Author: Apostolos Tentolouris Piperas

Investigation of Boundary Layer Suction on a Wind Turbine Airfoil using CFD

Supervisor: Martin O.L. Hansen

Wind Energy Building 403 Kongens Lyngby

Master’s Thesis 5th August 2010

Acknowledgements

There is not much to acknowledge really. People without whom I would never have survived my studies and who helped me realize that there is plenty of beauty to be shared despite the smothering workload of these past two years, a period that eventually lead to the present document, do not need this page to be aware of it and most likely will never read it in the first place. I would like however to express my gratitude to my supervisor Martin O.L. Hansen, probably the smartest person on the planet, for taking the time to bother with me and my questions, and Dalibor Cavar with Juan Pablo Murcia without whom my work would have taken twice the time and effort. Finally, I would like to thank whoever was responsible for my admittance to DTU. I may not have become a better engineer in the direction I was hoping, but I ended up becoming a better person, which is something I could have never hoped for.

i

Preface

This report is part of the requirements to achieve the Master of Science in Engineering (M.Sc.Eng.) at the Technical University of Denmark. It represents 30 ECTS points and was carried out at the Department of Mechanical Engineering at the Technical University of Denmark from Fe- bruary until August 2010.

iii

Abstract

The present Master Thesis deals with the investigation of suction as a mean of boundary layer control on a wind turbine root airfoil using CFD. Flow around a NACA 4415 airfoil is simula- ted in ANSYS CFX 12.1 environment and transition to turbulence as well as flow separation are studied for various arrangements of suction. The coefficients of lift and drag are computed for different angles of attack and the lift and drag curves after applying suction are compared with the corresponding values of the clean airfoil. Finally, a simplistic analysis is carried out in order to evaluate the impact and the usability of boundary layer suction on a wind turbine blade.

v

Table of Contents

List of Figures xi

List of Symbols 1

1 Introduction 1 1.1 General ...... 1 1.2 Previous Work ...... 1 1.3 Scope ...... 2

2 Boundary Layer Theory 3 2.1 Boundary Layer Basics ...... 3 2.2 Laminar and Turbulent flows...... 5 2.3 Boundary Layer Thickness - Drag ...... 7 2.4 Transition ...... 10 2.5 External Pressure Gradient ...... 14 2.6 Boundary Layer Separation ...... 15 2.7 Separation Bubbles ...... 17 2.8 Boundary Layer Control ...... 18 2.9 Boundary Layer Suction ...... 21

3 CFD Implementation 25 3.1 Setting up the model ...... 25 3.1.1 Geometry ...... 25 3.1.2 Mesh ...... 25 3.1.3 Setup ...... 27 3.1.4 Solver ...... 30

4 Results 37 4.1 Suction Location ...... 38 4.2 Discrete Suction versus Distributed Suction ...... 39 4.3 Suction Quantity ...... 45 4.4 Finer Analysis ...... 47 4.5 Wind Turbine Performance Enhancement ...... 51

vii viii TABLE OF CONTENTS

4.5.1 Blade Element Momentum Method ...... 52 4.5.2 BEM algorithm ...... 52 4.5.3 BEM results ...... 55 4.6 The Blade as a Centrifugal Pump ...... 59

5 Conclusions and Perspectives 63 5.1 Conclusions ...... 63 5.2 Suggestions for Further Work ...... 63

A Appendix 69 List of Figures

2.1 Boundary layer development...... 4 2.2 Thickness and shear variation ...... 5 2.3 Laminar and turbulent non-dimensionalised velocity profile...... 6 2.4 Turbulent boundary layer profile...... 6 2.5 Turbulent boundary layer structure...... 7 2.6 Diplacement thickness...... 8 2.7 Boundary layer thicknesses...... 9 2.8 Shear stress coefficient...... 9 2.9 Shear stress distribution...... 10 2.10 Transition from laminar flow to turbulent...... 11 2.11 Tollmien Schlichting waves...... 11 2.12 Ribbon frequency effect on boundary layer response...... 12 2.13 Neutral Stability Curve...... 13 2.14 Pressure distribution on an airfoil...... 13 2.15 Effect of pressure gradient on boundary layer...... 14 2.16 Velocity profiles and gradients...... 15 2.17 Boundarly layer profiles and point of inflection...... 16 2.18 Flow separation on an airfoil...... 16 2.19 Effect of adverse pressure gradient on the boundary layer...... 17 2.20 Separation bubbles...... 18 2.21 Vortex generators...... 20 2.22 Boundary layer aceleration...... 20 2.23 Boundary layer control via suction...... 21 2.24 Comparison between continuous and discrete suction...... 22 2.25 Critical value of suction coefficient...... 22 2.26 Skin friction variation under optimum suction ...... 23

3.1 Relative error...... 26 3.2 Generated Mesh...... 29 3.3 Image of the domain for the LE suction case prior the import into the Solver.. 30 3.4 No suction for 0 degrees angle of attack...... 31 3.5 No suction for 15 degrees angle of attack...... 33

ix x LIST OF FIGURES

3.6 Transient simulation for no suction case at 15 degrees angle of attack. . . . . 33

3.7 Leading edge distributed suction (Cq = 0.03) for 15 degrees angle of attack. . 34 3.8 Leading edge distribution - Tight convergence, higher number of iterrations . 34

3.9 Transient simulation for (Cq = 0.03) at 15 degrees angle of attack ...... 35

4.1 Eddy viscosity for 10o angle of attack ...... 37 4.2 Point of transition ...... 38 4.3 Non dimensionalized eddy viscosity and shear stress ...... 39 4.4 Application of suction at maximum thickness point and at leading edge . . . 40 4.5 Point of transition to turbulent flow at different angles of attack ...... 41 4.6 Location of distributed suction ...... 41 4.7 Velocity gradient for clean airfoil and distributes suction ...... 42 4.8 Flow separation at 17o angle of attack for a clean airfoil...... 42 4.9 Pressure coefficients for different angles of attack ...... 43 4.10 Pressure coefficient at 17o angle of attack for different suction cases...... 43 4.11 Flow separation for different distributed suction cases ...... 44 4.12 Lift and drag curves for discrete suction ...... 45 4.13 Lift and drag curves for distributed suction ...... 45 o 4.14 CLand CD values for different suction coefficients at 15 angle of attack . . . 46 4.15 CL ratio for different suction coefficients at 15o angle of attack ...... 46 CD 4.16 Pressure coefficient for different suction coefficients at 15o angle of attack . . 47 4.17 Eddy viscosity for different suction coefficients at 15o angle of attack . . . . . 47 du o 4.18 Velocity gradient dy for different suction coefficients at 15 angle of attack . . 50 4.19 Streamlines for different suction coefficients at 15o angle of attack ...... 50 4.20 Lift coefficient response for different angles of attack ...... 50

4.21 Lift and drag curves for the clean airfoil and Cq = 0.08 case ...... 51 4.22 Suction effect on aerodynamic coefficients ...... 51 4.23 Velocities at rotor plane...... 52 4.24 Tjaereborg wind turbine characteristics ...... 55 4.25 Angle of attack variation ...... 56 4.26 Chord distribution of the Tjaereborg blade ...... 56 4.27 Lift and drag curves of root segment ...... 57 4.28 Power contribution of each of the three first segments ...... 58 4.29 Power curve of the Tjaereborg wind turbine after suction ...... 58 4.30 Power ratio between the clean blade and suction cases ...... 59 4.31 Weibull distribution with A = 8 and k = 2...... 59 4.32 Power contribution of each of the two close to hub segments for reduced chord 60 4.33 Tjaereborg power curve after suction and 25%chord reduction ...... 60 4.34 Tjaereborg power coefficient curve after suction and 25%chord reduction . . 61 4.35 Thrust on the rotor for a range of wind speeds from cut-in speed to rated power 61

5.1 Mass flow distribution at suction location...... 64 LIST OF FIGURES xi

A.1 Distributed suction location ...... 69 A.2 Eddy viscosity for different turbulence models...... 70 A.3 Eddy viscosity for normal and 45o inclined suction for different angles of attack 71 A.4 Sensitivity check for steady state simulations ...... 72 A.5 FFT of lift coefficient response...... 72 A.6 Lift coefficient response at 60o angle of attack...... 73 A.7 Suction arrangement for pump driven suction on a glider plane ...... 73

List of Symbols

a ...... axial induction coefficient [] a! ...... tangential induction coefficient [] A ...... rotor area [m 2] AEO...... annual energy output [GWh]

CD ...... drag coefficient []

C fx ...... local shear stress coefficient []

C fL ...... averaged shear stress coefficient []

CL ...... lift coefficient []

Cn ...... normalized normal to the rotorplane force []

Cp ...... pressure coefficient []

CP ...... powercoefficient []

Ct ...... normalized tangential to the rotorplane force [] l ...... distance along the wall [m] L ...... lift force [N] D ...... drag force [N] F ...... Prandtl’s correction factor [] M ...... torque [Nm] P ...... power[W] Q kg ...... suction flux [ m3 ] Re ...... Reynolds number []

Rex ...... Reynolds number based on x representative length [] m u, v, w...... velocity components [ s ] m uw ...... suction velocity [ s ] m U0 ...... undisturbed velocity [ s ] m U f ...... friction velocity [ s ] m v ...... transversal velocity component [ s ] y+ ...... non dimensional wall distance [] x, y, z...... cartesian coordinates [] α ...... angle of attack [radian] δ ...... boundary layer thickness [m] δ ...... displacement thickness [m] ∗ δ ...... kinetic energy thickness [m] ∗∗ xiii xiv LIST OF FIGURES

θ ...... momentum thickness [m] when referred in chapter 2 θ ...... twist angle[radian] when referred in chapter 4 µ ...... dynamic viscosity [Pa s] ν m2 ...... kinematic viscosity [ s ] ρ kg ...... density [ m3 ] σ ...... solidity [] τ ...... shear stress [Pa]

τ0 ...... shear stress at the wall [Pa] φ ...... flow angle [radian] ω ...... angular velocity [radian/s] Chapter 1

Introduction

1.1 General

Wind turbines are capable of transforming the kinetic energy of the wind to mechanical energy in a shaft and finally into electric energy in a generator. The rotation of the shaft is achieved by the aerodynamic forces acting on the blades as the wind is passing through the rotor. Maxi- mizing the lift component of these wind forces allows the turbine to yield its rated power for lower wind speeds or using thinner blades, whereas minimizing the drag component results in smaller bending moments at the root of the blade, thus allowing the reduction of the material needed to withstand the created stresses. Using suction as a mean of boundary layer control, it is possible to delay stall to higher angles of attack, thus enhancing the airfoil’s lifting capabilities. In addition, suction of the boundary layer can extend its laminar region along the airfoil, i.e. move the transition to turbulent boundary layer further downstream, thus reducing the drag.

1.2 Previous Work

As early as in his first paper published in 1904, Prandtl demonstrated the effect of boundary layer suction by applying it via a slit on one side of a cylinder. On the suction side the flow adhered to the surface wall over a significantly longer part of the cylinder arc compared to the no suction side, and separation was supressed. This lead to the reduction of drag and the creation of lift, a perpendicular to the flow force caused by the asymmetry of the flow patttern. This was a first indication that adverse pressure gradients and wall friction, which determine the seperation process, can be effectively countered with boundary layer suction. From then on and throughout the twentieth century, extensive research has been carried out within the aviational industry on the application of boundary layer suction on airplane wings in order to minimize fuel consumption, as documented by Braslow [1]. In recent years, considerable effort has been devoted to the investigation of the applica- tion of suction either through open slots or porous wall strips for the purpose of skin friction drag reduction and boundary layer control in general, resulting to the conclusion that suction could indeed delay transition and separation and consequently control the flow . A significant number of studies (including Eppler [2], Oyewola [3] and Gad el Hak [4]) have focused on the effect of distributed low suction rates as well as concentrated wall suction through short porous wall strips on turbulent boundary layers. Results show that if the suction rate is sufficiently high, relaminarisation of the flow occurs almost immediately downstream the suction location. Some researchers, including Abbot and Doenhoff [5], have related the momentum thickness Reynolds number at the suction location with the suction rate coefficient and postulate that relaminarisation can take place only under certain correlation of the two.

1 2 1. Introduction

Numerous designs have been suggested for the implementation of suction. The two main ideas that have been investigated in the past are discrete suction through slots and distributed suction. The former allows an abrupt pressure increase at the location of the slot whereas the latter is achieved via a porous surface through which the air is sucked. The exact location where the suction is taking place along the airfoil as well as the amount of fluid that is being sucked is of crucial importance to the performance of the airfoil.

1.3 Scope

The present Master Thesis will attempt to model suction at a typical wind turbine blade root airfoil using ANSYS CFX 12.1. After modeling a clean (no suction applied) airfoil and ve- rifying the validity of the results, suction will be implemented in the form of normal to the airfoil’s surface velocity boundary conditions, and new lift and drag curves will be derived. If suction can improve C and Cl , it could lead to the production of more slender blades, lmax Cd which are cheaper to build and present lower extreme loads due to a reduced chord. Using the BEM algorithm the turbine’s new power curve will be derived, and subsequently the quanti- fication of the chordline’s reduction along the spanwise direction ( c(r) ) while maintaining the clean blade power output will be computed. In addition, the possiblity of using the rota- ting turbine blade as a centrifugal pump by cutting off its tip, in order to create the necessary sub-pressure within it that would drive the suction, will be investigated. Chapter 2

Boundary Layer Theory

Boundary layer theory has been for over a hundred years one of the most important achieve- ments of fluid mechanics. Its significance stems from the fact that it provides a high degree of correlation between theory and experiment and thus unifies theoretical hydrodynamics with hydraulics, two divergent branches of fluid dynamics which used to contradict one another. The former evolved from the equations of motion assuming frictionless and non-viscous flow, whereas the latter was a highly empirical science based on a large number of experimental data. It was evident in most cases that the discordance between classical hydrodynamics and experiments was due to the fact that the theory neglected completely fluid friction. In addi- tion, as far as air and water were concerned, the two most important and commonly used fluids, their viscosity was very small and as a result the forces due to viscous friction were very low compared to the gravitational and pressure forces. It was therefore difficult to comprehend that by omitting the frictional forces the behavior of the fluid would alter at such an extent. It was Ludwig Prandtl in 1904 that first presented an analysis of viscous flows concerning cases of practical importance. His paper proved that the flow around a body fully immersed in a fluid can be divided into two regions, one thin layer in the very close vicinity of the body called boundary layer, in which frictional forces play an important role, and the remaining outer region where friction forces can be neglected and the flow can be approximated as po- tential flow. This approach of the phenomenon allowed Prandtl to theoretically interpret the experimental results with simplified mathematics. The numerous applications of boundary layer theory include the calculation of skin friction drag, the interpretation of the phenomena occurring at the maximum lift point of airfoils as well as phenomena connected with stall. Boundary layer flow under certain ambient and geometric conditions can become reversed and subsequently detach from the surface of the solid wall. This phenomenon, known as boundary layer separation, is linked with the creation of eddies in the wake and is connected with a great drag increase in addition to the sudden drop of lift, on streamlined bodies such as an airfoil. Various methods of boundary layer control have been proposed to confront this problem, such as motion of the solid wall, acceleration of the boundary layer (blowing) and suction. The present case study deals with the latter.

