The influence of cornering on the
vortical wake structures of an inverted
wing
James Keogh
1
, Graham Doig
1,2
, Sammy Diasinos
3
and Tracie Barber
1
Abstract
The aerodynamic performance of inverted wings on racing-car configurations is most critical when cornering; however,
current wind tunnel techniques are generally limited to the straight-line condition. The true cornering condition intro-
duces complexity because of the curvature of the freestream flow. This results in an increase in the tangential velocity
with increasing distance from the instantaneous centre of rotation and causes the front wing to be placed at a yaw angle.
Numerical simulations were used to consider an 80% scale front wing when steady-state cornering with radii ranging
from 60 m to 7.5 m, and yaw angles ranging from 1.25° to 10°. The changes to the pressure distribution near the end-
plates caused the wake structure to become highly asymmetric. Both the primary longitudinal vortices and the second-
ary longitudinal vortices differed in strength, and the vortex core positions shifted in the vertical direction and the
spanwise direction. The change in the position became more substantial further downstream as the structures tended
toward the freestream direction. The effects on the wing surface pressure distribution resulted in the introduction of
yawing and rolling moments, as well as a side force and an increase in drag. The results demonstrate the importance of
evaluating the cornering condition if that is where a good performance is most sought after.
Keywords
Vehicle aerodynamics, cornering, ground effect, aerodynamics, computational fluid dynamics
Introduction
Aerodynamic evaluation of bodies while cornering
In motorsport, aerodynamic devices are used to pro-
duce a downforce which increases the tyre adhesion and
ultimately enables higher levels of acceleration to be
achieved.
1,2
This permits modern racing cars to corner
at much higher speeds.
Despite the fact that the aerodynamic performance
is most critical when cornering, designs will typically be
evaluated in the straight-line condition, including com-
binations of yaw. This is largely because the wind tun-
nel remains the primary tool for aerodynamic
development. There have been previous attempts to
replicate the cornering condition in a wind tunnel with
the use of bent models
3
and curved test sections,
4
but
these methods are not capable of representing all
aspects of true cornering flow. Industry is aware of the
limitations of these methodologies.
4
At present, the
true condition has not been achieved experimentally in
the public domain, meaning that numerical simulations
are typically preferable for this type of analysis.
The real-world conditions experienced by an open-
wheel racing car have been identified to have a signifi-
cant effect on the aerodynamic performance.
Parameters such as the pitch, the yaw, and the ride
height are already known to have dramatic effects.
5
An
entire open-wheel racing-car geometry was numerically
analysed for three specific corners at the Fuji Speed
Way Circuit.
6
The study incorporated the changes in
the pitch and the ride height, in addition to cornering.
Variation occurred in the lift force and the drag force,
as well as in the yawing moment and the side force. No
1
School of Mechanical and Manufacturing Engineering, University of New
South Wales Australia, Sydney, New South Wales, Australia
2
Aerospace Engineering Department, California Polytechnic State
University, San Luis Obispo, California, USA
3
Department of Engineering, Macquarie University, Sydney, New South
Wales, Australia
Corresponding author:
James Keogh, School of Mechanical and Manufacturing Engineering,
UNSW Australia, Sydney, NSW, 2052, Australia.
Email: j.keogh@unsw.edu.au
Keough, Doig, et al. Published in Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering.
February 26, 2015. 1-13.
fur
ther details regarding the flow structures responsible
for these changes was presented, and the effects due to
cornering were not clearly distinguished from the
effects due to other parameters.
Okada et al.
7
and Tsubokura et al.
8
demonstrated
the importance of evaluating the high-speed cornering
condition during the aerodynamic design phase for a
commercial vehicle. Considering a medium-sized sedan
geometry, the outboard pressure losses were identified
that contributed to a negative yawing moment and side
force. This caused a damping effect that restrained the
vehicle during cornering. For two different geometries
the magnitude of this force varied for various vehicle
shapes. A temporal variation in the vehicle reacting to
the change in the conditions also occurred. A 49% dif-
ference in the aerodynamic damping toward the steer-
ing motion existed between the two geometries; this
was largely attributed to the increased space around
the wheels in the wheel well.
