Numerical study on aerodynamic and noise performance of bionic asymmetric airfoil with surface grooves Open Access

Many structural and operational engineering problems of aircraft, such as continuous flight and flight maneuverability, are directly related to the aerodynamic performance of aircraft wings.¹ Although researchers have made great achievements in improving airfoil performance through theoretical analysis, numerical simulation, and experimental measurements, there are still much work to be done in the development of aircraft, such as longer flight, more efficient takeoff and landing, and lower noise.

In order to obtain high efficiency and low noise airfoils of aircraft, especially to improve aerodynamic performance of airfoils at high angle of attack, people have begun to search for answers and inspirations from the wings of birds in nature. As we know, birds have existed on the earth since the Cretaceous era.² After years of evolution, birds have evolved special wings that adapted to their respective environments and become the flight leader. For example, seagulls can fly much longer because of their wings, which just cost little energy for the flight,³ and long-eared owls can fly to their prey in an almost silent way.⁴ By extracting and analyzing the wing characteristics of the seagull and long-eared owl, the special flight mechanism of these birds is revealed. Then, the wing characteristics are applied to improve the airfoil performance. Ge et al.⁵ found that the bionic airfoils usually have better aerodynamic performance and/or lower noise compared to the original airfoil.

Previous research has mostly focused on the modification of the leading and trailing edges of airfoils. For example, seagulls have long wings and low energy consumption during flight. They are suitable for long-term gliding. Gu et al.⁶ analyzed the performance of the bionic airfoil at low Reynolds number by computational fluid dynamics (CFD) numerical simulations. The studied results show that the bionic airfoil exhibits better aerodynamic performance and is more suitable for small wind turbines. The long-eared owls can fly silently at night. The noise reduction ability of long-eared owl wings provides a useful reference for noise reduction design of Rotary Turbine Machinery. Gruschka et al.⁷ carried out a series of experimental studies to measure the noise produced by the owls during flight gliding. Lilley⁸ pointed out that the low noise flight of the owls is mainly due to the leading-edge wavy structure of owl wings, the trailing-edge serration structure of owl wings, and the feather of wing surface. For the leading edge, Tong et al.⁹ adopted a numerical method to study the effects of the wavy leading edge of the airfoil on noise reduction. They found that the lift and drag of the airfoil are increased when the wavy leading edge is added on the airfoil. At the same time, the wavy leading edge has a significant noise reduction effect, and the average noise of the airfoil with the wavy leading edge is reduced by 9.5 dB. On the other hand, for the trailing edge, Howe^10,11 pointed out that the serrated trailing edge has noise reduction performance. Avallone et al.^12,13 applied different types of serrated trailing edge on the airfoil and found that the aerodynamic noise of the airfoil is reduced effectively. Chong and Joseph¹⁴ confirmed that the aerodynamic performance of the airfoil with cutoff serrated trailing edge is better than that of the airfoil with add-on serrated trailing edge. Liu et al.¹⁵ reconstructed the serrated non-smooth structures of the leading edge and trailing edge to the NACA0012 airfoil. The results show that for the NACA0012 airfoil, the serrated structure not only has better effect on noise reduction, but also improves the airfoil lift–drag ratio. Geyer et al.¹⁶ conducted an experimental study on the trailing-edge noise of a set airfoils made of different porous materials.

In addition to the above studies on the structure and function of leading edge and trailing edge, the function of surface ridges formed by the intertwined feathers on the bird wings has also been studied.^17–19 Wang et al.¹⁸ designed a bionic airfoil inspired by the wing surface ridges of bird. It is found that the noise is reduced by 13.1–13.9 dB when the surface ridges are introduced. Lin et al.¹⁹ studied the aerodynamic performance of the airfoils with wavy surface ridges. Through numerical simulations, they claimed the presence of the surface ridges can effectively suppress the surface pressure fluctuation. Gao et al.²⁰ designed bionic blades for the wind turbine. Their study shows that the herringbone groove structure enhances the flow attachment by generating vortices, which reduces the pressure on the leeward surface of bionic blades. The ridges formed by the intertwined feathers are another surface structure that has received attention. Lin et al.¹⁹ studied the aerodynamic performance of some airfoils with wavy surface ridges. They pointed out that the surface ridges can suppress the surface pressure fluctuation of the airfoil. Smith et al.²¹ compared a smooth airfoil and four variants with different span-wise surface waves, and found that the wavy surface reduces the span-wise correlation of the pressure fluctuations and also modifies the boundary layer dynamics, which contributes to the large reduction of noise. The surface ridges are also combined with the serrated LE and TE by some researchers, which shows a good noise reduction performance.^18,22 In practice, the asymmetric airfoils are used more widely than the symmetrical airfoils.^23–25 At the same time, the wing profile of birds is also asymmetric.²⁶ Therefore, the studies on the function of the non-smooth structure of feather slots and its application in the asymmetrical airfoil are still necessary.