2.1 Boundary Layer Basics

During the flow of a frictionless and incompressible fluid, no tangential forces and therefore no shear stresses are present between two consecutive layers. The only interaction with one another is via normal forces. This means that an ideal fluid does not present any internal resistance to a change of shape, which leads to the inability of the frictionless, incompressible approach of the flow to account for the drag of a body. The absence of tangential forces implies that in the close region of the solid wall, there is a difference between the tangential velocity of the fluid and the wall surface, in other words there is a slip. This slip does not exist in

3 4 2. Boundary Layer Theory real flows due to the fact that in a microscopic level the fluid particles adhere to the wall, thus producing shear stresses. The property of the fluid that accounts for these friction forces is viscosity, it is heavily dependent on the fluid’s temperature and, according to Newton’s law of friction, it is the proportionality factor between the shear stress between layers of a uniform flow and the velocity gradient in the direction normal to the layers :

∂u τ = µ . (2.1) ∂y

µ in known as dynamic viscosity, however when frictional and inertial forces interact it µ is important to take into account the viscosity to density ratio ν = ρ known as kinematic viscosity. The no slip condition implies that fluid particles are being retarded by the frictional forces, ∂u and is responsible for the velocity gradient ∂y . This thin layer around the body within which the flow velocity increases from the zero value until the free stream velocity is the boundary layer. The thickness of this boundary layer δ increases along the downstream direction of the flow over the wall, as seen in figure 2.1 taken from [6].

Figure 2.1 – Boundary layer development.

The continuously increasing thickness of the boundary layer can be explained by the fact that as the flow proceeds downstream, larger quantities of fluid become affected by the fric- tional forces, and the adjacent to the wall particles are continuously being subject to retarding force from the shear stress. These particles, due to their lower velocity, retard adjacent par- ticles further out from the wall, thus making the boundary layer thicker. As the boundary layer becomes thicker, the velocity gradient at the wall becomes smaller and therefore, as seen in figure 2.2 taken from [7], the shear stress decreases. There is also a correlation between the boundary layer thickness and the viscosity, presented in section2.3. However, even at high Reynolds numbers, i.e. for relative low viscosity values, the shearing stresses in the boundary layer still have a considerable effect on the flow, due to the high velocity gradient in the y direction, equation 2.1, at the immediate wall neighborhood, which diminishes in the outer regions of the flow. The retarded fluid particles of the boundary layer do not remain within it for the entire wet- ted length of the boundary wall. In some cases the flow becomes reversed and the decelerated particles are forced outwards, thus separating the flow from the wall. This boundary layer se- paration, described in section 2.6, is always linked with vortex generation in the body’s wake, as well as with great energy losses. The decelerated flow at the wake of the body induces large drag due to the large deviation of the pressure distribution in respect with the potential flow. 2.2. Laminar and Turbulent flows 5

Figure 2.2 – a) Thickness variation along a flat plate. b) Shear variation along a flat plate - effect of transition.

2.2 Laminar and Turbulent flows

Boundary layer flows can exist in two different regimes, laminar and turbulent. In laminar flow the fluid layers slide over one another without any fluid mass interchange taking place between neighboring layers. Therefore, the developed shear produced by the velocity gradient is entirely due to viscosity, and there is no momentum interchange between the layers. On the other hand in turbulent flow, velocity fluctuations both in the streamwise as well as in the per- pendicular to the flow direction are taking place resulting in significant mass and momentum transfer between neighboring layers. Due to these fluctuations the velocity profile is varying with time, however it is possible for a time averaged profile to be defined. The interchange of the streamwise component of the momentum between adjacent layers results in shearing stresses between them, the magnitude of which, at regions of the boundary layer away from the wall, is greater than those developed as a result of the fluid’s viscosity as seen in figure 2.9. Therefore, the shape of the velocity profile of a turbulent boundary layer is dominated by these stresses, termed Reynolds stresses. Assuming zero pressure gradient, figure 2.3 taken from [8] depicts two typical boundary layers, one for each of the aforementioned regimes. For the laminar case it is evident that a considerable portion of the boundary layer has significantly reduced velocity, since viscosity is the only medium with which energy from the free stream is transferred towards the inner retarded particles. In the turbulent boundary layer the Reynolds stresses are responsible for the penetration of energy from the free stream to the layers close to the wall surface, which results in a relatively high value of fluid velocity in the layers close to the wall seen in figure 2.3. Within the layers closer to the wall the perpendicular velocity fluctuations are dampened down and viscosity dominates the flow. In this region, called viscous sublayer, the shearing stresses become purely viscous and the velocity decreases rapidly until zero in a linear manner. Since ∂u τwall = µ( ∂y )wall, it is evident that the friction stress of the turbulent boundary layer is greater than the laminar one, owing to the much higher velocity gradient. It should be noted that for a flat plate, i.e. zero pressure gradient, the laminar profile 6 2. Boundary Layer Theory

Figure 2.3 – Laminar and turbulent non-dimensionalised velocity profile.

has a constant shape at each point along the surface, with the thickness growing along the downstream direction. In other words, the nondimensional velocity distribution ( u over y ) U0 δ does not vary from section to section along the plate.

The velocity distribution in the turbulent boundary layer, presented in figure 2.4 taken from [7], can be segregated into three main zones, each of which described by a different set of equations. The zone adjacent to the surface is the viscous sublayer, wherein the flow is essentially laminar and the shear is virtually constant and equal to the shear stress at the wall. The flow outside the viscous sublayer is turbulent, it can be described by the logarithmic law and is therefore called logarithmic layer. Between the aforementioned zones lies the buffer zone, which can mainly be described by empirical expressions.

Figure 2.4 – Turbulent boundary layer profile.

Figure 2.5 from [9] depicts the structure of the boundary layer and the different velocities distributions inside it. The dimensionless wall distance y+ quantity refers to the law of the wall + yU f τ0 + and is equal to y = ν where U f = ρ is the friction velocity. The corresponding y to each region is presented in table 2.1. In! the outer region, the velocity distribution is satisfied by the velocity defect law as seen in 2.5b. 2.3. Boundary Layer Thickness - Drag 7

Table 2.1 – y+ values per region for the turbulent boundary layer

Viscous sublayer Buffer zone Logarithmic layer y+ 0 - 5 50 - 70 70 - 500 1000 ∼

(a) Velocity distribution in a turbu- (b) Flow regions within a turbulent boundary layer lent boundary layer

Figure 2.5 – Turbulent boundary layer structure.

2.3 Boundary Layer Thickness - Drag

Due to the fact that the velocity values of the outer regions of the boundary layer tend to ac- quire the free stream value asymptotically, the boundary layer thickness is used to be defined as the distance from the wall where the velocity is equal to 99% of the value of the undisturbed mα du flow. The inertia force per unit volume in the x axis can be expressed as V = ρα = ρ dt where u is the horizontal component of the free stream velocity. For steady flow the aforementioned du ∂u dx ∂u ∂u relation becomes ρ dt = ρ ∂x dt = ρu ∂x . For a flat plate of length l the gradient ∂x is propor- U U2 tional to l and therefore the inertia force per unit volume is in the order of ρ l . In a similar 2 ∂τ = ∂ µ ∂u = µ ∂ u manner, the friction force per unit volume is ∂y ∂y ( ∂y ) ∂2y . The velocity gradient in the U normal to the plate direction is proportional to δ , therefore the friction force per unit volume µU is in the order of δ2 . Equalizing the friction and the inertia forces and solving for the boundary layer thickness the following relation is acquired:

νl δ , (2.2) ∼ "U where ν is the kinematic viscosity. It is evident that the boundary layer thickness over a flat plate is dependent on the fluid characteristics, the flow conditions of the free stream and the running distance from the plates leading edge. Blasius has shown that the numerical factor missing from the above relation is approximately equal to 5, figure 2.10, therefore for laminar flow in the boundary layer we have δ = 5 νl and after non dimensionalising we get δ = 5 . U l √Rel Evidently, δ increases with the square root! of the downstream running distance x. In addition, 8 2. Boundary Layer Theory having in mind that the Reynolds number expresses the ratio of the inertia forces over the fric- tional forces, as Re approaches infinity the previous equation suggests that the boundary layer δ 0.16 thickness diminishes. For the turbulent case , the corresponding relation is l = 1 . Due to 7 Rel the vagueness of the boundary layer thickness concept, more precise definitions can be given, each one offering different information regarding its characteristics.

Displacement thickness ( δ = ∞(ρU ρu) dx ) ∗ 0 0 − Due to the presence of the boundary layer over a surface, the mass flow within a stream tube # that prior to its encounter with the boundary layer had a value of ρU0 is now decreased to a smaller value ρu. Therefore, for continuity reasons, the crossection of the streamtube must increase, which for the 2D case means that the widths of the streamtubes within the boundary layer will increase thus displacing the streamtubes of the free flow away from the surface. The effect on the free flow will be equivalent with the displacing of the surface into the stream with no boundary layer present. Under such conditions, this into the stream displacement is called boundary layer displacement thickness δ∗, and is presented in figure 2.6 taken from [10].

Figure 2.6 – Diplacement thickness.

Momentum thickness (θ = ∞( u )(1 u ) dx) 0 U0 − U0 This term is connected with the momentum flow rate within the boundary layer, which owing # to the presence of the boundary layer is less than the momentum flow rate if no boundary layer existed, since in that case the velocity near the wall would be equal to the free stream velocity. The distance through which the surface must be displaced into the stream in order for the total flow momentum at that particular position when no boundary layer is present to be equal with the actual flow momentum is called momentum thickness θ. This quantity is often used for the calculation of the skin friction losses.

u u 2 Kinetic energy thickness (δ∗∗ = ∞( )(1 ( ) ) dx) 0 U0 − U0 The kinetic energy thickness is connected with the kinetic energy defect within the boundary # layer and is defined in a similar manner with the momentum thickness.

The aforementioned thicknesses can be seen in 2.7 taken from [8].

The shear stress on the wall can be computed by Newton’s law of friction. Following the same proportionality train of thought, the shear stress on the surface for tha laminar case ρU 2 is proportional to µU µl and after non dimensionalizing with ρU it is evident that it is dependent on the Reynolds! number alone: 2.3. Boundary Layer Thickness - Drag 9

Figure 2.7 – Boundary layer thicknesses.

τ µ 1 0 = . (2.3) ρU2 ∼ ρUl √Re " l

τ0 The local shear stress coefficient, cfx = 1 2 , is heavily dependent on the wall roughness 2 ρU and differs from laminar to turbulent flows. Figure 2.8 from [7] depicts the variation of the averaged shear stress coefficient CfL with the Reynolds number, indicating the significance of the flow regime on the shear.

Figure 2.8 – Shear stress coefficient.

As far as the drag force is concerned, by multiplying the shear with the plate surface, the relation D b ρµU3l is derived, where b is the surface width, which shows that the laminar ∼ 3 1 frictional drag$ is proportional to U2 and l 2 . The non linear dependence of the drag with the body length can be explained by the fact that as the flow proceeds downstream, its thickness increases thus producing lower shear at the regions close to the trailing edge compared to the leading edge. 10 2. Boundary Layer Theory

Adjacent to the surface, i.e. at the base of the boundary layer, the shear stress in the fluid is ∂u entirely dependent on viscosity and is equal to µ(∂y )wall as seen in figure 2.9 from [9], whereas in further away from the wall the Reynolds stresses dominate the shear.

Figure 2.9 – Shear stress distribution.

2.4 Transition

As the fluid proceeds on a flat plate, the laminar boundary layer continues to grow and viscous stresses are less capable of damping disturbances in the flow. Therefore a point is reached where these disturbances are amplified and lead to a turbulent state. Irregular patterns appear after a critical Reynolds number is reached and radial fluctuations occur, causing the mixing of the fluid laminae and thus making the flow turbulent. The exchange of momentum across the thickness of the boundary layer produces a more even cross-sectional area, as seen in figure 2.3. For the case of the flat plate, which implies no pressure gradient in the downstream di- rection as in the case of airfoils, the transition from laminar to turbulent flow is taking place for high values of the external velocity. A severe increase in the boundary layer thickness as well as in the shear stress is taking place at the point of transition, as depicted in figure 2.10 from [6]. Evidently, the based on the running distance variable x critical Reynolds number is approximately 3.2x105 which corresponds to a critical Reynolds number based on the displa- cement thickness Reδ = 2800. The point of transition along the plate can be derived through Rexcrit. However, it should be noted that the numerical value of the critical Reynolds number depends on the amount of disturbance in the external flow, and for extremely low disturbances in the flow higher critical Reynolds values can be reached. According to the one-step method 0.4 U(x)θ(x) of Michel found in [10] transition occurs when Reθ = 2.9Rex where Reθ = ν and U(x)x Rex = ν . As mentioned earlier, transition occurs because of the amplification of small disturbances in the boundary layer. These disturbances may originate from surface roughness, turbulence in the free stream or vibrations of the surface itself. Experiments have shown that the boundary layer can be simulated as a nonlinear oscillator that under certain conditions has an initially linear response to external stimuli [8]. Figure 2.11 from [8] presents the transition of a boundary layer over a flat plate with disturbances generated by a harmonic line source. The conversion of these disturbances into low amplitude waves is very complex due to the fact that that wave length of a typical external disturbance is much larger than the wave length of the 2.4. Transition 11

Figure 2.10 – Transition from laminar flow to turbulent. response of the boundary layer.

Figure 2.11 – Tollmien Schlichting waves.

After these low amplitude waves within the boundary layer have been generated, they will propagate downstream and will be either damped and eventually decayed or amplified and eventually lead to turbulent flow. While their amplitude remains small, these growing waves are mainly two-dimensional and are known as Tollmien Schlichting waves in honor of the researchers who studied them. As depicted in figure 2.11 the linear phase extends to a great portion of the transitional region. The linearity is based on the fact that due the very small value of the wave amplitudes their products may be neglected, however as the disturbance amplitude increases so does the complexity of the boundary layer response. In addition to the dissipative effect of viscosity in removing energy from a disturbance, Prandtl realized that it also plays a significant role in the development of wave disturbances by causing energy to be transferred to the disturbance. This energy transfer process is termed energy production by the 12 2. Boundary Layer Theory

Reynolds stress. For the proper study of Tollmien-Schlichting waves, artificially generated waves had to be generated in a controlled manner. A vibrating ribbon with controlled frequency was therefore placed within the boundary layer in order to generate waves, as opposed to studying the waves generated by natural causes such as the ones mentioned earlier. It was found that the boundary layer response was dependent on the wave frequency as seen in figure 2.12 from [8]. High ribbon frequencies resulted in the dampening of the generated waves, whereas waves produced by intermediate ribbon frequencies attenuated downstream of the ribbon, then began to grow and eventually they decayed. Low frequencies however produced waves of growing amplitude which eventually lead to transition to turbulence.

