19th Brazilian Congress of Thermal Sciences and Engineering

November 6th–10th, 2022, Bento Gonçalves - RS - Brazil

ENC-2022-0225
AERODYNAMIC INVESTIGATION OF A MIRA FASTBACK MODEL
GEOMETRY USING CFD TECHNIQUES BASED ON EXPERIMENTAL
WIND TUNNEL ANALYSIS
Luckyan Kanigoski Quintino
luckyanquintino@gmail.com
Jorge Esteban Chavez Gutierrez
jorge.chavez@labmci.ufsc.br
Leonel R. Cancino
leonel.cancino@labmci.ufsc.br
Internal Combustion Engines Laboratory - Joinville Technological Center - Federal University of Santa Catarina - LABMCI/CTJ/UFSC.
Rua Dona Francisca 8300, Joinville, SC, CEP 89219-600, Brazil.

Abstract. Aerodynamics is a high applicability type of science, used in the development of energy efficient automobiles
and, airplanes, even considered in the design of great infrastructures such as tall buildings and bridges. On the rise of the
computer era, computational tools were then developed to calculate the effects of fluid dynamics on virtual bodies without
manufacturing a prototype or using a wind tunnel. Experimentalists have been working together, using testbenches as
wind tunnels in order to better understand the fluid flow around vehicles. In function of the car shape diversity, it was
necessary to define some automotive reference geometries, it means, some geometry that is not actually a car geometry
but is a body that can be used to better understand the flow pattern around a real car. In this work, the MIRA reference
fastback type model was numerically investigated. Its geometry differs in the rear with a smooth transition between the
roofline and the rear end of the body, eliminating the three-volume characteristic of a traditional sedan car body. Mesh
and computational domain independence test were then performed to guarantee reliable numerical data. The obtained
fluid flow pattern, using the commercial ANSYS FLUENT™ software, is then discussed in terms of aerodynamic behavior
and compared to experimental data available at the literature. The set-up was built using wind tunnel experimental data
available at the literature. Flow structures like vortices, separation and reattachment were numerically visualized and
analyzed. Four turbulence models where then used for numerical simulations: κ - ε Realizable, κ - ε RNG, κ - ω and
Reynolds Stress Model were tested to compare and validate the numerical results as well as numerical procedures. The κ -
ε Realizable turbulence model shows the better numerical predictions for cD and cL , when compared to the experimental
data.

Keywords: Computational Fluid Dynamics, MIRA fastback body, Aerodynamic behavior, Turbulence model

1. INTRODUCTION

Nowadays fuel prices had increased considerably, and this kind of situations normally highlight fuel efficient kind of
cars. Although a low drag coefficient is possible, it’s not always achievable in a car project because of the air flow around
the body that also has direct impact in the vehicle stability as well as in noise generation, both vital to the success of the
car as a product in safety and comfort categories (Schutz, 2015). It is clear that the along the design of a car, several
steps are followed and each one of steps involves several tools, also, it is normal nowadays to hear about the potential
of computational fluid dynamics as a main tool in the automotive industry, covering and being applied to several areas
in the hole car project: combustion and electrical propulsion systems, powertrain system and aerodynamics (Heywood
(2018); Schutz (2015); Merker et al. (2012) and references therein). Along this process, experimentalists have been
working together, obviously investing big funds applied to testbenches as wind tunnels in order to better understand the
fluid flow around vehicles. At the beginning “normal” wind tunnels were then built, today is “normal” to find completely
sophisticated wind tunnels trying to, in-laboratory, reproduce the natural ambient of a car, some examples of this kinds
of wind tunnels can be found at Schutz (2015). In function of the car shape diversity in the automotive industry, it
was necessary to define or create some automotive reference bodies, it means, some geometry that is not actually a car
geometry (involving all the complexities) but is a body that can be used to better understand the flow pattern around a real
L.K. Quintino, J.E.C. Gutierrez, L.R. Cancino.
Aerodynamic Investigation of a MIRA Fastback Model Geometry Using CFD Techniques based on Experimental Wind Tunnel Analysis

