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Hydrodynamic Forces on a Horizontal Cylinder Under Waves and Current Are Examined

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Hydrodynamic Forces on a Horizontal Cylinder Under Waves and Current Are Examined AN ABSTRACT OF THE THESIS OF Chung-Chu Teng for the degree ofMaster of Ocean Engineering in Civil Engineering presented on March 10, 1983 Title: HYDRODYNAMIC FORCES ON A HORIZONTAL CYLINDER UNDER WAVES AND CURRENT Redacted for Privacy ABSTRACT APPROVED: Dr. John H. Nath By assuming the linear superposition principle to be valid, the hydrodynamic forces on a horizontal cylinder under waves and current are examined. In this study, towing a cylinder in waves is used to simulate a cylinder underwaves and current. The experimental technique is proved valid throughtheoretical considerations and experimental investigations. For large current velocity (or high tow speed), the drag coefficient for waves and current approaches that for steady flow. If the current is large enough, these two values are nearly identical. In addition, the behavior of force coefficientsfor a horizontal cylinder in waves only with moderately large Reynolds number, Keulegan-Carpenter number and frequency parameter is examined. The results show that the forces ona horizontal cylinder in waves are smaller than those for planar oscillatory flow. Whether the totalacceleration or localacceleration should be used in the inertia term is a debatable point for using the Morison equation. To study this problem, the similarities and differences between these two accelerations for different water depths and wave heights are examined. The results show there is no evident difference in force prediction if the related force coefficients are used. To check the suitability of this data for determining Cd and/or Cm,an indicator, RR, is developed for the horizontal smooth cylinder in waves and current. HYDRODYNAMIC FORCES ON A HORIZONTAL CYLINDER UNDER WAVES AND CURRENT by Chung-Chu Teng A THESIS submitted to Oregon State University in partial fulfillment of the requirements for the degree of Master of Ocean Engineering Commencement June 1983 APPROVED: Redacted for Privacy Professor of Civil Engineering in Charge of Major Redacted for Privacy Head OrDepartmehnitCivil Engineer9g Redacted for Privacy Dean of Graduate/ chool Date thesis is presented MNc 101/1(P3 Typed by Word Processing Specialists for Chung-Chu Teng ACKNOWLEDGEMENTS The author would like to express his sincere gratitude to his major professor, Dr. JohnH. Nath, for hisguidance, encouragement and support throughout this study. Acknowledgements must be made to Dr. Robert T. Hudspeth and Dr.Charles K. Sollitt for their review and advice on the writing of this thesis. During the study, the author received graduate research assistantship funds from the American Petroleum Institute, National Science Foundation, OSU Sea Grant Program and NOAA Data Buoy Program. Their support is gratefully acknowledged. The author would also like to express his thanks to his brother Chung-Chian, his sisters Nai-Jan and Ming-Hwa, his cousin Louise Yu and some friends in OSU for their concern and encouragement. This thesis and the greatest thanks are dedicated to his parents, Pao-Shin and Mien-Yuan, for their love and patience throughout all these years. TABLE OF CONTENTS Page 1. INTRODUCTION 1.1 Horizontal Cylinder in Waves 1 1.2 Current Effect 2 1.3 Scope of the Present Study 5 2. THEORETICAL CONSIDERATIONS 2.1 Combined Flow Field under Waves and Current 6 2.2 Modified Morison Equation 12 2.3 Dimensional Analysis 17 2.4 Force Coefficient Dependence on the Governing Parameters 21 2.5 Accelerations in the Inertia Term 34 3. EXPERIMENT 3.1 Description of the Experiment 37 3.2 Similarity between "waves and Towing" and the Linear Superposition Principle 43 4. DATA ANALYSIS 4.1 Determination of Force Coefficients 46 4.2 Conditioning of Force Coefficients 49 5. RESULTS AND DISCUSSION 5.1 Hydrodynamic Forces on a Horizontal Cylinder in Waves 56 5.2 Hydrodynamic Forces on a Horizontal Cylinder under Waves Plus Towing (Application: Hydrodynamic Forces under Waves and Current) 71 5.3 Similarity Between "Waves and Towing" and the Linear Superposition Principle 82 5.4 Total and Local Acceleration in the Force Prediction 87 6. CONCLUSIONS 102 REFERENCES 104 APPENDIX A. Comparison of Force Coefficients Obtained through Different Techniques 107 APPENDIX B. List of Notations 112 LIST OF FIGURES Figure Page 2-1 Definition sketch for waves and current 6 2-2 Kinematics and forces on a horizontal cylinder 13 2-3 Definition sketch for a horizontal cylinder under waves and current 15 2-4 Variation of drag coefficients with Reynolds number for a smooth cylinder in steady flow 22 2-5 Roughness effect on drag coefficient for steady flow 22 2-6 (a) Drag and (b) Inertia coefficients vs. Reynolds number for various values of K for planar oscillatory flow 24 2-7 (a) Drag