apostolis%20mek-fm-ep-2010-07

Author:Apostolos Tentolouris Piperas

Investigation of Boundary Layer Suction on aWind Turbine Airfoil using CFD

Supervisor:Martin O.L. Hansen

Wind EnergyBuilding 403

Kongens Lyngby

Master’s Thesis5th August 2010

Acknowledgements

There is not much to acknowledge really. People without whom I would never have survivedmy studies and who helped me realize that there is plenty of beauty to be shared despitethe smothering workload of these past two years, a period that eventually lead to the presentdocument, do not need this page to be aware of it and most likely will never read it in the firstplace. 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 myquestions, and Dalibor Cavar with Juan Pablo Murcia without whom my work would havetaken twice the time and e!ort. Finally, I would like to thank whoever was responsible for myadmittance 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 theMaster of Science in Engineering (M.Sc.Eng.)at the Technical University of Denmark. It represents 30 ECTS points and was carried out atthe 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 layercontrol 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 separationare studied for various arrangements of suction. The coe"cients of lift and drag are computedfor di!erent angles of attack and the lift and drag curves after applying suction are comparedwith the corresponding values of the clean airfoil. Finally, a simplistic analysis is carried outin order to evaluate the impact and the usability of boundary layer suction on a wind turbineblade.

v

Table of Contents

List of Figures xi

List of Symbols 1

1 Introduction 11.1 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Previous Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.3 Scope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

2 Boundary Layer Theory 32.1 Boundary Layer Basics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32.2 Laminar and Turbulent flows . . . . . . . . . . . . . . . . . . . . . . . . . . 52.3 Boundary Layer Thickness - Drag . . . . . . . . . . . . . . . . . . . . . . . 72.4 Transition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102.5 External Pressure Gradient . . . . . . . . . . . . . . . . . . . . . . . . . . . 142.6 Boundary Layer Separation . . . . . . . . . . . . . . . . . . . . . . . . . . . 152.7 Separation Bubbles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172.8 Boundary Layer Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182.9 Boundary Layer Suction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

3 CFD Implementation 253.1 Setting up the model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

3.1.1 Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253.1.2 Mesh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253.1.3 Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273.1.4 Solver . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

4 Results 374.1 Suction Location . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 384.2 Discrete Suction versus Distributed Suction . . . . . . . . . . . . . . . . . . 394.3 Suction Quantity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 454.4 Finer Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 474.5 Wind Turbine Performance Enhancement . . . . . . . . . . . . . . . . . . . 51

vii

viii TABLE OF CONTENTS

4.5.1 Blade Element Momentum Method . . . . . . . . . . . . . . . . . . 524.5.2 BEM algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 524.5.3 BEM results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

4.6 The Blade as a Centrifugal Pump . . . . . . . . . . . . . . . . . . . . . . . . 59

5 Conclusions and Perspectives 635.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 635.2 Suggestions for Further Work . . . . . . . . . . . . . . . . . . . . . . . . . . 63

A Appendix 69

List of Figures

2.1 Boundary layer development. . . . . . . . . . . . . . . . . . . . . . . . . . . 42.2 Thickness and shear variation . . . . . . . . . . . . . . . . . . . . . . . . . . 52.3 Laminar and turbulent non-dimensionalised velocity profile. . . . . . . . . . 62.4 Turbulent boundary layer profile. . . . . . . . . . . . . . . . . . . . . . . . . 62.5 Turbulent boundary layer structure. . . . . . . . . . . . . . . . . . . . . . . . 72.6 Diplacement thickness. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82.7 Boundary layer thicknesses. . . . . . . . . . . . . . . . . . . . . . . . . . . 92.8 Shear stress coe"cient. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92.9 Shear stress distribution. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102.10 Transition from laminar flow to turbulent. . . . . . . . . . . . . . . . . . . . 112.11 Tollmien Schlichting waves. . . . . . . . . . . . . . . . . . . . . . . . . . . 112.12 Ribbon frequency e!ect on boundary layer response. . . . . . . . . . . . . . 122.13 Neutral Stability Curve. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132.14 Pressure distribution on an airfoil. . . . . . . . . . . . . . . . . . . . . . . . 132.15 E!ect of pressure gradient on boundary layer. . . . . . . . . . . . . . . . . . 142.16 Velocity profiles and gradients. . . . . . . . . . . . . . . . . . . . . . . . . . 152.17 Boundarly layer profiles and point of inflection. . . . . . . . . . . . . . . . . 162.18 Flow separation on an airfoil. . . . . . . . . . . . . . . . . . . . . . . . . . . 162.19 E!ect of adverse pressure gradient on the boundary layer. . . . . . . . . . . . 172.20 Separation bubbles. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182.21 Vortex generators. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202.22 Boundary layer aceleration. . . . . . . . . . . . . . . . . . . . . . . . . . . . 202.23 Boundary layer control via suction. . . . . . . . . . . . . . . . . . . . . . . . 212.24 Comparison between continuous and discrete suction. . . . . . . . . . . . . . 222.25 Critical value of suction coe"cient. . . . . . . . . . . . . . . . . . . . . . . 222.26 Skin friction variation under optimum suction . . . . . . . . . . . . . . . . . 23

3.1 Relative error. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263.2 Generated Mesh. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293.3 Image of the domain for the LE suction case prior the import into the Solver. . 303.4 No suction for 0 degrees angle of attack. . . . . . . . . . . . . . . . . . . . . 313.5 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. . . . . 333.7 Leading edge distributed suction (Cq = 0.03) for 15 degrees angle of attack. . 343.8 Leading edge distribution - Tight convergence, higher number of iterrations . 343.9 Transient simulation for (Cq = 0.03) at 15 degrees angle of attack . . . . . . 35

4.1 Eddy viscosity for 10o angle of attack . . . . . . . . . . . . . . . . . . . . . 374.2 Point of transition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 384.3 Non dimensionalized eddy viscosity and shear stress . . . . . . . . . . . . . 394.4 Application of suction at maximum thickness point and at leading edge . . . 404.5 Point of transition to turbulent flow at di!erent angles of attack . . . . . . . . 414.6 Location of distributed suction . . . . . . . . . . . . . . . . . . . . . . . . . 414.7 Velocity gradient for clean airfoil and distributes suction . . . . . . . . . . . 424.8 Flow separation at 17o angle of attack for a clean airfoil. . . . . . . . . . . . 424.9 Pressure coe"cients for di!erent angles of attack . . . . . . . . . . . . . . . 434.10 Pressure coe"cient at 17o angle of attack for di!erent suction cases. . . . . . 434.11 Flow separation for di!erent distributed suction cases . . . . . . . . . . . . . 444.12 Lift and drag curves for discrete suction . . . . . . . . . . . . . . . . . . . . 454.13 Lift and drag curves for distributed suction . . . . . . . . . . . . . . . . . . . 454.14 CLand CD values for di!erent suction coe"cients at 15o angle of attack . . . 464.15 CL

CD ratio for di!erent suction coe"cients at 15o angle of attack . . . . . . . . 46

4.16 Pressure coe"cient for di!erent suction coe"cients at 15o angle of attack . . 474.17 Eddy viscosity for di!erent suction coe"cients at 15o angle of attack . . . . . 474.18 Velocity gradient dudy for di!erent suction coe"cients at 15

o angle of attack . . 504.19 Streamlines for di!erent suction coe"cients at 15o angle of attack . . . . . . 504.20 Lift coe"cient response for di!erent angles of attack . . . . . . . . . . . . . 504.21 Lift and drag curves for the clean airfoil and Cq = 0.08 case . . . . . . . . . . 514.22 Suction e!ect on aerodynamic coe"cients . . . . . . . . . . . . . . . . . . . 514.23 Velocities at rotor plane. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 524.24 Tjaereborg wind turbine characteristics . . . . . . . . . . . . . . . . . . . . . 554.25 Angle of attack variation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 564.26 Chord distribution of the Tjaereborg blade . . . . . . . . . . . . . . . . . . . 564.27 Lift and drag curves of root segment . . . . . . . . . . . . . . . . . . . . . . 574.28 Power contribution of each of the three first segments . . . . . . . . . . . . . 584.29 Power curve of the Tjaereborg wind turbine after suction . . . . . . . . . . . 584.30 Power ratio between the clean blade and suction cases . . . . . . . . . . . . . 594.31 Weibull distribution with A = 8 and k = 2 . . . . . . . . . . . . . . . . . . . 594.32 Power contribution of each of the two close to hub segments for reduced chord 604.33 Tjaereborg power curve after suction and 25%chord reduction . . . . . . . . 604.34 Tjaereborg power coe"cient curve after suction and 25%chord reduction . . 614.35 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 . . . . . . . . . . . . . . . . . . . . . . . . . . . 69A.2 Eddy viscosity for di!erent turbulence models. . . . . . . . . . . . . . . . . 70A.3 Eddy viscosity for normal and 45o inclined suction for di!erent angles of attack 71A.4 Sensitivity check for steady state simulations . . . . . . . . . . . . . . . . . 72A.5 FFT of lift coe"cient response. . . . . . . . . . . . . . . . . . . . . . . . . . 72A.6 Lift coe"cient response at 60o angle of attack. . . . . . . . . . . . . . . . . . 73A.7 Suction arrangement for pump driven suction on a glider plane . . . . . . . . 73

List of Symbols

a . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . axial induction coe"cient []a! . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . tangential induction coe"cient []A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . rotor area [m 2]AEO. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . annual energy output [GWh]CD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . drag coe"cient []C f x . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . local shear stress coe"cient []C f L . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . averaged shear stress coe"cient []CL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . lift coe"cient []Cn . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . normalized normal to the rotorplane force []Cp . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . pressure coe"cient []CP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . power coe"cient []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 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . suction flux [ kgm3 ]Re . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Reynolds number []Rex . . . . . . . . . . . . . . . . . . . . . . . . . . .Reynolds number based on x representative length []u, v,w. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . velocity components [ ms ]uw . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . suction velocity [ ms ]U0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . undisturbed velocity [ ms ]Uf . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . friction velocity [ ms ]v . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . transversal velocity component [ms ]y+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . non dimensional wall distance []x, y, z. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . cartesian coordinates []! . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . angle of attack [radian]" . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . boundary layer thickness [m]"" . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . displacement thickness [m]" " ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . kinetic energy thickness [m]

xiii

xiv LIST OF FIGURES

# . . . . . . . . . . . . . . . . . . . . momentum thickness [m] when referred in chapter 2# . . . . . . . . . . . . . . . . . . . . . . . . . . twist angle[radian] when referred in chapter 4µ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . dynamic viscosity [Pa s]$ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . kinematic viscosity [ m2s ]% . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . density [ kgm3 ]& . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . solidity []' . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . shear stress [Pa]'0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . shear stress at the wall [Pa]( . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . flow angle [radian]) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .angular velocity [radian/s]

Chapter 1

Introduction

1.1 General

Wind turbines are capable of transforming the kinetic energy of the wind to mechanical energyin a shaft and finally into electric energy in a generator. The rotation of the shaft is achievedby 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 forlower wind speeds or using thinner blades, whereas minimizing the drag component results insmaller bending moments at the root of the blade, thus allowing the reduction of the materialneeded to withstand the created stresses.

