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Random Wave Forces on Cylinders

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Random Wave Forces on Cylinders AN ABSTRACT OF THE THESIS OF Ming-Kuang Hsu for the degree of Doctor of Philosophy in Civil Engineering presented on October 16, 1986. Title: Random Wave Forces on Cylinders Redacted for Privacy Abstract approved: John H. Nath The in-line force power spectrum is predicted by the frequency domain maximum force coefficient [Cun(z,fn)] vs. Keulegan-Carpenter number [Kn(z,fn)] relationship. The frequency domain Keulegan- Carpenter number is defined as the velocity from the amplitude spectrum at fn divided by the respective frequency and diameter of the cylinder [Kn(z,fn) = un(z,fn)/(fn x D)].When Kn(z,fn) is small, the frequency domain maximum force coefficient closely follows the 2 (z,f ) = 21-/Kn(z,fn) for a smooth cylinder. The force relation Cpn n power spectrum can be estimated from a given wave spectrum by using linear wave theory and the above relation for Cnn(z,fn). The non- dimensionalized rms errors between measured and predicted spectra are used to evaluate the predictions. The force time history can be predicted from the wave profile and an inverse Fast Fourier Transform method. This method is valid when Kn(z,fn) is less than 10 for smooth cylinder. Force time histories predicted by using this method compare reasonably well with measurements. RANDOM WAVE FORCES ON CYLINDERS by MingKuang Hsu A THESIS submitted to Oregon State University in partial fulfillment of the requirements for the degree of Doctor of Philosophy Completed October 16, 1986 Commencement June 1987 APPROVED: Redacted for Privacy Professor of Civil Engineering in Charge of Major Redacted foriPrivacy Head of artment sf /Civil Engineerin Redacted for Privacy Dean of Graduate $1ool Date thesis is presented October 16, 1986 Typed by Ming -Kuang Hsu ACKNOWLEDGEMENTS The author wishes to express his deep appreciation to Professor John H. Nath for his guidance and support during the course of this research. During his graduate studies, the author received financial support from the American Petroleum Institute, the Chevron Oil Field Research Company, the National Science Foundation, and computer funds from the OSU Milne Computer Center to all of whom he expresses his appreciation. Finally, the author expresses his deep thanks to his parents and Mr. and Mrs. Minore for their love. TABLE OF CONTENTS Chapter 1Talt 1.0 INTRODUCTION 1 1.1 Predicting Ocean Wave Forces 1 1.2 Scope 2 2.0 THEORETICALCONSIDERATIONS FOR OCEAN WAVE FORCES 5 2.1 The Time Domain Force-Phase Method 9 2.1.1 The Time Domain Force-Phase-. Method 11 2.1.2 The Time Domain Force-Phase-S Method 16 2.2 The Frequency Domain Force-Phase Method 23 2.2.1 The Frequency Domain Force-Phase-. Method 27 2.2.2 The Frequency Domain Force-Phase-S Method 28 2.3 The Prediction of Force Power Spectra 28 2.4 The Prediction of Force Time History 31 2.5 Force-Phase Method Extension 31 2.5.1 Vertical Cylinders 32 2.5.2 Horizontal Cylinders 32 3.0 DESCRIPTION OF EXPERIMENTS 36 3.1 Laboratory Experiments 36 3.1.1 The SMC12 Cylinder 39 3.1.2 The SRC.02 Cylinder 39 3.1.3 The SP3-55D Cylinder 39 3.2 Field Experiments 43 3.2.1 NMI Second Christchurch Bay Tower 43 3.2.2 Wave Force Project II Tests 46 4.0 RESULTS AND DISCUSSION 49 4.1 The Cpn(Kn) Regression Lines 49 4.1.1 The Amplitude Filter 51 4.1.2 The Frequency Filter 60 4.1.3 Reynolds Number Effects 62 4.2 Force Coefficients 66 4.2.1 Laboratory Test Results 68 4.2.2 Field Test Results 74 4.2.2.1 NMI Second Christchurch Bay Tower 74 4.2.2.2Wave Force Project II Tests 78 4.3 The Prediction of Force Power Spectra 78 4.3.1 Evaluation Criteria for Predicted Force Power Spectra 80 4.3.2 Laboratory Tests 80 4.3.3 Field Tests 89 4.3.3.1 NMI Second Christchurch Bay Tower 89 4.3.3.2 Wave Force Project II Tests 94 4.4 The Prediction of Force Time Histories 101 TABLE OF CONTENTS (continued) Chapter page 5.0 CONCLUSIONS 107 6.0 REFERENCES 108 APPENDIX A Constructing the Cu(K) Hyperbola 112 APPENDIX B The Derivative of C(K) with Respect to a 115 u APPENDIX C Comparison of Force Coefficients Obtained through Different Methods 123 LIST OF FIGURES Figure page 1.1-1 Wave induced hydrodynamic loading regimes as determined by individual size (from Shield and Hudspeth, 1985) 3 2.0-1 Definition sketch of wave force on a vertical cylinder 6 2.0-2 Definition sketch for the phases and magnitudes of the wave profile, velocity and local force measurements on a vertical cylinder in periodic waves (from Nath, 1985b) 7 2.0-3 The Wave Force Project II wave record 10 2.1-1 Maximum force coefficient for smooth cylinders as a function of K (from Sarpkaya, 1976) 15 2.1-2 Maximum force coefficients for the VSMC12 and VSMC8 Cylinders (from Nath, 1985a) 17 2.1-3 Non-dimensionalized phase shift for the VSMC12 and VSMC8 cylinders (from Nath, 1985a) 17 2.1-4 Values of C and C from Eqs.