Computational Modelling of Rectangular Sub-Boundary Layer Vortex Generators

applied sciences

Article Computational Modelling of Rectangular Sub-Boundary Layer Vortex Generators

Unai Fernandez-Gamiz 1,* ID , Iñigo Errasti 1 ID , Ruben Gutierrez-Amo 1, Ana Boyano 2 and Oscar Barambones 3 ID 1 Nuclear Engineering and Fluid Mechanics Department, University of the Basque Country, Nieves Cano 12, 01006 Vitoria-Gasteiz, Araba, Spain; [email protected] (I.E.); [email protected] (R.G.-A.) 2 Department of Mechanical Engineering, University of the Basque Country (UPV/EHU), Nieves Cano 12, 01006 Vitoria-Gasteiz, Spain; [email protected] 3 Automatic control and System Engineering Department, University of the Basque Country, Nieves Cano 12, 01006 Vitoria-Gasteiz, Araba, Spain; [email protected] * Correspondence: [email protected]; Tel.: +34-945-014-066

Received: 22 November 2017; Accepted: 16 January 2018; Published: 19 January 2018

Abstract: Vortex generators (VGs) are increasingly used in the wind turbine manufacture industry as flow control devices to improve rotor blade aerodynamic performance. Nevertheless, VGs may produce excess residual drag in some applications. The so-called sub-boundary layer VGs can provide an effective flow-separation control with lower drag than the conventional VGs. The main objective of this study is to investigate how well the simulations can reproduce the physics of the flow of the primary vortex generated by rectangular sub-boundary layer VGs mounted on a flat plate with a negligible pressure gradient with an angle of attack of the vane to the oncoming flow of β = 18◦. Three devices with aspect ratio values of 2, 2.5 and 3 are qualitatively and quantitatively compared. To that end, computational simulations have been carried out using the RANS (Reynolds averaged Navier–Stokes) method and at Reynolds number Re = 2600 based on the boundary layer momentum thickness θ at the VG position. The computational results show good agreement with the experimental data provided by the Advanced Aerodynamic Tools of Large Rotors (AVATAR) European project for the development and validation of aerodynamic models. Finally, the results indicate that the highest VG seems to be more suitable for separation control applications.

Keywords: vortex generators; ﬂow control; computational ﬂuid dynamics; Computational Fluid Dynamics (CFD)

1. Introduction In order to achieve the aim of 100% renewable energy consumption, wind energy, as a leader toward the way of renewable energy, is developing rapidly all over the world. To decrease the levelized cost of energy (LCOE), the size of a single wind turbine has been increased to 10 MW nowadays, and it will increase further in the near future. Large wind turbines and their related wind farms have many challenges in aerodynamics, aero-elasticity and aero-acoustics. Therefore, the introduction of new designs and upgrading methods will be also needed to make this possible [1,2]. According to Aramendia et al. [3,4] and Fernandez-Gamiz et al. [5], either the use of passive controllers (vortex generators (VGs), microtabs, spoilers, etc.) or active controllers (trailing-edge ﬂaps, synthetic jets and air jet vortex generators) can be introduced. One of the best options is the introduction of VGs on the blades to improve the aerodynamic performance needed. The use of this passive ﬂow device helps to reduce the load distribution, and the blade has to undergo and obtain the optimal creation of energy. Øye [6] compared the measured power curves with VGs and without on a 1-MW wind turbine. Although quite rough methods were used for the VG design optimization,

Appl. Sci. 2018, 8, 138; doi:10.3390/app8010138 www.mdpi.com/journal/applsci Appl. Sci. 2018, 8, 138 2 of 16 the experiment showed that, for a stall-regulated wind turbine, power increased nearly 24% by using VGs through field tests. Furthermore, Sullivan [7] conducted an experiment on a 2.5-MW wind turbine to test the effects of adding VGs on the power conversion performance. An increase of 11% in the annual energy production was found. In the work of Fernandez-Gamiz et al. [8], Blade Element Momentum BEM-based computations were carried out on the National Renewable Energy Laboratory (NREL) 5-MW baseline wind turbine with and without flow control devices. The results obtained from the clean wind turbine without any device for flow controlling were compared with the ones obtained from the wind turbine equipped with vortex generators and Gurney flaps. A best configuration case is proposed, which has the largest increase of the average power output. In that case, increments on the average power output of 10.4% and 3.5% have been found at two different wind speed realizations VGs were first introduced by Taylor [9], and their principle of operation relies on the increased mixing between the external stream and the boundary layer due to longitudinal vortices produced by the VGs. Fluid particles with high momentum in the streamwise direction mix with the low-momentum viscous flow inside the boundary layer; therefore, the mean streamwise momentum of the fluid particles in the boundary layer is increased. The process provides a continuous source of momentum to counter the natural boundary layer momentum decrease and the growth of its thickness caused by viscous friction and adverse pressure gradients (Doerffer et al. [10] and Steijl et al. [11]). Vortex generators can reduce or eliminate flow separation in moderate adverse pressure gradient environments (Velte et al. [12,13]). Even when separation does occur for cases of a large adverse pressure gradient, the mixing action of trailing vortices will restrict the reversed flow region in the shear layer and help maintain some pressure recovery along the separated flow. Thus, the effects of separation may be minimized or even removed. Fernandez-Gamiz et al. [14] and Urkiola et al. [15] studied the behavior of a rectangular VG on a flat plane and the streamwise vortices produced by them to investigate how the physics of the wake behind VGs in a negligible streamwise pressure gradient flow can be reproduced in Computational Fluid Dynamics CFD simulations and their accuracy in comparison with experimental observations. In the work carried out by Gao et al. [16] and Baldacchino et al. [17] on a 30% thick DU97-W-300 airfoil (Delft University of Technology, Delft, The Nederlands), the maximum lift coefficient was substantially increased due to the implementation of passive VGs. When the angle of attack increases, both lift and drag coefficients rise up to values higher than the ones reached in steady state conditions. The concept of micro vortex generators was most probably first introduced by Keuthe [18]. In that study, wave-type micro VGs with a height of 27% and 42% of the local boundary layer (BL) thickness were mounted on an airfoil to decrease trailing edge noise by suppressing the formation of a Karman vortex street and by reducing the velocity deficit in the airfoil wake. Since the late 1980s, these devices appeared in the literature under different names such as sub-boundary layer vortex generator (SBVG), presented by Holmes et al. [19], the submerged vortex generator of Lin et al. [20], the low-profile vortex generator Martinez-Filgueira et al. [21] and the micro vortex generator (Lin [22]). As stated in the review of Kenning et al. [23], the potential applications of VGs and SBVGs include control of leading edge separation, shock-induced separation and smooth surface separation. Vortex generators are applied on wind turbine blades with the major aim to delay or prevent the separation of the flow and to decrease the roughness sensitivity of the blade. They are usually mounted in a spanwise array on the suction side of the blade and have the advantage that they can be added as a post-production fix to blades that do not perform as expected. Therefore, adding VGs is a straightforward solution to improve the rotor performance (Bragg et al. [24]). The main contribution of this work is the computational study of the primary vortex generated by three different rectangular VGs, where it has been found that the highest vane is the most suitable actuator for flow control applications. The goal of this study is to investigate how well the simulations can reproduce the physics of the flow behind a rectangular VG to characterize the primary vortex generated by the vane mounted on a flat plate with three different device heights. The aspect ratio (AR) Appl. Sci. 2018, 8, 138 3 of 16

