1
Chapter 1
INTRODUCTION TO VEHICLE AERODYNAMICS
1.1 Introduction
The continuing increase in fuel price coupled with uncertainty of future supply
has created widespread interest in vehicles with high efficiency including pickup trucks.
Pickup trucks, vans and SUVs account for 48% of sales fraction of light duty vehicle in
United States while light 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 rises.
Today auto 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 structural
mass, using engine with higher thermally efficiency, or altering the exterior body shape
to reduce the aerodynamic drag. According to US department of energy [10], in urban
driving aerodynamic drag accounts for 2.6% of the 12.6% of fuel energy being used to
propel the car as shown in Figure 1.1. Since the aerodynamic drag increases at higher
speeds, the aerodynamic drag on a highway driving accounts for 11% of 20% fuel energy
needed to propel the vehicle. Therefore improving vehicle aerodynamics is one of the
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factors that play crucial role for getting better mileage and better performance including
the handling of the vehicle especially at high speeds.
The body shapes of pickup 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.
The use of add-on devise enables us to reduce the aerodynamic drag of the vehicle
without compromising on its main design features. Studying 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.
With the use of CFD these 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 truck with add-on device such as Aerocap,
Tonneau cover, Tail plates and Rear Roof Garnish for drag reduction.
Figure 1.1 Typical energy uses and losses in a vehicle [9].
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1.2 Flow around a vehicle
External flow past objects encompass an extremely wide variety of fluid
mechanics phenomena and the characteristic of the flow fields is a function of shape of
the body. For a subsonic flow past a given shaped object, the characteristic of the flow
typical depends on the Reynolds number Re. Figure 1.2 shows flow over a cylinder at
Re=0.1, 50 and 105. For low Reynolds number, Re= 0.1, the flow is laminar and the
viscous effect plays important role throughout the flow. As Reynolds number is increased
to Re=105 , the flow separates and the viscous effect is limited in boundary layer and the
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]
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As opposed to streamlined bodies such as airfoils, road vehicle exist as blunt
bodies in close proximity to ground. The 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 turbulent wind that is almost constantly present. Furthermore, road 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
complexity to the flow field. Clearly, flow fields from a flow past vehicles are much
more complex compared to the flow past a simple geometry cylinder or more streamlined
body-shape of aircraft and ships.
Figure 1.3 shows flow streamlines 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, above 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 the separation point
is located at the rear edge of the roof as shown in Figure 1.3. Actually any sharp surface
irregularity can trigger the separation to form a wake.
5
Figure 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 boundary 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 manner. Friction drag formed between 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
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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 transmitted 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
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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 resultant flow encounters a
sharp edge and that is why it is always important for ground vehicles to have smoothly
rounded edges everywhere. Each type of separation can form a separation-bubble zone
either by reattaching itself downstream to the flow or being transmitted 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.
Vehicle aerodynamics operates mainly in the Reynolds number region in excess
of 106 according 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 vehicle and in the wheel 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 into 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
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separated flow occur on the A-pillar, at the rear of the vehicle, underneath the vehicle and
around the wheel region. In 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]
.
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Flow separations that lead to a pressure drag can be divided in two different
groups, according to Hucho [5]. If the separation line is located perpendicular to the flow
direction as shown in Figure 1.6, the vortices generated will have the axis perpendicular
to the outer flow and parallel 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. The
kinetic energy of the vortex field is rapidly dissipated by the turbulent mixing and
irreversibly converted 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.
The second type of flow separation is characterized by separation line inclined
with respect to the flow as shown in Figure 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,
contains a lot of kinetic energy which corresponds to the work necessary to overcome
pressure drag.
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Figure 1.6 Flow separations on a
bluff body (separation line
perpendicular 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]
1.4 Aerodynamic forces on vehicles
The air flow over a vehicle transmits 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 Figure 1.8 acting on a principal axis of a vehicle. Each one is described as
follows.
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Figure 1.8 Aerodynamic force and moments acting on a vehicle [17]
Drag
Drag is force acting on the surface of the vehicle by the flow in direction
opposing the motion of the vehicle. The 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. Direct 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 surface 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.
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Thus the non-dimensional coefficient is introduced to compare aerodynamic
performances of a vehicle. The non-dimensional drag coefficient 𝐶𝐷 is defined as
𝐶𝐷 =
2𝐷
𝜌𝑉 2 𝐴
(1.1)
Where:
𝐶𝐷
𝐴
𝜌
𝑉
=
=
=
=
Aerodynamic Drag Coefficient
Frontal Area of the Vehicle
Air Density
Total Wind Velocity
According to Hucho [5], the 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 equation represents aerodynamic lift Coefficient:
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𝐶𝐿 =
2𝐿
𝜌𝑉 2 𝐴
(1.2)
where:
= Lift Force
𝐶𝐿 = Lift Coefficient
L
Sideforce
Sideforce 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:
𝐶𝑆 =
2𝑆
𝜌𝑉 2 𝐴
(1.3)
Where:
S
𝐶𝑆
=
=
Sideforce acting on the vehicle
Sideforce Coefficient (Function of the Relative Wind Angle)
Pitching moment
Pitching moment affects the weight distribution between the front and the non
dimensional pitching moment coefficient is:
𝐶𝑃𝑀 =
2𝑃𝑀
𝜌𝑉 2 𝐴𝐿
(1.4)
Where:
𝐶𝑃𝑀
PM
L
=
=
=
Pitching Moment Coefficient
Pitching Moment
Wheelbase
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Yawing moment
Crosswinds produce a side force on a vehicle that acts at the middle of the
wheelbase. When 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:
𝐶𝑌𝑀 =
2𝑌𝑀
𝜌𝑉 2 𝐴𝐿
(1.5)
Where:
𝐶𝑌𝑀
YM
A
L
=
=
=
=
Yawing Moment Coefficient (Varies with Wind Direction)
Yawing Moment
Frontal Area of the Vehicle
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:
𝐶𝑅𝑀 =
2𝑅𝑀
𝜌𝑉 2 𝐴𝐿
(1.6)
Where:
𝐶𝑅𝑀
RM
A
L
=
=
=
=
Rolling Moment Coefficient
Rolling Moment
Frontal Area of the Vehicle
Wheelbase
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1.5 Fuel economy
Fuel economy is the measure of how many miles a vehicle can travel 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.
Vehicle 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. Vehicle aerodynamics have a role on the demand side of
the equation and lowering the aerodynamic drag lowers the Road load part of the tractive
force needed to drive the car. The tractive force 𝐹𝑇𝑅 required at the tire/road interface of
a car's driving wheels is defined as (Sovran and Bohn, [12]
(1.7)
Where: 𝐹𝑇𝑅 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= ƒ𝑅 G
(1.8)
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Where: G= mg the gravitational force the vehicle exerts on the road, ƒ𝑅 is the coefficient
of rolling resistance of the vehicle which needs to be determined experimentally and it
depends on the speed of the vehicle as shown in Figure 1.9.
