F_A Thesis -finishedx

liftdroveMechanics

Oct 24, 2013 (3 years and 9 months ago)

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1



C
hapter

1

INTRODUCTION TO VEHICLE AERODYNAMICS


1.1
Introduction

The continuing increase in fuel price coupled with uncertainty of future supply
has cr
eated widespread interest in

vehicles

with high efficiency

including pickup trucks.

P
ickup trucks,
vans and SUVs

account
for 48%

of
sale
s

fraction of light duty vehicle in
United States

while

l
ight duty vehicles account for approximately 40% of all US oil
consumption

[
9
]
.

Therefore improving

the fuel economy of pickup trucks
will
have
tremendous impact
on energy security
,
emission

of green house gas and cost of fueling
when gasoline price rise
s
.

Today

a
uto manufacturers are competing intensely to produce a powerful
pickup
truck with better gas mileage in the market regulated with law reinforcement on fuel
emissions and consumers’ need
for
bigger size truck with more horse powers

and cargo
capacity.

Energy efficiency of vehicles can be improved by reducing the total structur
al
mass, using engine with higher thermally efficiency, or altering the exterior body shape
to reduce the aerodynamic drag.
A
ccording to
US

department of
energy

[10]
, in urban
driving

aerodynamic drag accounts for 2.6% of the 12.6% of fuel energy being use
d to
propel the car as shown in
Figure
1.1
.

Since t
he aerodynamic drag increases at higher
speeds
,

the aerodynamic drag
on a high
way driving
accounts for 11% of 20% fuel energy
needed to propel the
vehicle
.

T
herefore improving vehicle aerodynamics is one of the
2


factors that play crucial role for getting better mileage

and better
performa
nce
including
the
handling of the vehicle especially at high speeds
.

The body shapes of p
ickup trucks
are primarily designed
to meet the functional,
economic and aesthetic requirements. Aerodynamic

drag
is
often
the consequence of the
body shape designed to meet the functional, economic and aesthetic design constraints.
T
he use of add
-
on devise enables us to reduce the aerodynam
ic
drag of

the vehicle
without
compr
omis
ing

on its
main design

features.
S
tudying flow over a pickup truck
with add
-
on devices
is
costly in wind tunnel due to cost
for
the setup


as well as
number
of runs required for successful drag reduction

and optimization of
the
add on devises
.
W
ith
the
use of CFD th
ese

costs are avoided and multiple runs can be set up at the same

time for

comparison and optimization.

It is motivated for this thesis by
using a CFD
approach

to
analyze the flow over pickup t
ruck with add
-
on device
such as Aerocap,
Tonneau cover, Tail plates and Rear Roof G
arnish
for drag reduction.










Figure 1.1 Typical energy uses and losses in a vehicle
[9
].

3


1.2
Flow around a vehicle

External

flow past objects encompass an extremely wide variety of fluid
mechani
cs phenomena and the

characteristic

of the flow

fields is a function of shape of
the body
.
F
or a
subsonic flow past a
given shaped object
,
the characteristic of the

flow
typical de
pends

on the Reynolds number Re. F
igure
1.
2
shows flow over a cylinder at
Re=0.1, 50 and 1
0
5
. For low Reynolds number
,

Re= 0.1, the flow is laminar and the
viscous effect plays important role throughout the flow
. A
s Reynolds number
is
increase
d
to

Re
=


,
the flow separates and the viscous effect is limited in
boundary layer and t
he
wake region

is

formed behind the cylinder
.

The separation point is where the flow starts
to separate as shown in
Figure 1.2
.





Figure1.2 Flow

over a cylinder at different Reynolds
number

[
20
]

4


A
s

opposed to streamlined
bodies such as air
foils
, road
vehicle exist as blunt
bodies in close proximity to ground.
T
he complex geometries of the vehicle associated
with the rotating wheels,
engine compartment and
cooling vents add to complexity of the
flow over the vehicle
, which
makes
the
flow over ground vehicle fully turbulent and three
dimensional with steep pressure gradient
.

Road vehicles also operate in the surrounding
ambient turbulen
t wind that is almost constantly present. Furthermore
, r
oad vehicles
travel at various yaw angles depending on the nature of the cross wind which
increase the
chance for the flow to separate
on the leeward side of the vehicle

and thus

adding more
complexit
y to the flow field.


Clearly, f
low field
s from a flow past vehicles are much
more complex compared to the flow past a
simple geometr
y c
ylinder

or more streamlined
body
-
shape
of aircraft and ships.

F
igure
1.
3

shows
flow
streamline
s

over
a
passenger vehicle

in the symmetry
plane. As air flow approaches

the

stagnation
point
A
, where

the static pressure equals the
total pressure
,
the flow divides
into two,
abov
e and below
the vehicle
.

At point B, the
pressure lowers than the total pressure, even lower than the

ambient pressure, as the
velocity of the flow increases. After point C, the flow detaches from the vehicle surface

and then
attach again at point D
which is
located on the windscreen. On the roof the
pressure
between
points E and F
is again low

but the pressure
distribution
will
depend on
the roof
shape and curvature. At the end of the roof the flow must slow down and
pressure should rise
.

After
point

F
,

the flow gets easily detached

and t
he separation point
is located at the rear edge of the ro
of

as shown in
Figure 1.3
.

Actually

any
sharp
surface
irregularity ca
n trigger the separation to form a wake.

5



F
igure
1.
3 Streamline about passenger vehicle in the
symmetry plane
[8]


1.3
Boundary

layer and separation

of flow over a vehicle

The air flow
movement causes bounda
ry layer to develop on the

surface of the
vehicle and
it thickness as flow over the vehicle progress.
In

this relatively small region

adjacent to the vehicle, the effect of viscosity must be taken in to account.
This concept

was introduced by Ludwig Prandtl in 1904.
Outside

this
region

the boundary layer
is
assumed to be inviscid or frictionless.

As shown in Figure 1.4,
during

the initial stage,
the boundary layer flow near the
front edge of the vehicle exists in a laminar
ma
nner.

Friction drag formed betwee
n the
layers of the airflow and

the surface of the vehicle will create a velocity gradient and
as
the

result

outer layer moves faster the inner one. This slowing
-
down

effect spreads
outwards and the boundary later gradually

become thicker. According to
Bernard

[6]
, on
most ground vehicles the laminar boundary layer does not extend for much more than
about 30mm from the front of the vehicle. Further down the flow transition to turbulent
flow take place

after passing the

critical distance
. In the turbulent boundary layer, eddies
are formed resulting in rapid mixing of fast and slow moving masses of air (
i.e.

turbulent

6


diffusion). The turbulent mixing will then move further outwards from the surface.
However, very close to
the surface with in a turbulent boundary layer flow, a thin sub
layer
of

laminar flow still exists. The two distinct differences between the flow
mechanisms in the laminar and turbulent flow is that in laminar flow, the influence of the
surface is transmit
ted outward mainly by a process of molecular impacts, whereas in the
turbulent flow the influence is spread by turbulent mixing.


