Numerical study on flow characteristics of airfoil with bionic micro-grooves

Three airfoil models with bionic micro-grooves were developed to investigate the effect of the bionic micro-grooves on the airfoil flow field and aerodynamic performance. Large eddy simulation (LES) was used to predict the flow field around the airfoil. The Re were 1.6 × 105 and 2 × 105, and the angle of attack was 6°. The results show that all three airfoils reduce the velocity gradient at the airfoil suction surface near the wall and the energy loss in the boundary layer. The area of the recirculation zone of the H1 and H2 airfoils is significantly reduced. However, when the Re is 1.6 × 105, the area of the recirculation zone of the H3 airfoil increases. The aerodynamic performance of all three airfoils was improved. When the Re is 1.6 × 105, the aerodynamic performance of the H1 airfoil is improved most significantly, and the drag reduction rate reaches 16.41%. When the Re is 2 × 105, the aerodynamic performance improvement of H2 is the most obvious, and the drag reduction rate reaches 17.45%. In order to achieve the best drag reduction effect, the position of the bionic micro-grooves should gradually approach the wing's tail with the increase of Re.


Introduction
Airfoil drag reduction technology has been widely used in fluid machinery, aerospace, etc. In the past decades, a variety of techniques have been used to achieve desired drag reduction. The main methods of controlling drag include active and passive control.
The passive control methodology is effective and requires a small investment [1]. The more common passive control methods include vortex generator [2], bionic leading edge [3], serrated trailing edge [4], and bionic micro-grooves [5]. Researchers have conducted a lot of research on passive control technology. Some scholars have investigated the control of vortex generators on the separation of the airfoil boundary layer through experiments. The study showed that the vortex generator has a significant drag reduction effect and reduces the separation vorticity of the wing at a suitable installation angle and mounting position [6]. Jumahadi et al. [7] investigated the airfoil surface hybrid vortex generator and found that the hybrid micro vortex generator increased the lift by 21.2%, increased the drag by 11.3%, and increased the lift-to-drag ratio by at least 8.6%. Tian et al. [8] simulated the aerodynamic characteristics of an owl prototype wing by numerical methods. The results indicated that the lift coefficient and stall performance of the owl-like airfoil is improved, and the efficiency of the bionic airfoil blade increased by 12%. Zou et al. [9] studied the flow separation of a wing with a sinusoidal shape and found that the modification of the leading and trailing edges increases the level of the mixture and delays the flow separation on the surface of the wing. Xu et al. [10] simulated the aerodynamic performance of the airfoil with the leading edge of the owl. The aerodynamic performance of the airfoil was improved, and the lift coefficient increased by 19.8%. Yang et al. [11,12] simulated the external flow of a serrated trailing edge bionic wing by LES and found that the relative tooth height of the trailing edge has a large effect on the aerodynamic characteristics of the wing. The separation of the boundary layer was delayed, thus accelerating the mixing of the fluid and energy transfer in the wake region. Zhang [13] investigated the aerodynamic performance of a serrated trailing edge wing blade and found that the serrated trailing edge leads to fluid vortex pairs near the trailing edge of the airfoil and the spanwise correlation of the vortex structure near the trailing edge is weakened.
Bionic groove structure drag reduction is a popular topic in current drag reduction research work. By changing the shape of the wing, the flow in the near-wall region of the wall is improved and the energy dissipation in the turbulent boundary layer is reduced. The current research work analyzes and discusses the drag reduction mechanism of bionic micro-grooves from different perspectives. For the geometry of micro-structures arranged downstream, Walsh [14] experimentally investigated the drag reduction effect of micro-grooves of different sizes arranged downstream and found that longitudinal grooves can bring some drag reduction when the dimensionless height h + ≤ 25 and dimensionless spacing s + ≤ 30 of the grooves. Sutardi [15], Amy [16], Ching [17], and others also studied the groove dimensions, and the results showed that the drag reduction was more satisfactory when the dimensionless size of the groove was s + ≤ 50 and h + ≤ 30. Song et al. [18] found that the V-shaped ridge structure on the airfoil surface can significantly reduce the turbulent intensity and turbulent kinetic energy in the airfoil boundary layer, which proves the drag reduction effect of the ridge structure. Wu et al. [19] investigated the aerodynamic performance of NACA0012 airfoil with different grooves structure sizes and found that there exists an optimal value of grooves spacing, and the drag reduction rate reaches 9.65% with the optimal structure. Shi [20] has carried out the numerical simulation of the airfoil with a V-shaped groove structure. The results showed that the grooves arranged at the back of the airfoil have a good drag reduction effect, and the drag reduction rate is 16.2%.
The mechanism of micro-groove drag reduction is very complex. Yuan [21] simulated a dedicated wind turbine wing with micro-slots and found that the V-slots achieved drag reduction mainly by reducing differential pressure drag. Serson et al. [22] studied the method of wing span corrugation to improve the aerodynamic performance of the airfoil with the help of DNS method and found that the corrugation would reduce the lift-drag ratio of the airfoil. Liu et al. [23] analyzed the drag reduction mechanism of micro-grooves from the perspective of entropy generation. The results showed that the groove structure can reduce entropy generation in the flow process. Domel et al. [24] arranged a new type of tooth structure on the suction side of the airfoil and found that the airfoil drag can be reduced, the lift increased, and the momentum loss in the boundary layer can be supplemented. Zhang et al. [25] conducted a simulation study on the micro-textured airfoil and proved that the micro-texture layout had a positive impact on the airfoil drag reduction. Harun et al. [26] presented a wind tunnel experiment on the airfoil with an oblique staggered grid structure and found that the convergence and divergence staggered grid structure would significantly change the turbulence characteristics and reduce the airfoil drag. Chamorro et al. [27] investigated the drag variation of wind turbine airfoil blades with partially covered groove structures by wind tunnel test. This study found that the arrangement of grooves on the wing surface can reduce friction. The height and geometry of the grooves can affect this effect. Interestingly, their work showed that in some cases, the grooves were more effectively partially covered than completely covered.
Despite the significant number of studies on this problem, a definite explanation of how the bionic micro-groove affects the flow is still absent. In this paper, the effect of the bionic micro-groove structure arranged at different locations of the airfoil suction surface on the flow of the airfoil surface and the mechanism of the effect are investigated.

