applied sciences

Article Analysis of the Effect of Vortex Generator Spacing on Boundary Layer Flow Separation Control

Xin-kai Li 1,*, Wei Liu 1, Ting-jun Zhang 1, Pei-ming Wang 1 and Xiao-dong Wang 2

1 China Huadian Engineering Co., LTD (CHEC), Beijing 100160, China; [email protected] (W.L.); [email protected] (T.-j.Z.); [email protected] (P.-m.W.) 2 College of Energy, Power and Mechanical Engineering, North China Electric Power University, Beijing 102206, China; [email protected] * Correspondence: [email protected]; Tel.: +86-010-63918174



Received: 31 October 2019; Accepted: 9 December 2019; Published: 13 December 2019


Abstract: During the operation of wind turbines, flow separation appears at the blade roots, which reduces the aerodynamic efficiency of the wind turbine. In order to effectively apply vortex generators (VGs) to blade flow control, the effect of the VG spacing (λ) on flow control is studied via numerical calculations and wind tunnel experiments. First, the large eddy simulation (LES) method was used to calculate the flow separation in the boundary layer of a flat plate under an adverse pressure gradient. The large-scale coherent structure of the boundary layer separation and its evolution process in the turbulent flow field were analyzed, and the effect of different VG spacings on suppressing the boundary layer separation were compared based on the distance between vortex cores, the fluid kinetic energy in the boundary layer, and the pressure loss coefficient. Then, the DU93-W-210 airfoil was taken as the research object, and wind tunnel experiments were performed to study the effect of the VG spacing on the lift–drag characteristics of the airfoil. It was found that when the VG spacing was λ/H = 5 (H represents the VG’s height), the distance between vortex cores and the vortex core radius were approximately equal, which was more beneficial for flow control. The fluid kinetic energy in the boundary layer was basically inversely proportional to the VG spacing. However, if the spacing was too small, the vortex was further away from the wall, which was not conducive to flow control. The wind tunnel experimental results demonstrated that the stall angle-of-attack (AoA) of the airfoil with the VGs increased by 10◦ compared to that of the airfoil without VGs. When the VG spacing was λ/H = 5, the maximum lift coefficient of the airfoil with VGs increased by 48.77% compared to that of the airfoil without VGs, the drag coefficient decreased by 83.28%, and the lift-to-drag ratio increased by 821.86%.

Keywords: vortex generators; wind turbine; airfoil; aerodynamic performance; large eddy simulation

1. Introduction During the operation of wind turbines, flow separation occurs at the blade root, which reduces the wind turbine efficiency [1]. Flow control technologies, such as VGs [2], plasma flow control [3], microflaps [4], microtabs [5], blowing and suction [6], synthetic jets [7], and flexible walls [8], have been increasingly applied to the design or optimization of wind turbine blades, aiming to improve their aerodynamic performance. Barlas [9] and Johnson [10] compared these flow control methods, while Lin [11] and Wang [12] found that VGs are one of the most effective devices for improving the aerodynamic performance of blades. In 1947, Taylor [13] was the first to apply VGs to wing flow control. The basic principle of flow separation control using VGs is that when the fluid passes through a VG, a concentrated vortex will be generated downstream. Under the action of the concentrated vortex, the high-energy fluid

Appl. Sci. 2019, 9, 5495; doi:10.3390/app9245495 www.mdpi.com/journal/applsci Appl. Sci. 2019, 9, 5495 2 of 22 outside the boundary layer will enter the bottom of the boundary layer, increasing the mixing of the fluids inside and outside the boundary layer. This will increase the kinetic energy of the fluid at the bottom of the boundary layer and delay its separation [14,15]. Due to their simple structure and convenient installation, VGs have been widely applied in fields such as flow control [16–18] and heat transfer [19,20]. In 1995, Reuss et al. [21] conducted two-dimensional wind tunnel tests on the National Advisory Committee for Aeronautics (NACA) 4415 airfoil in the subsonic wind tunnel of the Aerospace Research Laboratory. The aim of these tests was to record the cross-sectional lift and bending moment characteristics under different airflow conditions. The effect of the airfoil leading-edge roughness and VGs on the aerodynamic performance of the airfoil was investigated. In 2006, Godard and Stanislas [22–24] experimentally studied the control effect of triangular VGs on the boundary layer flow separation on a curved plate. Their experimental set-up could change the installation angle of VGs and measure the wake structure of small wings. In 2010, Yang et al. [25] performed numerical simulations to study a blunt trailing edge airfoil with and without VGs, and the performance of the airfoil was analyzed. The interaction between vortices generated by the VGs and wake vortices or separation vortices was investigated, while a mechanism for suppressing the boundary layer separation using VGs was revealed. In 2011, Zhen et al. [26] studied the effect of VGs on the aerodynamic performance of airfoils using numerical simulations, where the Spalart–Allmaras (SA) turbulence model and the standard wall function were employed. Their study results demonstrated that when the VGs were close to the separation point, the airfoil had a high maximum lift coefficient, and the performance of the rectangular and curved edge VGs was better than that of the triangular VGs. Lishu et al. [27] designed two types of VG combinations and conducted wind tunnel experiments in order to investigate airfoil flow control in depth. Their results revealed that the reasonable combination of a flap and VGs can significantly improve the aerodynamic performance of the airfoil, providing an ideal form of combined control. In 2012, Delnero et al. [28] experimentally investigated the effects of triangular VGs on airfoil aerodynamic performance. The VGs were located 10% and 20% away from the airfoil leading edge. The results showed that VGs can improve the airfoil aerodynamic characteristics, and the effect is better when the VGs are arranged 20% away from the leading edge. In 2013, Velte and Hansen [29] performed wind tunnel experiments using three-dimensional particle image velocimetry to observe the effect of VGs on the near-stall flow behavior of the DU91-W2-250 airfoil. Their aim was to study the flow structures induced by the VGs on the wing. It was found that the VGs transfer the high momentum fluid to the near-wall region, and the variation of the velocity component direction in the boundary layer along the flow increases. In 2014, Sørensen et al. [30] conducted numerical simulations on the FFA-W3-301 and FA-W3-360 airfoils. The calculated results were compared with wind tunnel measurements, and the variation of lift and drag with the angle of attack was obtained. Although their method was not able to capture the flow details accurately, it can be used to qualitatively compare the effects of different VG settings on airfoil aerodynamic performance. In 2015, Manolesos and Voutsinas [31] employed passive VGs as a simple and effective method to delay or suppress airfoil flow separation, and carried out an experimental study on the optimized blades. Flow visualization of triangular VGs through three-dimensional particle image velocimetry was carried out. Overall, the results demonstrated that the maximum lift increased by 44%, while the drag increased by 0.2%. Lin et al. [17] experimentally evaluated a boundary layer separation control method using miniature surface VGs. Wind tunnel tests were carried out in a low-turbulence pressure tunnel at the NASA (The National Aeronautics and Space Administration) Langley research center. The measured parameters included lift, drag, surface pressure, wake profile, and surface heat flux fluctuations. The results indicated that small VGs can effectively reduce the flow separation in the boundary layer of the flaps. Gao et al. [32] performed computational fluid dynamics (CFD) simulations to study the effect of the physical characteristics and magnitudes of flow from VGs on the aerodynamic performance of the DU97-W-300 blunt-trailing-edge wing. The effect of the VG size was analyzed in terms of the trailing edge thickness and the VG length. The results demonstrated that the drag loss was more sensitive to the increase in the VG’s height than lift, while Appl. Sci. 2019, 9, 5495 3 of 22 an increase in the VG’s length had a negative impact on both lift and drag. Analysis of the streamlines and vortices further revealed the flow field characteristics in the wake region. In 2016, Omar et al. [33] experimentally studied the NACA 4415 airfoil equipped with VGs. The results showed that triangular VGs were more suitable for controlling the boundary layer separation, while micro VGs can effectively control the flow. Zhang et al. [34] studied the effect of VGs on the aerodynamic performance of thick blades. In particular, the effects of height and chord position of VGs and double-row VGs on airfoil aerodynamic performance were investigated. The results demonstrated that after the VGs were installed on the airfoil leading edge, the maximum lift coefficient increased. In addition, the lift coefficient of the double-row VGs could be further improved at high angles of attack due to the different installation positions and sizes. In 2017, Wang et al. [12] studied the aerodynamic performance of the S809 airfoil with and without VGs using CFD simulations. The results showed that the VGs can effectively improve the aerodynamic performance of the S809 airfoil, reduce the thickness of the boundary layer, and delay stall. The double-row VG arrangement demonstrated a good performance in controlling flow separation, which further improved the aerodynamic performance of the S809 airfoil. Martínez-Filgueira et al. [35] studied the motion of micro VGs in the boundary layer of a flat plate using numerical simulations. The installation angle of the VGs was 18.5◦. The trajectory and size of the vortices on the plate were analyzed. Brüderlin et al. [36] improved airfoil aerodynamic efficiency by means of passive VGs placed on the control surface. First, the aerodynamic characteristics of the airfoil were simulated using a Reynolds-averaged Navier–Stokes solver (RANS). Then, through the parameterization study of different VG sizes, the effectiveness of the VGs under certain flow conditions were studied. In 2018, Gageik et al. [37] used a numerical visualization method to investigate whether appropriate micro VGs can suppress the pressure wave. The flow around the VGs was characterized using numerical schlieren visualization. Baldacchino et al. [38] performed wind tunnel experiments on the DU97-W-300 airfoil, where the oil flow visualization method was used to verify the effect of VGs on airfoil stall separation suppression. The results demonstrated that VGs can delay stall, while under a stall condition, the presence of VGs increases the load fluctuation. In 2019, Kundu et al. [39] used the numerical simulation method to study the performance of the S1210 airfoil with VGs under improved trailing edge conditions. The results showed that by adding counter-rotating VGs near the airfoil trailing edge, the lift coefficient of the wing can be increased by 17% and the stall angle can be delayed from 10◦ to 12◦. Moreover, a rounder and thicker trailing edge can increase the lift coefficient by 13.5%, thus improving the performance. Nowadays, VGs are becoming an important part of wind turbine blade design. However, the challenges involved in calculating the flow field around VGs have not yet been satisfactorily addressed. Mereu et al. [40] used the scale decomposition method to simulate the stall behavior of the DU97-W-300 airfoil at high Reynolds numbers. In addition, a detailed sensitivity analysis was performed to evaluate the effects of time integration, grid width resolution, and region width on the simulation accuracy. Using this method, the flow on the airfoil surface with VGs was numerically simulated. Manolesos et al. [41] proposed a numerical model of VGs for RANS simulations. The performance and application of the VG numerical model were also investigated. A wind turbine impeller was taken as an example to study the reliability of the model. Without considering the mesh-induced errors, the results showed that the vortices generated in the numerical simulation were weaker than those in the fully analytical calculation. The technical development of VGs as a means of flow control has been analyzed since the 1990s. Although many scholars have investigated the flow control mechanism of VGs, in the practical application of VGs, there are still some problems to be solved. When VGs are used to control the flow of wind turbine blades, an optimal VG spacing needs to be determined since there is flow interference between VGs and the spacing between VGs may affect the development and dissipation of concentrated vortices. The effect of VG spacing on vortex characteristics and wind turbine airfoil aerodynamic characteristics has not yet been reported. Therefore, in this paper, the effect of VG spacing on vortex characteristics and the aerodynamic characteristics of special airfoils for wind turbines is investigated using numerical simulations and wind tunnel experiments. Appl. Sci. 2019, 9, 5495 4 of 22