car. Obviously some main car shape characteristics must be leave in to account in order to define a realizable automotive
reference body. For passengers and sportive cars there are two well knowledge references: (i) the Ahmed body (Ahmed
et al., 1984) and (ii) the MIRA reference bodies Carr and Stapleford (1986). The Motor Industry Research Association -
MIRA reference geometries were developed after production models of the early 80’s initially with three rear body type
variation: fastback, notchback and estate-back/wagon and were firstly introduced to calibrate wind tunnels using scale
models and full-sized models, those geometry also became a great reference for CFD software validation some decades
later. The Motor Industry Research Association - MIRA fastback reference car was first presented by Carr and Stapleford
(1986) as a simplified vehicular model used for aerodynamics investigations regarding the blockage effects in wind tunnel
testing. The fastback model was one of four conceived by Carr and Stapleford (1986) for their studies, the others were
the notch-back (very similar to a sedan model), the van or square-back and the pick-up (less used in posthumous studies).
All models share the same front-end and lower rear dimensions and geometry and are distinguished by the upper rear
geometry only. According to Le Good and Garry (2004), those models’ proportions were based on family-sized cars of
the early 80’s with a final geometry much more similar to the real-world cars than the Ahmed body for example. Le Good
and Garry (2004) commented that all the MIRA reference cars had a great contribution on understanding the influence of
test section and investigating blowing and suction effects on ground plane boundary layer and its influence on the car’s
behavior, in helping to refine and calibrate wind-tunnels and also testing numerical CFD.

Figure 1. Flow around a car in details - rear body in its variants: (a) hatchback, (b) fastback, and (c) notchback; schematic.
Adapted from Schutz (2015)

This study is focused on the analysis of external aerodynamic behavior of the MIRA fastback model geometry using
CFD tools. Firstly, the validation of the computational domain independence and later the number of mesh elements
independency were done using the κ - ε Realizable turbulence model. After that κ - ε RNG and κ - ω standard were
investigated and compared. Schutz (2015) presents some images indicating the wake characteristics according to the rear
end of a vehicle (Figure 1(b)), pointing the notchback type design capable of creating short and closed wakes, especially
when compared to the hatchback and fastback rear types.

2. EXPERIMENTAL DATA FROM THE LITERATURE

Wang et al. (2014) gathered multiple experimental data for the cD values from the TJ-2 wind tunnel of Tongji Univer-
sity (the MIRA models at the TJ-2 and IVK wind tunnel facilities) and also Hoffman et al. (2001) results to compare with
their own measurements and CFD analysis. All those values are shown at Table 1, alongside with the cL data measured
by Wang et al. (2014)

Table 1. Drag and Lift coefficients of MIRA reference geometries - Experimental data presented by Wang et al. (2014)

HD-2 TJ-2 IVK Hoffman et al. (2001) CFD HD-2 CFD

Wind Tunnel Wind Tunnel Wind Tunnel Sim. Sim. Wind Tunnel Sim.
Rear body cD cL
Fastback 0.2849 0.2631 0.2795 ≈0.26 0.2738 0.0460 0.0410
Notchback 0.3183 0.3016 0.3204 ≈0.29 0.3048 0.0416 0.0397
Squareback 0.3842 0.3668 0.3874 ≈0.36 0.3742 -0.3633 -0.3592

The data presented by Wang et al. (2014) includes five different values for the Drag coefficient of the MIRA Fastback
with a maximum of 0.2849, measured at the HD-2 wind tunnel (Figure 2), and a minimum of 0.2631 measured at the TJ-2
wind tunnel of Tongji University, presenting a 7.65% difference between themselves. In the other hand, the only reference
for lift coefficients presented were those measured by Wang et al. (2014)) by experimental and CFD methods. For those
reasons, the cD were chosen as primary reference value to validate the simulations used for mesh and computational
domain size independence. Other data were collected in order to have a primary reference over other important parameters
 19th Brazilian Congress of Thermal Sciences and Engineering
November 6th–10th, 2022, Bento Gonçalves - RS - Brazil

and consequently facilitate the verification of the final results such as the surface pressure on longitudinal symmetry plane
and the expected wake structure and air behavior at the rear end of the model. Zhengqi et al. (2011) measured the pressure
distribution over a MIRA Fastback model at the HD-2 wind tunnel at the Hunan University using 58 m/s as the flow
speed input for a 1/3 scale model. Although Zhengqi et al. (2011) used the same wind tunnel, model and scale of this
paper study, the numeric results for those cases are not directly comparable because of the difference of velocity. But the
pressure distribution should be very similar, especially at the front and of the car, considering that Zhengqi et al. (2011)
were capable of maintaining a laminar flow approaching the frontal area of the model.

