2\alpha }{\sin \alpha }$$

(19)

$$C_d=C_{d, max}{\sin }^2\alpha +K_B\cos \alpha$$

(20)

where, $K_L$ and the $K_D$ are:

$$K_L=\left[C_{l,s}-C_{d,max}\sin {\alpha }_s\cos {\alpha }_s\right]\frac{\sin {\alpha }_s}{{\cos }^2{\alpha }_s}$$

(21)

$$K_D=\frac{C_{d,s}-C_{d, max}{\sin }^2{\alpha }_s}{\cos {\alpha }_s}$$

(22)

where, $C_{l,s}$ and $C_{d,s}$ are, respectively, the lift and drag coefficients at an angle of attack ${\alpha }_s$ of 20° in which $C_{d,max}$ depends on the aspect ratio, as follows [15]:

$$C_{d,max}=\{\begin{array}{c}1.11+0.018 AR, AR\le 50\\ 3.01, AR>50\end{array}$$

(23)

Spera’s Correction

In the turbulent wake state, Spera recognized an empirical link between the thrust coefficient ($C_T$) and the angle of attack, which is expressed as [15]:

$$C_T=\frac{{\sigma }_r{\left(1-a\right)}^2{C}_x}{{\sin }^2\varphi }$$

(24)

If $C_T>0.96$, the axial induction factor is:

$$a=0.143+\sqrt{0.0203-0.6427(0.889-C_T}$$

(25)

whereas if $C_T<0.96$, then the axial induction factor is solved using Equation (19).

2.1.2. BEMT-Based Software

Several multibody dynamic analysis and simulation codes are available in the literature for wind turbine design and performance. These codes depend on the BEMT to estimate the rotor power throughout extrapolating polar data to $360°$ of airfoil incidence. The extrapolated polar data are then to be used to simulate the rotor. Most of these codes are free or open-source programs. Some are products from the National Renewable Energy Laboratory (NREL), such as OpenFAST and WT_Pef. The latter was later removed from distribution and replaced with AeroDyn software. The specifications of the most common BEMT-based codes are summarized below:

• XFOIL is an interactive program based on the panel method to design and analyze subsonic isolated airfoils. Given the geometry of a 2D airfoil, Reynolds, and Mach numbers, XFOIL can calculate the airfoil’s pressure distribution and lift and drag coefficients. JavaFoil, Vortexje, and QBlade are examples of similar panel method-based software.
• XTurb-PSU is a free BEMT code developed and distributed at the Pennsylvania State University. It provides a simplified analysis of BEMT, which has been used and validated for iced airfoil applications [21].
• BLADED is an MBS design software for onshore and offshore wind turbines from DNV-GL.
• PROPID: is a command prompt-based software (under MS-DOS) capable of generating power curves from the geometry of each section of the blade along with airfoil polars resulting from CFD analysis.
• OpenFast: is an open-source wind turbine simulation tool built on FAST v8. It was created, tested, and documented by the National Renewable Energy Laboratory (NREL) as a community model developed and used by research laboratories, academia, and industry.
• QBlade is open-source software for wind turbine blade design and aerodynamic simulation. It is coupled with XFOIL (for aerodynamics coefficients) and FAST (for power curve generation). The use of XFOIL to calculate the aerodynamic properties of the iced airfoils is not recommended since XFOIL is based on the panel method, which has drawbacks with the separation of flow in the boundary layer or the stall on the airfoil.
• AeroDyn: is an aerodynamics software library (module) from NREL for designers of horizontal-axis wind turbines. It is written to be interfaced with several dynamics analysis software packages (such as FAST, ADAMS, SIMPACK, and FEDEM) for the aeroelastic analysis of wind turbine models.

Section three of this paper discusses the application of these codes for BEMT calculations in the literature.

2.2. Numerical CFD Approach for Ice Accretion on An Airfoil

CFD analysis is a widely used technology in fluid dynamics for analyzing fluid flows and providing numerical solutions for complex phenomena governed by complex differential equations. It has become a fundamental technology for icing research on wind turbines. Using commercial CFD software to model the behavior of ice around wind turbine blades is the primary focus of researchers today. The main goal is to investigate the effects of ice on the overall performance of wind turbines and optimize the efficiency of the implemented ice prevention systems. Numerous published research [5,15,22,23,24,25] have examined and analyzed the use of the CFD for the aerodynamic assessment of wind turbine icing. However, the published articles on wind turbine icing simulation do not provide enough information on the setting up of the model for the pre-processing phase of the simulation. The use of CFD to estimate ice accretion on wind turbine blades is covered in detail in this section to provide knowledge on grid optimization and to set up the model configuration for icing.

2.2.1. Computational Domain

For a CFD analysis, a substantial control domain and a suitable discretization must always be used to account for all variables and minimize the undesirable influence of external boundary conditions. It is also advantageous to utilize the model in fully turbulent mode, allowing the solver to emphasize the laminar and turbulent models together with the software’s models for transition [26]. For the model’s validity, it is essential to define the boundary limits properly. As an external flow CFD problem, the icing simulation control domain represents the space around the geometry of interest (airfoil, blade, or complete wind turbine) for which a flow solution is needed. Its form and size are determined mainly by the aerodynamic properties of its geometry and the influence it has on the surrounding flow field. For the icing modeling of the whole wind turbine, we need to incorporate, for example, the large size of low-energy wakes behind the turbine. In the case of an airfoil, the separation of streamlines due to geometric deformation caused by ice accumulation at relatively high angles of attack must be considered. Therefore, the computational domain boundaries should be placed a sufficient distance away from the geometry to guarantee that the outer domain does not affect the flow next to it and thus affects the result’s quality. Without ignoring the significance of low-cost computing, the farther the borders are from the airfoil, the more room is available for the turbulence to dissipate before reaching the boundary limits [18]. We observe that the larger the angle of incidence, the higher the turbulence and the greater the homothety ratio required for stability [18,27].

Because of its more remarkable ability to account for turbulence and larger range in the angle of attack, the C-type geometry of the control domain is often implemented to model clean and iced airfoils [18,28]. For ice accretion modeling on blade airfoils, a C-grid domain extending 20 chord lengths upstream and 30 chord lengths downstream would be reasonable to assume that all flow disturbance consequences are taken into account in the fluid zone of the domain [29]. Figure 3 illustrates the recommended size, airfoil position, and boundary conditions. The recommended domain characteristics are based on ice simulation studies showing excellent consistency with experimental results [29,30,31].

2.2.2. Grid Generation

In general, meshing is a crucial stage in a numerical simulation. However, the choice between unstructured, structured, or cartesian mesh types depends on the problem’s nature and complexity. For example, structured grids are often employed when modeling an airfoil under icing conditions due to their adaptability to be adjusted and regenerated during ice growth and airfoil shape deformation. Figure 4. presents an example of a structured grid created for use with FENSAP-ICE (Finite Element Navier–Stokes Analysis Package) to simulate icing on a NACA 0012 symmetric airfoil.

Whatever the type of meshing used, wall-proper local refinement is a critical aspect of the accuracy of the simulations. Figure 5 presents an example of a hybrid grid containing a smooth transition between a refined structured grid of layers of homogeneous prismatic elements at airfoil walls and an unstructured grid of tetrahedral elements in the rest of the control domain. For a practical implementation of the turbulence models and to capture the velocity profile in the airfoil boundary layer, it is often necessary to satisfy the condition $y+<1$ in order to account for viscosity and turbulence effects in the boundary layer on airfoil walls [15]. The evaluation of $y+$ depends on air density, free-stream velocity, dynamic viscosity, and the boundary layer length. It is noteworthy that air properties are defined for the atmospheric temperature considered in the simulation. Turbulence models such as the Spalart–Allmaras and k-ω SST have been discussed thoroughly in previously published papers discussing modeling approaches for wind turbine icing [18,32].

