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

ON THE EFFECT OF FREE-STREAM TURBULENCE ON THE
AERODYNAMIC DRAG AND WAKE DYNAMICS OF AN AHMED BODY

Pierre-Yves Passaggia, Nicolas Mazellier, Azeddine Kourta
University of Orléans, INSA-CVL, PRISME, EA 4229, 45072, Orléans, France
pierre-yves.passaggia@univ-orleans.fr

1

ABSTRACT

play extremely complex (Bonnavion et al., 2017). Althoughsignificant drag reduction was reported at the laboratory scaleusing either passive or active control methods (see e.g., Pujals
et al., 2010; Barros et al., 2016; McNally et al., 2019; LoriteDı́ez et al., 2020, to only cite a few), these achievements wereobtained in operating conditions which are far from being representative of real-life applications, which evolve in strongly
turbulent upwind.

We report an extensive experimental investigation on theeffect of inflow turbulence on a square-back Ahmed body.
Variations reaching up to +16% and −17% of the drag coefficient are observed for free-stream turbulence representative of
open-road conditions (Saunders & Mansour, 2000). Regular
turbulence grids are mounted upstream the body and turbulence intensity together with the integral length scale of turbulence are varied using different mesh, bar sizes, and solidity.
The role of free-stream turbulence on the drag coefficient andthe wake meandering dynamics is investigated. In particular,
the statistics associated with the dynamics of the reflectional
symmetry breaking of the wake are analysed using a proper
orthogonal decomposition method. Increasing free-stream turbulence leads to a drastic change in the meandering dynamics of the wake which evolves from intermittent to essentially
Gaussian. Interestingly, the amplitude, the frequency of themeandering and the spatial distribution of the wake are foundto decrease when increasing free-stream turbulence. Wake meandering is shown to be strongly receptive to free-stream turbulence. More importantly, we draw a link between the receptivity of the shear-layer instabilities and the wake meandering which hints to important conclusions in the scope offlow-control strategies.

2

The role of external conditions on the aerodynamics ofvehicles and in particular the near wake remains largely unexplored because of the facilities required to run such large-scale
experiments. Most of the previously cited studies took placein low-free-stream turbulence intensities Tu ≈ 0.5%, which
are at least one order of magnitude lower than values observed in open-road conditions where Tu varies between 2%
and 15% (Watkins & Saunders, 1995; Saunders & Mansour,2000). Higher turbulence intensities may even be found inheavy traffic and/or wind gusts conditions. Moreover, the onroad integral lengthscale (Lu ), which can be seen as the dimension of the energy-containing eddies, of the incoming flow
ranges between 0.3H (with other cars) and 3.5H (open-roadand light winds) where H is the typical height of the tested
vehicles (Saunders & Mansour, 2000). In this study, the effect of free-stream turbulence on the near-wake meandering isinvestigated for nearly isotropic and homogeneous turbulence
conditions.

Introduction

The transportation industry, and in particular, road vehicles, remains one of the main contributors to global energy
consumption and pollutant emissions. Car manufacturers must
therefore comply with environmental regulations such as CO2 emissions standards which are becoming increasingly strict.
Reducing the aerodynamic drag through flow control strategies stands as an appealing solution to comply with these policies. Heavy commercial vehicles are considered aerodynamically inefficient compared to other ground vehicles due totheir unstreamlined body shapes. A large commercial vehicle travelling at 100 km/h consumes about approximately 52%of the total fuel to provide power to overcome the aerodynamic
drag (Schoon & Pan, 2007). The aerodynamic drag of a semitrailer truck typically accounts for about 75-80% of the totaldrag for a driving speed of 100 km/h (Hucho, 1998). It istherefore of the utmost importance to understand the dynamics of such wakes to free-stream turbulence in order to establish robust flow-control methods. Over the past two decades,
substantial efforts have been invested to control the vehicle
wake, which is characterised by both large pressure drag andthree-dimensional (3D) coherent structures (Hucho & Sovran,1993). Altogether, these phenomena contribute in large parts
to performance losses and make the physical mechanisms at