Figure
1.
4

Boundary layer velocity
profiles

[14]


In the turbulent boundary layer, some of the energy is dissipated in friction,
slowing airflow velocity, resulting in a pressure increase. If the increase in pressure is
gradual, the process of turbulent mixing will cause a transfer of energy from the fast

moving eddies
to slower ones
in the turbulent boundary layer. If the rate of change in
pressure is too great, for example in sharp corners, the mixing process will be too slow to
push the slower air molecules moving. When this happens, the boundary layer
flow stops
following the contours of the surface, resulting in separation. Air particles downstream of
7


the separation region will then move towards the lower pressure region in the reverse
direction to the main flow, the separation region will reattach.
In

the region
between
separation and reattachment

points
,
air flow is circulating and this

is called the

‘separation bubble’. Separation will normally occur if the resulta
nt flow encounters a
sharp edge and that is why i
t is always important for ground vehic
les to have smoothly
rounded edges everywhere. Each type of
separation can form a
separation
-
bubble zone
either by reattaching itself dow
nstream to the flow or being

tra
nsmitted into a wake,
where the separation bubble

re
-
circulates

frequently. Hucho

[5]

named this frequent
circulation as “dead water” zone. Separation bubble zone happens normally on
the
surface
area in front of the windshield and on the side of the fenders while “dead water”
zone normally happens on the rear surface of the ground vehicles
.

V
ehicle aerodynamics operates mainly in the Reynolds
number region in excess
of



a
ccording to Ahmed [11],
and
the
effect

of separation and reattachment dominates
most of the ground
vehicles

surface region.

As shown in the Figure 1.5
,
typical

areas
around the vehicle that exhibit small region
of

separation are the body appendages such
as the mirrors, headlights, windshield wipers, door
handles and

windshield junction.
Larger flow separation regions around the

vehicle include

the A
-
pillar, body

under side,
rear body
of

the v
ehicle and in the whee
l wells [5]
.

In a similar prospective, Ahmed [11]
defined the airflow as three dimensional with steep pressure gradients and having regions
of separated flow. Regions of separated flow are categorized in
to small and large regions.
Small regions of separated flow occur normally around attached component on a vehicle
body such as headlights, mirror, door handles and windshield wipers. Large regions of
8


separated flow occur on the A
-
pillar, at the rear of the

vehicle, underneath the vehicle and
around the wheel region.

I
n present study, the focus
will be
on the wake near the rear of
the vehicle




Figure
1.
5

Areas of flow separation around a vehicle

[5]



.

9


F
low separations that
lead to a pressure drag can be divided in t
wo different
groups
,
according to
H
ucho [5]
.
If

the separation line is located perpendicular to the flow
direction as
shown

in F
ig
ure

1.
6
,

the vortices generated will have
the
axis

perpendicular
to the outer
flow
and

parall
el to the line of separation.
Figure 1.6 shows that a
symmetrical flow exists only for low Reynolds number
.

For

larger
Reynolds

number,
periodic vortex shedding occurs, and the flow in the

separated region is unsteady. T
he
kinet
ic energy of the v
ortex field is

rapidly dissipated by the turbulent mixing and
irreversibly conve
rted into frictional heat

[
5]
,

and it leads to considerable total pressure
loss in the region behind the body and the corresponding deficit in kinetic energy is equal
to the work needed to overcome the pressure drag.
Behind

the body a wake is formed in
which, time averaged, relatively
uniform suction and very low flow velocities are present.

T
he second type of
flow separation is characterized by separation line inclined
with respect to the flow as shown in
F
ig
ure
1.
7
,

the
vortex

generated have

axis nearly
parallel to the
line

of

separation with

vortex shedding

[5]
.
In

this case a well
-
ordered
steady three
dimensional flow

separation is found and on the rearward surface of the
body
and
the separated flow induces suction which
leads

to pressure drag.
On

the
inclined surface the flow

is attached and behind the body only relatively small total
pressure losses are observed.
The

flow field of the concentrated vortices, however,
conta
ins a lot of kinetic energy
which corresponds to the work necessary to overcome
pressure drag.


10














1.4
Aerodynamic
forces
on vehicles

The

air flow over a vehicle

t
ransmit
s

an aerodynamic force
to the vehicle
through
pressure and shear stress distribution acting on the surface of the vehicle.
Pressure

and
shear

stress act at

every point on the body with pressure

normal to the surface of the

vehicle, the shear stress
tangential to the surface.
The net effect
of
the aerodynamic force

includes
drag

D
, lift

L
, side force component

S,

and

various

moments

PM, RM, YM

as
shown in Fig
ure 1.8
a
cting on a principal axis of a vehicle.

Each one is described as
follows
.









Figure 1.6 Flow separations on a
bluff body (separation line
pe
rpendicular to the flow
direction) [5]

Figure 1.7

Flow separation on a
bluff body with oblique blunt base
(separation line at an angle to the
flow direction) [5]


11







Figure
1.8 Aerodynamic

force and moments acting on a vehicl
e

[17]


Drag

D
rag is
force

acting
on the surface of the vehicle

b
y the flow in direction
opposing the motion of the vehicle.
T
he drag
is the integral of local stream
-
wise
component of normal (pressure) and tangential (skin friction) surface forces over all
surface exposed to the
stream.

D
irect evaluation
of
drag requires

knowledge of the
detailed stress distribution
and also integrating the pressure distribution over the complex
surface of the vehicle which
is
extremely

difficult

to obtain
.

But
with the help of CFD
detailed surfac
e pressure distribution for a flow over
an

object can be easily obtained
after

the CFD set up is adequately validated.

During the analysis of aerodynamics performance of two vehicles,
comparing the
drag and lift forces do not yield much
.
One

vehicle can generate less drag or lift
than
other
depending on test speed, density of air and projected frontal area of the vehicle.

12


Thus the non
-
dimensional
coefficient is introduced to compare

aerodynamic
performances of a vehicle.
The

non
-
dime
nsional
drag coefficient



is defined as





















































































































































Where:





=

Aer潤onamic Drag C潥fficient



=

Fr潮tal Area 潦 the Vehicle



=

Air Densi
ty



=

Total Wind Velocity


A
ccording to H
ucho

[5]
,

t
he contribution of the front
body to drag is usually
small
, the rear shape of

the vehicle contribute greatly

to the aerodynamic drag because of
the low pressure turbulent wake region
is
formed at the rear creating large pressure
difference between the front and rear ends of the vehicle.



Lift

Aerodynamic lift is the
component of
aerodynamic

force
perpendicular

to the
free
stream velocity.
It

is
mainly
created by the
pressure difference
on

the top and bottom
surface
of a vehicle. Aerodynamic lift has a strong influence on driving stability and it is
very important not to negatively affect it so that the vehicle

remains stable. If
aerodynamic lift increases too much then it will cause the
vehicle
wheels to have less
traction
force with the road, and this will cause the vehicle to become very unstable and
risk rollover. The following equat
ion represents aerodyna
mic lift Coefficient:


13




















































































































































where:



L

=

Lift Force





=

Lift Coefficient


Sideforce

S
ideforce is
produced by the
crosswind acting on the vehicle and under steady
state wind conditions
and the non dimensional
side force

coefficient is given by
:
























































































































































Where
:



S

=

Side
force

acting

on the vehicle





=

Sideforce Coefficient (Function of the Relative Wind Angle)


Pitching moment

P
itching moment
affects
the
weight

distribution
between the front and
the non
dimensional pitching moment coefficient is:









































































































































Where
:






=

Pitching Moment Coefficient


PM

=

Pitching Moment


L

=

Wheelbase




14


Yawing moment

Crosswinds produce a
side force

on a vehicle that acts

at the middle of the
wheelbase.

