Numerical study on aerodynamic performance and noise of protrusions structures near the trailing edge

Based on the NACA0012 airfoil, different types of protrusions namely serrated protrusions and arc-shaped protrusions are set near the trailing edge. Both new airfoils have a certain decrease in flow performance however there is a significant reduction in aerodynamic noise of airfoils. This is because the protrusions damage the vortex near the trailing edge. In addition, the noise reduction of serrated protrusions is more significant than t of arc-shaped protrusions, about 2.7dB.


Introduction
The aerodynamic noise of fluid machinery has always been a focused research topic.The traditional noise reduction method is to analyze the flow of fluid machinery, optimize the overall structure, improve the impact of unreasonable flow to achieve noise reduction.In addition, there are also interventions in the propagation of noise, where the noise is absorbed, silenced or treated with sound absorption after it is generated, resulting in a significantly lower noise level at the receiving source than that at the sound source.However, these methods did not intervene from the source of noise, which do not control the flow on the blade surface, resulting in poor noise reduction efficiency compared to the cost of noise reduction.Low sound pressure level will make our environment more suitable, like airport noise and home noise.And the study of noise reduction will make some application in military and civilian.So, this is an extremely important study to reduce noise of fluid machinery.
At present, studies based on trailing and leading-edge structures are mostly focused.Howe [1][2] first proposed the theoretical analysis of the sawtooth trailing-wing airfoils that mimic owl wings, and presented a prediction model for sawtooth tail-edge noise reduction.Afterwards, many researchers began to study the zigzag trailing edge.Carlos Arce Leon et al. [3] studied the zigzag trailing edge based on the NACA0018 airfoil, observed an increase in the noise level, and explained the increase in noise level by means of particle image velocimetry.Ye et al. [4] numerically studied the effect of different serrated trailing-edges on aerodynamic performance and noise, they found serrated trailingedges could improve fan efficiency and significantly reduce the noise in the middle-and lowfrequency by splitting large-scale vortices into small ones.Liu et al. [5] investigated the effect of trailing-edge flap on the aerodynamic performance and noise of NACA0018 airfoil, the research indicated that the trailing-edge flap could effectively suppress flow separation, thus improve the dynamic stall characteristics and reduce the noise.Ananthan et al. [6] changed the position of finlets, they found the finlets near the trailing edge provide a 'lifting-up' effect for the most energetic eddies which could weaken the edge scattering and reduce the trailing-edge noise.Based on the NACA0012 airfoil, Walter Arias Ramirez et al. [7] studied the obtuse trailing edges of different radii of curvature and analyzed the effects of compressibility on sound generation and propagation.It was found that thick trailing edges would produce higher noise levels and increase scattering far-field noise.In the experiment, RYI Jaeha et al. [8] applied a sawtooth trailing edge to the 10kw wind turbine and conducted a wind tunnel test, confirming the noise reduction effect of the sawtooth trailing edge and Howe's prediction model of the sawtooth trailing edge noise reduction on the small size fan.Some people also studied the different forms of the leading edge.Weijie Chen et al. [9] studied the NACA0012 airfoil with straight and wavy leading edges through experiments and found that the wavy leading edge has a good noise reduction effect and the reduction of sound power is particularly sensitive to the parameters of the wavy leading edge.JR Mathews et al. [10] conducted a study by adding serrations to the leading edge of the airfoil.After comparing the zigzag leading edge and the straight leading edge, it was found that the zigzag leading edge was more complex and resulted in the effect of noise is difficult to predict, and it is found that the sawtooth front has little effect at large angles of attack.There are also some improvements on the serration trailing edge.Ge et al. [11] added a porous structure to the trailing edge of the airfoil.It was found that such a structure can suppress the noise generated by vortex shedding and can reduce the scattering noise of the turbulent boundary layer.Chong et al. [12] found that the non-flat serrations trailing edge have better structural strength than the flat serration trailing edge, and they confirmed that the non-flat serration trailing edge will eliminate high-frequency noise and reduce narrow-band noise by using a combination of non-flat serration trailing edge and woven mesh sieve.
However, to the best knowledge of the authors, no study has been carried out yet to investigate the effect of different types protrusions on the aerodynamic performance and noise.This article will study the adjustment of the surface structure of the airfoil with the NACA0012 airfoil as a prototype.Based on the original airfoil, serrated protrusions and arc-shaped protrusions will be used, and numerical simulation research will be conducted on the original and improved airfoils.The effectiveness of airfoil modification will be evaluated from the aspects of aerodynamic performance and aerodynamic noise.

