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Abstract

The number of computational uid dynamics (CFD) simulations

performed during the vehicle aerodynamic development process

continues to expand at a rapid rate. One key contributor to this trend

is the number of analytically based designed experiments performed

to support vehicle aerodynamic shape development. A second

contributor is the number of aerodynamic optimization studies

performed for vehicle exterior components such as mirrors,

underbody shields, spoilers, etc. A third contributor is the increasing

number of “what if” exploratory studies performed early in the design

process when the design is relatively uid. Licensing costs for

commercial CFD solutions can become a signicant constraint as the

number of simulations expands. A number of alternative products

(e.g., independently developed, supported and documented forks of

the popular open-source OpenFOAM® toolbox [1]) have become

available in recent years, offering a lower cost alternative to

traditional commercial CFD products. This paper summarizes results

from a broad and deep evaluation of the capability of iconCFD® to

substitute for the more traditional commercial CFD solutions

currently used to support vehicle aerodynamic development early in

the program development cycle. Included in this study were detailed

B-car, sedan, SUV and truck shapes as well as multiple variants of

each shape. The study investigated both static and moving ground

boundary conditions as well as alternative turbulence models. Trends

of the predicted aerodynamic drag coefcients (Cd) are compared

against experimental data. Both transient and steady state simulation

ranking accuracy of total vehicle Cd were found to be equivalent to

that historically observed with more traditional commercial solver

results. A consistent upward bias in absolute Cd values was observed

in the transient results.

Introduction

Aerodynamic loading on vehicles has a signicant inuence on fuel

economy. Wind tunnel testing and computational uid dynamics

simulations are widely used to evaluate the aerodynamic forces

exerted on a vehicle. There are two metrics by which the accuracy of

CFD solvers have traditionally been evaluated. The rst metric is

visualization—the ability to accurately predict and visualize surface

pressures, surface ow lines and ow eld structures for potential

insights into Cd reduction actions prior to test. CFD is now a widely

accepted tool for this type of pretest analysis. The second metric is

the absolute accuracy of the predicted aerodynamic coefcients.

Numerous validation studies have been performed by both academia

and automotive OEMs over the last two decades for the purpose of

determining if the predictive accuracy of CFD could consistently and

reliably replicate experimental results. Accuracy levels have

signicantly improved over the years as a function of increasing

model denition, mesh resolution, etc., however, absolute replication

of experimental force measurements remains somewhat challenging.

It should be noted that repeatability of wind tunnel measurements

between different facilities can also be an issue. In particular, test

section replication, small tire modications, etc. can have a

signicant effect on the measured forces.

Today’s aerodynamicist continues to depend on CFD to visualize

ow eld data for insight into potential Cd reduction actions. As

experimental aerodynamicists acknowledge that results can often be

tunnel dependent and CFD proponents acknowledge that certain

phenomena are extremely challenging to simulate, a third metric,

ranking accuracy, has become increasingly important. Today’s

aerodynamicists depend on CFD to correctly rank aerodynamic

coefcients across both multiple vehicle shapes and conguration

variations within a given shape.

An Extensive Validation of an Open Source Based Solution for

Automobile External Aerodynamics

2017-01-1524

Published 03/28/2017

Robert Lietz, Levon Larson, Peter Bachant, John Goldstein, Rafael Silveira, and Mehrdad

Shademan

Ford Motor Company

Pete Ireland and Kyle Mooney

ICON

CITATION: Lietz, R., Larson, L., Bachant, P., Goldstein, J. et al., "An Extensive Validation of an Open Source Based Solution for

Automobile External Aerodynamics," SAE Technical Paper 2017-01-1524, 2017, doi:10.4271/2017-01-1524.

