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

REGIMES OF NEAR WAKE INTERACTIONS OF A SQUARE BACK BLUFFBODY.
CONSEQUENCES FOR DRAG.

Di Bao, Jacques Borée, Yann Haffner* and Christophe Sicot
Institut Pprime
UPR 3346, CNRS-ENSMA-Université de Poitiers
86360 Futuroscope-Chasseneuil, France
Corrsponding address: jacques.boree@ensma.fr(*)Present address: Centre Scientique et Technique du Bâtiment, Nantes, France

ABSTRACT

for the same car geometry. Therefore, there is a need for intermediate model configurations that allow a rigorous parametricstudy using reference underflow perturbations.
Our choice has been to use a Windsor body (e.g. Pavia
et al. (2020)) and to perturb the wake of this simplified squareback geometry by placing, in the underflow, a pair of streamlined “D-shaped” obstacles of varying width. The two obstacles are mounted at varying relative distances from the base of
the body. In a companion experiment, the length of the same
body but equipped with rotating wheels and wheelhouses isvaried, allowing the relative distance between the rear wheels
and the base to be varied. Our goal is first to analyse how
the main wake of the body is modified by the wakes of these
perturbations, of much smaller size, developing along the underflow. The final goals are to understand how the drag of the
body is modified due to the presence of the obstacles and tovalidate the main findings on the body with wheels and wheelhouses.

The impact of underflow perturbations on the wake andaerodynamic drag of a 3-D square-back bluff body is investigated in order to analyse wheel-vehicle interactions. Two configurations are considered by placing either a pair of D-shaped
obstacles or four rotating wheels under the body. For the obstacle configuration, the obstacle width w and the distance fromthe base to the obstacles l are systematically varied. We reveal
two drag-sensitive regimes for l/w < 2.5, where the pressuredrag of the body is increased up to 22 %. These two regimes
present different flow dynamics downstream the obstacles anddifferent scaling properties for the pressure drag. For the wheel
configuration with a wheel width w, a similar pressure drag increase is also observed for l/w < 2.5. When the wheels wererotated, a scaling for the pressure drag, taking into account thedecrease in the wheel wake size, is proposed. In both configurations, the drag increase is associated to a mean mass transferfrom the near wake of the body to the wakes of the obstacles
or rear wheels.

Experimental set-up
Introduction

The experimental setup is shown in figure 1. A squareback Windsor body with height H = 0.289 m and width W =0.389 m is placed on a raised floor in the S620 closed-loop
wind tunnel at ENSMA with a ground clearance G = 50 mm.
The blockage ratio over the floor caused by the model is 2.4%. The length of the body can be modified L/H = {3.41,
3.49, 3.59, 3.68, 3.78, 3.87, 3.97}. A free-stream velocity
U0 = 25ms−1 is considered, corresponding to a height-based
Reynolds number Re = 4.8 × 105 . The origin O of the coordinate system (x, y, z) is shown in figure 1(a).
Two configurations are considered as shown in figure1(b). Firstly, when the wheelhouses of the body with length
L/H = 3.97 are plugged, a pair of D-shaped obstacles is placed
upstream the base of the body, between the underside of the
body and the floor. Five values of the width of the obstacles
w/H={0.12, 0.16, 0.19, 0.22, 0.26} are tested. The distancefrom the base of the obstacle to the base of the body is defined
as l, which ranges from l = 0w to l = 5w. Secondly, when thewheelhouses are not plugged, four electric motors are installedon the floor and are detached from the main body. The rotational speed of the motors Φ, normalized by the speed 3187
RPM matching the free-stream velocity, is varied from 0% to
100%. On each motor, a sharp edge wheel with width w/H= 0.19 and diameter d/H = 0.52 is installed and is flush to

The driving range of ground vehicles at highway speeds
is mainly dictated by the aerodynamic drag, which accounts
for over 50% of the vehicle’s total energy consumption. The
dominant contribution to the total pressure drag is the largescale near wake. The complex interaction between the wheels
and this main body wake, however, remains to be understoodin detail. This interaction was recently studied in Wang et al.
(2020) with a basic question: what are the salient features ofthe flow perturbations induced by wheels that drives this interaction? Starting from rotating/stationary wheels having representative deformable tires, it was shown that the momentum
deficit created in the underflow by the wheels, in particular therear wheels, is an important enabler to this interaction. At firstorder, it is therefore believed that wheels can be seen as underbody perturbations and that the key aerodynamic features are
the underflow blockage, the wheel’s wake development in theunderflow and its interaction with the near wake of the vehicle.
Even in very simplified reduced scale model studies using reference academic automotive geometries, it is very difficult to achieve a systematic and rigorous survey of the flowmechanisms driving wheel-wake interactions. For example,
for obvious mechanical reasons, it is very difficult to change
the width of the wheels and their location relative to the base1