Figure 2. HD-2 Boundary Layer Wind Tunnel (HD-2BLWT) schematic configuration (adapted) used by Wang et al.
(2014) for PIV measurement

3. METHODOLOGY

3.1 The MIRA fastback geometry used in this work

The MIRA fastback reference car used for the CFD analysis is very similar to the model used by Wang et al. (2014)
on their wind tunnel experiment: an 1:3 scale model respecting mostly dimensions. Some angles and dimensions were
not informed by Wang et al. (2014) and therefore were gathered from Carr and Stapleford (1986) for the same scale and
also from the Zhang et al. (2019) paper, converting the last missing dimensions to 1:3 scale. The body dimensions are
informed in Figure 3 below
Other modifications were necessary due some ANSYS FLUENT™ limitations when setting the enclosure as the
control volume of the wind tunnel. An error occurred when a symmetry plane was set to limit the volume under the car,
as it could not put the wheels of the model in contact with the ground due a tangential condition. The solution applied
is shown at Detail A of Figure 3, which consisted in modifying the wheels geometry in order to create a flat surface and
eliminate the single line tangential contact. This solution was chosen over other two alternatives, because it resulted later
in a better meshing skewness. Although this modification deviates a bit from the original MIRA body design, it could be
interpreted as tire deformation effects due vertical load, a regular behavior for a pneumatic tire according to Wong (2001).
In this case the main contributor is the body weight. The frontal area calculated for this 1:3 MIRA model equals 0.20637
m2 .
The fluid domain was created in ANSYS Design Modeler™ using the enclosure tool and based on the HD-2 Boundary
Layer Wind Tunnel (HD-2BLWT) in Wind Engineering Research Center, Hunan University, same used by Wang et al.
(2014) and shown at Figure 2. Using the model’s origin location as reference it was possible to apply symmetry conditions
to the enclosure tool at XZ and YZ planes, which resulted in a half car model with the wheels touching the floor. The total
height of the virtual wind-tunnel was set as 2.5 m, and the total width set as 1.5 m due to the symmetry condition applied
in the YZ plane, both representing the dimensions of the HD-2 tunnel. Since there are no clear indications of the position
of the model along the length of the wind tunnel, the distance between the velocity inlet and the model most forward
point was set following the recommendations of Agarwal (2013) work, which suggests a length of 3 times of the model
length ahead of it, and therefore this dimension was defined as 4167 mm. A convergence test on the tunnel rear length
were executed, using 8, 10, 12 and 14 times the model total length for the distance between the model’s most rearward
point and the pressure outlet. Smaller lengths were not used in this comparison, because they are more likely to produce
questionable results as showed by Gutierrez et al. (2020).
L.K. Quintino, J.E.C. Gutierrez, L.R. Cancino.
Aerodynamic Investigation of a MIRA Fastback Model Geometry Using CFD Techniques based on Experimental Wind Tunnel Analysis

Figure 3. MIRA Fastback reference car dimensions in mm

3.2 Meshing procedures and Boundary conditions

Three boxes were created near the car in order to increase meshing refinement in their respective regions. The boxes
are shown below in the Figure 4:

Figure 4. Dimensions of virtual wind tunnel and the boxes (a) Carbox, (b) Wakebox, (c) Underbox for mesh refinement
purposes. The w and h correspond to the real wind tunnel used by Wang et al. (2014) (see Figure 2), and “ L " represents
the MIRA fastback length = 1389 mm.

The carbox (Figure 4(a)) and the Underbox (Figure 4(c)) used fixed parameters for all the executed simulations, the
first one used 15 mm and the second one used 10 mm mesh sizing. Both boxes were configurated as body of influence
for each respective sizing over the full computational domain. The Wakebox (Figure 4(b)) used different sizing for the
simulations, because it was the variable modified for the mesh convergence test. Other two special refinements were
applied to the domain, one using the faces of the MIRA Fastback model as reference for a 10 mm sizing and a special 5
mm sizing applied only to the wheels of the model. Both sizing were configured with a soft behavior. Mesh Defeaturing
was set active alongside with Capture Curvature with 12° of normal angle and Capture Proximity for faces and edges.
 19th Brazilian Congress of Thermal Sciences and Engineering
November 6th–10th, 2022, Bento Gonçalves - RS - Brazil

The remaining parameters for the mesh generation process were kept as default values.

