tesi triennale

UNIVERSITÀ DEGLI STUDI DI NAPOLI FEDERICO II

FACOLTÀ DI INGEGNERIA

CORSO DI LAUREA TRIENNALE IN

INGEGNERIA AEROSPAZIALE

DIPARTIMENTO DI INGEGNERIA AEROSPAZIALE

TESI DI LAUREA

ANALYSIS OF AIRFOILS FOR APPLICATIONS IN VAWT AND

ASSESSMENT OF THEIR

AERODYNAMIC COEFFICIENTS

RELATORE

CH.MO PROF. CANDIDATO

FABRIZIO NICOLOSI CAIAZZO ANTONIO

MATRICOLA N 35/460

CORRELATORE

ING. PIERLUIGI DELLA VECCHIA

ANNO ACCADEMICO 2011/2012

Analysis of airfoils for applications in VAWT and assessment of their aerodynamic coefficients Caiazzo Antonio

2

Index

Index……..……………………………………………………………………………………………………………………………………………………2

Summary.……………………………………………………………………………………………………………………………………………………3

1 Overview Turbine ......................................................................................................................................... 4

1.1 Introduction ............................................................................................................................................... 4

1.2 Vertical-axis turbines ................................................................................................................................. 5

2 Analysis of airfoils used for vertical axis turbines…….................................................................................. 6

2.1 CFD Methodology ...................................................................................................................................... 6

2.2 Computational code Fluent ....................................................................................................................... 7

3 Computing Grid ............................................................................................................................................ 7

3.1 The turbulence models .............................................................................................................................. 9

3.2 Spalart-Allmaras model............................................................................................................................. 9

3.3 Settings used for the analysis .................................................................................................................. 10

4 Results of Analysis ..................................................................................................................................... 13

4.1 Naca 0018………………………….…………….……….……………………………………………...………………………....…………..13 4.2 GT 10………………..…………..………………………………….……...……………………………………………………………………….15 4.3 Hlift………………………….…..……….……..……………………………………………………………………………………………………17 4.4 S809….……..………………..….……………….…………………………………………………………………………………………….…..19

5 Appendix..……………….….…………………………………………………………………………………………………………………………..21

5.1 Sc_Wlet…………….……………………………………………...…………………………………………………………....………….........21 5.1.1 Sc wlet_root………...…………………………………………………..….……………………………………………………………...21 5.1.3 Sc wlet_tip………..…………………………………………..…….……………………………………………………………...........23

6 Conclusions…………………………………………………………………………….................................................................25


3

Summary

This thesis focuses on the aerodynamic analysis of airfoils used for vertical wind

turbines or vertical marine turbines.

The airfoils aerodynamic analysis has been performed using the commercial

Fluent CFD code, while the airfoils meshes have been performed by the ADAG

group staff of the University of Naples Federico II.

The main goal of this thesis has been the Fluent settings in terms of Physics

condition, Aerodynamic conditions and analysis Results. Vertical wind turbine

airfoils have been analyzed in a wide range of angles of attack (-20 °<α<110°),

to have more reliable results in the operative range of these machines.

The wind turbine airfoils analyzed have been the classic NACA 0018, the GT10,

the Hlift airfoil(designed by the ADAG Group) and the Selig S809 airfoil. At the

end of this thesis two supercritical airfoils have been investigated to have low

speed results of these kind of airfoils.


4

1 Overview on turbines

1.1 Introduction

Wind or marine turbines are devices used to convert the mechanic energy into electrical energy.

They can be divided into two main category, which differ each other by the axis of rotation: vertical

axis turbines and horizontal axis turbines.

This work deals with the vertical axis turbines, in particular with the airfoils employed in this kind

of turbines.

The propeller blade of vertical axis turbines, like a thin wing offers minimal resistance to

advancement, does not create dangerous turbulence, has a high-lift: this translates into a high

coefficient of power and very high speed of rotation (some rotors have propellers with peripheral

speeds close to the sound’s).