3

Experimental setup

The bluff body is a full-scale square-back Ahmed bodywith dimensions [L,W, H] = [1.044, 0.340, 0.288] m (Ahmed
et al. (1984)). Experiments were carried out in the S1 windtunnel at PRISME laboratory (Orléans, France). The test
section of this closed-loop wind tunnel is a 2×2 m2 squareand extends over 5 m. The ground clearance G was set to
G = 50 mm and a flap is mounted along the trailing edgeof the raised floor (see figure 1(a)). The investigated freestream velocity, monitored by a Pitot probe located at 2mfrom the grids, is U∞ = 25 ± 0.2 m/s, which corresponds to
ReH = U∞ H/ν ≈ 4.8 × 105 , with ν the kinematic viscosity ofair. Free-stream turbulence is generated by regular bi-planar
grids placed at the inlet of the test section (1.5 m upstream ofthe leading edge of the raised floor). In this study, eight gridswith square bars were considered, each of them being characterised by a solidity defined as χ = b/M(2 − b/M) where M
and b stand for the grid mesh and the bar thickness, respectively. The grid properties are summarised in Passaggia et al.
(2021).

1

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

(b)
b

0.42

55

0.4

50

0.38

45

0.36

40

M

U∞
p∞
z

5.2H
3.2H

BL-type hotwire
at x=-0.7H
Pressure taps
PIV plane
at y=0

35

0.34

30

0.32
25

0.3

y

20

0

0.28
x

15

0.26
0.15

Aerodynamic balance

0.2

0.25

0.3

0.35

Figure 1. (a) Experimental setup showing the pressure taps (red circles), PIV plane (green rectangle), and positions of the streamwise
velocity profiles measured by a BL-type hot-wire probe. (b) CD as a function of Cb for all cases including the reference case denotedby a pentagram.

Grid ref.

b/H(%)

M/H

χ(%)

Lu /H

Tu (%)

Cb

CD

ln(G)

N

A

No Grid

/

/

/

/

0.5

-0.2600.341

0.0204164

6.40

B25M10

8.68

0.35

43.8

20

4.77

-0.3190.391

0.0218173

6.95

B25M20

8.68

0.69

23.4

10

5.58

-0.3090.380

0.0187232

6.56

B25M30

8.68

1.04

16.0

6.6

5.56

-0.3300.397

0.020794

6.96

B25M40

8.68

1.39

12.1

5

5.13

-0.2850.313

0.0192

304

6.55

B58M32

20.1

1.10

33.0

6.25

8.72

-0.2490.350

0.0121

232

5.94

B70M26

24.3

0.97

43.7

7.7

10.16

-0.2800.384

0.0172

322

6.00

B90M32

31.2

1.10

48.3

6.25

11.04

-0.2400.299

0.00801094

5.06

B120M36

41.7

1.25

55.5

5.6

12.90

-0.1900.282

0.00421489

4.37

Table 1. Summary of main physical parameters covered in this study. Free-stream turbulence characteristics are measured at x =11.4H from the grid.

4Free-stream turbulence and dragin the free-stream by the Pitot tube, respectively. The precision of the pressure scanner is given with a 1.6% accuracy,
which corresponds to an error bar equivalent to the size of thepoints used in figure1(b). The resulting base pressure coeffi1 R
cient is Cb = HWS C p (y, z)dS. Note that the values of CD and
Cb for the reference case are slightly different than previously
reported in Volpe et al. (2015) because the position of the Pitot
tube was different than in their experiment which was locatedat x = 8.4H from the grid.

