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DownloaIntroductionIn open-wheel racing series, such as Formula 1 and Indy Rac-

ng, a front wing is inverted to produce downforce, that is, nega-ive lift, leading to an enhancement of traction and cornering abil-ty of cars. The front wing is operated in close proximity to a solidoundary, known as the ground effect regime, where differentow features are exhibited, compared with the freestream condi-

ion. Since aerodynamic performance plays a significant role inpen-wheel race cars, investigations and testing are typically con-ucted via wind tunnel testing, computational simulations, andrack-based testing 1. Although wind tunnel testing remains aignificant tool for aerodynamic development, computational fluidynamics CFD plays an important role because of its efficientost performance compared with wind tunnel testing, and the de-ailed flow information that is available.

The first computational investigations of an inverted wing inround effect were performed by Katz 2 and Knowles et al. 3,sing a potential flow-based panel method to simulate a single-lement wing in ground effect. Katz 2 observed an enhancementf downforce as the wing is brought closer to the ground. Previ-usly conducted experimental investigations 47 show down-orce reduction below the height where the maximum downforces produced due to flow separation and breakdown of edge vorti-es around end plates of a wing. No downforce reduction phe-omenon, however, was observed even at excessively low rideeight in the study of Katz 2; viscous effects were not simulated,

thus, no flow separation was captured. Zerihan and Zhang 8performed a Reynolds-averaged NavierStokes RANS simula-tion for a two-dimensional single-element wing, using a fullystructured grid with the SpalartAllmaras S-A 9 and shearstress transport SST k- turbulence models. The computationalresults of pressure and velocity distributions were compared withtheir previously performed experiments 4,10. The computationscaptured the trends of the pressure distributions at the center por-tion of the wing span, as well as wake characteristics. Mahon andZhang 11 conducted a further computational analysis for thesurface pressure and wake characteristics, using multiblock hybridgrids. Various types of turbulence models were compared with theresults of the experiments 4,10. The results of the SST k-model showed the most accurate prediction of the pressure distri-butions and force slope. For the wake flow, the realizable k-model showed the most accurate prediction. More recently, Kief-fer et al. 12 examined effects of the incidence of a single-element wing, modeling a Formula Mazda wing. The turbulencewas modeled by the standard k- model. The numerical results,however, were obtained by using a fixed ground boundary, andthere was no experimental validation. In addition to the computa-tional investigations of a single-element wing, some extendedstudies for an inverted wing in ground effect have been conducted,including studies of a double-element wing 3,13 and interactionsbetween a wing and a rotating wheel 14,15.

In the current investigation, an inverted single-element wingwith vortex generators VGs in ground effect is computed usingRANS simulations. Kuya et al. 7,16 experimentally investigatedthe performance and characteristics of such configuration. In thispaper, the computational approach is comprehensively validatedwith the experimental results. The computations are then used to

Contributed by the Fluids Engineering Division of ASME for publication in theOURNAL OF FLUIDS ENGINEERING. Manuscript received September 14, 2009; finalanuscript received November 20, 2009; published online February 3, 2010. Assoc.ditor: Zvi Rusak.

ournal of Fluids Engineering FEBRUARY 2010, Vol. 132 / 021102-1Copyright 2010 by ASMEYuichi Kuyae-mail: yuichi@soton.ac.uk

Kenji TakedaSenior Lecturer

e-mail: ktakeda@soton.ac.uk

Xin ZhangProfessor

e-mail: x.zhang1@soton.ac.uk

School of Engineering Sciences,University of Southampton,Southampton SO17 1BJ, UK

ComputRace CaGeneratVortex generators cgradients, such as wtations for an invermain aim is to provhow they affect the oexperimental studielayer and large-scalincluding both counfidence, Reynolds-avbulence model are vand wake charactermental results. Thevortex acts to supprgenerators featuresvortex generated bysize and breaks docounter-rotating larstream, indicating tco-rotating sub-bouthe spanwise flow cpating as it develoexperimental measucan help control flovortex generator typded 11 Mar 2010 to 152.78.214.194. Redistribution subject to ASMtional Investigation of aWing With Vortexrs in Ground Effectbe applied to control separation in flows with adverse pressures. In this paper, a study using three-dimensional steady compu-wing with vortex generators in ground effect is described. Theunderstanding of the flow physics of the vortex generators, andall aerodynamic performance of the wing to complement previousf the same configuration. Rectangular vane type sub-boundaryortex generators are attached to the suction surface of the wing,rotating and co-rotating configurations. In order to provide con-ged NavierStokes simulations using the SpalartAllmaras tur-