In order to have a constant and high performance, the propeller should always be able to steer in the

wind.

There are two methods used: by a rudder of appropriate size which directs the whole complex

(propeller upwind or wind-up), or, by putting the propeller posteriorly to the complex formed by a

generator and rotation pin and using the gyroscopic torque of the engine itself to orient the mill

(bow downwind or down-wind).

The propeller has a streamlined airfoil easily obtainable from books and popular publications.

In practice standard airfoils are used for modest applications.


5

1.1 Vertical axis wind turbines

The vertical-axis wind turbines (VAWT) have the axis of rotation perpendicular to the current

direction, and consist of turbines of differential action: using aerodynamic drag or lift as the

propulsive force.

In particular the Darrieus, a vertical axis type turbine,

uses aerodynamic lift as propulsive force.

This model has blades which are vaguely of a

parabolic shape to reduce the high centrifugal force

that develops during operation but where the radius is

small (at the ends), is also small the developed power.

In general the VAWT consist of a set of blades

arranged vertically which are connected, (in some

cases) with radial arms, to a vertical rotation axis.

The vertical-axis turbines have some advantages over

the horizontal ones, in particular the weight of the set

composed by transmission unit and the alternator can

be reduced and the blades of the turbine with vertical

axis should not be in a specific position, thanks to the

using of the wind in an arc of 360 °.

Fig.1.1 turbine with vertical axis

They are small, very aesthetic, and better adapted to turbulent wind ranges typical of cities (wind

direction and flow variables) than horizontal-axis turbines, but also in utilization in mountain areas,

with very intense wind gusts, the vertical axis is preferred, since the horizontal axis turbines are

limited, owing to inertia of the masses in tangential and vertical motion, while the vertical axis

turbine is indifferent to the rotation of the wind so the weight of the support structures can be

reduced.

The main advantages of the vertical axis are:

the continuous operation regardless of wind direction,

the best resistance even at high wind speeds and their turbulence,

the low noise production, the easy and relative inexpensive maintenance.


6

2 Analysis of airfoils used for vertical axis turbines

The fluid-dynamic performance analysis of a wind turbine consists of a series of investigations on

the aerodynamic behavior of the wing airfoil which constitute the blades of the turbine.

It is important to know what happens to an airfoil under certain conditions, which are specifically

characterized by relatively low Reynolds numbers.

These Reynolds number values represent a big problem since under these conditions is rather

difficult to find or calculate the

aerodynamic profiles, and this can create

several problems in the design phase.

Another big problem appears with high

angles of attack of the airfoil of the blade

during a complete revolution of the turbine.

From these considerations it is necessary to

find a computational method that could

analyze the airfoils aerodynamic in these

operating conditions.

So it is organized a methodology for CFD

analysis.

Fig.2.1 Principle of operation of the turbine blade

2.1 Methodology CFD

The CFD methods offer the highest degree of accuracy and description of the phenomena involved;

they are in fact able to reproduce fully the field unsteady and the onset of the phenomena of

dynamic stall of which the vertical axis turbines are affected.

The results obtained, in terms of accuracy and description, depend strongly on the mesh-size used

and implemented by the model to describe the physics.

The time required for the solution must consider both the time required for the creation of the grid

and the time required for the solution of the field by the solver; they are generally very long.

It is also necessary to consider the possible time required for the Replacement of the airfoil adopted

for the blades. In this work, the airfoils meshes have been performed by the ADAG group staff of

the University of Naples Federico II.


7

2.2 Computational code Fluent

Fluent is a commercial software , now widely used in engineering, physics and chemistry in both

industrial and academic field.

It is a solver able to process and post-process a problem, previously defined by boundary conditions

assigned on a computing grid, thanks to the finite volume method.

For all the fluid-dynamics problems, Fluent always solves the balance equations of mass and

momentum, while in the cases in which they are involved heat transfers or density changes, the

code adds an additional equation of energy balance.