2.2.3. Grid Adaption for Iced Airfoils

When ice accumulates on wind turbine blades, airfoil-shape boundaries deform, causing certain grid elements around the airfoil wall to become distorted and inappropriate for the continuity of the solution. According to the estimated ice shape, the airfoil geometry is updated. To account for the altered airfoil boundary and prevent convergence issues during the subsequent simulation process or when calculating the aerodynamic characteristics of the iced airfoil, re-meshing becomes essential when utilizing the iced airfoil geometry generated from ice accretion simulation. When modeling ice accretion, the researcher must build a mesh adaptable to geometric deformation as the ice form evolves. After every given time-scale step of ice accretion, the grid must be modified by morphing to accommodate the new resulting ice shape. The adaptive grid will be able to conform to the updated geometry without distorting or degenerating elements throughout the elements mapping process. ANSYS-FENSAP-ICE incorporates the Arbitrary Lagrangian-Eulerian (ALE) method for moving boundaries, including grid displacement due to ice accretion [33]. Grid adaption methods are detailed in ANSYS-FENSAP-ICE documentation and other associated research [34]. Costa et al. [35] suggest a grid morphing-based method for effectively modifying and improving the grid to handle complex ice growth simulations.

Before conducting the final simulation for airfoil aerodynamic parameter estimation, the grid should be adapted to conform to the newly created iced boundary. Once the entire ice accretion has been assessed for a specific accretion duration, performance evaluation may be conducted. Final aerodynamic calculations determine the performance deterioration due to the airfoil’s shape and roughness modification. The grid for the overall shape may be generated once after the complete ice accretion process. However, this simplifies the process and results in inaccurately generated boundaries.

Alternatively, multiple intervals can be considered by dividing the total duration of ice accretion into shorter periods. The grid is updated regularly to account for the intermittent ice growth before conducting the overall numerical analysis [36]. Once the ice thickness is calculated, a new surface grid must be created and modified with the updated geometry. This must be done repeatedly for the iced boundary reconstruction to be accurate. Over the entire period of ice accretion, the overall computations estimate ice’s total mass and shape. A procedure of multiple updates is more computationally costly. At the same time, it produces a better representation of the shape of the ice than doing a single simulation session for the entire duration of ice accretion. The two solution schemes for ice accretion calculations are available in ANSYS-FENSAP-ICE as Multi-Shot and Single-Shot Approaches [33]. If the solver permits it, the aerodynamic, the trajectory, and the thermodynamic modules may automatically mesh and update the governing parameters in sequences of multiple cycles. Alternatively, the procedure can be carried out manually by transmitting the solution files for each shot of the simulation. This will make it possible for the other computations (flow, impingement, and ice formation) to be repeated without having to re-mesh for each possible iteration of the modular design. Recently released publications used this feature of the sophisticated icing CFD software [37,38]. By modifying the regions of the grid close to the vulnerable wall borders, the STAR-CCM+ commercial software offers a 3D morphing motion approach to estimate the time-scale evolution of ice formation [38]. ANSYS-FENSAP-ICE also offers this functionality through the “Multi-shot Ice Accretion with Automatic Mesh Displacement” feature, which makes it possible to combine configuration and execution into a single setup with automatic feedback loops using the most updated governing parameters. For instance, a single shot will take 21 min to estimate the ice thickness based on the initial geometry and governing parameters if the icing event lasts for 21 min. In contrast, if a multi-shot is used with three discrete time steps, the simulation’s governing parameters and geometry will be changed every seven minutes [33]. Furthermore, it is advised for each shot of ice accretion calculation to incorporate surface roughness height while executing the flow solution. This can be done in FENSAP-ICE using the “Beading model” feature [32]. This option enhances the calculated ice accretion forms by considering the impacts of surface roughness on the shear stress, heat flux, and predicted aerodynamic parameters for the final ice shape [32,33].

2.2.4. Grid Independency Study

For ice accretion modeling, accuracy is essential to reduce reliance on costly experimental analyses. A critical phase in a CFD investigation of icing is the creation of the appropriate grid because of how it affects the calculated solution. A high-quality grid is required to produce precise, reliable, and relevant computation results. Meshing errors significantly affect convergence, solution accuracy, and processing time. The reduction in elements that exhibit distortions or skewness is associated with high-quality meshes, while adjacent to the airfoil surface, it is crucial to attaining zero or negligible skewness [34]. In other words, accuracy relies mainly on the grid employed, not only in terms of its refinement and element size but also the elements’ orientation and aspect ratio. Additionally, grid refinement is necessary for the areas showing a significant gradient, such as the boundary layer.

An appropriate grid should result from a grid refinement study and be adequately smooth. A grid convergence study, also known as a grid independency study, is essential to determine the optimal number of grid elements for specific parameter estimation to reduce possible errors and minimize computational costs [38]. In a grid refinement study, computations are performed using incremental grid refinements until valid convergence is attained for the significant parameters. The size of the elements will decrease with each grid refinement, meaning that each element will be replaced with a smaller element. Each step includes an observation of the outcomes for each relevant parameter. When a precision criterion is met, the iterative process reaches convergence. However, no matter how refined the grid is, the numerical solution will not reach an exact solution as the Reynolds-averaged Navier–Stokes (RANS) equations are nonlinear. Since the precise solution is uncertain, each iteration’s error depends on how the computed quantity changed between two iterations. Therefore, a solution error should be validated and assessed depending on the required precision.

The estimation of aerodynamic characteristics is of the utmost importance for icing modeling. Therefore, a convergence analysis must be conducted on the lift coefficient ($C_l$) and drag coefficient ($C_d$) at a given angle of attack, typically the nominal angle of the selected wind turbine operational design. Likewise, for the simplicity of icing simulation, it is recommended to do this convergence analysis for both aerodynamic coefficients $C_l$ and $C_d$ of the iced airfoils. As examples from the wind turbine icing literature, Zanon et al. [31] performed a convergence test on the lift coefficient to simulate ice accretion on the airfoil NACA 64-618 on the NREL 5 MW baseline wind turbine. Hildebrandt [29] observed a discretization error across grids convergence study conducted on the lift coefficient ($C_l$) and drag coefficient ($C_d$) for both clean and iced airfoils, while incorporating simulation duration as an additional determining parameter in grid selection. In commercial software, grid refinement convergence is achieved using integrated tools. The adaptive meshing tool supplied by the program may be used to automate mesh refining until a user-specified degree of precision is attained.

One may opt for a refinement study over the whole domain or locally, wherever refinement is necessary. For example, for icing modeling on airfoils, enough grid resolution must be implemented around the stagnation zone to adequately capture the local properties of water droplet impingement, as seen in Figure 5. Therefore, a convergence study may be done locally to account for airfoil deformation caused by ice accumulation in specific locations (around the airfoil or near the stagnation region within the impingement limits). Only a mesh convergence analysis can show that the mesh has good refinement in this area for assessing the required density implemented in the regions of interest. In general, smooth transitions between zones of varying densities must be observed. Rapid variations in mesh density or improperly shaped elements produce solution instability and unsatisfactory outcomes. When the regenerated grid must conform to the ice accretion, effort must be taken to ensure that the shape of the elements in these locations does not deviate too much from the reference shape.

2.2.5. Boundary Conditions

Each module (aerodynamic, droplet trajectory, and thermodynamic) for the ice accretion simulation involves a system of partial differential equations whose solution requires the definition of proper boundary conditions. The most common boundary conditions are velocity-inlet, pressure-outlet, and anti-slip wall. In the icing problem, some boundaries require more than one condition. Ice accretion is a multiphase flow problem, where supercooled water droplets are dispersed particles in the air. In the CFD simulation of multi-phase flows, when air is designated as a continuous phase, this is automatically assigned to the droplets dispersed in the air. This causes inaccuracies in estimating the water droplets’ impingement limits and, subsequently, the ice form since the droplets will be driven to circumvent the airfoil to escape collision. Therefore, the airfoil should perform as both a porous wall for droplets and a wall for air. Some CFD software permits coupling a User Defined Function (UDF) with the computations to account for the droplets’ continuity, momentum, and energy equations to address this problematic issue [30].