dated against the experimental results regarding force, pressure,s, with the validation exhibiting close agreement with the experi-amwise friction shows the downwash induced by the generatedflow separation. The flow field survey downstream of the vortexakdown and dominance of the generated vortex in the flow. The

counter-rotating sub-boundary layer vortex generator grows inas it develops downstream, while the vortex generated by the

scale vortex generator shows high vorticity even further down-persistence of the vortex in the flow. The flow field behind thery layer vortex generator is dominated by a lateral flow, havingponent rather than a swirling flow, and the vortex quickly dissi-downstream. The results from this paper complement previousents by highlighting the flow physics of how vortex generators

eparation for an inverted wing in ground effect, and how criticalnd size are for its effectiveness. DOI: 10.1115/1.4000741E license or copyright; see http://www.asme.org/terms/Terms_Use.cfm

ec

2

csopr

mcrSpiicmdhuhArft

FacKGas

are given in the study of Zerihan 18. The ride height h is definedas the distance from the lower boundary to the lowest point on the

FV

.)

.)

ingand

0

Downloaxamine the detailed flow physics of the VG separation controlharacteristics to support the experimental studies.

Computational Modeling2.1 Governing Equations and Turbulence Modeling. The

omputations are performed by solving the three-dimensionalteady RANS equations. A commercial RANS solver, FLUENT 6.217, which uses the finite volume method, is used here. A second-rder upwind scheme is used to interpolate values between com-utational nodes. The SIMPLEC pressure-velocity coupling algo-ithm 17 is employed.

Mahon and Zhang 11 compared various types of turbulenceodels using the same wing profile used here. In this study, the

haracteristics of an inverted wing is mainly examined at the wingide height of 0.090c, and Mahon and Zhang 11 showed that theST k- model presents the best prediction at the ride height inressure distributions and wake profiles. The S-A model, however,s employed here, since it has been found that the SST k- models unstable at some ride heights examined, leading to unconvergedomputations. The S-A model exhibits the second best perfor-ance in the work of Mahon and Zhang 11, and is originally

esigned for wall-bounded aerodynamic flows. In addition, Zeri-an and Zhang 8 also compared the S-A and SST k- modelssing the same wing profile used by Mahon and Zhang 11 andere, and showed a comparable performance of the two models.lthough one-equation models may induce a larger numerical er-

or than two-equation models, a careful validation study is per-ormed here so as to provide sufficient confidence of the compu-ations, and to estimate an amount of the errors.

2.2 Computational Geometries and Boundary Conditions.igure 1 shows a schematic of an inverted single-element wingnd its coordinate used in the computations, which has the sameross section profile as the wing used in the experimental study ofuya et al. 7,16. The wing profile is based on that of a NASAAW profile, type LS1-0413, and has a chord c of 223.4 mm

nd a finite trailing edge of 1.65 mm. The origin of the coordinateystem is set at the leading edge of the wing; the wing coordinates

xz

UMoving wall

symmetric boundary (zb)or

periodic boundary (zc)

symmetric boundary (za)or

periodic boundary (zc)

4hVG

2hVG2hVG

hVG

VG

h

y

UFreestream

ig. 1 Computational grid of inverted single-element wing andG

za(symmetric B.CU

Symmetrically imaged VG

(a)

zb(symmetric B.C

Symmetrically imaged VG

2hVG

4hVG

15

2hVG

Fig. 2 Configurations of VGs on wwise ends: a counter-rotating VGs

21102-2 / Vol. 132, FEBRUARY 2010ded 11 Mar 2010 to 152.78.214.194. Redistribution subject to ASMsuction surface of the wing, and is varied between 0.067c and0.448c in this study. The incidence is measured relative to a linefrom the trailing edge to the most swelled point on the pressuresurface, which corresponds to 2.6 deg relative to the chord line,and is fixed at 1 deg in this study, corresponding to the true inci-dence of 3.6 deg. A further description can be found in Refs.7,16.

Rectangular vane type of sub-boundary layer vortex generatorsSVGs and large-scale vortex generators LVGs are studied herewith a device height of 2 mm hVG /c=0.009 and 6 mm hVG /c=0.027, respectively. Figure 2 shows a schematic of VG configu-rations. The VGs attached on the suction side of the wing areoriented at 15 deg relative to the streamwise direction. The trailingedge of the VGs is set at x=120 mm, corresponding to x /c=0.537. The height and chord ratio of the VGs is fixed at 1:4, andthe distance between the spanwise ends of the computational do-main and the trailing edge of the VGs is fixed at 2hVG. Since theCtLVG configuration demands a grid three times wider than theother configurations in the spanwise direction, the CtLVG compu-tational domain has additional cells along both the spanwise endsso that the grid expansion ratio from the VG is the same in boththe computational domains. For the clean wing configuration, thesame computational grid as the SVG configurations is used, wherethe computational cells for the VG are not set as a solid boundary.The computational VGs are modeled as a zero-thickness solidboundary because it is much simpler to generate, easier to modify,and can decrease the number of grid points significantly. Allan etal. 19 compared a simply modeled rectangular vane having zerothickness with a fully modeled trapezoidal vane with finite thick-ness. The comparison showed that the performance of the simplymodeled rectangular vane is similar to that of the fully modeledtrapezoidal vane, and hence, the simplified model is employedhere.

