Abstract – Semi-trailer trucks are the backbone of any freight
system throughout the world. Annually, a large portion of the cargo is
transported through semi-trailer trucks. These trucks spend most of their
useable life traveling at motorway speeds. Most of the energy consumed by the trucks
is used to overcome the aerodynamic drag force. The power required to overcome
the drag force must be supplied by the truck’s powerplant. Therefore, it is of
the utmost importance to minimize the drag force. By using computational fluid
dynamics, it is shown in this paper that the application of curved plate below
the floor along with side-skirts on the semi-trailer truck can significantly
reduce the drag force. We show that by removing the exposure of the blunt
bodies on the underside of the semitrailer such as the axle, differential and
suspension components to the oncoming air considerably reduces the drag force
experienced by the semi-trailer truck. A reduction in the drag force will
directly result in improved energy consumption of the truck. An improved fuel
consumption would result in relatively cheaper goods for the consumers. An
improved fuel consumption will also lead to a reduction in the in the emission
of harmful gases, leading to greener and healthier environment.
I.
Introduction
It
is shown by the drag equation (equation 1) that, while moving through the air
the drag force relates directly to the square of an object’s velocity, for the
present study the object is a semi-trailer truck. As a result, the power
required from a truck’s powerplant to overcome the aerodynamic drag varies with
the cube of the truck’s velocity (equation 2). For example, a semi-trailer
truck cruising on a highway at 40 Km/h might require 10 bhp to overcome
aerodynamic drag, but that same truck now travelling at 80 Km/h would require 80
bhp from the truck’s powerplant. The powerplant can be an internal combustion
engine, batteries or a combination of both. In the usual real-world situations
for example, when the truck is moving into a headwind, the dependence of drag
force on velocity is even more critical. The headwind has to be added to the
velocity of the truck before the velocity is squared for the aerodynamic drag
calculation. Thus, it is very crucial to reduce the aerodynamic drag. It is
shown by research that up to 65% of the fuel is used to overcome aerodynamic
drag [17].
where
is
the aerodynamic drag force,
is
the fluid density,
is
the fluid velocity,
is
the surface area,
is
the drag coefficient and
is
the power required to overcome drag [18].
The
idea to reduce drag and/or improve downforce on a vehicle using various
aerodynamics devices such as side-skirts and fairings has been around for
decades. In this paper, we present an explanation as to why placing a flat
plate below the floor of the truck can be used to improve fuel economy. Crosswinds
have a high impact on semi-trailer trucks. Crosswinds lead to an increase in
the drag coefficient and direction instability which can lead to capsizing of
the trucks in some extreme cases. In this paper we also study the effect the
drag reduction devices in the case of a crosswind. Various passive flow control
methods have been implemented and are under consideration for the purpose of
drag reduction in semi-trailer trucks, as explained in the following
paragraphs.
As
a part of the research conducted by [3], experiments are conducted to study the
wake in various portions of a tractor-trailer. The locations of interest in
this study include the region at the back of tractor and front of trailer; and at
the back of trailer. The Generic Conventional Model (GCM) is the truck used in
this study. The modifications to the truck include a combination of side
extenders and the boat-shaped tail. Up to 60% reduction in drag coefficient is
noticed at higher yaw angles of around 10°. Various aerodynamics fuel saving
devices are tested experimentally by [6] on heavy vehicles, primarily
semi-trailer trucks. The results from wind tunnel experiments show that the
fairings and side coverings reduce aerodynamics drag by up to 26%. It is found
in this study that, among all the configurations tested, the modified truck
with a fairing in between cabin and the container and side covers cause a
maximum amount of reduction in the drag force.
Different
drag reduction devices have been numerically tested by [7] using commercially
available computational fluid dynamics (CFD) code STAR-CCM+. The results show
that the largest drag reduction is achieved for the under-carriage treatment.
The under-carriage treatment includes the addition of side-skirts, wheel covers
and complete underbody redesign. The study concluded that it is not beneficial
to change the shape of trailer, both aerodynamically and financially as simple
addon devices can be added to the tractor-trailer with equivalent effect.
Quantitatively, it is shown that side-skits and sealed wheels cause a maximum
reduction in the drag coefficient of up to 77%.
As
a part of this study [8], several devices to reduce drag force on class-8
tractor-trailers is analyzed. This study is completed via wind tunnel testing
of reduced scale models of the tractor-trailers. By combining various
aerodynamic devices, a reduction in the drag coefficient of 11.5% in the
highway fuel economy is noted. The wind averaged drag coefficient improvements
of 22 to 23% are observed for the aerodynamic (modified) trailer. The
modifications include the installation of a trailer forebody device and side
extenders of variable lengths.
