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Ice accretion on the cold airfoil blade surface, such as wind turbines working in winter, affects its performance and degrades its aerodynamic characteristics and efficiency. Therefore, it is necessary to study the icing characteristics on the cold blade surface. At present, many pieces of research on wind turbine blade icing have been explored on the macroscale but seldom on the microscale. In this chapter, the icing process of a single water droplet on the cold aluminum plate surface was examined by a visualized method. The effects of volume and temperature on the icing characteristics were tested and acquired. After that, the profile parameters of iced water droplets were drawn and analyzed by MATLAB software, including the contact diameter, the maximum diameter and height of iced water droplets, the contact angle, and so on. The research findings provide experimental and theoretical foundations to deeply study the icing characteristics of wind turbine blades on a microscale.
Northeast Agricultural University, College of Engineering, Harbin, China
Yuxin Xu
Northeast Agricultural University, College of Engineering, Harbin, China
Wenfeng Guo
Northeast Agricultural University, College of Engineering, Harbin, China
*Address all correspondence to: zhangyingweineau@163.com
1. Introduction
Fuel energy is an important basis related to human and economic development. However, the problems of non-renewability and pollution to the environment promote the rapid development of renewable energy worldwide. Wind energy, a type of renewable energy, has the characteristics of abundance, wide scope of distribution, and cleanness. It has been paid more attention by many countries. Wind turbine, a type of power generation equipment, is the main utilization in the field of wind energy. The total capacity of installation increases annually. According to the distribution of wind resources worldwide, high-quality wind resource is mainly located in high-altitude and high-latitude regions. In these regions, low temperature and humid environment exist. When the wind turbines work under this condition, ice accretion occurs on the blade surface. Then, the profile of the blade surface changes, and the dynamic characteristic of the blade degrades, decreasing the power efficiency of wind turbines [1, 2]. Therefore, it is necessary to explore the icing problem of wind turbines.
Currently, many scholars have studied the icing events of wind turbines, and the research methods include experiments and simulation. Yan Li simulated a quasi-3D ice model of a horizontal axial wind turbine using a 2D simulation method [3]. K. Pope simulated the ice shape on the airfoil S809 with FENSAP ICE software and obtained the load distribution law of the blade surface [4]. Zhaohui Du examined the growth process of ice on the leading edge of the NREL Phase VI blade using the simulation method. These research findings showed that the weight of ice increased along the wingspan. At the tip of the blade, the power efficiency decreased dramatically [5]. Fernando Villalpando explored the growth process of ice accretion on the 2D airfoil blade profile by combining FLUENT with MATLAB. In the aspect of the icing test, Yan Li conducted the ice distributions on the straight blade surface of a vertical axial wind turbine under low and high tip speed ratio conditions. The research findings validated that rotating velocity and relative angle of attack were key factors that affect the change of ice distribution [6, 7]. Additionally, Hu Hui also performed many tests of ice accretions on wind turbine blades. In assessing the power losses because of ice accretion, the field studies of research were performed in the wind farm based on the real horizontal axial wind turbine [8, 9]. Therefore, exploring the icing characteristics of wind turbines can provide theoretical and experimental foundations for developing de-icing technology for wind turbines. Nevertheless, in the previous research, scholars mainly focused on the macroscale ice shape and ice distribution on the blade surface, but the microscale ice process, such as water droplets, also needed to be researched and observed. In the microscale scope, the interactive relation between the iced water droplet and substrate can be explored and the icing mechanism be disclosed. It lays a research basis for developing de-icing technology for wind turbines. In the previous works, it was examined that there were four stages in the icing process, including supercooling of the droplet, nucleation, re-glowing, and freezing and solid cooling [10]. By using visualization methods, it was found that there existed even nuclei in the water droplet at the moment of nucleation, and the water droplet changed from transparent to opaque. In the process of freezing, the interface between ice and water increased, and the profile of water droplets varied. Finally, a tip was generated on the top of the water droplet, and the iced water droplet exhibited a peach-like shape [11]. Zheyan Jin also performed a similar test based on the wind turbine icing problem [12]. In this research, scholars mainly explored the icing process and phenomena of water droplets on a cold surface, and the profile of water droplets is seldom analyzed parametrically. In this present study, not only the icing processes of water droplets were tested under different icing conditions, but the profiles of iced water droplets were also acquired and analyzed by image processing technology.
