12th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan (Online), July 19-22, 2022

YAWED AHMED BODY: IMPACT OF VERTICAL FLAPS ON FLOWSTRUCTURES

Sukruth Satheesh
Laurent Cordier
Franck Kerhervé
sukruth.satheesh@univ-poitiers.fr laurent.cordier@univ-poitiers.fr franck.kerherve@univ-poitiers.fr

Andreas Spohnandreas.spohn@ensma.fr

Département Fluides, Thermique et Combustion, Institut Pprime, UPR 3346 CNRS,ENSMA, Université de Poitiers, 86360 Futuroscope-Chasseneuil, France

ABSTRACTof the middle plane.
Flaps in various configurations and control mechanisms
have been studied for drag reduction. However, there are very
limited studies that correlate forces to the physics of flow separation, both on the leading and trailing parts of Ahmed-body.
This phenomenon is of greater relevance when the body is at
an angle with respect to the flow direction (i.e. yaw). The
present work therefore focuses on identifying the variation offlow separation regions and their effect on horizontal forcesusing visualization techniques, on Ahmed body models withsquare-back configuration and with vertical flaps mounted onlateral edges at a fixed deflection angle.
A significant amount of literature on flaps of various
sizes and different configurations, and their effect on generated forces exists. The work by Fourrié et al. (2011) presents
a detailed explanation regarding the effect of a single horizontal deflector on Ahmed body with a fixed, slanted rear window
on lift and drag forces. It indicated existence of an optimum
deflector angle at which drag is minimized due to the disruption of counter-rotating vortices generated by the lateral edges.
Littlewood & Passmore (2010) studied the effect of chamfering implemented only on a small part of the upper trailingedge of a bluff body and reported significant drag reduction
due to change in flow orientation resulting in higher base pressures. de la Cruz et al. (2017) conducted a series of wind tunnel tests on Ahmed body with vertical flaps mounted on thelateral edges over a range of flap angles, with both flaps moving in a symmetric or even an asymmetric manner, and bodyyaw angles. They found that minimum drag is achieved when
the flaps are deflected asymmetrically in cases involving modelyaw due to a smoother taper (boat-tailing), resulting in wakesize reduction. Grandemange et al. (2015) have conductedwind tunnel experiments to look at the effect of chamfering
the top and bottom sections of the base region of a squareback Ahmed body over different yaw angles, and found thatchamfering contributes significantly to drag reduction. Beaudoin & Aider (2008) have studied a range of deflectors operating in various combinations, and their effect on lift and dragon a Ahmed body with a slant-back. They found that verticaldeflectors mounted about the slant surface have greatest effectin reducing drag and lift due to recirculation area enlargement.

The vortical structures and aerodynamic drag generated
by an Ahmed body with square back are studied for various
yaw angles. To reduce the impact of yaw and drag the rear-end
is equipped with two trailing edge flaps along the lateral sides.
The experiments combine force measurements and flow visualizations inside a low-speed water tunnel at Reynolds numbers of O[104 ]. Under yaw conditions strong vortical structures form on the rounded front part, while drag increases.
Inclining the flaps inwards towards the middle plane of themodel leads to a drag reduction of about 2.5%. The resultsfrom flow visualization also highlight the yaw dependency ofconical vortices existing on the model roof.

INTRODUCTION
Reducing drag and lift of ground vehicles remains a major challenge to improve energy efficiency and thus pollution.
The so-called Ahmed body (Ahmed et al. (1984)) has becomea standard configuration to experiment new techniques in viewof aerodynamic improvement. The sharp corners at the rearend of the Ahmed body with square back lead to massively
separated flow and high pressure drag. Therefore, most attempts are directed to increase base pressure along the rear
panel. To achieve this goal many recent studies used injectionof momentum to do virtual form shaping by acting on the mixing process shortly upstream and downstream of flow separation. Another well-known technique is to change the shape ofthe rear-end by adding flaps. Flaps allow to increase pressure
before flow separation and thus increasing the base pressure.
All these techniques must be optimized to get the best compromise between energy expended and/or detrimental geometric deformation of the base configuration. When transposing
results from all these studies under controlled flow conditions
without yaw to more realistic road conditions, with fluctuating
side-wind, the obtained results are often too optimistic. The
aim of the present study is to investigate the impact of yaw
on the vortical flow structure and drag forces of Ahmed body.
In order to minimize the aerodynamic drag under yaw the rearend is equipped with trailing edge flaps along each lateral side.
These flaps can be inclined at various angles inward or outward