Appl.of the Sci. vane 2018, 8 defined, 138 as the relation between the height and length of the VG will consequently3 vary,of 16 maintaining the angle of attack constant. The baseline VG has an aspect ratio of ARH = 2.5, and two twoheight height variations variations are are also also investigated, investigated, those those corresponding corresponding to to AR ARH2H2= = 2 2 and and AR ARH1H1 = 3, as as sketched sketched inin Figure Figure 11.. For this purpose,purpose, computational simulationssimulations have been carried out using thethe RANSRANS (Reynolds(Reynolds averaged averaged Navier–Stokes) Navier–Stokes) method method and and at at a a Reynolds Reynolds number number Re Re = = 2600. 2600. The The case case consists consists ofof a a single single vortex vortex generator generator on on a a flat flat plate plate with with th thee angle angle of of attack attack of of the the vane vane to to the the oncoming oncoming flow flow ββ == 18°. 18◦ .The The flow flow over over the the flat flat plate plate without without the the VG VG has has been been previously previously simulated simulated to to calculate calculate the the boundaryboundary layer layer thickness thickness at at the the VG VG position. position.

FigureFigure 1. 1. SketchSketch of of the the vortex vortex generator generator (VG) (VG) dimensions dimensions with with respect respect to the to local the local boundary boundary layer layer(not to(not scale). to scale).

2.2. Baseline Baseline Experimental Experimental Data Data TheThe current studystudy is is based based on on Advanced Advanced Aerodynamic Aerodynamic Tools Tools of Large of RotorsLarge (AVATAR)Rotors (AVATAR) European Europeanproject, and project, the parameters and the parameters used for the used validation for th ofe validation the computational of the computational results are the results following are ones: the following ones: • Streamwise velocity profiles at different locations (AVATAR Task 3.1 [25]) • • StreamwiseVelocity fields velocity at streamwise profiles at planes differe 10H,nt locations 25H and (AVATAR 50H (AVATAR Task Task3.1 [25]) 3.1 [ 25]) • • VelocityFields of fields the normalized at streamwise vorticity planes at 10H, different 25H streamwiseand 50H (AVATAR planes (AVATAR Task 3.1 Task[25]) 3.2, [26]) • Fields of the normalized vorticity at different streamwise planes (AVATAR Task 3.2, [26]) • Turbulence kinetic energy fields at streamwise planes (AVATAR Task 3.2 [26]) • Turbulence kinetic energy fields at streamwise planes (AVATAR Task 3.2 [26]) Taking into account the previous configuration and in order to characterize the primary vortex Taking into account the previous configuration and in order to characterize the primary vortex generated by the three different VGs, the following parameters have been proposed: generated by the three different VGs, the following parameters have been proposed: • Streamwise velocity profiles at different streamwise locations. • Streamwise velocity profiles at different streamwise locations. • Primary vortex vertical and lateral positions to define the vortex trajectory. • Primary vortex vertical and lateral positions to define the vortex trajectory. • Peak vorticity ωx,max development. • Peak vorticity ωx,max development. •• WallWall shear shear stress (WSS). AccordingAccording to to the the experimental experimental data data available available in in the the AVATAR AVATAR project project and and to to reproduce reproduce the the experimentsexperiments of of the the VG VG on on a flat a flat plate plate performed performed in that in thatproject, project, the numerica the numericall simulations simulations have been have carriedbeen carried out at outa Reynolds at a Reynolds number number Re = 26 Re00 = based 2600 based on local on BL local momentum BL momentum thickness thickness θ = 2.4θ =mm 2.4 and mm withand witha free a freestream stream velocity velocity of U of∞U =∞ 15m/s.= 15 m/s. A negligible A negligible pressure pressure gradient gradient onon the the plate plate isis assumed. assumed. ◦ TheThe angle angle of ofincidence incidence of the of vane the vane to the to oncoming the oncoming flow is flow18°. The is 18calculation. The calculation of the local ofBL themomentum local BL thicknessmomentum θ was thickness made byθ was the madeapplic byation the of application Equation (1): of Equation (1): Z ∞ u u θ== x 11 −− xdy (1)(1) 0 U∞ U∞ where ux is the streamwise velocity component, U∞ the free stream velocity and y the vertical where ux is the streamwise velocity component, U∞ the free stream velocity and y the vertical coordinatecoordinate normal normal to to the the wall. wall. InIn order order to to validate validate the the numerical numerical model model of of the the VG, VG, the the results results of of the the numerical numerical simulations simulations are are comparedcompared to to the the experimental experimental data data of of the the AVATAR AVATAR Project [25,26]. [25,26]. The The experiments experiments were were carried carried out out in the Boundary Layer Wind Tunnel of the Delft University of Technology. The tunnel can attain a maximum speed of 38 m/s in the wide-walled test section of 1.5 × 0.25 m2. The large separation of the side walls (1.5 m) minimizes end effects on the flow region of interest along the centerline zone. An adjustable back wall allows adjustment of the pressure gradient, ensuring a truly null pressure Appl. Sci. 2018, 8, 138 4 of 16 in the Boundary Layer Wind Tunnel of the Delft University of Technology. The tunnel can attain a maximum speed of 38 m/s in the wide-walled test section of 1.5 × 0.25 m2. The large separation of the side walls (1.5 m) minimizes end effects on the flow region of interest along the centerline zone. An adjustable back wall allows adjustment of the pressure gradient, ensuring a truly null pressure gradient when desired. The turbulence level at maximum free stream velocity was determined as Appl. Sci. 2018, 8, 138 4 of 16 0.5%. Vortex generator dimensions were designed according to the previous research made by m, wheregradient the rectangular when desired. vortex The generators turbulence werelevel at designed maximum according free stream to thevelocity study was of determined Godard et as al. [28] and are0.5%. summarized Vortex generator in Table dimensions1. were designed according to the previous research made by Baldacchino et al. [27], where the rectangular vortex generators were designed according to the study Tableof Godard 1. etVortex al. [28] generator and are summarized geometry inin Table the Advanced 1. Aerodynamic Tools of Large Rotors (AVATAR) project. Table 1. Vortex generator geometry in the Advanced Aerodynamic Tools of Large Rotors (AVATAR) project.Vortex Generator (VG) Property Symbol Value (mm) Size in h Units VortexVG Generator height (VG) Property Symbol H Value (mm) 5.0 Size in h Units 1 Vane lengthVG height L H 5.0 12.5 1 2.5 Distance betweenVane VG length pairs D L 12.5 30 2.5 6 Trailing edge separation d 12.5 2.5 Distance between VG pairs D 30 6 Incident angle β 18◦ - Trailing edge separation d 12.5 2.5 Local boundary layer thickness δ 20 4 Incident angle β 18° - Local boundary layer thickness δ 20 4 The placement of the VGs is such that flow impinges on the vanes in a divergent manner, producingThe counter-rotating, placement of the common VGs is such down-flow that flow embedded impinges on vortices. the vanes For in each a divergent test case, manner, 25 pairs of rectangularproducing VGs counter-rotating, were mounted common in an array down-flow configuration, embedde sided vortices. by side, For as showneach test in case, Figure 252 pairs, covering of a spanwiserectangular distance VGs of were 0.75 mounted m and centered in an array on configuration, the tunnel centerline. side by side, This as wasshown done in Figure in order 2, covering to minimize a spanwise distance of 0.75 m and centered on the tunnel centerline. This was done in order to end-effects from the finite array. The vortex generator height is H = 5 mm and considering a negligible minimize end-effects from the finite array. The vortex generator height is H = 5 mm and considering pressurea negligible gradient. pressure gradient.

