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Skin Friction Drag and Shear Stress Distribution on Several Streamlined Bodies of Revolution with Varied Fineness Ratio

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Skin Friction Drag and Shear Stress Distribution on Several Streamlined Bodies of Revolution with Varied Fineness Ratio Calhoun: The NPS Institutional Archive Theses and Dissertations Thesis Collection 1964 Skin Friction Drag and Shear Stress Distribution on Several Streamlined Bodies of Revolution With Varied Fineness Ratio. Dunning, Cleveland L. Monterey, California. Naval Postgraduate School http://hdl.handle.net/10945/26252 NPS ARCHIVE 1964 DUNNING, C. RKIN FRICTION DRAG AND SMEAR STRESS DISTRIBUTION ON SEVERAL STREAMLINED BODIES OF REVOLUTION WITH VARIED FINENESS RATIO E v'". .i VI LAND L PUNNING ROBERT F. OVERMYER COLBEN K. SIME, JR. is s A ffWmmM' LIBRARY U.S. NAVAL POSTGRADUATE SCHOOL MONTEREY, CALIFORNIA SKIN FRICTION DRAG AND SHEAR STRESS DISTRIBUTION Oil SEVERAL STREAMLINED BODIES OF REVOLUTION WITH VARIED FINENESS RATIO 3)C >fC >f< 3fC 3fi Cleveland L. Dunning Robert F. Overmyer and Colben K. Sime, Jr. f t mm* # LIBRARY OS. NAVAL POSTGRADUATE SCHOOL MONTEREY, CALIFORNIA SKIN FRICTION DRAG AND SHEAR STRESS DISTRIBUTION ON SEVERAL STREAMLINED BODIES OF REVOLUTION WITH VARIED FINENESS RATIO by Cleveland L. Dunning Captain, United States Marine Corps Robert F. Overmyer Captain, United States Marine Corps and Colben K. Sime, Jr. Captain, United States Marine Corps Submitted in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE with major in Aeronautics United States Naval Postgraduate School Monterey, California 1964 SKIN FRICTION DRAG AND SHEAR STRESS DISTRIBUTION ON SEVERAL STREAMLINED BODIES OF REVOLUTION WITH VARIED FINENESS RATIO by Cleveland L. Dunning Robert F. Overmyer and Colben K. Sime, Jr. This thesis is accepted in partial fulfillment for the degree of MASTER OF SCIENCE with major in Aeronautics from the United States Naval Postgraduate School ACKNOWLEDGEMENT The authors wish to express their sincere gratitude to Professor George J. Higgins for his great interest, help and encouragement in the completion of this work. Professor Higgins., in addition to his full schedule as a faculty member and on short notice, proposed this project and has graciously provided time and guidance toward the fulfillment of this objective. In addition, many stimulating discussions by Professor Higgins in previous courses in fluid mechanics and aerodynamics are acknowledged. 11 ABSTRACT Experimental techniques were employed to determine the coefficient of skin friction drag and the distribution of local frictional intensity for several low drag bodies of revolution with mixed laminar and turbulent flow The data were obtained as a function of fineness ratio and Reynolds number from experiments conducted in the U. S. Naval Postgraduate School subsonic wind tunnel under conditions equivalent to incomDressible flow. Skin friction drag coefficients were determined first by the indirect method of subtracting pressure drag from total drag. A second more direct method was the deter- mination of local shear distributions and integration over the surface area to obtain total frictional drag* The possibility of inaccuracies introduced by assumptions and agreement between results of the two methods are discussed 111 TABLE OF CONTENTS Section Title Page 1. Introduction 1 2. Equipment and Procedures 2 a. Total Drag Measurements 3 b. Support Drag Lf c. Local Pressure Distribution Measurements 5 d. Boundary Layer Probe 6 3. Presentation of Results 3 h. Skin Friction Determined From Total Drag Minus Pressure Drag 8 a. Total Drag 3 b. Pressure Drag 13 c. Skin Friction Drag 18 5. Direct Determination of Local Skin Friction Intensity 21 a. Analytical and Theoretical Methods 26 b. Experimental Estimate of Shear Stresses 30 6. Comparison of Results 38 7. Conclusion *+0 References *+3 Tables ^5 Illustrations 9^ IV LIST OF TABLES Table Page I Diameter-Length Coordinates, Streamlined Bodies, 66(215) - OXX h5 II Model Characteristics, 66(215) - CXX 1+6 III Pressure Orifice Locations, Streamlined Bodies, 66(215) - OXX h7 IV Coefficient of Drag Streamlined Body of Revolution, L/D 1 hS V Coefficient of Drag Streamlined Body of Revolution, L/D = 2 h9 VI Coefficient of Drag Streamlined Body of Revolution, L/D = 3 50 VII Coefficient of Drag Streamlined Body of Revolution, L/D = h 51 VIII Coefficient of Drag Streamlined Body of Revolution, L/D = 5 52 IX Coefficient of Drag Streamlined Body of Revolution, L/D = 6 53 X Distribution of Normal Pressure Forces and Local Velocities, L/D = 1 5h XI Distribution of Normal Pressure Forces and Local Velocities, L/D = 2 59 XII Distribution of Normal Pressure Forces and Local Velocities, L/D = 3 6k XIII Distribution of Normal Pressure Forces and Local Velocities, L/D = h 69 XIV Distribution of Normal Pressure Forces and Local Velocities, L/D = 5 7h XV Distribution of Normal Pressure Forces and Local Velocities, L/D = 6 79 XVI Lengthwise Velocity Distribution In The Boundary Layer At 0.009 Inches From Surface Table Page XVII Experimentally Estimated Skin Friction, Body of Revolution, L/D =3 36 XVIII Experimentally Estimated Skin Friction, Body of Revolution, L/D = h 88 XIX Experimentally Estimated Skin Friction, Body of Revolution, L/D =5 90 XX Experimentally Estimated Skin Friction, Body of Revolution, L/D =6 92 vi LIST OF ILLUSTRATIONS Figure Page 1. The Streamlined Bodies Tested 9^ 2. Schematic Diagram of the U. So Naval Post- graduate School Closed Circuit Wind Tunnel 95 3. Aerolab Three Component Eeam Balance 96 ha. Equipment Set Up For Total Drag Measurement 97 hl>. Side View of Model And Test Section 98 kc. Front View of Model and Test Section 98 5. Model With Dummy SupDort Strut 99 6. Equipment Set Up For Pressure Measurement 99 7. Drag Coefficients For Bodies of Revolution, CDwet Versus RL , 100 8. Orientation of Mutually Perpendicular Pressure and Frictional Forces 101 9. Distribution of Normal Pressure And Inte- gration of Pressure Drag On A Body of Revolution 102 10. Pressure Drag Coefficients For Bodies Of Revolution, Cd versus R^ 108 11. Skin Friction Drag Coefficients For Bodies Of Revolution, C - 109 Df = CDwet Cop 12. Percentage of Friction Drag to Total Drag Versus The Ratio of Diameter Over Length 110 13. Comparison of Laminar Boundary Layer Profile Slopes on Bodies of Revolution with a Flat Plate 111 Ik, Pressure Distribution Over Bodies of Revolution = L/D 1, 2, 3, *+i 5, and 6 112 15. Lengthwise Velocity Distribution in The Boundary Layer of Streamlined Bodies of Revolution, L/D = 3, h, 118 vi 1 Figure Page 16. Lengthwise Velocity Distribution in The Boundary Layer of Streamlined Bodies of Revolution, L/D = 5, 6. 119 17. Estimated Lengthwise Variation of Non- dimensional Shear Stress on a Body of Revolution, L/D = 3. 120 18. Estimated Lengthwise Variation of Non- dimensional Shear Stress on a Body of Revolution, L/D = k. 121 19. Estimated Lengthwise Variation of Non- dimensional Shear Stress on a Body of Revolution, L/D = 5. 122 20. Estimated Lengthwise Variation of Non- dimensional Shear Stress on a Body of Revolution, L/D = 6. 123 21. Skin Friction Drag Coefficients From the Integration of Local Frictional Shear Stress* 12m- 22. Comparison of Estimated Friction Drag Coef- ficients with Differences Between Total and Pressure Drag Coefficients, L/D = 3, 5- i2 5 23. Comparison of Estimated Friction Drag Coef- ficients With Differences Between Total and Pressure Drag Coefficients, L/D - M-, 6 C 126 viii TABLE OF SYKBCLS Symbol Definition Units Skin friction drag coefficient based on wetted surface area CDwet Total drag coefficient based on vetted surface area CDp Pressure drag coefficient based on wetted surface area CDt Coefficient of total drag - includes support and buoyancy drag ^Dsupp Coefficient of support drag Cf Flat plate drag coefficient Cflam Laminar flat plate drag coefficient cfturb Turbulent fla>t plate drag coefficient cftrans Flat plate drag coefficient at transition Coefficient of buoyancy drag ^CDs+B Coefficient of buoyancy plus supnort drag Df Friction drag •*' lbs Dt Total drag lbs„ D Diameter fto L Axial length fto 2 P Local static pressure Ibo/fto Po Stream static pressure lb /ft AP Local static minus stream static pressure Ibc/fto 2 Qo Free stream dynamic pressure Ibo/fto r Radius . ft c RL Reynolds number based on axial length Local Reynolds number based on developed length ix Symbol Definition Units s Variable developed length ft. S Developed length fto S Frontal area ft. 2 Sw Wetted surface area fto V Local velocity f to/sec. V Free stream velocity f to/seco X Variable axial length fto (r£) gradient surface f e Velocity at to/seCo fto m Slone of non-dimensional velocity profile 1/ft1/fto 2 f> Density of air lb s =<sec a fteA Angle between local tangent to surface and body axis dego ^ Absolute viscosity lbo°sec *° Local shear stress at the surface lbo/fto 2 1. Introduction, The aerodynamic forces on a body immersed in an incom- pressible fluid flow consist of contributions from normal pressures and tangential shear stresses The problem of de= termining the coefficient of skin friction drag and distri- bution of local frictional intensity for several bodies of revolution as a function of fineness ratio and Reynolds number was undertaken at the United States Naval Postgraduate School, Monterey, California . Data for this analysis were obtained from subsonic wind tunnel tests on six models with fineness ratios from one to six at zero angle of attack and through a Reynolds number range of Ool to 5°0 x 10 . The model shapes were based upon the NACA 66(215) -0XX airfoilo The skin friction drag based on wetted surface area was to be initially determined from the difference of the total drag and pressure drag. A second method involving the inte- gration of the local shear stresses in the boundary layer over the developed length of the body was later utilized to deter- mine the skin friction drag. The expected agreement in results from the two methods was dependent upon an accurate determination of the drag com- ponents of the mutually perpendicular pressure and shearing forces acting normal and tangential to the model surface c It was hoped that these results could be correlated with and com- pared to other analytically and experimentally determined skin friction drag coefficients of a flat plate at zero incidence and other axially symmetric bodies* 2.
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