Inspired by the feather slots of bird wings, we proposed a novel bionic airfoil with non-smooth grooves based on the NACA4412 asymmetric airfoil. The large eddy simulation (LES) method is used to investigate the flow characteristics over the NACA4412 airfoil and the bionic airfoil numerically. The Ffowcs Williams and Hawkings (FW-H) acoustic analogy is adopted to study the acoustic performance of the original airfoil and the bionic airfoil. The numerical simulations are performed at different angles of attack, α = 0° and 14°, respectively, and the Reynolds number based on the airfoil chord, Re = 1.2 × 10⁵. Through analyzing and comparing the aerodynamic performance of the bionic airfoil and NACA4412 airfoil, we also hope to provide a useful reference for revealing the noise reduction effect of the non-smooth structure of feather slots at the rear of the bird wings. These results will be an effective technical scheme for the design of low noise and high efficiency turbomachine.

The grooves on the surface of bird wings can provide certain aerodynamic effects, helping birds better adapt to changes in airflow during flight.¹⁹  Figure 1 shows the size parameters of the bionic prototype and the bionic groove airfoil, the corresponding radius of grooves is 5.29 mm, and the width of a feather slot is 38.13 mm. For the studied bionic airfoil, three grooves are constructed by cutting off the airfoil. The span-wise length of the airfoil is 114.39 mm. The thickness of the pinnae is 0.25 mm in the process of model building.

A C-type computational domain is used to ensure the validity and accuracy of numerical simulation results. As shown in Fig. 2, the coordinate origin is set at the center of the semi-circle in the middle section of the computational domain. The airfoil is located at the origin of coordinate. The chord length is 0.1 m. As the computational domain, the circle radius is 10 times the chord length of airfoil. The distance from the coordinate origin to the outlet of the domain is set to 20 times the chord length of airfoil. The span-wise width of the computational domain is 0.1 m. X, Y, and Z directions are flow direction, lateral direction, and span-wise direction, respectively. The velocity, total pressure, and turbulent intensity are given at the inlet boundary. The mean static pressure is set at the outlet boundary. The adiabatic and no-slip conditions are used on the airfoil surfaces. The periodic boundary conditions are applied along both span-wise and pitch-wise directions of the computational domain.

In the numerical calculation, the non-uniform and unstructured grids are adopted and refined near the airfoil surface. The grid distribution of computational domain is shown in Fig. 3. To ensure the reasonable accuracy and efficiency of numerical calculation, grid-independence verification on NACA4412 airfoil and bionic airfoil is performed at first. Figure 4 shows the variation of lift-to-drag ratio of airfoil with the number of grids and the accuracy of numerical calculations. In order to verify the accuracy of numerical calculations, the static stall characteristics of the NACA4412 airfoil were conducted at a Reynolds number of 5 × 10⁴, referring to the operating conditions in the experiment of Koca et al.³¹ It is seen that when the number of grids is greater than 3.36 × 10⁶, the lift-to-drag ratio of NACA4412 airfoil has not changed substantially with the increase in the number of grids. When the number of grids is greater than 3.8 × 10⁶, the lift-to-drag ratio of the bionic airfoil does not change. Therefore, in the present study, the number of grids used for NACA4412 airfoil and bionic airfoil is 3.36 × 10⁶ and 3.8 × 10⁶, respectively.

To monitor the aerodynamic noise generated by the flow around the airfoils, twelve noise receivers are arranged in the circumferential direction of the airfoil. As shown in Fig. 5, the radius of the circle with the receivers is 1 m, which is 10 times the chord length of the airfoil.

Here, $p$ is the static pressure, $p ∞$ is the reference pressure, $ρ$ is the fluid density, and $V ∞$ is the flow velocity.