Figure 2. Vortex generator array layout. Figure 2. Vortex generator array layout. 3. Computational Setup 3. Computational Setup The present study consists of a rectangular VG positioned on a flat plate with an incident angle Theto the present oncoming study flow. consists The height of a of rectangular the VG located VG at positioned the flat plate on in a flatthe simulations plate with anis going incident to be angle to thedifferent, oncoming and flow.the AR The will heightconsequently of the change, VG located whereas at the the angle flat plateof attack in will the remain simulations constant. is goingThe to be different,ARs of the and three the cases AR willare AR consequentlyH2 = 2, ARH = 2.5 change, and AR whereasH1 = 3, and the the angle heights of attackare going will to remainbe H2 = 4.16, constant. H = 5 and H1 = 6.25 mm, respectively. The computational domain dimensions are represented in The ARs of the three cases are ARH2 = 2, ARH = 2.5 and ARH1 = 3, and the heights are going to Figure 3 normalized by the baseline VG case height H. be H = 4.16, H = 5 and H = 6.25 mm, respectively. The computational domain dimensions are 2 Wake symmetry behind1 the VGs is assumed in the current simulations. Thus, the computational represented in Figure3 normalized by the baseline VG case height H. domain includes only one VG inclined to the oncoming flow instead of a pair. In that way, meshing Wakeand computational symmetry behind time can the be VGsconsiderably is assumed reduced. in the Figure current 2 illustrates simulations. in green Thus, color the the computational spanwise domainlocations includes of the only domain one VG consisting inclined of to only the one oncoming vane. The flow symmetry instead ofassumption a pair. In used that way,in the meshing present and computations can be justified by the previous studies of Sorensen et al. [29] and Velte et al. [12]. Appl. Sci. 2018, 8, 138 5 of 16 computational time can be considerably reduced. Figure2 illustrates in green color the spanwise locations of the domain consisting of only one vane. The symmetry assumption used in the present computationsAppl. Sci. 2018 can, 8, 138 be justified by the previous studies of Sorensen et al. [29] and Velte et al. [512 of ].16

Appl. Sci. 2018, 8, 138 5 of 16

FigureFigure 3. Sketch 3. Sketch of the of the computational computational domain. domain. DimensionsDimensions are are scaled scaled byby the the baseline baseline VG VGheight height H H (not to scale). (not to scale). Figure 3. Sketch of the computational domain. Dimensions are scaled by the baseline VG height H The computational domain is divided into 28 blocks. The mesh has been refined near the VG (not to scale). Theand computationalin the corners of domain the vane is where divided the intovelocity 28 blocks. gradients The are mesh large. has In beenregions refined far away near from the the VG and VG and the wake, the mesh density is lower. Five blocks are located around the VG and six blocks in the cornersThe computational of the vane where domain the is velocity divided gradientsinto 28 blocks. are large. The mesh In regions has been far refined away fromnear the VG VG and downstream of the vane to capture the generated primary vortex. The same block-based meshing the wake,and in the the mesh corners density of the is vane lower. where Five the blocks velocity are gradients located around are large. the In VG regions and six far blocksaway from downstream the strategy as in the study of Urkiola et al. [15] has been followed. The total amount of cells is eight of theVG vane and to the capture wake, the mesh generated density primary is lower. vortex. Five blocks The same are located block-based around meshingthe VG and strategy six blocks as in the million, with a height of the first cell of Δy/H = 3.23 × 10−6, normalized according the baseline VG studydownstream of Urkiola etof al.the [ 15vane] has to beencapture followed. the generate Thed total primary amount vortex. of cellsThe same is eight block-based million, withmeshing a height height. Around the vane, the mesh has 1.7 million cells, while the mesh downstream the VG for of thestrategy first cell as ofin the∆y/H study = 3.23of Urkiola× 10− et6, al. normalized [15] has been according followed. the The baseline total amount VG height. of cells Aroundis eight the capturing the wake has approximately 2.4 million cells; see Figure 4. In order to resolve the boundary million, with a height of the first cell of Δy/H = 3.23 × 10−6, normalized according the baseline VG vane,layer, the mesh cell clustering has 1.7 million has been cells, used while close to the the mesh wall, downstreamand the wall dimensionless the VG for capturing distance of the the wake first has height. Around the vane, the mesh has 1.7 million cells, while the mesh downstream the VG for approximatelylayer of cells 2.4 is less million than cells;y+ < 1. see Figure4. In order to resolve the boundary layer, cell clustering capturing the wake has approximately 2.4 million cells; see Figure 4. In order to resolve the boundary has been used close to the wall, and the wall dimensionless distance of the first layer of cells is less layer, cell clustering has been used close to the wall, and the wall dimensionless distance of the first than y+ < 1. layer of cells is less than y+ < 1.

Figure 4. View of the meshing around the rectangular VG.

Each surface of the domain has been assigned to a type of boundary condition. The vane’s four Figure 4. View of the meshing around the rectangular VG. different patches andFigure the bottom 4. View of the of thedomain meshing were around defined the as rectangulara wall with VG.a non-slip condition. The roof of the domain and the two lateral surfaces were defined as slip surfaces (symmetrical Each surface of the domain has been assigned to a type of boundary condition. The vane’s four different patches and the bottom of the domain were defined as a wall with a non-slip condition. The roof of the domain and the two lateral surfaces were defined as slip surfaces (symmetrical Appl. Sci. 2018, 8, 138 6 of 16

Each surface of the domain has been assigned to a type of boundary condition. The vane’s four different patches and the bottom of the domain were defined as a wall with a non-slip Appl. Sci. 2018, 8, 138 6 of 16 condition. The roof of the domain and the two lateral surfaces were defined as slip surfaces (symmetricalhypothesis). The hypothesis). velocity inlet The was velocity chosen inlet for the was entr choseny of the for fluid the and entry pressure of the outlet fluid andfor the pressure exit of outletthe fluid for downstream the exit of the the fluid VG. downstream the VG. The quality of the mesh was evaluatedevaluated by fivefive mainmain indicatorsindicators to analyze whether it can be classifiedclassified as a high quality mesh; seesee Table2 2.. ThisThis setset ofof parametersparameters isis aa mixmix ofof industryindustry standards,standards, solver manuals and academia standards and should consequently not be regarded as the only choice of parameter selection. Equiangular skewness is an indicator of how optimal the cell shape is related toto the corner angles.angles. For hexahedral cells, skewness should not exceed 0.85 to obtain a fairly accurate solution. The cell aspect ratio of a cell is typically the ratio between thethe widthwidth andand height.height. For critical flowflow areas, exceptexcept thosethose closeclose toto thethe wall,wall, thethe cellcell aspectaspect ratioratio shouldshould notnot exceedexceed anan averageaverage ofof 10.10.

Table 2.2. Quality meshingmeshing parameters.parameters.

