RESEARCH ARTICLE

Experimental aerodynamic study of a car-type bluff body

Boris Conan Jerome Anthoine Philippe Planquart

Received: 6 February 2010 / Revised: 28 September 2010 / Accepted: 4 October 2010 / Published online: 16 October 2010

Springer-Verlag 2010

Abstract The Ahmed body is used as a reference model

for fundamental studies of car-type bluff body aerody-

namics, in particular focused on the influence of the rear

slant angle on the drag coefficient. The objectives of the

present work are to obtain reliable drag coefficient com-

parable to the literature and to explain, based on the nature

of the flow, its variation when changing the rear slant angle

from 10 to 40. The drag coefficients measured in both anopen and a closed test sections differ by less than 0.5%

which proves the reliability and reproducibility of the

results. The sensitivity of the drag coefficient to some

parameters such as the model roughness or the oncoming

boundary layer and the lack of precise information on these

parameters in the literature could explain the difference

observed with the Ahmed drag coefficient data. The vari-

ous types of measurement techniques used in the study

underline their complementarity. The combination of par-

ticle image velocimetry and oil visualization provides a

deeper understanding of the flow behaviour around the

Ahmed body and a physical interpretation of the drag

coefficient evolution.

List of symbols

A Prontal area

CD Drag coefficient

CDcorr Corrected drag coefficient

CDmeas Measured drag coefficient

FD Drag forceFD Mean drag force

Ti Turbulence intensity

Uref Reference velocityUref Mean reference velocity

Dt Separation timeq Air densityk2 Vortex detection criteriaxz Vorticity in z direction

1 Introduction

1.1 Context of the study

For ground vehicles, air resistance is responsible for more

than 75% of the total resistance to the motion at 100 km/h

(Hucho and Sovran 1998). First investigated as an impor-

tant aspect of vehicle performance, the two oil crisis

changed the issue of drag reduction studies to the reduction

in the consumption. Even after decades of investigations on

vehicle aerodynamics, drag reduction considerations are

still a concern as the major source of energy consumption.

An important number of papers are still published every

year on this subject using both experimental and numerical

approaches.

Since full-scale wind tunnel tests are expensive and

allow poor flexibility in terms of modification of parame-

ters, their use is limited to detailed analysis and final per-

formance investigations. As an alternative, reduced-scale

wind tunnel tests are an interesting way to study global

shape modifications on a vehicle. In the major part of these

B. Conan (&) J. Anthoine P. Planquartvon Karman Institute, Chaussee de Waterloo, 72,

1670 Rhode Saint Genese, Belgium

e-mail: boris.conan@vki.ac.be

J. Anthoine

e-mail: jerome.anthoine@vki.ac.be

P. Planquart

e-mail: philippe.planquart@vki.ac.be

123

Exp Fluids (2011) 50:12731284

DOI 10.1007/s00348-010-0992-z

experimental aerodynamic studies, the idea is to quantify

the improvement generated by a design evolution. The test

consists in comparing the drag of the basic configuration

with the modified version to find the effect of the modifi-

cation and in choosing the best option. Even if, in this case,

the relative value is most of the time enough to conclude

about a design evolution, the exact value is not to neglect

when comparing to numerical simulation or literature data.

The need for a common car shape model appears in order

to have a universal basis for investigations.

In 1984, Ahmed et al. (1984) proposed a very simple

and easily evolutive model with a cubical shape that no

longer really looks like a car but reproduces its global

behaviour: a large three-dimensional displacement in the

front, a relative uniform flow in the middle, and a large

structured wake at the rear. Thanks to this model and

previous work from Morel (Sovran et al. 1978), Ahmed

described the evolution of drag coefficient with the rear

slant angle. For a small angle between 0 and 20, the dragcoefficient (CD) is relatively constant, with a minimum at

around 12.5. At this angle, the wake is mainly constitutedby two longitudinal vortices. While increasing the rear

angle, the drag coefficient rises dramatically, up to 50% for

a rear slant angle of 30. This important drag increase isdue to a flow separation at the rear edge of the model that

reattaches on the slant, combined with pre-existing longi-

tudinal vortices. 30 is the so-called critical angle becausetwo flow behaviours can occur associated either with a

high drag (just described) or with a low drag coefficient.

The low drag coefficient is comparable to 0 rear angle.The drag reduction, a 45% drop, is due to the fact that the

separation cannot reattach to the rear slant, that leads to a

global wake. Above 30, the drag coefficient does notchange significantly and stays at a low level.

