CFD Analysis of the Characteristics of a Shrouded Turbine

Ganis, Maximilian Ludwig

CFD Analysis of the Characteristics of a Shrouded Turbine

Zusammenfassung

Inhaltsangabe:Abstract:
Wind energy is an increasingly import source of renewable, clean energy. In spite of this, only the methods and the materials of construction have improved over time, while the basic working principle of the wind turbine is still the same as it was centuries ago. In this thesis we have increased the power of a wind turbine by a factor of 4 in a fluid dynamic simulation, using a very simple external shroud system.
We have also extended the theory of wind turbines (limit of Betz), to include this new kind of device and show why past attempts to augment the power of a wind turbine by means of shroud systems have failed.
A detailed analysis of the device and its functioning principle is presented in this thesis - optimization studies need to be done in the future.

Inhaltsverzeichnis:Table of Contents:
AbstractI
IndexII
List of FiguresIV
List of SymbolsVI
Introduction1
1.Theory of Wind Turbines5
1.1Introduction5
1.2The Betz Law6
1.3Aerodynamics of the rotor13
1.4Rotor Power Characteristics18
1.5Number of Rotor Blades20
1.6Horizontal Axis Wind Turbines (HAWT)22
1.7Shrouded / Ducted Wind Turbines28
1.7.1Ducted Rotor29
1.7.2Turbine with a Diffuser Duct29
2.Methodology33
2.1Introduction33
2.2Computational Domain34
2.3Computational Code41
2.3.1Conservation Equations42
2.3.2K-Epsilon Turbulence Model43
2.3.3Discretization of the Conservation Equations45
2.4MFR - Multiple Frame of Reference45
2.5Parallel Processing46
2.6Simulations47
3.Results48
3.1Introduction48
3.2Conventional Turbine49
3.2.1Velocity Field49
3.2.2Static Pressure Field52
3.2.3Total Pressure Field53
3.2.4Power of the Conventional Turbine55
3.2.5Energy and Momentum Transfer57
3.3Shrouded Turbine59
3.3.1Velocity Field59
3.3.2Static Pressure Field62
3.3.3Total Pressure Field63
3.3.4Power of the Shrouded Turbine65
3.3.5Energy and Momentum Transfer66
3.3.6The Betz Limit68
3.3.7Cross Check Analysis with Traditional Shrouded Turbines69
Conclusions72
Bibliography73
Acknowledgments

Leseprobe

Inhaltsverzeichnis

ID 7044

Maximilian Ludwig Ganis

CFD Analysis of the Characteristics

of a Shrouded Turbine

Diplomarbeit

an der UNIVERSITÀ DEGLI STUDI DI UDINE

Fachbereich Faculty of Engineering

National Institute for Nuclear Physics/Department of Physics of Udine

Juni 2003 Abgabe

ID 7044

Ganis, Maximilian Ludwig: CFD Analysis of the Characteristics of a Shrouded Turbine

Hamburg: Diplomica GmbH, 2003

Zugl.: Fachhochschule Südwestfalen, Universität, Diplomarbeit, 2003

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Abstract

L'energia elettrica è un elemento indispensabile per lo sviluppo e il mantenimento

della società moderna. Il fabbisogno energetico dipende in modo molto forte da fonti

di energia non rinnovabili, ma l'attuale tasso di consumo delle fonti fossili fa

presumere un loro esaurimento nel giro di alcuni decenni. Per questo motivo le

risorse rinnovabili, quali energia solare, eolica e geotermica, stanno riscuotendo un

grande interesse da parte della ricerca scientifica e di quella industriale.

L'energia eolica è fra le fonti di energia rinnovabili su cui si sta investendo

maggiormente poiché è pulita, disponibile in grandi quantità e soprattutto economica.

Forti di studi teorici iniziati quasi cento anni fa congiunti con recenti sviluppi

tecnologici atti ad aumentarne l'efficienza, gli impianti a turbine eoliche sono oggi

una risorsa energetica di primaria importanza nell'ambito delle fonti alternative.

L'incremento della potenza di una turbina eolica può essere ottenuto non solo

aumentando l'area spazzata dal suo rotore ma anche applicando un profilo statorico

alla sua struttura. L'ottimizzazione della struttura statorica comporterebbe notevoli

vantaggi dal punto di vista del costo (l'investimento per metro quadro di rotore è

notevolmente superiore a quello dello statore) e dal punto di vista della realizzazione

(ingombri minori dell'intera macchina e sollecitazioni minori sugli organi

meccanici).