Governing equation
The incompressible Navier-Stokes equations are filtered in Fourier space to obtain the LES control equations used in the simulation. The filtered control equations can be written as: Using Smagorinsky-Lilly model: In the above formula, Δ is the filter function and C s is the wall friction coefficient, here taken as 0.1.

Geometric model and boundary conditions
By scanning a single shield scale structure of the shark skin, and using curve fitting to obtain the cross-sectional profile curve formula at its middle position: First specify the wall unit K: Equations (11) and (12) are empirical formulas. In the above formula, ν is the fluid kinematic viscosity, μ τ is the airfoil wall shear velocity, τ w is the airfoil wall shear stress and ρ is the fluid density. Equations (11) and (12) are for ZPGTBL (Zero Pressure Gradient Turbulent Boundary Layer). The applicability of these two formulas is verified here. The results are shown in Fig. 1. It shows that the two formulas can be compatible with the airfoil.
According to dimensional analysis: By organizing the above formula, we can get: By scaling Eq. (8) in equal proportions, the groove size is determined as s = 0.25 mm, so h = 0.11 mm.
The two main freestream velocity values simulated in the current work (U ∞ = 24 m/s and U ∞ = 30 m/s) correspond to Reynolds number (Re) values of 1.6 × 10 5 and 2 × 10 5 , assuming a fluid kinematic viscosity ν = 1.5 × 10 −5 m 2 /s, the density is ρ = 1.225 kg/m 3 . Substituting Eqs. 15 and 16, one can also calculate h + and s + . The results are shown in Table 1.
It can be found from Table 1 that the selected groove size can meet the size parameters required for drag reduction in the literature [15][16][17].
The original airfoil is NACA0012(airfoil chord length C = 100 mm). The flow field of a smooth airfoil with an angle of attack of 5° and a Re of 1.6 × 10 5 was simulated by LES, and velocity contours and streamline diagrams were obtained (see Fig. 2). It can be found that the flow separation phenomenon of the wing mainly occurs at 0.2-0.8 times of the chord length.
In order to explore the influence of bionic micro-grooves arranged at different positions on the suction surface of the airfoil for the flow characteristics, three geometries would be tested. In the front of the airfoil flow separation zone (between 0.35 and 0.40 times the chord length), 20 bionic micro-grooves structures are arranged and named as H1  (11) and (12)  airfoil. H2 airfoil is equipped with 20 bionic micro-grooves in the middle of the separation zone (between 0.50 and 0.55 times the chord length). H3 airfoil is equipped with 20 bionic micro-grooves in the tail of the separation zone (between 0.65 and 0.70 times the chord length). The threedimensional H2 airfoil geometry with bionic micro-grooves is indicated in Fig. 3. The computational domain and boundary conditions were described in Fig. 4. We used Fluent software to complete the simulation. The pressure-velocity coupling method uses the SIMPLEC scheme. To achieve a lower numerical dissipation, a central difference algorithm was used for spatial dissipation. In the current work, in order to reduce the computational cost, the SST k-ω turbulence model is used for the steady-state solution, and then the LES method is used for unsteady calculation. The time step is set to 5 × 10 −5 s. Table 2 shows the grid information and validation results required for grid independence validation. N x , N y, and N z are the numbers of cells in the streamwise, wall-normal, and spanwise directions. A uniform mesh was used in streamwise and spanwise while in the wall-normal direction an expanding mesh was used in the expected boundary layer regions. The dimensionless wall-normal discretization y + < 1.