Figure 1.9 𝐟𝐑 versus road speed V for typical radial tires [5]
The effective mass of the vehicle, M, is given by
M= m (1+𝜀𝑖 )
(1.9)
Where 𝜀𝑖 . 𝑚 is the equivalent translational mass of the rotating parts of the power train of
the vehicle? The mass fraction 𝜀𝑖 depends on the gear engaged and the suffix i denotes
the gear engaged.
The corresponding tractive power 𝑃𝑇𝑅 is:
𝑃𝑇𝑅 = 𝐹𝑇𝑅 *V
(1.10)
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Where V= velocity of the car. And the tractive energy required for propulsion during any
given driving period is:
𝑇
𝐸𝑇𝑅 = ∫0 𝑃𝑇𝑅 𝑑𝑡
(1 .11)
From the above equations, 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. These two methods can be related using Equation 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 𝑏̇ [L/s] over a period of time T [s] and then
averaging the integral over the distance travelled during the period of T[s].
𝐵=
𝑇
∫0 𝑏̇𝑑𝑡
𝑇
∫0 𝑉𝑑𝑡
Where: V is the velocity of the vehicle.
(1 .13)
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Since 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.
During Powered drive, 𝐹𝑇𝑅 >0, the amount of fuel consumed is
𝑏 + [𝐿] = 𝜌
1
𝑓𝑢𝑒𝑙
𝑏𝑒
𝑇 >0
∫𝐹
𝐹𝑇𝑟 ∙𝑉
(
𝜂𝐷
+ 𝑃𝑏,𝐴 ) 𝑑𝑡
(1 .14)
where 𝑃𝑏,𝐴 is the engine power required to drive vehicle accessories like air conditioning,
𝜌𝑓𝑢𝑒𝑙 is the density of fuel, 𝑏𝑒 is the specific fuel consumption also known as bsfc brake
specific fuel consumption and typical bsfc maps for gasoline and diesel engine is shown
in Figure [1.10] as below, 𝜂𝐷 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]
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During breaking the 𝐹𝑇𝑟 < 0 and the total volume of fuel consumed is given by:
𝑏 − [𝐿] = ∫𝐹
𝑇 <0
𝑏̇𝑏 𝑑𝑡
(1 .15)
Where: 𝑏̇𝑏 𝑖𝑠 brake volume fuel rate.
During idles the velocity of the vehicle V=0 and the amount of fuel consumed is:
𝑏𝑖𝑑𝑙𝑒 [𝐿] = ∫𝑉=0 𝑏̇𝑖𝑑𝑙𝑒 𝑑𝑡 = 𝑏̇𝑖𝑑𝑙𝑒 ∙ 𝑡𝑖𝑑𝑙𝑒
(1 .16)
Where: 𝑏̇𝑖𝑑𝑙𝑒 is idle volume flow rate.
By adding equations 1.15, 1.16 and 1.17the total fuel consumed B:
𝐵[𝐿⁄100𝑘𝑚 ] = 𝐶
𝐹 ∙𝑉
1
𝑏 ( 𝑇 +𝑃𝑏,𝐴 )𝑑𝑡+∫𝐹 <0 𝑏̇𝑏 𝑑𝑡+𝑏̇𝑖𝑑𝑙𝑒 ∙𝑡𝑖𝑑𝑙𝑒
∫
𝜌𝑓𝑢𝑒𝑙 𝐹𝑇 >0 𝑒 𝜂𝐷
𝑇
𝑇
∫0 𝑉 𝑑𝑡
(1 .17)
To 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 highway driving cycles
shown in Figure 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.
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Figure 1.11 EPA driving cycle [5]
To determine numerically the effects of improved aerodynamics on fuel economy
by using Equation 1.17 is a complex task. Sovran and Bohn [12] developed a method to
determine tractive energy equation for EPA urban and highway driving schedules. Later
Sovran [13] used Equation 1.17 and tractive energy Equation 1.11 to developed charts
that show the impact of changes in aerodynamic drag on composite fuel consumption for
the EPA schedules. The composite fuel consumption for EPA driving schedules is given
by equation 1.18.
𝐹𝐸𝐶𝑂𝑀𝑃𝑂𝑆𝐼𝑇𝐸 =
1
0.55
𝐹𝐸𝑢𝑟𝑏𝑎𝑛
+
0.44
𝐹𝐸ℎ𝑖𝑔ℎ𝑤𝑎𝑦
(1 .18)
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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 (𝐶𝐷 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]
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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 has 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 aerodynamic 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 oil would be saved and also reduce carbon emission to the
environment.
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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 the 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 1975 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 been 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.
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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-Garni, Bernal and
Khalighi [2] to address the issue if the two-equation k-ε turbulence model could capture
steady flow around the pickup truck. They compared the data from CFD simulations with
excremental data collected form Al-Garni, Bernal and Khalighi‘s experiment [2] and
stated that the steady state formulation was good enough to study vehicle aerodynamics.
Cooper [3] investigated 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 presented 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 were 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 primary 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 mounted 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, the 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 plates, Airdam, Traditional canopy, Aerocap with rear inclination angel of
5⁰,10⁰,12⁰,15⁰ and 18.77⁰. 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 consuming and expensive to operate as multiple tests are usually required in
achieving the desired aerodynamic shape or characteristic 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 over simple 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 direct numerical solution of Navier-stoke
equation is not yet possible even with modern day computers. In order to come up with
reasonable solution, a time averaged Navier-Stokes equation was being used (Reynolds
Averaged Navier-Stokes Equations – RANS equations) together with turbulent models to
resolve the issue involving Reynolds Stress resulting from the time averaging process.
With the reduction on computational cost today, 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 pickup truck model. This k-ε turbulence model is very
robust, having reasonable computational turnaround time, and widely used by the auto
industry. Since the main aerodynamics force acting on road 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. It 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
object causes friction drag on the object. Skin friction is dominant on 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 boundary 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. The 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 flow
separation. For non-streamlined bluff bodies such as pickup trucks immersed in a
flow, the flow separates from the body near sharp edges and creates a wake region
of turbulence. Pressure will drop in the turbulence region, resulting 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 increases as lift
increases. Thus minimum drag occurs when the lift on the body is zero. As road
vehicle are bluff bodies in close proximity 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 degree relative 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 degree,
resulting in smaller 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.
Figure 3.1 Flow past a circular cylinder: (a) laminar separation; (b) turbulent separation; (c)
theoretical and actual surface-pressure distribution, [7]
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
32
flow field and improve the aerodynamic of the model. However, before 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 flow over the same generic
model [1]. Yang and Khaligi’s [1] CFD simulation of flow over a pickup truck 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
present CFD simulation. The full size generic pick up is 5.184m long, 1.824m wide,
1.786 m high and with a projected frontal area of 2.809m2. The origin of the coordinate
axis used in present simulation was attached to the bumper of the vehicle. The pickup
truck box 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 outlet 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 simulation, 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 1/12th-scale generic pickup truck model used in [1] and [2].
Figure 3.3 1/12th scale of flow domain used in present simulation, 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 commercial volumetric meshing software TGrid to descretize the domain with a
hybrid meshes. Prismatic layer was created over the vehicle surface to capture the
boundary layer characteristics 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. Further hex refinement was
created between the floor of pickup truck and the ground face of the virtual wind tunnel.
