investigation of 2d airfoils equipped with a trailing edge flaps msc in wind energy

Master Thesis

Investigation of 2D Airfoils equipped with a trailing

edge flaps

MSc in Wind EnergyTeodor Kaloyanov

October 7, 2011

Department of Mechanical Engineering

Author: Teodor KaloyanovSupervisors: Jens Sørensen and Robert MikkelsenTitle: Investigation of 2D Airfoils equipped with a trailing edge flapsDivision: Wind Energy Division

Technical University of DenmarkOctober 7, 2011

Abstract

Wind power is the most developed industry from the renewable energies presently.It has already established its place in the society and the market, thus it is pub-licly accepted and widely spread all over the world. Therefore the optimizationand further development within the field is crucial for the economic fusibility ofthe future wind power projects.

There are various aspects to be considered in order to optimize the overall impactof a wind turbines. Beyond all question the most important are power productionand lifetime. In this project have been investigated an idea for a device whichwill have a positive impact on those aspects. The project was inspired by thework of Peter Bjørn Andersen and his Ph.D. thesis ”Advanced Load Alleviationfor Wind Turbines using Adaptive Trailing Edge Flaps: Sensoring and Control.”[1]. His research has shown that using a moving trailing edge flaps on an windturbine blades, similar to those on the airplane wings can significantly reducethe aerodynamic loads and increase the life time of the turbine. The purpose ofthis thesis is to research further on that mater and give better inside to this newtechnique.

Contents

1 Introduction 1

2 Modeling 22.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22.2 OpenFOAM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22.3 Model Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32.4 Mesh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

2.4.1 Mesh selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42.4.2 Mesh generation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

2.5 Boundary conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82.6 Solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2.6.1 Finite Volume Schemes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92.6.2 Finite Volume Solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102.6.3 Solvers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102.6.4 Turbulence Model K-Omega SST . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112.6.5 Time control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

2.7 Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132.7.1 NACA0012 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142.7.2 NACA64318 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

3 Experiment 273.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273.2 Experimental setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273.3 Main components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

3.3.1 Airfoil . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283.3.2 Linear Motor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283.3.3 Rotational Motor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 303.3.4 DAQ unit and LabVIEW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 303.3.5 Pressure transducer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

3.4 Major Challenges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 323.4.1 Data acquisition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 323.4.2 Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

3.5 Uncertainty Assessment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 333.6 Test Cases and Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

4 Summary 38

A Turbulence Models 40

B Meshing 41

C OpenFOAM 51

D Experiment 54

i

List of Figures

2.1 Overview of OpenFOAM structure [2] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22.2 Basic structure of OpenFOAM program folders . . . . . . . . . . . . . . . . . . . . . . . . 32.3 Sketch of the model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32.4 C-mesh of NACA0012 airfoil, [9] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42.5 O-mesh of NACA0012 airfoil, [11] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52.6 Sketch of airfoil O-mesh for OpenFOAM . . . . . . . . . . . . . . . . . . . . . . . . . . . 52.7 Final mesh used for the simulations of NACA0012 airfoil, ParaV iew . . . . . . . . . . . . 82.8 Airfoil coordinates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132.9 Laminar simulations NACA0012, Pressure distribution, P , for Re = 1e2 and Re = 1e3 . . 152.10 Laminar simulations NACA0012, Boundary layer view in terms of velocity, U , for Re = 1e2

and Re = 1e3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162.11 Lift coefficient, cL over NACA0012, at Angle of Attack, AoA = −4 : 16 . . . . . . . . . . 172.12 Drag coefficient, cD over NACA0012, at Angle of Attack, AoA = −4 : 16 . . . . . . . . . 172.13 Lift-drag ratio, cL/cD over NACA0012, at Angle of Attack, AoA = −4 : 16 . . . . . . . . 172.14 Pressure distribution, Cp over NACA0012, for Reynolds number, Re = 1e6, and Angle of

Attack, AoA = 5, and Flap angle, flap = 0 . . . . . . . . . . . . . . . . . . . . . . . . . 192.15 Pressure distribution, Cp over NACA0012, for Reynolds number, Re = 1e6, and Angle of


Attack, AoA = 5, and Flap angle, flap = −5 . . . . . . . . . . . . . . . . . . . . . . . . 192.17 Pressure distribution, Cp over NACA0012, for Reynolds number, Re = 1e6, and Angle of



Attack, AoA = 5, and Flap angle, flap = −5 . . . . . . . . . . . . . . . . . . . . . . . . 202.20 Pressure distribution, Cp over NACA0012, for Reynolds number, Re = 1e6, and Angle of

Attack, AoA = 0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212.21 Pressure distribution, Cp over NACA0012, for Reynolds number, Re = 1e6, and Angle of


Attack, AoA = 0, and Flap angle, flap = 5 . . . . . . . . . . . . . . . . . . . . . . . . . 212.23 Forces coefficients from OpenFOAM simulations . . . . . . . . . . . . . . . . . . . . . . . 232.24 Pressure distribution, Cp over NACA64318, for Reynolds number, Re = 3e6, Free stream

velocity, AoA = 6 and AoA = 10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242.25 Pressure distribution, Cp over NACA64318, for Reynolds number, Re = 3e6, Free stream

velocity, AoA = 12 and AoA = 14 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 252.26 Pressure distribution, Cp over NACA64318, for Reynolds number, Re = 3e6, Free stream

velocity, AoA = 16 and AoA = 18 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

3.1 Experiment setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273.2 Pictures of NACA 63418 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283.3 Picture of the linear motor - LinMot . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293.4 Installation scheme of the linear motor [17] . . . . . . . . . . . . . . . . . . . . . . . . . . 293.5 Mac Motor connection scheme [20] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

ii

LIST OF FIGURES iii

3.6 Voltage generator control panel LabV IEW.vi (left), LabV IEW.vi for monitoring the con-trol signals (right) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

3.7 Pressure telemetry setup, [21] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 313.8 Pressure monitoring LabV IEW panel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 323.9 Location of the pressure tab on the surface of the NACA63418 airfoil . . . . . . . . . . . . 343.10 Pressure coefficient distribution on the airfoil surfaces for each pressure tab, Re = 3.1888e5 353.11 Pressure coefficient distribution comparison, Re = 3.1888e5, experiment flap position V =

2.0, OpenFOAM flap position 0[deg] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 363.12 Pressure coefficient distribution comparison corrected, Re = 3.1888e5, experiment flap

position V = 2.0, OpenFOAM flap position 0[deg] . . . . . . . . . . . . . . . . . . . . . . 373.13 Force coefficients comparison Experiment and OpenFOAM results . . . . . . . . . . . . 37

D.1 Airfoil flap motion sketch, by Clara Vette . . . . . . . . . . . . . . . . . . . . . . . . . . . 54D.2 Sketch of the central section with the pressure tabs, by Clara Vette . . . . . . . . . . . . . 54D.3 Linear motor specification [19] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

List of symbols

Vectors will be given in bold font, for example: U - Velocity vector. Dimensions are given in squarebrackets [] and [−] implies non-dimensionality. Some large or small numbers given will be given as usingexponential part, and are considered multiplied by 10 to the power of the value, e.g. 1e1 = 10

Ux x, velocity componentUy y, velocity componentRe Reynolds numberc Airfoil ChordAoA Angle of attackCp Pressure coefficientcL Lift coefficientcD Drag coefficientµ Dynamic viscosityν Kinematic viscosityρ Densityνt Turbulent viscosityκ Turbulent kinetic energyω Specific dissipation rate of turbulence kinetic energyI Turbulence intensityl Turbulent length scaley+ Dimensionless wall distanceUf Friction velocityg Ratio between the first and the last cell of an edge, of the block in a meshδs First cell of particular blockδe Last cell of particular blockrays Number of cells perpendicular to the airfoil surfaceglow Number of cells parallel to the airfoil surface

iv

Chapter 1

Introduction

The atmospheric boundary layer where the wind turbines are located is a highly turbulent environment.For this reason the blades and the other mechanical components constantly experience unsteady loadingsand therefore under fatigue loads. The engineers are trying to reduce this effect by controlling and opti-mizing different turbine elements. For instance, pitch control of the blades, tip brakes, vortex generators,use of special materials, etc. Among those only the pitch control is actually a real time control whichcan alter the aerodynamic properties of the turbine blades to take into account the changes in the windspeed. A pitch regulated turbine typically can achieve fatigue load reduction in the order of 20 to 30percent. However the new turbine blades are progressively becoming larger and larger and the wind flowaround them is not uniform, so dealing with the unsteady loads cannot be achieved with pitch controlall along. Thus the need of smart rotor blades with a local flow control is already widely discussed topicwithin the wind energy field.

The are various mechanisms which can be applied for local control of the flow around the turbine blade. Agood discussion of some classical boundary layer control devices is presented in ”Adaptive wing and flowcontrol technology” [5]. A relatively simple and efficient solution is the trailing edge movable flaps whichalters the camber of the airfoil and therefore changes its aerodynamic properties. Furthermore since thistechnology is widely used on aircraft applications, one can find research on the topic which dates from1930s. Thus there are numerous available sources of information and results from experiments and models.

Following this idea Peter Bjrn Andersen made his Phd dissertation [1] where he investigates the impactof an adaptive trailing edge flaps on the wind turbine blade similar to the flaps of airplane blade. Theauthor [1] argues that a blade with added trailing edge flaps significantly reduces the fatigue loads on theturbine. He concludes that attaching flaps on the wind turbine blades have significant influence on thewing aeroelastic stability. As a result, a single flap with a length of 10% the blade length based on thecontrol achieves up to 30% load reduction, and for three flaps up to 40%.

In addition this technology would provide much faster and cheaper capability of tracking optimum liftbecause the motion requires sufficiently less energy to move the flaps, rather than the whole wing. More-over the change in the pitch angle would change the flow over the whole blade, while the flaps alter theflow around a specific section of the blade.

In order to analyze the flow around a blade with moving flaps is important to know how the wind behaveswhen passing through an airfoil equipped with a movable trailing edge. Thus the purpose of this thesisis to give better inside on the flow around a section of the blade using the current state technology andsoftware. The investigation includes computational fluid dynamics (CFD) modeling via OpenFOAM ,and experiments in a wind tunnel laboratory. The CFD computations include turbulence modelingbecause of the high Reynolds number flows around the turbines.

1

Chapter 2

Modeling

2.1 Overview

In this chapter the model used for the CFD modeling is thoroughly explained. This includes shortdescription of the used software tools, along with the equations and the models which are involved in thecoding. The program used for the CFD analysis is OpenFOAM together with additional programmingand scripting on Fortran90, Shellscript andOctave used to generate the mesh file, control the simulationsand plot the results. The goal of the CFD model is to simulate the experiment conditions and to reproducecomparable data for open discussions.

2.2 OpenFOAM

OpenFOAM is an open source commercial CFD code written on C++. It was chosen for this particularcase because of its flexibility and accessibility. It consists of various embedded libraries which are acces-sible for review and modifications. The libraries consists of numerous mathematical models and CFDtools organized in directories. Furthermore the program runs under linux environment and it is free touse [2].

Figure 2.1: Overview of OpenFOAM structure [2]

In order to facilitate the reader with the content, the basics of the program are briefly explained. Figure2.1 presents the overall structure of OpenFOAM and figure 2.2 shows a block diagram of the OpenFOAMcase folder structure. The system directory is hosting the control tools, the finite volume schemes andthe finite volume solutions. The control tools are used to identify parameters as time step, simulationtime, creating time directors and sampling physical quantities. The constant directory contains the fileswhich define the mesh and the dimensional fluid properties as dynamic and kinematic viscosity, as well asthe setup of the turbulent models. Since the program requires an initial conditions (boundary conditions(BC)) for the major fluid parameters one have to specify the initial vectors and fields within the initialtime directory at start time. Then based on the control of the simulation are created new time directorieswhich contain the solutions for the same parameters for the requested time steps. There are various postprocessing utilities which can additionally calculate important parameters for each time directory afterthe simulation is finished.

