Open access peer-reviewed chapter

Experimental Study on the Ultrasonic De-Icing Method of Wind Turbine Blades

Written By

Jianlong Ma, He Shen and Wenfeng Guo

Submitted: 14 June 2023 Reviewed: 28 September 2023 Published: 05 November 2023

DOI: 10.5772/intechopen.113305

From the Edited Volume

Wind Turbine Icing - Recent Advances in Icing Characteristics and Protection Technology

Edited by Yan Li

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Abstract

Ice accretion on the wind turbine blade degrades the aerodynamic performance and power efficiency of wind turbines. Therefore, developing a high-efficiency de-icing method with low energy consumption is necessary to stabilize their operation in winter. Now, there are several types of de-icing methods being developed. Among these methods, ultrasonic de-icing method is suitable for wind turbines because of its low energy consumption, simple structure, and easy installation. In this chapter, the theoretical and experimental studies on ultrasonic de-icing of wind turbines are introduced. The de-icing vibration modes of plate element and airfoil blade with NACA0018 were analyzed and determined. The anti-icing and de-icing effects of ultrasonic vibration on the iced plate and blade segment were tested by the experimental methods. An icing wind tunnel system and two kinds of de-icing measurement devices were designed and built. The adhesive strengths of ice on the plate and airfoil blade surface were measured with variation in frequency. The experimental results show that ultrasonic vibration could decrease the amount and the adhesive strength of ice dramatically and had de-icing capability at the frequency of de-icing vibration mode. The research findings are useful and helpful to the development of ultrasonic de-icing technology in future works.

Keywords

  • wind turbine
  • anti-icing
  • de-icing
  • ultrasonic
  • experimental method

1. Introduction

With the rapid development of technology, air pollution and global warming have become serious problems for each country. Therefore, clean and renewable energies are important to us. Wind energy, as one of the most successful and widely used renewable energies, is mainly applied to wind power generation. However, for wind turbines working in humid and cold environments, ice accretion sometimes occurs on the blade surface. It changes the profile and degrades the aerodynamic performance of the airfoil blade. Then the power efficiency of wind turbines decreases. Moreover, icing on the blade increases the weight and destroys the dynamic balance of the rotor, which shortens the lifespan of wind turbine. Occasionally, ice-shedding events threaten the surrounding buildings or people [1, 2, 3]. Thus, it’s necessary to develop anti- and de-icing technologies for wind turbines.

At present, there are several kinds of de-icing methods in development, such as electro-thermal de-icing, fluid thermal de-icing, pneumatic de-icing, electric-pulse de-icing, microwave de-icing, surface coating de-icing, and ultrasonic vibration de-icing [4, 5, 6, 7]. Among these de-icing methods, electro-thermal de-icing method is widely used because of its simple structure, but it costs a great amount of electric energy in the process of de-icing. It’s not available for wind turbines, which are a kind of power generation equipment that decreases power efficiency. Similarly, the microwave de-icing method also costs a large amount of energy. Moreover, fluid thermal de-icing and pneumatic de-icing methods have large volumes and complex structures. For the electric-pulse de-icing method, it’s complicated due to the high distribution density of the coil. Additionally, it’s only available on metal surfaces. When it works, the metal surface will generate large deformation. The surface coating method uses the hydrophobic material to decrease the amount of ice. It’s a kind of active de-icing method. However, the coating is fragile and prone to falling off. After that, it’s failure to protect the surface. In contrast, the ultrasonic de-icing method has the features of low energy cost, small vibration amplitude, long lifespan, lightweight, no noise, simple structure, easy installation, and so on [8]. A wind turbine is a power generation device that transforms wind energy into electricity. Therefore, conversion efficiency is an important parameter for it. If the de-icing method consumes a lot of energy in operation, the power generation efficiency will decrease overall. Therefore, it’s necessary to find a low–energy-cost de-icing method for wind turbines. In this case, the ultrasonic de-icing method is considered one of the available de-icing methods, especially for wind turbines. Nevertheless, the de-icing mechanism of it has not been explored clearly, and the technology of it is in development. Now, scholars have carried out some research on ultrasonic de-icing by theoretical and experimental methods [9, 10]. Simulation is the most widely used method. In this way, the stress distributions at the interface between substrate and ice were analyzed. Experimental method is commonly used to validate the effect of theoretical findings. In these tests, the parameter of de-icing time was always used to assess the de-icing effect. However, the effect of ultrasonic vibration on the adhesive strength of ice was seldom tested by experiment.