In this chapter, the icing process of a water droplet on a cold aluminum surface was studied based on the previous works. The low-temperature environment was simulated by a refrigerator. The icing process of water droplets was observed and acquired by a high-resolution industrial camera. The effects of the water droplet’s volume and ambient temperature on the icing process and ice shape were tested. After that, image processing was conducted by MATLAB software, and the variations of profile, contacting area, and contact angle of water droplets were analyzed. Then, the regressions were performed and parametrically analyzed based on the image processing results. The research finding lays theoretical and experimental foundations for studying the icing characteristic and the adhesive characteristic of ice on the wind turbine blade surface.
The sketch map of the experimental system is shown in Figure 1. The system is composed of a refrigerating equipment, an experimental bench for icing, and an image acquisition system.
Figure 1.
Sketch map of the experimental system.
As shown in Figure 1, a refrigerator, BD/BC-305E model, is selected to simulate icing conditions. The temperature scope of the equipment is from 0 to −20°C, and the resolution is 1°C. In this present study, the icing temperature was in the range of −5 to −15°C, satisfying the experimental condition. The experimental bench for the icing test is a high-precision mobile platform with XYZ directions. The maximum mobile range in each direction is 9 mm. An aluminum plate is fixed on the mobile platform, which is used to modulate the focal distance between the water droplet and the camera. The image acquisition and transaction system are comprised of a high magnification factor camera and a computer. The camera is used to capture the icing process of water droplets, and the computer is used to get the profile of iced water droplets and analyze the shape parameters. The experimental system is shown in Figure 2.
Figure 2.
Experimental system.
2.2 Image acquisition system
As shown in Figure 1, an image acquisition system is used to get the icing process of water droplets and conduct image processing. The system is comprised of a computer, a high magnification factor camera, and a supplementary light device. The camera is a type of CMOS camera having 16,000,000 pixels, and the frame rate of acquisition is 30 fps. The image resolution is 1920 × 1080, and the magnification factor is 100. The acquisition results are stored in the computer.
In this present study, the experimental scheme is listed in Table 1.
Volume of water droplet (μL)
Temperature (°C)
30
−10, −12, −14, −16, −18, −20
40
−10, −12, −14, −16, −18, −20
50
−10, −12, −14, −16, −18, −20
Table 1.
Experimental scheme.
As listed in Table 1, in this present study, the effects of water droplet volume and ambient temperature on the icing process and the shape of the iced water droplet are the key research content. Three kinds of water droplet volumes, including 30, 40, and 50 μL and five kinds of temperatures, such as −10, −12, −14, −16, −18, −20°C, were selected. The experimental procedure is shown in Figure 3.
Figure 3.
Experimental procedure.
As shown in Figure 3, before testing, the experimental temperature was set, and the refrigeration system began to work. When the temperatures of the environment and aluminum plate surface reached the target temperature, the image acquisition system was started. Then, the icing test of the water droplet was performed. After that, the image acquisition and transaction were conducted.
3.2 Image identification of iced water droplets
In this present study, automatic image processing technology was used to acquire the profile of iced water droplets, which is an innovative method. It was different from the manual processing method by using drawing software, such as AUTOCAD, Photoshop, and so on. Based on the procedure of image acquisition, the image analysis was performed using image processing technology developed in MATLAB, and the profile of iced water droplets was obtained. Furthermore, the Gaussian filter in the Canny algorithm was replaced by the Wiener self-adaptive filter. In the icing process of water droplets, an image processing program can self-adapt to the variations of environmental brightness and transparency of water droplets in order to intensify the accuracy of identifying the profile of iced water droplets. Based on the image processing, a coordinate was set up and the profile of iced water droplets was regressed by a polynomial. The flowchart identifying the profile of the iced water droplet is shown in Figure 4.
