Analysis of the Characteristics of Ice Accretion on the Surface of Wind Turbine Blades Under Different Environmental Conditions

Abstract

The problem of ice accretion on wind turbine blades seriously affects the safe operation and efficiency of wind farms. In this paper, FENSAP-ICE software is adopted to conduct research on this issue. The mechanism of ice accretion on wind turbine blades is analyzed, including the formation process of ice accretion, as well as three types of ice accretion, namely glaze ice, rime ice, and mixed ice, and their occurrence conditions. A prediction method for ice accretion on the blades is elaborated. A numerical calculation method is employed, and the accuracy of the numerical model is verified through the design of multiple groups of numerical simulation calculations for ice accretion on the NACA0012 airfoil. Using this model, the laws governing how environmental temperature, incoming flow rate, liquid water content, and droplet diameter influence ice accretion on wind turbine blades are studied. It is found that reducing the environmental temperature and increasing the incoming flow rate and the liquid–liquid water content will increase the ice accretion mass and area. Increasing the droplet diameter will increase the ice accretion mass, but the ice-covered area will decrease and will concentrate towards the leading edge.

1. Introduction

Wind energy, as a renewable energy source, is an important part of the transformation of the energy structure, and its development can help to improve the diversity and security of energy supply, reduce dependence on external energy sources, and enhance energy security. As global wind energy resources are mainly concentrated in high-*latitude and high-altitude areas, wind turbines are prone to blade icing in cold and low-temperature conditions in winter, especially in areas with low temperatures and high humidity [1]. Ice cover on wind turbine blades increases the blades’ weight, reduces the turbine’s speed and power generation efficiency, and affects the overall energy output [2]. Secondly, the presence of ice can alter the aerodynamic characteristics of the blades, leading to unbalanced airflow distribution, increased vibration and noise, and possibly even equipment damage [3]. Blade ice cover may also affect the safety of the wind turbine, increase the risk of failure, and lead to downtime for maintenance, thus affecting the continuity of power generation and economic benefits, which greatly affects the safe operation and power output of wind farms. Therefore, wind turbine blade ice cover has become a problem that needs to be solved urgently.

In the early days, research on ice covering problems mainly focused on aircraft wings and power transmission cables. In recent years, with the rapid development of global wind power, wind turbine blade ice covering problems have also attracted a great deal of attention from scholars around the world. The problem of ice covering wind turbine blade surfaces mainly focuses on the following aspects: (1) research on the growth process of ice covering the blade surface and the ice-covering mechanism; (2) the prediction of the shape of ice covering the blade surface; (3) the analysis of the difference in aerodynamic performance before and after a blade surface is covered by ice. For the above research directions, researchers mainly adopt the two methods of model testing and numerical simulation.

There are two main methods for conducting a wind turbine blade surface icing test: one is to use an ice wind tunnel in the laboratory for a wind turbine blade model test; the other is to observe the natural icing phenomenon at wind farms that have been built and put into operation. Li et al. selected a cylinder rotating around the longitudinal axis as an object and analyzed the various icing characteristics of the two rotational modes of the vertical and horizontal axes [4]. Zhang et al. carried out related experiments in the icing and snow wind tunnel of Central South University and concluded that the distribution and mass of ice columns on the backwind surface of the bogie grew rapidly during the experiments. They analyzed the distribution and mass of the snow and ice and concluded that the melt water sprayed from the rotating brake disc flew everywhere, leading to the rapid growth of icicles on the leeward side of the bogie during the experiment [5]. Honlly et al. observed the influence of ice covering the surface of an NACA0012 airfoil on its surrounding flow field through the method of oil smoke visualization, and analyzed the influence of a separation vortex on its stability after ice covering [6]. For a prediction of the shape and extent of ice cover, Guo et al. designed a rotor test rig with two NACA0018 airfoil blades in a wind tunnel and found that when the tip rate ratio is lower than 1, the ice covers the whole surface of the blade and grows layer by layer [7]. Feng et al. carried out a wind tunnel test on the wind turbine blades of the NACA7715 airfoil. The results showed that the maximum icing rate of the NACA7715 is 6.6%, and the maximum icing area ratio is 21.8% at an angle of attack of −80° [8]. Zhang et al. conducted a test on the NACA0018 blade and the results show that salinity can reduce the icing area and ice thickness, and the icing range mainly focuses on the relative position of the blade chord within the range of −20%~20% [9]. Hochart et al. conducted ice coating tests on the blades of a 1.8 MW horizontal axis wind turbine and found that the amount of ice coating on the blades was the lowest at the blade roots and the greatest at the blade tips [10]. Han et al. carried out ice wind tunnel tests on rotating NREL series wind turbine blades under different environmental conditions and reproduced the ice coating process on a blade surface. The experimental ice type was compared with the ice type predicted by the LEWICE simulation, and it was found that the prediction results of ice frosting were in good agreement with the experimental results [11]. For the analysis of aerodynamic performance before and after icing, Dai et al. used an S8025 airfoil blade as the research object and found that the centrifugal load significantly affects the aerodynamic performance of wind turbines with tip icing. The results can be used as a reference to improve the blade tip de-icing of wind turbines [12]. Mu et al. chose the NACA0018 blade to conduct their test in a reflow icing wind tunnel, and the study showed that salinity can greatly inhibit the icing area and ice thickness [13]. Farzaneh et al. obtained the mass, shape, and profile of ice accumulation as a function of cylinder inclination in a horizontal icing wind tunnel for their study [14]. However, due to the size of the wind tunnel and the test environment, it was difficult to achieve a full-size model for wind tunnel tests of ice formation. And it is difficult to accurately control the environmental variable parameters in scaled-down model tests.

