cfd simulations of an airfoil with leading edge ice accretion

CFD Simulations of an Airfoil

With Leading Edge Ice Accretion

Kasper Mortensen s021998

Supervisors

Jens Nørkær Sørensen, DTUKenneth Thomsen, Siemens Wind Power

August 2008

Section of Fluid MechanicsDepartment of Mechanical EngineeringTechnical University of Denmark, DTU

ii

Abstract

The accretion process of three ice protrusions have been simulated using the nu-merical ice accretion code Lewice. The protrusions are accreted on a NACA63418airfoil and two of them represent rime ice and one accounts for a glaze ice accre-tion. Multiblock structured grids using mainly quadrilateral cells are constructedin Gambit for the clean airfoil as well as the three ice accretion cases. Simulationsof the cases are performed in the commercial CFD code Fluent mainly utilizingthe Spalart Allmaras turbulence model. Furthermore a simulation of a clean air-foil with jets of air being blown from the surface through holes on the leadingedge has been performed. This is intended as a way of avoiding the ice accretion.The results of the various simulations are analysed and compared to experimentalresults by (Abbott & Von Doenhoff 1959) and to results of the panel method codeXFOIL.

iv

Dansk resume

Isopbygningen af tre forskellige isformer pa et NACA63418 vingeprofil er simuleretved brug af den numeriske isopbygningskode Lewice. To af formerne repræsentererrim mens den sidste form er repræsentativ for en slags isslag. Beregningsnet tilhhv. det rene vingeprofil og de tre is-cases er genereret i Gambit som struktureredemultibloknet. Simuleringer af de forskellige cases er foretaget i den kommercielleCFD kode Fluent fortrinsvis med brug af Spalart Allmaras turbulensmodellen.Derudover er der foretaget beregninger pa et rent vingeprofil hvor der blæses luft-strømme gennem huller pa fronten. Formalet med dette er at undga opbygningenaf is pa profilet. De forskellige simuleringsresultater er analyseret og sammen-lignet med eksperimentelle resultater fra (Abbott & Von Doenhoff 1959) samtmed resultater fra panel-koden XFOIL.

vi

Preface

This report is prepared at the Technical University of Denmark, DTU, and servesas the authors Master’s Thesis in Energy Engineering. The work has been carriedout from January 2008 to August 2008 as a cooperation between the author, theFluid Mechanics Section of DTU and Siemens Wind Power.

First of all I would like to thank my supervisor Professor Jens Nørkær Sørensen,Dept. of Mechanical Engineering, DTU, for his guidance and support during theproject and Associate Professor Wen Zhong Shen, Dept. of Mechanical Engineer-ing, DTU, for always having an open door.

I also owe a great thank you to Associate Professor Jianhua Fan, Dept. of CivilEngineering, DTU, for his counseling concerning the Fluent simulations and toProfessor Lorenzo Battisti, Dept. of Mechanical and Structural Engineering, Uni-versity of Trento, for his help and ideas concerning the ice accretions.

Furthermore I am grateful to Kenneth Thomsen, Jesper Laursen and others atSiemens Wind Power for providing me with blade data, discussing the computa-tional grids and taking an active interest throughout the project phase.

Kasper Mortensen.Kgs. Lyngby, August 2008.

Contents

Abstract ii

Dansk resume iv

Preface vi

Nomenclature xi

1 Introduction 1

2 Theory 5

2.1 Airfoil Flow and Boundary Layer Separation . . . . . . . . . . . . 6

2.1.1 Airfoil Geometry Terminology . . . . . . . . . . . . . . . . 6

2.1.2 Forces and Force Coefficients on an Airfoil . . . . . . . . . 7

2.1.3 Boundary Layer Effects and Flow Separation . . . . . . . . 8

2.2 Numerical Methods for Flow Computations . . . . . . . . . . . . 12

2.2.1 Computational Fluid Dynamics . . . . . . . . . . . . . . . 12

2.2.2 Panel Methods . . . . . . . . . . . . . . . . . . . . . . . . 15

2.3 Ice Accretion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

2.3.1 Fundamentals of Icing . . . . . . . . . . . . . . . . . . . . 17

2.3.2 Collision Efficiency . . . . . . . . . . . . . . . . . . . . . . 18

2.3.3 Collection Efficiency . . . . . . . . . . . . . . . . . . . . . 19

2.3.4 Accretion Efficiency . . . . . . . . . . . . . . . . . . . . . . 19

2.3.5 Meteorological Quantities . . . . . . . . . . . . . . . . . . 22

2.3.6 Comparison of Parameter Influence . . . . . . . . . . . . . 26

viii

CONTENTS ix

3 Numerical Setup 29

3.1 Definition of the Simulation Cases . . . . . . . . . . . . . . . . . . 30

3.1.1 Clean Airfoil . . . . . . . . . . . . . . . . . . . . . . . . . . 30

3.1.2 Ice Case A . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

3.1.3 Ice Case B . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

3.1.4 Ice Case C . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

3.1.5 Blowing Surface . . . . . . . . . . . . . . . . . . . . . . . . 34

3.2 Geometry and Grids . . . . . . . . . . . . . . . . . . . . . . . . . 35

3.2.1 Generation of the Grid - Clean Airfoil . . . . . . . . . . . . 35

3.2.2 Generation of the Grid - Ice Case A . . . . . . . . . . . . . 38

3.2.3 Generation of the Grid - Ice Case B . . . . . . . . . . . . . 39

3.2.4 Generation of the Grid - Ice Case C . . . . . . . . . . . . . 40

3.2.5 Generation of the Grid - Blowing Surface . . . . . . . . . . 40

3.2.6 Grid Dependency Check . . . . . . . . . . . . . . . . . . . 40

3.3 Simulation Procedures and Settings . . . . . . . . . . . . . . . . . 42

3.3.1 Residual History and Estimation of Convergence . . . . . . 43

4 Results and Discussion 46

4.1 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . 47

4.1.1 Clean Airfoil . . . . . . . . . . . . . . . . . . . . . . . . . . 47

4.1.2 Ice Case A . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

4.1.3 Ice Case B . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

4.1.4 Ice Case C . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

4.1.5 Blowing Surface . . . . . . . . . . . . . . . . . . . . . . . . 81

5 Conclusion 89

6 Perspectives and Future Work 91

Bibliography 93

Appendix A - Calculations I

CONTENTS x

Appendix B - Matlab scripts III

Appendix C - Lewice VII

CONTENTS xi

Nomenclature

α - Angle of attackη1 - Collision efficiencyη2 - Collection efficiencyη3 - Accretion efficiencyε - Turbulent dissipation rateκ - Constant equal to 0.622λ - Liquid fraction of iceµ - Dynamic viscosityν - Kinematic viscosityρ - Densityρa - Air densityρw - Water densityτ - Stress tensorτw - Wall shear stressω - Specific turbulent dissipation

A - Areac - Chord (length of airfoil)cp−a - Specific heat capacity of aircp−w - Specific heat capacity of waterCD - Drag coefficientCf - Skin-friction coefficientCL - Lift coefficientCM - Moment coefficientCP - Pressure coefficientCs - Roughness constantd - DiameterD - Diameter (if related to smaller diameter, d)D - Drag forcee0 - Vapour pressure of aires - Saturation water vapour pressureg - Acceleration of gravitationh - Convective heat transfer coefficientk - Turbulent kinetic energyKL - Modified Langmuir parameterKs - Roughness heightL - Lift forceL - LengthLf - Latent heat of freezingLvap - Latent heat of vaporization

CONTENTS xii

LWC - Liquid water contentmw - Mass rate of waterM - Pitching momentM - MassMV D - Median volume diametern - Number of panelsp - PressureQaero - Aerodynamic heatQcon - Convective heatQevap - Evaporative heatQkin - Kinetic heatQlat - Latent heatQsens - Sensible heatR - Surface recovery factorRe - Reynolds numberRec - Reynolds number with respect to chordRed - Reynolds number with respect to diameterRH - Relative humidityt - Timet - ThicknessT0 - Temperature of ambient airTd - Droplet temperatureTs - Surface temperatureTstatic - Static temperatureu - Cartesian velocity componentu′ - Turbulent velocity fluctuationv∗ - Wall-friction velocityV - VelocityV0 - Freestream velocityw - Mass concentrationx - X-coordinate or length in Cartesian x-directiony - Y-coordinate or length in Cartesian y-directionY + - Dimensionless wall coordinate

Chapter 1

Introduction

The subject of ice build-up on structures is a well known phenomenon to amongothers the aeronautics field where ice accretion on airplane wings have been ob-served numerous times. Ice accretion can be a problem during certain weatherand flight conditions and the presence of which should be avoided due to thepossible risk of decreased lift and/or increased drag on the wing. Therefore coun-termeasures including thermal or mechanical anti- or deicing systems are takeninto account for operating airplanes.

Within the field of civil engineering icing on structures such as lattice towers,suspension bridges and power cables has proven to be an area of concern in somegeographic regions. As an interesting eye opener for the reader Figures 1.1 - 1.3are presented in this introductory part to give an impression of just how severe acase of extreme ice accretion can be.

Also within the area of wind turbines accretion of ice can cause severe problemswith ice shed, increased loads on the structural parts as well as altered aerody-namic behaviour. This is of course a subject of concern in regions with cold climatewhere the weather conditions make certain structures prone to ice accretion.

Most investigations of the subject have been performed using either ordinary windtunnels with artificial ice templets attached to airfoil models or NASA’s icing windtunnel. Common to the vast majority of these investigations is the choice of airfoilshape, flight and meteorological conditions etc. to represent the case of an aircraftflying through a problematic atmospheric layer in a relatively short time interval.In the last decade or so CFD codes have begun to play a significant role in theinvestigations but the emphasis is to date still in favour of aircraft situations.

A number of papers describe the process of ice accretion. (Langmuir & Blodgett1946) and (McComber & Touzot 1981) calculate the trajectories and impingementof droplets in an airflow while (Poots & Rodgers 1976) deal with both impingementand freezing process on a cable. (Ackley & Templeton 1979) and (Arnold et

1

CHAPTER 1. INTRODUCTION 2

Figure 1.1: Rime on a power line in Voss, Norway. From (Makkonen 2000).

al. 1997) in detail describe the modeling parameters included for an icing eventand (Makkonen 2000) gives a thorough review on rime and glaze ice growth onstructures. (Makkonen et al. 2001) focus on ice accretion for wind turbines andincludes wind tunnel tests in comparison with the predictions of a numerical code.

Also several works concern wind tunnel tests of iced airfoils and computer codeforecasting of ice accretions but as stated above most of these approach the sub-ject with the aeronautics field in mind. (Potapczuk & Berkowitz 1989) describe acomprehensive series of experimental investigations performed in the NASA IcingResearch Tunnel (IRT), (Wright & Chung 2000) correlate the geometric ice shapewith the aerodynamic performance degradation while (Addy et al. 1997) per-formed IRT-tests on airfoils used on modern aircrafts. (Seifert & Richert 1997) and(Jasinski et al. 1997) performed ordinary wind tunnel experiments using mouldedtemplets for different ice accretions and predicted the wind turbine power per-formance change as a result of the ice accretions. Finally (Shin et al. 1994)investigated the effect on airfoil drag for various ice accretions using numericaltools.

In the last decade or so CFD codes have played an increasing role in the lit-erature. (Bak et al. 1999) and (Ferrer & Munduate 2007) utilize custom-madeand commercial, respectively, 3D CFD codes for the purpose of investigating rotoraerodynamics for the wind turbine field. (Klausmeyer & Lin 1997) compare the re-sults of different CFD codes and turbulence models for airfoil flow in general, (Chiet al. 2004) use several turbulence models in order to analyse the aerodynamics of


Figure 1.2: Glaze ice sample on aerial cables taken after a freezing-rain event inSlovenia. From (Makkonen 2000).

an airfoil with ice accretion and (Kwon & Sankar 1997) compare experimental andCFD results for a wing with leading edge ice accretion. (Zhu et al. 2007) use CFDfor comparing different methods of predicting drag while (Chung & Addy 2000)and (Chung et al. 1999) both describe results of CFD simulations of iced airfoilsand wings performed by NASA.

Empirical data concerning atmospheric icing events is collected and presented bye.g. (Cober et al. 2001), (Isaac et al. 2001) and (Fikke et al. 2006).

This report concerns the aerodynamics of a wind turbine blade with leading edgeice accretion. In order to perform these investigations within a reasonable timespan the commercial CFD code Fluent has been utilized to simulate the flowaround an airfoil. In the case of the reference or clean airfoil the results from theCFD code have been compared to a computational code using the panel method.The results for the clean airfoil are then compared to several cases of leading edgeice accretion and the influence of the ice on the specific airfoil is analysed.

Furthermore an anti-icing system for the wind turbine blade is introduced. Thisconcept constitutes of a series of holes in the leading edge area through whichwarm air is blown. The effect on the boundary layer stability is analysed sincethis approach might lead to unwanted boundary layer separation and thus stalling


Figure 1.3: A fully iced lattice communication tower on Yllas, Finland. From(Makkonen 2000).

of the blade.

The following sections concern the theory needed to understand the physicalprocess of ice accretion on structures and the different methods for the com-putational codes used for the flow analysis in this report. Some general airfoiland flow theory is briefly explained in Section 2.1. Section 2.2 briefly explain theconcepts behind computational fluid dynamics and the panel method. Section 2.3introduces the topic of atmospheric icing and how this relates to the ice accreationon structures.

The ice accretions to be simulated are presented in Section 3.1 and the generationof the computational grids for the CFD simulations are described in Section 3.2.The modeling procedure is described in Section 3.3 and the full analysis anddiscussion of the obtained results is presented in Chapter 4.

Hereafter a conclusion of the prepared works and some perspectives on furthertasks in relation to this report are given in Chapters 5 - 6, respectively.

Chapter 2

Theory

5

CHAPTER 2. THEORY 6

2.1 Airfoil Flow and Boundary Layer Separation

In this section the basic theory concerning the flow around an airfoil is presented.This includes the introduction of forces on an airfoil, dimensionless force andmoment coefficients and the concept of flow separation.

2.1.1 Airfoil Geometry Terminology

An airfoil is a 2D vertical cut of a given wing or blade section. Referring toFigure 2.1 the chord designates the distance between the leading and trailingedge.