In this paper, an aluminum plate and airfoil blade segment were selected as research objects, and the de-icing effects of ultrasonic vibration on the adhesive strength of ice on the plate and blade segment were explored. First, the de-icing vibration mode and the distribution of shear stress at the adhesive interface between ice and substrate were analyzed by simulation. Based on the simulation results, two types of devices measuring the adhesive force of ice were designed and manufactured. Then the effects of ultrasonic vibration on the adhesive strength of ice covering on the plate and airfoil blade were examined by experiments.

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2. Ultrasonic de-icing effect on plate element

In this part, the effect of ultrasonic vibration on the iced plate is introduced. For the large-scale wind turbine, the surface profile of the blade can be simplified into two kinds of shapes, which are the plane and the volume, as shown in Figure 1.

Figure 1.

Sketch map of large-scale blade segment.

As shown in Figure 1, at the leading edge, the curvature at this position is highest all over the blade surface. In contrast, the curvature of the blade body surface is the lowest, which is approximately a plane surface. Therefore, it can be considered a plane surface. That’s why the de-icing effect of ultrasonic vibration on the adhesive strength of the iced blade was explored in the present study. Therefore, an aluminum plate was selected as a research object to carry out the relevant research. The reason for the selection of aluminum material is that the thermal conductivity of metal is isotropic. It’s helpful to carry out essential research. For real wind turbine blades, most of them are mainly made of composite material, such as carbon fiber or glass fiber-reinforced plastics. These materials are anisotropic in physical and thermal characteristics, which brings out difficulties in the initial test. Moreover, some small-scale wind turbines, such as vertical-axis wind turbines, are made of aluminum material, and many scholars conducted research on the icing characteristics of wind turbines using the aluminum airfoil blade segment. In these cases, aluminum material was used in the present study.

2.1 Simulation on the iced plate

The principle of the ultrasonic de-icing method is shown in Figure 2. As shown in Figure 2, the piezoelectric ceramic patch (PZT patch) is adhered to opposite surface without icing. When the PZT patch is excited by alternating current (AC) voltage, it stretches and contracts alternatively, resulting in high-frequency vibration. In this case, the iced plate vibrates and deforms along with the PZT patch. Then there is shear stress at the adhesive interface between ice and plate. When the shear stress is higher than the adhesive shear strength of ice, the adhesive strength of ice is weakened, or the ice is removed even more.

Figure 2.

Model of iced plate element for ultrasonic de-icing.

For exploring the mechanism of ultrasonic de-icing, an aluminum plate was selected as the simulation object. The configuration parameters are listed in Table 1.

Side length of plateThickness of plateThickness of ice
60mm × 60 mm1 mm2 mm

Table 1.

Configuration parameters of iced plate.

Based on the iced plate model, the model analyzes were conducted by ANSYS. The simulation parameters are listed in Tables 2 and 3, and the vibration modes of the plate, the first vibration mode and the fourth one, are shown in Figure 3.

ObjectsElement types
IceSOLID186
Aluminum plateSOLID186
PZT patchSOLID226

Table 2.

Element type in simulation.

MaterialsItemsValues
IceDensity0.9 × 103 kg/m3
Elastic modulus8.7 × 109 Pa
Poisson ratio0.33
AluminumDensity2.7 × 103 kg/m3
Elastic modulus7 × 1010 Pa
Poisson ratio0.3
Piezoelectric ceramicDensity7.5 × 103 kg/m3

Table 3.

Material parameters.

Figure 3.

Vibration modes.

As shown in Figure 3, the four sides of plate were constrained in the process of the simulation, which were the boundary conditions in the simulation. For each vibration mode, the deformation distributes symmetrically. The symmetry axes of them are along horizontal and vertical directions. In the present study, the first vibration mode was selected as a research object. According to the vibration mode, the position of the PZT patch was decided to be located at the center of the plate, which is similar to the one in Figure 2.

As shown in Figure 2, the position and size of the PZT patch are decided according to the first vibration mode. From the cloud picture of the first vibration mode, the highest bending amplitude is located in this position. Therefore, when there is an excitation load impacting this position, the largest bending deformation of plate can be realized. In this case, the higher shear stress can be generated at the adhesive interface between ice and plate.