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

W

L

x
z

H

y
O

G

O

Figure 1. Experimental set-up. (a) Arrangement of the model and the raised floor. (b) Configurations with the use of obstacles andthe rotating wheels. (c) Locations of pressure taps on the base and underside of the body. (d) Positions of the particle image velocimetry
fields of view.
served. For the longest body with underflow perturbed by the
obstacle pair, the variation of the base drag ∆CB = CB − CB0
for different obstacle widths w/H with varying obstacle-tobase distance l/w is presented in figure 2(a). Here the relative distance l/w is the relevant scaling as the distance to thebase is concerned. Based on the mean and fluctuating properties measured downstream the obstacles (discussed later), two
successive drag-sensitive regimes are identified for obstacleto-base distances l/w < 2.5, where pressure drag of the bodyis increased up to 22%. In different regimes, different scaling
properties for the base drag are observed (see figure 5 in Bao
et al. (2022) for the scalings). In regime I, the base drag increase from the plateau (l/w > 2.5) scales quadratically with
w. In regime II, the base drag increase relative to the unperturbed case scales linearly with w.

the floor. A 3 mm deep recess is designed to prevent the contact between the wheel and the floor. However, preliminary
tests showed that the resulting gap flow has influence on thebase pressure, maximally leading to ∼ 5% base drag decrease.
The gap flow is therefore prevented by placing a sealing kraft
paper between each wheel and the floor, producing negligible
differences in pressure measurements compared to the situation when the recess is fully sealed by high-density foam. The
distance from the rear wheels to the base is varied thanks to thevariation in the body length, which gives l/w = { 0.65, 1.08,
1.58, 2.08, 2.58, 3.08, 3.58}.
The pressure on the base and underside is monitored byseveral pressure taps shown in figure 1(c) connected to twopressure scanners. Four differential pressure sensors are additionally used for time-resolved measurements. For these sensors, the tubing leads to a cut-off frequency of 150 Hz which
is sufficient for resolving the presented time scales. The pressure coefficient C p = (p − p0 )/(0.5ρU02 ) is used to express
the pressure measurements, where the reference pressure p0
is obtained from a pitot tube installed at the ceiling of thetest section. The pressure drag of the body is quantified by
25 pressure taps over the base, defined as base drag coeffi1 25
cient: CB = − 25
∑i=1 C p (yi , zi ,t). The velocity fields in thenear-wake are measured by a PIV (Particle image velocimetry) system over three FOVs (fields of view) as depicted infigure 1(d). These three FOVs are respectively located at thesymmetry plane of the model (y/H = 0), the symmetry planeof the left-hand wheels (y/H = -0.58) and a cross-flow plane inproximity to the base (x/H = 0.03). Two-component (2D2C)
and stereoscopic (2D3C) PIV set-ups are respectively used forthe first two FOVs and the last FOV.

Results and discussion

The base drag sensitivity observed using obstacles is also
witnessed in the more applied situation when the wheels andwheelhouses are installed. The base drag evolution relative
to the unperturbed cases CB (l/w)/CB0 (l/w) for different rotational speed Φ is presented in figure 2(b). The obstacle configuration with the same w/H = 0.19 as the wheel is also shownfor comparison. With decreasing l/w, the base drag presents
first a plateau with a slight increase in base drag, followed bya rapid base drag increase, maximally leading to a base dragincrease of ∼ 13% for l/w = 0.65. The trend of base drag increase is very similar to regime I of the obstacle configuration.
Moreover, we also notice a slight decrease in base drag with
the increase in the rotational speed Φ. Considering that thewake of rotating wheels is shorter and narrower compared tostationary ones (Wäschle, 2007; Wang et al., 2020), an empirical scaling for the base drag, validated later by local pressureand velocity measurements, is simply obtained by defining anequivalent width w∗ = w/(1 + 0.2Φ). Figure 2(b) shows a collapse of all data on a single evolution when l/w∗ is used.

