vawt thermal stresses analysis

THERMAL ANALYSIS OF VERTICAL AXIS WIND TURBINE 2010-2011

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CONTENTS

I. LIST OF FIGURES 3

II. LIST OF SYMBOLS 4

III. ABSTRACT 5

IV. PROJECT OBJECTIVES 6

CHAPTER 1

INTRODUCTION 7

1.1. Straight-bladed Darrieus Type VAWT 7

1.2. Advantages and limitations 9

CHAPTER 2.

TERMINOLOGY 10

2.1. Tip Speed Ratio 10

2.2. Betz Limit 11

2.3. Power Coefficient 11

2.4. Torque Coefficient 11

2.5. Solidity (σ) 11

CHAPTER 3.

LITERATURE REVIEW 12

3.1.Performance Analysis of a Darrieus Rotor 12

3.2. Aerodynamic Analysis Of Darrieus Rotors 13

3.3. Effect of Wind Turbulence and Atmospheric Stability on Wind turbine Output 14

3.4. Wind Turbine Airfoil Flow Simulations 15


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CHAPTER 4.

VAWT AERODYNAMICS 16

4.1. The Actuator Cylinder 16

4.2. Momentum Theory 17

4.3. Blade Element Theory 19

CHAPTER 5.

DARRIEUS TURBINE PARAMETERS AFFECTED BY THERMAL CONDITIONS 21

5.1. Tower Height 21

5.2. Material Selection 22

5.2.1. Factors affecting material selection 22

CHAPTER 6.

COMPUTATIONAL METHODOLOGY AND SOLUTIONS OF ANALYSIS 24

6.1. VAWT Model . 24

6.2. Mesh Generation in Gambit 26

6.3. Solution of flow problem in FLUENT 28

6.3.1 FLUENT Solver Input and Solution Control Parameters 30

6.3.2. Results 30

6.4. Thermal Stress Analysis in ANSYS 33

6.4.1. Procedure 33

CONCLUSION 38

REFERENCES 39

APPENDIX A 40

APPENDIX B 41

APPENDIX C 42


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I. LIST OF FIGURES

Page No.

Figure 1.1. H-Darrieus Vertical Axis Wind Turbine 9

Figure 2.1. Forces, velocities and incident angles for various blade

positions during the rotation of Darrieus wind turbine.

10

Figure 3.1. Variation of power coefficient with respect to blade angle at

V=9 m/s [1]

13

Figure 4.1. Geometry of a Vertical Axis Wind Turbine. 16

Figure 4.2. Plan view of actuator cylinder 17

Figure 4.3. Lift and drag forces acting on a blade on a blade of a VAWT 19

Figure 4.4. Nomenclature used to represent the geometry of the variable

pitch blade for the VAWT blade (upper right quadrant)

19

Figure 6.1. Overall dimensions of the H-Darrieus rotor. 24

Figure 6.2. Pro/E model of the H-Darrieus rotor 25

Figure 6.3. Boundary conditions and computational domain of the rotor. 26

Figure 6.4. Unstructured mesh for the flow domain in GAMBIT 27

Figure 6.5. Unstructured mesh for the flow domain in GAMBIT showing

the concentrated meshing around the airfoil.

28

Figure 6.6. Variation of absolute pressure along the airfoil surface of Foil1

31

Figure 6.7. Variation of absolute pressure in the flow domain. 31

Figure 6.8. Variation of velocity magnitude near the airfoil blades. 32

Figure 6.9. Elemental nodes on the hollow, twisted airfoil blade as imported from GAMBIT

34

Figure 6.10. Contour plot of thermal gradient near the trailing edge of the

airfoil.

35

Figure 6.11. Contour plot of von Mises mechanical stress over the airfoil

solid.

36

Figure 6.12. Contour plot of von Mises mechanical stress over the airfoil

solid showing the stress concentration at the inner wall of blade.

37

Figure 6.13. Contour plot of total von Mises mechanical and thermal

stress over the airfoil solid showing the stress concentration

at the inner wall of blade.

37


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II. LIST OF SYMBOLS

AD : area of actuator disc

a : interference factor

C : airfoil cord length

CD : drag coefficient

CL : lift coefficient

: normal force coefficient

: tangential force coefficient

Fi : force component on each element of blade

N : number of blades

r : radius of blade- distance from rotor

U : effective flow passing through rotor

U∞ : upstream wind velocity

: wind speed on actuator disk

: downstream wind velocity

a : axial flow induction factor

Vθ : blade speed

W : apparent wind speed

α : attack angle

ω : angular velocity

αi : induced attack angle

αL : attack angle (infinite wing theory)

χ : tip speed ratio

δ : induced drag coefficient

θ : the angle location of blade

ζ : solidity

ψi : polar parameter of blade element i


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III. ABSTRACT

For efficient utilization of the available wind energy, it is imperative to study the behavior

and performance of the wind turbines subjected to aerodynamic and ambient conditions to

understand the possible behavior of the system such that the modifications in design, if any,

can be incorporated so that the extraction of energy from the wind is maximized.