Model and Construction
Protrusions are set near the trailing edge on the upper surface of the airfoil based on the NACA0012 airfoil.Two airfoils with arc-shaped protrusions and serrated protrusions respectively are constructed.
As shown in Figure 1 below, the cross-sectional profiles and the 3D model of the airfoils with protrusions in the spanwise direction are displayed.An unstructured mesh is adopted to the computational grid because the good adaptability to complex features which covering the airfoil surfaces.And the boundary layer of the wall is encrypted to ensure the grid scale of the first normal dimensionless network of the airfoil surface  ( ≤ 1。The grid independence test was performed in order to ensure the effective calculation accuracy and reasonable calculation efficiency.When the number of grids is greater than 3.35 million, the lift-todrag ratio of the NACA0012 airfoil basically does not change with the increase of the number of grids.When the number of grids is greater than 3.86 million and 4.03 million, the lift-to-drag ratio of the airfoil with arc-shaped protrusions and serrated protrusions respectively no longer changes with the increasing of the number of grids.Thus, the number of grids of NACA0012 airfoil, the airfoil with arc-shaped protrusions and serrated protrusions used in this paper is approximately 3.35 million, 3.86 million and 4.03 million respectively.
The numerical method for transient calculation is a SIMPLE algorithm based on the finite volume method.The Green-Gauss Node Based gradient scheme is used.In order to reduce the numerical dissipation of the solution, the second-order upwind scheme is used in the discrete format.The time step selected for the transient calculation is 1×10 *$ s.

Results
It can be seen from figure 3 that the lift coefficient of NACA0012 is generally the highest, followed by the airfoil with arc-shaped protrusions, and the lift coefficient of the airfoil with serrated protrusions is the lowest.Three airfoils show similar lift coefficient when the angle of attack is below 16 degree.The lift coefficient of NACA0012 airfoil is the highest at both small and large angles of attack, and it's almost 1.3 times of the lift coefficient of the airfoil with serrated airfoil at 18 degree.However, the lift coefficient of airfoils with protrusions is higher at some angles of attack.This is because the existence of the protrusions destroys the flow on the original airfoil surface, making the flow more chaotic, thus affecting the lift coefficient, but in the case of small to medium angles of attack, the impact on the lift coefficient is not significant.To demonstrate the effect of the protrusions on the flow state and sound pressure level around the airfoil in an unsteady flow field, the Q-criterion is used to analyze and compare the vortex movement of the suction and the pressure surfaces of the NACA0012 airfoil and the airfoil with protrusion at an angle of attack of 17°, and the vortex corn regions of the airfoil with arc-shaped protrusions are similar with these of the airfoil with serrated protrusions.As shown in figure 4, the airfoil with protrusions weakens the eddy intensity in the upper middle section of the airfoil suction surface, while the reduction in eddy intensity can effectively reduce the noise generated by the airfoils, so the airfoil with protrusions will have a better act on noise reduction.This phenomenon may be caused by the presence of protrusions, which make a larger vortex divides after the separation of the airflow.The insufficient energy of the airflow makes the vortex intensity on the suction surface of the airfoil with protrusions lower than that on the suction surface of the NACA0012 airfoil.As a result, the airfoil with protrusions has a lower sound pressure level.The aerodynamic noise of the airfoils is calculated by simulation.The sound pressure levels of the airfoils' noise are shown in table 1.From the table, it is found that the airfoil with serrated protrusions produce the lowest sound pressure level, and NACA0012 airfoil produce the highest sound pressure level.The noise of the airfoil with arc-shaped protrusions reduced by 1.6dB compared to NACA0012 airfoil, and the noise of the airfoil with serrated protrusions reduced by 2.7dB compared to NACA0012 airfoil.Twelve acoustic pressure signal receivers are evenly arranged on a circle that is 10 times the chord length of the bionic airfoil in order to obtain the distribution of noise in the propagation direction accurately.Figure 5 shows the directional distribution of the sound pressure level.The sound pressure level changes significantly with direction of the airfoil with different protrusions, with the highest peak on the upper and lower sides and the lowest peak on the front and back sides, indicating that the airfoil noise is modeled by a dipole source and the main radiation area of the noise is on the upper and lower sides.Figure 6 compares the effect of protrusions on the noise production.As can be seen from the comparison contours, the NACA0012 airfoil produces the highest noise.The high frequency noise produced by the airfoil with protrusions are almost the same, while the airfoil with serrated protrusions produces lower low-frequency noise than that with arc-shaped protrusions, so the overall noise generated by the airfoil with serrated protrusions will be lower than the noise generated by the airfoil with arc-shaped protrusions.By comparing the noises generated by the airfoil with arc-shaped protrusions and NACA0012, it can be seen that the airfoil with protrusions and NACA0012 airfoil produce the same low-frequency noise basically, but the airfoil with protrusions produce lower medium-frequency noise than NACA0012 airfoil, and at high-frequency, NACA0012 airfoil produce the lowest one.Overall, the airfoil with serrated protrusions produces lower aerodynamic noise than others.

