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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:
[email protected]
Kenji TakedaSenior Lecturer
e-mail: [email protected]
Xin ZhangProfessor
e-mail: [email protected]
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,
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-
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
21102-8 / Vol. 132, FEBRUARY 2010ded 11 Mar 2010 to
152.78.214.194. Redistribution subject to ASMRace Cars, Appl. Mech.
Rev., 59, pp. 3349.2 Katz, J., 1985, Calculation of the Aerodynamic
Forces on Automotive Lifting
Surfaces, ASME J. Fluids Eng., 107, pp. 438443.3 Knowles, K.,
Donoghue, D. T., and Finnis, M. V., 1994, A Study of Wings in
Ground Effect, Proceedings of the Loughborough University
Conference onVehicle Aerodynamics, Vol. 22, pp. 113.
4 Zerihan, J., and Zhang, X., 2000, Aerodynamics of a Single
Element Wing inGround Effect, J. Aircr., 376, pp. 10581064.
5 Zerihan, J., and Zhang, X., 2001, Aerodynamics of Gurney Flaps
on a Wingin Ground Effect, AIAA J., 395, pp. 772780.
6 Soso, M. D., and Wilson, P. A., 2006, Aerodynamics of a Wing
in GroundEffect in Generic Racing Car Wake Flows, Proc. Inst. Mech.
Eng., Part D J.Automob. Eng., 2201, pp. 113.
7 Kuya, Y., Takeda, K., Zhang, X., Beeton, S., and Pandaleon,
T., 2009, FlowSeparation Control on a Race Car Wing With Vortex
Generators in GroundEffect, ASME J. Fluids Eng., 131, p.
121102.
8 Zerihan, J., and Zhang, X., 2001, A Single Element Wing in
Ground EffectComparisons of Experiments and Computation, AIAA Paper
No. 2001-0423.
9 Spalart, P. R., and Allmaras, S. R., 1992, A One-Equation
Turbulence Modelfor Aerodynamic Flows, AIAA Paper No.
1992-0439.
10 Zhang, X., and Zerihan, J., 2003, Off-Surface Aerodynamic
Measurements ofa Wing in Ground Effect, J. Aircr., 404, pp.
716725.
11 Mahon, S., and Zhang, X., 2005, Computational Analysis of
Pressure andWake Characteristics of an Aerofoil in Ground Effect,
ASME J. Fluids Eng.,127, pp. 290298.
12 Kieffer, W., Moujaes, S., and Armbya, N., 2006, CFD Study of
Section Char-acteristics of Formula Mazda Race Car Wings, Math.
Comput. Model. Dyn.Syst., 43, pp. 12751287.
13 Mahon, S., and Zhang, X., 2006, Computational Analysis of a
InvertedDouble-Element Airfoil in Ground Effect, ASME J. Fluids
Eng., 128, pp.11721180.
14 Diasinos, S., Barber, T. J., Leonardi, E., and Hall, S. D.,
2004, A Two-Dimensional Analysis of the Effect of a Rotating
Cylinder on an InvertedAerofoil in Ground Effect, Proceedings of
the 15th Australian Fluid Mechan-ics Conference.
15 Diasinos, S., Barber, T., Leonardi, E., and Gatto, A., 2006,
The Interaction ofa Rotating Cylinder and an Inverted Aerofoil in
Ground Effect: Validation andVerification, AIAA Paper No.
2006-3325.
16 Kuya, Y., Takeda, K., Zhang, X., Beeton, S., and Pandaleon,
T., 2009, FlowPhysics of a Race Car Wing With Vortex Generators in
Ground Effect, ASMEJ. Fluids Eng., 131, pp. 121103.
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
Ground Effect, Ph.D. thesis, University of Southampton, UK.19
Allan, B. G., Yao, C.-S., and Lin, J. C., 2002, Simulation of
Embedded
Streamwise Vortices on a Flat Plate, NASA Technical Report No.
CR-2002-211654, ICASE Report No. 2002-14.
20 Lin, J. C., 1999, Control of Turbulent Boundary-Layer
Separation UsingMicro-Vortex Generators, AIAA Paper No.
1999-3404.
21 Pauley, W. R., and Eaton, J. K., 1988, Experimental Study of
the Develop-ment of Longitudinal Vortex Pairs Embedded in a
Turbulent Boundary Layer,AIAA J., 267, pp. 816823.
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