4. Empirical formula for noise reduction prediction in 2D airfoils with serrated trailing edges

In this chapter, we confirmed the noise reduction effect induced by serrated trailing edges and identified changes in aerodynamic performance and noise performance. Thus, this study confirmed changes in the frequency components in the wake and the velocity distribution when a serrated trailing edge was attached to a 2D airfoil.

Noise in a 2D airfoil is caused by the boundary layer between the surfaces of the blades, the vortex in the blades, and blade interference. The noise in the wind turbine blade cross-section is defined as self-noise, and different characteristics of self-noise were observed depending on the cross-sectional shape of the blade, flow conditions, and angles of attack. As 2D airfoil selfnoises are usually caused by a combination of multiple factors, it is difficult to identify the exact cause of changes. Brooks et al. [13] suggested an empirical prediction formula based on the results of an aerodynamic noise experiment conducted on an NACA0012 airfoil.

The current study suggests a noise prediction formula for serrated trailing edges using the acoustic model suggested by Brooks, thickness and material for serration strip based on the results of the aerodynamic noise test and the wind tunnel test conducted on serrated trailing edges [14].

$$SPL\_{Total} = SPL\_{TBLTE} - SPL\_{\text{semantion } TE} \tag{4}$$

Figure 12. Mean velocity distribution for the plate with different serrations measured in the z axis direction [8].

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(a) Nor-mal-type serrations; (b) skewed type serrations; (c) multi-type serrations.

The 2D airfoil noises which occur in the wind tunnel test are often heavily influenced by turbulent boundary layers. Based on this fact, Eq. (4) was designed to exclude those noise components which can be altered by serrated trailing edges. Figure 13 presents information on the noise components of 2D airfoils with serrated trailing edges.

Figure 14 shows the "Bell-Type" function for serration trailing edge about Frequency Domain. As seen in Eqs. (5)–(10), the results confirmed noise reduction effect for various aspect ratios of serrations trailing edge [10] (Figure 14).

4. Empirical formula for noise reduction prediction in 2D airfoils with

In this chapter, we confirmed the noise reduction effect induced by serrated trailing edges and identified changes in aerodynamic performance and noise performance. Thus, this study confirmed changes in the frequency components in the wake and the velocity distribution when a

Noise in a 2D airfoil is caused by the boundary layer between the surfaces of the blades, the vortex in the blades, and blade interference. The noise in the wind turbine blade cross-section is defined as self-noise, and different characteristics of self-noise were observed depending on the cross-sectional shape of the blade, flow conditions, and angles of attack. As 2D airfoil selfnoises are usually caused by a combination of multiple factors, it is difficult to identify the exact cause of changes. Brooks et al. [13] suggested an empirical prediction formula based on

The current study suggests a noise prediction formula for serrated trailing edges using the acoustic model suggested by Brooks, thickness and material for serration strip based on the results of the aerodynamic noise test and the wind tunnel test conducted on serrated trailing edges [14].

The 2D airfoil noises which occur in the wind tunnel test are often heavily influenced by turbulent boundary layers. Based on this fact, Eq. (4) was designed to exclude those noise components which can be altered by serrated trailing edges. Figure 13 presents information on

Figure 14 shows the "Bell-Type" function for serration trailing edge about Frequency Domain. As seen in Eqs. (5)–(10), the results confirmed noise reduction effect for various aspect ratios of

ð4Þ

the results of an aerodynamic noise experiment conducted on an NACA0012 airfoil.

the noise components of 2D airfoils with serrated trailing edges.

serrations trailing edge [10] (Figure 14).

serrated trailing edges

Figure 11. Layout of serration plate [8].

132 Stability Control and Reliable Performance of Wind Turbines

serrated trailing edge was attached to a 2D airfoil.

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Figure 12. Mean velocity distribution for the plate with different serrations measured in the z axis direction [8]. (a) Nor-mal-type serrations; (b) skewed type serrations; (c) multi-type serrations.

• The predicted sound field spectrum [10]

$$S(f) \approx \frac{1}{8\pi^2 R^2} \left(\frac{U\_\text{c}L}{c\_0}\right) l\_\nu(f)\Phi(f) \tag{5}$$

• Oscillatory function of trailing edge

$$l\_y(f) = \frac{U\_c}{\xi 2\pi f} \tag{6}$$

• Surface pressure Term: Frequency domain

$$\Phi(f) = \frac{\Phi(\mathcal{S}^\*)l\varrho^2}{U\_{\text{max}}} \tag{7}$$

• Strouhal number function

$$\mathcal{H}^\* = \frac{fL(x)}{U\_{\text{max}}} \tag{8}$$

To analyze the noise prediction performance of the NACA0012 airfoil, an experiment was conducted under the conditions given in Table 2, and the results were used for a comparative analysis. A comparative analysis of the differences between the experimental results and the

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Figure 14. Bell function for serration trailing edge about frequency domain.