Conclusion
Through this study, the effect of protrusions on the airfoil surface is studied.The of protrusions can impact the aerodynamic performance and noise of the airfoil.
1) Setting protrusions on the airfoil surface can cause a certain degree of damage to the flow on the airfoil surface at high angle of attack, leading to a decrease in the aerodynamic performance of the airfoil.
2) The periodic protrusions can achieve a reduction in overall aerodynamic noise.Compared to NACA0012 airfoil, the noise of the airfoil with arc-shaped protrusions and serrated protrusions reduced by 1.6dB and 2.7dB respectively.
3) The airfoils with protrusions produce lower noise than NACA0012 airfoil, especially at low-and medium-frequency.The airfoil with serrated protrusions can also have good noise reduction effects even when the aerodynamic performance is not significantly affected.
In this article, we only studied airfoils with two types of protrusions, provided direction for the study of surface protrusions on airfoils.The optimal protrusion may not be among them and further work is needed to explore, however the infinity of the structure may result in the inability to easily obtain the optimal structure.

Figure 1 .
Figure 1.Section of the airfoils with protrusions.A C-shaped structure is used to create the computational domain, as shown in figure6, to ensure the effectiveness of numerical simulation results and reduce numerical dissipation.The outlet boundary is setting at the downstream of the model with a distance of 20 times of the length of the chord.The front (upstream) of the model is a semi cylindrical model, with a distance of 10 times of the chord length from the root of the airfoil.The width of the model is 0.1m, and the rear of the model is a cuboid.The velocity boundary condition is given to the inlet, the pressure boundary condition is given to the outlet with an outlet pressure of 1.013× 10 $ Pa, the side surface in contact with the calculation model is set as a periodic boundary condition, and the model surface is set as a non-slip wall boundary condition.The Reynolds number of this model is about 1.2× 10 $ .

Figure 2 .
Figure 2. Computational domain of the simulation.

Figure 3 .
Figure 3. Lift coefficient of NACA0012 airfoils and the airfoils with protrusions.To demonstrate the effect of the protrusions on the flow state and sound pressure level around the airfoil in an unsteady flow field, the Q-criterion is used to analyze and compare the vortex movement of the suction and the pressure surfaces of the NACA0012 airfoil and the airfoil with protrusion at an angle of attack of 17°, and the vortex corn regions of the airfoil with arc-shaped protrusions are similar with these of the airfoil with serrated protrusions.As shown in figure4, the airfoil with protrusions weakens the eddy intensity in the upper middle section of the airfoil suction surface, while the

4 .
(a) NACA0012 airfoil (b) airfoil with serrated protrusions Figure Vortex corn regions of the NACA0012 airfoil(a) and the airfoil with protrusions(b).

Figure 5 .
Figure 5.The OASPL of the airfoils.Figure6compares the effect of protrusions on the noise production.As can be seen from the comparison contours, the NACA0012 airfoil produces the highest noise.The high frequency noise produced by the airfoil with protrusions are almost the same, while the airfoil with serrated protrusions produces lower low-frequency noise than that with arc-shaped protrusions, so the overall noise generated by the airfoil with serrated protrusions will be lower than the noise generated by the airfoil with arc-shaped protrusions.By comparing the noises generated by the airfoil with arc-shaped protrusions and NACA0012, it can be seen that the airfoil with protrusions and NACA0012 airfoil produce the same low-frequency noise basically, but the airfoil with protrusions produce lower medium-frequency noise than NACA0012 airfoil, and at high-frequency, NACA0012 airfoil produce the lowest one.Overall, the airfoil with serrated protrusions produces lower aerodynamic noise than others.

Figure 6 .
Figure 6.One-third octave of NACA0012 airfoil and the airfoil with protrusions.

Table 1 .
The sound pressure level of the airfoils.