2

CHAPTER 2. MODELING 3

CASE

System

Control Dictinary

Finite Volume

Schemes

Finite Volume

Solutions

Constant

Transport Properties

Polymesh

Block Mesh

Boundaries

Time

Directories

Initial and boundary

conditions

Sample Dictinary

Variable solutions for

each time step

Figure 2.2: Basic structure of OpenFOAM program folders

2.3 Model Description

Figure 2.3 shows a simple sketch of model - airfoil with a moving flap. The movable part is shaded indark gray at its initial position, while the lighter gray tip presents its position for a certain angle. Asproposed in [6] the trailing edge flaps accounts for 10% of the airfoil, where the trailing flap is modeledas a flexible part which bends its sides when it flaps. However in this particular model for simplificationthe flap motion will not provoke changes in its shape. In practice this effect depends on the mechanicaldesign of the airfoil as there are many different ways how a flaps can be attached to a wing. As positivedirection of the flap motion is consider clockwise rotation, e.g. the airfoil on the figure has been rotatedon flap angle of around minus ten degrees.

Ux

Uy

x

y

U

Figure 2.3: Sketch of the model

The airflow will be presented in terms of two vectorial components, Ux along the chord of the airfoil, andUy perpendicular to it. Thus the angle of attack will depend on the magnitude and direction of thoseterms. The purpose is to simulate a two dimensional flow at realistically high Reynolds numbers (Re)around an airfoil at different angles of attack, and different flap positions. The model will be first imple-mented for NACA0012 standard airfoil and compared with experimentally acquired data. Subsequently,simulations will be carried out for airfoil NACA-63418 used in the experiment, chapter 3.As a standard CFD modeling routine, all of the parameters will be in non-dimensional form. However,since OpenFOAM source code uses dimensional quantities, in order to insure consistency, all of theparameters will be assigned to a constant values of 1 or 0, except the kinematic viscosity, ν. This waythe Reynolds number will be controlled by changing only the viscosity of the fluid (equation 2.1).Thus the major parameters are given in table 2.1:


Table 2.1: Initial parameters, boundary conditions

Quantity Value DimensionFree stream velocity 1 [m/s]Airfoil chord, c 1 [m]Reference pressure 0 [N/m2]Kinematic viscosity variable [m2/s]

Re =Uc

ν=

1

ν(2.1)

2.4 Mesh

2.4.1 Mesh selection

One of the most important aspects when dealing with a CFD problem is the mesh. There are variousprograms which can generate mesh and which are compatible with OpenFOAM [2]. However the projectrequires a moving mesh in order to simulate the flow around a airfoil with a moving flap. This implies theneed for facilitation of a mesh which is easily modifiable even during simulations. OpenFOAM itself isequipped with a mesh generation tool for structured meshes called blockMesh [2]. Since this tool allowseasy mesh manipulations it is the best choice for this particular problem. A disadvantage is the fact thatone cannot monitor the creation of the mesh before completion. Once the mesh is generated it can bereviewed via Paraview, the program which is generally used for visual post processing for OpenFOAM .[2].

2.4.2 Mesh generation

There are various kinds of meshes which are used to simulate a flow around airfoil. Among those themost popular are the C-mesh, shown on figure 2.4, and O-mesh, presented on figure 2.5. Although theC-mesh it easier to produce and control, as can be seen from figure 2.4 it will not provide as accuratesolution as the O-mesh in the wake for different angles of attack. Since the O-mesh is not dependenton the flow direction, it is the preferred option. However in the case of the O-mesh, it is a challengeto supply meshing lines perpendicular to the surface of the airfoil close to the trailing and leading edge.Fortunately, the solvers like OpenFOAM can take into account non orthogonal edges, and can find thesame solution.

Figure 2.4: C-mesh of NACA0012 airfoil, [9]


Figure 2.5: O-mesh of NACA0012 airfoil, [11]

It uses three dimensional coordinate systems as all geometries are implemented in three dimensions. Thuswhen building a two dimensional mesh on of the dimension is an empty dimension, i.e. just an extruded2D mesh. This grid is composed by blocks and has several others features which defines it.

0

1 2

34

56

7 8

9

0

1

2

3

4

Figure 2.6: Sketch of airfoil O-mesh for OpenFOAM

• Vertexes - Labeled major points which define the blocks of the mesh

• Edges - A line which connects two vertexes, as it can take a selected shape. It is not recommendedto have cross section

• Blocks - The mesh have to be composed by the use of hexagon blocks. If needed they can becompressed to other shapes, but that’s not required for this project. Each hexagon is defined byselection of 8 vertex labels. The block are meshed individually as the user can selects the numberof cells in each direction of the block (x, y coordinates), as well as their cell expansion ration whichis defined as the ration between the last and the first cell.

• Patches - The sides of the blocks which are not neighboring each other have to be defined as patches.


Table 2.2: Mesh Major Points

Point DescriptionVertex 0 The x coordinate is found as the circle radius from the center, y is zeroVertex 1 The coordinates are calculated based on the required length of the arc between vertex 0 and 1Vertex 2 The coordinates are calculated based on the required length of the arc between vertex 1 and 2Vertex 3 The coordinates are calculated based on the required length of the arc between vertex 2 and 3Vertex 4 The coordinates are calculated based on the required length of the arc between vertex 0 and 4Vertex 5 The point of the airfoil coordinates with maximum thicknessVertex 6 Leading edge coordinatesVertex 7 The point of the airfoil coordinates with maximum thicknessVertex 8 Point from the airfoil for 90% of the airfoil chord, positive y directionVertex 9 Point from the airfoil for 90% of the airfoil chord, negative y direction

Those patches are used to define the boundaries of the mesh and therefore the boundary conditionsfor the fluid quantities.

Vertexes

Based on those parameters have been build a blockMeshDict file which generates airfoil O-mesh. Howeverthis tool requires careful bookkeeping in order to attain accuracy and consistency. Thus to control thesize of the mesh and to change the airfoil shape automatically, the use of additional programing isrecommended. The code is given in appendix B. A sketch of the mesh model is presented on figure 2.6.The vertexes are twenty overall given with small numbers from 0 to 9, as there are ten more in theextruded dimension z and the blocks are five marked as big numbers in gray circles. In order to define acircle and an airfoil inside the middle of it, the locations of the major points have been chosen in a waywhich assures consistency in the size of the neighboring cells. The circle center has the x coordinate ofthe airfoil maximum thickness, while y is zero. The leading edge of the airfoil has coordinates (0 0) andthe trailing edge (1 0) so the chord length is 1[m]. The coordinates of the airfoil have been taken fromthe UIUC Airfoil Coordinates Database [10]. The locations of points 1, 2, 3 and 4 has been calculated ina sense that the ration between lengths of the arcs they form and the corresponding section of the airfoilare the same for each block. This way is insured the consistency in the cells neighboring cell sizes. Thefunction used for the computation is given in the end of appendix B subroutine points. It computes therequired angle between the vertexes based on the distance between the major points of the airfoil andcalculates the coordinates of the points on the circle. The vertexes are summarized in table 2.2.

Edges

Consequently the edges are formed by calculating additional points and using the points of the airfoil.In order to create the shape of the airfoil is used polySpline tool, which connects requested points witha spline. The trailing edge is exception because at this last 10% region the airfoil surface is considered astraight line. Additionally in order to allow easy adjustments to the airfoil flap position the two points at90% chord are connected though a spline passing by the last two points of the trailing edge. Therefore theflap angle is controlled by the position of those two points in y direction. Moreover, by connecting thosetwo points with a spline it is ensured that even the small line between the last two points is a curvature.Creating a circle as a shape for the mesh is required in order to have better shaped mesh lines parallel tothe airfoil. The vertexes in table 2.2 have been already placed in such way so that they form a circle. Thenext step is to connect them using arcs by finding points on the same circle. This is implemented by thesame subroutine points, in appendix B, but instead it is using the half distance which finds a point onthe same circle between the two points. Then the edges which shaped the inner part of the blocks havebeen build in a way which ensures that the parallel mesh lines are perpendicular to the airfoil surface.This is implemented by connecting the point of the airfoil and the point of the circle with a spline whichcontains a point between them near the airfoil that makes the line perpendicular to its surface. Suchpoint is found by finding the angle between two points of the airfoil (vertex 9 for example, and the pointjust before it in the leading edge direction - equation 2.2). Then based on the selected distance to thepoint are calculated the coordinates (subroutine arcs appendix B). Table 2.3 presents a summery of the


Table 2.3: Mesh Edges

Edges (points) DescriptionEdge (0 1) An arc based on a middle pointEdge (1 2) An arc based on the southern point of the main circleEdge (2 3) An arc based on the eastern point of the main circleEdge (3 4) An arc based on the northern point of the main circleEdge (4 0) An arc based on a middle pointEdge (4 5) A spline which yields perpendicularity with both endsEdge (3 9) A spline which yields perpendicularity with both endsEdge (2 8) A spline which yields perpendicularity with both endsEdge (1 7) A spline which yields perpendicularity with both endsEdge (5 6) A spline composed from the airfoil coordinatesEdge (6 7) A spline composed from the airfoil coordinatesEdge (7 8) A spline composed from the airfoil coordinatesEdge (8 9) A spline composed from the airfoil coordinates

edges.

β = tan−1abs(y(pi)− y(pi−1)

abs(x(pi)− x(pi−1)(2.2)

Blocks

The blocks shape and position have been chosen in a way which implies consistency in the size of theneighboring cells. Since the grading ration and number of cells are the input parameters for meshing eachblock, those parameters can be select in way which yields consistency between the neighboring blocks.The mesh around the leading and trailing edge should be finner because of the high gradients of thevelocities and pressure in those regions. Since the meshing of each block depends on the number of cellsand the grading ration between the first and the last cell, one can derive the size of those cells using thelength of the meshing side and vice versa. This is implemented in a subroutine grading at appendix Bwhich compute the following equations using arithmetic progression, equation 2.3.

s =n

2(2δs+ (n− 1)d)(2.3)

Where s is the sum of progression, n is the number of terms, δs is the value of the first term, and dis the difference between two terms. Based on that one can derive the number of mesh cells and theirprogression ratio, g.

g =δs

δe(2.4a)

S =l

δs(2.4b)

l =

np∑i

√(x(i)− x(i+ 1))

2+ (y(i)− y(i+ 1))

2(2.4c)

pr =g(g + 4δs)

(2(4S + g))(2.4d)

rays =g

2pr(2.4e)

Where np is the number of points on the airfoil; x(i) coordinate on the airfoil surface; g is the rationbetween the first and the last cell (δe); S is the sum of the elements; l is the length of the airfoil curve;pr is the progress rate of the arithmetic progression; and rays is the number of cells perpendicular to theairfoil surface. The equation for pr has been derived using V olframMathematica.


Table 2.4: Patches

Patch (points) DescriptionInlet Starting field of the flux, composed of sides with edges (4 0) and (1 0)Outlet Final field of the flux, composed of sides with edges (1 2), (2 3) and (3 4)Airfoil The wall of the airfoil, consisting of side with edges (5 6) (6 7) (7 8) (8 9) (9 5)

Patches

As described above the patches are the sides of the hexagons with no neighboring blocks and they areused to define boundaries conditions. OpenFOAM allows assigning various kinds of patches which havespecific properties. For this project the patches of particular interest are inletOutlet and wall. Thefirst option will switch the velocity and the pressure between either a fixed value and a zero gradientdepending on the direction of the flux. The wall condition is a no slip condition, constant velocity andpressure no gradient. The patches geometry is summarized in table 2.4.

Review

Based on the description above the mesh have been created using the Fotran90 scrip B as it createsthe file blockMeshDict which the OpenFOAM utility blockMesh uses to create the mesh. The codegenerates supporting files in the constant directory which contains all the information for the mesh andactually presents the mesh itself. Once the mesh is created one can review it with the post processingtool ParaV iew.Figure 2.7 presents the resulting mesh.

Figure 2.7: Final mesh used for the simulations of NACA0012 airfoil, ParaV iew

2.5 Boundary conditions

The variables of particular interest, and which require BC are the fluid quantities - velocity and pressure.Furthermore for the turbulence modeling will be used K-omega SST model therefore there is a need forsetting BC for the turbulent viscosity, kinematic energy and dissipation rate. This implies that therenear the airfoil surface for the computations will be used wall functions, which will be briefly explainedin section 2.6.4The boundary conditions are summarized in table 2.5 where I is the turbulence intensity, and l is themixing length. For this model the turbulence intensity have been set to 5%, and the mixing length havebeen estimated as a quarter of the chord.