Figure 13. Estimation of serration trailing edge noise.

• Span-wise length scale function

$$L(x) = \left[ \log \left( \frac{\lambda\_s}{h} \right)^{0.015} + 0.12 \right]^2 \tag{9}$$

• Estimation function for serration trailing edge noise reduction effect

$$\begin{aligned} \text{SPL}\_{\text{servationTE}} \\ &= \mathbf{3.5} - \mathbf{8} \lceil \log(\text{St}^{\ast}) + \mathbf{0.3} \rceil^{2} - \left[ \log(\frac{\lambda\_{\text{s}}}{h}) + \mathbf{0.4} \right]^{2} \\ &\therefore \text{SPL}\_{\text{servationTE}} \geq \mathbf{0} \end{aligned} \tag{10}$$

#### 4.1. Verification of performance of NACA0012 airfoil

The empirical formula for prediction of 2D airfoil self-noises by Brooks was developed based on the results of an experiment conducted on an NACA0012 airfoil. If an airfoil with a camber or a serrated trailing edge is used, it is impossible to directly apply the prediction model suggested by Brooks, because there can be changes not in the blade of a symmetric airfoil but in aerodynamic performance. To predict noise under such conditions, the lift slope was calibrated to the baseline lift coefficient. Figure 15 gives information about the NACA0012 airfoil with a serrated trailing edge in the wind tunnel test.

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Figure 13. Estimation of serration trailing edge noise.

ð5Þ

ð6Þ

ð7Þ

ð8Þ

ð9Þ

ð10Þ

• The predicted sound field spectrum [10]

134 Stability Control and Reliable Performance of Wind Turbines

• Oscillatory function of trailing edge

• Strouhal number function

• Span-wise length scale function

• Estimation function for serration trailing edge noise reduction effect

The empirical formula for prediction of 2D airfoil self-noises by Brooks was developed based on the results of an experiment conducted on an NACA0012 airfoil. If an airfoil with a camber or a serrated trailing edge is used, it is impossible to directly apply the prediction model suggested by Brooks, because there can be changes not in the blade of a symmetric airfoil but in aerodynamic performance. To predict noise under such conditions, the lift slope was calibrated to the baseline lift coefficient. Figure 15 gives information about the NACA0012 airfoil

4.1. Verification of performance of NACA0012 airfoil

with a serrated trailing edge in the wind tunnel test.

• Surface pressure Term: Frequency domain

Figure 14. Bell function for serration trailing edge about frequency domain.

To analyze the noise prediction performance of the NACA0012 airfoil, an experiment was conducted under the conditions given in Table 2, and the results were used for a comparative analysis. A comparative analysis of the differences between the experimental results and the

airfoil with a serrated trailing edge). The measurement of noises collected through the microphones was used to calculate the cross spectrum between CH00 and CH02, utilizing a noise prediction program which was developed based on the empirical formula suggested by Brooks et al. [13].

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Figure 16 shows the results of comparative analysis of the noise prediction values of the NACA0012 airfoil with the actual measured values. The measured values are consistent with the predicted values. Differences in the low frequency domain (300 Hz or below) can be

As seen in Figure 17, the noise reduction effect produced by a serrated trailing edge was analyzed by applying the contents of the noise prediction formula for the NACA0012 airfoil and the empirical formula suggested by Brooks et al. [13] for prediction of noises in the serrated trailing edge, as seen in Eqs. (5)–(10). After conducting an experiment under the narrow condition, the predicted values were compared with the experimental values. According to the prediction, noises ranging from 500 Hz to 10 kHz should be reduced by the inclusion of a serrated trailing edge. Figures 17 and 18 shows the results of the experiment conducted under the wide condition, as well as the results of the comparative analysis of the predicted values and the measured values. In accordance with the prediction, it was found that

ascribed to the background noise of the anechoic wind tunnel test facility.

noises ranging from 300 Hz to 8 kHz were reduced (Figure 18).

Figure 17. The wind tunnel test and estimation for NACA0012 with narrow serration plate.

Figure 15. NACA0012 airfoil with serration trailing edge.


