Feasibility Study of a 3D CFD Solution for FSI …786912/FULLTEXT01.pdfii Master of Science Thesis EGI 2015-006MSC EKV1077 Feasibility Study of a 3D CFD Solution for FSI Investigations

Master of Science Thesis

KTH School of Industrial Engineering and Management

Energy Technology EGI-2015-006MSC EKV1077

Division of Heat and Power Technology

SE-100 44 STOCKHOLM

Feasibility Study of a 3D CFD

Solution for FSI Investigations on

NREL 5MW Wind Turbine Blade

Giacomo Bernardi

ii

Master of Science Thesis EGI 2015-006MSC

EKV1077

Feasibility Study of a 3D CFD Solution for

FSI Investigations on NREL 5MW Wind

Turbine Blade

Giacomo Bernardi

Approved

Examiner

Björn Laumert

Supervisor

Nenad Glodic

Commissioner

Contact person

Abstract

With the increase in length of wind turbine blades flutter is becoming a potential design constrain, hence the interest in computational tools for fluid-structure interaction studies. The general approach to this problem makes use of simplified aerodynamic computational tools. Scope of this work is to investigate the outcomes of a 3D CFD simulation of a complete wind turbine blade, both in terms of numerical results and computational cost. The model studied is a 5MW theoretical wind turbine from NREL. The simulation was performed with ANSYS-CFX, with different volume mesh and turbulence model, in steady-state and transient mode. The convergence history and computational time was analyzed, and the pressure distribution was compared to a high fidelity numerical result of the same blade. All the model studied were about two orders of magnitude lighter than the reference in computation time, while showing comparable results in most of the cases. The results were affected more by turbulence model than mesh density, and some turbulence models did not converge to a solution. In general seems possible to obtain good results from a complete 3D CFD simulation while keeping the computational cost reasonably low. Attention should be paid to mesh quality.

iii

Acknowledgments

First and foremost I wish to thank my supervisor, Nenad Glodic, for his support throughout this

project with his knowledge and comments and for his help managing its many changes.

This achievement would not have been possible without the support of my parents, and would

have been much more difficult without all my friends at KTH. Thank you all!

Contents

Contents v

List of Figures vii

List of Tables ix

Abbreviations xi

1 Introduction 11.1 Renewable energy and power generation . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Wind energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.2.1 Wind energy history . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41.2.2 The wind turbine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71.2.3 Offshore wind turbines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101.2.4 Floating wind turbines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

1.3 The NREL offshore 5 MW baseline wind turbine . . . . . . . . . . . . . . . . . . . . 14

2 Background 172.1 Aeroelasticity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172.2 Aeroelastic modeling for wind turbine rotor . . . . . . . . . . . . . . . . . . . . . . . 20

2.2.1 Aerodynamic models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202.2.1.1 BEM model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202.2.1.2 3D CFD model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

2.2.2 Structural models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232.2.2.1 FEM model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232.2.2.2 Multy-body and modal shape approach . . . . . . . . . . . . . . . 23

2.3 Turbulence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242.3.1 Statistical Turbulence models (RANS) . . . . . . . . . . . . . . . . . . . . . . 25

2.3.1.1 Eddy-viscosity models . . . . . . . . . . . . . . . . . . . . . . . . . . 27Zero-equation models . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28One-equation models . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28Two-equation models . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

The k-εmodel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29The k-ω model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30The Shear Stress Transport model . . . . . . . . . . . . . . . . . 30Production limiter and curvature correction . . . . . . . . . . 32

2.3.1.2 Explicit Algebraic Reynolds Stress Models . . . . . . . . . . . . . 33

v

vi Contents

3 Objectives 35

4 Method of Attack 37

5 Numerical techniques 395.1 Workflow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 405.2 ICEM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

5.2.1 Inner and outer mesh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 425.3 CFD simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

5.3.1 Steady-state simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 455.3.1.1 Effect of turbulence models . . . . . . . . . . . . . . . . . . . . . . 465.3.1.2 Effect of meshing techniques . . . . . . . . . . . . . . . . . . . . . . 465.3.1.3 Effect of turbulence correction factors . . . . . . . . . . . . . . . 47

5.3.2 Transient simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

6 Results and Discussion 496.1 Steady-state results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

6.1.1 Turbulence models comparison . . . . . . . . . . . . . . . . . . . . . . . . . . 496.1.2 Mesh sets comparison . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

6.1.2.1 Inner domain mesh . . . . . . . . . . . . . . . . . . . . . . . . . . . . 516.1.2.2 Outer domain mesh . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

6.1.3 Correction factor comparison . . . . . . . . . . . . . . . . . . . . . . . . . . . 576.1.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

6.2 Transient results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 606.2.1 CP results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

6.2.1.1 Comparison with steady-state results . . . . . . . . . . . . . . . . 606.2.1.2 Inner domain mesh comparison . . . . . . . . . . . . . . . . . . . 616.2.1.3 Outer domain mesh comparison . . . . . . . . . . . . . . . . . . . 63

6.2.2 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

7 Final discussion and Conclusions 677.1 Future work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

Bibliography 71

List of Figures

1.1 Estimated renewable energy share of global electricity production, 2011 . . . . . 11.2 Renewable power capacities, EU-27, BRICS, 2011 . . . . . . . . . . . . . . . . . . . . 21.3 Renewable energy share of installed capacity of electricity production, 2011 . . 21.4 Electrical generating capacity of renewable energy plant . . . . . . . . . . . . . . . 31.5 Persian windmill . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41.6 C. Brush’s wind turbine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51.7 Smith-Putnam wind turbine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61.8 Wind turbine components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71.9 Aerodynamic force near the blade tip . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81.10 Loads on a wind turbine blade . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91.11 Cumulative offshore wind capacity and capacity share in Europe . . . . . . . . . . 111.12 Tower/foundation/anchor cost, including installation . . . . . . . . . . . . . . . . . 121.13 Floating wind turbine structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

2.1 Collar diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172.2 Increase of wing incidence due to wing twist . . . . . . . . . . . . . . . . . . . . . . . 192.3 Coupling of bending and torsional oscillations . . . . . . . . . . . . . . . . . . . . . . 19

4.1 Blade geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

5.1 Inner and outer domain geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 415.2 Domain boundary conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 415.3 Inner domain mesh, blade section . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 435.4 Outer domain mesh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 445.5 Span positions for results analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

6.1 Pressure distribution: steady-state, turbulence models . . . . . . . . . . . . . . . . . 506.2 Pressure distribution: steady-state, inner domain mesh . . . . . . . . . . . . . . . . 526.3 Residuals time history: steady-state, inner domain mesh . . . . . . . . . . . . . . . 536.4 Pressure distribution: steady-state, outer domain mesh . . . . . . . . . . . . . . . . 546.5 Residuals time history: steady-state, outer domain mesh . . . . . . . . . . . . . . . 556.6 Pressure distribution: steady-state, outer domain mesh (2) . . . . . . . . . . . . . . 566.7 Residuals time history: steady-state, outer domain mesh (2) . . . . . . . . . . . . . 576.8 Pressure distribution: steady-state, turbulence correction factors . . . . . . . . . . 586.9 Pressure distribution: steady-state and transient on Case 1 . . . . . . . . . . . . . . 616.10 Pressure distribution: transient, inner domain mesh . . . . . . . . . . . . . . . . . . 626.11 Pressure distribution: transient, outer domain mesh . . . . . . . . . . . . . . . . . . 646.12 Pressure distribution: transient, outer domain mesh (2) . . . . . . . . . . . . . . . . 65

vii

List of Tables

1.1 Load factor for renewable and conventional energy . . . . . . . . . . . . . . . . . . . 31.2 Physical and operational characteristics of the NREL 5 MW wind turbine . . . . 15

5.1 Inner domain mesh sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 425.2 Outer domain mesh sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 435.3 Physical values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 455.4 Inner mesh studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 465.5 Outer mesh studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 475.6 Turbulence correction factors studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

6.1 Computational time: steady-state, turbulence models . . . . . . . . . . . . . . . . . 516.2 Computational time: steady-state, inner domain mesh . . . . . . . . . . . . . . . . . 536.3 Computational time: steady-state, outer domain mesh . . . . . . . . . . . . . . . . . 566.4 Computational time: steady-state, turbulence correction factors . . . . . . . . . . 586.5 Computational time: reference and transient . . . . . . . . . . . . . . . . . . . . . . . 606.6 Computational time: transient, inner domain mesh . . . . . . . . . . . . . . . . . . 636.7 Computational time: transient, outer domain mesh . . . . . . . . . . . . . . . . . . 65

ix

Abbreviations

AC Aerodynamic Center

BEM Blade Element Momentum method

CFD Computational Fluid Dynamics

CG Center of Gravity

DES Detached Eddy Simulation

DNS Direct Numerical Solution

DRSM Differential Reynolds Stress Model

EARSM Explicit Algebraic Reynolds Stress Model

EVTE Eddy-Viscosity Transport Equation

FEM Finite Element Method

FSI Fluid Structure Interaction

HAWT Horizontal Axis Wind Turbine

LES Large Eddy Simulation

PS Blade Pressure Side

RANS Reynolds Averaged Navier-Stokes equations

SS Blade Suction Side

SST Shear Stress Transport

xi

Chapter 1

Introduction

1.1 Renewable energy and power generation

According the International Energy Agency renewable energy is: “. . . derived from natural pro-

cesses that are replenished constantly. In its various forms, it derives directly from the sun, or from

heat generated deep within the earth. Included in the definition is electricity and heat generated

from solar, wind, ocean, hydropower, biomass, geothermal resources, and biofuels and hydrogen de-

rived from renewable resources” [1]. In 2010 renewable energy supplied approximately 16.7% of

the global final energy consumption (power generation, heating and cooling, transport fuels,

and rural/off-grids energy services)[2], and the share of renewable energy in power production

is even bigger.

At the end of 2011 renewable energy accounted

for more than 25% of the global generating ca-

pacity and provided an estimated 20.3% of the

total consumption (fig. 1.1). This difference be-

tween generating capacity and power produc-

tion is caused by the variability of most of the

renewable energy sources, such as wind and so-

lar energy [2].

Hydropower is the main source of renewable

power worldwide, followed by wind power,

FIGURE 1.1: Estimated renewable en-ergy share of global electricity produc-

tion, 2011 [2]

1

2 Chapter 1. Introduction

biomass power and solar photovoltaic. For the EU-27 countries the photovoltaic capacity is

higher than biomass power (fig. 1.2).

FIGURE 1.2: Renewable power capacities, EU-27, BRICS, 2011 [2]

The success of renewable energy for power

FIGURE 1.3: Renewable energy share of installedcapacity of electricity production, 2011 [2]

generation can be seen in its fast growth.

During 2011 renewable energy has been al-

most half of the new electric production ca-

pacity globally installed, estimated in 208 GW.

Wind power, solar photovoltaic, and hydropower

are in order the most installed renewable sources

during 2011, see figure 1.3.

Some useful data about renewable energy and

load factor can be found in the Digest of United

Kingdom energy statistics (DUKES) for 2012 [3], issued by the Department of Energy and Cli-

mate Change (DECC), a British government department. Table 1.1 shows the plant load factor

for different renewable and conventional electricity generation, as comparison. Plant load fac-

tor is defined as the plant actual yearly energy output over the potential output if the plant

operates at full capacity for one year.

Hydropower is the most reliable among the renewable sources but is not expected to grow

much more, as can be seen in figure 1.4. Photovoltaic is growing at a fast pace, but it is still

the renewable energy with the lowest plant load factor. Certainly photovoltaic is the youngest

renewable technology, but so far it cannot withstand the comparison with wind energy. Wind

energy shows a fast, longer, growth in installed capacity, a more mature technology and a more

1.1. Renewable energy and power generation 3

Renewables

Wind 27.1%- onshore 26.2%- offshore 29.8%Photovoltaic 8.3%Hydro 35.4%- small scale 37.1%- large scale 35.1%

Conventional

Combined cycle gas turbine 61.9%Nuclear 60.1%Coal fired 42.2%

TABLE 1.1: Plant load factor for renewable and conventional electricity generation (average2007-2011) [3]

favorable plant load factor. Can also be observed the steady growth in offshore wind energy,

which as well features a higher load factor. This important characteristic, liable to be quickly

improved, and the limitation in new onshore wind farms, makes offshore wind energy the

most interesting renewable energy source for the next future [3].