Figure 2.12 – Ribbon frequency effect on boundary layer response.

A neutral stability curve is therefore possible to be mapped out, which can separate the frequencies that produce wave amplification from the ones that will get damped out. Figure 2.12 presents such a curve of non dimensional frequency over the local Reynolds number, which denotes whether a boundary layer is stable or unstable. Within the neutral stability curve the energy produced by the Reynolds stresses exceeds viscous dissipation whereas the opposite occurs outside the curve. Evidently, there is a critical frequency and a critical Reynolds number that act as a barring threshold to the Tollmien Schlichting wave propagation, however it has been observed that the transitional Reynolds number is greater than the critical one. This is due to the fact that it takes some time, and therefore distance, for the amplified disturbance, denoted by the critical Re, to evolve into turbulence, signified by the transitional Re. An approach to increase the transitional Reynolds number, and thus mitigate turbulence phenomena, is through wave cancellation via appropriately located disturbance generators. A control system would detect the dominant element of the disturbance spectrum (phase, orientation, frequency) and the generators would be used to suppress or cancel out the detected disturbance [4]. Neutral stability curves can also be used in order to study the effect of an external pressure gradient on the boundary layer, which in turn is presented in section2.5. As presented in 2.4. Transition 13

Figure 2.13 – Neutral Stability Curve.

figure 2.13 from [8], after replacing the local Reynolds number with the one referring to the U0δ boundary layer thickness Reδ = ν which also grows along the surface, an adverse pressure gradient results in a smaller critical Reynolds number as well as a very wide range of unstable disturbance frequencies. The opposite holds for a favorable pressure gradient, i.e. low critical frequency and high critical Reynolds number. For streamline bodies such as airfoils, for 105 < 7 ReL < 10 the transition to turbulence will occur shortly downstream of the point of minimum pressure, and for a constant ReL an increase of the angle of attack would mean the upstream displacement of the point of minimum pressure and subsequently the moving forward of the transition point. By designing an airfoil with its minimum pressure point further aft, as seen in figure 2.14 from [8] it is possible to postpone transition, however this would give rise to a more severe adverse pressure gradient after that point which could cause separation of the flow. In order to prevent separation and maintain laminar flow as long as possible the use of suction methods can be implemented.

Figure 2.14 – Pressure distribution on an airfoil. 14 2. Boundary Layer Theory

This boundary layer transition is of great aerodynamical interest when it comes to blunt bodies. The turbulent mixing makes the flow more resistant to separation and thus the accele- ration effect of the flow on the suction side of the airfoil lasts longer. The further downstream movement of the boundary layer detachment point produces a significant decrease of the indu- ced vortices region at the wake and thus reduces pressure drag. The more slender a body is the less profound the reduction of drag will be since the gradual pressure increase in the downs- tream direction may be overcome without separation. The separation point in streamlined bodies is greatly affected by the pressure conditions of the external flow, as described in sec- tion 2.5. For a negative pressure gradient along the downstream direction, i.e. for decreasing pressure along the flow, the boundary layer is laminar until the point of minimum pressure. The pressure gradient then becomes positive and the pressure increases further downstream making the flow turbulent. A laminar boundary layer can support only a small pressure in- crease, it is therefore preferable for an airfoil to have developed a turbulent boundary layer on it suction side in order to achieve high values of lift, but in the same time and in order to reduce skin friction (which is higher for turbulent flows), the point of transition needs to be displaced as far downstream as possible.

2.5 External Pressure Gradient

The effect of a pressure change in the streamwise direction has a great effect on the behavior of the boundary layer. A decreasing pressure along the surface is called a favorable pressure gradient due to the fact that the streamwise pressure forces tend to help the flow to counter the shearing effects, thus resulting in a less retarded flow close to the wall and subsequently a fuller profile. When the pressure is increasing along the wall, the pressure gradient becomes adverse due to the fact that the streamwise pressure forces now enhance the shearing action. Consequently, the flow decelerates even more at the wall region and the boundary layer grows more rapidly as depicted in figure 2.15, taken from [8].

Figure 2.15 –Effect of pressure gradient on boundary layer.

The velocity profile under these conditions is much less full and may develop a point of ∂u inflexion, i.e. a point where the velocity gradient ∂y changes sign, in other words a point where 2 2 ∂ u = µ ∂ u = dp ∂2y 0. Owing to the boundary layer equations, at the wall surface we have : (∂2y )y=0 dx therefore in the immediate neighborhood of the wall, the velocity profile curvature is solely 2.6. Boundary Layer Separation 15

2 dp < ∂ u < dependent on the pressure gradient. For a favorable pressure gradient dx 0, ( ∂2y )wall 0 and therefore the curvature will maintain its negative sign throughout the entire boundary layer. ∂2u > For an adverse pressure gradient however the curvature at the wall is positive, (∂2y )wall 0, ∂2u < but since at a large distance from the wall ∂2y 0, it follows that a point must exist where 2 ∂ u = ∂2y 0. These arguments can be visualized in figure 2.16, taken from [6].

(a) Favorable pressure gradient (b) Adverse pressure gradient

Figure 2.16 – Velocity profiles and gradients.

For a sufficiently strong or prolonged adverse pressure gradient the flow near the wall is so greatly decelerated that it begins to reverse direction, indicating that the flow has separated from the surface, as seen in figure 2.17 from [10]. The point of separation can be defined as the limit between the upstream and downstream flow within the adjacent to the wall layer:

∂u ( ) = 0. (2.4) ∂y y=0 In the region of retarded potential flow an inflexion point will always be present in the velocity profile, and since the profile exhibits a zero tangent at the point of separation, it follows that separation can only occur when the potential flow is retarded.

2.6 Boundary Layer Separation

The main cause of boundary layer separation in streamlined bodies such as an airfoil is adverse pressure gradient, which may be impressed on the boundary layer by the external pressure conditions. The significance of separation in airfoils is great since it is strongly connected with its lifting capabilities. Figure 2.18 from [6] depicts an airfoil at different angles of attack. An increase in the incidence produces a steeper pressure gradient and after a certain value causes the separation of the flow. Furthermore, the prevention of boundary layer separation reduces the total drag to such an extent that a symmetrical airfoil that achieves laminar boundary layer for most of its wetted length can produce the same drag as a circular cylinder with a diameter nearly 150 times smaller than the airfoil’s chordline [6]. Figure 2.19 from [8] depicts a boundary layer flow over a surface with gradual, convex curvature, such as the surface of an airfoil past the maximum thickness point. Owing to the Bernoulli principle, the velocity in the vicinity of the surface is decreasing and the pressure is rising. It should be noted however that there is no pressure variation in the direction normal to the surface, which means that the pressure at the edge of the boundary layer is imprinted to ∂p the layer adjacent to the surface. Since ∂x > 0, the net pressure at the depicted fluid element ABCD is tending to decelerate it and in combination with the viscous shears acting on the 16 2. Boundary Layer Theory

Figure 2.17 – Boundarly layer profiles under different pressure gradients. Effect on point of inflection.

Figure 2.18 – Flow separation on an airfoil. sides AB and CD the element is further retarded as it moves downstream. This slowing down effect has a more profound effect at the layers close to the solid wall resulting in a change in the shape of the velocity profiles. ∂u After the separation point S where (∂y )wall = 0, the boundary layer thickness increases rapidly in order to satisfy continuity. After the separation point, the direction of the flow in 2.7. Separation Bubbles 17

Figure 2.19 –Effect of adverse pressure gradient on the boundary layer. the close vicinity of the wall is in the upstream direction thus creating a circulatory movement in the near surface region. Due to the greater extent of lower energy fluid at the wall region in laminar boundary layers,presented in 2.3, separation due to adverse pressure gradient will occur sooner in comparison with turbulent boundary layers. Boundary layer separation in the rear half of an airfoil results in a significant increase of the wake flow thickness, which subsequently results in a decrease of the pressure rise that should occur in the trailing edge. This means that the forward acting pressure components of the rear part of the airfoil do not develop and therefore the rearward acting pressure forces of the frontal stagnation point are not countered. As a result the pressure drag of the airfoil increases greatly. For large angles of attack, separation takes place at a point located a small distance downstream of the point of minimum pressure, thus creating a large wake which in turn diminishes the low pressure conditions at the area downstream the leading edge which is responsible for the creation of lift. Favorable pressure gradients has the exact opposite effect, since energy is added to the slow moving flow near the solid wall thus making the flow more resistant to separation.

2.7 Separation Bubbles

Laminar separation might occur in airfoils with large upper surface curvature when relatively high angles of attack are reached. Small disturbances in separated flows grow easily in small Reynolds numbers, therefore the transition to turbulent flow that may subsequently take place leads to a rapid thickening of the detached boundary layer which might be sufficient for the lower edge to reach the solid wall once again, thus leading to the reattachment of the separated flow, which is now within the turbulent regime. As seen in figure 2.20, taken from [8], a bubble of fluid is trapped between the separation point and the point where the flow comes back into contact with the surface and reattaches. Within this bubble two regions exist : A pocket of stagnant fluid within which the pressure is constant, and downstream of that pocket, an area where circulatory motion is taking place and within which the pressure is increasing significantly towards the point of reattachment. Two distinct categories of separation bubbles have been observed to occur, a short bubble 18 2. Boundary Layer Theory

Figure 2.20 – Separation bubbles. extending over 1% of the chordline (100 displacement thicknesses at the separation point) and a long bubble extending over a greater portion of the chordline, around 10000 displacement thicknesses at the separation point. The former has a negligible effect on the peak suction whereas the latter’s effect is significant. The criterion as to which bubble is formed is the value of the displacement thickness based Reynolds number at the separation point. If Reδ∗ < 400 a long bubble is most likely to occur while for Reynolds values over 550 a short bubble is more probable. The length of long bubbles increases rapidly with increasing angle of attack and might extend up until the trailing edge of the airfoil, thus causing a continuous reduction of the leading edge suction peak or even stall. On the other hand, the response of short bubbles at an increase of the angle of attack is to move slowly upstream without changing their length. Stall might occur either due to the upstream movement of the rear separation point or by breakdown of the short bubble near the leading edge due to the failure of the separated flow to reattach onto the wall surface.

2.8 Boundary Layer Control

Laminar boundary layers can support very small adverse pressure gradients before flow se- paration occurs. According to [4], for a deceleration of ambient incompressible fluid greater than U x 0.09 the boundary layer will separate from the surface. For the case of turbulent 0 ∼ − boundary layers this value is much greater and separation is avoided up until U x 0.23, thus 0 ∼ − making them capable of overcoming larger adverse pressure gradients, owing to the conti- nuous flow of momentum from the free stream towards the wall. However, even in turbulent flow separation cannot always be prevented, therefore numerous methods of boundary layer control have been developed in order to tackle the problem, such as:

Motion of the solid wall This method can in a way prevent the development of the boundary layer by eliminating the difference between the fluid’s velocity and the velocity of the solid wall. By taking advantage of the no slip condition, the wall moves along with the stream and the velocity gradient is suppressed. Experimental investigations of a moving boundary on an airfoil, by forming a part of the upper surface into an endless belt, have yielded very high maximum lift coefficients o (Clmax = 3.5) at very high angles of attack (α = 55 ) [6]. 2.8. Boundary Layer Control 19

Shaping As mentioned earlier, transition from laminar to turbulent flow can be delayed with the use of suitably designed airfoils which relegate the point of transition further downstream thus redu- cing the total frictional drag of the body. The favorable pressure gradient extends up until the point of minimum pressure, it is therefore desirable to move the latter as far back as possible. However, the more aft that point is located the steeper the adverse pressure gradient will be- come beyond it. As a result, the range of angles of attack within which this gradient change can be achieved without separation is very narrow. Depending on the Reynolds number, the airfoil shape, the surface roughness and the incidence angle, the boundary layer beyond the minimum pressure point either becomes turbulent shortly after or it temporarily dettaches for- ming the separation bubbles mentioned earlier.

Wall cooling Generally, an increase in air temperature will result in an increase of its viscosity. Therefore, ∂µ the removal of heat from the body surface results in ∂y < 0, causing an increase of the velocity gradient on the wall which produces a more full and stable profile [4]. In addition, the critical Reynolds number is increased and the range of frequencies that lead to disturbance amplifica- tion is reduced.

Turbulators As mentioned in section 2.2, a turbulent boundary layer is more resistant to separation and therefore transition may be desirable in lifting devices in order to avoid stall. Transition usually occurs for values of the local distance from the leading edge Reynols number close to 106. It can be advanced by exposing the boundary layer to large disturbances, in connection with section 2.4, by placing single, multiple or distributed roughness elements on the wall. The u(κ)κ height of these elements can be quantified by the corresponding Reynolds number Reκ = ν , where κ denotes the roughness length. Reκ is used to assess the effect of surface roughness on transition, signified by the based on the displacement thickness Reynolds number Reδ∗ . For a smooth surface, transition occurs at Re 2600 whereas for Re = 600 transition δ∗ ≈ κ takes place at Re 1000 , and increasing Re to 1000 Re decreases even more at 300 δ∗ ≈ κ δ∗ [4]. It is important for the turbulator however to suppress laminar separation without making the boundary layer unnecessarily thick, since thick turbulent boundary layers are more prone to separation than thin ones. This limits the range of Reynolds numbers wherein roughness 5 U0c elements can aid airfoils to achieve higher performance to Rec < 10 , where Rec = ν . In general, roughness will enhance turbulence, which is much needed in high angles of attack, but it also increases skin drag so great care should be put into their design. Vortex generators, seen in figure 2.21 from [11], also can be used for the energy enrichment of the near wall flow, by creating a tip vortex which draws air from the outer flow regions into the boundary layer. They are typically rectangular or triangular, with a height comparable to the boundary layer thickness, and are positioned near the leading edge, upstream of where laminar separation is expected. As a result, fluid particles with high streamwise momentum are swept along helical paths towards the surface where they mix with the near wall flow and replace the retarded particles. If however the separation location can be accurately predicted, the vortex generetors can be placed accordingly and their size can be greatly reduced, thus reducing the drag. 20 2. Boundary Layer Theory

Figure 2.21 – Vortex generators.

Boundary layer acceleration By supplying additional energy to the retarded fluid particles near the surface and thus modi- fying the velocity profile, it is possible to delay separation until larger angles of attack. This can be achieved either by the discharge of fluid from within the airfoil or through the imple- mentation of a slat in the leading edge, as depicted in figure 2.22a, taken from [6].