Using suction as a mean of boundary layer control, it is possible to delay stall to higherangles of attack, thus enhancing the airfoil’s lifting capabilities. In addition, suction of theboundary layer can extend its laminar region along the airfoil, i.e. move the transition toturbulent 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 e!ect of boundarylayer suction by applying it via a slit on one side of a cylinder. On the suction side the flowadhered to the surface wall over a significantly longer part of the cylinder arc compared tothe no suction side, and separation was supressed. This lead to the reduction of drag and thecreation 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 determinethe seperation process, can be e!ectively countered with boundary layer suction. From thenon and throughout the twentieth century, extensive research has been carried out within theaviational industry on the application of boundary layer suction on airplane wings in order tominimize fuel consumption, as documented by Braslow [1].

In recent years, considerable e!ort 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 frictiondrag reduction and boundary layer control in general, resulting to the conclusion that suctioncould indeed delay transition and separation and consequently control the flow . A significantnumber of studies (including Eppler [2], Oyewola [3] and Gad el Hak [4]) have focused on thee!ect of distributed low suction rates as well as concentrated wall suction through short porouswall strips on turbulent boundary layers. Results show that if the suction rate is su"cientlyhigh, relaminarisation of the flow occurs almost immediately downstream the suction location.Some researchers, including Abbot and Doenho! [5], have related the momentum thicknessReynolds number at the suction location with the suction rate coe"cient and postulate thatrelaminarisation 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 mainideas that have been investigated in the past are discrete suction through slots and distributedsuction. The former allows an abrupt pressure increase at the location of the slot whereas thelatter is achieved via a porous surface through which the air is sucked. The exact locationwhere the suction is taking place along the airfoil as well as the amount of fluid that is beingsucked 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 rootairfoil 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 theairfoil’s surface velocity boundary conditions, and new lift and drag curves will be derived.If suction can improve Clmax and Cl

Cd , it could lead to the production of more slender blades,which are cheaper to build and present lower extreme loads due to a reduced chord. Using theBEM 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 maintainingthe clean blade power output will be computed. In addition, the possiblity of using the rota-ting turbine blade as a centrifugal pump by cutting o! its tip, in order to create the necessarysub-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 degreeof correlation between theory and experiment and thus unifies theoretical hydrodynamics withhydraulics, 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 experimentaldata. It was evident in most cases that the discordance between classical hydrodynamics andexperiments 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 lowcompared to the gravitational and pressure forces. It was therefore di"cult to comprehend thatby 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 concerningcases of practical importance. His paper proved that the flow around a body fully immersedin a fluid can be divided into two regions, one thin layer in the very close vicinity of the bodycalled boundary layer, in which frictional forces play an important role, and the remainingouter 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 theexperimental results with simplified mathematics. The numerous applications of boundarylayer theory include the calculation of skin friction drag, the interpretation of the phenomenaoccurring 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 reversedand subsequently detach from the surface of the solid wall. This phenomenon, known asboundary layer separation, is linked with the creation of eddies in the wake and is connectedwith a great drag increase in addition to the sudden drop of lift, on streamlined bodies suchas an airfoil. Various methods of boundary layer control have been proposed to confront thisproblem, such as motion of the solid wall, acceleration of the boundary layer (blowing) andsuction. 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 thereforeno shear stresses are present between two consecutive layers. The only interaction with oneanother is via normal forces. This means that an ideal fluid does not present any internalresistance to a change of shape, which leads to the inability of the frictionless, incompressibleapproach of the flow to account for the drag of a body. The absence of tangential forces impliesthat in the close region of the solid wall, there is a di!erence between the tangential velocityof 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, thusproducing shear stresses. The property of the fluid that accounts for these friction forces isviscosity, it is heavily dependent on the fluid’s temperature and, according to Newton’s law offriction, it is the proportionality factor between the shear stress between layers of a uniformflow and the velocity gradient in the direction normal to the layers :

' = µ*u*y. (2.1)

µ in known as dynamic viscosity, however when frictional and inertial forces interact itis important to take into account the viscosity to density ratio $ = µ% known as kinematicviscosity.

The no slip condition implies that fluid particles are being retarded by the frictional forces,and is responsible for the velocity gradient *u*y . This thin layer around the body within whichthe flow velocity increases from the zero value until the free stream velocity is the boundarylayer. The thickness of this boundary layer " increases along the downstream direction of theflow 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 factthat as the flow proceeds downstream, larger quantities of fluid become a!ected by the fric-tional forces, and the adjacent to the wall particles are continuously being subject to retardingforce 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 layerbecomes thicker, the velocity gradient at the wall becomes smaller and therefore, as seen infigure 2.2 taken from [7], the shear stress decreases. There is also a correlation between theboundary layer thickness and the viscosity, presented in section2.3. However, even at highReynolds numbers, i.e. for relative low viscosity values, the shearing stresses in the boundarylayer still have a considerable e!ect on the flow, due to the high velocity gradient in the ydirection, equation 2.1, at the immediate wall neighborhood, which diminishes in the outerregions 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 deceleratedparticles 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 largedrag 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 -e!ect of transition.

2.2 Laminar and Turbulent flows

Boundary layer flows can exist in two di!erent regimes, laminar and turbulent. In laminarflow the fluid layers slide over one another without any fluid mass interchange taking placebetween neighboring layers. Therefore, the developed shear produced by the velocity gradientis entirely due to viscosity, and there is no momentum interchange between the layers. On theother 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 momentumtransfer between neighboring layers. Due to these fluctuations the velocity profile is varyingwith time, however it is possible for a time averaged profile to be defined. The interchangeof the streamwise component of the momentum between adjacent layers results in shearingstresses between them, the magnitude of which, at regions of the boundary layer away fromthe wall, is greater than those developed as a result of the fluid’s viscosity as seen in figure2.9. Therefore, the shape of the velocity profile of a turbulent boundary layer is dominated bythese stresses, termed Reynolds stresses.Assuming zero pressure gradient, figure 2.3 taken from [8] depicts two typical boundarylayers, one for each of the aforementioned regimes. For the laminar case it is evident that aconsiderable portion of the boundary layer has significantly reduced velocity, since viscosityis the only medium with which energy from the free stream is transferred towards the innerretarded particles. In the turbulent boundary layer the Reynolds stresses are responsible for thepenetration of energy from the free stream to the layers close to the wall surface, which resultsin 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 downand viscosity dominates the flow. In this region, called viscous sublayer, the shearing stressesbecome purely viscous and the velocity decreases rapidly until zero in a linear manner. Since'wall = µ(*u*y )wall, it is evident that the friction stress of the turbulent boundary layer is greaterthan 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


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 thedownstream direction. In other words, the nondimensional velocity distribution ( uU0 over

y" )

does not vary from section to section along the plate.

The velocity distribution in the turbulent boundary layer, presented in figure 2.4 takenfrom [7], can be segregated into three main zones, each of which described by a di!erent setof equations. The zone adjacent to the surface is the viscous sublayer, wherein the flow isessentially 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 lawand is therefore called logarithmic layer. Between the aforementioned zones lies the bu!erzone, 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 di!erent velocitiesdistributions inside it. The dimensionless wall distance y+ quantity refers to the law of the walland is equal to y+ = yU f

$ where Uf =!'0% is the friction velocity. The corresponding y

+ toeach region is presented in table 2.1. In the outer region, the velocity distribution is satisfiedby 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 Bu!er zone Logarithmic layer

y+ 0 - 5 50 - 70 70 - 500 #1000

(a) Velocity distribution in a turbu-lent boundary layer

(b) Flow regions within a turbulent 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 definedas the distance from the wall where the velocity is equal to 99% of the value of the undisturbedflow. The inertia force per unit volume in the x axis can be expressed asm!V = %! = %

dudt where

u is the horizontal component of the free stream velocity. For steady flow the aforementionedrelation becomes %dudt = %

*u*x

dxdt = %u

*u*x . For a flat plate of length l the gradient

*u*x is propor-

tional to Ul and therefore the inertia force per unit volume is in the order of %

U2l . In a similar

manner, the friction force per unit volume is *'*y =**y (µ

*u*y ) = µ

*2u*2y . The velocity gradient in the

normal to the plate direction is proportional to U" , therefore the friction force per unit volumeis in the order of µU

"2. Equalizing the friction and the inertia forces and solving for the boundary

layer thickness the following relation is acquired:

" #"$lU, (2.2)

where $ is the kinematic viscosity. It is evident that the boundary layer thickness over aflat plate is dependent on the fluid characteristics, the flow conditions of the free stream andthe running distance from the plates leading edge. Blasius has shown that the numerical factormissing from the above relation is approximately equal to 5, figure 2.10, therefore for laminarflow in the boundary layer we have " = 5

!$lU and after non dimensionalising we get

"l =

5$Rel.

Evidently, " increases with the square root of the downstream running distance x. In addition,


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 layerthickness diminishes. For the turbulent case , the corresponding relation is "l =

0.16

Re17l

. Due to

the vagueness of the boundary layer thickness concept, more precise definitions can be given,each one o!ering di!erent information regarding its characteristics.

Displacement thickness ( "" =# %0 (%U0 & %u) dx )

Due to the presence of the boundary layer over a surface, the mass flow within a stream tubethat prior to its encounter with the boundary layer had a value of %U0 is now decreased to asmaller value %u. Therefore, for continuity reasons, the crossection of the streamtube mustincrease, which for the 2D case means that the widths of the streamtubes within the boundarylayer will increase thus displacing the streamtubes of the free flow away from the surface. Thee!ect on the free flow will be equivalent with the displacing of the surface into the stream withno boundary layer present. Under such conditions, this into the stream displacement is calledboundary layer displacement thickness "", and is presented in figure 2.6 taken from [10].

Figure 2.6 – Diplacement thickness.

Momentum thickness (# =# %0 (

uU0 )(1 &

uU0 ) dx)

This term is connected with the momentum flow rate within the boundary layer, which owingto the presence of the boundary layer is less than the momentum flow rate if no boundary layerexisted, 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 totalflow momentum at that particular position when no boundary layer is present to be equal withthe actual flow momentum is called momentum thickness #. This quantity is often used for thecalculation of the skin friction losses.

Kinetic energy thickness (""" =# %0 (

uU0 )(1 & (

uU0 )

2) dx)The kinetic energy thickness is connected with the kinetic energy defect within the boundarylayer 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. Followingthe same proportionality train of thought, the shear stress on the surface for tha laminar caseis proportional to µU

!%Uµl and after non dimensionalizing with %U

2 it is evident that it isdependent on the Reynolds number alone:

2.3. Boundary Layer Thickness - Drag 9

Figure 2.7 – Boundary layer thicknesses.

'0%U2

#"µ

%Ul=

1$Rel. (2.3)

The local shear stress coe"cient, cf x = '012%U2

, is heavily dependent on the wall roughnessand di!ers from laminar to turbulent flows. Figure 2.8 from [7] depicts the variation of theaveraged shear stress coe"cient Cf L with the Reynolds number, indicating the significance ofthe flow regime on the shear.

Figure 2.8 – Shear stress coe"cient.

As far as the drag force is concerned, by multiplying the shear with the plate surface, therelation D # b

$%µU3l is derived, where b is the surface width, which shows that the laminar

frictional drag is proportional to U32 and l 12 . The non linear dependence of the drag with the

body length can be explained by the fact that as the flow proceeds downstream, its thicknessincreases thus producing lower shear at the regions close to the trailing edge compared to theleading edge.


