CHARACTERISTICS OF FLOW IN THE WAKE REGION OF A BLUFF VERTICAL CYLINDER IN THE PRESENCE OF WAVES, CURRENTS AND COMBINED WAVE-CURRENT FLOWS JIMMY NG KEONG TARK M. Eng., National University of Singapore B. Eng. (Hons), National University of Singapore A THESIS SUBMITTED FOR THE DEGREE OF DOCTOR OF PHILOSOPHY DEPARTMENT OF CIVIL AND ENVIRONMENTAL ENGINEERING NATIONAL UNIVERSITY OF SINGAPORE 2012 Dedicated to my Late Father i Acknowledgements This dissertation would not be possible without the very kind help of several people. I like to express my heartfelt gratitude and thanks to my PhD supervisors, Prof Chan Eng Soon and Dr. John E. Halkyard for their confidence, patience and faith in me during the course of this study. Special thanks are extended to Professor Chan Eng Soon for his very kind support that had enabled me to carry out research on a full time basis. I am especially appreciative of Dr. John E. Halkyard for his vast insight and knowledge in offshore structures and hydrodynamics, his patient guidance and encouragement, and mentoring that had in so many ways, made me a better and stronger person. Much of the experimental work had been kindly assisted by the outstanding personnel of the Hydraulics Laboratory. I give thanks to Sit Beng Chiat, Krishna Sanmugam, Shaja Khan, Semawi Sadi and Roger Koh for their synergy, dedication and untiring help, and being great colleagues and friends. The set up of the parallel cluster and STAR CCM+ CFD system is credited to the excellent knowhow of Adrian Tan Seck Wei, who is a whiz in these systems. I am extremely grateful to my ‘Bro’ Kanaram Roopsekhar of TMSI, who had rendered great help and advice in both experiments and CFD simulations. I am very grateful for the technical and research advice given by Dr. Allan Magee of Technip Inc. who had spent many hours with me to fine tune my research study, despite his busy schedule, as well as the modelling help rendered by Ms. Jaime Tan of Technip KL. Invaluable lessons were learnt from Dr. Mike Khoo of TSI, who is an excellent instructor and specialist in PIV systems. Your time has been much appreciated. I like to extend my gratitude to a buddy and old classmate Professor Ng How Yong, who is always there with a listening ear and great advice when the going got tough. My family had been my pillar of strength during the five years of this PhD study, and this is credited to the unwavering faith and support of my wife and mother. Thank you, Lih Jiuan and Irene, for being there all the time, and believing in me. ii Summary This study is concerned with the flow in the wake of a bluff vertical cylinder, in combined wave and current flows. Past model tests in the industry had revealed the existence of a beat phenomenon in the relative motion responses of two tandem offshore structures in collinear waves and currents. The beat phenomenon gave rise to high responses that posed potential risks to mooring and tethering systems. The present work explores the beat phenomenon further, for flow parameters of Uc / Uw of 0.8 to 2.8, and wave KC numbers of 0.25 to 0.50. Flow kinematics in the wake flow is mapped out for the range of flows, where the beat phenomenon is identified. The experiments are performed using a specially built tow carriage system to simulate currents in the 39m long wave flume, by towing the models and instrumentation. Noise and sound insulation, as well as intelligent electronic controls are incorporated in the design and implementation of the tow carriage so that steady uniform currents are simulated. Kinematics mapping over the cylinder wake region revealed selected locations in the wake where beat phenomenon is obvious. Forces acting on a downstream cylinder placed at these identified locations are measured using a purpose built instrumented downstream cylinder, where a 50 mm section of the cylinder measured hydrodynamic forces. Results of measured forces showed that amplitude modulation in the transverse force signatures is very pronounced at x/D = ½, y/D = 0.6 offset, and the inline and transverse force amplitudes can be much larger than wave only flows. The physics of the wake characteristics in the beat phenomenon is captured through the PIV flow visualization method, which offers quantitative measure of the flows. Experimental