(a) Boundary layer control via (b) High lift devices. blowing.

Figure 2.22 – Boundary layer aceleration.

Different movable elements that permit the alteration of the airfoil geometry and subse- quently its aerodynamic characteristics can be seen in figure 2.22b, taken from [5]. Through the delay of stall they allow higher lift coefficients and higher angles of attack.

Transpiration Another method to avoid separation is by changing the curvature of the velocity profile via the withdrawal of the near wall fluid through slots or porous surfaces. The effect of suction consists of the removal of the retarded fluid particles located at the region close to the surface thus preventing the reversal of the flow. The resulting boundary layer, depicted in figure 2.23 from [8], that is created is much thinner and more capable of overcoming the adverse pressure gradient, allowing the flow to progress further downstream the surface wall without separating. The implementation of suction techniques allows the suppression of separation at higher 2.9. Boundary Layer Suction 21

Figure 2.23 – Boundary layer control via suction. angles of attack, thus achieving high lift coefficients. In addition, suction can result in the shif- ting of the transition point further downstream thus reducing frictional drag, since an extended laminar region implies smaller shear on the surface. A more detailed presentation of boundary layer suction is presented in the chapter 2.9,

2.9 Boundary Layer Suction

The kinetic energy of the fluid layers adjacent to the surface can be increased by removing low energy air through suction slots or a porous surface. Suction suspends boundary layer growth and leads to a fuller velocity profile. It can therefore be used to delay transition, postpone separation or relaminarize an already turbulent flow. By changing the curvature of the velocity profile at the wall the stability characteristics of the flow can be enhanced, thus preventing the critical Reynolds number Reδcrit, referring to the neutral stability curves seen in figure2.13, to be reached. The quantity of fluid sucked away can be expressed by the ratio of the suction velocity u at the wall over the free stream velocity C = | w| . The transition delay and the separation q U0 prevention should be achieved with the minimum suction flow rate possible in order to reduce the power needed for the suction. According to [4] separation on a symmetrical airfoil can be 0.5 prevented for Cq = 1.12Re−L when distributed suction is implemented, whereas for discrete suction the maximum effectiveness, according to [5], can be reached when the sucked air is equal to the air quantity that would pass through the diplacement thickness δ∗ at the slot location with the local external velocity. For typical airfoils Cq values between 0.002 and 0.004 are sufficient for separation prevention [4]. The position along the airfoil where suction is taking place should be a short distance downstream the nose where, at large angles of attack, steep adverse pressure gradients occur. By concentrating the suction shortly downstream of the minimum pressure point, the extending of the airfoil’s lift curve to higher angles of attack can become possible. Figure 2.24 from [6] presents the increase of maximum lift ∆CLmax over the suction coefficient. Evidently, for the same lift increase, continuous suction needs much less air quantity removed compared to the discrete case. A minimum suction coefficient can be derived by assuming a uniformal suction along the whole extent of a surface and applying as a boundary condition the wall-normal velocity to be equal to the suction velocity. The equations that describe such a flow, according to [6], result 22 2. Boundary Layer Theory

Figure 2.24 – Comparison between continuous and discrete suction.

uwy in a velocity profile in the form of u(y) = U [1 e ν ] and a displacement thickness equal to 0 − δ = ν . This solution is realized at some point downstream the leading edge, despite the fact ∗ uw that suction− is applied earlier on, and it does so in an asymptotic manner. It is therefore termed asymptotic suction profile. U0δ∗ After investigating the stability of this profile, the critical Reynolds number Reδ∗ = ν was found to acquire the very high value of 70000, which can then be used in order to calcu- late the asymptotic displacement thickness and subsequently the suction velocity. Finally the uw 1 condition of stability forms at − = C > , however experiments have shown that the U0 q 70000 quantity of air that needs to be removed in order for laminar flow to be maintained is higher. 2 U0 x Introducing the parameter ξ = Cq ν , the resulting critical Reynolds numbers are derived, and presented in figure 2.25, taken from [6]. Evidently the limit of stability is never crossed at any 1 4 point along the length if Cq > 8500 which results in Cqcrit = 1.2.10− .

Figure 2.25 – Critical value of suction coefficient.

The variation of the skin friction coefficient for the aforementioned case, in connection with figure 2.8, under the condition of optimal suction which denotes the smallest Cq that 2.9. Boundary Layer Suction 23 suffices for transition prevention, is depicted in figure 2.26, found in2 [6]. The save in drag corresponds to the distance between the turbulent and the optimum suction curve at any given Reynolds number.

Figure 2.26 – Skin friction variation under optimum suction

The stabilizing effect of suction on the boundary layer can also be detected in the induced large increase of the critical Reynolds number. The corresponding neutral stability curves, according to [6], denote a critical Re over 100 times larger than the no suction case.

Chapter 3

CFD Implementation

The programm used for the investigation of airfoil suction is ANSYS CFX 12.1 and the results are subsequently processed within MATLAB environment. For the purposes of the present case study, the NACA 4415 airfoil is used, and the suction effect on lift and drag will be extrapolated for the Tjaereborg blade root airfoil. The notation NACA 4415 suggests that the airfoil has a maximum camber of 4% located at a distance from the leading edge equal to 40% of the chord length with a maximum thickness of 15% of the chord.

3.1 Setting up the model

Within ANSYS CFX 12.1 environment, the ANSYS Workbench tool will be used. It segre- gates the modeling process into 5 steps, Geometry, Mesh, Setup, Solution and Results.

3.1.1 Geometry

The geometry of the airfoil is created in Autodesk Inventor Professional 11 via the import of the point coordinates that define the airfoil profile. For this purpose 47 points were used for the suction side of the airfoil and 49 for the pressure side, which were subsequently connected via a spline curve. The airfoil has a chord length equal to 1m and its leading edge is located 10m from the domain inlet, whereas the flow domain consists of a 30mx10m parallelogram. The design is saved as an .igs file and is imported into ANSYS. Due to the inability of CFX to simulate 2D cases, the flow domain along with the airfoil itself are created as an extrusion of unit length. The produced parallelepiped will then be meshed with a single element depth so that the third dimension is diminished, and the top and bottom faces of the extrusion will be set as symmetry planes later in the process. It should be noted that that the extrusion length should not exceed the maximum lenghtscale of the mesh, but in the same time it should have a value that will not cause visibility problems later in the building process of the model. The proposed dimensions result in a relatively low blockage ratio factor, as the boundaries are not too close to the airfoil and the flow is not constrained.

As far as the suction region is concerned, it will be created as a cut-in in the airfoil in order for the definition of different boundary conditions along the airfoil curve to become possible.

3.1.2 Mesh

During the creation of the mesh, great care must be taken at the vicinity close to the airfoil surface since it is there where the boundary layer will be formed. The accuracy of the model increases with the total number of elements used, however so does the simulation time nee- ded to produce results. In addition, by refining the mesh, convergence issues may arise since

25 26 3. CFD Implementation smaller flow features such as shedding phenomena are resolved, which coarser meshes cannot capture. Depending on the scope of the study, these issues should be handled with the proper setup of the simulation.

After the regions of the model have been defined, the background mesh length scale of the model is specified by using the Body Spacing option. This length scale corresponds to the coarsest length scale required anywhere in the domain, before any Face Spacing or Controls are applied to any regions of the model. The Maximum Spacing within the Body Spacing menu specifies the maximum element size which will be used when creating triangles on the domain’s surface and tetrahedra in the domain’s volume. The default value for this parameter is around 5% of the maximum extent of the model.

A Face Spacing is used to specify the mesh length scale on a face and in the volume ad- jacent to that face. The Default Face Spacing applies to all faces that have not been explicitly assigned a specific length scale. In the present case study the Volume Spacing option is used for Default Face Spacing, which implements the same spacing on the face as the Maximum Spacing specified in Body Spacing. For the airfoil however an explicit Face Spacing is applied and the Relative Error option is used, due to the fact that it allows the edge length on parti- cular faces to vary depending upon the local curvature. It is therefore possible for the mesh at the curved surfaces of the airoil to be automatically refined. The value of the relative error ∆x specifies the level of the curvature resolution as the ratio x , reffering to figure 3.1 from [12], which specifies the maximum deviation of the resulting mesh away from the geometry face.

Figure 3.1 – Relative error.

The refinenment of the mesh in specific regions of the model can be accomplished via the use of Mesh Controls. The mesh refining effect decays with distance from the control region, and progressively coarser elements are produced. Two types of Control have been implemen- ted in the present case study, Point Control for the close vicinity of the airfoil, and Triangle Control for the broader neighborhood around the airfoil extending from a few meters upstream of the leading edge until several chord lengths downstream, while in the same time the mesh refinement is broadening downstream. The spacing attributes for the aforementioned controls differ from one another, and are specified via the Point Spacing option, which in turn requires three definition values : the Length Scale, which determines the mesh size in the locality of the point, the Radius of Influence which defines the radial extent of meshed spaced filled with elements the size of which was defined in Length Scale, and the Expansion Factor, which de- termines the coarsening rate of the mesh outside the Radius of Influence.

In near wall regions, the velocity gradients produced by boundary layer phenomena need elements with high aspect ratios, in order to be resolved in a computationally efficient manner. 3.1. Setting up the model 27

For this reason, CFX-Mesh implements prisms to create a mesh that is finely resolved normal to the wall but coarse parallel to it, by inflating the 2D local face elements into 3D prism elements. In the present case study, this Inflation is applied on the airfoil surface in order to take into account the effect of the boundary layer on its aerodynamic behavior. The parameters that control the Inflation should be carefully chosen in order to capture the flow phenomena within the boundary layer, such as transition or separation. The Number of Inflated Layers denotes the number of inflation layers applied and must not exceed 100. If the inflation layer thickness is specified by the First Layer Thickness option, which in the present simulation is indeed the case, then Number of Inflated Layers specifies the maximum number of inflation layers. The Expansion Factor determines the relative thickness of adjacent inflation layers, i.e. each successive layer in the normal to the wal direction is thicker than a previous one by one Expansion Factor. By selecting First Layer Thickness as the option that will control the creation of the in- flation layer instead of Total Thickness, the transition from the inflated prism elements to the tetrahedral mesh elements is smoother [12]. First Layer Thickness however does not control the total height of the inflation layer, but it creates prisms based upon the first layer thickness, the Expansion Factor and the Number of Inflated Layers. The first layer thickness is defined in the present report by a target y+ value, given the Reynolds Number and a Reference Length. + 13 ANSYS CFX calculates the first layer thickness (∆y) using the formula ∆y = L∆y √80Re −14 . After the first layer is created, thicker layers, the height of which is defined by the Expansion Factor, are added on top of it until the ratio of height over base length reaches unity. Additio- nal prisms are then added in case the Extended Layer Growth option is enabled, which is the case in the present case study, until the Number of Inflated Layers is reached. Advanced quality checking can be done by changing the Number of Spreading Iterations, that controls how far the effects of deleted elements propagate, which which is of no iportance the present simulation since no adjacent inflation boundaries are overlapping, the Minimum Internal Angle, which controls the minimum allowed angle in the triangular face of a prism nearest to a surface before it is marked unacceptable and up for deletion, and the Minimum External Angle, which controls the respective element property for a prism farthest from a surface. The aforementioned parameters have not been changed from their default values. Proceeding to Surface Meshing, the Delauny Surface Mesher has been selected due to its speed and its ability to mesh closed faces. The Meshing Strategy selected is Extruded 2D Mesh in order to generate a 2D mesh of one element thickness. The 2D Extrusion Option is set to Full so the mesh is generated using the full extent of the geometry and the Number of Layers is set to 1. The proper planes are then selected for the Extruded Periodic Pair and the Periodic Type Option is set to Translational. Finally the Surface Meshes and the Volume Mesh are generated. Figure 3.2 presents the final mesh of the domain. Table 3.1 presents the properties chosen for the creation of the mesh using CFX-Mesh. Fields that do not appear in the table have been left with their default values. In order to check the effect the mesh quality has on the results of the simulation, a refined mesh is created, by halving the element sizes of the previous mesh, and some cases are run twice using two different meshes.

3.1.3 Setup The first thing to do in the Setup is to specify the Analysis Type of the simulation. Steady state analysis should be used to model flows that do not change over time, whereas transient analysis should be used to model time dependent flows. Flows around streamlined bodies may exhibit dynamic phenomena due to the vortex shedding that will occur after certain angles of attack, it is therefore preferable to use transient analysis for the simulation, with a carefully 28 3. CFD Implementation

Table 3.1 – Mesh properties

Spacing Default Body Spacing Maximum Spacing [m] 1.0 Default Face Spacing Option Volume Spacing Option Relative Error Relative Error 0.0123116 Minimum Edge Length [m] 0.001 Airfoil Spacing Maximum Edge Length [m] 1.5 Radius of Influence [m] 1.0 Expansion Factor 1.2

Controls Length Scale [m] 0.01 Airfoil Vicinity Radius of Influence [m] 1 Expansion Factor 1.2 Length Scale [m] 0.1 Broader Vicinity Radius of Influence [m] 1 Expansion Factor 1.2 Point Control Point 0.5[m], 0[m], 0[m] Spacing Airfoil Vicinity Point -3[m], 0[m], 0[m] Triangle Control Point 7[m], 3.5[m], 0[m] Point 7[m],-3.5[m], 0[m] Inflation Inflation Number of Inflated Layers 60 Expansion Factor 1.1 Number of Spreading Iterations 0 Minimum Internal Angle [Degrees] 2.5 Maximum Internal Angle [Degrees] 10.0 Option First Layer Thickness Define First Layer By y+ y+ 1.0 Reynolds Number 1.5e6 Inflation Options Reference Length [m] 1.0 First Prism Height [m] 1.646695e-5 Extended Layer Growth Yes Layer by Layer Smoothing No Options Surface Meshing Option Delaunay Meshing Strategy Option Extruded 2D Mesh 2D Extrusion Option Option Full Number of Layers 1 3.1. Setting up the model 29

(a) Flow Domain. (b) Airfoil Vicinity

(c) Inflation Layer.

Figure 3.2 – Generated Mesh. chosen timestep in order to capture the vortex shedding and avoid aliasing with the Strouhal frequency. The total time of the simulation should be long enough so that parameters like the lift or drag on the body reach a relatively constant value. Transient analyses however occupy extreme amounts of disk space until these fluctuations over time diminish, therefore when used in the present project, the results will not be stored at each timestep but only at the beginning and the end of the simulation. The forces acting on the airfoil however will be monitored throughout the run in order to be utilized later on. Steady state analyses will be used throughout the present case study, with a supplementary transient simulation for some cases for comparison reasons. Once a general trend of the airfoil’s response to suction has been es- tablished using steady state simulations, the optimal cases will be simulated once again using transient analysis.