The Ahmed body is nowadays largely used as reference

model for both experimental and numerical investigations.

Thanks to its simplicity, the model is used to study the flow

unsteadiness or to implement new technologies like passive

or active control for drag reduction (Duell and George

1999; Bayraktar et al. 2001; Roumeas et al. 2009).

1.2 Objectives of the investigation

In the context of aerodynamic experiments, the present

work objective is to reproduce as closely as possible a

reference study in the VKI low-speed wind tunnel. The

study chosen is the investigation of the influence of the rear

angle of an Ahmed body on the drag coefficient. The

experiment is done in the very same condition as Ahmed

(Fig. 1). Two types of test sections being available, another

contribution is the investigation of the test section depen-

dency; the original test is reproduced in both an open and

closed test section. Experiments are also dedicated to

complement the Ahmed body experimental database.

In addition to classical drag investigation, the study is

also devoted to the physical understanding of drag evolu-

tion by coupling oil visualization and PIV measurements to

explain the nature of the flow.

2 Experimental methodology

2.1 Model description

The model was built following Ahmed description (Ahmed

et al. 1984). Final dimensions are very close to the original

one. It was built so to allow an easy removal and

replacement of the rear part while keeping the model

attached to the balance, which avoid calibrating it before

each configuration.

The model is divided into three independent parts: the

frame, fixed to the balance with four supports, the main

body, made up of the front nose and the middle part joined

together, and the rear part, attached to the middle part and

that can be replaced easily. Five different rear parts were

built with rear angles (h) equal to: 10, 20, 25, 30 and40 (Fig. 2).

The complete model was fabricated at the VKI with

22 mm MDF (medium density fibreboard) boards. In order

to perform oil visualization and to decrease the surface

roughness, the wood was covered with black photo paper.

The main part is screwed to the rear part internally, and the

junction zone is moved away from the rear angle to min-

imize any interference in the rear part. Final global defi-

nition, dimensions and uncertainties of the VKI model are

listed in Figs. 2, 3 and Table 1.

Fig. 1 The Ahmed body in the VKI L-1A open test section, the set-upclosely reproduces the original Ahmed configuration

1274 Exp Fluids (2011) 50:12731284

123

2.2 VKI-L1 wind tunnel facility and set-up

All experimental studies are carried out in the VKI-L1 low-

speed wind tunnel. Two configurations are available, a free

jet test section of 3 m diameter (mentioned hereafter as

L-1A) and a closed test section of 2 m 9 3 m (L-1B).

These two configurations have a common return circuit

with a contraction ratio of 4 and are powered by a variable

speed DC motor of 580 kW driving two contra-rotative

fans of 4.2 m diameter. Experiments are performed in both

test sections with a velocity range from 13 to 60 m/s. The

turbulence intensity was measured at a level under 0.5%.

In order to be comparable to Ahmed experiment, the

wind tunnel set-up reproduces as closely as possible the

original configuration. For both wind tunnel configurations,

the model is installed on a 1.8 m wide 9 5 m long floor

very similar to the one used by Ahmed to simulate the

ground effect. To avoid separation, the leading edge of the

floor is rounded in an elliptical way (radius a and b in

Table 1) and the floor is exactly the same in the two test

sections. (Figs. 4, 5)

In the closed test section L-1B, a diffuser was built at the

end of the elevated floor to accelerate the flow below it and

control any separation at the leading edge due to blockage

under the floor (Fig. 5). The angle of the diffuser is set

experimentally to around 30 by visualizing the behaviourof wool tuft at the leading edge at low speed.

For technical constraints, the model is not positioned at

the very same distance from the leading edge of the floor:

