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Subject: Computer-Based Analytical Tools B Student: Rodrigo Folgueira Lecturer: Dr Xiaogang Yang
TURBULENT FLOW AROUND A LORRY
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INDEX
1.- Abstract .................................................................................................................................... 3
2.- Introduction............................................................................................................................... 4
3.- Background Theory .................................................................................................................. 5
3.1.- Turbulence ........................................................................................................................ 5
3.2.- CFD ................................................................................................................................... 6
3.3.- Fluid Mechanics ................................................................................................................ 7
3.4.- Pressure ............................................................................................................................ 7
3.4.1 Dynamic pressure ......................................................................................................... 8
3.5.- Viscosity ............................................................................................................................ 8
3.6.- Reynolds Number ............................................................................................................. 9
3.7.- Turbulent Kinetic Energy ..................................................................................................... 10
3.8.- Drag ................................................................................................................................. 11
3.8.1.- Drag Force ................................................................................................................ 11
3.8.2.- Drag coefficient ......................................................................................................... 11
4.- Methodology ........................................................................................................................... 13
4.1.-Specifying the geometry of the problem .......................................................................... 13
4.1.1.- Lorry without modifications ....................................................................................... 13
4.1.2.- Definitive lorry ........................................................................................................... 13
4.2.- Boundary Conditions ....................................................................................................... 14
5.- Result comments and discussions ......................................................................................... 16
5.1.- Static Presure .................................................................................................................. 16
5.2.- Dynamic pressure ........................................................................................................... 18
5.3.- Total pressure ................................................................................................................. 20
5.4.- Velocity magnitude - Velocity vectors ............................................................................. 22
5.5.- Turbulence intensity ........................................................................................................ 24
6.- Conclusions ............................................................................................................................ 26
7.- References ............................................................................................................................. 27
TURBULENT FLOW AROUND A LORRY
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1.- Abstract
This report consists in the analysis of the turbulence flow around a lorry.
The aim of this project is to design different models of a lorry that offer less
aerodynamic drag compared with the original. The first model is designed in
Gambit and solved in Fluent program. The second and definitive lorry is
designed in AutoCAD Inventor 2011.
The aim of the project is to make a comparison between the data obtained in
the study of both lorries.
In the back of the truck there is a separation of flow and this creates a low
pressure area. Spoilers are used to create high pressure in the back and reduce
the pressure difference on both sides.
The models are placed in wind tunnels to study airflow; we study the flow on the
sides and up the model for a study of flow in the bottom.
The purpose of the project is to reduce the high and the low pressure behind
the lorries to obtain a model with less amount of drag and fuel economy edible.
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2.- Introduction
During this research project is an attempt to reduce aerodynamic drag on lorries
using numerical simulation methods and analyzing the aerodynamic flow.
In the front of the lorry, the incoming air undergoes a series of steps-stagnation,
deceleration and increased pressure. There are parts of the flow that remain in
the truck while others fall below it.
The air moves over the truck and slides down the hood, but when it comes to
the windshield base undergoes a great change of direction. Then suddenly
drops behind the cab. At this point the lorry, the air pulse is usually not enough
to keep the air flow and separates the flow over the trailer. This causes low
pressure created over the back. This effect continues throughout the trunk of
the truck to get to the back where it comes with low pressure.
In the front area creates a high pressure area and vice versa, at the back of the
truck creates a low pressure area, there is a pressure difference is what creates
a driving force called drag.
Another force that is created is called drag that is created due to the stagnation
under the lorry that creates a net force along the lorry.
Both forces increase with increasing speed of the lorry.
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3.- Background Theory
3.1.- Turbulence
In fluid dynamics, turbulence or turbulent flow is a fluid regime characterized by
chaotic, stochastic property changes. This includes low momentum diffusion,
high momentum convection, and rapid variation of pressure and velocity in
space and time. While there is no
theorem relating Reynolds number
to turbulence, flows with high
Reynolds numbers usually become
turbulent, while those with low
Reynolds numbers usually remain
laminar. For pipe flow, a Reynolds
number above about 4000 will most
likely correspond to turbulent flow,
while a Reynold's number below
2100 indicates laminar flow. The
region in between (2100 < Re < 4000) is called the transition region. In turbulent
flow, unsteady vortices appear on many scales and interact with each other.