Table 2.5: Boundary conditions

Quantity Equation Inlet/Outlet Airfoil DimensionU - free stream fixed value [m/s]p - free stream fixed value [N/m2]

νt

√32 (UIl) or 5ν free stream wall function [m2/s]

κ 32 (UI)

2free stream wall function [m2/s2]

ω√kl free stream wall function [1/s]

Table 2.6: Divergence terms

Term Equation Interpolation schemeConvection, U ∇ · (ρUU) Upwind second order linearConvection, κ ∇ · (kU) Linear limitedConvection, ω ∇ · (ωU) Linear limited

SST transport γωκ τij

∂ui

∂xjLinear

2.6 Solution

This section explains the numerical algorithms and models built in OpenFOAM which are used for thisparticular case.

2.6.1 Finite Volume Schemes

The finite volume method is used to evaluate and solve partial differential equations as it estimates valuesat discrete locations (volumes) on a particular mesh. Thus a finite volume is the area surrounding thecentral point of the mesh cells. [7]. Then the equations are solved using conservation of momentum fluxthrough this control volume(CV).The finite volume method in OpenFOAM is presented by several numerical schemes for different mathe-matical operator in the differential equations [2]. Depending on the particular application the user specifyhow to model each of those numerical schemes. One can review the options for those tools even online[3], where the source code is presented.

First and second time derivatives

The time derivatives ∂∂t and ∂2

∂t2 are estimated by the use of simple Euler scheme, which is a first order,bounded, implicit scheme. However in order to estimate initial fields for the velocity, the pressure andthe flux, it is used a steady state condition which does not solve for time derivatives.

Gradient Schemes

The gradient numerical scheme models the gradient of the pressure for ∇p and the velocity for ∇U .There are several options for selection of the gradient schemes which include the leastSquares methodas second or fourth order scheme, or Gaussian interpolation. Furthermore those schemes can be limitedonly to the grid faces or cells.

Divergence Schemes

Each divergence term for the particular model have to be presented as the user have to specify also itsinterpolation scheme. OpenFOAM has a default divergence schemes for steady state k-omega SST modelwhich will be used for this project. In order to solve each term OpenFOAM uses Gauss discretization,and prescribed interpolation scheme. The terms are given in table 2.6.

Laplacian Schemes

It models the Laplacian terms, as it requires the selection of interpolation and normal surface gradientschemes.


Point-to-point interpolations of values

Based on the case one can select different finite difference method in order to perform the interpolationsrequired for each finite volume scheme. The upwind difference scheme is the most commonly used sinceit is one order more accurate than the central difference scheme.

Component of gradient normal to a cell face

The surface normal gradient is calculated at the cell face. It is the component which is normal to theface of the gradient of the central cell values for those two cells that this face connects. A surface normalgradient requires evaluation of Laplacian term by the use of Gaussian integration.

2.6.2 Finite Volume Solutions

OpenFOAM is equipped with solutions and algorithm control for various applications. It specifies eachlinear solver which is used for each discretized equation [2]. Thus the user specifies an individual methodand its properties of number-crunching to solve the set of linear equations for each variable of particularinterest.

2.6.3 Solvers

The fluid dynamics solver applications in OpenFOAM are based on pressure-implicit split-operator(PISO) or semi-implicit method for pressure-linked equations (SIMPLE) algorithms. These algorithmsare iterative procedures for solving equations for velocity and pressure, as PISO is being used for transientproblems and SIMPLE for steady-state. Both algorithms are based on evaluating initial solutions andthen correcting them by the use of finite volume schemes. SIMPLE only makes one correction whilePISO requires around four as the user can specify this number.

Steady State Solution

The steady state solution is implemented by the OpenFOAM semi-implicit method for pressure-Linkedequations SimpleFoam. It solves the Navier-Stokes equations with the following iterative procedure:

1. Boundary conditions (BC) setup

2. Momentum equation solved in order to compute the intermediate velocity field

3. Mass fluxes evaluated for each cell face

4. Pressure equation solved (under-relaxation)

5. Mass fluxes corrected for each cell face

6. Velocities updated by for the updated pressure field

7. Boundary conditions updated

8. The process is repeat until convergence

* Steps 4 and 5 could be looped for a prescribed time in order to correct in case of non-orthogonality.

Navier-Stokes equations (2.5 and 2.6) for incompressible flow, constant density and viscosity:

∇ · (ρU) = 0 (2.5)

∂U

∂t+∇ · (uu)−∇ · (ν∇u) = −∇p (2.6)

The solution is implemented by deriving an equation for the pressure, using the divergence of the mo-mentum equation, and then it is substituted in the continuity equation.Then the momentum equation (2.7) where H(U) (2.8) is combination of the matrix coefficients of anneighbor cells ap times their velocities Un and then this is added to the unsteady term eq : continuity.

apUp = H(U)−∇p⇐⇒ Up =H(U)

ap− ∇pap

(2.7)


H(U) = −∑n

anUn +Uo

∆t(2.8)

The continuity equations in discrete form (2.9) is given as the sum of the velocity on the face Uf (2.10)times its outward-pointing face area vector S:

∇U = −∑f

SUf (2.9)

Uf =

(H(U)

ap

)f

− (∇p)f(ap)f

(2.10)

Finally substituting equation 2.10 in equation 2.9 one can obtained an equation for the pressure (2.14).

∇(

1

ap∇p)

= ∇(H(U)

ap

)=∑f

U

(H(U)

ap

)f

(2.11)

2.6.4 Turbulence Model K-Omega SST

In order to imitate realistic flow conditions similar to those in the wind tunnel experiment, the simulationshave to be executed for high Reynolds numbers. The flow around airfoil is laminar for Reynolds numberslower than 200. For Reynolds numbers between 200 and 1000 one can witness the laminar vortex shedding,and for Reynolds numbers above 1000 the flow becomes turbulent. In order to simulate a turbulent flowaround an object should use a special model which take into account the turbulent fluid quantities whichoccur in the equations. OpenFOAM repository offers numerous Raynolds-Averaged equations models(RAS) as for high Reynolds numbers those are standard κ−ω, κ− ε, κ−ωSST , as well as the 1 equationmixing-length Spalart-Allmaras model. Appendix A offers a brief overview and discussion about thosemodels.The simulations for this project are implemented using the k − ω shear stress transport (SST) model asthe most suitable for high Reynolds flows pressure gradient flows.The equations of the model are presented below, the way they are interpreted in OpenFOAM .The specific dissipation of turbulent kinetic energy is given in equation 2.12

∂ω

∂t+∇ · (uω) = ∇2[(ν + νtσω)ω] +

γω

κτij

∂ui∂xj− βω2 + 2(1− F1)σω2

1

ω∇κ · ∇ω + Psas (2.12)

The turbulent kinetic energy is modeled as (eq. 2.13):

∂κ

∂t+∇ · (uκ) = ∇2[(ν + νtσκ)κ] + τij

∂ui∂xj− β∗ωκ (2.13)

∇(

1

ap∇p)

= ∇(H(U)

ap

)=∑f

U

(H(U)

ap

)f

(2.14)


Psas = 1.25max(T1 − T2, 0) (2.15a)

T1 = 1.755κS2 L

Lνκ(2.15b)

T2 = 3κ max

(1

ω2∇ω · ∇ω, 1

κ2κ · κ

)(2.15c)

L =κ

12

ωcµ14

(2.15d)

Lνκ = κS

|κ2u|(2.15e)

νt =α1κ

max(α1ω,ΩF2)(2.15f)

F2 = tanh

[[max

(2√κ

β∗ωy,

500ν

y2ω

)]2](2.15g)

F1 = tanh

min

[max

(2√κ

β∗ωy,

500ν

y2ω

),

4σω2κ

CDκωy2

]4

(2.15h)

CDκωy2 = max

(2ρσω2

1

ω

∂k

∂xi

∂ω

∂xi, 10−10

)(2.15i)

γ1 =5

9(2.15j)

γ2 = 0.44 (2.15k)

β1 =3

40(2.15l)

β2 = 0.0828 (2.15m)

β∗ =9

100(2.15n)

ακ1 = 0.85 (2.15o)

ακ2 = 1 (2.15p)

αω1 = 0.5 (2.15q)

αω2 = 0.856 (2.15r)

a1 = 0.31 (2.15s)

C1 = 10 (2.15t)

2.6.5 Time control

The selection of proper time control depends on the mesh properties in terms of number of cells, size andshapes, as well as the properties of the flow, and the main solver. For the steady state solutions, it isimportant that the simulation runs for sufficient amount of time until it converges to the desired value.The process of selecting the proper time control is manual and includes initial calculations and testingwith different relaxation parameters. The relaxation parameters allow the user to specify how fast shouldone quantity converge.


Table 2.7: Mesh parameters based on the different case scenarios

Parameter NACA0012 laminar NACA0012, κ− ω SST NACA64318, κ− ω SSTNumber Cells 5700 11350 22850Airfoil CVs 114 227 457δs 1e-2 5e-3 5e-3δe 1e-1 5e-2 2e-2

2.7 Simulations

In this section are presented the simulation scenarios of particular interest to the model. The resultsfrom OpenFOAM will be compared to experimental data and other programs. First starting with asteady state laminar simulations which aims to inspect the quality of the mesh, and if the acknowledgedfinite volume schemes and solutions generate acceptable results. For this purpose is used the standardNACA0012 symmetric airfoil. Then the Reynolds number will be increased, and the turbulence modelwill be included in order to analyze the properties of the flow in terms of lift, drag and pressure distri-bution. Once those results are resolved the simulations are being done for NACA-63418 airfoil used inthe experiment, chapter 3. First the results from OpenFOAM are compared to some experimental dataand other computer programs. Finally, in chapter 3 the conditions of the experiment will be mimickedin order to compare the acquired data with the data from the model.The coordinate profiles of both airfoils involved in the simulations are shown on figure 2.8. The majorparameters of the meshes are presented in 2.7. A common parameters for the meshes is the circle radiusof 5 [m], and the minimum cell height neighboring the airfoil wall of 0.00015 [m]. The minimum cell ischosen so it yields non-dimension wall distance, y+ (equation 2.16) of average 1 along the surface.

y+ =Ufy

ν(2.16)

Where Uf is the friction velocity, and y is the height of the nearest cell to the wall.

-0.4

-0.2

0

0.2

0.4

0 0.2 0.4 0.6 0.8 1

y [-

]

x [-]

NACA0012NACA63418

Figure 2.8: Airfoil coordinates


2.7.1 NACA0012

The laminar cases which aim to clarify the quality of the mesh and the validity of the model are donefor low Reynolds numbers of 100 and 1000. On figure 2.9 one can observe the wind speed behavioralong the airfoil for different angles of attack. At small angles of attack the boundary layer for the lowerReynolds number is significantly thicker, and this effect is reduced for higher AoA. The area aroundthe stagnation point where the flow speed is reduced is much larger in the case of the lower Reynoldscase. Important implication is the instability of the boundary layer at 14 degrees angle of attack, andthe complete separation at 20 degrees for Reynolds number of 1000, while for Re = 100 the flow staysattached for each of those inclinations. Figure 2.9 presents the pressure distribution of the above cases.As can be inferred from the velocity plots the lower Reynolds number cases influence the pressure aroundthe airfoil in a wider area. However the most interesting are the cases of Re = 1000 and angles of attack14 and 20 degrees on figures 2.10h and 2.10j where one can see the formation of vortex structures in thewake of the airfoil in terms of low pressure regions.The validation of the κ − ω SST model is implemented on NACA0012. Simulations are done for twoReynolds numbers - 200000 and 1000000, and for three different flap positions of -5, 0 and 5 degrees.This is done for angles of attack from -4 to 16, 17 degrees, in order to capture the 0 lift angle of attack,and the optimum lift for each case.

The force coefficients for those cases are presented on figures 2.11, 2.12 and 2.13. Figure 2.11a presents theresults for the lift curves of NACA0012 mesh for the three flap positions, at Reynolds number of 200000.One can observe that the change in the flap angle results in translation the lift curve along the y axis. Theflap deflection of plus 5 degrees (clockwise rotation) changes the camber of the airfoil in such a way thatincrease the lift for each angle of attack with approximately 0.1 non-dimensional units cL. The sampleeffect holds for flap deflection in the other direction (contra-clockwise) as minus 5 degrees results in liftreduction of around 0.1. Then on figure 2.11b one can review a comparison between OpenFOAM resultsand synthesized data from a combination of experimental results and computer calculations (source [14]).The lift coefficient behavior is given for different Reynolds numbers. One can see how as Re increasesthe rated cP is rising up. The OpenFOAM results and the experiment data are in a good agreement inthe linear part of the cP curve as they have almost identical values. However as it is common the CFDmodel typically overestimate the stall point, and predict much higher optimum lift. This is because fullyturbulent models, cannot predict the complex stall phenomenon and the separation behavior on an airfoilaccurately which leads to over prediction of the aerodynamic characteristics. Figure 2.12a shows the dragcoefficient behavior for different flap positions. It slightly increases for positive rotation and decreases fornegative, as the change tends to have linear behavior. On figure 2.12b one can observe cD comparison. Asexpected the drag coefficient decreases for higher Reynolds number as for the OpenFOAM result thus forthe experiment data. The slope of the curves are in a good agreement, however the CFD computationstend to overestimate the drag force. In order to correct this effect the turbulence quantities in the modelhave to additionally tunned.