In present simulation, the flow domain was descretized with about 9 to 10 million hybrid
cells.
3.4 Baseline pickup truck CFD method and setup
The CFD simulation by Yang 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, boundary condition settings and solution controls
for present simulation respectively. The Reynolds number of the air flow was Re=
7.8*106 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*105 ,based on the length of
the model, the flow properties will be similar and one will be able to compare results
from CFD simulation[1] with any Reynolds number above the critical Reynolds number.
The assumptions made in present simulation were the air flow was steady state with
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 virtual wind tunnel.
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
Pressure
Outlet
Magnitude (Measured normal to
Boundary)
Turbulence Specification Method
Turbulence Intensity
Turbulence Viscosity Ratio
22 m⁄s (constant)
Intensity and Viscosity Ratio
1.00%
20
0 pascal
Gauge Pressure magnitude
Gauge Pressure direction
normal to boundary
Turbulence Specification Method
Backflow Turbulence Intensity
Intensity and Viscosity Ratio
10%
Backflow Turbulent Viscosity Ratio
Wall Zones
- vehicle surface-noslip wall B/c
- Ground face- invicisd wall B/C
-Side faces -inviscid wall B/C
Fluid
Properties
Fluid Type
10
Air
ρ = 1.175 (kg⁄m^3 )
Density
Kinematic viscosity
v = 1.7894×10^(-5) (kg⁄(m∙s))
Table 3.3 Boundary condition settings
Equations
Flow and Turbulence
Discretization
Monitor
 Pressure: Standard
 Momentum: Second Order Upwind
 Turbulence Kinetic Energy: Second Order Upwind
 Turbulence Dissipation Rate: Second Order Upwind
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 results and discussion
Figure 3.4a 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 simulations have a
tendency to overshoot the Cp value at stagnation point. The Maximum Cp value obtained
in present simulation was Cp= 1.01 and from Yang and Khalighi [1] the maximum
pressure coefficient value was approximately Cp= 1.15 as shown in Figure 3.5a. These
indicate that the present simulation was reasonably accurate in predicting the pressure
distribution over the top surface of the vehicle.
Figure 3.4b 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%.
1.5
1
0.5
0
-0.5 0
-1
-1.5
-2
-2.5
0
0
100
200
300
-0.5
-1
100
200
300
-1.5
-2
-2.5
Figure 3.4 (a) Pressure on pickup cab (b) Pressure on pickup floor
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 coefficient 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 these figures, the pressure coefficient distribution on 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 than the case of leaving the tailgate open. This findings confirms the
conclusion made by Cooper “Pickup truck aerodynamics-keep your tailgate up” [3].
39
60
50
40
30
20
Cp-TailgateOuter
simulated
expermental
10
0
-0.09
-0.11
-10
-0.13
-0.15
-0.17
-0.19
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 tailgate (inside) from [1]
Figures 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 match very well with nearly identical plots. Figure 3.12 shows static pressure
distribution over the pickup truck surfaces, indicating that pressure was very high on the
grill of the vehicle where the velocity of the flow becomes zero and stagnation point was
created. Figure 3.12 also shows relatively high static pressure created at the junction of
40
the windshield with the hood of the vehicle. Both front and rear tires also experience high
static pressure but the front wheels were subjected to slightly higher static pressure than
the rear. On the sharp edges 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.
140
U, x=400mm ,y=0
120
100
80
60
40
20
-0.6
0
-0.1
0.4
0.9
1.4
Figure 3.8 (a) u-velocity in y=0 plane (inside box). (b) u-velocity in y=0 plane (inside box) from [1].
41
U,x=500mm,y=0
140
90
40
-10
-60
0
0.5
1
Figure 3.9 (a) u-velocity in y=0 plane (outside box). (b) u-velocity in y=0 plane (outside box) from [1].
U,x=450mm,z=73mm
1.2
1
0.8
0.6
0.4
0.2
0
-120
-80
-40
0
40
80
120
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].
42
U,x=450mm,z=15mm
1.2
1
0.8
0.6
0.4
0.2
-120
-70
0
-20
-0.2
30
80
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 3.13 Wake profile for baseline
truck (velocity vector on iso-velocity
surface at 3m/s)
Figures 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. Figures
3.15(a) and (b) compare the velocity magnitude vectors in the symmetry plane from
43
present simulation with that of Yang and Khalighi [1]. The vectors indicate the flow
separation occurring at the rear edge of the cab and the vortex created in the box of the
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 and 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
also 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 Static 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 recirculation 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
𝐶𝐷 = 0.345 and 𝐶𝐿 = 0.28 respectively. However, in the real world pickup trucks
manufactured today have a drag coefficient at 𝐶𝐷 = 0.463 ~ 0.491 [1]. The drag
coefficient from CFD simulation was predicted less than the real life drag coefficient of
pickup 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 pickup model
lacks 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 inside 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 tunnel 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 nonequilibrium wall function was selected 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 pickup truck were compared with those of Yang and
47
Khalighi [1]. Results 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
The cargo 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 comparing 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 distribution plot
over the rear end of the Tonneau cover is larger than the pressure distribution plot over
the under body of the vehicle. This causes a reduction on lift force in the case of the
model with Tonneau cover. Pressure distributions in symmetry plane over the under body
of the vehicle are similar for both cases.
Tonneau
Cover
Garnish
Figure 4.1.1 Pickup truck with Tonneau cover
49
The Cp plot over the rear end of
the Tonneau cover is higher than
that of the under body
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
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*102
Pascal and it is higher than the static pressure of -1.32*102 Pascal for the baseline truck.
This contributes to reduce the lift and drag coefficient of the model with Tonneau cover.
Similarly, the total pressure behind the cab of the truck with Tonneau cover is about 6.39*101 Pascal as shown in Figure 4.1.4 and it is higher than that of the baseline truck,
which is -8.71* 101 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 Static 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 on the symmetry plane for air
flow over the pickup truck with Tonneau cover, indicating a small three dimensional flow
circulation formed 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 with Tonneau cover.
53
Figure 4.1.5 Velocity magnitude vector over symmetry plane for pickup with Tonneau cover
Figure 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
comparing the wake profile of the truck with Tonneau cover in Figure 4.1.6 with that of
baseline truck in Figure 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 Wake 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 𝐶𝐷 by 1.16% and of lift coefficient 𝐶𝐿 by 6.64% when compared with
the baseline truck model.
55
Configurations
Drag
Coefficient
% 𝐶𝐷 diff. from
baseline
Lift
Coefficient
% 𝐶𝐿 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 Pickup truck model with Rear Roof Garnish
A Rear Roof Garnish, 15cm long, was attached to the 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.
Rear Roof
Garnish
Figure 4.2.1 Pickup 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 comparing 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
Garnish suddenly decreases. This tends to increase the pressure difference between the
56
pickup underbody and top surfaces, which causes more lift in the case of pickup model
with Rear Roof Garnish.