Adjacent to the surface, i.e. at the base of the boundary layer, the shear stress in the fluid isentirely dependent on viscosity and is equal to µ(*u*y )wall as seen in figure 2.9 from [9], whereasin 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 viscousstresses are less capable of damping disturbances in the flow. Therefore a point is reachedwhere these disturbances are amplified and lead to a turbulent state. Irregular patterns appearafter a critical Reynolds number is reached and radial fluctuations occur, causing the mixing ofthe fluid laminae and thus making the flow turbulent. The exchange of momentum across thethickness of the boundary layer produces a more even cross-sectional area, as seen in figure2.3.

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 placefor high values of the external velocity. A severe increase in the boundary layer thickness aswell as in the shear stress is taking place at the point of transition, as depicted in figure 2.10from [6]. Evidently, the based on the running distance variable x critical Reynolds number isapproximately 3.2x105 which corresponds to a critical Reynolds number based on the displa-cement thickness Re" = 2800. The point of transition along the plate can be derived throughRexcrit. However, it should be noted that the numerical value of the critical Reynolds numberdepends on the amount of disturbance in the external flow, and for extremely low disturbancesin the flow higher critical Reynolds values can be reached. According to the one-step methodof Michel found in [10] transition occurs when Re# = 2.9Rex0.4 where Re# = U(x)#(x)

$ andRex = U(x)x

$ .As mentioned earlier, transition occurs because of the amplification of small disturbances

in the boundary layer. These disturbances may originate from surface roughness, turbulence inthe free stream or vibrations of the surface itself. Experiments have shown that the boundarylayer can be simulated as a nonlinear oscillator that under certain conditions has an initiallylinear response to external stimuli [8]. Figure 2.11 from [8] presents the transition of aboundary layer over a flat plate with disturbances generated by a harmonic line source. Theconversion of these disturbances into low amplitude waves is very complex due to the fact thatthat 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 willpropagate downstream and will be either damped and eventually decayed or amplified andeventually lead to turbulent flow. While their amplitude remains small, these growing wavesare mainly two-dimensional and are known as Tollmien Schlichting waves in honor of theresearchers who studied them. As depicted in figure 2.11 the linear phase extends to a greatportion of the transitional region. The linearity is based on the fact that due the very smallvalue of the wave amplitudes their products may be neglected, however as the disturbanceamplitude increases so does the complexity of the boundary layer response. In addition to thedissipative e!ect of viscosity in removing energy from a disturbance, Prandtl realized that italso plays a significant role in the development of wave disturbances by causing energy to betransferred to the disturbance. This energy transfer process is termed energy production by the


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 thereforeplaced within the boundary layer in order to generate waves, as opposed to studying the wavesgenerated by natural causes such as the ones mentioned earlier. It was found that the boundarylayer response was dependent on the wave frequency as seen in figure 2.12 from [8]. Highribbon frequencies resulted in the dampening of the generated waves, whereas waves producedby intermediate ribbon frequencies attenuated downstream of the ribbon, then began to growand eventually they decayed. Low frequencies however produced waves of growing amplitudewhich eventually lead to transition to turbulence.

Figure 2.12 – Ribbon frequency e!ect on boundary layer response.

A neutral stability curve is therefore possible to be mapped out, which can separate thefrequencies that produce wave amplification from the ones that will get damped out. Figure2.12 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 curvethe energy produced by the Reynolds stresses exceeds viscous dissipation whereas the oppositeoccurs outside the curve. Evidently, there is a critical frequency and a critical Reynolds numberthat act as a barring threshold to the Tollmien Schlichting wave propagation, however it hasbeen observed that the transitional Reynolds number is greater than the critical one. This is dueto the fact that it takes some time, and therefore distance, for the amplified disturbance, denotedby the critical Re, to evolve into turbulence, signified by the transitional Re. An approach toincrease the transitional Reynolds number, and thus mitigate turbulence phenomena, is throughwave cancellation via appropriately located disturbance generators. A control system woulddetect the dominant element of the disturbance spectrum (phase, orientation, frequency) andthe 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 e!ect of an external pressuregradient on the boundary layer, which in turn is presented in section 2.5. 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 theboundary layer thickness Re" = U0"

$ which also grows along the surface, an adverse pressuregradient results in a smaller critical Reynolds number as well as a very wide range of unstabledisturbance frequencies. The opposite holds for a favorable pressure gradient, i.e. low criticalfrequency and high critical Reynolds number. For streamline bodies such as airfoils, for 105 <ReL < 107 the transition to turbulence will occur shortly downstream of the point of minimumpressure, and for a constant ReL an increase of the angle of attack would mean the upstreamdisplacement of the point of minimum pressure and subsequently the moving forward of thetransition point. By designing an airfoil with its minimum pressure point further aft, as seenin figure 2.14 from [8] it is possible to postpone transition, however this would give rise toa more severe adverse pressure gradient after that point which could cause separation of theflow. In order to prevent separation and maintain laminar flow as long as possible the use ofsuction methods can be implemented.

Figure 2.14 – Pressure distribution on an airfoil.


This boundary layer transition is of great aerodynamical interest when it comes to bluntbodies. The turbulent mixing makes the flow more resistant to separation and thus the accele-ration e!ect of the flow on the suction side of the airfoil lasts longer. The further downstreammovement 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 theless 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 streamlinedbodies is greatly a!ected 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 decreasingpressure 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 downstreammaking 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 layeron it suction side in order to achieve high values of lift, but in the same time and in order toreduce skin friction (which is higher for turbulent flows), the point of transition needs to bedisplaced as far downstream as possible.

2.5 External Pressure Gradient

The e!ect of a pressure change in the streamwise direction has a great e!ect on the behaviorof the boundary layer. A decreasing pressure along the surface is called a favorable pressuregradient due to the fact that the streamwise pressure forces tend to help the flow to counterthe shearing e!ects, thus resulting in a less retarded flow close to the wall and subsequently afuller profile. When the pressure is increasing along the wall, the pressure gradient becomesadverse 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 growsmore rapidly as depicted in figure 2.15, taken from [8].

Figure 2.15 – E!ect of pressure gradient on boundary layer.

The velocity profile under these conditions is much less full and may develop a point ofinflexion, i.e. a point where the velocity gradient *u*y changes sign, in other words a point where*2u*2y = 0. Owing to the boundary layer equations, at the wall surface we have : µ(

*2u*2y )y=0 =

dpdx

therefore in the immediate neighborhood of the wall, the velocity profile curvature is solely

2.6. Boundary Layer Separation 15

dependent on the pressure gradient. For a favorable pressure gradient dpdx < 0, (*2u*2y )wall < 0

and therefore the curvature will maintain its negative sign throughout the entire boundary layer.For an adverse pressure gradient however the curvature at the wall is positive, (*2u

*2y )wall > 0,but since at a large distance from the wall *2u

*2y < 0, it follows that a point must exist where*2u*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 su"ciently strong or prolonged adverse pressure gradient the flow near the wall isso greatly decelerated that it begins to reverse direction, indicating that the flow has separatedfrom the surface, as seen in figure 2.17 from [10].

The point of separation can be defined as the limit between the upstream and downstreamflow within the adjacent to the wall layer:

(*u*y)y=0 = 0. (2.4)

In the region of retarded potential flow an inflexion point will always be present in thevelocity profile, and since the profile exhibits a zero tangent at the point of separation, itfollows 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 adversepressure gradient, which may be impressed on the boundary layer by the external pressureconditions. The significance of separation in airfoils is great since it is strongly connected withits lifting capabilities. Figure 2.18 from [6] depicts an airfoil at di!erent angles of attack. Anincrease in the incidence produces a steeper pressure gradient and after a certain value causesthe separation of the flow. Furthermore, the prevention of boundary layer separation reducesthe total drag to such an extent that a symmetrical airfoil that achieves laminar boundary layerfor most of its wetted length can produce the same drag as a circular cylinder with a diameternearly 150 times smaller than the airfoil’s chordline [6].

Figure 2.19 from [8] depicts a boundary layer flow over a surface with gradual, convexcurvature, such as the surface of an airfoil past the maximum thickness point. Owing to theBernoulli principle, the velocity in the vicinity of the surface is decreasing and the pressure isrising. It should be noted however that there is no pressure variation in the direction normalto the surface, which means that the pressure at the edge of the boundary layer is imprinted tothe layer adjacent to the surface. Since *p*x > 0, the net pressure at the depicted fluid elementABCD is tending to decelerate it and in combination with the viscous shears acting on the


Figure 2.17 – Boundarly layer profiles under di!erent pressure gradients. E!ect on point ofinflection.

Figure 2.18 – Flow separation on an airfoil.

sides AB and CD the element is further retarded as it moves downstream. This slowing downe!ect has a more profound e!ect at the layers close to the solid wall resulting in a change inthe shape of the velocity profiles.

After the separation point S where (*u*y )wall = 0, the boundary layer thickness increasesrapidly in order to satisfy continuity. After the separation point, the direction of the flow in

2.7. Separation Bubbles 17

Figure 2.19 – E!ect of adverse pressure gradient on the boundary layer.

the close vicinity of the wall is in the upstream direction thus creating a circulatory movementin the near surface region. Due to the greater extent of lower energy fluid at the wall regionin laminar boundary layers,presented in 2.3, separation due to adverse pressure gradient willoccur sooner in comparison with turbulent boundary layers.

Boundary layer separation in the rear half of an airfoil results in a significant increase ofthe wake flow thickness, which subsequently results in a decrease of the pressure rise thatshould occur in the trailing edge. This means that the forward acting pressure componentsof the rear part of the airfoil do not develop and therefore the rearward acting pressure forcesof the frontal stagnation point are not countered. As a result the pressure drag of the airfoilincreases greatly. For large angles of attack, separation takes place at a point located a smalldistance downstream of the point of minimum pressure, thus creating a large wake which inturn diminishes the low pressure conditions at the area downstream the leading edge which isresponsible for the creation of lift. Favorable pressure gradients has the exact opposite e!ect,since energy is added to the slow moving flow near the solid wall thus making the flow moreresistant to separation.

2.7 Separation Bubbles

Laminar separation might occur in airfoils with large upper surface curvature when relativelyhigh angles of attack are reached. Small disturbances in separated flows grow easily in smallReynolds numbers, therefore the transition to turbulent flow that may subsequently take placeleads to a rapid thickening of the detached boundary layer which might be su"cient for thelower edge to reach the solid wall once again, thus leading to the reattachment of the separatedflow, which is now within the turbulent regime.

As seen in figure 2.20, taken from [8], a bubble of fluid is trapped between the separationpoint 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 pressureis constant, and downstream of that pocket, an area where circulatory motion is taking placeand 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


Figure 2.20 – Separation bubbles.

extending over 1% of the chordline (100 displacement thicknesses at the separation point) anda long bubble extending over a greater portion of the chordline, around 10000 displacementthicknesses at the separation point. The former has a negligible e!ect on the peak suctionwhereas the latter’s e!ect is significant. The criterion as to which bubble is formed is the valueof the displacement thickness based Reynolds number at the separation point. If Re"" < 400 along bubble is most likely to occur while for Reynolds values over 550 a short bubble is moreprobable. The length of long bubbles increases rapidly with increasing angle of attack andmight extend up until the trailing edge of the airfoil, thus causing a continuous reduction ofthe leading edge suction peak or even stall. On the other hand, the response of short bubblesat 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 bybreakdown of the short bubble near the leading edge due to the failure of the separated flow toreattach 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 greaterthan U0 # x&0.09 the boundary layer will separate from the surface. For the case of turbulentboundary layers this value is much greater and separation is avoided up until U0 # x&0.23, thusmaking 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 turbulentflow separation cannot always be prevented, therefore numerous methods of boundary layercontrol have been developed in order to tackle the problem, such as:

Motion of the solid wallThis method can in a way prevent the development of the boundary layer by eliminating thedi!erence between the fluid’s velocity and the velocity of the solid wall. By taking advantageof the no slip condition, the wall moves along with the stream and the velocity gradient issuppressed. Experimental investigations of a moving boundary on an airfoil, by forming apart of the upper surface into an endless belt, have yielded very high maximum lift coe"cients(Clmax = 3.5) at very high angles of attack (! = 55o) [6].