2.2.6. Modules of Ice Accretion CFD Calculations

The numerical study of ice accretion on airfoils includes the computation of the mass flux of supercooled water droplets and the determination of the icing accumulation. These can be numerically simulated with integrated thermo-fluid dynamic models involving fluid flow simulation, droplet displacement, surface thermodynamics, and phase change [32]. Generally, numerical approaches for ice accretion calculations represent an iterative time-step procedure. As illustrated in Figure 6, four successive computation modules should always be considered: flow field aerodynamic calculations considering the air as a continuous phase, trajectory calculations of the supercooled water droplets in the air, thermodynamic analysis, and generation of new airfoil iced geometry. For example, ANSYS FENSAP-ICE operates in a modular system where each module performs a specific task: the FENSAP module carries out the flow calculation; DROP3D the droplets impingement and ICE3D the ice accretion and the mesh displacement [33]. In addition, each of these simulation modules includes numerical calculations of partial differential equations.

The numerical study of airflow behavior is carried out by solving nonlinear partial differential equations (PDE) for the conservation of mass (Equation (26)), momentum (Equation (27)), and energy (Equation (28)) [33,39]:

$$\frac{\partial {\rho }_a}{\partial t}+\overrightarrow{\nabla }·\left({\rho }_a\overrightarrow{V_a}\right)=0$$

(26)

$$\frac{\partial {\rho }_a\overrightarrow{V_a}}{\partial t}+\overrightarrow{\nabla }·\left({\rho }_a\overrightarrow{V_a}\overrightarrow{V_a}\right)=\overrightarrow{\nabla }·{\sigma }^{ij}+{\rho }_a\overrightarrow{g}$$

(27)

$$\frac{\partial {\rho }_a{E}_a}{\partial t}+\overrightarrow{\nabla }·\left({\rho }_a\overrightarrow{V_a}{H}_a\right)=\overrightarrow{\nabla }·\left({\kappa }_a\left(\overrightarrow{\nabla }{T}_a\right)+{\mathrm{v}}_{\mathrm{i}}{\tau }^{ij}\right)+{\rho }_a\overrightarrow{g}·\overrightarrow{V_a}$$

(28)

where $\overrightarrow{V_a}$ is the air velocity vector, $\rho$ is the air density, the subscript $a$ denotes the air solution, $T$ is the static air temperature in Kelvin, ${\sigma }^{ij}$ is the stress tensor, ${\kappa }_a$ is the thermal conductivity, E is the total initial energy, and H is the total enthalpy.

In FENSAP-ICE, the droplets’ behavior is numerically simulated using the Eulerian approach. The Eulerian two-fluid model is termed Eulerian–Eulerian since it considers both the droplets and the air to be continuous phases using the concept of water volume fraction [40]. Water conservation equations are developed similarly to the air as a fluid phase [32,41]. The general Eulerian–Eulerian two-fluid model consists of the Navier–Stokes equations augmented by the droplet’s continuity (Equation (29)) and momentum equations (Equation (30)) [33]:

$$\frac{\partial \alpha }{\partial t}+\overrightarrow{\nabla }·\left(\alpha \overrightarrow{V_d}\right)=0$$

(29)

$$\frac{\partial \left(\alpha \overrightarrow{V_d}\right)}{\partial t}+\overrightarrow{\nabla }·\left[\alpha \overrightarrow{V_d}⨂\overrightarrow{V_d}\right]=\frac{C_d{\mathrm{Re}}_d}{24K}\alpha \left(\overrightarrow{V_a}-\overrightarrow{V_d}\right)+\alpha \left(1-\frac{{\rho }_a}{{\rho }_d}\right)\frac{1}{F{r}^2}$$

(30)

where $\alpha$ is the water volume fraction, and $\overrightarrow{V_d}$ is the droplet velocity. The first term of the right-hand side of the equation Equation (30) represents the drag acting on droplets proportional to the relative droplet velocity, drag coefficient, and the droplets’ Reynolds number. The second term represents buoyancy and gravity forces proportional to the local Froude number ($Fr$). The drag coefficient for flow around spherical droplets can be calculated using several empirical relations [42]. Clift and Gauvin developed a simple empirical correlation in 1970 for droplet Reynolds numbers below 300,000 (Equation (31)):

$$C_d=\left(\frac{24}{{\mathrm{Re}}_d}\right)\left(1+0.15{\mathrm{Re}}_d{}^{0.687}\right)+\frac{0.42}{1+42500{\mathrm{Re}}_d{}^{-1.16}}{ \mathrm{for} \mathrm{Re}}_d\le 300000$$

(31)

However, for a very small diameter of the water droplet, a correction factor must be applied to the empirical correlation [43]. The drag coefficient drops sharply for Reynolds numbers close to 300,000 [44].

In FENSAP-ICE [33], the “Water-default” drag coefficient is based on an empirical correlation for flow around spherical droplets for ${\mathrm{Re}}_d>250$(Equation (32)):

$$C_d=\{\begin{array}{c}\left(\frac{24}{{\mathrm{Re}}_d}\right)\left(1+0.15{\mathrm{Re}}_d{}^{0.687}\right) for {\mathrm{Re}}_d\le 1300\\ 0.24 for {\mathrm{Re}}_d>1300 \end{array}$$

(32)

Finally, surface thermodynamics is calculated by solving a system of two PDEs on all solid surfaces. The first equation expresses the mass conservation (Equation (33)). The three terms on the right-hand side of the equation represent the mass transfer by water droplet impingement, evaporation, and ice accretion, respectively [45]. The second PDE expresses energy conservation (Equation (34)). The first three terms on the right-hand side of the equation are the heat transfer generated by the impinging supercooled water droplets, evaporation, and ice accretion. The last three terms are the radiative, convective, and one-dimension conductive heat fluxes [33,46].

$${\rho }_f\left[\frac{\partial h_f}{\partial t}+\overrightarrow{\nabla }\left({\overrightarrow{V}}_f{h}_f\right)\right]=V_{a}LWC\beta -{\dot{m}}_{evap}-{\dot{m}}_{ice}$$

(33)

$${\rho }_f\left[\frac{\partial h_f{c}_f{\dot{T}}_f}{\partial t}+\dot{\nabla }\left(V_f{h}_f{c}_f{\dot{T}}_f\right)\right]=\left[c_f\left({\tilde{T}}_a-{\tilde{T}}_f\right)+\frac{\Vert {\overrightarrow{V}}_d^2\Vert }{2}\right]V_{a}LWC\beta -L_{evap}{\dot{m}}_{evap}+\left(L_{fusion}-c_s\tilde{T}\right){\dot{m}}_{ice}+\sigma \epsilon (T_a^4-T_f{}^4)-c_h\left({\tilde{T}}_f-{\tilde{T}}_{ice. rec}\right)+Q_{anti-icing}$$

(34)

Here, the coefficients ${\rho }_f$, $c_f$, $c_s$, $\sigma$, $\epsilon$, $L_{evap}$, $L_{fusion}$ are the physical properties of the fluid and the solid. ${\tilde{T}}_f$ is the equilibrium temperature at the air/water film/ice/wall interface, $h_f$ is the film (ice) thickness, and $\beta$ is the local collision efficiency provided by the DROP3D module.

In this module, it is essential to consider the roughness. Two approaches to simulate this parameter were used, the Shin et al. model [47] for the single-shot approach and the Beading model for the multi-shot approach. More information about the last one can be obtained in FENSAP-ICE_User_Manual [33].