Drag
reduction using platooning is analyzed numerically by [9] for semi-trailer
trucks. In this study, the effect of varying the offset of the trailing truck with
the leading truck and the linear distance between the trucks are investigated
in detail. It is found that platooning configuration in which the two trucks
are aligned with each other results in most drag reduction. The study also
concluded that as the distance between the trucks increases, the drag reduction
decreases. Furthermore, it is noted that the stagnation pressure on the rear
truck increases and the pressure at the rear of the front truck decreases as
the distance between the trucks increases.
Various
trailer attachments for the semi-trailer trucks are considered by [10] in
search of an optimal configuration w.r.t. maximum drag reduction. CFD software
Fluent is used to simulate flow around a Mercedes Benz Actros truck. The
results of the simulation show that adding relatively inexpensive addons to the
truck is more beneficial as compared with redesigning of the truck and trailer
bodies. A substantial increase in the fuel economy of 17.74% is noted.
Moreover, regions of low pressure behind the trailer are observed to have
reduced contribution to the stability of the truck.
Drag
reduction for Heavy Goods Vehicles (HGVs) is the subject of research conducted
by [11]. The drag reduction devices used in this research work include a boat
tail, a deflector and a fin. As a result of adding these modifications, the
drag coefficient decreased by 7.2%. As a part of research conducted in [12-13],
a deflector plate of variable height is designed and implemented on a
semi-trailer truck. Under the proposed control system, the adjustment to the
drag coefficient of the truck can be done online. Quantitively, when in the
optimized position, the deflector reduces drag coefficient by 7.4%. An
additional 2% reduction in drag coefficient takes place with the implementation
of an active system.
Vortex
generators are added to the rear of the semi-trailer trucks to investigate
their effects of the aerodynamics drag by [16]. The study is carried out
numerically using a commercially available CFD package. The authors investigate
size, location and geometry of the vortex generators. It is found that by the
addition of vortex generators, an increase in the surface pressure can be
observed. The vortex generators also reduce the amount of recirculation in the flow
in the aft of the vehicle. The results from this study indicate that drag can
be reduced by up to 10% by addition of these devices.
The
effects of investigating drag reduction by injection of a low velocity jet of
air near the floor of a vehicle is investigated by [19]. The effects of flow
rate and cavity position and distribution have been investigated. It is found
that a major portion of drag force reduction arises from the presence of a
cavity in the model. A drag reduction of up to 13% is achieved in this study
[19]. Various fuel-saving potentials of drag-reducing devices installed on
heavy vehicles are experimentally explored by [20]. The devices include a
combination of a cab roof and side fairings, trailer-front fairings, tractor
and trailer side-skirts, boat-tails and base-flaps, and gap splitters. It is
found that up to 9% of the fuel can be saved in case of a vehicle being driven
for an annual mileage of 80,000 miles. It is also found that vehicles operated
on motorway speeds save almost twice as much fuel as compared to the vehicles
being driver inside the cities.
We
explain our methods and modifications to the GCM in the methodology section. In
the results and discussion section we present our results while comparing the
two configurations both quantitatively and quantitively.
II.
Methodology
The GCM designed and developed by the National
Aeronautics and Space Administration (NASA) exclusively to examine in detail,
the semi-trailer truck aerodynamics is used as a validation case for this paper.
We analyze the GCM using a commercially available CFD code, Flow Simulation
Premium [14]. The Flow Simulation Premium employs cell-centered finite volume
method. The ΞΊ-Ξ΅ model with damping functions is used to model turbulence (equations
6-7). The solution algorithm employed is SIMPLE-R (modified). The
discretization of the convective terms is obtained by using the Upwind scheme
with second level order of accuracy. Meanwhile, the diffusive terms are
discretized using the Central-Differencing scheme. Time is discretized using
the implicit first order accurate Euler scheme. The Favre-averaged
Navier-Stokes equations (equation 3-5) are used to predict turbulent flows.
where,
is a mass-distributed external force per unit
mass due to a porous media resistance
, a buoyancy
is the gravitational acceleration component
along the i-th coordinate direction) and the coordinate system’s rotation
, i.e.,
[14]. The subscripts are used to denote
summation over the three coordinate directions. While,
and
are source terms. The
subscripts are used to denote summation over the three coordinate directions. The
simulations are performed to predict three-dimensional steady-state flow around
the GCM.