2. Methods

2.1. Numerical Conditions

2.1.1. Large Eddy Simulation A large eddy simulation (LES) is a spatial average of turbulent fluctuations, that is, large-scale vortices and small-scale vortices are separated using a filtering function [42]. More specifically, large-scale vortices are simulated directly, while small-scale vortices are closed using models. The theoretical basis of an LES is the existence of inertial sub-scale vorticity in turbulent flows with high Reynolds numbers. The vorticity of such scale has statistical isotropy. It transfers the energy of vortices with an energy scale to vortices with a dissipation scale. After filtering the Navier–Stokes equation with a filter function, the governing equation of the LES method for an incompressible flow can be derived:

∂ρ ∂ρui + = 0 (1) ∂t ∂xi ! ∂(ρui) ∂(ρuiuj) ∂ ∂σij ∂p ∂τij + = µ (2) ∂t ∂xj ∂xj ∂xj − ∂xi − ∂xj where σij is the stress tensor and τij is the subgrid stress. In this paper, the Smagorinsky–Lilly model was used for the subgrid model. This model was first proposed by Smagorinsky [43]. The eddy viscosity can be defined as follows:

2 µt = ρLs s (3) q  1  where Ls is the mixed length of the grid and s 2sijsij, Ls = min kd, CsV 3 , where k is a constant, d is the nearest distance from the wall, Cs is the Smagorinsky constant (in this study, Cs = 0.1), and V is the volume of the calculation unit.

2.1.2. Mesh Development The ICEM software (ANSYS 16.0, Canonsburg, PA, USA) was employed to mesh the computational domain. The number of mesh nodes corresponding to the length, width, and height of the computational domain was 220 120 100, respectively, and the total number of elements was 2,640,000. The × × height of the first layer mesh was 0.001 mm and Y+ < 1, which met the calculation requirements. The mesh around the VGs consisted of 50 nodes along the length direction and 40 nodes along the height direction. The mesh distribution can be seen in Figure1. The applied boundary conditions were the velocity inlet and pressure outlet. The upper boundary of the computational domain was set as an Euler wall, the bottom boundary and the VGs were set as adiabatic non-slip walls, and the two sides of the computational domain were set as symmetrical boundaries. The dimensions of the computational domain are shown in Figure2. A turbulent velocity boundary condition was set at the inlet, where the inlet turbulence velocity type is given as follows:

   1/7  y  U δ y < δ u =  , (4)  U y δ ≥ where u is the local velocity, δ is the thickness of the boundary layer, U is the main velocity, and y is the normal height of the wall. Appl. Sci. 2020, 10, x FOR PEER REVIEW 5 of 24

Appl. Sci. 2020, 10, x FOR PEER REVIEW 5 of 24 Appl. Sci. 2019, 9, 5495 5 of 22

Figure 1. Computational domain mesh and detail of the mesh around the vortex generators (VGs).

The applied boundary conditions were the velocity inlet and pressure outlet. The upper boundary of the computational domain was set as an Euler wall, the bottom boundary and the VGs were set as adiabatic non-slip walls, and the two sides of the computational domain were set as symmetrical boundaries. The dimensions of the computational domain are shown in Figure 2. A turbulent velocity boundary condition was set at the inlet, where the inlet turbulence velocity type is given as follows:

1/7  y U y < δ u = δ ,   ≥ δ (4)  y  U where u is the local velocity, δ is the thickness of the boundary layer, U is the main velocity, and y is the normalFigureFigure height1. 1. ComputationalComputational of the wall. domain domain mesh mesh and and detail detail of of the the mesh mesh around around the the vortex vortex generators generators (VGs). (VGs).

The applied boundary conditions were the velocity inlet and pressure outlet. The upper boundary of the computational domain was set as an Euler wall, the bottom boundary and the VGs were set as adiabatic non-slip walls, and the two sides of the computational domain were set as symmetrical boundaries. The dimensions of the computational domain are shown in Figure 2. A turbulent velocity boundary condition was set at the inlet, where the inlet turbulence velocity type is given as follows:

1/7  y Figure 2. Computational domain dimensionsU y and< δ applied boundary conditions. u = δ , Figure 2. Computational domain dimensions and≥ δ applied boundary conditions. (4)  y 2.1.3. Computational Setup  U 2.1.3.The Computational FLUENT software Setup (ANSYS 16.0, Canonsburg, PA, USA) was used for the simulation. The where u is the local velocity, δ is the thickness of the boundary layer, U is the main velocity, and y is finite volume method was used to discretize the equations and the finite centered di erence scheme the normalThe FLUENT height of software the wall. (ANSYS 16.0, Canonsburg, PA, USA) was used for the ffsimulation. The wasfinite used volume to discretize method was the used space. to Becausediscretize for the LES equations computing, and the the finite SIMPLE centered (Semi-Implicit difference Methodscheme forwas Pressure used to discretize Linked Equations) the space. algorithm Because for saves LES more computing, computing the SIMPLE resources (Semi-Implicit than the PISO Method (Pressure for ImplicitPressure withLinked Splitting Equations) of Operators) algorithm algorithm, saves more the computing pressure–velocity resources coupling than the was PISO based (Pressure on the 5 SIMPLEImplicit algorithmwith Splitting in this of paper.Operators) The time algorithm, step was the set pressure–velocity as ∆t = 3 10− s. coupling After statistical was based stability on the in × Appl.theSIMPLE flow Sci. 2020 fieldalgorithm, 10 was, x FOR achieved, in PEER this REVIEW paper. time-averaged The time statisticsstep was were set as performed. Δt = 3 × 10 In−5 s. particular, After statistical the six cyclesstability6 afterof in24 the flowflow fieldfield was was stabilized achieved, were time-a time-averagedveraged statistics with thewere fluid performed. sweeping In across particular, the lower thewall six cycles of the offlatafter the plate the flat flow as plate a field cycle. as wasa Figurecycle. stabilized 3Figure illustrates were 3 illustrates time-average the structural the structurd parameterswithal the parameters fluid of VGs,sweeping of where VGs, across lwhereis thethe l VGlower is the length, wall VG Hlength,is the H VG is the height, VG height,S is the S distance is the distance between between VGs, and VGs,λ andis the λ is spacing the spacing of the of VGs the (seeVGs Figure (see Figure3 for 3the for di thefference difference between betweenS and Sλ and). The λ). present The present study study focused focused on the on e fftheect effect of the of VG the spacing VG spacing on flow on flowseparation separation control. control. Table 1Table lists the1 lists geometric the geometric parameters parameters of the VGs, of the while VGs, the while inflow the velocity inflow velocity was set wasas U set= 82 as mU/ s,=Figure 82 and m/s, the 2. Computationaland Reynolds the Reynolds number domain number based dimensions on based the VG andon heighttheapplied VG was heightboundary about was conditions. 3 about104. 3 × 104. × 2.1.3. Computational Setup

The FLUENT software (ANSYS 16.0, Canonsburg,H PA, USA) was used for the simulation. The λ finite volume method was used to discretize the equationsl S and the finite centered difference scheme was used to discretize the space. Because for LES computing, the SIMPLEβ (Semi-Implicit Method for Pressure Linked Equations) algorithm saves more computing resources than the PISO (Pressure Implicit with Splitting of Operators) algorithm, the pressure–velocity coupling was based on the SIMPLE algorithm in this paper. The time step was set as Δt = 3 × 10−5 s. After statistical stability in Figure 3. VG geometric model. the flow field was achieved, time-averagedFigure 3. statisticsVG geometric were model. performed. In particular, the six cycles after the flow field was stabilized were time-averaged with the fluid sweeping across the lower wall Table 1. VG geometric parameters.

Setting Angle β (°) Length l (mm) Height H (mm) S/H λ/H 20 17 6 7 3, 5, 7, 9

The pressure loss coefficient at the inlet and outlet of the calculation domain was defined as

CΔp , which can be calculated according to Equation (5), where Pinlet is the total pressure at the

inlet and Poutlet the total pressure at the outlet. The pressure difference coefficient reflects the magnitude of pressure difference loss in the computational domain. For flow control, the smaller the pressure loss difference, the smaller the corresponding energy loss.

()− = Pinlet Pinlet CΔp (5) Pinlet

In order to verify the mesh independence, three meshes with different densities were developed with 1,320,000 (coarse), 1,980,000 (medium), and 2,640,000 (fine) elements. The Richardson extrapolation method was used to verify the convergence of the mesh, and the results are presented in Table 2, where RE is the value obtained using a Richardson extrapolation, p is the order of accuracy, and R is the ratio of errors. The convergence conditions are 0 < R < 1 (monotonic convergence), R < 0 (oscillation convergence), and 1 < R (divergence). As it can be seen, the R = 0.22 result indicates monotonic convergence. Therefore, in this paper, the finest mesh was used for the numerical simulations.

Table 2. Mesh independence study results.

Mesh Richardson Extrapolation Variables Coarse Medium Fine RE p R

CΔp 0.3635 0.3628 0.3622 0.3620 2.75 0.22

2.2. Experimental Setup An experiment of an airfoil with VGs was carried out in the wind tunnel of North China Electric Power University (NCEPU), which contains a 2-D airfoil measurement section. The size of the test section is 1.5 × 3 × 4.5 m3, and the maximum wind speed of the wind tunnel is 62 m/s. The measurement section is equipped with 256- and 64-channel electronic scanning valves and a PXI (Platform PCI eXtensionsfor Instrumentation) data acquisition system. A pitot tube was installed on the wall of the upstream wind tunnel of the airfoil and provided a measurement of the total pressure of the inflow. The sidewall of the pitot tube was punctured to provide air holes, which Appl. Sci. 2019, 9, 5495 6 of 22

Table 1. VG geometric parameters.

Setting Angle β (◦) Length l (mm) Height H (mm) S/H λ/H 20 17 6 7 3, 5, 7, 9

The pressure loss coefficient at the inlet and outlet of the calculation domain was defined as C∆p, which can be calculated according to Equation (5), where Pinlet is the total pressure at the inlet and Poutlet the total pressure at the outlet. The pressure difference coefficient reflects the magnitude of pressure difference loss in the computational domain. For flow control, the smaller the pressure loss difference, the smaller the corresponding energy loss.

(Pinlet Pinlet) C∆p = − (5) Pinlet

In order to verify the mesh independence, three meshes with different densities were developed with 1,320,000 (coarse), 1,980,000 (medium), and 2,640,000 (fine) elements. The Richardson extrapolation method was used to verify the convergence of the mesh, and the results are presented in Table2, where RE is the value obtained using a Richardson extrapolation, p is the order of accuracy, and R is the ratio of errors. The convergence conditions are 0 < R < 1 (monotonic convergence), R < 0 (oscillation convergence), and 1 < R (divergence). As it can be seen, the R = 0.22 result indicates monotonic convergence. Therefore, in this paper, the finest mesh was used for the numerical simulations.