For this purpose, the CFD analysis in FLUENT and structural analysis in ANSYS of a

twisted three bladed H-Darrieus rotor has been undertaken. Due to limitations on

experimentation, the computational approach has been used to get the wind loads on the

blades. On further application of these loads, in addition with temperature conditions, the

structural behavior of the aforementioned blade is obtained for a predetermined set of

operating conditions.

The results from the analysis are compared with pre-existing ones for the purpose of

validation and are found to be confirming within acceptable error limits. This holistic

approach, thus, gives an insight to the behavior of similar systems subjected to identical

conditions.


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IV. PROJECT OBJECTIVES

(i) To implement a CAD model depicting the true blade profile for a given configuration

possible for the Darrieus type wind turbine.

(ii) Acquisition and implementation of the exact working constraints and parameters to

address the current state of wind turbine development

(iii) To identify and apply the exact data obtained on the turbine in an analysis software

(basically FLUENT or ANSYS) to achieve the goal of thermal simulation under loaded

conditions.

(iv) Post-processing of the results to identify the optimum blade design and configurations

that will be able to handle the thermal conditions ambient to the turbine.


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CHAPTER 1.

INTRODUCTION

Aerodynamics is an active and influential science, contributing to major aspects of wind

turbine design. The art of manipulating and adapting a moving fluid to optimize energy

extraction is of prime importance. Wind turbines have been studied since the earliest known

ancient humans attempted to harness wind energy through diversified means. One of the

manners to achieve this goal was through Vertical-Axis Wind Turbines (VAWT).

Recently, there has been a resurgence of interest regarding sources of renewable energy, with

numerous universities, companies and research institutions carrying out extensive research

activities. These activities have led to a plethora of designs of wind turbines based mostly on

computational aerodynamic models. Still largely restricted to an experimental subject,

vertical-axis wind turbines are appearing more frequently in the civilian and military market

as research into their cost-effectiveness and simplicity progresses.

At present, there are two primary categories of modern wind turbines, namely horizontal-axis

(HAWTs) and vertical-axis (VAWTs). The main advantages of the VAWT are its single

moving part (rotor) where no yaw mechanisms are required, its low-wind speed operation and

the elimination of the need for extensive supporting tower structures, thus significantly

simplifying the design and installation. Blades of straight-bladed VAWTs can be of uniform

airfoil section and untwisted, making them relatively easy to fabricate or extrude, unlike the

blades of HAWTs, which are commonly twisted and tapered airfoils for optimum

performance.

1.1. Straight-bladed Darrieus Type VAWT

Currently there are two main categories of modern wind turbines, namely the Horizontal Axis

Wind Turbines (HAWT) and the Vertical Axis Wind Turbines (or VAWT). These are used

mainly for electricity generation and water pumping. For the HAWT machines, the axis of

rotation of blades is horizontal and for the VAWT, the axis of rotation is vertical. Unlike

HAWT, VAWTs are insensitive to direction of wind and thus they do not need any


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complicated yawing mechanisms. There have been many designs of vertical axis windmills

over the years. Currently the vertical axis machines can be broadly divided into three basic

types –

1) Savonius type,

2) Darrieus type, and

3) H-Rotor type.

The Darrieus type VAWT was invented by French engineer George Jeans Mary Darrieus in

1925 and it was patented in the USA in 1931 [8]. It comes in two configurations, namely egg-

beater (or curved-bladed) and straight-bladed.

1.2. Advantages and limitations

Though HAWTs work well in rural settings with steady uni-directional winds, VAWTs have

numerous advantages over them.

They do not require additional components (like yaw mechanics, pitch control

mechanism, wind-direction sensing device). VAWTs are insensitive to wind-

direction.

Almost all of the components requiring maintenance are located at the ground level,

facilitating the maintenance work appreciably.

They also eliminate the costs (both initial and recurring maintenance) of the auxiliary

components (like diesel gensets) and risks associated with the failure or malfunction

of these components.

All these factors make them ideal candidate for rooftop (rural and urban) and certain

mechanical applications.

VAWTs have the simplest blade geometry, and thus are easier to manufacture.

Unlike HAWTs, fixed-pitch straight-bladed VAWTs are mechanically much simpler

and aesthetically more attractive.

Can be mounted to roofs without special provisions & support PVs & other

renewables without vibrations/noise concerns.


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Nevertheless, it is commonly believed that small-capacity straight-bladed VAWTs are

inherently unable to self-start properly. This notion is true for older designs which were

constructed by using old NACA airfoils and commonly available materials like aluminium or

wood. According to some researchers, the problem of self-starting can be alleviated by

i) using high-lift low-drag special-purpose airfoil; and

ii) by incorporating a Savonius rotor or torque tube.

Several prototypes and commercial models have been designed and deployed in the field

which have a self-starting feature. These prototypes and models have benefited from

advances in aerodynamic tools and lightweight composite materials.

Figure 1.1. H-Darrieus Vertical Axis Wind Turbine


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CHAPTER 2.

VAWT TERMINOLOGY

2.1. Tip Speed Ratio

Tip-speed ratio is the ratio of the speed of the rotating blade tip to the speed of the free stream

wind.