Copyright © 2017 SAE International

Numerically driven designed experiments and optimization studies

are driving the number of CFD simulations performed to increase at a

rapid rate. As High Performance Computing (HPC) resources

continue to expand, the main constraint on increasing CFD

simulations becomes the cost and availability of commercial CFD

licenses. These cost and licensing constraints are driving an ever-

increasing interest in open source CFD solvers. SAE Technical Paper

2011-01-0163 [2] was a limited investigation into the capability of

open source CFD. That study reported that open source steady state

simulations based on the Reynolds Averaged Navier–Stokes (RANS)

approach did a good job at predicting Cd while transient simulations

(detached eddy simulation; DES) were required for more accurate lift

predictions. This paper expands on that material as it examines the

viability of open source CFD as an alternative to today’s commercial

CFD solvers. The evaluation metrics used in the study were Cd

ranking accuracy and ow visualization. Two questions were

investigated. First, can an open source, nite volume, transient CFD

code provide the same level of ranking accuracy as more traditional

commercial CFD solvers? In other words, can open source transient

analyses correctly rank not only different vehicle shapes but also

variations in the conguration of each shape? Second, is the ranking

accuracy of steady state analyses adequate enough to provide design

direction early in the vehicle development process? The relative

correctness of the ow structures predicted by the steady state

analyses is evaluated by comparison against those from the transient

analyses. The steady state simulations employed the k–ω SST

turbulence model, and the transient simulations employed the

Spalart–Allmaras detached eddy simulation model (SA-DES). Both

turbulence models are commonly recommended for ows with large

rotation, separation and reattachment. A total of 54 vehicle variants

(including B-cars, sedans, SUVs and trucks) were evaluated in this

study. Results from simulations were compared against results from

wind tunnel experiments. Static ground wind tunnel testing was

performed at the Ford Motor Company Dearborn Test Facility.

Moving ground wind tunnel testing was performed at the Windshear

facility in North Carolina. Images of the performance vehicle in the

test section of both facilities are shown in Figure 1.

Figure 1. Wind tunnel test facilities.

The structure of the paper is as follows. The Methods section of this

paper discusses numerical methods, geometry modeling, boundary

condition setup and the governing equations. Ranking accuracy and

ow visualization for the total data set (as well as specic subsets of

the data) are presented in the Results section of this paper.

Observations and potential next steps are discussed in the

Conclusion/Summary section of this paper.

Methods

There have been a growing number of validation studies published on

open source CFD in recent years. Most have been limited in scope to

a small number of either vehicle shapes or variants of a single shape.

This paper reports the results of a study conducted across a wide

range of vehicle shapes, conguration variants and boundary

conditions. All CFD analyses were performed using a single common

modeling and simulation best practice. A high level schematic of the

process is shown in Figure 2.

Figure 2. Schematic of the process involved in each simulation.

Numerical Method

Governing Equations

RANS Method

In the current study, the three-dimensional incompressible Reynolds

Averaged Navier-Stokes (RANS) equations were used for simulating

turbulent ow over different vehicles. The continuity and momentum

equations used are as follows:

(1)

(2)

In these equations ui, p, ρ and μ represent the velocity, pressure,

density and kinematic viscosity, respectively, and the overbar

represents a time-averaged quantity. In RANS in order to calculate

the shear stresses, the Boussinesq hypothesis (which relates the

stresses to the mean velocity gradients) is used, i.e.,

(3)

where μt is the turbulent viscosity, k is the turbulent kinetic energy

and ϵ is the dissipation rate. Among the RANS turbulence models

available, the Spalart-Allmaras, k–ϵ and k–ω use the Boussinesq

hypothesis. These approaches are employed when low computational

cost is required.

For the RANS portion of this study, Menter’s k–ω SST model was

used [3]. The k–ω SST model is designed in a way to activate the

standard k–ω model in the inner region of the boundary layer and the

standard k–ϵ model in the outer region. It also uses a modied

turbulent viscosity equation to take into consideration the transport

effects of the shear stresses. In this model the turbulent viscosity is

calculated from

(4)

where F2 is a blending function, s is the strain-rate magnitude, α1

=0.31 and α* is given by

(5)

where

, Rk = 6.0, , in high-Re ows and

ω is the turbulence specic dissipation rate. These features make the

k–ω SST model more robust and accurate for ows with adverse

pressure gradients and separation and reattachment comparing to the

standard case.

Second-order spatially accurate schemes were used to discretize the

governing RANS equations within the framework of the nite

volume method (FVM). The SIMPLEC algorithm is used for

pressure-velocity coupling, and iconCFD’s iconSimplecFoam version

3.0.17, based on OpenFOAM’s simpleFoam, was used to solve the

governing equations. The RANS simulations were run for about 3000

iterations each on 144 processors on high performance computing

clusters, and the combined meshing and simulation time for each case

was approximately 12 hours. The behavior of the drag force on the

vehicles was monitored, and the solution was assumed to be nalized

and converged when the drag coefcient exhibited either a repeatable

behavior or showed no signicant change with each successive

iteration. Based on this criterion, the simulations were observed to be

converged before reaching the above mentioned iteration number.