A three-dimensional multiblock structured grid is used in thisstudy. A grid generation package, Gridgen V15, is used to buildthe grid, and any special functions in the package are not used,although the functions may provide an optimized grid, leading toquicker convergence. The upstream boundary is modeled with afreestream velocity inlet of 30 m/s, corresponding to the Reynoldsnumber of 450,000, based on the wing chord. The turbulent vis-cosity ratio of 8 is used as a result of preliminary studies to simu-late previous experimental studies of the same configuration. Forthe downstream boundary, a condition of zero flux diffusion isapplied, where the boundary plane is extrapolated from the down-stream values and there is no gradient in the streamwise direction.A no-slip boundary condition is applied to the wall boundaries,which are the wing, VGs, and lower boundary. A moving wallcondition is simulated at the lower boundary where a movingvelocity is equal to the freestream. The initial cell spacing on thewall boundaries is fine enough to solve the viscous sublayer of theflow on the wall properly, maintaining y+ of O1. The upperboundary is modeled with a symmetric condition. To simulate thecounter-rotating VG configurations, both spanwise ends of theboundary are defined as symmetric conditions; meanwhile, peri-odic conditions are applied for the co-rotating VG configuration.

Periodically imaged VG

Periodically imaged VG

U

(b)

zc(periodic B.C.)

zc(periodic B.C.)

2hVG2hVG4hVG

15

and boundary conditions at span-b co-rotating VGs

Transactions of the ASMEE license or copyright; see http://www.asme.org/terms/Terms_Use.cfm

AaVc

tVtmtsce1sho1cdAatfrcfe1dit

3

toao

sctrmspt

1.57

Number of cells (3D)

0.3

Number of cells (3D)2e+6 3e+61e+6 4e+6 5e+64e+62e+6 6e+6

win

(b) x/c0.2 0.40 0.6 0.8 1

1Clean_CFDCoSVG(z=zc)_CFD

J

Downloas shown in Fig. 2, z=2hVG and 2hVG are referred to as zand zb at the spanwise end boundaries for the counter-rotatingG configuration, respectively, and zc for the co-rotating VG

onfiguration.The convergence criteria for all simulations are carefully moni-

ored, allowing the numerical residuals to decrease by O104.ariations of downforce are lower than O106 for the final itera-

ions. Both two-dimensional and three-dimensional grid refine-ent studies have been conducted with the clean wing configura-

ion at the ride height of 0.179c regarding downforce. Figure 3hows the grid convergence history with respect to the downforceoefficient. For the two-dimensional study, the number of cells isxamined between 75,000 cells and 600,000 cells, and the grid of50,000 cells is chosen; the difference between the finest andelected grids is less than 0.1%. The three-dimensional grid studyas been conducted for a grid based on the two-dimensional gridf 150,000 cells. The number of cells examined is between,500,000 cells and 6,000,000 cells, and the grid of 3,000,000ells is employed for the clean wing and SVG configurations; theifference between the finest and selected grids is less than 0.1%.s described above, for the CtLVG configuration, 1,500,000 cells

re added to the grid of the clean and SVG configurations alonghe spanwise ends, resulting in a total of 4,500,000 cells. The gridor the CtLVG configuration also shows a small difference withespect to the finest grid, being less than 0.1%. The size of theomputational domain has been also examined. The distancesrom the wing to the upstream and downstream boundaries arexamined between 5c and 20c, and are respectively set as 5c and0c with differences from the largest grids of less than 0.01%. Theistance between the upper and lower boundaries has been exam-ned between 5c and 20c, and is set as 10c with differences fromhe largest grid of less than 0.05%.

ResultsTo examine an application of RANS simulations to computa-

ions of an inverted wing with VGs in ground effect, validationsf the computations against the experiments of Kuya et al. 7,16re presented here. This is followed by the detailed investigationsf the flow physics based on the computations.

3.1 Chordwise Surface Pressure Distributions. Figure 4hows comparisons of chordwise pressure distributions of theomputations and experiments on the wing of the four configura-ions at h /c=0.090. Note that the vertical lines in the figures rep-esent the leading and trailing edges of the VGs, and the experi-ental results of the VG configurations are averaged in the

panwise direction. It should also be noted that the computationalressure of the counter-rotating VG configurations show distribu-ions at two spanwise positions z=za and zb.

