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Application of Viscous-Inviscid Interaction Methods to Transonic Turbulent Flows Daesung Lee Iowa State University

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Application of Viscous-Inviscid Interaction Methods to Transonic Turbulent Flows Daesung Lee Iowa State University Iowa State University Capstones, Theses and Retrospective Theses and Dissertations Dissertations 1986 Application of viscous-inviscid interaction methods to transonic turbulent flows Daesung Lee Iowa State University Follow this and additional works at: https://lib.dr.iastate.edu/rtd Part of the Mechanical Engineering Commons Recommended Citation Lee, Daesung, "Application of viscous-inviscid interaction methods to transonic turbulent flows " (1986). Retrospective Theses and Dissertations. 8265. https://lib.dr.iastate.edu/rtd/8265 This Dissertation 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]. INFORMATION TO USERS While the most advanced technology has been used to photograph and reproduce this manuscript, the quality of the repr^uction is heavily dependent upon the quality of the material submitted. For example; • Manuscript pages may have indistinct print. In such cases, the best available copy has been filmed. • Manuscripts may not always be complete. In such cases, a note will indicate that it is not possible to obtain missing pages. • Copyrighted material may have been removed from the manuscript. In such cases, a note will indicate the deletion. Oversize materials (e.g., maps, drawings, and charts) are photographed by sectioning the original, beginning at the upper left-hand comer and continuing from left to right in equal sections with small overlaps. Each oversize page is also filmed as one exposure and is available, for an additional charge, as a standard 35mm slide or as a 17"x 23" black and white photographic print. Most photographs reproduce acceptably on positive microfilm or microfiche but lack the clarity on xerographic copies made from the microfilm. For an additional charge, 35mm slides of 6"x 9" black and white photographic prints are available for any photographs or illustrations that cannot be reproduced satisfactorily by xerography. 8703724 Lee, Daesung APPLICATION OF VISCOUS-INVISCID INTERACTION METHODS TO TRANSONIC TURBULENT FLOWS Iowa State University PH.D. 1986 University Microfilms 1nternational 300 N. zeeb Road, Ann Arbor, Ml 48106 Application of viscous-inviscid interaction methods to transonic turbulent flows by Daesung Lee  Dissertation Submitted to the Graduate Faculty in Partial Fulfillment of the Requirements for the Degree of DOCTOR OF PHILOSOPHY Major: Mechanical Engineering Approved: Signature was redacted for privacy. In Charge of Major Work Signature was redacted for privacy. :or the Major Department Signature was redacted for privacy. For the Graopate College Iowa State University Ames, Iowa 1986 ii TABLE OF CONTENTS PAGE NOMENCLATURE x I. INTRODUCTION 1 A. Overview of the Problem 1 B. Literature Review 8 1. Experimental work 9 2. Analytical work 16 a. General 16 b. Navier-Stokes solutions-general 17 c. Navier-Stokes solutions-boattails and bumps ... 18 d. Viscous-inviscid interaction-general 22 e. Viscous-inviscid interaction- boattails and bumps 25 C. Scope and Contributions of the Present Study 32 II. VISCOUS ANALYSIS 38 A. Laws of Conservation 38 1. Conservation, of mass 38 2. Conservation of momentum 39 3. Conservation of energy 39 4. Equation of state 40 B. Turbulent Flows 41 C. Coordinate System 44 D. Boundary-Layer Approximation .... 47 1. Governing equations 49 2. Boundary conditions 51 E. Turbulence Modeling 53 1. The structure of the turbulent boundary layer .... 53 2. Turbulence modeling 60 3. Algebraic model 64 4. Nonequilibrium turbulence model 69 F. Mathematical Model 78 1. Prandtl's transposition theorem 79 2. Nondimensionalization 80 3. Coordinate transformation 81 G. Numerical Method 86 1. Computational grid 87 iii 2. Finite-difference representation 89 a. Continuity and momentum equations 90 b. Energy equation 95 c. Johnson and King turbulence model 97 3. Method of solution 98 III. INVISCID ANALYSIS 104 A. Velocity Potential Equation 104 1. Coordinate system 108 2. Governing equations and boundary conditions .... 108 a. Governing equations 108 b. Boundary conditions 108 3. Nondimensionalization 113 4. Coordinate transformation 114 B. Relaxation Methods 117 C. Numerical Grid Generation 122 1. Governing equations 122 2. Solution procedure 125 D. Algorithms for the Velocity Potential Equation 128 E. Numerical Method 135 1. Finite-difference representation 135 a. Governing equations 135 b. Boundary conditions 138 2. Method of solution 141 a. SLOR method 141 b. AF2 method 146 IV. VISCOUS-INVISCID INTERACTION METHOD 153 A. Semi-Inverse Method 158 • B. Simultaneous Method 162 V. RESULTS AND DISCUSSION 170 A. Incompressible Laminar Flow 171 B. Transonic Turbulent Flow 179 1. Boattail flow 179 2. Bump flow 196 VI. CONCLUSIONS 235 A. Concluding Remarks 235 iv B. Recommendations for Future Study 238 VI r. REFERENCES 240 VIII. ACKNOWLEDGMENTS 257 IX. APPENDIX A: COEFFICIENTS IN THE FINITE-DIFFERENCE REPRESENTATIONS OF THE CONTINUITY AND MOMENTUM EQUATIONS . 