3.3 Simulation set-up

Figure 5 shows kinds of boundary conditions used in this work for all the simulations. The velocity inlet was set
to 20 m/s according to Wang et al. (2014) experiments, and since this value is under Mach 0.3, allowing the despise of
compressibility effects (Cengel and Cimbala, 2017). With this consideration, a pressure-based solver was selected being
the most adequate solver for incompressible flows at low velocity due also to its capacity to operate at low Mach numbers,
(Mangani et al., 2016).

Virtual wind tunnel - MIRA Fastback Model

Wind tunnel ceiling (Symmetry)

Wind tunnel symmetry plane (Symmetry)

Inlet (Velocity Inlet)

Outlet (Pressure Outlet)

Wind tunnel lateral wall (Symmetry)

Road (Wall)

Influence body - Carbox

Influence body - Wakebox

Influence body - Underbox

Figure 5. Boundary conditions used in this work for all the simulations

The use of a turbulence model is necessary to approach the solution achieved in experimental analysis. For this
reason, the simulations of this project were developed with three turbulence models: κ - ε Realizable, κ - ε RNG and κ -
ω Standard, being the first model used for the independence tests and also used by Wang et al. (2014) simulation. A hybrid
initialize method was selected, using the default parameters for 10 iterations. Following the initialization, 100 iterations
using first order upwind equations for momentum, turbulent dissipation rate and turbulent kinetic energy were executed
and after conclusion those parameters were changed to second order equations and the turbulence viscosity modified to
0.95 set to iterate until achieving a convergence status. The coupled pressure-velocity method were selected, using a least
squares cell based gradient and standard pressure. The inlet was configured with 1% of turbulent intensity and a ratio
of 10 for the turbulent viscosity. The outlet set to prevent reverse flow with 0.0 Pa of gauge pressure, 5% of backflow
turbulent intensity and a ratio of 10 for the backflow turbulent viscosity. The floor (road) and the model were considered
as no slip stationary walls, and the remaining faces considered as symmetry. The viscous model for the κ - ε Realizable
considered non-equilibrium wall functions, C2-ε as 1.9, TKE and TDR Prandtl Number equal to 1 and 1.2 respectively.
All the values for boundary conditions were obtained from the literature at similar flow configurations (Lanfrit (2005);
Gutierrez et al. (2020); Zhang et al. (2019); Wilcox (1994) and references therein)
All the simulations were initially set to iterate until the residual values of all the transport variables decreased below
1x10−4 , unfortunately the continuity residual was reducing very slowly after 600 iterations, so a target of at least 1000
iterations were set, and if the other residual values were below 1x10−4 , than the simulation was considered convergent.
Before testing others turbulence models, two independence tests were performed using the κ - ε Realizable turbulence
model: one varying the computational domain size and the other varying the mesh sizing at the Wakebox.

4. RESULTS AND DISCUSSION

In this section, all the numerical results of this work are presented. For all the simulations, convergence was considered
“acceptable" when the residuals of all the transport variables were below 1x10−4 . In order to identify the virtual tunnel
length and the minimum mesh size, two independence test where then performed. The virtual tunnel cross section area is
the same as in the experimental procedures of Wang et al. (2014), resulting in a blockage ratio of ≈2.75% which meets
the requirement that the blockage ratio of the experimental model should be less than 5% (Choi and Lee, 2000). Four
turbulence models where then used in order to identify the “ strong and weak " points of each turbulence model for road
vehicle aerodynamics under the flow conditions of this work.
L.K. Quintino, J.E.C. Gutierrez, L.R. Cancino.
Aerodynamic Investigation of a MIRA Fastback Model Geometry Using CFD Techniques based on Experimental Wind Tunnel Analysis

4.1 Computational domain length and Mesh size independence tests

The distance from the rear surface of the MIRA Fastback reference geometry to the exit of the numerical wind tunnel
(12L in the upper part of Figure 4) was defined for domain length independence analysis. To develop this study, the rear
length [L] was varied between 8L and 14L, where L denotes the total length of the MIRA fastback length geometry (1389
mm), as shown in Figure Figure 4. On the other hand, the same dimensions and refinement parameters were maintained
for the underbody-box and car-box influence volumes (Figure 4), while the dimensions and refinement parameters of the
wake-box were varied proportionally with the back length of the computational domain, this means that the size of this
volume of influence was varied as the study of independence of the length of the computational domain was executed,
once this length was defined, the study of mesh independence test was carried out. The drag coefficient cD was selected
to analyze the convergence and independence criteria. Figure 6 shows the results of independence test performed in this
work.
0.288 0.2790
cD cD
0.286
Drag coefficient - cD [--]