In this paper it will be assumed the Mach number is small enough so that it can neglect the effects

of compressibility, and thus consider the constant density in the flow field.

Moreover in the fields in question chemical reactions and phase transitions will not be considered.

The motion, however, cannot be considered laminar, so you will need to model in a timely manner

the effects of the presence of turbulence in the field and this will require the resolution of an

additional equation at least.

3 Computing Grid

The equations of fluid dynamics are not generally solvable analytically in their domain of

definition.

Therefore, for the analysis of the evolution of fluid involved, numerical solution techniques are used

(finite volume, finite element, finite difference, etc..).

The basic idea of these techniques consists in dividing the initial domain into smaller subdomains

and simpler geometry to solve the equations respecting the initial conditions set on the edge of the

original domain.

The term mesh indicates the set of subdomains (or cells) in which the initial domain has been split

and it determines the spatial integration step for the solution of linearized and discretized equations,

resulting from the system of differential equations that describe the behavior of the system.

A proper mesh must satisfy 2 requirements:

It must present locally the resolution necessary and sufficient for the proper representation

of local variables, so it must be dense in areas of strong gradients and sparse in areas of low

gradients;

It must be of good quality, so the cells must be little distorted and the variation of

the characteristic parameters must be continuous and gradual.


8

In the finite volume methods, the solver calculates the average value of the variables in each cell

(discrete solution) and places it in the center cell; the continuous solution is then reconstructed by

interpolation.

The creation of the mesh can follow two directions: 1) one can implement a structured mesh, or

ordered, in this case its cells can be considered as elements of an array, 2) or use a unstructured

mesh in which there is no order between the cells and is faster and easier to implement, but less

efficient in terms of accuracy and speed of resolution of the field.

Often it is more advantageous to generate an unstructured mesh because it is faster in the

calculations , but they give only indications of the orders of magnitude of the physical variables of

interest in the simulation, with lower accuracy.

In this case you can save time by creating an unstructured mesh but you cannot determine the

position of a cell according to the one of the neighbor cells.

In all CFD methods also the distortion of the cells represents a significant source of error in a

simulation, so great attention is necessary in the creation of the mesh.

The following table presents a brief analysis of the advantages and disadvantages of structured

mesh:

Table 1.1: Comparison of advantages and disadvantages of structured mesh

The definition of mesh of good quality is essential for obtaining reliable results by the solver.

Structured Mesh

Advantages Disadvantages

Greater accuracy,

especially if aligned to the

flow

Density also prevalent

in areas at low

gradient

More efficient numbering

resulting in more efficient

solution algorithms

Difficulty of

discretization of

complex domains

More effectively control

over the size of the cells

On complex

geometries it requires

a considerable

expenditure of time


9

3.1 The turbulence models

Turbulence indicates a state of motion of the fluid characterized by strong irregularities, both spatial

and temporal of the physical sizes, a coexistence of a wide range of length, speed and time scales,

the three-dimensionality of motion, high capacity mixing, unpredictability.

Such motion, although solution of the Navier-Stokes equations, therefore presents a higher level of

complexity compared with laminar motion.

The problem is to determine the most appropriate description of this state both for the

understanding of physical phenomena, and for the modeling required to predict the condition of

turbulence.

For the purposes of the present study it is necessary to emphasize especially the large capacity of

turbulent flows to dissipate kinetic energy (this property affects greatly on the strength of the body).

The simulation of turbulence implies a choice of model definitely dependent on the particular

problem to be addressed. Fluent is able to implement different models of turbulence, in particular

the Spalart-Allmaras model.

3.2 Spalart-Allmaras Model

The Spalart-Allmaras model is the simplest among those implemented in Fluent: in fact it resolves a

single additional equation, or the transport of a modified form of the kinematic turbulent viscosity.

Indicating with the kinematic turbulent viscosity as the viscosity of a turbulent flow in which a

turbulence model is implemented and defining ν the kinematic turbulent amended viscosity, it is

affirmed the following relation where is a function known of damping.