258 X. APPENDIX B: "COEFFICIENTS IN THE FINITE-DIFFERENCE REPRESENTATION OF THE ENERGY EQUATION 261 XI. APPENDIX C: RESULTING COEFFICIENTS BY THE USE OF THE MODIFIED THOMAS ALGORITHM 262 XII. APPENDIX .D: TRANSFORMATION FORMULAS USED FOR THE BOUNDARY CONDITIONS IN THE NUMERICAL GRID GENERATION 263 XII. APPENDIX E: COEFFICIENTS IN THE FINITE-DIFFERENCE REPRESENTATIONS USED IN THE NUMERICAL GRID GENERATION ... 265 XIII. APPENDIX F: COEFFICIENTS IN THE FINITE-DIFFERENCE REPRESENTATION OF THE POTENTIAL EQUATION OBTAINED BY THE SLOR SCHEME 267 XIV. APPENDIX G: COEFFICIENTS IN THE FINITE-DIFFERENCE REPRESENTATION OF THE POTENTIAL EQUATION OBTAINED BY THE ÀF2 SCHEME 271 V LIST OF FIGURES PAGE FIGURE 1. Transonic flow field through the interaction 3 FIGURE 2. Coordinate system for the viscous analysis 45 FIGURE 3. Shear-layer coordinate system 46 FIGURE 4. Finite-difference grid for the viscous analysis 88 FIGURE 5. Coordinate system for the inviscid analysis 109 FIGURE 6. Inviscid computational domain in physical coordinates . 110 FIGURE 7. Inviscid computational domain in transformed coordinates 116 FIGURE 8. Grid system for the inviscid analysis 129 FIGURE 9. Differencing molecule for operators 143 FIGURE 10. Coupling algorithms for the interaction method 154 FIGURE 11. Flow chart for the semi-inverse method 161 FIGURE 12. Flow chart for the simultaneous method 168 FIGURE 13. Geometric configuration of a flat plate with a trough . 172 FIGURE 14. Pressure coefficient distribution for an incompressible laminar separation bubble flow over a flat plate with a trough (Re^ = 8 x 10^) 176 FIGURE 15. Displacement thickness distribution for an incompressible laminar separation bubble flow over a 4 flat plate with a trough (Re^ = 8 x 10 ) 177 FIGURE 16. Skin-friction coefficient distribution for an incompressible laminar separation bubble flow over a 4 flat plate with a trough (Re^ = 8 % 10 ) 178 FIGURE 17. Geometric configuration of a boattail 181 FIGURE 18. Computational domain for the inviscid solution of the vi boattail flow 182 FIGURE 19. Pressure coefficient distribution for a transonic turbulent flow over a boattail (Config. 3, = 0.8, Re = 1.22 X lo/) 185 00 ^ FIGURE 20. Skin-friction coefficient distribution for a transonic turbulent flow over a boattail (Config. 3, = 0.8, Re = 1.22 X ic/) 186 00 FIGURE 21. Pressure coefficient distribution for a transonic turbulent flow over a boattail (Config. 1, = 0.7, Re = 1.16 X lo/) 189 00 FIGURE 22. Skin-friction coefficient distribution for a transonic turbulent flow over a boattail (Config. 1, = 0.7, Re = 1.16 X lo/) 190 00 FIGURE 23. Displacement thickness distribution for a transonic turbulent flow over a boattail (Config. 1, = 0.7, Re = 1.16 X lo/) 192 00 FIGURE 24. Maximum Reynolds shear stress distribution for a transonic turbulent flow over a boattail (Config. 1, M = 0.7, Re = 1.16 x lo/) 193 00 00 FIGURE 25. Mean velocity profiles for a transonic turbulent flow over a boattail (Config. 1, M^ = 0.7, Re^ = 1.16 X lo/) 194 FIGURE 26. Geometric configuration of a bump 197 FIGURE 27. Comparison of measured pressure coefficients with predictions for inviscid flow for a transonic turbulent flow over a bump (M^ = 0.875) 200 FIGURE 28. Pressure coefficient distribution for a transonic turbulent flow over a bump (M^ = 0.6) 206 FIGURE 29. Pressure coefficient distribution for a transonic turbulent flow over a bump (M^ = 0.8) 207 FIGURE 30. Pressure coefficient distribution for a transonic turbulent flow over a bump (M = 0.875) 208 - vil FIGURE 31. Pressure coefficient distribution for a transonic turbulent flow over a bump (M^ = 0.9) 209 FIGURE 32. Skln-friction coefficient distribution for a transonic turbulent flow over a bump (M^ = 0.6) 211 FIGURE 33. Skln-friction coefficient distribution for a transonic turbulent flow over a bump (M^ = 0.875) 212 FIGURE 34. Skln-friction coefficient distribution for a transonic turbulent flow over a bump = 0.9) 213 FIGURE 35. Comparison of separation and reattachment locations for a transonic turbulent flow over a bump 214 FIGURE 36. Displacement thickness distribution for a transonic turbulent flow over a bump = 0.6) 217 FIGURE 37. Displacement thickness distribution for a transonic turbulent flow over a bump (M^ = 0.875) 218 FIGURE 38. Maximum Reynolds shear stress distribution for a transonic turbulent flow over a bump (M^ =0.6) .... 219 FIGURE 39. Maximum Reynolds shear stress distribution for a transonic turbulent flow over a bump (M^ = 0.875) . 220 FIGURE 40. Mean velocity profiles for a transonic turbulent flow over a bump (1) (M^ = 0.875) 223 FIGURE 41. Mean velocity profiles for a transonic turbulent flow over a bump (2) (M^ = 0.875) 224 FIGURE 42. Reynolds shear stress profiles for a transonic turbulent flow over a bump (1) (M^ = 0,875) 225 FIGURE 43. Reynolds shear stress profiles for a transonic turbulent flow over a bump (2) (M^ = 0.875) 226 FIGURE 44.
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