IndicatorIndicator Acceptable Acceptable ValuesValues Current Research Research Values Values CellCell aspect aspect ratio ratio 1–10 5.92 5.92 EquiangularEquiangular skewness skewness <0.85 0.169 0.169 MaximumMaximum included included angle angle <120<120°◦ 105.24 105.24°◦ ◦ ◦ MinimumMinimum included included angle angle >20 >20° 74.75 74.75°

Figure5 5 represents represents thethe wall wall y+ y+ ﬁeldfield distributiondistribution onon thethe VGVG and and bottom bottom walls. walls. ForFor thethe currentcurrent study, thethe maximummaximum valuevalue ofof y+y+ correspondscorresponds toto 0.3660.366 andand itsits averageaverage isis 0.044.0.044.

Figure 5. Wall y+ field distribution on the VG and bottom walls. Figure 5. Wall y+ field distribution on the VG and bottom walls. In this work, the open source code OpenFOAM (Version 2.4.0, The OpenFOAM Foundation Ltd., London,In this UK) work, [30] thehas openbeen sourceused for code simulating OpenFOAM a rectangular (Version 2.4.0,VG on The a flat OpenFOAM plate with Foundation negligible Ltd.,pressure London, gradient. UK) This [30] hasCFD been code used is an for object-oriented simulating a rectangularlibrary written VG in on C++ a flat to platesolve withcomputational negligible pressurecontinuum gradient. mechanics This problems. CFD code The is an solver object-oriented potential Foam, library which written solves in C++ potential to solve flows, computational was used continuumto generate mechanicsstarting fields problems. (initia Thelization solver of potentialfields) in Foam,order whichto speed solves up potentialthe convergence flows, was process. used toThis generate solver is starting suitable fields to generate (initialization initial condit of fields)ions for in ordermore advanced to speed upsolvers the convergencesuch as the one process. used Thisin the solver present is suitable work named to generate simpleFoam. initial conditions The simple forFoam more solver advanced has been solvers applied such for as thesteady-state, one used inincompressible the present work and turbulent named simpleFoam. flows using Thethe simpleFoamRANS (Reynolds solver averaged has been Navier–Stokes) applied for steady-state, equations. incompressibleSecond order discretization and turbulent schemes flows usingwere employed the RANS in (Reynolds the CFD simulations. averaged Navier–Stokes) The k-omega SST equations. (shear Secondstress transport) order discretization turbulence schemesmodel developed were employed by Ment iner the [31] CFD was simulations. used for all The the k-omegacomputations. SST (shear This stressturbulence transport) model turbulence is a combination model of developed two models: by Wilcox’s Menter [ 31k-ω] wasmodel used for forthe allnear the wall computations. region and Thisthe k- turbulenceε model for model the outer is a combinationregion and in of free two shear models: flows. Wilcox’s k-ω model for the near wall region and theSimulations k-ε model were for the performed outer region on a andpersonal in free server-clustered shear flows. parallel machine with Intel® Core i7- 6700 CPU 3.40 GHz × 8 cores and 32 GB RAM on 64-bit Linux. The domain was automatically divided into eight subdomains to solve in parallel and to reduce the simulation time. The computational cost was approximately 12 days per simulation. A mesh independency study has been done with the boundary layer velocity profile at the plane 10 H downstream of the VG and at z = 0 cross-wise position. Figure 6a shows a comparison between Appl. Sci. 2018, 8, 138 7 of 16

Simulations were performed on a personal server-clustered parallel machine with Intel® Core i7-6700 CPU 3.40 GHz × 8 cores and 32 GB RAM on 64-bit Linux. The domain was automatically divided into eight subdomains to solve in parallel and to reduce the simulation time. The computational cost was approximately 12 days per simulation. A mesh independency study has been done with the boundary layer velocity profile at the plane 10 HAppl. downstream Sci. 2018, 8, 138 of the VG and at z = 0 cross-wise position. Figure6a shows a comparison7between of 16 the CFDthe CFD curves curves of three of three studied studied meshes: meshes: 2 2 millionmillion (coarse), 4 4million million (medium) (medium) and and 8 million 8 million (fine) (fine) cells forcells the for baselinethe baseline case case with with a VGa VG height height of of HH == 5 mm. mm. Figure Figure 6b6b represents represents the the BL BLvelocity velocity profiles profiles of theof fine the meshfine mesh (blue) (blue) versus versus the the experimental experimental oneone (black) provided provided by by [25]. [25 ].

(a) (b) 30 30

25 25

20 20

15 15

10 10 Wall-normal position y (mm) position Wall-normal

5 5

0 0 0 0.5 1 1.5 0 0.5 1 1.5 u /U [-] u /U∞ [-] x ∞ x

FigureFigure 6. Comparison 6. Comparison of theof the normalized normalizedstreamwise streamwise ve velocitylocity profile profile at atthe the 10H 10H downstream downstream plane plane position and spanwise position of z = 0 corresponding to the baseline case of H = 5 mm. (a) CFD curves position and spanwise position of z = 0 corresponding to the baseline case of H = 5 mm. (a) CFD for three different meshes: coarse (green), medium (red) and fine (blue); (b) Boundary layer (BL) curves for three different meshes: coarse (green), medium (red) and fine (blue); (b) Boundary layer (BL) velocity profiles of the fine mesh (blue) versus the experimental one (black). velocity profiles of the fine mesh (blue) versus the experimental one (black). Verification of sufficient mesh resolution was performed based on the Richardson extrapolation Verificationmethod and applied of sufficient to the meshnormalized resolution peak vorticity was performed ωx/(U∞/H) based at the on plane the position Richardson of 10H extrapolation behind the vane. Table 3 shows the results of the mesh independency study. A monotonic convergence method and applied to the normalized peak vorticity ωx/(U∞/H) at the plane position of 10H behind the vane.was achieved. Table3 shows the results of the mesh independency study. A monotonic convergence was achieved. Table 3. Results of the mesh independency study 1.

Table 3. Results Mesh Resolution of the mesh independency Richardson study Extrapolation1. Coarse Medium Fine p R RE ωx/(U∞/H) 0.35Mesh Resolution 0.62 0.66 2.75 Richardson 0.15 Extrapolation0.66 1 RE represents the extrapolatedCoarse solution, Medium R the ratio Fine of errors p and p the R order of accuracy. RE ω /(U /H) 0.35 0.62 0.66 2.75 0.15 0.66 The normalizedx ∞ streamwise velocity curve of the fine mesh and the experimental one presented 1 in Figure 6bRE fit representsreasonably the well. extrapolated This higher solution, resolu Rtion the ratiomesh of has errors been and used p the for order the current of accuracy. computations and applied to the three low profile vanes H, H1 and H2. The normalized streamwise velocity curve of the fine mesh and the experimental one presented in Figure4.6 Resultsb fit reasonably well. This higher resolution mesh has been used for the current computations and appliedNumerical to the three simulations low profile of the vanes vortex H, generating H1 and H vane2. on a flat plate were performed. Three dimensions of a single low-profile vane H = 5 mm, H1 = 6.25 mm and H2 = 4.16 mm at an incident 4. Results angle to the oncoming flow of β = 18° were computed and compared with experimental results. The Numericalextraction of simulationsthe data from ofthe the computations vortex generating was conducted vane in ona similar a flat way plate to the were procedure performed. described in [14], in planes normal to the wall downstream of the VG to capture the development of Three dimensions of a single low-profile vane H = 5 mm, H1 = 6.25 mm and H2 = 4.16 mm at an incidentthe vortex. angle Table to the4 shows oncoming the height flow H of theβ = baseline 18◦ were VG computedand the heights and in compared the other simulated with experimental cases H1 and H2. The VG H1 has been designed with an aspect ratio AR = 2, which is the highest one, and results. The extraction of the data from the computations was conducted in a similar way to the the VG H2 with an aspect ratio AR = 3.