(2.1)

Where,

ω = rotational speed (in radians /sec)

R = rotor radius (in m)

U = wind “free stream” velocity (in m/sec)

Figure 2.1. Forces, velocities and incident angles for various blade positions during the rotation

of Darrieus wind turbine.


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2.2. Betz Limit

All wind power cannot be captured by rotor or air would be completely still behind rotor and

not allow more wind to pass through. Theoretical limit of rotor efficiency is 59%. Most

modern wind turbines are in the 35 – 45% range

2.3. Power Coefficient

The power coefficient is defined as,

(2.2)

where, P = rotor power

2.4. Torque Coefficient

The torque coefficient is defined as,

(2.3)

where, T = rotor torque

The relation between the two coefficients is,

(2.4)

2.5. Solidity (σ)

The solidity of a wind turbine is the ratio between blade area to swept area in a full rotation.

(2.5)


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CHAPTER 3.

LITERATURE REVIEW

The current wind turbine research is primarily driven towards proposing performance

optimizations of horizontal-axis wind turbines, however substantial progress has also been

observed towards vertical-axis wind turbine applications concerning aerodynamic efficiency

and performance regarding energy production by assessing operational characteristics in sub-

scale testing. There remains no extensive availability of literature concerning specific

Darrieus model applications, but rather there is literature concerning the general study of the

concept of the Darrieus rotor with very few authors analyzing in-depth the aerodynamic

phenomena that these models create as observed with thermal effects. A representative

selection therefore, relevant to supporting the theoretical and numerical results and thermal

effects involved in the project are reviewed and summaries provided of how the literature is

incorporated into the study.

3.1.Performance Analysis of a Darrieus Rotor

Debnath et al. [1] have predicted the performance characteristics of three-bladed Darrieus

rotor for various overlap conditions. The aerodynamic coefficients, such as lift coefficient,

drag coefficient, and lift-to-drag coefficient, were evaluated with respect to angle of attack.

Subsequent validation by using experimental values for the twisted three-bladed H-Darrieus

rotor was also presented. The study is used for identifying the design aspects that influences

the economics of the rotor such as evaluation of aerodynamic coefficients, like lift, drag, and

lift-to-drag coefficients for the blades.

Fig. 3.1 shows that power coefficients are positive at the blade azimuthal positions where

positive thrust coefficients are obtained. Moreover, Fig. 3.1 also confirms that blade twist of

30° results in higher average power coefficient for the rotor.

With the superiority of the lift-driven devices established as well as the fact that maximum

power is obtained when the device is moving perpendicular to the wind, the concept of

placing lifting surfaces on a rotating machine is seen to be an obvious method of deployment.


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Figure 3.1. Variation of power coefficient with respect to blade angle at V=9 m/s [1]

3.2. Aerodynamic Analysis Of Darrieus Rotors

The differences between cross-wind rotors and the wind-axis type is that there is a

continuously varying local wind as a blade rotates from "upwind" to "downwind". A quasi-

steady condition is usually assumed and the effects of the upwind blade on the blade in

downwind position is neglected, as shown by Wilson, R [2].

Two group of mathematical model for analysing and predicting Darrieus rotor performance

are the simple momentum (streamtube) model and the complex vortex models.

The simple momentum model is simple and straightforward and results in good agreement

with the available test data. It treats the flow as a single streamtube with the induced velocity

constant across the rotor, which allows a closed solution, but which limits its use to lightly

loaded blades and circumstances in which there is no significant variation of wind velocity

across the flow area. The analysis includes aerodynamic drag of the blades and it shows that

performance is sensitive to drag, particularly at high values of TSR.


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Another method is the multiple-streamtube concept, for which an iteration procedure is

required, as the ratio of wind speed u at the rotor to the freestream velocity V∞. is not constant

and must be obtained by matching of momentum and blade-element relationships.

Among the two, the momentum models are known to be unable to describe flow field around

the turbine correctly. Strangely it seems to be the most widely used tool mostly because of

the acceptable accuracy of the result, widely available literature, and code simplicity.

To date, very little work has been done on establishing the influence that fundamental

thermal parameters such as temperature gradients, heat transfer etc. have on the aerodynamic

performance and structural integrity of a VAWT. This type of study can only be carried out if

a suitably comprehensive prediction scheme is available.

To account for the temporal variation in angle of attack on the wind turbine blades Coton et

al. [3] suggested fully unsteady three-dimensional analysis scheme which has been validated

against existing machines to provide the required level of aerodynamic detail over the full

range of tip-speed ratio.

3.3. Effect of Wind Turbulence and Atmospheric Stability on Wind turbine

Output

Rohatgi et al. [4] studied the impact of wind turbulence on wind turbine operation. Wind

profile variations may cause random, fluctuating loads and stresses over the whole structure,

resulting into power instabilities and fatigue life of the wind turbine.

Information regarding the atmospheric stability is also important considering the fatigue life

and the power generation from a wind turbine. The vertical wind profile models are governed

by the vertical temperature distribution resulting from radiative heating or cooling of the

earth’s surface and the subsequent convective mixing of the air adjacent to the surface.