FIGURE 1.4: Electrical generating capacity of renewable energy plant [3]


1.2 Wind energy

1.2.1 Wind energy history

Wind energy has accompanied mankind for most of its history. At about 3100 B.C. Egyptians

were using sails of linen or papyrus to propel small boats southward against the stream of river

Nile, and sailboats were replaced only many centuries later by steamboats [4]. From this ini-

tial use as boat propulsion, wind energy later became also source of mechanical power. The

first windmills (fig. 1.5) appeared in the Persian region of Sistan, between seventh and ninth

century [5]. From there windmills spread to central Asia and later in China and India [6].

Windmills started to be used in northwestern Europe during the twelfth century [7].

FIGURE 1.5: Persian windmill [8]

The first windmill in Europe was built in England in 1137 by William of Almoner, of Le-

icester. The original design, called post-mill, where the whole tower rotates to face the wind,

is thought to be developed independently from the carousel design used in Persia and most

likely inspired by the design of waterwheels. From England, post-mills spread in the rest of

Europe in a west-to-east direction; in the 1300s windmills were used in Spain, France, Belgium,

the Netherlands, Denmark, the German principalities and the Italian states. As they became

more common, windmills became also bigger and their design had to be improved for that;

hence the tower-mill design was developed, where only the upper part of the tower with the

sails, the wind shaft and the brake wheel rotate to the wind [4].

With migration from Europe to the New World, windmills were introduced in the colonies,

but they were not as successful as in Europe. Beside being big and expensive to build, a tower-

mill requires constant human attention, a problem in the rural areas in the colonies with their

1.2. Wind energy 5

lack of labor force. Furthermore, the abundance of rivers made watermills more suitable for

the development of the colonies. Windmills were more common on islands and along the shore

for grain grinding. As the migration moved to the arid and windy West, wind power became

more important [4]. Here the American windmill design was developed during the 19th cen-

tury by D. Halladay (1854) and by Reverend L. H. Wheeler (1867) [9]. Light, small, movable,

self-regulating, cheap and easy to maintain, these windmills were used for grain grinding and

water pumping across the West plains. Railroad companies were the first users of Halladay’s

windmills, used to supply water to steam locomotives [4]. About two decades later, the first

experiments of wind energy production were performed in Europe and US. In July 1887, in the

town of Marykirk in Aberdeenshire, Scotland, Professor James Blyth of Anderson’s College

installed the first windmill for electricity

production, a 33-feet tall cloth-sailed tur-

bine, charging accumulators developed by

Camille Alphonse Faure to power the lights of

his cottage. Later he built a wind turbine to

supply emergency power to the Montrose Lu-

natic Asylum [10].

Few months later the Blyth’s experiment,

in winter 1887-1888 in Ohio, US Professor

Charles F. Brush built a massive 12 kW wind

turbine, with a rotor diameter of 50 meters and

144 rotor blades (fig. 1.6). The machine served

for twenty years, until Brush decided to take

down the sails in 1908 [4].

FIGURE 1.6: C. Brush’s wind turbine [4]

In 1890s, danish scientist Poul la Cour began test on wind turbines, he was the first to discover

that a fast rotating wind turbine with fewer blades is more efficient in electricity production.

In 1903 he founded the Society of Wind Electrician, with the first course held the following

year [11]. Commercial use of wind power had to wait until 1927, when Joe and Marcellus

Jacobs opened in Minneapolis the Jacobs Wind factory, selling wind turbines used on farms to

charge batteries and power lighting.


FIGURE 1.7: Smith-Putnam wind turbine[12]

Year 1941 saw the first megawatt-size wind tur-

bine, the Smith-Putnam wind turbine, installed

at Grandpa’s Knob, Castelton, Vermont. It was

a two-bladed, variable pitch, downwind wind

turbine, with a 53-meters diameter rotor and

1.25 MW power output (fig. 1.7). It was af-

fected by a succession of problems and never

run unattended. It was dismantled in 1945 af-

ter a blade failure [13]. In 1956 la Cour’s stu-

dent Johannes Juul built in Gedser, Denmark

a three-bladed, upwind wind turbine capable

of 200 kW inspiring the design of later wind

turbines. He is also the inventor of the emer-

gency aerodynamic tip brake. The turbine run

for eleven years and was refurbished in the mid

1970s at the request of NASA.

The Oil Crisis in 1970s drove the United States government to begin, in cooperation with

NASA, research into large commercial wind turbines, resulting in the first windfarm, con-

sisting of 20 turbines, built in 1980 in New Hampshire. Eleven years later, the first offshore

windfarm was built in Vindeby, in the southern part of Denmark, with eleven turbines of

450 kW each [11].

At these days, the Enercon E–126 is the world’s biggest wind turbine, capable of 7.5 MW

of electricity output, featuring a 135-meters high concrete tower and three segmented steel-

composite hybrid blades for its 127-meters wide rotor [14].

1.2. Wind energy 7

1.2.2 The wind turbine

Wind turbines transform the kinetic energy of the wind in electrical energy, rotating the shaft

of a generator. The maximum theoretical power available for the turbine is:

PM AX = 1/2mV 20 = 1/2ρAV 3

0

where V0 is the wind speed, ρ the air density and A the rotor area; showing the importance of

wind speed for the power output. To extract all the power available, the wind turbine should

bring down to zero the speed of the air flowing through the turbine disc, which is physically

impossible. Therefore a theoretical maximum power coefficient is imposed by the mass and

energy conservation, called Betz limit, equal to 0.593. Modern wind turbines are capable of

really high power coefficient, up to 0.5 [15]. The main components of a HAWT can be seen

in fig.1.8.

1. Foundation

2. Connection to the electric grid

3. Tower

4. Access ladder

5. Yaw control

6. Nacelle

7. Generator

8. Anemometer

9. Brake

10. Gearbox

11. Rotor blade

12. Blade pitch control

13. Rotor hub

FIGURE 1.8: Wind turbine components [16]

The rotor, generally made of three blades, generates the torque necessary to rotate the shaft by

means of the tangential component of the total aerodynamic force acting on the blades. Since

the rotational speed of the rotor is much lower than the speed of the generator, a gearbox has to

be used to connect the slow shaft of the former with the fast shaft of the latter. On the fast shaft,


between the gearbox and the generator, sits a brake, either electric or mechanical, to prevent the

rotor from overspeeding in case of failure in the generator or in the grid connection. Usually

the generator employed in wind turbines is of the asynchronous type, so the shaft rotational

speed has to be bigger and really close to the synchronous speed, requiring the turbine to work

at constant speed. To maximize the power output, a control unit reads the wind direction and

actuate a yaw motor in order to keep the turbine always against wind. Another purpose of the

control unit is to prevent the generator from operating above its rated nominal power, causing

a possible failure. To do so, when the nominal power is reached and the wind speed is high

enough to exceed the maximum torque, the control unit increases the blade pitch (they rotate

against the wind), reducing the angle of attach of the blade and hence the torque generated by

the rotor. In case the wind speed is too high for a safe operation (cut-off speed), the controller

brakes the rotor and put the blades in neutral position [17].

v

A

v

B

u

w

Plane of rotation

F

F

FIGURE 1.9: Aerodynamic force near the blade tip, redrawn from [17]

When the wind turbine is stationary, the wind generates on the blades a small aerodynamic

force, almost perpendicular to the rotor plane; the small tangential component generates the

torque necessary to start the wind turbine, which slowly accelerates(fig.1.9 A). As the rotor

accelerates, the total air speed w seen by the blade, sum of the wind speed v and the tangential

speed u, rotates towards the rotor plane and increases in magnitude; the effect is a reduction

of the high angle of attach the blade experiences at start up, hence the blade becomes more

efficient and produce a high lift force L and a relatively small drag D (fig.1.9 B). The projection

of these two forces on the rotor plane create the tangential force PT , and consequently the

1.2. Wind energy 9

torque that drives the generator; the orthogonal component PN tends to bend the tower and

the blades and does not produce work (fig.1.10) [17].

Rotor planeφ

PT

D

PNR

L

w

FIGURE 1.10: Loads on a wind turbine blade, redrawn form [15]

The strategies to control the rotational speed of the rotor and prevent it form overspeeding

are:

• stall regulation;

• pitch regulation;

• yaw control.

The first two are the most common.

Stall regulation is the most simple mechanically, since the blade does not need to be pitched

and can hence be rigidly fixed to the hub. This type of turbine generally operates at almost

constant speed, therefore as the wind speed increases the angle of attack also increases, eventu-

ally leading to stall. In this way the tangential load can be reduced to keep the rotor at nominal

speed. This control strategy lacks in finely controlling the power output; at start up, when the

generator is connected instantaneously to the grid, the turbine causes an overshoot in power

output. To prevent the turbine from overspeeding in case of a generator failure, an aerody-

namic brake is needed. In case of stall regulated wind turbines, the blade tip can be rotated

towards the wind, acting as a brake. This system is activated by centrifugal force.

Pitch regulation uses some sort of actuators to change the pitch of the blade, resulting in a

smoother power output at start up. On the other hand, the pitch regulation system is not fast

enough to filter all the turbulence from the airflow, hence the power output has a bigger fluc-

tuation about the nominal value, compared to a stall regulated wind turbine. Since the blade


pitch can be changed, the blade can act as an aerodynamic brake, so tip brakes are no longer

necessary.

Yaw control is used in stall and pitch regulated wind turbines to rotate the nacelle against

wind and hence extracting the maximum power from the wind. For this reason the yaw con-

trol can also be used to reduce the power extraction by turning the rotor away from the wind

and therefore reducing the airflow trough the rotor. This control method is not commonly

used for large machines [15].

1.2.3 Offshore wind turbines

Wind turbines need flat areas with strong, constant wind and proper separation to avoid recip-

rocal interference; sea is the natural answer to these requirements. The flat, smooth water sur-

face creates much less turbulence than any land surface, allowing the wind to flow undisturbed

and faster. While onshore wind turbines rely on winds from the irregular cyclonic-anticyclonic

structures in the atmosphere, offshore wind turbines harvest the energy of the regular breezes

from land and sea and vice-versa caused by the uneven heating of land and water masses. Fur-

thermore, offshore wind turbines are not constrained in the maximum dimension by road

transport of their components, unlike onshore wind turbines.

On the other hand, offshore wind turbines are more expensive to manufacture, place and main-

tain. The basic onshore wind turbine has to be modified in order to withstand the harsher en-

vironment: corrosion protection of the tower and the blades; sealing of the nacelle to protect

the sensitive internal components from seawater spray and, in case, heating units for low tem-

perature operation; more reliable mechanical components for longer maintenance intervals.

To connect the turbine tower to the foundation in the seabed, a support structure has to be

built and transported to the final site; particular, and often expensive vessels, are used during

the installation of the complete structure. Clearly, sending the personnel and the equipment

necessary for the maintenance of an offshore wind turbine is much more expensive than for

an onshore wind turbine. The connection to the power grid with underwater cables, further

increases the complexity, and hence the cost, of an offshore wind farm. For these reasons big

wind turbines are used for offshore energy production, in order to minimize the number of

supporting structures and grid connection points required for total power output; this results

also in more complex turbines and structures.

1.2. Wind energy 11

In 1991 Denmark inaugurated the first offshore wind farm, capable of 4.95 MW with eleven

turbines. Twenty years later the total installed capacity was about 3 GW, almost all of it in

Europe. United Kingdom is the leading country in offshore wind energy production, with

more than half of the total European capacity (fig.1.11) [18].

FIGURE 1.11: Cumulative offshore wind capacity 1991-2010 and share of installed capacityin Europe in 2010 [18]

The support structures used for offshore wind turbines have been previously well tested in

the oil and gas industry, but so far only grounded structures are used in wind energy [19].

Different designs are available, depending on the depth and soil characteristic, the main are:

gravity-based: durable and simple but heavy and expensive for depth above ten meters [20];

monopile: simple and well documented, requires scour protection and is affected by large

hydrodynamic loads [21];

suction bucket: cheap and suitable for high depth, difficult to transport and install, not suit-

able for rocky soil [22];

tripile: simple and more stiff than monopile, it is heavy and requires a large amount of steel

[23];

tripod: good stiffness and resistance against overturning, complex structure with risk of fa-

tigue [24];

jacket: light and good overturning resistance, complex to manufacture and transport [25].

The main problem with grounded offshore wind turbines is that the cost of the support struc-

ture grows with the water depth, because of the bigger amount of material used but also because


of the larger overturning moment at their foundations (fig.1.12). Some countries, e.g., USA,

Japan, Korea, have small amount of shallow waters for wind energy production and a big po-

tential of strong, constant winds lies in deep water areas; this is the reason of the recent big

interest in floating structures for wind turbines [19].