(a) AoA = −5, Re = 1e2 (b) AoA = −4 : 16, Re = 1e3

(c) AoA = 0, Re = 1e2 (d) AoA = 0, Re = 1e3

(e) AoA = 10, Re = 1e2 (f) AoA = 10, Re = 1e3

(g) AoA = 14, Re = 1e2 (h) AoA = 14, Re = 1e3

(i) AoA = 20, Re = 1e2 (j) AoA = 20, Re = 1e3

Figure 2.9: Laminar simulations NACA0012, Pressure distribution, P , for Re = 1e2 and Re = 1e3


(a) AoA = −5, Re = 1e2 (b) AoA = −4 : 16, Re = 1e3

(c) AoA = 0, Re = 1e2 (d) AoA = 0, Re = 1e3

(e) AoA = 10, Re = 1e2 (f) AoA = 10, Re = 1e3

(g) AoA = 14, Re = 1e2 (h) AoA = 14, Re = 1e3

(i) AoA = 20, Re = 1e2 (j) AoA = 20, Re = 1e3

Figure 2.10: Laminar simulations NACA0012, Boundary layer view in terms of velocity, U , for Re = 1e2and Re = 1e3


(a) cL, flap comparison OpenFOAM ,Re = 2e5

-0.5

0

0.5

1

1.5

-5 0 5 10 15 20

Cl [

-]

AoA [deg]

OpenFOAM Re2e5OpenFOAM Re1e6

Exp Re1.6e5Exp Re3.6e5

Exp Re7e5Exp Re1e6

(b) cL, Re comparison with experiments

Figure 2.11: Lift coefficient, cL over NACA0012, at Angle of Attack, AoA = −4 : 16

(a) cD, flap comparison OpenFOAM ,Re = 2e5

0

0.02

0.04

0.06

0.08

0.1

-5 0 5 10 15 20

Cd

[-]

AoA [deg]



Exp Re7e5Exp Re1e6

(b) cD, Re comparison with experiments

Figure 2.12: Drag coefficient, cD over NACA0012, at Angle of Attack, AoA = −4 : 16

(a) cL/cD, flap comparison OpenFOAM ,Re = 2e5

-0.5

0

0.5

1

1.5

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16

Cl[-

]

Cd[-]



Exp Re7e5Exp Re1e6

(b) cL/cD, Re comparison with experiments

Figure 2.13: Lift-drag ratio, cL/cD over NACA0012, at Angle of Attack, AoA = −4 : 16


Figures 2.14, 2.15 and 2.16 present the pressure distribution over the airflow for different trailing edgeposition, at an angle of attack of 5 degrees, and Re of one million. Furthermore the same results of cPare compared with the result from previous experiments and modeling in figures 2.17, 2.19 and 2.18, [6].A screen shots of the corresponding mesh at the trailing edge for each flap angle is given on figures 2.14a,2.15a and 2.16a, where the boundary layer can bee seen in terms of velocity (dark red zero velocity, greenfree stream velocity).

The pressure distribution along the airfoil itself is given on figures 2.14b, 2.15b and 2.16b, where cP isplotted ”upside-down” with negative values (suction). This is done for facilitation since the upper surfaceof a conventional lifting airfoil corresponds to the upper curve. The pressure coefficient at the stagnationpoint is around 1, as then it rises rapidly on both surfaces until it finally recovers to a small positive valueat the trailing edge (pressure recovery region). The upper surface pressure is shown with gray circlesand it is revered as suction, while the dark circles indite the lower pressure surface. The circles presentthe surface pressure applied the airfoil taken in the centers of each control volume edge. A close look atthose plots reveals the behavior of the cP for the different flap positions. Applying a flap deflection of5 degrees results in increase in the pressure and the curves go apart of each other (figure 2.14b), whilea negative flap angle of 5 degrees causes the pressure to decrease on both sides and the curves to comecloser together (figure 2.15b). Additionally the bended surface around the trailing edge experiences asmall anomaly in the cP , a local pressure peak with a coordinates position of the flap hinge.

On the comparison plots, figures 2.17, 2.19 and 2.18 one can observe that the OpenFOAM results holdwell together with the results from [6]. There is a small obvious overestimation for the suction surface ofthe airfoil for each flap case, which most likely caused by the mesh quality. In addition, one can see thatat the trailing edge the curves on figures 2.17a, 2.19a and 2.18a are smooth, while those of OpenFOAMhave a sharp peak. The reason for that is the geometry of the movable flaps.Finally the pressure distribution along NACA0012 computed in OpenFOAM is presented as viewed inParaV iew for flap angles of 0 and 5 degrees, on figures 2.20a and 2.20b. One can observe the significantchange in the pressure distribution produced by the flap deflection. On figure 2.20a the pressure is thesame along both surfaces since NACA0012 has a symmetric profile, so flow around it is equally oscillatedon both sides and the pressure is in equilibrium and lift force is 0. However just rotation of 5 degrees onthe trailing edge flap alters the flow to such extend that the lift coefficient is around 0.11, which is similarto airfoils like NACA 23012, [16]. Furthermore a comparison of cP distribution for the same conditionsare given on figure 2.21 for zero flap angle and 2.22 for 5 degrees flap angle.


(a) Trailing edge mesh, boundary layer, U

-2

-1.5

-1

-0.5

0

0.5

10 0.2 0.4 0.6 0.8 1

Cp

[-]

x/c [-]

Pressure Disctribution

SuctionPressure

(b) Pressure distribution

Figure 2.14: Pressure distribution, Cp over NACA0012, for Reynolds number, Re = 1e6, and Angle ofAttack, AoA = 5, and Flap angle, flap = 0


-2

-1.5

-1

-0.5

0

0.5

10 0.2 0.4 0.6 0.8 1

Cp

[-]

x/c [-]


SuctionPressure




-2

-1.5

-1

-0.5

0

0.5

10 0.2 0.4 0.6 0.8 1

Cp

[-]

x/c [-]


SuctionPressure


Figure 2.16: Pressure distribution, Cp over NACA0012, for Reynolds number, Re = 1e6, and Angle ofAttack, AoA = 5, and Flap angle, flap = −5


(a) Exp data, source [6]

-2

-1.5

-1

-0.5

0

0.5

10 0.2 0.4 0.6 0.8 1

Cp

[-]

x/c [-]


SuctionPressure

(b) OpenFOAM



-2

-1.5

-1

-0.5

0

0.5

10 0.2 0.4 0.6 0.8 1

Cp

[-]

x/c [-]


SuctionPressure

(b) OpenFOAM



-2

-1.5

-1

-0.5

0

0.5

10 0.2 0.4 0.6 0.8 1

Cp

[-]

x/c [-]


SuctionPressure

(b) OpenFOAM

Figure 2.19: Pressure distribution, Cp over NACA0012, for Reynolds number, Re = 1e6, and Angle ofAttack, AoA = 5, and Flap angle, flap = −5


(a) Pressure, flap = 0 (b) Pressure, flap = 5

Figure 2.20: Pressure distribution, Cp over NACA0012, for Reynolds number, Re = 1e6, and Angle ofAttack, AoA = 0


-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

10 0.2 0.4 0.6 0.8 1

Cp

[-]

x/c [-]


SuctionPressure

(b) OpenFOAM



-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

10 0.2 0.4 0.6 0.8 1

Cp

[-]

x/c [-]


SuctionPressure

(b) OpenFOAM



(a) cL comparison of NACA64318 (b) cD comparison of NACA64318

2.7.2 NACA64318

This section is to show the validity of the model as it is compared to data from different sources takenfrom the ”Risø airfoil catalog” [15]. The data sources consists of experimentally acquired data from thelocal wind tunnel and two models by XFOIL and EllipSys2D. The simulations in OpenFOAM areexecuted for Reynolds number of three million so it is consistent with those from the catalog. They aremade for every angle of attack in the range of 0 to 20 degrees, in order to compute the force coefficientcurves. Additionally, the pressure distribution along the airfoil will be compared at selected AoAs.

Figure 2.23a shows the lift coefficient estimated by OpenFOAM along with the experimental and com-puted data. From the plot one can infer that the XFOIL and EllipSys2D models overestimate theexperimental data and OpenFOAM underestimates it. It is important that the slope is the same in thelinear part of the curve (up to AoA = 10[deg]) for all of the results, which is the case here. The stallpart of the curves for angles of attack higher than fourteen degrees wide varies for each model, and itseem like EllipSys2D has the best estimation according to the experiments. In fact the values which arecomputed based on the OpenFOAM model are estimated using averaging. That is because at this highangles of attack the solutions does not converge to a single value, but rather a series of repeating values.The reason for that is separation of the flow which cannot reach a steady state solution, similar to whatis shown on figure 2.10j.

The drag coefficient shown on figure 2.23b estimated by OpenFOAM slightly overestimates all of theother models but resembles the shape of the curves in a good manner. An overview of all force coefficientsis shown on figure 2.23.The following plots (figures 2.24, 2.25 and 2.26) present different pressure distributions depending on theangle of attack. The results from OpenFOAM are compared to two models used in [15] for angles ofattack of 6, 10, 12 , 14, 16 and 18 degrees. In addition, for better visualization the flow is given as seenin ParaV iew in terms of velocity and pressure.

From the plots one can infer that as the angle of attack is increasing, the pressure difference betweenthe suction and the pressure side of the airfoil is increasing. Another phenomenon is the flow separationwhich occurs after a certain transitional point based on the angle of attack. As can be seen on figures2.24c and 2.24d the flow at AoA = 6 and 10 is still fully attached and thus the cP curves on figures2.24e and 2.24f indicate an adverse pressure gradient as they slowly reach the recovery point. Howeverafter certain critical point, separation occurs and those curves flattens close to the trailing edge, sincethere is no pressure gradient to sustain the flow. This separation becomes greater as the angle of attackis getting higher, and at certain point, a full separation can be reached suction curve will be completelyflat. On figures 2.25 and 2.26, one can notice that there is a difference in the point of separation betweenthe OpenFOAM results and those from the other models. For the OpenFOAM based data it occursslightly later because as can been seen on figure 2.23a the critical angle of attack for the lift coefficientis higher for this CFD model. In addition, the difference in the geometry for the different models at thetrailing edge, causes the formation of a local sharp peak at 90% chord length. In order to correct thatthe shape of the trailing edge flaps have to be tuned.


-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0 5 10 15 20

Cm

[-]

AoA [deg]

Pitch Moment

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

0 0.02 0.04 0.06 0.08 0.1

Cl [-

]

Cd [-]

Lift Drag Ratio

0

0.02

0.04

0.06

0.08

0.1

0 5 10 15 20

Cd

[-]

AoA [deg]

Drag Coefficient

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

0 5 10 15 20

Cl [-

]

AoA [deg]

Lift Coefficient

Figure 2.23: Forces coefficients from OpenFOAM simulations


(a) Pressure, AoA = 6 (b) Pressure, AoA = 10

(c) Velocity, AoA = 6 (d) Velocity, AoA = 10

-6

-5

-4

-3

-2

-1

0

10 0.2 0.4 0.6 0.8 1

Cp [-]

x/c [-]

SuctionPressure

-6

-5

-4

-3

-2

-1

0

10 0.2 0.4 0.6 0.8 1

Cp [-]

x/c [-]

SuctionPressure

(e) OpenFOAM , cP distribution, AoA = 6 left, AoA = 10 right

(f) Airfoil Catalog [15], cP distribution, AoA = 6 left, AoA = 10 right

Figure 2.24: Pressure distribution, Cp over NACA64318, for Reynolds number, Re = 3e6, Free streamvelocity, AoA = 6 and AoA = 10




-6

-5

-4

-3

-2

-1

0

10 0.2 0.4 0.6 0.8 1

Cp [-]

x/c [-]

SuctionPressure

-6

-5

-4

-3

-2

-1

0

10 0.2 0.4 0.6 0.8 1

Cp [-]

x/c [-]

SuctionPressure




Chapter 3

Experiment

3.1 Overview

The experiment is conducted in the wind tunnel laboratory at the Technical University of Denmark(DTU). The purpose of this research is to investigate the flow behavior around an airfoil with a movableflap. Moreover the flapping airfoil should be able to retain optimum lift at variable angles of attack.The hardware components and its control software as well as the airfoil has been designed and build byRobert Mikkelsen at DTU. The students enrolled in the experiment have been assigned to implementmonitoring and controlling systems for the airfoil.

