Control of separated flow at low Reynolds number around NACA0012 airfoil by boundary layer suction

The separated flow at low Reynolds number around the NACA0012 airfoil is numerically studied by large-eddy simulation. Strategies of boundary layer suction to control flow separation are investigated. A method of using two-zone suctions, near the leading edge and near the trailing edge, are calculated. Based on verification with direct numerical simulation (DNS) and experimental data, the results of the lift and the drag, the vortices, and the strength of near-field pressure fluctuations, are checked. The results show that the two-zone suctions can supress flow transition and separation, thereby increase the lift and reduce the drag. The shedding of vortices is weakened, and the near-field pressure fluctuations are attenuated. For comparison with the two-zone suctions, the strategies of suction near the leading edge only and suction near the trailing edge only are also studied. It is found that suction near the leading edge only may suppress transition and delay separation when the suction zone is large enough, but the flow property deteriorates due to shedding vortices in the wake. The suction near the trailing edge only may improve the flow performance by reducing the size of the vortices in the rear section of the airfoil and in the wake region, but it has little effect on the separation bubble and transition.


Introduction
Airfoil is the fundamental element of impeller blades, wind turbine blades, and aircraft wings.Its aerodynamic performance has an important impact on the energy efficiency of these devices.At low Reynolds numbers, the boundary layer over the airfoil surface is easy to separate because of the adverse pressure gradient, leading to unexpected effects such as the reduced lift, the increased drag, and additional noises.In response to this problem, the active flow control method of boundary layer suction has been proposed by people to improve the flow and lower down the noises.
In 1927, Prandtl [1] suggested the possibility of improving the performance of lifting devices by boundary layer suction, which was subsequently verified by experiments of McLafferty [2] and Owens [3].In recent years, many scholars had applied boundary layer suction to airfoil flow control.Kornilov [4] investigated the classical symmetric airfoil of suction control, Fatahian et al. [5] explored the control effect of suction on the flier shape, and Tadjfar et al. [6] conducted suction control on the airfoil in the dynamic stall.The above scholars had achieved the effect of increasing lift and reducing drag through boundary layer suction.Some scholars had researched aerodynamic noise.Szőke [7] found that suction could reduce the trailing edge noise of a flat airfoil.Abbasi et al. [8] proved that suction control was also applicable to the flow around the airfoil with the addition of rod interference.
The above work verified the control effect of suction in both flow and noise, but most scholars only used the suction method of a single area and rarely expanded the suction to multiple areas.
The "White Paper on the Development of Electric Aircraft" issued in 2021 proposed a green aviation technology strategy for the joint development of advanced aerodynamic technology and noise reduction technology.In this context, evaluating flow control methods must consider flow and noise simultaneously.In addition, developing advanced pneumatic technology requires more effective flow control methods.
In this paper, the method of applying suction to the near leading edge and near trailing edge of the airfoil simultaneously is discussed.Considering the separation flow often occurs at low Reynolds numbers, the NACA0012 airfoil with different suction methods is studied using large eddy simulation.Two-zone suctions, near leading edge suction and near trailing edge suction are calculated and compared.The control effect of boundary layer suction on the flow and noise of the airfoil is explored by analyzing the lift drag variation, surface flow characteristics, development process of vortex structure and pressure pulsation intensity at monitored points.