Lo scopo di questa tesi è la valutazione tramite analisi numerica dell'incremento di

potenza di una turbina convenzionale grazie all'applicazione di una struttura statorica

di piccole dimensioni. L'interpretazione dei risultati verrà fatta utilizzando le leggi di

conservazione dell'energia e della quantità di moto presenti nella teoria di Betz, e

analizzando le grandezze microscopiche (campi di moto e campo di pressione) e

macroscopiche (potenza, portata, energia trasportata e quantità di moto).

Index

Abstract I

Index II

List of Figures IV

List of Symbols VI

Introduction...1

Chapter 1: Theory of Wind Turbines...5

1.0 Introduction...5

1.1 The Betz Law...6

1.2 Aerodynamics of the rotor...13

1.3 Rotor Power Characteristics...18

1.4 Number of Rotor Blades...20

1.5 Horizontal Axis Wind Turbines (HAWT)...22

1.6 Shrouded / Ducted Wind Turbines...28

1.6.1 Ducted Rotor...29

1.6.2 Turbine with a Diffuser Duct...29

Chapter 2: Methodology...33

2.0 Introduction...33

2.1 Computational Domain...34

2.2 Computational Code...41

2.2.1 Conservation Equations...42

2.2.2 K- Turbulence Model...43

INDICE

III

2.2.3 Discretization of the Conservation Equations...45

2.3 MFR - Multiple Frame of Reference...45

2.4 Parallel Processing...46

2.5 Simulations...47

Cap 3: Results...48

3.0 Introduction...48

3.1 Conventional Turbine...49

3.1.1 Velocity Field...49

3.1.2 Static Pressure Field...52

3.1.3 Total Pressure Field...53

3.1.4 Power of the Conventional Turbine...55

3.1.5 Energy and Momentum Transfer...57

3.2 Shrouded Turbine...59

3.2.1 Velocity Field...59

3.2.2 Static Pressure Field...62

3.2.3 Total Pressure Field...63

3.2.4 Power of the Shrouded Turbine...65

3.2.5 Energy and Momentum Transfer...66

3.2.6 The Betz Limit...68

3.2.7 Cross Check Analysis with Traditional Shrouded Turbines...69

Conclusions...72

Bibliography...73

Acknowledgments

List of Figures

Chapter 1

1.0 Wind-Rotor

System... 5

1.1 Horizontal Axis Pressure Variation...

1.2 Wind-Rotor Stream Tube...

1.3 Power coefficient and efficiency curves as a function of a... 12

1.4 High and low pressure zones on an airfoil...

1.5 Velocity

Triangles...