FIGURE 1.12: Tower/foundation/anchor cost, including installation [26]

1.2. Wind energy 13

1.2.4 Floating wind turbines

In a floating structure the support is provided by the water by means of buoyancy, while some

mooring lines are only used to keep the platform in place. As grounded structures, floating

structures are widely used in the oil and gas industry for deep water operation, and these de-

signs, plus some hybrids, are under study for wind turbine support. So far only prototypes

have been built. This section is based on [27].

The spar buoy structure consists of a long cylinder with air in its top and ballast in its bottom

(fig.1.13 A–left). The big volume of air provides the buoyancy required to support the whole

structure, while the ballast keeps the center of gravity below the center of buoyancy, making

the structure stable. The longer is the cylinder and the heavier is the ballast, the more stable

is the structure. This kind of structure, with its small cross section at sea surface, is poorly

affected by wave motion. The Hywind prototype, by Statoil, is an example of this structure.

The tension leg platform (TLP) is an underwater structure anchored to the sea bed by some

tension legs (fig.1.13 A–center). The buoyancy force is bigger than the weight of the structure,

hence the mooring cables are under tension, stabilizing the structure. The whole platform is

kept underwater, with only the connection structure to the wind turbine tower affected by the

wave loads. Blue H is testing a 3/4 scale prototype of this design.

The barge floater is a semi-submersible floating structure, widely used in oil and gas industry

(fig.1.13 A–right). The structure can be sailed to the site already completely installed, and can

be sailed back to a harbor for maintenance purpose, making it cheaper to install and operate.

On the other hand, its big floating structure at sea surface makes it sensitive to wave motion.

A possible improvement of this design, is to add to the barge a wave energy device. These com-

ponents are used to extract the energy of the waves and convert it in electricity. The structure

becomes clearly more complex and expensive, but generates more energy and the wave energy

device greatly reduces the movements of the platform, improving the efficiency of the wind

turbine. Due to the particular design, the structure rotates autonomously against the waves,

which are usually propagating in the same direction of the wind, so the yaw motor will not be

necessary. A prototype is under study, the Poseidon 37 [28].

A possible improvement of the spar buoy is to strengthen it with tension wires, as in the Sway

prototype (fig.1.13 B). In this way the structure can be made stiff enough while saving steel

and weight. If the rotor is placed downwind of the tower, the tension wires can continue up

to the top of the structure, making it more stiff; with the downwind rotor, the structure will

turn against wind, not requiring any yaw control.


The tri-floater uses three shorter semi-submerged spars (fig.1.13 C). To compensate the loads

from the waves, a dynamic ballast is used to stabilize the structure. A full scale prototype,

WindFloat, is under test with a 2 MW wind turbine.

FIGURE 1.13: Floating wind turbine structures [26, 29, 30]

1.3 The NREL offshore 5 MW baseline wind turbine

The United States, among others, are interested in the big potential of offshore wind energy.

The Mineral Management Service published in 2006 the results of a study about offshore wind

energy [31]. According data from the U.S. Department of Energy (DOE), a potential available

energy of 900 GW, almost the total capacity installed in the U.S., is available in waters beyond

five nautical miles from shore; the so called Outer Continental Shelf (OCS), defined as “all

submerged lands, its subsoil, and seabed that belong to the United States and are lying seaward and

outside of the states’ jurisdiction”[32].

This report [31] showed also that only about 10% of this energy potential is in shallow waters

area (depth< 30 m). In order to study and evaluate available and new technologies in offshore

wind energy, the DOE’s National Renewable Energy Laboratory (NREL) defined a realistic

standardized design of a wind turbine for offshore operation [33]. NREL based its design on

publicly available data from real wind turbines and theoretical designs used in offshore wind

energy simulations. In particular NREL used data from the largest wind turbine prototypes

available at that time1, the Repower 5M and the Multibrid M5000, both rated at a power out-

put of 5 MW. Many theoretical studies (DOWEC, RECOFF, WindPACT among others) are

based on conceptual design of 5-6 MW. The resulting design is a 5 MW, upwind, three-bladed

1February 2009

1.3. The NREL offshore 5 MW baseline wind turbine 15

wind turbine, operating at variable speed and pitch controlled [33]. The main physical and

operational characteristics are listed in table 1.2.

Blade

Length (w.r.t. Root Along Preconed Axis) 61.5 mMass 17,740.0 kgFirst Mass Moment of Inertia (w.r.t. Root) 363,231.0 kg mSecond Mass Moment of Inertia (w.r.t. Root) 11,776,047.0 kg m2

Rated tip speed 80.0 m s−1

Rotor

Diameter 126.0 mMass 110,000.0 kgShaft tilt 5.0 degPrecone 2.5 deg

Hub

Diameter 3.0 mMass 56,780.0 kgHub Inertia about Low-Speed Shaft 115,926.0 kg m2

Height above ground 90.0 m

Nacelle

Mass 240,000.0 kgNacelle Inertia about Yaw Axis 2,607,890.0 kg m2

Tower

Mass 347,460.0 kgHeight above ground 87.6 m

Operation

Cut-in (@ 6.9 rpm) 3.0 m s−1

Rated (@ 12.1 rpm) 11.4 m s−1

Cut-out 25.0 m s−1

TABLE 1.2: Physical and operational characteristics of the NREL offshore 5 MW baselinewind turbine [33]

Chapter 2

Background

2.1 Aeroelasticity

Aeroelasticity can be considered as the result of the mutual interaction of three main disci-

plines: dynamics, solid mechanics and (unsteady) aerodynamics.[34] This can be easily visual-

ized with the Collar diagram (fig.2.1).

Elastic forces

Inertial forces

Aerodynamic forces

(Dynamics)

(Solid mechanics)(Fluid)

FIGURE 2.1: Collar diagram [34]

Pairing the vertices of the triangle, three important scientific fields can be found:

• Stability and control: inertial and aerodynamics forces,

• Structural vibrations: inertial and elastic forces,

• Static aeroelasticity: aerodynamic and elastic forces.

17

18 Chapter 2. Background

The Collar diagram can be further expanded to include, for example, the stress induced by

high temperature (aerothermoelasticity) or the dynamics of the control system (aeroservoelas-

ticity)[34].

Aeroelastic problems can be divided in dynamic and static aeroelasticity, respectively if inertial

and unsteady aerodynamic loads are or not involved. In case of a long, slender wing in subsonic

flow they are [35, 36]:

• static aeroelasticity:

– divergence,

– control reversal;

• dynamic aeroelasticity:

– flutter

classical flutter,

stall flutter,

– buffeting.

The aeroelastic results and methods used in wing design can be used also in wind turbine blades,

since they share similar geometric and aerodynamic characteristics. While control reversal is

of no interest in case of wind turbine blades, buffeting, caused by the interaction of a lifting

surface with a strongly turbulent flow, is generally expected only in downwind wind turbines.

Furthermore, classical flutter mainly affects pitch–regulated wind turbines while stall flutter

mainly stall–regulated wind turbines. Here static aeroelastic torsional divergence and dynamic

aeroelastic bending–torsional flutter will be studied [37].

Divergence is the case of a statically unstable fluid-structure interaction. In the case of a wing

section with its aerodynamic center ahead of its center of torsion (fig.2.2) the lift force will

twist the section to a higher angle of attach and hence further increase the lift and so on. The

torsional stiffness counteracts this torsion, if the air speed is smaller than a limit speed called

divergence speed the internal elastic force and the external aerodynamic force converge to an

equilibrium point [36]; if this speed is exceeded the section will indefinitely twist beyond the

elastic limit and eventually causing the structure to fail [34]. Even if aeroelastic divergence

is avoided, in straight wing, and therefore wind turbine blades, often this torsion causes an

increase of the aerodynamic load on the outer section of the blade and hence an higher bending

moment at the blade root, possibly causing a collision between the blade and the supporting

tower in an upwind HAWT.

Flutter occurs in case of unfavorable coupling between flexural and torsional modes. While

an elastic system with one degree of freedom cannot be unstable without negative spring or

2.1. Aeroelasticity 19

Lift

Center of twistWing twist

Aerodynamic center

FIGURE 2.2: Increase of wing incidence due to wing twist, redrawn from [36]

damping force, in case of two degrees of freedom the force associated with each degree of free-

dom can interact with each other causing a diverging oscillation. While pure bending and pure

torsional oscillation are quickly damped by aerodynamic forces, the inertial and aerodynamic

forces in case of a combined torsional–flexural oscillation can excite the structure beyond its

structural damping.

For example if the torsional and bending oscillation are 90° out of phase, i.e. the torsion is at

its maximum at zero bending and vice versa (see fig. 2.3) the twisting causes a positive angle

of attack and therefore a force in the direction of motion. The situation is reversed when the

wing moves downwards. In practical cases the difference in phase angle would not be as large

as 90°, but the same effect applies [36].

Motion

Flexural axis

Positive geometric Negative geometricincidence producing positive lift incidence producing

negative lift

of wing

FIGURE 2.3: Coupling of bending and torsional oscillations and destabilizing effect of geo-metric incidence, redrawn from [36]


2.2 Aeroelastic modeling for wind turbine rotor

In order to perform a computational simulation of the dynamic performance of a wind tur-

bine, an aerodynamic model has to be used in order to determine the loads necessary for a

structural model to determine the dynamic response of the rotor.

Some common aerodynamic and structural models are available and used in different aeroelas-

tic codes developed by universities, research centers and private companies. Both time-domain

and frequency-domain codes are used.

2.2.1 Aerodynamic models

Typically two types of aerodynamic computational models are used for wind turbine aeroelas-

tic codes: BEM model and CFD model.

2.2.1.1 BEM model

The Blade Element Momentum (BEM) method is widely used because of its low computational

cost. In its classic formulation, the BEM method takes in account the angular momentum of

the flow trough a wind turbine and the deflection in the incoming near flow caused by the

presence of the blade; it is then an improvement of the simpler 1D-momentum disk actuator

model. Two important assumptions, and hence limits, of the BEM method is that it assumes

the disk to be of an infinite number of blades and no radial dependency, neglecting tip and 3D

effects. Furthermore it can not model transient effects, like dynamic stall. With the Prandtl’s

tip loss factor, the effect of a finite number of blades can be simulated, and usually this modified

BEM model is used to compute the torque and drag acting on the wind turbine. For aeroelastic

simulations the unsteady aerodynamics have to be modeled by means of different models as

dynamic wake model and dynamic stall model.

2.2.1.2 3D CFD model

With a 3D CFD model, the three governing equations of fluid dynamics - the continuity, mo-

mentum and energy equations - are numerically solved. The equations for a viscous flow, also

known as Navier-Stokes equations are [38]:

2.2. Aeroelastic modeling for wind turbine rotor 21

Continuity equation

∂ ρ

∂ t+∇ · (ρV) = 0 (2.1)

Momentum equations

x component:∂ (ρu)∂ t

+∇ · (ρuV) =−∂ p∂ x+∂ τx x

∂ x+∂ τy x

∂ y+∂ τz x

∂ z+ρ fx (2.2a)

y component:∂ (ρv)∂ t

+∇ · (ρvV) =−∂ p∂ y+∂ τxy

∂ x+∂ τyy

∂ y+∂ τzy

∂ z+ρ fy (2.2b)

z component:∂ (ρw)∂ t

+∇ · (ρwV) =−∂ p∂ z+∂ τx z

∂ x+∂ τy z

∂ y+∂ τz z

∂ z+ρ fz (2.2c)

Energy equation

∂

∂ t

ρ

e +V 2

2

+∇ ·

ρ

e +V 2

2

V

= ρq +∇ · (k∇T )−∇ · (Vp)+∂ (uτx x )∂ x

+∂

uτy x

∂ y+∂ (uτz x )∂ z

(2.3)

+∂

vτxy

∂ x+∂

vτyy

∂ y+∂

vτzy

∂ z+∂ (wτx z )∂ x

+∂

wτy z

∂ y+∂ (wτz z )∂ z

+ρf ·V

The system includes seven unknown variables, ρ, p, u, v, w, T and e and five equations. The

relation between the thermodynamic variables ρ, p, T and e can be found first assuming the

gas to be a perfect gas, which equation of state is:

p = ρRT

where R is the specific gas constant. To close the model an equation for internal energy is

required, like for example

e = e(T , p)

and in case of a calorically perfect gas it will be

e = cvT

where cv is the specific heat at constant volume [38].