Number of cells (2D)2e+50 4e+5 6e+5

1.56

1.565

(a)

2D3D3D_LVG

CLs

Fig. 3 Grid refinement study with cleancoefficient and b convergence ratio

ournal of Fluids Engineering0.2 0.4x/c

0 0.6 0.8 1

0

-2

-3

-4

-5

-6

-1

Clean_experimentCoSVG_experiment

(c)

CP

CoSVG

Fig. 4 Comparisons of computational and experimentalchordwise surface pressure distributions on wing at h /c=0.090: a CtSVG, b CtLVG, and c CoSVG

FEBRUARY 2010, Vol. 132 / 021102-3ded 11 Mar 2010 to 152.78.214.194. Redistribution subject to ASMNumber of cells (2D)2e+50

CLs(%)

1e+5 3e+5

0

0.1

0.2

-0.1

(b)

2D3D3D_LVG

g configuration: a sectional downforce

(a) x/c

Clean_CFDCtSVG(z=za)_CFDCtSVG(z=zb)_CFDClean_experimentCtSVG_experiment

Clean_CFDCtLVG(z=za)_CFDCtLVG(z=zb)_CFDClean_experimentCtLVG_experiment

0.2 0.40 0.6 0.8 1

1

0

-2

-3

-4

-5

-6

-1

1

0

-2

-3

-4

-5

-6

-1

Counter-rotatingza(symmetric B.C.)U

zb(symmetric B.C.)

Co-rotatingzc(periodic B.C.)

zc(periodic B.C.)

U

CP

CP

CtSVG

CtLVGE license or copyright; see http://www.asme.org/terms/Terms_Use.cfm

ecerg

ptpt=

cCtisttecti

ssftCr

ewcatttwcta

perimental sectional downforce is calculated by integrating thepressure around the center portion of the wing performed in Ref.7.

Table 1 Sectional downforce at h /c=0.090

Clean CtSVG CtLVG CoSVG

CC

(

ed

0

DownloaOn the pressure surface, all the computations capture the gen-ral trend of the experimentally obtained distributions, while theomputational values indicate underpredictions compared with thexperiments. The computation of the clean wing shows flow sepa-ation at about 70% chord, characterized by a constant value re-ion on the suction surface.

For the CtSVG configuration, the computation predicts theressure distributions on the suction surface fairly well, includinghe gradient of the pressure recovery, in particular, the suctioneak, while the experiments show somewhat less suction near therailing edge. For both the counter-rotating configurations at zza, a spike near the leading edge of the VG is noticeable in theomputations. The size of the spike is more remarkable in thetLVG configuration. The computation of the CtLVG configura-

ion predicts the distribution upstream of the VG relatively well,ncluding a prediction of the suction peak, while the computationshow more suction near the trailing edge. The CtSVG configura-ion predicts more suction on the suction surface compared withhe CtLVG configuration, which is in good agreement with thexperiments. Of interest here is that both the counter-rotating VGonfigurations show a moderate pressure recovery slope towardhe trailing edge and eliminate the constant value region, indicat-ng the reduction in flow separation.

The computations of the clean wing and CoSVG configurationhow apparently similar pressure distributions, indicating the floweparation region as featured by the experimental results. There-ore, there appears little or no effect of the CoSVGs in terms ofhe separation control. The spike near the leading edge of theoSVGs is smaller than that of the counter-rotating VG configu-

ations.

3.2 Sectional Force Characteristics. The wing used in thexperiments has generic end plates at both spanwise ends of theing, and the force characteristics are affected by the edge vorti-

es induced around the end plates. Meanwhile, the computationsre performed with symmetric or periodic boundary conditions athe spanwise ends of the computational domain. The end plates,herefore, are not simulated in the computations, so the computa-ions correspond to a simulation around the center portion of theing where there is no effect of the edge vortices. Accordingly, a

omparison of the force values of downforce and drag betweenhe experiments and computations is not sufficient. Alternatively,

comparison of sectional downforce is presented here. The ex-

Ls_CFD 1.63 2.29 2.25 1.70Ls_experiment 1.91 2.46 2.37 1.68CLs % 15 7 5 1

(a)0.1 0.2 0.3 0.4 0.50

2.0

1.5

1.0

2.5

h/c

CLs

Clean_CFDCtSVG_CFDCtLVG_CFDCoSVG_CFD

Fig. 5 Characteristics of computheights: a downforce and b drag

21102-4 / Vol. 132, FEBRUARY 2010ded 11 Mar 2010 to 152.78.214.194. Redistribution subject to ASMA validation for the sectional downforce is given in Table 1,presenting the sectional downforce of the computations, experi-ments, and differences between them at h /c=0.090. The compu-tations of the three VG configurations show reasonable predictioncompared with the experiments. Although the computation of theclean wing shows the highest deviation from the experimentalresult, the errors of VG configurations are less than 7%.