Numerical procedure
The filtered Navier-Stokes equation is the governing equation of large eddy simulation (LES).Considering that the flow around the airfoil is mainly wall flow, the WALE subgrid model with better prediction ability for wall flow, especially the turbulent transition process, is selected in this paper, and its subgrid viscosity is modeled as follows: L min d C V   represents the mixing length for the SGS, d represents the distance to the proximate wall, κ is the von Karman constant, V is the computational cell volume, and w 0.325 where ij S  is average strain tensor, d ij S  is the untraced symmetric part of the squared velocity gradient.
The WALE subgrid-scale model is suitable for the simulation of laminar flows.Choi et al. [9] used the WALE model to calculate the axisymmetric sudden expansion flow at low Reynolds numbers, and the simulation results agreed with experimental data.As shown in Figure 1, the three-dimensional NACA0012 airfoil with chord length c=75 mm is selected for calculation, and the spanwise length is 0.2c.Inflow velocity v=20 m/s, Angle of attack AoA=4°, and Reynolds number Re=1×10 5 based on chord length.Fourteen slit suction areas with a width of 0.003c are set in the two areas with the position x/c=0.15~0.4 and 0.6~0.95 of the suction surface at every 0.05c intervals.These areas are defined as a velocity inlet with a direction toward the negative Y-axis and a suction speed vs = 5 m/s to suck fluid into the airfoil.As shown in Figure 2, the grid of the flow area adopts the C-type body painting method, and the whole area is the hexahedral grid.According to the grid quality standards of ICEM, the global grid quality is more significant than 0.9.In order to meet the calculation requirements of large eddy simulation, the dimensionless wall distance of the mesh y + ≈1.The boundary conditions are shown in Figure 3, where the distance between the boundary and the center of the airfoil is 20c.The far-field boundary and suction region are the velocity inlet, the outlet is the pressure outlet, the airfoil surface uses the non-slip wall condition, and the spanwise is defined by the periodic boundary condition.
The numerical method for solving the flow field is the Semi-Implicit Method for Pressure Linked Equations, where the pressure terms are solved in second order format, the momentum equations are solved in second order windward format, and the time terms are discretized in second order implicit To determine the appropriate number of grids, four sets of progressively encrypted grids Ⅰ, Ⅱ, Ⅲ, and Ⅳ are used to calculate the lift coefficient of the airfoil and compared with the experimental value of Ohtake [10], as shown in Figure 4.The calculated data show that the difference between Mesh Ⅲ and Mesh Ⅳ is only 0.6%, and the error between Mesh Ⅲ and experimental values is less than 1.5%.Considering the accuracy and economy of numerical simulation, Mesh III is selected for this calculation, and the total number is 2 million.In order to verify the calculation's correctness, the large eddy simulation results based on Mesh Ⅲ are compared with the LES results of Zhang [11] and the DNS results of Shan et al. [12], as shown in Figure 5. Figure 5 (a) shows the curve of the time average pressure coefficient of the airfoil surface at z/c=0.5.The calculated results capture the "pressure platform" [13] representing the transition region at x/c≈0.55, which agrees with the reference value.

Time average characteristics
Eight different suction conditions shown in Table 1 are used to study the effect of the suction area on airfoil performance, with the suction position representing the center of the slit.According to the suction positions, they can be divided into three types: two-zone suctions, near leading edge suction and near trailing edge suction.Figure 6 shows the time history of the lift coefficient and drag coefficient of the airfoil.These coefficients are expressed as follows: where S is the projected surface of the airfoil, Fl and Fd are the lift and drag forces around the airfoil.
Compared to the non-suction condition, the lift coefficient of the airfoil with two-zone suctions applied is increased by 12.53%, and the drag coefficient is decreased by 27.93%.The two near leading edge suction (Suc.2;Suc.4) reduce the lift coefficient by 29.13% and 9.47%, and the drag coefficient decreases by 5.96% and increases by 22.82%, respectively.In addition, the fluctuation of both coefficients increased.An increase in the lift coefficient (5% to 25%) and a change in the drag coefficient (-9% to 9%) are observed for all the rear section suction conditions.Considering a large number of near trailing edge suction conditions and the absence of significant abrupt changes in the aerodynamic characteristics, only Suc.3 and Suc.6, which correspond to the suction areas of two-zone suctions and near leading edge suction, are selected for further study.The time-averaged streamlines of the airfoil surface with different suction applications are extracted and shown in Figure 7.There is a long laminar flow separation bubble on the surface of the non-suction airfoil, and there are two Separation Lines (SL) and two Reattachment Lines (RL).The streamlines between SL1 and RL1 develop only in the flow direction, and distortion of the streamlines spanwise is observed near SL2 and RL2.This phenomenon can be interpreted as the two-dimensional unstable wave generated by the free shear layer on the surface of the separation bubble growing linearly downstream, triggering the three-dimensional motion.In Figure 7 (b), the flow is tightly attached to the airfoil surface with the two-zone suctions, there is no flow separation on the surface, and the wall flow line presents a single flow direction.In Figures 7 (c) and 7 (d), both near leading edge suction delay the starting position of separation.The suc.2, with a more extensive suction range, also inhibits the development of the spreading of the flow in the back section.The near trailing edge suction in Figures 7 (e) and 7 (f) has little effect on the separation bubble.It only changes the flow from the suction area to the trailing edge, limiting the flow direction to one direction.

