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Validation and Comparison of Modern Lifting-Line and Lifting-Surface Methods for Application to Clean and Iced Wings Nicholas James Crist Iowa State University

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Validation and Comparison of Modern Lifting-Line and Lifting-Surface Methods for Application to Clean and Iced Wings Nicholas James Crist Iowa State University Masthead Logo Iowa State University Capstones, Theses and Retrospective Theses and Dissertations Dissertations 1-1-2006 Validation and comparison of modern lifting-line and lifting-surface methods for application to clean and iced wings Nicholas James Crist Iowa State University Follow this and additional works at: https://lib.dr.iastate.edu/rtd Recommended Citation Crist, Nicholas James, "Validation and comparison of modern lifting-line and lifting-surface methods for application to clean and iced wings" (2006). Retrospective Theses and Dissertations. 18966. https://lib.dr.iastate.edu/rtd/18966 This Thesis is brought to you for free and open access by the Iowa State University Capstones, Theses and Dissertations at Iowa State University Digital Repository. It has been accepted for inclusion in Retrospective Theses and Dissertations by an authorized administrator of Iowa State University Digital Repository. For more information, please contact [email protected]. Validation and comparison of modern lifting-line and lifting-surface methods for application to clean and iced wings by Nicholas James Crist A thesis submitted to the graduate faculty in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE Major: Aerospace Engineering Program of Study Committee: Richard G. Hindman, Major Professor Tom I-P. Shih Alric Rothmayer Adin Mann Iowa State University Ames, Iowa 2006 Copyright ©Nicholas James Crist, 2006. All rights reserved. 11 Graduate College Iowa State University This is to certify that the master's thesis of Nicholas James Crist has met the thesis requirements of Iowa State University Signatures have been redacted for privacy 111 TABLE OF CONTENTS LIST OF TABLES v LIST OF FIGURES vi ACKNOWLEDGEMENTS ix ABSTRACT x CHAPTER 1. INTRODUCTION 1 CHAPTER 2. CHRONOLOGICAL PROGRESSION OF LIFTING-LINE METHODS 3 2.1 Lifting-Line Theory 4 2.1.1 Prandtl 5 2.1.2 Weissinger 6 2.1.3 Blackwell 7 2.1.4 Lifting Surface 8 22 Viscous Coupling 9 2.2.1 I' correction 9 2.2.2 a correction g CHAPTER 3. Q3D-WING THEORY 12 3.1 Lifting-Line Method 12 3.1.1 Local horseshoe vortex arrangement 15 3.2 Viscous Coupling Method 17 CHAPTER 4. VORTEX LATTICE DECAMBERING THEORY 20 4.1 Lifting Surface 21 1V 4.2 Viscous Coupling Methods 22 4.2.1 Scheme one 23 4.2.2 Scheme two 26 4.3 Modified Decambering Method 28 4.3.1 Decambering algorithm 30 CHAPTER 5. VALIDATII~N 32 5.1 Potential Methods 32 5.2 Viscous Coupling 34 5.2.1 Clean wings 36 5.2.2 Iced wings 42 5.3 Multiple Solutions 44 CHAPTER 6. CONCLUSIONS 51 CHAPTER 7. FUTURE v'~ORK 54 APPENDIX . HORIZONTAL TAIL RESULTS 55 BIBLIOGRAPHY 59 V LIST of TABLES Table 5.1 Wing planform shapes for span loading validation 32 Table 5.2 Clean wing validation cases 36 Table 5.3 Iced wing validation cases 43 V1 LIST OF FIGURES Figure 1.1 2D mesh of an iced airfoil 1 Figure 2.1 Finite wing effects 3 Figure 2.2 Velocity gradient created by a point vortex superimposed in a uniform flow 4 Figure 2.3 Multiple horseshoe vortices along the wing quarter-chord 5 Figure 2.4 Blackwell's staggered horseshoe vortices 7 Figure 2.5 Lifting surface theory 8 Figure 2.6 Decambering approach 11 Figure 3.1 Induced velocity from a straight vortex filament segment 13 Figure 3.2 Induced drag 15 Figure 3.3 Horseshoe arrangement 16 Figure 3.4 Viscous correction 19 Figure 4.1 Vortex Lattice Method 21 Figure 4.2 CIVLM and Cl~is~ intersection. 24 Figure 4.3 Convergence problems with the decambering method 26 Figure 4.4 'I~ajectory lines 27 Figure 4.5 Large changes in target Cl for scheme 2. 28 Figure 5.1 Span loading for rear swept wings 33 Figure 5.2 Span loading fora 0.9° swept wing 33 Figure 5.3 Span loading for forward swept wings 34 V11 Figure 5.4 NACA 64A010 airfoil 37 Figure 5.5 NACA 64A010 airfoil 40 Figure 5.6 Comparison of NACA 23012 and 64A010 airfoils 40 Figure 5.7 Results for a wing having an AR of six, taper ratio of 1.0, and a sweep of 0.0° 41 Figure 5.8 Results for a wing having an AR of six, taper ratio of 0.2, and a sweep of 6.34° 41 Figure 5.9 Drag results for the NACA 23012 wings 42 Figure 5.10 2D iced airfoil aerodynamics 43 Figure 5.11 Results for a clean wing having an AR of four, taper ratio of 1.0, and a sweep of 0.0° 44 Figure 5.12 Results for the 212 rime ice wing 