The Ahmed body is linked to a six-components strain
gauge balance through its feet, avoiding any contact withthe ground. We focus here on the drag force FD and theyaw Fy , the coefficients of which are CD = 2FD /(ρU∞2 S) andCy = 2Fy /(ρU∞2 S), where ρ is the air density and S = HW thefrontal area. The drag coefficient is measured with a 2% precision and is well within the range reported in the literature
for a similar geometry and flow condition (Volpe et al., 2015;
Lucas et al., 2017). Note that the mean side forces are nearlynull and that the lift coefficient is also one order of magnitude
lower, as reported in Passaggia et al. (2021). Pressure distributions over the rear surface S are measured through 81 pressure taps connected to three Chell MicroDAQ pressure scanners recording pressure fluctuations at 50 Hz. The pressuretaps are identified in figure 1(a) by red circles. The acquisition frequency was set to 50 Hz and allowed for measuring the
dynamics of meandering wake. In addition, 5 Kulite pressure
sensors we mounted near the four corners of the body to measure pressure fluctuations at a frequency of 1 kHz as well as
an additional one located at the centre of the body. The pressure coefficient is defined as C p = 2(P − P∞ )/(ρU∞2 ) where P
and P∞ are the wall pressure and the static pressure measured

Varying the characteristics of turbulence in the freestream (i.e. varying χ) modifies the base pressure coefficient
Cb and the drag coefficients CD with a linear relation(see figure 1(b)) where the linear regression provides
CD ≈ −Cb + 0.078, as shown in figure 1(b) which is inagreement with previous studies (Lorite-Dı́ez et al., 2020;
Haffner et al., 2021). These relations therefore point to thestrong sensitivity of the flow to free-stream turbulence and inparticular, the drag coefficient, which is essentially controlled
by the pressure at the base. In turn, base pressure is known
to be controlled by both the geometry of the wake and the
Reynolds stresses (Grandemange et al., 2012). Since theReynolds stresses were already analysed in Passaggia et al.
(2021), we tie a first link between the wake stability and212th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan (Online), July 19-22, 2022(a) 1.2
1
0.8
0.6
0.4
0.2

0.5
0
-0.5

-0.5

0

(b)

1.2
1
0.8
0.6
0.4
0.2

0.5

0.8

0.5

0.6
0

0.4

-0.5

0.2

-0.5

0

0.5
0

1.2
1
0.8
0.6
0.4
0.2

0.5
0
-0.5

-0.5

0

1.2
1
0.8
0.6
0.4
0.2

0.5

-0.2
0.5

-0.4

0

-0.6

-0.5

-0.5

0

-0.8

0.5

0

0.5

1

1.5

2
107

√
Figure 2. (a) Contours of pressure coefficient for the second POD mode U2 (y, z) Σ2 for χ = 0 (reference, top left), χ = 43.8%(largest drag increase, top right), χ = 33.0% (mild drag decrease, bottom left), χ = 55% (largest drag decrease, bottom right). (b)√Sample temporal evolution of the second POD mode V2 (t) Σ2 for the reference case (χ = 0) and the strongest free-stream turbulent
condition (χ = 55%).

(a) 7

10-3

6

55

(b) 7.5

55

50

7

50

45

45

5

6.5
40

40

4

6
35

35

3

30

5.5

30

2

25

5

25

20

20

1

4.5
15

0
0.6

0.7

0.8

0.9

1

15

4
0.6

1.1

0.7

0.8

0.9

1

1.1

Figure 3. (a) Non-dimensional switching frequency NH/TU∞ as a function of the spatial growth rate of shear-layer instabilities ln(G).
√(b) RSB mode amplitude A = Σ2 also reported as a function of ln(G). The black pentagram reports the reference case, without grid.

the loss of symmetry caused by the so-called reflectional
symmetry breaking mode which drives the meandering of the
wake.

5

(2021) together with its contribution to the drag, we investigate
the wake meandering which is known to induce a large dragdecrease when the wake switches between each possible side(i.e. left or right in the present case (Haffner et al., 2020)).
In order to carry out this analysis, we use 81 pressure sensors
located on the flat back of the body using a proper orthogonal
decomposition such that

Wake meandering dynamics

The meandering of the wake is analysed by means of amodal decomposition based on modes computed through a
Proper Orthogonal Decomposition (POD). These modes arelater used to split the pressure fluctuations between a mean,
the RSB mode, and the remainder from the shear layer modes
and incoherent fluctuations. In particular, we show that the
RSB mode is essentially controlled by the mean-flow properties. The intermittent dynamics of the shear-layer modes andincoherent fluctuations are analysed through their statistics.