Figure 5 shows computationally calculated sectional downforceand drag of the four configurations at various ride heights. Theexperimental force characteristics for the full scale model aregiven in Ref. 7. All the downforce curves feature the downforceenhancement phenomenon, as the ride height is decreased due tothe Venturi effect. At much smaller ground clearances, the cleanwing and CoSVG configuration exhibit the downforce reductionphenomenon. The CoSVG configuration produces similar orslightly higher downforce compared with the clean wing. Thedownforce reduction phenomenon is not observed in computa-tions of the counter-rotating VG configurations, showing a con-tinuous increase in downforce as the wing is brought closer to theground. Both the counter-rotating VG configurations generatesimilar downforce. For the curves of the computational drag, allthe computations indicate an increase in drag as the ride heightdecreases, as shown in the experiment 7. The computations pre-dict the same order of the degree of drag as the experiment withthe CtLVG configuration producing the highest drag, and theclean wing producing the lowest drag.

3.3 Wake Velocity Profiles. Figure 6 shows comparisons ofmean streamwise velocity profiles at x /c=1.5 of the four configu-rations at h /c=0.090, including the computational and experimen-tal results. The thick and thin lines respectively indicate the com-putational and experimental results. The figure for the counter-rotating VG configurations shows profiles at two spanwisepositions z=za and zb.

All the computations overpredict in terms of the maximum ve-locity deficit of the wake. The boundary layer growth on the mov-ing ground is captured well by all the computations. In the com-putations, the CtSVG configuration shows a larger velocity deficitcompared with the clean wing and a small variance in the span-wise direction, which is in good agreement with the experimentalresults. The comparison between the clean wing and CtLVG con-figuration show that the computations can predict the generaltrend and correlation between the three profiles very well, show-ing a large variance in the spanwise direction. The computationsof the CoSVG configuration shows a larger velocity deficit thanthe clean wing, as the experimental results show, while its differ-ence is more apparent in the experimental results.

3.4 Streamwise Friction Distributions. Streamwise frictiondistributions on the suction surface of the four configurations at

b)0.1 0.2 0.3 0.4 0.50

0.10

0.08

0.06

0.04

0.02

0.12

h/c

CDs

Clean_CFDCtSVG_CFDCtLVG_CFDCoSVG_CFD

sectional forces at various ride

Transactions of the ASMEE license or copyright; see http://www.asme.org/terms/Terms_Use.cfm

hz

o

srcd

vccsotvfli

The friction slope of the CtSVG configuration at z=za indicatesa spike around 60% chord, and decreases the value along the

Counter-rotatingza(symmetric B.C.)U

Co-rotatingzc(periodic B.C.)U

Fs

J

Downloa/c=0.090 are shown in Fig. 7. Note that the vertical and hori-ontal lines in the figures represent the leading and trailing edgesf the VGs, and the value of CFx =0, respectively.The friction of the clean wing shows negative values down-

tream of 70% chord, corresponding to a region of the flow sepa-ation. The experimentally obtained separation point is at 6580%hord of the clean wing; the wide range of the separation point isue to the strong three-dimensionality of the separated flow.

Both the counter-rotating VG configurations indicate higheralues than the clean wing. This is because suction of both theounter-rotating VG configurations is stronger than that of thelean wing, and therefore, a larger amount of flow runs along theuction surface, resulting in the increase in the friction. A variancef the value in the spanwise direction is observed downstream ofhe VG, due to the secondary flow induced by the VG-generatedortex. The downwash toward the suction surface suppresses theow separation, leading to higher values of the friction, as shown

n the distributions at z=za.