Related research results^32,33 found that the 33% and 50% cross-sectional airfoil of the bionic airfoil has a larger lift. So, the aerodynamic performance of the 33% and 50% cross-sectional airfoil is studied to analyze the aerodynamic characteristics of airfoils. It can be found from Fig. 7 that the pressure coefficient of NACA4412 airfoil changes smoothly as the chord position changes. After the air flows over the leading edge of airfoil, the pressure coefficient changes smoothly because the flow fits the surface of the airfoil. Compared to the NACA4412 airfoil, the first 50% part of the bionic airfoil is the same as the NACA4412 airfoil, so does the pressure coefficient. Because of the presence of the feather slots, the surface pressure coefficient of the bionic airfoil fluctuates. The pressure coefficient on the upper and lower surfaces decreases simultaneously. This is due to the drastic change of the airfoil structure. Vortices with opposite directions are generated at the upper and lower slots of bionic airfoil. Although there is a change in the surface pressure coefficient, the difference of pressure coefficient between the upper and lower surfaces of airfoil does not change much. The structure behind the feather slots does not change drastically, so the pressure coefficient at the rear of the bionic airfoil changes relatively smoothly.

Figure 7 shows the pressure coefficient distribution of the NACA4412 airfoil and the bionic airfoil at an angle of attack, α = 14°. The surface pressure coefficient of NACA4412 airfoil changes smoothly as the span position changes. The lift mainly occurs by the first 50% part of the airfoil. Compared to the NACA4412 airfoil, the change of surface pressure coefficient of the bionic airfoil is relatively smooth. In the first half of the airfoil, the surface pressure coefficients of the NACA4412 airfoil and the bionic airfoil are basically the same. The figure indicates that the lifts generated in the first half of the airfoils are basically the same. In the middle of the airfoil, the difference in pressure coefficient between the upper and lower surfaces of the NACA4412 airfoil is greater than the differences of the 33.3% and 50% cross sections of the bionic airfoil. This is because the sharp change at the initial part of the feather slots of airfoil. Thereby, the difference in surface pressure coefficient of the bionic airfoil is smaller than that of the original airfoil. In the second half of the airfoil, the surface pressure coefficient difference of the two sections of the bionic airfoil is greater than the difference of the NACA4412 airfoil. The total lift generated by the bionic airfoil is greater than the NACA4412 airfoil because of the large angle between the incoming flow and the airfoil. The flow separation is obvious when the airfoils faced with the large angle flow. As a result, the influence of the flow caused by the feather slots is relatively small, and the surface pressure distribution of the bionic airfoil is also relatively smooth. For the top and the bottom of the feather slots, the difference in surface pressure coefficient between two sections is not large, so the lifts produced by these two sections are basically the same.

The sound pressure level (SPL) of the twelve receivers of the NACA4412 airfoil and bionic airfoil varies with frequency (20–20 000 Hz) as shown in Fig. 8. At α = 0°, the sound pressure level of the bionic airfoil in the low-frequency band is larger than that of NACA4412 airfoil. The difference of SPL is not too large in the middle- and high-frequency bands. It is observed that noise received by receiver 1 and receiver 7 is the smallest, and the values of receiver 4 and receiver 10 are the biggest. The figures indicate that the noise radiates mainly along the upper and lower directions. Thus, the aerodynamic noise of NACA4412 airfoil is slightly higher than the noise of bionic airfoil at an angle of attack of 0°. Similarly, the sound pressure level of the NACA4412 airfoil is basically the same as the sound pressure level of the bionic airfoil when faced at an angle of attack of 14°. The noise radiates mainly along the upper and lower directions. From the comparison, we found that the presence of the feather slots could decrease the noise generated by birds flying.

Figure 9 shows the OASPLs diagrams of NACA4412 airfoil and bionic airfoil. At 0°, the noise distribution directions of NACA4412 airfoil and bionic airfoil are basically similar. The forward and backward sound pressure levels of the airfoil are the lowest, and the upper and lower sound pressure levels of the airfoil are the highest. The figures indicate that the noise radiates mainly along the upper and lower directions. Compared with NACA4412 airfoil, the sound pressure level of bionic airfoil is slightly lower in upper and lower directions than that of NACA4412 airfoil, and the sound pressure level of bionic airfoil is slightly higher in front and back directions than that of NACA4412 airfoil. At 14°, the radiation direction of noise does not change much, the main radiation direction is still upper and lower directions, and the forward and backward sound pressure levels are the lowest. However, at high angle of attack, the sound pressure level of each receiving point of bionic airfoil is lower than that of NACA4412 airfoil with the difference, which is about 2.0 dB.