(2.1-9) and (2.1-10) c4 m(1) using the cutves shown in Figs. 2.1-2 and 2.1-3. The and C data points are the least squares values of Cd for the VSMC12 and VSMC8 cylinders (from Nath,1985a51 18 2.1-5 The maximum force coefficients data points and their hyperbola for the VSMC12 and VSMC8 cylinders 21 2.2-6 Non-dimensionalized phase data points and the curve of predicted nondimensionalized phase 21 2.1-7 Drag and inertia force coefficients Cdd, and Cmdi calculated by TFPS method then convert4d into Cdi, and The data points are CmLby using Eqs. (C-8) and (C-9). the least-squares values of Cd and Cm for the VSMC12 and VSMC8 cylinders 22 2.2-1 The amplitude spectrum of WPII record-6887 26 2.5.1 Definitions of forces on vertical and horizontal cylinders 33 3.1-1 The OSU wave flume (from Nath, 1985a) 38 LIST OF FIGURES (continued) Figure Page 3.1-2 Sectional elevation of a VSMC12 test cylinder (from Hudspeth et al., 1984) 40 3.1-3 Sectional elevation of a vertical 8.625-in. test cylinder (from Nath, 1983) 41 3.1-4 Side view of a horizontal 8.625-in. test cylinder (from Nath, 1985a) 42 3.2-1 NMI Christchurch Bay Tower side view (from Bishop, 1984a) 44 3.2-2 NMI Christchurch Bay Tower top view (from Bishop, 1984a) 45 3.2-3 Platform layout of Wave Project II (from Blank, 1969) 47 3.2-4 Location of WPII dynamometers and wave staff (from Blank, 1969) 48 (K) hyperbola and their asymptotes 50 4.1-1 The Cpn n 4.1-2 The velocity-force cross-amplitude spectrum 52 4.1-3 The velocity-force cross-phase spectrum 53 4.1-4 The amplitude filter: (a) before filter, (b) after filter 55 4.1-5 The band pass frequency filter: (a) before filter, (b) after filter 56 The C ) data points and their regression line 4.1-6 pn(Kn (before filter) 57 4.1-7 The C (K) data points and their regression line, afteru passing through an amplitude filter (cut-off amplitude = 0.01 spectral peak) 58 ) data points and their regression line, 4.1-8 The Cpn(Kn after passing through an amplitude filter (cut-off amplitude = 0.1 spectral peak) 59 The C 4.1-9 pn(Kn) data points and their regression line, after passing through an band pass (0.1 Hz to 1.0 Hz) filter 61 LIST OF FIGURES (continued) Figure Page 4.1-10 In-line force coefficient vs. K (from Bearman et al., 1985) 63 4.1-11 Maximum force coefficient for smooth cylinders as a function of K (from Sarpkaya, 1986b) 64 4.1-12 The C (Kn) data points and their regression lines for NMI larpn ge and small cylinder (11 records at three locations) 65 4.1-13 Maximum force coefficient for rough cylinders (from Sarpkaya, 1986b) 67 4.2-1 In-line force coefficients and phases for the VSMC12 cylinder (Run 32) 69 4.2-2 Transverse force coefficients of the VSMC12 cylinder (Run 32) 70 4.2-3 In-line force coefficients and phases for the API84 VSRC.02 cylinder (Run 23) 71 4.2-4 Transverse force coefficients for the API84 VSRC.02 cylinder (Run 23) 72 4.2-5 Horizontal force coefficients for the API84 HSRC.02 cylinder (Run 55) 73 4.2-6 Vertical force coefficients for the API84 HSRC.02 cylinder (Run 55) 75 4.2-7 In-line force coefficients for the NMI large cylinder level-3 (Record 71) 76 4.2-8 In-line force coefficients for the NMI small cylinder level-3 (Record 71) 77 4.2-9 In-line force coefficients and phases for the WPII cylinder position-7 (Record 6887) 79 4.3-1 Raw in-line force power spectra for the VSMC12 cylinder (pseudo prediction) 81 4.3-2 Smoothed in-line force power spectra for the VSMC12 cylinder (pseudo prediction) 82 LIST OF FIGURES (continued) Figure Page 4.3-3 Raw in-line force power spectra for the VSRC.02 cylinder (pseudo prediction) 83 4.3-4 Smoothed in-line force power spectra for the VSRC.02 cylinder (pseudo prediction) 84 4.3-5 Raw horizontal force power spectra for the HSRC.02 cylinder (pseudo prediction) 85 4.3-6 Smoothed horizontal force power spectra for the HSRC.02 cylinder (pseudo prediction) 86 4.3-7 Raw vertical force power spectra for the HSRC.02 cylinder (pseudo prediction) 87 4.3-8 Smoothed vertical force power spectra for the HSRC.02 cylinder (pseudo prediction) 88 4.3-9 Raw in-line force power spectra for the VSMC12 cylinder (true prediction) 90 4.3-10 Smoothed in-line force power spectra for the VSMC12 cylinder (true prediction) 91 4.3-11 In-line force power spectra for the NMI large cylinder level-3, record-71 (pseudo prediction) 92 4.3-12 In-line force power spectra for the NMI small cylinder level-3, record-71 (pseudo prediction) 93 4.3-13 In-line force power spectra for the NMI large cylinder level-3, Record-71 (true prediction) 95 4.3-14 In-line force power spectra for the NMI small cylinder level-3, Record-71 (true prediction) 96 4.3-15 Raw in-line force power spectra for the WPII cylinder position-7, record-6887 (pseudo prediction) 97 4.3-16 Smoothed in-line force power spectra for the WPII cylinder, position-7
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