Top surface
Floor surface
Figure 4.2.2(a) Pressure coefficient plot on symmetry plane for flow over a pickup truck with Rear
Roof garnish
Top surface
Floor surface
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. On the top surface of the Rear Roof Garnish, the
pressure is about -1.24*102 Pascal and from the pressure distribution over baseline truck
57
in Figure 3.16, the pressure at the rear of the cab is about -8.36* 101 Pascal, which is
higher than that of the pick truck mounted with Rear Roof Garnish. This indicates that the
Rear Roof Garnish tends to increase the lift force on the vehicle. Figure 4.2.4 shows the
total pressure 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 pressure contour over the pickup with Rear Roof Garnish and symmetry plane
58
Figure 4.2.4 Total pressure contour over the pickup with Rear Roof Garnish and symmetry plane
Figure 4.2.5 shows the velocity magnitude vector in the symmetry plane for
airflow over the pickup truck attached with Rear Roof Garnish. By comparing velocity
magnitude vector shown in Figure 4.2.5 with that 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 profiles 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
relatively 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 𝐶𝐷 was reduced by about 2.4%;
howeve,r the lift coefficient 𝐶𝐿 was increased by about 33%.
59
Figure 4.2.5 Velocity magnitude vector for a pickup truck with Rear Roof Garnish on the symmetry
plane
Figure 4.2.6 Wake profile over a pickup truck with Rear Roof Garnish (velocity vector on isovelocity surface at 3m/s).
Configurations
Baseline
Rear Roof
Garnish
Drag
Coefficient
0.3453
0.337
% 𝐶𝐷 diff. from
baseline
0
Lift
Coefficient
0.2193
% 𝐶𝐿 diff.
from Baseline
0
-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 Pickup truck model with Tail plates
In 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 rear 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.
Tail
Plates
Figure 4.3.1 Pickup truck with attached Tail plates
By comparing 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*101
Pascal which have a suction effect at the rear of the vehicle. However, the static pressure
on the tail gate of the pickup truck with tail plates is about 4.52 Pascal. This indicates
that, in the case of model with the tail plates, the pressure difference between the front
and rear end of the truck is smaller than that of the baseline truck, contributing to the
reduction of drag force acting on the vehicle. Figure 4.3.3 shows the total pressure
contour over the model with the tail plates and it can be read that the total pressure on the
61
tail gate is -1.28*101 Pascal and from the total pressure contour of baseline truck in
Figure 3.17 the pressure on the tail gate of the baseline truck is about -4.58*101 Pascal.
This indicates the rise of total pressure behind the tailgate of the model with tail plates.
Figure 4.3.2 Static pressure distribution over model with tail plates and symmetry plane
Figure 4.3.3 Total pressure distribution over model with tail plates and symmetry plane
62
Figure 4.3.4 shows the velocity magnitude vector in the symmetry plane for air
flow over the truck with tail plates, indicating that the underbody flow was deflected
upwards and the velocity of the downwash flowing over the edge of the tailgate was
reduced. This tends to increase the static pressure behind the tailgate which contributes
positively to the reduction of drag force acting on the vehicle. By comparing the wake
profile over the truck with tail plates in Figure 4.3.5 with wake profile of the baseline
truck in Figure 3.13, the wake profile seems to be similar in the box but behind the truck
the wake profile in case of the model with tail plates become longer and flatter. The
overall effect of tail plated is summarized in Table 4.3.1. It indicates that, by attaching a
tail plate to the baseline model, a reduction of aerodynamic drag coefficient 𝐶𝐷 by 3.48%
and lift coefficient 𝐶𝐿 by 40.54% was achieved.
Figure 4.3.4 Velocity magnitude vector on the symmetry plane for model with tail plates
63
Figure 4.3.5 Wake profile over pickup truck with tail plates (velocity vector on iso-velocity surface at
3m/s)
Drag
Coefficient
% 𝐶𝐷 diff. from
baseline
Lift
Coefficient
Baseline
0.3453
0
0.2193
0
Tail Plates
0.3333
-3.475238923
0.1304
-40.5380757
Configurations
% 𝐶𝐿 diff.
from Baseline
Table 4.3.1 Comparison of drag and lift coefficient of baseline pickup truck with a model attached
with Tail plates.
4.4 Pickup truck model with Airdam
Figure 4.4.1 shows the pickup truck mounted with airdam that has 6 in clearance
from the ground. Two airdam configurations, one with 6 in clearance from the ground
and the other with 3 in clearance, were used to investigate the effect of airdam on the
aerodynamic drag of the vehicle. The aim to attach an airdam was to reduce the drag
coming from the underside of the vehicle with the premise that by reducing the air speed
under the vehicle it is likely to minimize the contribution of the underbody flow to the
overall drag. However, the front projected area of the vehicle is increased with the airdam
64
attached and this could increase the drag. Therefore, careful attention was required to
achieve the desired net effect.
Airdam with 6in
clearance from the
ground
Figure4.4.1 Pickup truck with Airdam
Figures 4.4.2 shows the pressure coefficient plots in the symmetry plane for the
truck mounted with airdam; Figure 4.4.2(a) is for the case having a 3-in clearance from
the ground and Figure 4.4.2(b) is for the case having 6in clearance from the ground
respectively. Comparison between Figures 4.4.2 (a), Figure 4.4.2(b) and Figure 4.1.2 (b)
indicates that the stagnation area in the model with airdams is longer along the X-axis.
Also in the case of the airdam with 3 in clearance from the ground, the Cp plot in Figure
4.4.2(a) shows that the Cp plot in the box has a higher value than the Cp plot over the
underbody. This will lower the lift force acting on the model.
65
The Cp plot in the box is higher
than that of the under body
Figure4.4.2 (a) Pressure coefficient plot over a model with Airdam (3in clearance from the ground)
Figure 4.4.2(b) Pressure coefficient plot over model with Airdam (6in clearance from the ground)
Figure 4.1.2(b) Pressure coefficient plot over baseline pickup in the symmetry plane
66
Figures 4.4.3 shows the pressure contour over the vehicle with airdam. By
comparing the model case of having airdams with that of baseline truck in Figure 3.12, it
indicates that in the frontal area over which stagnation of flow occurs, the pressure is
larger when the airdams are used. This tends to increase the drag force acting on the
vehicle.
Figure4.4.3 (a) Pressure contour over pickup with Airdam (3in clearance from the ground)
Figure4.4.3 (b) Pressure contour over pickup with Airdam (6in clearance from the ground)
67
Figure 3.12 Pressure distributions over the pickup
Table 4.4.1 shows drag and lift coefficient reduction achieved by the Airdam.
Airdam with 6 inch clearance from the ground increased drag of the model. But, airdam
with 3 inch clearance from the ground have reduced drag by 0.35% and the drag
reduction is very small to merit the cost and the risk of bumping onto objects on the road.
On the other hand, the lift reduction coefficient achieved by employing airdam with 3in
clearance from the ground is 326.45% and from airdam with 6in clearance is 36.48%.
This indicates airdams are very effective in reducing lift force acting on a vehicle and
should be employed on a race car to increase traction and handling while maneuvering
curves or slippery roads.