With the rapid development of computer technology, researchers have been using numerical simulation methods to study the problem of ice cover since the 1960s. At the same time, the methods of flow field, droplet impact characteristics, and ice cover analysis based on computational fluid dynamics have become more mature, and numerical simulation methods have been more widely used. Although wind turbines were first adopted as early as the 18th century, due to the large-scale application of thermal power and hydroelectric power, attention was at first not widely paid to research on wind turbines. And research on the icing problem on the surfaces of objects started mainly around transmission lines and the aerospace field. For the prediction of icing models, Wang et al. proposed a new residual-based unsupervised domain adaptive method for multi-turbine blade icing detection, which significantly improves the performance of icing detection in multi-turbine scenarios by using a combination of deep residual grids and maximum mean difference [15]. Wu et al. developed a three-dimensional numerical method for a two-phase flow of air and water under rotating conditions and established a thermodynamic model for icing in the environment of aircraft engines [16]. In IMSICM, Wang et al. used a 3D Free Wake Lifting Line, and a 2D Viscous and Inviscid Interaction method to calculate the flow field and proposed an efficient dynamic icing calculation model [17]. The wind shear effect has a large impact on the shape of glaze ice, which is mainly manifested by the suppression of ice protrusion behind the main ice angle. Wang et al. proposed an icing risk assessment method combined with wind power generation and used the C-means clustering algorithm to provide a more effective and accurate method for blade icing diagnosis [18]. M. Ibrahim et al. modeled wind turbine blades using the blade element momentum theory, which provided new insights into the modeling of glaze ice on large wind turbine blades [19]. Pope et al. used a CFD icing simulation, proposed a methodology for freezing ice scaling on rotating blades, and suggested parameters for the glaze ice profile on rotating blades [20]. Chankyu Son et al. proposed a model that takes into account the flow transition caused by blade surface roughness, which coupled the Langtry–Menter model and included roughness amplification with the boundary conditions of k and u [21,22]. Jin J Y et al. divided the blades of a 300 kW wind turbine into nine airfoils, and carried out two- and three-dimensional numerical simulations of ice coating on them, respectively. It was found that the ice thickness obtained by the two-dimensional ice coating simulation was greater than that found by the three-dimensional simulation [23]. Manatbayev et al. used FENSAP-ICE to obtain the shape of the ice accumulation over a range of angles of attack between −25 °C and 25 °C to predict the shape of ice accumulation on the VAWT. The results showed that the VAWT could not generate power under glaze ice conditions [24]. However, with the rising position of wind power in the global energy structure, the operational stability of wind turbine blades in extreme climates has become a pressing issue. Most of the research on ice formation on wind turbine blades borrows from the experience of studying ice formation on aircraft wings. The relevant scholars often simplify the three-dimensional problem into a two-dimensional airfoil ice formation problem for their studies using the blade element theory. In this way, the blade’s span-wise velocity is not fully taken into account. Calculation using a three-dimensional model can more accurately restore the ice covering process on a blade surface, due to the simulation being more complex; research on the three-dimensional numerical prediction of overall blade ice coverage is less common. Therefore, by establishing an accurate prediction model for wind turbine blade ice covering, the distribution characteristics and impacts of ice adhesion under different meteorological conditions can be effectively assessed.

In this study, we will carry out meteorological icing environment analysis and analyze the icing conditions based on meteorological observation data, calculate the icing process of NACA0012 airfoils by a numerical simulation method, and study the influences of incoming flow speed, ambient temperature, air water content, and water droplet diameter on the icing of wind turbine blades, so as to provide a certain theoretical basis for the prevention and anti-icing of wind farms and the management of early warning of icing. The NACA0012 blade model used in the experiment is stationary, and its detailed information is as follows: The blade model dimensions are 110 mm × 920 mm, the twist angle ranges from −6° to 6°, and the taper ratio is 0.5. This blade is a symmetric model. When the chord length c is taken as 1, some of the coordinates are as follows: when x/c = 0.005, y/c = 0.01223; when x/c = 0.01, y/c = 0.017; when x/c = 0.03, y/c = 0.0284; when x/c = 0.04, y/c = 0.0323; and when x/c = 0.05, y/c = 0.0355.

2. Wind Turbine Blade Ice Covering Mechanism

2.1. Ice Cover Formation

Ice is a product of the exothermic solidification of a liquid under the influence of low temperature. Currently, most research on wind turbine blade icing is based on the icing mechanism of airplanes in high-altitude flight. The two icing mechanisms are the same from a microscopic point of view, both involve the process of freezing on the surface of the structure after a large number of super-cooled water droplets are captured by the structure. However, the meteorological conditions and processes of wind turbine blade icing and aircraft icing are quite different. The environmental conditions for aircraft icing are composed of atmospheric suspensions such as water vapor mass condensation and ice crystals, and the main feature of the icing process is the high-speed impact of super-cooled water droplets with the structural surface for a short period of time [25]. The climatic conditions of wind turbine blade icing are characterized by freezing rain, wet snow or icy fog, clouds, and rime and other water vapor condensate deposits; the main feature of the icing process is the process of long-duration impacts between the super-cooled water droplets and the structural surface. There have been a large number of mature results in aircraft icing research. However, under rain and rime conditions, there are fewer studies on the icing mechanism and ice shape prediction of wind turbine blades, and no design standards for blade icing have been formed.