DES Method

Three-dimensional incompressible DES simulations were also carried

out to solve the transient ow over different vehicles. DES is a hybrid

method which combines the benet of using RANS-based methods in

the wall proximity region and LES in the rest of the domain. The

popularity of this method is growing rapidly for many industrial

applications due to its comfort for satisfying the mesh requirements

compared to the LES method. The DES approach used in the current

analyses employs a ltered approach where the sub-grid scale model

used is the Spalart–Allmaras turbulence model with a higher

inuence near the wall and a decay far from the wall.

As with the RANS simulations, a second-order nite volume

discretization was used. Second-order temporal discretization was

also employed, and the PISO algorithm was used for pressure-

velocity coupling. A time step of 0.0001 seconds was chosen for the

transient cases, and simulations were conducted on 144 and 240 cores

on the HPC system. Transient simulations were run for 1.5 seconds of

simulated time (which corresponded to 3-5 days of wall clock time),

and statistical averages were computed over the last 1.0 seconds of

simulated time.

Determination of the ranking accuracy of the predicted aerodynamic

drag coefcient was the primary focus of the study. Flow eld

visualization comparisons were conducted in order to conrm the

correctness of the solution and inspect for possible offsetting errors.

Geometry Modeling and Boundary Conditions

An example of one geometry modelled in the current study is

presented in Figure 3. The size of the domain is kept constant in all

cases and only the vehicle is changed. To minimize the inuence of

the inlet, outlet, sides and top boundaries on the pressure and velocity

elds, the computational domain is considered to be 60 m in length,

50 m in width and 30 m in height. Based on this dimensions, the

maximum blockage ratio for all vehicles analyzed is between 1.5% to

2.5%, which is smaller than the 3% maximum suggested by Franke et

al. [4]. Note that a constant numerical setup was applied to all cases.

Figure 3. Computational domain and boundary conditions.

For consistency, a single user independent meshing strategy was

applied to all vehicle models. iconCFD’s hexahedral dominant

unstructured mesh generator iconHexMesh, derived from

OpenFOAM’s snappyHexMesh, was used for creating the hybrid

mesh inside the domain. There are different approaches in CFD for

accounting the wall effect. In the current study, the wall function

approach, which uses the law of the wall, was used for modeling the

ow in the wall region. This approach was used for both k–ω SST

and DES methods. In order to use a wall function, a grid spacing with

30 < y+ < 300 is required. Here, y+ = uτy/ν is a non-dimensional wall

distance, where uτ = (τw/ρ)0.5 is the friction velocity, y is the wall

normal distance, ν is the kinematic viscosity, ρ is the density and τw is

the wall shear stress.

In order to capture the inuence of the high velocity gradients in the

wall regions, a ner mesh is used for regions close to the walls

(ground surface and vehicle parts); while for the rest of the domain, a

coarser mesh is used. Cells adjacent to most parts of the vehicle were

rened 9 times, with cells next to ner-detailed parts such as tires and

grilles being rened 10 times. Near all vehicle parts a boundary layer

mesh with 6 high aspect ratio layers was generated with an expansion

ratio of approximately 1.3, such that the rst cell center was located

in the log law region of the boundary layer, consistent with the high

Reynolds number wall function strategy. Additional renement

regions were added to capture the vehicle wake, an example of which

is shown in Figure 4. On average, the vehicle models were simulated

with about 15 million surface mesh elements, and the entire

computational domain contained approximately 100 million volume

mesh elements.

Figure 4. Constructed mesh around a model.