Table 2. Mesh independence study results.

Mesh Richardson Extrapolation Variables Coarse Medium Fine RE p R

C∆p 0.3635 0.3628 0.3622 0.3620 2.75 0.22

2.2. Experimental Setup An experiment of an airfoil with VGs was carried out in the wind tunnel of North China Electric Power University (NCEPU), which contains a 2-D airfoil measurement section. The size of the test section is 1.5 3 4.5 m3, and the maximum wind speed of the wind tunnel is 62 m/s. The measurement × × section is equipped with 256- and 64-channel electronic scanning valves and a PXI (Platform PCI eXtensionsfor Instrumentation) data acquisition system. A pitot tube was installed on the wall of the upstream wind tunnel of the airfoil and provided a measurement of the total pressure of the inflow. The sidewall of the pitot tube was punctured to provide air holes, which were used to measure the static pressure of the incoming flow. There were 96 pressure taps in the middle section of the airfoil to measure the static pressure distribution on the surface of the airfoil. The static pressure coefficient (Cp) was the time-averaged result found with a sampling time interval of 0.1 seconds. The experimental sampling time was 10 seconds for each working condition. There were 111 total pressure piezometric holes and 5 static pressure piezometric holes (called the wake rake) downstream of the airfoil, which were used to calculate the drag coefficient of the airfoil. The geometric dimensions of the wind tunnel and test airfoils are shown in Figure4. The test airfoil used in the experiment is a special wind turbine airfoil: the DU93-W-210 airfoil. The airfoil was developed and designed by Delft University. The DU93-W-210 airfoil is very representative of the aerodynamic characteristics of wind turbine airfoils in general. The thickness of the airfoil was 21% of C, the chord length of the tested airfoil was 0.8 m, and the span of the airfoil was 1.5 m. The VGs were arranged at 0.2 times the chord length from the leading edge of the airfoil. Figure5 shows the test airfoil with the VGs installed. The geometric dimensions of the VGs are shown in Table3. The tunnel wind speed was set to 18.2 m/s, and the Reynolds number based on the chord of the airfoil was 1 106. The AoA of the airfoil ranged from 10 to 25 . × − ◦ ◦ Appl. Sci. 2020, 10, x FOR PEER REVIEW 7 of 24 were used to measure the static pressure of the incoming flow. There were 96 pressure taps in the middle section of the airfoil to measure the static pressure distribution on the surface of the airfoil. The static pressure coefficient (Cp) was the time-averaged result found with a sampling time interval of 0.1 seconds. The experimental sampling time was 10 seconds for each working condition. There were 111 total pressure piezometric holes and 5 static pressure piezometric holes (called the wake rake) downstream of the airfoil, which were used to calculate the drag coefficient of the airfoil. The geometric dimensions of the wind tunnel and test airfoils are shown in Figure 4.

Appl. Sci. 2020, 10, x FOR PEER REVIEW 7 of 24

4.5 m were used to measure the static pressure of the incoming flow. ThereMovable were along96 pressure axis taps in the Test airfoil middle section of the airfoil to measure the static3 m pressure distribution on the surface of the airfoil. 0.8 m The static pressure coefficient (Cp) was1.5 the m time-averaged result foundTrail with rake a sampling time interval of 0.1 seconds. The experimental sampling time was 10 seconds for each working condition. Wind Pitot tubes There were 111 total pressure piezometric holes and 5 staticPressure pressure taps piezometric0.75 m holes (called the wake rake) downstream of the airfoil, which were used to calculate the drag coefficient of the airfoil. Umax = 62 m/s Turntable Appl.The Sci.geometric2019, 9, 5495 dimensionsTurbulence of the intensity wind =tunnel 0.3 % and test airfoils are shown in Figure 4. 7 of 22 Meas uring section 1.5 ×3 ×4.5 m3

4.5 m Movable along axis Test airfoil 3 m 0.8 m 1.5 m Trail rake Figure 4. Wind tunnel measurement section size and test airfoil. Wind Pitot tubes Pressure taps 0.75 m The test airfoil used in the experiment is a special wind turbine airfoil: the DU93-W-210 airfoil. The airfoil was developedU maxand = 62 m/sdesigned by Delft University.Turntable The DU93-W-210 airfoil is very Turbulence intensity = 0.3 % representative of the aerodynamicMeas uring sectioncharacteristics of wind turbine airfoils in general. The thickness of the airfoil was 21% of C1.5, ×the3 × chord4.5 m3 length of the tested airfoil was 0.8 m, and the span of the airfoil was 1.5 m. The VGs were arranged at 0.2 times the chord length from the leading edge of the airfoil. Figure 5 shows the test airfoil with the VGs installed. The geometric dimensions of the VGs are shown in Table 3. The tunnel wind speed was set to 18.2 m/s, and the Reynolds number based Figure 4. Wind tunnel measurement section size and test airfoil. on the chord of the airfoil was 1 × 106. The AoA of the airfoil ranged from −10° to 25°. Figure 4. Wind tunnel measurement section size and test airfoil.

The test airfoil used in the experiment is a special wind turbine airfoil: the DU93-W-210 airfoil. The airfoil was developed and designed by Delft University. The DU93-W-210 airfoil is very representative of the aerodynamic characteristics of wind turbine airfoils in general. The thickness of the airfoil was 21% of C, the chord length of the tested airfoil was 0.8 m, and the span of the airfoil was 1.5 m. The VGs were arranged at 0.2 times the chord length from the leading edge of the airfoil. Figure 5 shows the test airfoil with the VGs installed. The geometric dimensions of the VGs are shown in Table 3. The tunnel wind speed was set to 18.2 m/s, and the Reynolds number based on the chord of the airfoil was 1 × 106. The AoA of the airfoil ranged from −10° to 25°.

Figure 5. Test airfoil with VGs. Figure 5. Test airfoil with VGs. Table 3. VG geometric parameters and arrangement. Table 3. VG geometric parameters and arrangement. Installation Angle β (◦) Length l (mm) Height H (mm) Spacing S/H Pitch Distance λ/H Installation20 Angle β (°) Length 17 l (mm) Height 5H (mm) Spacing 5 S/H Pitch Distance 3, 5, 7, 9 λ/H 20 17 5 5 3, 5, 7, 9 Figure6 shows the wind tunnel test results of the DU93-W-210 airfoil without the VGs. NCEPU provided the test results in this paper. NPU is the wind tunnel test results from the Northwest Polytechnic University, and Delft is the wind tunnel test results from Delft University. By comparing the results of the three wind tunnels, it can be seen that the wind tunnel test results in this paper were close to those obtained by NPU and DelftFigure before 5. Test a stallairfoil AoA with (8 VGs.◦) for the airfoil lift coefficient. After the stall AoA, the lift coefficient measured in the wind tunnel was slightly higher than that measured in the other two wind tunnels.Table For the 3. VG drag geometric coefficient, parameters before theand stallarrangement. AoA, the drag coefficient matched the resultsInstallation of the other Angle wind β (°) tunnels.Length However, l (mm) Height after the H (mm) stall AoA,Spacing the wind S/H tunnelPitch Distance test results λ/H in this paper were closer20 to the Delft University 17 wind tunnel test 5 results. Since 5 the aerodynamic 3, 5, 7, characteristics 9 of airfoils fluctuate after a stall, the lift and drag coefficients must be revised, and the mechanism of each correction method is different. However, the present study is focused on the aerodynamic characteristics of the airfoil before the stall. Appl. Sci. 2020, 10, x FOR PEER REVIEW 8 of 24

Figure 6 shows the wind tunnel test results of the DU93-W-210 airfoil without the VGs. NCEPU provided the test results in this paper. NPU is the wind tunnel test results from the Northwest Polytechnic University, and Delft is the wind tunnel test results from Delft University. By comparing the results of the three wind tunnels, it can be seen that the wind tunnel test results in this paper were close to those obtained by NPU and Delft before a stall AoA (8°) for the airfoil lift coefficient. After the stall AoA, the lift coefficient measured in the wind tunnel was slightly higher than that measured in the other two wind tunnels. For the drag coefficient, before the stall AoA, the drag coefficient matched the results of the other wind tunnels. However, after the stall AoA, the wind tunnel test results in this paper were closer to the Delft University wind tunnel test results. Since the aerodynamic characteristics of airfoils fluctuate after a stall, the lift and drag coefficients must be

Appl.revised, Sci. 2019 and, 9 ,the 5495 mechanism of each correction method is different. However, the present study8 of 22is focused on the aerodynamic characteristics of the airfoil before the stall.

0.35 a) b) NCEPU 1.5 0.30 NPU Delft 1.0 0.25 l C NCEPU d 0.20 0.5 NPU C Delft 0.15 0.0 0.10 -15-10 -5 0 5 10 15 20 25 30 0.05 -0.5 α (°) 0.00 -15-10 -5 0 5 10 15 20 25 30 -1.0 α (°)

Figure 6. Comparison of experiments: (a) lift coefficient and (b) drag coefficient. Figure 6. Comparison of experiments: (a) lift coefficient and (b) drag coefficient. 3. Results and Discussion 3. Results and Discussion 3.1. Analysis of the CFD Calculation Results 3.1. AnalysisFigure7 ofshows the CFD time-averaged Calculation Results axial velocity contours on the symmetrical plane of the computationalFigure 7 domain.shows time-averaged As it can be observed, axial velocity the channel contours expanded on the between symmetrical 0–35H, which plane led of to the an adversecomputational pressure domain. gradient As (APG), it can be and obse a continuousrved, the channel decrease expanded in fluid velocity.between Under0–35H,the which action ledof tothe an APGadverse and pressure wall viscosity, gradient flow (APG), separation and a occurred continuous at the decrease lower wall, in fluid and velocity. a low-velocity Under zone the appeared.action of The flow separation position was approximately at x 20H. Since the free-slip wall boundary condition the APG and wall viscosity, flow separation occurred1 ≈ at the lower wall, and a low-velocity zone wasappeared. adopted The on flow the upperseparation wall ofposition the computational was approximately domain, at no x1 flow ≈ 20 separationH. Since the occurred. free-slip In wall the 35–135H section, there was a zero pressure gradient (ZPG), and flow reattachment occurred at x 60H. boundary condition was adopted on the upper wall of the computational domain, no2 ≈ flow Theseparation axial velocity occurred. contours In the with 35–135 VGsHrevealed section, thatthere the was VGs a inhibitedzero pressure flow separationgradient (ZPG), in all fourand cases.flow When the VG spacing was λ/H = 7, a small low-speed region appeared at x 30H. When the VGs reattachment occurred at x2 ≈ 60H. The axial velocity contours with VGs revealed≈ that the VGs spacinginhibited was flowλ/ Hseparation= 9, the area in ofall thefour low-speed cases. When region the at VG the samespacing location was λ increased./H = 7, a Thissmall showed low-speed that whenregionλ appeared/H = 9, the at e xff ectiveness≈ 30H. When of thethe concentratedVGs spacing vorticeswas λ/H at= 9, this the location area of becamethe low-speed weak, whileregion the at hydrodynamicthe same location energy increased. was already This showed low under that the when inverse λ/H pressure= 9, the effectiveness gradient due of to the largeconcentrated spacing betweenvortices at VGs. this No location low-velocity became zone weak, appeared while the at thehydrodynamic other two installations energy was with already a smaller low under spacing. the inverseFigure pressure8 shows gradient the distribution due to the large of the spacing pressure between coe ffi VGs.cient No (C low-velocityp) on the bottom zone appeared wall of the at computational domain. In the no VG case, the inflection point of Cp appeared at x 20H, and the slope the other two installations with a smaller spacing. ≈ of the Cp change decreased. In the cases where the boundary layer flow was controlled by the VGs, the Cp on the wall increased in the APG section. Since no flow separation occurred, no alteration in the slope of Cp change in the APG section was observed. The Cp in most positions of the ZPG segment was basically 0. The difference between different VG spacings was primarily reflected in the turning position of the Cp curve. In particular, the larger the VG spacing, the smaller the slope of the wall pressure drop and the worse the flow control effect. After the fluid passed through the expansion section, the Cp increased. According to Figure7, the flow separation occurred at x 20H. After the ≈ flow separation, the slope of the Cp drop decreased, while after the flow reattachment, no significant changes in Cp were observed in the ZPG section. Appl. Sci. 2020, 10, x FOR PEER REVIEW 9 of 24