Figure 4.
The flowchart identifies the profile of iced water droplets.
As shown in Figure 4, the image processing system reads first the images from memory. Then, the colorful image is processed into a gray mode, which is used by the Canny algorithm in image processing [13]. Based on the gray image, the Wiener filter is applied to the image in self-adaption mode. The filter can self-adapt to local variation in the image, such as estimating the local average value and variation around each pixel, which are expressed in the following Eqs. (1) and (2).
μ=1NM∑n1,n2∈ηan1n2E1
σ2=1NM∑n1,n2∈ηa2n1n2−μ2,E2
where η is a local neighborhood in the range of N × M; μ is the local average value around a pixel; N is the length of the local neighborhood; M is the width of the local neighborhood; α is the image matrix; σ2 is the local variation around a pixel; n1 is the abscissa of image matrix; and n2 is the ordinate of image matrix.
Based on Eqs. (1) and (2), the Wiener filter in the magnitude of pixel is set up by estimated value, which is expressed in Eq. (3).
bn1n2=μ+σ2−υ2σ2an1n2−μ,E3
where ν2 is the variation of noise; b is the Wiener filter in the magnitude of pixel; and a is the local standard deviation around a pixel.
In image processing, the variation of noise cannot be predicted, so the average value of all the local variations was used in this present study. When the variation is high, the smoothing method is not used; conversely, the smoothing method is used when the variation is low [14, 15]. In this method, the processing result is better than the one processed by the linear filtering method. Therefore, the self-adaption filter is better than the linear filter in the aspect of processing the object profile. It can reserve the object edge and other parts with high frequencies in the image.
For the object edge in the image, the value can vary in different directions. Therefore, the classic Canny algorithm uses four gradient operators to calculate the gradients along the directions: horizontal, vertical, and diagonal. This kind of algorithm uses different operators of edges to calculate the modulus and direction which are expressed in Eqs. (4) and (5).
G=Gx2+Gy2E4
θ=atan2GyGx,E5
where G is the gradient; Gx is the difference along the horizontal direction; Gy is the difference along the vertical direction; θ is the included angle between the differences in the horizontal and vertical.
In the image gray processing, there exists a concentration region for gray variation. It needs to perform non-maximum suppression for gradient results and detect object edges. Then, the local maximum value needs to be found by comparing the gradient values along the gradient direction. After that, the maximum value is reserved, and the object edge with multiple pixels is changed into the one with a single pixel, making the width decrease.
In the border edge detection algorithm, a threshold value is commonly used to filter noise or variation of color, which results in a low gradient value. In the Canny algorithm, two threshold values, the high one and the low one, are selected to distinguish the edge pixel. When the gradient value is higher than the high threshold value, the pixel is marked as a strong edge pixel. Conversely, when the gradient value is lower than the low threshold value, the pixel is depressed. However, the pixel with a strong edge value can be considered as the real border, and the one with a weak edge value can be considered as noise or inference caused by color variation. Commonly, the pixel with a weak value caused by a real border is connected with the one with a strong value, but the one caused by noise is isolated. Based on this characteristic, the delay edge following algorithm is selected in this present study, which detects eight domains connected with a pixel having a weak edge value. In these connected domains, if there exist pixels with strong-edge values, these pixels will be reserved. In this algorithm, all the connected borders with weak-edge values are detected. If there exists a pixel in the weak border connecting with a pixel in the strong border, then the weak border is reserved; otherwise, it is depressed. The breadth-first search and depth-first search detection methods are used in this present study [16, 17].
