Numerical Analysis of Broadband Noise Generated by an Airfoil with Spanwise-Varying Leading Edges
<p>Schematic illustration of the leading-edge serrations.</p> "> Figure 2
<p>Comparison between the measured axial velocity spectra and theoretical spectra.</p> "> Figure 3
<p>SPL comparison for analytical and experimental results of trailing-edge self-noise.</p> "> Figure 4
<p>SPL generated by the analytical results in view of self-noise and experimental results at <math display="inline"><semantics> <mrow> <mover accent="true"> <mrow> <mi>h</mi> </mrow> <mo>¯</mo> </mover> <mo>=</mo> <mn>0.5</mn> </mrow> </semantics></math>.</p> "> Figure 5
<p>SPL generated by the analytical results in view of self-noise and experimental results at <math display="inline"><semantics> <mrow> <mover accent="true"> <mrow> <mi>h</mi> </mrow> <mo>¯</mo> </mover> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>.</p> "> Figure 6
<p>SPL generated by the analytical results in view of self-noise and experimental results at <math display="inline"><semantics> <mrow> <mover accent="true"> <mrow> <mi>h</mi> </mrow> <mo>¯</mo> </mover> <mo>=</mo> <mn>2</mn> </mrow> </semantics></math>.</p> "> Figure 7
<p>The serration profiles of diverse leading edges.</p> "> Figure 8
<p>Comparison of decay rates of <math display="inline"><semantics> <mrow> <mfenced open="|" close="|" separators="|"> <mrow> <msub> <mrow> <mi>E</mi> </mrow> <mrow> <mn>0</mn> </mrow> </msub> </mrow> </mfenced> </mrow> </semantics></math> for different leading-edge serrations.</p> "> Figure 9
<p>Comparison of decay rates of <math display="inline"><semantics> <mrow> <mfenced open="|" close="|" separators="|"> <mrow> <msub> <mrow> <mi>E</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msub> </mrow> </mfenced> </mrow> </semantics></math> for different leading-edge serrations.</p> "> Figure 10
<p>SPL spectra of different leading-edge serrations at <math display="inline"><semantics> <mrow> <mover accent="true"> <mrow> <mi>h</mi> </mrow> <mo>¯</mo> </mover> <mo>=</mo> <mn>0.5</mn> </mrow> </semantics></math>.</p> "> Figure 11
<p>SPL spectra of different leading-edge serrations at <math display="inline"><semantics> <mrow> <mover accent="true"> <mrow> <mi>h</mi> </mrow> <mo>¯</mo> </mover> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>.</p> "> Figure 12
<p>SPL spectra of different leading-edge serrations at <math display="inline"><semantics> <mrow> <mover accent="true"> <mrow> <mi>h</mi> </mrow> <mo>¯</mo> </mover> <mo>=</mo> <mn>2</mn> </mrow> </semantics></math>.</p> "> Figure 13
<p>The serration profiles of the diverse leading edge with different values of b in Equation (16).</p> "> Figure 14
<p>The serration profiles of the diverse leading edge with different values of b in Equation (17).</p> "> Figure 15
<p>SPL spectra of leading-edge serrations with different b values in Equation (16) at <math display="inline"><semantics> <mrow> <mover accent="true"> <mrow> <mi>h</mi> </mrow> <mo>¯</mo> </mover> <mo>=</mo> <mn>2</mn> </mrow> </semantics></math>.</p> "> Figure 16
<p>SPL spectra of leading-edge serrations with different b values in Equation (17) at <math display="inline"><semantics> <mrow> <mover accent="true"> <mrow> <mi>h</mi> </mrow> <mo>¯</mo> </mover> <mo>=</mo> <mn>2</mn> </mrow> </semantics></math>.</p> "> Figure 17
<p>Schematic diagram of a double-wavelength serration.</p> "> Figure 18
<p>The serration profiles of leading edges with minimum test value (SPL) at <math display="inline"><semantics> <mrow> <mover accent="true"> <mrow> <mi>h</mi> </mrow> <mo>¯</mo> </mover> <mo>=</mo> <mn>0.5</mn> </mrow> </semantics></math>.</p> "> Figure 19
<p>The serration profiles of lading edges with minimum test value (SPL) at <math display="inline"><semantics> <mrow> <mover accent="true"> <mrow> <mi>h</mi> </mrow> <mo>¯</mo> </mover> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>.</p> "> Figure 20