The conclusive inferences regarding the thermal aspects of turbine operational parameters are

incorporated in the subsequent analysis that will result from this project.


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3.4. Wind Turbine Airfoil Flow Simulations

Implementation of design improvements for the wind turbines is hampered by the lack of

practical prediction tools having the appropriate level of complexity. The fact that the flow is

incompressible, three-dimensional, unsteady, turbulent, and very often separated to a large

extent, means that its numerical analysis is very complex and costly.

Bermúdez et al [6] proposed a viscous–inviscid interaction method that allows for the

efficient computation of unsteady airfoil flow. The numerical robustness as offered by the

algorithm will aid in more generalised calculations when incorporated into the simulation

program.


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CHAPTER 4.

VAWT AERODYNAMICS

A single blade of a vertical axis wind turbine, viewed from above, is illustrated in Fig.4.1. In

the figure the blade is shown rotating in the counter-clockwise direction, and the wind is seen

impinging on the rotor from left to right. As is typical in vertical axis wind turbines, the

airfoil is symmetric. The blade is oriented so that the chord line is perpendicular to the radius

of the circle of rotation. The radius defining the angular position of the blade (normally

meeting the chord line at the quarter chord) makes an angle of φ with the wind direction, as

shown in the figure.

Figure 4.1. Geometry of a Vertical Axis Wind Turbine.

4.1. The Actuator Cylinder

Vertical axis blade configurations are many but, for the purpose of this exercise, we shall

assume that the blades are straight and vertical. Such a machine sweeps out a cylinder,

instead of a disk as is the case with HAWT, and so intersects any given streamtube twice. As

shown in the Fig.4.2, this means that there are effectively, two elemental actuator disks in

tandem, each set at an angle to the flow and each extracting some of the flow’s energy.

Various theories have been put forward to deal with the presence of the two actuator disks.

The simplest theories lump the two disks together and assume that all the energy is being

extracted at the mid-vertical plane of the cylinder. Such an approach can be treated in either a

single or multiple streamtube manner. However, an analysis which takes account of the


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double intersection is able to provide much greater detail about the aerodynamic response,

such as the variation of the torque and blade normal loading and it is an approach which will

be described in this text.

Figure 4.2. Plan view of actuator cylinder

4.2. Momentum Theory

The air which passes through the disc undergoes an overall change in velocity, U – Uw and a

rate of change of momentum equal to the overall change of velocity times the mass flow rate.

Rate of change of momentum = (4.1)

The force causing this change of momentum comes entirely from the pressure difference

across the actuator disk, because the streamtube is otherwise surrounded by air at atmospheric

pressure, which gives zero net force. Therefore

(4.2)

To obtain the pressure difference , Bernoulli’s equation is applied separately to

the upstream and downstream sections of the streamtube; separate equations are necessary

because the total energy is different upstream and downstream.


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For a VAWT, the momentum theory has to be applied to each intersection of the air stream

with the actuator cylinder. However, conditions vary greatly around the cylinder and so it is

common to consider a multiplicity of streamtubes which pack together to fill the cylinder

volume.

The two intersections are treated as two actuator disks in tandem. The disk areas are different

because of the expansion of the streamtubes and, although the disks are not normal to the

flow direction, these areas are taken to be normal cross-section.

It is assumed that at a point somewhere between the disks, the static pressure the static

pressure rises through the atmospheric level , and at this point the streamtube velocity is

Ua. By momentum theory therefore, at the actuator disk,

and,

(4.3)

(4.4)

The rate of change of momentum for the upstream part of the streamtube is then,

(4.5)

The speed U now becomes the upstream velocity (instead of U) or the downstream disk and

hence

and,

(4.6)

(4.7)

So the rate of change of momentum is

(4.8)


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4.3. Blade Element Theory

Blade element theory relies on two key assumptions:

1. There are no aerodynamic interactions between different blade elements.

2. The forces on the blade elements are solely determined by the lift and drag

coefficients.

Each blade has an airfoil cross-section and produces lift which has a component in the

tangential direction, thus providing a torque which is not constant but varies with blade

position and, when the blades are few in numbers, this means that the shaft torque fluctuates.

Figure shows the blade element forces and velocities at points in each quadrant of a

revolution.

Figure 4.3. Lift and drag forces acting on a

blade on a blade of a VAWT

Figure 4.4. Nomenclature used to represent

the geometry of the variable pitch blade for

the VAWT blade (upper right quadrant)

As can be seen, the lift always has a component in the forward direction but the blade surface

facing the wind changes between the upstream and downstream passes. This means that the

angle of incidence changes sign and so it would seem that the airfoil should be symmetrical.

A cambered airfoil would give an increased torque on one pass but a decreased torque on the

other, and experiment has shown that the latter predominates whichever way the blade is

cambered. Pitching the blades nose-in or nose-out should, in principle, give similar results,

but a small advantage can be obtained with a little nose-out pitch, especially at very low tip

speed ratios. This is useful because vertical axis machines generally have low starting


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torques. For simplicity, however, we shall assume zero set pitch, that is, the chord line is a

tangent to the circle of rotation and moreover, touches the circle at the mid-point chord.