The meteorological conditions for the icing of wind turbine blades need to be met by freezing droplet temperatures (below 0 °C) and the presence of water in the atmosphere in three states (water vapor, liquid water, and solid water). When a wind turbine operates in a cold and humid area, super-cooled water droplets in the atmosphere will drift over the wind turbine with the wind. Due to the different diameters of water droplets of different mass and inertia forces, the impact on the blade has a different trajectory. These trajectories determine the characteristics of the ice cover such as ice volume, ice thickness, and ice density. Therefore, the environmental conditions for blade ice cover and the different kinds of ice cover need to be clarified.

2.2. Ice Cover Types and Conditions

On wind turbine blades, icing occurs when tiny liquid droplets in the air, or rain and snow, carried by the airflow in low-temperature conditions, strike the blade surface. They then continuously freeze and accumulate. This is a highly complex process involving both mass and heat transfer. Based on the ice formation process and ambient conditions, surface ice on a wind turbine blade can be divided into three types of ice: glaze ice, rime ice, and mixed ice [26].

Glaze Ice: When the icing environment temperature is between −10 °C and 0 °C, the relative incoming speed is faster, and the liquid–liquid water content is higher. The irregular ice shape changes the aerodynamic profile of the blade, which leads to drastic changes in the airflow on the surface of the blade after covering it with glaze ice, which has a large impact on its aerodynamic performance. The quantity of air inside the glaze ice is smaller, the surface is smooth, the texture is harder, and the density is larger, usually more than 900 kg/m³, which means it is not easy to remove compared with other ice types.

Rime Ice: The environmental temperature of rime ice formation is generally lower than −10 °C, the relative speed of the incoming flow is faster, and the liquid–liquid water content is higher. In the above environment, the liquid water droplets in the air are all frozen into ice instantly after hitting the surface of the blade, and there is no liquid water on the surface of the blade to produce overflow. So, the rime ice can be considered to be undergoing linear growth on the surface of the blade, the original aerodynamic design of the blade will be changed to a lesser extent, and the impact on the aerodynamic performance will be lower. As the rime ice freezes into ice in a shorter time, there is more air inside after freezing, so the surface of rime ice is rougher and its density is lower, about 300~600 kg/m³, which means it is easier to remove than glaze ice.

Mixed Ice: The physical properties of mixed ice are between glaze ice and rime ice, which means it can be regarded as a mixture of glaze ice and rime ice, and the environmental factors for its formation are also between glaze ice and rime ice.

Table 1. Characteristics of glaze ice and rime ice.

Type	Environmental Temperature	Approach Rate	Liquid Water Content in Air	Impact on Aerodynamic Performance	Background (Texture)	Density
glaze ice	−10~0 °C	Quicker	High	Larger	Stiff	Larger
rime ice	<−10 °C	Quicker	High	Smaller	Rough	Smaller

shows the comparative analysis of glaze ice and rime ice. (An approach rate higher than 10 m/s is considered relatively fast, while an approach rate lower than 5 m/s is regarded as relatively slow. A liquid–liquid water content higher than 0.5 g/m³ is deemed to be high, and that lower than 0.3 g/m³ is considered low.)

3. Prediction Methods for Blade Ice Cover

3.1. Numerical Calculation Methods

The more mature numerical simulation process of ice cover formation at this stage is divided into 3 steps [27]: (1) obtaining the winding flow field outside the airfoil through the control equations; (2) solving the water droplet impact process to obtain the water droplet collection rate of the structure in this flow field; (3) carrying out the calculation of ice cover growth on the surface of the airfoil.

The main calculation of the ice covering process lies in the droplet impingement characteristics, which are mainly governed by the winding flow field. In this paper, the Fluent software 2022R1 was used to calculate the flow field outside the airfoil, considering the viscous influence of the air bypass flow field. The turbulence model was chosen to be the SST k-ω model, which combines the advantages of the k-ω model and the k-ε model, and uses the robustness of the k-ω model to capture the viscous boundary layer flow in the near-wall area [28]. The robustness of the k-ω model is used to capture the viscous boundary layer flow at the near-wall surface, while the k-ε model is used to simulate the airflow field of the blade more accurately in the main flow region. The transport variables of the model are the turbulent kinetic energy k and the specific dissipation rate ω, and the transport equations are

$$\rho {\displaystyle \frac{\partial k}{\partial t}}+\rho \left(u\cdot \nabla \right)k=\nabla \cdot \left[\left(\mu +{\mu }_T{\sigma }_k\right)\nabla k\right]+P_k-{\beta }^{\ast }\rho \omega k$$

(1)

$$\nabla \cdot \left[\left(\mu +{\mu }_T{\sigma }_{\omega }\right)\nabla \omega \right]+P_{\omega }-\beta \rho {\omega }^2+2\left(1-F_1\right){\displaystyle \frac{{\partial }_{\omega 2}\rho }{\omega }}\nabla k\nabla \omega =\rho {\displaystyle \frac{\partial \omega }{\partial t}}+\rho \left(u\cdot \nabla \right)\omega$$

(2)

where μ is the air rate; ρ is the air density; μ_T is the fluid viscosity at the actual temperature; t is the time; P_k is the effective generation rate of k; P_ω is the effective generation rate of ω; β, β*, σ_k, σ_ω, and σ_ω2 are empirical coefficients; and F₁ is the mixing function.