Instantaneous characteristics
In order to judge the flow in the wake region of the airfoil, a monitoring point is placed at x/c=1.1, y=0 on the cross-section of z/c=0.5.Based on the pulsation velocities ', ', ' u v w , the turbulent kinetic energy is calculated, and its power spectral density is obtained, the results are shown in Figure 8.The four groups of power spectrum lines in Figure 8 (a) all have multi-scale characteristics, and the value of the power spectrum decreases with the increase of frequency, which reflects the phenomenon of energy transfer from large-scale vortices to small-scale vortices in turbulence.In addition, the spectral lines have attenuation segments with an approximate slope of -5/3 in a particular range, which is an essential feature of turbulence.Multiple peaks can be seen in the power spectrum value in Figure 8 (b), indicating that the energy is mainly contained in some specific scale vorticity, which does not reflect turbulence's multi-scale and energy cascade characteristics.In order to reveal the morphology of the vortex, Figure 9 shows the isosurface calculated based on the "Q" criterion, and the colors on the isosurface represent the pressure distribution.The "Q" criterion is defined as follows:  Without suction, in Figure 9 (a), the flow on the airfoil surface before x/c=0.55 is spanwise uniform.At the same time, after x/c=0.55, the three-dimensional pulsation gradually increases, and the twodimensional vortex structure that falls off from the separation shear layer begins to distort and break, developing into a three-dimensional "Λ" vortex structure.At this time, unsteady waves of vortices in the wake area propagate upstream, which is the main reason for unsteady aerodynamic performance and the primary source of aerodynamic noise [14].Figure 9 (b) shows that the transition on the airfoil surface is inhibited after adding two-zone suctions.The vortices on the airfoil surface maintain spanwise uniformity and fall off periodically and alternately in the trailing edge region.In Figure 9 (c), the near leading edge suction also achieves transition inhibition, but the scale of the shedding vortex is more extensive than that of the two-region suction.If the suction range is halved, as shown in Figure 9 (d), the transition inhibition is no longer possible, and only the separation point is shifted backward.The near trailing edge suction in Figure 9 (e) and Figure 9 (f) does not affect the transition process.
Figure 10 shows the spatial distribution of the pressure pulsation, which can provide a reference for finding the noise source around the airfoil.In Figure 10 (a), the distribution of pressure pulsation on the airfoil surface coincides with the turbulent region after transition, indicating that the primary source of aerodynamic noise in the absence of suction is the three-dimensional vortex structure at the rear of the airfoil.When the two-zone suctions are added, the pressure pulsation in Figure 10 (b) moves back to the wake region, and the pulsation range and intensity are reduced because the twozone suction inhibits transition.Complex vortices are no longer generated in the rear section.The near leading edge suction in Figures 10 (c) and 10 (d) also shifts the pressure pulsation back to the wake region but with greater intensity and range than the two-zone suction.The increased pulsation in Figure 10 (c) is due to the large-scale shedding vortex in the wake region, while the increase of pulsation in Figure 10 (d) is due to the narrow suction range, and the transition process is not inhibited.In Figures 10 (e) and 10 (f), the near trailing edge suction does not change the position of the pressure pulsation.However, it decreases the pulsation intensity, which is consistent with the previously observed phenomenon that the near trailing edge suction reduces the size of the vortex structure.
In order to study the distribution of pressure pulsation in the near field, a total of 36 monitoring points are set at intervals of 10° at a distance of 10c from the center of the airfoil at a cross-section of z/c=0.5.Since the monitoring point is located in the calculation domain, the pressure pulsation ' p at the monitoring point is directly extracted, and its intensity is calculated as follows:  is the reference pressure, and ' p is the pulsation pressure.
The formula for calculating the spectrum of pressure pulsation intensity is: where PSD is the unilateral power spectral density of the pulsating pressure '( ) p t , which means that only the positive frequency part of the power spectral density is considered in the frequency domain, and the calculation formula is as follows: where N is the length of the time domain signal, 1 / ( ) f N t     is the frequency resolution.Figure 11 shows the directivity comparison of the near-field pressure pulsation intensity of the airfoil, and all cases show the prominent dipole source directivity characteristics of the "8" font.The two-zone suctions have the best effect in reducing the pressure pulsation intensity, with a reduction of about 26.67%.Two near leading edge suctions (Suc.2;Suc.4) increase the intensity of pressure pulsation by 9.83% and 18.82%, respectively.Among all kinds of near trailing edge suction, the best Suc.3 reduces the pulsation intensity by about 8.93%, and the control effect of the remaining postsuction is not pronounced.Figure 12 shows the spectrum of pressure pulsation intensity of the airfoil at 30° azimuth.The spectrum of two-zone suctions is lower than without suction except for the peak at 4000 Hz.In addition, similar peaks can be observed in the two near leading suctions, indicating that the suction in the front segments causes the peaks.It is known from the previous section that both near leading edge suction increases the intensity of pressure pulsation.However, it can be found in the spectral diagram that the spectral values are distributed differently in frequency.Suc.2 inhibits transition, reduces lowfrequency pulsation, and increases high-frequency pulsation, while the spectral value of Suc.4 is observed to increase the full frequency.The near trailing edge suction reduces the pulsatile intensity at all frequencies, but the reduction is smaller than that of the two-zone suctions.