Fig.4.3 and Fig.4.4 show the forces on a blade element in the first quadrant, measuring the

azimuth angle β clockwise (direction of rotation), from the downstream direction.

The angle θ is not the blade azimuth but the angle between the radius vector and the local

streamline. This streamline is assumed to be straight as it crosses the turbine and so the angle

θ is the same at both actuator disks/blade elements. The forces resolved into the local

streamline sense, give

(4.9)

The terms in brackets are normal (N) and chordwise (T) components of the resultant force on

the airfoil and it is usual to use these rather than L and D.

(4.10)

(4.11)

As CL and CD are known functions of , then CN and CT can be calculated and used instead.

(4.12)

(4.13)

Note that N, T, L and D are forces per unit of length of blade

Therefore,

(4.14)


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CHAPTER 5.

DARRIEUS TURBINE PARAMETERS AFFECTED BY

THERMAL CONDITIONS

5.1. Tower Height

Tower Height is governed by the “wind profile power law”. It is a relationship between the

wind speeds at one height, and those at another.

The power law is often used in wind power assessments where wind speeds at the height of a

turbine (>~ 50 meters) must be estimated from near surface wind observations (~10 meters),

or where wind speed data at various heights must be adjusted to a standard height prior to

use. Wind profiles are generated and used in a number of atmospheric pollution dispersion

models.

The wind profile of the atmospheric boundary layer (surface to around 2000 meters) is

generally logarithmic in nature and is best approximated using the log wind profile equation

that accounts for surface roughness and atmospheric stability. The wind profile power law

relationship is often used as a substitute for the log wind profile when surface roughness or

stability information is not available.

The wind profile power law relationship is:

(5.1)

where u is the wind speed (in meters per second) at height z (in meters), and ur is the known

wind speed at a reference height zr. The exponent (α) is an empirically derived coefficient

that varies dependent upon the stability of the atmosphere. For neutral stability conditions, α

is approximately 1/7, or 0.143.

In order to estimate the wind speed at a certain height x, the relationship would be rearranged

to:

(5.2)


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The value of 1/7 for α is commonly assumed to be constant in wind resource assessments,

because the differences between the two levels are not usually so great as to introduce

substantial errors into the estimates (usually < 50 m).

Doubling the altitude of a turbine, then, increases the expected wind speeds by 10% and the

expected power by 34%.

At night time, or when the atmosphere becomes stable, wind speed close to the ground

usually subsides whereas at turbine hub altitude it does not decrease that much or may even

increase. As a result the wind speed is higher and a turbine will produce more power than

expected from the 1/7th power law: doubling the altitude may increase wind speed by 20% to

60%.

5.2. Material Selection

The typical operating temperature of a wind turbine may vary from -200C to 40

0C. Taking

this range into consideration, a suitable material must be selected that can provide maximum

blade life under fluctuating temperature conditions. The continuous dimensional changes

experienced by the rotor during a low-to-high temperature cycle, such as those prevalent in

desert areas, may induce cracking in the blades. By suitable material selection and subsequent

treatments, the material may be made adaptable to such temperature fluctuations so that the

wind turbine operates with desired efficiency throughout its predicted life.

5.2.1. Factors affecting material selection

Many factors are considered while selecting material for wind turbine blades. These include

physical properties such as, low density, performance requirements, safety, environmental

conditions, economic factors, etc.

The principal properties pursued from a technical point of view are:

1. High material stiffness to maintain optimal performance.

2. A long fatigue life to reduce material degradation.


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3. High thermal conductivity.

4. Moderate density.

5. High specific heat.

6. Low coefficient of thermal expansion.

On comparison of various materials, epoxy-fibre reinforced plastic was found to satisfy most

of these properties adequately. As such, we have used this material in our analysis.

Table 5.1. Material Properties of epoxy-fibre reinforced plastic (EFRP)

PROPERTIES TEST

METHOD UNIT VALUES

(a) PHYSICAL

Density IS 10192 kg/m3 1850

Water Absorption IS 10192 - Max. 0.13

Mass fraction - % fibre 61

Volume fraction - % fibre 52

(b) MECHANICAL

Tensile Strength IS 1998 N/mm2 250

Flexural Strength IS 1998 N/mm2 350

Flexural Strength after keeping at 150°C for

one hour and tested at 150°C IS 1998 N/mm2 175

Shear Strength IS 1998 N/mm2 120

Compressive strength IS 1998 N/mm2 400

Impact Strength Charpy (Type Test) 10mm IS 10192 kJ/mm2 75

(c) THERMAL

Thermal conductivity - W/m-K 3.46

Coefficient of linear expansion - m/m 0C 1.2 x 10

-5

Specific heat - kJ/kgK 1.170


24

CHAPTER 6.

COMPUTATIONAL METHODOLOGY AND SOLUTIONS

OF ANALYSIS

6.1. VAWT Model

To exhaustively depict the use splines for reproducing the twisted blade profile, the model of

H-Darrieus rotor was drawn using Pro/E software.

Figure 6.1. Overall dimensions of the H-Darrieus rotor.