In motorsport, the aerodynamic performance when
cornering becomes even more critical.
2,9,10
Typical
racing-car configurations consist of multiple compo-
nents which interact to produce a desired aerodynamic
outcome. The front wing is most likely to have access
to relatively clean flow and has a significant influence
on the aerodynamic performances of the downstream
components.
9,11
The vortical wake leaving the front
wing then becomes a critical consideration.
Inverted wing aerodynamics
The most comprehensive set of straight-line experimen-
tal results were conducted by Zerihan.
12
He used an
inverted T026 aerofoil with endplates, considered across
various ground clearances. Studies of this geometry
were presented by Zerihan,
12
Zerihan and Zhang,
13
and Zhang and Zerihan,
10,14
considering both the
single-element configuration and the double-element
configuration. Investigations presented the surface pres-
sures, the forces, and the wake measurements, defining
several key aerodynamic characteristics.
Close proximity to the ground resulted in increased
acceleration of the flow beneath the inverted suction
surface, creating a strong low-pressure region beneath
the wing surface. Near the midspan location the flow
tended toward a two-dimensional state and the adverse
pressure gradient increased as the ground clearance
was reduced. A critical point was reached where signifi-
cant trailing-edge separation resulted in the occurrence
of the ‘downforce loss phenomenon’ at approximately
h/c = 0.112.
The flow near the endplate was characterized by the
primary and secondary vortices, as well as by a number
of smaller flow structures.
10
The primary vortex formed
inside the endplate, as shown in Figure 1, owing to the
large pressure gradient. The primary vortex was identi-
fied as an important flow structure for operating effi-
ciently in close proximity to the ground. The vortex
alleviated the adverse pressure gradient and permitted
lower ground clearances to be achieved.
15
The second-
ary vortex formed outside the upper edge of the end-
plate. Increased pressure inside the endplate over the
pressure surface resulted in a smaller pressure gradient,
which produced a weaker vortex.
Soso and Wilson,
16
however, highlighted the sensi-
tivities of an inverted wing to change in the oncoming
flow. When a wing was positioned in the wake of a gen-
eric racing car, a significant loss in the downforce was
found to occur.
These findings, together with the little research con-
ducted into aerodynamics when cornering,
6–8
strongly
suggest that a significant change will occur for an
inverted wing in the cornering condition. In a practical
sense, understanding the aerodynamic performance in
Figure 1. Location of the primary vortices and the secondary vortices in the straight-line condition.
Figure 2. (a) The cornering flow conditions; (b) the effect of
understeer toward the flow seen by the front wing; (c) the
effect of oversteer toward the flow seen by the front wing.
this condition could be argued as more critical than in
the straight-line condition.
4
Dynamics of cornering
Modern aerodynamicists have become familiar with a
stationary model where the flow field is in motion.
When cornering, obviously this relative motion is no
longer in a straight line. As the vehicle follows a curved
path, so does the flow relative to the vehicle, as is shown
in Figure 2(a). The relative velocity of the flow increases
with increasing distance from the centre of rotation. In
percentage terms, corners with tighter radii will increase
the velocity gradient across the span. The flow curva-
ture will also vary and is greater as it becomes closer to
the centre of rotation. The variation in the curvature
means that the yaw angle of the wing will also vary
slightly across the span.
The attitude of the vehicle will have a significant
effect. Understeer or oversteer, shown in Figure 2(b)
and Figure 2(c) respectively, can cause the wing to be
correspondingly closer to or further away from the cen-
tre of rotation. This causes changes in both the velocity
and the effective angle of the oncoming flow.
In corners with the tightest radii, the aerodynamic
forces are reduced in magnitude as the speed of the
vehicle is limited by the acceleration able to be
sustained. Despite this, some racing cars will spend
much time in this condition, making small gains very
advantageous.
4
As a result, the aerodynamic perfor-
mance in this condition can become crucial.