5.1

C p (y, z,t) = ∑ Ui (y, z) Σi Vi (t),(1)

iwhere Ui (xi ) is the spatial distribution of the ith POD mode,
while Σi and Vi (t) represent the energy and the temporal evolution of the ith POD modes, respectively. Note that U and V
are orthonormal matrices while Σ is a diagonal matrix. Notethat here, the first mode is the mean base pressure while thesecond mode is always associated with the RSB mode, whatever the level of free-stream turbulence.
The spatial distribution of the POD modes for different
turbulence grids is shown in Figure 2(a). The pressure associated with the RSB mode is found to be either slightly increased
for the grid with the smaller mesh size (i.e. the smaller turbulence intensity and the smaller integral lengthscale) while it

POD modes dynamics

The dynamics of the the wake are known to be driven by
an RSB mode which switches between the left and the rightside of the wake, reported in several studies (Volpe et al., 2015;
Grandemange et al., 2012). While the instability dynamics of
the upper shear layer was recently reported in Passaggia et al.

3

12th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan (Online), July 19-22, 2022(a) 0.6

(b)
10-1

0.5
0.4

10-2

0.3
10-3
0.2
10-4

0.1
0
-6

-4

-2

0

2

4

-6

6

-4

-2

0

2

4

6

Figure 4. (a) Probability density functions of the RSB mode temporal dynamics Σ2V2 (t). Note that all PDFs were normalised with
their density. (b) Probability density functions of the high-pass dynamics C′p − C˜p where C˜p is computed using a moving average witha window of 0.1 s, extracted from the Kulite sensors located near the roof. The PDFs are normalised with respect to their integral while
the width is rescaled using the variance of the signals.

is clearly decreased when the bar and the mesh size increase.
However, it is interesting to note that the pressure signatureof the mode is only weakly affected by free-stream turbulence, even for the stronger free-stream turbulence conditions.
Figure 2(b) shows the temporal evolution of the second POD
mode for the case without grid. It is compared with the temporal evolution for the largest turbulence grid where the amplitude is clearly decreased and where the number of switches
has also increased.

by ln(G), where G is the spatial energy gain of the shear-layer
modes Passaggia et al. (2021).
Both the RSB mode amplitude and the non-dimensionalswitching frequency are found to scale linearly with the growthrate of the shear-layer instabilities (i.e. see Figure 3) whichhints to the receptivity of free-stream turbulence by the theshear layers.

5.2

The characteristic non-dimensional number of switches
per unit time between each state NH/TU∞ , is shown in Figure 3(a) and is the related to inverse of the mean residence timeon either the left or the right side of body’s flat back. Here,N is the number of switches recorded by the pressure scanner through the temporal evolution of the mode V2 (t) while
T is the recording time which was set to half an hour. In theworst case scenario, more than 90 switches were still recorded
which provides a good convergence of the statistics. The amplitude of√the modes is shown in Figure 3(b) where the amplitude A = Σ2 is found to either increase or decrease dependingon the characteristics of the free-stream turbulence. This result
was very recently reported in Burton et al. (2021) for different
turbulence grid arrangements which may not lead to homogeneous and isotropic free-stream turbulent conditions. However, nor the mean residence time, nor the amplitude of thereflectional symmetry breaking mode seems to scale with thedrag coefficient. However, we show that both the amplitude of
the wake and the mean switching time scale linearly with thegrowth rate of the Kelvin-Helmholtz instabilities originatingfrom the wake Passaggia et al. (2021).