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Figure 6.2. Pro/E model of the H-Darrieus rotor

The main parts of the model are:

(a) the twisted blades

(b) the shaft

(c) the retaining discs

The chord length of the blades was 10 cm and height of the blades was 40 cm. The actual

shape of the airfoil blade of unit size is shown in Fig. 6.1. An angular twist of 30° was

provided at the trailing ends of the blades, such that the twist on each blade was symmetrical.

The blades were mounted in such a fashion that the concave face of the twist end is facing the

upstream flow. The profile of the airfoil resembles to NACA 0012 having twist at the trailing

end. Although such cambered section at negative incidence (which happens in the downwind

pass) develops a little lift, such blades are better off than symmetrical NACA airfoil blades

where upwind and downwind phenomena are more or less even, especially at low Reynolds

number flows.


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The H-Darrieus rotor used for the analysis is modelled in Pro/E and the data-points were then

transferred to Gambit for further development of mesh on it.

6.2. Mesh Generation in Gambit

The Computational Fluid Dynamic package used was FLUENT while the mesh was

generated in GAMBIT of the FLUENT 6.3.26 software. Fig.6.3 shows the computational

domain, which has three bladed rotor along with surrounding four edges resembling the test

section of the wind tunnel. Velocity inlet and pressure outlet conditions were taken on the left

and right boundaries, respectively. The top and bottom boundaries, which signify the

sidewalls of the wind tunnel, had symmetry conditions on them. The blades and shaft were

set to standard wall conditions. Two-dimensional unstructured (triangular-mesh)

computational domain was developed. The vertical axis wind rotor blades rotate in the same

plane as the approaching wind.

Figure 6.3. Boundary conditions and computational domain of the rotor.

For an H-Darrieus rotor, the general geometric properties of the blade cross-section are

usually constant with varying span section, unlike original Darrieus rotor as invented and

patented by Darrieus in 1931, for which these geometric properties vary with the local radius.


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The density of mesh was high at the blade ends and also on the blade peripheries to capture

the flow physics near the wall boundaries. On the blades of the rotor, near wall boundary

layers were built in gambit such that the distance of the first row of grid points in direction

normal to the boundary was 0.001 cm. Wind velocity of 9 m/s were taken for simulating the

wind flow. The tip speed ratio corresponding to this wind velocity is 4.26.

Table 6.1. Mesh Entities

Total mesh faces 300562

Total mesh edges 2150

Total mesh nodes 150873

Figure 6.4. Unstructured mesh for the flow domain in GAMBIT


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Figure 6.5.Unstructured mesh for the flow domain in GAMBIT showing the concentrated

meshing around the airfoil.

6.3. Solution of flow problem in FLUENT

Any computational formulation of a physical process is based on mathematical modelling. In

the CFD formulation as well, the conservative forms of continuity and Navier–Stokes’

equations in integral form for incompressible flow of constant viscosity were solved by the

built-in functions of the FLUENT 6.2 CFD software. The simplest and most widely used two-

equation turbulence model is the standard k-ɛ model that solves one transport equation to

allow the turbulent kinetic energy and its dissipation rate to be independently determined.

The standard k-ɛ model is particularly suitable for flows though sharp corners, straight and

curved edges like the rotor blades, as the model uses wall functions based on the law of the

wall. The standard k-ɛ equation can be represented as:

For turbulent kinetic energy (k):

(6.1)


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For dissipation (Є):

(6.2)

Turbulent viscosity (µT) is modelled as:

(6.3)

Model constants:

In the present study, steady-state, incompressible two-dimensional flow was assumed. The

numerical simulations were carried out by solving the conservation equations for mass and

momentum by using an unstructured-grid finite volume methodology.

The sequential algorithm, semi-implicit method for pressure linked equation (SIMPLE), was

used in solving all the scalar variables. For the convective terms of the continuity and

momentum equations, and also for the turbulence equations, the second order upwind

interpolating scheme was applied in order to achieve more accurate results. The

computational conditions are given in Section 6.3.1.


30

6.3.1 FLUENT Solver Input and Solution Control Parameters

(a) Material: air (fluid)

Property Value(s)

Density 1.225 kg/m3

Cp (Specific Heat) 1006.43 J/kg-K

Thermal Conductivity 0.0242 W/m-K

Viscosity 1.7894E-05 kg/m-s

(b) Boundary Conditions:

Wind velocity 9 m/s

Pressure 1.013 bar

Rotational speed 146 rad/sec

(c) Solver Settings

6.3.2. Results

The absolute pressure results are obtained from the analysis is Fig. 6.6. The important parameter is the

absolute pressure values along the curved length of Foil1 which will suffice for mechanical pressure

loading in the thermal stress analysis.

(1)Relaxation

Variable Relaxation

Pressure 0.3

Density 1

Body Forces 1

Momentum 0.7

Turbulent Kinetic Energy 0.8

Turbulent Dissipation Rate 0.8

Turbulent Viscosity 1

(2)Method

Pressure-Velocity Coupling SIMPLE

Turbulence Model Standard k-ɛ

Near Wall Treatment Enhanced

(3)Discretization Scheme

Pressure Standard

Momentum Second Order Upwind

Turbulent Kinetic Energy Second Order Upwind

Turbulent Dissipation Rate First Order Upwind


31

Figure 6.6. Variation of absolute pressure along the airfoil surface of Foil1

Figure 6.7. Variation of absolute pressure in the flow domain.