W
hen the crosswinds do not act at the middle of the wheelbase a yawing
moment is produced. The yawing moment
coefficient
is represented by the following
equation:
















































































































































Where
:






=

Yawing Moment Coefficient (Varies with Wind Direction)


YM

=

Yawing Moment



A

=

Frontal Area of the Vehicle


L

=

Wheelbase


Rolling
moment

When the crosswind produces a
side force

at an elevated point on a vehicle, a
rolling moment is produced and

the rolling moment
coefficients varies with wind
direction and
it
is

represented by the following equation:















































































































































Where
:






=

Rolling Moment
Coefficient



RM

=

Rolling Moment


A

=

Frontal Area of the Vehicle


L

=

Wheelbase




15


1.5
Fuel

economy

Fuel economy

is the measure of how many miles a vehicle can tra
vel in certain
amount of fuel. In
United States

it is measured in mile per
gallon.

Fuel

economy and
increasing global warming are the current key arguments to reduce aerodynamic drag

of
vehicles
.


V
ehicle fuel consumption

is

a matter of demand and supply

[5]
.
On

the demand
side is

the mechanical energy to propel the vehicle forward and on supply side
is
the
efficiency with which the energy can be generated and transmitted through the power
train to the point of application.

V
ehicle aerodynamics have a role on the demand side of
th
e equation and lowering the aerodynamic drag lowers the Road load part of the tractive
force needed to drive the car. T
he tractive force





required at the tire/road interface

of
a car's driving wheels is
defined as
(Sovran and
B
ohn
, [
12]



Where
:




is tractive
force, R

the tire rolling resistance
,

D the
aerodynamic

drag, M the
vehicle
effective
mass, g the acceleration of gravity,
θ is

the inclination angle of the road.

The

rolling resistance of the
vehicle, R

is given by
:


R=


G



(1.8
)




(1.7)

16


W
here
:

G= mg the gravitational force th
e vehicle exerts on the road,




is the coefficient
of rolling resistance of the vehicle which needs
to be determined
experimentally and

it
depends on the spee
d of the vehicle as shown in
Figure

1.9
.



Figure 1.9




versus road speed V for typical radial tires [5]

T
he effective mass of the
vehicle,
M
,

is given by




M=
m

(
1+


)









(1.9
)

Where






is the equivalent translational mass of the rotating parts of the power train of
the
vehicle?

The

mass fraction



d
epends on the gear engaged and the suffix i denotes
the gear engaged.

T
he
corresponding

tractive power



is:








=


*
V



(1.10
)

17


Where

V
= velocity of the car
. A
nd

the tractive energy required for propulsion during any
given driving period is
:






















(1 .11
)


From

the
above

equation
s, equation 1.8 to 1.12
, if the drag
force
acting
on the
vehicle
increase
,

the amount of energy needed to propel the vehicle through the air
will

also

increase
. This

means
that
burning more fuel is needed.


Fuel

consumption of a road vehicle is a measure of volume of fuel consumed to
travel a specific unit of distance.
In

Europe, fuel consumption of the vehicles is specified
as liter of fuel consumed to travel 100 Km.
However
in USA different method is used to
measure fuel
economy
;
it is measured by the amount of miles a vehicle can travel with
a
gallon of fuel.
The
se
two

method
s

can be related using E
quation
1.12 as


MPG
=235.2
/ (
L/100KM)


L/100Km =235.2/mpg





(
1 .12
)

Fuel

consumption
of
a vehicle
B [
L/100km] can be evaluated analytically by
integration the instantaneous fuel consumed

̇

[L/s] over a period of time T [s] and
then
averaging the integral over the distance travelled
during the period of T[s].







̇















(1 .13
)


Where
:

V is the velocity of the vehicle.

18


S
ince driving a vehicle on the road, involves acceleration, deceleration and idle,
fuel consumption of the vehicle should be determined based on these three different
modes

of vehicle operations: power drive, Braking and Idle.

D
uring Powered
drive,




>0, the amount of fuel consumed is







[

]











(











)








(1 .14
)


where





is the engine power required to drive vehicle accessories like air conditioning,



is the density of fuel,



is the specific fuel consumption also known as bsfc brake
specific fuel consumption

and typical bsfc

maps for gasoline

and diesel engin
e is shown
in
Figure [
1.
10
]

as below
,




is the efficiency of the
drive train

between the transmission
input and the tire patch of the drive wheels.


Figure 1.10 Typical bsfc maps for a gasoline and a diesel engine [5]


19


During
breaking

the



< 0
and the total volume of fuel consumed is given by:












[

]



̇














(1 .15
)


Where:


̇




brake volume fuel
rate.

During

idles the
velocity

of the vehicle V=0 and the amount of fuel consumed
is:





[

]



̇







̇













(
1 .16
)

Where
:


̇



is
idle volume flow rate.


By

adding equation
s 1.15
, 1.16

and 1.17
the total fuel consumed B:












[




]












(











)




̇




̇
















(
1 .17
)


T
o maintain
uniformity

in the process of determining the fuel consumption of
vehicles,

a
standard driving cycles

has to be used.

In

U
.
S
.,

fuel economy is determined
based the EPA driving schedule which consists

of

Urban and h
ighway driving cycles
shown in
F
ig
ure

1.
11
.

Vehicles fuel economy is tested in a US EPA
laboratory by

placing
the vehicle drive wheels on a dynamometer which simulate the EPA'
s driving schedule
and measure

the
carbon content in the vehicles exhaust pipe to calculate the amount of
fuel consumed during the test.


20



Figure 1.11 EPA driving cycle [5]


To determine
numerically

the effects

of improved

aerodynamic
s on fuel economy
by using
E
quation
1.17

is a complex task
.
Sovran and
B
ohn [
12
]

developed a method to
determine tractive energy
equation for

EPA urban and highway driving schedu
les.
Later
Sovran

[
13
]

used
E
quation
1.17

and tractive energy
E
quation
1.11

to developed charts
that show the impact of changes in aerodynamic drag on
composite
fuel cons
umption for
the EPA
schedules
.
The composite fuel consumption for EPA driving schedules is given
by equation 1.18.




=





























(
1 .18
)








21


Figure 1.12

shows G.
Sovran [13]

charts to determine the impacts of changes in
aerodynamic drag on fuel consumption for

EPA schedules given the change in the
product of aerodynamic drag coefficient and

frontal area of the vehicle (


A).





Figure 1.12 G. Sovran charts for the impact of changes in aerodynamic drag on the fuel consumption
for vehicles

driving on the EPA schedules [5]

22


Chapter 2

BACKGROUND AND OBJECTIVE

2.1 Motivation

Most ground vehicle research has been performed on passenger automobiles, race
cars and commercial truck tractor assembly. Research conducted on a pickup truck by
large
automakers was mainly for commercial use and the results are not accessible for
researchers. However with advancement in computer and CFD tools institutional
researchers are able to study the complex three
-
dimensional (3
-
D) turbulent flow
structure around
blunt bodies like pickup trucks.

The pickup
truck segment now accounts for about
15 percent

of

annual

vehicle
sales

in
the
U
.
S
.