Figure 2.1: Airfoil geometry and its nomenclature. From (Bertin & Smith 1998).

The camber of the airfoil determines the curvature such that a symmetric airfoilhas zero camber. The maximum thickness and the chordwise location of this isimportant as well since this affects the flow over/under the airfoil.

The US institution National Advisory Committee for Aeronautics, NACA, hassince the start of the 20th century been one of the forerunners in the researchand classification of airfoils and many airfoils are named by a certain NACA digitdesignation. In the NACA five-digit classification the first integer indicates thecamber in terms of the relative magnitude of the design lift coefficient which intenths is three halves of the first integer. The second and third integer togetherindicate the distance from the leading edge to the position of maximum camber.The distance in per cent of the chord is one half the number represented by theintegers. The last two integers indicate the section thickness in per cent of thechord (Abbott & Von Doenhoff 1959).

The NACA63418 airfoil, for instance, is thus an airfoil where the design lift co-

CHAPTER 2. THEORY 7

efficient equals 0.9 (integer 6 times 3/2 divided by 10), the location of maximumcamber is at 17% distance from the leading edge along the chord line (integers3-4 divided by 2 in per cent) and the thickness is 18% of the chord (integers 1-8in per cent).

2.1.2 Forces and Force Coefficients on an Airfoil

When air flows around an airfoil pressure and velocity variations are produced inthe surrounding flow field. Normal pressure forces and tangential shear forces acton the surface of the airfoil due to airflow. Integrating these forces over the sur-face gives the resultant aerodynamic force which can be resolved into componentsparallel and perpendicular to the incoming airflow vector. The force componentperpendicular to the velocity vector, V0, is denoted the lift force and the compo-nent parallel to V0 is called the drag force. The forces are seen in Figure 2.2.

Figure 2.2: Definition of lift, drag, pitching moment and angle of attack on anairfoil. From (Hansen 2000).

By changing the angle of attack, α, which is defined as the angle between thevelocity vector V0 and the chord line of the airfoil, it is possible to change themagnitude of lift and drag.

The relationship between pressure and velocity is for an incompressible, inviscid(frictionless), steady flow situation along a streamline described by the famousBernoulli equation, Eq. (2.1), (Fox et al. 2004).

p

ρ+

V 2

2+ gy = constant (2.1)

with p being the air pressure, ρ the density, V velocity, g acceleration of gravitationand y the height. When neglecting the height difference between upper and lower

CHAPTER 2. THEORY 8

side of an airfoil and keeping density constant, Eq. (2.1) in a simplified situationtells that if the velocity on the upper side of an airfoil exceeds the velocity onthe lower side the pressure on the upper side must be lower than the pressureon the lower side of the airfoil. This principle is exploited in airfoil theory werethe flow is forced to run a longer way along the upper airfoil side thus increasingthe flow velocity on this side relative to the lower side and hereby creating anet underpressure over the airfoil. Because of this the upper side of an airfoil isreferred to as the suction side and the lower airfoil side is correspondingly referredto as the pressure side.

If the lift and drag forces are designated L and D, respectively, it it possible tonon-dimensionalize these into coefficients by Eqs. (2.2) - (2.3).

CL =L

1/2 · ρV 20 c

(2.2)

CD =D

1/2 · ρV 20 c

(2.3)

where c is the chord of the airfoil. CL and CD are the lift and drag coefficients,respectively. Non-dimensionalizing gives a set of coefficients readily comparablefrom airfoil to airfoil regardless of size (chord) and flow characteristics (densityand velocity).

In a similar manner a moment coefficient is given in Eq. (2.4). The pitchingmoment, M , is a moment about an axis through the airfoil, defined at c/4 andpositive when it turns the airfoil nose up.

CM =M

1/2 · ρV 20 c2

(2.4)

It is common to plot the three above mentioned force coefficients as functions ofangle of attack for a given airfoil.

2.1.3 Boundary Layer Effects and Flow Separation

When air moves over the surface of the airfoil the stability of the flow is influencedby the course of the airfoil as well as whether the flow is in the laminar or turbulentflow regime. The latter is characterized by the dimensionless Reynolds number,Re given in Eq. (2.5)

CHAPTER 2. THEORY 9

Re =V L

ν(2.5)

where L is a characteristic length for the concerned geometry and ν is the kine-matic viscosity of the present fluid.

The Reynolds number is the ratio between inertial and viscous forces. The tran-sition from laminar to turbulent flow occurs at approximately Re=500,000 fora smooth flat plate and L in Eq. (2.5) is normally the airfoil chord (Bertin &Smith 1998). Furthermore phenomena such as surface roughness, heating andblowing can influence the transition criteria and promote transition at a lowerReynolds number.

The region next to a solid surface is dominated by viscous forces. This region iscalled the boundary layer. In a laminar boundary layer the velocity is zero at thesurface (no slip) and increases in normal direction until the height of the bound-ary layer where the velocity reaches 99% of the freestream velocity (White 2006).The boundary layer thickens downstream and at some distance from the leadingedge may undergo transition and become turbulent. This happens if the viscousforces can no longer dampen the disturbances in the flow. The turbulent flow-field is among other things characterized by velocity fluctuations and a ”chaotic”appearance with vorticity and flow structures of many length scales.

For an angle of attack of zero the stagnation point is at the leading edge of theairfoil. Here the velocity is locally zero and a pressure peak is present. Forincreasing angles of attack the stagnation point moves along the pressure side ofthe airfoil. As the air travels over the airfoil the course of the surface determineswhether the flow accelerates or decelerates locally. An acceleration leads to apressure decrease and a deceleration comes with a pressure increase. The pressuregradient is very important for the ability of the flow to stay attached to the airfoilsurface. Concentrating on the suction side only it is apparent that the flow velocitywill increase in the region from the leading edge to a certain location. Aft of thisposition the flow velocity decreases towards the trailing edge. The first part of theairfoil is therefore governed by a favourable pressure gradient (pressure decreasesdownwards) and the last part by an adverse pressure gradient (pressure increasesin downward direction). This is illustrated for the flow around a cylinder inFigure 2.3 where the flow accelerates and pressure drops from point D to E whilethe flow decelerates and pressure increases from point E to F.

Adverse pressure gradients can result in boundary layer separation and where theadverse pressure gradient is the strongest the risk of separation is at maximum.If the boundary layer is turbulent it can better overcome the pressure rise with-out separation. Therefore a turbulent boundary layer often results in, if any atall, a separation bubble far downstream near the trailing edge while a laminarboundary layer is more prone to earlier and more pronounced separation. When

CHAPTER 2. THEORY 10

Figure 2.3: Schematics of the pressure progress for flow around a cylinder. Sdenotes the point of separation. From (Schlichting & Gersten 2003).

the boundary layer separates recirculation zones might appear and the overall liftis lost (Bertin & Smith 1998). This is called stall and occurs for increased anglesof attack. A flow visualization of a stalled and unstalled airfoil is depicted inFigure 2.4 together with the schematics of the separation of a laminar boundarylayer.

Figure 2.4: Flow visualization of an unstalled (upper left) and stalled airfoil (lowerleft) and the schematics of a laminar boundary layer separation (right). S denotesthe point of separation. From (Schlichting & Gersten 2003).

Separation also influences the drag of the airfoil. A laminar boundary layer haslower skin drag (viscous friction) than a turbulent one but if separation of theboundary layer occurs the total drag, the sum of skin and pressure drag, increasessignificantly. A turbulent boundary layer thus increases the skin drag but is lessprone to separation and therefore more stable for increasing angles of attack. Bothskin and pressure drag is rather difficult to compute accurately since determination


of the skin friction needs a very high grid resolution and a tuned turbulence modelwhile small deviations between the computed and actual pressure can cause largeinaccuracies when integrating for the pressure drag (Bertin & Smith 1998).

For a more detailed discussion of boundary layer effects and laminar-turbulenttransition the reader is referred to (Schlichting & Gersten 2003).

Blowing Boundary Layer

The introduction of suction or blowing from the airfoil surface can have an effecton the boundary layer stability. Suction always increases the stability of theboundary layer since the low-energy particles are removed before they can causeseparation. The separation point moves downwards with increasing suction orseparation is altogether avoided. This is exploited in airfoil cases for increasing themaximum lift coefficient. Furthermore, suction reduces friction drag and therebystabilises the laminar-turbulent transition (Schlichting & Gersten 2003). Theeffect of suction on one side of a cylinder is seen in Figure 2.5.

Figure 2.5: The effect of suction on the upper side of a cylinder upon the boundarylayer separation. From (Schlichting & Gersten 2003).

Blowing from the surface can on the other hand, in general, thicken the boundarylayer since the normal component of the velocity is increased and promotes thedisturbances in the flow to grow, thus enhancing the danger of boundary layer sep-aration. The blowing can although also increase the stability if injected correctly.Blowing in the front part of an airfoil where the pressure is dropping is one suchcase. Furthermore a tangential injection can rather than promote separation havethe opposite effect if the injected air is of higher velocity. Hereby the low-energyparticles are supplied with kinetic energy which helps them overcome the adversepressure gradient (Schlichting & Gersten 2003).


2.2 Numerical Methods for Flow Computations

In the following sections the concepts of two numerical approaches utilized in thisproject are briefly explained.

2.2.1 Computational Fluid Dynamics

Computational Fluid Dynamics, CFD, is a numerical technique which is basedon the theoretical equations of fluid dynamics but the results of a CFD simula-tion is analogous to the results of experimental work such as wind tunnel tests.The equations describing the fluid behaviour of any single phase problem are theNavier-Stokes equations. Unfortunately these equations are much to complex tobe analytically solved unless for some special cases where the nature of the prob-lem simplifies the equations greatly. These problems are rarely of any practicaluse and therefore a numerical solution of the equations are sought.

Again, the complexity of the Navier-Stokes equations requires a large computa-tional effort in order to obtain a, for many purposes, usefull solution. In the 1960’sand 70’s progress in the development of computers made it possible to performsimulations for 2D cases and only during the 90’s solutions described in 3D havebeen enabled by the fast increase in computational speed (Anderson 1995). Sincethe fluid dynamics community is confident in the Navier-Stokes equations, whichhave been known for more than a century, being the full solution to any fluid re-lated problem only the computational power limits solving even the most complexcases.

In order to obtain a numerical solution it is necessary to discretize the domain.This means that the resolution of the discretized domain will have an influence onthe accuracy and resolution of the solution. Furthermore the algebraic equationswhich are to be solved by the computer are only approximations of the originaldifferential equations solved by an iterative procedure (Ferziger & Peric 2002).

No matter what specific flow case one is dealing with a numerical solution willalways be a compromise between accuracy and computational time. The uti-lized approach with its benefits and drawbacks should reflect the required level ofinformation and sofistication needed for the individual task.

If a solution to the full Navier-Stokes equations is desired by numerical simulationthis involves the turbulent eddies from the complete time dependent equations.This approach is termed Direct Numerical Simulation, DNS, and requires a domaindiscretization fine enough to capture the smallest length scales of the turbulenteddies; the Kolmogoroff scale (Bertin & Smith 1998). DNS solutions to mostpractical cases take years to simulate even for the fastest of present day super-computers but are also the most accurate and detailed of all CFD approaches.


By time averaging the equations the critical parameters are the highly unsteadyturbulent quantities of momentum and energy. This technique is called ReynoldsAveraged Navier-Stokes, RANS, and brings the subject of turbulence models intoplay. Since this is the approach used in this project it will receive the attention inthe following and further techniques such as e.g. LES will not be discussed here.The time scale over which the averaging is done must be large compared to thetypical time scale of the flow fluctuations and the flow must be statistically steady(Ferziger & Peric 2002).

The Navier-Stokes equations are a set of equations derived from the three funda-mental equations; conservation of mass, Newtons second law (momentum equa-tion) and conservation of energy (first law of thermodynamics). When the flowregime is turbulent, as most practical cases are, and averaged over time the mo-mentum terms contain Reynolds stress tensors. This leads to the fact that moreunknown than equations are present and the set of equations is not closed. Theclosure problem is dealt with by modeling the mean turbulent quantities (Versteeg& Malalasekera 1995).

The Navier-Stokes equations for incompressible flow in 2D is written in tensorform in Eq. (2.6), (White 2006).

ρDV

Dt= ρg −∇p +∇ · τij (2.6)

where

τij = µ

(∂ui

∂xj

+∂uj

∂xi

)︸︷︷︸

laminar

− ρu′iu

′j︸︷︷︸

turbulent

(2.7)

with ρ being the density, V the velocity, t time, g gravitational acceleration, ppressure, τ stress tensor, µ viscosity, u Cartesian velocity component, x Cartesiancoordinate and u′ the turbulent velocity fluctuations. The indices ij represent theEinstein notation and the¯denote time-mean of the terms.

Turbulent eddy-viscosity models require the determination of the velocity (or en-ergy content) and length scale. The velocity scale is often determined by cal-culating the turbulent kinetic energy, k, and the length scale could be found byusing the turbulent dissipation rate, ε. In this case the turbulent model is calleda k-ε model. Another approach is to use the specific turbulent dissipation, ω, asa way of determining the turbulent length scales. In that case the model is calleda k-ω model. Both turbulence models are termed two-equation models since twoturbulent quantities need modeling. An example of a one-equation model is the


Spalart Allmaras turbulence model which, basically, models a variable similar tothe eddy-viscosity.

The simulations in this project are carried out using the Spalart Allmaras turbu-lence model since this was designed for aeronautical purposes and the k-ω SSTmodel since this performes better in the near-wall region compared to the similark-ε model. A good solution in the area near the airfoil and ice surface is expectedto be a necessity.


2.2.2 Panel Methods

A much simpler mean to obtain an approximative solution of the flowfield aroundan airfoil than the RANS in combination with turbulence models is the potentialtheory. Here it is assumed that the flow is incompressible, inviscid and irrotational.Potential theory is therefore an approximate explanation of the flow externally ofthe viscous boundary layer and thus a reasonable assumption for high-Reynoldsnumber flows where the boundary layer is thin. This section is based upon (Meyer2004) and (Katz & Plotkin 2001).

By dividing the geometry into a number of finite line segments, panels, startingfrom the trailing edge lower side and proceeding clockwise around the airfoil, theaim of the panel method is to compute the general flow. Figure 2.6 shows aschematic overview of an airfoil divided into n number of panels.