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12th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan (Online), July 19-22, 2022
They also report that vertical flaps operating in tandem withother specific flaps offer greater force reduction when compared only to vertical ones. In a recently published study, Tran
et al. (2022) have performed force and skin-friction measurements on a slant-back Ahmed body in yaw. Their drag andlift measurements presents certain distinct characteristics. The
plots present minimal changes in drag and lift magnitudes overa small range of angles (β = 0◦ − ±3◦ ), post which the trends
are linear. This hints at yaw insensitivity of forces over a small
range of angles. However, no further analyses has been presented to elucidate this aspect.
In all, this indicates that a gap in understanding with regards to the flow topology in a yawed Ahmed body. The focusof this work involving Ahmed body is to identify the effectof vertical flaps on the observed flow structures quantitatively
and qualitatively, and comparing it against that presented by aconfiguration without flaps.

Figure 1.

Experimental setup

on Ahmed body in yaw, operating both with and without flaps.
Figure 1 presents the experimental setup. Rectangular flaps
spanning 3 cm in length (s), height equal to that of the Ahmed
body, and deflection of ±5◦ (measured w.r.t. the flow direction) were fabricated and fixed onto the vertical edges of the
Ahmed body. These dimensions were selected based on the results in literature wherein flaps with these specific dimensions(s/l = 10.3%) presented the best trend in drag reduction.

EXPERIMENTAL SETUP
The paper is organized as follows. First, the experimental setup is explained followed with a description and discussion of the drag forces and the flow structures obtained
through visualization, for the different Ahmed body configurations tested here. Experiments are conducted in the freesurface water channel Hydra III at Institut Pprime (Poitiers,
France). The overall test section- 2.1 m long and 0.51× 0.33
m2 in cross-section is made of glass windows to allow opticalaccess, with the freestream velocity ranging from 0.05 to 0.45
ms−1 . A square-back Ahmed body model (0.292 (l)× 0.109(w)× 0.0806 (h) m) is installed in the front portion of the test
section. The model is mounted on a plate to replicate the effectof ground, with the leading edge of the plate located ∼ 0.65h
ahead of the model. The leading edge of the plate is chamfered
to fix and stabilize the front stagnation point, and the height ofmodel legs being ∼ 0.18h. This model-plate combination is
also elevated from the channel floor by ∼ 0.68h to avoid theground boundary layer from affecting the flow across model.
Experiments are performed over a range of model yaw angles (0◦ − 15◦ ) and Reynolds numbers Reh , based on the freestream velocity and model height (Reh ∼ O[103 − 104 ]). The
yaw angle (β ) is defined classically as the angle between theincoming flow direction and Ahmed body main axis. Hydrogen bubble-flow visualizations are performed in the horizontal
plane at mid-body height to characterize the flow in terms of
separation along lateral sides of the body and wake development. A 50 µm stainless steel wire mounted taut between 2
supports is used as cathode– source of hydrogen bubbles when
supplied with a voltage of 80 V from a regulated power source.
The wire is located just at the front of body and in contact withthe leading face to seed the boundary layer developing on themodel. Pulsed or continuous bubble sheets can be generatedusing a computer-controlled electronic switch. Image acquisition is through a 2048×2048 pixels USB3 camera operating at
80 Hz.
For force measurements, the entire setup was mounted in
an inverted direction, i.e. the model was suspended from a
vertical strut and connected to a piezoelectric load-cell rated
for 10 N and with a resolution of 0.002 N. The blockage ratio, computed as the ratio of model area to the water channel
cross-sectional area was 5% when β = 0◦ , and increases withyaw reaching around 9% at β = 15◦ , the maximum yaw angle tested here. All the force measurements were conducted at
Reh = 16 × 103 , while the flow visualizations at Reh of 8×103
in order to elaborate on the various flow structures observed