flow visualization methods had a limited time capture window, and this work is extended numerically using a computational fluid dynamics software package STAR CCM+. The complexity and turbulence in the cylinder wake require a Detached Eddy Simulation (DES) solver, together with Volume of Fluid (VOF) method for surface waves. CFD simulations are performed for iii a single upstream cylinder, as well as tandem cylinders for the downstream cylinder locations x = ½ D, y = and 0.6 D, for current only flow, wave only flow, as well as combined wave current flows. CFD results showed similar beating characteristics in the kinematics, forces and wave elevation time signatures in combined flows. As CFD permits a full record for the flow characteristics from initialization of simulation to steady beating, analyses of the wake flow field, together with vorticity plots and isosurface plots conclude that the beat phenomenon arise from a time dependent wavecurrent-structure interaction, that causes asymmetrical flow patterns in the upstream cylinder wake, that results in periodic differentials in the wake flow that correspond with the beat frequency. Both experiments and CFD simulations show that beating evolved as a gradual process that lead to steady beat modulation. Similar flow characteristics and beat parameters are obtained from both experiments and CFD simulations, attesting to the suitability of CFD simulation as a numerical tool to predict the beat phenomenon obtained in combined wave current flows around bluff cylinders in low Uc /Uw and KC flows. A dynamic one degree of motion model is developed in this study, where kinematics measured in the upstream cylinder wake is used to estimate the surge and sway motion responses of a flexibly suspended downstream cylinder. This model demonstrated that the downstream cylinder response is greatly enhanced in combined wave current flows, as compared to wave only conditions. This model is extended to use measured forces on the downstream cylinder to predict its motion responses. Again, the amplified effects contributed by combined wave current flows are demonstrated. This study establishes the existence of a beat phenomenon occurrence around a bluff cylinder body in the presence of wave and currents, at selected Uc / Uw ratios and low KC flows. It is hoped that the findings from this study will encourage further interest in research of combined wave current flows in the said flow parameters, which are commonly encountered in the offshore environment. iv Table of Contents Page Acknowledgements ii Summary iii Table of Contents v List of Figures x List of Tables xix List of Symbols xxi List of Abbreviations xxiii Chapter 1. Introduction 1.1 Background 1.2 Review of Past Research 1.2.1 Cylinders in Uniform Flow 1.2.2 The Phenomenon of lock-In for Flows Past Cylinders 1.2.3 Cylinder in Waves 10 1.2.4 Combined Waves and Currents on a Cylinder 14 1.2.5 Tandem Cylinders in Current Flows 17 1.2.6 Kinematics Characteristics in Cylinder Near Wake 19 1.2.7 Kelvin Waves Estimation in Bluff Cylinder Wake 22 1.2.8 Flow Parameters in Present Study 23 Objectives of the Present Study 25 2.1 Questions leading to the objectives of this study 25 2.2 Objectives of this study 26 Chapter v Chapter 3. 3.1 Experiments - Design, Construction and Implementation 28 Similitude, Scaling and Flow Regimes 28 3.1.1 Currents 29 3.1.2 Waves 31 3.2 Dimensions, Ranges and Undisturbed Flow Characteristics 32 3.3 Wave generation 33 3.4 Tow Carriage Design 36 3.4.1 Ladder Chassis 38 3.4.2 Drive Train 38 3.4.3 Cable Train and Cabling 40 3.4.4 Model and Instrumentation frame 41 3.4.5 Structural Response of Tow Carriage 42 3.4.6 Ramp Up acceleration rates 43 3.4.7 Controls and Safety 43 3.5 Kinematics Measurement 44 3.6 Wave Elevation Measurements 45 3.7 Force Measurements 46 3.8 Flow Visualization 51 3.8.1 PIV Technique 51 3.8.2 PIV system overview 52 3.8.3 PIV Measurements in the Flume 54 3.8.4 Seedling material 58 3.8.5 Timing Setup 58 3.8.6 Processing of PIV Raw Images 59 Experimental Study of Flow Field in the Wake of a Bluff Cylinder 61 Chapter 4. 