3.2 Experimental setup

PC

Wind Tunnel

Airf

oil

Local Power

LinMot Controller Transformer

Pressure Device

National Instuments DAC

unit

LinMot

MacMot

Pressure scanners

Power supply cable (high voltage)

Power supply cable (low voltage)

Control signal

Figure 3.1: Experiment setup

Figure 3.1 shows a block diagram of the major components involved in the experiment. The airfoil ismounted in a wind tunnel, as it is attached to a pitch mechanism with a rotational motor. The trailingedge movable flap is operated by the use of a liner motor. Both mechanism are controlled by computerprograms which can use a voltage signal as a control signal. In order to measure the flow behavior

27

CHAPTER 3. EXPERIMENT 28

(a) Airfoil Closed (b) Airfoil Opened

Figure 3.2: Pictures of NACA 63418

around the airfoil are used pressure tabs located on the surface of the airfoil which are connected topressure scanners and the readings are captured using specific software. Figure 3.1 presents how themajor components involved in the setup are connected.

3.3 Main components

3.3.1 Airfoil

The airfoil NACA-63418 used for the model is shown on figure 3.2 and some practical information isgiven in appendix D. It is made of carbon fiber and it has a typical hallow structure. As it is mentionedabove the airfoil is equipped with a movable flexible flap on the trailing edge. The rotation of the flapis implemented by the means of reciprocating motion. A scheme of the mechanism is shown in appendixD on figure D.1. Furthermore on the surface of the airfoil have been drilled pressure tabs which areused to measure the local pressure. Those pressure tabs are located in tree parallel sections in order toconfirm the 2D flow inside the wind tunnel, figure 3.2b. The pressure scanners are connected to the tabsvia plastic tubes and the tabs which are not connected are blocked with a small dead-end tubes. Theinterface cables of the linear motor and the pressure scanners along with the tubes which input referencepressures into the scanners are taken out of the airfoil throughout the pitch hallow beam.

3.3.2 Linear Motor

A picture of the motor assembled on the airfoil which is used for the flap motion is shown on figure 3.3and its specification is given in the appendix, figure D.3. It is controlled by an electromagnetic field viavoltage signal generation. Figure 3.4 presents the wiring of the motor to the other components. In thisparticular case the digital control signal is generated via LabV IEW on the local computer and throughthe DAQunit device is sent to the motor controller (X4 on the figure - Logic supply). Then the signal issent to the motor via the motor connection X3 (Thick coaxial cable and flat cable).The software used in order to control and monitor the engine is called LinMotTalk. It is used to setupthe motor parameters depending on the experimental case, to specify the type of input signal and totrack the operation. As mentioned above the signal is generated via LabV IEW virtual instruments, V I.The graphical interface of the VI - the control panel is shown on figure 3.6 and it is explained in section3.3.4.


Figure 3.3: Picture of the linear motor - LinMot

Figure 3.4: Installation scheme of the linear motor [17]


3.3.3 Rotational Motor

The rotational motor is used to manipulate the pitch rotation of the blade via worm-gear mechanism.Figure 3.5 describes the wiring of the rotational motor. The power/analog input is connected to theNational Instruments DAQ unit so it can receive the voltage signal generated via the LabV IEW.vi.However for the power supply is used the LinMot controller. The connection between the PC and theservo motor is realized using a digital COM cable. The software interface for the rotational servo motoris called MacTalk where the user can specify the type of control method. For this particular experimentthe most appropriate is to use analog signal (voltage) to position. This way a specific voltage correspondsto specific number of revolutions in terms of pulses (1 revolution = 4096 pulses).

Figure 3.5: Mac Motor connection scheme [20]

3.3.4 DAQ unit and LabVIEW

The Data acquisition National Instruments(DAQ unit) unit has the function of interfacing the computerwith the sensor and actuator systems. It is connected to the personal computer via serial port. Its analogoutputs are connected to LinMot Controller input and to the pitch servo motor input. They are alsoconnected to the analog inputs of the DAQ unit, in order to monitor the signal generation. The pressuretransducer is also connected to the data acquisition unit via its digital input/output.As mentioned above both motors are control by analog voltage signal generation realized in LabV IEWand send to the motors through the DAQ unit. The LabV IEW.vi control panel for the signal generatoralong with the LabV IEW monitoring program is shown of figure 3.6. It is programmed in a way that itcan generate different voltage signal on the analog outputs of the DAQ unit. Thus one of the signals is sentto the flap motor and the other to the pitch motor. The control allows the user to select the propertiesof signal in terms of shape, amplitude, frequency, offset and phase. For security reasons before sendingthe signal to the motors as well as during the simulations, the signal is monitored by the programmedLabV IEW.vi which reads the signals on the analog inputs.

3.3.5 Pressure transducer

In order to captured the pressure on the surface of the airfoil is used DTCInitium pressure transducerwith two pressure scanners. Figure 3.7 presents the system configuration of those devices. One of thescanners has a high range pressure capability and measures the pressure on the suctions side of the airfoil,while the other has a low range pressure capability and measures the pressure side of the airfoil.Figure 3.8 presents the major control panel of the experiment. On the major chart on the screen onecan monitor the pressure distribution along the airfoil as it is presented as a function of the chord


Figure 3.6: Voltage generator control panel LabV IEW.vi (left), LabV IEW.vi for monitoring the controlsignals (right)

Figure 3.7: Pressure telemetry setup, [21]


in millimeters. Additionally the LabV IEW.vi is programmed in a way so one can observe the otherimportant parameters as the lift and drag force on the airfoil, the angle of attack and the position of theflap. The forces are calculated in terms of pressure integrated over the surface area. The angle of attackand the flap angle are estimated as a function of the voltage signal of the motors.

Figure 3.8: Pressure monitoring LabV IEW panel

3.4 Major Challenges

3.4.1 Data acquisition

Ground loop all of the devices involved in the experiment have to use a common ground in order toavoid ground loop problems. It is important to check the manual for each device to connect it properly tothe overall system. Having a ground loop result in capturing external signals, like the 50[Hz] frequencyof the local power grid white considerable amplitude compared to the pressure signal.Observation: As an examples of a ground loop were recorded to major errors. The corpus of the lowvoltage DC transformer was connected to the ground of the high voltage DC converter. In addition thedigital ground of the DAQ unit was connected to the ground of the control wire of the Initium pressuresystem. It is important to notify that since the computer is connected to most of the devices, and alsoto ground, they are all already grounded and further grounding wound result in a ground loop.Mechanical vibrations there are various sources of mechanical vibrations on the overall system whichresults in fluctuations in the output data. In order to avoid such negative influence one have to insurethat the tubes of the pressure system are not disturbed.Observation: Since the airfoil is just a section of a blade, it has opened sections which have to be covered(for example typed) to avoid incoming flow in the airfoil. It was observed that this problem resulted notjust in moving the pressure tubes, but inducing turbulence around the airfoil. Another problem is the aircooling of the linear motor which flow was pushing the tubes and produces fluctuations on the pressuresignal in the order of (1 to 5 volts).Electromagnetic disturbances since the pressure scanners are sensitive to electromagnetic fields, itis vital to screen all sources of such kind or to protect the scanners.


Observation: In this particular case, it was noticed that the flat control cable of the linear motor washad a great impact on the pressure system as it increased the noise of the system up to 2-5 times. Thesolution to this problem was to screen the flat cable with a Faraday cage and ground it to the thick cableground.

3.4.2 Setup

Linear Motor - The greatest challenge by any means is the linear LinMot motor. It is a highly sensitivepiece of technology which requires extra attention to all of it hardware connections and software setup.Additionally the motor is not designed for moving high loads which implies that the airfoil flap mechanismshould not load the motor slider more than it is prescribed (around 50[N ]). Furthermore it is crucialthat the power signal wires and the control signal wires from the controller to the motor are placed inseparated shields within the cabling in order to avoid interference.

3.5 Uncertainty Assessment

The experiment involves the use of high variety of electrical equipment. Therefore the quality of theexperiment data depends on how the signal is carried out from one device to another. For example,the signal generation is send from the computer to the DAQ unit device and then to the controller ofthe linear motor. Instead, since the controller and the computer are already connected through a COMport connection, the signal could have been directly send from the PC to the motor. Further research isrequired for this can be accomplished, because of the difficult software compatibility.There are various sources of noise in all the devices cause by mechanical and electrical disturbances. Forexample, the flap motion itself provokes motion of the tubes which cannot be avoided, and it insurancesthe signal for the trailing edge pressure.


3.6 Test Cases and Results

This section presents the results from the experiment in the wind tunnel. The following results are takenfor wind speed, U = 20[m/s], which yields Reynolds number Re = 3.1888e5. Figure 3.9 shows thelocations of the pressure tabs on the airfoil surface. The measurements have been taken in time seriesof 10 to 20[s], for eight angles of attack of AoA = 0, 2, 5, 7, 10, 12, 15, 17[deg], and four flap positionscorresponding to different voltage flap = 1.0, 2.0, 2.5, 3.0[V ]. The zero flap position is defined for a volt-age signal of 2.0[V ]. However, since it is hard to determine manually the zero angle of attack position,and the movable flaps is flexible and it bends its surface. This implies that the data have to thoroughlyexamined and compared with simulation results, in order to clarify the position of the airfoil and its flaps.

-0.4

-0.2

0

0.2

0.4

0 0.2 0.4 0.6 0.8 1

y/c

[-]

x/c [-]

PressureTab

Figure 3.9: Location of the pressure tab on the surface of the NACA63418 airfoil

On figure 3.10 one can observe the pressure distribution over the airfoil in the wind tunnel for eachmeasurement location. The results are presented for different pitch position as it was considered duringthe experiment. Thus for each angle of attack are shown the two most distinct of the four flap positionsgiven in voltage signal. As can been seen on the plots the pressure curves starts to have a flat end aroundangle of attack of twelve degrees, as this occurs after chord length of 80%. The separation moves towardsthe leading edge as the angle of attack is increased, thus for angle of attack of 17 degrees reaches beyond60% chord length.

Figure 3.11 shows a comparison between the experiment data of flap angle corresponding to voltage signalV = 2.0[V ] and post-processed data from OpenFOAM for the same Reynolds number. It is obvious thatthe two sets of data are not in a very good agreement in the first 50% chord length of the airfoil. Howeverin the other part of it, the OpenFOAM results predict quite well the point of separation. It was alreadyobserved that the OpenFOAM model overestimates the angle of attack when separation occurs, and dueto the fact that the pressure distribution at zero angle of attack is supposed to be similar on both sur-faces of the airfoil, one can conclude that the initial angle of attach of the experiments have been mistaken.

On figure 3.12 one can see the pressure distribution as it is shifted -7 degrees of angle of attack for themeasurement data. This one can notice that the experimental and computed data now is in much betteragreement.Thus based on the pressure distribution, the lift and drag coefficients are estimated and compared to theOpenFOAM results. This comparison is given on figure 3.13. The lift coefficient from the experimentaldata is calculated using pressure integration over the surface area, and this way are computed the twoforce components on the airfoil, one parallel to the chord and one perpendicular. Those forces aretransposed over the lift and drag vectors and thus the force coefficients are computed. This explains theodd results on the drag plot, since for stream bodies 90% of the drag is due to drag friction, which isnot take into account for when computing the forces based on the experimental data. One can see asignificant difference in the lift curves as well. A possible explanation is that in fact the error in settingzero the angle of attack was even grater, and the data is still shifted several degrees.