RESULTS & DISCUSSION
The model was mounted within the water channel suchthat the main axis of the body is aligned with the channel
axis, thus ensuring that the model was equidistant to the channel sidewalls, and the model yaw angle implemented using a
servo. The specified yaw angle and the actual implemented
yaw angle were compared using a camera, the difference being less than ± 0.25◦ . The force data from the piezoelectric
sensor was sampled at 1 kHz, and the measured force signal
filtered to account for the effect of noise and drift. The filtereddrag force signal was averaged (F) and non-dimensionalizedusing dynamic pressure and the exposed area (A, at β = 0◦ ) toobtain drag coefficient, as seen in equation 1 and ρ being fluid
density. The data was acquired for 180 seconds at each yaw
angle, the acquisition undertaken after the flow unsteadinessdue to model rotation minimized.

F
2
ρU
∞ ·A
2

CD = 1(1)

Reynolds number (Reh = ρU∞ h/µ) is calculated based onmodel height and µ the dynamic viscosity of water.

Effect of yaw and vertical flaps on horizontal
forcesOver the years significant amount of numerical and experimental studies on ground vehicles have been conducted.
This has resulted in a wide range of datasets involving various
configurations of Ahmed body– square-back, slant-back, basecavity profiles, and deflector configurations amongst others,
over different Reynolds numbers. However, there are limited
works on Ahmed body in cross-flow. Figure 2 presents thevariation of drag coefficient with yaw angle of the different
configurations under consideration here. The -5◦ flap angle
corresponds to the scenario wherein flaps are directed towards
the model centerline, while +5◦ flap angle the opposite. From
figure 2, it can be observed that CD for all the configurations
increases with yaw, as expected. This is due to the creationof pressure difference about the lateral model faces (windward
and leeward flow regions) with yaw, resulting in drag force increase. The plot also highlights the fact that the drag generated
by the +5◦ flap configuration is consistently higher than that by2

12th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan (Online), July 19-22, 2022
the square-back or -5◦ flap configurations. In terms of magnitude, the drag values obtained over these experiments are
consistent with that available in literature. Lorite-Dı́ez et al.
(2020) have conducted wind-tunnel tests to study the effect ofbase cavity profiles on drag and compared it against a squareback model at Reh = 105 over yaw angles 0◦ to 10◦ . Theirmeasurements for square-back configuration match well withthe current data. Verzicco et al. (2002) and Grandemange et al.
(2015) have conducted numerical and experimental studies onsquare-back configuration without yaw at Reh of 105 and 106
respectively, and the results are well in agreement. Although
the experiments by Bello-Millán et al. (2016) are on Ahmed
body with a slant-back profile at Reh = 2 × 105 , the change inmagnitude of model blockage and the associated drag rise with
yaw are similar to that in current experiments. Owing to theabsence of ground plate in the current force experiments, it isessential to eliminate the effect of free surface waves from dragvalues. Based on the works of Chaplin & Teigen (2003) onvertical, surface piercing cylinders and by Satheesh & HueraHuarte (2019) on the effect of free surface on flat plates of different aspect ratios operating in cross-flow, it has been foundthat a model generates approximately 25% higher drag near
the free surface than when located away from the boundaries.
These results are applicable over a specific range of Reynolds
numbers (O[103 −105 ]) and Froude numbers and has been utilized in the current measurements to minimize the contributionof wave drag to the total drag. Although the results by Tran
et al. (2022) mention insensitivity in drag over a small range ofyaw angles for a slant-back Ahmed body, no such trends havebeen observed in the current scheme. This is due to greater
yaw angle resolution and lower blockage ratio in their work
compared to the current one. However, their drag coefficientsat low yaw angles are close to the current measurements.

