Contents Contents i List of Figures iii List of Tables ix Abstract xi Preface xiii 1 Thesis introduction 1 2 Theory 3 2.1 The Navier-Stokes Equations . . . . . . . . . . . . . . . . . . . 3 2.2 Reynolds number . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.3 Reynolds Averaged Navier-Stokes equation, RANS . . . . . . . 5 2.4 Turbulence modelling . . . . . . . . . . . . . . . . . . . . . . . 6 2.5 Transition prediction model . . . . . . . . . . . . . . . . . . . . 8 2.6 Near wall treatment . . . . . . . . . . . . . . . . . . . . . . . . 11 2.7 Airfoil parameters . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.8 Force Coefficients . . . . . . . . . . . . . . . . . . . . . . . . . . 14 2.9 Numerical schemes . . . . . . . . . . . . . . . . . . . . . . . . . 15 2.10 XFOIL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 2.11 Creating the flatback airfoils . . . . . . . . . . . . . . . . . . . 19 3 Meshing 21 4 NACA0012 - Sensitivity Studies 25 4.1 NACA0012 vs NACA0012 blunt . . . . . . . . . . . . . . . . . 25 4.2 Comparisonofbothk−ω SSTandSpalart-Allmarasturbulence models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 4.3 Introducing the transition prediction model . . . . . . . . . . . 34 4.4 y+ dependence study . . . . . . . . . . . . . . . . . . . . . . . . 41 4.5 Domain extent . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 i ii CONTENTS 4.6 Cell count dependence study . . . . . . . . . . . . . . . . . . . 45 4.7 Numerical schemes dependence . . . . . . . . . . . . . . . . . . 47 5 Thick-blunt airfoils validation 49 5.1 Fully Turbulent vs Free Transition . . . . . . . . . . . . . . . . 50 5.2 Comparison of different CFD codes for the airfoil FX-77-W-343 53 5.3 Comparison of different CFD codes for the airfoil FX-77-W-400 58 5.4 Comparison of different CFD codes for the airfoil FX-77-W-500 60 5.5 Comparison of the performance of the airfoils FX-77-W studied 62 6 Thick-flatback airfoils validation 65 6.1 Comparison of different CFD codes for the airfoil FB-3500-0050 66 6.2 Comparison of different CFD codes for the airfoil FB-3500-0875 68 6.3 Comparison of different CFD codes for the airfoil FB-3500-1750 70 6.4 Comparison of the performance of the airfoils FB-3500 studied 72 6.5 Study of the flow around flatback airfoils. . . . . . . . . . . . . 81 7 Thick-flatback airfoils study 89 7.1 Flatbacking of the airfoils studied . . . . . . . . . . . . . . . . . 89 7.2 NEW flatback airfoils . . . . . . . . . . . . . . . . . . . . . . . 92 7.3 NEWsym flatback airfoils . . . . . . . . . . . . . . . . . . . . . 94 7.4 NEWthick flatback airfoils . . . . . . . . . . . . . . . . . . . . . 97 7.5 NACA8648 flatback airfoils . . . . . . . . . . . . . . . . . . . . 100 8 Comments to the convergence of the solution 107 8.1 Initialization of the field with potentialFoam . . . . . . . . . . . 107 8.2 Sensitivity Study . . . . . . . . . . . . . . . . . . . . . . . . . . 109 9 Conclusion 111 9.1 Future work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 9.2 Future work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114 Bibliography 115 Appendices 118 A Meshing a NACA0012 with a sharp trailing edge 119 B Results computed with ANSYS CFX and Ellipsys for the airfoils FX-77-W 125 C Results computed with ANSYS CFX and Ellipsys for the airfoils FB-3500-XXXX 129 D Comparison of the results obtained with OpenFOAM and ANSYS CFX for the airfoils NEW TE X% 133 E Comparison of the results obtained with OpenFOAM and ANSYS CFX for the airfoils NEWsym TE X% 137 F Comparison of the results obtained with OpenFOAM and ANSYS CFX for the airfoils NEWthick TE X% 141 G Mesh dependence study for the airfoil FX-77-W-400 145 H Mesh dependence study for the airfoil FB-3500-0875 149 I Example of the fvSolution file of OpenFOAM 153 List of Figures 2.1 Notation used to obtain the stress tensor. Obtained from reference [17] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.2 Boundary layer on a flat plate. y scale greatly enlarged. Obtained from reference [22]. . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.3 Typical velocity profile of a turbulent boundary layer. Obtained from reference [18] . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 2.4 Possibilities of near wall treatment in CFD. Obtained from refe- rence [21]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.5 Parameters describing the geometry of an airfoil. . . . . . . . . . . 14 2.6 Aerodynamic forces on an airfoil. Obtained from reference [23]. . . 15 2.7 Control volume around a node P. Obtained from [19]. . . . . . . . 16 2.8 Gradients at the faces for a linear scheme. Obtained from [19]. . . 17 2.9 Gradients at the faces for a quadratic scheme. Obtained from [19]. 17 2.10 Sketch of the parameters used by the function TGAP of XFOIL. Created by Alejandro Gómez. . . . . . . . . . . . . . . . . . . . . . 20 3.1 Zoom of the airfoil FB-3500-0875 meshed using an O-mesh. . . . . 21 3.2 ZoomoftheairfoilFB-3500-0875meshedusingaC-mesh. Example of a mesh not optimal for flatback airfoils. . . . . . . . . . . . . . . 22 3.3 ZoomatthetrailingedgeoftheAirfoilFB-3500-0875meshedusing a C-mesh. Example of a mesh not optimal for flatback airfoils. . . 22 4.1 GeometryoftheNACA0012airfoilandtheNACA0012airfoilwith the blunt trailing edge. . . . . . . . . . . . . . . . . . . . . . . . . . 25 iii iv List of Figures 4.2 Aerodynamic coefficient curves for the airfoil NACA0012 original andtruncated,forRe=3.000.000. CurvesobtainedwithOpenFOAM. 27 4.3 Lift coefficient curves for the airfoil NACA0012 with the blunt trailing edge using the k−ω SST turbulence model. Re=3.000.000 28 4.4 Drag coefficient curves for the airfoil NACA0012 with the blunt trailing edge using the k−ω SST turbulence model. Re=3.000.000. 29 4.5 ResidualsduringthecomputationperformedfortheSpalart-Allmaras turbulence model and an angle of attack of 8 degrees. Simula- tion run for the airfoil NACA0012 with the blunt trailing edge at Re=3.000.000 using OpenFOAM. . . . . . . . . . . . . . . . . . . . 30 4.6 Residuals during the computation performed for the k − ω SST turbulence model and an angle of attack of 8 degrees. Simula- tion run for the airfoil NACA0012 with the blunt trailing edge at Re=3.000.000 using OpenFOAM. . . . . . . . . . . . . . . . . . . . 31 4.7 Force coefficients history for the Spalart-Allmaras turbulence mo- del and an angle of attack of 8 degrees. Simulation run for the airfoil NACA0012 with the blunt trailing edge at Re=3.000.000. . 31 4.8 Force coefficients history for the k−ω SST turbulence model and an angle of attack of 8 degrees. Simulation run for the airfoil NACA0012 with the blunt trailing edge at Re=3.000.000. . . . . . 32 4.9 Aerodynamic coefficient curves for the computations using both turbulence models using OpenFOAM. NACA0012 with blunt trai- ling edge at Re=3.000.000. . . . . . . . . . . . . . . . . . . . . . . 33 4.10 Aerodynamic coefficient curves for the computations with Open- FOAM with and without transition model for the boundary layer. NACA0012 at Re=3.000.000. . . . . . . . . . . . . . . . . . . . . . 35 4.11 CurvesofthepressurecoefficientCpfortheNACA0012atanangle ofattackof10degreesandRe=3.000.000. Experimentaldatataken from [12]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 4.12 Friction coefficient curves for the airfoil NACA0012 at an angle of attack of 10 degrees and Re=3.000.000. . . . . . . . . . . . . . . . 37 4.13 C curves at both pressure and suction side for the different cases f specified for a NACA0012 at an angle of attack of 2 degrees at Re=3.000.000. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 4.14 C curves for the different cases specified for a NACA0012 at an p angle of attack of 2 degrees at Re=3.000.000. . . . . . . . . . . . . 