-5

-4

-3

-2

-1

0

10 0.2 0.4 0.6 0.8 1

Cp

[-]

x/c [-]

AoA = 17 [deg]

flap 1[V]flap 3[V]

-5

-4

-3

-2

-1

0

10 0.2 0.4 0.6 0.8 1

Cp

[-]

x/c [-]

AoA = 15 [deg]

flap 1[V]flap 3[V]

-5

-4

-3

-2

-1

0

10 0.2 0.4 0.6 0.8 1

Cp

[-]

AoA = 12 [deg]

flap 1[V]flap 3[V]

-5

-4

-3

-2

-1

0

10 0.2 0.4 0.6 0.8 1

Cp

[-]

AoA = 10 [deg]

flap 1[V]flap 3[V]

-5

-4

-3

-2

-1

0

10 0.2 0.4 0.6 0.8 1

Cp

[-]

AoA = 7 [deg]

flap 1[V]flap 3[V]

-5

-4

-3

-2

-1

0

10 0.2 0.4 0.6 0.8 1

Cp

[-]

AoA = 5 [deg]

flap 1[V]flap 3[V]

-5

-4

-3

-2

-1

0

10 0.2 0.4 0.6 0.8 1

Cp

[-]

AoA = 2 [deg]

flap 1[V]flap 3[V]

-5

-4

-3

-2

-1

0

10 0.2 0.4 0.6 0.8 1

Cp

[-]

AoA = 0 [deg]

flap 1[V]flap 3[V]

Figure 3.10: Pressure coefficient distribution on the airfoil surfaces for each pressure tab, Re = 3.1888e5


-5

-4

-3

-2

-1

0

1

0 0.2 0.4 0.6 0.8 1

Cp

[-]

x/c [-]

AoA=17[deg]

Exp, flap 2.0 [V]OpenFOAM flap 0 [deg]

-5

-4

-3

-2

-1

0

1

0 0.2 0.4 0.6 0.8 1

Cp

[-]

AoA=15[deg]


-5

-4

-3

-2

-1

0

1

0 0.2 0.4 0.6 0.8 1

Cp

[-]

AoA=12[deg]


-5

-4

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-1

0

1

0 0.2 0.4 0.6 0.8 1

Cp

[-]

AoA=10[deg]


-5

-4

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-1

0

1

0 0.2 0.4 0.6 0.8 1

Cp

[-]

AoA=7[deg]


-5

-4

-3

-2

-1

0

1

0 0.2 0.4 0.6 0.8 1

Cp

[-]

AoA=5[deg]


-5

-4

-3

-2

-1

0

1

0 0.2 0.4 0.6 0.8 1

Cp

[-]

AoA=2[deg]


-5

-4

-3

-2

-1

0

1

0 0.2 0.4 0.6 0.8 1

Cp

[-]

AoA=0[deg]


Figure 3.11: Pressure coefficient distribution comparison, Re = 3.1888e5, experiment flap position V =2.0, OpenFOAM flap position 0[deg]


-5

-4

-3

-2

-1

0

1

0 0.2 0.4 0.6 0.8 1

Cp

[-]

x/c [-]

AoA=10[deg]


-5

-4

-3

-2

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0

1

0 0.2 0.4 0.6 0.8 1

Cp

[-]

AoA=7[deg]


-5

-4

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-2

-1

0

1

0 0.2 0.4 0.6 0.8 1

Cp

[-]

AoA=5[deg]


-5

-4

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0

1

0 0.2 0.4 0.6 0.8 1

Cp

[-]

AoA=3[deg]


-5

-4

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0

1

0 0.2 0.4 0.6 0.8 1

Cp

[-]

AoA=0[deg]


-5

-4

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-2

-1

0

1

0 0.2 0.4 0.6 0.8 1

Cp

[-]

AoA=-2[deg]


-5

-4

-3

-2

-1

0

1

0 0.2 0.4 0.6 0.8 1

Cp

[-]

AoA=-5[deg]


Figure 3.12: Pressure coefficient distribution comparison corrected, Re = 3.1888e5, experiment flapposition V = 2.0, OpenFOAM flap position 0[deg]

-0.5

0

0.5

1

1.5

2

2.5

-10 -5 0 5 10

Cl [

-]

AoA [deg.]

Flap 1.0[V]Flap 2.0[V]Flap 2.5[V]Flap 3.0[V]

OpenFOAM Flap 0 [deg]OpenFOAM Flap -5 [deg]OpenFOAM Flap 5 [deg]

(a)

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

-10 -5 0 5 10

Cl [

-]

AoA [deg.]

Flap 1.0[V]Flap 2.0[V]Flap 2.5[V]Flap 3.0[V]

OpenFOAM Flap 0 [deg]OpenFOAM Flap -5 [deg]OpenFOAM Flap 5 [deg]

(b)

Figure 3.13: Force coefficients comparison Experiment and OpenFOAM results

Chapter 4

Summary

A CFD steady state model was implemented using the open source commercial code OpenFOAM , inorder to predicted the flow behavior around airfoils with a movable flaps. The CFD code uses the fullturbulent Shear Stress Transport κ − ω model to simulate the high Reynolds number airfoil flows usedfor the wind energy applications. Additionally, a script for creating an airfoil O-mesh was developedwith an option for a trailing edge flap rotation. The code can draw any airfoil shape based on airfoilnormalized coordinates as the first point should start from the trailing edge and the points should followin a contra-clockwise order. The mesh allow easy control over the size of the domain, the number of cellsand their grading as automatically calculates them based on the desired size of the smallest cell.The CFD code can predict the steady flow behavior around different airfoils. For validation were usedNACA0012 and NACA63418 and the result were compared with data from experiments and other com-puter models. As it was expected, the CFD model overestimates the angle of attack when stall occursand cannot provide accurate estimate for separating flows. It was shown that the model can generategood results for attached flows. For the NACA0012 case, the estimated lift curves were matching the ex-perimental data. In the case of NACA63418 the model predicted the slope of the lift curve but in generalunderestimates the lift force, contrary on the other models used for comparison. The reason for that canbe found on the pressure distribution plots. The results from OpenFOAM are in good agreement withthe data from the other models, but there some anomalies cause by the quality of the mesh.

The final goal of the CFD model is to predict dynamic flow behavior of a flow around airfoil equipped witha movable flap by the use of a moving mesh. The model developed for this master thesis was implementedin way which offers the opportunity to be easily upgraded to a transient solver code. However the movingmesh problems require large computer resources, and to simulate moving mesh cases with a fine meshgeometry will be needed cluster of parallel running machines. OpenFOAM is equipped with tools forthis purpose which makes it a favorable chose.Another very import aspect for future developed is the airfoil mesh, especially in the trailing edge sector.The trailing edge flap is now modeled only with leaner surfaces, which creates sharp local peaks on thepressure curves. This can be deal with by adding a function which bends the points in a particular way.Additionally, the code can be tested for different trailing edge shapes and features which change theaerodynamics of the airfoil flow.

In the wind tunnel laboratory an airfoil NACA63418 is used for the analysis of a flow around an air-foil with a movable flaps. In order to setup the sensors and actuators for this project, their interfacesoftware was investigated and configured. Additionally LabV IEW programs were implemented to mon-itor and control each device and acquire experimental data. In order to improve the signal quality forthe control and the data acquisition, different sources of disturbances were investigated and taken care of.

The results from experiment are showing that there is a need of further measures for improving thequality of the signal. The trailing edge movable flaps requires decreasing of stiffness in order to reducethe load on the linear motor.The final goal of the experiment is to control the trailing edge flaps so that it can follow optimum lift fora change in the angle of attack. For this purpose to the current LabV IEW.vi have to be added a PIDcontrol toolbox which uses the PID control algorithm.

38

Bibliography

[1] Peter Bjrn Andersen Advanced Load Alleviation for Wind Turbines using Adaptive Trailing EdgeFlaps: Sensoring and Control, Risø DTU, February 2010

[2] Open FOAM User Guide, Version 1.6, 24th July 2009

[3] Source code online, http://foam.sourceforge.net/

[4] OpenFOAM, http://www.openfoam.com/

[5] Adaptive wing and flow control technology, E. Stanewsky, Pregress in Aerospace Sciences 37, 2001

[6] Wei Jun Zhu, Tim Behrens, Wen Zhong Shen and Jens Sørensen, A Hybrid Immersed BoundaryMethod for Studying Airfoils with Trailing Edge Flap Department of Mechanical Engineering, Tech-nical University of Denmark

[7] Harry B. Bingham, Poul S. Larsen and V. Allan Barker, Computational Fluid Dynamics, LectureNote for Course no. 41319, Technical University of Denmark, DK-2800 Lyngby, Denmark, August26, 2009

[8] Frank M. White, Viscous fluid flow , Third Edition, 2006

[9] NASA homepage, http://www.nasa.gov/

[10] UIUC Airfoil Coordinates Database ,http://www.ae.illinois.edu/

[11] CERFACS homepage, http://www.cerfacs.fr/

[12] Hansen, M.H., Data for aeroelastic modeling of the Nordtank 500 kW turbine with LM19.1 blades,Risø DTU, Roskilde, Denmark, August 2010

[13] Sumer, B. M., Lecture notes on turbulence, DTU 2007

[14] http://www.cyberiad.net/, original source: Sheldahl, R. E. and Klimas, P. C., Aerodynamic

[15] Wind Turbine Airfoil Catalog, Risø National Laboratory, August 2001

[16] The Characteristics of 78 related airfoil sections from test in the variable-density wind tunnel, E.Jacobs, K. Ward, R. Pinkerton

[17] LinMot Installation guide, Document version 3.10 / November 2009

[18] LinMot Homepage, http://www.linmot.com/

[19] LinMot Data Book, Industrial Linear Motors, Edition 15

[20] User Manual, Integrated Servo Motors

[21] User Manual, Pressure Systems, Inc., ISO-9001:2000 Certified, Web: PressureSystems.com

39

Appendix A

Turbulence Models

The turbulent models use extra transport equations which define the turbulent properties of the flow. In the caseof the two equation models, the turbulent energy equation performs better if it is coupled with a second equationmodeling its rate of dissipation. The turbulence models which can be used for the CFD computation for thisproject are the standard κ−ω, κ− ε, κ−ωSST , as well as the 1 equation mixing-length Spalart-Allmaras model.

k − ω standard model

The κ − ω BSL model is based on Wilcox original κ − ω omega model and is developed by Menter in order toimprove Wilcoxs original model so that an even higher sensitivity could be obtained for adverse-pressure-gradientflows. The main issue with the Wilcox model is the strong sensitivity to free stream conditions. Based on thevalues specified for the inlet, one can obtain a significant variation in the models results. In order to solve thisproblem Menter develops, a combination between the κ − ω model near the surface and the κ − ω model in theouter region. As a result the BSL model is identical to the Wilcox model in the inner half of the boundary-layerbut it can change gradually to the higher Reynolds numbers towards the boundary-layer edge.

k − ε model

The model is usually used for free-shear layer flows with relatively small pressure gradients and for wall-boundedand internal flows. Experiments show that there are significant computational errors in case of flows containinglarge adverse pressure gradients [13]. Therefore one can conclude that the k - model will be an inappropriatechoice for inlet flows.

k − ω shear-stress transport model

The SST κ−ω turbulence model as the κ−ω BSL model are developed to improve Wilcoxs original model so thatan even higher sensitivity could be obtained for adverse-pressure-gradient flows [13]. The main reason is that theother two models do not account for the transport of the turbulent shear stress. This results in an over-predictionof the eddy-viscosity. The use of a κ − ω formulation in the inner parts of the boundary layer makes the modelapplicable all the way down to the wall through the viscous sub-layer, therefore the SST κ − ω model can beused as a low Reynolds turbulence model without any additional damping functions. The SST formulation alsoswitches to a k- behavior in the free-stream and this way avoids the common κ−ω problem that the model is toosensitive to the inlet free-stream turbulence properties. The SST κ− ω model is popular for its good behavior inadverse pressure gradients and separating flow. However the model produce a bit too large turbulence levels inregions with large normal strain, like stagnation regions and regions with strong acceleration. This tendency ismuch less pronounced than with a normal k- model though.

Model comparison

Menter (1993) made an extensive comparison between (1) the classic k- model; (2) the original κ− ω model; (3)the κ − ω BSL model; and (4) the κ − ω SST model for various well documented flows. The tested flows were,among others, two kinds of adverse pressure gradient flow (one having a very strong adverse pressure gradient,so strong that separation occurs); the backward- facing-step flow; and the flow past a NACA 4412 airfoil at anangle of attack near maximum lift condition. The main conclusion from this inter-comparison exercise was thatthe κ− ω, SST model gave the most accurate results while the k - model did not yield as accurate results as theother three for the tested adverse-pressure-gradient flow cases [13].

40

Appendix B

Meshing

Mesh NACA0012, κ− ω SST geometry statisticsMesh stats

points: 23154

internal points: 0

faces: 45627

internal faces: 22473

cells: 11350

boundary patches: 4

point zones: 0

face zones: 0

cell zones: 0

Overall number of cells : 11350

Checking topology...