2.8. Boundary Layer Control 19

ShapingAs mentioned earlier, transition from laminar to turbulent flow can be delayed with the use ofsuitably 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 thepoint 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 changecan be achieved without separation is very narrow. Depending on the Reynolds number, theairfoil shape, the surface roughness and the incidence angle, the boundary layer beyond theminimum pressure point either becomes turbulent shortly after or it temporarily dettaches for-ming the separation bubbles mentioned earlier.

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

TurbulatorsAs mentioned in section 2.2, a turbulent boundary layer is more resistant to separation andtherefore transition may be desirable in lifting devices in order to avoid stall. Transition usuallyoccurs for values of the local distance from the leading edge Reynols number close to 106. Itcan be advanced by exposing the boundary layer to large disturbances, in connection withsection 2.4, by placing single, multiple or distributed roughness elements on the wall. Theheight of these elements can be quantified by the corresponding Reynolds number Re+ = u(+)+

$ ,where + denotes the roughness length. Re+ is used to assess the e!ect of surface roughnesson transition, signified by the based on the displacement thickness Reynolds number Re"" .For a smooth surface, transition occurs at Re"" ' 2600 whereas for Re+ = 600 transitiontakes place at Re"" ' 1000 , and increasing Re+ to 1000 Re"" decreases even more at 300[4]. It is important for the turbulator however to suppress laminar separation without makingthe boundary layer unnecessarily thick, since thick turbulent boundary layers are more proneto separation than thin ones. This limits the range of Reynolds numbers wherein roughnesselements can aid airfoils to achieve higher performance to Rec < 105, where Rec = U0c

$ . Ingeneral, 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 ofthe near wall flow, by creating a tip vortex which draws air from the outer flow regions into theboundary layer. They are typically rectangular or triangular, with a height comparable to theboundary layer thickness, and are positioned near the leading edge, upstream of where laminarseparation is expected. As a result, fluid particles with high streamwise momentum are sweptalong helical paths towards the surface where they mix with the near wall flow and replace theretarded particles. If however the separation location can be accurately predicted, the vortexgeneretors can be placed accordingly and their size can be greatly reduced, thus reducing thedrag.


Figure 2.21 – Vortex generators.

Boundary layer accelerationBy 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. Thiscan 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 viablowing.

(b) High lift devices.

Figure 2.22 – Boundary layer aceleration.

Di!erent 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]. Throughthe delay of stall they allow higher lift coe"cients and higher angles of attack.

TranspirationAnother method to avoid separation is by changing the curvature of the velocity profile viathe withdrawal of the near wall fluid through slots or porous surfaces. The e!ect of suctionconsists of the removal of the retarded fluid particles located at the region close to the surfacethus preventing the reversal of the flow. The resulting boundary layer, depicted in figure 2.23from [8], that is created is much thinner and more capable of overcoming the adverse pressuregradient, 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 coe"cients. In addition, suction can result in the shif-ting of the transition point further downstream thus reducing frictional drag, since an extendedlaminar region implies smaller shear on the surface. A more detailed presentation of boundarylayer 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 lowenergy air through suction slots or a porous surface. Suction suspends boundary layer growthand leads to a fuller velocity profile. It can therefore be used to delay transition, postponeseparation or relaminarize an already turbulent flow. By changing the curvature of the velocityprofile at the wall the stability characteristics of the flow can be enhanced, thus preventing thecritical Reynolds number Re"crit, referring to the neutral stability curves seen in figure2.13, tobe reached.

The quantity of fluid sucked away can be expressed by the ratio of the suction velocityat the wall over the free stream velocity Cq = |uw |

U0 . The transition delay and the separationprevention should be achieved with the minimum suction flow rate possible in order to reducethe power needed for the suction. According to [4] separation on a symmetrical airfoil can beprevented for Cq = 1.12Re&0.5L when distributed suction is implemented, whereas for discretesuction the maximum e!ectiveness, according to [5], can be reached when the sucked airis equal to the air quantity that would pass through the diplacement thickness "" at the slotlocation with the local external velocity. For typical airfoils Cq values between 0.002 and0.004 are su"cient for separation prevention [4]. The position along the airfoil where suctionis 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 ofthe minimum pressure point, the extending of the airfoil’s lift curve to higher angles of attackcan become possible. Figure 2.24 from [6] presents the increase of maximum lift #CLmax overthe suction coe"cient. Evidently, for the same lift increase, continuous suction needs muchless air quantity removed compared to the discrete case.

A minimum suction coe"cient can be derived by assuming a uniformal suction along thewhole extent of a surface and applying as a boundary condition the wall-normal velocity to beequal to the suction velocity. The equations that describe such a flow, according to [6], result


Figure 2.24 – Comparison between continuous and discrete suction.

in a velocity profile in the form of u(y) = U0[1 & euwy$ ] and a displacement thickness equal to

"" = $&uw . This solution is realized at some point downstream the leading edge, despite the fact

that suction is applied earlier on, and it does so in an asymptotic manner. It is therefore termedasymptotic suction profile.

After investigating the stability of this profile, the critical Reynolds number Re"" = U0""$

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 thecondition of stability forms at &uwU0 = Cq >

170000 , however experiments have shown that the

quantity of air that needs to be removed in order for laminar flow to be maintained is higher.Introducing the parameter , = C2q

U0x$ , 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 anypoint along the length if Cq > 1

8500 which results in Cqcrit = 1.2.10&4.

Figure 2.25 – Critical value of suction coe"cient.

The variation of the skin friction coe"cient for the aforementioned case, in connectionwith figure 2.8, under the condition of optimal suction which denotes the smallest Cq that

2.9. Boundary Layer Suction 23

su"ces for transition prevention, is depicted in figure 2.26, found in2 [6]. The save in dragcorresponds to the distance between the turbulent and the optimum suction curve at any givenReynolds number.

Figure 2.26 – Skin friction variation under optimum suction

The stabilizing e!ect of suction on the boundary layer can also be detected in the inducedlarge 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 resultsare subsequently processed within MATLAB environment. For the purposes of the presentcase study, the NACA 4415 airfoil is used, and the suction e!ect on lift and drag will beextrapolated for the Tjaereborg blade root airfoil. The notation NACA 4415 suggests that theairfoil 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 ofthe point coordinates that define the airfoil profile. For this purpose 47 points were used forthe suction side of the airfoil and 49 for the pressure side, which were subsequently connectedvia a spline curve. The airfoil has a chord length equal to 1m and its leading edge is located10m 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 CFXto simulate 2D cases, the flow domain along with the airfoil itself are created as an extrusionof unit length. The produced parallelepiped will then be meshed with a single element depthso that the third dimension is diminished, and the top and bottom faces of the extrusion willbe set as symmetry planes later in the process. It should be noted that that the extrusion lengthshould not exceed the maximum lenghtscale of the mesh, but in the same time it should havea value that will not cause visibility problems later in the building process of the model. Theproposed dimensions result in a relatively low blockage ratio factor, as the boundaries are nottoo 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 orderfor the definition of di!erent 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 airfoilsurface since it is there where the boundary layer will be formed. The accuracy of the modelincreases 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 cannotcapture. Depending on the scope of the study, these issues should be handled with the propersetup of the simulation.

After the regions of the model have been defined, the background mesh length scale ofthe model is specified by using the Body Spacing option. This length scale corresponds to thecoarsest length scale required anywhere in the domain, before any Face Spacing or Controlsare applied to any regions of the model. The Maximum Spacing within the Body Spacingmenu specifies the maximum element size which will be used when creating triangles on thedomain’s surface and tetrahedra in the domain’s volume. The default value for this parameteris 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 explicitlyassigned a specific length scale. In the present case study the Volume Spacing option is usedfor Default Face Spacing, which implements the same spacing on the face as the MaximumSpacing specified in Body Spacing. For the airfoil however an explicit Face Spacing is appliedand 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 meshat the curved surfaces of the airoil to be automatically refined. The value of the relative errorspecifies the level of the curvature resolution as the ratio #xx , re!ering 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 theuse of Mesh Controls. The mesh refining e!ect 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 TriangleControl for the broader neighborhood around the airfoil extending from a few meters upstreamof the leading edge until several chord lengths downstream, while in the same time the meshrefinement is broadening downstream. The spacing attributes for the aforementioned controlsdi!er from one another, and are specified via the Point Spacing option, which in turn requiresthree definition values : the Length Scale, which determines the mesh size in the locality ofthe point, the Radius of Influence which defines the radial extent of meshed spaced filled withelements 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 needelements with high aspect ratios, in order to be resolved in a computationally e"cient manner.

3.1. Setting up the model 27

For this reason, CFX-Mesh implements prisms to create a mesh that is finely resolved normalto the wall but coarse parallel to it, by inflating the 2D local face elements into 3D prismelements. In the present case study, this Inflation is applied on the airfoil surface in order totake into account the e!ect of the boundary layer on its aerodynamic behavior.

The parameters that control the Inflation should be carefully chosen in order to capturethe flow phenomena within the boundary layer, such as transition or separation. The Numberof 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 thepresent simulation is indeed the case, then Number of Inflated Layers specifies the maximumnumber of inflation layers. The Expansion Factor determines the relative thickness of adjacentinflation layers, i.e. each successive layer in the normal to the wal direction is thicker than aprevious 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 thetetrahedral mesh elements is smoother [12]. First Layer Thickness however does not controlthe 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 definedin the present report by a target y+ value, given the Reynolds Number and a Reference Length.ANSYS CFX calculates the first layer thickness (#y) using the formula #y = L#y+

$80Re&1314 .

After the first layer is created, thicker layers, the height of which is defined by the ExpansionFactor, 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 thecase 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 e!ects of deleted elements propagate, which which is of no iportancethe present simulation since no adjacent inflation boundaries are overlapping, the MinimumInternal Angle, which controls the minimum allowed angle in the triangular face of a prismnearest to a surface before it is marked unacceptable and up for deletion, and the MinimumExternal Angle, which controls the respective element property for a prism farthest from asurface. The aforementioned parameters have not been changed from their default values.

Proceeding to Surface Meshing, the Delauny Surface Mesher has been selected due to itsspeed and its ability to mesh closed faces. The Meshing Strategy selected is Extruded 2DMesh in order to generate a 2D mesh of one element thickness. The 2D Extrusion Option isset to Full so the mesh is generated using the full extent of the geometry and the Number ofLayers is set to 1. The proper planes are then selected for the Extruded Periodic Pair and thePeriodic Type Option is set to Translational. Finally the Surface Meshes and the Volume Meshare 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 e!ect the mesh quality has on the results of the simulation, a refinedmesh is created, by halving the element sizes of the previous mesh, and some cases are runtwice using two di!erent meshes.