Appl. Sci. 2019, 9, 5495 9 of 22 Appl. Sci. 2020, 10, x FOR PEER REVIEW 9 of 24

Figure 7. Spanwise mean velocity contours on the plane of symmetry of the computational domain.

Figure 8 shows the distribution of the pressure coefficient (Cp) on the bottom wall of the computational domain. In the no VG case, the inflection point of Cp appeared at x ≈ 20H, and the slope of the Cp change decreased. In the cases where the boundary layer flow was controlled by the VGs, the Cp on the wall increased in the APG section. Since no flow separation occurred, no alteration in the slope of Cp change in the APG section was observed. The Cp in most positions of the ZPG segment was basically 0. The difference between different VG spacings was primarily reflected in the turning position of the Cp curve. In particular, the larger the VG spacing, the smaller the slope of the wall pressure drop and the worse the flow control effect. After the fluid passed through the expansion section, the Cp increased. According to Figure 7, the flow separation occurred at x ≈ 20H.

After the flow separation, the slope of the Cp drop decreased, while after the flow reattachment, no Figure 7. Spanwise mean velocity contours on the plane of symmetry of the computational domain. significantFigure changes 7. Spanwise in C meanp were velocity observed contours in the on ZPG the plane section. of symmetry of the computational domain.

Figure 8 shows the distribution of the pressure coefficient (Cp) on the bottom wall of the -0.8 λ/H = 5 computational domain. In the no VG case, the inflection point ofλ/H C = p7 appeared at x ≈ 20H, and the slope of the Cp change decreased. In the cases where the boundary λ/H layer= 9 flow was controlled by the -0.6 λ/H = 11 VGs, the Cp on the wall increased in the APG section. Since Nono control flow separation occurred, no

alteration in the slope of Cpp change in the APG section was observed. The Cp in most positions of the ZPG segment was basicallyC -0.40. The difference between different VG spacings was primarily reflected in the turning position of the Cp curve. In particular, the larger the VG spacing, the smaller the slope of the wall pressure drop and-0.2 the worse the flow control effect. After the fluid passed through the expansion section, the Cp increased. According to Figure 7, the flow separation occurred at x ≈ 20H. After the flow separation, the0.0 slope of the Cp drop decreased, while after the flow reattachment, no significant changes in Cp were observed in the ZPG section. 0 40 80 120 x/H

-0.8 λ/H = 5 Figure 8. Distribution of Cp on the bottom wall of the computational λ/H = 7 domain. Figure 8. Distribution of Cp on the bottom wall of the computational λ/H = 9 domain. Although in some simple-0.6 flows, the existence of vortices can λ/H = be 11 determined by intuition and No control visualization, in three-dimensional viscous flows, especially in complex flows, a large number of p experimental or numericalC simulation-0.4 data are required to show the structure, evolution, and interaction of vortices. Therefore, it is necessary to give an objective discrimination of the vortices’ criteria. At present, the Q criterion is more commonly used, where the region of Q > 0 is defined as a vortex, that -0.2 is Ω 2 > E 2. Its physical meaning is that the fluid rotation in the region of the vortex plays a leading k k k k role in comparing the strain rate. The specific formula is as follows: 0.0

1 2 2 0Q = ( 40Ω E 80) 120 (6) 2 k k x−/H k k

Figure 8. Distribution of Cp on the bottom wall of the computational domain. Appl. Sci. 2020, 10, x FOR PEER REVIEW 10 of 24

Although in some simple flows, the existence of vortices can be determined by intuition and visualization, in three-dimensional viscous flows, especially in complex flows, a large number of experimental or numerical simulation data are required to show the structure, evolution, and interaction of vortices. Therefore, it is necessary to give an objective discrimination of the vortices’ criteria. At present, the Q criterion is more commonly used, where the region of Q > 0 is defined as a vortex, that is Ω 2 > E 2 . Its physical meaning is that the fluid rotation in the region of the vortex plays a leading role in comparing the strain rate. The specific formula is as follows:

1 2 2 Q = ( Ω − E ) (6) 2

Appl. Sci. 20192 =, 9, 5495 2 1 2 Ω 10 of 22 where E eije ji and Ω = Ω Ω = ω , eij , ij are the strain rate tensor and the vorticity ij ji 2 tensor, respectively. where E 2 = e e and Ω 2 = Ω Ω = 1 ω 2, e , Ω are the strain rate tensor and the vorticity k k ij ji k k ij ji 2 | | ij ij tensor,In this respectively. study, the Q criterion was used to identify the three-dimensional vortices in the flow field. In this study, the Q criterion was used to identify the three-dimensional vortices in the flow field. Figure9 shows the Q isosurfaces colored according to the velocity in the flow field (Q = 1 105). Figure 9 shows the Q isosurfaces colored according to the velocity in the flow field (Q = 1 ×× 105). Many disordered vortices were observed in the turbulent flow field without VGs. However, typical Many disordered vortices were observed in the turbulent flow field without VGs. However, typical turbulent coherent structures could be distinguished. In the initial flow stage, under the fluid viscosity turbulent coherent structures could be distinguished. In the initial flow stage, under the fluid and shear stress, the vortices were rolled up near the wall (as indicated by A). Due to self-rotation of the viscosity and shear stress, the vortices were rolled up near the wall (as indicated by A). Due to vortices, the radius of the vortex cores increased gradually downstream. At the same time, disturbed self-rotation of the vortices, the radius of the vortex cores increased gradually downstream. At the by the three-dimensional flow field, the vortices fluctuated extensively, twisted, and protruded upward same time, disturbed by the three-dimensional flow field, the vortices fluctuated extensively, along the normal direction. The protrusion was induced by the self-rotation of the spanning vortices, twisted, and protruded upward along the normal direction. The protrusion was induced by the which intensified the protrusion height (as indicated by B). Under the action of a shear flow, the vortices self-rotation of the spanning vortices, which intensified the protrusion height (as indicated by B). continued to stretch and lift, and gradually developed into closed upper end hairpin vortices with an Under the action of a shear flow, the vortices continued to stretch and lift, and gradually developed opening at the lower end (as indicated by C). Moving backwards, the legs of the vortices extended and into closed upper end hairpin vortices with an opening at the lower end (as indicated by C). Moving the head of the hairpin vortices became larger, forming a local high-shear layer. Under the action of the backwards, the legs of the vortices extended and the head of the hairpin vortices became larger, mainstream fluid, the vortex was stretched along the flow direction into a tube (as indicated by D). forming a local high-shear layer. Under the action of the mainstream fluid, the vortex was stretched This indicated that in turbulent flows, the average length of the vortex tube was generally increased. along the flow direction into a tube (as indicated by D). This indicated that in turbulent flows, the The energy transport process from larger to smaller vortices and the viscous dissipation into heat is average length of the vortex tube was generally increased. The energy transport process from larger called the cascade principle. to smaller vortices and the viscous dissipation into heat is called the cascade principle.

Figure 9. Q isosurfaces (Q = 1 105) colored according velocity without VGs: (a) computational × Figuredomain 9. andQ isosurfaces (b) inlet section. (Q = 1 × 105) colored according velocity without VGs: (a) computational domain and (b) inlet section. Figure 10 shows Q isosurfaces colored according to the velocity in the flow field (Q = 1 105) × as aFigure result of10 theshows VG Q control. isosurfaces First, colored by comparing according Figures to the9 andvelocity 10, it in can the be flow found field that (Q without= 1 × 105) the as aVG result control, of the many VG control. irregular First, vortices by comparing were generated Figures downstream 9 and 10, it of can the be computational found that without domain, the while VG control,this number many was irregular reduced vortices when were the flow generate was controlledd downstream by VGs. of the By computational comparing the domain, vortices while under thisdiff erentnumber VG was spacings, reduced it when can be the found flow that was with controlled the increase by VGs. of By the comparing VG spacing, the the vortices height under of the differentvortices increased.VG spacings, As itit cancan bebe seenfound in Figurethat with 10b, the the increase presence of of the VGs VG created spacing, longitudinal the height vortices, of the vorticesand this increased. fact organized As it thecan local be seen vortex in Figure structure 10b, and the further presence hindered of VGs the created development longitudinal and movement vortices, of the spanwise vortices. The vortices generated between two VGs rotated in opposite directions, thus the outward vortices of the VGs were “suppressed.” On the other hand, the upward forces at the inner side of the VGs were toward the center. Under the action of the two concentrated vortices, the inner extended vortices were “raised” to form hairpin-like vortices, and as the flow developed downstream, the concentrated vortices gradually merged with the leg of the hairpin-like vortices. The legs of the concentrated and hairpin-like vortices played an important role in the exchange of kinetic energy and energy dissipation near the wall. When λ/H = 3, the centralized vortices generated by the two VGs were so close to each other that the spanning vortices inside the VGs were not “raised,” but instead were fused together at a downstream location under a reverse pressure gradient, forming hairpin-like vortices. When λ/H = 5, the outer spreading vortices of the VGs were “suppressed,” while the inner spreading vortices were “raised,” forming regular hairpin-like vortices that moved downstream. When Appl. Sci. 2020, 10, x FOR PEER REVIEW 11 of 24 and this fact organized the local vortex structure and further hindered the development and movement of the spanwise vortices. The vortices generated between two VGs rotated in opposite directions, thus the outward vortices of the VGs were “suppressed.” On the other hand, the upward forces at the inner side of the VGs were toward the center. Under the action of the two concentrated vortices, the inner extended vortices were “raised” to form hairpin-like vortices, and as the flow developed downstream, the concentrated vortices gradually merged with the leg of the hairpin-like vortices. The legs of the concentrated and hairpin-like vortices played an important role in the exchange of kinetic energy and energy dissipation near the wall. When λ/H = 3, the centralized vortices generated by the two VGs were so close to each other that the spanning vortices inside the VGs were not “raised,” but instead were fused together at a downstream location under a reverse

Appl.pressure Sci. 2019 gradient,, 9, 5495 forming hairpin-like vortices. When λ/H = 5, the outer spreading vortices11 of of the 22 VGs were “suppressed,” while the inner spreading vortices were “raised,” forming regular hairpin-like vortices that moved downstream. When λ/H = 7 and λ/H = 9, no regular hairpin-like λvortices/H = 7 and wereλ/ Hdeveloped= 9, no regular on the hairpin-like inner side vorticesdue to the were large developed VG spacing. on the Such inner disordered side due to turbulent the large VGstructures spacing. were Such not disordered conducive turbulent to the energy structures exchange were in not the conducive near-wall to region, the energy which exchange became inprone the near-wallto flow separation. region, which became prone to flow separation.

a)

?/H =3= 3 ??//HH =5= 5

??//HH=7 = 7 ??/H/H=9 = 9

Inside Outside b) ?? ??