(a)

(b)

(c)

zb(symmetric B.C.) zc(periodic B.C.)

u/U0.5

-0.1

y/c

0.6 0.7 0.8 0.9 1.0 1.1

0.1

0

u/U0.5

-0.1

y/c

0.6 0.7 0.8 0.9 1.0 1.1

0.1

0

Clean_experimentCtSVG(z=za)_experimentCtSVG(z=zb)_experiment

Clean_CFDCtSVG(z=za)_CFDCtSVG(z=zb)_CFD

Clean_experimentCtLVG(z=za)_experimentCtLVG(z=zb)_experiment

Clean_CFDCtLVG(z=za)_CFDCtLVG(z=zb)_CFD

u/U0.5

-0.1

y/c

0.6 0.7 0.8 0.9 1.0 1.1

0.1

0

Clean_experimentCoSVG(z=zc)_experiment

Clean_CFDCoSVG(z=zc)_CFD

ig. 6 Comparisons of computational and experimentaltreamwise velocity profiles of wake at h /c=0.090 at x /c=1.5:a CtSVG, b CtLVG, and c CoSVG

ournal of Fluids Engineeringded 11 Mar 2010 to 152.78.214.194. Redistribution subject to ASMstreamwise direction as the vortex becomes weaker downstream.Meanwhile, the upwash from the VG-generated vortex induceslow friction, as indicated by the slope at z=zb, indicating a smallnegative spike around 60% chord. Although the upwash weakensthe friction, the value is positive at most of the regions, henceindicating a very small adverse effect.

For the CtLVG configuration, the friction is enhanced by thedownwash at z=za as with the CtSVG configuration. The reducedgradient of the slope downstream of 60% chord is less steep com-pared with the CtSVG configuration, indicating that the vortex isstill dominant. The friction slope at z=zb shows a relatively widerange of a negative region between 60% and 87% chord, wherethe flow separation is enhanced by the upwash.

For the CoSVG configuration, a small variance is observed,compared with the clean wing. Although the CoSVG configura-tion shows the flow separation slightly further downstream com-pared with the clean wing, the effect for the separation control isapparently less than that of the CtSVG configuration. The separa-tion point of the clean and CoSVG configuration is respectivelyobserved at 70% and 75% chord.

3.5 Characteristics of VG-Generated Vortex. Figure 8shows velocity vectors and streamwise vorticity contours at x /c=0.63, 0.72, and 0.81 of the CtSVG, CtLVG, and CoSVG con-figurations at h /c=0.090. Note that yw in the figures denotes thenormal distance from the wing surface, and hence, the upper edgeof the figures corresponds to the suction surface of the wing.z /c=0 is the spanwise center of the computational domain. Itshould also be noted that the scale of the figures for the CtLVGconfiguration Fig. 8b is three times larger than the other con-figurations due to the size difference of the computational domain.

The results presented here feature breakdown and dominance ofthe VG-generated vortex in the flow. At x /c=0.63, the velocityvectors of the CtSVG configuration show the downwash to thesuction surface at the left hand side of the contour; the downwashpumps the momentum into the boundary layer flow. The vortexcenter moves in the positive spanwise direction as it developsdownstream, and the swirling motion mostly dissipates at x /c=0.81. Meanwhile, for the CtLVG configuration, the swirling mo-tion of the velocity vectors can be observed even at x /c=0.81,indicating that the vortex is still dominant in the flow. The veloc-ity vectors of the CoSVG configuration shows that the downwashto the suction surface is shown at x /c=0.63, however, the flownear the suction surface has a strong lateral component. Furtherdownstream, the flow field is completely dominated by the lateralflow running in the positive spanwise direction. This is becausethe interaction between neighboring co-rotating vortices tends tocancel each others downwash and upwash, and enhances the lat-eral component of the flow. Therefore, the lateral flow, rather thanthe swirling flow, becomes predominant.

For the streamwise vorticity contours, it is shown that the VG-generated vortex represented by negative vorticity induces thepositive vorticity region on the suction surface. The vortex centerof the CtLVG configuration is further from the wing surface thanthat of the CtSVG configuration, and the distance from the suctionsurface increases as the vortex develops downstream. Of greatinterest is that the vortex of the CtSVG grows and breaks down asit develops downstream, while the vortex of the CtLVG showshigh vorticity values even further downstream, therefore indicat-ing that the vortex of the CtLVG is still dominant in the flow, asalso shown by the velocity vectors. For the CoSVG configuration,the vortex is likely to develop in the positive spanwise direction,and the second vortex is observed at x /c=0.72, which is generatedby a neighboring VG and develops in the positive spanwise direc-tion due to the lateral flow. The distance between the vortex andthe suction surface increases as the vortex develops downstream,

FEBRUARY 2010, Vol. 132 / 021102-5E license or copyright; see http://www.asme.org/terms/Terms_Use.cfm

aTs

4

wtdrwcds

dTssbetsaCmfTgsatfc

1

0.03Clean_CFDCtSVG(z=za)_CFDCtSVG(z=zb)_CFD

1

CtLVG(z=za)_CFD

CtSVG

ictiVG

0

Downloand it completely detaches from the suction surface at x /c=0.81.he vortex size of the CoSVG configuration at x /c=0.63 ismaller than the other configurations.