2.3. A Hybrid CFD-BEM Mixed Approach for Estimating Wind Turbine Power Production Loss Due to Icing

In 2D simulations, ice accretion is replicated over a single airfoil section. It offers essential information on the aerodynamic performance loss when the airfoil shape deforms due to ice accumulation. However, this kind of analysis does not accurately assess the power production loss caused by ice. Some references consider that the ice accreted over the airfoil section at 85% spanwise position of a wind turbine blade represents the average ice accretion impact on the blade power generation [36,48,49]. At that radius, the most substantial contribution to the power generation of turbines occurs [50]. For instance, Turkia et al. [51] considered that the section at a radius of 85% of the total blade radius represents the average accretion of ice on a blade. Based on this assumption, they established a simplified relationship between ice accretion on a standard cylinder and that on a rotating blade. Results were used to create a Finnish icing atlas in 2012.

Nonetheless, 2D simulations do not account for the 3D flow effects. Fully 3D solutions replicate the whole blade in a 3D domain. They account for 3D flow effects [7]. This simulation is challenging to construct, particularly in several icing situations. The Quasi-3D simulation is a reasonable alternative approach that combines the ease of 2D analysis with the capabilities of the BEMT to capture the 3D flow effects [52]. A wind turbine’s power curve can be generated by combining the BEMT with the 2D airfoil CFD simulation solution. Adopting the CFD-BEM method to construct the power curves for clean and iced WT aids in estimating wind turbine output losses due to icing, resulting in a computationally less costly solution. Both approaches, the Quasi-3D simulation, and the Fully 3D simulation, have a similar theoretical background, but they describe and represent ice effects on wind turbine blades differently.

The Quasi-3D simulation approach combines the CFD-calculated aerodynamic coefficients for the selected sections’ airfoils with the BEMT to generate the wind turbine’s power curves for both clean and icing situations [16]. A typical Quasi-3D simulation approach for power losses estimation passes through the following steps (See Figure 7 and Figure 8):

• Selection of different sections along the blade’s span of the studied wind turbine.
• Identification of the input parameters for ice accretion conditions:

  -

  The far-field atmospheric conditions

  -

  Wind turbine operational parameters

  -

  Icing conditions

• Ice accretion simulation on the airfoil of each selected section to determine airfoil sectional properties. Icing CFD software is employed, such as FENSAP-ICE, LEWICE, TURBICE, etc.
• Aerodynamic coefficients’ calculation for a specific range of angles of attack, also known as partial polar: C_l(α) and C_d(α), and for each selected section for both scenarios, clean and iced airfoils. General Multiphysics CFD simulation tools can be used for this purpose, such as FLUENT, CFX, FENSAP, etc. The decrease in C_l and the increase in C_d describe the aerodynamic performance loss caused by ice accretion on airfoils. Typically, they are illustrated by plotting airfoil polar curves C_l(α) and C_d(α) for both clean and iced wind turbines. Nevertheless, what determines the drop in aerodynamic performance is the decrease in the lift-to-drag ratio, expressed by C_l/C_d, owing to ice-induced roughness [5].
• Application of the improved BEMT for both clean and icing conditions:

  -

  Generation of circular foils and extrapolation of the aerodynamic coefficients C_l(α), C_d(α) over 360° AoA. To estimate power and load in varying operating scenarios, the polar must be extended to 360° for each blade’s section [38]. This is accomplished within the polar extrapolation module by applying the Viterna equation [38,53,54]. Only polar data that has been extrapolated may be utilized to model a wind turbine.

  -

  Estimation of flow induction factors iteratively and calculation of C_T(TSR), C_p(TSR). The iterative BEM methodology is outlined and described by Switchenko et al. [12].

  -

  Calculation of 3D-effects corrections to improve the BEM accuracy of prediction.

• Generation of power curve P(V) as described in Figure 7 for the clean (no-ice) wind turbine using an MBS code. Alternatively, if available, the wind turbine theoretical power can be employed for comparison with the iced-up power curve.
• Generation of power curve P(V) for the wind turbine of iced-up blades using an MBS code, such as OpenFAST, Bladed, etc., which is presented in Section 2.1.2. Due to ice, the deterioration of the power curve represents the wind turbine’s power losses. Typically, they are shown by plotting, for both clean and iced wind turbines, the power curve P(V) or the power coefficient as a function of the wind speed C_P(V), or the power coefficient C_P(TSR) or the torque coefficient T(TSR) as a function of the Tip Speed Ratio. Figure 8 presents the overall process of the Quasi-3D approach for icing simulation. CFD solver is used to compute the aerodynamic coefficients C_l (α) and C_d (α) for each section’s iced airfoils. A BEMT code is used to generate the iced wind turbine’s power curves using the CFD computed polar C_l(α) and C_d(α) for the iced airfoils.

2.4. Full-Scale 3D Modeling of a Wind Turbine in Rotation

To generate the power curve P(V) for a horizontal-axis wind turbine, 3D simulation for the entire turbine with rotation using CFD icing simulation software is desirable. We can obtain torque and momentum coefficients from the simulations and generate the power curve. However, due to complexity and expensive computational costs, the fundamental research for evaluating icing consequences on wind turbines is a two-dimensional simulation of blade airfoils for a particular set of weather and operational parameters. Until very recently, most published research on wind turbine icing simulation relied on 2D models for selective parametric analysis and to acquire a better understanding of the phenomenon. Various simulation scenarios are required to assess the drop in power generation under any icing conditions; a 2D simulation will no longer be appropriate. The aerodynamic performance, for example, should be tested under each specific condition at each section of the blade for each angle of attack, pitch angle, rotor speed of rotation, and other relevant parameters [5]. A typical horizontal-axis wind turbine (HAWT) has twisted blade geometry of usually multiple sections’ forms, starting with a cylindrical form at the root with a smooth transition to airfoils and extending for tens of meters long [55]. This complex aerodynamic form of blade geometry requires exclusively 3D simulations. However, icing affects not only the blade but the entire wind turbine with various types of 3D effects, such as the radial flow [9].

Moreover, the rotation of the blades will highly affect ice accretion, from which the need for a full 3D simulation of a rotating turbine comes from. Even a simulation for the entire wind farm is also important to consider the effect of the aerodynamic wakes behind the turbines and to account, with adequate accuracy, for production losses during every specific icing condition. Therefore, a three-dimensional numerical simulation of ice accretion on the entire envelope (the complete turbine with the rotating blades) is indispensable to account for the influence of the affecting parameters on the ice formation on the blades and the degradation in wind turbine performance [10].

Very few published research have accomplished complete 3D ice simulation [7]. The modest efforts in this regard are almost for comparison purposes with the 2D approach rather than for icing impact investigation [11,12,56]. It is also worth noting that in all the consulted 3D simulation studies, modeling was performed only on a single blade and not on the complete turbine. The simulation was performed based on periodic settings and assuming that all blades behave identically regardless of location. Testing wind turbine performance under several icing conditions is time-consuming and computationally expensive.

Due to the complexity of the physics of a highly time-varying phenomenon, it would be challenging to conduct such scenarios of simulations, particularly considering the uncertainty of the ice accretion process [57]. To perform a fully 3D icing simulation on the wind turbine, it is highly recommended to use a reliable and powerful 3D multi-physics simulation tool adapted to evaluate effectively icing impact on wind turbine performance and operation in cold climates. With the presence of that powerful tool, it could be possible to develop methodologies that help to understand the conditions that lead to ice formation on the wind turbine. In addition, this helps examine the effectiveness of the IPS used to reduce the impact of icing on wind turbines. Recent advancements in CFD for in-flight icing simulation and the revolution in information technology and hardware capabilities brought much potential to step toward the fully 3D icing simulation. As a result, in-Flight icing 3D simulation recently moved from just accident investigation to design, prevention, and certification [58]. Furthermore, the advancement in the 3D icing simulation codes developed for aeronautics can capture various 3D effects and other icing disturbances in aircraft, such as ice break-up and shedding that can also be advantageous for the simulation of the 3D effects of icing on wind turbines [10,59].