The kinematic turbulent modified viscosity is therefore, according to the model, identical to the

kinematic turbulent viscosity except in areas near the walls, where they occur phenomena of

production and destruction of the turbulent viscosity.

This model is designed for aeronautical applications and has been shown to provide good results in

the presence of strong adverse pressure gradients and modeling of transonic flows.

It has proven successful in applications concerning the turbo machinery, and the rotating objects

too; for these peculiarities, together with the robustness and economy of computation (it consist of a

single evolution equation and not two) it has been chosen among the models implemented in Fluent

for the present work.


10

3.3 The Settings Used for analysis

Airfoils NACA 0018, Hlift, GT10, S809 and Sc Wlet

In this chapter the settings of the Fluent code for the airfoil aerodynamic analysis will be presented.

The use of the Spalart-Allmaras model, has necessitated the creation of a particularly dense mesh

near the body.

The transition phenomenology is an unsteady fluid-dynamic event happened when the turbulence

level of the upstream current is high or in the presence of a surface particularly wrinkled or made to

vibrate.

The circumstances mentioned above often occur in the operation of a turbine with a vertical axis,

and because there is a strong swirling interaction between the blades both because the mechanical

parts, placed in rotation, hardly be balanced by a dynamic point of view, so then the blades are

subjected to vibratory phenomena.

In the table we can see the numerical values of the fluid-dynamic constants used:

Table 2.1: Values of the simulation flow conditions

The conditions of Mach and Reynolds are set forth below for each airfoil in analysis.

Flow conditions

1.225

4.17 e-5

(For airfoils Naca0018, GT10,

Hlift S809)

6.25 e-6

(For airfoils Sc wlet root and

tip)

Depending on the Reynolds

number desired

288 K


11

In particular, starting from the knowledge of the Mach, it has been able, from the formulation

, easily derive the fluid velocity V from the speed of sound (in air at 20 ° C) √

, and then the viscosity μ as to ensure the desired Reynolds, by the

with c = 1

(unitary chord of the airfoil).

Here are the settings used for the Fluent simulations, it is worth to note that the parameters used are

the result not only of a laborious literary research, but also an equally laborious research work of

setting that would guarantee computational speed and accuracy of the solution.

Table2.2: Settings used in Fluent

Turbulence Model Spalart Allmaras

Boundary conditions Airfoil = wall

Farfield = pressure-far-field

Int_farfield = interior

Outflow = pressure-far-field

Material Air, density ideal gas,

viscosity Sutherland

Solid, aluminum

Models Energy-On

Viscous-Spalart-Allmaras

(1 eqn)

Solution method Pressure velocity coupling scheme

= SIMPLE

Spatial discretization Second order upwind

Convergence criterion 10e-8

Under-relaxtion factor default


12

As it has been highlighted clearly, the external grille

consists of two parts, called "Farfield" and "outflow" both

placed at a distance of approximately 30 times the chord

from the edges of the airfoil.

Below it is shown an example, a detail of the grid on the

edge of the airfoil Naca0018, in order to highlight both the

necessary condensation inside the boundary layer, both the

quality of the cells in terms of perpendicularity to the

airfoil and in terms of aspect ratio.

Fig.3.1 Mesh

Figure 3.2: Mesh around the airfoil NACA 0018

Figure 3.2: Mesh around the leading edge of the airfoil NACA 0018 Figure 3.3: Mesh around the trailing edge of the airfoil Naca 0018


13

4 Results of the analysis

Airfoils NACA 0018, GT10, Hlift, S809

It is presented below the results of the simulation carried out in terms of lift, drag, and momentum

(with the center of the momentum located to 25% of the chord of the profile) coefficient as a

function of the angle of attack, according to the parameters and settings denoted previously. Then

you will report graphs of numerical results in Fluent CFD.