<p>The serration profiles of leading edges with minimum test value (SPL) at <math display="inline"><semantics> <mrow> <mover accent="true"> <mrow> <mi>h</mi> </mrow> <mo>¯</mo> </mover> <mo>=</mo> <mn>2</mn> </mrow> </semantics></math>.</p> "> Figure 21
<p>OASPLs of representative serrations with double wavelengths at <math display="inline"><semantics> <mrow> <mover accent="true"> <mrow> <mi>h</mi> </mrow> <mo>¯</mo> </mover> <mo>=</mo> <mn>0.5</mn> </mrow> </semantics></math>.</p> "> Figure 22
<p>OASPLs of representative serrations with double wavelengths at <math display="inline"><semantics> <mrow> <mover accent="true"> <mrow> <mi>h</mi> </mrow> <mo>¯</mo> </mover> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>.</p> "> Figure 23
<p>OASPLs of representative serrations with double wavelengths at <math display="inline"><semantics> <mrow> <mover accent="true"> <mrow> <mi>h</mi> </mrow> <mo>¯</mo> </mover> <mo>=</mo> <mn>2</mn> </mrow> </semantics></math>.</p> "> Figure 24
<p>SPL<sub>CA</sub> and SPL<sub>0</sub> distributions of representative serrations with double wavelengths at <math display="inline"><semantics> <mrow> <mover accent="true"> <mrow> <mi>h</mi> </mrow> <mo>¯</mo> </mover> <mo>=</mo> </mrow> </semantics></math> 0.5.</p> "> Figure 25
<p>SPL<sub>CA</sub> and SPL<sub>0</sub> distributions of representative serrations with double wavelengths at <math display="inline"><semantics> <mrow> <mover accent="true"> <mrow> <mi>h</mi> </mrow> <mo>¯</mo> </mover> <mo>=</mo> </mrow> </semantics></math> 1.</p> "> Figure 26
<p>SPL<sub>CA</sub> and SPL<sub>0</sub> distributions of representative serrations with double wavelengths at <math display="inline"><semantics> <mrow> <mover accent="true"> <mrow> <mi>h</mi> </mrow> <mo>¯</mo> </mover> <mo>=</mo> </mrow> </semantics></math>2.</p> "> Figure 27
<p>Cloud chart of <math display="inline"><semantics> <mrow> <msup> <mrow> <mfenced open="|" close="|" separators="|"> <mrow> <msub> <mrow> <mi>E</mi> </mrow> <mrow> <mi>n</mi> </mrow> </msub> </mrow> </mfenced> </mrow> <mrow> <mn>2</mn> </mrow> </msup> </mrow> </semantics></math> built for the smooth leading edge.</p> "> Figure 28
<p>Cloud charts of <math display="inline"><semantics> <mrow> <msup> <mrow> <mfenced open="|" close="|" separators="|"> <mrow> <msub> <mrow> <mi>E</mi> </mrow> <mrow> <mi>n</mi> </mrow> </msub> </mrow> </mfenced> </mrow> <mrow> <mn>2</mn> </mrow> </msup> </mrow> </semantics></math> for different double-wavelength serrations at <math display="inline"><semantics> <mrow> <mover accent="true"> <mrow> <mi>h</mi> </mrow> <mo>¯</mo> </mover> <mo>=</mo> </mrow> </semantics></math>2, including (<b>a</b>) traditional serrations, (<b>b</b>) ogee-shaped serrations, (<b>c</b>) sinusoidal serrations, and (<b>d</b>) iron-shaped serrations.</p> "> Figure 29
<p>SPL spectra of representative double-wavelength serrations at <math display="inline"><semantics> <mrow> <mover accent="true"> <mrow> <mi>h</mi> </mrow> <mo>¯</mo> </mover> <mo>=</mo> </mrow> </semantics></math> 2.</p> "> Figure 30
<p>Sound pressure reduction levels of representative double-wavelength serrations at <math display="inline"><semantics> <mrow> <mover accent="true"> <mrow> <mi>h</mi> </mrow> <mo>¯</mo> </mover> <mo>=</mo> </mrow> </semantics></math> 2.</p> "> Figure 31
<p>Integration of OASPLs of representative double-wavelength serrations over different frequency bands at <math display="inline"><semantics> <mrow> <mover accent="true"> <mrow> <mi>h</mi> </mrow> <mo>¯</mo> </mover> <mo>=</mo> <mn>2</mn> </mrow> </semantics></math>.</p> "> Figure 32
<p>Surface pressure generating outgoing acoustic waves for double-wavelength serrations at <math display="inline"><semantics> <mrow> <mover accent="true"> <mrow> <mi>h</mi> </mrow> <mo>¯</mo> </mover> <mo>=</mo> </mrow> </semantics></math> 2.</p> "> Figure 33