Grid independence and model accuracy verification
We performed a grid-independent validation exercise, and the results are shown in Table 2. In order to balance both computational cost and solution quality, the simulation chose a grid of 2.175 million cells (see Fig. 5).
According to the experimental conditions in the literature [28], the flow field of a smooth wing with chord length C = 100 mm was simulated with an angle of attack of 5° and the freestream velocity of 25 m/s. The time-averaged pressure coefficient of the smooth airfoil wall was compared with the experimental data, and the results were indicated in Fig. 6. Figure 7 shows the near-wall time-averaged velocity distribution curves at different locations on the suction surface at Re of 1.6 × 10 5 and 2 × 10 5 . The velocity distribution within the boundary layer at different locations of the airfoil suction surface is similar. As indicated in Fig. 7, it can be seen It is shown in Fig. 7 that the velocity distribution curve in the near-wall region of the airfoil surface rises more intensely while the two tend to be consistent in the outer boundary layer region. Compared with the smooth airfoil, the boundary layer momentum loss thickness of the airfoil with grooves in the recirculation zone decreases more significantly, and the boundary layer displacement thickness and boundary layer momentum loss thickness in the reattachment zone also decrease significantly. This means that the energy loss in the boundary layer decreases, indicating the drag reduction effect of bionic micro-grooves. The velocity variation near the smooth airfoil wall is more intense, indicating that the velocity gradient is larger than the groove surface. The decrease of velocity gradient reduces the turbulence intensity, reduces the loss of wall turbulent kinetic energy, and achieves the purpose of drag reduction. The aerodynamic performance of airfoil is improved to some extent.

Time-averaged velocity distribution of airfoil surface boundary layer
As the Re was increased, the drag reduction effect of the H1 and H2 airfoils has been maintained. However, the drag reduction effect of the H3 airfoil is insignificant compared with other airfoils, but it also reduces the thickness of the boundary layer, so that the flow at the trailing edge is improved compared with the smooth airfoil.

Time-averaged wall shear stress distribution on the airfoil surface
The time-averaged wall shear stress distribution of a single bionic groove is described in Fig. 8. Figure 8a is a schematic diagram of the vortex structure in a single bionic groove. It can be seen from the figure that since the vortex does not fill the entire groove structure, and the contact area with the inner wall surface of the groove is limited during the rotational movement of the vortex, it leads to a greater variety of tangential stress in the inner wall of the trench than the smooth airfoil. During the rotation, the contact area between the vortex and the inner wall of the trench is limited, so the shear stress on the inner wall of the trench structure remains stable, but there is a large variation at points A and B in the figure, which is because the vortex is tangential to the trench wall, so the wall shear stress here is relatively large. Figure 8b shows the magnitude of the time-averaged wall shear stress for the grooved airfoil and the smooth airfoil. It shows the wall shear stress curve calculated at the same distance from the leading edge and therefore at an equivalent position. The integral of this curve represents the work of the wall shear stress, which clearly shows that the grooved surface is smaller than the smooth surface. This means that the energy dissipation on the grooved surface is smaller than that of the smooth one, which may be an important reason for the drag reduction of the grooved structure. Table 3 shows specific data on the time-averaged shear stress values at the walls of the three bionic and smooth airfoils. It can be seen from the table that the average wall shear stress on the groove surface is smaller than the smooth When the Re is 2 × 10 5 , the time-averaged wall shear stresses of H1 and H2 wings are slightly smaller than Re = 1.6 × 10 5 , but not very significant. However, the time-averaged wall shear stress of the H3 airfoil is significantly greater than Re = 1.6 × 10 5 . Figure 9 shows the average wall shear stress values for H1 and H2 airfoils with smooth airfoils. We can find that the wall shear stress fluctuations on the surface of the groove are regular and the curve integral value is smaller than that of the smooth one. Therefore, it is reasonable to assume that it is the change in wall shear stress that produces the drag reduction effect of the groove. Figure 10 shows the time-averaged velocity contours in the recirculation zones of four airfoils. Figure 11 shows the area of the recirculation zone of four airfoils It is shown in Fig. 10a, c, e and g that the thickness and flow direction length of the recirculation zone on the suction surface of the smooth airfoil are larger than those of H1 and H2 airfoils, but the thickness of the recirculation zone is significantly smaller than H3 airfoil. This leads to the recirculation zone area of the H3 airfoil being larger than the smooth airfoil. The H1 airfoil has a significant suppression effect on the thickness and flow length of the recirculation zone, moving the reattachment position of the fluid upstream. The decrease in the recirculation zone area means that the additional drag and loss caused by boundary layer separation are reduced, and the flow near the airfoil wall is improved. From a b c d of Fig. 4, it can be seen that the thickness and flow length of the recirculation zone of the smooth are larger than the others at Re of 2 × 10 5 . At this operating condition, the thickness and flow length of the recirculation zone of the H2 airfoil are the smallest. The results show that the suppression effect is stronger for the H2 airfoil and less for the H3 airfoil than the other two wings.