4.1 NACA0018

Fig:4.1 Airfoil Naca0018

Table 3.1: Aerodynamic coefficients obtained by numerical simulation Fluent of the airfoil Naca0018

Afterwards the curves of main aerodynamic coefficients of the airfoil in question are shown.

α [deg] Cm Cl Cd

0 6.2307e-05 -3.0787e-04 1.3290e-02

2 5.8353e-03 1.9592e-01 1.3539e-02

4 1.1263e-02 3.8970e-01 1.4292e-02

6 1.6395e-02 5.7632e-01 1.5616e-02

8 2.1363e-02 7.5076e-01 1.7617e-02

10 2.6359e-02 9.0721e-01 2.0501e-02

12 3.1444e-02 1.0378e+00 2.4691e-02

14 3.6263e-02 1.1311e+00 3.1175e-02

16 3.8879e-02 1.1660e+00 4.3006e-02

18 3.1527e-02 1.0910e+00 7.1091e-02

20 2.6645e-03 9.2068e-01 1.3178e-01

25 -6.3226e-02 7.9519e-01 3.1260e-01

30 -9.9451e-02 8.0429e-01 4.6215e-01

35 -1.3181e-01 8.5483e-01 5.9975e-01

40 -1.6302e-01 8.7588e-01 7.3515e-01

50 -2.2316e-01 8.1799e-01 9.8044e-01

60 -2.8066e-01 6.5518e-01 1.1867e+00

70 -3.3754e-01 4.2386e-01 1.3534e+00

80 -3.8047e-01 9.3714e-02 1.5341e+00

90 -5.0321e-01 -1.7616e-02 1.8145e+00

100 -6.2374e-01 -6.8379e-01 2.3359e+00


14

Fig.4.1.1: Cm-α curve for Mach 0.1 and Reynolds Fig 4.1.2: Cl-α curve for Mach 0.1 and Reynolds

The curves of the coefficients are obtained

starting from processing of the data

obtained in Fluent with the Matlab

software, to vary the angle of attack α and

for a value of equal to Mach 0.1, with

Reynolds number value of equal to one

million.

Figure 4.1.3: Cd-α curve for Mach 0.1 and Reynolds

Below the images relating to conditions of pressure and turbulence on the airfoil considered for

certain structures, derived by the software fluent, and this will be proposed in the following for each

profile examined.

Pressure conditions to α = 0 ° Fig. 1 to the left and to α = 10 ° Fig. 2 to the right for Mach 0.1 and Reynolds


15

4.2 GT10

Fig:4.2 Airfoil GT10

Table 3.2: Aerodynamic coefficients obtained by numerical simulation Fluent of the aerodynamic airfoil GT10

At 80 ° by means of non-convergence, the data are obtained according to the arithmetic mean of those

obtained from a population of approximately 1000 elements (belonging to the same "cycle"), resulting from

the simulation. In order to obtain good graphics, an arithmetic average of the data has also been applied for

high angles such as 90 ° and 100 °.