4.1 Kinematics in the Wake of a Bluff Cylinder vi 61 4.1.1 Wake Characteristics in Current Flows 63 4.1.2 Wake Characteristics in Wave Flows 65 4.1.3 Wake Characteristics in Combined Wave and Current Flows 66 4.2 Wave Surface Elevations Alongside Bluff Cylinder 69 4.3 Forces Acting on a Slender Cylinder in the Wake of a Bluff Cylinder 71 4.3.1 72 4.4 Force Characteristics on a Downstream Slender Cylinder in Current Flows 4.3.2 Force Characteristics on a Downstream Slender Cylinder in Wave Only Flows 72 4.3.3 Force Characteristics on a Downstream Slender Cylinder in Combined Wave Current Flows 73 Flow Vector Visualization using PIV 84 4.4.1 Test Matrix 84 4.4.2 Visualization frame of reference 84 4.4.3 Flow Vector Characteristics in the Bluff Cylinder Wake 85 4.4.3.1 Typical Flow Vector Visualization Plot 85 4.4.3.2 Single Bluff Cylinder Wake Flow Characteristics, T = 0.7s 86 4.4.3.3 Bluff Cylinder Wake Characteristics with Slender Cylinder at x = ½ D, y = 0. T = 0.7s 87 4.4.3.4 Bluff Cylinder Wake Characteristics with Slender Cylinder at x = ½ D, y = 0. T = 0.7s 88 Computation Fluid Dynamics Modelling 97 Chapter 5. 5.1 Model and Meshing 98 5.2 Turbulence Modelling in STAR CCM+ 99 5.3 Free Surface Modelling 100 5.4 101 Boundary Conditions 5.5 Initial Conditions 102 5.6 Wave Absorption and Reflection in the Numerical Wave Tank 103 vii 5.7 Mesh Convergence and Time Step Sensitivity Tests 104 5.8 Test Matrix and Data Monitoring on CFD Runs 107 Chapter 6. 6.1 Results of Numerical Modelling Wave Elevations at Locations in the Wave Tank 110 110 6.2 Flow Field in the Wake of the Bluff Cylinder 117 6.3 Forces on the Downstream Cylinder 129 6.4 Vector and Vorticity Plots 136 6.5 Iso – Surface Plots 146 6.5.1 Evolution of Iso – surface Patterns for T = 0.7s, C = 50 mm/s Flows 146 6.5.2 Periodicity of Distorted Iso – surface Patterns 146 6.6 Comparison of Results Obtained in Experiments and CFD Simulations 153 6.6.1 Kinematics in the Wake of the Bluff Upstream Cylinder 153 Forces on Downstream Cylinder in the Wake of a Bluff Cylinder 159 Flow Vector Visualization around Downstream Cylinder in PIV and CFD. 163 6.6.2 6.6.3 6.7 Wake Flow Characteristics in Beat Phenomenon 167 6.7.1 Features of Flow around Slender Downstream cylinder at x = ½ D, y = 167 6.7.2 Features of Flow around Slender Downstream cylinder at x = 1½ D, y= 0.6D 170 Discussion on Beat Phenomenon in a Bluff Cylinder Wake 172 Chapter 7. 7.1 Origins of the Beat Phenomenon 172 7.2 Beat Periods in Combined Wave Current Flows 183 7.3 Drag Coefficients in the Bluff Cylinder Wake 186 7.4 Velocity Spectrum in Measured Flow Velocities at x = ½ D Downstream 187 7.5 Effects of Beat Phenomenon on Simulated Motions of Downstream Cylinder 190 7.5.1 190 One Degree of Freedom Model viii 7.5.2 7.6 Surge Responses of Downstream Cylinder Vorticity patterns in Upstream Cylinder Wake, with Downstream Cylinder at x = ½ D, y = Chapter 8. Conclusions and Recommendations 192 195 197 8.1 Conclusions of this study 197 8.2 Recommendations for future work 199 References 201 Appendices Appendix A Time Series of Experimental Kinematics 208 Appendix B Time Series of Experimental Forces on Downstream Cylinder 280 Appendix C Flow Visualization from PIV Experiments (Fixed PIV Frame of Reference) 299 Appendix D Time Series of CFD Calculated Wake Velocities 318 Appendix E Time Series of CFD Calculated Forces on Downstream Cylinder 335 Appendix F Time Series of CFD Calculated Wave Elevations 344 Appendix G CFD Calculated Velocity Vector and Vorticity Plots 357 Appendix H Iso Surface Plots of Numerical Wave Tank 374 Appendix I Deviation of Similarity Scale factors using Dimensional Analysis 399 ix (a) (b) Currents only runs C = 50 mm/s Location x = ½ D, y = x = ½ D, y = 0.6 D Figure 110. X Velocity Experiments CFD Mean Std Dev Mean Std Dev -0.0268 0.0155 -0.0001 0.0146 -0.0081 0.0204 0.0199 0.0199 Y Velocity Experiments CFD Mean Std Dev Mean Std Dev -0.0034 0.0349 0.00 0.0151 0.0035 0.0207 -0.0045 0.0163 Comparison of experimental and CFD simulated Kinematics in the upstream cylinder wake at (a) x = ½ D, y = 0, (b) x = ½ D, y = 0.6 D, for current only flow, C = 50mm/s. 156 (a) (b) Waves and Currents T = 0.7 s, C = 50 mm/s Location x = ½ D, y = x = ½ D, y = 0.6 D Figure 111. X Velocity Experiments CFD Mean Std Dev Mean Std Dev -0.0268 0.0155 -0.0001 0.0146 -0.0081 0.0204 0.0199 0.0199 Y Velocity Experiments CFD Mean Std Dev Mean Std Dev -0.0034 0.0349 0.00 0.0151 0.0035 0.0207 -0.0045 0.0163 