Method
Numerical method
The present study utilizes numerical simulations to
investigate the aerodynamics of an isolated inverted
wing when cornering at a constant radius and a steady
state. All results were generated with the use of the
commercial finite-volume solver ANSYS Fluent 14.5,
17
as is prominent throughout industry. Reynolds-aver-
aged Navier–Stokes simulations were used. Previous
studies have proven this technique to be effective for
simulating the same geometry in the straight-line condi-
tion,
15,18–21
and it remains the preferred technique
within industry, as it is more computationally feasible
for development. This study represents the first investi-
gation into the aerodynamic performance of an isolated
inverted wing in the cornering condition.
The pressure-based implicit coupled solver was
utilized to achieve steady-state simulations.
Compressibility effects at the simulated Mach numbers
were deemed negligible, in accordance with the conclu-
sions of previous studies.
19,21,22
Simulations were run
using a second-order node-based upwinding discretiza-
tion scheme across 64 processors. Convergence was
deemed to be met when the aerodynamic forces ceased
to change by more than 0.02% over 1000 continued
iterations, and a point velocity monitor placed near the
centre of the primary vortex also ceased to change by
more than 0.02%. For all simulations, the scaled resi-
dual errors fell below 8 3 10
25
.
The coordinates of the aerofoil can be found in the
thesis by Zerihan.
12
A chord length of 223.4 mm and a
span of 1100 mm gave an aspect ratio of 4.92. The wing
also features a rectangular endplate measuring 250 mm
3 100 mm 3 4 mm. The wing features a blunt trailing
edge 1.5 mm thick. The wing was described as being at
an incidence of 3.45°. Since the wing is symmetric, vali-
dation and straight-line cases were run for the semispan
with a symmetry plane placed at the midspan location.
The present numerical study was validated against
the published experimental results
12
. These experiments
were conducted in the Southampton Low-Speed Wind
Tunnel, which had test-section dimensions of 2.1 m
3 1.7 m with an octagonal cross-section. The oncoming
air was reported at 30 m/s within an error of 60.2%.
The freestream turbulence intensity was given as 0.2%.
An overhead force balance was utilized for measure-
ment of all the forces. For the numerical validation
cases conducted in the current study, a simplified rec-
tangular cross-section was utilized that matched the
maximum extents of the wind tunnel.
23
A further sim-
plification of the numerical model was the use of a
moving ground plane across the entire width of the test
Figure 3. Examples of the mesh structure: (a) isometric view; (b) midspan location; (c) straight-line condition; (d) cornering
condition.
section. The boundary layer growth on the walls was
not reported from the experiments but can be expected
to have a minimal influence owing to the low blockage
ratio. As a result, the walls and the roof of the domain
were modelled as zero-shear slip walls. The domain
was modelled 7c upstream and 15c downstream.
A density of 1.22 kg/m
3
gave a Reynolds number Re
of 4.54 3 10
5
which fell within the reported range for
the experimental data. In the published experiments a
grit strip was located at 0.1c on both the pressure and
the suction surfaces of the wing. This enabled the the
present computational model to be designed such that
laminar and turbulent boundary layer regions were
replicated.
A multi-block, fully structured meshing technique
was employed. Cells were concentrated near the bound-
aries and four chord lengths downstream of the trailing
edge to ensure that the near-wake behavior was accu-
rately represented. Cells were additionally concentrated
near the endplate region to obtain the prominent upper
+
and lower vortices. The y value remained below 1
over the wing, the endplate, and the ground plane.
Three mesh densities were assessed at h/c = 0.179 to
determine the required resolution; an omnidirectional
refinement ratio of 1.2 was applied to successive mesh
densities. The medium mesh consisted of a total of
7.6 3 10
6
cells with 117 spanwise cells and 185 chord-
wise cells. The fine mesh and the coarse mesh consisted
of 13.6 3 10
6
cells and 4.7 3 10
6
cells respectively.
Examples of the mesh construction in an isometric view
and at the symmetry plane are shown in Figure 3(a)
and Figure 3(b) respectively. Efforts were particularly
concentrated on ensuring that high-aspect-ratio cells
existed only parallel to the flow at the boundary.