Boundary conditions must be applied to all the regions in the domain. They can be Inlets, Outlets, Openings, Walls or Symmetry Planes. The values and properties applied to each boundary of the simulation are presented in table3.2. It should be noted that the flow is always m subsonic and from Left to Right, with a value of 23.52 s in order to achieve a Reynolds number of 1.5e106 which typical for wind turbines, and the implementation of the different angles of attack is achieved by the modification of the inlet velocity from the Left and Down inlet with the corresponding trigonometric functions. For the 0 angle of attack case, the boundary conditions at the Upper and Down faces have been set to Free Slip Wall. Pressure boundary conditions are applied at the domain outlets and the Average Static Pressure option is used in order to allow the pressure to vary locally on the boundary. Suction is implemented by setting the corresponding location along the airfoil as an outlet and setting velocity boundary conditions in order to control the suction quantity. The image of the domain in the 3D Viewer window of ANSYS, after the setup process is finished, is depicted in figure 3.3. As far as the domain and model properties are concerned, they are presented in table3.3. The Gamma Theta transitional turbulence model has been chosen for advanced turbulence control of the Shear Stress Transport model (SST), due to its ability to capture the influence of different factors that affect transition such as the free stream turbulence and pressure gradients. It implements the use of experimental correlations that relate the turbulence intensity in the free 30 3. CFD Implementation

Figure 3.3 – Image of the domain for the LE suction case prior the import into the Solver. stream to the momentum thickness based Reynolds number [12]. Other models are also tried out and presented in chapter 4 in order to justify the superiority of the Gamma Theta model in regards to the purpose of the present case study. For convergence control, the value of the 4 root mean square normalized residual over the whole domain is chosen to be below 10− , and the maximum amount of iterations has been set to 750. A sensitivity check will be carried out 6 later on by reducing the RMS residual to 10− in order to check its effect on the results. Table 3.3 presents the values and the properties used for the analysis.

3.1.4 Solver The simulations are run in HP MPI Distributed Parallel mode on the DTU cluster of com- puters, and the result files after the simulation ends are transferred back to the PC for further process. The monitoring of the residuals allows the estimation of the level of correspondance of the results to reality, since convergence indicates whether the equations have been solved. In most of the cases studied in the present report the steady state residuals do not converge, indicating the need for transient simulations. Figure 3.4 presents the residuals of the mass and momentum equations as well as the force applied on the body in the Y direction as shown in figure 3.3, for the 0 angle off attack case with no suction. It is evident that despite the fact that the relatively loose convergence target 4 of 10− is not reached, the Lift force stabilizes at approximately 150 N, which deems the simulation relatively accurate. For the 15o angle of attack case however, the Y force is fluctuating with an amplitude of approximately 60N as seen in figure 3.5, suggesting that boundary layer separation has made the steady state simulation impossible to converge and indicating in a clear manner the need for transient simulations. 3.1. Setting up the model 31

Table 3.2 – Boundary Conditions

Location Boundary Type Body No Slip Wall Smooth Wall Inlet Flow Regime Subsonic Mass and Momentum Cart. Vel. Components U = Vrelcos(α) [m/s] Down V = Vrelsin(α) [m/s] W = 0[m/s] Turbulence Low (Intensity=1%) Inlet Flow Regime Subsonic Mass and Momentum Cart. Vel. Components U = Vrelcos(α) [m/s] In V = Vrelsin(α) [m/s] W = 0[m/s] Turbulence Low (Intensity=1%) Outlet Flow Regime Subsonic Out Mass and Momentum Average Static Pressure Relative Pressure 0 [Pa] Outlet Flow Regime Subsonic Up Mass and Momentum Average Static Pressure Relative Pressure 0 [Pa] Suction Outlet Flow Regime Subsonic Mass and Momentum Normal Speed Vsuc = CqVrel[m/s] Symmetry Planes Symmetry

(a) Residuals (b) Y force

Figure 3.4 – No suction for 0 degrees angle of attack.

Figure 3.6 presents the residuals and the Y force for such an analysis. A time step of 0.01 seconds has been used and a total simulation time of 3 seconds which, given the fact that m the flow has a velocity of 23.52 s , allows the fluid to travel apporoximatelly 70 chordlines throughout the simulation, thus providing enough time for the development of the flow. Small oscillations in the Y component of the aerodynamic force can be observed, in the order of 20N, which can be linked to the vortex shedding. 32 3. CFD Implementation

Table 3.3 – Steady State Setup properties

Analysis Type Option Steady State Default Domain Basic Settings Material Air at 25 C Morphology Continuous Fluid Reference Pressure [atm] 1 Domain Motion Stationary Fluid Models Heat Transfer Option Isothermal Fluid Temperature [C] 25 Turbulence Option Shear Stress Transport Transitional Turbulence Gamma Theta Model Initialization Velocity Type Cartesian Cartesian Velocity Components [m/s] U = Vrelcos(α) V = Vrelsin(α) W = 0 Solver Control Advection Scheme High Resolution Turbulence Numerics High Resolution Convergence Control Min. Iterations 1 Max. Iterations 750 Convergence Criteria Residual Type RMS Residual Target 1.e-4 3.1. Setting up the model 33

(a) Residuals (b) Y force

Figure 3.5 – No suction for 15 degrees angle of attack.

(a) Residuals (b) Y force

Figure 3.6 – Transient simulation for no suction case at 15 degrees angle of attack.

It appears that applying suction as a mean of boundary layer control on the NACA 4415 airfoil, the convergence criteria are met even for higher angles of attack, as seen in figure3.7, and therefore the results appear to be usable for further analysis. 6 As a verification of the validity of the results, the residual target is reduced to 10− and the maximum number of iterations is increased to 1500. The results are presented in figure3.8. The mass and momentum equations residuals as well as the Y force, fluctuate in a periodic 5 manner around the value of 10− and 450N respectively, indicating convergence problems, and therefore a transient simulation supplements the results, using again a time step of 0.01 seconds and a total simulation time of 3 seconds, and presented in figure3.9. Figure A.4 in the appendix reveals the inability of the steady state simulations to accurately predict the separation point at 15o angle of attack for the leading edge suction case. Evidently, depending on the residuals target value and the mesh element size, separation occurs at 60%, 70% or 90% of the chord. For this reason, the majority of the simulations will be run in steady 34 3. CFD Implementation

(a) Residuals (b) Y force

Figure 3.7 – Leading edge distributed suction (C q = 0.03) for 15 degrees angle of attack.

(a) Residuals (b) Y force

Figure 3.8 – Leading edge distributed suction (C q = 0.03) for 15 degrees angle of attack - Tight convergence, higher number of iterrations state mode and after a reasonable pattern has been established regarding the airfoil’s behavior when different kinds of suction are applied, the optimal suction arrangement will be run once again using transient analysis in order to derive more accurate results. 3.1. Setting up the model 35

(a) Residuals (b) Y force

Figure 3.9 – Transient simulation for leading edge distributed suction (C q = 0.03) for 15 degrees angle of attack

Chapter 4

Results

Before moving on to the investigation of the effect of suction on the boundary layer, some further validation of the Setup options chosen is carried out. The choice of the Shear Stress Transport Gamma Theta transitional turbulence model over the SST Fully Turbulent and the Kappa Omega model is justified in figures 4.1 and 4.2. As mentioned in section 2.9, suction is expected to enhance the airfoil’s performance by delaying transition and preventing sepera- tion or at least producing a more narrow wake. The delay of transition would create a shorter turbulent regime thus decreasing skin friction. It is therefore necessary for the CFD simulation to use a model that can capture transition in order for comparisons with the clean (no suction) airfoil to be possible. The quantity used to detect transition is the eddy viscosity, which can be defined as the proportionality factor that relates the Reynolds stresses and the mean velocity gradient. When transition to turbulence takes place, the Reynolds stresses values will rise due the existence of fluctuating horizontal and transversal velocities and therefore a jump in the values of eddy viscosity will be observed. The point along the airfoil where this eddy viscosity jump takes place will be considered as the transition point to turbulence.

Figure 4.1 depicts the eddy viscosity distribution along the upper side of the NACA 4415 airfoil at 10o angle of attack for a Reynolds number of 1.5e6. It is evident that when using the SST Fully Turbulent as well as the Kappa Omega model, the flow is turbulent right from the leading edge, whereas the SST Gamma Theta model is able to simulate the laminar flow that takes place for a short extent downstream the leading edge before the transition to turbulence takes place. The low eddy viscosity values of the graph can be explained by the fact that they are measured on the layer adjacent to the surface of the airfoil.

ï7 x 10 2.5 Gamma Theta Kappa Omega Fully Turbulent 2

1.5

1 Eddy Viscosity [Pa s]

0.5

0 0 0.2 0.4 0.6 0.8 1 x [m]

Figure 4.1 – Eddy viscosity for 10o angle of attack

37 38 4. Results

In order to verify the CFX results, a comparison against the results from XFOIL is un- dertaken. XFOIL is an interactive program for the design and analysis of subsonic isolated airfoils with the use a simple linear-vorticity stream function panel method combined with an integral boundary layer analysis, [13]. Figure 4.2 depicts the variation of the transition point along the airfoil over the angle of attack. Due to the increasing steepness of the adverse pres- sure gradient, transition to turbulence occurs closer to the leading edge for an increasing angle of attack. It is clear that from the three aforementioned models, only the SST Gamma Theta model is able to capture adequately the transitional behavior of the boundary layer, and follow the same trend as the XFOIL results, and will therefore be used henceforth.

0.7 Xfoil SST Gamma Theta 0.6 Kappa Omega SST Fully turbulent

0.5

0.4

0.3

0.2

0.1 Distance between point of transition and LE [m]

0 0 5 10 15 20 25 Angle of attack [deg]

Figure 4.2 – Point of transition

Figure A.2 in the Appendix presents the variation of the eddy viscosity along the airfoil surface, for the three turbulence models for different angles of attack. It is evident in the SST Gamma Theta case that the eddy viscosity jump occurs closer to the leading edge as the angle of attack increases. In connection with figure2.2, the shear stress along with the eddy viscosity over the airfoil surface (non dimensionalized by their maximum values) are plotted in figure du 4.3. Both quantities depend on the velocity gradient dy and consequently are suitable for the detection of transition, however only the eddy viscosity will be used in the present case study for that purpose.

4.1 Suction Location

As mentioned in section 2.4 the adverse pressure gradient, which essentially is the cause of flow separation and therefore stall, starts downstream the minimum pressure point on the upper airfoil surface. It is therefore a reasonable assumption to apply suction at that point in order to enhance the airfoil’s efficiency. For that purpose, a 0.007m suction slot, as suggested by [5], is implemented at the miminum pressure point, corresponding to 0o angle of attack, and a normal to the wall velocity is applied as a boundary condition to the suction outlet, such that the suction coefficient is equal to Cq = 0.03. CFX results however reveal that suction will delay transition only for those angles of attack where the clean airfoil transition point is downstream the suction location, whereas for higher angles of attack where the transition point has moved upstream the suction location, suction has no effect. Changing the directionality of the suction from normal to 45o inclined also has no effect on transition, as can be seen in figure A.3 in the Appendix. Results however differ significantly when suction is applied upstream 4.2. Discrete Suction versus Distributed Suction 39

5 degrees AoA 1 Wall shear Eddy viscosity 0.5

0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 x [m] 12 degrees AoA 1 Wall shear Eddy viscosity 0.5

0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 x [m] 17 degrees AoA 1 Wall shear Eddy viscosity 0.5

0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 x [m]

Figure 4.3 – Non dimensionalized eddy viscosity and shear stress the earliest transition point. For the same slot dimensions and the same suction coefficient, CFX shows that slot suction applied close to the leading edge can greatly improve tha airfoil’s aerodynamic behavior. Transition is delayed almost until the trailing edge for small angles of attack and for higher angles the transition point is notably moved downstream. Figure 4.4 presents the eddy viscosity distribution along the airfoils surface for these cases, clearly indicating the beneficiary effect of leading edge suction. Figure 4.5 shows the variation of the distance of the transition point from the leading edge over the angle of attack. Evidently, the application of discrete suction at the leading edge upstream from the point of transition results in significant transition delay. The importance of the suction location can be also seen by the behavior of the suction at the 0 degrees minimum pressure point curve, where it is clear that transition is delayed only for the angles of attack where transition occurs downstream the suction location. For higher angles of attack, the curve almost coincides with the clean airfoil curve.

4.2 Discrete Suction versus Distributed Suction

As shown in figure 2.24, when distributed suction is used the maximum lift obtained is much higher than the corresponding value obtained by applying discrete suction for the same suction coefficient Cq. Two different cases of distributed suction will be applied in ANSYS, leading edge suction and trailing edge suction. Leading edge distributed suction will be appplied in a region that extends mostly on the upper side but a small portion of it will be located in the lower side of the airfoil. More specifically it extends over 5.7% of the airfoil’s upper side length and 2.6% of the pressure side. The choice of such an arrangement is based on the results found in [6], depicted in figure A.1. Trailing edge distributed suction will extend downstream 40 4. Results

ï7 x 10 6 0 degrees 5 degrees 10 degrees 5 12 degrees 15 degrees 17 degrees 4

3

Eddy viscosity [Pa s] 2

1

0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 x [m]

(a) No suction

ï7 x 10 4.5 0 degrees 4 5 degrees 10 degrees 12 degrees 3.5 15 degrees 17 degrees 3 Suction slot location

2.5

2

Eddy viscosity [Pa s] 1.5

1

0.5

0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 x [m]

(b) Discrete suction at maximum thickness

ï7 x 10 8 0 degrees 5 degrees 7 10 degrees 12 degrees 6 15 degrees 17 degrees Suction slot location 5

4

3 Eddy viscosity [Pa s]

2

1

0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 x [m]

(c) Discrete suction at leading edge

Figure 4.4 – Application of suction (C q = 0.03) at maximum thickness point and at leading edge 4.2. Discrete Suction versus Distributed Suction 41

1 Xfoil results 0.9 No suction Suction with C = 0.03 at min. pressure point q 0.8 Suction with C = 0.03 at Leading Edge q 0.7

0.6

0.5

0.4

0.3

0.2

Distance between point of transition and LE [m] 0.1

0 0 5 10 15 20 25 Angle of attack [deg]

Figure 4.5 – Point of transition to turbulent flow at different angles of attack of the clean airfoil seperation point for the 15o case, as presented in figure 4.6.