1.
Validation
and Verification
The data from [1-5, 15] is used for validate the
computational mesh for the present study. A thick flat plate is added on below
the wheels of the GCM to simulate the functionality of a road. Slip boundary
condition is applied to a portion of the flat plate to prevent a boundary layer
from forming at the leading edge of the flat plate while no-slip boundary
condition is applied to the portion of the flat plate directly under and after
the rear of the GCM to allow for the formation of the boundary layer. This is
done to keep the CFD simulation as close to the physically occurring phenomenon
as possible.
The slip region is marked by red squares in Fig. 1.
Far-field pressure conditions are applied to the boundaries of the
computational domain. The computational domain with the boundary conditions
applied is shown in Fig. 1. Within Fig. 1, the blue arrow represents the
direction of the ambient velocity, with no cross-wind. The ambient velocity is
kept at 115.875 mph (51.5 m s-1), similar to [2]. To study the
effect of the cross-wind, the ambient velocity direction is varied.
Fig. 1, Computational domain and the boundary
conditions
A Cartesian computational mesh with immersed boundary
method is employed in the present work. Separate mesh controls are employed to
refine the mesh in the areas of interest such as between the road and the truck
floor, the gap between the cabin rear and the container front, the wake of the
truck etc. to ensure solution accuracy. The mesh around the GCM is shown in
Fig. 2, along with the mesh of the GCM superimposed. It should be noted that
the results of the present simulations are within 4% of [1-5]. The drag
coefficient from the present simulations comes out to be 0.421 while the drag
coefficient from literature is 0.398 [1], 0.402 [2], 0.427 [3] and 0.399 [5], respectively.
This drag coefficient is for the case with no cross-winds. The drag coefficient
from the present simulations with cross-winds at 8° is at 0.759 while the values
from experimental data are at 0.725 [3] and 0.700 [5]. This places our
simulation results within 7% of the published experimental data, at high
cross-winds.
Fig. 2, The computational mesh
The streamwise velocity contour from the present
simulation is compared with the contours obtained from [3-4] in Fig. 3. It is
clear from Fig. 3 that the results from present simulation are in close
agreement with the previously published experimental and numerical simulation
results [3-4]. A comparison of the vertical velocity contours between
experimental data [3] and the present simulation is shown in Fig. 4. The
results are in also close agreement with each other. The location of the plots
w.r.t. semi-trailer truck, used in Fig. 3-4 is shown in Fig. 5.
Fig. 3, L-R, Streamwise velocity contours from literature.
Experimental [3], numerical simulation [4] and present study
Fig. 4, L-R, Streamwise velocities contours from experiments
[3] and present simulation
Fig. 5, L-R, Locations of the plots
2. Mesh
and Time Independence Test
The final mesh cell count is selected keeping under
consideration that a very negligible change is noticed in the drag coefficient
after increasing the cell count. It should also be noted that the amount of
core hours required to complete the solution with a higher cell count increase
considerably, as explained in the following paragraph.
The mesh employed in the validation of the numerical
simulation comprises of 2,113,458 cells. There are 224,741 cells on the truck’s
body. As a result of increasing the mesh cell count to 5,213,889 cells with 405,242
on the truck’s body, the drag coefficient improved by less than 1%, as compared
to the experimental data [1-3, 5] and the initial mesh. It should be noted that
the solution time for the mesh with a higher cell count is more than twice as
compared to the selected mesh. Keeping the initial mesh, a transient simulation
is performed to ensure that there are no transient effects in the study. It
should be noted that the difference in the drag coefficient from the transient
analysis and the steady-state simulation is less than 1%. An initial time-step
of 6.95e-6 s employed for the transient analysis is gradually
increased to 3.39e-1 s, as the solution approached the steady-state.
It should be noted that the simulations employing an adaptive time-step are, by
their nature, time-step independent.
3.
Modification
to the GCM
The proposed plate along with side-skirts is added at
the bottom of the truck’s floor, in a single assembly. The added plate
completely covers the blunt and drag producing components on the sides and the underside
of the truck. The modification is shown in as shown in Fig. 6.
Fig. 6, T-B, GCM and the modified GCM geometry
III.
Results and
Discussion
The
numerical simulations predict that the baseline configuration produces 8.36%
more drag than the modified configuration. This improvement is noted at the
highway cruise speed and without any crosswinds. At the higher yaw angle, the
baseline configuration is predicted to have 6.3% more drag as compared to the
modified configuration. Thus, the addition of a simple and cost-effective passive
flow control device i.e. a flat plate with side skirts, has the potential to
significantly improve heavy vehicle fuel economy at a variety of flow
conditions.
