A Brief Review of Blade Surface Icing Adhesive Theories for Wind Turbines

Abstract

In cold and humid areas, ice easily accumulates on the blade surface of the wind turbine. The icing on the blade surface causes the power efficiency of wind turbines to decline, even leading to safety accidents. In order to research and develop efficient anti-icing and de-icing technologies, exploring the adhesive properties between ice and the blade surface is necessary. Therefore, in this paper, the main theories of the icing adhesive mechanism have been briefly summarized, including mechanical, electronic, and wetting theories, from the aspechts of theory and experimental research, which can provide a reference for researching icing mechanisms and the development of anti-icing and de-icing technologies for wind turbines.

1. Introduction

Wind energy is one of the renewable energies of the best successful commercial operation. However, ice easily accumulates on the blade surface in cold and humid areas. An icing example of the wind turbine operating in Northeast China is shown in Figure 1. Icing affects the output power and the safe operation of wind turbines, causing severe economic loss and security risks to the power grid [1, 2]. Therefore, to research and develop efficient anti-icing and de-icing systems, the icing mechanism must be explored [3, 4].

Figure 1.

An example of icing on wind turbines.

The icing research of wind turbine mainly draws lessons from that of aircraft, including aerodynamics and heat transfer theory, etc. As is shown in Figure 2, the supercooled droplets impact the blade’s surface following air movement [5]. The energy exchange occurs among droplets, blades, and flow field. The droplets freeze into ice in the phase transition and accumulate on the blade surface. This process can be obtained by numerical simulation or icing test [6]. However, there is a problem in the icing process needing to go a step further to explore, which is the icing mechanism. Therefore, in this chapter, some literature has been consulted, the significant theories of the icing mechanism have been briefly summarized, which can provide a reference for researching icing mechanisms and the development of anti-icing and de-icing technologies for wind turbines.

Figure 2.

Schematic diagram of water droplets impacting a blade [5].

2. Overview of adhesion theories

Adhesion is a complex phenomenon related to the interaction of physics and chemistry from microscale to macroscale [7]. According to the research of Schultz and Nardin, the main adhesion theories are listed as follows: mechanical interlocking, electronic or electrostatic theory, adsorption (thermodynamic) or wetting theory, diffusion theory, chemical (covalent) bonding theory, and theory of weak boundary layers and interphases [8]. In contrast, Fourche [9] separated mechanical adhesion from specific adhesion, the latter including the subcategories of the electronic model, diffusion model, thermodynamic adsorption or wetting model, rheological model, chemical adhesion model, and the model of weak boundary layers. Although the classification and naming of Schultz and Fourche differ, their depiction of the main theories is similar. This chapter considered that mechanical theory and other adhesion theories explain the adhesive properties from different angles. The decision to separate mechanical theory from other adhesion theories is arbitrary. Therefore, this chapter uses the classification method of Schultz and Nardin to discuss adhesion theories.

At present, adhesion theories are applied to the research of icing mechanisms, mainly including mechanical, electronic, and wetting theories. The following part of this chapter will focus on mechanical, electronic, and wetting theories. The mechanical theory holds that adhesion results from mechanical interlocking between ice and the microscopic feature of the substrate surface. According to electronic theory, adhesion is generated by the double electron layer on the interface between ice and substrate surface. The wetting theory argues that the adhesion between the ice and the substrate surface depends on the wettability of the substrate surface [7, 8]. The above theories are not mutually exclusive. In the icing process, those mechanisms may occur simultaneously, depending on the specific conditions.

3. Mechanical theory

The mechanical theory is one of the oldest theories. In 1925, McBain and Hopkins first proposed the concept of “mechanical adhesive” in “On adhesive and adhesive action.” [8]. The mechanical theory holds that the substrate surface is uneven. On the microscale, the surface topography of substrate is similar to that of terrain. Many peaks and valleys of different shapes are randomly distributed on the substrate surface. When water freezes on the substrate surface, the peaks and valleys are like tiny dowels to bond the ice with the substrate. The schematic diagram of the mechanical adhesive mechanism is shown in Figure 3 [9].