[9]

and this indicates that pickup

trucks
have a larger weighting on the
national oil consumption. Current pickup truck design h
as higher aerodynamic drag and
exhibit suboptimal fuel economy. The pickup trucks in the market today have higher
aerodynamic drag than other type of light vehicle
with
the same projected frontal area.
For example
,

current production pickup trucks have aer
odynamic drag coefficient in the
range
of 0.463
-
0.491 and in comparison

the aerodynamic coefficient for typical SUV
would be in the range of 0.414
-
0.44

[1
].

Previous research

[19]

suggests that drag coefficient for light trucks can be
reduced. Reduction in
drag has been

shown to improve fuel economy by several miles
per gallon

on average. If all trucks were to improve their drag coefficients by this margin,
billions of barrel of oi
l would be saved and also reduce carbon emission to the
environment.

23


2.2 Pickup truck history

Pickup trucks have been around almost since the advent of the automobile. There
was a Ford model TT that was sold in 1916. It has just been in recent years that t
he light
duty truck, pickup trucks, SUV and vans, has gained a large market share in US. In 1990
,
47.5 million light trucks were registered in US and by year 2000 the number of light
trucks registered were increased by 63.8% to 77.8 million [18]. Since 197
5 pickup trucks
account for a stable 13% vehicle sales fraction in US

[16] and in 2005 there were 40
million registered pickup trucks. The sales of pickup trucks are expected to be stable
despite the current rise in fuel price. However this trend has not b
een translated to the
level of effort placed on improving light truck aerodynamics although many
improvements have been made from
the initial Model
-
TT in 1916
shown in Figure

2.2
.1
.







Figure 2.2
.1 Ford Model
-
TT from 1916

After 30 years of development, covered wheels and curved front appear in the
ford

trucks as shown in Figure 2.2
.2
, the Ford F
-
100
.

24






Figure 2.2
.2

Ford F
-
100 from 1951

The F
-
100 of 1966 was boxier and less aerodynamic but it
provided the consumer
with greater capacity in terms of payload and towing.








Figure 2.2
.3

Ford F
-
100 from 1966

The 1997 Ford F
-
150 from was proclaimed (by all automotive journalists) to be
the most aerodynamic light truck form
to date. This may be obvious to the casual
observer based upon its almost car
-
like curves. Ironically, the curved shape was cited as
one of the reasons that Ford’s newest design lost market share, due to consumer
preference for “tough” looking trucks.

25





Figure 2.2
.4

Ford F
-
100 from 1997

The newer ford F100 2008
-
2009 model had improved aerodynamic design with
better engines and better fuel management electronic systems. However, aesthetic feature
gave a sturdy look to it.




Figure 2.2
.5

Ford F
-
100 from 2008
-
2009


2
.3 Previously conducted research

Unlike researches on sedan and SUVs, only fewer publications of flow over
pickup trucks are available to the public. Al
-
Garni, Bernal, and Khalighi conducted
experiment to investigate the flow in the near wake of a generic pickup truck [2]. The
experiment
was conducted in a 2X2 wind tunnel at Aerospace Engineering Department at
University of Michigan. They used PIV velocity measurement method to measure the
26


turbulent flow in the near wake of a generic truck. The objective of their experiment was
to provide
qualitative data for CFD validation. Later Yang and Khalighi [1] conducted
CFD simulations using the same vehicle models as those of
Al
-
G
arni, Bernal and
Khalighi [2] to address the issue if the two
-
equation k
-
ε turbulence model could capture
steady flow a
round the pickup truck. They compared the data from CFD simulations with
excremental data collected form
Al
-
G
arni, Bernal and Khalighi‘s experiment [2] and
stated that the steady state formulation was good enough to study vehicle aerodynamics
.

Cooper [3] i
nvestigated the effect of tail gate position at different yaw angles as
well as the effect of different box configurations on aerodynamic drag of a pickup truck.
He conducted a full scale test in National Research Council of Canada (NRC) wind
tunnel and pr
esented the results with CFD analysis to visualize the flow structure of
tailgate up and tail gate off configuration at zero degree yaw angle.

Recently, Mukhtar, Britcher and Camp [4] conducted experimental investigation
and CFD simulation to analyze the
flow around pickup truck with several configurations.
Their objective was to determine the influence of these configurations on aerodynamic
drag of the vehicle. They simulated the airflows at different yaw angles and the CFD
results from the simulation wer
e compared with the experimental data they obtained from
a full scale experiment conducted at Langley full scale wind tunnel.


2.4 Objective

The objective of this thesis is to investigate the effect of add
-
on devices on a flow
over a pickup truck. The pri
mary tool that will be used to accomplish this will be
27


computational fluid dynamics (CFD). In effort to reduce the aerodynamic drag of pickup
trucks, aerodynamic add
-
on devices such as canopies, Rear Roof Garnish, Tail plates,
Airdam and Aerocap will be mo
unted on the baseline pickup truck and the air flow will
be simulated. This paper will quantify the effect of the aerodynamic accessories on the
pickup truck aerodynamics through CFD modeling. Once general effects of the
accessories have been quantified, t
he accessory that yields the best drag reduction will be
optimized.


2.5

Outlines

The rest of chapters will be arranged as follows. The next chapter discusses CFD
problem formulation and results from a flow over the baseline truck. The CFD result
from
present simulation was compared and validated against those from Yang and
Khalighi [1]. In Chapter 4, the problem formulation developed in Chapter 3 were used to
study flow over a pickup trucks with add
-
on devises: Tonneau cover, Rear Roof Garnish,
tail pl
ates,

Airdam, Traditional canopy, Aerocap with rear inclination angel of
5

,10

,12

,15


and 18.77

. Also In Chapter 4, flow over 3D curved Aerocap was
investigated to quantify the impact of drag reduction achieved by the 3D curved Aerocap
on fuel economy.
Chapter 5 presents conclusion and offers some recommendations for
future research




28


Chapter 3

PROBLEM FORMULATION


3.1 Introduction

Traditionally
, wind tunnel and road tests are

required to investigate the
aerodynamics performance of the vehicles. However, Full
-
scale wind tunnel and road
tests are time consu
ming and expensive to operate as

multiple tests are usually required in
achieving the desired aerodynamic shape or character
istic
during the
design

process of
vehicles.

Aerodynamic evaluation of air flow over an object
can
be performed
using
analytical method or
CFD

approach
.
On one hand, analytical method of solving

air flow
over an object
can be done
only
for
simple
flows ove
r simp
le geometries like laminar
flow over a flat plate. If air flow gets complex
as
in
flows over a bluff body, the flow
becomes turbulent and it is impossible to solve Navier
-

Stokes
and continuity equations
analytically. On the other hand,
obtaining dir
ect numerical solution of Navier
-
stoke
equation is not yet possible

e
ven with modern day computers. In order to come up with
reasonable solution
, a

time a
veraged Navier
-
Stokes equation was being
used (Reynolds
Average
d Navier
-
Stokes Equations


RANS equati
ons) together

with turbulent model
s

to
resolve

the issue i
nvolving Reynolds Stress resulting from the time averaging process.