(a) Leading edge suction (b) Trailing edge suction

Figure 4.6 – Location of distributed suction

The suction coefficient is kept constant at CQ = 0.03 and the simulations are run again with different boundary conditions in order to maintain the same mass flow with the discrete case. Flow separation will be evaluated using the velocity gradient along the aifoil’s upper du surface and will be detected by regions where dy is negative for a significant extent. Figure4.7 depicts the velocity gradient distribution at 0, 10 and 17 degrees angle of attack for the clean airfoil and the leading edge distributed suction cases. For the clean airfoil at 0o angles of attack, no separation is present apart from a small bubble at approximately the middle of the airfoil. At 10o, the bubble has moved upstream, in accordance with section 2.7. At 17o however, the flow appears to be reversed over a region that starts from apporoximately the middle of the chord and extends up until the trailing edge, indicating that the flow has dettached from the surface. The separation of the flow for this case can be visualized in figure 4.8. The application of distributed suction at the leading edge clearly enhances the airfoil in that regard, as no separation bubble occurs for the first two angles of attack, and for the third one flow dettachment is significantly delayed from the middle of the airfoil to approximately 70% of the chord, as can be seen in figure4.11b. The zero values of the gradient close to the leading edge are explained by the fact that the velocity boundary 42 4. Results

4 5 x 10 Clean airfoil x 10 Leading edge slot suction 14 3.5 0 degrees 0 degrees 10 degrees 10 degrees 12 3 17 degrees 17 degrees 10 2.5

8 2 6 1.5 4

du/dY gradient du/dY gradient 1 2

0.5 0

ï2 0

ï4 ï0.5 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 x [m] x [m]

Figure 4.7 – Velocity gradient at different angles of attack for clean airfoil and leading edge distributed suction. conditions at that region have been set in a way that the air is sucked with a perpendicular to the surface direction, and therefore the gradient is approximately zero.

Figure 4.8 – Flow separation at 17o angle of attack for a clean airfoil.

The benefficiary effect of suction can be also depicted with pressure coefficient curves. Fi- gure 4.9 reveals that the application of suction can increase the lifting force due to the pressure difference between the upper and the lower side of the airfoil, only for high angles of attack. Figure 4.10 presents the pressure curves for the NACA 4415 airfoil at 17o angle of attack as were derived from CFX. Once again it is evident that discrete suction has no effect when applied downstream the transition point, whereas the pressure difference between the upper and lower sides increases when slot suction is applied close to the leading edge. Distributed suction at the trailing edge produces better results than the discrete cases, while leading edge suction enhances the airfoil performance even more. The narrower wake produced by leading edge suction can be visualised in figure 4.11. Apparently, a suction coefficient at the trailing edge of Cq = 0.03 is not enough for the flow 4.2. Discrete Suction versus Distributed Suction 43

7 7 0 degrees 0 degrees 6 10 degrees 6 10 degrees 17 degrees 17 degrees 5 5 p p C C

ï 4 ï 4

3 3

2 2

1 1 Pressure Coefficient Pressure Coefficient

0 0

ï1 ï1

ï2 ï2 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 x [m] x [m]

(a) Clean airfoil (b) Discrete leading edge suction

7 0 degrees 6 10 degrees 17 degrees 5 p C

ï 4

3

2

1 Pressure Coefficient

0

ï1

ï2 0 0.2 0.4 0.6 0.8 1 x [m]

(c) Distributed leading edge suction

Figure 4.9 – Pressure coefficients for different angles of attack

7 No suction 6 Slot suction at minimum pressure point Slot suction at leading edge Distributed suction at trailing edge 5 Distributed suction at leading edge

Cp 4 ï

3

2

1 Pressure coefficient

0

ï1

ï2 0 0.2 0.4 0.6 0.8 1 x [m]

Figure 4.10 – Pressure coefficient at 17o angle of attack for different suction cases. to reattach on the airfoil surface, however if the suction is applied before transition the flow is more resistant to the adverse pressure gradient and remains attached for a larger portion of the airfoil. 44 4. Results

(a) Trailing edge distributed suc- (b) Leading edge distributed suc- tion tion

Figure 4.11 – Flow separation at 17o angle of attack for trailing and leading edge distributed suction

Higher velocity gradients on the wall, in addition to making the flow more resilient to separation, also produce higher skin drag according to equation (2.1). If however the pressure drag decrease from the narrower wake is high enough then the flow control through boundary layer suction is deemed succesful. The aerodynamic coefficients of lift and drag are the final criteria of whether the application of suction can enhance the performance of the airfoil. Lift and drag forces can be derived via the X and Y force components that CFX calculates, modified by the corresponding angle of attack as seen in equations (4.1) and (4.2).

FY cos(α) FX sin(α) CL = − . (4.1) 1 2 2 ρV

FY sin(α) + FXcos(α) CD = . (4.2) 1 2 2 ρV

Figures 4.12 and 4.13 present the lift and drag coefficients of the discrete an distributed suction cases respectively. Apparently, inclined discrete suction at 45o induces higher lift values without increasing the drag compared to the normal suction case, whereas the normal leading edge slot suction although it extends the airfoil’s lifting capabilities to higher angles of attack, it induces higher drag values possibly related to the skin friction drag caused by the higher velocity gradients. Distributed suction on the other hand expands the range of the lift producing angles of attack even more for both the trailing and leading edge suction. Due to the narrower wake created by the leading edge suction, the lift values are higher for higher angles of attack com- pared to the trailing edge results, while at the same time keeping drag low, even below the clean airfoil values. The high drag values of the trailing edge case, especially for the low angles of attack, can be explained by the fact that the distributed suction in that case extends for almost 40% of the chord (figure 4.6b) thus creating high skin friction due to the high values du of dy . 4.3. Suction Quantity 45

Lift Curve Drag Curve 2 0.2 No Suction Normal suction with C = 0.03 0.18 q 1.8 Inclined suction with C = 0.03 q Leading edge suction with C = 0.03 0.16 q 1.6 Xfoil results 0.14

1.4 0.12

1.2 0.1 Lift coefficient

Drag coefficient 0.08 1

0.06 0.8 No Suction Normal suction with C = 0.03 q 0.04 Inclined suction with C = 0.03 0.6 q Leading edge suction with C = 0.03 0.02 q Xfoil results 0.4 0 0 5 10 15 20 25 0 5 10 15 20 25 Angle of attack [deg] Angle of attack [deg]

Figure 4.12 – Lift and drag curves for discrete suction

Lift Curve Drag Curve 1.8 0.2 No Suction Trailing edge distributed suction with C = 0.03 0.18 q 1.6 Leading edge distributed suction with C = 0.03 q Xfoil results 0.16 1.4 0.14

1.2 0.12

1 0.1 Lift coefficient

Drag coefficient 0.08 0.8

0.06 0.6

No Suction 0.04 Trailing edge distributed suction with C = 0.03 0.4 q Leading edge distributed suction with C = 0.03 0.02 q Xfoil results 0.2 0 0 5 10 15 20 25 0 5 10 15 20 25 Angle of attack [deg] Angle of attack [deg]

Figure 4.13 – Lift and drag curves for distributed suction

4.3 Suction Quantity

Having derived that distributed suction at the leading edge of the NACA 4415 airfoil increases its performance to a higher extent than the other suction arrangements that were tried out, a simple analysis is carried out with the suction coefficient Cq as a parameter in order to derive the optimum suction quantity. Figure 4.14 presents the lift and drag coefficient for a varying suction coefficient Cq. It appears that beyond Cq = 0.08 the drag of the airfoil increases. Figure 4.15 depicts the CL ratio, indicating that a suction coefficient of 0.08 would produce the highest performance CD since the lift to drag ratio beyond that point remains approximately constant, despite the fact that the suction quantity is increased. However, if the use of the airfoil is such that the increased drag can be withstood, for instance if the root of the wind turbine blade can hold the created bending moments, then higher suction coefficients can be used, assuming of course that the suction mechanism can reach the corresponding values of Cq. The pressure curves are presented in figure 4.16, indicating that higher Cq induces higher 46 4. Results

2 0.11

1.9 0.105

1.8 0.1

1.7 0.095

1.6 0.09

1.5 0.085

1.4 0.08 Lift coefficient Drag coefficient 1.3 0.075

1.2 0.07

1.1 0.065

1 0.06 0 0.05 0.1 0.15 0.2 0 0.05 0.1 0.15 0.2 Suction coefficient C = V /V Suction coefficient C = V /V q suc 0 q suc 0

o Figure 4.14 – CLand CD values for different suction coefficients at 15 angle of attack

28

26

24

22

20 ratio D /C

L 18 C 16

14

12

10 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 Suction coefficient C = V /V q suc 0

Figure 4.15 – CL ratio for different suction coefficients at 15o angle of attack CD

Cp, while the eddy visocosity distribution, figure 4.17, reveals that only for high Cq is transi- tion delayed. Figure 4.18 presents the velocity gradient along the upper side of the airfoil at 15o angle of attack. It appears that for the high suction case, except from a small separation bubble downs- tream the leading edge, no flow separation is observed since the velocity gradient does not acquire negative values for a significant extent, whereas for Cq = 0.08 separation is observed du approximately at 85% of the chord. The high values of dy however, exept from preventing separation are also responsible for the high drag values observed in figure4.14. A better visualization of the suction effect is achieved when the flow streamlines are pre- sented in CFX. Figure 4.19 shows that higher Cq can allow the flow to remain attached to the airfoil for an increasing extent. The flow velocity values are also higher for higher suc- tion coefficients, suggesting that the increase in the lift is caused by the enhancement of the acceleration of the flow on the upper side of the airfoil. 4.4. Finer Analysis 47

7 C = 0.02 q 6 C = 0.04 q C = 0.08 q 5 C = 0.15 q p C

ï 4

3

2

1 Pressure Coefficient

0

ï1

ï2 0 0.2 0.4 0.6 0.8 1 x [m]

Figure 4.16 – Pressure coefficient for different suction coefficients at 15 o angle of attack

ï6 x 10 1.5 C = 0.02 q C = 0.04 q C = 0.08 q C = 0.15 q 1

Eddy viscocity [Pa s] 0.5

0 0 0.2 0.4 0.6 0.8 1 x [m]

Figure 4.17 – Eddy viscosity for different suction coefficients at 15 o angle of attack

4.4 Finer Analysis

More accurate results can be acquired if finer meshes and transient analyses are implemented. Table 4.1 presents the mesh properties that result after halving the element size compared to the previous cases presented in table 3.1, while table 4.2 presents the setup properties of the transient simulations. It should be noted that the implementation of the normal to the wall velocity for the distributed suction has been modified, and is presented in table4.3. Using transient analysis and a finer mesh, the clean airfoil and the Cq = 0.08 cases are simulated once again. With a timestep of 0.01 seconds, 3 seconds of flow around the NACA 4415 airfoil were simulated in CFX. Apparently, as presented in figure4.20, some algorithmic fluctuations occur at the beginning of the simulation. For this reason, the values of the lift and drag forces that will be used further will consist of the mean value of the last second of the force time series, i.e. timesteps 201 to 300 . Evidently, the clean airfoil has gone into stall at 20o since heavy fluctuations caused by the vortex shedding can be observed. It is possible to derive the Strouhal frequency by such a si- gnal, however longer simulation data should be acquired. FigureA.5 in the Appendix presents 48 4. Results

Table 4.1 – Finer mesh properties

Spacing Default Body Spacing Maximum Spacing [m] 1.0 Default Face Spacing Option Volume Spacing Option Constant Constant Edge Length [m] 0.0123116 Airfoil Spacing Radius of Influence [m] 1.0 Expansion Factor 1.2 Controls Length Scale [m] 0.005 Airfoil Vicinity Radius of Influence [m] 1 Expansion Factor 1.2 Length Scale [m] 0.05 Broader Vicinity Radius of Influence [m] 1 Expansion Factor 1.2 Point Control Point 0.5[m], 0[m], 0[m] Spacing Airfoil Vicinity Point -3[m], 0[m], 0[m] Triangle Control Point 7[m], 3.5[m], 0[m] Point 7[m],-3.5[m], 0[m] Inflation Inflation Number of Inflated Layers 60 Expansion Factor 1.1 Number of Spreading Iterations 0 Minimum Internal Angle [Degrees] 2.5 Maximum Internal Angle [Degrees] 10.0 Option First Layer Thickness Define First Layer By y+ y+ 0.5 Reynolds Number 1.5e6 Inflation Options Reference Length [m] 1.0 First Prism Height [m] 8.23347e-6 Extended Layer Growth Yes Layer by Layer Smoothing No Options Surface Meshing Option Delaunay Meshing Strategy Option Extruded 2D Mesh 2D Extrusion Option Option Full Number of Layers 1 4.4. Finer Analysis 49

Table 4.2 – Transient Setup Properties

Analysis Type Option Transient Time Duration Option Total Time Total Time 3 [s] Time Steps Option Timesteps Timesteps 0.01[s] Initial Time Option Automatic with Value Timesteps 0 [s] Material Air at 25 C Basic Settings Morphology Continuous Fluid Reference Pressure 1 [atm] Domain Motion Stationary Heat Transfer Option Isothermal Fluid Models Fluid Temperature 25 C Turbulence Option Shear Stress Transport Transitional Turbulence Gamma Theta Model Velocity Type Cartesian Initialization Cartesian Velocity Components [m/s] U = Vrelcos(α) U = Vrelsin(α) W = 0 Advection Scheme High Resolution Transient Scheme Second Order Backward Euler Timestep Initialization Automatic Turbulence Numerics High Resolution Convergence Control Solver Control Min. Coeff. Loops 1 Max. Coeff. Loops 10 Timescale Control Coefficient Loops Convergence Criteria Residual Type RMS Residual Target 1e-4

Table 4.3 – Suction boundary conditions

Outlet Flow Regime Option Subsonic Suction Mass and Momentum Option Mass Flow Rate Mass Flow Rate 0.0156 [kg/s] Mass Flow Update Option Constant Flux 50 4. Results

5 x 10 4 C = 0.02 q 3.5 C = 0.04 q C = 0.08 q 3 C = 0.15 q 2.5

2

1.5

1 Velocity gradient du/dy

0.5

0

ï0.5 0 0.2 0.4 0.6 0.8 1 x [m]

du o Figure 4.18 – Velocity gradient dy for different suction coefficients at 15 angle of attack

(a) Cq = 0.01 (b) Cq = 0.08 (c) Cq = 0.15

Figure 4.19 – Streamlines for different suction coefficients at 15 o angle of attack

3.5 3.5 0 degrees AoA 0 degrees AoA 15 degrees AoA 15 degrees AoA 3 20 degrees AoA 3 20 degrees AoA

2.5 2.5

2 2

1.5 1.5 Lift coefficient Lift coefficient

1 1

0.5 0.5

0 0 0 0.5 1 1.5 2 2.5 3 0 0.5 1 1.5 2 2.5 3 Time [s] Time [s]

(a) Clean airfoil (b) Distributed suction at leading edge with Cq = 0.08

Figure 4.20 – Lift coefficient response for different angles of attack the power spectrum of this short 3 seconds signal, revealing a small peak at approximately 5 Hz, which is relatively close to the corresponding value of a flow around a cylinder with a diameter equal to the airfoil’s chord ( f = StV, where St 0.23 according to [6]). Taking the L ( mean value of the last second for each of the angles of attack, figure 4.21 can be produced 4.5. Wind Turbine Performance Enhancement 51 which depicts the aerodynamic curves of such an analysis.