Drag due to boundary layer skin friction increases. The structure and location of
boundary layer separation often changes, sometimes resulting in a reduction of
overall drag. Although laminar-turbulent transition is not governed by Reynolds
number, the same transition occurs if the size of the object is gradually
increased, or the viscosity of the fluid is decreased, or if the density of the fluid
is increased.
TURBULENT FLOW AROUND A LORRY
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3.2.- CFD
The computational fluid dynamics (CFD) is a branch of fluid mechanics that
uses numerical methods and algorithms to solve and analyze problems on the
flow of substances. Computers are used to perform millions of calculations
required to simulate the interaction of fluids and gases with surfaces designed
for engineering complex. Even with simplified equations and high-performance
supercomputers, only approximate results can be achieved in many cases.
Ongoing research, however, allows the incorporation of software that reduces
the speed of calculation as well as the margin of error in analyzing situations
while allowing more complex fluids such as transonic and turbulent flows. The
verification of the data obtained by CFD is usually carried out in wind tunnels or
other physical scale models.
TURBULENT FLOW AROUND A LORRY
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3.3.- Fluid Mechanics
Fluid mechanics is the study of fluids and the forces on them.
Fluid mechanics can be mathematically complex. Sometimes it can best be
solved by numerical methods, typically using computers. A modern discipline,
called computational fluid dynamics (CFD), is devoted to this approach to
solving fluid mechanics problems.
The study of fluids - liquids and gases. Involves various properties of the fluid,
such as velocity, pressure, density and temperature, as functions of space and
time.
3.4.- Pressure
Pressure is defined as force per unit area. It is usually more convenient to use
pressure rather than force to describe the influences upon fluid behavior. The
standard unit for pressure is the Pascal, which is a Newton per square meter.
TURBULENT FLOW AROUND A LORRY
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3.4.1 Dynamic pressure
In incompressible fluid dynamics dynamic pressure (indicated with q, or Q, and
sometimes called velocity pressure) is the quantity defined by:[1]
where :
= dynamic pressure in pascals,
= fluid density in kg/m3 (e.g. density of air),
= fluid velocity in m/s.
Dynamic pressure is closely related to the kinetic energy of a fluid particle, since
both quantities are proportional to the particle's mass and square of the velocity.
Dynamic pressure is in fact one of the terms of Bernoulli's equation, which is
essentially an equation of energy conservation for a fluid in motion. Another
important aspect of dynamic pressure is that, as dimensional analysis shows,
the aerodynamic stress experienced by an aircraft traveling at speed “v” is
proportional to the air density and square of “v”, in others words proportional to
“q”.
3.5.- Viscosity
Informally, viscosity is the quantity that describes a fluid's resistance to flow.
Fluids resist the relative motion of immersed objects through them as well as to
the motion of layers with differing velocities within them.
The more usual form of this relationship, called Newton's equation, states that
the resulting shear of a fluid is directly proportional to the force applied and
TURBULENT FLOW AROUND A LORRY
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inversely proportional to its viscosity. The similarity to Newton's second law of
motion (F = ma) should be apparent.
The SI unit of viscosity is the pascal second [Pa s], which has no special name.
Despite its self-proclaimed title as an international system, the International
System of Units has had very little international impact on viscosity.
3.6.- Reynolds Number
Reynolds number can be defined for a number of different situations where a
fluid is in relative motion to a. These definitions generally include the fluid
properties of density and viscosity, plus a velocity and characteristic dimension.
This dimension is a matter of convention - for example a radius or diameter are
equally valid for spheres or circles, but one is chosen by convention.