39 4.15 PositionpredictedforthetransitionpointontheairfoilNACA0012 at Re=3.000.000. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 4.16 y+ sensitivitystudyontheNACA0012airfoilwiththetrailingedge blunt at Re=3.000.000. . . . . . . . . . . . . . . . . . . . . . . . . 42 4.17 Topologyviewofthemeshesdoneinordertodothedomainextent sensitivity study. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 4.18 Sensitivity study of the domain extent. Simulations for the airfoil NACA0012 with the blunt trailing edge at Re=3.000.000. . . . . . 44 List of Figures v 4.19 Mesh dependence study for the NACA0012 with the blunt trailing edge for an angle of attack of 2 degrees at Re=3.000.000. . . . . . 45 4.20 Mesh dependence study for the NACA0012 with the blunt trailing edge for an angle of attack of 8 degrees at Re=3.000.000. . . . . . 46 4.21 Mesh dependence study for the NACA0012 with the blunt trailing edge for an angle of attack of 14 degrees at Re=3.000.000. . . . . . 46 4.22 Aerodynamiccoefficientsobtainedfordifferentdifferencingschemes intheconvectivetermsoftheRANSequation. Testedattheairfoil NACA0012 with the blunt trailing edge at Re=3.000.000. . . . . . 48 5.1 Comparison of the geometry of the airfoil FX-77-W studied. . . . . 50 5.2 Aerodynamic coefficients for the airfoil FX-77-W-343 with and wi- thout transition model applied at Re=3.000.000. . . . . . . . . . . 51 5.3 Aerodynamic coefficients for the airfoil FX-77-W-343 with and wi- thout transition model applied at Re=3.000.000. Results obtained with ANSYS CFX . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 5.4 AerodynamiccoefficientsfortheairfoilFX-77-W-343atRe=3.000.000. 54 5.5 Contour plot of the velocity field for the airfoil FX-77-W-343 at Re=3.000.000 and an angle of attack of 14 degrees. . . . . . . . . . 55 5.6 Numerical schemes dependence study for the airfoil FX-77-W-343 at the stall region at Re=3.000.000. . . . . . . . . . . . . . . . . . 57 5.7 AerodynamiccoefficientsfortheairfoilFX-77-W-400atRe=4.000.000. 59 5.8 Aerodynamic coefficients for the airfoil FX-77-W-500 at the Rey- nolds number specified. . . . . . . . . . . . . . . . . . . . . . . . . 61 5.9 Comparison of the results for the lift coefficient of the airfoils FX- 77-WatthedifferentReynoldsnumberspecified. OpenFOAM=solid line. Experiments=broken line. . . . . . . . . . . . . . . . . . . . . 63 5.10 ComparisonoftheresultsforthedragcoefficientoftheairfoilsFX- 77-WatthedifferentReynoldsnumberspecified. OpenFOAM=solid line. Experiments=broken line. . . . . . . . . . . . . . . . . . . . . 63 6.1 Comparison ofthe geometryof theairfoil flatbackFB-3500-XXXX studied. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 6.2 AerodynamiccoefficientsfortheairfoilFB-3500-0050atRe=666.000. 67 6.3 AerodynamiccoefficientsfortheairfoilFB-3500-0875atRe=666.000. 69 6.4 AerodynamiccoefficientsfortheairfoilFB-3500-1750atRe=666.000. 71 6.5 Comparison of the the lift coefficient for the airfoils FB-3500 at Re=666.000. OpenFOAM = solid line, Experiments = broken line. 73 6.6 ComparisonofthedragcoefficientfortheairfoilsFB-3500atRe=666.000. OpenFOAM = solid line, Experiments = broken line. . . . . . . . 73 6.7 Comparison of the lift to drag ratio of the airfoils FB-3500 at Re=666.000. OpenFOAM = solid line, Experiments = broken line. 74 6.8 Streamlines for the airfoil FB-3500-0050 at an angle of attack of 14 degrees at Re=666.000. . . . . . . . . . . . . . . . . . . . . . . . 74 vi List of Figures 6.9 Streamlines for the airfoil FB-3500-0875 at an angle of attack of 14 degrees at Re=666.000. . . . . . . . . . . . . . . . . . . . . . . . 75 6.10 Streamlines for the airfoil FB-3500-1750 at an angle of attack of 14 degrees at Re=666.000. . . . . . . . . . . . . . . . . . . . . . . . 76 6.11 Cp curves for the airfoils FB-3500 simulated with OpenFOAM for an angle of attack of 14 degrees at Re=666.000. . . . . . . . . . . . 