0.75 m instead of 1.33 m in Ahmed study. This can influ-

ence the inlet boundary layer. Giving the lack of information

about the original boundary layer thickness at the position of

the model, it was approximated supposing a turbulent

attached flow. On the other hand, measurements were

Fig. 2 Top and side view of the model and axis definition

Fig. 3 Front view and angle description

Table 1 Description of the VKI model

Dimension Description VKI model Uncertainty

L Total length 1,043 mm 2 mm

W Total width 390 mm 1 mm

H Total high 289 mm 1 mm

R Main front radius 100 mm 1 mm

D Support diameter 30 mm 1 mm

S Rear slant length 222 mm 1 mm

a Floor ellipse diam. 20 mm 1 mm

b Floor ellipse diam. 30 mm 1 mm

d Support distance 1 202 mm 1 mm

d Support distance 2 672 mm 1 mm

e Support spacing 297 mm 1 mm

h Support high 50 mm 1 mm

l Length to junction 660 mm 1 mm

r Sec. front radius 20 mm 1 mm

l Surface roughness 10 lm 1 lm

h Rear angle 10 to 40 0.1u Model yaw angle 0.53 0.1w Model pitch angle 0.13 0.1

Fig. 4 Set-up in the open test section L-1A

Fig. 5 Set-up in the closed test section L-1B with the elevated floor

Exp Fluids (2011) 50:12731284 1275

123

carried out on the floor, without the model, but at its future

position. Table 2 summarizes the boundary layer thickness.

It can be concluded that the boundary layer thickness is less

than half the height of the model support. So, considering

turbulent attached flow on the floor, the consequence of

positioning differently the model is limited because the

boundary layer thickness for the VKI model is thinner. This

should not affect the measurement and ensure the wind

tunnel set-up similarity with the original experiment.

2.3 Drag coefficient measurements

The drag coefficient CD is defined as:

CD FD0:5 A q U2ref

The frontal area A being constant, two values are

necessary to compute CD, the drag force FD and the

reference velocity Uref.

To measure the drag, the model is attached to a balance.

In L-1B, the test section is equipped with an aerodynamic

six components balance used here only to acquire the drag.

In L-1A, the drag is obtained from a single component

balance. In both configurations, the model is connected to

the balance through its 4 supports passing within holes in

the floor. The reference velocity is the free-stream velocity,

upstream of the model, measured with a Pitot probe. The

Pitot is placed outside of the boundary layer of the floor, in

front of the model and enough on the side so that it is

outside of any perturbation created by the body.

For both test campaigns, the computation to obtain the

final drag coefficient consists, for a given rear angle, of

doing several independent runs (the wind tunnel is stopped

between two runs) at a given reference velocity. Drag

coefficients are computed from a constant velocity after 10

s averaging.

CD FD10s

0:5 q A U210sThe final averaged drag coefficient is computed from

different independent runs, at least two.

2.4 PIV measurements

PIV measurements are carried out in the closed test section

L-1B in the same conditions as the drag measurements but,

for practical reasons, at a reference velocity of 13 m/s.

Some developments were needed to be able to install the

laser, to have a proper seeding and to get the test section

L-1B dark. To achieve the objective of having additional

information on the rear part in the symmetry plane, the

laser is enlighting the model from the roof of the test

section. The optical bench, placed in the continuation of

the Mini-Yag laser, is composed of a spherical lens of

2.4 m focal distance to focus the beam on the model, a

cylindrical lens to create the laser sheet and a prism to

reflect the laser down to the rear part of the model (Fig. 6).

To avoid perturbation upstream the model, the best

option achieved for the seeding is to fill the complete wind

tunnel with smoke from a rake downstream the model.

After a while, the wind tunnel is full of smoke that ensures

an homogeneous seeding. Giving the high distance from

the laser to the model and the relative low power of the

laser, the laser sheet is concentrated in a small area.

Therefore, the area of interest is divided into four different

planes that overlap. For each of these planes, the image

recording is performed with a two photo sensor PCO

camera equipped with 50 mm CANON lens with a pixel

definition of 1,280 9 864. It is positioned outside the test

section on the side. Final pictures are 260 mm 9 175 mm.

Laser and camera are externally synchronized, the sepa-

ration time Dt is optimized to have a displacement of about8 pixels in the free flow (Table 3).

Table 2 Boundary layer thickness: measurement in VKI set-upcompared to an estimation from Ahmed description

Distance VKI Ahmed

0.75 m 1.33 m

40 m/s 15.5 mm 24.1 mm

60 m/s 14.31 mm 22.2 mm

Fig. 6 PIV set-up in L-1B anddecomposition of the area of

interest in four overlapping

planes

1276 Exp Fluids (2011) 50:12731284

123

At each position, a series of 1,000 image pairs are taken,

which has been proved to be sufficient to have a repre-

sentative average.

Even if precautions are taken to improve the darkness

and the quality of the background, a pre-processing is

applied to original images. It consists in calculating the

mean value of the 1,000 images and subtracting it from all

the images. This removes a constant background and a

possible reflection.