For aircraft or ships, the length or width can be used. For flow in a pipe or a
sphere moving in a fluid the internal diameter is generally used today. For fluids
of variable density (e.g. compressible gases) or variable viscosity (non-
Newtonian fluids) special rules apply. The velocity may also be a matter of
convention in some circumstances, notably stirred vessels.
where:
is the mean fluid velocity (SI units: m/s)
TURBULENT FLOW AROUND A LORRY
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L is a characteristic linear dimension, (traveled length of fluid, or
hydraulic diameter when dealing with river systems) (m)
μ is the dynamic viscosity of the fluid (Pa·s or N·s/m² or kg/(m·s))
ν is the kinematic viscosity (ν = μ / ρ) (m²/s)
is the density of the fluid (kg/m³)
3.7.- Turbulent Kinetic Energy
In fluid dynamics, turbulence kinetic energy (TKE) is the mean kinetic energy
per unit mass associated with eddies in turbulent flow.
In Reynolds-averaged Navier Stokes equations, the turbulence kinetic energy
can be calculated based on the closure method, turbulence model. Generally,
the TKE can be quantified by the mean of the turbulence normal stresses:
TKE can be produced by fluid shear, friction or buoyancy, or through external
forcing at low-frequency eddie scales(integral scale). Turbulence kinetic energy
is then transferred down the turbulence energy cascade, and is dissipated by
viscous forces at the Kolmogorov scale. This process of production, transport
and dissipation can be expressed as:
where:
Dk / Dt is the mean-flow material derivative of TKE;
is the turbulence transport of TKE;
P is the production of TKE, and
ε is the TKE dissipation.
TURBULENT FLOW AROUND A LORRY
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3.8.- Drag
3.8.1.- Drag Force
The surrounding fluid exerts pressure forces and viscous forces on an object.
The drag force is due to the pressure and shear forces acting on the surface of
the object. In order to predict the drag on an object correctly, we need to
correctly predict the pressure field and the surface shear stress.
3.8.2.- Drag coefficient
The drag coefficient expresses the drag of an object in a moving fluid
Any object moving through a fluid experiences drag - the net force in the
direction of flow due to pressure and shear stress forces on the surface of the
object.
Drag force can be expressed as:
Fd = cd 1/2 ρ v2 A ; where:
TURBULENT FLOW AROUND A LORRY
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Fd = drag force (N)
cd = drag coefficient
ρ = density of fluid
v = flow velocity
A = characteristic frontal area of the body
The drag coefficient is a function of several parameters like shape of the body,
Reynolds Number for the flow, Froude number, Mach Number and Roughness
of the Surface.
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4.- Methodology
4.1.-Specifying the geometry of the problem
To specifying the geometry of the problem, we have to take into account the
critical flow regions for drag.
4.1.1.- Lorry without modifications
The geometry of the first model, is a really simple geometry and is designed in
gambit. The lorry has a cabin and a trailer that are independent each other.
Dimensions for the cabin: 1.8 m length and 3 m tall.
Dimensions for the trailer: 13.5 m length and 4.5 m tall.
4.1.2.- Definitive lorry
The design and geometry of the definitive lorry is the most complex. It has been
designed with AutoCAD Inventor 2011 as the second one.
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We can see the design in this figure:
4.2.- Boundary Conditions
The lorry is placed at the center of a wind tunnel at a distance “X” enough large
to facilitate steady flow around vehicle. This “X” distance will be 30 meters in
our case. Increasing these distance only changes the computational time, it
does not change any other results.
The distance from the bottom to the underbody of the lorry is 075 meters and
the distance from the cabin to the trailer is one meter by the standard version of
the construction.
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The lorry speed was set to 22.2 m/s to 80 km/h.
The first model and the last and definitive one lorries has been designed by
AutoCAD Inventor 2011 and then, the files were imported into Gambit.
The size of the lorry I meters and the tunnel channel has 106.3 meters length,
30 meters high and 15 meters width. The width of the lorry is 3 meters.
After creating the air channel, it is necessary to import the files fron the Aucad
Inventor. After creating the boundary conditions in Gambit the files are imported
to Fluent.
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5.- Result comments and discussions
This are the different results obtained with the different models that have been designed:
5.1.- Static Presure
Especially in the cabin, but also in the trailer you can see that there is a
stagnation of flow velocity decreases and increases with pressure.
High pressures are responsible for the drag.
Static Pressure of the lorry without modifications in 3D.