Figure 2.6: Airfoil divided into panels and panel method terminology. From(Meyer 2004).

Superposition of a freestream flow and one or more singularities, e.g. source, sink,point vortex or doublets, represents the flow around the airfoil. At each pointthe Neumann condition, i.e. that no flow can penetrate the panel and thus thevelocity component in normal direction equals zero, is applied.

A geometry having a sharp edge like the trailing edge of an airfoil will for certainangles of attack produce infinite velocities at the sharp edge because the flowis assumed inviscid. This problem is solved by introducing the Kutta conditionwhich states that the tangential velocity at first and last line segment, panels 1and N , respectively, should be equal. The Kutta condition is satisfied for instanceby placing a constant vortex strength on each panel.

First the velocities in tangential and normal direction for the midpoint of eachpanel i are calculated. Hereafter the solution of panel j induced on panel i isdetermined and added for all panels. When the tangential velocity in all panelsis known the pressure distribution can be calculated and by integrating this over


the entire geometry the lift force is known.

The numerical code XFOIL utilizes the panel method described above coupledwith a viscous solution for the boundary layer in the vicinity of the airfoil (Drela &Youngren 2001). XFOIL has proven excellent results given its relatively simplifiedapproach to a flowfield solution. For this reason the code is widely used in thefluid dynamics and aeronautics community and will also be used as a validationtool for the CFD results for the clean airfoil in this project.


2.3 Ice Accretion

The following section serves as an introduction to the subject of atmospheric iceaccretion on structures. The topic has been under investigation for decades withrespect to the aeronautics field as well as building structures such as lattice towers,suspension bridges, power cables etc. In the light of wind turbines the topic isrelatively new though and most of the research has its foundation on NASA’saeronautical results.

An ice accretion process can be divided into three overall steps; collision, collectionand accretion of water particles and the entire process is clearly time dependentwith the ice growing in layers. The outcome of the accretion process can beclassified as rime or glaze depending on various meteorological parameters such astemperature, liquid water content and droplet size. Rime is overall characterizedas being a dry and frosty ice with a white, rough surface whereas glaze is a wetand smooth, glassy type of ice often being transparent. Visual examples of rimeand glaze cases were given in Figure 1.1 and Figure 1.2, respectively.

The section is, unless otherwise stated, based upon (Makkonen 2000) and (Ackley& Templeton 1979).

2.3.1 Fundamentals of Icing

For an icing event to take place some form of water must be present in the at-mosphere. The most essential sources are those of cloud droplets, i.e. fog, super-cooled raindrops and snow particles. Condensation of water vapour is normallyconsidered negligible compared with impingement of liquid water droplets andsnow.

The mass rate of ice accreted on a structure is given by

dM

dt= η1η2η3wV A (2.8)

where η1, η2 and η3 represent the collision, collection and accretion efficiencies,respectively. w is the mass concentration of particles in air, V the particle velocityrelative to the object and A the cross-sectional area of the object. The factorsη1, η2 and η3 all have values between 0 and 1 and are dealt with in the followingsections.

The accreted mass of ice is clearly time dependent; two otherwise identical icestorms of different duration will of course create different amounts of ice with thelargest amount accreted in the longest lasting storm. Furthermore the alreadyaccreted ice will change the flowfield around the object, hence influencing thecollision efficiency, cf. Section 2.3.2.


2.3.2 Collision Efficiency

The factor η1 in Eq. (2.8) is the collision efficiency representing the part of theparticles which actually hit the object (relative to the maximum number of parti-cles in front of the object area). The reason for this value to be less than 1 is thatsmall particles tend to follow the streamlines around the object. Larger particleson the other hand have a large inertia and tend to collide with the object. Thisis illustrated in Figure 2.7.

Figure 2.7: Streamlines and droplet trajectories around a cylindrical object. From(Makkonen 2000).

The classical article of (Langmuir & Blodgett 1946) was the first to describe thedroplet trajectories around an object. A droplet moving in an air stream is in-fluenced by the forces of drag and inertia when neglecting gravity and buoyancy.If drag dominates the droplet will follow the streamlines whereas a particle in-fluenced mainly by inertia will not be deflected significantly and therefore tendto hit the object. The ratio of inertia to drag is dependent on the droplet size,velocity of the airstream and dimensions of the object in question.

A modified Langmuir parameter, KL, is defined in Eq. (2.9) (Battisti Class IV2006)

KL =1

18

24

CD ·Red

ρw

ρa

(d

D

)2

Rec (2.9)

where CD is the drag coefficient, Red the droplet Reynolds number, ρw and ρa

denote the water and air density, respectively. d and D are the droplet and object(airfoil) diameter, respectively, and Rec is the Reynolds number with respect tothe chord. The modified Langmuir parameter describes the inertia effects of waterdroplets relative to the drag force. For small droplets relative to the object size,

i.e.(

dD

)2<< 1, icing will therefore not be a crucial issue. Hence the tip region

of a wind turbine blade will be much more prone to icing than the root section


due to the size of the tip compared to the root of the blade both relative to thedroplet size. This effect relates to aeronautics where icing can be a big problemfor smaller aircrafts whereas large aircrafts experience less problems due to icing.

Furthermore, by realising that KL ∝ Vc≈ V

t, where V is the incoming wind speed

and t is the thickness of the blade section, the tip of a wind turbine blade is evenmore prone to ice accretion due to the increased flow velocity at this section.

Since the collection efficiency depends strongly on the particle size relative to theobject size it is reasonable to estimate that η1 = 1, i.e. all particles hit the object,for the case of supercooled raindrops unless the structure is very big. This leavesan estimation of η1 when dealing with cloud droplets as the source of icing.

Finally it should be noted that the Langmuir parameter predicts that the size ofthe water droplets relative to the object size is important whereas the shape ofthe object has almost no effect (Battisti Class IV 2006).

2.3.3 Collection Efficiency

The collection or sticking efficiency, η2 in Eq. (2.8), is the ratio of the particlesthat stick to the object to the particles that hit the object. When a supercooleddrop hits an object it will freeze instantaneously. A snowflake hitting the objectcan on the other hand bounce and thereby not stick to the surface. For liquidparticles it is reasonable to assume that η2 = 1, i.e. all hitting particles freezeupon impact. The sticking efficiency for snow particles depends on the conditionsof the snow. Dry and hard snow will tend to bounce off, η2 = 0 whereas wetsnow is very prone to stick upon impact, especially at low velocity and for certaintemperature and humidity conditions.

2.3.4 Accretion Efficiency

Assuming that a number of particles have collided and stuck to the structure theactual growth or accretion of ice is the next step in the process. This part isconsidered a thermodynamical problem involving the heat balance. The accretionefficiency is sometimes referred to as the freezing fraction. If all particles freezeon impingement the accretion efficiency, η3 in Eq. (2.8), will be 1 and the iceis characterized as rime. If on the other hand the freezing rate is controlled bythe transfer of the latent heat released during the freezing process the growthis characterized as being wet and the resulting ice is termed glaze. In this caseη3 < 1. A sketch of rime and glaze formation is shown in Figure 2.8.

The main thermodynamic contributions to the heat balance consist of

• Latent heat, Qlat, is the heat released during freezing of the liquid water


Figure 2.8: Formation of glaze and rime. From (Battisti Class III 2006).

droplet.

• Aerodynamic heat, Qaero, is the heat caused by viscous friction of the air.

• Kinetic heat, Qkin, is due to the collision of the water droplets.

• Convective heat, Qcon, is the heat loss caused by convection to the air.

• Evaporative heat, Qevap, is a heat loss due to the evaporation of water.

• Sensible heat, Qsens, is a heat loss caused by the temperature differencebetween droplet and object surface.

This leads to the overall heat balance given by Eq. (2.10)

Qlat + Qaero + Qkin = Qcon + Qevap + Qsens (2.10)

with the individual terms given by Eqs. (2.11) - (2.17)

Qlat = (1− λ)η3mwLf (2.11)

where λ is the liquid fraction of the accretion (normally set to a constant value of0.3) and Lf the latent heat of freezing (Makkonen 2000). mw, given in Eq. (2.12),is the flux density of water to the surface known from Eq. (2.8).


mw = η1η2wV A (2.12)

Qaero =hRv2

2cp−a

(2.13)

where h is the convective heat transfer coefficient, R the surface recovery factor(0.79 for a cylinder), V the incoming velocity and cp−a the specific heat of air(Ackley & Templeton 1979).

Qkin =mwV 2

2(2.14)

Qcon = h(Ts − T0) (2.15)

where Ts is the surface temperature and T0 is the ambient air temperature (Makkonen2000).

Qevap =hκLvap(es − e0)

cp−ap(2.16)

where κ is a constant equal to 0.622, Lvap the latent heat of vaporization, es thesaturation water vapour pressure at the surface, e0 the vapour pressure of theambient air and p the air pressure (Makkonen 2000).

Qsens = mwcp−w(Ts − Td) (2.17)

where cp−w is the specific heat of water and Td is the droplet temperature (Makkonen2000).

A plot of the individual heat contributions is seen in Figure 2.9 1.

It can be seen that the evaporation and convection on the cooling side and theaerodynamic heating are the most important contributions to the thermal balancealong the blade (especially in the tip region) while the kinetic heating and sen-sible cooling contributions are almost neglegible. The total heat flux is negativemeaning that the blade is cooled.

1The plot is a reproduction of previous work prepared by the author during the DTU course41326 Wind Turbine Ice Prevention Systems Selection and Design.


Figure 2.9: Heat flux contributions along a wind turbine blade.

2.3.5 Meteorological Quantities

In addition to the above mentioned factors some meteorological quantities arerelevant to address. These include the liquid water content of air, LWC, airtemperature and droplet size.

Liquid Water Content is a measure of the amount of liquid water in a volumeof air, often given in g/m3. The LWC is typically in the range of 0 − 0.6 g/m3

(Cober et al. 2001) and depends on the classification of the cloud, elevation andtemperature. Investigations include values of LWC = 1.3 g/m3 (Makkonen etal. 2001) while (Battisti Class III 2006) mention values up to 3.0 g/m3 in cumulusclouds and NASA’s Lewice code is validated between 0.31 − 1.8 g/m3 (LewiceManual 2002). Both rime and glaze can be produced for LWC of most values al-though very large values of LWC tend to produce glaze (Battisti Class III 2006).This is due to the temperature dependency of LWC which is depicted in Fig-ure 2.10.

A logical dependency between temperature and LWC is shown since temperaturesmuch below the freezing point will make the liquid water freeze and thereby reducethe LWC. The risk of an icing event increases with increasing LWC because thereis simply more water which might freeze and accrete present.


Figure 2.10: Distribution of liquid water content as a function of droplet diameterfor different air temperatures. From (Battisti Class III 2006).

Temperature is of course a very important factor in the field of icing. Ingeneral the risk of icing lies in an interval between zero and -20 ◦C accordingto (Ackley & Templeton 1979) while (Cober et al. 2001) report the temperatureinterval between zero and -15 ◦C to be the most crucial. Figure 2.11 shows thecorrelation between reported icing cases and air temperature.

While the air temperature determines the state of the particles in the air it isthe surface temperature of the object, as discussed in Section 2.3.4, that dictateswhether the accreted ice will be rime or glaze. A surface temperature whichcreates a film of liquid water, i.e. temperatures just around freezing, will result inglaze while temperatures further below zero result in rime as the outcome. Therelation between type of ice and temperature (combined with wind speed) is seenin Figure 2.12.

Droplet Size is often given by the median volume diameter, MVD, which isused as a single droplet size instead of performing weighted calculations for eachdroplet size within a given droplet size distribution. (Makkonen et al. 2001) men-tion the interval 1.5−50 µm as being the critical MVD for icing events and (Coberet al. 2001) characterize a drop as being large when MV D > 50 µm. Clouds andfog which have smaller droplet sizes than raindrops are able to supercool more andwill therefore tend to accrete rime whereas larger supercooled drops are associatedwith glaze accretion (Ackley & Templeton 1979).

A correlation between droplet size and LWC with temperature influence indicatedis presented in Figure 2.10 and Figure 2.13. The former of these shows the ten-dency that LWC decreases for increasing droplet size. This is reported by (Cober


Figure 2.11: Relative frequency of observed icing cases related to air temperature.From (Battisti Class III 2006).

et al. 2001) as well.

Due to the explanation given in Section 2.3.2 the most severe icing events areobserved for large droplets, i.e. for freezing rain rather than fog. The droplet sizetherefore effects the impingement limits of the ice accretion as well as the amountof ice accreted.


Figure 2.12: Relation between type of ice, air temperature and wind speed. From(Battisti Class III 2006).

Figure 2.13: Relation between droplet size, liquid water content and air temper-ature. Measured data from (Cober et al. 2001).


2.3.6 Comparison of Parameter Influence

As a way of showing the influence of the above mentioned and other relevantparameters on ice accretion a reference case has been made and hereafter eachparameter has been changed individually while maintaining the other parameters.The parameters in the reference and changed cases are listed in Table 2.1.

Reference value Compared valueLWC [g/m3] 0.4 0.6Temperature [ ◦C ] -10 -5MVD [µm] 30 45Velocity [m/s] 50 75Relative humidity [%] 100 50Pressure [Pa] 101325 151987.5Time [s] 1000 1500α [◦] 0 5

Table 2.1: List of reference and compared values for different influence factors.

All parameters have been increased by a factor of 0.5 when using zero as a referencepoint. Exceptions from this are for the cases of temperature and relative humiditywhich have both been decreased by 0.5 in value and for the angle of attack whichhas simply been changed from 0 to 5◦.

In this project the ice accretions are simulated using a numerical code Lewicewhich is described in Appendix C. This code uses the parameters given in e.g.Table 2.1 as input and outputs the shape of airfoil and ice as Cartesian coordinatesets. These coordinates are in turn used as inputs for Matlab and the geometryand grid generator Gambit. The results on the accreted ice are seen in Figure 2.14.

When comparing the reference case to a similar case except for an increase inliquid water content it is seen that the ice shape and thickness is affected. Theamount of accreted ice increases with LWC.