Table 2. NACA0012 airfoil test condition.

predicted results was carried out under a total of three conditions (one, a 2D airfoil without a serrated trailing edge; and, two and three, the narrow and wide conditions of a normal tri-shaped

Figure 16. The wind tunnel test and estimation for NACA0012 airfoil condition.

airfoil with a serrated trailing edge). The measurement of noises collected through the microphones was used to calculate the cross spectrum between CH00 and CH02, utilizing a noise prediction program which was developed based on the empirical formula suggested by Brooks et al. [13].

Figure 16 shows the results of comparative analysis of the noise prediction values of the NACA0012 airfoil with the actual measured values. The measured values are consistent with the predicted values. Differences in the low frequency domain (300 Hz or below) can be ascribed to the background noise of the anechoic wind tunnel test facility.

As seen in Figure 17, the noise reduction effect produced by a serrated trailing edge was analyzed by applying the contents of the noise prediction formula for the NACA0012 airfoil and the empirical formula suggested by Brooks et al. [13] for prediction of noises in the serrated trailing edge, as seen in Eqs. (5)–(10). After conducting an experiment under the narrow condition, the predicted values were compared with the experimental values. According to the prediction, noises ranging from 500 Hz to 10 kHz should be reduced by the inclusion of a serrated trailing edge. Figures 17 and 18 shows the results of the experiment conducted under the wide condition, as well as the results of the comparative analysis of the predicted values and the measured values. In accordance with the prediction, it was found that noises ranging from 300 Hz to 8 kHz were reduced (Figure 18).

Figure 17. The wind tunnel test and estimation for NACA0012 with narrow serration plate.

predicted results was carried out under a total of three conditions (one, a 2D airfoil without a serrated trailing edge; and, two and three, the narrow and wide conditions of a normal tri-shaped

Model Lift coefficient AOA\* Remark NACA0012 0.50 5.03 N/A Serration narrow 0.43 4.43 λ=h ¼ 0:5 Serration wide 0.42 4.40 λ=h ¼ 2

Figure 15. NACA0012 airfoil with serration trailing edge.

136 Stability Control and Reliable Performance of Wind Turbines

Wind speed = 30 m/s.

Table 2. NACA0012 airfoil test condition.

Figure 16. The wind tunnel test and estimation for NACA0012 airfoil condition.

condition of a 2D airfoil without a serrated trailing edge, and the narrow condition and wide conditions of the normal tri-shaped airfoil with a serrated trailing edge, as was done with the NACA0012 airfoil. The noises collected through the microphones were used to calculate the cross-spectrum between CH0 and CH2, and a noise prediction program which was developed based on the empirical formula suggested by Brooks et al. [13] was utilized to predict 2D airfoil

Model Lift coefficient AOA\* Remark Baseline 0.59 4.60 N/A Serration narrow 0.51 4.48 λ=h ¼ 0:5 Serration wide 0.55 4.49 λ=h ¼ 2

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Figure 20 shows the results of the comparison between the predicted values of the baseline airfoil and the measured values. It was revealed that the disparities between the measured values of the baseline airfoil and the predicted values were wider than those between the measured and predicted values of the NACA0012 airfoil. Figures 21 and 22 show the predicted results when a serrated trailing edge was applied to a 2D airfoil. As there were larger

self-noises, as for the NACA0012 airfoil.

Figure 20. The wind tunnel test and estimation for baseline airfoil condition.

Wind speed = 30 m/s.

Table 3. Baseline airfoil test condition.

Figure 18. The wind tunnel test and estimation for NACA0012 with wide serration plate.

#### 4.2. Verification of baseline airfoil performance

In this study, using the NACA0012 airfoil, experimentally tested Brooks' noise prediction formula and the noise prediction equation for the serrated tail edge are proposed. The prediction of noise reduction in the baseline airfoil with the shape seen in Figure 19 was conducted, and the predicted results were compared with the experimentally obtained values. Based on the results of the wind tunnel test, the lift slope was calibrated to the baseline lift coefficient in order to predict airfoil self-noises.

For the analysis of noise prediction of the baseline airfoil, an experiment was conducted under the conditions given in Table 3, and the measured results were compared with the predicted results. For a comparative analysis between the predicted values and the experimentally obtained values, the experiment was conducted under a total of three conditions, the single

Figure 19. Baseline airfoil with serration trailing edge.


Table 3. Baseline airfoil test condition.

4.2. Verification of baseline airfoil performance

138 Stability Control and Reliable Performance of Wind Turbines

Figure 19. Baseline airfoil with serration trailing edge.