POD modes and pressure-fluctuations
statistics

Next, we analyse the statistics of the fluctuations where
the dynamics are now split in a triple decomposition between
the mean base pressure, the RSB mode, and the remainder ofthe pressure fluctuations. This decomposition writes
C p (y, z,t) = C p (y, z) + C˜p (y, z,t) +C′′p (y, z,t),(2)where C p (y, z) = U1 (y, z)Σ1 = Cb , C˜p (y, z,t) = U1 (y, z)Σ2V2 (t).
Figure 4(a) shows the probability√ density function associatedwith the RSB mode dynamics Σ2V2 (t) for different turbulent free-stream conditions. For the reference case without
free-stream turbulence, the PDF is essentially symmetric andshows two= distinct peaks which correspond to the left andright states associated with the RSB mode. As free-stream turbulence increases, the amplitude of the peaks progressively decreases and both peaks tend to merge. For the larger values offree-stream turbulence, the PDF evolves towards a Gaussian,particularly visible for χ = 55%. This result is important as it
shows that for Tu > 10% and Lu ≈ H, the meandering of thewake is strongly affected by the dynamics of the free-stream
turbulence which is indeed Gaussian for scales in the range ofthe integral lengthscale.
This is also visible in the dynamics of the C′′p (y, z,t) measured near the roof, on the back of the body using the fast
Kulite sensors. Figure 4(b) reports the statistics of the shearlayer modes and the incoherent dynamics given by C′′p (y, z,t).
For the reference case, without free-stream turbulence, the
PDF is clearly not Gaussian. The tails of the PDF extend by
two standard deviations when compared with the Gaussian reference. The tails are the trace of the shear-layer fluctuations asshown in Haffner et al. (2020) leading to the switching of the

As recently shown in Haffner et al. (2020), the switch
between the left and the right state is caused by a set of KelvinHelmholtz modes located in the shear layer. The stability ofthe shear layer was recently investigated in Passaggia et al.
(2021). The shear-layer modes were found to be be associatedwith Strouhal numbers in the range St = [0.1, 1]. The samemodes where also identified in Haffner et al. (2020) and caused
the switch between the left and the right state of the RSB mode.
As shown in Passaggia et al. (2021), it is the receptivity of theshear layer to free-stream turbulence that controls these shearlayer modes and the amplitude of these modes is found to becontrolled by the energy gain of the dominant instability given

4

12th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan (Online), July 19-22, 2022
mode from one side to the other, whence its intermittent nature.
As free-stream turbulence increases, the tails of the PDFs
quickly narrow, even for Tu < 5%, and approach the Gaussian
distribution. For the largest grid, fluctuations fit nearly perfectly the Gaussian distribution, which further hints to the factthat the shear-layer display a strong receptivity to free-stream
dynamics and thus, the meandering, together with the shearlayer modes and the incoherent fluctuations.
These results hint to the fact that the dynamics of the wake
are further influenced when increasing free-stream turbulence
and that the shear-layer receptivity is an important mechanism
in explaining the wake dynamics of bluff bodies in turbulent
free streams.