Drag coefficient - cD [--]

0.284
0.2759
0.282
0.280
0.278 0.2728
0.276
0.274
0.2697
0.272
0.270
0.268 0.2666
8L 10L 12L 14L 4.0x106 6.0x106 8.0x106 1.0x107 1.2x107 1.4x107
(a) (b)
Rear Length [m] (L = 1.389 m) Number of elements [--]
Figure 6. Computational domain length and Mesh size independence tests.

The train observed in Figure 6(a) indicates that for rear length bigger that 12L no significant cD variation is elucidated,
of this form, the rear length of 12L was selected for numerical simulations from this point and forward. The Figure 6(b)
shows the mesh size independence test results, here is possible to observe that for a mesh with a elements number among
1.0x107 and 1.4x107 there is no cD representative variation. The final computational mesh used for analysis in this work
has 13’790.730 elements and the rear length is 12L (Figure 4)

4.2 Drag, lift and pressure coefficients

The methodology described for the preparation of the CFD simulation were reproduced using different turbulence
models, those were the κ - ω and the Reynolds Stress Model (RSM). The κ - ε RNG model were also simulated, but the
convergence parameters for the residual values were not fulfilled, consequently those results will not be presented. The
final values calculated for cD and cL are displayed at Table 2 below:

Table 2. Drag and Lift coefficients calculated for different turbulence models

This work Wang et al. (2014)

Aerodynamic Numerical Numerical Numerical Experiment Numerical
Coefficient κ - ε realizable κ-ω RSM HD-2 Wind Tunnel κ - ε realizable
cD 0.2671 0.2814 0.3214 0.2849 0.2738
cL 0.0381 0.0890 0.0596 0.0460 0.0410

All the turbulence models resulted in quite distant values from those from the Wang et al. (2014) reported in their paper
and none of them could match precisely the values for both cD and cL . The κ - ε Realizable turbulence model presented
the closest result for lift, with 7% difference to the Wang et al. (2014) CFD results and 17% for the experimental results.
The other two turbulence models simulated resulted in considerably distant lift values, being the experimental coefficient
30% less than the indicated by the Reynolds Stress Turbulence model (RMS) simulation and 94% to the κ - ω turbulence
model simulation. In relative comparison, the difference between the κ - ω and RSM to the Wang et al. (2014) lift
coefficient is considerably big, but confronting the values directly the difference stands in 10−2 order, being this the same
 19th Brazilian Congress of Thermal Sciences and Engineering
November 6th–10th, 2022, Bento Gonçalves - RS - Brazil

order of magnitude, thus the high percentage differences between values. The drag coefficients in the other hand are closer
to the results registered by Wang et al. (2014), being κ - ω the more accurate turbulence model with only 1% less than
the experimental value an 3% more than the CFD results obtained by Wang et al. (2014). The κ - ε Realizable turbulence
model also presented a good result with only 2% difference to the CFD results and 6% to the experimental results. The
RSM turbulence model presented the worst results compared to the values of drag presented by Wang et al. (2014) and
also the highest, being 13% bigger than the experimental and 17% bigger than the CFD results.
The results of this study over drag and lift indicates that the κ - ε Realizable is the best turbulence model to reproduce
Wang’s wind tunnel experiment when analyzing both drag and lift together. If the focus of the simulation go only towards
the drag parameters the κ - ω turbulence model is the best choice, but analyzing any other lift dependent parameter like
the aerodynamic balance, it becomes a bad choice, since its results shown a high inaccuracy regarding the lift coefficient.
Lastly, the RSM model also seems not to be a suitable turbulence model for this study, not only because the results obtained
for both drag and lift coefficients are not accurate with the data presented by Wang et al. (2014) for the same experiment
condition, but also because this model demands much more computational capacity for the calculations. This means that,
for the same computer, the final results would take longer to be achieved when compared to the other turbulence models.
Figure 7 shows the pressure coefficient contours in the MIRA fastback geometry surface. The rear angle in this
geometry is about 22.5°, it means below the critical angle (∼ 30°) related to automotive fastback geometries (Hucho,
1998), of this form, the MIRA fastback geometry analyzed in this work must return a low drag coefficient, as explained
by Ahmed et al. (1984) using the classical Ahmed body reference geometry.