Changing only the temperature from -10 ◦C to -5 ◦C reduces the amount of iceaccreted due to a decreased value of η3, the accretion efficiency. This is because ahigher temperature changes the heat balance of the freezing process. Furthermorethe type of ice can change from rime into glaze with increasing temperature.

Increasing the median volume diameter of the droplets leads to a change in thedroplet impingement limits so that a larger front area of the airfoil is hit byparticles. This is due to the change in the ratio between the droplet inertia anddrag as explained by Langmuir’s parameter, cf. Eq. (2.9).

An increase in wind speed also increases the amount of accreted ice since theparticles gain more inertia. As a result more particles hit the airfoil and the ice


accretion increases. Furthermore the shape of the ice changes and the impinge-ment limits increase.

Changing the relative humidity of the air does not have a large influence on theamount of accreted ice. This fact seems intuitively wrong but by realising that therelative humidity is only a measure for how much water vapour a volume of aircan contain this makes sence. Instead the amount of liquid water in the air, theLWC, plays a role. Relative humidity is normally set to 100% in icing analysis.

Pressure does not play a significant role and is only included in this analysis forinformative reasons.

Increasing the duration of the icing event has the straightforward result of in-creasing the amount of ice. The relative change when compared to the influenceof the above mentioned factors stresses that time is an important factor.

A change in angle of attack obviously alters the accretion since the streamlinesaround the airfoil are changed with the flow angle.


Figure 2.14: First row: LWC=0.6 g/m3 (left) and T=-5 ◦C (right). Second row:MVD=45 µm (left) and V=75 m/s (right). Third row: RH=50% (left) andP=151987 Pa (right). Fourth row: t=1500 s (left) and α=5◦ (right).

Chapter 3

Numerical Setup

29

CHAPTER 3. NUMERICAL SETUP 30

3.1 Definition of the Simulation Cases

In this section the simulation cases, their parameters and objectives for choosingsuch cases are presented. First of all the objective is to simulate how the aerody-namic properties of an airfoil with leading edge ice accretion will change comparedto the same clean, unaffected airfoil.

3.1.1 Clean Airfoil

The airfoil used for all cases is the NACA63418 airfoil which is a cambered airfoilwith a sharp trailing edge. This airfoil could be used in the tip region of a windturbine blade and is therefore representative for this project. A plot of the airfoilis given in Figure 3.1.

Figure 3.1: The NACA63418 airfoil used for the simulations.

In the calculations a unit chord and zero roughness on the airfoil surface is used.Furthermore a freestream velocity of 33 m/s (Re=2.2·106) and standard conditionsare applied for all simulation cases which are performed from α=0-20◦ in intervalsof 2◦.


3.1.2 Ice Case A

The first ice case, ice case A, is the result of meteorological quantities represen-tative for a classic rime-producing ice storm. Also the duration of such a stormis taken into consideration and the accretion time of 3 hours as seen in Table 3.1is quite typical. All parameters influencing the accretion shape are given in Ta-ble 3.1.

Quantity ValueTime, t 10800 sDroplet size, MVD 20 µmAngle of attack, α 0◦

Wind speed, V 90 m/sLiquid water content, LWC 0.2 g/m3

Static temperature, Tstatic 254.11 KRelative humidity, RH 100%Pressure, p 101325 Pa

Table 3.1: The influencing parameters for the ice accretion of ice case A. Typicalparameters for accreting rime.

These parameters are given as input to the ice accretion code Lewice. Note thatthe input temperature is the static temperature, Tstatic calculated by Eq. (3.1)

Tstatic = T0 −V 2

0

2cp−a

(3.1)

where T0 is the ambient total temperature, V0 the velocity and cp−a the specificheat capacity of air.

The wind speed is set to 90 m/s since this would be of the order of magnitude forthe tip speed of a running wind turbine in the MW-size. The values for dropletsize, liquid water content and temperature (corresponding to a total ambienttemperature of -15 ◦C) are all representative for a rime-ice accretion according tothe literature, cf. (Makkonen 2000), (Ackley & Templeton 1979), (Battisti ClassIII 2006) and (Makkonen et al. 2001). In Section 2.3.6 it was shown that neitherrelative humidity nor pressure had a significant effect on the accretion shape andthey are only included in Table 3.1 for coherence.

Figure 3.2 shows the ice shape accreted on the airfoil and a zoom plot of theleading edge area.

The ice protrusion increases the total length in chordwise direction of airfoil andice with approximately 11% of the original chord. The rather severe shape is


Figure 3.2: The accreted ice shape for case A.

primarily due to the accretion duration of 3 hours. At low angles of attack it ispossible that the total lift force is increased due to the enhanced chordwise lengthwhile at medium and higher angles of attack it is expected to reduce the lift forcedue to leading edge separation.

3.1.3 Ice Case B

Ice case B has parameters representative for a glaze-producing ice storm. Theused quantities are given in Table 3.2.

Quantity ValueTime, t 10800 sDroplet size, MVD 20 µmAngle of attack, α 0◦

Wind speed, V 90 m/sLiquid water content, LWC 0.6 g/m3

Static temperature, Tstatic 267.61 KRelative humidity, RH 100%Pressure, p 101325 Pa

Table 3.2: The influencing parameters for the ice accretion of ice case B. Typicalparameters for accreting glaze.

Most of the quantities are the same as for the previous case except for the liquidwater content and temperature (corresponding to a total ambient temperature of-5 ◦C). These values are changed in order to be representative of a typical glaze-iceaccretion situation.


The ice shape is plotted on the airfoil in Figure 3.3.

Figure 3.3: The accreted ice shape for case B.

The accreted ice shape is somewhat different compared to the shape in case A.The protrusion does not extent further in chordwise direction than approximately1% of the original chord but the shape is less streamlined than case A and causesa more abrupt non-airfoil shape with the beginning of two horns. It is expectedthat this will cause a larger reduction in lift force and an increase in drag.

3.1.4 Ice Case C

This case has input parameters and an ice shape identical to case A. But unlikecase A and B this case will be simulated with a given surface roughness dictatedon the ice protrusion while maintaining the smooth surface of the actual airfoil.

The surface roughness in Fluent is determined by the roughness height, Ks, anda dimensionless roughness constant, Cs, which is dependent upon the type ofsurface roughness. The latter is maintained at the default value of Cs=0.5 sinceno references of this value in relationship to surface roughness of ice is, to theauthors knowledge, available.

(Jasinski et al. 1997) use roughness heights of Ks=9-19·10−4 m for rime ice butsince these values are larger than the desired first cell height in the computationalgrid, cf. Section 3.2, the order of this magnitude does not make sense. Thereforea roughness height of Ks=5·10−6m has been used for ice case C.


3.1.5 Blowing Surface

As means of mitigating ice accretions several techniques are used for wind turbinesin particularly cold locations. Most common is electrical heating of the outer sur-face of the blade or sections around the leading edge of the blade. This approachconsumes a part of the produced electric energy and is often the cause of lightningstrikes (Battisti Class VII 2007).

An alternative anti-icing system inspired by transpiration cooling from the gasturbine industry could utilize jets of warm1 air being blown from a series of smallholes arranged on the leading edge. The warm air could be taken from e.g. thegenerator and directed to the tip area of the blade where it could exit to theouter blade surface through holes on the leading edge. This way the warmer airblown from inside could possibly avoid the accretion of ice by increasing the airtemperature in the vicinity of the blade surface.

The influence of such a system on the flow and aerodynamic properties of theclean airfoil is investigated in this case which in the remainder of the report isreferred to as the blowing surface case.

Since the blowing of warm air aims at entirely avoiding the accretion of ice thesimulations are performed on the clean airfoil with 3 holes of 3 mm diameterlocated on the airfoil leading edge. The holes are treated as velocity inlets inFluent and the boundary conditions given are the velocity and direction of the jets.The direction of the flow is perpendicular to the airfoil surface and the velocity is3 m/s. For this case the energy equation is enabled and the temperature is givenas a boundary condition for the airfoil surfaces, inlet and outlet as well as theholes. The temperature of the blown air is set to 4 ◦C while the ambient air andsurfaces are set to -15 ◦C .

1The term warm air should be seen respectively to the temperature of the ambient air. Atemperature of approximately 4 ◦C is regarded to be sufficient for the jets in order to avoid anice accretion.


3.2 Geometry and Grids

A numerical code needs to solve the given equations for a number of discrete pointsin the domain. The resolution of the discretization will influence the accuracy ofthe solution as well as the computation time. The position of the discrete pointsis determined by the grid, or mesh, created for the specific problem.

3.2.1 Generation of the Grid - Clean Airfoil

The generated grid consists of several blocks confined in an outer circular domain.Overall the surroundings have been divided into three domains in normal direction.The first layer of blocks are placed in the direct vicinity of the airfoil in orderto give the desired wall Y+ distribution of approximately unity. Hereafter theactual inner mesh is constructed with the boundary at an approximate distanceof 0.5·chord from the airfoil surface. The outer domain is comprised of a circlewith a radius of 25·chord with the circular centre located at the airfoil leadingedge, (x,y)=(0,0).

A total of 288 nodes have been distributed onto the surface of the airfoil clusteredaround the leading edge and in particular at the trailing edge sections. The gridconstitutes of a total of 107142 cells whereof the vast majority are quadrilateralcells in a mapped structure. Only under the trailing edge a total of 140 triangularcells are placed in two wedge shaped blocks positioned between the wall blocksand inner grid.

The multiblock structure has been made in order to deal with the concave shapeof the trailing edge which combined with the wish for a grid resolution in theY+=1 order forced the grid lines to cross each other when the domain was notdivided into blocks. Furthermore the need for a multiblock structure proved itselfright when meshed without. This resulted in the fact that the grid lines becamestretched in the normal direction and that these were far from orthogonal ontothe airfoil surface in most areas.

Wall Blocks A series of wall blocks constitute the first 50 cell layers next tothe airfoil surface. The height of each layer in these blocks is approximately10−5·chord corresponding to a Y+ value of 1 for a Reynolds number of 2.2·106.The reason for making this first block in the normal direction is the fact that adictated first cell height of 10−5·chord when using a larger first domain did notresult in the desired value at all points around the airfoil. The reason for thisdiscrepancy between the dictated and the actually created first cell height mustbe due to the difference in distance from the airfoil surface to domain boundaryalong certain positions. A total of 9 blocks are distributed around the airfoil inaddition to an extra two blocks behind the trailing edge. The total number of


cells within the wall blocks is 19980 cells. All of these are quadrilateral cells ina mapped structure. Figure 3.4 shows the wall blocks around the leading andtrailing edge of the airfoil.

Figure 3.4: Wall blocks and grid near the leading (left) and trailing edge (right)for the clean airfoil.

It is seen how the grid under the trailing edge was constructed in order to dealwith the above mentioned problems with crossing grid lines.

Inner Grid The inner grid cells grow from the wall blocks away from the airfoil.2 half ellipses grow together at the position x=0.3 and together with a sharpvertical cut-off make up the inner grid domain. This boundary is placed at anapproximate distance of 0.5·chord from the airfoil surface. The 9 wall blockscontinue into 9 blocks in the inner grid with an extra 2 blocks behind the airfoiltrailing edge. The cell height of these 11 blocks are dictated to start at 10−5·chordwith an increase of 5% per layer. This way a total of 149 cells are distributed inthe normal direction of the inner grid. A total of 50362 cells make up the innergrid. Due to the concave shape of the trailing edge of the pressure side it hasbeen necessary to construct a part of this area with triangular cells. The innergrid and full airfoil is seen in Figure 3.5.

Outer Grid From the ellipse shape with abrupt vertical cut-off of the innergrid the cells grow into the outer grid in which a circular boundary ends thetotal domain. 7 blocks constitute this outer grid which have 50 nodes in normaldirection clustered at the transition from the inner grid. The clustering ratio isdecided such that the last cell layer in the inner grid and first cell layer in theouter grid gives a smooth transition without abrupt jumps in cell size. The outergrid has a total of 36800 quadrilateral cells in a mapped structure. In Figure 3.6the full domain grid is seen.


Figure 3.5: Inner grid around the clean airfoil.

Figure 3.6: Full grid around the clean airfoil.


3.2.2 Generation of the Grid - Ice Case A

The general structure of the grid has been maintained for the cases with iceaccretion on the leading edge and only the grid area directly in front of the airfoilhas been changed. Hence 2 wall blocks make up the layer next to the ice surface.These blocks again constitute of 50 cell layers and the cell height is in mostplaces equal to 10−5·chord but varying due to the outer course of the wall blockswhich has been constructed in a near-straight way in order to avoid problems withoverlapping and streched grid lines caused by the complex concave and convex iceshape. Another benefit of the near-straight course of the wall blocks is that thetransition to the inner grid is very smooth. The grid around the leading edge andice accretion is shown in Figure 3.7.

Figure 3.7: Grid around the leading edge and ice accretion for ice case A.

The inner grid first cell height is set to 10−5·chord with an increasing cell heightof 5% per layer until this grows smoothly into the outer grid block.

A division into an upper and lower half of the ice has been made for the purposeof calculating the pressure distribution over the airfoil. In this way the upperhalf of the accreted ice is formally a part of the suction side of the airfoil whencalculating pressure distribution and lift coefficient. The lower part of the ice isin a similar way a part of the airfoil pressure side.

50 evenly distributed nodes have been placed on both upper and lower ice shape.The total number of nodes on the airfoil/ice surface is thereby increased from the288 nodes in the clean airfoil case to 313. Therefore the number of nodes in theadjacent inner and outer grid blocks has also been increased to 50 instead of 25for the clean airfoil case. The total number of cells in the full grid is 119592.


3.2.3 Generation of the Grid - Ice Case B

The shape of the protrusion for ice case B is somewhat more complex with twohorn-like structures deviating from the airfoil shape. Again only the area aroundthe leading edge and ice accretion has been changed and the general structure withwall blocks on the surface has been maintained. Figure 3.8 shows the constructedgrid around the leading edge of ice case B.

Figure 3.8: Grid around the leading edge and ice accretion for ice case B. The redcircles indicate areas of high node density.

The walls blocks following the surface again constitute of 50 cell layers in nor-mal direction but in four areas it has been necessary to furthermore make blockstructures before the inner grid. These areas are the very front and immediatelybehind the protrusion on both lower and upper side. Each of these blocks containssome triangular grid cells in order to obtain a smooth transition to the inner gridwhile stepwise going from the complex ice shape.