1.6 Decomposition of the lift and drag forces... 15

1.7 Strip Theory... 16

1.8 Characteristic Curve Approximation... 17

1.9 Schematics of a typical horizontal axis wind turbine... 19

1.10 Power characteristics for the most common HAWT... 19

1.11 Power characteristics variation as a function of the number blades... 20

1.12 One, two and three blade horizontal axis wind turbines... 22

1.13 Lattice pole HAWT... 23

1.14 Guyed tower HAWT... 23

1.15 Self-supporting steel-tube tower HAWT's... 24

1.16 Cantilever self-supporting steel-tubes towers in construction... 24

1.17 Variation in height for different HAWT's... 25

1.18 Different HAWT configurations... 26

1.19 CG Image of the Maxi Vortec Shrouded wind turbine... 28

1.20 CG Image of a shrouded wind turbine plant... 28

1.21 Shrouded Wind Turbine... 29

1.22 Wind turbine with diffuser... 29

1.23 Electrical output vs. free stream velocity of shrouded wind turbine... 30

1.24 Prototype of the first experimental shrouded turbine... 32

Chapter 2

2.0 Virtual Model of the Shrouded Wind Turbine... 34

2.1 Discretization of the Simulated Parts... 35

2.2 72° Simulated Portion Slice... 35

2.3 Geometrical Model Schematics... 36

2.4 Isometric view of the CFD model...

INDICE

2.5 y-axis view of the CFD model... 37

2.6 y-axis view of the refined rotor zone of the CFD model... 38

2.7 Inlet

Conditions... 39

2.8 Pressure Conditions in the back... 39

2.9 Pressure Conditions on the top... 40

2.10 Cyclic Conditions on left side... 40

2.11 Cyclic Conditions on right side and detail close-up... 41

Chapter 3

3.0 Cross section through the turbine along x-axis... 48

3.1 Cross section through the z-axis... 49

3.2 Axial Component of the Velocity... 49

3.3 Air Velocity Along the x-axis of the Wind Turbine... 50

3.4 Air Velocity Along the x-axis of the Wind Turbine (Detail)... 51

3.5 Comparison between v

,v and v

velocities... 51

3.6 Profile of the Static Pressure... 52

3.7 Profile of the Static Pressure (View from Top)... 52

3.8 Profile of the Total Pressure... 53

3.9 Total Pressure Along the x-axis of the Wind Turbine... 54

3.10 Total Pressure Along the x-axis of the Wind Turbine (Detail)... 54

3.11 Torque on the Wind Turbine... 55

3.12 Power of the Wind Turbine... 56

3.13 Characteristic Curve of the Wind Turbine... 57

3.14 Axial Component of the Velocity... 59

3.15 Air Velocity Along the x-axis of the Shrouded Wind Turbine... 60

3.16 Air Velocity along the x-axis of the Shrouded Wind Turbine (Detail)...

3.17 Comparison of the Rotor Stream Tube Air Velocity Both Turbines... 61

3.18 Profile of the Static Pressure... 62

3.19 Profile of the Static Pressure (View from Top)... 62

3.20 Profile of the Total Pressure... 63

3.21 Total Pressure Along the x-axis of the Shrouded Wind Turbine... 64

3.22 Total Pressure Along the x-axis of the Shrouded Turbine (Detail)... 64

3.23 Comparison of the Rotor Stream Tube Total Pressure of the Shrouded

and Conventional Wind Turbines...

3.24 Torque of the Shrouded Wind Turbine... 65

3.25 Power Comparison for Shrouded and Conventional Turbines... 66

3.26 Profile of the Total Pressure with Particle Track... 68

3.27 Traditional Shrouded Turbine (No Space Between Shroud and Blade)... 70

3.28 Power of the Traditional Shrouded Wind Turbine... 71

List of Symbols

Section of Reference

Velocity of the Fluid

Mass flow

F Force

W Power

E Energy

Flow

T Torque

Q Volume

Flow

Axial Reduction Factor

Cp Power

Coefficient

S Rotor

Solidity

C Cord

Length

B Blade

Step

D Diameter

Number of Blades

p Pressure

t Temporal

Coordinate

, y

, z

Spatial

Coordinates

Strain Rate Component

Turbulent Kinetic Energy

Greek Letters

Density

Rotational

Speed

Efficiency

Tip Speed Ratio

µ Molecular

Viscosity

Stress Tensor Coordinate

Symbol of Kronecker

Turbulent Viscosity

Dissipation

Rate

Introduction

Most countries in the world today rely mostly on coal, oil, and natural gas for energy.

Fossil fuels are nonrenewable, that is, they draw on finite resources that will

eventually drain, becoming too expensive or too environmentally damaging to

retrieve. In contrast, renewable energy resources are constantly replenished.

Most renewable energy comes either directly or indirectly from the sun. Sunlight, or

solar energy, can be used directly for heating and lighting buildings, for generating

electricity, and a variety of commercial and industrial uses; vapor, generated by

water evaporation, can be treated by hydro electrical plants when it turn to rain or

snow. Rain and snow together with sunlight cause plants to grow. Vegetable organic

matter, whose growth is deeply linked to solar energy, can produce biomass

derivatives (energy, fuels, chemicals, etc.).

However not all renewable energy resources, come from the sun, such as geothermal

energy, which taps the Earth's internal heat, the energy produced from the ocean's

tides, which comes from the gravitational forces between the moon, sun and Earth.

All these forms of energy constitute renewable energy sources and can be used to

produce clean energy. Their use therefore provides important benefits which are not

only relative to the renewable aspect of the energy but also to the environmental and

economic advantages gained by their use. These technologies make use of clean

sources of energy and therefore have a much lower environmental impact than

conventional energy technologies. The use of these technologies also brings the

obvious advantage of a reduced dependency on foreign, fossil based energy supplies.