The water droplet collection process and the blade surface icing process were calculated by FENSAP-ICE, in which the water droplet collection process is solved by the super-cooled water droplet two-phase flow control equation. Roughness is considered relative to an ideal smooth surface. The shallow-water icing model was chosen for the icing model, which is based on the water film movement model, considering the droplet backflow phenomenon on the blade surface, and calculating the water droplet mass and heat transfer problems at each node on the blade surface.

3.2. Numerical Simulation and Validation

3.2.1. Airfoil Boundary Conditions and Meshing

In order to fully compare the numerical simulation results with NASA experimental data, and to ensure the accuracy of the numerical model for ice cover, this paper designs three sets of numerical simulations of ice cover on the NACA0012 blade. It chooses three ambient temperatures of −5.56, −11.11, and −26.11 °C, and gives full consideration to the three types of ice, glaze ice, rime ice, and mixed ice, with the rest of the conditions remaining the same (an incoming speed of 67 m/s, an angle of attack of 4°, a liquid–liquid water content of 1 g/m³, a droplet diameter of 20 μm, and an icing time of 360 s). In particular, the wing chord length is 0.5334 m, which is consistent with the wing type chosen for the NASA test.

As shown in Figure 1a, the boundary conditions for the wing calculation are set as follows: the left-curved boundary, the upper and lower boundaries, and the right boundary are set as far-field pressure boundaries. The front and rear boundaries perpendicular to the paper surface are set as symmetry plane boundaries, and the wing is set as a no-slip wall.

In order to ensure that there is no backflow at the outlet, the outlet should be more than 15 times the chord length of the airfoil from the tail of the airfoil. Due to the constant shape of the airfoil spreading direction, this paper only constructs a layer with a thickness of 2 mm in the spreading direction. The first layer of the grid outside the airfoil wall thickness is 0.001 mm to ensure that the y+ is less than 1 under each working condition, and the grid outside the wall is shown in Figure 1b.

In general, the grid quality and density determine the calculation accuracy and efficiency. In order to ensure the accuracy of the calculation results and save the calculation cost as much as possible, this paper chooses the first group of simulations to verify the grid independence of the model. Among them, the influence of the number of grids on the quality of the ice cover is shown in Figure 2. It can be seen that the number of grids is more than 2.5 × 10⁵, and the quality of the ice cover tends to be stabilized.

To ensure the accuracy and efficiency of the numerical simulation of wind turbine blade surface ice cover, the number of cells of the blade model is about 1.8 × 10⁶, and the mesh encryption is carried out for the blade part, as shown in Figure 3. The thickness of the first grid of the boundary layer is set to 0.2 mm, and the computational verification y+ is in the range of 30 to 300.

The external flow field region is of a CH type and the distance from the flow field outlet to the trailing edge of the blade is greater than 10 times the maximum chord length of the blade, and the overall model computational domain is shown in Figure 4.

3.2.2. Analysis of Numerical Simulation Results for NACA0012 Airfoils

Using the above meshing method, three sets of numerical simulation results are compared with NASA test data as shown in Figure 3, where c is the chord length of the NACA0012 airfoil. As shown in Figure 5 (the black line represents the NACA 0012 airfoil, the blue line is the numerical simulation model, and the red line is the NASA experimental model), when the temperature is −5.56 °C, a liquid droplet does not freeze immediately when it hits the surface of the airfoil, and under the influence of the incoming flow, the water film moves upward and freezes gradually, forming an upwardly curved ice corner at the leading edge of the airfoil, which is in a state of open ice, with an irregular ice shape, which has a greater impact on the aerodynamic performance of the airfoil. When the temperature is −11.11 °C, the upward ice corner phenomenon is weakened, and the overflow phenomenon at the bottom of the airfoil is more serious, and it is in a state of mixed ice. At −26.11 °C, the liquid droplets freeze immediately when touching the surface of the airfoil, and almost no water droplets move upward with the airflow. Therefore, at lower temperatures, the overlying ice is in the form of rime ice and the ice pattern is more consistent with the aerodynamic design of the airfoil and has less impact on the aerodynamic performance of the airfoil.

As can be seen from Figure 5, the numerical simulation of the ice type in this paper fits well with the ice type of the NASA test. The relative errors of the maximum ice thickness of the three groups of simulations are shown in

Table 2. Relative errors in maximum ice thickness for numerical modeling.

Number	Maximum Ice Thickness Tested/mm	Modeled Maximum Ice Thickness/mm	Relative Error/Percent
1	12.828	13.852	7.980
2	12.620	13.618	7.910
3	15.197	14.439	4.990

. The larger relative error of the maximum ice thickness in the environment of −5.56 °C in No. 1 is due to the fact that the N-S equations have a certain amount of error in calculating the adherent flow, but the error of 7.98% is still within the acceptable range.

4. Analysis of Factors Affecting Wind Turbine Blade Icing

From the above analysis, it was found that the accuracy of the numerical simulation in terms of the calculation of wing icing is relatively high. So, this paper uses a numerical simulation to analyze the influence of different environmental factors on the surface icing of wind turbine blades. The target blade is a 2 MW wind turbine blade, and the relevant geometric parameters are shown in

Table 3. Sectional airfoil data.