Figure 18. The wind tunnel test and estimation for NACA0012 with wide serration plate.

predict airfoil self-noises.

In this study, using the NACA0012 airfoil, experimentally tested Brooks' noise prediction formula and the noise prediction equation for the serrated tail edge are proposed. The prediction of noise reduction in the baseline airfoil with the shape seen in Figure 19 was conducted, and the predicted results were compared with the experimentally obtained values. Based on the results of the wind tunnel test, the lift slope was calibrated to the baseline lift coefficient in order to

For the analysis of noise prediction of the baseline airfoil, an experiment was conducted under the conditions given in Table 3, and the measured results were compared with the predicted results. For a comparative analysis between the predicted values and the experimentally obtained values, the experiment was conducted under a total of three conditions, the single condition of a 2D airfoil without a serrated trailing edge, and the narrow condition and wide conditions of the normal tri-shaped airfoil with a serrated trailing edge, as was done with the NACA0012 airfoil. The noises collected through the microphones were used to calculate the cross-spectrum between CH0 and CH2, and a noise prediction program which was developed based on the empirical formula suggested by Brooks et al. [13] was utilized to predict 2D airfoil self-noises, as for the NACA0012 airfoil.

Figure 20 shows the results of the comparison between the predicted values of the baseline airfoil and the measured values. It was revealed that the disparities between the measured values of the baseline airfoil and the predicted values were wider than those between the measured and predicted values of the NACA0012 airfoil. Figures 21 and 22 show the predicted results when a serrated trailing edge was applied to a 2D airfoil. As there were larger

Figure 20. The wind tunnel test and estimation for baseline airfoil condition.

Figure 21. The wind tunnel test and estimation for baseline airfoil with wide serration plate condition.

differences between the predicted values and the measured values in comparison to those of the NACA0012 airfoil, the study showed a similar performance prediction ability under the conditions of interest.

the beginning of Section 4, however, this study has certain limitations, such as the range of noise

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Figure 22. The wind tunnel test and estimation for baseline airfoil with wide serration plate condition.

There were differences in the installation angles of serrated trailing edges depending on the shapes of the 2D airfoils, which may have caused variations in the frequency ranges of noise reduction, even when the same serrated trailing edge was used. Such an effect was noted in previous studies conducted from 1997 to 1999 in the JOULE-III program in Europe to measure the noises generated by a wind turbine rotor [12]. If follow-up studies take this effect into account, it may be possible to propose a more accurate noise prediction empirical formula than

Another limitation is related to the prediction formula defined as "Bell-type" by this study. This study conducted a 2D wind tunnel test on the noise reduction effect induced by serrated trailing edges, based on the baseline 2D airfoil used in actual wind turbine rotors. The contents of Figure 23 show the noise reduction prediction function of serrated trailing edges

previously conducted baseline airfoil and the serrated airfoil. The results confirmed that the noise reduction effect appeared as 'Bell-type' in various aspect ratios (λ=h) of serrated trailing

) and the differences in the noise reduction prediction results between the

experiment results and the limited types of 2D airfoils.

the one reviewed by this study.

(SPL serration <sup>T</sup>:E:

edges.

When a serrated trailing edge was applied, noise reduction effects were observed both in the experimental results and the predicted results obtained by the empirical formula, under the same angles of attack. Also, they showed a similar frequency range where noises were reduced. However, it was found that the predicted values were smaller than the experimental values.

#### 4.3. Review of noise reduction effects of 2D airfoils with serrated trailing edges

This study examined the noise reduction effects between the NACA0012 airfoil and the baseline airfoil used by a wind turbine rotor, which is considered a standard airfoil, following the application of serrated trailing edges. In this study, the validity of the noise reduction effect was confirmed under the angle of attack set as a precondition. This study utilized Brooks' empirical formula for noise reduction in 2D airfoils and the 'Bell-type' noise prediction empirical formula in order to examine the noise reduction effect of serrated trailing edges. As mentioned in Estimation Method to Achieve a Noise Reduction Effect of Airfoil with a Serrated Trailing Edge for Wind… http://dx.doi.org/10.5772/intechopen.73608 141

Figure 22. The wind tunnel test and estimation for baseline airfoil with wide serration plate condition.

differences between the predicted values and the measured values in comparison to those of the NACA0012 airfoil, the study showed a similar performance prediction ability under the

When a serrated trailing edge was applied, noise reduction effects were observed both in the experimental results and the predicted results obtained by the empirical formula, under the same angles of attack. Also, they showed a similar frequency range where noises were reduced. However, it was found that the predicted values were smaller than the experimental values.