77 nodes are placed on the upper half of the ice and 82 nodes are placed on thelower half. The large number of nodes is due to the back side of the protrusionwhere 50 nodes are placed on both upper and lower part as indicated by the redcircles in Figure 3.8.

The inner grid first cell height is set to 10−5·chord with an increasing cell height of5% per layer until this grows smoothly into the outer grid block. The full domainconsists of a total of 125151 cells.


3.2.4 Generation of the Grid - Ice Case C

This grid is the same as for ice case A. The roughness parameters Ks and Cs aregiven in Fluent as a boundary condition for the wall entities of the ice protrusion.

3.2.5 Generation of the Grid - Blowing Surface

This grid is essentially the same as for the clean airfoil case. The difference lies inthe fact that the leading edge surface has practically been split into smaller indi-vidual sections in order to simulate holes in the airfoil surface. This is illustratedin Figure 3.9.

Figure 3.9: Grid around the leading edge for the blowing surface case.

Figure 3.9 shows the location of the 3 holes but in the actual grid the holes arereplaced by straight lines which each represents a velocity inlet in the simulations.It is important to note that in Figure 3.9 the wall block grid in front of the holeshas momentarily been removed in order to visualize the holes. The meshing ofthe wall blocks as well as the rest of the grid is the same as for the clean airfoilseen in Figures 3.4 - 3.6.

3.2.6 Grid Dependency Check

In order to make sure that the solution is not dependent on the resolution of thecomputational grid certain parameters can be plotted as a function of number of


grid cells. Therefore several grids with same basic block structure but varyingcell size growth rate and thereby number of cells have been constructed and asolution for ice case A, α=16◦ with Spalart Allmaras turbulence model, usingidentical solver settings has been run for each grid. The significant parameters inthis case are the force coefficients for lift, drag and moment. Figure 3.10 showsthe result of these simulations.

Figure 3.10: Grid dependency checked using lift (left) and drag and moment(right) coefficients.

It should be noted that the simulations for the grid dependency check were per-formed using 1st order discretization schemes since the coarse grids were non-converging when using 2nd order discretization. This influences the accuracy ofthe simulation but is not the focus of these simulations. The difference betweenthe CL-solution with 1st and 2nd order discretization is seen by comparing theresults of Figure 3.10 and the value for ice A, α=16◦ in Figure 4.16, Section 4.1.2.

In order to save time when running the computations the grid with the small-est number of cells displaying an independent solution should be used for thecalculations. This is seen to be the case for a grid with around 120,000 cells.


3.3 Simulation Procedures and Settings

During simulations some procedures or approaches have been followed in order toincrease the accuracy and decrease the computation time needed for each individ-ual simulation.

The clean airfoil was simulated using both Spalart Allmaras and k-ω SST tur-bulence models. For all ice cases and the blowing surface only Spalart Allmaraswas used since this is the best performing model when simulating ice accretions(Chung & Addy 2000) (Klausmeyer & Lin 1997). All simulations were performedas steady solutions.

A solution using Spalart Allmaras often converged faster and easier than with thek-ω SST turbulence model and therefore the former of these were normally run asa first solution until convergence. Hereafter the turbulence model was switchedto k-ω SST for the clean airfoil case. This procedure gave a faster convergence ofthe k-ω SST model since it started from the already converged Spalart Allmarassolution. Furthermore the simulations were run for α=0 first and the angle ofattack was hereafter gradually increased while running from the results of theprevious solution.

When running the simulations with ice accretion it proved necessary to use arather conservative approach in order to avoid simulation errors such as floatingpoint errors from Fluent. The simulations were therefore often started with rel-atively low under relaxation factors and first order discretization schemes. If thesolution residuals seemed to decrease steadily the discretization factors could bechanged to the desired schemes.

Grid adaption with respect to Y+ was performed in order to ensure that the gridresolution around the surface was in the desired order when this was not alreadythe case from the initial grid. Often a grid adaption with respect to gradientsof mean velocity or turbulent kinetic energy was performed as well. Figure 3.11shows the wall Y+ distribution on the pressure and suction side of the airfoil withice (case A) for the initial grid and after a Y+ adaption has been performed.

As boundary conditions for the inlet (velocity inlet type) the magnitude andcomponents of the flow velocity were given together with the modified turbulentviscosity for the Spalart Allmaras cases and turbulence intensity and turbulentviscosity ratio for the k-ω SST model. The latter values were set to 10% and 10,respectively, while the modified turbulent viscosity was kept at the default valueof 0.001 m2/s.

The outlet (pressure outlet type) boundary conditions were defined by flow direc-tion being orthogonal to the boundary and modified turbulent viscosity (SpalartAllmaras) or turbulence intensity and turbulent viscosity ratio (k-ω SST) with val-ues being the same as for the specified inlet conditions. The boundary conditions


Figure 3.11: Wall Y+ distribution as function of chordwise position on the airfoiland ice (case A) for the initial (left) and adapted grid (right).

for the outlet were only used in the case of flow reversal.

Boundary conditions for all wall zones (airfoil and ice surfaces) were defined byno-slip and a surface roughness height of zero except for ice case C where theroughness height on upper and lower ice surface was set to 5·10−6m, cf. Section 3.1.

Furthermore it should be noted that the meshing program Gambit sometimesproduced faulty grids when exporting these. Often it was necessary to export themesh file twice in order to get rid of these errors which resulted in extreme valuesof for instance Y+ and velocity or pressure gradients when running a solution inFluent. A grid check in Fluent or manual inspection of the grid did not show anyproblems however.

3.3.1 Residual History and Estimation of Convergence

A plot of the residual history for a convergent simulation is shown in Figure 3.12.

Changing between discretization schemes causes momentary spikes in the residualsbut due to the large number of iterations these are not seen in Figure 3.12. Thepressure scheme was changed from standard to 2nd order2 and the momentum andmodified turbulent viscosity schemes (Spalart Allmaras) or momentum, turbulentkinetic energy and specific dissipation rate (k-ω SST) were changed from 1st to2nd Order Upwind.

The convergence criteria for the residuals were set to 10−5 but were never usedas a sole estimation of whether the solution had converged or not. This wasinstead estimated by plotting the lift and drag coefficient as a function of numberof iterations. When a stable level had been observed over a longer period of

2For a few random simulations the solution converged better using a PRESTO! pressurediscretization scheme.


Figure 3.12: Residual history for a simulation of ice case A.

iterations the solution was estimated as having converged. A plot of the CL andCD history for the same simulation as Figure 3.12 is seen in Figure 3.13.

Figure 3.13: Convergence history for the lift (left) and drag coefficients (right) fora simulation of ice case A.

The monitoring of the lift and drag coefficients is not enabled from the beginning.This is because both CL and CD need some thousands of iterations to reach theapproximate values. After a while the coefficient plots were cleared in order tominimize the scale of the 2nd axis and further ease the estimation of convergence.The plots in Figure 3.13 are therefore not for the final convergence but only a stepon the way.

Finally is should be noted that although a solution with second order discretizationschemes was wanted this was not always possible. For the clean airfoil simulatedwith k-ω SST, ice cases A and C the solutions would not converge with secondorder schemes for α=18◦ and α=20◦. For ice case B this was already the case


from α=16◦. The results presented for these values are therefore converged witha standard pressure discretization scheme and 1st Order Upwind schemes formomentum and turbulent quantities. In general these first order schemes arenot considered good enough for the desired solution. This was mentioned inSection 3.2.6.

Figure 3.14 shows a plot of the lift coefficient when running ice case A for α=18◦.

Figure 3.14: Lift coefficient course for 1st order (left side) and 2nd order dis-cretization schemes (right side) for a solution of ice case A, α=18◦.

The straight line to the left is the level when running with 1st order discretizationschemes and the fluctuating curve to the right is after switching to 2nd orderschemes. It is obvious that the solution using 2nd order discretization is non-convergent.

Chapter 4

Results and Discussion

46

CHAPTER 4. RESULTS AND DISCUSSION 47

4.1 Simulation Results

In this section the results from the various simulations are presented. Each flowcase is discussed separately and plots of velocity contours and streamlines areshown. A comparison of the aerodynamic properties of the airfoil with and withoutice is given in terms of the pressure coefficient distribution followed by polars oflift, drag and moment coefficients.

4.1.1 Clean Airfoil

The results from the two turbulence models are treated separately for a betteroverview. First the results from the Spalart Allmaras simulations are presented.

Spalart Allmaras

Figures 4.1 - 4.2 show the velocity contours and streamlines, respectively, for theflow around the clean airfoil.

The plots for 2-6◦ are omitted since these virtually show no flow development ofinterest. The scale of all plots in Figure 4.1 is fixed for better comparison acrossthe different angles of attack plots. Maximum value in the velocity scale is 94.1m/s (for α=20◦) indicated by red colours and minimum is zero indicated by darkblue colours. The reason for the streamline unit kg/s and not kg/m · s is the 2Dgeometry. The missing m in the denominator denotes per unit depth.

From Figure 4.1 areas of high velocities are seen over the surface of the airfoil andlow velocities are seen at the stagnation point at the leading edge and furthermoreat the trailing edge. The latter area grows bigger with increasing angle of attackwhile the stagnation point moves downstream along the pressure side. At thesame time the area of high velocity on the suction side grows bigger and increasesin value while moving upstream.

It is evident from Figure 4.2 that the flow from α=0◦ to around 10◦ is rathersmooth and well attached to the surface of the airfoil. At α=12◦ a separationbubble starts to form at the trailing edge and at α=16◦ the bubble is fixed,growing and moving upstream for bigger angles of attack. Also at approximatelyα=16◦ yet another bubble forms downstream of the first separation bubble.

The pressure coefficient distribution for various angles of attack for the clean airfoilcalculated by Fluent is presented in Figure 4.3 together with the results for thepanel method code XFOIL at same angles of attack.


Figure 4.1: Velocity contours for the clean airfoil using Spalart Allmaras. 1st row:α=0◦ (left) and α=8◦ (right), 2nd row: α=10◦ (left) and α=12◦ (right), 3rd row:α=14◦ (left) and α=16◦ (right), 4th row: α=18◦ (left) and α=20◦ (right). Valuesare in m/s.


Figure 4.2: Streamlines for the clean airfoil using Spalart Allmaras. 1st row: α=0◦

(left) and α=8◦ (right), 2nd row: α=10◦ (left) and α=12◦ (right), 3rd row: α=14◦

(left) and α=16◦ (right), 4th row: α=18◦ (left) and α=20◦ (right). Values are inkg/s.


Figure 4.3: Pressure coefficient distribution along the airfoil. Simulated resultsfor the clean airfoil at selected angles of attack using Spalart Allmaras turbulencemodel (top) and XFOIL (bottom).


In general the CP distribution predicted by the Spalart Allmaras turbulence modelcorresponds very well with the XFOIL results. Only for high angles of attack aresmall discrepancies observed. This serves as a form of validation for the Fluentresults since XFOIL is generally considered to give believable results.

A negative pressure peak at the stagnation point near the leading edge is observed.Only at α=0 and 4◦ is a favourable pressure gradient in the leading edge suctionarea present. It is interesting to note that the suction side curve (upper curve) forα=20◦ crosses the curves for α=12 and 16◦ approximately 14 and 18% downstreamof the chord, respectively. These are the positions from where the high angleof attack flow starts loosing its local lifting ability compared to α=12 and 16◦.Upstream of these positions the lift force is stronger for α=20◦ as indicated bythe higher flow velocity in the front part of the suction side seen in Figure 4.1.

Plots of the force and moment polars are presented in Figures 4.4 - 4.5 where thesimulation results for the clean airfoil are compared with XFOIL and experimentalresults from (Abbott & Von Doenhoff 1959). It should be noted that the lattervalues are read of from a graph and the procedure in doing so introduces someinaccuracies.

In the following the lift coefficient will gain the most attention since this is by farthe most important value for wind turbines.


Figure 4.4: Lift coefficient as function of the angle of attack. S.A. denotes SpalartAllmaras turbulence model.

Figure 4.5: Drag (left) and moment (right) coefficients as functions of the angleof attack. S.A. denotes Spalart Allmaras turbulence model.


Concentrating on the lift coefficient it is observed that the simulated results agreeexcellently with the XFOIL results. This was clear already from the comparisionof the CP curves since the lift is obtained by integrating the pressure coefficientover the airfoil. Only at the highest angle of attack the Spalart Allmaras modelpredicts noticably less than XFOIL. In general the results also agree very wellwith the experimental results by (Abbott & Von Doenhoff 1959) although thetendency that the simulations underpredict the lift is clear. It should be notedthat at flow separation the situation becomes highly 3-dimensional and neitherXFOIL nor this Fluent model will be able to predict the flow with great accuracy.The lift is increasing roughly linearly until α=10◦ and maximum lift capacity isreached at α=14◦ with a value of 1.33.

Turning to the drag coefficient it is evident that the agreement between the sim-ulated clean airfoil and XFOIL or (Abbott & Von Doenhoff 1959) is not particu-larly well. Spalart Allmaras predicts significantly higher values of drag than bothXFOIL and (Abbott & Von Doenhoff 1959) for all angles of attack1. It should benoted that the XFOIL and experimental results are spot on identical for α =0, 2and 8◦.

For the moment coefficient taken around (x,y)=(0.25,0) the simulated clean airfoilagrees fairly well with (Abbott & Von Doenhoff 1959) for α .10◦ and hereafter theSpalart Allmaras model predicts higher CM . The XFOIL results are much higherthan both the simulated and experimental results for nearly all angles of attack.The course of the curves itself also differs significantly. While the experimentallyobtained CM values decrease with angle of attack this is not the case for neitherXFOIL nor the Spalart Allmaras results which either increase or level out forincreasing angle of attack.

Fortunately it is the lift coefficient which exhibits the best agreement with thecompared sources. While this parameter showed very similar results both dragand moment coefficients had some discrepancies and in the remainder of the reportthe actual values of these significant figures should not be taken to literally. Theappearance of the curves and their results relative to the Spalart Allmaras cleanairfoil results still give valuable information though.

1The experimental results only include values for α ≤10◦ for drag and α ≤18◦ for moment.


k-ω SST

For selected angles of attack are the velocity contours and streamlines over theairfoil seen in Figures 4.6 - 4.7, respectively.