Based on the border detection, it also needs to carry out morphology closing to deal with the problem of leaking edge. First, image dilation and erosion are conducted to connect the tiny breakpoints and delete the small remnant regions. Then, the image of iced water droplets was transformed into a binary image of an edge with a single connected domain. In this case, the coordinates of pixels with non-zero values in binary images are all obtained, and the tip of the iced water droplet is detected. According to the coordinate values, the origin of the coordinate is established at the tip of iced water droplets. For an iced water droplet, it has an axially symmetric profile. Therefore, the x-axis of the established coordinate has coincided with the symmetry axis of the profile, and the y-axis is vertical to the x-axis in this present study [18]. In the established coordinate system, the curved profile of iced water droplets is expressed by a polynomial fitting equation, which is expressed as Eq. (6).
px=p1xn+p2xn−1+⋯+pnx+pn+1,E6
where n is the highest power in the polynomial and pi is the coefficient in the polynomial.
Based on the polynomial fitting result in the profile of iced water droplets, the ratio of pixel number in the image to the real size of the object should be established, which is expressed by Eq. (7).
μ=ln,E7
where μ is the ratio of pixel number to real size of the object; l is the real size of the object; and n is the pixel number in the image.
Combining image processing with profile identification, the profile of iced water droplets can finally be shown in Figure 5. As shown in Figure 5a, it shows the image of iced water droplets. Figure 5b shows a half profile of iced water droplets in Figure 5a after rotating the iced water droplet anticlockwise. From this figure, the symmetric axis of iced water droplets is located at the x-axis of the coordinate, and the upper half profile is obtained by the polynomial method. Figure 5c shows the variation of the included angle between the tangent line of the iced water droplet profile and the substrate plane. The value of the y-axis is the included angle, and the value of the x-axis is the position along the profile of iced water droplets. Figure 5d shows the 3D profile of iced water droplets generated from the 2D profile in Figure 5b.
According to the experimental scheme in Table 1, three kinds of water droplet volumes and six kinds of temperatures were selected in the icing tests. The process of icing is shown in Figure 6.
Figure 6.
Icing process of water droplets.
Figure 6 shows the icing process of a droplet of water with a volume of 40 μL under −15°C conditions. The icing time for a droplet of water is 41 s from contacting the cold surface to freezing fully. The time interval between the two pictures is the same. As shown in the figure, the water droplet was transparent when contacting the cold surface initially. After fully freezing, it became opaque. At the initial stage of icing, the interface between ice and water was nearly parallel to the substrate surface. With the development of the icing process, the interface changed from plane to curve. The experimental results show that the icing time in the outer region of the water droplet, being close to the water surface, is shorter than the one in the inner region of the water droplet. The reason for this result is that heat transfer in the outer region of the water droplet happened not only between the water droplet and substrate but also between the water droplet and environmental air. In this instance, the water in the surface region froze faster than the one in the inner region. Additionally, at the initial stage of the icing process, the shape of water droplets did not change significantly; it was kept in the shape of a spherical cap, as shown from Picture 1 to Picture 5 in Figure 6. However, at the later stage of the icing process, the top of the water droplet presented a convex shape, looking like a tower tip at last. The reason for this result is that the surface of the water droplet is almost frozen at the end of the icing process, but the inner water has not fully frozen. In this instance, the frozen surface constrained the volume inflation of inner water in the icing process, which squeezed the water from the inner region to the tip surface. Finally, the tip surface of the water droplet became a sharp shape. Similarly, for other volumes of water droplets, the icing processes had the same phenomena.
4.2 Effect of substrate temperature on the shape of iced water droplets
Based on the icing test of the water droplet, the profile of iced water droplets was acquired using the Canny algorithm and fitted using the polynomial equation. The profile of iced water droplets with a volume of 40 μL is shown in Figure 7.
Figure 7.
Profile of the iced water droplet with a volume of 40 μL fitted by polynomial.