44 Figure 5.13 Results for the 944 glaze ice wing 45 Figure 5.14 Multiple solutions for. viscous coupling procedures 45 Figure 5.15 Potential span loading for different initial correction values at 20° angle of attack 46 Figure 5.16 Target span loading at 20° angle of attack 47 Figure 5.17 Overcompensation for the initial value of the viscous correction term 47 Figure 5.18 Converged span loading at 20° angle of attack 48 Figure 5.19 Effective angle of attack for first and final iteration 48 Figure 5.20 Converged span loading at 5° angle of attack for different initial S1 values 49 Figure 5.21 Cancellation of over compensation for initial bl 50 Figure A.1 Results for a wing having an AR of two, taper ratio of 0.5, and a sweep of 16.7° 55 Figure A.2 Results for a wing having an AR of two, taper ratio of 0.5, and a sweep of 45.0° 55 Figure A.3 Results for a wing having an AR of three, taper ratio of 0.5, and a sweep of 11.3° 56 viii Figure A.4 Results for a wing having an AR of three, taper ratio of 0.5, and a sweep of 35.0° 56 Figure A.5 Results for a wing having an AR of four, taper ratio of 0.5, and a sweep of 7.6° 57 Figure A.fi Results for a wing having an AR of four, taper ratio of 0.5, and a sweep of 35.0° 57 Figure A.7 Results for a wing having an AR of six, taper ratio of 0.5, and a sweep of 5.7° 58 Figure A.8 Results for a wing having an AR of six, taper ratio of 0.5, and a sweep of 35.0° 58 1X ACKNOWLEDGEMENTS I would like to extend my sincere thanks to Dr. Richard Hindman for his guidance and encouragement during my graduate and undergraduate studies. Dr. Hindman's daily excite- ment and enthusiasm for his work has been an inspiration. My sincere thanks to Dr. Tom I-P. Shih for his contributions to this work and his never ending energy and passion for research. Dr. Shih's encouraging remarks and continual good nature have made the long late nights of work worthwhile. I would also like to thank the other members of my committee, Dr. Alric Rothmayer and Dr. Adin Mann, whose valuable comments improved the quality of this work. I am very grateful for the hard work and dedication of my fellow graduate research partner, Brandon Williams, who was instrumental in the development and validation of the lifting-line method (Q3D) . My thanks to Kyle Chi who provided all the icing data. I thank Ashvin Mahajan for always taking the time to help me with any technical problems. His excitement for teaching and his passion for inspiring undergraduate students, including myself, has been an incredible asset to the department. And above all, a sincere thanks to my friends and family whose love and patience have carried me through the late nights and long weeks of the past few years. X ABSTRACT Computational fluid dynamics (CFD) has become a valuable tool for predicting the aero- dynamics of finite wings. However, wings with ice accretion require an incredible amount of resolution to capture the intricate details of the ice shape. This can lead to an overwhelming amount of grid points and CFD analysis can become impractical or even impossible for such problems. Therefore, two fast and accurate methods have been developed for predicting the aerodynamics of clean and iced wings. The present methods combine known viscous airfoil data with a modern lifting-line or lifting-surface method. Validation against experimental and computational results show both methods to provide accurate predictions of the aerodynamics for clean and iced wings. The present methods experienced non-unique solutions at high an- gles of attack, a phenomenon noted by other researchers but never thoroughly explained. The present work provides an explanation for these multiple solutions. 1 CHAPTER 1. INTRODUCTION Between 1990 and 2000 there where 388 aircraft accidents attributed to aircraft icing, 105 of which where fatal. 10 Aircraft icing disrupts the flow over the surfaces causing reduced lift, decreased angle of attack for maximum lift, and significantly increased drag. Tests have shown that ice no thicker or rougher than a piece of coarse sandpaper can reduce lift by 30 percent and increase drag by 40 percent. Larger ice accretions can increase drag by 80 percent or more. Performance degradation due to icing is incredibly difficult to predict with Computational Fluid Dynamics (CFD) because of the large number of grid points required to resolve the intricate ice shapes. Efficient methods for meshing 2D iced airfoils have recently been developed and presented by Chi, et a1.5 More than a one hundred thousand grid points are required for a typical mesh of an iced airfoil.
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