Based on the model analysis, harmonic analysis was carried out, and the maximum shear stress at the adhesive interface between ice and aluminum plate was calculated. Some results with higher shear stress are shown in Figure 4.

Figure 4.

Variations of the maximum shear stresses at the adhesive interface.

As shown in Figure 4, it shows the variations of maximum stresses at the adhesive interface with excitation frequency under different side lengths of PZT patches. The side length of PZT patch varies from 12 to 17 mm. From the figure, it is found that the size of PZT patch has an effect on the maximum stress, and there are some conditions where the maximum shear stresses are far higher than the other conditions. In the previous works, it was concluded that the shear adhesive strength of ice was the lowest in comparison with the ones along other directions. That’s why the shear stress at the adhesive interface was selected as the de-icing parameter.

2.2 Experimental scheme

According to the previous experiments, the adhesive shear stress is about 0.3 ∼ 1.8 MPa. Combining the simulation results with the previous experimental result, the effect of ultrasonic vibration on the adhesive strength of ice was determined by experiment. The experimental scheme is listed in Table 4.

Thickness of ice (mm)Thickness of the PZT patch (mm)Experimental temperature (°C)Excitation voltage Vp-p (V)Side length of PZT patch (mm)Excitation frequency (kHz)
22−18400160
85
87
89
140
77
79
81

Table 4.

De-icing experimental scheme for iced plate.

In the present study, an alloy aluminum plate with material model 7075 was used as a test coupon, and the size of it was 60 mm × 60 mm × 2 mm. The PZT patch with the material model PZT4 was selected, and two kinds of side lengths, 16 mm × 16 mm × 2 mm and 14 mm × 14 mm × 2 mm, were selected as listed in Table 4. For the ice sample, the thickness was 2 mm, and the ambient temperature was −18°C. Additionally, the sinusoidal voltage was used as excitation voltage, and the peak-to-peak voltage Vp-p is 400 V. According to the harmonic analysis results for the maximum shear stress, several frequencies were selected in the present experiment as listed in Table 4.

2.3 Experimental system

The experimental system in the present study is shown in Figure 5.

Figure 5.

Sketch map of experimental system.

As shown in Figure 5, the experimental system is comprised of a signal generator, an ultrasonic power amplifier, a device for measuring the adhesive torque of ice, and so on. The signal generator, whose model is RIGOL DG1022Z, is used to generate low sinusoidal signal voltage. The ultrasonic power amplifier, whose model is LONG YI DGR-3001, is used to amplify the power of the sinusoidal signal from the signal generator and drive the PZT patch to vibrate at high frequency. The device for measuring the adhesive strength of ice is used to measure the adhesive torque of ice. In this way, the adhesive shear strength of ice can be measured.

2.4 Experimental results

Based on the above experimental system, the adhesive torques of ice were measured under different conditions. However, for analyzing the de-icing effect of ultrasonic vibration in comparison, the adhesive torque in the unit area, which is the adhesive shear stress, is calculated. The analytical formula is expressed by Eq. (1).

τa=12M22+ln3+22L3E1

where, M is the adhesive torque of ice covering on the whole aluminum alloy plate surface; L is the side length of an iced aluminum alloy plate.

Then the adhesive shear stresses under different experimental conditions are calculated according to the experimental results. The variation in frequency is shown in Figure 6.

Figure 6.

Variation of shear stress with frequency.

As shown in Figure 6, when the iced plate was not excited by ultrasonic vibration, the adhesive shear stress was higher than that under ultrasonic vibration. The adhesive shear stress was about 0.21 MPa. In comparison, when the PZT patch is 14 mm × 14 mm × 2 mm, the adhesive shear stress is only 0.014 MPa under the vibration frequency of 79 kHz. It’s just 7% of that without ultrasonic vibration. However, when the vibration is 81 kHz the adhesive shear stress is similar to that without ultrasonic vibration. Ultrasonic vibration did not have de-icing effect. It validates that high shear stresses only exist at special frequencies, such as 79 kHz. Under these conditions, ultrasonic vibration can increase the shear stress at the interface between ice and substrate, which decreases the adhesive strength of ice. On the contrary, at the other frequency, such as 81 kHz, the shear stress is low at the interface, and the adhesive shear strength of ice did not change at all. The experimental results agreed with the simulation results as listed in Figure 4 and Table 2. Figure 6 also validates the ultrasonic de-icing effect, as the size of the PZT patch was 16 mm × 16 mm × 2 mm. Under the excitation frequencies of 85 and 87 kHz, the adhesive shear stresses were just 0.037 and 0.021 MPa, respectively, which were far lower than that without ultrasonic vibration.