Differences in the predicted ice shapes via 2D and 3D simulations are demonstrated in a study on complex icing events using FENSAP-ICE Simulation. Switchenko et al. [12] employed Quasi-3D and fully 3D simulations to compare the operational performance of an NREL Phase VI scaled to Wind-PACT 1.5 MW wind turbine with on-site observation data. The Quasi-3D results were comparable to fully 3D simulations but at a reduced computational cost. Jin et al. [11] explained that in 2D simulations, a higher ice growth was observed than in 3D simulations. This behavior was associated with the absence of the flow interaction in the radial direction in 2D simulations. Costa et al. [35] performed a 2D and 3D icing simulation study adopting a mesh morphing approach to handle model complexity. The 2D scenario demonstrated accuracy with a standard workflow based on ice generation from scratch. In contrast, the 3D scenario primarily demonstrated the viability of its application given the challenging nature of the replicated ice growth. Inconsistencies could be noticed, that might be explained by the quasi-3D approach’s underlying assumptions, which highlight the prominence of considering the three-dimensional effects of flow in simulation.

We may summarize the benefits of the quasi-3D in low-time computational penalties related to simplification and simulation consistency that allows examining more scenarios of ice accretion in various weather conditions. While considering assumption and ignoring transition and the various 3D effects in flow, particularly in the radial direction of blades’ span, could result in shortcomings in simulation, resulting in an underestimating of aerodynamic performance and generated power. In contrast, a fully 3D simulation that accounts for transition and the 3D effect of flow in the radial direction might lead to more accuracy and replication reliability, eventually at the expense of excessive computing requirements.

2.5. Assessment of the Annual Energy Production (AEP) in Icing Conditions

In the feasibility study of a wind farm in Nordic conditions, it is necessary to estimate the production losses due to icing on the blades of the wind turbines to determine its productivity. Different methods are adopted for assessing the production losses of wind turbines during icing events. Among these are wind tunnel measurement and real-time site observations of power production, which require matured techniques for detecting icing events and identifying their severity [60].

The conventional method for predicting losses follows two steps: the first is to determine the likely amount of icing events per year, and the second is to calculate the reduction in the efficiency of wind turbines [10]. The realization of the second stage requires experimental tests and numerical simulations to predict and analyze the iced airfoils of the blades of the wind turbines to calculate the aerodynamic degradation due to frost in specific weather conditions [5]. With the high cost of wind tunnel tests, a numerical simulation approach makes it possible to quickly provide information on the reduction in aerodynamic and energy performance according to different wind turbine configurations and weather conditions. Combining numerous and precise meteorological measurements with powerful numerical models is essential to adequately assess the impact of icing on the functioning of a wind turbine and its annual production [15]. However, due to the complexity of the physics of a very variable phenomenon in time and the difficulty in the analysis of icing profiles, as well as the difficulty of performing three-dimensional numerical simulations of the accretion of ice on the rotating blades, it is presently not possible to use numerical simulations in real-time for optimizing performance and operating wind turbines.

When operating under icing conditions, the aerodynamic performance of wind turbine blades is subject to different levels of degradation depending on the operating conditions, such as air temperature, wind speed, and the severity and duration of the icing event. The icing-induced losses of a wind turbine’s Annual Energy Production (AEP) may be determined at a specific site using the local wind speed frequency data and the power curves generated for the clean and iced wind turbines. For estimating the annual production losses related to icing, the power curves of clean and iced wind turbines generated using the Quasi-3D simulation approach are associated with the wind speed annual distribution to estimate the energy captured in both cases. The power curves resulting from CFD-BEM mixed approach for both clean and iced wind turbines are coupled with given site information to estimate the wind farm annual energy losses due to icing. The wind farm site is represented here by the wind speed annual distribution (number of hours per year for which wind flows at each operational velocity) and the number of icing hours per year for representative events. The latter is found through the duration of the classed icing events (rotor icing) and the frequencies of every icing scenario. The annual energy production of a wind turbine can be found by coupling the power curve with the wind speed annual distribution. The losses are calculated by coupling the power curve of the iced wind turbine with the wind speed annual distribution and the icing scenarios. The assessment process of the annual wind turbine production loss on account of icing is illustrated in Figure 9.

As an example of the method, we present the study of Dimitrova et al. [61] on a numerical model to calculate the annual energy production for a wind turbine generic model during two light icing occurrences. The model (PROICET) is developed at the Anti-icing Materials International Laboratory (AMIL) at the University of Quebec at Chicoutimi in collaboration with the Wind Energy Research Laboratory (WERL) at the University of Quebec at Rimouski. The numerical simulations are based on icing weather data collected at a Murdochville site in Quebec, Canada. Averaged parameters for annually repeated light icing representative events are considered. The annual production losses of the wind turbine during two light icing events are presented for three representative cases of the duration of ice melting on the wind turbine generic model’s blade. In the three cases, the icing events last 74 h per year, and the ice disappears either immediately after icing, or remains on the blades one or two days after icing.

2.6. Strategy for the Assessment of Wind Turbine Production Losses due to Icing

Over the last decades, research has provided a better understanding of the physics of atmospheric ice accretion on structures. The most common icing model is the Makkonen model [62], developed by Lasse Makkonen for predicting ice accretion over a cylinder as a reference collector, as the study of ice accretion on the cylinder, for which numerous analytical and experimental results are available, is fundamental for this field of research [25,41,51]. This model, based on three fractions: collision efficiency, sticking efficiency, and accretion efficiency, is referenced in the ISO 12494 standard [7] and has been employed in many icing problems [63].

As a simplified, rapid estimation method of ice accretion [64], this empirical model is often coupled with Numerical Weather Prediction (NWP) models to provide an estimate of risk under different weather conditions [7,65,66]. NWP model results for icing research have seen rapid growth in recent years [67,68,69]. NWP models are required to forecast cloud hydrometeors, key input parameters for icing forecasts that include in-cloud icing. NWP models can also provide data at locations where the required observations are unavailable [70,71]. Weather Research and Forecasting (WRF) model is a Numerical Weather Prediction (NWP) system developed to assist in atmospheric research and operational forecasting needs. As a recommended strategy to assess wind turbine production losses (Figure 10), the WRF model [72] developed for research purposes and operational weather forecasts is employed to determine icing conditions at the tested site for a specific period. The resulting values of the icing event parameters (T, LWC, V) and the MVD estimated by measurements or using climatological values are used to simulate ice mass accreted on a cylindrical structure [73]. The power curves of clean and iced wind turbines estimated using the Quasi-3D simulation approach are linked to time-dependent weather conditions resulting in similar ice formation to that estimated using CFD simulation. Estimation of power loss resulting from ice build-up on wind turbine blades is performed rapidly in the energy production model using the Makkonen model [62]. The model should be optimized to account for all relevant elements, from detecting the icing event and evaluating the type, form, and severity of ice build-up to determining the optimal scenario of protection and the energy necessary for the process. The overall simulation-based process of production loss estimation in connection to weather modeling is illustrated in Figure 10 Using weather prediction data, statistical methods based on a supervised learning algorithm and artificial neural networks (ANNs) can also be integrated to predict icing-induced production loss [64,74].

As a notable example of the proposed approach, Turkia et al. [51] presented a methodology for developing the reduced power curves for an iced reduced-scale variable speed pitch-controlled wind turbine. First, the icing conditions were specified using a numerical weather forecast model. Then, using the ice accretion model provided in ISO 12494 (2001), a relationship between a stationary standard cylinder and the rotating wind turbine blade was developed [75]. Next, the VTT-developed software TURBICE was employed to model ice accretion on two blade sections during three distinct icing episodes, while the aerodynamic was modeled using ANSYS FLUENT. Finally, the power curves were estimated for the clean and iced wind turbine using FAST software. The power loss due to icing was estimated for three different phases: short, intermediate, and long periods of ice accretion. For validation, field observations were used to confirm the findings.