?/H =3= 3 ?/?H/H ==5 5

??//HH =7= 7 ??/H/H ==9 9

Figure 10. Q isosurfaces (Q = 1 105) colored according to velocity with VGs: (a) computational × domain and (b) inlet section.

Figure 11 shows vorticity isolines and spatial streamlines at five cross-sectional locations downstream of the VGs. First, as it can be seen in Figure 11a, the concentrated vortices generated by the VGs scrolled around the vortex core center and rotated in spirals. When λ/H = 7, at x > 20H, the streamlines began to bend due to the counter-pressure gradient effect, and the flow became unsmooth. When λ/H = 9, at x > 20H, the streamlines were twisted, which indicated that the VGs were not able to adequately suppress the flow separation. In Figure 11b, it can be observed that with the increase of the VG spacing, the distance between the two vortices gradually increased. Downstream of x/H = 15, when λ/H = 7 and λ/H = 9, the shape of the vortices was irregular with no obvious vortex center, while the area surrounding the vortices increased. When λ/H = 3 and λ/H = 5, the two vortices were closer to each other, and the shape of the concentrated vortices was still intact. Since the concentrated Appl. Sci. 2020, 10, x FOR PEER REVIEW 12 of 24

Figure 10. Q isosurfaces (Q = 1 × 105) colored according to velocity with VGs: (a) computational domain and (b) inlet section.

Appl. Sci. 2020, 10, x FOR PEER REVIEW 13 of 24 Figure 11 shows vorticity isolines and spatial streamlines at five cross-sectional locations downstream of the VGs. First, as it can be seen in Figure 11a, the concentrated vortices generated by the VGs scrolled around the vortex core center and rotated in spirals. When λ/H = 7, at x > 20H, the streamlines began to bend due to the counter-pressure gradient effect, and the flow became unsmooth. When λ/H = 9, at x > 20H, the streamlines were twisted, which indicated that the VGs were not able to adequately suppress the flow separation. In Figure 11b, it can be observed that with the increase of the VG spacing, the distance between the two vortices gradually increased. Downstream of x/H = 15, when λ/H = 7 and λ/H = 9, the shape of the vortices was irregular with no obvious vortex center, while the area surrounding the vortices increased. When λ/H = 3 and λ/H = 5, Appl. Sci. 2019, 9, 5495 12 of 22 the two vortices were closer to each other, and the shape of the concentrated vortices was still intact. Since the concentrated vortices rotated upward at the inner side of the VGs and were subjected to vorticesupward rotated forces, upwardthe highest at the vortex inner sidecore ofheight the VGs from and the were wall subjected was observed to upward at λ forces,/H = 3. the When highest the vortexdistance core between height fromthe vortices the wall was was small observed enough, at λ /theH = upward3. When rotation the distance force betweenmade the the vortices vortices lift was off smallthe wall. enough, This theimplies upward that rotationin order forceto restrain made the the flow vortices separation lift off the using wall. VGs, This the implies vortices that need in order to be tocloser restrain to the the wall flow separationto give a stronger using VGs, energy the vorticesexchange need effect to be in closer the near-wall to the wall area, to give and a the stronger more energybeneficial exchange the flow effect control. in the near-wallWhen λ/ area,H = and3, the the spacing more beneficial was somewhat the flow control.small, which When wasλ/H =not3, theconducive spacing to was flow somewhat control. small, which was not conducive to flow control.

a)

λ/H=3 λ/H=5

λ/H=7 λ/H=9

Figure 11. ((aa)) Vorticity Vorticity streamlines and and contours in in the flow flow domain and ( b) vorticity contours at differentdifferent cross-sections. Figure 12 shows the relationship between the vortex core radius and vortex core spacing with Figure 12 shows the relationship between the vortex core radius and vortex core spacing with flow distance, where r represents the vortex radius and ∆z represents the distance between the two flow distance, where r represents the vortex radius and Δz represents the distance between the two vortex cores. With the increase of the VG spacing, the ∆z increased gradually. The vortex core radius represents the radial range of action. Theoretically, when VGs are used to suppress flow separation, the optimal distance is when the vortex radius r is equal to the distance between the two vortex cores ∆z/2 (half the distance). However, the radius of the vortices increased along the flow direction, and the vortices slightly deviated toward the flow direction. Therefore, the radius of the vortices and spacing between vortices cannot be equal everywhere along the flow direction. When the distance between vortices was ∆z/2 < r, VGs hindered the development of vortices. When ∆z/2 > r, a region where the vortices could not act was developed, which led to the decrease of the added value of fluid kinetic Appl. Sci. 2020, 10, x FOR PEER REVIEW 14 of 24

vortex cores. With the increase of the VG spacing, the Δz increased gradually. The vortex core radius represents the radial range of action. Theoretically, when VGs are used to suppress flow separation, the optimal distance is when the vortex radius r is equal to the distance between the two vortex cores Δz/2 (half the distance). However, the radius of the vortices increased along the flow direction, and the vortices slightly deviated toward the flow direction. Therefore, the radius of the vortices and spacing between vortices cannot be equal everywhere along the flow direction. When the distance betweenAppl. Sci. 2019vortices, 9, 5495 was Δz/2 < r, VGs hindered the development of vortices. When Δz/2 > r, a region13 of 22 where the vortices could not act was developed, which led to the decrease of the added value of fluid kinetic energy in the boundary layer. By comparing the four different VG spacing results, it can beenergy seen inthat, the except boundary at x layer./H = 1, By the comparing distance thebetween four dithefferent vortices VG spacingΔz was results,smaller it than can bethe seen vortex that, radiusexcept r at atx/ Hthe= 1,other thedistance locations between when theλ/H vortices = 3. This∆z was shows smaller that than this the VG vortex spacing radius hinderedr at the otherthe developmentlocations when of λvortices/H = 3. at This most shows positions that this along VG th spacinge flow hindereddirection, the and development that the VG of spacing vortices was at mosttoo smallpositions to facilitate along the flow flow control. direction, When and λ/ thatH = 7 the and VG 9, spacing Δz > r for was each too smalldirection, to facilitate which reduced flow control. the effectiveWhen λ /rangeH = 7 of and the 9, vortices∆z > r for and each was direction, not conducive which reducedto flow control. the effective When range λ/H of= 5, the it vorticeswas found and thatwas Δ notz > conduciver before x/ toH flow= 10, control.while after When x/Hλ /=H 10,= 5,Δz it < was r. Consequently, found that ∆z >a VGr before spacingx/H =of10, λ/H while = 5 was after morex/H = suitable10, ∆z

r Δz/2 2 λ/H = 3 H

/

z 1

0 5 10 15 20 2 λ/H = 5

H /

z 1

0 5 10 15 20 4 λ/H = 7 H

/ 2 z

0 5 10 15 20 6 H / λ/H = 9 z

4 2 0 5 10 15 20 x/H Figure 12. Relationship between the vortex core radius and vortex core spacing with flow direction. Figure 12. Relationship between the vortex core radius and vortex core spacing with flow direction. Second-order spatial correlation is a statistical method commonly used to study turbulence. Two-pointSecond-order spatial spatial correlation correlation can reflect is a thestatistical spatial method relationship commonly of one used or more to study pulsations turbulence. in the Appl. Sci.Two-pointturbulent 2020, 10, xflowspatial FOR field. PEER correlation This REVIEW method can canreflect be used the tospatial analyze relationship the correlation of one of theor more structural pulsations characteristics in the 15 of 24 turbulentof the downstream flow field. VG This vortices. method The correlationcan be used function to analyze is defined the as correlation follows: of the structural that theycharacteristics are completely of the downstream unrelated. VG vortices. For uniformThe correlation turbulence, function isthe defined correlation as follows: coefficient is D E independent of the coordinate position,Rij(r, xand) = relateui0(x, t)du 0j(onlyx + r ,tot) ,the correlation distance. In (7)order to ()= ' ' + investigate the correlation of the turbulentRij r, x momeui (x,t)ntumu j (x downstreamr,t) , of the VGs, the correlation(7) where u and u are components of the pulsating velocity, and x and r are vectors. When i = j, this characteristicsi of thej turbulent momentum v′ along the flow direction at certain points at different whereexpresses ui and the u autocorrelationj are components of of a certain the pulsating pulsation, velocity, and when and ix ,andj, it r means are vectors. that the When two pulsationsi = j, this heightsexpressesare on correlated. a pair the ofautocorrelation Thecentrosymmetric autocorrelation of a certain diagramplanes pulsation, of is shownthe VGsand in when Figurewere i compared.13≠ j., it means that the two pulsations are correlated. The autocorrelation diagram is shown in Figure 13. The above formula can be transformed into dimensionless correlation coefficients as follows:

u' (x,t)u ' (x + r,t) = i j Rij . (8) '2 '2 + ui (x,t)u j (x r,t)

The correlation coefficient magnitude represents the statistical similarity between two random variables or the probability that the fluctuation takes the same sign at different positions in the flow field. R' = ±1 denotes that twoFigure random 13. Autocorrelation variables are completely of pulse velocity correlated,u. while R' = 0 denotes ij Figure 13. Autocorrelation of pulse velocity u. ij The above formula can be transformed into dimensionless correlation coefficients as follows:   ' Figure 14 illustrates the autocorrelation coefficient curve R ' ' (r ) for the calculation of the ( ) ( + ) v v 1 ui0 x, t u0j x r, t R = . (8) fluctuating velocity v′ at different positionsij r on the central symmetry plane of the domain. Five 2( ) 2( + ) reference points at different heights and differentui0 x, tpointsu0j x alongr, t the flow direction were selected for coherence analysis (Figure 14a). The minimum correlation distance was 0.5 mm, the maximum correlation distance was 675 mm, and the VGs were placed at the 0 position. According to Figure 14b, the coherence coefficient at the reference point is 1, indicating that the reference point was correlated with itself. In addition, the larger the correlation coefficient near the reference point, the larger the correlation coefficient amplitude, and the higher the correlation between the fluctuation and the reference point. A comparison between the following four cases demonstrated that when λ/H = 3, the magnitude of the correlation coefficient was the largest at most locations, which indicated that at this VG spacing, the structure of turbulence in the downstream domain preserved a high organization. When λ/H = 7 and 9, the magnitude of the correlation coefficient was larger at most locations, while that of λ/H = 5 was closer to ' = at most locations. The correlation Rv'v' (r1) 0 between the turbulent vortices downstream of the VGs and the reference point was poor, indicating that this VG spacing (λ/H = 5) was more suitable for suppressing flow separation. The width between the correlation coefficient curve and the two intersections reflected the scale of the coherent structure in the downstream turbulent flow field. It can be observed that the scale of the vortices increased gradually as the flow developed downstream.