Figure 7 shows the profiles under different ambient temperatures, including −10, −12, −14, −16, −18, and − 20°C. When the ambient temperatures are different, the shapes of iced water droplets are significantly different, such as the height, diameter, contact angle, and so on.
According to the fitting results of profiles, in quantitatively analyzing the variations of profile parameters with substrate temperature, four parameters including the contact angle of iced water droplets, contact diameter between the iced water droplet and substrate, and the maximum height and diameter of iced water droplets were selected in this present study. The variations of these parameters with substrate temperature are shown in Figure 8.
Figure 8.
Variations of contact angle and contact diameter along with temperature.
Figure 8a shows the variations in contact angle and diameter of an iced water droplet with ambient temperature. When the volume of the water droplet was constant, the contact diameter increased along with the substrate temperature, and the contact angle decreased with the increase in the substrate temperature. The reason for these results is that the temperature difference between the water droplet and substate increases as the substrate temperature decreases. In this instance, the heat quantity increases in unit time, and the icing time shortens. Additionally, the characteristic of water flowability degrades as the temperature decreases, which results in a decrease in the contact diameter and an increase in the contact angle. For this reason, the adhesive strength of iced water droplets decreases. The research finding indicates that impacting ice generated by water droplets impinging on the cold surface, such as wind turbine icing and aircraft icing, has low adhesive strength in comparison with glaze ice frozen by liquid water.
As shown in Figure 8b, the height of iced water droplets increases, and the maximum diameter of it decreases along with the substrate temperature. The reason for this result is the same as the above one. When the substrate temperature decreases, the icing time of water droplets shortens and the flowability of water degrades. However, the volume of water droplets is constant, which results in an increase in the height and a decrease in the maximum diameter of iced water droplets.
4.3 Effect of water volume on the shape of iced water droplets
Similarly, the profiles of iced water droplets with volumes of 30, 40, and 50 μL were also fitted by the Canny algorithm under the substrate of temperature of −16°C. The fitting results are shown in Figure 9.
Figure 9.
Fitting profile of iced water droplets with volumes of 30, 40, and 50 μL.
As shown in Figure 9, when the substrate temperature was constant, the profiles of iced water droplets with different volumes were significantly different. Based on the results of image identification, the profile parameters of iced water droplets were analyzed comparatively with variations of water droplet volume, which are shown in Figure 10.
Figure 10.
Variation of profile parameter with water droplet volume.
As shown in Figure 10a, when the substrate temperature is constant, the contact angle and the contact diameter of iced water droplets increase along with the water droplet volume. In Figure 10b, the maximum diameter of iced water droplets increases along with the water droplet volume, but the height decreases a little.
In exploring the problem of wind turbine icing under a microscope, the icing process of water droplet on the cold aluminum plate surface was explored, and some conclusions are listed as follows:
An experimental system for icing tests was designed and built. The ambient temperature scope in the system is in the range of 0 to −20°C. The icing process of water droplets was acquired by an industrial camera with a high magnification factor of 100. In enhancing the effectiveness and accuracy of image processing, automatic edge detection technology was used in this present study. Based on the MATLAB software, the profile of iced water droplets was identified and acquired using the Canny algorithm. In this way, the contact angle of water droplets was obtained, and the profile function was fitted using the polynomial equation.
The effects of water droplet’s volume and substrate temperature on the profile and contact angle of iced water droplets were analyzed based on the image processing. When the substrate temperature was constant, both contact angle and contact diameter between the iced water droplet and substrate surface increased along with the water droplet volume. In contrast, when the water droplet volume was constant, the contact angle increased with the decrease in the substrate temperature, but the contact diameter decreased.
This work was supported by the National Natural Science Foundation of China (NSFC) [grant number 51976029].
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Written By
Yingwei Zhang, Yuxin Xu and Wenfeng Guo
Submitted: 14 June 2023Reviewed: 23 August 2023Published: 29 September 2023
Open access peer-reviewed chapter