76 6.12 Friction coefficient curves for the airfoils FB-3500 simulated with OpenFOAM for an angle of attack of 14 degrees at Re=666.000. . 77 6.13 Turbulent kinetic energy field for the airfoil FB-3500-0050 at an angle of attack of 14 degrees at Re=666.000. . . . . . . . . . . . . 78 6.14 Turbulent kinetic energy field for the airfoil FB-3500-1750 at an angle of attack of 14 degrees at Re=666.000 . . . . . . . . . . . . . 78 6.15 Comparison of the location of the transition point for the different airfoils specified at Re=666.000.. . . . . . . . . . . . . . . . . . . . 80 6.16 Comparisonofthemagnitudeofthevelocityatthewakeoftheair- foilFB-3500-1750atadistancexfromthetrailingedge. Re=666.000 and angle of attack 14 degrees. . . . . . . . . . . . . . . . . . . . . 81 6.17 Vector field of the velocity at the wake of airfoil FB-3500-1750 at Re=666.000 and an angle of attack of 14 degrees. . . . . . . . . . . 82 6.18 Comparison of the geometry of the airfoil FB-3500-1750 and the airfoilsgeneratedaddingchorddownstreaminthedeadwaterregion. 82 6.19 Vector field of the velocity at the wake of airfoil FB-3500-1750 at Re=666.000 and an angle of attack of 14 degrees. . . . . . . . . . . 83 6.20 Comparison of the geometry of the airfoil FB-3500-1750 and the airfoilsgeneratedaddingchorddownstreaminthedeadwaterregion. 84 6.21 Velocity field and streamlines for the airfoil FB-3500-1750 with an addition of 20 % of the chord length into the dead water region shown in figure 6.10. Re=666.000 and angle of attack of 14 degrees. 84 6.22 Velocity field and streamlines for the airfoil FB-3500-1750 with an addition of 35 % of the chord length into the dead water region shown in figure 6.10. Re=666.000 and angle of attack of 14 degrees. 85 6.23 Turbulent kinetic energy field for the airfoil FB-3500-1750 with an addition of 20 % of the chord length into the dead water region shown in figure 6.10. Re=666.000 and angle of attack of 14 degrees. 86 6.24 Turbulent kinetic energy field for the airfoil FB-3500-1750 with an addition of 35 % of the chord length into the dead water region shown in figure6.10. Re=666.000 and angle of attack of 14 degrees. 87 7.1 Different openings done by Risø DTU at the airfoil DU-97-W-300 (shown in red color). Figures obtained from [27]. . . . . . . . . . . 90 7.2 Results for the different flatback airfoils created by Risø DTU, shown in figures 7.1. Figures obtained from [27]. . . . . . . . . . . 91 7.3 Lift coefficient normalized for the airfoil NEW at Re=4.000.000. . 92 7.4 Drag coefficient normalized for the airfoil NEW at Re=4.000.000.. 93 List of Figures vii 7.5 Lift-to-drag ratio normalized for the airfoil NEW at Re=4.000.000. 93 7.6 Lift coefficient normalized for the airfoil NEWsym at Re=4.000.000. 95 7.7 DragcoefficientnormalizedfortheairfoilNEWsym atRe=4.000.000. 95 7.8 Lift-to-dragrationormalizedfortheairfoilNEWsymatRe=4.000.000. 96 7.9 Lift coefficient normalized for the airfoil NEWthick at Re=4.000.000. 98 7.10 DragcoefficientnormalizedfortheairfoilNEWthick atRe=4.000.000. 98 7.11 Lift-to-dragrationormalizedfortheairfoilNEWthick atRe=4.000.000. 99 7.12 Comparison of the geometry of the flatback airfoils NACA8648. . . 100 7.13 LiftcoefficientnormalizedfortheairfoilNACA8648atRe=4.000.000.101 7.14 DragcoefficientnormalizedfortheairfoilNACA8648atRe=4.000.000.102 7.15 Lift-to-dragrationormalizedfortheairfoilNACA8648atRe=4.000.000.102 7.16 Location of the transition point for laminar to turbulent boundary layer at the airfoil NACA8648 at Re=4.000.000.. . . . . . . . . . . 103 7.17 Pressure coefficient at the airfoil NACA8648 at Re=4.000.000 and an angle of attack of 10 degrees. . . . . . . . . . . . . . . . . . . . 104 7.18 Friction coefficient at the airfoil NACA8648 at Re=4.000.000 and an angle of attack of 10 degrees. . . . . . . . . . . . . . . . . . . . 105 8.1 Solution for the flow around a flat plate at time step 15, field initialized with potentialFoam. . . . . . . . . . . . . . . . . . . . . 