Airfoil Designation	Wind Turbine Radius/m	Blade Span/m	Chord Length/m	Relative Thickness/Percent
DU86-1	5.46	0.50	0.50	35.39
DU86-2	15.46	0.50	0.50	18.70
DU86-3	30.56	0.50	0.50	12.20

. The blade is composed of an S-shaped airfoil, which has a larger wind energy utilization rate and lower roughness requirements and is widely used in the selection of wind turbine blades. The wind turbine blade is shown in Figure 6.

By changing the ambient temperature, incoming flow rate, liquid water content, and water droplet diameter, the growth of ice cover on the blades under different environmental factors was simulated. This revealed the influence of various environmental factors on the law governing three-dimensional static blade surface ice cover. This paper combines the actual environmental conditions of the project and the four above-mentioned environmental factors, and designs 18 groups of working conditions for numerical simulation calculations, as shown in

Table 4. The conditions influencing wind turbine blade surface ice cover.

Number	Temperature/°C	Incoming Flow Rate/(m∙s−1)	Liquid Water Content/(g∙m−3)	Droplet Diameter/μm
1	−5	60	1.0	20
2	−10	60	1.0	20
3	−15	60	1.0	20
4	−20	60	1.0	20
5	−25	60	1.0	20
6	−30	60	1.0	20
7	−10	70	1.0	20
8	−10	80	1.0	20
9	−10	90	1.0	20
10	−10	100	1.0	20
11	−10	60	1.5	20
12	−10	60	2.0	20
13	−10	60	2.5	20
14	−10	60	3.0	20
15	−10	60	1.0	25
16	−10	60	1.0	30
17	−10	60	1.0	35
18	−10	60	1.0	40

, with a simulation time of 900 s. Groups 1 to 6 are mainly considered for the influence of temperature, groups 2 and 7 to 10 are mainly considered for the influence of the incoming flow velocity, groups 2 and 11 to 14 are mainly considered for the influence of the water content of the air, groups 2 and 15 to 18 are mainly considered for the influence of the water content of the air. Groups 2 and 11 to 14 consider the effect of liquid water content, and Groups 2 and 15 to 18 consider the effect of water droplet diameter.

Table 5. The relationship between the incoming flow rate and the Reynolds number.

Incoming Flow Rate/(m∙s−1)	Reynolds Number	Critical State
60	2.03 × 106	Super-critical state
70	2.37 × 106
80	2.70 × 106
90	3.04 × 106
100	3.38 × 106

shows the change in Reynolds number.

4.1. Effects of Ambient Temperature

The ambient temperature is an important factor affecting the ice overlay on the surface of wind turbine blades and, considering the climatic conditions of wind farms in alpine regions, groups 1 to 6 are selected. Calculate when the temperature is −5, −10, −15, −20, −25, −30 °C, when the overlying ice generation and quality changes, and when the simulation and calculation time is 900 s.

The variation in ice cover on the blade surface is shown in Figure 7, demonstrating three sets of typical ice cover conditions. The variation in ice cover mass with temperature is shown in Figure 8.

As can be seen in Figure 7, with the gradual decrease in ambient temperature, the ice-covered area on the blade surface shows an overall expansion trend, and the thickness of the ice-covered area at the leading edge of the blade thickens significantly with the decrease in temperature. The maximum thickness of ice cover at the leading edge of the blade is 1.290 mm at −5 °C, and the maximum thickness of ice cover at the leading edge is 29.23 mm at −30 °C. As can be seen in Figure 8, the temperature has a greater influence on the quality of ice cover on the blade surface when the ambient temperature is above −20 °C, and the average increase in ice cover quality is 3.700 kg for every 5 °C decrease. As the temperature continues to decrease, when the ambient temperature is below −20 °C, the temperature has a greater influence on the quality of ice cover on the blade surface, and the average increase in ice cover quality is 3.700 kg for every 5 °C decrease. As the temperature continues to decrease, when the ambient temperature is lower than −20 °C, the influence of temperature on the quality of the ice-covered blade surface gradually decreases, and the average increase in ice-covered mass is 1.140 kg for every decrease of 5 °C. This is because the liquid water content is constant. When the ambient temperature is above −20 °C, decreasing the temperature raises the collection rate of water droplets on the blades, and the content of the remaining liquid water in the air decreases. When the temperature is lower than −20 °C, decreasing the temperature cannot obviously improve the collection rate of water droplets, resulting in an increase in the ice-covered mass rate, resulting in a slower increase in the mass of the ice cover.

4.2. Influence of Incoming Flow Rate

The rotational speed of the wind turbine in operation is not fixed. In order to simulate the actual incoming rate of the blades during operation, this paper sets up five incoming rates, which, respectively, correspond to 60, 70, 80, 90, and 100 m/s in the calculation of group 2 and groups 7–10. After 900 s of simulation, the distribution of the overlying ice on the surface of the blades with the change in the mass is shown in Figure 9 and Figure 10.

As can be seen from Figure 9, with the gradual increase in the incoming flow rate, the ice-covered area of the blade surface shows an overall expansion trend. The expansion of the range of change is small and is mainly distributed on the leading edge of the blade.