and (b) Inertia coefficients vs. Keulegan-Carpenter number for constant values of R and B 25 2-8 (a) Drag and (b) Inertia coefficients vs. Reynolds number for various K(=a/D) by oscillating a cylinder in still water 26 2-9 (a) Drag and (b) Inertia coefficient vs. Reynolds number for various values of E/D 27 2-10 (a) Drag and (b) Inertia coefficients vs. Keulegan-Carpenter number for a horizontal cylinder in waves 29 2-11 (a) In-line and (b) transverse coefficients vs. Keulegan-Carpenter number for a horizontal cylinder in waves 30 2-12 (a) Drag and (b) Inertia coefficients vs. Keulegan-Carpenter number for various values of w/u for a horizontal cylinder in waves 32 m m LIST OF FIGURES (Continued) 3-1 Cross-section of specimen set-up in the OSU Wave Research Facility 38 5-1 (a) Drag and (b) Inertia coefficients vs. Reynolds number for a smooth horizontal cylinder in waves....59 5-2 (a) Drag and (b) Inertia coefficients vs. Reynolds number for a smooth horizontal cylinder in waves for 25 > K > 15 61 5-3 (a) Drag and (b) Inertia coefficients vs. Keulegan- Carpenter number for various values of Wm/Um for a smooth cylinder in waves 63 5-4 (a) Drag and (b) Inertia coefficients vs. Keulegan-Carpenter number for a smooth horizontal cylinder in waves 64 5-5 (a) In-line and (b) Transverse coefficient vs. Keulegan-Carpenter number for a smooth horizontal cylinder in waves 66 5-6 Comparisons of force coefficients between a smooth and a sand roughened cylinder in waves 69 5-7 RR values vs (FD)max /(F1)max 70 5-8 (a) Drag and (b) Inertia coefficients vs. Reynolds number for a smooth cylinder under waves and towing (current) 75 5-9 (a) Drag and (b) Inertia coefficients vs. Reynolds number for a sand roughened cylinder under waves and towing (current) 76 5-10 Comparison between drag coefficients obtained from steady state flow and those under waves and towing for (a) smooth and (b) sand roughened cylinder 77 5-11 (a) Drag and (b) Inertia coefficients vs. Verley and Moe number for a cylinder under waves and towing (current) 79 LIST OF FIGURES (Continued) 5-12 (a) Drag and (b) Inertia coefficients vs. Keulegan-Carpenter number for a smooth and a sand roughened cylinder under waves and towing (current) 80 5-13 (a) In-line and (b) Transverse coefficients vs. Keulegan-Carpenter number for a smooth cylinder under waves plus towing 81 5-14 Measurements of horizontal velocity under waves and towing (a) U=0.71 ft/sec. (b) U=3.24 ft/sec 84 5-15 Comparisons between predicted values and measured data for horizontal velocity under waves and towing (a) U=0.71 ft/sec (b) U=6.25 ft/sec 85 5-16 Comparison between predicted values and measured data for the vertical velocity under waves and towing at low tow speed (U=0.71 ft/sec) 88 5-17 Comparison between predicted values and measured data for the vertical velocity under waves and towing at high tow speed (U=6.25 ft/sec) 89 5-18 Ratios of total acceleration to local acceleration 91 5-19 Influence of current on acceleration ratios aand a 97 x z 5-20 Acceleration ratios vs. Cm's ratios [(Cm) total/(Cm) local] 98 5-21 Effect of current on Cm's ratio 99 LIST OF TABLES Table Page 3-1 Summary of Force Dynamometer Calibration Constants 41 5-1 Summary of Data for a Smooth Horizontal Cylinder in Waves 57 5-2 Summary of Data for a Sand Roughened Horizontal Cylinder in Waves 68 5-3 Summary of Data for a Horizontal Cylinder under Waves and Current (Smooth and Sand Roughened) 72 5-4 Summary of error indicators for horizontal velocity under waves and towing 86 5-5 Summary of Data for a Smooth Horizontal Cylinder in Waves by Using Different Accelerations 92 5-6 Summary of Data for a Smooth Horizontal Cylinder under Waves and Current by Using Different Accelerations 95 5-7 Influence of Current on the Force Prediction 101 HYDRODYNAMIC FORCES ON A HORIZONTAL CYLINDER UNDER WAVES AND CURRENT 1. INTRODUCTION 1.1 Horizontal Cylinder in Waves Wave induced forces on cylinders have been investigated mostly for vertical cylinders or horizontal cylinders in planar oscillatory flow. Little research has been done on horizontal cylinders in waves in spite of the common use of horizontalmembersin many offshore structures and ocean pipelines. The significantdifferencebetween a horizontal cylinder in waves and a vertical cylinder (or a horizontal cylinder subjected to planaroscillatory flow) is that the formerexperiences orbital motion of the fluid particles around the axis of the cylinder. In wavy flow,the wake formed over a horizontal cylinder will rotate around the cylinder. It will be swept back and forth in an oscillatory way only for cylinders near the sea bottom or in shallow water. The stagnation point on the cylinder willrotate around the horizontal cylinder as the waves pass. For vertical smooth cylinders, the vertical force component par- allel to the cylinder axis is probably negligible compared to the in- line force and the transverse vortex force.
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