108 8.2 Solution for the flow around a flat plate at time step 15, field not initialized with potentialFoam. . . . . . . . . . . . . . . . . . . . . 108 A.1 Different C-meshes tried for the airfoil NACA0012. . . . . . . . . . 120 A.2 Lift coefficient curves for the airfoil NACA0012 at Re=3.000.000 with different distribution of cells, cases from table A.1. Curves obtained with ANSYS CFX. . . . . . . . . . . . . . . . . . . . . . 122 A.3 Drag coefficient curves for the airfoil NACA0012 at Re=3.000.000 with different distribution of cells, cases from table A.1. Curves obtained with ANSYS CFX. . . . . . . . . . . . . . . . . . . . . . 122 A.4 Lift coefficient curves for the airfoil NACA0012 at Re=3.000.000 for the mesh from figure A.1d, case 5 from table A.1. . . . . . . . . 123 A.5 Drag coefficient curves for the airfoil NACA0012 at Re=3.000.000 for the mesh from figure A.1d, case 5 from table A.1. . . . . . . . 123 B.1 Comparison of the results obtained with ANSYS CFX and Ellip- sys of the lift coefficient for the airfoils FX-77-W at the different Reynolds number specified. . . . . . . . . . . . . . . . . . . . . . . 126 B.2 ComparisonoftheresultsobtainedwithANSYSCFXandEllipsys for the drag coefficient of the airfoils FX-77-W at the different Reynolds number specified. . . . . . . . . . . . . . . . . . . . . . . 126 B.3 ComparisonoftheresultsobtainedwithANSYSCFXandEllipsys for the lift-to-drag ratio of the airfoils FX-77-W at the different Reynolds number specified. . . . . . . . . . . . . . . . . . . . . . . 127 C.1 Comparison of the the lift coefficient for the airfoils FB-3500 at Re=666.000. ANSYS CFX = solid line, Ellipsys = broken line. . . 130 C.2 ComparisonofthedragcoefficientfortheairfoilsFB-3500atRe=666.000. ANSYS CFX = solid line, Ellipsys = broken line. . . . . . . . . . . 130 C.3 Comparison of the lift to drag ratio of the airfoils FB-3500 at Re=666.000. ANSYS CFX = solid line, Ellipsys = broken line. . . 131 D.1 Lift coefficient normalized for the airfoil NEW at Re=4.000.000. OpenFOAM=solid line, ANSYS CFX=broken line. . . . . . . . . . 134 D.2 Drag coefficient normalized for the airfoil NEW at Re=4.000.000. OpenFOAM=solid line, ANSYS CFX=broken line. . . . . . . . . . 134 D.3 Lift-to-dragrationormalizedfortheairfoilNEW atRe=4.000.000. OpenFOAM=solid line, ANSYS CFX=broken line. . . . . . . . . . 135 E.1 LiftcoefficientnormalizedfortheairfoilNEWsymatRe=4.000.000. OpenFOAM=solid line, ANSYS CFX=broken line. . . . . . . . . . 138 E.2 DragcoefficientnormalizedfortheairfoilNEWsymatRe=4.000.000. OpenFOAM=solid line, ANSYS CFX=broken line. . . . . . . . . . 138 E.3 Lift-to-dragrationormalizedfortheairfoilNEWsymatRe=4.000.000. OpenFOAM=solid line, ANSYS CFX=broken line. . . . . . . . . . 139 F.1 LiftcoefficientnormalizedfortheairfoilNEWthick atRe=4.000.000. OpenFOAM=solid line, ANSYS CFX=broken line. . . . . . . . . . 142 F.2 DragcoefficientnormalizedfortheairfoilNEWthick atRe=4.000.000. OpenFOAM=solid line, ANSYS CFX=broken line. . . . . . . . . . 142 F.3 Lift-to-dragrationormalizedfortheairfoilNEWthick atRe=4.000.000. OpenFOAM=solid line, ANSYS CFX=broken line. . . . . . . . . . 143 G.1 Mesh dependence study for an angle of attack of 0 degrees for the airfoil FX-77-W-400 at Re=4.000.000. . . . . . . . . . . . . . . . . 146 G.2 Mesh dependence study for an angle of attack of 8 degrees for the airfoil FX-77-W-400 at Re=4.000.000. . . . . . . . . . . . . . . . . 147 H.1 Mesh dependence study for an angle of attack of 0 degrees for the airfoil FB-3500-0875 at Re=666.000. . . . . . . . . . . . . . . . . . 150 H.2 Mesh dependence study for an angle of attack of 8 degrees for the airfoil FB-3500-0875 at Re=666.000. . . . . . . . . . . . . . . . . . 151 H.3 Mesh dependence study for an angle of attack of 16 degrees for the airfoil FB-3500-0875 at Re=666.000. . . . . . . . . . . . . . . . . . 151 viii