After improving the image quality, the VKI WIDIM

processing algorithm (Scarano 2002) is applied. This

algorithm is based on an improved cross-correlation

method applied in several steps where interrogation areas

are distorted and displaced. Sub-pixel interpretation is used

as well in this post-processing. Inlet post-processing

parameters are set like described in Table 4. Statistical

quantities are computed from the average of the 1,000

image pairs. The turbulent kinetic energy is defined as

TKE 0:5 u0 v0 . Instantaneous images are also ana-lysed in terms of vorticity xz and vortex detection using thek2 criteria from: Jeong and Hussain (1995); Jiang et al.(2004); Depardon et al. (2005); Raffel et al. (2007).

Local near-wall PIV data are post-processed with an

improved adaptative method (Theunissen et al. 2007)

where windows are adapted to the surface. This allows to

describe more details very next to the wall.

3 Influence of the rear angle on drag

3.1 Drag measurements

As described before, final values of drag measurements are

the result of an averaging of independent runs. Tests are

performed for five rear angles in L-1B, only two in L-1A.

Notice that the velocity of the test is not the same in the

two test sections (40m/s in L-1A and 50m/s in L-1B) that

leads to a Reynolds correction discussed hereafter.

In wind tunnel testing, infinite free-flow conditions are

not verified because of the existence of an open or closed

test section boundaries. This is obvious in closed test sec-

tion but it is as well present in open-jet wind tunnels. In the

correction proposed for L-1B, only solid blockage effect is

considered, the correction, based on Maskell theory

(Maskell 1963), leads to the decrease of the drag coeffi-

cient by 1.1%. In the open test section, a positive correction

for blockage (corrected drag higher than measured drag) is

applied, equivalent to an increase in the drag coefficient by

0.75%.

The second correction is related to a Reynolds effect

since the tests in the two test sections are not done at the

same velocity. In the literature (Bayraktar et al. 2001), the

Reynolds effect on drag coefficient is very low: a decrease

of 1% for 1 million Reynolds increase. The compensation

is applied to reach a Reynolds number of 4.29. 106, that

is around 60 m/s. That leads to a decrease in the value by

-0.5% for L-1B and by -1.2% for L-1A. In summary,

corrections lead to:

CDcorrL1B CDmeas :1 0:016CDcorrL1A CDmeas :1 0:0045After corrections, (Fig. 7), results from L-1A and L-1B are

matching: the difference is less than 0.5%. However, pre-

caution applies giving the uncertainty of the drag mea-

surement in L-1A: the error of the balance, calculated with

the calibration and the statistic error, is 4.91% with 95%

confidence level. This is important compared to L-1B

aerodynamic balance that is more precise and gives only an

error of 1% with 95% confidence level.

As described previously, the two tests are performed

with the same model but the set-up, the balance and the

measurement chain are different. It is therefore very

interesting to see that, after correction, results obtained are

Table 3 Laser and camera configurations

Frequency (Hz) Duration (ls) Dt (ls)

Laser 3 100 140

Camera 3 222 140

Table 4 PIV post-processing parameters

Parameter Value

Magnification factor 0.206 mm/px

Free stream displacement &8 px

Initial window size 64 px

Number of refinement steps 1

Final window size 32 px

Overlapping 75%

Final number of vectors 33,300

Fig. 7 Comparison of final VKI-L1 results with Ahmed literature

Exp Fluids (2011) 50:12731284 1277

123

independent of the test facility and reproducible, which

proves a certain reliability of the results.

Similarly to Ahmed experiment, the evolution of the

drag coefficient presents three major parts (Fig. 7).

Between 10 and 20, the drag coefficient is not changingvery much, almost constant. From 20 to 30, it presents animportant increase, rising by almost 50% from 0.27 to

reach 0.40 at 30. At that precise rear angle, two behav-iours are observed independently. They are after called

low drag and high drag configurations. From one run

to another, it is not possible to predict whether the drag

measured will be high or low. That enlightens the bista-

ble state at that angle called critical angle. Experimen-

tally, the low drag state is more probable than the high drag

state (3/1 ratio). The state while running the wind tunnel

can be determined thanks to tufts glued on the rear side of

the model. If the tufts are tilted up, it is high drag, and if

they are straight, it is the low drag configuration. After 30,the drag coefficient remains low and almost constant.

3.2 Comparison with literature and discussions

Final results obtained in the two VKI test sections L-1A

and L-1B are consistent with each other and with the ori-

ginal Ahmed data as plotted in Fig. 7. After applying

blockage corrections, data obtained at VKI have really the

same tendency as described by Ahmed. The plot given in

Fig. 7 clearly shows the drag coefficient rising from 10 to30. In VKI experiment, the 30 crisis is also present andhas more impact on drag than in the original Ahmed result.