The boundary conditions considered include a constant velocity of 80

mph at the inlet with a turbulence intensity of 0.5%, which matches

the wind tunnel condition. A symmetry boundary condition is applied

to both the top and side walls. The ground surface is split two

sections, one with slip condition and the other with the no-slip

condition. In order to consider the boundary layer growth in the

upstream of the domain, a distance of 9.6m in the upstream ahead of

the vehicle is set to have no-slip condition. For the rest of the ground

surface, a slip condition is used. A pressure outlet condition that lets

the ow to exit to the atmosphere is applied at the outlet. For static

ground cases, static boundary conditions were used on the oor and

the tires. For other cases, in order to correctly consider the car

movement, moving ground and rotating tire boundary conditions

were used. The numerical wind tunnel was tuned to generate

measured empty tunnel boundary layer growth for static conditions in

order to best replicate wind tunnel measurements.

Table 1. Summary of validation models.

Validation Models

The objective of this study was to determine the capability of an

open-source CFD solver to support aerodynamic development across

all vehicle programs. It was therefore necessary to evaluate the solver

across a wide range of vehicle shapes and variants. Detailed B-car,

sedan, SUV and truck shapes, as well as multiple variants of each

shape, are included in this study. A select set of simplied models

(DrivAer notchback, fastback and wagonback) are also included [5].

A summary of all cases simulated and their setup information is

provided in Table 1.

Model Geometry

Model geometry for each of the base models are presented in Figure

5. The details of each model variant are presented in Figure 5 to

Figure 15.

Figure 5. Validation set of base models.

Figure 6. DrivAer models with configuration variants.

Figure 7. B-car SUV base model and configuration variants.

Figure 8. B-car base model and configuration variants.

Figure 9. Sedan 1 base model and configuration variants.

Figure 10. Sedan 2 base model and configuration variants.

Figure 11. Sedan 3 base model and configuration variants.

Figure 12. Truck 1 base model and configuration variants.

Figure 13. Truck 2 base model and configuration variants.

Figure 14. Performance vehicle base model and configuration variants.

Figure 15. SUV base model and configuration variants.

Metrics

Cd ranking accuracy is the primary metric for comparing simulated

and measured results. It provides a measure of the capability of the

simulation tool to correctly predict the Cd trends across the vehicle

sample set used in this study. Cd development plots and ow

visualization were used to identify any signicant differences

between the steady state and transient simulation results.

Cd Ranking Accuracy

In this paper ranking accuracy is dened as the number of correctly

predicted positional rankings divided by the total number of

positional rankings. A visual example is presented in Figure 16. The

blue bars show ve sample measurements of increasing value. The

red line shows the predicted values for each sample measurement.

Each measurement has a rank order position relative to the other four

samples, leading to a total of 20 positional rankings for this data set.

The rank order of samples 1, 2 and 3 were correctly predicted four

times. The rank order of samples 4 and 5 were correctly predicted

three times. The net result is a total of 18 correctly predicted sample

rank orders and a ranking accuracy of 90%.

Figure 16. Ranking accuracy example.

Two metrics are used in this paper to compare the results of the

steady state and transient simulations.

Cd Development Plots

The rst comparison metric is the Cd development plot, an example

of which is given in Figure 17. This plot is essentially a visual

representation of drag accumulation moving from the front to the rear

of the vehicle. This plot is used to assist in identifying locations on

the vehicle with notable differences between steady state and

transient local drag force predictions.

Figure 17. Cd development plot example.

Flow Visualization

The second comparison metric used in identifying signicant

differences between steady state and transient simulation results is

ow visualization. A combination of velocity distributions and

isosurfaces of wake structure were used in this study.

Results

A total of 54 unique vehicle and vehicle variants were evaluated. Cd

trends versus experimental measurements are plotted in Figure 18. A

positive bias in the absolute Cd values was observed in both the

transient and steady state simulation results. The values in the plot

have been adjusted by subtracting the average bias from the drag

values. The simulation results reveal a high level of correlation to the

experimental trends for both the transient and steady state results.

Figure 18. Normalized Cd trend predictions versus experimental

measurements.

Cd Ranking Accuracy - All Cases

The correlation presented in Figure 18 is further supported by the

ranking accuracy bar graph shown in Figure 19. The steady state and

transient ranking accuracy results from the entire data set were very

good and generally equivalent to similar studies performed on

commercial CFD solver applications.

Figure 19. Steady state and transient Cd ranking accuracy for all data sets.