are of greater benefit in this scenario wherein identifying theeffect of vertical flap on the flow around body is the prime
objective. Thus, the model roof was imaged in different configurations to study the flow. Image-averaging was undertaken
to sort the instantaneous flow structures from long-term ones.
Sectors of higher light intensity indicate regions wherein theobservable flow structures are steady, while the diffuse regions
are an indication of increased mixing and/or flow separation.
The images for one of the configurations is inset in figures 3aand 3b to highlight the presence of conical vortices– one that
extends along the model length, and another that undergoes
skewing. It is observed that the conical vortices gain prominence with increasing yaw, with significant skewing of one ofthese vortices. Most of the previous visualizations have focused on the wake in order to correlate them with the measured force trends and not much attention given to flow acrossthe model roof, especially the conical vortices and their skewing. Figure 3a presents a plot indicating the change in flow
separation location with yaw on the leeward side, for different configurations. The separation location is measured withrespect to the model front-face and non-dimensionalized using model length, the separation location being measured fromimages post averaging. Therefore x/l = 0 corresponds to a
scenario where the flow separation occurs at the leading edgeof the model while x/l = 1 to when the separation occurs at
model’s trailing edge. The plot indicates that the separation
point moves upstream with yaw in all configurations, as expected. It also indicates that the presence of flaps has an influence on the separation point, forcing it further upstream whencompared to the square-back configuration. No measurements
have been performed on the windward side due to the absenceof flow separation post a particular yaw angle. Similarly, figure 3b presents the location of skewed conical vortex, measured with respect to the left lateral edge of model and nondimensionalized using model width. It is explicitly clear fromthis plot that vortex skewing increases with yaw in all configurations, its magnitude higher when flaps are used. From theinset images of β > 0◦ , it is also seen that the origin of skewed
vortex is on the leading edge/face of body.

Effect of vertical flaps & yaw
Figure 4 presents instantaneous snapshots (viewed fromunderneath) highlighting the effect of yaw on Ahmed bodymodels at a fixed Reh . Each column corresponds to a particular yaw angle, and each row to a specific model configuration–
square-back, and with flaps at fixed deflection angles (∓5◦ ).
Even from these instantaneous results, it is observed in all
configurations that an increase in model yaw angle results inwake to be yawed as well, as expected. The interesting partis the presence of conical vortex (observed in background, on
the roof) that appears prominently when the yaw angle is 10◦ ,with this feature being more conspicuous in models with flaps(figures 4f and 4i). Flow separation and/or reattachment on
leeward sides in all configurations is also apparent with theincrease in yaw angle (figures 4c, 4f, 4i).
Figure 5 presents a set of time-averaged flow visualization images obtained in order to observe the variation in flow
evolution and existing wake structures over a range of modelyaw angles, Reh being fixed at 8×103 . It is observed that
all the model configurations present a strong flow from themodel roof into the wake. The flow is laterally symmetric,
as expected when there is no yaw. Increasing the yaw angle results in an asymmetry– leading to observable conicalvortices that extend along the entire model length, and theskewed vortex. This is observed in all the model configura-

Figure 2. Drag coefficient variation with yaw for different
Ahmed body configurations

Yaw effectEven though Reynolds numbers provided by water tunnels are lower than those by wind tunnels, the ability to correlate the visualized flow structures with the measured forces3