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3. Ultrasonic de-icing effect on airfoil blade

Based on the ultrasonic de-icing effect on the iced plate element, the de-icing effect on the airfoil blade was also explored in the present study.

3.1 Simulation

In this paper, an airfoil blade segment was selected as research object. The sketch map of it is shown in Figure 7.

Figure 7.

Sketch map of an airfoil blade.

As shown in Figure 7, the blade segment with airfoil of NACA0018 has a hollow structure. The reason for the selection of this airfoil is that NACA0018 has a symmetric profile, which is widely used to carry out basic research such as aircraft icing and wind turbine icing. For this airfoil, there is a hollow structure at the leading edge that is used to lay out the PZT patches. In the previous work, it was found that ice accretion often occurred on the leading edge, such as on aircraft wings and wind turbine blades. Icing destroys the profile of airfoil and results in the degradation of aerodynamic performance. Therefore, it’s necessary to explore the de-icing technology of airfoil blades. In the previous work, it was found that the ice accretion position along the chord length was less than 30%. Therefore, in the present design, the ratio of chord length l at the hollow position to the whole chord length C is 30%. Moreover, aluminum alloy is selected as the material of airfoil blade. The reason for the selection is that the aluminum alloy has isotropic and high heat transfer coefficient, which was widely used by many scholars to carry out airfoil blade icing.

Based on the structure of airfoil blade with a hollow structure, the model analysis of it was carried out by ANSYS, and the de-icing vibration mode was decided. The vibration mode is shown in Figure 8.

Figure 8.

De-icing vibration mode of airfoil blade.

As shown in Figure 8, the natural frequency of this vibration mode is 22,779 Hz. There exist two reasons for its selection. First, the natural frequency of de-icing vibration mode must be higher than 20,000 Hz. In this range, the vibration belongs to ultrasonic range. Second, under this vibration mode, the leading edge of airfoil blade bends alternatively, and the bending deformation alters positively and negatively. In this case, the bending deformation distributes along the whole leading edge surface, which can generate shear stress at the adhesive interface between the ice and airfoil substrate. Additionally, the amplitude of the bending deformation is the same along the direction of the wing span.

Based on the modal analysis, for exciting the bending deformation of airfoil blade, the PZT patches were laid out at the vibration amplitude in the present study. A test coupon of airfoil blade segment with PZT patches is shown in Figure 9.

Figure 9.

Test coupon of airfoil blade segment with PZT patches.

3.2 Experimental scheme

After manufacturing the test coupon of airfoil blade, the impedance analysis of it was carried out by an impedance analyzer, whose model is ZX70A. The measuring scope of frequency is from 20 to 30 kHz. After that, three frequencies were selected as experimental parameters, which were 21,228, 25,604, and 27,254 Hz. Under these three frequencies, the impedances were higher than those under other natural frequencies. Based on them, the experimental scheme was designed and listed in Table 5.

Experimental conditionsValues
Experimental temperature−12°C
Wind speed4 m/s
Excitation frequency21,228 Hz、25,604 Hz、27,254 Hz
Excitation voltage Vp-p400 V
Angle of attack

Table 5.

De-icing experimental scheme for iced blade.

3.3 Experimental system

In the present study, a de-icing system with ultrasonic excitation device for airfoil blade segment was designed and built. There are two parts in this system: the icing sub-system and the ultrasonic de-icing sub-system.

The icing sub-system is shown in Figure 10, which is used to simulate the icing environment of airfoil blade. As shown in Figure 10, it’s a return-flow icing wind tunnel, and the working parameters are listed in Table 6. As listed in Table 6, the working parameters can meet the icing demand of airfoil blade segment.

Figure 10.

Return flow icing wind tunnel.

Working parametersValues
Cross-section of the test section250 × 250 mm2
Temperature0°C ∼ −20°C
Wind speed0 ∼ 20 m/s
Diameter of the water droplet50 μm

Table 6.

Working parameters of the icing wind tunnel.