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Static Pressure of the definitive lorry in 3D
It is possible to observe which the static pressure in the first improved
aerodynamics of the lorry is lower than the lorry without modifications.
Static Pressure Comparison among the two different lorries.
Lorry without modifications Definitive lorry
Max Static Pressure (N/m2) 341 334
Min Static Pressure (N/m2) -358 -474
TURBULENT FLOW AROUND A LORRY
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5.2.- Dynamic pressure
You can see that the highest value of the dynamic pressure is at the top of the
trailer. In the front of the cabin and in the end of the lorry is concentrated the
smaller dynamic pressure.
Dynamic Pressure of the lorry without modifications in 3D.
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Dynamic Pressure of the definitive lorry in 3D
Lorry without modifications Definitive lorry
Max Dynamic Pressure (N/m2) 389 504
Min Dynamic Pressure (N/m2) 1.30 3.22
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5.3.- Total pressure
The total pressure in the first improved aerodynamics of the lorry is lower than
the lorry without modifications.
Total Pressure of the lorry without modifications in 3D.
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Total Pressure of the definitive lorry in 3D
Lorry without modifications Definitive lorry
Max Total Pressure (N/m2) 367 356
Min Total Pressure (N/m2) -250 -94.6
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5.4.- Velocity magnitude - Velocity vectors
We show that the aerodynamics in the first lorry with no modifications is less
than in the definitive lorry.
It is noted that the final truck is better than the first in terms of the velocity vector
magnitude.
Velocity vectors of the lorry without modifications in 3D.
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Total Pressure of the definitive lorry in 3D
Lorry without modifications Definitive lorry
Max Velocity magnitude
vectors (m/s) 28.6 30.3
Min Velocity magnitude
vectors (m/s) 34.3 1.2
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5.5.- Turbulence intensity
It is possible to observe that the Definitive lorry has been improved in the issue
of the turbulences.
Turbulence intensity of the lorry without modifications in 3D.
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Turbulent intensity of the definitive lorry in 3D
Lorry without modifications Definitive lorry
Turbulent Intensity (m/s) 21.3 25
Turbulent Intensity (m/s) 1.77 23.6
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6.- Conclusions
In this project, we have studied the drag reduction by different systems and
devices. This report presents the results of the study of a lorry, the drag
coefficient and flow in the near wake.
Noting the study of the behavior of turbulence, taking the points where they
were the higher pressures in different parts of the lorry, you can analyze what
parts of the geometry of the lorry significantly increased the drag coefficient.
The following conclusions are drawn:
There is a region of stagnation pressure in front of the lorry, at the corner
of the front of the lorry is high speed and low pressure flow and this is the
same case in the top of the cab.
It is shown that there is a large formation of turbulence at the base of the
trailer, dramatically increasing the drag coefficient. This base has been
modified, reducing turbulence and drag coefficient.
Under the lorry, the surface distribution of pressure shows the desired
behavior. The local pressure is round about static pressure environment.
It has been decreased the space between the cab and trailer, thus
reducing possible turbulence in the gap. It also tilts the front of the truck
and added a spoiler for the same purpose.
Finally, it is possible to say that the aim of this project has been reached and I
have obtain a model with lest amount of drag so that it gives fuel economy
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7.- References
Internet
o Fluid mechanics: http://www.engineeringtoolbox.com/fluid-mechanics-t_21.html
o http://hyperphysics.phy-astr.gsu.edu/hbase/press.html
o Viscosity: http://physics.info/viscosity/
o Drag coefficient: http://www.engineeringtoolbox.com/drag-
coefficient-d_627.html
o Wikipedia
Turbulence: http://en.wikipedia.org/wiki/Turbulence
Computacional Fluid Dynamics: http://es.wikipedia.org/wiki/Dinamica_de_fluidos_computacional
Fluid mechanics:
http://en.wikipedia.org/wiki/Fluid_mechanics
Reynolds Number: http://en.wikipedia.org/wiki/Reynolds_number
Turbulent Kinetic Energy:
http://en.wikipedia.org/wiki/Turbulent_kinetic_energy
Dynamic Pressure: http://en.wikipedia.org/wiki/Dynamic_pressure
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