3. Summary and Discussion of Research on the Estimation of Wind Turbine Power Loss

This section presents a synthesis of the research in the last two decades on the Quasi-3D method for power loss estimation due to ice accretion on the HAWT. The purpose of this section is to survey, discuss and summarize recent attempts to quantify ice’s influence on wind turbines’ energy output using Fully 3D or Quasi-3D modeling approaches for different operational scenarios and icing conditions. The output of each of these studies is summarized along with other valuable information, such as the type of ice treated, the software used for both CFD and BEMT simulation, the type of wind turbine and airfoils considered, along with the output considerations of the examined studies. Numerous research on common wind turbines and airfoils can be found in the literature. From reviewing hundreds of references available in the literature on wind turbine icing, investigations have been carried out focusing on the Quasi-3D simulation approach and its application on wind turbines in icing conditions. A matrix of the reviewed icing modeling studies for wind turbines is provided in tables. This section of the paper surveys and discusses these attempts by evaluating their contribution.

Starting from 1998 with a study by Jasinski et al. [76] for investigating the impact of ice on HAWT performance, the Quasi-3D simulation approach is still progressing as this work is being written. Jasinski et al. [76] employed PROPID, a command prompt-based software capable of using airfoil polars results from CFD analysis to estimate the effects of the dry regime of ice on the performance of a three-bladed wind turbine of a 450-kW rated power. In addition, they conducted 2D simulations on S809 airfoils using LEWICE software for ice accretion and aerodynamic calculations. The study concluded a considerable performance reduction for thin layers of ice accretion at wind speeds below the wind turbine-rated power. This exemplary study continued to be replicated using different tools on various models in the subsequent research on wind turbine icing.

In 2009, Dimitrova et al. [61] presented numerical research to predict energy losses caused by low-severity icing conditions on a 1.8 MW Vestas V80 wind turbine. The study combined three codes to simulate icing conditions in a wind farm in Murdochville-Quebec. The CIRA-LIMA code was developed in collaboration between the CIRA (Italian Center for Aerospace Investigations) and the LIMA (International Laboratory of Anti-icing Materials). It was used by Dimitrova [20] in 2009 to create the iced airfoils, XFOIL was used to calculate the airfoils’ aerodynamic coefficients, then PROPID was used to generate the power curves. However, Dimitrova et al. [61] recommended using another tool for aerodynamic simulation, given that XFOIL, based on the panel method, has drawbacks in modeling flows with large separation zones, such as flows around iced airfoils. Furthermore, the power curve generated using the BEMT has limitations considering additional losses related to the three-dimensional effects of geometrical design and rotation of the wind turbine. These losses aggravate in the presence of ice. Upon that, Dimitrova et al. [61] recommended correction equations to account for these losses, referred to as “improved BEMT” in the second section of this paper.

Homola et al. [16] conducted a Quasi-3D analysis of power performance losses on the NREL 5 MW wind turbine under rime ice conditions. They used the stand-alone version of FENSAP-ICE for CFD icing simulations and an in-house code for generating the power curves for a clean and iced wind turbine. The authors mentioned that they performed a comparison between results on rime ice shapes obtained from FENSAP-ICE (formerly from Newmerical Technologies International, Inc, Montreal, Quebec, Canada), LEWICE (NASA, Cleveland, Ohio, USA), and TURBICE (VTT, Espoo, Finland) with good agreement found between all these codes. They also predicted the severity of ice accretion on the different sections of the blade and its penalty on power production in different control scenarios.

Turkia et al. [51] investigated three temporal phases of rime ice formation on a scaled-down NREL 5 MW to WWD-3 MW wind turbine. They used ANSYS FLUENT for aerodynamic calculations and TURBICE for ice accretion simulation, a panel method-based software developed by VTT. In addition, for BEMT calculations, they used FAST, an open-source CAE software managed by a dedicated team at NREL, for simulating the coupled dynamic response of wind turbines. In addition, the authors presented a method developed for estimating wind turbine production losses by correlating power production loss with the ice mass accretion on a referenced collector using the Makkonen model [77] for ice accretion around a cylinder. Turkia et al. [51] highlighted the importance of considering surface roughness distribution when assessing the aerodynamic loss due to icing, even at the onset of icing events, especially for drag coefficient estimation. However, limiting the investigation to dry ice led to an underestimation of the influence of icing on power generation.

Sagol [56] performed a critical analysis of NREL Phase VI wind turbine blades utilizing both a Quasi-3D and a Fully 3D simulation approaches for estimating icing-induced power loss. The objective was to determine if the improved accuracy of the results compensates for the additional computer resources needed by the Fully 3D simulations. She used for both analysis ANSYS FLUENT and the extended Messinger [77] model for the mass and energy balances of the ice accretion process. A single blade was only used for the Fully 3D simulation. To account for the blade’s rotation, a rotating reference frame method with periodic boundary conditions was adopted. This is a procedure adopted by almost all the examined Fully 3D approach studies. The research demonstrated that the two approaches resulted in distinct ice forms and, thus, distinct blade performance when iced. Sagol [56] found that estimating ice buildup on the blade using the Quasi-3D method yields more reasonable results with difficulty validating iced-up wind turbines without experimental data. At the same time, the Fully 3D approach gives more reliable results for the ice-free blade. However, when using the Quasi-3D approach, the ice shape and associated power loss are disturbed by neglecting the 3D effects.

Etemaddar et al. [54] examined the impact of ice accretion on the performance of the NREL 5 MW baseline wind turbine and icing- related additional loads. They used LEWICE for 2D ice accretion simulations, while FLUENT analyzed the resulting iced airfoils to estimate the aerodynamic characteristics. The BEMT calculations were performed using WT-Perf software from NREL. To assess the performance degradation on account of icing, the results were obtained for the power loss and the power coefficient for several cases around the rated wind speed as a function of the tip speed ratio. In addition, Etemaddar et al. [54] examined the effect of several icing parameters on the resulting iced airfoils under a wide range of conditions and compared their results with experimental data for both clean and iced conditions, which led later to the study’s broad citation. However, the authors mentioned uncertainty in experimental drag coefficient measurements for the results presented on selected segments of the tested wind turbine.

Additional research studies may also be featured in this survey to highlight the multi-sidedness applications of the discussed approaches. O. Yirtici published three papers [78,79,80] investigating power loss for the NREL 5MW and Aeolos-H 30 kW wind turbines. An in-house tool is developed for the Quasi-3D simulation using XFOIL and an open-source panel code coupled with a turbulent boundary layer model. Jin et al. [11] studied the effect of ice accretion on the CQU 300kW wind turbine. They compared the ice shape and power coefficient results using 2D and 3D CFD simulation schemes using ANSYS FENSAP-ICE. Francesco Caccia [81,82] conducted a Quasi-3D rime ice simulation on the NREL 5MW wind turbine using OpenFAST for the BEMT calculations and an open-source code for the CFD simulations. The power losses due to icing are discussed by comparing the power curves for both clean and iced turbines. At low Reynolds numbers, Richard Hann [83] performed 2D simulations for S826 airfoils that compose an NREL wind turbine. Additionally, experimental tests were conducted to validate the numerical results. The performance deterioration of an S826 airfoil is analyzed along with the power production losses. Cao et al. [84] followed the methodology of Etemaddar et al. [54]. They conducted 2D simulations for multiple sections of the NREL 5 MW blade to extrapolate polars for $360°$ of airfoil rotational position. Their results were limited to the ice shape of the studied sections and the extrapolated polars. Villalpando et al. [85] conducted 2D simulations for a blade’s three NACA 63−415 airfoils. The polars resulting from the simulations with FLUENT were used to deduce the power coefficient curve. To investigate the aeroelastic effects of an NREL 5 MW WT with iced blades, Gantasala et al. [86] used FAST software from NREL for BEMT calculations and ANSYS CFX for CFD simulations. The icing consequences were evaluated through the demonstration of the power curve and the ice loads. Son and Kim [87] presented a numerical analysis code, WISE (Wind turbine Icing Simulation code with performance Evaluation), integrated into OpenFOAM for the NREL phase VI turbine. Their results were limited to ice shape and power coefficient. Kangash et al. [88] present a Quasi-3D icing simulation on the NREL 5 MW wind turbine at various velocities. The FENSAP-ICE module integrated into ANSYS software is used for the CFD simulations of ice, while QBlade is used for the BEMT calculations. The outcomes of such investigations are questionable in the absence of experimental validation. Furthermore, QBlade software is coupled with XFFOIL for aerodynamic coefficient calculations. XFFOIL has drawbacks at the separation zones, a condition that is always present with ice accretion. The panel method used by XFOIL cannot converge beyond the flow separation, a likely occurrence with iced airfoils due to leading-edge deformation. Using the Panel method to estimate aerodynamic coefficients for iced airfoils is not recommended, especially at high angles of attack [20].