x/H

(a) Reference points of self-correlation Appl. Sci. 2019, 9, 5495 14 of 22

The correlation coefficient magnitude represents the statistical similarity between two random variables or the probability that the fluctuation takes the same sign at different positions in the flow field. R = 1 denotes that two random variables are completely correlated, while R = 0 denotes ij0 ± ij0 that they are completely unrelated. For uniform turbulence, the correlation coefficient is independent of the coordinate position, and related only to the correlation distance. In order to investigate the correlation of the turbulent momentum downstream of the VGs, the correlation characteristics of the turbulent momentum v0 along the flow direction at certain points at different heights on a pair of centrosymmetric planes of the VGs were compared. Figure 14 illustrates the autocorrelation coefficient curve R0 (r1) for the calculation of the v0v0 fluctuating velocity v0 at different positions on the central symmetry plane of the domain. Five reference points at different heights and different points along the flow direction were selected for coherence analysis (Figure 14a). The minimum correlation distance was 0.5 mm, the maximum correlation distance was 675 mm, and the VGs were placed at the 0 position. According to Figure 14b, the coherence coefficient at the reference point is 1, indicating that the reference point was correlated with itself. In addition, the larger the correlation coefficient near the reference point, the larger the correlation coefficient amplitude, and the higher the correlation between the fluctuation and the reference point. A comparison between the following four cases demonstrated that when λ/H = 3, the magnitude of the correlation coefficient was the largest at most locations, which indicated that at this VG spacing, the structure of turbulence in the downstream domain preserved a high organization. When λ/H = 7 and 9, the magnitude of the correlation coefficient was larger at most locations, while that of λ/H = 5 was closer to R0 (r1) = 0 at most locations. The correlation between the turbulent vortices v0v0 downstream of the VGs and the reference point was poor, indicating that this VG spacing (λ/H = 5) was more suitable for suppressing flow separation. The width between the correlation coefficient curve and the two intersections reflected the scale of the coherent structure in the downstream turbulent flow field. It can be observed that the scale of the vortices increased gradually as the flow developed downstream. Figure 15 shows the average velocity distribution at different positions along the downstream direction. /U represents the ratio of the time-averaged velocity to the mainstream velocity and ∞ y/H is the ratio of the normal wall height to the VG height. It can be observed that the increase in the kinetic energy of the fluid at the bottom of the boundary layer corresponded to a decrease in the kinetic energy of the fluid above the boundary layer. The S-type velocity profile took the center of the vortex core as the symmetrical point, which is the main principle of using VGs to control flow separation. In particular, due to the rotation of the concentrated vortices, the high-energy fluid outside of the boundary layer was transferred into the bottom of the boundary layer, inhibiting the boundary layer separation. By comparing the velocity profiles developed under the four VG spacings, it can be seen that the kinetic energy of the fluid at the bottom of the boundary layer increased with the decrease of the VG spacing. However, when λ/H = 3, downstream of x/H = 15, the center of the vortex core was higher than the wall, and the high-energy fluid in the boundary layer was also higher than the wall height. When λ/H = 5, the kinetic energy at the bottom of the boundary layer was the largest. Appl. Sci. 2020, 10, x FOR PEER REVIEW 15 of 24 that they are completely unrelated. For uniform turbulence, the correlation coefficient is independent of the coordinate position, and related only to the correlation distance. In order to investigate the correlation of the turbulent momentum downstream of the VGs, the correlation characteristics of the turbulent momentum v′ along the flow direction at certain points at different heights on a pair of centrosymmetric planes of the VGs were compared.

Figure 13. Autocorrelation of pulse velocity u.

' Figure 14 illustrates the autocorrelation coefficient curve R ' ' (r ) for the calculation of the v v 1 fluctuating velocity v′ at different positions on the central symmetry plane of the domain. Five reference points at different heights and different points along the flow direction were selected for coherence analysis (Figure 14a). The minimum correlation distance was 0.5 mm, the maximum correlation distance was 675 mm, and the VGs were placed at the 0 position. According to Figure 14b, the coherence coefficient at the reference point is 1, indicating that the reference point was correlated with itself. In addition, the larger the correlation coefficient near the reference point, the larger the correlation coefficient amplitude, and the higher the correlation between the fluctuation and the reference point. A comparison between the following four cases demonstrated that when λ/H = 3, the magnitude of the correlation coefficient was the largest at most locations, which indicated that at this VG spacing, the structure of turbulence in the downstream domain preserved a high organization. When λ/H = 7 and 9, the magnitude of the correlation coefficient was larger at most locations, while that of λ/H = 5 was closer to ' = at most locations. The correlation Rv'v' (r1) 0 between the turbulent vortices downstream of the VGs and the reference point was poor, indicating that this VG spacing (λ/H = 5) was more suitable for suppressing flow separation. The width between the correlation coefficient curve and the two intersections reflected the scale of the coherent structure in the downstream turbulent flow field. It can be observed that the scale of the vortices Appl. Sci. 2019, 9, 5495 15 of 22 increased gradually as the flow developed downstream.

x/H Appl. Sci. 2020, 10, x FOR PEER REVIEW 16 of 24 (a) Reference points of self-correlation ?/H = 3 ?/H = 5 ?/H = 7 ?/H = 9

y/H = 0.5 x/H = 1

y/H =1 x/H = 5

y/H = 2 x/H = 10

y/H = 4 x/H = 15

y/H = 6 x/H = 20

(b) Correlation coefficients

Figure 14. Correlation coefficient distribution of fluctuating velocity v0. Figure 14. Correlation coefficient distribution of fluctuating velocity v′.

Figure 15 shows the average velocity distribution at different positions along the downstream direction. /U∞ represents the ratio of the time-averaged velocity to the mainstream velocity and y/H is the ratio of the normal wall height to the VG height. It can be observed that the increase in the kinetic energy of the fluid at the bottom of the boundary layer corresponded to a decrease in the kinetic energy of the fluid above the boundary layer. The S-type velocity profile took the center of the vortex core as the symmetrical point, which is the main principle of using VGs to control flow separation. In particular, due to the rotation of the concentrated vortices, the high-energy fluid outside of the boundary layer was transferred into the bottom of the boundary layer, inhibiting the boundary layer separation. By comparing the velocity profiles developed under the four VG spacings, it can be seen that the kinetic energy of the fluid at the bottom of the boundary layer increased with the decrease of the VG spacing. However, when λ/H = 3, downstream of x/H = 15, the center of the vortex core was higher than the wall, and the high-energy fluid in the boundary layer was also higher than the wall height. When λ/H = 5, the kinetic energy at the bottom of the boundary layer was the largest. Appl.Appl. Sci.Sci. 20192020,, 910, 5495, x FOR PEER REVIEW 1716 of 2224 Appl. Sci. 2020, 10, x FOR PEER REVIEW 17 of 24

FigureFigure 15.15. SpanwiseSpanwise meanmean velocityvelocity profiles.profiles. Figure 15. Spanwise mean velocity profiles.

FigureFigure 1616 showsshows thethe relationshiprelationship betweenbetween thethe pressurepressure lossloss coecoefficientfficient CC∆ΔPP and the VG spacing. Figure 16 shows the relationship between the pressure loss coefficient CΔP and the VG spacing. TheThe percentagepercentage decreasedecrease ofof CC∆ΔPP with VGs compared to that without VGs (clean) can be observed. The percentage decrease of CΔP with VGs compared to that without VGs (clean) can be observed. WhenWhen VGsVGs were were installed, installed, the theC∆ CPΔinP in the the calculation calculation domain domain decreased decreased compared compared to that to withoutthat without VGs. When VGs were installed, the CΔP in the calculation domain decreased compared to that without AmongVGs. Among them, thethem,C∆ Pthewas CΔ theP was smallest the smallest when λ when/H = 5, λ/ andH = the5, and maximum the maximumC∆P was C reducedΔP was reduced by 30.95%. by VGs. Among them, the CΔP was the smallest when λ/H = 5, and the maximum CΔP was reduced by When30.95%.λ/ HWhen= 9, theλ/HC ∆=P 9,was the the CΔ largest,P was the which largest, was reducedwhich was by 2.37%reduced compared by 2.37% to thatcompared without to VGs.that 30.95%.Therefore,without When VGs.λ/H Therefore,λ=/H5 was= 9, morethe λ/H C suitable=Δ P5 was formorethe flowlargest, suitable control. which for flow was control. reduced by 2.37% compared to that without VGs. Therefore, λ/H = 5 was more suitable for flow control.