<p>Phase distribution of surface pressure along the spanwise-varying leading edge of double-wavelength serrations at <math display="inline"><semantics> <mrow> <mover accent="true"> <mrow> <mi>h</mi> </mrow> <mo>¯</mo> </mover> <mo>=</mo> </mrow> </semantics></math> 2, M = 0.17, k<sub>1</sub> = 62.83, k<sub>3</sub> = 0.</p> "> Figure 34
<p>Spatial distribution of OASPL integrated over the frequency bands of (<b>a</b>) 0~10,000 Hz, (<b>b</b>) 0~500 Hz, (<b>c</b>) 500~5000 Hz, and (<b>d</b>) 5000~10,000 Hz at <math display="inline"><semantics> <mrow> <mover accent="true"> <mrow> <mi>h</mi> </mrow> <mo>¯</mo> </mover> <mo>=</mo> </mrow> </semantics></math> 2.</p> ">
Abstract
:1. Introduction
2. Analytical Formulation
3. Comparison with Experiments
4. Acoustic Performance of Single-Wavelength Serrations
5. Acoustic Sensitivity of Double-Wavelength Serrations
6. Results and Discussion
6.1. The Behavior of the Functions
6.2. Sound Pressure Level (SPL)
6.3. Sound Pressure Level Integrated with Different Frequency Bands
6.4. Surface Pressure and Phase Distributions
6.5. Directivity Characteristic of OASPL
7. Conclusions
- (1)
- Combined with the function associated with the shape factor, noise reduction at specific frequencies can be obtained in the low- and intermediate-frequency bands for serrations with a small curvature at non-smooth points. Moreover, it should be mentioned that spanwise-varying leading edges coping with a subsonic airflow interact with sharp serrations, resulting in an increase in additional broadband noise in the low-frequency regime compared with traditional serrations. And the performance in the high-frequency region is reversed. However, when the influence of trailing-edge self-noise is gradually enhanced with the increase in , the noise reduction advantage of large-curvature serrations at non-smooth points in the high-frequency region is weakened to a certain degree. For a single-value piecewise function in the unit wavelength range of 1 and 1/4 period, one must meet the condition in order to design a serration with excellent noise reduction performance at low and intermediate frequencies, while the opposite represents a good noise reduction level in the high-frequency region.
- (2)
- Aside from this, the acoustic optimality of double-wavelength serrations of different frequencies and phases is the key focused discussion. The noise reduction levels of shape factors, wavelengths, and amplitudes at different tip-to-root ratios are obtained through the design of trial numbers. It turns out that the shape factor was dominant at different tip-to-root ratios. The amplitude gradually replaces the wavelength with the increase in the tip-to-root ratio and transforms into the second most influential factor. Based on the premise of fixed wavelength and amplitude, the noise reduction level at performed best. This indicates that the larger the amplitude of the superimposed serrations, the more conducive it is to increasing the phase difference.
- (3)
- Both the sinusoidal function and the iron-shaped function performed well at different double-wavelength serrations, reducing the overall sound pressure level by up to 5.2 dB. Broadband noise in the 500–5000 Hz band was significantly reduced by 6.7 dB. The root-destructive interference was enhanced by the ogee-shaped serrations, increasing the local noise reduction effect and suppressing noise emissions in specific high-frequency regions. In the design of serrations, one can refer to the source cut-off mechanism of source radiation and introduce sharp structures such as narrow slits at the root to achieve local noise control, satisfying the design requirement of reducing high-frequency noise.