Renewable energy can be obtained capturing energy from the winds which are

directly generated by the sun's effect. Wind turbines are the most important devices

for harnessing this form of energy.

The earth receives 1.74 x 10

watts of power from the sun. About 1 to 2 per cent of

the energy is converted into wind energy. That is about 50 to 100 times more than the

energy converted into biomass by all plants on earth. In fact, the plant net primary

production is about 4.95 x 10

calories per square meter per year. This is global NPP,

Global net primary production, i.e. the amount of energy available to all subsequent

links in the food/energy chain. The earth's surface area is 5.09 x 10

. The net

power output stored by plants is thus 1.91 x 10

W, or 0.011% of the power emitted

to earth.

Regions round equator, at 0° latitude receive most of this solar energy. Hot air is

lighter than cold air and will rise into the sky until it reaches approximately 10 km

altitude and will spread to the North and the South. If the globe did not rotate, the air

would simply arrive at the North Pole and the South Pole, sink down, and return to

the equator. Since the globe rotates, any movement on the Northern hemisphere is

Introduction

diverted to the right and in the southern hemisphere it is bent to the left. This

apparent bending is caused by the Coriolis force.

Coriolis effect is an inertial force described by the 19th-century French engineer-

mathematician Gustave-Gaspard Coriolis in 1835. Coriolis showed that, if the

ordinary Newtonian laws of motion of bodies are to be used in a rotating frame of

reference, an inertial force--acting to the right of the direction of body motion for

counterclockwise rotation of the reference frame or to the left for clockwise rotation

must be included in the equations of motion. The effect of the Coriolis force is an

apparent deflection of the path of an object that moves within a rotating coordinate

system. The object does not actually deviate from its path, but it appears to do so

because of the motion of the coordinate system.

Around 30° latitude in both hemispheres the Coriolis force prevents the air from

moving much farther. At this latitude a high pressure area forms, as the air begins

sinking down again. As the wind rises from the equator a low pressure area will form

close to ground level attracting winds from the North and South. At the Poles, there

will be high pressure due to the cooling of the air. Keeping in mind the bending

caused by the Coriolis force, the following prevailing Global wind directions result:

Latitude 90-60°N 60-30°N 30-0°N

0-30°S

30-60°S

60-90°S

Direction NE

The prevailing Global wind directions are important when deciding where to place

wind turbines.

The winds we have been considering up till now are geostrophic winds. Geostrophic

winds are largely driven by temperature differences, and thus pressure differences,

and are not influenced allot by the earth's surface. Geostrophic winds are found at

altitudes above 1000 meters .On the other hand, winds up to altitudes of 100 meters,

known as surface winds, are very much influenced by the earth's surface,such as

obstacles and roughness. The wind's directions near the surface will be slightly

different from the direction of the geostrophic wind because of the earth's rotation.

When dealing with wind energy, we are mainly interested with surface winds.

Although the global wind directions are important in determining the prevailing

winds in a given area, local climatic conditions may influence the most common

wind directions or local winds. Basically the winds direction is influenced by the

sum of global and local effects. When larger scale winds are light, local winds may

dominate the wind patterns. Sea breezes and land breezes are both examples of local

winds and the monsoon in South-East Asia is really a large-scale form of sea breeze

and land breeze.

Introduction

The Energy from the Wind

The kinetic energy of a moving body is as follows:

(0.0)

As can be seen from equation 0.0, the kinetic energy of a moving body is

proportional to its mass. The kinetic energy in the wind thus depends on the density

of the air. At normal atmospheric pressure and at 15° C air has a density of 1.225

kilograms per cubic meter. Air density however decreases with humidity rise,

increases with temperature drop, and decreases with lower pressure.

A wind turbine obtains its power input by converting the force of the wind into a

torque acting on the rotor blades. The amount of energy which the wind transfers to

the rotor depends on the density of the air, the rotor area, and the wind speed.

Wind energy is a free, renewable resource, so no matter how much is used today,

there will still be the same supply in the future. Wind energy is also a source of

clean, non-polluting, electricity. Unlike conventional power plants, wind plants emit

no air pollutants or greenhouse gases. In 1990, California's wind power plants offset

the emission of more than 1.1 billion kilograms of carbon dioxide, and 6.8 million

kilograms of other pollutants that would have otherwise been produced. It would take

a forest of 90 million to 175 million trees to provide the same air quality.