68
Configurations
Baseline
Airdam -3in
Airdam-6in
Drag
Coefficient
0.3453
0.3441
0.3661
% 𝐶𝐷 diff. from
baseline
0
-0.35
6.03
Lift
Coefficient
0.2193
-0.4966
0.1393
% 𝐶𝐿 diff. from
Baseline
0
-326.45
-36.48
Table 4.4.1 Comparison of drag and lift coefficient of baseline pickup truck with a model attached
with Airdam-3in and Airdam-6in.
4.5 Pickup truck model with Traditional Canopy
The baseline pickup truck was mounted with a traditional canopy as shown in
Figure 4.5.1. The air flow was then simulated to investigate the flow structure around the
vehicle. The traditional canopy was also used as reference for the design of aerocap.
Figure 4.5.1 Pickup truck with traditional canopy
Figure 4.5.2 shows the pressure coefficient plots in the symmetry plane for the
model with traditional canopy. By comparing with the case of baseline truck as shown in
Figure3.4, it indicates that near the rear of the vehicle the pressure over the top surface of
the canopy is higher than the underbody. Thus the truck with the traditional canopy will
have lesser lift force than the baseline truck.
69
Figure 4.5.2 Pressure coefficient plot on symmetry plane for model with Traditional Canopy
Figure 4.5.3 shows the static pressure contour over model with canopy. By
Comparing the static pressure at the base of the vehicle with canopy with the pressure at
the rear of the cab and tail of the baseline truck in Figure 3.16, it indicates that the
pressure at the base of the truck with the canopy is -3.44*101 Pascal and it is higher than
that of the baseline truck which equals to -8.36*101 Pascal. This contributes to reducing
the pressure difference between the front and base of the model with canopy and results
in lesser drag.
Figure 4.5.3 Static pressure distribution over model with Traditional Canopy
70
Figure 4.5.4 shows the wake profile behind the truck with canopy, indicating that
the wake region behind the base is larger than that of the baseline truck shown in
Figure3.13. In case of the model with traditional canopy, flow separation occurs at the
top edge of the base while for the baseline truck the flow separation occurs at the rear
edge of the roof.
Figure 4.5.4 Wake profile behind the pickup truck with traditional canopy (velocity vector on isovelocity surface at 3m/s)
Table 4.5.1 summarizes the overall effect of traditional canopy on the drag and
lift. It can be seen that the computed drag coefficient for pickup truck mounted with
traditional canopy was 𝐶𝐷 = 0.3157, a reduction of 8.57% when compared to baseline truck.
Configurations
Drag Coefficient
% 𝐶𝐷 diff. from baseline
Baseline
0.3453
0
Traditional canopy
0.3157
- 8.57
Table 4.5.1 Comparison of drag and lift coefficient of baseline truck model with a model attached
with Traditional canopy.
71
4.6 Pickup truck model with Aerocap
Figure 4.6.1 shows the pickup truck fitted with Aerocap attached to the box of the
baseline truck. The aim of using Aerocap is to improve the flow structure around the
vehicle so as to reduce aerodynamic drag (𝐶𝐷 ). CFD simulation of the air flow over the
model with Aerocap was conducted under the setting that the rear inclination angle is
varied for α=5⁰,10⁰,12⁰,15⁰ and 18.77⁰. The size of the wake region behind the vehicle is
determined by the pressure and velocity relationship which depends on the rear
inclination angle α. The optimum rear inclination angle should increase the static pressure
at the rear end while the flow remain attached the vehicle surfaces.
Figure 4.6.1 Pickup truck model with Aerocap of a rear inclination angle α= 10°
Figure 4.6.2 only shows the pressure coefficient plot over the symmetry plane for
rear inclination angle α=5⁰,12⁰ and 18.77⁰. The plots indicates as rear inclination angle α
increase the pressure near the top edge of the inclined face of aerocap decreases while
the pressure plots remain similar over the rest of the surfaces.
72
Figure 4.6.2 Pressure coefficient plot in symmetry plane over model with Aerocap at different 
Figures 4.6.3, 4.6.4, 4.6.5, 4.6.6, and Figure 4.6.7 shows the total pressure contour
in the symmetry plane and over the surface of the pickup model with Aerocap when the
rear inclination angle is specified as α=5⁰, 10⁰, 12⁰, 15⁰ and 18.77⁰ respectively. It
indicates that a lower total pressure area was created at the base of the model when
Aerocap was set with different inclination angles. The total pressure contours also
indicate that as the rear inclination angle α increases the region with total pressure
gradient at the base of the model decreases. This region is also associated with the size of
the wake region.
73
Figure 4.6.3 Total pressure on symmetry plane when rear inclination angle α=5°
Figure 4.6.4 Total pressure on symmetry plane when rear inclination angle α=10°
74
Figure 4.6.5 Total pressure on symmetry plane when rear inclination angle α=12°
Figure 4.6.6 Total pressure on symmetry plane when rear inclination angle α=15°
75
Figure 4.6.7 Total pressure on symmetry plane when rear inclination angle α=18.77°
Figure 4.6.8 to Figure 4.6.12 shows the static pressure contour in the symmetry
plane and over the surface of the model truck with Aerocap when the rear inclination
angles α=5⁰, 10⁰, 12⁰, 15⁰ and 18.77⁰ are specified, respectively. The pressure contours
indicate that as the rear inclination angle α increases the pressure on the cab roof
decreases. This tends to increase lift as the rear inclination angle α increases.
76
Figure 4.6.8 Pressure on symmetry plane when rear inclination angle α=5°
Figure 4.6.9 Pressure on symmetry plane when rear inclination angle α=10°
77
Figure 4.6.10 Pressure on symmetry plane when rear inclination angle α=12°
Figure 4.6.11 Pressure on symmetry plane when rear inclination angle α=15°
78
Figure 4.6.12 Pressure on symmetry plane when rear inclination angle α=18.77°
Figure 4.6.13 to Figure 4.6.17 shows the velocity magnitude streamline for the
rear inclination angle α=5⁰, 10⁰, 12⁰, 15⁰ and 18.77⁰, respectively. The streamlines
indicate that turbulent wake region develops at the base of the vehicle have two vertices,
one on top and the other in the wake region. When the rear inclination angle reaches
α=10⁰ the two vertices are of similar size as shown in Figure 4.6.14. However, as the rear
inclination angle increases the vortex on the top became larger than the one in the bottom
and the center the bottom vortex slightly moves towards the tail of the vehicle. The
stream lines also shows that as the rear inclination angle increases the height and the
length of the wake region decrease.
79
Figure 4.6.13 Velocity magnitude path line on symmetry plane when rear inclination angle α=5°
Figure 4.6.14 Velocity magnitude path line on symmetry plane when rear inclination angle α=10°
80
Figure 4.6.15 Velocity magnitude path line on symmetry plane when rear inclination angle α=12°
Figure 4.6.16 Velocity magnitude path line on symmetry plane when rear inclination angle α=15°
81
Figure 4.6.17 Velocity magnitude path line on symmetry plane when rear inclination angle α=18.77°
Figure 4.6.18 to Figure 4.6.22 shows the wake profile for air flow over pick up
with Aerocap at inclination angle α=5⁰, 10⁰, 12⁰, 15⁰ and18.77⁰, respectively. These
figures indicate that as the rear inclination angle α increases the size of the wake region
behind the vehicle decreases. For Aerocap with rear inclination angle α= 5⁰, 10⁰ and 12⁰,
there is a formation of horse-shoe shaped vortices at the rear of the vehicle, however, as
the rear inclination angle increases to the angle α=15⁰ and 18.77⁰, these horse-shoe
shaped vertices are not present.