Qualitatively, VKI results are comparable to reference

Ahmed data.

Quantitatively, VKI results (Table 5) give an overesti-

mation before 30 by less than 8%, except the 25 valuethat is much more overestimated: around ?20%. On the

other hand, drag coefficients after the 30 crisis, includingthe 30 in low drag configuration, are also overestimated,by 12% in average.

Drag coefficient measurements carried out in VKI wind

tunnel were successful in the sense that the evolution of the

absolute values is quite well correlated by literature results.

In average, drag coefficients are overestimated by around

12%. Because similar in the two measurement campaigns

in an open and closed test section, this shift might be due to

a boundary condition created by the elevated floor or by a

geometrical difference between the VKI model and the

original one (front part, roughness...). The important dif-

ference for the 25 rear angle could be due to the highsensitivity on the separation due to the sharpness of the rear

edge. However, except for 25, differences are limitedgiving the sensitivity to operating conditions of a parameter

like drag coefficient. Additionally, the lack of description

of the Ahmed model does not allow to conclude.

The only interpretation of the drag coefficient data is not

enough to understand completely the flow around the

model. Other means are carried out on the rear part of the

model to fill this gap. Oil visualization and PIV are two

techniques complementary in the sense that oil gives

information on the wall streamlines while PIV gives a

velocity vector field in the plane perpendicular to the

model surface. Information on two directions can therefore

be extracted.

4 Physical interpretation

4.1 Surface visualizations

Oil visualization is applied to the body and tested at 40m/s.

Shaped lines created by the oil displacement are repre-

sentative of wall streamlines if the momentum generated

by the flow on the oil is stronger than body forces like

gravity. An unknown is the effect of the oil on the flow

behaviour, especially in this case, where the rear edge

sharpness seems to play an important role. Specific oil

patterns are described according to Perry and Chong (1987)

as positive or negative bifurcation lines.

First, visualization is performed on the front of the body

where the experiment does not show any important dif-

ference while changing the rear part. A separation line,

characterized by the accumulation of oil, is clearly what

happens in Fig. 8 (left), at the junction between rounded

and straight parts. While not described by the very first

studies using an Ahmed body, Spohn and Gillieron (2002)

observed the same behaviour. Krajnovic and Davidson

(2004) in a LES simulation came out with wall streamlines

Table 5 VKI and Ahmed drag coefficient comparison

Angle 5 10 12.5 20 25 30 30 40

Ahmed 0.2310 0.2300 0.2500 0.28 0.3780 0.26 0.255

L-1A 0.2684 0.2828

L-1B 0.2601 0.2690 0.3433 0.3932 0.2967 0.2839

L-1A/L1-B \0.5% \0.5%L-1/Ahmed ?7.6% ?22% ?4% ?14% ?11%

1278 Exp Fluids (2011) 50:12731284

123

very similar to those obtained with oil visualization. These

studies confirm that the separation in the front part of the

body even though not observed by Ahmed is linked to the

definition of the model itself. This detachment can be

easily removed by gluing a strip of sand paper before the

separation line, the roughness forcing the transition to

turbulent and avoiding the flow separation, (Fig. 8 (right)).

However, this changes the type of flow on the model to

fully turbulent and the drag calculated is changed in con-

sequence. This effect has been measured but is not reported

here, all visualizations and results of the present paper are

obtained without sand paper.

For a rear angle of 20 (Fig. 9), the middle wallstreamline goes straight away in the direction of the flow.

While going outward to the edges, streamlines are

diverging (positive bifurcation line or PBL) and converg-

ing (negative bifurcation line or NBL) with an S shape

in between. This is the materialization of a vortex. In

addition to the slant, visualization on the side of the model

shows that the flow is deviated to the top, Fig. 10. The

description of the visualization is summarized in Fig. 11, at

20, the flow structure is composed by a pair of longitu-dinal vortices rolling in opposite direction from the edge to

the centre. There is no separation on the rear slant.

For a rear angle of 30 (Fig. 12), the flow being muchmore complex behind the rear slant and velocities rela-

tively low, the visualization needs more effort. The video

taken during the test is a real advantage to describe pre-

cisely the direction of the wall streamlines. For this angle,

the middle streamline goes up, against the mean flow,

which is the signature of a recirculation. On the left and on

the right, similar patterns as in the 20 configuration areobserved indicating the presence of longitudinal vortices at

each edge (Fig. 13). The positive bifurcation line is here

more important than in the other configurations and makes

a boundary between the recirculation part and side vortices.