Appl. Sci. 2018, 8, 138 8 of 16 procedure described in [14], in planes normal to the wall downstream of the VG to capture the development of the vortex. Table4 shows the height H of the baseline VG and the heights in the other simulated cases H1 and H2. The VG H1 has been designed with an aspect ratio AR = 2, which is the highest one, and the VG H2 with an aspect ratio AR = 3.

Table 4. Vortex generator dimensions and aspect ratios (AR). Appl. Sci. 2018, 8, 138 8 of 16

Table 4. VortexVG generator h/δ dimensionsHeight(mm) and aspect ARratios (AR). H1 0.31 6.25 2.0 VG h/δ Height (mm) AR H 0.25 5.00 2.5 H1 0.31 6.25 2.0 H2 0.21 4.16 3.0 H 0.25 5.00 2.5 H2 0.21 4.16 3.0 First of all, a comparison between experimental and CFD streamwise velocity profiles has been carried outFirst for of the all, baseline a comparison case H between at the planes experimental 10H, 25H and and CFD 50H streamwise downstream velocity of theprofiles vane; has see been Figure 7. Additionally,carried out four for differentthe baseline cross-wise case H at locations the planes are 10H, analyzed, 25H and which 50H downstream are at z = 0, of z =the TE vane; (VG see trailing edge),Figure z = D/3 7. Additionally, and z = D/2, four where different D = cross-wise 30 mm. At locations the crosswise are analyzed, location which of zare = 0,at thez = 0, numerical z = TE (VG results trailing edge), z = D/3 and z = D/2, where D = 30 mm. At the crosswise location of z = 0, the numerical fit quite well to the experimental ones. As the flow moves away from the center z = 0 to the spanwise results fit quite well to the experimental ones. As the flow moves away from the center z = 0 to the direction, some differences can be found between the experimental and the numerical streamwise spanwise direction, some differences can be found between the experimental and the numerical velocitystreamwise profiles. velocity profiles.

CFD Exp D=0 +TE D/3 D/2 30 30 30 30

25 25 25 25

20 20 20 20 10H 15 15 15 15

10 10 10 10

5 5 5 5

0 0 0 0 0 0.5 1 1.5 0 0.5 1 1.5 0 0.5 1 1.5 0 0.5 1 1.5

30 30 30 30

25 25 25 25

20 20 20 20 25H 15 15 15 15

10 10 10 10

5 5 5 5

0 0 0 0 0 0.5 1 1.5 0 0.5 1 1.5 0 0.5 1 1.5 0 0.5 1 1.5 Wall-normal position y (mm) 30 30 30 30

25 25 25 25

20 20 20 20

15 15 15 15 50H

10 10 10 10

5 5 5 5

0 0 0 0 0 0.5 1 1.5 0 0.5 1 1.5 0 0.5 1 1.5 0 0.5 1 1.5 Normalized streamwise velocity, u /U [-] x ∞ Figure 7. Normalized streamwise velocity profiles () at different streamwise locations 10H (top), 25H Figure 7. Normalized streamwise velocity proﬁles () at different streamwise locations 10H (top), (middle) and 50H (bottom) behind the VG. Solid black lines (–) correspond to the experimental data 25H (middle) and 50H (bottom) behind the VG. Solid black lines (–) correspond to the experimental and the blue ones (–) to numerical profiles. data and the blue ones (–) to numerical proﬁles. According to the information available in the AVATAR project, three variables have been chosen for qualitative comparison between the numerical and the experimental results: the streamwise velocity, the normalized streamwise vorticity and the turbulence kinetic energy. The experimental fields were only available at the downstream plane positions from 10H–50H. Appl. Sci. 2018, 8, 138 9 of 16

According to the information available in the AVATAR project, three variables have been chosen for qualitative comparison between the numerical and the experimental results: the streamwise velocity,Appl. Sci. 2018 the, 8 normalized, 138 streamwise vorticity and the turbulence kinetic energy. The experimental9 of 16 ﬁelds were only available at the downstream plane positions from 10H–50H. Figure8 8 shows shows thethe out-of-planeout-of-plane streamwisestreamwise velocityvelocity ﬁelds fields on on spanwisespanwise planesplanes atat threethree differentdifferent locations 5H, 10H, 25H andand 50H50H downstreamdownstream ofof thethe vortexvortex generator.generator. TheThe comparisoncomparison includesincludes thethe results of the simulations corresponding to the three different VG heights and the experimental data.

Figure 8. Comparison of the out-of-plane streamwise velocity fields ux between experimental and Figure 8. Comparison of the out-of-plane streamwise velocity ﬁelds ux between experimental and numerical simulations of the three cases H, H1 and H2. Streamwise plane positions from top to bottom: numerical simulations of the three cases H, H1 and H2. Streamwise plane positions from top to bottom: 5H, 10H, 25H, 50H.

The height of the vortex generated by the vane increases as the vortex is moving away from the The height of the vortex generated by the vane increases as the vortex is moving away from the flat plate in the streamwise direction. At the farthest plane position studied 50H, the two vortexes flat plate in the streamwise direction. At the farthest plane position studied 50H, the two vortexes that are visible in the near wake plane positions seem to be unique. The roll-up process largely occurs that are visible in the near wake plane positions seem to be unique. The roll-up process largely occurs before the 10H location. The wake evolution is typical of the induced flow field where the velocity before the 10H location. The wake evolution is typical of the induced flow field where the velocity deficit is clearly observed in the places nearer the core of the vortex. The vortex size and the velocity deficit is clearly observed in the places nearer the core of the vortex. The vortex size and the velocity at its center increase as it moves away from the flat plate. The velocity in the middle of the vortex at its center increase as it moves away from the flat plate. The velocity in the middle of the vortex increases as it goes away, and the vortex increases, as can be seen by the reduction of the yellow. increases as it goes away, and the vortex increases, as can be seen by the reduction of the yellow. The normalized vorticity ωx/(U∞/H) fields at different streamwise planes are illustrated in The normalized vorticity ω /(U /H) fields at different streamwise planes are illustrated in Figure 9. The vorticity is a pseudovectorx ∞ field, which describes the local spinning motion of a continuum Figure9. The vorticity is a pseudovector field, which describes the local spinning motion of a near some point (the tendency of something to rotate), as would be seen by an observer located at continuum near some point (the tendency of something to rotate), as would be seen by an observer that point and traveling along with the flow. As shown in Figure 9, the experimental data and the located at that point and traveling along with the flow. As shown in Figure9, the experimental data CFD case of H = 5 mm are very similar, endorsing the accuracy of the current computations. As and the CFD case of H = 5 mm are very similar, endorsing the accuracy of the current computations. expected, the vorticity in the core of the vortex decreases as the distance increases, and that decrease As expected, the vorticity in the core of the vortex decreases as the distance increases, and that decrease is more significant at the planes 25H and 50H. The higher the vane, the larger is the vorticity in the is more significant at the planes 25H and 50H. The higher the vane, the larger is the vorticity in the vortex core. vortex core. Appl. Sci. 2018, 8, 138 10 of 16 Appl. Sci. 2018, 8, 138 10 of 16

Figure 9. Comparison of the normalized streamwise vorticity ωx/(U∞/H) between experimental and Figure 9. Comparison of the normalized streamwise vorticity ωx/(U∞/H) between experimental and numericalnumerical simulations. simulations. Streamwise Streamwise plane plane positions positions from top top to to bottom: bottom: 5H, 5H, 10H, 10H, 25H 25H and and50H. 50H.