As Figure 19 shows, the ranking accuracy for the transient results

was 94.3%, while the ranking accuracy for the steady state results

was 91.3%. The ranking accuracies of both methods were

approximately equivalent overall, and were in alignment by

expectations based on previous results from more traditionally

utilized commercial solvers. The broad range of shapes and boundary

conditions within the data set, however, creates the potential for

making lower accuracy results within subsets of the data. To that

extent, the data was divided into different specic groupings as

following and the ranking accuracies recalculated for each case:

1. Static Ground

2. Moving Ground

3. Sedans

4. SUVs

5. Trucks

6. Open AGS

7. Closed AGS

8. Closed Grille

9. B-cars

A total of 39 samples were included for the static ground cases, 15 for

the moving ground cases, 21 for sedans, 5 for SUVs, 12 for trucks, 6

for B-cars, 9 for open AGS, 23 for closed AGS and 13 for closed

grille cases. The following observations were made:

• Ranking accuracy for the static ground cases was equal or

slightly higher than the ranking accuracy calculated for the

entire data set. DES results were 1.4% greater. Results from the

k–ω SST model simulations were 1.4% greater.

• For the moving ground cases, the ranking accuracy was

approximately equal to the number calculated for the entire data

set. DES results were 0.9% greater. k–ω SST results were 1.8%

less.

• For sedan cases the ranking accuracy number was lower than

the one calculated for the entire data set. DES results were 6.7%

lower. k–ω SST results were 12.3% lower.

• Ranking accuracy for the SUV subset of cases was lower than

the ranking accuracy calculated for the entire data set. DES

results were 14.3% lower. k–ω SST results were 21.3% lower.

• DES ranking accuracy for the truck subset of cases, at 86.4%,

was 7.9% lower than the ranking accuracy of the entire data set.

k–ω SST ranking accuracy, at 77.3%, was 14.0% lower.

• For the open AGS cases the ranking accuracy was slightly lower

than the ranking accuracy calculated for the entire data set. DES

results were 2.6% lower. k–ω SST results were 8% lower.

• Ranking accuracy for the closed AGS subset of cases was

slightly lower than the ranking accuracy calculated for the entire

data set. DES results were 2.2% lower. k–ω SST results were

3.9% lower.

• Ranking accuracy for the closed grille subset of cases was

slightly lower than the ranking accuracy calculated for the entire

data set. DES results were 5.8% lower. k–ω SST results were

6.7% lower.

• Ranking accuracy for the B-car subset of cases was higher than

the ranking accuracy calculated for the entire data set. DES

results were 5.7% higher. k–ω SST results were 8.7% higher.

The 100% ranking accuracies are most likely an anomaly

attributable to the small size of the subset and to the types of

variants included in the subset.

Cd Development Plots - Static Ground Cases

Cd development plots for the 12 base models simulated with static

ground conditions (with both the k–ω SST and DES turbulence

models) are presented in Figure 20 to Figure 31. The experimentally

measured total vehicle Cd is included for reference in each plot.

Key observations:

1. Both DES and k–ω SST closed front end simulations generated

similar results (Figure 20 to Figure 22) from the front bumper to

the midpoint of the wheelbase (x = 0).

2. Both DES and k–ω SST open front end simulations (Figure 23

to Figure 31) generated similar results from the front bumper to

the heat exchangers.

3. Both turbulence models capture the same overall Cd

development pattern in the under hood region, although some

differences are seen in absolute Cd values predicted in that

region.

4. Cd development patterns were similar for most vehicles from

the rear of the engine compartment to the B-pillar with the

exception of the performance vehicle (Figure 29). Further

investigation is required to understand the mechanisms behind

these differences.

5. Cd development with the DES model increased at a slightly

greater rate than the k–ω SST model between the B-pillar and

the rear corners of the models. Initial review of the ow elds

indicate that this may be the result of differences in underbody

ow rates.

6. No consistent pattern in the Cd development differences between

DES and k–ω SST simulations was observed in the data at the

base of the models. This result is not totally unanticipated given

the complexity of the ow eld in that region.

7. A positive bias in the DES predicted total vehicle Cd is observed

in the data.

Figure 20. Cd development plot for the fastback variant of the simplified

reference model (detailed floor, static ground condition).

Figure 21. Cd development plot for the notchback variant of the simplified

reference model (detailed floor, static ground condition).