82
Figure 4.6.18 Wake profile behind the pickup truck with Aerocap when rear inclination angle α=5°
(velocity vector on iso-velocity surface at 3m/s)
Figure 4.6.19 Wake profile behind the pickup truck with Aerocap when rear inclination angle α=10°
(velocity vector on iso-velocity surface at 3m/s)
83
Figure 4.6.20 Wake profile behind the pickup truck with Aerocap when rear inclination angle α=12°
(velocity vector on iso-velocity surface at 3m/s)
Figure 4.6.21 Wake profile behind the pickup truck with Aerocap when rear inclination angle α=15°
(velocity vector on iso-velocity surface at 3m/s)
84
Figure 4.6.22 Wake profile behind the pickup truck with Aerocap when rear inclination angle
α=18.77° (velocity vector on iso-velocity surface at 3m/s)
Table 4.6.1 and Figure 4.6.23 show the comparison of drag and lift coefficient for
pickup truck model with Aerocap at rear inclination angle α= 5⁰, 10⁰, 12⁰, 15⁰ and
18.77⁰. Compared to the baseline model, pickup truck with the entirely studied Aerocap
configurations have a reduction in drag coefficient. The drag coefficient for model with
aerocap decreases quickly for the rear inclination angle between 5⁰ and ⁰10 and it slightly
decrease when the rear inclination angle is between 10⁰ and 12⁰. However, when the rear
inclination angle is greater than 12⁰ the drag coefficient increases dramatically as shown
in Figure 4.6.23(a). The minimum lift coefficient achieved is for aerocap with the rear
inclination angle of 5⁰ and the lift coefficient increase with the increase of rear inclination
angle as shown in Figure 4.6.23(b).
85
Drag
Coefficient
0.3453
0.2957
0.2894
0.2892
0.2987
Configurations
Baseline
Aerocap α=5°
Aerocap α=10°
Aerocap α=12°
Aerocap α=15°
Aerocap
α=18.77°
% 𝐶𝐷 diff. From
baseline
0.3091
0
-14.36432088
-16.18882131
-16.24674196
-13.49551115
Lift
Coefficient
0.2193
0.0497
0.1097
0.1579
0.2296
% 𝐶𝐿 diff. from
Baseline
0
-77.3369813
-49.97720018
-27.99817601
4.696762426
-10.48363742
0.3587
63.56589147
Table 4.6.1 Comparison of drag and lift coefficient of pickup truck with Aerocap at different rear
inclination angle α with the baseline truck.
0.32
Lift coefficient Vs rear inclination angle
0.4
drag coefficient
0.3
0.3
0.2
0.28
drag
coefficient
0.26
0.1
0
5
10
12
15
18.77
0
5
10
15
20
Figure 4.6.23: (a) Drag Coefficient (𝑪𝑫 ) versus rear inclination angle α. (b) Lift Coefficient (𝑪𝑳 )
versus rear inclination angle α.
4.7 Pickup truck model with 3D curved Aerocap
From the aerodynamic analysis of Aerocap with 5 different rear inclination
angles, Aerocap with the rear inclination angle α= 12⁰ has the smallest drag coefficient
𝐶𝐷 = 0.2892 as shown in Table 4.6.1. By decreasing the rear width of the aerocap it is
possible to further reduce the aerodynamic drag. It is motivated for a study of using 3D
curved Aerocap. The aim of using 3D curved Aerocap is to make static base pressure at
the end of the vehicles body as high as possible but at the base itself, this base pressure is
86
made as small as possible which would require tapering the rear end. In the present study,
tapering the rear end of Aerocap was made with rear inclination angle α= 12⁰.
Experimental investigation by Gaylard and Howell [19] from Jaguar Land Rover
showed that possible combination of shape modification on SUV as shown in Figure4.7.1
could improve aerodynamic drag. One of the recommended solutions was to decrease the
width of the SUV side frames at the rear. Since the flow over a pickup truck with
Aerocap is similar to the flow over SUV, this recommendation also holds for the pickup
trucks fitted with Aerocap. Thus Aerocap with the rear inclination angle of α= 12⁰ is
modified by narrowing the rear width and streamlining the Aerocap as shown in Figure
4.7.2.
Figure 4.7.1 Shape changes to reduce drag of SUV [19]. Figure 4.7.2 Pickup truck with 3D
curved Aerocap
For a pickup with 3D curved aerocap, it was expected that its aerodynamics
improvement over a model truck with Aerocap inclination angle α= 12⁰ is due to the
87
improvement in the flow structure at the rear of the model as well as the increase of static
pressure at the base of the model. Figure 4.7.3 shows the static pressure contour over a
symmetry plane for pickup truck with 3D curved Aerocap. It can be seen that the pressure
at the rear of the vehicle is about -6.54 Pascal. From Figure 4.6.10, the static pressure is
about -8.34 Pascal at the base of the pickup truck with Aerocap α= 12⁰ and the pressure
value is even lower in some areas on the tailgate. The negative pressures have more
suction effect in the case of the vehicle mounted with Aerocap α= 12⁰ and this verifies
aerodynamic drag improvement of model with 3D curved aerocap over the model with
Aerocap α= 12⁰.
Figure 4.7.3 Pressure distribution over pickup with 3D curved Aerocap in the symmetry plane
Figure 4.7.4 shows the total pressure contour over the model with 3D curved
aerocap and on symmetry plane. By comparing with Figure 3.17, it indicates that the total
88
pressure at the rear of the vehicle is -2.16*101 Pascal which is higher than total pressure
of the baseline truck at -8.71*101 Pascal.
Figure 4.7.4 Total pressure distribution over pickup with 3D curved Aerocap in the symmetry plane
Figure 4.7.5 shows the velocity magnitude path line on symmetry plane for flow
over model with 3D curved Aerocap. By comparing with the streamline flow over a
symmetry plane for airflow over a model with 2D Aerocap at α=12⁰ in Figure 4.6.15, it
indicates that the vortexes behind the trucks are very similar. Figure 4.7.6 shows the
wake profile behind the model with 3D curved aerocap and by comparing with the case
of the mode with Aerocap α= 12⁰ in Figure 4.6.20 it indicates that the horse-shoe shaped
vortices presented at the rear of the model with Aerocap α= 12⁰ is not present in the case
of the model with 3D curved aerocap..
89
Figure 4.7.5 Velocity magnitude path line on symmetry plane for flow over model with 3D curved
Aerocap
Figure 4.7.6 Wake profile behind the pickup truck with 3D curved Aerocap (velocity vector on isovelocity surface at 3m/s)
Table 4.7.1 shows drag and lift coefficients for the truck mounted with Aerocap
α=12⁰ and 3D curved Aerocap. It can be seen that aerodynamic drag reduction of 19.84%
90
and lift reduction of 40.72 % were achieved by mounting 3D curved Aerocap on the
truck. The table also shows that the 3D curved Aerocap has better aerodynamic
characteristic than that of Aerocap α=12⁰.