Lift Curve Drag Curve 2 0.2

0.18 1.8 0.16 1.6 0.14 1.4 0.12

1.2 0.1

0.08 Lift coefficient

1 Drag coefficient 0.06 0.8 0.04 0.6 0.02

0.4 0 0 5 10 15 20 25 0 5 10 15 20 25 Angle of attack [deg] Angle of attack [deg] No Suction No Suction Leading edge distributed suction with C = 0.08 Leading edge distributed suction with C = 0.08 q q Xfoil results Xfoil results

Figure 4.21 – Lift and drag curves for the clean airfoil and C q = 0.08 case

Apparently, the lift capabilities of the NACA 4415 airfoil have been extended to higher angles of attack whereas figure 4.22a reveals that an increase of the lift coefficient up to 20% is possible, while CD can decrease up to 30%. It is worth mentioning that maximum lift occurs at higher angles than the clean airfoil, implying that in the case of applying suction on a wind turbine blade, the pitch angle should be modified accordingly.

1.25 1.4

1.3 1.2 1.2

1.1 1.15 L, clean D, clean /C /C 1

1.1 L, suction D, suction 0.9 C C

0.8 1.05 0.7

1 0 5 10 15 20 0 5 10 15 20 Angle of attack [deg] Angle of attack [deg]

(a) Effect on Lift ( CL,suction ) due to the applica- (b) Effect on Drag ( CD,suction ) due to the appli- CL,clean CD,clean tion of leading edge distributed suction cation of leading edge distributed suction

Figure 4.22 – Suction effect on aerodynamic coefficients

4.5 Wind Turbine Performance Enhancement

The aerodynamic coefficients of the NACA 4415 airfoil after suction is applied were derived in section 4.4 and will be used to estimate the impact of suction on a wind turbine. For this purpose, the Tjaereborg wind turbine will be used, the aerodynamic data of which were provi- ded by DTU. The NACA 4415 suction results will act as a starting point for the modification 52 4. Results of the Tjaereborg root airfoil coefficients, which will in turn be used as an input in the Blade Element Momentum method (BEM). After the Lift and Drag forces on the root segments of the Tjaereborg blade have been derived, a new power curve corresponding to a turbine where boundary layer suction is applied in the root airfoils will be computed. Moreover, the possible reduction of the modified airfoil’s chordline will be quantified, while maintaining the same Lift force with the clean airfoil case.

4.5.1 Blade Element Momentum Method The BEM method combines the 1-D momentum theory with with the actual geometry of the rotor by implementing in the algorithm various local attributes of the blade, such as the twist and chord distribution and the aerodynamic behavior of the specific airfoils used. The blade is segregated in segments, each with its own properties and independent of the others. Figure 4.23 from [14] presents the components and the angles related to the relative velocity at the rotor plane of a wind turbine airfoil. θ denotes the twist angle, α the angle of attack and φ the flow angle.

Figure 4.23 – Velocities at rotor plane.

For a given wind speed, the following procedure is followed in order to calculate the turbine’s power output.

4.5.2 BEM algorithm 1. The first step of the BEM method is the initialization of the induction factors at zero. They will later be recalculated and their final value will be defined when two consecutive induction factors (axial or tangential, a or a! respectively, not to be confused with the angle of attack α) acquire identical values.

2. The solidity of the turbine σ is calculated via :

c(i)B σ(i) = , (4.3) 2πr(i)

where c is the chordline, B the number of blades and r is the segment’s distance from the hub. The index ’i’ signifies the radial position along the blade.

3. Calculation of the flow angle φ.

(1 a)V φ(i) = atan − 0 . (4.4) (1 + a!)ωr(i) 4.5. Wind Turbine Performance Enhancement 53

4. Due to the fact that BEM assumes that the force from the blades on the flow is constant in each annular element, which corresponds to a rotor with an infinite number of blades, Prandtl’s tip loss factor is implemented in order to correct this assumption.

B(R r(i)) 2 − F = arccos(e− 2r(i)sin(φ(i)) ). (4.5) π

5. The angle of attack α is calculated via the earlier derived flow angle φ and the local pitch angle of the blade θ. The latter is a combination of the pitch angle and the twist of the blade

α(i) = φ(i) θ(i). (4.6) −

6. Using the lift and drag coefficients, Cn and Ct are calculated which correspond to the non-dimensionalised normal and tangential to the rotor plane forces.

Cn(i) = CL(i)cos(φ(i)) + CD(i)sin(φ(i)). (4.7)

C (i) = C (i)sin(φ(i)) C (i)cos(φ(i)). (4.8) t L − D

7. Due to the fact that for high values of the axial induction factor the simple momen- tum theory breaks down and does not produce results that are verified experimentaly, Glauert’s correction is implemented in order to acquire results that are closer to reality. The recalculated value of the axial induction factor is :

1 2 a 0.2 4Fsin φ(i) +1 ≤ anew = σCN (4.9)  CT > .  4F(1 0.25(5 3a)a) a 0 2  − −  2  = (1 a) CN σ where CT −sin2φ . The tangential induction factor is then computed :

σCt a! = . (4.10) new 4Fsinφ(i)cosφ(i) σ(i)C (i) − t A relaxation method is implemented so that the newly calculated values of the induction factors consist of 90% of the previous value and 10% of the new.

8. The difference between the old and the new values of the axial induction factor is com- puted and as long as it is above a certain threshold value, the induction factors of the last step are substituted in the first one the and the process is repeated until two consecutive values converge. 54 4. Results

9. For the axial induction factor computed, the relative velocity can be calculated and sub- sequently the lift and the drag forces which will lead to the tangential to the rotor plane force pt :

(1 a)V V = − 0 . (4.11) rel sinφ(i)

1 L(i) = c(i)C (i)V 2. (4.12) 2 L rel

1 D(i) = c(i)C (i)V 2. (4.13) 2 D rel

p (i) = L(i)sinφ(i) D(i)cosφ(i). (4.14) t −

pn(i) = L(i)cosφ(i) + D(i)sinφ(i). (4.15)

10. The torque of each blade is computed via :

1 1 M(i) = A(r 3 r3) + B(r 2 r2), (4.16) 3 i+1 − i 2 i+1 − i

where

p , + p , A = t i 1 − t i . (4.17) r r i+1 − i

p , r + p , + r B = t i i 1 − t i 1 i . (4.18) r r i+1 − i 11. Lastly the power of each segment is computed via:

P(i) = ωM(i). (4.19)

Subsequently, the power contributed by each blade segment is summed and the result is multiplied by the total number of blades.

12. The same procedure is followed for a range of free wind velocities until the turbine’s power curve is derived. 4.5. Wind Turbine Performance Enhancement 55

2500 0.6

0.5 2000

0.4 1500 p

C 0.3

Power [kW] 1000 0.2

500 0.1

0 0 0 5 10 15 20 25 0 5 10 15 20 25 Wind speed [m/sec] Wind speed [m/s]

(a) Power curve (b) Power coefficient curve

Figure 4.24 – Tjaereborg wind turbine characteristics

4.5.3 BEM results

Figure 4.24 presents the power curve and the power coefficient curve of the 2MW Tjaereborg rad fixed speed wind turbine. The turbines angular velocity is ω = 2.3195 s and the twist angle distribution varies from 8o at the root to 0.16o at the blade tip. Apparently rated power is reached at 15m/s and the maximum power coefficient is reached at 9m/s. Due to the fact that the beneficiary effect of suction takes place for a certain range of angles of attack, it is important to know at which angles of attack does the turbine blade operate. According to figure 4.22, the angle of attack should be above 15o in order for the airfoil’s performance to be enhanced. Figure 4.25a depicts the variation of the angle of attack over the free wind speed for different radial positions, whereas4.25b presents the variation of the angle of attack over the span of the blade for different free wind speeds. Evidently, only the root segments of the blade operate in the range of angles of attack wherein suction could have an improving effect. This can be explained by the fact that the tangential component of the relative velocity of each segment, in connection with figure4.23, is proportional to its distance from the hub and since the normal to the rotorplane component of the velocity does not vary radially, segments close to the tip will experience small angles of attack. This can be mitigated by the twisting of the blade, however the twist angle distribution over the blade has not been designed for such purpose. The chord distribution of the blade is presented in figure4.26. It should be noted that the airfoils used for the two segments closest to the hub are identical. The aerodynamic data of the Tjaereborg blade root airfoil are modified following the trend of the CFX results of the NACA 4415 airfoil, in order to simulate the effect suction would have on them. Figure 4.27 depicts the new lift and drag curves which were produced based on figure 4.22. After a certain angle of attack, suction is expected to not have any effect on neither lift or drag. ANSYS simulations reveal that the CL,suction ratio approcahes unity (1.077) at a 60o CL,clean angle, as presented in figure A.6 in the Appendix, therefore beyond that point the suction and the clean curve will coincide. The power contribution of each of the three first segments is presented in figure4.28. In accordance to figure 4.25, figure 4.28 reveals that for blade segments away from the hub, suction can improve the segment’s power output only for high free wind speeds. The turbine’s power curve after the application of suction on its first two segments is presented in figure 4.29. Apparently rated power is reached for a lower wind speed, however 56 4. Results

50 50 V = 6 m/s 6.46m ï 9.46m segment 0 45 9.46m ï 12.46m segment 45 V = 9 m/s 0 12.46m ï 15.46m segment V = 12 m/s 40 40 0 24.46m ï 27.46m segment V = 15 m/s 0 35 35

30 30

25 25

20 20 Angle of attack [deg] Angle of attack [deg] 15 15

10 10

5 5

0 0 5 10 15 20 25 10 15 20 25 30 Free wind speed [m/s] Radial distance from rotor center [m]

(a) Angle of attack over free wind speed (b) Angle of attack over blade span

Figure 4.25 – Angle of attack variation

3.5

3

2.5

2

1.5 Chord length [m]

1

0.5

0 0 5 10 15 20 25 30 Blade span [m]

Figure 4.26 – Chord distribution of the Tjaereborg blade no significant increase of the total power is observed. Figure 4.30 presents the power gain due to suction as a function of the free wind speed. Only a 2% increase can be obtained at the rated power wind speed. The total energy gain due to the application of suction can be also quantified via the annual energy output (AEO) computation. Assuming that the wind speed within one year follows a Weibull distribution with a shape coefficient equal to 2 and a size coefficient equal to 8, as presented figure4.31, the AEO can be computed using equations 4.20 and 4.21, according to [15].

AEO = AT w(Vi)CP(Vi), (4.20) )Vi where A is the rotor plane area and T is the time within the frame of interest in seconds, in the present case a year, and

1 w = ρV3 pd f (V). (4.21) 2 4.5. Wind Turbine Performance Enhancement 57

1.5 1.4

1.2

1 1

0.8

0.6 Lift coefficient Drag coefficient 0.5 0.4

0.2

0 0 0 20 40 60 80 100 0 20 40 60 80 100 Angle of attack [deg] Angle of attack [deg] LE suction LE Suction Clean segment Clean segment

Figure 4.27 – Lift and drag curves of the Tjaereborg root blade segment located from 6.46m until 12.46m from the rotor center

Under these conditions, the Tjaereborg turbine produces 4.1029GWh per year, whereas when suction is applied the AEO rises to 4.1197GWh, i.e. there is a gain of 0.0168GWh or a 0.4096% increase. However, this minimal gain of the power output is not the only way to exploit boundary layer suction. Due to the increased lift forces, a decrease of the chord of the root segments while maintaining their power output contribution is possible. After reducing the chord length of the segments located between 6.46m 9.46m and 9.46m 12.46m to the 75% of their initial − − length, their power curves are computed and presented in figure4.32 The wind turbine power curve is then computed and, as seen in figure4.33, no significant difference between the clean blade and the suction with reduced root chord length cases is evident. The case of the clean blade with the same chord reduction is also plotted for compa- rison reasons. In order to acquire a better view of the effect of suction on the turbine’s performance, the power coefficient for the cases of the clean blade, the blade with suction, and the reduced root chord blade with suction, are presented in figure4.34. The annual energy output of the Tjaereborg wind turbine when suction is applied and the close to the hub segments of the blades are reduced by 25% is almost equal to the original Tjaereborg turbine, with a 0.2% deviation. It is important to note that due to the lift force increase produced by the application of boundary layer suction, the thrust force acting on the rotor would also rise. Figure4.35 depicts the variation of the thrust force. This increase in thrust will create higher bending moments on the wind turbine tower root which must be accounted for in the final design of the wind turbine. 58 4. Results

80 120 Clean airfoil Clean airfoil LE sution LE sution 70 100

60

80 50

40 60 Power [kW] Power [kW] 30 40

20

20 10

0 0 0 5 10 15 20 25 0 5 10 15 20 25 Free wind speed [m/s] Free wind speed [m/s]

(a) Segment located between 6.46m and (b) Segment located between 9.46m and 9.46m 12.46m

120 Clean airfoil LE sution 100

80

60 Power [kW]

40

20

0 0 5 10 15 20 25 Free wind speed [m/s]

(c) Segment located between 12.46m and 15.46m

Figure 4.28 – Power contribution of each of the three first segments

2500 LE suction for 6.46m ï 12.46m segment LE suction for 6.46m ï 12.46m segment Clean airfoil 2150 Clean airfoil

2000 2100

2050 1500

2000 Power [kW] 1000 Power [kW] 1950

1900 500 1850

0 5 10 15 20 25 13 13.5 14 14.5 15 15.5 Free wind speed [m/s] Free wind speed [m/s]

(a) Power curve (b) Zoom-in at rated power

Figure 4.29 – Power curve of the Tjaereborg wind turbine after suction is applied over the range 6.46m 12.46m from the rotor’s center − 4.6. The Blade as a Centrifugal Pump 59

1.1

1.08

1.06

1.04

1.02

1

Power ratio 0.98

0.96

0.94

0.92

0.9 5 10 15 20 25 Free wind speed [m/s]

Figure 4.30 – Power ratio between the clean blade case and the LE suction over the range 6.46m 12.46m from the rotor’s center −

12 Weibull distribution Cutïin speed 10

8

6 Probability [%] 4

2

0 0 5 10 15 20 25 Free wind speed [m/s]

Figure 4.31 – Weibull distribution with A = 8 and k = 2

4.6 The Blade as a Centrifugal Pump

An idea for the application of suction on the wind turbine blades is to not implement it via a power consuming pump, but to achieve it by cutting off the blade tip. The centrifugal forces created by the turbine’s rotation would then produce an inner blade spanwise flow which could drive the suction. Assuming that the blade itself acts as a radial impeler blade, the necessary torque M that needs to be delivered in order to create a flow rate Q according to [10] is equal to:

M = ρQω(r 2 r 2), (4.22) 2 − 1

where r2 and r1 signify the distance from the hub of the blade tip and the blade root respec- tively. The flow rate Q can be computed via the total area of the suction location multiplied by the wind speed the blade experiences, after the latter is multiplied with the suction coefficient Cq. It is important to note that the velocity each segment of the blade experiences is not the 60 4. Results

60 70 Clean airfoil Clean airfoil LE sution LE sution 60 50

50 40

40 30 30 Power [kW] Power [kW]

20 20

10 10

0 0 0 5 10 15 20 25 0 5 10 15 20 25 Free wind speed [m/s] Free wind speed [m/s]

(a) Segment located between 6.46m and (b) Segment located between 9.46m and 9.46m 12.46m

Figure 4.32 – Power contribution of each of the two close to hub segments after 25% chord reduction

2500 LE sution reduced chord LE sution reduced chord 2100 Clean blade Clean blade 2000 Clean blade reduced chord Clean blade reduced chord 2050

1500 2000

Power [kW] 1000 Power [kW] 1950

1900 500

1850

0 0 5 10 15 20 25 12 13 14 15 16 17 Free wind speed [m/s] Free wind speed [m/s]

(a) Power curve (b) Zoom-in at rated power

Figure 4.33 – Power curve of the Tjaereborg wind turbine after suction is applied over the range 6.46m 12.46m from the rotor’s center and the corresponding chord- lengths have been− reduced by 25% same due to its rotation, as can be visualised in figure4.23, and therefore the suction velocity along the blade must vary accordingly.