Figure 4.6: Velocity contours for the clean airfoil using k-ω SST. 1st row: α=0◦


(left) and α=20◦ (right). Values are in m/s.

The scale of all plots in Figure 4.6 is fixed with a range between 0 and 88 m/swhich is the maximum value appearing for α=16◦. For α=6◦ a low velocity area isvisual at the trailing edge. This area thickens and grows upstream for increasingangle of attack. The development is as expected very similar to the one predictedby the Spalart Allmaras turbulence model. The difference in observed maximum


velocity between the Spalart Allmaras results (94.1 m/s for α=20◦) and k-ω SST(88 m/s for α=16◦) might be because the simulations for α=18 and 20◦ for thelatter turbulence model were only convergent using 1st order discretization whileall simulations for the clean airfoil using Spalart Allmaras converged with 2ndorder schemes. The maximum velocity for the Spalart Allmaras model at α=16◦

was 85.8 m/s.

Figure 4.7: Streamlines around the clean airfoil using k-ω SST. 1st row: α=10◦


(left) and α=20◦ (right). Values are in kg/s.

The streamlines in Figure 4.7 reveal trailing edge separation with the vortex mov-ing upstream for increasing angle of attack. This development is very much alike


the Spalart Allmaras computations until α=18 and 20◦ where the k-ω SST showsmore severe separation. Again, this might be because of the difference in dis-cretization schemes.

Figure 4.8 depicts the streamlines in the trailing edge area from α=8◦ were thesestart to release from the suction side of the airfoil.

Figure 4.8: Streamlines around the trailing edge of the clean airfoil using k-ω SST.1st row: α=8◦ (left) and α=12◦ (right), 2nd row: α=14◦ (left) and α=16◦ (right),3rd row: α=18◦ (left) and α=20◦ (right). Values are in kg/s.

Here the development of the vortex at the trailing edge is clearly seen. Theboundary layer separates and a vortex develops. The recirculation zone movesupstream and another vortex forms at the trailing edge.


The CP distribution along the airfoil is plotted in Figure 4.9 together with theSpalart Allmaras results for comparison.

It is seen that the curves of the pressure coefficient are identical except for thehighest angle of attack. For α=20◦ the pressure increase in the front zone on thesuction side is quite dramatic compared to the Spalart Allmaras results.

The force and moment polars are plotted in Figures 4.10 - 4.11.

The polars for the clean airfoil simulated with Spalart Allmaras and XFOIL aswell as the experimental results from (Abbott & Von Doenhoff 1959) are includedfor easier comparison.

CL generally agrees well with the compared results except for α=18-20◦. Maxi-mum lift is obtained for α=14◦ with a value of 1.33.

Also CD roughly coincide with the Spalart Allmaras except for α=18-20◦ wherea sharp rise is observed. This corresponds well with the larger separation area atthe trailing edge for these angles of attack.

The moment coefficient is similar to the Spalart Allmaras predictions althoughthe values are generally higher for the k-ω SST model. Again, at α=18-20◦ thevalues drop significantly.

Most likely the discrepancies between the Spalart Allmaras and k-ω SST resultsfor the clean airfoil are due to the 1st order discretization schemes utilized for thelatter model at α=18 and 20◦.


Figure 4.9: Pressure coefficient distribution along the airfoil. Simulated resultsfor the clean airfoil at selected angles of attack using Spalart Allmaras turbulencemodel (top) and k-ω SST (bottom).


Figure 4.10: Lift coefficient as function of the angle of attack. S.A. denotes SpalartAllmaras while SST denotes k-ω SST turbulence model.

Figure 4.11: Drag (left) and moment (right) coefficients as functions of the angleof attack. S.A. denotes Spalart Allmaras while SST denotes k-ω SST turbulencemodel.


4.1.2 Ice Case A

Figures 4.12 - 4.13 depict the velocity contours and streamlines, respectively.

The velocity contours in Figure 4.12 show the flow development from α=0◦ toα=20◦ with only α=2◦ left out due to layout reasons. The scale of all plots isfixed and have a maximum value of 65.9 m/s obtained for α=12◦. From aroundα=4◦ a low velocity area is developing from the leading edge and downstreamwhile a separation bubble over the ice protrusion starts building up from α=6◦.Up to approximately α=14◦ the leading edge bubble reattaches to the suctionside of the airfoil and hereafter this merges with the upstream growing trailingedge separation area. For increased angles of attack the low velocity area growssteadily.

The flow pattern is also shown using a streamline plot in Figure 4.13. Here theleading edge separation bubble as well as the course of the trailing edge separationis clearly seen. Furthermore it is observed how the second trailing edge separationbubble develops as the first one moves upstream along the upper airfoil surface.This happens around α=12◦ and is similar to the clean airfoil case described aboveexcept for the fact that it takes place at a lower angle of attack. At α=16◦ a rapidgrowth in the separated area behind the protrusion is observed. Comparing thecourse of the trailing edge separation with the clean airfoil it is evident that the iceaccretion changes the flow downstream and results in earlier and more pronouncedtrailing edge separation.

In order to follow the development of the important flow around the ice protrusionthree zoomed streamline plots of the leading edge area are presented in Figure 4.14.

At α=6◦ a separation bubble has established on the suction side of the ice accre-tion. At α=10◦ the bubble has thickened and grows downstream until it mergeswith the trailing edge vortex at around α=14◦.


Figure 4.12: Velocity contours for ice case A. 1st row: α=0◦ (left) and α=4◦

(right), 2nd row: α=6◦ (left) and α=8◦ (right), 3rd row: α=10◦ (left) and α=12◦

(right), 4th row: α=14◦ (left) and α=16◦ (right), 5th row: α=18◦ (left) and α=20◦

(right). Values are in m/s.


Figure 4.13: Streamlines for ice case A. 1st row: α=0◦ (left) and α=4◦ (right), 2ndrow: α=6◦ (left) and α=8◦ (right), 3rd row: α=10◦ (left) and α=12◦ (right), 4throw: α=14◦ (left) and α=16◦ (right), 5th row: α=18◦ (left) and α=20◦ (right).Values are in kg/s.


Figure 4.14: Streamlines around the leading edge and ice protrusion for ice caseA. Top: α=6◦, Middle: α=10◦, Bottom: α=14◦. Values are in kg/s.


The pressure coefficient distribution along the airfoil and ice protrusion is plottedin Figure 4.15.

Figure 4.15: Pressure coefficient distribution along the airfoil. Simulated resultsfor selected angles of attack for ice A.

It is clearly seen that the ice accretion disturbs the flow and results in pressurefluctuations especially visible immediately after the small bump located aroundx=0, cf. Figure 3.2, and at the accretion limit. In general the suction side pres-sure curves are increasing more rapidly and the suction/pressure side differenceis smaller compared to the clean case presented in Figure 4.3. This is true forpractically all angles of attack at all positions along the airfoil. For smaller an-gles of attack the pressure recovers and a favourable pressure gradient is observeddownstream of the accretion limit while this is not the case for higher angles ofattack. The strong adverse pressure gradient for α=4◦ results in the separatingvortex at the leading edge.

The force and moment polars are shown in Figures 4.16 - 4.17.


The results for the clean airfoil simulated with the Spalart Allmaras turbulencemodel are included in the plots for better comparison.

It is evident that the ice A lift coefficient for virtually all angles of attack is lowerthan for the clean airfoil due to the early leading edge separation and the moresevere trailing edge vortices which developed at lower angles of attack than forthe clean airfoil. The maximum CL of 1.02 is reached already at approximatelyα=10◦ and hereafter the airfoil stalls and the lift decreases and stagnates. This isno surprise bearing Figures 4.12 - 4.14 in mind.

The drag coefficient is also for ice A increasing with angle of attack and thishappens significantly faster than for the clean airfoil. The drag increase is a resultof the flow separation and the vortices’ influence on the pressure drag.

The moment coefficient increases rapidly and reaches positive values (nose turnedup) until α=12◦. Hereafter the values decrease and reaches the level of the cleanairfoil moment for the largest angles of attack.


4.1.3 Ice Case B

Velocity contours are seen in Figure 4.18.

Note that every second angle of attack has been omitted in Figure 4.18 and thatthe scale of the plots is fixed with a maximum value of 56.8 m/s which occursfor α=8◦. The velocity contours show areas of very low velocity behind the iceprotrusion from α=0◦ and at the trailing edge from approximately α=4◦. Withincreasing angle of attack the latter area thickens and moves upstream as observedfor the previous cases but this development happens faster for ice B. For instancethe trailing edge separation bubble has fully merged with the leading edge lowvelocity area around α=12◦ while this only started to happen at α=14◦ for ice A.

Figure 4.19 depicts the streamlines around the airfoil starting from α=6◦.

The streamlines show the development of the vortices at leading end trailing edge.Focusing on the trailing edge separation this happens sooner and more pronouncedfor ice B when comparing the individual angle of attack plots with the ones forthe clean airfoil and ice case A. The development of the trailing edge vortices isquite similar in appearance but comparing size and shape qualitatively it is seenthat ice B leads by at least 2◦ compared to ice A and by at least 6◦ comparedto the trailing edge development for the clean airfoil. By ”leads” is meant thata roughly similar trailing edge vortex situation is observed for the clean airfoil ate.g. α=16◦, while this same situation is seen for ice A at approximately α=12◦

and for ice B at α=10◦.

Figure 4.20 focuses on the leading edge separation by depicting streamlines in azoomed area for α=0-12◦.

It is evident that a separation bubble establishes behing the protrusion hornsalready for α=0◦. The vortex reattaches to the airfoil and does not merge withthe trailing edge vortex until approximately α=10◦. At α=12◦ the flow is obviouslyfully separated which was also seen in Figure 4.19. For increasing angle of attackthe vortex on the suction side of the airfoil grows downstream while the oppositeis seen for the pressure side leading edge vortex.


Figure 4.18: Velocity contours for ice case B. 1st row: α=0◦ (left) and α=4◦


(right). Values are in m/s.


Figure 4.19: Streamlines for ice case B. 1st row: α=6◦ (left) and α=8◦ (right), 2ndrow: α=10◦ (left) and α=12◦ (right), 3rd row: α=14◦ (left) and α=16◦ (right),4th row: α=18◦ (left) and α=20◦ (right). Values are in m/s.


Figure 4.20: Streamlines around the leading edge and ice protrusion for ice caseB. 1st row: α=0◦ (left) and α=2◦ (right), 2nd row: α=4◦ (left) and α=8◦ (right),3rd row: α=10◦ (left) and α=12◦ (right). Values are in m/s.


A plot of the CP distribution along the airfoil and ice accretion is seen in Fig-ure 4.21.

Figure 4.21: Pressure coefficient distribution along the airfoil. Simulated resultsfor selected angles of attack for ice B.

The flow is clearly disturbed by the protrusion horns and the pressure gradient isadverse on the suction side downstream of the ice accretion except for α=0 and4◦ which exhibit a favourable pressure gradient from approximately 10 to 30%downstream position. In general the difference between suction and pressure sideis smaller compared to the clean airfoil distribution.

The force and moment coefficients are plotted and presented in Figures 4.22 - 4.23with the results for the Spalart Allmaras simulated clean airfoil as well as ice caseA.


It is seen that the lift coefficient is generally considerably lower than both the cleanairfoil and ice case A. CL increases with angle of attack until α=8◦ whereafterthere is a decrease followed by another increase. The maximum value of CL is0.83. The course of the curve with the lower angle of attack for maximum lift andthe value for maximum lift corresponds well with the flow development describedand compared to the clean airfoil and ice A above. The horn-like protrusion shapeseverely affects the flow and thus the aerodynamic properties of the airfoil.

The drag coefficient is higher than both the clean airfoil and ice A for all anglesof attack. This comes as no surprise since the flow separation significantly affectsthe pressure drag.

The moment coefficient displays a similar course as for ice case A with an increasein CM for the lower half of angle of attack followed by a decrease for the largesthalf or so. The CM values are generally lower than for ice A and higher than forthe clean airfoil for the first half of the angle of attack interval while for the lasthalf CM is lower than for the clean airfoil.


4.1.4 Ice Case C

Figures 4.24 - 4.25 depict the velocity contours and streamlines for ice case C,respectively.

The velocity contours in Figure 4.24 have a fixed scale with 65.5 m/s as themaximum value obtained for α=12◦.

From approximately α=6◦ a low velocity area is developing over the ice accretion.At the same time a low velocity area near the trailing edge starts being visible.Both areas grow with increasing angle of attack. Up to approximately α=14◦

the leading edge bubble reattaches to the suction side of the airfoil and hereafterthis merges with the upstream growing trailing edge separation area. The flowdevelopment is very similar if not completely identical to ice case A.

Figure 4.25 shows the leading edge separation bubble as well as the course ofthe trailing edge separation. It is observed how a second trailing edge separationbubble develops as the first one moves upstream along the upper airfoil surface,approximately at α=12◦. At α=14◦ the leading and trailing edge vortices mergeand the flow is fully separated. Again it should be noted that the development isalmost identical to ice A.

Zoomed streamline plots of the leading edge area for α=4-14◦ are presented inFigure 4.26.

At α=6◦ a separation bubble has been established on the suction side of the ice ac-cretion. For increasing angles of attack the vortex thickens and grows downstreamuntil it merges with the trailing edge vortex at approximately α=14◦.

It is quite clear how the flow is identical to case A for each individual angle ofattack. The obvious reason is that the roughness height used for the ice accretionin case C has been too small for having a noticeable effect on the flow. Theconsideration for the grid density in the immediate vicinity of the surfaces thusconflicted with a desired investigation of the effect of surface roughness.

The pressure coefficient distribution along the airfoil and ice protrusion is plottedin Figure 4.27 together with the results for ice A.


Figure 4.24: Velocity contours for ice case C. 1st row: α=0◦ (left) and α=6◦


(right), 4th row: α=16◦ (left) and α=20◦ (right). Values are in m/s.


Figure 4.25: Streamlines for ice case C. 1st row: α=6◦ (left) and α=8◦ (right), 2ndrow: α=10◦ (left) and α=12◦ (right), 3rd row: α=14◦ (left) and α=16◦ (right),4th row: α=18◦ (left) and α=20◦ (right). Values are in kg/s.