3.1.3 Setup

The first thing to do in the Setup is to specify the Analysis Type of the simulation. Steadystate analysis should be used to model flows that do not change over time, whereas transientanalysis should be used to model time dependent flows. Flows around streamlined bodies mayexhibit dynamic phenomena due to the vortex shedding that will occur after certain angles ofattack, it is therefore preferable to use transient analysis for the simulation, with a carefully


Table 3.1 – Mesh properties

Spacing Default Body Spacing Maximum Spacing [m] 1.0

Default Face Spacing Option Volume SpacingOption Relative Error

Relative Error 0.0123116Minimum Edge Length [m] 0.001

Airfoil Spacing Maximum Edge Length [m] 1.5Radius of Influence [m] 1.0Expansion Factor 1.2

Controls Length Scale [m] 0.01Airfoil Vicinity Radius of Influence [m] 1

Expansion Factor 1.2Length Scale [m] 0.1

Broader Vicinity Radius of Influence [m] 1Expansion Factor 1.2

Point Control Point 0.5[m], 0[m], 0[m]Spacing Airfoil VicinityPoint -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 60Expansion Factor 1.1

Number of Spreading Iterations 0Minimum Internal Angle [Degrees] 2.5Maximum Internal Angle [Degrees] 10.0

Option First Layer ThicknessDefine First Layer By y+

y+ 1.0Reynolds Number 1.5e6

Inflation Options Reference Length [m] 1.0First Prism Height [m] 1.646695e-5Extended Layer Growth YesLayer by Layer Smoothing No

Options Surface Meshing Option DelaunayMeshing Strategy Option Extruded 2D Mesh2D Extrusion Option Option Full

Number of Layers 1


(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 Strouhalfrequency. The total time of the simulation should be long enough so that parameters likethe lift or drag on the body reach a relatively constant value. Transient analyses howeveroccupy extreme amounts of disk space until these fluctuations over time diminish, thereforewhen used in the present project, the results will not be stored at each timestep but only atthe beginning and the end of the simulation. The forces acting on the airfoil however will bemonitored throughout the run in order to be utilized later on. Steady state analyses will be usedthroughout the present case study, with a supplementary transient simulation for some casesfor 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 usingtransient 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 eachboundary of the simulation are presented in table3.2. It should be noted that the flow is alwayssubsonic and from Left to Right, with a value of 23.52ms in order to achieve a Reynolds numberof 1.5e106 which typical for wind turbines, and the implementation of the di!erent anglesof attack is achieved by the modification of the inlet velocity from the Left and Down inletwith the corresponding trigonometric functions. For the 0 angle of attack case, the boundaryconditions at the Upper and Down faces have been set to Free Slip Wall. Pressure boundaryconditions are applied at the domain outlets and the Average Static Pressure option is usedin order to allow the pressure to vary locally on the boundary. Suction is implemented bysetting the corresponding location along the airfoil as an outlet and setting velocity boundaryconditions in order to control the suction quantity. The image of the domain in the 3D Viewerwindow 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 turbulencecontrol of the Shear Stress Transport model (SST), due to its ability to capture the influence ofdi!erent factors that a!ect 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


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 triedout and presented in chapter 4 in order to justify the superiority of the Gamma Theta modelin regards to the purpose of the present case study. For convergence control, the value of theroot mean square normalized residual over the whole domain is chosen to be below 10&4, andthe maximum amount of iterations has been set to 750. A sensitivity check will be carried outlater on by reducing the RMS residual to 10&6 in order to check its e!ect on the results. Table3.3 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 furtherprocess. The monitoring of the residuals allows the estimation of the level of correspondanceof 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 forceapplied on the body in the Y direction as shown in figure 3.3, for the 0 angle o! attack casewith no suction. It is evident that despite the fact that the relatively loose convergence targetof 10&4 is not reached, the Lift force stabilizes at approximately 150 N, which deems thesimulation relatively accurate.

For the 15o angle of attack case however, the Y force is fluctuating with an amplitude ofapproximately 60N as seen in figure 3.5, suggesting that boundary layer separation has madethe steady state simulation impossible to converge and indicating in a clear manner the needfor transient simulations.


Table 3.2 – Boundary Conditions

Location Boundary Type

Body No Slip Wall Smooth WallInlet Flow Regime Subsonic

Mass and Momentum Cart. Vel. Components U = Vrelcos(!) [m/s]Down V = Vrelsin(!) [m/s]

W = 0[m/s]Turbulence Low (Intensity=1%)

Inlet Flow Regime SubsonicMass and Momentum Cart. Vel. Components U = Vrelcos(!) [m/s]

In V = Vrelsin(!) [m/s]W = 0[m/s]

Turbulence Low (Intensity=1%)Outlet Flow Regime Subsonic

Out Mass and Momentum Average Static PressureRelative Pressure 0 [Pa]

Outlet Flow Regime SubsonicUp 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 0.01seconds has been used and a total simulation time of 3 seconds which, given the fact thatthe flow has a velocity of 23.52ms , allows the fluid to travel apporoximatelly 70 chordlinesthroughout the simulation, thus providing enough time for the development of the flow. Smalloscillations in the Y component of the aerodynamic force can be observed, in the order of20N, which can be linked to the vortex shedding.


Table 3.3 – Steady State Setup properties

Analysis Type Option Steady State

Default DomainBasic Settings Material Air at 25 C

Morphology Continuous FluidReference Pressure [atm] 1

Domain Motion StationaryFluid Models Heat Transfer

Option IsothermalFluid Temperature [C] 25

TurbulenceOption Shear Stress Transport

Transitional Turbulence Gamma Theta ModelInitialization Velocity Type Cartesian

Cartesian Velocity Components [m/s] U = Vrelcos(!)V = Vrelsin(!)

W = 0Solver Control Advection Scheme High Resolution

Turbulence Numerics High ResolutionConvergence Control

Min. Iterations 1Max. Iterations 750

Convergence CriteriaResidual Type RMSResidual Target 1.e-4



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


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 4415airfoil, 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.

As a verification of the validity of the results, the residual target is reduced to 10&6 and themaximum 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 periodicmanner around the value of 10&5 and 450N respectively, indicating convergence problems,and therefore a transient simulation supplements the results, using again a time step of 0.01seconds 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 accuratelypredict 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



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


Figure 3.8 – Leading edge distributed suction (Cq = 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 behaviorwhen di!erent kinds of suction are applied, the optimal suction arrangement will be run onceagain using transient analysis in order to derive more accurate results.



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

Chapter 4

Results

Before moving on to the investigation of the e!ect of suction on the boundary layer, somefurther validation of the Setup options chosen is carried out. The choice of the Shear StressTransport Gamma Theta transitional turbulence model over the SST Fully Turbulent and theKappa Omega model is justified in figures 4.1 and 4.2. As mentioned in section 2.9, suctionis 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 shorterturbulent regime thus decreasing skin friction. It is therefore necessary for the CFD simulationto 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 bedefined as the proportionality factor that relates the Reynolds stresses and the mean velocitygradient. When transition to turbulence takes place, the Reynolds stresses values will rise duethe existence of fluctuating horizontal and transversal velocities and therefore a jump in thevalues of eddy viscosity will be observed. The point along the airfoil where this eddy viscosityjump 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 4415airfoil at 10o angle of attack for a Reynolds number of 1.5e6. It is evident that when using theSST Fully Turbulent as well as the Kappa Omega model, the flow is turbulent right from theleading edge, whereas the SST Gamma Theta model is able to simulate the laminar flow thattakes place for a short extent downstream the leading edge before the transition to turbulencetakes place. The low eddy viscosity values of the graph can be explained by the fact that theyare measured on the layer adjacent to the surface of the airfoil.

0 0.2 0.4 0.6 0.8 10

0.5

1

1.5

2

2.5x 10 7

x [m]

Eddy

Visc

osity

[Pa

s]

Gamma ThetaKappa OmegaFully Turbulent

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 isolatedairfoils with the use a simple linear-vorticity stream function panel method combined with anintegral boundary layer analysis, [13]. Figure 4.2 depicts the variation of the transition pointalong 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 angleof attack. It is clear that from the three aforementioned models, only the SST Gamma Thetamodel is able to capture adequately the transitional behavior of the boundary layer, and followthe same trend as the XFOIL results, and will therefore be used henceforth.

0 5 10 15 20 250

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Angle of attack [deg]

Dist

ance

bet

ween

poi

nt o

f tra

nsitio

n an

d LE

[m]

XfoilSST Gamma ThetaKappa OmegaSST Fully turbulent

Figure 4.2 – Point of transition

Figure A.2 in the Appendix presents the variation of the eddy viscosity along the airfoilsurface, for the three turbulence models for di!erent angles of attack. It is evident in the SSTGamma Theta case that the eddy viscosity jump occurs closer to the leading edge as the angleof attack increases. In connection with figure2.2, the shear stress along with the eddy viscosityover the airfoil surface (non dimensionalized by their maximum values) are plotted in figure4.3. Both quantities depend on the velocity gradient dudy and consequently are suitable for thedetection of transition, however only the eddy viscosity will be used in the present case studyfor that purpose.

4.1 Suction Location

As mentioned in section 2.4 the adverse pressure gradient, which essentially is the cause offlow separation and therefore stall, starts downstream the minimum pressure point on the upperairfoil surface. It is therefore a reasonable assumption to apply suction at that point in orderto enhance the airfoil’s e"ciency. 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, anda normal to the wall velocity is applied as a boundary condition to the suction outlet, suchthat the suction coe"cient is equal to Cq = 0.03. CFX results however reveal that suctionwill delay transition only for those angles of attack where the clean airfoil transition point isdownstream the suction location, whereas for higher angles of attack where the transition pointhas moved upstream the suction location, suction has no e!ect. Changing the directionality ofthe suction from normal to 45o inclined also has no e!ect on transition, as can be seen in figureA.3 in the Appendix. Results however di!er significantly when suction is applied upstream

4.2. Discrete Suction versus Distributed Suction 39

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.5

15 degrees AoA

x [m]

Wall shearEddy viscosity

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.5

112 degrees AoA

x [m]


0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.5

117 degrees AoA

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 coe"cient,CFX shows that slot suction applied close to the leading edge can greatly improve tha airfoil’saerodynamic behavior. Transition is delayed almost until the trailing edge for small anglesof attack and for higher angles the transition point is notably moved downstream. Figure4.4 presents the eddy viscosity distribution along the airfoils surface for these cases, clearlyindicating the beneficiary e!ect of leading edge suction.