Figure 3.

The schematic diagram of the mechanical adhesive mechanism. (a) Complete wetting state. (b) Incomplete wetting state [9].

According to mechanical theory, the substrate surface is rougher, the ice adhesion strength is stronger. However, the mechanical theory does not consider the wettability of the substrate surface. The above assumption is valid under the premise of complete wetting of the substrate surface, as shown in Figure 3a. Conversely, there will exist many defects on the interface between ice and substrate, as shown in Figure 3b.

For mechanical theory, scholars such as Fortin, Knuth, and Shen explored the icing mechanism. In addition, some scholars, such as Chaudhury and Kim [10], have studied the elastic modulus, which is an important parameter affecting ice adhesive strength. The model of Fortin and Perron [11] is established based on the behavior of water before and after freezing, substrate roughness, and the type of ice. The model assumes that the ice near the freezing point is affected by internal and external strain, and its cohesive strength corresponds to the failure stress. The failure stress is related to the grain size and creep of grain boundary sliding in polycrystalline substrates at elevated temperatures. The ice adhesion shear stress on the substrate with only a single level of roughness is expressed as Eq. (1) [11].

$${\tau }_{\mathrm{adh}}=\left.\begin{array}{l}{\left\{{\alpha }_{\mathrm{ice}}\left(\frac{{\chi }_{\text{oxygen}}-{\chi }_{\text{coating}}}{{\chi }_{\text{xoygen}}-{\chi }_{\text{substrate}}}\right)\right.}^2\frac{T_{\mathrm{f}}-T}{T_{\mathrm{f}}-T_{\mathrm{ref}}}\frac{4{\gamma }_{\mathrm{LV}}}{{\delta }_0}\\ \times \left[f_{\mathrm{RMS}}+\frac{{\delta }_0}{\kappa }\left(1-f_{\mathrm{RMS}}\right)\left(1-f_{\text{cramp}}\right)\right]+\left(1-f_{\mathrm{RMS}}\right)f_{\text{cramp}}{\tau }_{\mathrm{f}}\end{array}\right\}{f}_{\mathrm{por}}$$E1

Where α_ice is the proportionality constant due to phase change; χ is electronegativity; T is temperature; T_f is solidification temperature; T_ref is reference temperature; γ is surface tension; L is liquid; V is vapor; δ₀ is a molecular distance; f_RMS is the fraction of ice in contact with the substrate; κ is root mean square roughness height; f_cramp is fraction of mechanical locking; τ_f is Ice shear strength; f_por is porosity fraction.

Knuth’s model [12] is established based on Young’s modulus, thermal expansion, and static friction. The model assumes that when the water droplets freeze on the substrate surface, the water droplets expand and freeze in the surface topography, creating a “clamping” mechanism. In order to separate ice from the substrate, the clamping mechanism must be overcome. Assuming there are two methods to separate the ice. The first method assumes that the shear force is perpendicular to the valley on the substrate surface at the microscale. The perpendicular shear force of ice covering the substrate surface is expressed as Eq. (2). The second method assumes that the shear force is parallel to the valley on the substrate surface at the microscale. The parallel shear force of ice covering the substrate surface is expressed as Eq. (3) [12].

$$S_0={\mathit{EA}}_0\alpha \mathrm{\Delta }T\left({\mu }_{0}cos{\theta }_0+sin{\theta }_0\right)$$E2

$$S_0=2{\mu }_0{\mathit{EA}}_0\alpha \mathrm{\Delta }T$$E3

Where S₀ is the shear force required to shed ice; E is Young’s modulus of ice; A₀ is the Initial area of surface and ice contact; α is the thermal coefficient of expansion; ∆T is the change in ambient temperature; μ₀ is the coefficient of static friction; θ₀ is the slope of surface topography, defined as negative with respect to the horizontal plane.