With the reduction on computational cost t
oday, aerodynamic simulation using
CFD have
a faster turnaround time
and
will only be at a
small
fraction of the cost of the
wind tunnel or road tests. One can analyze the flow over vehicles by solving RANS

29


equations

and turbulence modeling equations and yet get a near realistic result. In present
work the k
-
ε

turbulence model
with
non
-
equilibrium wall function was

selected to
analyze the flow over the generic
p
ickup truck model
.
Th
is
k
-
ε

turbulence model is very
robust, hav
ing

reasonable computational turnaround time, and widely used by the auto
industry.
S
ince the main aerodyn
amics force acting on r
o
ad vehicle is aerodynamic drag,
this

thesis project focuses on studying
aerodynamic drag along with generated lift
due to
air
flow over the vehicle

at zero degree yaw angle.



3.2

Aerodynamic drag on vehicles

Aerodynamic drag is generated
by the interaction of a solid body with a fluid

which results in
the difference in velocity between the solid object and the fluid
. I
t can be
regarded as aerodynamic resistance to motion of the object through the fluid medium.

To
reduce Aerodynamic drag of ground vehicle, it is very important to understand the source
of aerodynamic drag for a flow over a vehicle

which is described as follows:

1
. Skin friction: the interaction between the flowing air molecule and the solid
objec
t causes friction

drag on the object
. Skin friction is dominant
o
n streamlined
objects like airplane wing

while pressure drag is dominant
on bluff bodies.

2
. Boundary layer pressure loss: as the air flows over the body, boundary layer
develops. The boundar
y layer is a

thin

layer over the body

where the
velocity of
the flow varies from zero on the surface of the object to free flow velocity at the
edge of the boundary layer
. T
he viscous effect

within the boundary layer

is very
important
.
Boundary layer gets
thicker as it progress from the front to rear of the
30


vehicle. The thicker boundary layer at the rear of the vehicle makes the rear
stagnation pressure of the flow less than the front stagnation pressure, so there is
effective pressure drop along the length

of the body, which causes
f
low
separation
. F
or non
-
streamlined bluff bodies suc
h

as pickup
trucks

immersed in a
flow
, the
flow separates from the body near sharp edges and creates
a wake region
of t
urbulence. Pressure will drop in the turbulence region
, r
esulting in
the pressure
difference between the front and rear of the vehicle



the pressure
the drag.

Since
blunt
bodies have a larger rear area
, they

have larger pressure drag. For
streamlined body
,

this term is less significant.

3. Induced drag: when

a body

such as a

vehicle

spoiler is

immersed

in
a flow it
generates

a lift

which also induces

drag. The

drag on a body

increase
s

as lift
increases. Thus minimum drag occurs when the lift on the body is zero
.

As
road
vehicle are bluff bodies in close proxi
mity to the ground and the pressure
difference between the under body and upper surface of the vehicle create lift
which
could
induce drag.

4
. Interference drag: it is caused by imperfection on the body of the
vehicle
surfaces

as windshield wipers, door handles.


As mentioned previously, separation of the boundary layer and the ensuing
turbulence complicates the problem dramatically. In
White [7],

it is demonstrated that a
cylinder with a laminar separation oriented 82 deg
ree

r
elative to the free

stream had a
coefficient of drag of 1.2. The same cylinder has a coefficient of drag of
0
.3 when the
31


Reynolds number increased to allow the turbulent

flow

separation to occur at
120
deg
ree,
resulting
in
sma
ller wake and higher pressure
at

the rear
, and thus reduced drag
. The
same premises of reducing the wake region and
also
increasing
the pressure at the rear
were
used in this paper to improve the aerodynamic drag of the vehicle.


















3.3
. CFD problem formulation

The greatest benefit from computational fluid dynamics
is
to gain insight into a
particular phenomenon by establishing the trends in the aerodynamic characteristics.
It is
valuable in
understanding and exploiting the trends of shape change that will affect the
Figure 3.1

Flow past a circular cylinder: (a) laminar separation; (b) turbulent separation; (c)
theoretical and actual surface
-
pressure distribution
, [7]


32


flow field and improve the aerodynamic of the model.

However, b
efore the CFD model
with add on devise can be designed and simulated, CFD method

for flow over a generic
pickup truck
needs to
be
validated
against
CFD simulation of flo
w over the same generic
model [1].

Yang and Khaligi’s [1] CFD
simulation of

flow over a pickup tru
ck was

reproduced and used as bench
mark for the present CFD method, given that
the

results
from CFD
simulation [1]

agreed with experimental
data [2],
.

Figure 3.2

shows the generic pickup truck used by Yang and Khalighi [1
] and
the
p
resent CFD simulation. The full size generic pick up is 5.1
84m long, 1.824m wide,
1.786

m high
and
with a projected frontal area of 2.809m
2
.

T
he orig
in of the coordinate
axis used in present simulation was

attached to the bumper of the vehicle
. T
he pickup

truck bo
x floor lies on Z
-
zero axis as the
X axis lies along the length of the vehicle as
seen on Figure 3.2. Figure 3.3

shows the
1/12
scale of the
flow domain used in the
present simulation. The virtual wind tunnel has dimension of 10.4m wide, 5.4m high

and
58m long. The virtual wind tunnel

used by

Yang and Khalighi [1]
and by
present CFD
simulation
had

the same cross sectional area with area blockage ratio of 5%. However the
length of the wind tunnel used in

the study of Yang and Khalighi

[1] is 23 m which is
about 4
.6L, where L is

the length of

the full size generic pick up. That leaves only

3.
6L of
the
flow domain to be ahead and
back of the generic pickup truck
. These make the flow
over the vehicle

to be highly affected by
inlet and out
let boundary

condition set for the
CFD simulation.
Thus it is
a
good CFD practice to increase

the length of the virtual wind
tunnel
. In
present simul
ation, the length of the virtual wind tunnel was increased to 58m
instead of 23m used in the study of Yang
and Khalighi


[1], which leaves 3.6 times the
33


length of the vehicle (L)
ahead

of the model

and 6.6L

behind the model from the base of
the vehicle
.












Figure 3.2

Original 1/12
th
-
scale generic pickup truck model used

in [1] and [2]
.




Figure 3.3

1/12th scale of
f
low domain used in present simulatio
n, all dimensions are in mm.



The virtual wind tunnel

was

scaled down by 12

and imported in to Gambit to
create surface meshes on the vehicle and

the virtual
wind tunnel
surfaces. A

surface mesh
of 1.5 mm size was
created on the vehicle surface. On the ground face
,
a
size function
was used to vary the mesh size on the
face from 1.5 mm to 30mm with a growth rate

1.05. On the inlet, outlet, top and side
faces of the virtual
wind tunnel

a uniform mesh
34


size of 30 mm was

used.
The flow domain with the generated surface mesh was

imported
into
the c
ommercial volumetric meshing software TGrid

to

descretize the
domain with a
hy
brid meshes. Prismatic layer was

created over the vehicl
e surface to capture the
boundary layer characterist
ics and a layer of tetra cell was

created to connect the prism
layer with hex core domain. The hex core

cells were

refined in a 1m long, 0.25m wide
and 0.22 high box enclosing the

scaled down pickup model
. F
urther hex refinement
was
created
between the floor of pickup truck and the ground face of the virtual wind tunnel.
In prese
nt simulation, the flow domain was

descretized with
about
9 to 10 million hybrid
cells.