Figure 4.26: Streamlines around the leading edge and ice protrusion for ice caseC. 1st row: α=4◦ (left) and α=6◦ (right), 2nd row: α=8◦ (left) and α=10◦ (right),3rd row: α=12◦ (left) and α=14◦ (right). Values are in kg/s.


Figure 4.27: Pressure coefficient distribution along the airfoil. Simulated resultsfor selected angles of attack for ice A (top) and C (bottom).


In Figure 4.27 the results for ice A are reproduced for easier comparison to ice caseC. Again it is obvious that the results for ice case A and C are almost identicalwith only very small discrepancies. If nothing else, case C serves as validation ofthe simulation reproducibility of ice A. Because of the similarity between the twocases the CP distribution will not be commented further.

The force and moment polars are shown in Figures 4.28 - 4.29.

The results for the clean airfoil simulated with the Spalart Allmaras turbulencemodel, ice case A and B are included in the plots for better comparison. It isevident that the ice C lift coefficient for all angles of attack is spot on coincidentwith ice A. This is also true for both the drag and moment coefficient. The ap-pearance of the polars or comparisons to the clean airfoil or ice case B is thereforenot commented further and the reader is referred to Section 4.1.2 for a deeperdiscussion of the results.


4.1.5 Blowing Surface

Velocity contours for the airfoil with holes and air jets on the leading edge arepresented in Figure 4.30.

Figure 4.30: Velocity contours for the blowing surface. 1st row: α=0◦ (left) andα=8◦ (right), 2nd row: α=14◦ (left) and α=16◦ (right), 3rd row: α=18◦ (left) andα=20◦ (right). Values are in m/s.

The velocity scale is fixed for all plots and have a maximum value of 71.2 m/swhich was observed for α=16◦. At α=8◦ a low velocity area is building up over thetrailing edge. For increasing angle of attack this grows upstream and at α=20◦

the low velocity area spans the entire suction side from trailing to leading edge.


The development is similar to the clean airfoil case but the blowing surface isahead by approximately 2◦.

The streamlines around the blowing surface airfoil are shown in Figure 4.31.

Figure 4.31: Streamlines for the blowing surface. 1st row: α=10◦ (left) and α=12◦


(right). Values are in kg/s.

It is observed how the trailing edge separation vortex establishes and is clearlyfixed at α=14◦ where the second vortex starts forming downstream. At α=20◦

the flow is fully separated. The separation is thus more severe than for the cleanairfoil.


CP is depicted with the clean airfoil as comparison in Figure 4.32

The curves are very similar up to α=8◦ and hereafter the CP values on the suctionside of the blowing surface are lower than the clean airfoil. It is evident that thejets disturb the flow and cause a severe adverse pressure gradient near the leadingedge for medium to large angles of attack.

Figures 4.33 - 4.34 show the force and moment coefficient polars.

The polars for the clean airfoil as well as ice A and B are included in order to seehow severe the reduction/increase caused by the jets is compared to these cases.

The lift coefficient increases with angle of attack until α=12◦ where it reachesthe maximum value of 1.17. Hereafter the airfoil stalls. In general the values arelower than the clean airfoil but higher than the ice cases.

Drag is higher than for the clean airfoil due to the larger separation vortices butstill displays lower values than the ice cases. The moment coefficient is rather sim-ilar to the clean airfoil except for the largest angles of attack where this decreases,i.e. turns the airfoil more nose down.


Figure 4.32: Pressure coefficient distribution along the airfoil. Simulated resultsfor selected angles of attack for the clean airfoil (top) and blowing surface (bot-tom).


In order to see how the warmer air of the jets distributes along the airfoil a seriesof temperature contour plots are presented in Figures 4.35 - 4.36.

The plots are contours of static temperature and the scale is fixed between -15 ◦C(ambient air, airfoil surfaces) and 4 ◦C (jet air) for all plots.

Figure 4.35 shows the development in terms of temperature. It is seen that thewarmer air reaches far downstream and is attached to the airfoil surface untilα=20◦ where the fully separated flow tears the boundary layer away. Note alsohow the layer of warmer air over the surface thickens for increased angle of attack.This is due to the expansion of the boundary layer.

When zooming further in on the leading edge in Figure 4.36 one is able to followthe development of the area just in front and downstream of the holes. The plotis, just like all plots presented this way, taken for the exact same zoom intensityand therefore shows the exact same location of the airfoil. The arrows indicatethe position of the three holes.

It it observed that the area of warmer colours (red-yellowish) just in front of theholes is actually thicker for low angles of attack and that this moves downstreamfrom the injection locations. A bit downstream the whole temperature area thick-ens for increasing angle of attack though.

The results indicate that the overall method of an anti-icing system like the pre-sented could work as intented but that it is necessary to change the numbers andposition of holes as well as velocity and temperature of the injected air in order tofind the optimal configuration. When using the given parameters for these simu-lations a reduction in e.g. lift is observed compared to the clean airfoil predictionsbut it should also be noted that the performance of the airfoil is better than thesimulated ice cases.


Figure 4.35: Contours of static temperature for the blowing surface for α=0◦

(top), α=12◦ (middle) and α=20◦ (bottom). Values are in Kelvin.


Figure 4.36: Contours of static temperature for a zoom around the leading edgeholes on the blowing surface for α=0◦ (top), α=12◦ (middle) and α=20◦ (bottom).Values are in Kelvin.

Chapter 5

Conclusion

A NACA63418 airfoil has been simulated using CFD with and without ice accre-tions on the leading edge. For the clean airfoil trailing edge separation is observedfrom approximately α=12◦. The pressure coefficient distribution and lift coeffi-cient agree brilliantly with XFOIL and experimental values when compared. Amaximum CL of 1.33 is reached for α=14◦. Drag is overpredicted by the CFD sim-ulations compared to both XFOIL and the experimental results while the momentcoefficient agrees well with the latter for α ≤10◦.

Ice case A consists of a leading edge ice protrusion roughly following the airfoilshape and extending around 10% of the original chord in upstream direction. Theprotrusion clearly influences the flow and results in a separation bubble buildingup over the ice on the suction side of the airfoil from α=6◦. The vortex growsdownstream with increasing angle of attack and merges with the trailing edgeseparation at α=14◦. The trailing edge separation occurs at lower angle of attackcompared to the clean airfoil. CL increases with angle of attack until α=10◦ wherea maximum value of 1.02 is observed. The lift coefficient is generally lower thanfor the clean airfoil at all angles of attack. Drag is increased compared to the cleanairfoil due to the more severe separation resulting in increased pressure drag.

Ice case B is a less streamlined protrusion with two horn-like structures extendingapproximately 1% of the original chord. Separation bubbles are observed fromα=0◦ behind the horns. The vortices reattach to the airfoil surface up to α=10◦

where the suction side leading edge vortex merges with the trailing edge separa-tion. Again the trailing edge separation occurs at lower angles of attack comparedto the clean airfoil as well as to ice case A. The lift coefficient is generally lowerthan both the clean airfoil and ice A and reaches the maximum value of 0.83 forα=8◦. Drag is increased further compared to ice A. The protrusion of ice case Baffects the flow more than ice case A.

The last simulated ice protrusion, case C, has a shape identical to case A butis simulated with a surface roughness of the ice. The flow development and the

89

CHAPTER 5. CONCLUSION 90

results in terms of CP , CL, CD and CM are identical to ice A. Flow discrepanciesdue to the surface roughness are not captured by the simulation model for theused roughness height of 5·10−6m.

Simulations of a clean airfoil with three holes in the leading edge, through which19 ◦C warmer air relative to the ambient air and airfoil surfaces is blown with avelocity of 3 m/s, reveal that the warm air distributes relatively far downstreamalong the suction side of the airfoil. The injection of the air affects the flow andreduces the lift coefficient compared to the clean airfoil. CL reaches its maximumvalue of 1.17 for α=12◦ and drag is increased for all angles of attack comparedto the clean airfoil. The aerodynamic properties are affected less than for thesimulated ice cases.

Chapter 6

Perspectives and Future Work

The results presented in this report will hopefully make the producers of windturbines consider how much the accretion of ice can effect the aerodynamic prop-erties of the blades. And hereby are the subjects of increased structural loads orsafety issues if ice is being shed from the blades not even being addressed.

Owners and operators of wind turbines will have great economic interest in theinfluence on the power production. (Jasinski et al. 1997) report performancelosses up to 20% for ice protrusions less severe than the ones investigated in thepresent work. (Seifert & Richert 1997) calculate annual energy production (AEP)losses of same magnitude for an accretion resembling ice shape A in this report.The author has in a previous report done a similar analysis as e.g. (Seifert &Richert 1997) and obtained a power curve for an iced blade through a BEM code.With different assumptions regarding weather and site conditions a reduction inthe AEP of 10-15% was estimated.

Regarding some possible future work it would be obvious to extend the performedanalysis to a wide range of ice shapes in order to determine what types of accretionshapes are truly severe for the aerodynamic properties.

It could also be interesting to test just a couple of different airfoils to see whetherthe exact shape plays a role or not. Are any airfoils performing better than othersin terms of mitigating ice accretion? The theory presented in Section 2.3 predictedthat the shape is not important and that instead the size of the airfoil relative tothe droplets was the determining factor for the accretion.

The simulations of the blowing surface should be regarded as preliminary workand might interest developers of wind turbine blades. A deeper parametric studywhere the position, shape and size of the holes and the velocity and temperatureof the jets is needed before one can assess the perspectives of such an anti-icingsystem. The ultimate goal would be a fail-safe, low cost anti-icing system whicheliminated the self power consumption and did not affect the aerodynamics and

91

CHAPTER 6. PERSPECTIVES AND FUTURE WORK 92

energy output of the turbine.

A validation of the presented results in terms of wind tunnel tests would alsobe a relevant possible continuation of the project work. Does the flow in anexperimental setup behave as predicted by the results of the numerical code? Thecomparison between experimental and simulated results might lead to some finetuning of the model.

Finally it would be of great interest to develop the CFD model into a rotatingsystem in 3D and thus further tailor the results for use within the wind turbinecommunity.

Bibliography

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S.F. Ackley and M.K. Templeton (1979)Computer Modeling of Atmospheric Ice AccretionCRREL REPORT 1979 79.

H.E. Addy, M.G. Potapczuk and D.W. Sheldon (1997)Modern Airfoil Ice Accretions35th Aerospace Sciences Meeting & Exhibit, January 6-10, 1997, Reno,Nevada.

J.D. Anderson, JR. (1995)Computational Fluid Dynamics. The Basics with ApplicationsMcGraw-Hill Education.

K. Arnold, G. Tetzlaff and A. Raabe (1997)Modeling of ice accretion on a non-rotating cylinderMeteorol. Zeitschrift, N.F. 6, 120-129 (Juni 1997).

C. Bak, P. Fuglsang, N.N. Sørensen, H.A. Madsen, W.Z. Shen and J.N. Sørensen(1999)Airfoil Characteristics for Wind TurbinesRisø-R-1065(EN), Risø National Laboratory, Roskilde, March 1999.

L. Battisti (2006)Class III - Basics on Icing For Wind TurbinesLecture slides from course 41326 Wind Turbine Ice Prevention Systems Se-lection and Design. Technical University of Denmark, June 2007.

L. Battisti (2006)Class IV - Ice Formation on Wind Turbines (Part One)Lecture slides from course 41326 Wind Turbine Ice Prevention Systems Se-lection and Design. Technical University of Denmark, June 2007.

93

L. Battisti (2007)Class VII - Icing Mitigation TechnologyLecture slides from course 41326 Wind Turbine Ice Prevention Systems Se-lection and Design. Technical University of Denmark, June 2007.

J.J. Bertin and M.L. Smith (1998)Aerodynamics For EngineersThird Edition, Prentice-Hall International, Inc.

X. Chi, B. Zhu, T.I-P. Shih, H.E. Addy and Y.K. Choo (2004)CFD Analysis of the Aerodynamics of a Business-Jet Airfoil with Leading-Edge Ice Accretion42nd Aerospace Sciences Meeting and Exhibit, January 5-8, 2004, Reno,Nevada.

J. Chung, Y. Choo, A. Reehorst, M. Potapzcuk and J. Slater (1999)Navier-Stokes Analysis of the Flowfield Characteristics of an Ice Contami-nated Aircraft Wing37th Aerospace Sciences Meeting and Exhibit, January 11-14, 1999, Reno,Nevada.

J.J. Chung and H.E. Addy, Jr. (2000)A Numerical Evaluation of Icing effects on a Natural Laminar Flow AirfoilNASA TM-2000-209775, January 2000.

S.G. Cober, G.A. Isaaq and J.W. Strapp (2001)Characterization of Aircraft Icing Environments that Include SupercooledLarge DropletsJournal of Applied Meteorology, American Meteorological Society 2001.

M. Drela and H. Youngren 2001XFOIL 6.9 User PrimerNovember 2001.

E. Ferrer and X. Munduate (2007)Wind turbine blade tip comparison using CFDJournal of Physics: Conference Series 75 (2007) 012005.

J.H. Ferziger and M. Peric (2002)Computational Methods for Fluid DynamicsThird Edition, Springer.

S. Fikke, G. Ronsten, A. Heimo, S. Kunz, M. Ostrozlik, P.-E. Persson, J. Sabata,B. Wareing, B. Wichura, J. Chum, T. Laakso, K. Santti and L. Makkonen(2006)

COST 727: Atmosperic Icing on Structures. Measurements and Data Collec-tion on Icing: State of the Art.Publication of MeteoSwiss, 75, 110 pp. 2006.

Fluent 2006User Manual for Fluent version 6.3Fluent Inc. September 2006.

R.W. Fox, A.T. McDonald and P.J. Pritchard (2004)Introduction to Fluid MechanicsSixth Edition, Wiley.

M.O.L. Hansen (2000)Aerodynamics of Wind TurbinesJames & James.

G.A. Isaac, S.G. Cober, J.W. Strapp, A.V. Korolev, A. Tremblay and D.L. Mar-cotte (2001)Recent Canadian Research on Aircraft In-Flight IcingCanadian Aeronautics and Space Journal, Vol. 47, No. 3, September 2001.