The comparison of the turbulence kinetic energy fields is represented in Figure 10. The Theturbulence comparison kinetic of energy the turbulence (TKE) is the kinetic mean energykinetic energy fields is per represented unit mass associated in Figure 10with. The eddies turbulence in kineticturbulent energy flow (TKE) and is is the a measure mean kinetic of the energyintensity per of the unit turbulence. mass associated It is defined with as eddies follows: in turbulent flow and is a measure of the intensity of the turbulence.1 It is defined as follows: = + + (2) 2 1 2 2 2 where ux, uy and uz are the velocity fieldK components.= u + u + u (2) 2 x y z As shown in Figure 10, the TKE field comparison between the experimental case and the wheresimulationsux, uy and isu veryz are similar the velocity at the planes field components. 25H and 50H, whereas at the plane 10H, the experimental Ascase shown does not in have Figure a quick 10, development the TKE field as the comparison simulation has. between On the the one experimental hand, for the case case of andthe the simulationslargest vane is very height similar H1, the at the intensity planes of 25H turbulence and 50H, results whereas in a higher at the y plane coordinate 10H, thethan experimental the baseline case H and then the shortest VG H2. That means that as a consequence of the height of the VG, the does not have a quick development as the simulation has. On the one hand, for the case of the largest turbulent flow moves through at a higher elevation. On the other hand, as the flow moves away from vane height H1, the intensity of turbulence results in a higher y coordinate than the baseline H and the trailing edge of the actuator, the energy is dissipated to a greater extent in the smallest vane H2. then the shortest VG H . That means that as a consequence of the height of the VG, the turbulent flow Furthermore, it is clearly2 visible that for the case of H1 = 6.25 mm at the plane 5H behind the VG, movesthe through energy created at a higher as a consequence elevation. of On the the vortex other is hand,the maximum as the flowone in moves comparison away with from the the other trailing edgecases of the H actuator, and H2. the energy is dissipated to a greater extent in the smallest vane H2. Furthermore, it is clearlyFigure visible 11 thatshows for the the normalized case of H 1streamwise= 6.25 mm velocity at the plane(ux/U∞ 5H) profiles behind for the the VG, three the different energy VG created as a consequenceheights H1 = 4.16 of themm, vortex H = 5 ismm the and maximum H2 = 6.25 mm one at in the comparison 10H, 25H and with 50H the downstream other cases positions. H and H 2. As shown in Figure 11, at the downstream position 25H and spanwise position z = D/2 and at 50H Figure 11 shows the normalized streamwise velocity (ux/U∞) profiles for the three different VG and spanwise positions z = D/2 and z = D/3, the differences of the curves are notable. heights H1 = 4.16 mm, H = 5 mm and H2 = 6.25 mm at the 10H, 25H and 50H downstream positions. In order to analyze the vortex evolution, up to three parameters were previously identified in As shown in Figure 11, at the downstream position 25H and spanwise position z = D/2 and at 50H past studies made by Fernandez-Gamiz et al. [32] and Godard et al. [28] on the streamwise longitudinal and spanwise positions z = D/2 and z = D/3, the differences of the curves are notable. vortex embedded in turbulent boundary layers. Therefore, the proposed parameters to characterize In order to analyze the vortex evolution, up to three parameters were previously identified in past the primary vortex generated by a passive rectangular VG are the streamwise peak vorticity ωx,max , studiesthe madevortex bypath Fernandez-Gamiz and the wall shear etstress al. [(WSS).32] and The Godard peak vorticity et al. [28 is ]used on the to locate streamwise the center longitudinal of the vortexstreamwise embedded vortex in turbulent in each plane boundary position layers. downstream Therefore, of the VG the and, proposed subsequently, parameters to determine to characterize the the primary vortex generated by a passive rectangular VG are the streamwise peak vorticity ωx,max , the vortex path and the wall shear stress (WSS). The peak vorticity is used to locate the center of the streamwise vortex in each plane position downstream of the VG and, subsequently, to determine Appl. Sci. 2018, 8, 138 11 of 16

Appl. Sci. 2018, 8, 138 11 of 16 the vortexvortex trajectory. trajectory. InIn addition,addition, the the WSS WSS is is a aparame parameterter associated associated with with the thevortex vortex induced induced rate of rate of mixingmixing of the of outer the outer ﬂow flow with with the the boundary boundary layer. layer. The The trajectory trajectory of the the primary primary vortex vortex generated generated by by a vane-typea vane-type VG plays VG plays a determining a determining role role in thein the mixing mixing performance. performance.

2 Figure 10. Comparison of the normalized turbulence kinetic energy (TKE) K/(U∞) fields2 between Figure 10. Comparison of the normalized turbulence kinetic energy (TKE) K/(U∞) ﬁelds between experimental data and numerical simulations. Streamwise plane station from top to bottom: 5H, 10H, experimental data and numerical simulations. Streamwise plane station from top to bottom: 5H, 10H, 25H, 50H. 25H, 50H.

Figure 12 shows the normalized peak vorticity (ωx,max·H)/U∞ development of the three different

Figureheights 12 of showsthe VGs, the which normalized in fact represents peak vorticity the de (cayωx,max of the·H)/ vortexU∞ developmentalong the streamwise of the threedirection. different heightsAs ofexpected, the VGs, the whichvortex decay in fact seems represents to follow the an decay exponential of the law vortex in all alongcases. At the the streamwise closest positions direction. to the VG, the largest value corresponds to the lowest VG height of 4.16 mm, but that trend is turned As expected, the vortex decay seems to follow an exponential law in all cases. At the closest positions around at the distance of 50H in which the highest value is that corresponding to the case with a to the VG, the largest value corresponds to the lowest VG height of 4.16 mm, but that trend is turned 6.25-mm vane height. The values of the peak vorticity of the different VG cases almost overlap each aroundother, at theand distanceconsequently, of 50H no si ingnificant which variation the highest was valuefound. is that corresponding to the case with a 6.25-mm vaneBy observing height. the The location values of of the the vortex peak vorticitycenter as a of function the different of the downstream VG cases almost axis x, overlap one can each other,determine and consequently, the path of nothe signiﬁcantprimary vortex variation in both was lateral found. (z) and vertical (y) directions. The calculation Byof the observing vortex center the locationis made by of finding the vortex the maxi centermum as streamwise a function vorticity of the point downstream in the corresponding axis x, one can determinedownstream the path plane of the position; primary see vortex Fernandez-Gamiz in both lateral et (al.z) and[32] verticaland Martinez-Filgueira (y) directions. Theet al. calculation [21]. of theFigures vortex 13 center and is14 made show bya comparison ﬁnding the between maximum the streamwise trajectories vorticitydescribed pointby the in primary the corresponding vortex downstreamgenerated plane by the position; different seeVG Fernandez-Gamizheights. Streamwise et coordinates al. [32] and and Martinez-Filgueira both lateral and vertical et al. [21]. coordinates are normalized by the baseline VG height H. As illustrated in Figure 13, the lateral path Figures 13 and 14 show a comparison between the trajectories described by the primary vortex of the three cases tends to follow the direction in which the device is inclined, and the trajectories generated by the different VG heights. Streamwise coordinates and both lateral and vertical coordinates roughly collapse in the streamwise plane positions studied. The vortex paths in the vertical direction are normalizedare represented by the in Figure baseline 14. VGThey height collapse H. in As the illustrated near wake, in from Figure the formation13, the lateral of the path vortex of up the to three casesapproximately tends to follow the the downstream direction in plane which 18H. the As device the distance is inclined, increases and the far trajectoriesaway in the roughly streamwise collapse in thedirection, streamwise the higher plane vortex positions trajectory studied. corresponds The vortex clearly paths to the in higher the vertical VG H1 direction = 6.25. In the are far represented wake in Figurepositions, 14. They a clear collapse gap in the in vertical the near paths wake, is visi fromble between the formation the three of VG the cases, vortex which up does to approximately not occur the downstreamin the lateral planepaths. 18H. As the distance increases far away in the streamwise direction, the higher vortex trajectory corresponds clearly to the higher VG H1 = 6.25. In the far wake positions, a clear gap in the vertical paths is visible between the three VG cases, which does not occur in the lateral paths. Appl. Sci. 2018, 8, 138 12 of 16 Appl. Sci. 2018, 8, 138 12 of 16