Regardless of the purpose of the research, ice modeling studies for wind turbines should always be validated before adopting the outcomes of a CFD numerical solution. While most of the standard commercial CFD programs incorporating icing modules were initially created for aeronautics, it is essential to validate the adopted code for the range of Reynolds numbers and other operational conditions of wind turbines. To some extent, numerical methods used to estimate airplane ice accretion have been adopted for wind turbine icing applications. Several research studies have validated the CFD findings via experimental testing [12,28,30,31,36,38,39,49,51,85,89,90,91,92,93,94,95]. However, validation against experimental data for typical wind turbines in various icing situations and operating scenarios is still required and is crucial for model reliability.

Generally, for all kinds of numerical simulations, one should have an idea of the nature of the results to expect before performing the simulation. Therefore, applying simplified assumptions at the earliest stages would be convenient, starting with basic scenarios for which results are already known to streamline verification and validation and to have confidence in the simulation tool at the disposal. For example, numerical icing studies available in the literature, to validate their CFD tools, usually start with a simulation of ice accretion on a symmetric airfoil NACA-0012 and validate against published experimental results [36,37,39,41,42,56,62,87,89,93,96,97,98,99]. The most cited study in this category is Makkonen et al. [62], which used experimental tunnel tests on NACA 0012 airfoil to validate the TURBICE model. The results have also been compared with LEWICE simulation results. Then, a case study was carried out on the NACA 63-213 airfoil, followed by heating system calculations for anti-icing simulation. This became a typical study for wind turbine icing simulation.

Before developing a full-scale 3D model for simulating a complex phenomenon such as ice accretion on rotating wind turbines, some preliminary investigations must be performed. Numerous CFD-based published research validated their findings using experimental data for the symmetric NACA 0012 airfoil [11,39,41,42,89,96,98,99]. Several papers use the NACA 64-618 since it is selected for the outboard third part of the blade on the simulated 5-MW NREL offshore baseline wind turbine [31,38,70,82,100,101,102]. At this part of the blade, ice accumulates the most. Moreover, this airfoil type (NACA series 6-Digit) has been used for many large wind turbine blades [8]. Timmer [103] also outlined the characteristics of the airfoil series NACA 6-digit for large wind turbine blades. The first step is to validate the clean airfoil’s resulting aerodynamic coefficients. The literature contains references to the aerodynamic performance of clean airfoils derived from either theoretical research or experimental investigations. As a result, the validation of the clean airfoil occurs within the framework of satisfying the user of the simulation tool. Validation of an iced airfoil involves verifying the ice form acquired under identical icing conditions.

Now that numerical techniques are becoming more prevalent in wind turbine icing research [54], it is vital to compare experimental and numerical icing simulation findings for typical wind turbines operating under different icing conditions [104]. As we can realize from tables, over the last two decades, the most common available tested and documented reference wind turbines are the NREL 5 MW and the NREL Phase VI from the National Renewable Energy Laboratory. These two common types are accessible for validating numerical studies on icing, while other types were also evaluated.

3.1. NREL-Phase VI Horizontal-Axis Wind Turbine

This real wind turbine was characterized experimentally under normal conditions at NASA’s Ames Research Center wind tunnel. Many CFD studies use the NREL’s Phase VI wind turbine to test the adopted codes because such test data are available. The information on the characteristics required to quantify the full-scale wind turbine aerodynamic performance is available in a technical report distributed by the National Renewable Energy Laboratory (NREL) [105]. Han et al. [106] presented ice accretion tests on this model as an example of icing research on this turbine. In contrast to the operation mode of the variable-speed and variable-pitch-controlled wind turbine currently available in the industry, this two-bladed turbine, composed of S809 airfoils, often works with a constant rotor rotational speed at varying wind velocities [9].

3.2. NREL 5-MW Offshore Baseline Wind Turbine

This conventional upwind variable-speed, variable blade-pitch-to-feather-controlled virtual wind turbine comprises three blades of six different airfoils distributed along a span of 63 m, as demonstrated in

Table 1. Airfoil distribution on the NREL 5-MW baseline wind turbine blades.

Airfoils	Spanwise Position	Section Radius (m)	Chord Length (m)
DU W-405	19%	11.75	4.557
DU W-350	25%	15.85	4.652
DU W-350	32%	19.95	4.458
DU 97-W-300	38%	24.05	4.249
DU 91-W2–250	45%	28.15	4.007
DU 91-W2-250	51%	32.25	3.748
DU 91-W-210	58%	36.35	3.502
DU 91-W-210	64%	40.45	3.256
NACA 64–618	71%	44.55	3.010
NACA 64–618	77%	48.65	2.764
NACA 64–618	84%	52.75	2.518
NACA 64–618	89%	56.1667	2.313
NACA 64–618	93%	58.90	2.086
NACA 64–618	98%	61.6333	1.419

[107]. The specifications of this reference wind turbine are available in a technical report provided by the NREL laboratory [107]. Unlike the preceding turbine, this virtual model has not been the subject of deepened icing-related experiments. However, the NACA 64-618 airfoil, which comprises the last one-third of its blade, has been examined thoroughly over the past ten years.

In addition to the validation possibilities with experimental results available for the types mentioned above of wind turbines, it is also convenient to compare numerical studies with others that utilize similar solutions and, if accessible, with other solvers’ findings. Furthermore, As the primary objective of a potential Quasi-3D or Full-3D simulation approach is to assess the overall power loss of the wind turbine due to icing, these types of studies can benefit from real-time field measurements and observations, if available, to validate the results with the power production loss of the observed iced-up wind turbine based on the data measured during certain icing events. It might also be useful to state the benefits and drawbacks of each strategy.

The advantages of the Quasi-3D simulation can be summed up by the relatively low computational cost associated with simplification and simulation consistency to explore many scenarios of ice accretion in different weather conditions. While failing to take into account the transition and different 3D effects of flow, particularly in the radial direction of the blades’ span, may cause simulation inaccuracies that underestimate the loss in aerodynamic performance and power produced. A Fully 3-D simulation, on the other hand, might eventually produce improved accuracy and replication reliability at the expense of significant computational demands. Most of the recent research that performed Quasi-3D simulations using the CFD-BEM approach or Fully 3D simulations are listed and summarized in this section. In addition, the reviewed Quasi-3D and Fully 3D icing simulation studies are presented in

Table 2. Synopsis of the research on 3D and Quasi-3D wind turbine icing simulation.