For aerodynamic problems is often possible to consider the fluid newtonian, in which the


shear stress is proportional to the time rate of strain, i.e., velocity gradients. For such fluid the

viscous stresses are

τx x = λ (∇ ·V)+ 2µ∂ u∂ x

τyy = λ (∇ ·V)+ 2µ∂ v∂ y

τz z = λ (∇ ·V)+ 2µ∂ w∂ z

(2.4)

τxy = τy x =µ

∂ v∂ x+∂ u∂ y

τx z = τz x =µ

∂ u∂ z+∂ w∂ x

τy z = τzy =µ

∂ w∂ y+∂ v∂ z

where µ is the dynamic viscosity relating stresses to deformation and λ is the second viscosity

coefficient relating stresses to volumetric deformation. The second viscosity coefficient is dif-

ficult to determine, with Stokes estimated it to be λ = − 23µ, and is therefore often neglected

[39]. In this case the momentum equations become

x component:∂ (ρu)∂ t

+∇ · (ρuV) =−∂ p∂ x+∂

∂ x

2µ∂ u∂ x

+∂

∂ y

µ∂ v∂ x+∂ u∂ y

+∂

∂ z

µ

∂ u∂ z+∂ w∂ x

+ρ fx (2.5a)

y component:∂ (ρv)∂ t

+∇ · (ρvV) =−∂ p∂ y+∂

∂ x

µ

∂ v∂ x+∂ u∂ y

+∂

∂ y

2µ∂ v∂ y

+∂

∂ z

µ

∂ w∂ y+∂ v∂ z

+ρ fy (2.5b)

z component:∂ (ρw)∂ t

+∇ · (ρwV) =−∂ p∂ z+∂

∂ x

µ

∂ u∂ z+∂ w∂ x

+∂

∂ y

µ

∂ w∂ y+∂ v∂ z

+∂

∂ z

2µ∂ w∂ z

+ρ fz (2.5c)

And the energy equation becomes

∂

∂ t

ρ

e +V 2

2

+∇ ·

ρ

e +V 2

2

V

= ρq +∇ · (k∇T )−∇ · (Vp)+µ

2

∂ u∂ x

2

+ 2

∂ v∂ y

2

+ 2

∂ w∂ z

2

(2.6)

+

∂ u∂ y+∂ v∂ x

2

+

∂ u∂ z+∂ w∂ x

2

+

∂ v∂ z+∂ w∂ y

2

+ρf ·V

The result is a system of nonlinear partial differential equations, very difficult to solve analyt-

ically, since a general close-form solution to these equations has not been found yet [38]. For

this reason they are solved numerically integrating them over finite control volumes, which is

2.2. Aeroelastic modeling for wind turbine rotor 23

what a CFD code does.

With this method, the mass, momentum and energy conservation equations, for a viscous,

compressible flow are numerically solved, requiring high computational resources. The most

challenging part is to model the turbulence of the model, due to the wide range of vortex length

scales. A common approach is to split the total pressure and velocity fields in a (time)averaged

and a fluctuating part, the so called Reynolds decomposition, the famous RANS equations. Dif-

ferent turbulence models can be used with this method, modeling the whole range of turbu-

lence structures. In case of separation, more advanced and more computationally expensive

turbulence models are required. The Large Eddy Simulation (LES) model solves the exact

equations for the large scale turbulent structures, while the smaller scales are modeled in a sim-

plified manner. In order to model the strongly separated flow areas without affecting to much

the computational cost, an hybrid approach between RANS and LES, called DES (Detached

Eddy Simulation) can be used; in this case the LES model is used only in separated flow areas,

while the RANS model is used in the rest of the flow field.

2.2.2 Structural models

The blade structure can be modeled with a classic 3D FEM model or with simpler multi-body

and modal shape approach

2.2.2.1 FEM model

In rare cases this approach has been used to model the complete 3D structure of the blade,

leading to complex models of thousands of shell elements. Due to its high computational cost

a simple 1D model is preferred to the full 3D model. It consist of an elastic beam clamped

at the blade root and free at the tip. The model can also be extended to take in account non-

uniformity and anisotropic beam.

2.2.2.2 Multy-body and modal shape approach

A simpler approach is to consider the blade as a series of rigid elements hinged together and

linked with springs and dampers to model the structure stiffness and damping (multi-body

approach). Solving the equation of motion:


Mx+Cx+Kx= Fg (2.7)

where M is the mass matrix, C the damping matrix, K the stiffness matrix and Fg the gener-

alized force vector related to the external loads, the displacement vector x can be found. The

elements of the vector x are the degrees of freedom of the system.

To reduce the number of DOFs and hence the computational time of the problem, the modal

shape function can be used. A deflection shape in this method is defined as a linear combi-

nation of a few but physically realistic basic functions, which are often the deflection shapes

corresponding to the eigenmodes with the lowest eigenfrequencies; in this way only three or

four eigenmodes are used, two flapwise and one or two edgewise.

2.3 Turbulence

Turbulence is a chaotic fluctuation in time and space in the flow field. It is characterized by high

Reynolds number, meaning the inertia forces in the fluid are significant compared to viscous

forces [40].

Turbulent flows can be described with the Navier-Stokes equations, but their direct numerical

solution (DNS) is not computationally feasible at realistic Reynolds numbers, because of the

wide spectrum of sizes of the swirling flow structures (eddies). For example, in case of a tur-

bulent flow not undergoing any rapid change in the mean flow, the turbulence can be assumed

in quasi-equilibrium, meaning that the dissipation at small scales is in balance with the energy

transfer from the largest scale to the smaller. In this case the ratio between the largest scales Λ

(i.e. the thickness of the boundary layer of a wall-bounded shear flow) and the smallest scale η

(called the Kolmogorov1 length scale) can be estimated as [41]:

Λ

η∼Re3/4

and the smallest length scale would be much smaller than the smallest finite volume mesh that

can be practically used in numerical analysis.

1The smallest length scale is assumed to be independent of the outer geometrical restriction and depends onlyon the viscosity ν and viscous dissipation ε as: η=

ν3/ε1/4.

2.3. Turbulence 25

To predict the effect of turbulence without the use of direct simulation, different turbulence

models have been developed:

• RANS:

– Eddy-viscosity models,

– Reynolds stress models;

• LES;

• Hybrid LES-RANS.

2.3.1 Statistical Turbulence models (RANS)

When the timescale of the problem is much larger than the turbulent timescale, the turbulent

flow can be seen as some averaged characteristics with some time-dependent fluctuating com-

ponents. The so called Reynolds decomposition splits the total velocity and pressure fields into

a mean and a fluctuating part

ui (x, t ) =Ui (x)+ u ′i (x, t )

and

Ui =1∆t

t+∆t∫

t

ui d t

where∆t is a time scale that is large compared to the turbulence time scale but small compared

to the time scale to which the equations are solved.

For incompressible flows the continuity condition is

∂ ui

∂ xi= 0

and the same condition holds for both the mean velocity and the fluctuating part

∂ Ui

∂ xi= 0

∂ u ′i∂ xi

= 0

The mean flow equation, usually referred to as Reynolds equation, is derived from the incom-

pressible version of the Navier-Stokes equation for the total instantaneous velocity:

∂ ui

∂ t+ u j

∂ ui

∂ x j=− 1

ρ

∂ p∂ xi+ ν

∂ 2ui

∂ x j∂ x j(2.8)


and it is∂ Ui

∂ t+Uj

∂ Ui

∂ x j=− 1

ρ

∂ P∂ x j

+∂

∂ x j

ν∂ Ui

∂ x j− u ′i u ′j

(2.9)

where can be seen the turbulence interaction term in the mean flow equation in a role similar

to the viscous stress tensor. The turbulent stress, or Reynolds stress, tensor can be defined as

−ρu ′i u ′j

This tensor is symmetric and thereby has six independent components. Therefore, after aver-

aging there are ten unknowns: the three Ui components, pressure P and the six components

of the Reynolds stress tensor; but only four equations: the three components of the Reynolds

equation and the continuity equation. This is the so called turbulence closure problem, mean-

ing a model is needed for the Reynolds stress tensor.

The stress tensor for a Newtonian incompressible flow can be written

− pδi j +µ

∂ ui

∂ x j+∂ u j

∂ xi

(2.10)

where the pressure gives the isotropic part of the stress tensor.

The Reynolds stress tensor can also be rewritten to isolate the isotropic part. Introducing the

definition of kinetic energy (per unit mass) of the turbulent fluctuations

k ≡ 12

u ′k

u ′k

the Reynolds stress tensor becomes

−ρu ′i u ′j =−23ρkδi j −ρ

u ′i u ′j −23

kδi j

where the first term is the isotropic component, in analogy with the contribution form the

pressure, and accounts for two thirds of the turbulence stress, while the anisotropic component

can be described with an eddy-viscosity concept [41].

2.3. Turbulence 27

2.3.1.1 Eddy-viscosity based models of the turbulent stress tensor

The turbulence shear stress can be described in terms of a turbulent viscosity. In analogy to

the Newtonian fluid stress description(2.10), the turbulence stress can be written

−ρu ′i u ′j =−23ρkδi j +ρνT

∂ Ui

∂ x j+∂ Uj

∂ xi

(2.11)

While ν is a property of the fluid, νT is a property of the flow. The anisotropic part can be

rewritten as

ρνT

∂ Ui

∂ x j+∂ Uj

∂ xi

= 2ρνT Si j (2.12)

where Si j =12

∂ Ui∂ x j+∂ Uj

∂ xi

is the mean strain rate tensor.

Since the stress tensor is symmetric, it means that it can only depend on the symmetric, strain

part of the mean velocity gradient tensor. It thereby assumes the turbulent stress not to depend

directly on the antisymmetric mean rotation rate tensor Ωi j =12

∂ Ui∂ x j− ∂ Uj

∂ xi

[41].

To obtain the kinetic energy of the turbulent velocity fluctuation for the isotropic part of the

turbulence tensor, equation (2.9) is subtracted from (2.8) to obtain the fluctuating part of the

velocity, then multiplied by u ′i and averaged

∂

∂ t+Uj

∂

∂ x j

k =− ∂

∂ x j

12

u ′i u ′i u ′j +1ρ

u ′j p ′− ν ∂ k∂ x j

− ν∂ u ′i∂ x j

∂ u ′i∂ x j− u ′i u ′j

∂ Ui

∂ x j(2.13)

The first group of terms in the right hand side represents spatial redistribution (or transport);

the first is the net effect of turbulent diffusion of u ′i u ′i/2 by the velocity fluctuation u ′j , the

second can be seen as turbulent diffusion caused by the pressure fluctuation and the third as

the viscous diffusion of k. The second term in the right hand side of equation (2.13) is the

viscous dissipation, ε, of turbulence kinetic energy (the transfer of kinetic energy into heat)

and the last term is the transfer of energy from the mean flow to the turbulent fluctuation,

therefore named the production term.

∂

∂ t+Uj

∂

∂ x j

k =DkDt=P − ε+D


With the production, dissipation and diffusion terms defined as

P =−u ′i u ′j∂ Ui

∂ x j

ε= ν∂ u ′i∂ x j

∂ u ′i∂ x j

D = ∂

∂ x j

ν∂ k∂ x j− 1

2u ′i u ′i u ′j −

1ρ

u ′j p ′

Zero-equation models With this simple model, there is no transport of any component of

Reynolds stress tensor. The isotropic part of the turbulent stress tensor is incorporated in a

modified pressure

p∗ = p +23ρδi j k

and the turbulent viscosity of the anisotropic part is constant in the flow field and proportional

to a turbulent velocity scale and a geometric length scale (i.e. wall distance, wake thickness,

etc.)

νT ∼V · L

One-equation models In this kind of models, only one quantity is transported, k or νT .

For example in the Prandtl’s one equation model the kinetic energy transport equation is

∂ k∂ t+Uj

∂ k∂ x j

=P − ε+D = τi j∂ Ui

∂ x j−CD

k3/2

l+

∂

∂ x j

ν +νTσK

∂ k∂ x j

where

τi j = 2νT Si j −23

kδi j , CD = 0.08 , νT = k1/2 l , σK = 1.0

l is the turbulent length scale [42].