The flow over the basic Windsor body was first carefully measured. A detailed description for the basic bodywith length L/H = 3.97 can be found in Bao et al. (2022).
Briefly, the large-scale near wake presents a vertical wellbalanced mean topology with horizontal bi-stable dynamics(Grandemange et al., 2013). There is a slight base drag increase from CB0 = 0.189 to 0.198 with decreasing body lengthfrom L/H = 3.97 to 3.41, possibly due to the modifications in
the boundary layer profile at separation (Mariotti et al., 2015).
However no obvious changes in the wake properties are ob-

Local pressure measurements are now investigated in order to reveal the location of base drag increase. The base pressure distributions ⟨C p ⟩ (⟨⟩ denotes space-averaging from theleft-hand and the right-hand sides) and their changes relative
to the unperturbed cases ∆⟨C p ⟩ are shown in figure 3(a). The
selected representative cases are the wheel cases with maximum and minimum l/w and the w/H = 0.19 obstacle cases ofthe plateau and the two regimes. We first focus on the obstacle configuration. In the plateau, the base pressure decrease of∼ 5% from the unperturbed case is located at the bottom half2

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

Figure 2. (a) Impact of the position l and width w of the obstacles on the base drag of the body, darker color indicates wider obstacle,
different colors indicate different flow regimes (see text). (b) Base drag of the body ∆CB /CB0 as a function of the distance from thebase to the rear wheel l, darker color indicates higher rotational speed Φ, l is scaled with the width of the wheel w and a reduced width
depending on the rotating speed w∗ = w/(1 + 0.2Φ).

Figure 3. (a) Evolution of the base pressure distribution with the distance from the base to the obstacles or to the rear wheels l/w, themean values and the differences with respect to the unperturbed case are respectively presented at the left and right sides of the base.
(b) Comparison between the evolution of ⟨C p5 ⟩ and ⟨C p6 ⟩. The width of the obstacle pair is w/H = 0.19.

I. On the contrary, in regime II, ⟨C p6 ⟩ − ⟨C p5 ⟩ decreases withdecreasing l/w. For the wheel configuration, the same observation as the regime I of the obstacle configuration is achieved.

of the base with a slight pressure recovery at the top half. In
regime I, we observe a further pressure decrease at the bottom
half of the base with now also a slight decrease at the top half.
The pressure decrease is not homogeneous laterally but rather
located near the obstacles. In regime II, the base pressure isimportantly modified and the modification is mainly located at
the bottom half of the base and horizontally near the obstacle
pair. Indeed, both regimes share the same feature with pressure drop near the obstacle pair. This feature is also observed
for the wheel configuration.

The influence of the obstacles on the main wake aspresented using ⟨C p5 ⟩ changes rapidly in the drag-sensitive
regimes. The streamwise pressure development downstream
the obstacles or the wheels is therefore investigated. The pressure coefficients obtained from the available pressure taps behind the obstacles/wheels are used. Each pressure measurement is plotted against the relative distance xw /w from the tap
to the base of the obstacle or the most downstream positionof the rear wheels (detailed in figure 7 of Bao et al. (2022)).
For the obstacle configuration (figure 4(a)), a nice collapse
is found for all the cases with two different streamwise pressure developments of the obstacle wake in two regimes - green
symbols corresponds to transition between regimes. In regime
I (colored in red), the development is similar to the measurements for 2-D D-shaped bluff bodies (Bearman, 1967; Parket al., 2006) with comparable pressure level near the base.
The sharp pressure change in 1 < xw /w < 2 can be linked to
the vortex shedding motion of the obstacle through a streamwise momentum balance along the centerline of the obstacle
as shown in Bao et al. (2022). In regime II (colored in blue),the pressure near the obstacle base shows a higher level thanregime I, indicating that the obstacle wake is completely mod-In order to study the relation between local near wake interactions and base pressure variation, we consider the pressure distribution in the vicinity of the obstacles or the rear
wheels. In figure 3(b) a comparison is presented between theevolution of ⟨C p5 ⟩ and ⟨C p6 ⟩ for the reference configuration.
As shown in the sketch, pressure sensors numbered 5 and 6 aresituated in the symmetry plane of the rear wheels or obstacles
and are located at both sides of the bottom trailing edge. These
are the key locations for the problem considered here. For the
obstacle configuration, in the plateau, ⟨C p5 ⟩ is slightly higher
than ⟨C p6 ⟩. This is expected for a mean curved streamline after
separation, inducing a lower pressure inside the recirculating
bubble due to centrifugal effect. However in both regime I
and II, ⟨C p5 ⟩ is lower than ⟨C p6 ⟩. With decreasing l/w, thepressure difference ⟨C p6 ⟩ − ⟨C p5 ⟩ increases strongly in regime