Configurations
Baseline
Aerocap α=12°
3D curved
Aerocap
Drag
Coefficient
0.3453
0.2892
% 𝐶𝐷 diff. from
baseline
0
-16.24674196
Lift
Coefficient
0.2193
0.1579
% 𝐶𝐿 diff.
from Baseline
0
-27.99817601
0.2768
-19.83782218
0.13
-40.72047424
Table 4.7.1 Comparison of drag and lift coefficient of baseline pickup truck with Aerocap α=12⁰ and
3D curved aerocap
4.8 Impact of 3D curved Aerocap on fuel economy of pickup truck
In order to analyze the effect of mounting a 3D curved aerocap on the truck on the
fuel economy, G. Sovran's [13] method was used in present work. G. Sovran [13] used
the tractive energy equation (1.11) to develop charts as plotted in Figure 1.12 to show the
impact of changes in the product of drag coefficient and projected area (𝐶𝐷 A) on the fuel
consumption based on EPA driving schedule. The charts can be used to determine the
reduction in fuel consumption, the equivalent reduction in weight of the vehicle and the
equivalent reduction in vehicle resistance coefficient for any given change in 𝐶𝐷 A. The
composite fuel economy for EPA driving 𝐹𝐸𝑐𝑜𝑚𝑏𝑖𝑛𝑒𝑑 is given by equation (4.8.1) as
𝐹𝐸𝑐𝑜𝑚𝑏𝑖𝑛𝑒𝑑 = 𝑚𝐶 =
1
0.55
0.45
𝐹𝐸𝑢𝑟𝑏𝑎𝑛 + 𝐹𝐸ℎ𝑖𝑔ℎ𝑤𝑎𝑦
(4.8.1)
Consider the 2007 Ford F-150 pickup 2WD and 4.2 liter engine. It has 16mpg
urban and 20mpg EPA rating. Assuming the curb weight of the generic pickup truck M =
91
2000 kg, tire rolling resistance coefficient 𝑟𝑜 = 0.009, using equation 4.8.1 and the EPA
rating of the Ford Truck mentioned above, the composite fuel economy 𝑚𝑐 would be
7.58 mpg. The 𝐶𝐷 A term for the baseline pickup truck is 0.97𝑚2 and for pickup truck
with the 3D curved aerocap, 𝐶𝐷 A is 0.778 m2. Therefore the percentage reduction in 𝐶𝐷 A
is 19.83 between the pickup truck with 3D curved aerocap and the baseline truck. The
term 𝐶𝐷 𝐴 ⁄𝑀 for the base line truck is 4.85E-04𝑚2 ⁄𝑘𝑔. Using G. Sovran's [1] chart in
Figure 1.12, the impact of a 19.83% reduction on the composite fuel economy is
summarized in Table 4.8.1 and the reduction in fuel consumption is 0.003 [𝑔𝑎𝑙𝑠⁄𝑚𝑖].
Vehicle Variables
Reduction in Fuel Consumption
Increase in Fuel Economy
Equivalent Reduction in Weight
Equivalent Reduction in Tire Rolling
Resistance Coefficient
Aerodynamic Drag Coefficient, 𝐶𝐷 = 0.3453
Frontal Area, 𝐴 = 2.809 𝑚2
Curb Weight, 𝑀 = 2000 𝑘𝑔
Tire Rolling Resistance Coefficient, 𝑟𝑜 = 0.009
Composite Fuel Economy, 𝑚𝐶 = 17.58 𝑚𝑝𝑔
City Fuel Economy, 16 mpg
Highway Fuel Economy, 20 mpg
𝐶𝐷 𝐴⁄𝑀 = 4.85 × 10−4 𝑚2 ⁄𝑘𝑔
%𝐶𝐷 𝐴
1
= 0.275 (
) ( ) = 0.003 [𝑔𝑎𝑙𝑠⁄𝑚𝑖]
100
𝑚𝐶
(6
⁄
)𝑚
=
100 𝐶 = 1.055 𝑚𝑝𝑔
%𝐶𝐷 𝐴
= 0.55 (
) 𝑀 = 218.13 𝑘𝑔
100
%𝐶𝐷 𝐴
= (𝑟𝑜 )1 − 2 (
) (𝑟𝑜 )1 = 0.0054
100
Table 4.8.1 Impact of 19.83% reduction in𝑪𝑫 A on Composite Fuel Economy using G. Sovran [5]
charts in Figure 1.12.
Average driver in U.S. drive about 15,000 miles annually and according to
Federal Highway Administration [18] in year 2005, 39,987,802 pickup trucks were
registered in U.S. that was close to 40 million. Assuming all the 40 million pickup trucks
in U.S. had installed 3D curved aerocap; 1,800,000,000 gallons of fuel will be saved.
92
About 46% of each barrel of crude oil is refined into automobile gasoline and one barrel
of crude oil yields 19.3 gallons of gasoline [22]. Thus the amount of crude oil which
could have been saved equates to 92.26 million barrels. Inflation adjusted average price
of a barrel of crude oil in 2005 was 55.21 dollars [21], and had all the pickup trucks
registered in 2005 installed the 3D curved aerocap the U.S. had saved about 5.09 billion
dollars every year. This is significant contribution.
93
Chapter 5
CONCLUSIONS AND FUTURE WORK
5.1 Conclusions
The effects of different aerodynamic add-on devices on flow and its structure over
a generic pickup were analyzed using CFD approach. The objective is to reduce
aerodynamic drag acting on the vehicle and thus improve the fuel efficiency as well as
reduce the carbon print of pickup trucks.
Flow over the generic pickup model was simulated using CFD and the results
from the simulation were validated against CFD results of flow over the same generic
model from Yang and Khalighi [1]. The results from present simulation was compared
with results from Yang and khalighi[1] in chapter 3 and the results were found to be in
complete agreement.
The thesis studied the flows over a pickup truck with add-on devices: (1) Tonneau
cover, (2) Rear Roof Garnish, (3) Tail plates, (4) Airdam with 3in and 6 in clearance
from ground, (5) Traditional canopy, Aerocap at 5 different rear inclination angles, and
(6) a 3D curved Aerocap. Table A1 in Appendix 1 shows the drag and lift coefficient of
the entire studied add-on devices. Except for Airdam with 6in clearance from the ground,
all the studied add-on devices reduced the drag coefficient when it was compared to the
result of baseline truck.
The maximum reduction of aerodynamic drag coefficient,𝐶𝐷 , was 19.84% which
was achieved by employing 3D curved Aerocap and it was followed by Aerocap α=12⁰ at
94
CD=16.24%, the second maximum reduction. The impact of the 3D curved Aerocap on
the fuel economy of the pickup truck was analyzed in section 4.8. It was concluded that
installing 3D curved Aerocap on baseline truck will save 0.003𝑔𝑎𝑙𝑠⁄𝑚𝑖.