Author Contributions
Funding
Institutional Review Board Statement
Data Availability Statement
Conflicts of Interest
References
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Parameters | Shape | ||||
---|---|---|---|---|---|
Factors | A | B | C | D | E |
Level 1 | Serrated | 0.2 | 0.2 | 0.8 | 1 |
Level 2 | Ogee | 0.4 | 0.5 | 0.6 | 1 |
Level 3 | Sinusoidal | 0.6 | 0.8 | 0.4 | 1 |
Level 4 | Iron-shaped | 0.8 | 1 | 0.2 | 1 |
Trial Number | Code Name | SPL (dB) | SPL1 | SPL2 | SPLCA | Results | ||
---|---|---|---|---|---|---|---|---|
1 | A1B1C1 | 0.2 | 0.2 | 81.3600 | −0.3541 | −2.3381 | −1.3461 | I1 |
2 | A1B1C2 | 0.2 | 0.5 | 81.2934 | −0.4207 | −1.2235 | 0.8221 | I2 |
3 | A1B1C3 | 0.2 | 0.8 | 81.2534 | −0.4607 | 0.0759 | 0.1924 | I3 |
4 | A1B1C4 | 0.2 | 1 | 81.2595 | −0.4546 | 0.9309 | 0.2382 | I4 |
5 | A1B2C1 | 0.4 | 0.2 | 81.5507 | 0.7586 | −2.2048 | 0.7231 | I5 |
6 | A1B2C2 | 0.4 | 0.5 | 81.2268 | 0.4347 | −1.4466 | 0.5060 | I6 |
7 | A1B2C3 | 0.4 | 0.8 | 80.7423 | −0.0498 | −0.5733 | −0.3116 | I7 |
8 | A1B2C4 | 0.4 | 1 | 80.4740 | −0.3181 | −0.0542 | −0.1862 | I8 |
9 | A1B3C1 | 0.6 | 0.2 | 82.3493 | 1 8211 | −1.4556 | 0.1828 | I9 |
10 | A1B3C2 | 0.6 | 0.5 | 81.9631 | 1.4349 | −0.9077 | 0.2636 | I10 |
11 | A1B3C3 | 0.6 | 0.8 | 81.0968 | 0.5686 | −0.4463 | 0.0612 | I11 |
12 | A1B3C4 | 0.6 | 1 | 80.4483 | −0.0799 | −0.3438 | −0.2119 | I12 |
13 | A1B4C1 | 0.8 | 0.2 | 83.1816 | 2.8530 | −0.7657 | 1.0437 | I13 |
14 | A1B4C2 | 0.8 | 0.5 | 82.8609 | 2 5323 | −0.2522 | 1.1401 | I14 |
15 | A1B4C3 | 0.8 | 0.8 | 81.9630 | 1.6344 | −0.1386 | 0.7479 | I15 |
16 | A1B4C4 | 0.8 | 1 | 81.1964 | 0.8678 | −0.5177 | 0.1751 | I16 |
17 | original | — | — | 84.0530 | — | — | — | — |
Factors | A | B | C |
---|---|---|---|
0.809 | 0.342 | 0.171 | |
3.092 | 1.096 | 1.027 | |
4.301 | 1.481 | 1.627 | |
Order of the factors () | A > B > C | ||
Order of the factors (1) | A > B > C | ||
Order of the factors (2) | A > C > B |
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Wang, L.; Liu, X.; Tian, C.; Li, D. Numerical Analysis of Broadband Noise Generated by an Airfoil with Spanwise-Varying Leading Edges. Biomimetics 2024, 9, 229. https://doi.org/10.3390/biomimetics9040229
Wang L, Liu X, Tian C, Li D. Numerical Analysis of Broadband Noise Generated by an Airfoil with Spanwise-Varying Leading Edges. Biomimetics. 2024; 9(4):229. https://doi.org/10.3390/biomimetics9040229
Chicago/Turabian StyleWang, Lei, Xiaomin Liu, Chenye Tian, and Dian Li. 2024. "Numerical Analysis of Broadband Noise Generated by an Airfoil with Spanwise-Varying Leading Edges" Biomimetics 9, no. 4: 229. https://doi.org/10.3390/biomimetics9040229