Clemson University TigerPrints All Theses Theses 12-2009 2-D and 3-D Assessment of Cambered and Symmetric Airfoils: A CFD Study Tuncay Kamas Clemson University, [email protected] Follow this and additional works at:https://tigerprints.clemson.edu/all_theses Part of theOperations Research, Systems Engineering and Industrial Engineering Commons Recommended Citation Kamas, Tuncay, "2-D and 3-D Assessment of Cambered and Symmetric Airfoils: A CFD Study" (2009).All Theses. 693. https://tigerprints.clemson.edu/all_theses/693 This Thesis is brought to you for free and open access by the Theses at TigerPrints. It has been accepted for inclusion in All Theses by an authorized administrator of TigerPrints. For more information, please [email protected]. ABSTRACT: A two-dimensional and three-dimensional computational study has been carried out respectively regarding aerodynamic forces affecting a symmetric airfoil, NACA0015 and a cambered airfoil, NACA2414. The negative lift (down force) and drag forces were predicted through the simulation of airflows over inverted rear-wings in different configurations namely; varying incidences i.e. angles of attack of the airfoils -two dimensional cross-section of the inverted rear wings to be mounted on back of a car- and varying speeds of initial airflow. The downforce increases as the angle of attack increases however, if an inverted rear wing is fixed on a car at high angle of attacks the rear-wing starts to stall which is not a desired condition affecting the vehicle stability. Furthermore, the camberness added to the airfoil increased the downforce, which contributes more to the stability concept of the automobile. Consequently, three dimensional simulations have evaluated effects of the 3-D features of the airflow over the rear-wings of a road car. The features are tip vortices along the upper edge, the lower edge and at the tip in addition to the sheet vortex along the trailing edge. The visualizations of the vortex vectors and streamlines explicitly depicted the features. The contour and the 2-D plots of the pressure distribution over the inverted rear-wings, set at angle of attack of 4o illustrated the effects of the airflow features. The tip vortices and the vortex sheets decrease the downforce. ii ACKNOWLEDGEMENT: I would like to thank my supervisor, Dr. Mohammad Omar for his encouragement and contributions to me during this project. His attributes were very helpful. I would also like to thank my friends in the research group for sharing their knowledge and nice times together, while I was studying. iii TABLE OF CONTENTS: Abstract .......................................................................................................................................... ii Acknowledgement ........................................................................................................................ iii List of Figures ............................................................................................................................... vi List of Tables .................................................................................................................................. x Nomenclatures ............................................................................................................................... xi 1. Introduction ....................................................................................................................... 1 2. Literature Review .............................................................................................................. 4 2.1.Rearwings on Automobiles ......................................................................................... 4 2.1.1. Boundary Layer .......................................................................................... 5 2.1.2. Adverse Pressure Gradient ........................................................................ 6 2.1.3. Airfoils ......................................................................................................... 8 2.1.4. Effects of Airfoils Geometry .................................................................... 10 2.1.5. Three Dimenasional Aspects of Wings ................................................... 12 2.2. Computational Fluid Dynamics ............................................................................... 14 2.2.1. Reynolds Averaged Navier-Stokes (RANS) Equations ........................ 16 2.2.2. Turbulence Modeling Methods ................................................................. 18 2.2.2.1. One-Equation Turbulence Model ............................................... 19 2.2.2.1.a. Spallart Allmaras One-Equation Turbulence Model ............... 20 2.2.2.2. Two-Equation Turbulence Model ............................................... 24 iv 2.2.2.2.a. The Standard k-ε Two-Equation Turbulence Model .....................25 3. Two-Dimensional Assessment of Cambered and Symmetric Airfoils At Various Angles Of Attack And Speeds: A Cfd Study ...................................................27 3.1. Geometric Features of the Airfoils and Computational Domains and Flow Properties .........................................................................................................27 3.2. Validation of the Computational Process ...............................................29 3.3. Results and Discussion ..............................................................................30 3.4. Conclusions for Two-Dimensional Simulations Over the Symmetric And Cambered Airfoils ..................................................................................................41 4. Three-Dimensional Assessment of Cambered and Symmetric Airfoils at Various Angles of Attack and Speeds: A CFD Study ...................................................42 4.1. Conclusions for Two-Dimensional Simulations Over the Symmetric and Cambered Airfoils ...................................................................................................50 Appendix A .......................................................................................................................53 Appendix B .......................................................................................................................57 References .........................................................................................................................61 v List of Figures Figure 2.1. Velocity distribution