Figure 22. Cd development plot for the wagonback variant of the simplified

reference model (detailed floor, static ground condition).

Figure 23. Cd development plot for Sedan 1 (closed AGS, shields removed,

static ground condition).

Figure 24. Cd development plot for Sedan 2 (open AGS, static ground

condition).

Figure 25. Cd development plot for Sedan 3 (baseline, static ground

condition).

Figure 26. Cd development plot for the performance vehicle (closed AGS,

static ground condition).

Figure 27. Cd development plot for the B-car SUV (baseline, static ground

condition).

Figure 28. Cd development plot for the B-car (baseline, static ground

condition).

Figure 29. Cd development plot for the SUV (open AGS, static ground

condition).

Figure 30. Cd development plot for Truck 1 (baseline, static ground condition).

Figure 31. Cd development plot for Truck 1 (closed AGS, static ground

condition).

Flow Visualization - Static Ground Cases

Isocontours of zero total pressure for the 12 base models simulated

with static ground conditions (with both k–ω SST and DES

turbulence models) are shown in Figure 32 and Figure 33. Centerline

velocities (with the colorbar scale indicating the velocity magnitude

in meters per second) for the 12 base models are displayed in Figure

34 and Figure 35. These gures are useful in highlighting the

differences in the predicted ow structures around vehicles.

Key observations:

1. Based on these evaluations, the RANS-based k–ω SST creates

larger separation vortices (as compared to the transient DES

model) around tires. The k–ω SST model also creates wall-

attached vortices in the wake region.

2. It can be realized from the gures that the RANS-based k– ω

SST model creates higher underbody velocities.

3. For Sedan 1, 2 and 3, higher underbody velocities are observed

(marked with arrows in Figure 34) using the k–ω SST model,

as compared to the DES cases. This might be a possible reason

for the larger separation vortices from the front tires observed in

Figure 32. Low velocity regions can be seen over the backlight

in all three Sedans (k–ω SST cases). This is consistent with the

separation bubbles observed in that region.

4. The velocity contours for the SUV obtained from two models

are similar, except for the mid-underbody (marked with arrows

in Figure 34), where k–ω SST predicts much lower velocity.

5. For Truck 1 and 2, higher underbody velocities can be observed

using k–ω SST model (marked with arrows in Figure 34).

Similar to the phenomenon observed for SUV vehicles, low

velocities can be seen in the mid-underbody region (marked

with arrows in Figure 34) using the k–ω SST model.

Figure 32. Isocontours of zero total pressure generated using the steady, k–ω

SST turbulence model for static ground cases.

Figure 33. Isocontours of zero total pressure generated using the unsteady,

DES turbulence model for static ground cases.

Figure 34. Contours of velocity magnitude generate using the steady, k-ω SST

turbulence model for static ground cases.

Figure 35. Contours of velocity magnitude generated using the unsteady, DES

turbulence model for static ground cases.

Cd Development Plots - Moving Ground Cases

Cd development plots for the 5 base models simulated with moving

ground conditions (with both k–ω SST and DES turbulence models)

are presented in Figure 36 to Figure 40. The experimentally measured

total vehicle Cd is included for reference in each plot.

Key observations:

1. Both DES and k–ω SST open front end simulations generated

similar results from the front bumper to the heat exchangers

(Figure 36 to Figure 40).

2. Both turbulence models capture the same overall Cd

development pattern in the under hood region, although some

differences are seen in absolute Cd values predicted in that

region (Figure 36 to Figure 40).

3. Cd development patterns were similar for most vehicles from the

rear of the engine compartment to the B-pillar. DES and k–ω

SST patterns for the performance vehicle (Figure 38) showed

less variation than that seen under static ground conditions.

4. Cd development with the DES model increased at a slightly

greater rate than the k–ω SST model beginning at the C-pillar.

5. Cd development differences between DES and k–ω SST

simulations observed at the base of the models were much less

than those observed under static ground conditions.

6. A positive bias in the DES predicted total vehicle Cd is observed

in the data similar to that noted in the static ground simulations.

Figure 36. Cd development plots for Sedan 1 (closed AGS, shields removed,

moving ground condition).

Figure 37. Cd development plots for Sedan 2 (open AGS, moving ground

condition).

Figure 38. Cd development plots for performance vehicle (closed AGS,

moving ground condition).