For all further cases (post-validation), the boundary
layer was assumed to be fully turbulent, and the
domain was extended in all directions. A boundary sen-
sitivity study was undertaken and, as a result, the outlet
was extended to 50c downstream. The walls, the roof,
and the inlet were also extended to a distance of 10c.
Beyond these distances the aerodynamic forces ceased
to change by more than 0.01%. The mesh around the
body was reflected about the z axis and the x axis to
incorporate the whole geometry, as shown in Figure
3(a). This gave a total of 17.2 3 10
6
cells. The bound-
aries of the domain were modified to accommodate the
path of the freestream flow, and the cells were also
aligned in this direction. This transformation of the
domain is shown in Figure 3(c) and (d). A rotating ref-
erence frame was used for all cases with flow curvature.
The steady-state cornering condition was achieved by a
constant angular velocity about a fixed point, external
to the domain.
Validation
The results for the mesh study were generated using the
k2v shear stress transport (SST) turbulence model,
24
coupled with a low-Reynolds-number boundary adap-
tion. The different mesh sizes were found to have very
little effect on prediction of the aerodynamic forces,
shown in Table 1. From the medium mesh to the fine
mesh, the aerodynamic forces did not change by more
than 0.8%. The higher concentration of cells across
the span increased the resolution of the downstream
wake, a noted benefit in the case of the medium mesh
and the fine mesh.
The realizable k2e turbulence model
25
with the
enhanced wall function was also assessed against the
experimental data. The k2v SST model was found to
be particularly sensitive to the boundary layer mesh
construction, and a slow and consistent growth rate
away from the wall was required.
The results were assessed across nine ground clear-
ances from h/c = 0.045 to h/c = 0.448, as shown in
Figure 4. Particular emphasis was placed on whether
Table 1. Comparison of the experimental lift coefficients and
the experimental drag coefficients for the coarse mesh, the
medium mesh and the fine mesh at h/c = 0.179.
Mesh C
L
C
D
Coarse 1.228 0.052
Medium 1.241 0.052
Fine 1.248 0.052
Experimental
12
1.28 0.055
Medium (no transition) 1.236 0.052
Figure 4. Drag coefficients and lift coefficients: comparison of
the validation cases with the experimental results.
SST: shear stress transport.
the turbulence models were capable of representing the
trends in the aerodynamic forces from the published
experimental results. At ground clearances above
h/c = 0.224, both models were found to under-predict
lift and to over-predict drag. The over-prediction of
drag was more severe in the case of the realizable k2e
model, with the k2v SST model matching the experi-
mental results more closely. The under-prediction of lift
was found to be largely attributed to an under-
prediction of the suction peak for both models at the
higher ground clearances. Below h/c = 0.134, both
models predicted the early onset of vortex burst, associ-
ated with the ‘downforce loss phenomenon’.
10,13
In the
case of the realizable k2e, this separation was under-
predicted, and the result was an over-prediction of the
suction peak and lift in close proximity to the ground,
before a severe loss in efficiency between h/c = 0.067
and h/c = 0.045. The k2v SST model showed a similar
behavior in close proximity to the ground but demon-
strated a heightened level of sensitivity to separation
induced by the adverse pressure gradient. As a result,
lift predictions were matched more closely at low
ground clearances despite the fact that the suction peak
was also over-predicted.
An important point of difference for the two turbu-
lence models is their abilities to match primary vortex
Figure 5. Streamwise vorticity contours for h/c = 0.224 at
x/c = 1.2: (a) experimental;
12
(b) k–v SST; (c) realizable k–e.
formation. A comparison of streamwise vorticity con-
tours at x/c = 1.2, in which both models were com-
pared with the published particle image velocimetry
measurements, is shown in Figure 5. Both models were
found to under-predict the maximum streamwise vorti-
city for the considered ground clearances. The strength
of the counter-rotating vortical structures inside the
endplate was also greater in the experiments and led to
an increased distance between the endplate and the pri-
mary vortex, which is evident in Figure 5. Both numeri-
cal models predicted the development of the primary
vortex to occur further downstream and this contribu-
ted toward general discrepancies. In the case of the rea-
lizable k2e turbulence model, this difference was more