Boundary definition OK.

Point usage OK.

Upper triangular ordering OK.

Face vertices OK.

Number of regions: 1 (OK).

Checking patch topology for multiply connected surfaces ...

Patch Faces Points Surface topology Bounding box

inlet 52 106 ok (non-closed singly connected) (-4.70337 -4.1641 0) (-2.4711 4.1641 0.1)

outlet 175 352 ok (non-closed singly connected) (-2.4711 -4.99993 0) (5.29659 4.99993 0.1)

airfoil 227 454 ok (non-closed singly connected) (0 -0.06 0) (0.999969 0.06 0.1)

defaultFaces 22700 23154 ok (non-closed singly connected) (-4.70337 -4.99993 0) (5.29659 4.99993 0.1)

Checking geometry...

Overall domain bounding box (-4.70337 -4.99993 0) (5.29659 4.99993 0.1)

Mesh (non-empty, non-wedge) directions (1 1 0)

Mesh (non-empty) directions (1 1 0)

Boundary openness (2.61868e-20 1.04916e-20 -7.79731e-19) OK.

Max cell openness = 2.05272e-16 OK.

Max aspect ratio = 59.9866 OK.

Minumum face area = 5.63862e-08. Maximum face area = 0.319527. Face area magnitudes OK.

Min volume = 5.63862e-09. Max volume = 0.0319527. Total volume = 7.84156. Cell volumes OK.

Mesh non-orthogonality Max: 58.999 average: 22.3203

Non-orthogonality check OK.

Face pyramids OK.

Max skewness = 0.585886 OK.

Min/max edge length = 0.00015462 0.719724 OK.

All angles in faces OK.

Face flatness (1 = flat, 0 = butterfly) : average = 1 min = 0.999996

All face flatness OK.

Cell determinant (wellposedness) : minimum: 0.0107548 average: 1.53826

Cell determinant check OK.

Mesh NACA63418, κ− ω SST geometry statisticsMesh stats

points: 46614

internal points: 0

faces: 91857

internal faces: 45243

cells: 22850

boundary patches: 4

point zones: 0

face zones: 0

cell zones: 0

Overall number of cells: 22850

Checking topology...

Boundary definition OK.

Point usage OK.

Upper triangular ordering OK.

Face vertices OK.

Number of regions: 1 (OK).

Checking patch topology for multiply connected surfaces ...

Patch Faces Points Surface topology Bounding box

inlet 192 386 ok (non-closed singly connected) (-4.55057 -4.9886 0) (0.112528 4.9886 0.1)

outlet 265 532 ok (non-closed singly connected) (0.112528 -4.9997 0) (5.44939 4.9997 0.1)

airfoil 457 914 ok (non-closed singly connected) (0 -0.0681 0) (0.999983 0.1119 0.1)

defaultFaces 45700 46614 ok (non-closed singly connected) (-4.55057 -4.9997 0) (5.44939 4.9997 0.1)

Checking geometry...

Overall domain bounding box (-4.55057 -4.9997 0) (5.44939 4.9997 0.1)

41

APPENDIX B. MESHING 42

Mesh (non-empty, non-wedge) directions (1 1 0)

Mesh (non-empty) directions (1 1 0)

Boundary openness (-5.21416e-20 -3.19187e-20 -6.7389e-19) OK.

Max cell openness = 2.16162e-16 OK.

Max aspect ratio = 24.4342 OK.

Minumum face area = 6.24135e-08. Maximum face area = 0.0955576. Face area magnitudes OK.

Min volume = 6.24246e-09. Max volume = 0.00955576. Total volume = 7.84152. Cell volumes OK.

Mesh non-orthogonality Max: 63.3769 average: 22.1274

Non-orthogonality check OK.

Face pyramids OK.

Max skewness = 0.902093 OK.

Min/max edge length = 0.000147629 0.7091 OK.

All angles in faces OK.

Face flatness (1 = flat, 0 = butterfly) : average = 1 min = 0.999997

All face flatness OK.

Cell determinant (wellposedness) : minimum: 0.0172167 average: 1.35726

Cell determinant check OK.

Fortran 90 code

The following code is used to write the file required to build a mesh in OpenFOAM . It allows easy change of themesh geometry based on the sketch in figure 2.3. This includes different flap positions and airfoil shapes.

PROGRAM Mesh

c---------------------------------------------------------------------

c produces an OpenFOAM file (BlockMeshDict) for testing the airfoil flaps mesh

c

! Defining vars

double precision X(1000),Y(1000)

real ctm,g,f,f2

real l4,l3,ln,ls,lfl

real dels,dele

real dy

real per,s

real r

real phi

real lx,ly,hx,hy

real fl_n(2),fl_s(2)

integer i,rays,glow,mrays,brays

integer np,n0,fn,fs,cn,cs

! Dimensions

r = 5

z0 = 0

z1 = 0.1

! Change of flap

phi = 0

! Mesh parameters

ctm = 1

g = 0.001!0.0005

glow = 50!200

dels = 5e-3

dele = 5e-2

f = dele/dels

f2 = 1

! Load airfoil points

! open(unit=2,file="naca.data")

open(unit=2,file="naca.data")

read(2,*) np

do i=1,np

read(2,*) X(i), Y(i)

! write(*,*) ’X Y’,X(i),Y(i)

end do

X = X*ctm


Y = Y*ctm

! Finding leading edge position

n0 = np/2 + 1.5

! Points of the AIRFOIL

! Fing flap points

do i=1,np

fl_n(1) = X(i)

fl_n(2) = Y(i)

fn = i

if ((X(i).lt.0.905) .and. (Y(i).gt.0))exit

end do

do i=1,np

if ((X(i).lt.0.905) .and. (Y(i).lt.0))then

fl_s(1) = X(i)

fl_s(2) = Y(i)

fs = i

endif

end do

! Find points of maximum thinckness

do i=1,np

if (y5.lt.Y(i))then

x5 = X(i)

y5 = Y(i)

cn = i

endif

if (y7.gt.Y(i))then

x7 = X(i)

y7 = Y(i)

cs = i

endif

end do

call flap(phi,dy,X,Y,fn)

! Calculating mesh grading

call lenth(X,Y,cn,n0,l4)

call lenth(X,Y,fn,cn,l3)

call grading(l4,f,dels,rays)

call grading(l3,f,dels,mrays)

call lenth(X,Y,1,fn,ln)

call lenth(X,Y,fs,np,ls)

! lfl = Y(1) - Y(np)

call grading(ln,f2,dels,brays)

totalrays = rays + 2*mrays + 2*brays

! Changing flap coordinates

Y(1) = Y(1)+dy

Y(np) = Y(np)+dy

! Define Main Points of the MESH

! Point 0


x0 = x5 - r

y0 = 0

!arcs

call points(r,l4/2,lx,ly)

arc0x = x5 - lx

arc0y = -ly

! Point 1

call points(r,l4,lx,ly)

x1 = x5 - lx

y1 = -ly

!arcs

arc1x = x5

arc1y = -r

! Point 2

call points(r,0.1,lx,ly)

x2 = x5 + lx

y2 = -ly

!arcs

arc2x = r + x5

arc2y = 0

! Point 3

call points(r,0.1,lx,ly)

x3 = x5 + lx

y3 = ly

!arc

arc3x = x5

arc3y = r

! Point 4

call points(r,l4,lx,ly)

x4 = x5 - lx

y4 = ly

!arc

call points(r,l4/2,lx,ly)

arc4x = x5 - lx

arc4y = ly

! Point 5

x5 = x5

y5 = y5

! Point 6

x6 = X(n0)

y6 = Y(n0)

! Point 7

x7 = x7

y7 = y7

! Point 8

x8 = fl_s(1)

y8 = fl_s(2)

! Point 9

x9 = fl_n(1)

y9 = fl_n(2)


! Paralels

! arcs(r,X,Y,cn,cn+1,hx,hy)

pl5x = x5

pl5y = y5 + r/16

pl7x = x7

pl7y = y7 - r/16

! find corrdnates of arc for 9 4 and 8 3

call arcs(r,X,Y,fn,fn+1,hx,hy)

pl9x = x9 + hx + 0.05

pl9y = y5 + hy - 0.005

! Writing important info

write(*,*) ’----------------------------’

write(*,*) ’----------------------------’

write(*,*) ’----------------------------’

write(*,*) ’Number of points’,np

write(*,*) ’----------------------------’

write(*,*) ’Max Thickness ’,x5,y5,cn

write(*,*) ’Leading Edge ’,X(n0),Y(n0),n0

write(*,*) ’Trailing edge ’,X(1),Y(1),X(np),Y(np)

! write(*,*) ’Max Thickness ’,x7,y7,cs

write(*,*) ’Flapnode south ’,fl_s,fs

write(*,*) ’Flapnode north ’,fl_n,fn

write(*,*) ’Flap angle[deg]’,phi,dy

write(*,*) ’----------------------------’

write(*,*) ’----------------------------’

write(*,*) ’----------------------------’

write(*,*) ’Wall mesh points’,totalrays!,rays, mrays, brays

write(*,*) ’-------------’

c__________________________________________________________________

c______________________________________________________________________

c____ WRITING THE OpenFOAM File _____________________________

c______________________________________________________________________

open(unit=1, file=’blockMeshDict’,status=’unknown’)

c---------------------------------------------------------------------

write(1,*)’/*--------------------------------*- C++ -*----’,

1 ’--------------------------*\\’

write(1,*)’| ========= | ’,

1 ’ |’

write(1,*)’| \\ / F ield | OpenFOAM: The Op’,

1 ’en Source CFD Toolbox |’

write(1,*)’| \\ / O peration | Version*: 1.7.1 ’,

1 ’ |’

write(1,*)’| \\ / A nd | Web: http://w’,

1 ’ww.OpenFOAM.org |’

write(1,*)’| \\/ M anipulation | ’,

1 ’ |’

write(1,*)’\\*-----------------------------------------------’,

1 ’------------------------*/’

write(1,*)’ FoamFile’

write(1,*)’ ’

write(1,*)’ version 2.0;’

write(1,*)’ format ascii;’

write(1,*)’ class dictionary;’

write(1,*)’ object blockMeshDict;’

write(1,*)’ ’

write(1,*)’’


write(1,*)’ //* * * * * * * * * * * * * * * * * * * * * * *’,

1 ’ * * * * * * * * * * * * //’

! write(1,901) ’Test’,X(51)

c_____Convert to metres:

write(1,900)’convertToMeters’,ctm,’;’

900 format(A,F5.2,A)

write(1,*)’’

write(1,*)’’

c_____PLACE POINTS:

write(1,*)’vertices’

write(1,*)’(’

write(1,901)’(’,x0,y0,z0,’) //Pt 0’

write(1,901)’(’,x1,y1,z0,’) //Pt 1’

write(1,901)’(’,x2,y2,z0,’) //Pt 2’

write(1,901)’(’,x3,y3,z0,’) //Pt 3’

write(1,901)’(’,x4,y4,z0,’) //Pt 4’

write(1,901)’(’,x5,y5,z0,’) //Pt 5’

write(1,901)’(’,x6,y6,z0,’) //Pt 6’

write(1,901)’(’,x7,y7,z0,’) //Pt 7’

write(1,901)’(’,x8,y8,z0,’) //Pt 8’

write(1,901)’(’,x9,y9,z0,’) //Pt 9’

write(1,901)’(’,x0,y0,z1,’) //Pt 0’

write(1,901)’(’,x1,y1,z1,’) //Pt 1’

write(1,901)’(’,x2,y2,z1,’) //Pt 2’

write(1,901)’(’,x3,y3,z1,’) //Pt 3’

write(1,901)’(’,x4,y4,z1,’) //Pt 4’

write(1,901)’(’,x5,y5,z1,’) //Pt 5’

write(1,901)’(’,x6,y6,z1,’) //Pt 6’

write(1,901)’(’,x7,y7,z1,’) //Pt 7’

write(1,901)’(’,x8,y8,z1,’) //Pt 8’

write(1,901)’(’,x9,y9,z1,’) //Pt 9’