There are however some economic obstacles to greater wind power usage. Even

though the cost of wind power has decreased dramatically in the past 10 years, the

technology requires a higher initial investment than fossil-fueled generators. Roughly

80% of the cost is the machinery, with the balance being the site preparation and

installation. If wind generating systems are compared with fossil-fueled systems on a

"life-cycle" cost basis (counting fuel and operating expenses for the life of the

generator), however, wind costs are much more competitive with other generating

technologies because there is no fuel to purchase and minimal operating expenses.

The high costs associated with the design and production of the turbine, however still

limit the introduction and diffusion of this technology. More emphasis on the

economic aspects will be given in later discussions.

Other negative aspects that limit the implementation of wind turbines can be

attributed to factors such as the appearance and visual impact of a wind turbine on

the surrounding environment. This latter aspect can be solved through the

implementation of smaller more efficient turbines.

If the power output of a specific turbine could be augmented, given a specific

diameter, then the per-watt costs of the turbine would be reduced as the performance

of the system would be increased., or similarly for a given power output smaller

cheaper turbines could be built instead. It is possible to increase the power of a wind

turbine by installing a shroud or diffuser around the rotating propeller

Introduction

In the available literature one finds that attempts have been made in the past at

implementing diffuser arrays on wind turbines. These solutions could theoretically

increase the power while reducing the overall diameter of the turbine blade.

This has obvious advantages both from a power output point of view, as well as on a

design and construction basis. Smaller turbines mean less visual impact and less

deployment and implementation constraints. Thus if the added array has a per meter

square cost that is less than the corresponding per meter square cost of the turbine

blade, these solutions could reduce the cost of the entire wind turbine system,

effectively reducing the cost of wind energy. However these past attempts have not

as yet been successful.

The work done is this thesis will try to study why these attempts have not been

successful, explore the physics of the problem and consequently propose a better

solution, such as our shrouded wind turbine which has higher performance than the

traditional diffuser systems, with overall dimensions strongly reduced. The feasibility

of such a solution shall be explored using modern, commercial, computational fluid-

dynamics simulation code, which rapid technical progress has made available only in

recent years.

This thesis is articulated into 4 chapters. In the first chapter, the theory of the various

types of conventional wind turbines will be discussed. The second chapter will

explain the methodology of fluid-dynamic simulations and the characteristics of the

geometrical model that was utilized for the simulations. Chapter three will

summarize the results obtained from the simulations.

Chapter 1

Theory of Wind Turbines

1.0 Introduction

Fig.1.0: Wind-Rotor System

Fig.1.0 represents the stream tube that defines the wind-rotor system. Air

approaching the turbine gradually slows down and the stream tube section gets

larger. The wind turbine will deflect the wind, before the wind reaches the rotor

plane. This means that one can never be able to capture all of the energy in the wind

using a wind turbine. The wind turbine rotor must obviously slow down the wind as

it captures its kinetic energy and converts it into rotational energy. In other words the

wind will be moving more slowly behind the rotor than in front of the rotor. Since

the amount of air entering through the swept rotor area in front (every second) must

be the same as the amount of air leaving the rotor area behind, the air will have to

occupy a larger cross section (diameter) behind the rotor plane. The wind will not be

slowed down to its final speed immediately behind the rotor plane. The slowdown

will happen gradually behind the rotor, until the speed becomes almost constant.

If we look at the air pressure distribution, as the wind approaches the rotor in front of

the turbine, the air pressure increases gradually, since the rotor acts as a barrier to the

wind.

Fig.1.1: Horizontal Axis Pressure Variation

Wind Turbine Theory

Fig.1.1 shows the air pressure plotted vertically, while the horizontal axis indicates

the distance from the rotor plane. The air pressure will drop immediately behind the

rotor plane It then gradually increases to the normal air pressure level. If we move

farther downstream the turbulence in the wind will cause the slow wind behind the

rotor to mix with the faster moving wind from the surrounding area.