The ultrasonic de-icing sub-system is comprised of two parts, which are the ultrasonic excitation devices and a self-developed device for measuring the adhesive strength of ice covered on the airfoil blade surface. The ultrasonic excitation devices have been given in Figure 5, which are used to apply an excitation voltage to the PZT patches in order to generate ultrasonic vibration. The adhesive strength measurement device was developed specially for testing airfoil blades, as shown in Figure 11.

Figure 11.

Measurement device of adhesive strength of ice.

As shown in Figure 11, the shear method is used in the present study to measure the adhesive strength of ice. After icing on the blade segment in the icing wind tunnel, the iced blade segment is mounted on the slider of the device, as shown in Figure 12. Then it moves along the parallel rails. The slider is driven by a screw-driving mechanism where two pressure sensors are mounted on it. Under the driving of the pressure sensors, the iced airfoil blade goes through a de-icing hole, which has the same shape and size profile as the clean airfoil blade. In this case, the ice is removed by shear force, and the value is acquired by pressure sensors. In this way, the adhesive shear stress of ice covering the airfoil blade was measured. In the present study, the maximum value of measurement is determined as adhesive strength of ice.

Figure 12.

Ice distribution on the blade surface under (21.228 kHz, −4°C, 10 m/s).

3.4 Results and discussion

In the present study, the anti-icing and de-icing tests were conducted. The anti-icing test explored the effect of ultrasonic vibration on the amount of icing on the blade surface. The experimental scheme is listed in Table 5. The frequencies in the tests were 21,228z, 25,604, and 27,254 Hz. The excitation voltage was 400 V. The tests were conducted in the icing wind tunnel, and the icing process was recorded by a high-resolution camera. In this study, the ultrasonic vibration operated during the process of icing. And the ice distribution under different frequencies was obtained. For example, the one under the frequency of 21.228 kHz is shown in Figure 12.

In the present study, the type of ice is glaze ice. As shown in Figure 12, the ice grew layer by layer. The amount and covering area of ice on the lower blade surface were higher than those on the upper blade surface. When the water droplets impacted the blade surface, they did not freeze immediately. In this case, the water droplets converged and flew under the actions of wind and gravity. That’s why the amount of ice on the lower blade surface was higher than the one on the upper blade surface. For quantitatively analyzing the amount of ice, one parameter was used in the present study, which is dimensionless icing area. The sketch map of it is shown in Figure 13.

Figure 13.

Sketch map of dimensionless icing area.

As shown in Figure 13, the dimensionless icing area is expressed as Eq. (2).

ηs=SiSbE2

where ηs is the dimensionless icing area, Si is the cross-section area of ice and Sb is the cross-section area of the blade.

Based on the definition, the effect of ultrasonic vibration on the amount of ice was analyzed, which is shown in Figure 14.

Figure 14.

Variations of dimensionless icing areas under different frequencies.

As shown in Figure 14, under non-vibration conditions, the amount of ice was highest, which validated that ultrasonic vibration had anti-icing effect on wind turbines. Moreover, it also shows that frequency has an effect on the amount of ice. From Figure 14, when the frequency is 25.604 kHz, the amount of ice was lowest. It indicates that the ultrasonic vibration has an obvious effect on anti-icing at this frequency. Additionally, at the initial stage of icing, the amounts of ice were approximate under different frequency conditions. With the increase in icing time, the discrepancy in the amount of ice emerges gradually. For this result, the water droplets could impact the cold blade surface at the initial icing time, and the water droplets freeze in a short time because of high heat transfer of blade material, such as aluminum in the present study. After that, as the blade surface was covered by ice layer, the subsequent water droplets did not impact the blade surface directly. The water droplets could not freeze instantly. In this case, the ultrasonic had an obvious effect on anti-icing, which resulted in a decrease in the amount of ice. It was beneficial to the operation and aerodynamic performance of wind turbines.

Based on the anti-icing tests, the ultrasonic de-icing tests were also conducted in the present study. The icing process was carried out in the above icing wind tunnel. After icing, the effect of ultrasonic vibration on the adhesive strength of ice was carried in the refrigerator by the self-developed device shown in Figure 11. Based on the experimental system, the adhesive strength of ice on the airfoil blade was measured by the self-developed device in Figure 11. For analyzing the results under different icing conditions comparatively, the adhesive shear stress of ice was calculated by Eq. (3).

τ=FSE3

where τ is the adhesive shear stress of ice; F is the shear force of the ice adhering to the blade surface; S is the area of ice covering the blade surface.

According to Eq. (3), the variation of adhesive shear stress of ice with ultrasonic vibration is shown in Figure 15.