In the recirculation part, the flow seems to describe a

seashell shape like a mussel around the two upper corners

and joining along the rear slant centre. The description is

Fig. 8 Frontal separation (left) and effect of sand paper (right)

Fig. 9 Oil patterns, top view of the rear slant with 20 angle

Fig. 10 Side view after oil visualization with a rear slant of 20

Fig. 11 Drawing from test observations at 20

Exp Fluids (2011) 50:12731284 1279

123

summarized in Fig. 14. The flow structure at 30 for thehigh drag configuration is composed by a recirculation

bubble that reattaches on the rear slant surrounded by two

longitudinal vortices.

The numerical study made by Krajnovic and Davidson

(2005b) at 25 shows very similar behaviour with thepresence of longitudinal vortices and a smaller recircula-

tion bubble attached to the rear slant. Oil streamlines can

be easily compared to time-averaged trace lines. Patterns

are comparable, for example the convergence point in

Fig. 13 can be associated with the stable focus Pb

explained in the cited study. The description of the longi-

tudinal vortices is similar, but even if logical for the con-

tinuity of the flow, the presence of the three vortices is

difficult to confirm from oil patterns.

Visualizations at 30 in low drag configuration and at40 are more difficult to obtain. Nevertheless, a visualiza-tion at 30, of poorer quality, enlightens the bistable natureof the configuration by showing completely different pat-

terns from the one described previously. From Fig. 15, no

longitudinal vortexes can be seen and the flow is mainly a

reverse flow, proof a recirculation. At the lower part of the

rear slant, there is a zone where streamlines are in the

direction of the main flow (downward on the picture). In

between, oil patterns are diverging in a PBL forming a

semicircle shape linking the two extremes bottom right and

bottom left edges of the rear slant. This is a sign of a

attachment line and probably demonstrates a secondary

recirculation at the rear slant.

The possibility to meet randomly one or another con-

figuration at 30 is reinforced during the test by observingthe high drag configuration after turning on again the wind

tunnel without removing the oil used for the visualization

shown in Fig. 15.

To further understand the evolution of drag, oil visual-

ization is not enough, especially to describe the low drag

configuration at 30 and 40. Therefore, particle imagevelocimetry is performed in the vertical symmetry plane.

4.2 PIV results in the rear symmetry plane

For technical reasons, the PIV study is carried out at only

13 m/s with a 30 rear angle. In these conditions, the stateof the drag coefficient is always in the low drag configu-

ration. Sims-Williams and Dominy (1998) observed also

the predominance of low drag configuration at low Rey-

nolds number.

Generally speaking, the data quality is acceptable. The

mean signal/noise ratio is above 3 and lower only in the

shear layer where the flow is highly three dimensional.

Table 6 gives details on error and uncertainty analysis for

the instantaneous images and for the statistical error made

after averaging 1,000 images.

The instantaneous velocity vector field, Fig. 16, shows

an important velocity gradient and a significant quiet

region with low velocities downstream the model. Notice

that there is no time correlation in Figs. 16 and 17 between

two regions because velocity fields were taken at different

time instants. From the instantaneous data, two different

Fig. 12 Oil patterns, top view of the rear slant with 30 angle (highdrag)

Fig. 13 Zoom and description of the oil result at 30 (high drag)

Fig. 14 Final drawing of oil observation at 30 (high drag)

1280 Exp Fluids (2011) 50:12731284

123

techniques are applied to identify and characterize vortices

that can be expected in such a field. Figure 17 gives in the

same time the two criteria: xz (in flood) and k2 (in contourlines). These two criteria are complementary, xz givinghigh curl locations with the direction of rotation and k2providing the position of the actual vortex. The direction of

rotation is clockwise if xz \ 0 and counterclockwise whenxz [ 0. The two criteria are matching at some positions,these are the position of vortices, for example locations

A and B. However, no k2 criteria is detected at position S: itis a wall shear layer. The detection enlightens a vortex

shedding emanating from the upper rear edge. Vortices are

rolling in the clockwise direction (black in Fig. 17) and

moving in the streamwise direction. They are created in the

shear layer and similar to a KelvinHelmoltz instability.