3.4 Base
line
pickup truck
CFD method

and

setup

The CFD
simulation by Y
ang and

Khalighi [1] was

reproduced

in the

present
simulation.
Table 3.1
, Table 3.2,

Table 3.3

and Table 3.4

shows the
solver setup,

viscous
model and Turbulence model settings
,

b
oundary condition settings

and solution controls

for present simulation respectively.
The Reynolds number
of the air flow was
Re=
7.8*



based the

vehicle length L =5.184m
. According to Yang and
Khalighi [1],

if the
Reynolds number of the flow
is above the critical Re= 8.56*



,
b
ase
d

on the length of
the model, the flow properties will be similar and one wil
l be able to compare results
from
CFD simulation
[1] with

any Reynolds number above the crit
ical Reynolds number
.

The assumptions made in present simulation were
the
air
flow
was
steady state wit
h
constant velocity at inlet and with

zero degree yaw angle, constant pressure outlet, no slip

35


wall boundary conditions
at the vehicle surfaces, and inviscid flow
wall boundary
condition on the top, sidewalls

and ground face of the virt
ual wind tunne
l.





CFD Simulation

3ddp (3
-
D Double Precision)

Solver

Solver

Segregated

Space

3D

Formulation

Implicit

Time

Steady

Velocity Formulation

Absolute

Gradient Option

Cell
-
Based

Porous Formulation

Superficial Velocity

Table 3.1 Solver
setting


Turbulence Model

k
-
ε (2 eqn)

k
-
epsilon Model

Standard

Near
-
Wall Treatment

Enhanced wall Function

Operating Conditions

Ambient

Table 3.2 Viscous model and Turbulence model settings






36



Boundary Conditions

Velocity
Inlet

Magnitude (Measured
normal to
Boundary)

22 m⁄s (constant)



Turbulence Specification Method

Intensity and Viscosity Ratio



Turbulence Intensity

1.00%



Turbulence Viscosity Ratio

20

Pressure
Outlet

Gauge Pressure magnitude

0 pascal



Gauge Pressure direction

normal to boundary



Turbulence Specification Method

Intensity and Viscosity Ratio



Backflow Turbulence Intensity

10%



Backflow Turbulent Viscosity Ratio

10

Wall Zones

-

vehicle surface
-
noslip wall B/c

-

Ground face
-

invicisd wall B/C

-
Side faces
-
inviscid wall B/C

Fluid
Properties

Fluid Type

Air



Density

ρ = 1.175 (kg⁄m^3 )



Kinematic viscosity

v = 1.7894
×10^(
-
5) (kg⁄(m∙s))

Table 3.3 Boundary condition settings

Equations

Flow and Turbulence

Discretization



Pressure: Standard



Momentum:
Second Order Upwind



Turbulence Kinetic Energy: Second Order Upwind



Turbulence Dissipation Rate: Second Order Upwind

Monitor

Residuals & Drag Coefficient

Convergence
Criterion

-

Continuity = 0.001

-

X
-
Velocity = 0.001

-

Y
-
Velocity = 0.001

-

k = 0.001

-

epsilon =
0.001

Table 3.4
Solution Controls

37


3.5 Baseline
pickup truck r
esults and discussion

Figure 3.4
a

and Figure 3.5a

shows the pressure coefficient plot on the symmetry
plane

from present simulation
and

that of Yang and Khalighi

[1] respectively
. The
pressure
coefficient plot shows

that

the stagnation point
was
created on the front surface
of the pickup truck. The pressure coefficient also indicates
that
CFD simulation
s

have a
tendency t
o ov
ershoot the Cp value at stagnation
point
. The Maximum Cp value obtaine
d
in present simulation
was
Cp= 1.01 and
from
Yang and Khalighi


[1]

the maximum
pressur
e coefficient value was

approximately
Cp= 1.15

as shown in
Figure 3.5
a
.

These
i
ndicate that the present simulation was reasonably accurate

in predicti
ng
the pressure
di
stribution over the top surface of the vehicle.

Figure 3.4
b
and Figure 3.5b

show

the

pressure coefficient plot of the vehicle
underbody on the symmetry
from
present
simulation and
the study of Yang and Khalighi

[1].

Near the front end of the vehicle the pressure coefficient plots vary slightly
but it was
within acceptable error margin of less than 10%.





Figure 3.4

(a) Pressure on pickup
cab (b) Pressure on pickup floor





-2.5
-2
-1.5
-1
-0.5
0
0.5
1
1.5
0
100
200
300
-2.5
-2
-1.5
-1
-0.5
0
0
100
200
300
400
38






Figure 3.5 (a)
Pressure on pickup cab from [1]. (b) Pressure on pickup floor from [1].


Figure 3.6

and Figure 3.7

show
pressure coeffic
ient distribution on the tail
-
out
and tail
-
in

surface of the vehicle on symmetry plane
, respectively
.
Both the pressure plots
from the
present simulation
and

that of Yang and Khalighi

[1]
were

close to the
experimental data
obtained
by
Al
-
Garni, Bernal, and Khalighi

[2]

with
an
acceptable
error margin.
As seen in t
he
se

figures, the pressure coefficient distribution o
n the outer
tail gate
surface was

relatively higher than the pressure coefficient
on the inside of the
tailgate, which

indicates
if
leaving the tail gate up
it
increases the pressure at the rear of
the vehicle tha
n the case of leaving the tailgate open. This findings confirms t
he
conclusion made by
Cooper “Pickup truck aerodynamics
-
keep your tailgate up” [3].


3
9



Figure 3.6 (a) Pressure on tailgate (outside). (b) Pressure on the tailgate (outside) from [1]



Figure 3.7 (a) Pressure on tailgate (inside). (b) Pressure on the tai
lgate (inside) from [1]


Figure
s

3.8
, 3.9, 3.10, and
3.11

show the u
-
velocity plots at points inside and
outside of the pickup box from present
simulation and
that of Yang and Khalighi

[1]
.
,

they m
atch very well with
nearly identical

plots.

Figure 3.12 shows

static pressure
distribution over the pickup truck surfac
es, indicating that
p
ressure was

very high on the
grill of the vehicle where the velocity of the flow beco
mes zero and stagnation point was

created.
Figure 3.12 also

shows relative
ly high static pressure created at th
e junction of
-10
0
10
20
30
40
50
60
-0.19
-0.17
-0.15
-0.13
-0.11
-0.09
simulated
expermental
Cp
-
Tailgate
-
Outer

40


the windshield with

the hood of the vehicle. Both front and rear tires also experience high
static p
ressure but the front wheels were

subjected to slightly higher static pressure than
the rear. On the shar
p edge
s

of the
vehicle with
the A
-
pillar, the edges of the hood, grill
junctions

with
side
-
frame and
edges of the
wind shield,

flow separation was
expected to
occur

and the static pressure was

low. The pressure difference created between the front
and rear end of the vehicle causes the net aerodynamic force acting on the vehicle to
generate a drag against the motion of the
vehicle. Figure 3.13

shows the
wake profile for
baseline truck (velocity

vector on iso
-
velocity surface at 3m/s)
, indicating that turbulent
wake was formed inside the box and also behind the truck.




Figure 3.8 (a) u
-
velocity in y=0 plane (inside box). (b) u
-
velocity in y=0 plane (inside box) from [1].



0
20
40
60
80
100
120
140
-0.6
-0.1
0.4
0.9
1.4
U, x=400mm ,y=0

41




Figure 3.9
(a) u
-
velocity in y=0 plane (outside box). (b) u
-
velocity in y=0 plane (outside box) from [1].