Conclusions
This paper uses the large eddy simulation method to study the influence of three different suction methods (two-zone suctions, near leading edge suction, and near trailing edge suction) on the aerodynamic performance of NACA0012 airfoil.The lift and drag coefficient, the morphology of vorticity, and the pressure fluctuations are analyzed.The main conclusions are summarised as follows: (1) The near leading edge suction suppresses the transition and delays the separation point when the suction zone is large enough.However, the flow separation is not eliminated, and the flow performance deteriorates due to the two-dimensional shedding vortices in the separation zone.
(2) The near trailing edge suction reduces the size of the vortex structure in the rear section and wake area of the airfoil, so it increases the lift, reduces the drag and weakens the pulsation.However, it has little effect on the separation bubble and transition on the surface of the airfoil.
(3) Two-zone suctions suppress flow transition and eliminates flow separation.Compared with the two single-zone suction methods, it has a better flow control effect.
Figure 5 (b) is the time average surface pressure coefficient at the same position.The negative value in the figure corresponds to the reflux in the laminar flow separation bubble.The separation bubble's range is about 0.2≤x/c≤0.65,basically the same as the reference value.

Figure 8 .
Figure 8.The power spectral density of turbulent kinetic energy: (a) part with turbulence characteristics; (b) part without turbulence characteristics.

Figure 12 .
Figure 12. the spectrum of pressure pulsation intensity of the airfoil at 30° azimuth.

Table 1 .
Specific parameters of different suction conditions.