In order to compute the suction quantity for the Tjaereborg airfoil, the difference in geo- metry between the ANSYS simulated airfoil and the Tjaereborg airfoils needs to be taken into account. For this reason, the ratio of the suction surfaces will be assumed equal to the ratio of the chordlines, as seen in equation (4.23).

csegment Asegment = AANS YS (4.23) cANS YS

After taking into account each blade segment’s dimensions, the total suction quantity for m3 each blade is found equal to 3.82 s , which results in a torque needed equal to 9.65kNm, according to equation 4.22. 4.6. The Blade as a Centrifugal Pump 61

0.5 Clean airfoil Clean airfoil 0.45 LE Suction LE Suction LE Suction reduced chord 0.44 LE Suction reduced chord

0.4 0.42 0.35 ] ] ï ï 0.3 0.4

0.25

0.38 0.2 Power coefficient [ Power coefficient [

0.15 0.36

0.1

0.34 0.05

0 0 5 10 15 20 25 11 12 13 14 15 16 Free wind speed [m/s] Free wind speed [m/s]

(a) Power coefficient curve (b) Zoom-in at rated power

Figure 4.34 – Power coefficient curve of the Tjaereborg wind turbine after suction is applied over the range 6.46m 12.46m from the rotor’s center and the corresponding − chordlengths have been reduced by 25%

Thrust Thrust

220 225 200 220 180 215 160 210 140 205 120 200

Thrust [kN] 100 Thrust [kN] 195 80 Clean Blade 190 Clean Blade 60 LE Suction LE Suction 185 LE Suction ï reduced chord LE Suction ï reduced chord 40 180 20 4 6 8 10 12 14 16 13 13.5 14 14.5 15 15.5 Free wind speed [m/s] Free wind speed [m/s] (a) Thrust over free wind speed (b) Zoom-in at rated power

Figure 4.35 – Thrust on the rotor for a range of wind speeds from cut-in speed to rated power

The Tjaereborg wind turbine acquires its maximum power coefficient at a free wind speed m of 9 s , and for that wind speed the contributing torque of each blade after suction is applied and the chord of the close to the hub segments has been reduced by 25% is 89.275kNm. Therefore, cutting off the tip of the blade in order to implement boundary layer suction is deemed to be possible, since the torque needed to achieve the desired suction coefficients is m 10.8% of the total torque produced by the blade’s rotation. For a free wind speed of 14s the torque percentage drops to below 4%. It must be stressed however that the torque needed for the application of suction is a direct loss in power according to equation (4.19), and therefore the usability of this suction mechanism should be studied and optimized further. Of course, some form of control needs to be implemented as well in order to keep the suction coefficients within a satisfactory range. This can be achieved with a properly designed ducting in the interior of the turbine blade or with the use of vanes that would control the inner blade spanwise flow, depending on the turbine’s rotation and the relative velocities the blade encounters. Any additional power needed for the control of the boundary layer could be simulated by an additional equivalent drag coefficient in order to evaluate the feasibility of such an endeavor.

Chapter 5

Conclusions and Perspectives

5.1 Conclusions

Boundary layer control through different suction arrangements has been investigated for a NACA 4415 airfoil using ANSYS CFX 12.1. The applicability of the Gamma-Theta transi- tion model was verified with the XFOIL results, and it was concluded that suction affects the transition and separation of the flow only when it is applied upstream the clean airfoil transi- tion point. Due to the fact that the transition point is moving towards the leading edge as the angle of attack increases, it was deemed necessary to apply suction on the nose of the airfoil in order to enhance the airfoil’s performance at high angles of attack. The extent of the suction location as well as the suction quantity were also investigated and the results have shown that distributed suction produces superior results compared to discrete suction for the same suction quantity, reaching values of Clmax up to 20% higher than the clean airfoil.

Extrapolating the derived results from CFX to the airfoils used on the Tjaereborg wind turbine, a minor increase on the wind turbine’s power output was observed, rated power was reached for lower wind speed, but the contribution of suction to the total annual energy ou- tout was negligible. By applying suction however it was possible to reduce the chord length of the close to the hub segments of the blade by 25% while maintaining their initial power contribution. This chord reduction can lead to the production of slender blades which would subsequently present reduced bending moments at the root of the blade.

The possibility of using the rotating turbine blade as a centrifugal pump by cutting off its tip was also investigated, and results showed that the suction quantity needed for the enhancement of the blade performance can be achieved by the torque created by the blade’s rotation, but with a significant loss of power.

5.2 Suggestions for Further Work

Further analysis on boundary layer suction using CFD programs should include transient si- mulations in order to capture its effect on the dynamic phenomena of boundary layer transition to turbulence and flow separation. The time step as well as the number of itterations at each timestep must be such that the flow is properly resolved and the simulation converges. The directionality of the suction, both for the discrete as well for the distributed cases, is a topic that could be further investigated. The effect on the airfoil performance of the angle by which the air exits through the suction location could lead to imporved lift and drag results without the need of higher suction quantity. Given the use for which the airfoil is intended and depending on the dominating angle of attack during its operation, an optimal suction angle could be derived.

63 64 5. Conclusions and Perspectives

Since a solid conclusion of the present case study is that leading edge distributed normal suction enhances the airfoil’s behavior to a higher extent than other suction arrangements, more research could be done on the exact location it should be applied, the percentage of the airfoil surface it should cover, what portion of it should lie on either side of the airfoil, and the dependence of the above on the angle of attack. Moreover, further investigation could be done regarding the distribution of the mass flow along the suction area itself in order to achieve the optimal airfoil performance, as suggested by [2] for the active control case. Figure 5.1 presents the mass flow contour at the leading edge suction location. It appears that the outflow is not uniformally distributed, but there are certain location in the upper and lower side of the airfoil where the flow rate is higher than the rest of the suction area. By modifying the sucked air distribution, further enhancement of the airfoil’s performance may become possible.

o Figure 5.1 – Distribution of mass flow as it is sucked away for C q = 0.08 at 5 angle of attack

In practice, according to [16], the desired suction distribution can be realized by a suction sandwich structure on top of the usual structural sandwich structure. The suction sandwich structure can be divided in buffers within which the air is sucked through a carbon fiber ou- ter skin with many small holes, then flows through a perforated honeycomb core and finally through throttling holes of the structural sandwich faces, into the inner space of the wing, as presented in A.7. According to [16], the suction distribution can be controlled by varying the diameter of the holes in the honeycomb core and by the diameter of the throttling holes by which the sucked air is driven into the inner part of the blade. Cases of interest that could be studied in the future include different arrangements of suc- tion in order to derive high lift to drag ratios and high maximum lift coefficients with the minimum sucked air quantity possible. Multiple slot suction (as investigated by [3]) against distributed suction for the same suction coefficient can be compared, i.e. applying discrete suc- tion in multiple locations along the airfoil (leading edge, transition point, minimum pressure point, trailing edge) and while keeping the total sucked mass flow rate constant, investigate whether better results than the leading edge distributed suction can be reached. Furthermore, an analysis of how the airfoil’s roughness could alter the effect of suction could produce a roughness length threshold above which transition may not be influenced. The possibility that the suction location (slot, porous plate, permeable surface) could itself in- 5.2. Suggestions for Further Work 65 duce turbulence downstream (i.e. act as a turbulator) at certain flow conditions is also a topic that could be studied. Additionally, the effect of the free stream turbulence intensity and the Reynolds number may also produce useful results regarding the extent of the influence boun- dary layer suction can have on the flow around the airfoil.

Finally, the modeling of a 3D blade and the investigation of suction on all three compo- nents of the velocity profile should be the next step regarding the investigation of boundary layer suction since it will produce a much more accurate and detailed picture of how suction can affect the flow. For the wind turbine blade case, the effect of the local properties of the blade such as varying chord length, pitch angle and Reynolds number must be taken into ac- count, and transition and seperation lines along the spanwise direction of the blade can be derived for the clean blade and the suction cases. Moreover, the distribution of the suction flow rate along the spanwise direction of the blade can be studied in order to derive the op- timal performance. Furthermore, an attempt to detect and capture the Tolmienn Schlichting waves using CFD could be undertaken in order to investigate whether boundary layer suction can modify their frequency and consequently the boundary layer flow. The internal ducting of the blade (as seen in [17] for the active control case on airplane wings) is of crucial importance if suction is to be applied in a passive manner as suggested in section4.6, therefore great care needs to be taken in order to achieve the desired suction coefficient at the radial stations of interest along the blade span.

Bibliography

[1] A. L. Braslow, A History of Suction-Type Laminar-Flow Control with Emphasis on Flight Research. NASA History Division, 1999.

[2] R. Eppler, “Airfoils with boundary layer suction, design and off design cases,” Aerospace Sci. Technol., vol. 3, pp. 403–415, 1999.

[3] R. A. O. Oyewola, L. Djenidi, “Influence of localised double suction on a turbulent boundary layer,” Journal of Fluids and Structures, vol. 23, pp. 787 – 798, 2007.

[4] J.-P. B. Mohamed Gad-el Hak, Andrew Pollard, Flow Control, Fundamentals and Prac- tices. Springer, 1998.

[5] A. E. v. D. Ira H. Abbott, Theory of Wing Sections. Dover Publications, 1958.

[6] H. Schlichting, Boundary-Layer Theory. McGraw-Hill Book Company, seventh ed., 1979.

[7] J. A. R. Layton T. Crowe, Donald F. Elger, Engineering Fluid Mechanics. John Wiley and Sons, Inc., seventh ed., 2001.

[8] P. C. E. L. Houghton, Aerodynamics for Engineering Students. Butterworth Heinemann, fifth ed., 2003.

[9] B. M. Sumer, Lecture Notes on Turbulence. Technical University of Denmark, 2007.

[10] F. M. White, Fluid Mechanics. McGraw-Hill, fifth ed., 2003.

[11] “Vortex generator, aerospaceweb website. [online] [cited: 05 22, 2010.] http://www.aerospaceweb.org/question/aerodynamics/q0255.shtml.”

[12] ANSYS, “Cfx-mesh help,” January 2007.

[13] H. Y. Mark Drela, “Xfoil 6.9 user primer,” November 2001.

[14] M. O. Hansen, Aerodynamics of Wind Turbines. Earthscan, second ed., 2008.

[15] L. Battisti, “Lecture notes on wind turbine ice prevention systems selection and design,” June 2009.

[16] L. Boermans, “Practical implementation of boundary layer suction for drag reduction and lift enhancement.,” tech. rep., TU Delft, Faculty of Aerospace Engineering, The Netherlands.

[17] A. G. Rawcliffe, “Suction-slot ducting design,” tech. rep., Aeronautical Research Coun- cil, 1952.

67

Appendix A

Appendix

Figure A.1 – Different locations for distributed suction

69 70 A. Appendix

ï8 x 10 SST Fully Turbulent model 3.5 0 degrees 5 degrees 3 10 degrees 12 degrees 15 degrees 2.5 17 degrees

2

1.5 Eddy Viscosity [Pa s] 1

0.5

0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 x [m] (a) SST Fully Turbulent model

ï8 x 10 5 0 degrees 4.5 5 degrees 10 degrees 4 12 degrees 15 degrees 3.5 17 degrees

3

2.5

2 Eddy Viscosity [Pa s] 1.5

1

0.5

0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 x [m]

(b) SST Kappa Omega model

ï7 x 10 4.5 0 degrees 4 5 degrees 10 degrees 12 degrees 3.5 15 degrees 17 degrees 3

2.5

2

Eddy Viscosity [Pa s] 1.5

1

0.5

0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 x [m] (c) SST Gamma Theta model

Figure A.2 – Eddy viscosity for different turbulence models and different angles of attack 71

ï7 x 10 4.5 0 degrees 4 5 degrees 10 degrees 12 degrees 3.5 15 degrees 17 degrees 3 Suction slot location

2.5

2

Eddy visocity [Pa s] 1.5

1

0.5

0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 x [m]

(a) Normal suction

ï7 x 10 4.5 0 degrees 4 5 degrees 10 degrees 12 degrees 3.5 15 degrees 17 degrees 3 Suction slot location

2.5

2

Eddy visocity [Pa s] 1.5

1

0.5

0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 x [m]

(b) 45o inclined suction

Figure A.3 – Eddy viscosity for normal and 45 o inclined suction for different angles of attack 72 A. Appendix

5 x 10 5 Refined Mesh Convergence Threshold = eï6 Convergence Threshold = eï4 4

3

2

1 Velocity gradient du/dy

0

ï1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 x [m]

du o Figure A.4 – Velocity gradient dy for leading edge suction at 15 angle of attack using dif- ferent convergence criteria and different mesh element size

Figure A.5 – Fast Forrier analysis of the lift coefficient response at 15 o angle of attack for the clean airfoil 73

5.5 No suction 5 LE suction

4.5

4

3.5

3

Lift coefficient 2.5

2

1.5

1

0.5 0 0.5 1 1.5 2 2.5 3 Time [s]

Figure A.6 – Lift coefficient response at 60o angle of attack

Figure A.7 – Suction arrangement for pump driven suction on a glider plane