Figure 4.5 shows the variation of the distance of the transition point from the leading edgeover the angle of attack. Evidently, the application of discrete suction at the leading edgeupstream from the point of transition results in significant transition delay. The importance ofthe suction location can be also seen by the behavior of the suction at the 0 degrees minimumpressure point curve, where it is clear that transition is delayed only for the angles of attackwhere transition occurs downstream the suction location. For higher angles of attack, the curvealmost 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 muchhigher than the corresponding value obtained by applying discrete suction for the same suctioncoe"cient Cq. Two di!erent cases of distributed suction will be applied in ANSYS, leadingedge suction and trailing edge suction. Leading edge distributed suction will be appplied ina region that extends mostly on the upper side but a small portion of it will be located inthe lower side of the airfoil. More specifically it extends over 5.7% of the airfoil’s upper sidelength and 2.6% of the pressure side. The choice of such an arrangement is based on the resultsfound in [6], depicted in figure A.1. Trailing edge distributed suction will extend downstream

40 4. Results

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

1

2

3

4

5

6x 10 7

x [m]

Eddy

visc

osity

[Pa

s]

0 degrees5 degrees10 degrees12 degrees15 degrees17 degrees

(a) No suction

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.5

1

1.5

2

2.5

3

3.5

4

4.5x 10 7

x [m]

Eddy

visc

osity

[Pa

s]

0 degrees5 degrees10 degrees12 degrees15 degrees17 degreesSuction slot location

(b) Discrete suction at maximum thickness

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

1

2

3

4

5

6

7

8x 10 7

x [m]

Eddy

visc

osity

[Pa

s]


(c) Discrete suction at leading edge

Figure 4.4 – Application of suction (Cq = 0.03) at maximum thickness point and at leadingedge


0 5 10 15 20 250

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1


Dist

ance

bet

ween

poi

nt o

f tra

nsitio

n an

d LE

[m]

Xfoil resultsNo suctionSuction with Cq = 0.03 at min. pressure pointSuction with Cq = 0.03 at Leading Edge

Figure 4.5 – Point of transition to turbulent flow at di!erent 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 coe"cient is kept constant at CQ = 0.03 and the simulations are run againwith di!erent boundary conditions in order to maintain the same mass flow with the discretecase. Flow separation will be evaluated using the velocity gradient along the aifoil’s uppersurface and will be detected by regions where dudy is negative for a significant extent. Figure4.7depicts the velocity gradient distribution at 0, 10 and 17 degrees angle of attack for the cleanairfoil and the leading edge distributed suction cases.

For the clean airfoil at 0o angles of attack, no separation is present apart from a smallbubble at approximately the middle of the airfoil. At 10o, the bubble has moved upstream, inaccordance with section 2.7. At 17o however, the flow appears to be reversed over a regionthat 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 thiscase can be visualized in figure 4.8. The application of distributed suction at the leading edgeclearly enhances the airfoil in that regard, as no separation bubble occurs for the first two anglesof attack, and for the third one flow dettachment is significantly delayed from the middle ofthe airfoil to approximately 70% of the chord, as can be seen in figure4.11b. The zero valuesof the gradient close to the leading edge are explained by the fact that the velocity boundary

42 4. Results

0 0.2 0.4 0.6 0.8 14

2

0

2

4

6

8

10

12

14x 104 Clean airfoil

du/d

Y gr

adie

nt

x [m]

0 degrees10 degrees17 degrees

0 0.2 0.4 0.6 0.8 10.5

0

0.5

1

1.5

2

2.5

3

3.5x 105 Leading edge slot suction

du/d

Y gr

adie

nt

x [m]


Figure 4.7 – Velocity gradient at di!erent angles of attack for clean airfoil and leading edgedistributed suction.

conditions at that region have been set in a way that the air is sucked with a perpendicular tothe surface direction, and therefore the gradient is approximately zero.

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

The bene"ciary e!ect of suction can be also depicted with pressure coe"cient curves. Fi-gure 4.9 reveals that the application of suction can increase the lifting force due to the pressuredi!erence 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 attackas were derived from CFX. Once again it is evident that discrete suction has no e!ect whenapplied downstream the transition point, whereas the pressure di!erence between the upperand lower sides increases when slot suction is applied close to the leading edge. Distributedsuction at the trailing edge produces better results than the discrete cases, while leading edgesuction enhances the airfoil performance even more.

The narrower wake produced by leading edge suction can be visualised in figure4.11.Apparently, a suction coe"cient at the trailing edge of Cq = 0.03 is not enough for the flow


0 0.2 0.4 0.6 0.8 12

1

0

1

2

3

4

5

6

7

x [m]

Pres

sure

Coe

fficie

nt

C p


(a) Clean airfoil

0 0.2 0.4 0.6 0.8 12

1

0

1

2

3

4

5

6

7

x [m]

Pres

sure

Coe

fficie

nt

C p


(b) Discrete leading edge suction

0 0.2 0.4 0.6 0.8 12

1

0

1

2

3

4

5

6

7

x [m]

Pres

sure

Coe

fficie

nt

C p


(c) Distributed leading edge suction

Figure 4.9 – Pressure coe"cients for di!erent angles of attack

0 0.2 0.4 0.6 0.8 12

1

0

1

2

3

4

5

6

7

x [m]

Pres

sure

coe

fficie

nt

Cp

No suctionSlot suction at minimum pressure pointSlot suction at leading edgeDistributed suction at trailing edgeDistributed suction at leading edge

Figure 4.10 – Pressure coe"cient at 17o angle of attack for di!erent suction cases.

to reattach on the airfoil surface, however if the suction is applied before transition the flow ismore resistant to the adverse pressure gradient and remains attached for a larger portion of theairfoil.

44 4. Results

(a) Trailing edge distributed suc-tion

(b) Leading edge distributed suc-tion

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

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

CL =FYcos(!) & FXsin(!)

12%V2

. (4.1)

CD =FY sin(!) + FXcos(!)

12%V2

. (4.2)

Figures 4.12 and 4.13 present the lift and drag coe"cients of the discrete an distributedsuction cases respectively. Apparently, inclined discrete suction at 45o induces higher liftvalues without increasing the drag compared to the normal suction case, whereas the normalleading edge slot suction although it extends the airfoil’s lifting capabilities to higher anglesof attack, it induces higher drag values possibly related to the skin friction drag caused by thehigher velocity gradients.

Distributed suction on the other hand expands the range of the lift producing angles ofattack even more for both the trailing and leading edge suction. Due to the narrower wakecreated 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 theclean airfoil values. The high drag values of the trailing edge case, especially for the lowangles of attack, can be explained by the fact that the distributed suction in that case extendsfor almost 40% of the chord (figure 4.6b) thus creating high skin friction due to the high valuesof dudy .

4.3. Suction Quantity 45

0 5 10 15 20 250.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2Lift Curve


Lift

coef

ficie

nt

No SuctionNormal suction with Cq = 0.03Inclined suction with Cq = 0.03Leading edge suction with Cq = 0.03Xfoil results

0 5 10 15 20 250

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2Drag Curve


Drag

coe

fficie

nt

No SuctionNormal suction with Cq = 0.03Inclined suction with Cq = 0.03Leading edge suction with Cq = 0.03Xfoil results

Figure 4.12 – Lift and drag curves for discrete suction

0 5 10 15 20 250.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8Lift Curve


Lift

coef

ficie

nt

No SuctionTrailing edge distributed suction with Cq = 0.03Leading edge distributed suction with Cq = 0.03Xfoil results

0 5 10 15 20 250

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2Drag Curve


Drag

coe

fficie

nt

No SuctionTrailing edge distributed suction with Cq = 0.03Leading edge distributed suction with Cq = 0.03Xfoil results

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 increasesits performance to a higher extent than the other suction arrangements that were tried out, asimple analysis is carried out with the suction coe"cient Cq as a parameter in order to derivethe optimum suction quantity. Figure 4.14 presents the lift and drag coe"cient for a varyingsuction coe"cient Cq.

It appears that beyond Cq = 0.08 the drag of the airfoil increases. Figure 4.15 depicts theCLCD ratio, indicating that a suction coe"cient of 0.08 would produce the highest performancesince the lift to drag ratio beyond that point remains approximately constant, despite the factthat the suction quantity is increased. However, if the use of the airfoil is such that the increaseddrag can be withstood, for instance if the root of the wind turbine blade can hold the createdbending moments, then higher suction coe"cients can be used, assuming of course that thesuction 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

0 0.05 0.1 0.15 0.21

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

1.9

2

Suction coefficient Cq = Vsuc/V0

Lift

coef

ficie

nt

0 0.05 0.1 0.15 0.20.06

0.065

0.07

0.075

0.08

0.085

0.09

0.095

0.1

0.105

0.11


Drag

coe

fficie

nt

Figure 4.14 – CLand CD values for di!erent suction coe"cients at 15o angle of attack

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.1610

12

14

16

18

20

22

24

26

28


C L/CD ra

tio

Figure 4.15 – CLCD ratio for di!erent suction coe"cients at 15

o angle of attack

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 ofattack. 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 notacquire negative values for a significant extent, whereas for Cq = 0.08 separation is observedapproximately at 85% of the chord. The high values of dudy however, exept from preventingseparation are also responsible for the high drag values observed in figure4.14.

A better visualization of the suction e!ect 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 tothe airfoil for an increasing extent. The flow velocity values are also higher for higher suc-tion coe"cients, suggesting that the increase in the lift is caused by the enhancement of theacceleration of the flow on the upper side of the airfoil.

4.4. Finer Analysis 47

0 0.2 0.4 0.6 0.8 12

1

0

1

2

3

4

5

6

7

x [m]

Pres

sure

Coe

fficie

nt

C p

Cq = 0.02Cq = 0.04Cq = 0.08Cq = 0.15

Figure 4.16 – Pressure coe"cient for di!erent suction coe"cients at 15 o angle of attack

0 0.2 0.4 0.6 0.8 10

0.5

1

1.5x 10 6

x [m]

Eddy

visc

ocity

[Pa

s]

Cq = 0.02Cq = 0.04Cq = 0.08Cq = 0.15

Figure 4.17 – Eddy viscosity for di!erent suction coe"cients 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 tothe previous cases presented in table 3.1, while table 4.2 presents the setup properties of thetransient simulations. It should be noted that the implementation of the normal to the wallvelocity 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 aresimulated once again. With a timestep of 0.01 seconds, 3 seconds of flow around the NACA4415 airfoil were simulated in CFX. Apparently, as presented in figure4.20, some algorithmicfluctuations occur at the beginning of the simulation. For this reason, the values of the lift anddrag forces that will be used further will consist of the mean value of the last second of theforce time series, i.e. timesteps 201 to 300 .

Evidently, the clean airfoil has gone into stall at 20o since heavy fluctuations caused by thevortex 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 SpacingOption Constant

Constant Edge Length [m] 0.0123116Airfoil Spacing Radius of Influence [m] 1.0

Expansion Factor 1.2Controls Length Scale [m] 0.005

Airfoil Vicinity Radius of Influence [m] 1Expansion Factor 1.2Length Scale [m] 0.05

Broader Vicinity Radius of Influence [m] 1Expansion Factor 1.2

Point Control Point 0.5[m], 0[m], 0[m]Spacing Airfoil VicinityPoint -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 60Expansion Factor 1.1

Number of Spreading Iterations 0Minimum Internal Angle [Degrees] 2.5Maximum Internal Angle [Degrees] 10.0

Option First Layer ThicknessDefine First Layer By y+

y+ 0.5Reynolds Number 1.5e6

Inflation Options Reference Length [m] 1.0First Prism Height [m] 8.23347e-6Extended Layer Growth YesLayer by Layer Smoothing No

Options Surface Meshing Option DelaunayMeshing Strategy Option Extruded 2D Mesh2D 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 TimeTotal Time 3 [s]

Time Steps Option TimestepsTimesteps 0.01[s]

Initial Time Option Automatic with ValueTimesteps 0 [s]Material Air at 25 C

Basic Settings Morphology Continuous FluidReference Pressure 1 [atm]Domain Motion StationaryHeat Transfer

Option IsothermalFluid Models Fluid Temperature 25 C

TurbulenceOption Shear Stress Transport

Transitional Turbulence Gamma Theta ModelVelocity Type Cartesian

Initialization Cartesian Velocity Components [m/s] U = Vrelcos(!)U = Vrelsin(!)