As can be seen in Figure 10, with the increase in the incoming rate and other steps, the mass of ice cover on the surface of the wind turbine blade also increases linearly, and the mass of ice cover grows by 2.357 kg on average for every increase of 10 m/s in the incoming rate. The main reasons are: (1) The increase in the relative rate between the blade and the incoming flow makes the air flowing past the blade per unit of time increase. In icing conditions, the frequency of the super-cooled droplets impacting the blade increases, resulting in a gradual increase in the amount of ice cover. (2) The increase in the relative rate between the super-cooled water droplets and the blades leads to an increase in the ice-covered area on the surface of the blades.

4.3. Effect of Liquid Water Content

The liquid water content is another important environmental factor for the study of blade surface ice cover, and its magnitude can reflect the upper limit of icing under low temperatures. In this paper, we choose 1.0, 1.5, 2.0, 2.5, and 3.0 g/m³ as the five air water content cases for the simulation of blade surface ice cover; these correspond to group 2 and groups 11–14. After 900 s of ice cover simulation, the distribution and mass change in the blade surface ice cover are shown in Figure 11 and Figure 12.

As can be seen from Figure 11, with the gradual increase in liquid water content, the area of surface ice cover on the blade shows an overall expansion trend, and the expansion change range is large. As can be seen in Figure 12, the mass of the blade surface ice cover increases with the increase in liquid water content. The mass of the blade surface ice cover increases by 4.264 kg for every 0.5 g/m³ increase in liquid water content, which is mainly due to the fact that the density of the super-cooled water droplets in the air increases with the increase in liquid water content. This results in the frequency of the blade hitting the super-cooled water droplets increasing greatly, and thus the area of the blade surface covered by ice, as well as the mass of ice, both increase.

4.4. Effect of Median Volume Diameter

There is a significant difference in the inertia of water droplets with different diameters, and the distribution of ice cover is different after the impact of water droplets and the blade surface. Meanwhile, under the same liquid water content, the increase in water droplet diameter also reduces the density of the water droplets. In this paper, the five droplet diameters of 20, 25, 30, 35, and 40 μm were selected for the ice cover simulation, which, respectively, correspond to group 2 and groups 15–18 in Table 3. After 900 s of the numerical simulation of ice cover, the distribution and mass change in the ice cover on the blade surface are shown in Figure 13 and Figure 14.

As can be seen in Figure 13 and Figure 14, with the increase in droplet diameter, the ice-covered area on the blade surface gradually concentrates at the leading edge of the blade. The mass of the ice cover on the blade surface grows by 2.560 kg for every 10 μm increase in droplet diameter. The main reason for the linear growth of the mass of the ice cover is that the inertia of the droplets increases with the increase in droplet diameter, and the droplet collection rate on the surface of the blade rises as a result. The maximum droplet collection rate on the blade surface is 0.5321 for a droplet diameter of 20 μm, while the maximum droplet collection rate on the blade surface is 0.7146 for a droplet diameter of 40 μm.

5. Discussion

This section discusses and analyses in depth the effects of four aspects of wind turbine blade icing: ambient temperature, incoming flow rate, liquid water content, and water droplet diameter.

5.1. Ambient Temperature

As the ambient temperature gradually decreases, the area of the ice-covered blade surface shows an overall expansion. This phenomenon is closely related to the physical process of temperature change. When the ambient temperature drops, the water vapor in the air begins to condense into water droplets and attach to the blade surface to form an ice layer. Especially at low temperatures, the rate of condensation of water droplets is accelerated, leading to the gradual formation of a thicker ice layer on the surface of the blade. In the leading-edge region of the blade, the formation of the ice layer is particularly significant due to the characteristics of the airflow and the high flow resistance, so the thickness of the ice at the leading edge thickens significantly as the temperature is further reduced.

Specifically, the maximum ice thickness at the leading edge of the blade was 1.290 mm when the ambient temperature dropped to −5 °C. However, the maximum ice thickness at the leading edge of the blade increased significantly to 29.23 mm as the temperature continued to drop to −30 °C. This change can be attributed to the accelerated rate of condensation of the moisture in the airstream at the low temperature and the gradual accumulation of the ice layer on the surface of the blade.

In terms of changes in the mass of the ice cover, when the ambient temperature drops below −20 °C, the change in temperature has a significant effect on the mass of the ice cover on the blade surface. This was shown by an average increase of 3.700 kg in the mass of the overlying ice for every 5 °C decrease. At this time, the decrease in temperature caused more water droplets to accumulate on the blade surface, forming a thicker ice layer. This is because the attachment efficiency of the water droplets was low at higher temperatures, and the ability of the water droplets to condense and adhere to the ice layer was gradually increased as the temperature was lowered. However, when the ambient temperature is further reduced below −20 °C, the effect of temperature on the quality of the ice cover on the blade surface gradually diminishes. In this case, the average increase in ice cover mass was only 1.140 kg per 5 °C. This change can be physically explained by the fact that the moisture content in the air remains relatively constant in the temperature range below −20 °C. The temperature of the air is also lower than the temperature of the blades. Although the temperature was further reduced, the rate of water droplet collection in the air did not increase significantly. The low-temperature environment makes the ice on the blade surface stronger and denser. The remaining moisture in the air gradually decreases, leading to a stabilization of the number of water droplets that can accumulate on the blade surface even if the temperature continues to decrease, thus slowing down the rate of increase in the mass of ice cover.