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

Figure 4. Pressure evolution in the wakes of the obstacles (a) and of the rear wheels (b). xw /w is the relative distance from the baseof the obstacle or from the most downstream location of the rear wheel. For the cases of the wheel configuration with l/w < 2.5, therelative distance xw /w is either scaled with the wheel width w or the reduced width w∗ in (c) (see also fig. 7 of Bao et al. (2022)).

The investigation is then focused on the stereo PIV measurements in the cross-flow plane at x/H = 0.03 (figure 7).
For the obstacle configuration, in the plateau, the main wakeis bounded by shear layers. With decreasing l/w, an importantmomentum deficit is observed behind the obstacles in regime
II, followed by a wake merging in regime I. This is better illustrated by plotting the streamwise velocity along the symmetryline of the left-hand obstacle in figure 7(b). We notice first a
gradual reduction of shear between the wake of the body andthe wake of the obstacle from the plateau to regime I. Then thewakes are merged in regime II, with ux < 0 in the region downstream the obstacle. For the wheel configuration, the shear issubstantially reduced from the maximum l/w case to the minimum l/w case. However, no recirculating flow is captured in
the velocity field downstream the wheels.

ified by the near wake interactions. For the wheel configuration (figure 4(b)), a similar pressure decrease as regime I withxw /w is also measured but the slope is smaller than the obstacle. For the cases in the drag-sensitive regime l/w < 2.5 asshown in figure 4(c), the reduced width w∗ is able to collapse
the pressure developments of different cases involving different rotational speeds Φ and different l/w.
We now investigate the pressure dynamics in the wake ofthe obstacles or the wheels. The coherent dynamics of the obstacle wake are captured by taps 5L and 5R located downstreamof the obstacles or the wheels. The premultiplied spectra obtained from 5L and 5R are averaged and are shown in figure5(a). For the obstacle configuration, a clear distinction is noticed between the cases, where an important peak is noticed forthe case in regime I. This peak occurs at Stw = 0.26 which isin good agreement with the studies based on D-shaped cylinders (Bearman, 1967; Park et al., 2006). In these studies,
the authors interpret the peak frequency as the vortex shedding frequency. On the other hand in regime II, the peak at
Stw = 0.26 is barely discernible, implying suppression of theperiodic motion. For the wheel configuration, we notice a peakat Stw = 0.15. Interestingly, Croner et al. (2013) experimentally measured a dominant peak at Stw = 0.14 downstream anisolated wheel using a hotwire probe, numerically it matches
the fluctuation of the side force coefficient. Therefore in ourcase, the peak at Stw = 0.15 may represent horizontal coherent
motion of the wheel wake, in the same direction as the horizontal vortex shedding of the obstacles in regime I. The dynamics
of the obstacle or wheel wake has influence on the base pressure dynamics. This is shown in figure 5(b) by the premultiplied spectra obtained from 6L and 6R . For the wheel configuration, the dominant peak is observed down to l/w = 0.65
while a sharp change at l/w = 1.56 is observed for the 2-D
obstacle pair.