1.1 The Betz Law

The more kinetic energy a wind turbine pulls out of the wind, the more the wind will

be slowed down as it leaves the turbine in Fig.1.0. If all the energy were extracted

from the wind, the air would not move, i.e. the air could not leave the turbine. In that

case we would not extract any energy at all, since all of the air would also be

prevented from entering the rotor of the turbine. There must be some way slow down

the wind that is more efficient in converting the available energy to useful

mechanical energy. An explanation to this problem is given by Betz's law, which

states that an ideal wind turbine (rotating disk) would slow down the wind by 2/3 of

its original speed.[ref. 1]

Betz's law was first formulated by the German Physicist Albert Betz in 1919. His

book "Wind-Energie" published in 1926 gives a good account of the knowledge of

wind energy and wind turbines at that moment and is still frequently quoted today.

Fig.1.2: Wind-Rotor Stream Tube.

Wind Turbine Theory

Considering the stream tube represented Fig.1.2, the conservation of mass dictates

that mass flow remains constant therefore:

(1.0)

Where,

is the density of air [kg / m

is the area of the air stream before the rotor [m

is the wind velocity of the air stream before the rotor [m/s].

A is the rotor swept area [m

v is the velocity of the air at the rotor plane.

is the area of the air stream behind the rotor [m

is the wind velocity of the air stream behind the rotor [m/s].

is the mass flow [kg/s.].

From the conservation of momentum we then have:

)

(

)

(

(1.1)

That is the change in momentum creates a horizontal thrust force F [N] on the rotor.

It is a horizontal force exerted by the flow on the rotor.

Therefore from equation 1.1 the kinetic power W [Watt] extracted by the rotor is:

)

(

(1.2)

If we now take into account the conservation of kinetic energy and in particular the

variation of kinetic energy flow between the inlet and the outlet, we have:

)

(

)

(

(1.3)

The variation of kinetic energy flow between the inlet and the outlet is also equal to

the kinetic power W:

)

(

The power obtained from equation1.2 and the power obtained from equation 1.3

must be the same so:

)

(

)

(

(1.4)

Wind Turbine Theory

Power is also equal to torque T times the angular velocity , therefore, from this

equation we can extract the torque T as:

)

(

(1.5)

From equation 1.5 we therefore obtain:

)

(

(1.6)

Note that: 0 v

The result expressed in equation 1.6 is rather significant, as it cannot be easily

assumed prior to the considerations made on the conservation of mass, momentum

and energy.

The velocity of the wind in the rotor plane is, therefore, the average of the upstream

and downstream wind speeds, and as a consequence, the deceleration of the flow

stream happens half in the tract preceding the turbine and half in the tract following

the turbine.

One can sometimes find useful the definition of an axial reduction factor a, as the

factor by which one can measure how much the flow has been slowed down in the

tract preceding the turbine :

)

(

(1.7)

Note that: 0 a 1/2

And therefore all variables can be rewritten as a function of a and v

. In this

idealization it is assumed that v

, the velocity of the wind undisturbed, is constant

and a known quantity:

)

(

(1.8)

)

(

(1.9)

Wind Turbine Theory

the mass flow can be expressed as:

)

(

(1.10)

the force on the turbine can be rewritten as:

)

(

(1.11)

the torque then becomes

)

(

(1.12)

and finally the power can be expressed as:

)

(

(1.13)

Equation 1.13 shows the relationship between the power W and the axial reduction

factor a. We can therefore differentiate equation 1.13 with respect to a and obtain the

optimum value that maximizes the power. In other words:

But because 0 a ½ we obtain :

opt

(1.14)

The first direct implication of equation 1.14 is that to obtain maximum power, the

maximum velocity v that the turbine can extract from the wind v

has to be :

(1.15)

and the stream tube exit velocity is therefore:

(1.16)

Details

Seiten

Erscheinungsform

Originalausgabe

Jahr

2003

ISBN (eBook)

9783832470449

ISBN (Paperback)

9783838670447

DOI

10.3239/9783832470449

Dateigröße

1.9 MB

Sprache

Englisch

Institution / Hochschule

Università degli Studi di Udine – Faculty of Engineering, National Institute for Nuclear Physics and Department of Physics of Udine

Erscheinungsdatum

2003 (Juli)

Note

1,5

Schlagworte

windenergie erneuerbare energien windrad turbine clean energy

Autor

Maximilian Ludwig Ganis (Autor:in)