0.45 0.45 0.40 0.40 -2.37%

?P 0.35 -2.37% C

?P 0.35 C 0.30 -22.58% -11.44% 0.30 -22.58% -11.44% 0.25 0.25 -30.95% -30.95% 0.20 0.20 CleanClean ??//HH =3= 3 ?//H =5= 5 ?//H =7= 7 ??//H=9 = 9 CleanClean ??//HH =3= 3 ?//H =5= 5 ?//H =7= 7 ??//H=9 = 9 Figure 16. Relationship between the pressure loss coefficient C∆P and VGs spacings. Figure 16. Relationship between the pressure loss coefficient CΔP and VGs spacings. 3.2. AnalysisFigure of the Experimental16. Relationship Results between the pressure loss coefficient CΔP and VGs spacings. 3.2. AnalysisFigure 17 of shows the Experimental the lift–drag Results coeffi cient and lift–drag ratio curves of the airfoil with and without 3.2. Analysis of the Experimental Results VGs.Figure Figure 17 ashows demonstrates the lift–drag the lift coefficient coefficient and curve. lift–drag It can beratio seen curves that the of liftthe coe airfoilfficients with of and the airfoilwithoutFigure with VGs. and17 Figureshows without 17a the VGsdemonstrates lift–drag were almost coefficient the the lift samecoefficien and forlift–drag ant curve. angle-of-attack ratio It can curves be seen (AoA) of that the below theairfoil lift 8◦ .coefficientswith Above and 8◦ , withouttheof the VGs airfoil VGs. could Figurewith effectively and 17a withoutdemonstrates increase VGs the werethe lift oflift almost the coefficien airfoil. the tsame Incurve. Table for It 4 ancan, it angle-of-attack canbe seen be seen that that the (AoA) lift when coefficients belowλ/H = 8°.9, oftheAbove the stall airfoil 8°, AoA the with ofVGs the and could airfoil without effectively was 16VGs◦, whileincrwereease underalmost the lift the the of other samethe airfoil. VG for spacings, an In angle-of-attack Table the 4, it stall can AoA be(AoA) seen was belowthat 18◦ .when The8°. Abovemaximumλ/H = 9,8°, the the lift stall VGs coe AoAffi couldcient of effectively wasthe airfoil obtained incr wasease when 16°, the whileλ/ Hlift= ofunder5, the which airfoil. the wasother In increased Table VG spacings, 4, it by can 48.77% be the seen stall compared that AoA when was to λthat18°./H = ofThe 9, the the maximum clean stall airfoil.AoA lift of When coefficientthe airfoilλ/H = was3,wasλ /16°, Hobtained= while7, and underwhenλ/H = 9,λthe/H the other = maximum5, whichVG spacings, liftwas coe increasedffi thecient stall increased byAoA 48.77% was by 18°.45.67%,compared The 48.32%,maximum to that and of 30.20%,liftthe cleancoefficient respectively. airfoil. was When obtained Therefore, λ/H = 3,when λ the/H maximum =λ 7,/H and = 5,λ / liftHwhich = coe 9, theffi wascient maximum increased of the airfoil lift by coefficient was48.77% the comparedlargestincreased when toby that λ45.67%,/H of= the5. 48.32%, On clean the airfoil. otherand 30.20%, hand, Whenthe respectivelyλ/H drag = 3, coeλ/Hffi. =Therefore,cient 7, and was λ/ theH the = worst 9,maximum the maximum when liftλ/H coefficient =lift9. coefficient In Table of the3, increaseditairfoil can be was seen by the 45.67%, that largest when 48.32%, whenλ/H λand=/H3, =30.20%, the 5. On drag the respectively coe otherfficient hand, of. Therefore, thethe airfoildrag coefficientthe decreased maximum was by lift 82.06%the coefficient worst compared when of theλ/ toH airfoilthat= 9. In of was Table the the clean 3, largest it airfoilcan be when at seen an λ AoAthat/H = when of5. 18On◦ .λthe In/H addition,other= 3, the hand, drag it decreasedthe coefficient drag coefficient by of 83.28% the airfoil was when thedecreasedλ /worstH = 5, when by 78.43%82.06% λ/H =whencompared 9. In Tableλ/H =to 3,7, that it and ca ofn by bethe 13.06%seen clean that airfoil when when atλ /λanH/H =AoA =9. 3, The theof 18°. drag lift–drag In coefficient addition, ratio of itof decreased the the airfoilairfoil by increaseddecreased 83.28% bywhen by 741.03%82.06% λ/H = comparedcompared5, by 78.43% to to thatwhen that of of λthe/ theH clean= clean7, and airfoil airfoil by 13.06% at atan an AoA when AoA of ofλ18°./H 18 =In◦ 9.when addition, The lift–dragλ/H it= decreased3, ratio by 821.86% of bythe 83.28% airfoil when increasedwhenλ/H = λ5,/H byby = 5,612.06%741.03% by 78.43% whencompared whenλ/H λ =to/H7, that= and 7, andof by the by 55.06% clean 13.06% whenairfoil whenλ at/H λan/=H AoA9. = 9. Theof 18° lift–drag when λ ratio/H = of3, theby 821.86% airfoil increased when λ/ Hby = 741.03%5, by 612.06% compared when to λ that/H = of 7, theand clean by 55.06% airfoil whenat an AoAλ/H = of 9. 18° when λ/H = 3, by 821.86% when λ/H = 5, by 612.06% when λ/H = 7, and by 55.06% when λ/H = 9. Appl. Sci. 2019, 9, 5495 17 of 22 Appl. Sci. 2020, 10, x FOR PEER REVIEW 18 of 24

a) 2.5 b) Clean c) Clean λ/H = 3 λ/H = 3 0.3 2.0 λ/H = 5 2 λ/H = 5 λ/H = 7 λ/H = 7 λ/H = 9 λ/H = 9 l 1.5 d C C 0.2 1.0 Clean 1

λ/H = 3 l

λ/H = 5 C 0.5 λ/H = 7 λ/H = 9 0.1 0.0 0 -10 0 10 20 30 0.0 0.1 0.2 0.3 C -0.5 α (°) d 0.0 -10 0 10 20 30 -1.0 α (°) -1 FigureFigure 17. 17. (a() aCurves) Curves of the of thelift liftcoefficient, coefficient, (b) drag (b) dragcoefficient, coeffi cient,and (c) and lift–drag (c) lift–drag ratio with ratio and with without and VGs.without VGs.

Table 4. Relative variation of Cl, Cd, and lift–drag ratio under different VG spacings. Table 4. Relative variation of Cl, Cd, and lift–drag ratio under different VG spacings. Stall Increase of Decrease of C at Increase of Lift–Drag Case d Case Stall Angle-of-AttackAngle-of-Attack Increase of MaximumMaximum ClC l Decrease of 18Cd◦ at 18° IncreaseRatio of Lift–Drag at 18◦ Ratio at 18° Clean 8° 0% 0% 0% Clean 8◦ 0% 0% 0% λ/H = 3 λ/H = 3 18° 18◦ 45.67% 45.67% 82.06% 82.06% 741.03% 741.03% λ/H = 5 λ/H = 5 18° 18◦ 48.77% 48.77% 83.28% 83.28% 821.86% 821.86% λ/H = 7 λ/H = 7 18° 18◦ 48.32% 48.32% 78.43% 78.43% 612.06% 612.06% λ/H = 9 λ/H = 916° 16◦ 30.20% 30.20%13.06% 13.06% 55.06% 55.06%

p InIn Figure Figure 18,18 ,the the surface surface pressure pressure coefficient coefficient (C (C)p distribution) distribution of ofthe the airfoil airfoil is presented. is presented. It can It can be seen that the curves of Cp distribution on the airfoil surface with and without VGs coincided at 0° be seen that the curves of Cp distribution on the airfoil surface with and without VGs coincided at 0◦ and 5° AoA. At AoAs of 10°, 15°, and 18°, the VGs postponed the pressure plateau to some extent. and 5◦ AoA. At AoAs of 10◦, 15◦, and 18◦, the VGs postponed the pressure plateau to some extent. However,However, when λ//H = 9,9, the the effect effect of of the the VGs VGs flow flow control control was the worst, and and the pressure plateau p appearedappeared earlier than in the other thre threee cases. It It can can be observed that the Cp curvescurves of of the the other other three three VG spacings basically coincided. At an AoA of 20°, the Cp curves and the position of the pressure VG spacings basically coincided. At an AoA of 20◦, the Cp curves and the position of the pressure p platform of λλ//HH == 99 werewere similarsimilar to to those those of of the the clean clean airfoil, airfoil, while while the theCp curvesC curves of the of otherthe other three three VGs VGs spacings were similar. At 22°, the Cp curves of λ/H = 3 and λ/H = 5 basically coincided with the spacings were similar. At 22◦, the Cp curves of λ/H = 3 and λ/H = 5 basically coincided with the clean clean airfoil, while λ/H = 7 exhibited the best effect. When the AoA was equal to 25°, the Cp curves of airfoil, while λ/H = 7 exhibited the best effect. When the AoA was equal to 25◦, the Cp curves of the theairfoil airfoil with with VGs VGs coincided coincided with with those those of the of the clean clean airfoil. airfoil. Figure 19 shows the curve of the total pressure coefficient distribution at the wake rake. It can be -1.5 seen that at AoAs of α = 0◦, 5◦, and 10◦, for Clean an airfoil with-2.0 VGs, the total pressure loss at the wakeClean rake λ/H = 3 λ/H = 3 was larger-1.0 because the generators increased λ/H = the 5 thickness-1.5 of the boundary layer and thus λ increased/H = 5 λ/H = 7 λ/H = 7 the viscous losses. When the AoA was 15◦ and 18◦, the total pressure loss of the airfoil with VGs was -0.5 λ/H = 9 -1.0 λ/H = 9 smaller than that of the clean airfoil. Amongα = 0° the four VG spacings, the total pressure loss ofα the = 5° airfoil p p -0.5 C with VGsC 0.0 was the largest when λ/H = 9, and under the other three spacings, the total pressure loss was 0.0 similar. At α = 20◦, the total pressure loss was the largest when λ/H = 9 and the smallest when λ/H = 7. 0.5 0.5 At α = 22◦, the total pressure loss was the largest when λ/H = 7, which was larger than that of the clean 1.0 airfoil, while1.0 the total pressure loss of λ/H = 7 was the smallest. When α = 25◦, the total pressure loss 1.5 was the same,0.00.20.40.60.81.0 with or without VGs. 0.0 0.2 0.4 0.6 0.8 1.0 x/C x/C

Appl. Sci. 2020, 10, x FOR PEER REVIEW 18 of 24

a) 2.5 b) Clean c) Clean λ/H = 3 λ/H = 3 0.3 2.0 λ/H = 5 2 λ/H = 5 λ/H = 7 λ/H = 7 λ/H = 9 λ/H = 9 l 1.5 d C C 0.2 1.0 Clean 1

λ/H = 3 l

λ/H = 5 C 0.5 λ/H = 7 λ/H = 9 0.1 0.0 0 -10 0 10 20 30 0.0 0.1 0.2 0.3 C -0.5 α (°) d 0.0 -10 0 10 20 30 -1.0 α (°) -1 Figure 17. (a) Curves of the lift coefficient, (b) drag coefficient, and (c) lift–drag ratio with and without VGs.

Table 4. Relative variation of Cl, Cd, and lift–drag ratio under different VG spacings.

Case Stall Angle-of-Attack Increase of Maximum Cl Decrease of Cd at 18° Increase of Lift–Drag Ratio at 18° Clean 8° 0% 0% 0% λ/H = 3 18° 45.67% 82.06% 741.03% λ/H = 5 18° 48.77% 83.28% 821.86% λ/H = 7 18° 48.32% 78.43% 612.06% λ/H = 9 16° 30.20% 13.06% 55.06%

In Figure 18, the surface pressure coefficient (Cp) distribution of the airfoil is presented. It can be seen that the curves of Cp distribution on the airfoil surface with and without VGs coincided at 0° and 5° AoA. At AoAs of 10°, 15°, and 18°, the VGs postponed the pressure plateau to some extent. However, when λ/H = 9, the effect of the VGs flow control was the worst, and the pressure plateau appeared earlier than in the other three cases. It can be observed that the Cp curves of the other three VG spacings basically coincided. At an AoA of 20°, the Cp curves and the position of the pressure platform of λ/H = 9 were similar to those of the clean airfoil, while the Cp curves of the other three VGs spacings were similar. At 22°, the Cp curves of λ/H = 3 and λ/H = 5 basically coincided with the

Appl.clean Sci. airfoil,2019, 9 while, 5495 λ/H = 7 exhibited the best effect. When the AoA was equal to 25°, the Cp curves18 of of 22 the airfoil with VGs coincided with those of the clean airfoil.