Pressure Coefficient
1.030
0.667
0.323
- 0.030
- 0.384
- 0.738
- 1.090
- 1.450
- 1.800
- 2.150
- 2.510

Figure 7. Pressure coefficients - Numerical prediction using the κ - ε Realizable turbulence model.

4.3 Flow field

The flow field obtained using the κ - ε turbulence model is very close to the results presented by Wang et al. (2014)
for the fastback model. Figure 8(a) below shows the pathlines in the symmetry plane around the body. Than pathlines
indicates the formation of two vortex structures, a clockwise vortex coming from the upper flow and an anti-clockwise
vortex formatted by the air flow under the body, as mentioned in the classical work of Ahmed et al. (1984) for fastback
reference geometry.
The pathlines also shows that part of the upper airflow changes its trajectory in a limit line between the two generated
vortex structures centers, helping both the vortex to grow instead of only contributing to the expansion of the clockwise
vortex. Another parameter analyzed were the wind velocity magnitude (Figure 8(b)) around the body at the symmetry
plane. Focusing at the rear part of the body its possible to see a stagnation region, where the velocity values are very close
to zero. It is also possible to observe a high velocity region formed under the body due to the Venturi effect, consisting
in the acceleration of the airflow due to a transversal area expansion. In order to better understand the wake structure, 6
different planes behind the car body showing the pathlines are then plotted on Figure 9 (planes equivalents to Wang et al.
(2014) X/L 0.6 to 1.1 - (b) X/L = 0.6, (c) X/L = 0.7, (d) X/L = 0.8, (e) X/L = 0.9, (f) X/L = 1.0, and (g) X/L = 1.1).
That figure shows the vortex structures as depicted in the literature (Ahmed et al., 1984; Hucho, 1998; Gutierrez et al.,
2020; Schutz, 2015)
Illustratively, a simple comparison of Figure 9(a) to Figure 1(b) can elucidate the weak flow structure, predicted for
fastback reference geometries (Schutz, 2015; Hucho, 1998). In this work, all the turbulence model tested (κ - ε Realizable,
κ - ε RNG, κ - ω and Reynolds Stress Model) shows that behavior, even the κ - ε RNG turbulence model with residuals
around 10−2 . Additionally, both the vortices at the rear (Figure 8(a) also were reproduced for all turbulence models used
in this work, however, with different shapes. Figure 9(a) shows that two vortices for the numerical prediction using the κ
- ε Realizable turbulence models. Results for the other turbulence models used in this work are not exhibited because of
the big quantity of data. Figures 9 (b) to (g) shows the sequence of six planes ((b) X/L = 0.6, (c) X/L = 0.7, (d) X/L =
0.8, (e) X/L = 0.9, (f) X/L = 1.0, and (g) X/L = 1.1) illustrating the pair of trailing 3D vortices formed in the C-pillars
of the MIRA fastback geometry.
L.K. Quintino, J.E.C. Gutierrez, L.R. Cancino.
Aerodynamic Investigation of a MIRA Fastback Model Geometry Using CFD Techniques based on Experimental Wind Tunnel Analysis

(a)

Velocity Magnitude

35.0
31.5
28.0
24.5
21.0
17.5
(b) 14.0
10.5
7.0
3.5
0.0
[ m/s]

Figure 8. (a) Pathlines colored by velocity magnitude. (b) Velocity contours. Symmetry plane - Numerical prediction
using the κ - ε Realizable turbulence model.

(a)

Velocity Magnitude
35.0
31.5
28.0
24.5
21.0
17.5
14.0
10.5
7.0
3.5
0.0
[ m/s ]

(b) (c) (d)

(e) (f) (g)

Figure 9. Path lines colored by velocity - Numerical prediction using the κ - ε Realizable turbulence model.
 19th Brazilian Congress of Thermal Sciences and Engineering
November 6th–10th, 2022, Bento Gonçalves - RS - Brazil

The turbulent kinetic energy (κ) was also plotted in the same six planes, ((b) X/L = 0.6, (c) X/L = 0.7, (d) X/L =
0.8, (e) X/L = 0.9, (f) X/L = 1.0, and (g) X/L = 1.1), Figure 10 below show these results. The work from Wang et al.
(2014) reports experimental and numerical data of turbulent kinetic energy (κ), with maximum levels of κ ∼45 m2 /s2
(Figure 19(a) in the Wang et al. (2014) paper), in this work, the maximum turbulent kinetic energy (κ) numerical data was
around κ ∼35 m2 /s2 . Here is necessary to inform that the comparison of turbulent kinetic energy (κ) maximum levels is
done at the same turbulence model (κ - ε Realizable) and boundary conditions.