Shen [13] proposed and established an analytical model for expressing the icing adhesion strength based on the mechanical theory, the principles of substrate thermal deformation theory, and the tribology theory. Under a series of assumptions, the relationship between adhesion strength and some parameters, including thermal expansion, bulk modulus, and surface temperature difference of substrates, was established. The model characterizes the surface morphology of the substrate by surface roughness parameters. The adhesion strength of ice covering the surface of substrate material is expressed as Eq. (4) [13].

$$\tau =\frac{\mu K_{\mathrm{i}}{K}_m\mathrm{\Delta }{T}_{2}A\left({\gamma }_i{V}_{i1}-{\gamma }_m{V}_{m0}\right)}{S\left(cos{\theta }_1-\mu sin{\theta }_1\right)\left(K_i{V}_{m2}+K_m{V}_{i2}\right)}$$E4

Where μ is the static friction coefficient between the ice and the peak; K_i is the bulk modulus of ice; K_m is the bulk modulus of the substrate material; ΔT₂ is the difference in temperature between the beginning of ice contraction and the full ice contraction; A is the contact area between the ice and the peak; γ_i is the volume expansion coefficient of ice; V_i1 is the volume of ice before contraction when liquid water completely freezes; γ_m is the volume expansion coefficient of substrate material; V_m0 is the volume of the naked peak before the liquid water contacts the substrate material at the ambient temperature; S is the bottom area of a model unit; θ₁ is the included angle between the conical busbar and the diameter of the bottom; V_m2 is the volume of the peak after free contraction at the ambient temperature if there is no squeeze of the ice due to contraction; V_i2 is the volume of ice after free contraction at the ambient temperature if there is no obstacle of the peak.

Although scholars have carried out a lot of exploration, the calculation results of these models can not well predict the ice adhesion strength. The relationship between the ice adhesion strength, surface topography, and material parameters still needs in-depth exploration. Compared to theoretical research, the experimental method is also important for exploring the icing mechanism. Some scholars have researched the relationship between surface roughness and ice adhesion strength in experimental research but have not yet reached a consistent conclusion. In this chapter, according to the existing research results, the relationship between surface roughness and ice adhesion strength can be roughly classified into two categories.

1. There is a correlation between ice adhesion strength and surface roughness. The research of Druez et al. shows a correlation between ice adhesion strength and surface roughness in the range of surface roughness of industries. The ice adhesion strength increases with the increase of surface roughness. When the surface roughness is greater than 20 μm, the adhesion strength tends to extremum [14]. Zhu et al. [15]. found that the adhesion strength increases with surface roughness when surface roughness changes continuously from 3 to 33 μm. The study of Chu and Scavuzzo [16] shows that the ice adhesion strength depends on surface roughness to a great extent. The research of Ding et al. showed that the ice adhesion strength increases with the increase of surface roughness for the hydrophilic surface. In contrast, the changing trend of adhesion strength is the opposite for the hydrophobic surface. There is a significant linear relationship between ice adhesion strength and surface roughness [17]. The research of Guo et al. found that surface roughness greatly affects the ice adhesion strength. Generally speaking, with the increase of surface roughness, the ice adhesion strength of the substrate surface also increases [18]. Zou et al. [19]. found that the ice adhesion strength on the rough surface is much higher than that on the smooth surface.

2. There is no correlation between ice adhesion strength and surface roughness. The study of Sait Alansatan et al. showed that the ice adhesion strength varies with the surface roughness change, but there is no clear trend between them [20].

4. Electronic theory

The electronic theory was mainly proposed by Deryaguin [21]. The electronic theory holds that adhesion is the electrostatic force generated by the electron transfer forming the double-layer charges on the ice-substrate interface. The schematic diagram of the adhesion mechanism of electronic theory is shown in Figure 4 [9]. This theory is the most controversial of all adhesion theories since it is difficult to prove the existence of double-layer charges without destroying the ice.

Figure 4.

The schematic diagram of the electronic adhesive mechanism [9].