901 format (2X,A1,1X,F9.6,X,F8.4,1X,F6.2,A12)

write(*,*)’’

write(1,*)’);’

c-----PLACE BLOCKS:

write(1,*)’’

write(1,*)’blocks’

write(1,*)’(’

c BLOC 0:

write(1,903)’hex (’,0,1,7,6,10,11,17,16,’) (’,rays,glow,1,

1 ’)’,’simpleGrading (’,f,g,1,’)’!Face 0

write(1,903)’hex (’,1,2,8,7,11,12,18,17,’) (’,mrays,glow,1,

1 ’)’,’simpleGrading (’,1/f,g,1,’)’!Face 1

write(1,903)’hex (’,2,3,9,8,12,13,19,18,’) (’,brays,glow,1,

1 ’)’,’simpleGrading (’,f2,g,1,’)’!Face 2

write(1,903)’hex (’,3,4,5,9,13,14,15,19,’) (’,mrays,glow,1,

1 ’)’,’simpleGrading (’,f,g,1,’)’!Face 3

write(1,903)’hex (’,4,0,6,5,14,10,16,15,’) (’,rays,glow,1,

1 ’)’,’simpleGrading (’,1/f,g,1,’)’!Face 4

write(*,*)’’

write(1,*)’);’

903 format (2X,A5,8(X,I2),A3,2(I3,X),I1,A1,X,A15,2(F8.4,X),X,I1,A1)

c____ PLACE EDGES

write(1,*)’’

write(1,*)’edges’

write(1,*)’(’

! Section 0 6 7


write(1,*)’polySpline’,6,7,’(’

do i=n0+1,cs-1

write(1,909)’(’,X(i),Y(i),z0,’)’

enddo

write(1,*)’) ’


do i=n0+1,cs-1

write(1,909)’(’,X(i),Y(i),z1,’)’

enddo

write(1,*)’) ’

! Section 1 7 8


do i=cs+1,fs-1

write(1,909)’(’,X(i),Y(i),z0,’)’

enddo

write(1,*)’) ’


do i=cs+1,fs-1

write(1,909)’(’,X(i),Y(i),z1,’)’

enddo

write(1,*)’) ’

! Section 2 Trailing edge 9 8


write(1,909)’(’,X(1),Y(1),z0,’)’

write(1,*)’) // trailing edge’


write(1,909)’(’,X(np),Y(np),z1,’)’


! Section 3 9 5


do i=fn+1,cn-1

write(1,909)’(’,X(i),Y(i),z0,’)’

enddo

write(1,*)’) ’


do i=fn+1,cn-1

write(1,909)’(’,X(i),Y(i),z1,’)’

enddo

write(1,*)’) ’

! Section 4 4 0


do i=cn+1,n0-1

write(1,909)’(’,X(i),Y(i),z0,’)’

enddo

write(1,*)’) ’


do i=cn+1,n0-1

write(1,909)’(’,X(i),Y(i),z1,’)’

enddo

write(1,*)’) ’

! Arc 0

write(1,910)’arc’,0,1,’(’,arc0x,arc0y,z0,’)’


! Arc 1




! Arc 2



! Arc 3



! Arc 4



!

! ! 4 5

! write(1,910)’arc’,4,5,’(’,pl5x,pl5y,z0,’)’


!

! ! 1 7



!

!

! ! 9 3



!

! ! 9 3

! write(1,910)’arc’,8,2,’(’,pl9x,-pl9y,z0,’)’

! write(1,910)’arc’,18,12,’(’,pl9x,-pl9y,z1,’)’

! Arc 4 5

write(1,*)’polyLine’,4,5,’(’

write(1,909)’(’,pl5x,pl5y,z0,’)’

write(1,*)’)’


write(1,909)’(’,pl5x,pl5y,z1,’)’

write(1,*)’)’

! Arc 1 7


write(1,909)’(’,pl7x,pl7y,z0,’)’

write(1,*)’)’


write(1,909)’(’,pl7x,pl7y,z1,’)’

write(1,*)’)’

! Arc 9 3


write(1,909)’(’,pl9x,pl9y,z0,’)’



write(1,909)’(’,pl9x,pl9y,z1,’)’


! Arc 8 2


write(1,909)’(’,pl9x,-pl9y,z0,’)’



write(1,909)’(’,pl9x,-pl9y,z1,’)’



write(1,*)’);’

909 format(2x,A10,3(F7.4,X),A1)

910 format(A5,2(X,I2),A4,3(F9.6,2X),A12)

911 format(A5,2(X,I2),A4,3(F7.4,2X),A12)

c____ PLACE PATCHES

write(1,*)’’

write(1,*)’patches’

write(1,*)’(’

write(1,*)’patch inlet’

write(1,*)’(’

write(1,912)’(’,4,14,10,0,’)’

write(1,912)’(’,0,10,11,1,’)’

write(1,*)’)’

write(1,*)’patch outlet’

write(1,*)’(’

write(1,912)’(’,1,11,12,2,’)’

write(1,912)’(’,2,12,13,3,’)’

write(1,912)’(’,3,13,14,4,’)’

write(1,*)’)’

write(1,*)’wall airfoil’

write(1,*)’(’

write(1,912)’(’,5,15,16,6,’)’

write(1,912)’(’,6,16,17,7,’)’

write(1,912)’(’,7,17,18,8,’)’

write(1,912)’(’,8,18,19,9,’)’

write(1,912)’(’,9,19,15,5,’)’

write(1,*)’)’

write(*,*)’’

write(1,*)’);’

912 format (2X,A5 ,4(X,I2),A2)

c____ FINAL COMMAND

write(1,*)’’

write(1,*)’mergePatchPairs’

write(1,*)’(’

write(1,*)’);’

write(1,*)’’

write(1,*)’ //* * * * * * * * * * * * * * * * * * * * * * *’,

1 ’ * * * * * * * * * * * * //’

close(1)

END

subroutine lenth(X,Y,p1,p2,l)


real a,b,l

integer i,p1,p2

l = 0

do i=p1,p2-1

b = Y(i)-Y(i+1)

a = X(i)-X(i+1)

c = sqrt(a*a + b*b)

l = l + c

enddo


end

subroutine grading(l,g,dels,rays)

real l,g,dels,sm

integer rays

sm = l/dels

! pr = (2*(sm - (g/(2*pr))*dels))/((g/(2*pr))*((g/(2*pr))-1))

! x = (2*(a - (b/(2*x))*d))/((b/(2*x))*((b/(2*x))-1)), solve x

pr = g*(g + 4*dels)/(2*(4*sm+g))

rays = g/(2*pr)

! write(*,*)’sm’,sm,pr,rays

end

subroutine points(r,l,lx,ly)

real l,r,lx,ly,alpha

pi = 3.1416

alpha = l*pi

lx = cos(alpha)*r

ly = sin(alpha)*r

! write(*,*)’l,r,lx,ly,alpha’,l,r,lx,ly,alpha

end

subroutine arcs(r,X,Y,p1,p2,hx,hy)


real r,hr,hx,hy,beta

integer p1,p2

hr = r/64

beta = atan(abs(Y(p1)-Y(p2))/abs(X(p1)-X(p2)))

hx = sin(beta)*hr

hy = cos(beta)*hr

! write(*,*)’r,hr,hx,hy,beta’,r,hr,hx,hy,beta

end

subroutine flap(phi,dy,X,Y,fn)


real phi,dy,lf

integer fn

pi = 3.1416

phi = phi*pi/180

lf = abs(X(fn) - X(1))

dy = tan(phi)*lf

phi = (phi/pi)*180

! write(*,*)’phi,dy,lf’,phi,dy,lf

end

Appendix C

OpenFOAM

fvSchemes

/*--------------------------------*- C++ -*----------------------------------*\

| ========= | |

| \\ / F ield | OpenFOAM: The Open Source CFD Toolbox |

| \\ / O peration | Version: 1.7.1 |

| \\ / A nd | Web: www.OpenFOAM.com |

| \\/ M anipulation | |

\*---------------------------------------------------------------------------*/

FoamFile

version 2.0;

format ascii;

class dictionary;

object fvSchemes;

// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //

ddtSchemes

default steadyState;

gradSchemes

default Gauss linear;

grad(p) Gauss linear;

grad(U) Gauss linear;

divSchemes

default none;

div(phi,U) Gauss linearUpwind Gauss linear;

div(phi,k) Gauss upwind;

div(phi,omega) Gauss upwind;

div((nuEff*dev(grad(U).T()))) Gauss linear;

laplacianSchemes

default Gauss linear corrected;

interpolationSchemes

default linear;

51

APPENDIX C. OPENFOAM 52

snGradSchemes

default corrected;

fluxRequired

default no;

p;

// ************************************************************************* //

fvSolution

/*--------------------------------*- C++ -*----------------------------------*\

| ========= | |

| \\ / F ield | OpenFOAM: The Open Source CFD Toolbox |

| \\ / O peration | Version: 1.7.1 |

| \\ / A nd | Web: www.OpenFOAM.com |

| \\/ M anipulation | |

\*---------------------------------------------------------------------------*/

FoamFile

version 2.0;

format ascii;

class dictionary;

object fvSolution;

// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //

solvers

p

solver GAMG;

tolerance 1e-7;

relTol 0.1;

smoother GaussSeidel;

nPreSweeps 0;

nPostSweeps 2;

cacheAgglomeration on;

agglomerator faceAreaPair;

nCellsInCoarsestLevel 10;

mergeLevels 1;

U

solver smoothSolver;


tolerance 1e-8;

relTol 0.1;

nSweeps 1;

k



tolerance 1e-8;

APPENDIX C. OPENFOAM 53

relTol 0.1;

nSweeps 1;

omega



tolerance 1e-8;

relTol 0.1;

nSweeps 1;

SIMPLE

nOuterCorrectors 2;

nCorrectors 2;

nNonOrthogonalCorrectors 0;

pRefCell 0;

pRefValue 0;

residualControl

p 1e-2;

U 1e-3;

"(k|omega)" 1e-3;

relaxationFactors

p 0.3;

U 0.3;//0.6;

k 0.3;//0.6;

omega 0.3;//0.5;

cache

grad(U);

// ************************************************************************* //

Appendix D

Experiment

Airfoil NACA-63418

Figure D.1: Airfoil flap motion sketch, by Clara Vette

Figure D.2: Sketch of the central section with the pressure tabs, by Clara Vette

54

APPENDIX D. EXPERIMENT 55

Linear motor specifications

36 www.LinMot.com Edition 15subject to change

Motor Specification

P01-23Sx80/10x50

Stroke Max. mm (in) 50 (1.97)Stroke SS mm (in) 10 (0.39)Peak Force E1100 / E1001 N (lbf) 39 (8.7)Peak Force E100 N (lbf) 29 (6.5)Cont. Force N (lbf) 8 (1.7)Cont. Force Fan cooling N (lbf) 14 (3.2)Border Force % 71Force Constant N/A (lbf/A) 9.7 (2.17)Max. Current @ 72VDC A 4.0Max. Current @ 48VDC A 3.8Max. Velocity @ 72VDC m/s (in/s) 6.9 (270)Max. Velocity @ 48VDC m/s (in/s) 4.6 (180)Phase Resist. 25/80 °C Ohm 10.3/12.5Phase Inductance mH 1.4Thermal Resistance °K/W 7.0Thermal Time Const. sec 900Stator Diameter mm (in) 23 (0.91)Stator Length mm (in) 105 (4.13)Stator Mass g (lb) 245 (0.54)Slider Diameter mm (in) 12 (0.47)Slider Length mm (in) 130 (5.12)Slider Mass g (lb) 89 (0.20)Position Repeatability mm (in) ±0.05 (±0.0020)Linearity % ±0.70Position Rep. with ES mm (in) ±0.01 (±0.0004)Linearity with ES mm (in) ±0.01 (±0.0004)

Position-Time Diagram

P01-23Sx80/10x50

0

10

20

30

40

E1100, 72VDC &E1001, 72VDCE100, 48VDC

105

Max. Stroke: 50mmPeak Force: 39N

Max. Stroke 50

SS Stroke 10

5

15ZP=20

4525

0 10 20 30 40 500

20

40

60

80

100

120

1.5 kg1.0 kg0.5 kg0.0 kg

Dimensions in mm

ls=130

P01-23Sx80/10x50Standard Winding

Forc

e [N

]

Stroke [mm]

Tim

e [m

s]

Standard Winding:

Moving Slider

P01-

23Sx

80/1

0x50

Figure D.3: Linear motor specification [19]

investigation of 2d airfoils equipped with a trailing edge flaps msc in wind energy

Documents

1app h

upper triangular ordering

6e5exp re7e5exp re1e6

trailing edgewrite

domain bounding box

wind tunnel laboratory

trailing edge

closed singly connected