12th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan (Online), July 19-22, 2022
of conical vortex along the model length, and moves inward
towards model centerline at the slant surface, with increasing
model yaw. This results in increased interaction between theconical vortex and the separated flow on the slant surface, andis expected to be the source of increased drag. However, nosuch flow separation on roof of the square-back model (vis a
vis slant-back model) is known to exist. The flow topology
is further affected with the incorporation of vertical flaps, as
can be observed from figures 4c, 4f and 4i. Apart from this,the skewing of conical vortex and its dependence on yaw is anunobserved measurement hitherto. The work of Lorite-Dı́ez
et al. (2020) involving detailed force and pressure measurements on a square-back model indicates a linear correlation
between base pressure coefficient and the horizontal force coefficient, and their PIV measurements indicate developmentof an asymmetric recirculating flow that increases with yaw.
However, further experiments are needed to ascertain whether
all the drag rise associated with yaw can be attributed only tothe yaw-induced wake asymmetry or if the skewed vortex also
has a significant contribution. Thus, the current visualizationsattest to the fact that flow topology on a square-back model incross-flow is different compared to a slant-back.

CONCLUSIONS
The results obtained over these set of experiments involving a square-back Ahmed model and with vertical flaps incross-flow have provided an unique insight into the forces andflow structures observed on model roof. The increase in dragwith yaw for all the models is as expected, both in its trend
and magnitude. The conical vortices highlight the flow transition occurring on the model roof with increasing yaw. Oneof the conical vortex extend downstream into the wake in all
configurations, with its angle always lagging the imposed yaw
angle. The instantaneous global flow and the time-averaged
wake flow visualizations also indicate the prominence of conical vortex in cross-flow conditions. Meanwhile, another conical vortex skews increasingly with yaw, its skewing angle dependent on the presence of vertical deflectors. The skewing
process is expected to be directly related to the imposed yaw
angle. However, further experiments are necessary to elucidate this aspect and the reason for lag between the imposed
yaw angle and the conical vortex extending along the model
length, and are points of interest for future research. In all, thecurrent force measurements and flow visualization conducted
at Reh ∼ O[104 ] are in good agreement with literature wherein
Reh are even higher (O[105 − 106 ]).

Figure 3. Variation with yaw of (a) flow separation locationon leeward side and (b) conical vortex skew location

tions, their prominence increasing with yaw. Another aspectobserved from the images is that the angle subtended by theconical vortex that extends along the body length always lags
the model yaw angle. Studies (Large Eddy Simulation) by
Krajnović & Davidson (2005) and experiments by Spohn &Gilliéron (2002) involving electrolytic precipitation/ tin-flow
technique on a slant-back Ahmed body without yaw at Reh of
2×105 and ∼ 8 × 103 , respectively presents a detailed explanation regarding the different flow structures around Ahmed
body and the effect of slant-edge on the flow. These works
discuss the dynamics and trajectory of a conical vortex (Tr,lvortex systems in Krajnović & Davidson (2005)) in the presence of a slant-edge, indicating that the existence of conicalvortex and its extension along the entire model length. However, what is explicitly clear from the current work is that theconical vortex is not specific to a model geometry, and its evolution is dependent on model yaw.
Although the flow topology for the slant-back model has
been well described by several researchers, results are nonexistent for the square-back model, especially in cross-flow
condition. Besides force measurements, the work by Tran
et al. (2022) also estimated skin-friction drag on slant-backAhmed body using a luminescent oil, and report the extension

ACKNOWLEDGMENTS
The present work is funded by the French organization
ANR under the project COWAVE ANR-17-CE22-0008.

REFERENCES
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Bello-Millán, F. J., Mäkelä, T., Parras, L., Del Pino, C. & Ferrera, C. 2016 Experimental study on Ahmed’s body dragcoefficient for different yaw angles. Journal of Wind Engineering and Industrial Aerodynamics 157, 140–144.

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12th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan (Online), July 19-22, 2022

Figure 4. Instantaneous flow around different Ahmed body configurations at Reh = 8 × 103 (flaps highlighted in red) and different
yaw angles

Figure 5.

Time-averaged hydrogen bubble-flow visualization of Ahmed body wake plane in various configurations at Reh = 8 × 103

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