Taken together, the effect of temperature on the ice cover on the blade surface is complex and shows different patterns of change in different temperature intervals. When the temperature is above −20 °C, the low temperature can effectively promote the condensation and accumulation of water droplets, and the mass of the ice-covered layer increases rapidly. When the temperature is lower than −20 °C, the influence of the temperature on the collection efficiency of water droplets tends to weaken, and the growth of the mass of the ice-covered layer slows down accordingly.

5.2. Incoming Flow Rate

When the incoming velocity in the environment where the wind turbine blades are located gradually increases, the ice-covered area on the blade surface shows a tendency to expand. This expansion is mainly concentrated at the leading-edge part of the blade. Specifically, an increase in the incoming velocity leads to an increase in the relative velocity between the wind speed and the blade, which in turn affects the interaction of airborne water droplets with the blade surface. Although some degree of ice cover occurs over the entire blade surface, this ice build-up is concentrated at the leading-edge region of the blade, indicating that the airflow characteristics of the leading edge make it the most susceptible to ice build-up. With the increase in the incoming flow velocity, the ice layer on the blade surface also thickens gradually, showing a linear growth trend. According to the experimental data, the mass of ice on the blade surface increases by 2.357 kg for every 10 m/s increase in the incoming velocity, which is closely related to the dynamics of the airflow.

As the velocity of the incoming flow increases, the relative velocity between the blades and the incoming flow increases. When the amount of air flowing through the blades per unit time increases, the frequency of collisions between super-cooled water droplets and the blade surface during the icing process also rises. Here is how it works: As air passes over the blade surface, the water vapor it contains condenses into super-cooled water droplets. These droplets then hit the blade at a certain speed. When the relative velocity between the blade and the airflow goes up, the number of droplet impacts on the blade and the energy of these impacts increase. This enhanced collision effect speeds up the condensation of water droplets. As a result, more water droplets adhere to the blade surface per unit of time, leading to the formation of a thicker ice layer. Therefore, the amount of ice cover increases linearly as the incoming velocity increases.

In addition, as the incoming velocity increases, the relative velocity between the super-cooled water droplets and the blades becomes larger, and this change directly affects the way in which the water droplets attach to the blade surface. At higher relative velocities, water droplets no longer impact the blade at lower velocities, but at higher velocities, which not only increases the frequency of droplet impacts but also leads to an increase in the droplet attachment area. Water droplets impacting the blade surface at higher velocities are more likely to spread to form a larger area of ice on the surface, which results in a larger ice-covered area on the blade surface.

Taken together, the effect of increased incoming velocity on blade surface ice cover is significant. The increased relative velocity not only enhances the collision frequency between water droplets and the blade surface but also increases the energy of droplet impact and the attachment area, which accelerates the increase in the mass of the ice cover. As the incoming velocity increases, the linear increase in the mass of the ice cover on the blade surface becomes more pronounced, and this increase is mainly at the leading edge of the blade, as the airflow characteristics in this region are more likely to lead to the condensation and accumulation of water droplets.

5.3. Liquid Water Content

With the gradual increase in the water content in the ambient air, the ice-covered area on the surface of the wind turbine blades showed an obvious expansion trend. And the expansion range was relatively large, which indicates that the increase in the moisture content in the air has a significant effect on the formation of ice cover on the surface of the blades. At the same time, with the increase in liquid water content, the mass of the ice accumulated on the surface of wind turbine blades also grows, and this growth shows a certain regularity. According to the experimental data, for every 0.5 g/m³ increase in the liquid water content, the mass of the ice on the blade surface increases by 4.264 kg on average. This can be analyzed in depth from a physical point of view and is mainly reflected in the process of water vapor condensation into super-cooled droplets in the air, as well as the mechanism of interaction between these super-cooled water droplets and the blade surface.

As the water content of the air increases, the density of super-cooled water droplets in the air also increases. Super-cooled water droplets are droplets of water vapor that condense into a liquid state at temperatures below 0 °C. However, due to the low temperature, they do not freeze immediately but remain in a liquid state. As these super-cooled water droplets pass over the blade surface, they collide with the blade surface and freeze, forming an ice layer. When the liquid water content increases, the number of super-cooled water droplets in the air also increases, which leads to a significant increase in the frequency of collisions of super-cooled water droplets with the blade surface per unit time. Due to the increase in collision frequency, more super-cooled water droplets can accumulate on the blade surface, which in turn forms a thicker ice layer. At the same time, the kinetic energy of the water droplets is converted into thermal energy during the collision process, which causes more water droplets to condense and freeze in a short period of time, further accelerating the accumulation of the ice layer. With the increase in the frequency of water droplet impact, the adhesion effect on the blade surface is also enhanced. This not only leads to more water droplets attaching to the blade surface but also makes the area of water droplets spreading on the surface increase, which in turn enlarges the ice-covered area. Therefore, with the increase in liquid water content, both the ice-covered area and the mass of the ice cover on the blade surface show an increasing trend.

Taken together, the effects of airborne water content on blade surface ice cover are manifold. With the increase in liquid water content, the density and collision frequency of super-cooled water droplets increases significantly, which in turn leads to an increase in the mass and area of ice cover on the blade surface. This phenomenon is closely related not only to the number and density of the water droplets but also to the collision frequency and attachment ability of the water droplets, which ultimately leads to the thickening of the blade surface ice layer, indicating the significant influence of air humidity on the blade surface ice cover.