α[deg] Cm Cl Cd

-20 2.7282e-02 -5.2219e-01 2.5079e-01

-18 1.3591e-02 -5.9234e-01 2.0218e-01

-16 -7.2591e-02 -9.2115e-01 4.9811e-02

-14 -8.3980e-02 -9.0739e-01 3.0671e-02

-12 -8.6257e-02 -7.9172e-01 2.3146e-02

-10 -8.7056e-02 -6.3212e-01 1.8858e-02

-8 -8.8157e-02 -4.4415e-01 1.6157e-02

-6 -8.9755e-02 -2.3722e-01 1.4506e-02

-4 -9.1719e-02 -1.7587e-02 1.3656e-02

-2 -9.3783e-02 2.0732e-01 1.3497e-02

0 -9.5758e-02 4.3220e-01 1.3976e-02

2 -9.7475e-02 6.5189e-01 1.5076e-02

4 -9.8585e-02 8.5960e-01 1.6884e-02

6 -9.8851e-02 1.0481e+00 1.9603e-02

8 -9.8028e-02 1.2077e+00 2.3744e-02

10 -9.5493e-02 1.3186e+00 3.0777e-02

12 -9.1441e-02 1.3687e+00 4.2426e-02

14 -8.8048e-02 1.3866e+00 5.7542e-02

16 -8.6397e-02 1.3799e+00 7.6271e-02

18 -8.8499e-02 1.3538e+00 1.0032e-01

20 -9.3136e-02 1.2943e+00 1.3124e-01

25 -1.3003e-01 1.1095e+00 2.5493e-01

30 -1.8409e-01 9.8550e-01 4.4915e-01

35 -2.2281e-01 1.0244e+00 7.1073e-01

40 -2.4876e-01 1.0192e+00 8.5022e-01

50 -2.9746e-01 9.1102e-01 1.0972e+00

60 -3.4134e-01 7.1531e-01 1.2999e+00

70 -3.8590e-01 4.6922e-01 1.4635e+00

80 -4.5200e-01 2.0784e-01 1.6505e+00

90 -5.3893e-01 -1.5597e-01 1.9961e+00

100 -6.4503e-01 -7.0033e-01 2.4230e+00


16

Fig.4.2.1: Cm-α curve for Mach 0.1 and Reynolds Fig.4.2.2: Cl-α curve for Mach 0.1 and Reynolds

Fig.4.2.3: Cd-α curve for Mach 0.1 and Reynolds

Pressure conditions at α = -20 ° fig. 3 to the left and to α = 0 ° Fig. 4 to the right for Mach 0.1 and Reynolds


17

4.3 Hlift

Fig:4.3 Airfoil Hlift

α[deg] Cm Cl Cd

-20 -1.5763e-02 -3.7498e-01 2.3973e-01

-18 -2.6607e-02 -3.2490e-01 1.9846e-01

-16 -3.8427e-02 -2.8022e-01 1.5922e-01

-14 -5.4870e-02 -2.8374e-01 1.1438e-01

-12 -1.3805e-01 -4.0415e-01 2.2911e-02

-10 -1.5026e-01 -3.5888e-01 1.8476e-02

-8 -1.5144e-01 -1.8763e-01 1.6000e-02

-6 -1.5234e-01 2.8696e-02 1.4679e-02

-4 -1.5297e-01 2.5283e-01 1.4218e-02

-2 -1.5325e-01 4.7863e-01 1.4473e-02

0 -1.5314e-01 7.0088e-01 1.5405e-02

2 -1.5242e-01 9.1441e-01 1.6974e-02

4 -1.5092e-01 1.1131e+00 1.9316e-02

6 -1.4825e-01 1.2907e+00 2.2332e-02

8 -1.4520e-01 1.4401e+00 2.7197e-02

10 -1.4018e-01 1.5523e+00 3.4015e-02

12 -1.3282e-01 1.6048e+00 4.3803e-02

14 -1.2721e-01 1.5853e+00 6.2488e-02

16 -1.2679e-01 1.5070e+00 9.2349e-02

18 -1.3166e-01 1.4171e+00 1.2936e-01

20 -1.4211e-01 1.3369e+00 1.7328e-01

25 -1.7344e-01 1.1832e+00 2.9289e-01

30 -2.0853e-01 1.0758e+00 4.2695e-01

35 -2.4937e-01 1.0136e+00 6.0003e-01

40 -2.8172e-01 1.0034e+00 8.1011e-01

50 -3.2143e-01 9.2065e-01 1.1175e+00

60 -3.5873e-01 7.1957e-01 1.3266e+00

70 -3.9660e-01 4.6820e-01 1.4861e+00

80 -4.6909e-01 2.0876e-01 1.6940e+00

90 -5.5273e-01 -1.6011e-01 2.0730e+00

100 -6.7325e-01 -7.0400e-01 2.5246e+00

Table 3.3: Aerodynamic coefficients obtained by numerical simulation Fluent of the airfoil Hlift

At 80 ° by means of non-convergence, the data are obtained according to the arithmetic mean of those

obtained from a population of about 800 elements (belonging to the same "cycle"), resulting from the

simulation.