In section 4.8 it was also tried to quantify the impact of drag reduction on the
composite fuel economy and the amount of barrels of crude oil or dollars it could save in
the U.S. Assuming all the 40 million pickup trucks registered in 2005 in U.S. had
installed 3D curved Aerocap, 1.8 billion gallons of fuel will be saved based on average
driving of 15,000 miles annually. If this was converted to the amount of crude oil
consumption and the amount of money to spend on it, having all the pickup trucks
installed the 3D curved Aerocap the U.S. would have saved about 5.09 billion dollars
every year.
The minimum reduction of aerodynamic drag coefficient, CD, was 0.35% which
was obtained by employing Airdam with 3in clearance from the ground. It was flowed by
Tonneau cover in drag reduction by 1.16% when it was compared with the results of
baseline truck. However, Airdam with 3 in clearance from the ground is not practical to
mount on pickup trucks unless a devise was coupled with a sensor which moves the
Airdam up and down when the road condition permits. Apart from practicality, drag
reduction achieved by the Airdam is very small to merit the cost and risk of bumping on
to objects on the road. On the other hand, the lift coefficient reduction achieved by
employing Airdam with 3in clearance from the ground was 326.45%. This indicates that
Airdams are very effective in reducing lift force acting on a vehicle. It was recommended
95
to install the airarm on race cars to increase the traction and handling, especially during
the process of maneuvering curves or driving on slippery roads.
5.2 Future work
Although maximum reduction of aerodynamic drag coefficient,𝐶𝐷 , was achieved
as by using 3D curved Aerocap in the present study, improvement of 3D curved Aerocap
to further reduce the aerodynamic drag can be made possible by using the optimization
software or using synergetic effect of aerodynamic devices such as Tail plates with the
3D curved Aerocap.
The flow over the generic pickup truck in present CFD simulation was simplified
due to hardware limitation, including that the side mirrors were removed and non-rotating
wheals were used. It was also assumed a steady flow of air with zero degree yaw angle.
However, in reality the flow over the vehicle is unsteady and very turbulent. The next
step would be conducting unsteady flow over a realistic pickup truck with optimized 3D
curved Aerocap. Besides combing with Tail plates, the research study could continue to
analyze the synergetic effect of employing Side skirts, Vortex generators or other
aerodynamic devices with the optimized 3D curved Aerocap. If it is possible, the
experimental test will be conducted after the add-on devices are built and mounted on a
pickup truck.
96
APPENDIX
Configurations
Baseline
Aerocap α=5°
Aerocap α=10°
Aerocap α=12°
Aerocap α=15°
Aerocap
α=18.77°
Traditional
canopy
Airdam -3in
Airdam-6in
Tail Plates
Rear Roof
Garnish
Tonneau Cover
3D curved
Aerocap
Drag
% 𝐶𝐷 diff. from
Lift
% 𝐶𝐿 diff. from
Coefficient
baseline
Coefficient Baseline
0.3453
0
0.2193
0
0.2957
-14.36432088
0.0497
-77.3369813
0.2894
-16.18882131
0.1097
-49.97720018
0.2892
-16.24674196
0.1579
-27.99817601
0.2987
-13.49551115
0.2296
4.696762426
0.3091
-10.48363742
0.3587
63.56589147
0.3157
0.3441
0.3661
0.3333
- 8.57
-0.35
6.03
-3.475238923
-0.4966
0.1393
0.1304
-326.45
-36.48
-40.5380757
0.337
0.3413
-2.403706922
-1.158412974
0.2916
0.1828
32.96853625
-16.64386685
A0.2768
-19.83782218
0.13
-40.72047424
Table A1 Drag and lift coefficient of all studied Add-on devises
97
REFERENCES
1. Yang, Z., and Khalighi, B., “CFD Simulation for Flow Over Pickup Trucks”,
SAE Paper No. 2005-01-0547, 2005.
2. Al-Garni, A., Bernal, L., and Khalighi, B., “Experimental investigation of the
Near Wake of a Pick-up Truck”, SAE Paper No. 2003-01-0651, 2003.
3. Cooper, K., “Pickup trucks Aerodynamics - Keep your tailgate Up”, SAE Paper
No. 2004-01-1146, 2004.
4. Mokhtar, W., Britcher, C., Camp, R.,”Further Analysis of Pickup trucks
Aerodynamics”, SAE Paper No. 2009-01-1161, 2009.
5.
“Aerodynamics of Road Vehicles”, Edited by Wolf-Heinrich Hucho, SAE
International, Warrendale, PA, 1998.
6. Barnard, R.H., “Road Vehicle Aerodynamic Design-An Introduction”, 2nd
Edition, Longman ISBN 0-582-24522-2, 1996.
7. White, F.M.,”Fluid Mechanics 4th Ed.” Boston. MA. WCB McGraw-Hill, 1999
8. Giancarlo Genta “Motor vehicle dynamics: modeling and simulation-Vol43”
World scientific Publishing Co. ISBN: 978-981-02-2911-5
9. U.S. Environmental Protection Agency
http://www.epa.gov/oms/fetrends.htm#appendixes
Accessed: October 20, 2009
10. U.S. Department of Energy
Energy Efficiency and Renewable Energy
http://www.fueleconomy.gov/feg/atv.shtml
11. Ahmed, S.R., “Computational Fluid Dynamics”, Chapter XV in Hucho, W.H
(Ed.), Aerodynamics of Road Vehicles, 4th Edition, SAE International,
Warrendale, PA, USA, 1998
12. Sovran, G., Bohn, M.S., “Formula for Tractive Energy Requirements of Vehicles
During the EPA-Schedules,” SAE Paper No. 810184, Society of Automotive
Engineers, Warrendale, Pa., 1981
98
13. Sovran, G., “Tractive Energy Based Formulae for the Impact of Aerodynamics on
Fuel Economy over the EPA-Driving Schedules,” SAE Paper No. 830304,
Society of Automotive Engineers, Warrendale, Pa., 1983
14. Thomas R. Yechout “Introduction to Aircraft Flight Mechanics AIAA Education
Series” American Institute of Aeronautics and Astronautics Inc, 2003
ISBN 1-56347-577-4
15. http://www.fueleconomy.gov/feg/FEG2007.pdf
Accessed: October 20, 2009
16. U.S. Department of Transportation
Federal Highway Administration
http://www.fhwa.dot.gov/policy/ohim/hs05/htm/mv9.htm
Accessed: October 20, 2009
17. Hucho, Wolf-Heinrich., Sovran, Gino.”Aerodynamics of Road Vehicles” Annual.
Reviews Inc. Fluid Mech. 1993.25 :485-537
18. http://www.fhwa.dot.gov/ohim/onh00/line2.htm.
Accessed: October 20, 2009
19. Jeff Howell, Adrian Gaylard," Improving SUV Aerodynamics", Motor Industry
Research association (MIRA) Technical Paper.
20. Munson, Young, Okiishi “Fundamentals of Fluid Mechanics 4th Edition” John
Wiley and Sons, 2002
21. http://www.inflationdata.com/inflation/Inflation_Rate/Historical_Oil_Prices_Tabl
e.asp
Accessed: October 20, 2009
22. http://www.californiagasprices.com/crude_products.aspx
Accessed: October 20, 2009