In 1997, Ryzhkin and Petrenko [22] first applied the electronic theory to explore the adhesion mechanism between ice and substrates. They proposed and established an electrostatic model based on the existence of the surface states of protonic charge carriers on the surface of ice. The model reveals the relationship between the electrical and adhesive properties of the ice surface, calculating the order of magnitude of adhesive energy at distances greater than one intermolecular distance. The model calculates the order of magnitude of adhesive energy significantly greater than chemical bonding energy and van der Waals forces.

5. Wetting theory

Wetting theory, also known as adsorption (thermodynamic) theory, is currently a popular adhesion theory. The theory was proposed by Sharpe and Schonhorn in 1963. The wetting theory holds that adhesion is caused by the interaction between the molecules on the interface when the water droplets are in close contact with the substrate. Therefore, the standard of adhesive performance is essentially the standard of wettability. The contact angle is an important index for evaluating wettability. The schematic diagram of the adhesion of water droplets on the substrate surface is shown in Figure 5 [9].

Figure 5.

Schematic diagram of the interaction among solid, liquid, and gas interface [9].

As shown in Figure 5, when the droplet is on the substrate surface, the droplet adopts a balanced structure that minimizes the system’s energy. Young’s Equation first described this equilibrium condition, as shown in Eq. (5) [23].

$${\gamma }_{\mathrm{W},\mathrm{S}}+{\gamma }_{\mathrm{W}}cos\theta ={\gamma }_{\mathrm{S}}$$E5

Where γ_W is the surface energy of the liquid–vapor interface; γ_W,S is the surface energy of the solid–liquid interface; γ_S is the surface energy of the solid-vapor interface; θ is the contact angle formed by the liquid drop and solid.

As shown in Figure 5, if the droplet on the substrate surface (S) is frozen into ice (i), the work required to remove the ice from the substrate surface is called the thermodynamic work of adhesion W_a. The definition of W_a is shown in Eq. (6) [23].

$$W_{\mathrm{a}}={\gamma }_{\mathrm{S}}+{\gamma }_{\mathrm{ice}}-{\gamma }_{\mathrm{i},\mathrm{S}}$$E6

Where γ_ice is the surface energy of the ice-vapor interface; γ_i,S is the surface energy of the solid-ice interface.

According to Eqs. (5) and (6), Wa can be expressed as Eq. (7) [23].

$$W_{\mathrm{a}}={\gamma }_{\mathrm{ice}}+{\gamma }_{\mathrm{W}}cos\theta +\left({\gamma }_{\mathrm{W},\mathrm{S}}-{\gamma }_{\mathrm{i},\mathrm{S}}\right)$$E7

The surface energy of the solid–liquid interface of water is roughly same as that of ice, so γ_{W, S} ≈ γ_{i, S} [24]. Now assuming that the surface energy of the liquid–vapor interface of ice and water is also approximately the same, W_a can be expressed as Eq. (8) [23].

$$W_{\mathrm{a}}\approx {\gamma }_{\mathrm{W}}\left(1+cos\theta \right)$$E8

According to Eq. (4), the thermodynamic work of ice adhesion can be approximately calculated by the surface energy of the solid–liquid interface and the contact angle of water on the substrate surface. The relationship among the thermodynamic work of adhesion, the surface energy of the liquid–vapor interface, and the contact angle is shown in Figure 6 [23].

Figure 6.

Thermodynamic work of ice adhesion scaled by the surface tension of water as a function of water contact angle θ [23].

In experimental research, scholars have done much research on the relationship between water wettability and ice adhesive properties but have not formed a uniform conclusion. According to the existing research results, this chapter roughly classifies the relationship between water wettability and ice adhesive properties into three categories.

1. There is a correlation between ice adhesive properties and contact angle. Dotan et al [25]. found that the larger the contact angle, the lower the ice adhesion strength. Andersson et al. found that, for rubber substrates, when the contact angle is less than 90 degrees, the adhesion strength of ice decreases linearly with the increase of contact angle. When the contact angle is greater than 90 degrees, the adhesion strength of ice remains almost unchanged [26].