near a flat plate in a free stream [14]........................5 Figure 2.2. Transition of boundary layer along a flat plate [14] ...................................6 Figure 2.3. Illustration of the pressure gradients and streamlines of a flow over a circle ....................................................................................................................................7 Figure 2.4. Illustration of the effect of adverse pressure gradient on velocity profile... ...............................................................................................................................8 Figure 2.5. Streamlines in a steady flow over a cambered airfoil..................................8 Figure 2.6. Pressure distribution over symmetric and cambered airfoils [16] .........10 Figure 2.7. Effect of camber on an airfoil’s lift coefficient [16] ..................................11 Figure 2.8. Illustration of a wing with a rectangular section[16] ...............................13 Figure 2.9 . Contours of axial normal turbulence stress normalized on free stream velocity[17] .......................................................................................................................14 Figure 3.1. Geometry of the airfoils (a) NACA2414 cambered airfoil (b) NACA0015 symmetric airfoil ..............................................................................................................27 Figure 3.2. Geometry of the computational domain for NACA0015 correspond the values [13] ........................................................................................................................28 Figure 3.3. Pressure coefficient and velocity magnitude plots of NACA0015 at AOA=0 ..............................................................................................................................29 Figure 3.4. Distribution of Pressure coefficient versus position along the lower and upper surfaces of a-) NACA 0015 airfoil and b-)NACA 2414 airfoil at AOA=4 degree ................................................................................................................................30 vi Figure 3.5. Distribution of Pressure coefficient versus position along the upper surfaces of a-)NACA 0015 airfoil and b-) NACA 2414 airfoil at AOA=4 degree ......33 Figure 3.6. Distribution of Pressure coefficient versus position along the suction surfaces of a-)NACA 0015 airfoil and b-) NACA 2414 airfoil at AOA=4 degree ......34 Figure 3.7. Distribution of velocity magnitude versus position along the lower and upper surfaces of a-) NACA 0015 airfoil and b-) NACA 2414 airfoil at AOA=4 degree ................................................................................................................................36 Figure 3.8. The distribution of the pressure coefficient along the airfoil NACA2414 at different angle of attacks .............................................................................................38 Figure 3.9. The distribution of the velocity magnitude of the airflow at different angle of attacks .................................................................................................................39 Figure 4.1. Illustration of the 3-D inverted rear wing and the computational domain which represents a wind tunnel ......................................................................................43 Figure 4.2. Plot that depicts negative lift and drag forces over the rearwing versus iteration .............................................................................................................................45 Figure 4.3. 2D plot for pressure distribution versus length obtained from 3-D simulations of airflows over NACA0015 and NACA2415 inverted rearwings at angle of attack of 4o ....................................................................................................................46 vii Figure 4.4. Contour plots of pressure distribution on a-) the half-span fictitious plane b-) the wing-tip fictitious plane ............................................................................47 Figure 4.5. Visualization of tip vortices and vortex sheet ............................................48 Figure 4.6 Contour plot of velocity distribution obtained from the simulation of airflow over the NACA2415 cambered inverted rearwing ..........................................48 Figure 4.7. Visualizations of the streamlines generated by simulations of airflows over the NACA2415 and NACA0015 shown respectively ............................................49 Figure A1. Contour plots of a-) dynamic pressure b-) velocity magnitude of NACA2414 at AOA=0 .....................................................................................................53 Figure A2. Contour plots of a-) dynamic pressure b-) velocity magnitude of NACA2414 at AOA=4 .....................................................................................................53 Figure A3. Contour plots of a-) dynamic pressure b-) velocity magnitude of NACA2414 at AOA=8 .....................................................................................................53 Figure A4. Contour plots of a-) dynamic pressure b-) velocity magnitude of NACA2414 at AOA=12 ...................................................................................................54 Figure A5. Contour plots of a-) dynamic pressure b-) velocity magnitude of NACA2414 at AOA=16 ...................................................................................................54 Figure A6. Contour plots of dynamic pressure of NACA0015 at different angle of attacks ...............................................................................................................................55 viii Figure B1. Contour plots of a-) dynamic pressure b-) velocity magnitude of NACA0015 at different angle of attacks ........................................................................57 Figure B2. Contour plots of velocity magnitude of NACA2414 at different angle of attacks ...............................................................................................................................58 Figure B3. Pathlines of NACA2414 at different angle of attacks ................................59 Figure B4. Plots for pressure coefficient of NACA2414 at different speeds through Spallart Allmaras turbulence model ..............................................................................60 ix