Secondary vortices (white in Fig. 17) are present next to

the lower edge. In their numerical simulation with 25 rearangle, Krajnovic and Davidson (2005b) emphasis this

vortex shedding. At 30 in low drag configuration, thevortex shedding looks similar but, contrary to their case,

the flow does not reattach to the rear slant and counter-

clockwise vortices (B in Fig. 17) are much weaker

around the rear lower edge (x = 0). This instantaneous PIV

analysis emphasizes a regular vortex shedding at the rear

edge of the model and proves the highly unsteady nature of

the wake.

After averaging 1 000 pictures per plane, data from the

four different planes (but acquired at different time

instants) are joined together to recreate a complete field

around the model. Discontinuities are then very limited in

the patterns shown, thanks to the high number of pictures

used for the average.

Figure 18 is the time-averaged velocity vector field. Out

of the free flow (Uref = 12.5 m/s), the velocity gradient is

very important and in the wake, the velocity is very low,

around 2-3 m/s, less than 20% of the free stream. The

pattern is similar to the one described for instantaneous

images with an important shear layer separating the free

flow and the wake. The normalized velocity profiles (lon-

gitudinal component) plotted in Fig. 19 shows well the

recirculation area with the reverse flow. The turbulent

kinetic energy (TKE), computed with both longitudinal and

Fig. 15 Visualization at 30, in low drag configuration

Table 6 Measurement and statistical errors

Error Measurement error (%) Statistical error

U 1.28 \1.12% at 95%

Ti 1.95 6.2% at 95% Fig. 16 Instantaneous velocity field in the rear symmetry plane at 30rear angle

Fig. 17 Instantaneous vorticity field xZ (flood) and vortex detectionk2 criteria (contour line) in the rear symmetry plane

Exp Fluids (2011) 50:12731284 1281

123

vertical components, has a maximum value in the shear

layer downstream the rear upper edge. Results reported in a

normalized plots are comparable in behaviour and in

absolute value to those shown in Lienhart and Becker

(2003) by LDV measurements and with numerical data of

Krajnovic and Davidson (2005a) and Guilmineau (2008)

with a rear angle of 35.From the plot of the flow streamlines in Fig. 20, it can

be seem that the recirculation centre is out of the mea-

surement plane. Additionally, a deflection of the stream-

lines happens close to the surface at the lower rear edge

(x = -10) and might be a secondary recirculation area. The

normalized velocity field in Fig. 19 for x close to zero on

the rear slant also experiences a change very close to the

slant. An adaptative PIV post-processing is applied to

resolve better the flow close to the wall. This enlightens the

presence of a secondary recirculation flow at the lower

edge of the model and correlates oil visualization (Fig. 15)

and the work of Guilmineau (2008), which shows a very

similar behaviour at 35 rear angle in a numerical study.Streamline fields in the rear middle plane are directly

similar. The secondary recirculation in the present case

looks more extended than in the refereed work, this could

be explained by the difference of rear angle, at 30, thesecondary flow experiences a greater angle (60 instead of55 in the literature). This secondary behaviour would needfurther investigation (Fig. 21).

More generally speaking, the nature of the wake makes

no doubt: the flow is completely detaching at the rear

edge and not able to reattach on the rear slant, which

creates a global structure composed of an important

recirculation bubble behind the body and a secondary

circulation at the bottom of the rear surface. Notice that,

due to the perturbation, the free-stream flow is a little bit

bended downward. Following the literature and looking at

the oil visualization, the configuration is free of longitu-

dinal vortices.

The combination of two complementary techniques,

PIV and oil visualization, allows for a physical interpre-

tation of the drag measurement (Fig. 7). For a rear angle

of 20, the drag is mainly dependent on the formation oftwo longitudinal vortices at the rear of the model. From

20 to 30, the increase in drag is due to a separationappearing at the rear edge and reattaching on the rear

slant. The drag is rising due to the increase in the sepa-

ration in size combined with the longitudinal vortices,

until a rear angle for which the flow is not able to reattach

any more on the slant. At that angle, the wake is reor-

ganized in a global recirculation free of longitudinal

vortices. After 30, the flow is no longer attached to therear slant, the separation is set to the rear edge and the

drag coefficient remains constant.

Fig. 18 Time-averaged velocity field in the rear symmetry plane

Fig. 19 Normalized velocity in turbulent kinetic energy profilesextracted from PIV data. Vertical profile each 20 mm

1282 Exp Fluids (2011) 50:12731284

123

5 Conclusions

The aerodynamics of a car-type bluff body was investi-

gated through the so-called Ahmed body. Drag coefficient

measurements were performed within the VKI-L1 wind

tunnel using an open and closed test sections.