Analysis of aerodynamic performance of bionic airfoil
The bionic micro-groove structure not only changes the flow field on the airfoil surface but also further improves the aerodynamic performance of airfoils. Tables 4 and 5 are the time-averaged aerodynamic parameters of different airfoils. It is shown in Table 4 that the aerodynamic performance of three airfoils with bionic micro-grooves structure has been improved at Re of 1.6 × 10 5 and an attack angle of 6°. Among the three airfoils, the H1 airfoil has the best aerodynamic performance and the largest drag reduction rate, reaching 16.41%. Similarly, it is shown in Table 5 that the aerodynamic performance of the three airfoils has been improved. The difference is that in this operating condition, the airfoil with the greatest improvement in aerodynamic performance  To study the effect of Re variation on the aerodynamic performance of airfoils with bionic microgrooves, we added simulation work for H1 and H2 airfoils (Re = 1.7 × 10 5 ,1.8 × 10 5 ,1.9 × 10 5 ), and the aerodynamic performance parameters were obtained (see Table 6). We found that the aerodynamic performance of the H1 airfoil is better than H2 airfoil when the Re is 1.7 × 10 5 , and the lift-to-drag ratio is about 3.96% larger. When the Re is 1.8 × 10 5 , the lift-to-drag ratio of the H1 airfoil is about 2.90% larger than H2 airfoil. Gaps are decreasing. Finally, the aerodynamic performance of the H2 airfoil is better when the Re reaches 1.9 × 10 5 .
As is indicated in Tables 4, 5, and 6, it can be concluded that when Re is in the range of 1.6 ~ 1.8 × 10 5 , the aerodynamic performance of H1 is better than H2 airfoil; when Re is in the range of 1.8 ~ 2.0 × 10 5 (1.8 × 10 5 is the boundary Reynolds number), the opposite is true. When Re increases from 1.6 × 10 5 to 1.8 × 10 5 , the aerodynamic performance of the H1 gradually becomes worse, while the aerodynamic performance of the H2 gradually improves. When Re increases from 1.8 × 10 5 to 2.0 × 10 5 , the aerodynamic performance of the H1 gradually becomes worse compared with the H2 airfoil.
This indicates that the location of the arrangement of the bionic micro-grooves should be changed with the change of the operating conditions and there exists an optimal matching value. When the Re matches the position of the bionic micro-grooves, the aerodynamic performance of the airfoil can be improved and the airfoil with bionic micro-grooves has the best aerodynamic-dynamic performance. It can be inferred from the present work that the location of the arrangement of the bionic micro-grooves should gradually move toward the tail of the suction surface of the airfoil as the Re increases.

Conclusions
We have presented a simulation on the effect of the bionic micro-grooves arranged on the airfoil surface on the flow field and aerodynamic parameters of the airfoil. Our work shows that three airfoils with bionic micro-grooves reduce the flow loss in the boundary layer, reduce the flow resistance and improve the aerodynamic performance of the airfoil compared to a smooth airfoil.
In addition, we find that the three airfoils can effectively control the separation of the boundary layer on the airfoil surface, reduce the length of separated bubbles, and make the boundary layer reattachment point move upstream relative to the smooth airfoil. H1 airfoil performs best at Re = 1.6 × 10 5, and H2 airfoil performs best at Re = 2 × 10 5 . The case of H3 airfoil is somewhat different. For Re = 1.6 × 10 5 , the recirculation zone was increased, and when Re = 2 × 10 5 , it was decreased, but both improve the aerodynamic performance of the airfoil, although the effect is not obvious compared with the other two airfoils.
The results show that the groove position needs to match the airfoil operation condition to achieve the maximum drag reduction effect and effectively improve the aerodynamic performance of the airfoil. The groove arrangement position should gradually move to the airfoil tail with the increase of Re.
The research results of this paper have guiding significance for the arrangement of bionic micro-grooves on airfoil surfaces. However, we also have some shortcomings, such as the small sample size of data, and the unable to obtain an accurate relationship between Re and groove position. Therefore, this is also the improvement direction of our research work.