W.J. Jasinski, S.C. Noe, M.S. Selig and M.B. Bragg (1997)Wind turbine performance under icing conditionsAIAA, Aerospace Sciences Meeting and Exhibit, 35th, Reno, Nevada, Jan.6-9, 1997.

J. Katz and A. Plotkin (2001)Low-Speed AerodynamicsSecond Edition, Cambridge University Press.

S.M. Klausmeyer and J.C. Lin (1997)Comparative Results From a CFD Challenge Over a 2D Three-Element High-Lift AirfoilNASA Technical Memorandum 112858, May 1997.

O.J. Kwon and L.N. Sankar (1997)Numerical Simulation of the Flow About a Swept Wing With Leading-EdgeIce AccretionsComputers & Fluids Vol. 26, No. 2, pp. 183-192, 1997.

I. Langmuir and K.B. Blodgett (1946)A Mathematical Investigation of Water Droplet TrajectoriesArmy Air Forces technical Report, 1946.

L. Makkonen (2000)Models for the growth of rime, glaze, icicles and wet snow on structuresPhil. Trans. R. Soc. Lond. A (2000) 358, 2913-2939.

L. Makkonen, T. Laakso, M. Marjaniemi and K.J. Finstad (2001)Modelling and prevention of ice accretion on wind turbinesWind Engineering Volume 25, No. 1, 2001.

P. McComber and G. Touzot (1981)Calculation of the Impingement of Cloud Droplets in a Cylinder by the Finite-Element MethodJournal of the Atmospheric Sciences, Volume 38, May 1981.

K.E. Meyer (2004)Introduction to Potential FlowsLecture note from course 41323 Advanced Fluid Mechanics. Technical Uni-versity of Denmark, Spring 2007.

G. Poots and G.G. Rodgers (1976)The Icing of a CableJ. Inst. Maths Applied (1976) 18, 203-217.

M.G. Potapczuk and B.M. Berkowitz (1989)An Experimental Investigation of Multi-Element Airfoil ICe Accretion andResulting Performance DegredationAIAA, Aerospace Sciences Meeting and Exhibit, 27th, Reno, Nevada, Jan.9-12, 1989.

H. Schlichting and K. Gersten (2003)Boundary Layer Theory8th Revised and Enlarged Edition, Springer.

H. Seifert and F. Richert (1997)Aerodynamics of Iced Airfoils and Their Influence on Loads and Power Pro-ductionEuropean Wind Energy Conference, October 1997, Dublin Castle, Ireland.

J. Shin, B. Berkowitz, H.H. Chen and T. Cebeci (1994)Prediction of Ice Shapes and Their Effect on Airfoil DragJournal of Aircraft, Vol. 31, No. 2, March-April 1994.

H.K. Versteeg and W. Malalasekera (1995)An introduction to Computational Fluid Dynamics. The Finite VolumeMethodLongman Scientific & Technical.

F.M. White (2006)Viscous Fluid FlowThird Edition, McGraw-Hill Education.

BIBLIOGRAPHY 97

W.B. Wright (2002)User Manual for the NASA Glenn Ice Acccretion Code LEWICE Version2.2.2NASA/CR-2002-211793, August 2002.

W.B. Wright and J. Chung (2000)Correlation Between geometric Similarity of Ice Shapes and the ResultingAerodynamic Performance Degredation - A Preliminary Investigation UsingWIND38th Aerospace Sciences Meeting & Exhibit, January 10-13, 2000, Reno,Nevada.

Z. Zhu, X. Wang, J. Liu and Z. Liu (2007)Comparison of predicting drag methods using computational fluid dynamicsin 2d/3d viscous flowScience in China Series E: Technological Sciences, Vol. 50, No. 5, 534-549,Oct. 2007.

Appendices

Appendix A - Calculations

This appendix contains information and formulas regarding smaller calculationsperformed during the project.

Calculation of First Cell Height

Determination of the cell height of the first cell layer, y, in the computational gridis done by Eqs. (6.1) - (6.4) according to (Fluent Manual 2006) and (White 2006).

y =Y + ·ν

v∗(6.1)

v∗ =

(τw

ρ

)1/2

= V ·√

Cf/2 (6.2)

Cf/2 = 0.037 ·Re−1/5c (6.3)

Rec =V c

ν(6.4)

• Y +: Dimensionless wall coordinate, set to a value of 1

• ν: Kinematic viscosity of air, set to 1.5·10−5 m2/s

• v∗: Wall-friction velocity

• τw: Wall-shear stress

I

• V : Freestream velocity, set to 33 m/s

• Cf : Skin-friction coefficient

• Rec: Reynolds number with respect to chord

• c: Chord, set to 1 m

With the given values a first cell height is calculated to y=1.01·10−5 m for aReynolds number of Rec=2.2·106.

Calculation of Flow Components

When changing the angle of attack Fluent needs the input given as flow compo-nents for x- and y-direction.

x− comp = cos(α · π

180

)(6.5)

y − comp = sin(α · π

180

)(6.6)

• α: Angle of attack in degrees

II

Appendix B - Matlab scripts

This appendix contains the various Matlab scripts used for the project.

Script for Plotting the Ice Shape

clear all; close all; clc

data=load(’final1.dat’);

airfoil=load(’NACA63418.dat’);

%param=load(’finaltime.dat’);

figure

plot(data(:,1),data(:,2),’r--’,’LineWidth’,2), hold on

%plot(param(:,1), param(:,2),’r’,’Linewidth’,2)

plot(airfoil(:,1),airfoil(:,2),’k--’,’LineWidth’,2)

legend(’Ice B’,’Airfoil’)

axis equal, %grid on

data=[data(:,1) data(:,2) zeros(length(data(:,1)),1)];

save(’profile-for-gambit.dat’,’data’,’-ascii’)

Script for Plotting the Polars


aoa=[0 2 4 6 8 10 12 14 16 18 20];

aoa1=[0 2 4 6 8 10];

aoa2=[0 2 4 6 8 10 12 14 16 18];

CLxfoil=[0.346 0.579 0.7744 0.9507 1.0862 1.1875 1.2699 1.3106...

1.3239 1.3226 1.3216];

CDxfoil=[0.00609 0.00634 0.00916 0.0118 0.01386 0.01804 0.02509...

0.02794 0.02835 0.02844 0.02857];

CMxfoil=[-0.081 -0.078 -0.074 -0.067 -0.052 -0.037 -0.024...

-0.022 -0.024 -0.025 -0.025];

CLexp=[0.32 0.56 0.78 1.03 1.2 1.3 1.39...

1.39 1.37 1.34 1.3];

CDexp=[0.006 0.0063 0.0069 0.0086 0.0137 0.018];

CMexp=[-0.075 -0.078 -0.08 -0.085 -0.085 -0.085 -0.085...

III

-0.0875 -0.1 -0.112];

CLcleanSA=[0.3145 0.54646 0.7449 0.9235 1.0972 1.208 1.3008...

1.33796 1.31 1.301 1.218];

CDcleanSA=[0.0116 0.01409 0.0178 0.0235 0.03086 0.04023 0.05116...

0.06419 0.083 0.0998 0.1264];

CMcleanSA=[-0.0716 -0.078438 -0.0799 -0.0804 -0.082644 -0.07768 -0.07436...

-0.06978 -0.0665 -0.0644 -0.0678];

CLcleanSST=[0.324 0.53 0.7225 0.9025 1.0737 1.205 1.33...

1.335 1.315 0.95 0.893];

CDcleanSST=[0.01 0.0123 0.0158 0.0209 0.0273 0.036 0.045...

0.058 0.075 0.176 0.22];

CMcleanSST=[-0.0735 -0.075 -0.075 -0.075 -0.0758 -0.074 -0.071...

-0.062 -0.058 -0.081 -0.094];

CLiceASA=[0.3045 0.5489 0.7027 0.8814 0.9723 1.0247 1.022...

0.958 0.8359 0.8534 0.8855];

CDiceASA=[0.01939 0.01741 0.02605 0.0318 0.0481 0.0707 0.0983...

0.1445 0.2288 0.2827 0.3337];

CMiceASA=[-0.06888 -0.062062 -0.0382 -0.021 0.0017 0.0167 0.0211...

0.0065 -0.0492 -0.0634 -0.0746];

CLiceBSA=[0.3015 0.482 0.636 0.758 0.829 0.808 0.654...

0.641 0.697 0.734 0.778];

CDiceBSA=[0.0195 0.0218 0.029 0.0418 0.061 0.0913 0.1661...

0.2114 0.2562 0.296 0.3385];

CMiceBSA=[-0.0698 -0.0633 -0.0562 -0.0493 -0.044 -0.0462 -0.084...

-0.1006 -0.1114 -0.119 -0.128];

CLiceCSA=[0.3081 0.536 0.7375 0.878 0.9877 1.0255 1.021...

0.935 0.8358 0.854 0.885];

CDiceCSA=[0.0188 0.0157 0.0203 0.0326 0.0483 0.0709 0.0988...

0.1554 0.2294 0.2842 0.3335];

CMiceCSA=[-0.0691 -0.0557 -0.0408 -0.0199 0.0019 0.0168 0.0207...

-0.0012 -0.0496 -0.064 -0.0745];

CLblow=[0.3255 0.529 0.7159 0.8804 1.032 1.138 1.1729...

1.1176 1.033 0.9269 0.7669];

CDblow=[0.0031 0.0072 0.015 0.0269 0.0398 0.0562 0.0756...

0.1028 0.137 0.1862 0.298];

CMblow=[-0.0731 -0.0748 -0.0756 -0.0754 -0.0737 -0.0706 -0.0662...

-0.0641 -0.0698 -0.0864 -0.126];

IV

figure

%plot(aoa,CLexp,’ko’), hold on

%plot(aoa,CLxfoil,’bo’)

plot(aoa, CLcleanSA,’ro’), hold on

%plot(aoa, CLcleanSST,’rd’)

plot(aoa, CLiceASA,’rv’)

plot(aoa, CLiceBSA,’rs’)

%plot(aoa, CLiceCSA,’r+’)

plot(aoa, CLblow,’go’)

legend(’Clean S.A.’,’Ice A S.A.’,’Ice B S.A.’,’Blowing S.A.’...

,’Location’,’NorthWest’)%’Abbott & Von Doenhoff’,’XFOIL’,’Ice A S.A.’,’Ice C S.A.’)

grid on

xlabel(’\alpha’), ylabel(’C_L’)

hold off

figure

%plot(aoa1,CDexp,’ko’), hold on

%plot(aoa,CDxfoil,’bo’)

plot(aoa, CDcleanSA,’ro’), hold on

%plot(aoa, CDcleanSST,’rd’)

plot(aoa, CDiceASA,’rv’)

plot(aoa, CDiceBSA,’rs’)

%plot(aoa, CDiceCSA,’r+’)

plot(aoa, CDblow,’go’)


,’Location’,’NorthWest’)%,’Abbott & Von Doenhoff’,’XFOIL’,’Ice A S.A.’,’Ice C S.A.’)

grid on

xlabel(’\alpha’), ylabel(’C_D’)

hold off

figure

%plot(aoa2,CMexp,’ko’), hold on

%plot(aoa,CMxfoil,’bo’)

plot(aoa, CMcleanSA,’ro’), hold on

%plot(aoa, CMcleanSST,’rd’)

plot(aoa, CMiceASA,’rv’)

plot(aoa, CMiceBSA,’rs’)

%plot(aoa, CMiceCSA,’r+’)

plot(aoa, CMblow,’go’)


,’Location’,’NorthWest’)%,’Abbott & Von Doenhoff’,’XFOIL’,’Ice A S.A.’,’Ice C S.A.’)

grid on

V

xlabel(’\alpha’), ylabel(’C_M’)

hold off

Script for Plotting the Grid Dependency


N=[33888 39832 48932 119592 154320]; %351880];

CL=[1.141 1.0213 0.9283 0.8435 0.843];

CD=[0.3025 0.2706 0.2577 0.2354 0.235];

CM=[-0.0805 -0.064 -0.0594 -0.0492 -0.049];

figure

plot(N,CL,’bo’)

grid on

xlabel(’Number of grid cells’), ylabel(’Lift coefficient’)

figure

plot(N,CD,’ro’), hold on

plot(N,CM,’ko’)

grid on

legend(’C_D’,’C_M’)

xlabel(’Number of grid cells’), ylabel(’Force coefficient’)

VI

Appendix C - The Numerical Ice Accretion Code

Lewice

This appendix serves as information on how the ice accretions for the project weredetermined and is not intended to be a part of the official Master’s Thesis report.It should therefore not be evaluated as a part of the written thesis but insteadtreated as a means of enlighting the supervisors and other ”first row” readers.

The Icing Branch at the NASA Glenn Research Center has developed a numericalcomputer code for determining the ice accretion onto airfoils. This work is donewith the intended use of atmospheric airplanes in mind.

Briefly explained the code works in three overall steps: calculation of the flow fieldand trajectories using a Douglas Hess-Smith 2D panel method, determination ofthe distribution of liquid water impinging the airfoil and finally an icing modelcalculates the ice growth. This procedure is repeated in time steps until thespecified simulation time is reached. The icing model is using the same principlesexplained in the Section 2.3 concerning ice accretion.

As input the code uses a text file with a listed specification of the different pa-rameters determining the ice growth, such as temperature, liquid water contentand droplet size and distribution, and the output consists of different data fileswith information of e.g. ice thickness, coordinate distribution, surface roughnessand thermodynamic balance for each time step plus total value. These outputsare plotted using Matlab with the original airfoil in the figures in the thesis andare also used as direct coordinate input to Gambit when constructing the grid forthe ice cases.

The reason for not including this information in the relevant sections in the reportis due to the fact that most NASA work is available only to US citizens, universitiesand non-profit organisations. Since there seems to be a general consensus in theicing literature that Lewice is the state-of-the-art ice accretion code the authordecided to go through unofficial sources in order to acquire a version of the code.

Further information about the Lewice code and the general topic of ice accretioncan be found at www.icebox.grc.nasa.gov where also the user manual, listed below,for the utilized code version can be downloaded.

W.B. Wright (2002)User Manual for the NASA Glenn Ice Accretion Code Lewice. Version 2.2.2.NASA/CR-2002-211793, August 2002.

VII

cfd simulations of an airfoil with leading edge ice accretion

Documents