DiscussionThe computations exhibit good agreement with the experiments

7,16 to simulate the flow around an inverted single-elementing with VGs in ground effect. Among the validated computa-

ions, the flow field surveys, including the streamwise frictionistributions, velocity vectors, and streamwise vorticity contours,eveal the characteristics of the VG-generated vortex in the flowell. The computed force characteristics show that both the

ounter-rotating VG configurations can delay the onset of theownforce reduction phenomenon due to the suppression of floweparation, and produce higher downforce than the clean wing.

The vortex generated by the CtSVGs grows in size and breaksown as it develops downstream, reducing the swirling motion.his feature is in very good agreement with the result of theurface flow visualization in the experiment 16. The computedtreamwise friction also shows the decay of the vortex generatedy the CtSVG in the streamwise direction. Lin 20 suggested thatffective separation control is provided when VG-generated vor-ices are just strong enough to overcome separation, but are not sotrong that they dominate in the flow further downstream, passingfter an initial separation point. According to this criterion, thetSVG configuration investigated here exhibits the best perfor-ance in terms of separation control. The computed streamwise

riction provides further evidence of the advantage of the CtSVG.he downwash toward the suction surface induced by the VG-enerated vortex increases the friction on the surface, helping touppress the flow separation. Meanwhile, the upwash should haven adverse effect on the separation control. The friction distribu-ions at z=zb, however, indicates a very small region of negativeriction, and therefore, the unfavorable effect of the CtSVGaused by the upwash is rather small.

(b)

(a) x/c

x/c

0.2 0.40 0.6 0.8

0

0.01

0.02

-0.01

CFx

0.2 0.40 0.6 0.8

0

0.01

0.02

0.03

-0.01

CFx

CoSVG

CtLVG

Fig. 7 Computational streamwise frat h /c=0.090: a counter-rotatingconfiguration

21102-6 / Vol. 132, FEBRUARY 2010ded 11 Mar 2010 to 152.78.214.194. Redistribution subject to ASMThe vortex generated by the CtLVG shows high vorticity evenfurther downstream, indicating the dominance of the vortex. Thisstrong vortex significantly affects the flow in the spanwise direc-tion. The downwash induced by the CtLVG makes the flow attachon the suction surface at z=za, as with the CtSVG configuration,as observed in the result of the surface flow visualization in Ref.16. Indeed, the downwash induced by the CtLVGs might bemore effective than that generated by the CtSVGs, but the unfa-vorable effect caused by the upwash induced by the CtLVGs atz=zb significantly reduces the wing performance due to the accel-eration of flow separation on the suction surface. The frictiondistribution also shows the unfavorable effect of the upwash in-duced by the CtLVG configuration; a wider negative friction re-gion with lower values compared with the clean wing at z=zb. Thegreater strength of the vortex generated by the CtLVGs is alsoshown by the wake survey of the VGs, showing the dominance ofthe swirling flow downstream.

The flow field behind the CoSVG is dominated by the lateralflow component rather than the swirling flow, and the vortexquickly dissipates as it develops downstream. This lateral flow isidentified in the result of the surface flow visualization in Ref.16, where the spanwise flow pattern appeared. This is becausethe interaction between neighboring co-rotating vortices tends tocancel each others downwash and upwash, accelerating the decayof the vortices and enhancing the lateral component of the flow.Therefore, the CoSVG configuration has a lesser effect on sepa-ration control than the counter-rotating configurations in the cur-rent investigation. The quicker decay of the vortices induced bythe CoSVGs, compared with the CtSVGs captured here, is in goodagreement with the investigation of Pauley and Eaton 21. Theseresults suggest that wider device spacing between each vane couldinduce more effective co-rotating vortices on the separation con-trol, such that the interaction becomes less effective. In summary,the computational investigation reveals aerodynamic characteris-tics of an inverted single-element wing with VGs in ground effect,

Counter-rotatingza(symmetric B.C.)U

zb(symmetric B.C.)

Clean_CFDCoSVG(z=zc)_CFD

Co-rotatingzc(periodic B.C.)

zc(periodic B.C.)

U

CtLVG(z=zb)_CFD

on distributions on suction surfaceconfigurations and b co-rotating

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afp

5

ws

x/c

J

Downloand advantages of a use of the CtSVG configuration is presentedor the separation control, supported by a number of detailedhysical evidences.

Concluding RemarksThree-dimensional computations of an inverted single-element

ing with VGs in ground effect are performed by steady RANSimulations, and the following conclusions are drawn.

Validation for the computations is demonstrated, regardingforce, pressure, and wake characteristics compared with ex-periments. The computations show good agreement with theexperimental results, confirming the applicability of thecomputational approach used.