(a)

Turbulent Kinetic Energy

35.0
31.5
28.0
24.5
21.0
17.5
14.0
10.5
7.0
3.5
0.0
[ m2/s2 ]

(b) (c) (d)

(e) (f) (g)

Figure 10. Turbulent Kinetic Energy - Numerical prediction using the κ - ε Realizable turbulence model.

5. CONCLUSION

The experience of reproducing a wind tunnel experiment exploring other difference models involved several steps,
including the validation of the parameters such as mesh and computational domain independence, the calculation itself
and the critical analysis of the results. All the best practices recommended for CFD studies were also applied during the
pre-processing stage until the conclusion of the calculation, example given: the fulfillment of the convergence criteria
for the residual parameters in order to raise the simulation results credibility. Comparing the simulated models, the κ
- ε Realizable has an evident benefit towards the others, because it could reproduce the experimental values acceptable
precisely consuming a lower computational power. In this work, the ANSYS-FLUENT™ CFD software was used for
numerically analyze the aerodynamic response of the MIRA fastback reference automotive geometry. Along the numerical
procedure, independence tests (domain length and mesh size) were conducted in order to obtain reliable numerical data
with less (or without) influence of the dimensions used in the problem description and discretization. In this way, the
external aerodynamics of the reference geometry was then analyzed and understood. The Reynolds Stress Model shows
a poor behavior in this work, maybe related to the mesh quality refinement, however, is well knowledge that RSM model
usually performs better for vehicular aerodynamics (Hucho, 1998; Gutierrez et al., 2020; Schutz, 2015), specially for
lift prediction. The κ - ε Realizable turbulence model presented the closest result for lift, difference of 17% to the
experimental results of Wang et al. (2014). The other two turbulence models simulated resulted in considerably different
lift values, being the experimental coefficient 30% less than the indicated by the Reynolds Stress Turbulence model (RMS)
simulation and 94% to the κ - ω turbulence model simulation. The drag coefficients in the other hand are closer to the
results registered by Wang et al. (2014), being κ - ω the more accurate turbulence model with only 1% less than the
experimental value an 3% more than the CFD results obtained by Wang et al. (2014). The κ - ε Realizable turbulence
model also presented a good result with only 2% difference to the CFD results and 6% to the experimental results. The
L.K. Quintino, J.E.C. Gutierrez, L.R. Cancino.
Aerodynamic Investigation of a MIRA Fastback Model Geometry Using CFD Techniques based on Experimental Wind Tunnel Analysis

RSM turbulence model presented the worst results compared to the values of drag presented by Wang et al. (2014) and
also the highest, being 13% bigger than the experimental and 17% bigger than the CFD results. The κ - ε RNG turbulence
model does not show convergence below 10−4 and of this form its results were not presented in this work.

6. ACKNOWLEDGEMENTS

The authors would like to acknowledge the support of UFSC Joinville TI team (Mr. Kleber Carlos Francisco) for all
support given to the LABMCI computer network.