32

Figure 6.8. Variation of velocity magnitude near the airfoil blades.


33

6.4. Thermal Stress Analysis in ANSYS

Structural analysis comprises the set of physical laws and mathematics required to study and

predicts the behaviour of structures. The subjects of structural analysis are engineering

artifacts whose integrity is judged largely based upon their ability to withstand loads. From a

theoretical perspective the primary goal of structural analysis is the computation of

deformations, internal forces, and stresses. In practice, structural analysis can be viewed more

abstractly as a method to drive the engineering design process or prove the soundness of a

design without a dependence on directly testing it.

In a typical thermal stresses analysis, temperatures are calculated and then applied as load

conditions for the stress analysis. While it is possible to solve for the temperature using a

conjugate heat transfer capability of a CFD code, it can consume significant computational

resources. A reduced order model, assuming constant wall temperature on the inside of the

blade is used to estimate the thermal gradients in the solid domain of the blades.

6.4.1. Procedure

1. The blade profile data points are imported from Gambit into ANSYS software

package for stress analysis (Fig. 6.9). The bottom-up approach was then used to

model the hollow section of the airfoil. As the flow pattern is assumed identical across

the length of the blade, a 2-D planar analysis will suffice.

2. The relevant material properties for epoxy-fibre reinforced plastic were input from

table 5.1 using the Material Library.

3. For the purpose of establishing the thermal gradients across the solid section of the

blade profile, the area was meshed using PLANE55 elements (Appendix A). The

inside wall is maintained at a constant wall temperature of 300C and the outside

surface is provided with convective boundary condition, convective film coefficient

ha = 22 W/m2-

0C. This completes the thermal evaluation of the problem, Fig. 6.10.


34

Figure 6.9. Elemental nodes on the hollow, twisted airfoil blade as imported from GAMBIT

4. The thermal gradient values generated in the above analysis are used subsequently in

the thermal stress analysis of the blade.

5. For this purpose, the modelled area is meshed using the PLANE13 (Appendix B)

element types. The free area mesh was used. The mesh was further refined at the foil

surfaces.

6. The displacement degree of freedom (DOF) for the inner wall is set to zero.

7. Further, to incorporate the absolute pressure values, as obtained from the FLUENT,

the Table entries were made for 240 nodal points on the airfoil. For this, x,y nodal

coordinates and the corresponding absolute pressure values on the Foil1 airfoil

surface are imported from FLUENT analysis as the input. This completes the surface

loading of the blade.


35

Figure 6.10. Contour plot of thermal gradient near the trailing edge of the airfoil.

8. For thermal loading, the temperature gradients are incorporated as Table values at the

corresponding nodes.

9. The solution was then obtained in terms of total (thermal and mechanical) von Mises

stress and strain values.


36

Figure 6.11. Contour plot of von Mises mechanical stress over the airfoil solid.


37

Figure 6.12. Contour plot of von Mises mechanical stress over the airfoil solid showing the stress

concentration at the inner wall of blade.

Figure 6.13. Contour plot of total von Mises mechanical and thermal stress over the airfoil solid

showing the stress concentration at the inner wall of blade.


38

CONCLUSION:

The von Mises stress values obtained from the structural analysis shows that the location of

maximum value of stress corresponds to the position of maximum thermal gradient. Thus, by

evaluating the thermal profile of a wind turbine blade, under similar conditions, a rough

estimation of the location of the maximum stress concentration can be known.

FUTURE SCOPE:

The future scope of the project is to, possibly, develop a mathematical model governing the

performance parameters of a VAWT operation (such as lift coefficient, drag coefficient and

power) with respect to the temperature conditions imposed on to the turbine.


39

REFERENCES:

[1] Debnath B. K.; Biswas A. & Gupta R., Computational fluid dynamics analysis of a combined

three-bucket Savonius and three-bladed Darrieus rotor at various overlap conditions, Journal of

Renewable and Sustainable Energy, 2009, 033110, 1-13

[2] Wilson, R. Wind-turbine Aerodynamics Journal of lndustrial Aerodynamics, 1980, 5, 357-372

[3] Coton F. N.; Galbraith R. A. M. & Jiang D., The influence of detailed blade design on the

aerodynamic performance of straight-bladed vertical axis wind turbines, Proc Instn Mech Engrs,

1996, 210, 65-74

[4] Rohatgi J. & Barbezier G., Wind Turbulence and Atmospheric Stability - Their Effect on

Wind Turbine Output, Renewable Energy, 1999, 16, 908-911

[5] Ferreira C. S.; van Kuik G.; van Bussel G. & Scarano F., Visualization by PIV of dynamic

stall on a vertical axis wind turbine, Exp Fluids, 2009, 46, 97–108

[6] Bermudez L.; Velazquez A. & Matesanz A., Viscous–inviscid method for the simulation of

turbulent unsteady wind turbine airfoil flow, Journal of Wind Engineering and Industrial

Aerodynamics, 2002, 90, 643-661

[7] Barakos, G. and Mitsoulis, E., Numerical simulation of viscoelastic flow around a cylinder

using an integral constitutive equation, J. Rheol., 1995, 39, 1279

[8] Darrieus, G.J.M., Turbine having its rotating shaft transverse to the flow of the current. US

Patent No. 1835081,1931.