Two-equation models With two equation turbulence models, both the velocity and the

length scale are solved using separate transport equation. In these models the Reynolds stresses

are related to the mean velocity gradients and the turbulent viscosity (2.11). The turbulent

(eddy) viscosity is modeled as the product of turbulent velocity and turbulent length scale,

k1/2 and k3/2/ε respectively

νT =Cµk2

εor νT =

kω

2.3. Turbulence 29

In two equation models the turbulent velocity scale is related to the turbulent kinetic energy,

which is provided from the solution of its transport equation. The turbulent length scale is

computed from the turbulent kinetic energy and its dissipation rate. The dissipation rate of

the turbulent kinetic energy is provided from the solution of its transport equation [40].

The k-ε model The transport equations for the turbulent kinetic energy and its dissipation

rate are

∂ (ρk)∂ t

+∂

ρUj k

∂ x j=P −ρε+ ∂

∂ x j

µ+µT

σK

∂ k∂ x j

(2.14)

∂ (ρε)∂ t

+∂

ρUjε

∂ x j= (Cε1P −Cε2ε)

ε

k+

∂

∂ x j

µ+µT

σε

∂ ε

∂ x j

P = τi j∂ Ui

∂ x j

τi j =µT

2Si j −23∂ Uk

∂ xkδi j

− 23ρkδi j

(2.15)

Si j =12

∂ Ui

∂ x j+∂ Uj

∂ xi

µT =Cµρk2

ε

The model coefficients are

Cµ = 0.09 , Cε1 = 1.44 , Cε2 = 1.92 , σK = 1.0 , σε = 1.3

The k-εmodel is singular at the wall; hence it requires near-wall correction with a wall damping

function [40].


The k-ω model (Wilcox 1988) In this model, proposed by Wilcox, ω is interpreted as the

inverse timescale of the large eddies, and the transport equations are [43]

∂ (ρk)∂ t

+∂

ρUj k

∂ x j=P −β∗ρωk +

∂

∂ x j

µ+σKρkω

∂ k∂ x j

(2.16)

∂ (ρω)∂ t

+∂

ρUjω

∂ x j=γω

kP −βρω2+

∂

∂ x j

µ+σωρkω

∂ ω

∂ x j

The model coefficients are

β∗ = 0.09 , γ = 5/9≈ 0.56 , β= 3/40 , σK = 0.5 , σω = 0.5

The production term is defined in eq.(2.15), according the Boussinesq assumption. The k-

ω model is not singular on the wall, so can be integrated to the wall without wall damping

functions, but is unphysically sensitive to the free stream conditions [40].

The Shear Stress Transport (SST) model (SST-2003) Menter’s SST model is an evolution

of the baseline (BSL) model from the same author. In the BSL model the k-ω model is used

near the wall, switching to the k-εmodel for the outer region, in order to avoid the drawbacks

of these two models. The (modified) transport equations for k-ε are added to the transport

equations for k-ω, with a blending function F1, going from one near the surface to zero outside

the boundary layer.

∂ (ρk)∂ t

+∂

ρUj k

∂ x j=P −β∗ρωk +

∂

∂ x j

(µ+σKµT )∂ k∂ x j

(2.17)

∂ (ρω)∂ t

+∂

ρUjω

∂ x j=γ

νTP −βρω2+

∂

∂ x j

(µ+σωµT )∂ ω

∂ x j

+ 2 (1− F1)ρσω2

ω

∂ k∂ x j

∂ ω

∂ x j

The coefficients of the new model are a linear combination of the corresponding coefficients

of the underlying models, (1) for the k-ω model and (2) for the k-εmodel:

φ= F1φ1+(1− F1)φ2

2.3. Turbulence 31

The blending function is defined as:

F1 = tanh

arg41

arg1 =min

max

pk

β∗ωd,500νd 2ω

,4ρσω2k

C DKωd 2

C DKω =max

2ρσω21ω

∂ k∂ x j

∂ ω

∂ x j, 10−10

where d is the distance from the field point to the nearest wall.

The SST formulation accounts for the transport of the turbulent shear stress, in order to pre-

dict with higher accuracy the onset and the amount of flow separation under adverse pressure

gradients. The BSL model fails to precisely predict the flow separation from smooth surface,

not accounting for the transport of the turbulent shear stress, which results in an overproduc-

tion of the turbulent eddy viscosity. The proper transport behavior can be modeled with a

limiter to the formulation for the eddy viscosity [40]:

µT =ρa1k

max (a1ω, S F2)

where S =Æ

2Si j Si j . F2 is a blending function similar toF1, which restricts the limiter to the

wall boundary layer. Its formulation is:

F2 = tanh

arg22

arg2 =max

2

pk

β∗ωd,500νd 2ω

The coefficients are:

γ1 = 5/9 σK1 = 0.85 σω1 = 0.5 β1 = 0.075

γ2 = 0.44 σK2 = 1.0 σω2 = 0.856 β2 = 0.0828

β∗ = 0.09 a1 = 0.31


Production limiter and curvature correction The standard two equations turbulence

models overestimate the production term of the turbulent kinetic energy near stagnation points.

To prevent this, a limiter of the production term can be used; the one proposed by Menter is

P =min (P , 10β∗ρωk)

Eddy viscosity models are insensitive to rotation and curvature. In order to account the tur-

bulence production due to rotation and curvature, an empirical function fr 1 is multiplied to

the production term of the turbulent kinetic energy [40]. The function is

fr 1 =max [min ( frotation, 1.25) , 0.0]

where

frotation = (1+ cr 1)2r ∗

1+ r ∗

1− cr 3tan−1 (cr 2 r )

− cr 1

and

cr 1 = 1.0 cr 2 = 2.0 cr 3 = 1.0

All the variables and their derivatives are defined with respect to the reference frame of calcu-

lation, which may be rotating with rotation rate Ωrot. The remaining functions are [44]:

r ∗ =SΩ

r =2Ωi k S j k

ΩD3

DSi j

Dt+

εi mn S j n + ε j mn Si n

Ωrotm

Si j =12

∂ Ui

∂ x j+∂ Uj

∂ xi

Ωi j =12

∂ Ui

∂ x j−∂ Uj

∂ xi

+ 2εm j iΩrotm

and

S =Æ

2Si j Si j , Ω=Æ

2Ωi jΩi j , D =p

max (S2, 0.09ω2)

2.3. Turbulence 33

2.3.1.2 Explicit Algebraic Reynolds Stress Models

Explicit Algebraic Reynolds Stress Models (EARSM) are an extension of the standard two-

equation RANS models. While eddy-viscosity models relate linearly the anisotropic part of the

Reynolds stresses to the velocity strain-rate tensor via the turbulent viscosity νT , the EARSM

models give a nonlinear relation between the Reynolds stresses and the strain and rotation rate

tensors. The Reynolds stresses are: [40, 45]

ui u j = k

ai j +23δi j

where a≡ ai j is the anisotropy tensor, calculated with the following polynomial equation:

ai j =β1Si j +β3

Ωi kΩk j −13

I IΩδi j

+β4

Si kΩk j −Ωi k Sk j

+β6

Si kΩk lΩl j +Ωi kΩk l Sl j −23

IVδi j − I IΩSi j

(2.18)

where Si j and Ωi j are here the normalized (non-dimensional) strain-rate and vorticity tensors,

defined as:

Si j =12τ

∂ Ui

∂ x j+∂ Uj

∂ xi

, Ωi j =12τ

∂ Ui

∂ x j−∂ Uj

∂ xi

and τ is the time-scale given by τ = k/ε.

The β-coefficients are:

β1 =−NQ

β3 =−12 · IV

N ·Q (2 ·N 2− I IΩ)

β4 =−1Q

β6 =−6 ·N

Q (2 ·N 2− I IΩ)

The invariants are defined as:

I IS = Sk l Sl k , I IΩ =Ωk lΩl k , IV = Sk lΩl mΩmk

The denominator Q is:

Q =N 2− 2I IΩ

A1


N can be derived from:

N =

A3/3+

P1+p

P2

1/3+ sign

P1−p

P2

P1−p

P2

1/3for P2 ≥ 0

A3/3+ 2

P 21 − P2

1/6 cos

13 arccos

P1pP 2

1−P2

for P2 < 0

where

P1 =

A23

27+

A1A4

6I IS −

23

I IΩ

·A3, P2 = P 21 −

A23

9+

A1A4

3I IS −

23

I IΩ

3

and

A1 = 6/5, A2 = 0, A3 = 9/5, A4 = 9/4

Chapter 3

Objectives

Flutter is a relatively new topic in wind energy technology. This particular aeroelastic phe-

nomenon has been widely studied in aerospace (wings, rocket nozzles and turbojet engine

blades) as well as in civil engineering (towers, chimneys and bridges) because of the spectacu-

lar, and often dangerous, failures that it has caused to these structures, and the high cost asso-

ciated with the replacement or modification of the affected structure. Experience has shown

how flexible structures, and hence with low-valued characteristic frequencies, that are subject

to high aerodynamic loads can in some particular circumstances develop such an unstable and

destructive oscillation. In this case an unfavorable time-lag between the structure movement

and the unsteady aerodynamic forces will cause the structure to absorb energy from the flow

and therefore an increase in time of the amplitude of the vibration of the structure.

So far there are few cases of wind turbines affected by flutter. It is expected that as the blades

grow in length, their relatively flexible structure of fiberglass reinforced composite will en-

counter flutter instability, especially in the highly loaded pitch-regulated wind turbines. Many

studies have proved this possibility, making use of simplified aeroelastic stability codes, with

overall good results. Most of them use BEM method to solve the quasi-steady aerodynamic of

the undeformed structure, in no-wind condition and with rotational speed as only variable.

Some codes use unsteady 2D-aerodynamic solver for the blade sections.

This work is about a complete 3D CFD model of a large wind turbine blade for a fluid-structure

interaction study. This kind of aerodynamic simulation has been chosen in order to allow FSI

investigations with different values of wind speed and direction and different rotational speed.

Due to the highly iterative approach in FSI studies, the CFD model has to deliver the most

35

36 Chapter 3. Objectives

reliable results while minimizing the computational cost.

The main focus is to study the effect of different turbulence models and meshing techniques on

numerical results and computational cost. Numerical results will be compared with an high

fidelity CFD model results of the same blade. Computational cost of different models will be

compared and evaluated against numerical results.

The objectives of this work are:

• Evaluate the effect of different meshing techniques and turbulence models on conver-

gence speed and computational cost of the CFD simulation.

• Compare numerical results with a reference high fidelity CFD model.

Chapter 4

Method of Attack

The study case is a 61.5 meters long (from root to tip) wind turbine blade in a rotating frame

of reference. The technical data of the blade can be found in table 1.2 at page 15.

The simulation has been run at 11.7 rpm and 11.3 m/s wind speed with a simplified model of

the blade, neglecting precone and shaft tilt angles. The geometry of the blade can be seen in

figure 4.1.

The blade has been studied with ANSYS-CFX, varying different parameters.

The study was initially performed with steady-state simulations, using different mesh sets and

turbulence models. Based on the results of the steady-state simulations, some transient simu-

lations were performed, in order to investigate the effect of unsteady aerodynamics, like flow

separation and tip vortexes, on the numerical results. Transient simulations were performed

using all the mesh sets already used in steady-state runs, in order to investigate how this factor

can affect the numerical residuals and the convergence evolution.

Both steady-state and transient results were validated against an high-fidelity numerical simula-

tion. This result, called from now on reference, was obtained by a project partner at University

Stuttgart, Institute of Aerodynamics and Gas Dynamics (IAG). The simulation used the code

FLOWer, commonly used for helicopter aerodynamics. The model used has a physical time-

step of 1°revolution, with a C-shaped mesh designed for a y+ of 1 and 13 million cells for the

whole rotor. For the simulation of one revolution of the wind turbine rotor were required

about 3000 CPUh, and has been run on a cluster of 512 Intel Xeon E5-2680 processors.

37

38 Chapter 4. Method of Attack

x

y

z

FIGURE 4.1: Blade geometry

Chapter 5

Numerical techniques

The software used for this study was ANSYS–CFX 14 for the fluid dynamic computation,

some post-processing has been performed with MatLab.

ANSYS–CFX incorporates four tools, one for every step of a complete CFD simulation:

• ICEM is used to define the geometric input for the problem to be studied: here all the

geometries (0D, 1D, 2D and 3D) are created or imported from a CAD program, the

study domain and its subdomains are defined and eventually the mesh for the whole

domain is configured and created;

• ANSYS–Pre is used to define the physical input for the solver: here the flow is com-

pletely characterized, the different boundaries and the frames of reference (stationary,

translational or rotational) are defined, the parameters for the solver are set and at last

the input file for the solver is created;

• ANSYS–Solver Manager performs the simulation, keeps track of the residuals for con-

vergence, manages the pairings and the resources for parallel simulation and writes the

output file;

• ANSYS–Post is used to post-process the results: visualizing, manipulating and export-

ing numerical results and loading different results file, for example different timesteps of

a transient simulation.