Figure 15.

Variation of adhesive shear stress of ice with frequency(−12°C, 5 m/s).

As shown in Figure 15, without ultrasonic vibration, the adhesive shear stress of ice is about 0.14 MPa. The adhesive strength is lower than that shown in Figure 6. The difference was caused by the type of ice. For the test of iced plate in Section 2, the type of ice was glaze ice which was frozen by liquid water. However, in this test, the ice was generated by water droplets impinging on the blade surface. Additionally, the icing temperature was −12°C. Under this condition, the type of ice was rime ice. For rime ice, there are spaces among iced water droplets. It leads to a decrease in the adhesive area of ice. For this reason, the adhesive strength of ice decreased. In contrast, the glaze ice was generated from liquid water. There is no space in the body of ice, and the adhesive area with the substrate was large, which resulted in a high adhesive strength of ice.

Figure 15 also validates that ultrasonic vibration has a de-icing effect on the iced airfoil blade. The adhesive strength of ice decreased under the ultrasonic vibration. When the vibration frequency was 21.228 kHz, the adhesive strength of ice was at its lowest, which was approximately 0.084 MPa. The frequency was approximated by the theoretical one calculated in modal analysis. It validated that the leading edge bending alternately along the blade surface and symmetrically along the chord had a better de-icing effect. Additionally, under the other excitation conditions, such as 25.604 and 27.254 kHz, the adhesive strength of ice also decreased, but the values were higher than the one in the condition of 21.228 kHz. Especially for the one under the frequency of 27.254 kHz, the adhesive strength of the ice decreased a little. It also validates that the shear stress at the interface under this excitation condition was small, which has little effect on de-icing. Conclusively, for an airfoil blade, there exists a de-icing vibration mode, which is the best one for the ultrasonic de-icing method.

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4. Conclusions

In the present study, the de-icing effect of ultrasonic vibration on the plate element and airfoil blade was explored through simulations and experiments. Some conclusions are presented as follows:

  1. An aluminum plate element was selected as research object. The modal analysis and harmonic analysis of it were carried out. Based on the first vibration mode, the location of PZT patch was decided, and the maximum shear stresses at the adhesive interface between ice and substrate were calculated under different frequencies. The theoretical result shows that ultrasonic vibration has a de-icing effect. Based on the theoretical analysis, the experimental scheme was decided.

  2. An experimental system was designed and built for testing the de-icing effect of ultrasonic vibration on iced plate elements. A self-developed device was used to measure the adhesive strength of ice on the plate surface. Based on the system, the adhesive strengths of ice under different excitation frequencies were measured and calculated. The experimental results validate that ultrasonic vibration has a significant de-icing effect. The adhesive strength of ice has decreased by 93%.

  3. A blade segment with airfoil of NACA0018 was designed and manufactured. It has a hollow space at the leading edge, which is used to lay out PZT patches. The de-icing vibration mode and locations of PZT patches were decided by modal analysis. The vibration mode with alternative bending along the leading edge was selected as de-icing mode. The PZT patches were located at the locations with the highest deformation.

  4. Based on the modal analysis of airfoil blade, a test coupon with PZT patches was manufactured, and the natural frequencies were obtained by an impedance analyzer. Then the experimental scheme and system were designed and built. In the anti-icing tests, it was validated that ultrasonic vibration has an anti-icing effect. With the increase in icing time, the anti-icing effect grew obviously. The frequency has an effect on the icing amount. In the present study, when the frequency was 25.604 kHz, the amount of ice was lowest.

  5. Based on the anti-icing tests, a test of de-icing effect of ultrasonic vibration was conducted. A special, self-developed device was designed and manufactured to measure the adhesive strength of ice for airfoil blade. The experimental research findings validated the de-icing effect of ultrasonic vibration. The best de-icing frequency scanned by the impedance analyzer was approximated to the one obtained from the modal analysis. It also validates that the selected de-icing vibration mode is suitable for airfoil blade.

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Acknowledgments

This work was supported by the Open Fund of the Key Laboratory of Wind Energy and Solar Energy Technology [grant number 2020ZD03]; National Natural Science Foundation of China (NSFC) [grant number 51976029].

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Written By

Jianlong Ma, He Shen and Wenfeng Guo

Submitted: 14 June 2023 Reviewed: 28 September 2023 Published: 05 November 2023