Figure 3.10 (a) u
-
velocity for z=73mm

and x=450mm (scaled down model) (b) u
-
velocity for z=73mm

and x=450mm from [1].



-60
-10
40
90
140
0
0.5
1
U,x=500mm,y=0

0
0.2
0.4
0.6
0.8
1
1.2
-120
-80
-40
0
40
80
120
U,x=450mm,z=73mm

42




Figure 3.11 (a) u
-
velocity for
z=15mmand x=450mm (scaled down model) (b) u
-
velocity for z=15mm

and x=450mm from [1].



Figure 3.12 Pressure distributions over the pickup





Figure
s

3.14
(
a
) and (b)

compare the velocity magnitude vectors at z =73mm for a
1/12
-
scale vehicle mode from present simulation with that of Yang and Khalighi

[1]
. The
stream lines appear to be identical with the wake created in the pickup box
. Figure
s

3.15
(
a
) and (b) compare the velocity magnitude vectors in the symmetry plane from
-0.2
0
0.2
0.4
0.6
0.8
1
1.2
-120
-70
-20
30
80
U,x=450mm,z=15mm

Figure 3.13 W
ake profile for baseline
truck (velocity vector on iso
-
velocity
surface at 3m/s)

43


present simulation with that of Yang and Khalighi

[1]
.

The vectors indicate the flow
separation
occurring
at t
he rear edge of the cab and the
vortex created in the box of th
e
truck.
It
also indicates the downwash created at the outer edge of the tailgate behind the
truck
.



Figure 3.14 (a) Streamline on z=73 mm (scaled down model) plane. (b) Streamline on z=73mm plane
from [1].









Figure 3.15 (a)
Streamline on symmetry plane. (b) Streamline on symmetry plane from [1]




Figure 3.16 shows

the
static pressure distribution on the symmetry plane a
nd on
the surface of the pickup truck, indicating that
pressure dooms

were

created in front of
the vehicle and the maximum pressure

was

created on the front vehicle surface near the
bumper
.

The figure

also shows that the low pressure

was
created in the pickup box
and

44


a
lso over the cab of the vehicle, which tends to increase the
drag and lift coefficient of the
baseline truck
. Figure3.17

shows the total pressure distribution in the symmetry plane and
over the surface of the truck, indicating a high total pressure gradient region where the
flow separates with the flow

recirculation

created
.




Figure 3.16

S
tatic pressure distributions over the baseline truck and symmetry plane



Figure 3.17 Total pressure distributions over the baseline truck and symmetry plane

45


Figure 3.18

shows
the
velocity streamline around the pickup truck. The
streamlines are generated using a horizontal rack line located upstream the vehicle. Due
to interaction between the shear layer surrounding the separation region and the flow
around the vehicle,
a strong rec
irculation region was

generated and two contra rotating
voices

were

formed behind the vehicle
.




Figure 3.18 Streamline flow over the baseline pickup truck


The aerodynamic drag and lift coefficients
computed from the simulation were



= 0.345 and


= 0.28

respectively. However, i
n the real world pickup trucks
manufactured today have a drag coefficient
at


= 0.463

~
0.491 [1].
The drag
coefficient
from CFD simulation was predicted

less than the real life drag coefficient of
pi
ckup

trucks. This phenomenon was

also observed by
Mukhtar, Britcher and Camp [4],

when they

conducted CFD simulation on

generic model of the pickup truck used in

their
experimental investigation. These might be due to the fact that the generic pick
up model
lac
ks accessories such as side mirror and windshield wipers. Also in the case of the
46


generic pickup model there were no exposed axles,
underbody, radiator cooling vents and
many cavities on the surface of the vehicle that connects the in
side of the vehicle to

the
flow.



3.6 Summary

CFD Simulation for Flow over Pickup Trucks conducted by Yang and Khalighi
[1
] was reproduced in present study. The same generic pickup truck model was used in
present simulations by using a virtual wind tunnel that had the same cross section area as
the one used in [1]. The length of the virtual wind tunnel used
in [1]

is only 23m
, which
is about 4.4 times the length of the full
-
size pickup truck. However the virtual wind
tunnel used in present simulation is 58m long about 11 times the length of the full size
truck

which is 5.184m. The reason to increase the length of the wind tunn
el was to make
sure the flow over the pickup model would not be affected by inlet and outlet boundary
conditions imposed on the inlet and outlet of the flow domain.

After surface meshes were generated and boundary zones were defined on the
surfaces of the
flow domain in GAMBIT, the flow domain were imported in to
volumetric meshing software TGRID to generate hybrid mesh. The meshed file was
imported into FLUENT for simulations. A realizable k
-
ε turbulence model with non
-
equilibrium wall function was selecte
d to solve the Reynolds averaged Navier
-
stokes
equation in Fluent. The flow was assumed to be steady and incompressible with uniform
inlet velocity of 22m/s and turbulence intensity of 1%. The results from present CFD
simulation of flow over the generic pi
ckup truck were compared with those of Yang and
47


Khalighi

[1]
. R
esults

were
presented as pressure coefficient plot,

u
-
velocity plots and
velocity magnitude vector streamlines. The pressure coefficient and u
-
velocity plots
shown in Figure 3.4 to Figure 3.11
indicate the present CFD simulation of flow over
pickup truck was in good agreement with

that of Yang and Khalighi

[1]. The velocity
magnitude vectors shown in Figure 3.14 and Figure 3.15 also confirm the present

simulation was properly validated.


















48


Chapter 4

STUDY OF ADD
-
ON DEVICES


4.1 Pickup truck model with Tonneau cover

T
he car
go box of the base line truck was

covered with flat wall
under a
boundary
condition
similar to Tonneau cover as shown in Figure 4.1.1. This truck with Tonneau
cover was simulated using CFD. By c
omparing

the pressure distribution plot
on the
symmetry plane of
the

pickup truck with Tonneau cover, shown in Figure 4.1.2(a), with
that of

the
baseline model in Figure 4.1.2(b) it indicates that the pressure distributi
on plot
over the rear end of the Tonneau cover is larger than the pressure distribution plot over
the under body of the vehicle. This c
auses a reduction on lift force

in the case of
the
model with Tonneau cover.

Pressure distributions in symmetry plane ove
r the under body
of the vehicle are similar for both cases.









Figure
4.1
.1 P
ickup truck with Tonneau cover



Tonneau
Cover
Garnish


49



Figure 4.1
.2 (a)

Pressure coefficient plot in the symmetry plane for
pickup
truck with Tonneau cover




Figure 4.1
.2 (b)

Pressure coefficient plot in the symmetry plane for
baseline truck




The Cp plot over the rear end of
the Tonneau cover
is higher than
that of the under body

50


Figure 4.1.3

shows the static pressure distribution over the
truck with Tonneau
cover on the
symmetry

plane. By comparing Figure 4.1.3

with Figure3.16,
it shows that
the static pressure at cab rear of the vehicle with Tonneau cover is

about
-
1.02*



Pascal and it is
higher than
the static pressure of
-
1.32*



Pasc
al
for the
baseline truck
.
This
contributes to reduce the lift and drag
coefficient
of the mode
l with Tonneau cover.
Similarly,
the total
pressure behind the cab
of the truck with
Tonneau
cover is about
-
6.39*



Pascal as

shown

in
Figure
4.1.4 and it
is
higher than that of the baseline truck
,
which is
-
8.71*



Pascal as
shown in Figure

3.17
, signifying a reduced aerodynamic
drag and lift in the case of the pickup model mounted with Tonneau cover
.