5.4. Median Volume Diameter

With the increase in water droplet diameter, the area of ice cover on the surface of wind turbine blades gradually tends to be concentrated at the leading-edge part of the blade and shows an obvious correlation with the increase in water droplet diameter. Specifically, for every 10 μm increase in droplet diameter, the mass of ice cover accumulated on the blade surface increases by an average of 2.560 kg. This linear increase in the mass of the ice cover can be further explained by a physical principle. This is mainly due to the fact that the droplet inertia increases with the increase in droplet diameter, which in turn affects the efficiency of the collection of water droplets on the blade surface.

Physically, the kinetic energy and inertia of a water droplet are proportional to the square of its diameter. Therefore, as the diameter of a water droplet increases, the inertia of the droplet increases, which means that larger water droplets have more kinetic energy and are able to collide with and adhere to the surface of the wind turbine blades more readily. Larger water droplets are less likely to be deflected by the airflow from the wind turbine blades and are able to impact more directly onto the blade surface, which allows more water droplets to accumulate on the surface of the blade and form a thicker ice layer. As a result of this effect, the number of water droplets accumulating on the blade surface and the degree of adhesion increase as the diameter of the droplets increases, which in turn leads to a linear increase in the mass of the ice layer.

In addition, an increase in the diameter of the water droplets increases the collection rate of water droplets on the blade surface. The droplet collection rate is the efficiency of water droplet attachment on the blade surface, which is usually affected by the motion characteristics of the droplet (e.g., kinetic energy, velocity, mass, etc.) and the morphology of the blade surface. In the experiment, the maximum droplet collection rate on the blade surface is 0.5321 for a droplet diameter of 20 μm and this increases to 0.7146 when the droplet diameter increases to 40 μm. This means that larger droplets are able to attach to the blade surface over a wider area, especially in the leading-edge region of the blade. The leading-edge region is usually the most concentrated part of the airflow, where water droplets tend to concentrate and accumulate, further aggravating the icing process.

As the diameter of a water droplet increases, the mass and volume of the droplet increase, and the corresponding kinetic energy increases. Larger water droplets are more likely to overcome air resistance and airflow disturbances and directly impact the surface of the wind turbine blade and attach to it. This not only increases the number of water droplets on the blade surface but also increases the attachment area of each droplet. Due to the greater inertia of the larger water droplets, the frequency and energy of the water droplets impacting the blade increases, which results in the water droplets staying on the blade surface for a longer period of time and having a stronger attachment effect, thus increasing the rate of ice accumulation on the blade. At the same time, the collection efficiency of water droplets on the blade surface increases significantly as the droplet diameter increases. Especially at the leading-edge region of the blade, where the airflow is most concentrated, the aggregation effect of water droplets is more obvious, so larger water droplets have a higher proportion of attachment in this region, leading to the formation of a larger area of overlying ice.

In summary, as the diameter of the water droplets increases, the inertia and attachment capacity of the water droplets are enhanced, leading to a gradual increase in the mass of ice accumulated on the surface of the wind turbine blades. Behind this phenomenon is the enhancement of collision frequency and attachment effect due to the increase in droplet inertia, which promotes the acceleration of the ice-covering process, especially at the leading-edge region of the blade, where the droplets are collected more efficiently, which further exacerbates the accumulation of the ice layer.

6. Conclusions and Outlook

In this paper, based on the numerical calculation method of computational fluid dynamics, the surface ice-covering process of wind turbine blades is divided into three parts: the calculation of the flow field of the wall outward circling flow, the solution of the water droplet impact process, and the calculation of the growth of surface ice cover on the blades by using the FENSAP-ICE software. Combining the SST k-ω turbulence model and the shallow-water icing model, the surface icing process of the NACA0012 airfoil is reconstructed. The accuracy of the numerical model is verified by comparing it with the NASA test data. Based on this numerical icing model, the surface icing process of the overall wind turbine blade is simulated, and the effects of four major environmental parameters, including ambient temperature, incoming flow rate, the liquid–liquid water content, and the diameter of water droplets, on the surface icing characteristics of the blade are investigated. The main conclusions are as follows:

Through the surface ice cover calculation and analysis of 18 sets of integral wind turbine blades under different working conditions, lowering the ambient temperature, increasing the incoming flow rate, and increasing the liquid–liquid water content will increase the mass of the ice cover and ice-covered area of the blade. Increasing the diameter of the water droplets will also increase the mass of the ice cover on the blade, but the area of the ice cover decreases—and it gradually gathers towards the leading edge of the blade. In addition, increasing the incoming flow rate and the liquid water content of the air increases the mass of the ice on the blade surface linearly.

This paper analyses the influence of different environmental parameters on the characteristics of blade surface ice cover and provides a certain reference for the design of blade surface anti-icing systems. But due to the limited personal energy and ability, the research content of this topic can continue to improve and develop in the following aspects:

(1) In this paper, the overall blade surface ice cover prediction within 900 s uses the same ambient temperature, but the actual ambient temperature is continuously changing. Subsequent research can be carried out on blade surface ice cover prediction under the condition of drastic changes in ambient temperature.

(2) This paper analyses the effect of changes in a single environmental variable on the blade surface ice cover characteristics. Subsequently, we can consider changing multiple environmental factors at the same time to analyze the changes in the blade surface ice cover characteristics.

(3) A test platform can be set up for the blade surface ice cover characteristics to restore the environmental parameters under the 18 working conditions mentioned above. The results of the numerical simulation can be verified again with the test results, so as to make the results of the study of blade surface ice cover characteristics more reliable.