Figure 39. Cd development plots for SUV (open AGS, moving ground

condition).

Figure 40. Cd development plots for Truck 2 (closed AGS, moving ground

condition).

Flow Visualization - Moving Ground Cases

Isocontours of zero total pressure for the ve selected vehicles (Sedan

1 and 2, the performance vehicle, the SUV and Truck 2) simulated

with moving ground conditions (with both k–ω SST and DES

models) are shown in Figure 41 and Figure 43. Figure 42 and Figure

44 show the centerline velocity magnitude contours.

The key observations from these gures were:

1. For all ve vehicles, larger separation vortices from the front

tires can be observed using the k–ω SST model compared to

those from the DES model.

2. For all ve vehicles, higher underbody velocities are observed

(marked with arrows in Figure 42) using the k–ω SST model as

compared to DES.

3. The k–ω SST model predicts lower velocities for regions close

to the mid-underbody for the SUV and Truck 2 (marked with

arrows in Figure 42).

Figure 41. Isocontours of zero total pressure generated using the steady, k–ω

SST turbulence model for moving ground cases.

Figure 42. Contours of velocity magnitude generated using the steady, k–ω

SST turbulence model for moving ground cases.

Figure 43. Isocontours of zero total pressure generated using the unsteady,

DES turbulence model for moving ground cases.

Figure 44. Contours of velocity magnitude generated using the unsteady, DES

turbulence model for moving ground cases.

Summary and Conclusions

A combination of 54 different vehicle shapes and shape variants were

evaluated against both static and moving ground wind tunnel

experimental measurements. The ability of both transient DES and

steady k–ω SST RANS simulations to correctly rank all 54

congurations was evaluated using the ranking accuracy metric. Both

the DES and SST models achieved ranking accuracies greater than

90% overall, where DES showed an advantage of a few percentage

points.

Transient simulation ranking accuracy of total vehicle Cd was found

to be approximately equivalent to commercial transient lattice

Boltzmann solver results even though a consistent upward bias in

absolute Cd values was observed. This was true across the entire data

set as well as within specic subsets of the data. Steady state ranking

accuracy of total vehicle Cd was also found to be approximately

equivalent to commercial transient lattice Boltzmann solver results.

This was true across the entire data set as well as within specic

subsets of the data.

Cd development plot comparisons conrmed that similar Cd

development patterns were predicted by both steady state and

transient simulations. The most signicant variations were linked to

ow structure differences between steady state and transient

simulations observed in the tire wakes, underbody velocities and

body wakes.

Analysis of specic subsets of the data set highlighted the fact that

the ranking accuracy of transient simulations is slightly better than

steady state across all subsets with the most signicant improvement

seen for trucks and SUVs.

The results of this study indicate that both steady state and transient

simulations are capable of supporting general Cd trend analyses.

Transient analyses are recommended for maximum trend accuracy,

and in particular for truck and SUV models. However, the faster

turnaround time for steady state simulations makes this a very time

efcient option to support proportion studies and theme evaluations

early in the design cycle when absolute accuracy is less critical.

The next steps for this study would include an investigation of the

positive bias in absolute vehicle Cd, expansion of the validation set to

expand the number of samples in each subset to investigate more

subtle vehicle surface changes, and the addition of vehicle lift ranking

accuracy as an evaluation metric.

References

1. OpenFOAM, v2.1.1, 2012. www.openfoam.com.

2. Lietz, R., Hupertz, B., Lewington, N., Silveira, R., ,

“Benchmarking of an Open Source CFD Process for

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Contact Information

Robert Lietz

Vehicle Aerodynamics Technical Specialist and Core Supervisor

Ford Motor Company

rlietz@ford.com

Acknowledgments

The authors acknowledge support for this project from Burkhard

Hupertz and Neil Lewington of Ford Motor Company.

Definitions and Abbreviations

CFD - Computational Fluid Dynamics

HPC - High Performance Computing

DES - Detached-Eddy Simulation

AGS - Active Grille Shutters

RANS - Reynolds Averaged Navier-Stokes

OPENFOAM® - Registered trademark of OpenCFD Limited,

producer and distributor of the OpenFOAM software.

FVM - Finite Volume Method

LES - Large Eddy Simulation

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