18



Pressure conditions at α = -20 ° Fig 5 to the left and to α = 0 ° fig.6 right for Mach 0.1 and Reynolds


19

4.4 S809

Fig:4.4 Airfoil S809

α[deg] Cm Cl Cd

-20 1.2120e-02 -9.4111e-01 1.2500e-01

-18 5.2895e-03 -9.4550e-01 9.9042e-02

-16 7.6693e-04 -9.2625e-01 7.8852e-02

-14 -2.3236e-03 -8.8999e-01 6.2058e-02

-12 -4.7524e-03 -8.4673e-01 4.6904e-02

-10 -8.5139e-03 -8.1787e-01 3.1235e-02

-8 -1.7316e-02 -7.1928e-01 2.0615e-02

-6 -2.3006e-02 -5.3834e-01 1.6783e-02

-4 -2.8003e-02 -3.3019e-01 1.4818e-02

-2 -3.2846e-02 -1.0885e-01 1.3824e-02

0 -3.7448e-02 1.1750e-01 1.3562e-02

2 -4.1685e-02 3.4284e-01 1.3994e-02

4 -4.5185e-02 5.6050e-01 1.5158e-02

6 -4.7674e-02 7.6383e-01 1.7078e-02

8 -4.8866e-02 9.4557e-01 2.0077e-02

10 -4.8701e-02 1.0966e+00 2.4716e-02

12 -4.7509e-02 1.1968e+00 3.2799e-02

14 -4.7293e-02 1.2005e+00 5.0081e-02

16 -4.9582e-02 1.1728e+00 7.2933e-02

18 -5.5267e-02 1.1511e+00 9.9043e-02

20 -6.2097e-02 1.0053e+00 1.3930e-01

25 -1.5046e-01 9.1001e-01 4.3612e-01

30 -1.7919e-01 9.2943e-01 5.6830e-01

35 -2.0711e-01 9.7632e-01 7.0286e-01

40 -2.3502e-01 9.8963e-01 8.3807e-01

50 -2.8552e-01 9.0886e-01 1.0817e+00

60 -3.3167e-01 7.3447e-01 1.2936e+00

70 -3.7609e-01 4.9128e-01 1.4621e+00

80 -3.9993e-01 2.1053e-01 1.7277e+00

90 -5.0804e-01 -2.3670e-01 2.0415e+00

100 -6.0046e-01 -6.8406e-01 2.1553e+00

110 -6.1889e-01 -9.3513e-01 2.0963e+00

Table 3.4: Aerodynamic coefficients obtained by numerical simulation Fluent of the airfoil S809

At 0 ° and 80 ° by means of non-convergence, the data are obtained according to the arithmetic mean of

those obtained from a population of approximately 1000 elements (belonging to the same "cycle"), resulting

from the simulation.


20



Pressure conditions at α = -20 ° Fig 6 to the left and to α = 0 ° fig.7 right for Mach 0.1 and Reynolds


21

5 Appendix

The following profiles analyzed Sc Wlet, belong to the supercritical category, and are used for other

applications too, such as airfoils of airplanes that reach high speeds. The resulting curves of the

aerodynamic coefficients have been obtained from the simulation results of Fluent code.