As shown in Fig. 10, the figures are the pressure contours with streamlines of the 50% section of NACA4412 airfoil and the bionic airfoil at α = 14°. The pressure of the pressure side is higher than the pressure in suction side, shown in Fig. 10(a). The flow separates at nearly 1/3 of the chord from the leading. Compared to NACA4412 airfoil, bionic airfoil has a higher surface pressure in pressure side and a lower surface pressure in suction side, so bionic airfoil produces a higher lift coefficient than NACA4412 airfoil. Comparing the streamlines of Figs. 10(a) and 10(c), it can be seen that the flow separation point of NACA4412 airfoil is earlier than that of bionic airfoil. It indicates that compared to NACA4412 airfoil, the flow separation zone of bionic airfoil is smaller, the pressure drag of bionic airfoil is smaller, and the flow of the bionic airfoil is more stable than the flow of NACA4412 airfoil. Figures 10(b) and 10(d) are pressure contours with streamlines of the tails of NACA4412 airfoil and bionic airfoil, respectively. There are some significant tailing vortexes after the tail of the NACA4412 airfoil, while the vortexes of the bionic airfoil exist only at the tail of the airfoil. From the comparison, it shows that the tail flow of the NACA4412 airfoil is poor, and the vortexes also increases the noise generated by the NACA4412 airfoil.

For the NACA4412 airfoil, the fluid in the lower part of the airfoil is blended with the fluid in the upper part. This is because the pressure of the main stream of the pressure surface is larger than the pressure of the main stream of the suction surface. The pressure drag forces the fluid on the pressure side could against the suction side, thus creating a counterclockwise tip vortex at the end of the airfoil. For the bionic airfoil, the presence of the feather slots causes the fluid to directly hit the bottom of the feather slots. It creates a small range of high-pressure zones at the bottom of the feather slots. The presence of this high-pressure zone causes the fluid of the pressure side deflect slightly, so the fluid of the pressure side is hardly blended with the main stream of the suction surface.

Figure 11 shows the vorticity contour of the NACA4412 airfoil and the bionic airfoil. When the angle of attack is 0°, it can be seen that the fluid is flowing through the NACA4412 airfoil without separating from the surface, as shown in Figs. 11(a) and 11(b). Compared to the NACA4412 airfoil, there are some vortexes at the second half of the bionic airfoil because of the existence of the empty space of the wing groove. These vortexes not only increase the lift of the airfoil, but also slightly increase the drag of the airfoil. In Figs. 11(c) and 11(d), when the angle of attack is 14°, the flow separation on the NACA4412 airfoil surface is earlier than that on the bionic airfoil. The wake vortex of the NACA4412 airfoil is significantly larger than that of the bionic airfoil, which leads to the aerodynamic noise of NACA4412 airfoil higher than that of the bionic airfoil.

In this study, we proposed a bionic airfoil based on the NACA4412 airfoil. The aerodynamic performance and noise characteristics of the NACA4412 airfoil and the bionic airfoil are analyzed through the numerical method. The main conclusions obtained are as follows:

1. When the angle of attack is 0°, the aerodynamic performance of the NAC4412 airfoil and the bionic airfoil is almost similar. The lift of the bionic airfoil is slightly higher than that of the NACA4412 airfoil because of the vortex induced by the trailing-edge non-smooth structure, and the drag is also slightly higher than that of the NACA4412 airfoil. The aerodynamic noise generated by the NACA4412 airfoil is also slightly larger than that of the bionic airfoil. The noise radiates mainly upward and downward along the airfoil surfaces.

2. When the angle of attack is 14°, the overall performance of bionic airfoil is better than that of the NACA4412 airfoil. That is to say, compared with the NACA4412 airfoil, the lift of the bionic is higher and the drag is lower. The noise reduction of the bionic airfoil is about 2.0 dB. The flow separation occurred on the surface of NACA4412 airfoil. For the bionic airfoil, the flow separation point is pushed back because the non-smooth structure of feather slots is introduced near the trailing edge of the airfoil.

This work was supported by the Higher Education Science and Technology Innovation Plan Project of Shanxi Province (No. 2023L387).

The authors have no conflicts to disclose.

Mingjun Wen: Visualization (equal). Liming Wu: Methodology (equal); Writing – original draft (equal).

The data that support the findings of this study are available from the corresponding author upon reasonable request.