The clean wing shows flow separation downstream of 70%chord, represented by a constant pressure region on the suc-tion surface. Both the counter-rotating VG configurations,however, show a moderate pressure recovery slope toward

(a)

(b)

(c)

0

-0.01

-0.02

-0.03

yw/c

0

-0.01

-0.02

-0.03

yw/c

x/c=0.63

0.5U

0

-0.06

-0.08

-0.10

yw/c

-0.02

-0.04

z/c0-0.01 0.01 -0.01

z/c0-0.01 0.01 -0.01

z/c0-0.02 0.04-0.04 0.02 -0-0.04

-25 250x

Fig. 8 Characteristics of VG-generated=0.63, 0.72, and 0.81: a CtSVG, b CtLV

ournal of Fluids Engineeringded 11 Mar 2010 to 152.78.214.194. Redistribution subject to ASMthe trailing edge and eliminate the constant value region,indicating elimination or reduction in flow separation.

The computed force characteristics at =1 deg show thatboth the counter-rotating VG configurations can delay theonset of the downforce reduction phenomenon due to thesuppression of the flow separation, and produce higherdownforce than the clean wing at low ride heights.

Variances of the friction in the spanwise direction are ob-served downstream of the counter-rotating VGs due to thesecondary flow induced by the VG-generated vortices. Thedownwash on the suction surface induces higher values ofthe friction suppressing the flow separation; meanwhile, theupwash induces low friction. The adverse effect of the up-wash regarding the separation control is negligibly small inthe CtSVG configuration; meanwhile, the upwash generatedby the CtLVGs induces obvious unfavorable effects. TheCoSVG configuration exhibits a very small difference of thefriction distribution compared with the clean wing, however,

VG

x/c=0.72x/c=0.63 x/c=0.81

=0.72 x/c=0.81z/c0 0.01

z/c0-0.01 0.01

z/c0 0.01

z/c0-0.01 0.01

z/c0 0.040.02

z/c0-0.02 0.04-0.04 0.02

rtex in cross plane at h /c=0.090 at x /cand c CoSVG

FEBRUARY 2010, Vol. 132 / 021102-7.02

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the CoSVG configuration shows the flow separation slightlyfurther downstream.

The flow field survey downstream of the VGs features thebreakdown and dominance of the VG-generated vortex inthe flow. The vortex generated by the CtSVGs grows in sizeand breaks down as it develops downstream, while the vor-tex generated by the CtLVGs shows high vorticity even fur-ther downstream, indicating the dominance of the vortex inthe flow.

The flow field behind the CoSVGs is dominated by a lateralflow, having the spanwise flow component rather than aswirling flow, and the vortex quickly dissipates as it devel-ops downstream. This is because the interaction betweenneighboring co-rotating vortices is likely to enhance the lat-eral component of the flow. Due to this behavior of the

A

MoS

NR

G

densityx streamwise wall shear stress

x nondimensional streamwise vorticity =w /y

v /zc /U

GlossaryCoSVG co-rotating sub-boundary layer vortex

generatorCtLVG counter-rotating large-scale vortex generatorCtSVG counter-rotating sub-boundary layer vortex

generatorS-A Spalart-Allmaras

References1 Zhang, X., Toet, W., and Zerihan, J., 2006, Ground Effect Aerodynamics of

0

Downloavortex, the CoSVG configuration exhibits less effect interms of the separation control than the other VG configu-rations in the current study.

The computational investigation performed here revealsaerodynamic characteristics of an inverted single-elementwing with VGs in ground effect, and highlights the advan-tages of using the CtSVG configuration for flow separationcontrol.

cknowledgmentY. Kuya gratefully acknowledges the financial support of theinistry of Education, Culture, Sports, Science and Technology

f Japan and the School of Engineering Sciences, University ofouthampton.

omenclatureoman Symbols

CDs sectional drag coefficient =2Ds /U2 c

CFx streamwise friction coefficient =2x /U2

CLs sectional downforce coefficient =2Ls /U2 c

CP pressure coefficient =2p p /U2

c wing chordDs sectional drag

h wing ride heighthVG device height of vortex generator

Ls sectional downforcep pressure

p freestream static pressureU freestream velocity

ui Cartesian components of velocity: streamwise,lateral, and spanwise directions =u ,v ,w

xi Cartesian tensor system: streamwise, lateral,and spanwise directions =x ,y ,z

yw distance from wall or wing surfacey+ normalized wall distance

za ,zb ,zc spanwise ends of computational domain

reek Symbols wing incidence

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17 FLUENT, 2005, FLUENT 6.2 Users Guide, ANSYS Inc., Southpointe, PA.18 Zerihan, J. D. C., 2001, An Investigation Into the Aerodynamics of Wings in

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