D=0 +TE D/3 D/2 Appl. Sci. 2018, 8, 138 30 30 30 30 12 of 16

25 D=0 25 +TE 25 D/3 25 D/2 30 30 30 30 20 20 20 20 25 25 25 25 15 15 15 15 10H 20 20 20 20 10 10 10 10 15 15 15 15 10H 5 5 5 5 10 10 10 10 0 0 0 0 50 0.5 1 1.5 50 0.5 1 1.5 50 0.5 1 1.5 50 0.5 1 1.5

0 0 0 0 0 0.5 1 1.5 0 0.5 1 1.5 0 0.5 1 1.5 0 0.5 1 1.5 30 30 30 30

25 25 25 25 30 30 30 30 20 20 20 20 25 25 25 25 15 15 15 15 25H 20 20 20 20 10 10 10 10 15 15 15 15 25H 5 5 5 5 10 10 10 10 0 0 0 0 50 0.5 1 1.5 50 0.5 1 1.5 50 0.5 1 1.5 50 0.5 1 1.5 Wall-normal position y (mm) 0 0 0 0 0 0.5 1 1.5 0 0.5 1 1.5 0 0.5 1 1.5 0 0.5 1 1.5 30 30 30 30 Wall-normal position y (mm)

25 25 25 25 30 30 30 30 20 20 20 20 25 25 25 25 15 15 15 15 50H 20 20 20 20 10 10 10 10 15 15 15 15 50H 5 5 5 5 10 10 10 10 0 0 0 0 50 0.5 1 1.5 50 0.5 1 1.5 50 0.5 1 1.5 50 0.5 1 1.5

Normalised streamwise velocity, Rectangular 4.16 mm 0 0 0 0 0 0.5 1 1.5 0 u0.5/U1 [-]1.5 0 0.5 1 1.5 0 Rectangular0.5 1 5 1.5mm Normalised streamwisex ∞ velocity, Rectangular 6.25 mm Rectangular 4.16 mm Rectangular 5 mm x ∞ Figure 11. Normalized streamwise velocityu /U (u / U[-]) profiles for the 4.16-mm,Rectangular 5-mm 6.25 andmm 6.25-mm VG Figure 11. Normalized streamwise velocityx (ux∞/U∞) proﬁles for the 4.16-mm, 5-mm and 6.25-mm VG heights at the 10H, 25H and 50H downstream positions. heights at the 10H, 25H and 50H downstream positions. Figure 11. Normalized streamwise velocity (ux/U∞) profiles for the 4.16-mm, 5-mm and 6.25-mm VG heights at the 10H, 25H and 50HNormalized downstream Peak positions. vorticity development

1.2 Normalized Peak vorticity development Rectangular 4.16 mm 1.21 Rectangular 5 mm Rectangular 4.16 mm ∞ Rectangular 6.25 mm 0.81 Rectangular 5 mm H)/U ∞ Rectangular 6.25 mm 0.60.8 x,max H)/U ω ( 0.40.6 x,max ω ( 0.20.4

0.20 0 10 20 30 40 50 x/H 0 Figure 12. The normalized0 10peak vorticity20 development30 for40 the different50 VG heights. x/H

FigureFigure 12. The12. The normalized normalized peak peak vorticity vorticity development for for the the different different VG VG heights. heights. Appl. Sci. 2018, 8, 138 13 of 16 Appl. Sci. 2018, 8, 138 13 of 16 Appl. Sci. 2018, 8, 138 13 of 16

LateralLateral pathpath 0.56 0.56 0.555 0.555 0.55 0.55 0.545 0.545 0.54 0.54

z/h [-]z/h 0.535 Rectangular 4.16 mm z/h [-]z/h 0.535 Rectangular 4.16 mm Rectangular 5 mm 0.53 Rectangular 5 mm 0.53 Rectangular 6.25 mm Rectangular 6.25 mm 0.525 0.525 0.52 0.52

0 10 20 30 40 50 0 10 20 x/h [-]30 40 50 x/h [-] Figure 13. The development of the vortex center in the horizontal direction. Figure 13. The development of the vortex centercenter inin thethe horizontalhorizontal direction.direction. Vertical path Vertical path 1.8 1.8 1.6 1.6 1.4 1.4 1.2 1.2