This study examined the noise reduction effects between the NACA0012 airfoil and the baseline airfoil used by a wind turbine rotor, which is considered a standard airfoil, following the application of serrated trailing edges. In this study, the validity of the noise reduction effect was confirmed under the angle of attack set as a precondition. This study utilized Brooks' empirical formula for noise reduction in 2D airfoils and the 'Bell-type' noise prediction empirical formula in order to examine the noise reduction effect of serrated trailing edges. As mentioned in

4.3. Review of noise reduction effects of 2D airfoils with serrated trailing edges

Figure 21. The wind tunnel test and estimation for baseline airfoil with wide serration plate condition.

conditions of interest.

140 Stability Control and Reliable Performance of Wind Turbines

the beginning of Section 4, however, this study has certain limitations, such as the range of noise experiment results and the limited types of 2D airfoils.

There were differences in the installation angles of serrated trailing edges depending on the shapes of the 2D airfoils, which may have caused variations in the frequency ranges of noise reduction, even when the same serrated trailing edge was used. Such an effect was noted in previous studies conducted from 1997 to 1999 in the JOULE-III program in Europe to measure the noises generated by a wind turbine rotor [12]. If follow-up studies take this effect into account, it may be possible to propose a more accurate noise prediction empirical formula than the one reviewed by this study.

Another limitation is related to the prediction formula defined as "Bell-type" by this study. This study conducted a 2D wind tunnel test on the noise reduction effect induced by serrated trailing edges, based on the baseline 2D airfoil used in actual wind turbine rotors. The contents of Figure 23 show the noise reduction prediction function of serrated trailing edges (SPL serration <sup>T</sup>:E: ) and the differences in the noise reduction prediction results between the previously conducted baseline airfoil and the serrated airfoil. The results confirmed that the noise reduction effect appeared as 'Bell-type' in various aspect ratios (λ=h) of serrated trailing edges.

Figure 24 shows both the predicted results and the experimental results of the noise reduction effect induced by serrated trailing edges. The experimental results showed a 'Bell-type' distribution, but in some conditions, the distribution was more similar to 'Cone-type'. If further experiments are conducted based on the shape of serrated trailing edges, apart from the experimental conditions used in this study, it may be possible to improve the accuracy of the

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A wind tunnel experiment was conducted on 2D airfoils, and the noise reduction effect was examined based on aerodynamic performance. Using the wind tunnel test on 2D airfoils with serrated trailing edges, wake distribution measurements and an analysis of their relationship with acoustic characteristics were conducted in order to examine the restrictive conditions of Howe's theory. These experimental results confirmed that as changes occur in the boundary layer thickness of 2D airfoils, an empirical formula or a theoretical approach which can reflect these changes is necessary. This study suggested an empirical formula for the prediction of noises in serrated trailing edges by utilizing the wind tunnel results on 2D airfoils with serrated trailing edges, based on the acoustic model suggested by Brooks. Also, the wind tunnel test results and noise prediction results of the NACA0012 airfoil with serrated trailing edges were compared with those of the baseline airfoil, and, through this comparative analysis, the study suggested a new noise prediction empirical formula for 2D airfoils. The study confirmed the validity of the proposed noise prediction formula by carrying out aerodynamic performance testing and noise measurements on the NACA0012 airfoil, the baseline airfoil, and the serrated trailing edges. However, as the noise prediction formula for the serrated trailing edges was an empirical formula that was based on limited experimental conditions, errors may have arose because of factors including the installation angles of the serrated trailing edges and the cross-sectional shapes of the 2D blades. To make up for the shortcomings in the test results, additional wind tunnel tests need to be conducted, and in consideration of the test results, further studies need to be conducted on the formation of a more accurate noise predic-

This work was supported by research fund of 2014 Chungnam National University of the Korea.

noise prediction formula.

5. Conclusion

tion formula.

Acknowledgements

U velocity of the free stream (m/s)

λs span-wise wavelength (mm) h amplitude of serrations (mm)

Nomenclature

Figure 23. Cross spectrum of baseline airfoil with serration trailing edge.

Figure 24. The level difference of baseline airfoil with serration trailing edge.

Figure 24 shows both the predicted results and the experimental results of the noise reduction effect induced by serrated trailing edges. The experimental results showed a 'Bell-type' distribution, but in some conditions, the distribution was more similar to 'Cone-type'. If further experiments are conducted based on the shape of serrated trailing edges, apart from the experimental conditions used in this study, it may be possible to improve the accuracy of the noise prediction formula.