		Simulation Tool		Configuration and Output
Ref.	Type of Study	BEMT	CFD	IT	WT	AF	EV	Results
[78]	Quasi-3D	XFOIL	NA	R&G	Aeolos-H 30 kW	NACA 64618, S809, DU93-W-210	Y	IS, P(V)
[79]	Quasi-3D	XFOIL	SU2, an open-source RANS solver & METUDES, an in-house DDES solver	R&G	Aeolos-H 30 kW and NREL 5MW	Table 1	Y	IS, Polars, P(V)
[80]	Quasi-3D	In-house tool using XFOIL and an open-source panel code coupled with a turbulent BL model	SU2, an open-source RANS solver & METUDES, an in-house DDES solver	R&G	NREL Phase VI	NACA 23012, NACA 0012, DU93-W-210	Y	IS, T(r), Polars, PL
[49]	Quasi-3D	N.A.	LEWICE 2D	R	Enercon E40 600kW	S809	Y	IS, CP(TSR)
[61]	Quasi-3D	XFOIL and PROPID	CIRA-LIMA	R&G	Vestas V80 1.8 MW	NACA 63 415	Y	IS, Polars, P(V), PL
[16]	Quasi-3D	In-house code	FENSAP-ICE	R	NREL 5 MW	Table 1	NA	IS, Polars, CP(TSR), P(V), PL
[51]	Quasi-3D	FAST	TURBICE, FLUENT	R	NREL 5 MW scaled to WWD- 3 MW	Table 1	Y	IS, Polars, P(V), PL
[54]	Quasi-3D	WT-Perf	FLUENT and LEWICE	R&G	NREL 5 MW	Table 1	Y	IS, Polars, CP(TSR), CT(TSR), SR
[38]	Quasi-3D	BLADED	STAR-CCM+	R	NREL 5 MW	Table 1	Y	IS, Polars, P(V)
[31]	Quasi-3D	WT-Perf	CFX ICEAC2D	R&G	NREL 5 MW	Table 1	Y	IS, Polars, CP(TSR), T(TSR) P(V)
[21,29]	Quasi-3D	XTurb PSU	FENSAP-ICE	R&G	Wind-PACT 1.5 MW *	S825 NACA 64618	Y	IS, Polars, P(V)
[56]	Quasi-3D, Fully 3D	In-house code	FLUENT	R	NREL Phase VI	S809	NA	IS, T(r), Polars, PL
[12]	Quasi-3D, Fully 3D	NA	FENSAP-ICE	R&G	NREL Phase VI scaled to: Wind-PACT 1.5 MW *	S818 S825 S826	Y	IS, P(t)
[92]	Fully 3D	-	FLUENT	G	Small HAWT	NACA 4409	Y	IS, SR, CP(t), P(t)
[9]	Steady-state fully 3D	-	FLUENT	R&G	Variable-pitch/variable-speed 300 kW	-	Y	IS, CP(V), P(V)
[90]	Fully 3D	-	FENSAP-ICE	R&G	NREL Phase VI	-	Y	CP, CT, IS, PL
[81]	Quasi-3D	Open FAST	SU2, Open-source code	R	NREL 5 MW	Table 1	Y	IS, Polars, P(V), PL, CP(TSR)
[82]	Quasi-3D	Open FAST	SU2, Open-source code	R	NREL 5 MW	Table 1	Y	IS, P(V), Polars, PL, CP(TSR)
[76]	Quasi-3D	PROPID	LEWICE	R	450 kW	S809	Y	Polars, P(V)
[108]	Quasi-3D	In-house code	LEWICE FLUENT	R&G	600 kW	S816	Y	IS, Polars, P(V)
[98]	Fully 3D	-	FLUENT	R	NREL Phase VI	NACA0012 and S809	Y	IS, P(V)
[109]	Quasi-3D	In-house code	CFX	R	NREL 5 MW	Table 1	NA	CP(V)
[86]	Quasi-3D	FAST	ANSYS CFX	R	NREL 5 MW	Table 1	Y	IS, SR, P(V), T(V), Polars
[11]	Quasi-3D, Fully 3D	NA	ANSYS FENSAP-ICE	G	CQU 300 kW	NA	NA	IS, CP(r)
[83]	Quasi-3D	NA	LEWICE and FENSAP	R&G	NREL	S826	Y	IS, Polars, P(V)
[84]	Extrapolated polars from 2D simulations	NA	FLUENT and FENSAP-ICE	R&G	NREL 5 MW	Table 1	Y	IS, extrapolated polars
[85]	2D simulations for three blade sections	NA	FLUENT	R	NA	NACA 63−415	Y	Polars, CP(r)
[87]	Quasi-3D	NA	WISE—OpenFOAM	R&G	NREL Phase VI	S809 and NACA 0012	Y	IS, CP(r)
[94]	Fully 3D	-	In-house	R&G	NREL Phase VI	-	Y	IS
[110]	Quasi-3D	NA	ANSYS—FLUENT	R&G	NREL Phase VI	S809	Y	IS, Polars, CP(r)
[88]	Quasi-3D	QBlade	ANSYS-FENSAP-ICE	G	NREL 5 MW	Table 1	NA	IS, P(V), Polars, PL, CP(r)

Abbreviation: OB: One Blade Simulation; Full 3D: Full-scale wind turbine simulation; N-S: Navier–Stokes; IT: Ice Type; R: Rime Ice; G: Glaze Ice; WT: Wind Turbine; AF: Airfoils; EV: Experimental Validation; TR: Type of Results; TSR: Tip Speed Ratio; Y: Yes; N: No; NA: Not Available; Polars: $C_l\left(\alpha \right)$ Lift coefficient curve; $C_d\left(\alpha \right)$ Drag coefficient curve; P(V): Power Curve; IS: Ice shape; SR: Structural response on account of icing; PL: Power Loss; CP: Power Coefficient; T: Torque; r: section radius; t: time, V: velocity. DDES: Delayed-Detached-Eddy Simulation. BL: Boundary Layer. * NREL Phase VI Scaled to WindPACT 1.5 MW [111].

based on a literature review of numerical studies relating to icing on wind turbine blades. This review is restricted to HAWT research only.

4. Conclusions

The Quasi-3D is a practical simulation method that is less costly than the Fully 3D approach or experimental testing, which permits the examination of multiple scenarios of ice accretion in various conditions with reasonable computational requirements. This survey study revealed that the most recent icing simulation research had adopted the Quasi-3D simulation to quantify icing penalties on wind turbine power production. In contrast, the Fully 3D simulation studies were conducted exclusively on a single isolated blade instead of the entire turbine due to computational limitations. Generally, for both approaches, neglecting the rotational effects and considering stationary or quasi-stationary conditions remains a considerable simplification that results in inaccuracy. Additionally, most of the consulted studies focus on rime ice without considering the difficulties associated with the wet type of ice accretion, which impacts the accuracy of power loss estimation. Moreover, the absence of experimental results under real icing scenarios made it challenging to validate the results of numerical solutions.

The literature review revealed that most recent research studies focused on power loss estimation under various icing and operational conditions using Quasi-3D simulations for mainly two types of NREL wind turbines described briefly in this paper. For the computations of the CFD, BEMT, and aerodynamic modules, different software packages are employed. The study suggests that the existing inflight icing numerical codes require more experimental validations for wind turbines. At the same time, programs that use the BEMT are subject to limitations in ice-induced power curve calculations. Additional losses related to wind turbine geometry and operational conditions should be considered. A well-configured CFD solution of the RANS equations provides more accurate polar estimation as long as the BEMT does not account for 3D effects that may occur in the flow field. CFD offers more considerable modeling capabilities but a far higher computational cost than the BEMT. Another limitation lies in using panel method-based software (such as XFoil) to calculate the aerodynamic coefficients for iced airfoils. These programs cannot provide accurate results due to flow separation in the iced airfoils caused by leading-edge deformation. Moreover, coupling XFoil with QBlade makes it impossible to introduce the CFD-based estimated aerodynamic coefficients to QBlade. In fact, it will be more convenient to estimate $C_l\left(\alpha \right) and C_d\left(\alpha \right)$ using a CFD code and then using a BEMT code (such as PROPID, Bladed, and OpenFAST) to generate power curves.

In summary, advancements have been achieved in using CFD to comprehend the icing phenomena and its impact on the operation of wind turbines. However, a full turbine 3D simulation considering transient conditions is required to accurately replicate ice formation on the entire wind turbine to estimate overall performance under icing conditions. Finally, to better advance the research in this field, it is recommended to unify the research by adopting one of the NERL-characterized wind turbines, for which experimental results are available to validate a Fully 3D simulation for multiple actual events considering the recommended strategy described in this paper. Furthermore, the strategy benefits from the availability of simplified approaches and models like the Quasi 3D simulation along with the Makkonen model and numerical weather prediction for assessing wind turbine production losses due to icing.