W = 0Advection Scheme High ResolutionTransient Scheme Second Order Backward Euler

Timestep Initialization AutomaticTurbulence Numerics High ResolutionConvergence Control

Solver Control Min. Coe!. Loops 1Max. Coe!. Loops 10Timescale Control Coe"cient Loops

Convergence CriteriaResidual Type RMSResidual Target 1e-4

Table 4.3 – Suction boundary conditions

Outlet Flow Regime Option Subsonic

Suction Mass and Momentum Option Mass Flow RateMass Flow Rate 0.0156 [kg/s]

Mass Flow Update Option Constant Flux

50 4. Results

0 0.2 0.4 0.6 0.8 10.5

0

0.5

1

1.5

2

2.5

3

3.5

4x 105

x [m]

Velo

city

grad

ient

du/

dy

Cq = 0.02Cq = 0.04Cq = 0.08Cq = 0.15

Figure 4.18 – Velocity gradient dudy for di!erent suction coe"cients at 15o angle of attack

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

Figure 4.19 – Streamlines for di!erent suction coe"cients at 15 o angle of attack

0 0.5 1 1.5 2 2.5 30

0.5

1

1.5

2

2.5

3

3.5

Time [s]

Lift

coef

ficie

nt

0 degrees AoA15 degrees AoA20 degrees AoA

(a) Clean airfoil

0 0.5 1 1.5 2 2.5 30

0.5

1

1.5

2

2.5

3

3.5

Time [s]

Lift

coef

ficie

nt

0 degrees AoA15 degrees AoA20 degrees AoA

(b) Distributed suction at leading edge withCq = 0.08

Figure 4.20 – Lift coe"cient response for di!erent angles of attack

the power spectrum of this short 3 seconds signal, revealing a small peak at approximately5 Hz, which is relatively close to the corresponding value of a flow around a cylinder with adiameter equal to the airfoil’s chord ( f = S tV

L , where S t ( 0.23 according to [6]). Taking themean 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.

0 5 10 15 20 250.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2


Lift

coef

ficie

nt

Lift Curve

No SuctionLeading edge distributed suction with Cq = 0.08Xfoil results

0 5 10 15 20 250

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2


Drag

coe

fficie

nt

Drag Curve

No SuctionLeading edge distributed suction with Cq = 0.08Xfoil 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 higherangles of attack whereas figure 4.22a reveals that an increase of the lift coe"cient up to 20%is possible, while CD can decrease up to 30%. It is worth mentioning that maximum lift occursat higher angles than the clean airfoil, implying that in the case of applying suction on a windturbine blade, the pitch angle should be modified accordingly.

0 5 10 15 201

1.05

1.1

1.15

1.2

1.25


C L, s

uctio

n/CL,

cle

an

(a) E!ect on Lift (CL,suctionCL,clean) due to the applica-

tion of leading edge distributed suction

0 5 10 15 20

0.7

0.8

0.9

1

1.1

1.2

1.3

1.4


C D, s

uctio

n/CD,

cle

an

(b) E!ect on Drag (CD,suctionCD,clean) due to the appli-

cation of leading edge distributed suction

Figure 4.22 – Suction e!ect on aerodynamic coe"cients

4.5 Wind Turbine Performance Enhancement

The aerodynamic coe"cients of the NACA 4415 airfoil after suction is applied were derivedin section 4.4 and will be used to estimate the impact of suction on a wind turbine. For thispurpose, 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 coe"cients, which will in turn be used as an input in the BladeElement Momentum method (BEM). After the Lift and Drag forces on the root segments ofthe Tjaereborg blade have been derived, a new power curve corresponding to a turbine whereboundary layer suction is applied in the root airfoils will be computed. Moreover, the possiblereduction of the modified airfoil’s chordline will be quantified, while maintaining the sameLift 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 therotor by implementing in the algorithm various local attributes of the blade, such as the twistand chord distribution and the aerodynamic behavior of the specific airfoils used. The bladeis segregated in segments, each with its own properties and independent of the others. Figure4.23 from [14] presents the components and the angles related to the relative velocity at therotor plane of a wind turbine airfoil. # denotes the twist angle, ! the angle of attack and ( theflow angle.

Figure 4.23 – Velocities at rotor plane.

For a given wind speed, the following procedure is followed in order to calculate theturbine’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 consecutiveinduction factors (axial or tangential, a or a! respectively, not to be confused with theangle of attack !) acquire identical values.

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

&(i) = c(i)B2-r(i)

, (4.3)

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

3. Calculation of the flow angle (.

((i) = atan(1 & a)V0(1 + a!))r(i)

. (4.4)


4. Due to the fact that BEM assumes that the force from the blades on the flow is constantin 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.

F =2-arccos(e&

B(R&r(i))2r(i)sin(((i)) ). (4.5)

5. The angle of attack ! is calculated via the earlier derived flow angle ( and the local pitchangle of the blade #. The latter is a combination of the pitch angle and the twist of theblade

!(i) = ((i) & #(i). (4.6)

6. Using the lift and drag coe"cients, Cn and Ct are calculated which correspond to thenon-dimensionalised normal and tangential to the rotor plane forces.

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

Ct(i) = CL(i)sin(((i)) &CD(i)cos(((i)). (4.8)

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 :

anew =

%&&&'&&&(

14Fsin2((i)&CN

+1a ) 0.2

CT4F(1&0.25(5&3a)a) a > 0.2

(4.9)

where CT = (1&a)2CN&sin2( . The tangential induction factor is then computed :

a!new =&Ct

4Fsin((i)cos((i) & &(i)Ct(i). (4.10)

A relaxation method is implemented so that the newly calculated values of the inductionfactors consist of 90% of the previous value and 10% of the new.

8. The di!erence 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 laststep are substituted in the first one the and the process is repeated until two consecutivevalues 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 planeforce pt :

Vrel =(1 & a)V0sin((i)

. (4.11)

L(i) =12c(i)CL(i)Vrel2. (4.12)

D(i) =12c(i)CD(i)Vrel2. (4.13)

pt(i) = L(i)sin((i) & D(i)cos((i). (4.14)

pn(i) = L(i)cos((i) + D(i)sin((i). (4.15)

10. The torque of each blade is computed via :

M(i) =13A(ri+13 & r3i ) +

12B(ri+12 & r2i ), (4.16)

where

A =pt,i+1 & pt,iri+1 & ri

. (4.17)

B =pt,iri+1 & pt,i+1ri

ri+1 & ri. (4.18)

11. Lastly the power of each segment is computed via:

P(i) = )M(i). (4.19)

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

12. The same procedure is followed for a range of free wind velocities until the turbine’spower curve is derived.


0 5 10 15 20 250

500

1000

1500

2000

2500

Wind speed [m/sec]

Powe

r [kW

]

(a) Power curve

0 5 10 15 20 250

0.1

0.2

0.3

0.4

0.5

0.6

Wind speed [m/s]

C p

(b) Power coe"cient curve

Figure 4.24 – Tjaereborg wind turbine characteristics

4.5.3 BEM results

Figure 4.24 presents the power curve and the power coe"cient curve of the 2MW Tjaereborgfixed speed wind turbine. The turbines angular velocity is ) = 2.3195rads and the twist angledistribution varies from 8o at the root to 0.16o at the blade tip. Apparently rated power isreached at 15m/s and the maximum power coe"cient is reached at 9m/s.

Due to the fact that the beneficiary e!ect of suction takes place for a certain range ofangles of attack, it is important to know at which angles of attack does the turbine bladeoperate. According to figure 4.22, the angle of attack should be above 15o in order for theairfoil’s performance to be enhanced. Figure 4.25a depicts the variation of the angle of attackover the free wind speed for di!erent radial positions, whereas4.25b presents the variation ofthe angle of attack over the span of the blade for di!erent free wind speeds. Evidently, onlythe root segments of the blade operate in the range of angles of attack wherein suction couldhave an improving e!ect. This can be explained by the fact that the tangential componentof the relative velocity of each segment, in connection with figure4.23, is proportional to itsdistance from the hub and since the normal to the rotorplane component of the velocity doesnot vary radially, segments close to the tip will experience small angles of attack. This can bemitigated by the twisting of the blade, however the twist angle distribution over the blade hasnot been designed for such purpose.

The chord distribution of the blade is presented in figure4.26. It should be noted that theairfoils used for the two segments closest to the hub are identical.

The aerodynamic data of the Tjaereborg blade root airfoil are modified following the trendof the CFX results of the NACA 4415 airfoil, in order to simulate the e!ect suction wouldhave on them. Figure 4.27 depicts the new lift and drag curves which were produced based onfigure 4.22. After a certain angle of attack, suction is expected to not have any e!ect on neitherlift or drag. ANSYS simulations reveal that the CL,suctionCL,clean ratio approcahes unity (1.077) at a 60

o

angle, as presented in figure A.6 in the Appendix, therefore beyond that point the suction andthe clean curve will coincide.

The power contribution of each of the three first segments is presented in figure4.28. Inaccordance 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 ispresented in figure 4.29. Apparently rated power is reached for a lower wind speed, however

56 4. Results

5 10 15 20 250

5

10

15

20

25

30

35

40

45

50

Free wind speed [m/s]

Angl

e of

atta

ck [d

eg]

6.46m 9.46m segment9.46m 12.46m segment12.46m 15.46m segment24.46m 27.46m segment

(a) Angle of attack over free wind speed

10 15 20 25 300

5

10

15

20

25

30

35

40

45

50

Radial distance from rotor center [m]

Angl

e of

atta

ck [d

eg]

V0 = 6 m/sV0 = 9 m/sV0 = 12 m/sV0 = 15 m/s

(b) Angle of attack over blade span

Figure 4.25 – Angle of attack variation

0 5 10 15 20 25 300

0.5

1

1.5

2

2.5

3

3.5

Blade span [m]

Chor

d le

ngth

[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 gaindue 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 distributionwith a shape coe"cient equal to 2 and a size coe"cient equal to 8, as presented figure4.31,the AEO can be computed using equations 4.20 and 4.21, according to [15].

AEO = AT)

Vi

w(Vi)CP(Vi), (4.20)

where A is the rotor plane area and T is the time within the frame of interest in seconds, inthe present case a year, and

w =12%V3pd f (V). (4.21)


0 20 40 60 80 1000

0.5

1

1.5


Lift

coef

ficie

nt

LE suctionClean segment

0 20 40 60 80 1000

0.2

0.4

0.6

0.8

1

1.2

1.4


Drag

coe

fficie

nt

LE SuctionClean segment

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

Under these conditions, the Tjaereborg turbine produces 4.1029GWh per year, whereaswhen suction is applied the AEO rises to 4.1197GWh, i.e. there is a gain of 0.0168GWh or a0.4096% increase.

However, this minimal gain of the power output is not the only way to exploit boundarylayer suction. Due to the increased lift forces, a decrease of the chord of the root segmentswhile maintaining their power output contribution is possible. After reducing the chord lengthof the segments located between 6.46m&9.46m and 9.46m&12.46m to the 75% of their initiallength, 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 significantdi!erence between the clean blade and the suction with reduced root chord length cases isevident. 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 e!ect of suction on the turbine’s performance, thepower coe"cient for the cases of the clean blade, the blade with suction, and the reduced rootchord blade with suction, are presented in figure4.34.

