Subject: Computer-Based Analytical Tools B Student: Rodrigo Folgueira Lecturer: Dr Xiaogang Yang

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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

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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.

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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.

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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.

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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

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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)

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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.

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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:

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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

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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