5.1 Sc Wlet

5.1.1 Sc wlet_root

Fig:4.5 Airfoil Sc wlet_root

Table 3.5: Aerodynamic coefficients obtained by numerical simulation Fluent of the airfoil Sc wlet_root

α[deg] Cm Cl Cd

-18 5.5679e-02 -6.4653e-01 2.4390e-01

-16 5.3403e-02 -6.2728e-01 2.1387e-01

-14 5.0370e-02 -6.0515e-01 1.8300e-01

-12 4.4253e-02 -5.7554e-01 1.5127e-01

-10 2.6781e-02 -6.8220e-01 1.1212e-01

-8 -6.6806e-02 -6.5701e-01 1.4104e-02

-6 -6.7475e-02 -4.4875e-01 9.2556e-03

-4 -6.7557e-02 -2.2221e-01 7.6694e-03

-2 -6.7646e-02 1.1927e-02 7.1154e-03

0 -6.7068e-02 2.4384e-01 7.8482e-03

2 -6.6490e-02 4.7575e-01 8.5810e-03

4 -6.5912e-02 7.0767e-01 9.3139e-03

6 -6.3506e-02 9.2127e-01 1.1513e-02

8 -5.9244e-02 1.1155e+00 1.4890e-02

10 -4.9309e-02 1.2557e+00 2.3172e-02

12 -3.9662e-02 1.0662e+00 1.8846e-01

14 -4.4261e-02 1.1270e+00 2.9046e-01


22



Pressure conditions at α = -10 ° fig.9 left and to α = 0 ° fig.10 right for Mach 0.3 and Reynolds


23

5.1.2 Sc wlet_tip

Fig:4.6 Airfoil Sc wlet_tip

Table 3.6: Aerodynamic coefficients obtained by numerical simulation Fluent of the airfoil Sc wlet_tip

At 10°, 12° and 14° by means of non-convergence, the data are obtained according to the arithmetic mean of

those obtained from a population of approximately 1000 elements (belonging to the same "cycle"), resulting

from the simulation.

α[deg] Cm Cl Cd

- 20 6.1605e-02 -6.7797e-01 2.7407e-01

-18 5.8804e-02 -6.6010e-01 2.4417e-01

-16 5.6662e-02 -6.4043e-01 2.1476e-01

-14 5.4020e-02 -6.1698e-01 1.8494e-01

-12 4.8392e-02 -5.8819e-01 1.5284e-01

-10 3.8096e-02 -5.5404e-01 1.2101e-01

-8 -3.8173e-02 -6.5883e-01 7.3551e-02

-6 -6.8754e-02 -4.3924e-01 1.0441e-02

-4 -6.9111e-02 -2.1369e-01 7.8069e-03

-2 -6.9251e-02 1.9664e-02 7.0507e-03

0 -6.8767e-02 2.4446e-01 7.3818e-03

2 -6.8600e-02 4.8698e-01 7.9372e-03

4 -6.7228e-02 7.1106e-01 9.5582e-03

6 -6.2283e-02 8.9701e-01 1.4328e-02

8 -5.8672e-02 1.1050e+00 1.6813e-02

10 -4.8831e-02 1.0350e+00 3.6481e-02

12 -2.9914e-02 1.0580e+00 6.9308e-02

14 -2.5666e-01 1.0458e+00 1.8710e-01


24



Pressure conditions at α = -10 ° fig.11 left and to α = 0 ° fig.12 right for Mach 0.3 and Reynolds


25

6 Conclusions

Analyzing by CFD the aerodynamic performance of the airfoils used for vertical axis wind turbine

blades is a difficult problem to deal with.

The analysis in these operating conditions is strongly influenced by the turbulence model used and

by the quality of the grid; the low quality of grids or do not lead to the convergence of the results, or

they can provide completely wrong results.

Another important problem is represented by the high angle of attack to which the elements of

turbine blades work during one complete revolution. These angles are next to the aerodynamic stall

and often in post-stall.

It is preferred then investigate with the CFD method the aerodynamic behavior of the airfoils to

high angles of attack, and then use these results with the models for the performance analysis of the

turbines.

The results have been encouraging and from this work will be investigated in the wind tunnel

performance of the airfoils in the design phase, Naca 0018, GT10, Hlift, S809, under conditions of

laminar, turbulent, steady flow and in particular investigate the unsteady phenomena that

characterize the normal operation of the VAWT.

tesi triennale

Documents