39

40 Chapter 5. Numerical techniques

5.1 Workflow

The first step is to prepare the geometry for the mesh. The blade geometry is imported and

the remaining geometries necessary to define the domains and the boundaries are created. The

mesh is created on these geometries.

The mesh file is imported in the preprocessor to prepare the steady state simulation.

After the simulation converged to a solution, a new input file is prepared, now for a transient

simulation.

This new input file is used to define the transient simulation, with the result file from the steady

state simulation as initial condition. The result file is analyzed at last.

This procedure has been repeated for different meshing techniques and sizes and for different

turbulence models.

5.2 ICEM

In this study the aerodynamics of a wind turbine rotor is analyzed considering an isolated

blade with periodic boundaries, in order to simulate a complete three-blade rotor with a much

smaller domain, saving computational time. For this reason the domain is shaped as a cylin-

drical sector with a central angle of 120°.

Since the blade has to rotate about the hub of the wind turbine while the wind flows in the

domain, two subdomains were defined.

The inner domain contains the blade and rotates with it. It has the same central angle, centered

around the blade, and extends radially from the turbine hub to the inner shroud at 64 meters

radius, and axially of 5 meters upstream and downstream the blade, fig. 5.1(a).

The inner domain is enclosed in a much bigger outer domain, stationary. It extends radially

from the hub to the outer shroud at 500 meters radius and axially of 500 meters upstream and

downstream, fig. 5.1(b).

5.2. ICEM 41

(a) Inner domain (b) Outer domain

FIGURE 5.1: Inner and outer domain geometry

The wind flows in the system in positive x-direction, hence it was modeled as a constant speed

flow orthogonal to the inlet surface (black arrows in figure 5.2). The surface parallel to inlet

(outlet) and the outer shroud were modeled as openings (blue arrows), allowing both inflow

and outflow. The two side walls were defined as periodic boundaries. The hub was modeled

as a free-slip wall in the outer domain and as a no-slip wall in the inner domain.

FIGURE 5.2: Domain boundary conditions


The two domains have also different mesh density. The inner domain has a much finer mesh

to capture the strong gradients in velocity and pressure the flow has near the blade. The outer

domain, on the other hand, needs to have a much coarser mesh to keep the number of total

nodes reasonably low.

To mesh the volume in the two domains, hexahedron elements were chosen. To do so, the

volume has to be divided in blocks and on the edges of these blocks the mesh was defined

in terms of number of elements and an edge refinement factor, if needed. Edge refinement

has been used, for example, near the solid walls (blade and inner hub surface) to capture the

velocity boundary layer exists due to flow viscosity. In order to minimize the distortion of

the mesh near the blade, the O-grid tool has been used to match the blocks of mesh with the

curvilinear surface of the blade.

5.2.1 Inner and outer mesh

Three different meshes were created for the inner domain. The initial mesh (see tab 5.1) called

proj37, was modified in two different ways.

In the first modification, proj38, the mesh was refined along the blade span, increasing the

number of elements on the blade surface. This radial refinement, which propagate in the whole

inner domain, was limited to the blade only and was not extended on the volume between the

blade tip and the inner shroud; in order to minimize the number of mesh elements in the inner

domain.

The second modification, proj39, is based again on proj37 but refining the mesh orthogonally

to the blade surface. In this case was possible to modify only the blocks around the blade

geometry, so that the refinement will not propagate to the whole inner domain, where is not

necessary. The edges orthogonal to the blade surface were divided in 50 elements, with their

length exponentially decreasing moving towards the blade surface (see figure 5.3).

Mesh type Nodes Elements

proj37 1,194,608 1,150,254proj38 1,297,340 1,249,710proj39 1,687,880 1,640,364

TABLE 5.1: Inner domain mesh sets

5.2. ICEM 43

(a) proj37 (b) proj39

FIGURE 5.3: Inner domain mesh, blade section

For the outer domain were created two different meshes.

The initial mesh outer5 is homogeneous in most of the domain volume, the mesh density

was increased axially and radially at the interface with the inner domain (see figures 5.4(a) and

5.4(c)). These refinements will propagate, the former radially and the latter axially, to the

whole outer domain, also where this kind of refined mesh is not necessary.

The original mesh was further refined, obtaining mesh outer6. It was refined circumferentially

(see fig. 5.4(b)), axially at the downstream (right) interface with the inner domain; and radially

at the inner shroud radius and between the inner shroud and the hub, where tip vortexes will

move downstream (fig. 5.4(d)). These refinement drastically increased the number of mesh

nodes, as can be seen in table 5.2.

Mesh type Nodes Elements

outer5 332,000 315,315outer6 1,177,200 1,137,045

TABLE 5.2: Outer domain mesh sets


(a) outer5, radial (b) outer6, radial

(c) outer5, axial (d) outer6, axial

FIGURE 5.4: Outer domain mesh

5.3 CFD simulation

Several CFD simulations were performed, in order to find the most appropriate settings for the

aerodynamic model of the blade. Tests were conducted with different meshing techniques and

turbulence models, on a steady state simulation. Numerical results in terms of CP distribution

on some blade sections were compared with those found by partners at Stuttgart University.

Once the preferred turbulence model was found, further investigations on mesh size effect

were performed in transient simulations.

The pressure coefficient has been computed with the usual formula:

CP =p − p∞

q∞

where q∞ = 1/2ρ∞V 2∞ is the dynamic pressure.

The free-stream velocity considered is the total air speed seen by the blade, equal to the vector

sum of the wind speed and the tangential speed of the blade at the considered span position.

5.3. CFD simulation 45

The numerical results were extracted at four span positions (see table 5.3 and figure 5.5), with

the following physical parameters:

• v = 11.3 m/s: wind speed;

• ω = 11.7 rpm = 1.225 rad/s: rotational speed;

• p0 = 1 atm = 101325 Pa: static pressure;

• ρ0 = 1.225 kg/m3: air density;

• u : tangential speed;

• w : relative velocity.

Blade section spanposition

radius [m] u [m/s] w [m/s]

Station 3 50% 32.2 39.5 41.0Station 4 85% 53.9 66.0 67.0Station 5 95% 59.7 73.1 74.0Station 6 99% 62.7 76.8 77.6

TABLE 5.3: Physical values

123456

FIGURE 5.5: Span positions for results analysis

Sections closer to the blade root (stations 1 and 2) were not considered due to the heavily

turbulent and separated flow in that region; its strongly fluctuating characteristic cannot be

properly investigated with a steady state simulation.

5.3.1 Steady-state simulation

Steady-state simulations were run for maximum 1000 iterations with a convergence criteria of

a RMS residuals below 5 ∗ 10−5.


The hardware used for these simulations was a desktop computer with an Intel Core i7 860

processor and 8.00 GB RAM, running Microsoft Windows 7 Pro 64bit SP1.

5.3.1.1 Effect of turbulence models

First step was to investigate the effect of different turbulence models on the original mesh

(proj37 and outer5) of the system. They are:

• EVTE: a 1 equation model for eddy viscosity transport;

• k-ε: classic 2 equation model for transport of turbulent kinetic energy and dissipation;

• k-ω: Wilcox 2 equation model for transport of turbulent kinetic energy and turbulent

frequency;

• SST: Menter Shear Stress Transport model, blending of k-ω model near the wall with

k-εmodel in the outer region;

• EARSM: Explicit Algebraic Reynolds Stress Model, a non-eddy-viscosity RANS turbu-

lence model.

k-ω was also tested with two correction factors, a production limiter and a rotation correction

factor. The k-ε and EARSM failed to converge to a solution.

5.3.1.2 Effect of meshing techniques

The second step was to study how the mesh size affects the numerical results.

First the effect of different meshes on the inner domain was investigated, the study cases are

defined in table 5.4.

Study case Inner domain Outer domain

Case 1 proj37 outer5Case 2 proj38 outer5Case 3 proj39 outer5

TABLE 5.4: Inner mesh studies

Also the effect of the mesh size on the outer domain was studied. Table 5.5 shows the study

cases for the outer domain.

5.3. CFD simulation 47


Case 1 proj37 outer5Case 4 proj37 outer6


TABLE 5.5: Outer mesh studies

5.3.1.3 Effect of turbulence correction factors

The third step was to investigate the effect of some suggested turbulence correction factors

on the numerical result of the simulation. In this case the turbulence model and the mesh

size were not changed and the curvature correction and production correction factors were

added to a basic k-ω simulation on the original mesh (proj37 and outer5), first separately then

together (see table 5.6). For more information about used turbulence correction factors see

section 2.3.1.1 at page 31 in the turbulence models theory.

Study case Curvaturecorrection

Production limiter

Case 1 no noCase A yes noCase B no yesCase C yes yes

TABLE 5.6: Turbulence correction factors studies

5.3.2 Transient simulation

The transient simulations were run for seven complete revolutions (periods), lasting 64 time-

steps each, for a total of 36 seconds and 450 time-steps. The convergence criteria was the same

as the steady-state simulation, a RMS residuals below 5 ∗ 10−5; for every time-step was set a

minimum of three and a maximum of six coefficient loops. All five mesh study cases were

considered.

The hardware used for these simulations was a workstation with two Intel Xeon E5620 pro-

cessors and 23.50 GiB RAM, running CentOS 6.4.

To compare the numerical results of the different simulation with the reference case, the pres-

sure distribution of the last time-step was used.

Chapter 6

Results and Discussion

In this chapter will be shown and discussed the results from various numerical simulations.

They are divided between steady-state and transient simulations, and according the study cases

described in the previous chapter.

6.1 Steady-state results

This numerical study started with the steady-state aerodynamic simulation of the turbine

blade. Steady-state simulations are necessary to set the initial conditions for a transient simu-

lation, if required. In this study, steady-state simulations were also used to get a preliminary

insight into the effect of mesh and turbulence models on numerical results, because they are

less heavy on computational resources than transient simulation, while still producing mean-

ingful results.

The results are shown with the pressure distribution at four blade span-positions: the pressure

coefficient CP has been computed with the local total speed and has been plotted versus the

dimensionless chord position. The pressure on the suction side is the lower part of the graph.

6.1.1 Turbulence models comparison

Five different RANS turbulence models were tested on the same geometry and mesh; more

complex models (LES, DES, DRSM, ecc.) were not considered because of their high compu-

tational cost.

49

50 Chapter 6. Results and Discussion

Here can be seen the results from three of them: k-ω, EVTE and SST. EARSM and k-εmodels

did not converge to a solution.

0 0.2 0.4 0.6 0.8 1−3

−2.5

−2

−1.5

−1

−0.5

0

0.5

1

1.5

CP distribution at 32.2 m radius [ 50% span position]

chord position

CP

Referencek−ωEVTESST

(a) Station 3

0 0.2 0.4 0.6 0.8 1−3

−2.5

−2

−1.5

−1

−0.5

0

0.5

1

1.5


chord positionC

P


(b) Station 4

0 0.2 0.4 0.6 0.8 1−2.5

−2

−1.5

−1

−0.5

0

0.5

1

1.5


chord position

CP


(c) Station 5

0 0.2 0.4 0.6 0.8 1−4

−3.5

−3

−2.5

−2

−1.5

−1

−0.5

0

0.5

1

CP distribution at 62.7 m radius [100% span position]

chord position

CP


(d) Station 6

FIGURE 6.1: Pressure distribution: steady-state, turbulence models

All of the three models tested deliver very similar results, comparable to the reference case.

There are marginal differences between the SST and the EVTE model, while the k-ω approx-

imates slightly better the reference result.

All the three models show a very similar pressure distribution compared to the reference case,

also near the blade tip, slightly underestimating the blade load (which is proportional to the

area enclosed in the pressure distribution graph) compared to the reference result. The biggest

difference can be seen upstream the 40% chord point on the SS, which could affect the aero-

dynamic twisting of the blade, in particular at the section at 59.7 meters (fig. 6.1(c)). Here all

the three models show a reduction in the blade loading just downstream of the leading edge on

the suction side, probably suggesting a flow separation. Considering that this result is shared

6.1. Steady-state results 51

among all the turbulence models used, this is probably caused by problems with the blade ge-

ometry or with the mesh. It is interesting to observe that this section is located in the area near

the blade tip where the leading edge curves downstream and the blade chord length starts to

decrease more quickly (see figures 4.1 and 5.5).