The
qualitative results from the numerical simulations are presented in this
section. The three major fluid properties of interest discussed include
vorticity, pressure and velocity. At first, we present the results at
zero-degree yaw angle followed by a discussion at the higher yaw angle.
1.
Reduced Vorticity
The
contours showing vorticity magnitude superimposed by the velocity streamlines
are plotted in Fig. 7. The contours are plotted along the centerline of the GCM.
The direction of the flow is from the left to right of the reader. The scale
within Fig. 7 ranges from 0 – 1,000 s-1. The differences in
vorticity are quite clear. The large amounts of flow separation in the GSM
without modifications is evident at two important locations. The first region
where the flow separates is at the position where the tractor body meets with the
trailer section. A large vortex of magnitude ~500 s-1 can be seen in
the baseline GCM while the same vortex is absent in the modified GCM. The
addition of the flat plate below the floor of the GCM forms a continuous wall
below the modified tractor-trailer thus eliminating the blunt backward-facing
step like geometry from the flow path. This results in the elimination of the
vortex, which in turn leads to reduced drag force.
The
second location where vortex formation takes place below the baseline tractor-trailer
can be seen at the locations where fluid interacts with the blunt bodies like
axle, differential and suspension assemblies. In the baseline tractor-trailer
the vortices of magnitude ~1000 s-1 can be seen in the wake of the rear
axles. While at the same locations in the modified GCM, no such vortices can be
observed. The addition of flat plate removes, shields, these bluff bodies from the flow path thus contributing
towards reducing the drag force. It should be noted that the various small
vortices observed in the modified configuration have significantly less
strength as compared to the one’s observed in the baseline configuration.
This
effect can be clearly observed in Fig. 8. Within Fig. 8, the normalized
vorticity is plotted against normalized trailer length. The starting point on
the x-axis represents the point where the tractor body ends and the trailer
body starts. The line is plotted horizontally, along the center of the axles of
the tractor-trailer. The two rises in the vorticity for the baseline
configuration are the two axles. It should be noted that these axles are
shielded from the oncoming airflow by addition of the flat plate in the
modified configuration, hence the missing peaks in vorticity.
Fig. 7, T-B, GCM and the modified GCM
Fig. 8, T-B, GCM and the modified GCM
The
vorticity around the axis normal to the road, superimposed by velocity
streamlines is shown in Fig. 9. The scale in Fig. 9 ranges from -500 to 500 s-1.
The images in Fig. 9 are taken in a plane along the center of the axle of the
two configurations and parallel to the road. It can be seen from Fig. 9 that
the addition of the flat plate below the eliminates the pair of large and high
energy vortices from behind the tractor body in the modified configuration. The
magnitude of vorticity is also low for the modified configuration as compared
to the baseline configuration at the rear of the trailer, specially near the
axles and suspensions components. The reduction in size and strength of
unwanted flow separation leads to less drag force on the modified GCM as
compared to the baseline GCM, even in the case of a crosswind.
Fig. 9, L-R, GCM and the modified GCM
2.
Reduced Stagnation Pressure and
Pressure Difference
In terms of the pressure field around the two
configurations, three major differences can be observed between the baseline
and the modified configurations.
The contours of relative pressure are shown in Fig. 10.
The zoomed in view of the area of interest is shown in Fig. 11. The location of
the contours is same as in Fig. 7. The scale in Fig. 10-11 ranges from -500 – 200
Pa. The bluff bodies, rear axles in this
case, can be clearly seen to have their own stagnation regions marked by
high relative pressure as these bodies are directly in the path of the flow. This
phenomenon contributes towards the pressure drag. While the pressure distribution
in the same regions in the modified GCM configuration is much more uniform.
This reduces the pressure drag component of the total drag and thus contributes
to the overall drag reduction observed in the case of the modified GCM
configuration.
It can also be noted from Fig. 10 that the region of
relatively high-pressure at the aft and below the centerline of the baseline
configuration is far away from the body of the GCM. Meanwhile, in the
configuration with the plate installed at the bottom of the tractor-trailer
floor, the high-pressure region moves closer to the body of the GCM. This helps
to reduce the over all pressure difference between the rear and front of the
GCM. Thus, contributing to the reduction in drag force. As shown in Fig. 12, more
pressure for the modified configuration indicates less pressure difference
between front and rear of the tractor-trailer assembly, resulting in less drag
force.