A very good sign of the reproducibility and the reli-

ability of the results is the matching between the tests

realized in the open and closed test sections. Less than

0.5% of difference proves an independence of the test

section and the quality of the data that can be obtained in

the wind tunnel.

However, some differences are observed between the

VKI results and original data from Ahmed. Differences of

around 12% are present, they might be due to geometrical

difference on the model or on the floor. Unfortunately,

definitive conclusions cannot be set because complete

comparison with the original data is limited by the lack of

precise information on the literature: model roughness,

detailed frontal geometry or precise oncoming boundary

layer.

The physical understanding of the flow behaviour

around the rear of the model was analysed by various types

of measurement techniques. The combination of two

complementary techniques like oil visualization and PIV is

very helpful specially in the low drag configuration of

the 30 rear angle. More challenging to set-up, PIV hasthe other great advantage of giving information on the

unsteadiness structure of the flow, something not possible

with averaging techniques like oil visualization.

References

Ahmed S, Ramm G, Faitin G (1984) Some salient features of the

time-averaged ground vehicle wake. SAE-TP-840300

Bayraktar I, Landman D, Baysal O (2001) Experimental and

computational investigation of Ahmed body for ground vehicle

aerodynamics. In: Proceedings of the SAE international truck

and bus meeting and exhibition, Chicago, SAE paper 2001-01-

2742

Depardon S, Lasserre J, Brizzi L, Boree J (2005) Instantaneous skin

friction pattern analysis using a critical point detection algorithm

on near-wall piv data. Exp Fluids 39(5):805818

Duell E, George A (1999) Experimental study of a ground vehicle

body unsteady near wake. SAE paper 1999-01-0812

Guilmineau E (2008) Computational study of flow around a simplified

car body. J Wind Eng Ind Aerodyn 96(67):12071217

Hucho W, Sovran G (1998) Aerodynamics of road vehicles. Society

of Automotive Engineers, 400 Commonwealth Dr, Warrendale,

PA, 15096, USA

Jeong J, Hussain F (1995) On the identification of a vortex. J Fluid

Mech 285:6994

Jiang M, Machiraju R, Thompson D (2004) Detection and visuali-

zation of vortices. In: Johnson C, Hansen C (eds) Visualization

Handbook. Academic Press, New York, pp 287301

Krajnovic S, Davidson L (2004) Large-eddy simulation of the flow

around simplified car model. SAE paper 2004-01-0227

Krajnovic S, Davidson L (2005a) Flow around a simplified car, part 1:

large eddy simulation. J Fluids Eng 127:907

Krajnovic S, Davidson L (2005b) Flow around a simplified car, part 2:

understanding the flow. J Fluids Eng 127:919

Lienhart H, Becker S (2003) Flow and turbulence structures in the

wake of a simplified car model. SAE paper 2003-01-0656

Maskell E (1963) Theory of the blockage effect on bluff bodies and

stalled wings in closed wind tunnel. RAE Report and Memo-

randa 3400

Perry A, Chong M (1987) A description of eddying motions and flow

patterns using critical-point concepts. Annu Rev Fluid Mech

19(1):125155

Raffel M, Willert C, Wereley S, Kompenhans J (2007) Particle image

velocimetry: a practical guide. Springer, Berlin

Fig. 20 Streamlines in the rear symmetry plane

Fig. 21 Secondary recirculation, zoom next to the rear lower edge

Exp Fluids (2011) 50:12731284 1283

123

Roumeas M, Gillieron P, Kourta A (2009) Drag reduction by flow

separation control on a car after body. Int J Numer Methods

Fluids 60(11):12221240

Scarano F (2002) Iterative image deformation methods in piv. Meas

Sci Technol 13(1):119

Sims-Williams D, Dominy R (1998) Experimental investigation into

unsteadiness and instability in passenger car aerodynamics. SAE

paper 980391

Sovran G, Morel T, Mason W (1978) Aerodynamic drag mechanisms

of bluff bodies and road vehicles. Plenum, New York

Spohn A, Gillieron P (2002) Flow separations generated by a

simplified geometry of an automotive vehicle. In: IUTAM

symposium on unsteady separated flows, Toulouse

Theunissen R, Scarano F, Riethmuller M (2007) An adaptive

sampling and windowing interrogation method in PIV. Meas

Sci Technol 18:275

1284 Exp Fluids (2011) 50:12731284

123