7. REFERENCES

Agarwal, R., 2013. “Sustainable Ground Transportation: Technologies, Challenges and Opportunities”. American Society
of Mechanical Engineers Digital Collection. doi:10.1115/ES2013-18028.
Ahmed, S.R., Ramm, G. and Faltin, G., 1984. “Some Salient Features of the Time -Averaged Ground Vehicle Wake”.
SAE Transactions, Vol. 93, pp. 473–503. ISSN 0096-736X. URL https://www.jstor.org/stable/44434262.
Publisher: SAE International.
Carr, G.W. and Stapleford, W.R., 1986. “Blockage Effects in Automotive Wind-Tunnel Testing”. p. 860093. doi:
10.4271/860093. URL https://www.sae.org/content/860093/.
Cengel, Y. and Cimbala, J., 2017. Fluid Mechanics: Fundamentals and Applications. McGraw Hill, New York, NY, 4th
edition. ISBN 978-1-259-69653-4.
Choi, J.H. and Lee, S.J., 2000. “GROUND EFFECT OF FLOW AROUND AN ELLIPTIC CYLINDER IN A TURBU-
LENT BOUNDARY LAYER”. Journal of Fluids and Structures, Vol. 14, No. 5, pp. 697–709. ISSN 0889-9746.
doi:10.1006/jfls.2000.0290.
Gutierrez, J.E.C., Duarte, L.E.D., Oliveira, A.A.M. and Cancino, L.R., 2020. “The Ahmed Body’s External Aerodynamics
at 25° Slant Angle Rear Surface: A Numerical Analysis Using CFD”. In Proceedings of the 18th Brazilian Congress
of Thermal Sciences and Engineering. pp. ENC–2020–0060. URL https://repositorio.ufsc.br/bitstream/
handle/123456789/217969/ENCIT2020-0060-JECGutierrez.pdf?sequence=1&isAllowed=y.
Heywood, J.B., 2018. Internal Combustion Engine Fundamentals 2E. McGraw-Hill Education, 2nd edition. ISBN
978-1-260-11610-6.
Hoffman, J., Martindale, B., Arnette, S., Williams, J. and Wallis, S., 2001. “Effect of Test Section Configuration on
Aerodynamic Drag Measurements”. pp. 2001–01–0631. doi:10.4271/2001-01-0631.
Hucho, W.H., ed., 1998. Aerodynamics of Road Vehicles: From Fluid Mechanics to Vehicle Engineering. Sae Intl,
Warrendale, PA, 4th edition. ISBN 978-0-7680-0029-0.
Lanfrit, M., 2005. “Best practice guidelines for handling Automotive External Aerodynamics with FLUENT”.
Le Good, G.M. and Garry, K.P., 2004. “On the Use of Reference Models in Automotive Aerodynamics”. pp. 2004–01–
1308. doi:10.4271/2004-01-1308. URL https://www.sae.org/content/2004-01-1308/.
Mangani, L., Sanz, W. and Darwish, M., 2016. “Comparing the performance and accuracy of a pressure based
and a density-based coupled solver”. In Proceedings of the International Symposium on Transport Phenomena
and Dynamics of Rotating Machinery. ISROMAC 2016, Hawaii, Honolulu, pp. hal–01894391. URL https:
//hal.archives-ouvertes.fr/hal-01894391/document.
Merker, G.P., Schwarz, C. and Teichmann, R., eds., 2012. Combustion Engines Development - Mixture Formation,
Combustion, Emissions and Simulation. Springer-Verlag, Berlin Heidelberg. ISBN 978-3-642-02951-6.
Schutz, T., ed., 2015. Aerodynamics of Road Vehicles. SAE International, Warrendale, Pennsylvania, 5th edition. ISBN
978-0-7680-7977-7.
Wang, Y., Xin, Y., Gu, Z., Wang, S., Deng, Y. and Yang, X., 2014. “Numerical and Experimental Investigations on the
Aerodynamic Characteristic of Three Typical Passenger Vehicles”. Journal of Applied Fluid Mechanics, Vol. 7, No. 4,
pp. 659–671. ISSN 1735-3572. doi:10.36884/jafm.7.04.21460.
Wilcox, D.C., 1994. Turbulence Modeling for CFD. DCW Industries, Inc., La Cañada, California. ISBN 0-9636051-0-0.
Wong, J.Y., 2001. Theory of Ground Vehicles, 3rd Edition. Wiley-Interscience, New York, 3rd edition. ISBN 978-0-471-
35461-1.
Zhang, Y., Zhang, J., Wu, K., Wang, Z. and Zhang, Z., 2019. “Aerodynamic Characteristics of Mira Fastback Model
in Experiment and CFD”. International Journal of Automotive Technology, Vol. 20, No. 4, pp. 723–737. ISSN
1976-3832. doi:10.1007/s12239-019-0068-x.
Zhengqi, G., Wang, S., Qiu, J., Zhang, Q., Hu, P. and Chen, X., 2011. “Wind Tunnel Tests of MIRA Model Group for
Study of Vehicle’s Rear Shape”. Science & Technology Review. doi:10.3981/j.issn.1000-7857.2011.08.011. URL
http://en.cnki.com.cn/Article_en/CJFDTOTAL-KJDB201108023.htm.
8. RESPONSIBILITY NOTICE

The authors are solely responsible for the printed material included in this paper.