6

REFERENCES
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pp. 473–503.
Barros, D., Borée, J., Noack, B. R., Spohn, A. & Ruiz, T. 2016
Bluff body drag manipulation using pulsed jets and coanda
effect. J. Fluid Mech. 805, 422–459.
Bonnavion, G., Cadot, O., Évrard, A., Herbert, V., Parpais, S.,
Vigneron, R. & Délery, J. 2017 On multistabilities of real
car’s wake. J. Wind Eng. Ind. Aerodynamics 164, 22–33.
Burton, D, Wang, S, Smith, D Tudball, Scott, HN, Crouch, TN& Thompson, MC 2021 The influence of background turbulence on ahmed-body wake bistability. Journal of Fluid
Mechanics 926.
Grandemange, M., Gohlke, M., Parezanović, V. & Cadot, O.
2012 On experimental sensitivity analysis of the turbulent
wake from an axisymmetric blunt trailing edge. Phys. Fluids 24 (3), 035106.
Haffner, Y., Borée, J., Spohn, A. & Castelain, T. 2020 Mechanics of bluff body drag reduction during transient near-wakereversals. J. Fluid Mech 894 (A14).
Haffner, Y., Castelain, T., Borée, J. & Spohn, A. 2021 Manipulation of three-dimensional asymmetries of a turbulent
wake for drag reduction. J. Fluid Mech. 912.
Hucho, W. & Sovran, G. 1993 Aerodynamics of road vehicles.
Ann. Rev. Fluid Mech. 25 (1), 485–537.
Hucho, W.-H. 1998 Aerodynamics of road vehicles, society of
automotive engineers. Inc., Warrendale, PA .
Lorite-Dı́ez, M., Jiménez-González, J. I., Pastur, L., Martı́nezBazán, C. & Cadot, O. 2020 Experimental analysis of theeffect of local base blowing on three-dimensional wakemodes. J. Fluid Mech 883.
Lucas, J.-M., Cadot, O., Herbert, V., Parpais, S. & Délery,J. 2017 A numerical investigation of the asymmetric wakemode of a squareback ahmed body–effect of a base cavity.
J. Fluid Mech. 831, 675–697.
McNally, J., Mazellier, N., Alvi, F. & Kourta, A. 2019 Controlof salient flow features in the wake of a 25◦ ahmed modelusing microjets. Exp. Fluids 60 (1), 7.
Passaggia, Pierre-Yves, Mazellier, Nicolas & Kourta, Azeddine 2021 Aerodynamic drag modification induced by freestream turbulence effects on a simplified road vehicle.
Physics of Fluids 33 (10), 105108.
Pujals, G., Depardon, S. & Cossu, C. 2010 Drag reductionof a 3d bluff body using coherent streamwise streaks. Exp.
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Saunders, J. W. & Mansour, R. B. 2000 On-road and windtunnel turbulence and its measurement using a four-hole dynamic probe ahead of several cars. SAE Trans. pp. 477–496.
Schoon, R. & Pan, F. P. 2007 Practical devices for heavy truck
aerodynamic drag reduction. Tech. Rep.. SAE Technical Paper.
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SAE Technical Paper.

Conclusions and outlook

The near-wake dynamics of an Ahmed body and aerodynamic characteristics are analysed and compared for different
turbulence grids positioned upstream the body. It is shownthat free-stream turbulence strongly modifies the drag coefficient and thus the mean flow. We then address the role of thewake meandering which is the most energetic structure in thewake and which has been long speculated to play an importantin controlling drag. Although, free-stream turbulence is foundto be of key importance for controlling wake meandering andthe shear-layer dynamics, a clear link between drag and meandering is not clear. On the other hand, free-stream turbulence plays a key role in controlling the unsteady aerodynamic
in bluff-body wakes as shown by the dynamics of the first
Proper Orthogonal Decomposition (POD) mode, associatedwith the reflectional symmetry breaking (RSB) of the wake.
Free-stream turbulence is found to have little influence on the
structure of the pressure associated with the RSB mode on thebase of the body. However, the dynamics and the amplitudeof the mode is strongly affected. Increasing free-stream turbulence, the non-dimensional frequency of the RSB mode substantially increases while its amplitude follows a net decrease.
The statistics of the RSB mode are also found to evolve froma Probability Density Function (PDF) with two peaks whichmerge and evolve towards a Gaussian-type PDF. The remainder of the pressure fluctuations are also analysed and while
the dynamics of the shear layer are clearly non-Gaussian without free-stream turbulence, the intermittency disappears andthe pressure fluctuations become essentially Gaussian, hinting
to the strong receptivity of wake meandering and shear-layer
instabilities with increasing free-stream turbulence.
These results hint to important conclusions when investigating flow control strategies of bluff-body wakes. A possible
alley to perform flow control could aim at injecting turbulence
all around the base of the body, with a turbulence intensity
larger than 15% that extends far into the wake, its shear layer,
and a turbulent Gaussian-type forcing.

Acknowledgements
The authors warmly thank S. Loyer and Y. Haidous,
both engineers at PRISME, and E. Varon and W. Zeidan for
their technical contributions during the experiments. This
work was supported by the Agence Nationale de la Recherche(ANR) through the Investissements d’Avenir program under
the Labex CAPRYSSES Project (ANR-11-LABX-0006-01).

5