y/H [-]y/H 1 y/H [-]y/H 1 0.8 Rectangular 4.16 mm 0.8 Rectangular 4.16 mm Rectangular 5 mm Rectangular 5 mm 0.6 Rectangular 6.25 mm 0.6 Rectangular 6.25 mm 0.4 0.40 10 20 30 40 50 0 10 20 x/H [-]30 40 50 x/H [-] Figure 14. The development of the vortex center in the vertical direction. Figure 14. The development of the vortex centercenter inin thethe verticalvertical direction.direction. The WSS is the result of friction within the fluid and between the fluid and the walls and is related The WSS is the result of friction within the fluid and between the fluid and the walls and is related to theThe fluid WSS viscosity. is the result The magnitude of friction withinof the WSS the fluid is dependent and between on how the fluidfast the and velocity the walls increases and is related when to the fluid viscosity. The magnitude of the WSS is dependent on how fast the velocity increases when movingto the fluid away viscosity. from the The wall. magnitude The wall of shear the WSS stress, is dependentτω, can be determined on how fast by the Equation velocity increases(3): when moving away from the wall. The wall shear stress, τω, can be determined by Equation (3): moving away from the wall. The wall shear stress, τω, can be determined by Equation (3): = = (3) du (3) x τω = µ (3) where μ is the dynamic viscosity, ux is the axial flowdy velocityy=0 and y is the distance normal to the wall. where μ is the dynamic viscosity, ux is the axial flow velocity and y is the distance normal to the wall. The units in IS are Pa. Figure 15 represents the comparison of the wall shear stress for the three whereThe unitsµ is in the IS dynamicare Pa. Figure viscosity, 15 representsu is the axial the flowcomparison velocity of and they wallis the shear distance stress normal for the tothree the analyzed VG geometries on a flat plate.x Data were extracted from the VG trailing-edge up to the end wall.analyzed The unitsVG geometries in IS are Pa. on Figurea flat plate. 15 represents Data were the extracted comparison from of the the VG wall trailing-edge shear stress up for to the the three end of the domain and at a spanwise coordinate of z = 0. A dependency between the vane height and the analyzedof the domain VG geometries and at a spanwise on a flat coordinate plate. Data of were z = 0. extracted A dependency from the between VG trailing-edge the vane height up to theand end the wall shear stress produced in the VG wake is clearly seen in Figure 15. The largest value of the WSS ofwall the shear domain stress and produced at a spanwise in the coordinate VG wake is of clearl z = 0.y A seen dependency in Figure between15. The largest the vane value height of the and WSS the is reached by the highest VG H1 = 6.25 mm. According to Gad-el-Hak [33], transferring momentum wallis reached shear stressby the produced highest VG in theH1 = VG 6.25 wake mm. is According clearly seen to inGad-el-Hak Figure 15. [33], The largesttransferring value momentum of the WSS towards the near wall region means that the velocity is increased, which leads to an increase in the istowards reached the by near the highestwall region VG Hmeans= 6.25 that mm. the According velocity is toincreased, Gad-el-Hak which [33 ],leads transferring to an increase momentum in the wall shear stress. In the study of1 Lin et al. [34] on an airfoil with micro-VGs, it was demonstrated that towardswall shear the stress. near In wall the region study meansof Lin et that al. the[34] velocityon an airfoil is increased, with micro-VGs, which leads it was to demonstrated an increase in that the an increase of the WSS resulted in a lift increasing. wallan increase shear stress. of the In WSS the resulted study of in Lin a etlift al. increasing. [34] on an airfoil with micro-VGs, it was demonstrated that an increase of the WSS resulted in a lift increasing. Appl. Sci. 2018, 8, 138 14 of 16 Appl. Sci. 2018, 8, 138 14 of 16

Wall shear stress 1.2

1 (Pa) x

τ 0.8

0.6 Flat plate with rectangular VG 5 mm Flat plate with rectangular VG 6 mm 0.4 Flat plate with rectangular VG 4 mm Flat plate without VG Wall shear stress stress shear Wall 0.2

0 10 20 30 40 50 Streamwise distance x/h FigureFigure 15. 15. WallWall shear shear stress stress comparison comparison in in the the streamwise streamwise direction direction from from the the VG VG trailing-edge trailing-edge to to 50H 50H (spanwise(spanwise distance distance z z = = 0) 0) of of the the three three differen differentt VG VG heights heights and and without without any any vane vane on on the the wall. wall.

5.5. Conclusions Conclusions VorticesVortices generated generated by by a a passive passive rectangular rectangular vane-type vane-type VG VG on on a aflat flat plate plate have have been been studied. studied. NumericalNumerical simulations simulations at at a aReynol Reynoldsds number number Re Re = = 2600 2600 based based on on the the local local BL BL momentum momentum thickness thickness ∞ −1 −1 θθ == 2.4 2.4 mm mm and and free free stream stream velocity velocity UU∞ = =15 15 ms ms havehave been been carried carried out out using using the the RANS RANS method. method. ComputationalComputational fluid fluid dynamics dynamics simulations simulations are are able able to to reproduce reproduce the the physics physics of of the the primary primary vortex vortex generatedgenerated by by a arectangular rectangular passive passive VG VG with with reasonab reasonablyly good good reliability. reliability. As numerical As numerical methods methods are the are mostthe mostfrequently-used frequently-used ones ones applied applied in optimizi in optimizingng VGs VGs on onwind wind turbine turbine blades, blades, the the extensive extensive informationinformation presented presented in in the the current current study study can can be be used used as as guidance guidance for for successful successful design design and and implementationimplementation of of VGs VGs on on wind wind turbine turbine blades blades and and to to carry carry out out parametric parametric dependencies dependencies of of the the VGs VGs onon different different flowflow conditions.conditions. Because Because of of the the large larg rangee range of parameters of parameters inherent inherent in the problemin the problem (incident (incidentangle, interspacing angle, interspacing between between vanes, device vanes, orientation, device orientation, vane height vane and height length, and etc.),length, an etc.), in-depth an in-depthunderstanding understanding of the fluid of the flow fluid is needed flow is toneeded be correctly to be correctly applied. applied. Furthermore,Furthermore, a aqualitative qualitative comparison comparison of of the the spanwise spanwise velocity, velocity, normalized normalized vorticity vorticity and and turbulenceturbulence kinetic energyenergy fields fields at differentat different plane plane positions positions downstream downstream of the VGof hasthe beenVG introducedhas been introducedto see how to the see vortex how isthe developed. vortex is developed. It is verified It that is verified when using that when an appropriate using an mesh,appropriate fields suchmesh, as fieldsaxial such velocity, as axial vorticity velocity, and vorticity TKE are determinedand TKE are with determined reasonable with accuracy. reasonable accuracy. AA correlation correlation study study and and comparison comparison of the of vortex the vortex parameters parameters such as such vortex as vortextrajectory, trajectory, peak vorticitypeak vorticity and streamwise and streamwise BL velocity BL velocity profiles profileswith three with different three different VG heights VG has heights also hasbeen also carried been out.carried It should out. Itbe should noted bethat, noted in the that, development in the development of the center of the vortex center trajectory, vortex trajectory, the points the overlap points eachoverlap other each in the other lateral in the path lateral for the path three for thediffe threerent differentVG heights, VG but heights, not in but the not vertical in the path. vertical path. ItIt has has been been demonstrated demonstrated for for the the three three analyzed analyzed ge geometriesometries that, that, for for the the same same level level of of vorticity, vorticity, thethe vertical vertical path path of of the the primary primary vortex and thethe wallwall shearshear stressstress downstreamdownstream of of the the vane vane are are higher higher as asthe the actuator actuator height height increases. increases. TheThe wallwall shearshear stressstress has a direct influence influence on on the the quantity quantity of of energy energy transfer.transfer. Then, Then, if if a a delayed delayed stall stall is is desired, desired, the the best best geometry geometry will will be be the the one one with with the the best best wall wall shear shear stress increment. Thus, it could be concluded that the highest VG H1 = 6.25 mm is more suitable for stress increment. Thus, it could be concluded that the highest VG H1 = 6.25 mm is more suitable for separationseparation control control applications. applications.

Acknowledgments:Acknowledgments: TheThe funding funding from from the the Government Government of of the the Basq Basqueue Country Country and and the the University University of of the the Basque Basque CountryCountry UPV/EHU UPV/EHU through through the the SAIOTEK SAIOTEK (S-PE11UN112) (S-PE11UN112) and and EHU12/26 EHU12/26 research research prog programs,rams, respectively, respectively, is gratefullyis gratefully acknowledged. acknowledged.

Author Contributions: Unai Fernandez-Gamiz, Iñigo Errasti and Ruben Gutierrez prepared and ran the numerical part. They also wrote the manuscript. The post-processing was done by Ruben Gutierrez. Ana Boyano and Oscar Barambones provided constructive instructions in the process of preparing the paper. Appl. Sci. 2018, 8, 138 15 of 16

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