Both EVTE and SST have a lower computational cost compared to k-ω model (tab. 6.1), at

cost of lower numerical accuracy. This was expected for EVTE, a one-equation model, while

SST was expected to be closer to k-ω than to EVTE both in terms of computational cost and

numerical accuracy.

Model CPU time [sec] CPU cost

k-ω 1.69 · 105 100%EVTE 1.19 · 105 70%SST 1.37 · 105 81%

TABLE 6.1: Computational time: steady-state, turbulence models

Considering the numerical results, all the three models tested gave good outcome. EVTE

model is fast and delivers good results and should be chosen if computational cost is the main

constrain while k-ω gives the best results at a reasonably higher CPU time. Even if EVTE

seems to be the best option for steady-state simulation, delivering very similar results compared

to more complex turbulence models while being considerably lighter in computational cost,

k-ω has been chosen for the following simulations for its accuracy and for consistency with

reference results, also obtained with a k-ω model.

6.1.2 Mesh sets comparison

The choice of the mesh is one of the most important parameter for a numerical simulation, as

it can greatly affect both the numerical result and the computation time.

Here five different mesh will be studied, three for the inner domain and two for the outer

domain. The effect of mesh sets will be studied separately on inner and outer domain.

6.1.2.1 Inner domain mesh

For the inner domain, three different mesh were tested. From the initial mesh proj37 were

obtained two refined mesh: in proj38 the mesh was refined in the blade span direction, while

in proj39 the mesh was refined orthogonal to the blade surface. The details of these mesh can


be found in table 5.1 at page 42.

The study cases are defined in table 5.4, rewritten here.




0 0.2 0.4 0.6 0.8 1−3

−2.5

−2

−1.5

−1

−0.5

0

0.5

1

1.5


chord position

CP

ReferenceCase 1Case 2Case 3

(a) Station 3

0 0.2 0.4 0.6 0.8 1−3

−2.5

−2

−1.5

−1

−0.5

0

0.5

1

1.5


chord position

CP


(b) Station 4

0 0.2 0.4 0.6 0.8 1−2.5

−2

−1.5

−1

−0.5

0

0.5

1

1.5


chord position

CP


(c) Station 5

0 0.2 0.4 0.6 0.8 1−4

−3.5

−3

−2.5

−2

−1.5

−1

−0.5

0

0.5

1


chord position

CP


(d) Station 6

FIGURE 6.2: Pressure distribution: steady-state, inner domain mesh

All three mesh deliver the same results. Both refinements, span-wise and orthogonal to the

surface, did not improve the results, also at section 5 (fig. 6.2(c)). In chord-wise direction the

mesh seems enough dense.

In figure 6.3 can be seen the time evolution of the residuals for the mass and momentum equa-

tions. After about 80 timesteps residuals do not decrease or very slowly, and RMS residuals for

the momentum equation are just below 10−3, not reaching the target of 5.5 · 10−5. The three


inner mesh studied gave same results, and increasing the number of timesteps would not give

better results.

The computational cost increases with the density of the mesh, and it is significant for Case 3.

The computational cost is generally proportional to the number of nodes (tab. 6.2).

100 200 300 400 500 600 700 800 900 100010

−7

10−6

10−5

10−4

10−3

10−2

10−1

Timestep

RM

S r

esid

uals

P−Mass U−Mom V−Mom W−Mom

10−7

10−6

10−5

10−4

10−3

10−2

10−1

Case 1Case 2Case 3

FIGURE 6.3: Residuals time history: steady-state, inner domain mesh

Model CPU time CPU cost Nodes[sec]

Case 1 1.69 · 105 100% 100%Case 2 1.85 · 105 109% 107%Case 3 2.11 · 105 125% 132%

TABLE 6.2: Computational time: steady-state, inner domain mesh

6.1.2.2 Outer domain mesh

Two different mesh for the outer domain were tested, to investigate how they could affect

the numerical results on the blade and their effect on residuals and time to converge. The

initial mesh outer5 has been further refined at the interface with the inner domain and in

circumferential direction to obtain mesh outer6. The details of these mesh can be found in


table 5.2 at page 43.






Coarse inner mesh First the two mesh for the outer domain were tested on the original,

coarse, mesh for the inner domain (proj37): Case 1 and Case 4.

0 0.2 0.4 0.6 0.8 1−3

−2.5

−2

−1.5

−1

−0.5

0

0.5

1

1.5


chord position

CP

ReferenceCase 1Case 4

(a) Station 3

0 0.2 0.4 0.6 0.8 1−3

−2.5

−2

−1.5

−1

−0.5

0

0.5

1

1.5


chord position

CP


(b) Station 4

0 0.2 0.4 0.6 0.8 1−2.5

−2

−1.5

−1

−0.5

0

0.5

1

1.5


chord position

CP


(c) Station 5

0 0.2 0.4 0.6 0.8 1−4

−3.5

−3

−2.5

−2

−1.5

−1

−0.5

0

0.5

1


chord position

CP


(d) Station 6

FIGURE 6.4: Pressure distribution: steady-state, outer domain mesh

The refined mesh in the wake of the blade does not affect the pressure distribution on the blade,

as can be seen in figure 6.4, where the two different outer mesh give the same result.


The two mesh for the outer domain have also similar residuals, they do not reach the conver-

gence criterion and the residuals time evolution is the same (fig. 6.5).

100 200 300 400 500 600 700 800 900 100010

−7

10−6

10−5

10−4

10−3

10−2

10−1

Timestep

RM

S r

esid

uals


10−7

10−6

10−5

10−4

10−3

10−2

10−1

Case 1Case 4

FIGURE 6.5: Residuals time history: steady-state, outer domain mesh

Refined inner mesh Here the two mesh for the outer domain are tested with a refined mesh

for the inner domain (proj38), to see how they interact with a different inner mesh. The study

cases are Case 2 and Case 5.

The effect of the refined mesh in the outer domain with proj38 inner mesh is not as good as

with the original outer mesh (fig. 6.6). The pressure distribution for Case 5 seems shifted to

higher values than Case 2, with this gap decreasing to a negligible amount as moving towards

the blade tip. The results were controlled several times for computation errors in the post-

processing, without success. The reason of these discrepancies is unknown, it could be errors

in the interface between inner and outer domain. Was not possible to rerun the simulation to

investigate this issue.

The residuals time history does not show any meaningful difference between Case 2 and Case

5, and similar results to Case 1 and Case 4. The convergence criteria was met only by the

P-Mass equation (fig. 6.7).


0 0.2 0.4 0.6 0.8 1−3

−2.5

−2

−1.5

−1

−0.5

0

0.5

1

1.5


chord position

CP


(a) Station 3

0 0.2 0.4 0.6 0.8 1−3

−2.5

−2

−1.5

−1

−0.5

0

0.5

1

1.5


chord position

CP


(b) Station 4

0 0.2 0.4 0.6 0.8 1−2.5

−2

−1.5

−1

−0.5

0

0.5

1

1.5


chord position

CP


(c) Station 5

0 0.2 0.4 0.6 0.8 1−4

−3.5

−3

−2.5

−2

−1.5

−1

−0.5

0

0.5

1


chord position

CP


(d) Station 6

FIGURE 6.6: Pressure distribution: steady-state, outer domain mesh (2)

The refined outer mesh greatly increases the computational cost, for both cases. The increase of

computational cost is almost of the same proportion of the increase in nodes number (tab. 6.3).


Case 1 1.69 · 105 100% 100%Case 4 2.48 · 105 147% 155%

Case 2 1.85 · 105 109% 107%Case 5 2.80 · 105 166% 162%

TABLE 6.3: Computational time: steady-state, outer domain mesh


100 200 300 400 500 600 700 800 900 100010

−7

10−6

10−5

10−4

10−3

10−2

10−1

Timestep

RM

S r

esid

uals


10−7

10−6

10−5

10−4

10−3

10−2

10−1

Case 2Case 5

FIGURE 6.7: Residuals time history: steady-state, outer domain mesh (2)

6.1.3 Correction factor comparison

In order to overcome some known weaknesses of two-equation RANS turbulence models,

the basic model used for the simulation can be enhanced with some correction factors (see

section 2.3.1.1).

Here the basic k-ω model (Case 1) is compared with the same including correction factors,

first added separately and then with both correction factor included, as defined in table 5.6,

rewritten here.

Study case Curvaturecorrection

Production limiter

Case 1 no noCase A yes noCase B no yesCase C yes yes

TABLE 5.6: Turbulence correction factors studies


0 0.2 0.4 0.6 0.8 1−3

−2.5

−2

−1.5

−1

−0.5

0

0.5

1

1.5


chord position

CP

ReferenceBasic k−ωCase ACase BCase C

(a) Station 3

0 0.2 0.4 0.6 0.8 1−2.5

−2

−1.5

−1

−0.5

0

0.5

1

1.5


chord position

CP

ReferenceBasic k−ωCase ACase BCase C

(b) Station 5

FIGURE 6.8: Pressure distribution: steady-state, turbulence correction factors

The effects of these two correction factors on the base k-ω model are negligible. At all four

sections they underestimate the blade loading, with the usual problem at section 5 (fig. 6.8).

From these results can be seen that the increased complexity of the model (tab. 6.4) with the

introduction of correction factors does not show any useful improvement on the final result.

For this reason these correction factor were not considered in following simulations.

Model CPU time [sec] CPU cost

Case 1 1.69 · 105 100%Case A 1.77 · 105 105%Case B 1.72 · 105 102%Case C 1.76 · 105 104%

TABLE 6.4: Computational time: steady-state, turbulence correction factors


6.1.4 Discussion

Steady-state simulations gave good results compared to the reference case, obtained with a tran-

sient simulation on much more fine mesh. From the results seen in the previous pages can be

drawn the following conclusion:

• The turbulence model for the steady state simulation affects marginally the results of

the simulation; EVTE is fast with good results, while k-ω gives better results with good

computational cost.

• The effect of mesh density for the inner domain is not significant. Increasing the mesh

density does not improve neither numerical results nor convergence. Considering also

the computational cost the best option for the inner domain is mesh proj37.

• The refined mesh in the outer domain does not improve, in steady-state, the numeri-

cal results, both in terms of pressure distribution and residuals and convergence, while

considerably increasing the computational effort. The model does not reach the conver-

gence target with the momentum equations and underestimates the load on the first half

of the SS.

The more coarse mesh outer5 should be preferred for the outer domain. Similar results

were found using EVTE and SST as turbulence models. The best results came from the

original mesh using a k-ω model.

• Applying on the model any turbulence correction factor is not suggested. The differ-

ences in the results are very marginal, at the cost of a more complex model.

In case of a steady state simulation a simple and fast turbulence model is the best option. The re-

sults could be probably improved optimizing the mesh density, but the results already available

are not too far form the reference and should not affect the numerical results of the following

transient simulation based on them.


6.2 Transient results

In case of transient simulations the flow is solved along a predetermined period of time, unlike

steady-state where the solution represent a fixed moment in time. Transient simulations are

necessary in case of unsteady aerodynamics, as could be with flutter or flow separation. In case

of aeroelastic (static) divergence and RANS turbulence models, steady-state simulations could

be enough. In this section the effect of transient simulation will be studied, comparing them

with steady-state results and analyzing their residuals evolution and convergence.

6.2.1 CP results

For the transient simulation, data from the last time step were used; the differences from the

mean value over the last period are negligible.

To better understand the difference in numerical results between transient cases and reference

case, the computational cost should be considered. In table 6.5 can be seen the CPU time

required to model a complete revolution of the rotor.

Reference Case 1

1.08 · 107 CPUs 1.02 · 105 CPUs

TABLE 6.5: Computational time: reference and transient, one revolution

6.2.1.1 Comparison with steady-state results

In figure 6.9 can be seen the CP distribution on the blade for Case 1 from steady-state and tran-

sient simulation. The difference between the transient results and the reference are generally

small, and negligible at blade pressure side. The difference is bigger on the suction side.

Comparing transient result to steady-state of the same mesh, only small differences can be seen.

These differences are mainly located at the first half of the blade chord and are bigger at 50 %

span position (fig. 6.9(a)), decreasing towards the blade tip, which is the opposite of what was

expected, considering the vortexes and the spanwise flow near the tip. Both steady-state and

transient results show a possible separation on the suction side of section 5 (fig. 6.9(c)), without

any difference between steady-state and transient results.

Similar results were obtained with the other mesh.