The pressure difference between the top and bottom of
the GCM can also be clearly seen in Fig. 10. The higher-pressure difference
creates a net lift force which is more in the modified configuration as
compared to the baseline configuration. This phenomenon has two advantages. One
being the less load on the suspension of the modified GCM, increasing the
service life of the vehicle’s suspension. The other one being, the modified GCM
being able to carry additional load, equivalent
to the lift produced, while consuming less amount of fuel than the baseline
configuration.
As is the case with no cross-winds, the addition of
the plate at the bottom of the tractor-trailer completely eliminates the
stagnation zones at the rear of the trailer in the case with the cross-winds as
well. The pressure difference between rear and the front of the tractor-trailer
assembly is also reduced. The pressure difference is compared using the relative
pressure and is shown in Fig. 13. The scale for Fig. 13 is same as is for Fig.
10-11.
Fig. 10, T-B, GCM and the modified GCM
Fig. 11, T-B, GCM and the modified GCM
Fig. 12, The relative pressure plots
Fig. 13, The relative pressure plots
3.
Improved Momentum of the Flow
The
contours of the component of velocity in the direction of flow is presented in Fig.
14. The scale used in Fig. 14 ranges from -55, dark blue, to -1 m/s, red,
which is similar to scale chosen by [3]. The location of contours in Fig. 14 is
in the wake of the trailer. It can be seen that magnitude of the component of
velocity in the direction of flow is more in the case of modified configuration
as compared to the baseline configuration. This is indicated by the less amount
of region colored red in the wake of the trailer. The flow on the underside of
the GCM in the modified configuration is able to maintain significantly more
momentum in the desired direction. This less amount of restriction to the
oncoming flow is because of the plate that has been added in the modified
configuration. The component of velocity in the direction of flow is plotted in
the wake of the semi-trailer truck in Fig. 15, confirming the phenomenon. The
negative sign within Fig. 15 indicates the magnitude of velocity in the
negative – z direction i.e. the direction of flow.
Fig. 14, L-R, GCM, modified GCM
Fig. 15, Significantly more momentum in the flow for
the modified configuration
The
streamwise velocity superimposed by streamlines is shown in Fig. 16. The scale
within Fig. 16 ranges from -86, blue,
to 30 m/s, red. The location of the
images shown in Fig. 16 is same as that of Fig. 9. The streamwise flow within
Fig. 16 is from the bottom to top. It can be said that the addition of the
plate below the tractor-trailer delays stall. It can be seen form Fig. 16 that the
size of vortices in the case of the modified configuration is significantly
less in the wake of the right wheel assembly, wake of the trailer and around
the bluff bodies. The vortex beside the right wheel of the baseline
configuration for example, has size of ~0.06w where w is the width of the
trailer. Meanwhile, at the same location, the vortex is nonexistent in the
modified configuration and the flow is directed in the streamwise direction. The
vortices in the wake of the trailer beside the right wheel and the bluff bodies
i.e. suspension and axle assemblies, are almost completely eliminated as a
result of the proposed modification. Meanwhile, the vortices in the wake of the
tractor are also significantly reduced. The bulk of the flow in the wake of the
tractor-trailer can be clearly seen to have been directed towards the streamwise
flow. This reduced flow separation results in less drag force in the modified
configuration.
Fig. 16, L-R, GCM, modified GCM
Conclusion
In the present study we propose the addition of flat plate
with side-skirts plate to shield bluff bodies present on the underside of the
semi-trailer trucks from the oncoming flow. CFD simulations predict a drag
reduction of 7.71% in the modified GCM as compared to the baseline design. The
CFD simulations also predict that the addition of flat plate would also mitigate
the drag force in case of cross-winds. A reduction of up to 5.92% reduction of
drag is predicted by the CFD simulations for the case with a cross-wind. The
reduction in drag force in the modified GCM configuration as compared to the
baseline configuration can be attributed to the reduced vorticity, a reduced
pressure difference between front and rear of the truck and in general a more
streamlined flow in the underside of the modified truck. The reduction in drag
force would directly result in a reduced fuel requirement by the vehicle’s
engine. This
research has special significance for author’s home country where a number of light
and heavy-duty commercial vehicles would benefit from the implementation of the
proposed changes to the semi-trailer truck body work. This research can easily
be expanded to include smaller vehicles like the 4-6 wheelers and even 18-wheeler
heavy vehicles, which form the back bone of transport within the many countries
throughout the world.
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