A mean mass transfer from the main wake to the wakes ofthe obstacles is observed in figure 7(a) by considering the inplane vector fields. The strength of the mass flux is quantified
by space-averaging the mean vertical velocity in the present
plane over the width w at the interface between the main bodyand the obstacle, which is shown in figure 7(c). In regime II
the mass flux has a velocity of approximately 20 % of the freestream velocity. This is also observed – with lower intensity –in regime I as well as for the minimum l/w case of the wheel
configuration.
The aforementioned velocity measurements only focus on
the stationary wheel cases. Indeed, for those measurements,
only slight differences are noticed between the stationary cases
and the corresponding rotating cases. However, the streamwise velocity developments measured in the symmetry plane
downstream of stationary and rotating wheels are very different as shown in figure 8. In accordance with Wang et al.
(2020), the wake of the rotating wheel is shorter than that of
the stationary wheel. This is clearly shown in figure 8(b) byplotting the streamwise velocity ux evolution along the heightof the ground clearance G against the distance to the base of
the body x/H. A higher ux is measured near the base for the rotating case than for the stationary case. We then plot ux against
the distance from the most downstream location of the wheel
xw , which scales with the reduced width w∗ . This shows a nicecollapse in the interaction region xw /w∗ < 3. Moreover, themass transfer from the main wake to the wakes of the wheels is
also measured in this plane by the vertical velocity component
uz . The streamwise development along the ground clearance
line is plotted in a similar fashion as the ux evolution. The
reduced width w∗ collapses the region with negative uz .

Now the velocity fields are examined to reveal the flowmechanisms responsible for the base drag increase, startingfrom the mean topology of the main body wake in the symmetry plane as shown in figure 6. We notice a vertical asymmetry for the wheel configuration, possibly related to the presence of the front wheels that reduce the underbody flow rate.
The reduction in l/w brings slight changes in the topology
as indicated by the recirculation length (not discussed here
for brevity), defined as Lr = max(x/H)ux (x/H)≤0 . A more
pronounced change is observedin the strength of recirculaRtion, quantified by: R(x) = ux ≤0 |uxz (x, z)|dz, where |uxz | =pux 2 + uz 2 . For both configurations, we notice a substantial
increase in R with decreasing l/w.

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

Figure 5. Evolution of the premultiplied spectrum of the pressure signal C p5 (a) and C p6 (b) with the obstacle-to-base or wheel-tobase distance l/w.

Figure 6. (a) Evolution of the main wake topology with the obstacle-to-base distance or wheel-to-base distance l/w. (b) Comparisonof the recirculation strength R for the cases presented in (a).

Conclusiontransfer is always observed from the near wake of the body to
the wakes of the obstacles or rear wheels. Using our results
and the reference studies (Bearman, 1967; Hsu et al., 2021)
describing the effect of base suction on the pressure drag of
bluff bodies, a physical model based on a flow momentum balance of the wake is proposed in Bao et al. (2022) to explain
the scalings in different configurations. For the first regime(l/w < 1.5) of the obstacle configuration, the pressure dragscales with w. This implies that the size of the mass exchange
surface is governed by both the scale of the obstacle and thescale of the body. On the other hand, For the second regime(1.5 < l/w < 2.5), a w2 scaling is found which can be simply understood by stating that both the width and length of thesurface of the mass exchange are driven by the size of the obstacle w. For the obstacle configuration, the scaling points to adecrease in the length of the exchange surface with increasing
rotational speed. Our experimental data are all in agreementwith this model.

The impact of underflow perturbations on the wake andaerodynamic drag of a 3-D square-back bluff body was investigated in order to analyse wheel-vehicle interactions. Twoconfigurations were considered by placing either a pair of Dshaped obstacles or four rotating wheels under the body. For
the obstacle configuration, the obstacle width w and the distance from the base to the obstacles l were systematically varied. We revealed two drag-sensitive regimes for l/w < 2.5.
These two regimes present different flow dynamics downstream the obstacles and different scaling properties for thepressure drag. For the wheel configuration with a wheel
width w, a similar pressure drag increase is also observed forl/w < 2.5. When the wheels were rotated, a scaling for thepressure drag, taking into account the decrease in the wheel
wake size, was proposed.
Despite these important differences between either thetwo regimes or the shapes of the perturbations, a mean mass

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

Figure 7. (a) Evolution of the mean streamwise velocity ux with the obstacle-to-base or wheel-to-base distance l/w at x/H = 0.03
near the base of the body. The velocity distributions along the symmetry line of the left-hand obstacle/wheel are presented in (b)/(d).
The space-averaged vertical velocity ⟨ux ⟩ along the line indicated is plotted against l/w in (c).

Figure 8. (a) Velocity distributions in the symmetry plane of the left wheels (y/H = −0.58) for the stationary and full rotating cases(Φ = 100%), the wheel-to-base distance is l/w = 0.65. The streamwise velocity ux and the vertical velocity uz along the groundclearance line are plotted in (b) with different scalings.

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