-1.5 Clean -2.0 Clean λ/H = 3 λ/H = 3 -1.0 λ/H = 5 -1.5 λ/H = 5 λ/H = 7 λ/H = 7 -0.5 λ/H = 9 -1.0 λ/H = 9 α = 0° α = 5° p p -0.5 C C 0.0 0.0 0.5 0.5 1.0 1.0 1.5 Appl. Sci. 2020, 0.00.20.40.60.81.010, x FOR PEER REVIEW 0.0 0.2 0.4 0.6 0.8 1.019 of 24 x/C x/C

-4 Clean -6 Clean VGs installation location λ/H = 3 λ/H = 3 λ/H = 5 λ/H = 5 -3 Δx≈88H λ/H = 7 -4 Δx≈46.6H λ/H = 7 λ/H = 9 λ/H = 9

-2 α = 10° p α = 15° C

p Δ Flow separation position of Clean p -1 C ≈−0.77（ kpa m ） -2 -1 Δ Δp x ≈−1.62 Δx 0 0 1 2 0.00.20.40.60.81.0 0.0 0.2 0.4 0.6 0.8 1.0 x/C x/C

-8 -8 Clean Clean λ/H = 3 λ/H = 3 -6 λ/H = 5 -6 λ/H = 5 λ/H = 7 λ/H = 7 Δx≈30H λ/H = 9 Δx≈20H λ/H = 9

-4 α = 18° p -4 α = 20° p C C -2 -2 Δp Δp ≈−2.4 ≈−2.96 Δx Δx 0 0

2 2 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 x/C x/C

-8 Clean -6 Clean λ/H = 3 λ/H = 3 -6 λ/H = 5 λ/H = 5 λ/H = 7 -4 λ/H = 7 Δx≈10H λ/H = 9 λ/H = 9 -4 α = 25° p α = 22° Flow separation position ≈ 0.18C p C C -2 -2

Δp ≈−3.95 0 0 Δx

2 2 0.00.20.40.60.81.0 0.00.20.40.60.81.0 x/C x/C

Figure 18. Cp distribution on the airfoil surface. Figure 18. Cp distribution on the airfoil surface.

Figure 19 shows the curve of the total pressure coefficient distribution at the wake rake. It can be seen that at AoAs of α = 0°, 5°, and 10°, for an airfoil with VGs, the total pressure loss at the wake rake was larger because the generators increased the thickness of the boundary layer and thus increased the viscous losses. When the AoA was 15° and 18°, the total pressure loss of the airfoil with VGs was smaller than that of the clean airfoil. Among the four VG spacings, the total pressure loss of the airfoil with VGs was the largest when λ/H = 9, and under the other three spacings, the total pressure loss was similar. At α = 20°, the total pressure loss was the largest when λ/H = 9 and the smallest when λ/H = 7. At α = 22°, the total pressure loss was the largest when λ/H = 7, which was larger than that of the clean airfoil, while the total pressure loss of λ/H = 7 was the smallest. When α = 25°, the total pressure loss was the same, with or without VGs. Appl. Sci. 2019, 9, 5495 19 of 22 Appl. Sci. 2020, 10, x FOR PEER REVIEW 20 of 24

Clean λ/H = 3 λ/H = 5 λ/H = 7 λ/H = 9 Clean λ/H = 3 λ/H = 5 λ/H = 7 λ/H = 9

1.8 α = 0° 1.8 α = 5° 1.8 α = 10° 1.8 α = 15° 1.5 1.5 1.5 1.5 1.2 1.2 1.2 1.2 (m) (m)

(m) (m) z

z 0.9 0.9 0.9 0.9 z z 0.6 0.6 0.6 0.6 0.3 0.3 0.3 0.3 0.0 0.0 0.0 0.0 0.8 0.9 1.0 0.8 0.9 1.0 0.7 0.8 0.9 1.0 1.1 0.6 0.8 1.0 C C C C p p p p Clean λ/H = 3 λ/H = 5 λ/H = 7 λ/H = 9 Clean λ/H = 3 λ/H = 5 λ/H = 7 λ/H = 9

1.8 α = 18° 1.8 α = 20° 1.8 α = 22° 1.8 α = 25° 1.5 1.5 1.5 1.5 1.2 1.2 1.2 1.2

(m) (m) (m) (m) 0.9 0.9 0.9 0.9 z z z z 0.6 0.6 0.6 0.6 0.3 0.3 0.3 0.3 0.0 0.0 0.0 0.0 0.4 0.6 0.8 1.0 0.4 0.6 0.8 1.0 0.0 0.3 0.6 0.9 1.2 0.0 0.4 0.8 1.2 C C C C p p p p FigureFigure 19. 19. DistributionDistribution of of total total pressure pressure coefficient coefficient at at the the wake wake rake. rake. 4. Conclusions 4. Conclusions When VGs are used for the flow control of wind turbine blades, they are always installed under a When VGs are used for the flow control of wind turbine blades, they are always installed under certain arrangement. In this paper, the LES method was used to simulate the boundary layer separation a certain arrangement. In this paper, the LES method was used to simulate the boundary layer flow with and without VGs in an adverse pressure gradient environment. The large-scale coherent separation flow with and without VGs in an adverse pressure gradient environment. The large-scale structure of the boundary layer separation caused by the adverse pressure gradient and its evolution coherent structure of the boundary layer separation caused by the adverse pressure gradient and its process in the turbulent flow field were analyzed. The effect of different VG spacings on the suppression evolution process in the turbulent flow field were analyzed. The effect of different VG spacings on of the boundary layer separation were compared through the distance between vortex cores, the kinetic the suppression of the boundary layer separation were compared through the distance between energy of the fluid in the boundary layer, and the pressure loss coefficient. Subsequently, the effect of vortex cores, the kinetic energy of the fluid in the boundary layer, and the pressure loss coefficient. VG spacings on the lift–drag characteristics, airfoil surface pressure distribution, and airfoil pressure Subsequently, the effect of VG spacings on the lift–drag characteristics, airfoil surface pressure loss were investigated in a wind tunnel using the DU93-W-210 airfoil as the research object. distribution, and airfoil pressure loss were investigated in a wind tunnel using the DU93-W-210 According to the relationship between the vortex core radius and the distance between the vortex airfoil as the research object. cores, when the VG spacing was λ/H = 3, the distance between the vortex cores ∆z/2 was smaller than the vortexAccording core radiusto the rrelationshipin most positions between along the the vort flowex direction. core radius Therefore, and the this distance spacing between inhibited the the vortexdevelopment cores, when of vortices. the VG When spacingλ/H was= 7 andλ/H 9,= ∆3,z /the2 was distance always between larger than the rvortex. When coresλ/H =Δz5,/2 at wasx/H smaller= 10, the than∆z/ 2the and vortex the r werecore approximatelyradius r in most equal. positions Thus, along the λ/ Hthe= 5flow spacing direction. was more Therefore, suitable this for spacingflow control. inhibited The the increase development in fluid of kinetic vortices. energy When in theλ/H boundary = 7 and 9, layer Δz/2 was was inversely always larger proportional than r. Whento the λ VG/H = spacing. 5, at x/H However, = 10, the whenΔz/2 and the VGthe spacingr were approximately was λ/H = 3,the equal. distance Thus, between the λ/H vortices= 5 spacing was wassmall more and suitable the vortex for core flow was control. far from The the increase wall, resulting in fluid kinetic in the high-energy energy in the fluid boundary in the downstream layer was inverselyboundary proportional layer being higherto the VG from spacing. the wall. However, In the near-wall when the region, VG spacing the kinetic was energy λ/H = of3, the fluiddistance was betweenthe largest vortices when wasλ/H =small5, especially and the vortex at the x core/H = wa35s cross-section. far from the Whenwall, resultingλ/H = 5, thein theC∆ Phigh-energybetween the fluidinlet in and the outlet downstream of the computational boundary layer domain being was high the smallest,er from the which wall. was In by the 30.95% near-wall lower region, than that the in kineticthe computational energy of the domain fluid was without the VGs.largest when λ/H = 5, especially at the x/H = 35 cross-section. WhenIn λ/ theH = wind5, the tunnel CΔP between experimental the inlet results, and outlet it was of found the computational that the stall AoA domain of the was airfoil the withsmallest, VGs whichwas increased was by 30.95% by 10◦ comparedlower than to that that in of the the computational clean airfoil. When domainλ/H without= 5, the VGs. maximum lift coefficient of the airfoil with VGs increased by 48.77%, which was the largest increase. Furthermore, at an AoA In the wind tunnel experimental results, it was found that the stall AoA of the airfoil with VGs of 18◦, when λ/H = 5, the drag coefficient decreased by 83.28%, which was the largest reduction. At was increased by 10° compared to that of the clean airfoil. When λ/H = 5, the maximum lift an AoA of 18◦, the lift–drag ratio of the airfoil increased by 741.03% when λ/H = 3, 821.86% when coefficient of the airfoil with VGs increased by 48.77%, which was the largest increase. Furthermore, at an AoA of 18°, when λ/H = 5, the drag coefficient decreased by 83.28%, which was the largest reduction. At an AoA of 18°, the lift–drag ratio of the airfoil increased by 741.03% when λ/H = 3, Appl. Sci. 2019, 9, 5495 20 of 22

λ/H = 5, 612.06% when λ/H = 7, and 55.06% when λ/H = 9. Consequently, it can be deduced that, when the VG spacing was λ/H = 5, the comprehensive effect of airfoil flow control was the best. The optimization of the VG spacing was essentially the optimization of vortex scale and vortex core spacing. The vortex scale and vortex core spacing were related to the VGs installation angle, geometric height, and arrangement spacing.

Author Contributions: X.-k.L., W.L., T.-j.Z., and P.-m.W. conceived the research idea. X.-k.L. and X.-d.W. performed the numerical simulation. P.-m.W. and T.-j.Z. analyzed data and numerical results. All authors contributed to the writing, editing, and revising of this manuscript. Funding: This work was jointly supported by the National Natural Science Foundation of China (no. 51806221) and the Development Plan of Key Scientific and Technological Projects of China Huadian Engineering Co., LTD (CHEC) (no. CHECKJ 19-02-03). Conflicts of Interest: The authors declare no conflict of interest.

Nomenclature

∆t Unsteady computational physical time step (s) β Angle between vortex generators and incoming flow (◦) l Vortex generators chord length (mm) H Vortex generators height (mm) S Distance between the trailing edge of the vortex generators in the opposite direction λ Distance between the trailing edge of the vortex generators in the same direction C∆p Pressure loss coefficient at the inlet and outlet of the calculation domain Pinlet Total pressure at the inlet Poutlet Total pressure at the outlet RE The value obtained using the Richardson extrapolation R The ratio of errors p The order of accuracy Cp Airfoil surface static pressure coefficient Cl Lift coefficient of airfoil Cd Drag coefficient of airfoil Ulocal Local velocity U Inlet velocity Q Vortex core criterion Ω Vortex core vorticity r Vortex core radius ∆z The distance between the two vortex cores Time-averaged velocity Clean Airfoil without VGs

Abbreviations

VGs Vortex generators LES Large eddy simulation AoA Angle-of-attack CFD Computational fluid dynamics NCEPU North China Electric Power University NPU Northwest Polytechnic University Delft Delft University APG Adverse pressure gradient ZPG Zero pressure gradient Appl. Sci. 2019, 9, 5495 21 of 22

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