[9] Kuan-Chen Fu and Awad Harb, Thermal Stresses of a Wind Turbine Blade made of

Orthotropic Material, Computers & Structures, 1987, Vol. 27. No. 2. pp, 225-235.

[10] Freris L.L., Wind Energy Conversion Systems, Prentice Hall, 1990


40

APPENDIX A

PLANE55 Element Description

PLANE55 can be used as a plane element or as an axisymmetric ring element with a 2-D

thermal conduction capability. The element has four nodes with a single degree of freedom,

temperature, at each node.

The element is applicable to a 2-D, steady-state or transient thermal analysis. The element

can also compensate for mass transport heat flow from a constant velocity field. If the model

containing the temperature element is also to be analyzed structurally, the element should be

replaced by an equivalent structural element (such as PLANE42).

Figure A.1. PLANE55 Geometry

PLANE55 Input Data

The geometry, node locations, and the coordinate system for this element are shown in

Fig.A.1. The element is defined by four nodes and the orthotropic material properties.

Orthotropic material directions correspond to the element coordinate directions. Specific heat

and density are ignored for steady-state solutions.

Convection or heat flux (but not both) and radiation may be input as surface loads at the

element faces as shown by the circled numbers on Fig. A.1.

Heat generation rates may be input as element body loads at the nodes. If the node I heat

generation rate HG(I) is input, and all others are unspecified, they default to HG(I).


41

APPENDIX B

PLANE13 Element Description

PLANE13 has a 2-D magnetic, thermal, electrical, piezoelectric, and structural field

capability with limited coupling between the fields. PLANE13 is defined by four nodes with

up to four degrees of freedom per node. PLANE13 has large deflection and stress stiffening

capabilities. When used in purely structural analyses, PLANE13 also has large strain

capabilities.

Figure B.1. PLANE13 Geometry

PLANE13 Input Data

The geometry, node locations, and the coordinate system for this element are shown in Fig.

B.1. The element input data includes four nodes and magnetic, thermal, electrical, and

structural material properties.

Element loads are described in Node and Element Loads. Pressure, convection or heat flux

(but not both), radiation, and Maxwell force flags may be input on the element faces

indicated by the circled numbers in Fig. B.1 Geometry using the SF and SFE commands.

Positive pressures act into the element.

Body loads - temperature, heat generation rate, and magnetic virtual displacement - may be

input at the element's nodes or as a single element value [BF, BFE]. When the temperature

degree of freedom is active (KEYOPT(1) = 2 or 4), applied body force temperatures [BF,

BFE] are ignored. In general, unspecified nodal temperatures and heat generation rates

default to the uniform value specified with the BFUNIF or TUNIF command. Heat

generation from Joule heating is applied in Solution as thermal loading for static and transient

analyses.


42

APPENDIX C

Stress and Strain

Stress solutions allow you to predict safety factors, stresses, strains, and displacements given

the model and material of a part or an entire assembly and for a particular structural loading

environment.

A general three-dimensional stress state is calculated in terms of three normal and three shear

stress components aligned to the part or assembly world coordinate system.

The principal stresses and the maximum shear stress are called invariants; that is, their value

does not depend on the orientation of the part or assembly with respect to its world coordinate

system. The principal stresses and maximum shear stress are available as individual results.

The principal strains ε1, ε2, and ε3 and the maximum shear strain γmax are also available. The

principal strains are always ordered such that ε1> ε2> ε3. As with principal stresses and the

maximum shear stress, the principal strains and maximum shear strain are invariants.

Equivalent stress is related to the principal stresses by the equation:

Equivalent stress (also called von Mises stress) is often used in design work because it allows

any arbitrary three-dimensional stress state to be represented as a single positive stress value.

Equivalent stress is part of the maximum equivalent stress failure theory used to predict

yielding in a ductile material.

The von Mises or equivalent strain εe is computed as:

where:

ν' = effective Poisson's ratio, which is defined as follows:


43

Material Poisson's ratio for elastic and thermal strains computed at the reference

temperature of the body.

0.5 for plastic strains.

Thermal Strain

Thermal strain is computed when coefficient of thermal expansion is specified and a temperature load

is applied in a structural analysis.

Each of the components of thermal strain are computed as:

Where:

- thermal strain in one of the directions x, y, or z.

- Secant coefficient of thermal expansion defined as a material property in Engineering Data

- reference temperature or the "stress-free" temperature. This can be specified globally for the

model using the Reference Temperature field of Static Structural or Transient Structural (ANSYS)

analysis types. Optionally the reference temperature can be specified \as a material property for cases

such as the analysis for cooling of a weld or solder joint where each material has a different stress-free

temperature.

vawt thermal stresses analysis

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