Figure 4.1.
3

Static pressure distribution over
pickup

truck with Tonneau cover and symmetry plane


51




Figure 3.16

S
tatic pressure distributions over the baseline truck and symmetry plane


Figure 4.1.
4

Total pressure distribution over
pickup
truck with Tonneau cover and symmetry plane


52




Figure 3.17

Total pressure distributions over the baseline truck and symmetry plane



Figure 4.1.5

shows the velocity magnitude vector
o
n the symmetry plane for
air
flow
over the pickup truck

with Tonneau
cover, indicating a small
three dimensional flow
circulation f
ormed over the Tonneau cover and behind the truck
. By comparing the
velocity magnitude vectors in Figure 4.1.5 with that of the baseline truck shown in Figure
3.15, it indicates that the size of the circulation area behind the cab decreased for the
model w
ith Tonneau cover.


53




Figure
4.1.5

Velocity

magnitude vector over symmetry plane for pickup with Tonneau cover














F
igure 3.15 (a) Velocity magnitude vectors over the

symmetry plane

for the base line truck


Figure 4.1.
6

shows the wake profile for the vehicle with the Tonneau

cover. By
c
omparing
the wake profile of the truck with Tonneau cover in
Figure 4.1.
6

with

that of
baseline truck in
F
igure 3.13, the wake region appears to be

smaller
for the pickup truck
with
Tonneau cover

on both locations, where, one location is right behind the cab and the
other is right behind the truck
.


54








Figure 4.1.
6 Wake profile over a
pickup truck with Tonneau cover (velocity vector on iso
-
velocity
surface at 3m/s
).








Figure
3.13 W
ake profile for baseline truck (velocity vector on iso
-
velocity surface at 3m/s)


Overall effect of Tonneau cover on drag and lift is summarized in
Table 4.1.1
. It
indicates that the pickup truck

fitted with Tonneau cover has
reduction of aerodynamic

drag coefficient



by

1.16% and
of
lift coefficient



by
6.64%
when compared with
the baseline truck model.


55


Configurations

Drag
Coefficient

%



diff. from
baseline

Lift
Coefficient

%



diff. from
Baseline

Baseline

0.3453

0

0.2193

0

Tonneau Cover

0.3413

-
1.158412974

0.1828

-
16.64386685

Table 4.1.1 Comparison of drag and lift coefficient of baseline pickup truck model with a model
fitted with Tonneau cover.



4.2

P
ickup truck model with Rear Roof Garnish

A Rear R
oof

G
arnish,
15cm long,

was

attached to t
he rear of the cab at an
inclination angle of 12


as shown in
Figure
4.2.1. It was expected
that the Rear Roof
Garnish will delay the separation of flow that normally occurs at the rear edge of the roof
.
It will
also direct the air flow over the box to the edge of the tailgate.




Figure 4.2.1 P
ickup truck with
the
attached Rear Roof Garnish.


Figure 4.2.2
(a)

shows the pressure coefficient distribution over the pickup model
with Rear roof garnish.
By c
ompar
ing Figure 4.2.2(a) with Figure 4.2.2(b)
, the
plots of
pressure coefficient Cp
indicate that
the
pressure on the
top
surface
of the Rear Roof
G
ar
nish sudden
ly decreases. This tends to
increase the pressure difference between the
Rear Roof
Garnish


56


pickup underbody and top surface
s,

which causes
more
lift in

the case of pickup model
with Rear R
oof
G
arnish.





Figure 4.2.2
(a)

Pressure coefficient
plot
on symmetry plane for flow over a pickup truck

with Rear
Roof garnish




Figure 4.2.2(b)

Pressure coefficient plot
on top and floor surfaces of the base line truck
in the
symmetry

plane


Figure 4.2.3 shows
the
pressure distribution on the surface of the truck with Rear
Roof Garnish

in the symmetry plane
. O
n the top surface of the Rear Roof Garnish
, t
he
pressure is about
-
1.24
*



Pascal
and from
the
pressure distribution over baseline
truck

Floor surface

Top surface

Top surface

Floor surface

57


in
Figure 3.16, the pressure at the rear of the cab is about
-
8.36
*



Pascal,
which is
higher than

that of
the pick truck mounted with Rear Roof Garnish. Th
is
indicate
s that
the
Rear Roof Garnish tends to increase the lift force on the vehicle. Fig
ure 4.2.4 shows the
total pressu
re distribution over the model with Rear Roof Garnish in the symmetry plane,
indicating that the total pressure drop occurs in the box of the truck as well as in the
region behind the truck.




Figure 4.2.3 Static pressur
e
contour over the pickup with Rear Roof G
arnish and symmetry plane



58



Figure 4.2.4 Total pressur
e contour over the pickup with Rear Roof G
arnish and symmetry plane


Figure 4.2.5 shows
the
velocity magnitude vector in the symmetry plane
for
air
flow over
the

pickup truck
attached
with
Rear Roof Garnish
.

By c
omparing velocity
magnitude vector
shown in
Figure 4.2.5 with tha
t of the baseline model in Figure

3.15,
it
appears that
the flow circulation in the box
is
similar
,

except
for the region
very near to
the
Rear Roof Garnish. Comparison between the wake profile
s

in Figure 4.2.6 and Figure
3.13 indicates that the wake region in the box
of
pickup model with Rear Roof Garnish is
re
latively smaller in size
than that of the baseline truck. Table 4.2.1
presents the

overall
effect of using read roof garnish. It shows that
by attaching Rear Roof Garnish to the
baseline truck model, aerodynamic drag coefficient



was reduced by about 2.4%;
howeve
,
r the lift coefficient



was increase
d

by about 33%.



59




Figure 4.2.5 V
elocity mag
nitude vector for a pickup truck with Rear Roof G
arnish on the symmetry
plane




Figure 4.2.6 Wake
profile over a pickup truck with Rear Roof G
arnish (velocity vector on iso
-
velocity surface at 3m/s).



Configurations

Drag
Coefficient

%



diff. from
baseline

Lift
Coefficient

%



diff.
from Baseline

Baseline

0.3453

0

0.2193

0

Rear Roof
Garnish

0.337

-
2.403706922

0.2916

32.96853625

Table 4.2.1 Comparison of drag and lift coefficient of baseline pickup truck model
with a model
attached with Rear Roof Garnish.


60


4.3

P
ickup truck model with

Tail plates


I
n order to decrease the velocity of air flow from the underbody to the rear of the
vehicle,

a diffuser type tail plate was
mounted at the r
ear of the vehicle as shown
in
Figure 4.3.1
. A half foot long plate was

attached to the floor of the

vehicle and a 5cm
long plate was

attached to the top outer edge of the tailgate, both at 12 degree angle
inclination.




Figure 4.3.1 Pickup
truck with attached Tail plates


By c
omparing
the static pressure in
Figure 4.3.2
with that in Figure 3.16, it is seen
that
the static pressure
acting
on the tail gate of the
base line truck is about
-
3.55*



Pascal
which
have a suction effect at the rear

of the vehicle
. H
owever
,

the static pressure