The annual energy output of the Tjaereborg wind turbine when suction is applied and theclose to the hub segments of the blades are reduced by 25% is almost equal to the originalTjaereborg turbine, with a 0.2% deviation.

It is important to note that due to the lift force increase produced by the application ofboundary layer suction, the thrust force acting on the rotor would also rise. Figure4.35 depictsthe variation of the thrust force. This increase in thrust will create higher bending momentson the wind turbine tower root which must be accounted for in the final design of the windturbine.

58 4. Results

0 5 10 15 20 250

10

20

30

40

50

60

70

80


Powe

r [kW

]

Clean airfoilLE sution

(a) Segment located between 6.46m and9.46m

0 5 10 15 20 250

20

40

60

80

100

120


Powe

r [kW

]


(b) Segment located between 9.46m and12.46m

0 5 10 15 20 250

20

40

60

80

100

120


Powe

r [kW

]


(c) Segment located between 12.46m and15.46m

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

5 10 15 20 250

500

1000

1500

2000

2500


Powe

r [kW

]

LE suction for 6.46m 12.46m segmentClean airfoil

(a) Power curve

13 13.5 14 14.5 15 15.5

1850

1900

1950

2000

2050

2100

2150


Powe

r [kW

]

LE suction for 6.46m 12.46m segmentClean airfoil

(b) Zoom-in at rated power

Figure 4.29 – Power curve of the Tjaereborg wind turbine after suction is applied over therange 6.46m & 12.46m from the rotor’s center

4.6. The Blade as a Centrifugal Pump 59

5 10 15 20 250.9

0.92

0.94

0.96

0.98

1

1.02

1.04

1.06

1.08

1.1

Powe

r rat

io


Figure 4.30 – Power ratio between the clean blade case and the LE suction over the range6.46m & 12.46m from the rotor’s center

0 5 10 15 20 250

2

4

6

8

10

12


Prob

abilit

y [%

]

Weibull distributionCut in speed

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 apower consuming pump, but to achieve it by cutting o! the blade tip. The centrifugal forcescreated by the turbine’s rotation would then produce an inner blade spanwise flowwhich coulddrive the suction. Assuming that the blade itself acts as a radial impeler blade, the necessarytorque M that needs to be delivered in order to create a flow rate Q according to [10] is equalto:

M = %Q)(r22 & r12), (4.22)

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 bythe wind speed the blade experiences, after the latter is multiplied with the suction coe"cientCq. It is important to note that the velocity each segment of the blade experiences is not the

60 4. Results

0 5 10 15 20 250

10

20

30

40

50

60


Powe

r [kW

]


(a) Segment located between 6.46m and9.46m

0 5 10 15 20 250

10

20

30

40

50

60

70


Powe

r [kW

]


(b) Segment located between 9.46m and12.46m

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

0 5 10 15 20 250

500

1000

1500

2000

2500


Powe

r [kW

]

LE sution reduced chordClean bladeClean blade reduced chord

(a) Power curve

12 13 14 15 16 17

1850

1900

1950

2000

2050

2100


Powe

r [kW

]

LE sution reduced chordClean bladeClean blade reduced chord


Figure 4.33 – Power curve of the Tjaereborg wind turbine after suction is applied over therange 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 velocityalong the blade must vary accordingly.

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

Asegment =csegmentcANSYS

AANSYS (4.23)

After taking into account each blade segment’s dimensions, the total suction quantity foreach blade is found equal to 3.82m3s , 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 10 15 20 250

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5


Powe

r coe

fficie

nt [

]

Clean airfoilLE SuctionLE Suction reduced chord

(a) Power coe"cient curve

11 12 13 14 15 16

0.34

0.36

0.38

0.4

0.42

0.44


Powe

r coe

fficie

nt [

]

Clean airfoilLE SuctionLE Suction reduced chord


Figure 4.34 – Power coe"cient curve of the Tjaereborg wind turbine after suction is appliedover the range 6.46m & 12.46m from the rotor’s center and the correspondingchordlengths have been reduced by 25%

Thrust

4 6 8 10 12 14 1620

40

60

80

100

120

140

160

180

200

220


Thru

st [k

N]

Clean BladeLE SuctionLE Suction reduced chord

(a) Thrust over free wind speed

Thrust

13 13.5 14 14.5 15 15.5

180

185

190

195

200

205

210

215

220

225


Thru

st [k

N]

Clean BladeLE SuctionLE Suction reduced chord


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 coe"cient at a free wind speedof 9ms , and for that wind speed the contributing torque of each blade after suction is appliedand the chord of the close to the hub segments has been reduced by 25% is 89.275kNm.Therefore, cutting o! the tip of the blade in order to implement boundary layer suction isdeemed to be possible, since the torque needed to achieve the desired suction coe"cients is10.8% of the total torque produced by the blade’s rotation. For a free wind speed of 14ms thetorque percentage drops to below 4%. It must be stressed however that the torque needed forthe application of suction is a direct loss in power according to equation (4.19), and thereforethe 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 thesuction coe"cients within a satisfactory range. This can be achieved with a properly designedducting in the interior of the turbine blade or with the use of vanes that would control theinner blade spanwise flow, depending on the turbine’s rotation and the relative velocities theblade encounters. Any additional power needed for the control of the boundary layer couldbe simulated by an additional equivalent drag coe"cient in order to evaluate the feasibility ofsuch an endeavor.

Chapter 5

Conclusions and Perspectives

5.1 Conclusions

Boundary layer control through di!erent suction arrangements has been investigated for aNACA 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 a!ects thetransition 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 theangle of attack increases, it was deemed necessary to apply suction on the nose of the airfoil inorder to enhance the airfoil’s performance at high angles of attack. The extent of the suctionlocation as well as the suction quantity were also investigated and the results have shown thatdistributed suction produces superior results compared to discrete suction for the same suctionquantity, 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 windturbine, a minor increase on the wind turbine’s power output was observed, rated power wasreached 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 lengthof the close to the hub segments of the blade by 25% while maintaining their initial powercontribution. This chord reduction can lead to the production of slender blades which wouldsubsequently present reduced bending moments at the root of the blade.

The possibility of using the rotating turbine blade as a centrifugal pump by cutting o! its tipwas also investigated, and results showed that the suction quantity needed for the enhancementof the blade performance can be achieved by the torque created by the blade’s rotation, but witha 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 e!ect on the dynamic phenomena of boundary layer transitionto turbulence and flow separation. The time step as well as the number of itterations at eachtimestep 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, isa topic that could be further investigated. The e!ect on the airfoil performance of the angleby which the air exits through the suction location could lead to imporved lift and drag resultswithout the need of higher suction quantity. Given the use for which the airfoil is intended anddepending on the dominating angle of attack during its operation, an optimal suction anglecould be derived.

63

64 5. Conclusions and Perspectives

Since a solid conclusion of the present case study is that leading edge distributed normalsuction 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 theairfoil surface it should cover, what portion of it should lie on either side of the airfoil, and thedependence of the above on the angle of attack.

Moreover, further investigation could be done regarding the distribution of the mass flowalong the suction area itself in order to achieve the optimal airfoil performance, as suggestedby [2] for the active control case. Figure 5.1 presents the mass flow contour at the leadingedge suction location. It appears that the outflow is not uniformally distributed, but there arecertain location in the upper and lower side of the airfoil where the flow rate is higher than therest of the suction area. By modifying the sucked air distribution, further enhancement of theairfoil’s performance may become possible.

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

In practice, according to [16], the desired suction distribution can be realized by a suctionsandwich structure on top of the usual structural sandwich structure. The suction sandwichstructure can be divided in bu!ers 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 finallythrough throttling holes of the structural sandwich faces, into the inner space of the wing, aspresented in A.7. According to [16], the suction distribution can be controlled by varying thediameter of the holes in the honeycomb core and by the diameter of the throttling holes bywhich the sucked air is driven into the inner part of the blade.

Cases of interest that could be studied in the future include di!erent arrangements of suc-tion in order to derive high lift to drag ratios and high maximum lift coe"cients with theminimum sucked air quantity possible. Multiple slot suction (as investigated by [3]) againstdistributed suction for the same suction coe"cient can be compared, i.e. applying discrete suc-tion in multiple locations along the airfoil (leading edge, transition point, minimum pressurepoint, trailing edge) and while keeping the total sucked mass flow rate constant, investigatewhether better results than the leading edge distributed suction can be reached.

Furthermore, an analysis of how the airfoil’s roughness could alter the e!ect of suctioncould 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 topicthat could be studied. Additionally, the e!ect of the free stream turbulence intensity and theReynolds 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 boundarylayer suction since it will produce a much more accurate and detailed picture of how suctioncan a!ect the flow. For the wind turbine blade case, the e!ect of the local properties of theblade 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 bederived for the clean blade and the suction cases. Moreover, the distribution of the suctionflow 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 Schlichtingwaves using CFD could be undertaken in order to investigate whether boundary layer suctioncan modify their frequency and consequently the boundary layer flow. The internal ducting ofthe blade (as seen in [17] for the active control case on airplane wings) is of crucial importanceif suction is to be applied in a passive manner as suggested in section4.6, therefore great careneeds to be taken in order to achieve the desired suction coe"cient at the radial stations ofinterest along the blade span.

Bibliography

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

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

[3] R. A. O. Oyewola, L. Djenidi, “Influence of localised double suction on a turbulentboundary 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 Wileyand 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 reductionand lift enhancement.,” tech. rep., TU Delft, Faculty of Aerospace Engineering, TheNetherlands.

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

67

Appendix A

Appendix

Figure A.1 – Di!erent locations for distributed suction

69

70 A. Appendix

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.5

1

1.5

2

2.5

3

3.5x 10 8 SST Fully Turbulent model

x [m]

Eddy

Visc

osity

[Pa

s]


(a) SST Fully Turbulent model

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5x 10 8

x [m]

Eddy

Visc

osity

[Pa

s]


(b) SST Kappa Omega model

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.5

1

1.5

2

2.5

3

3.5

4

4.5x 10 7

x [m]

Eddy

Visc

osity

[Pa

s]


(c) SST Gamma Theta model

Figure A.2 – Eddy viscosity for di!erent turbulence models and di!erent angles of attack

71

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.5

1

1.5

2

2.5

3

3.5

4

4.5x 10 7

x [m]

Eddy

viso

city

[Pa

s]


(a) Normal suction

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.5

1

1.5

2

2.5

3

3.5

4

4.5x 10 7

x [m]

Eddy

viso

city

[Pa

s]


(b) 45o inclined suction

Figure A.3 – Eddy viscosity for normal and 45 o inclined suction for di!erent angles of attack

72 A. Appendix

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 11

0

1

2

3

4

5x 105

x [m]

Velo

city

grad

ient

du/

dy

Refined MeshConvergence Threshold = e 6Convergence Threshold = e 4

Figure A.4 – Velocity gradient dudy for leading edge suction at 15

o angle of attack using dif-ferent convergence criteria and di!erent mesh element size

Figure A.5 – Fast Forrier analysis of the lift coe"cient response at 15 o angle of attack forthe clean airfoil

73

0 0.5 1 1.5 2 2.5 30.5

1

1.5

2

2.5

3

3.5

4

4.5

5

5.5

Time [s]

Lift

coef

ficie

nt

No suctionLE suction

Figure A.6 – Lift coe"cient response at 60o angle of attack

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

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