2. There is a correlation between ice adhesive properties and contact angle only if the surface roughness is similar. Zou et al. reported that the adhesion strength of ice is only related to the contact angle when the surface roughness is similar. The adhesion strength of ice decreases with the increase of the contact angle [19]. Pang et al. found that higher contact angles lead to lower ice adhesion strength for coatings with the same surface roughness. For the coatings with different surface roughness, the adhesion strength of ice depends on the surface roughness rather than the contact angle [27].

3. There is a correlation between the ice adhesive properties and the contact angle hysteresis. Kulinich and Farzaneh [28, 29] found that the adhesion strength of ice has a good correlation with the contact angle hysteresis on the super-hydrophobic surface. When the contact angle hysteresis is low, the adhesion strength of ice is lower.

6. Summary

For the research on the icing mechanism of wind turbines, this chapter briefly summarizes the significant icing theories. The conclusions are as follows:

The icing adhesive theory mainly includes mechanical, electrostatic, and wetting theories. The three theories explain the icing adhesive properties from different viewpoints. However, each theory has its limitations and needs further improvement. Under actual conditions, the icing adhesive properties are also affected by environmental conditions, such as ambient temperature, wind speed, liquid water content, medium volumetric diameter, and liquid water composition, etc. In future research, the influence of environmental factors on adhesive properties should be considered. In addition, research on the icing adhesive theory of wind turbines has not been reported. The research on the icing adhesive theory of wind turbines should be based on the existing theories, introduce relevant theories, and carry out in-depth fusion research. This chapter can provide a reference for studying ice adhesive properties and anti-icing and de-icing technologies of wind turbines.

Acknowledgments

This research was funded by “National Natural Science Foundation of China (NSFC), grant number 51976029”.

Conflict of interest

The authors declare no conflict of interest.

Appendices and nomenclature

A	Contact area between the ice and the peak (m2)
A0	The initial area of surface and ice contact
E	Young’s modulus of ice
fcramp	Fraction of mechanical locking
fpor	Porosity fraction
fRMS	The fraction of ice in contact with the substrate
Km	Bulk modulus of the substrate substrate (Pa)
L	Liquid
S	The bottom area of a model unit (m2)
S0	The shear force required to shed ice
T	Temperature (K)
Tf	Solidification temperature (K)
Tref	Reference temperature (K)
ΔT	The change in ambient temperature (K)
∆T2	The difference in temperature between the beginning of ice contraction and the full ice contraction (K)
V	Vapor
Vi1	The volume of ice before contraction when liquid water completely freezes (m3)
Vi2	The volume of ice after free contraction at the ambient temperature if there is no obstacle of the peak (m3)
Vm0	The volume of the naked peak before the liquid water contacts the substrate substrate at the ambient temperature (m3)
Vm2	The volume of the peak after free contraction at the ambient temperature if there is no squeeze of the ice due to contraction (m3)
Wa	Thermodynamic work of adhesion
α	The thermal coefficient of expansion
αice	The proportionality constant due to phase change
γ	Surface tension
γi	Volume expansion coefficient of ice (K−1)
γi,S	The surface energy of the solid-ice interface.
γice	The surface energy of the ice-vapor interface
γm	Volume expansion coefficient of substrate substrate (K−1)
γS	The surface energy of the solid-vapor interface
γW	The surface energy of the liquid–vapor interface
γW,S	The surface energy of the solid–liquid interface
δ0	Molecular distance
θ-	The contact angle formed by the liquid drop and solid (degrees)
θ0	The slope of surface topography, defined as negative with respect to horizontal plane (degrees)
θ1	Included angle between the conical busbar and the diameter of the bottom (degrees)
κ	Root mean square roughness height
μ	Static friction coefficient between the ice and the peak
μ0	The coefficient of static friction
τ	Adhesion strength of ice (Pa)
τf	Ice shear strength (Pa)
χ	Electronegativity