6.2. Transient results 61

0 0.2 0.4 0.6 0.8 1−3

−2.5

−2

−1.5

−1

−0.5

0

0.5

1

1.5


chord position

CP

ReferenceStedy stateTransient

(a) Station 3

0 0.2 0.4 0.6 0.8 1−3

−2.5

−2

−1.5

−1

−0.5

0

0.5

1

1.5


chord position

CP


(b) Station 4

0 0.2 0.4 0.6 0.8 1−2.5

−2

−1.5

−1

−0.5

0

0.5

1

1.5


chord position

CP


(c) Station 5

0 0.2 0.4 0.6 0.8 1−4

−3.5

−3

−2.5

−2

−1.5

−1

−0.5

0

0.5

1


chord position

CP


(d) Station 6

FIGURE 6.9: Pressure distribution: steady-state and transient on Case 1

6.2.1.2 Inner domain mesh comparison

For the inner domain, three different mesh were tested, while the outer domain mesh was not

changed. The details of the three studied mesh can be found in table 5.1 at page 42.





It can be seen that there are very small differences between different mesh sizes. All three

models give good results if compared to the reference, with the exception of the suction side


0 0.2 0.4 0.6 0.8 1−3

−2.5

−2

−1.5

−1

−0.5

0

0.5

1

1.5


chord position

CP


(a) Station 3

0 0.2 0.4 0.6 0.8 1−3

−2.5

−2

−1.5

−1

−0.5

0

0.5

1

1.5


chord position

CP


(b) Station 4

0 0.2 0.4 0.6 0.8 1−2.5

−2

−1.5

−1

−0.5

0

0.5

1

1.5


chord position

CP


(c) Station 5

0 0.2 0.4 0.6 0.8 1−4

−3.5

−3

−2.5

−2

−1.5

−1

−0.5

0

0.5

1


chord position

CP


(d) Station 6

FIGURE 6.10: Pressure distribution: transient, inner domain mesh

of the blade just downstream of the nose at 95% span position, as already seen for steady state

simulations. That is probably caused by flow separation.

The differences between the three mesh models are negligible. The results are the same on the

pressure side, at all four sections considered. On the suction side there are very small differ-

ences between the three models, with Case 3 being the closest to the reference result and Case 1

the furthest; this difference increases towards the blade tip. The refined mesh seems to improve

the results only on the suction side and near the tip, negligible compared to the computational

cost (tab. 6.6).

Analyzing the results and comparing them to the reference results, the mesh size must be con-

sidered. The reference results were obtained with a mesh designed to have a y+ value of 1,

while the meshes used in this project are way more coarse, in order to keep the computational

cost at reasonable low levels.



Case 1 7.11 · 105 100% 100%Case 2 7.14 · 105 ∼ 100% 107%Case 3 8.29 · 105 117% 132%

TABLE 6.6: Computational time: transient, inner domain mesh

6.2.1.3 Outer domain mesh comparison

Two different mesh for the outer domain were tested, while the inner domain mesh was not

changed. The details of these mesh can be found in table 5.2 at page 43.






Coarse inner mesh Like the other cases, this results show a negligible difference on the

pressure side and a generally small difference on the suction side, compared to reference result.

The differences between the two mesh studied here are very small (fig. 6.11).

In details, the two cases do not show any difference on the pressure side, at all four sections. On

the suction side the differences are very small and restricted on the first half of the section, and

decreases moving towards the blade tip. Case 4 is the mesh which more closely approximates

reference result, at a slightly higher computational cost (tab: 6.7).


0 0.2 0.4 0.6 0.8 1−3

−2.5

−2

−1.5

−1

−0.5

0

0.5

1

1.5


chord position

CP


(a) Station 3

0 0.2 0.4 0.6 0.8 1−3

−2.5

−2

−1.5

−1

−0.5

0

0.5

1

1.5


chord position

CP


(b) Station 4

0 0.2 0.4 0.6 0.8 1−2.5

−2

−1.5

−1

−0.5

0

0.5

1

1.5


chord position

CP


(c) Station 5

0 0.2 0.4 0.6 0.8 1−4

−3.5

−3

−2.5

−2

−1.5

−1

−0.5

0

0.5

1


chord position

CP


(d) Station 6

FIGURE 6.11: Pressure distribution: transient, outer domain mesh

Refined inner mesh In figure 6.12 can be seen the CP distribution on the blade for Case 2

and Case 5. Both mesh gave good results compared to the reference case. Bigger differences can

be found on the suction side, especially at section 5 (fig. 6.12(c)).

The differences between the two studied cases are very small, and only on the SS. As already

seen with cases 1 and 4, the results from the refined outer mesh (outer6) are slightly closer

to the reference results than the coarse outer mesh (outer5), with this difference decreasing

towards the blade tip.

It should be noted that in these transient simulations there is not the anomaly between Case

2 and Case 5 seen in the steady-state simulations (fig. 6.6). This suggests that the anomaly was

not caused by an interference between proj38 inner mesh and outer6 outer mesh.

The more complex model of Case 5 comes with a considerably higher computational cost

(tab. 6.7).


0 0.2 0.4 0.6 0.8 1−3

−2.5

−2

−1.5

−1

−0.5

0

0.5

1

1.5


chord position

CP


(a) Station 3

0 0.2 0.4 0.6 0.8 1−3

−2.5

−2

−1.5

−1

−0.5

0

0.5

1

1.5


chord position

CP


(b) Station 4

0 0.2 0.4 0.6 0.8 1−2.5

−2

−1.5

−1

−0.5

0

0.5

1

1.5


chord position

CP


(c) Station 5

0 0.2 0.4 0.6 0.8 1−4

−3.5

−3

−2.5

−2

−1.5

−1

−0.5

0

0.5

1


chord position

CP


(d) Station 6

FIGURE 6.12: Pressure distribution: transient, outer domain mesh (2)


Case 1 7.11 · 105 100% 100%Case 4 7.77 · 105 109% 155%

Case 2 7.14 · 105 ∼ 100% 107%Case 5 1.38 · 106 194% 162%

TABLE 6.7: Computational time: transient, outer domain mesh


6.2.2 Discussion

Transient simulations gave good results compared to reference case, showing a possible flow

separation on the suction side of section 5.

In details transient simulations gave the following results:

• The comparison with steady-state simulation shows an improvement in numerical re-

sults. The differences are mainly located on the first half of the section and at mid-span

position. This suggests that transient simulations can resolve better than steady-state the

thin boundary layer downstream the leading edge. Near the blade tip and the trailing

edge the differences between transient and steady-state are negligible, both simulations

do not solve completely the complex flow in this area, as suggested by the difference with

reference case.

• Refining the mesh in the inner domain gave the expected effect of improving numerical

results, though the differences are marginal. Should be noted that the improvement

in numerical results seems more related to the number of nodes in the inner domain

than the actual refinement direction. Furthermore, the computational cost seems to

increase less than the number of nodes (tab. 6.6), suggesting that a further increase in

the number of nodes in the inner domain could improve the numerical results without

affecting excessively the computational cost.

• The refined outer mesh gave also better results. The improvements in numerical results

are really small compared to the increase in nodes number, and the effect in computa-

tional cost is particularly heavy for Case 5 (tab. 6.7). As already seen before, the dif-

ferences in numerical results are located only in the first half of the suction side, and

generally small. The improvement caused by the refined outer mesh is greater in case

of the coarse mesh for the inner domain, but the final results of Case 4 and Case 5 are

comparable.

Chapter 7

Final discussion and Conclusions

Aerodynamic loads and their accurate computation are extremely important for a reliable

aeroelastic simulation, but the highly iterative method for FSI simulations requires a fast aero-

dynamic simulation.

Often aerodynamic data for FSI simulations are obtained from 2D flow models, with correc-

tion factors for stall and 3D flow, in order to minimize the computational cost, but at the cost

of many approximations. On the other hand, a complete 3D CFD simulation can model di-

rectly not only these phenomena but also transients in wind speed and direction, rotor speed

and wind gradients, but can be really heavy on computational cost.

In this work were evaluated the possibilities and outcomes of 3D CFD simulations for aeroe-

lastic study of a complex, realistic wind turbine blade. Preliminary numerical results were

compared to more advanced CFD results, considering also their computational cost, in order

to give an introductory insight into the issues and possible strategies for 3D CFD simulation

for aeroelastic studies.

The model was tested with steady-state and transient simulation, changing mesh density and

turbulence model.

Turbulence models used gave similar results. Of the five different turbulence models tested,

the three that reached convergence had only minimal differences mainly on the suction side.

The computational cost generally scaled with the complexity of the turbulence model, with

EVTE one-equation model being the fastest. SST model, which uses a k-ω model near the wall

and a k-ε in the freestream showed to be faster than basic k-ω model.

EARSM and k-ε models diverged after about 15 iterations. Should be noted that EARSM is

67

68 Chapter 7. Conclusions

based on a k-ε model, which requires a wall function due to being singular on the wall. This

suggests that either there are problems with the surface or more probably with the mesh near

the surface. Scalable wall function used with k-ε should handle also finer mesh, but k-ωmodels

can switch to Low Reynolds method if the mesh is fine enough, and in this case proved to be

more robust.

From the results of these simulations EVTE model gave comparable good results with remark-

able lower computational cost and should be preferred.

Increasing the mesh density in the outer domain is not advisable. Due to the size of the outer

domain even a small increase in the mesh density in one direction propagates in the whole

domain generating a huge amount of nodes, also in areas where this density is not required.

This effect can be easily seen in results of Case 4 and 5, where the increase in the number of

nodes and computational cost gives only a marginal improvement in numerical results. For

this domain a good solution could be the use of an unstructured mesh, so that the element

length can quickly grow from the interface with the inner domain to the far-field boundary.

Inner domain is more sensitive to mesh density, but the improvement was very small. The

small difference in numerical results seems to be more linked to the number of nodes than the

actual mesh strategy. The results show also that the increase in computational cost is about

an half of the increase in number of nodes. The mesh density in the inner domain seems to

be sufficient to deliver reliable results, the difference with the reference case is probably caused

by the size of the elements near the blade surface, in terms of y+ and expansion ratio. The

former, in particular, affects how the boundary layer is solved and its transition from laminar

to turbulent. For a detailed study of the boundary layer and transition, the requirement is a

y+max ≈ 1 and an expansion ratio ≈ 0.1.

The most important factor for aeroelastic simulations is the aerodynamic load in terms of

force and torque w.r.t. the section flexural axis. These values are computed from the pressure

distribution on the blade surface, comparing transient results with the reference case shows

that the results are generally comparable but with a significant reduction in computation time

(table 6.5).

Analyzing the results, the blade loading from all the transient results is expected to be really

close to that computed with reference case, especially at mid-span region. The more coarse

mesh used in this study shows appreciable differences only at trailing edge of blade tip and on

suction side at section 5. The former can be explained with the highly turbulent flow in this

limited region and will have a minor effect on the global blade loading.

7.1. Future work 69

The underestimation of the aerodynamic load on the suction side of section 5 can potentially

be more detrimental to the local blade loading. This is probably caused by a localized flow

separation, due to the different way the boundary layer and its transition are computed in

this study and in the one used as benchmark. While it is important to properly model the

boundary layer in the first part of the SS, affected by transition and strong pressure gradient, it

will require a drastic increase in mesh density near the wall. Considering the results achieved

in this study, the increase in computation time will cause a significant improvement of the load

distribution only in a section near the blade tip, and marginally affect the loading in mid-span

region, and is therefore not suggested.

In conclusion can be seen that a overall good numerical result can be achieved with a model

simple enough to run on a common workstation, and hence allowing an FSI study of a com-

plete HAWT blade with a full 3D CFD simulation, despite the significant length of the blade.

Most of the mesh nodes should be in the inner domain and a possible improvement could be

the use of an unstructured mesh for the outer domain, in order to keep the element length

small only at the interface with the inner domain. The quality of the mesh in the inner do-

main is very important for the accuracy of the numerical results, as can be seen with failure of

ε-based turbulence models, and the geometry of the blade complicates this task. The turbu-

lence model affects marginally the numerical result with the mesh used in this study, therefore

the EVTE model should be preferred.

7.1 Future work

In this work, for technical reasons, only k-ω turbulence model was used for transient simula-

tions and comparison between turbulence models was based only on steady-state results. To

have a better insight in the effect of turbulence model, this comparison should be done with

transient results.

Due to the challenge posed by the meshing of the inner domain, other techniques than simple

block mesh should be studied. In particular C-shaped and unstructured mesh should be con-

sidered, also to obtain a fine control of y+ value over the entire blade surface.

With FSI simulations, mesh deformation has to be expected. This issue was not studied.

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