Comparison of experimental and CFD simulated Kinematics in the upstream cylinder wake at (a) x = ½ D, y = 0, (b) x = ½ D, y = 0.6 D, for combined wave current flow, T = 0.7 s, C = 50mm/s. 157 (a) (b) Waves and Currents T = 0.7 s, C = 100 mm/s Location x = ½ D, y = x = ½ D, y = 0.6 D Figure 112. X Velocity Experiments CFD Mean Std Dev Mean Std Dev -0.0570 0.0383 0.0193 0.0423 0.0947 0.0432 0.1271 0.0437 Y Velocity Experiments CFD Mean Std Dev Mean Std Dev 0.0003 0.0327 0.0070 0.0250 -0.0109 0.0288 -0.0185 0.0173 Comparison of experimental and CFD simulated Kinematics in the upstream cylinder wake at (a) x = ½ D, y = 0, (b) x = ½ D, y = 0.6 D, for combined wave current flow, T = 0.7 s, C = 100mm/s. 158 6.6.2 Forces on Downstream Cylinder in the Wake of a Bluff Cylinder In both experiments and CFD modelling, the forces acting on a 50 mm slice of downstream cylinder located at 80 mm below still water level are determined. Beat phenomenon is observed in combined wave and current flows. Figures 113 to 115 show the comparison plots between the forces measured in experiments and CFD. In waves only flows at T = 0.7s, no observable beat is noted in any of the force signatures. The X force signatures at both Y offsets compare very well between experiments and CFD. In the transverse direction, good agreement is also seen at y = 0.6 D offset, while experiments had higher Y force amplitudes at y = offset. In combined wave current flows at Uc / Uw < 1, a distinct modulated envelope is seen in the force signatures in both studies. The X force signatures show similar amplitudes, but sharper spikes in the data is observed in experiments. The transverse force signatures are smaller in CFD simulations. This disparity is largest at the y = offset location, where the lateral forces measured in experiments is an order larger than those observed in CFD. Similar observations are observed when currents is increased to C = 100 mm/s where Uc / Uw > 1. The beat period is greatly reduced at this wave current combination, the force signatures in experiments and CFD both show very comparable characteristics. 159 (a) (b) Waves only runs T = 0.7 s Location x = ½ D, y = x = ½ D, y = 0.6 D Figure 113. X Force (N) Experiments CFD Mean Std Dev Mean Std Dev 0.0054 0.1286 0.0006 0.1556 0.0013 0.1382 0.0008 0.1738 Y Force (N) Experiments CFD Mean Std Dev Mean Std Dev -0.0005 0.0200 0.0001 0.0071 0.0027 0.0300 0.0005 0.0259 Comparison of experimental and CFD simulated Forces on slender downstream cylinder placed at (a) x = ½ D, y = 0, (b) x = ½ D, y = 0.6 D, for wave only flow, T = 0.7 s. 160 (a) (b) Waves and Currents T = 0.7 s, C = 50 mm/s Location x = ½ D, y = x = ½ D, y = 0.6 D Figure 114. X Force (N) Experiments CFD Mean Std Dev Mean Std Dev -0.0062 0.1516 -0.0007 0.1505 0.0019 0.1542 0.0039 0.1608 Y Force (N) Experiments CFD Mean Std Dev Mean Std Dev 0.0000 0.0824 0.0002 0.0076 0.0064 0.0788 -0.0029 0.0384 Comparison of experimental and CFD simulated Forces on slender downstream cylinder placed at (a) x = ½ D, y = 0, (b) x = ½ D, y = 0.6 D, for combined wave current flow, T = 0.7 s, C = 50 mm/s. 161 (a) (b) Waves and Currents T = 0.7 s, C = 100 mm/s Location x = ½ D, y = x = ½ D, y = 0.6 D Figure 115. X Force (N) Experiments CFD Mean Std Dev Mean Std Dev -0.0038 0.1455 -0.0013 0.1580 0.0061 0.1650 0.0055 0.1702 Y Force (N) Experiments CFD Mean Std Dev Mean Std Dev 0.0058 0.0364 -0.0008 0.0142 0.0141 0.1056 -0.0039 0.0635 Comparison of experimental and CFD simulated Forces on slender downstream cylinder placed at (a) x = ½ D, y = 0, (b) x = ½ D, y = 0.6 D, for combined wave current flow, T = 0.7 s, C = 100 mm/s. 162 6.6.3 Flow Vector Visualization around Downstream Cylinder in PIV and CFD. In the preceding sections, it is determined that one of the factors contributing to the beat phenomenon on the forces on a slice of downstream cylinder is the existence of differential velocities in the flows past the top and bottom sides of the downstream cylinder. This differential in velocities followed a periodicity that follows the beat period in combined wave current flows. This beat observation is also reflected in the kinematics at selected points in the wake region, both in experiments and CFD simulations. To validate this observation in CFD, the flow around the downstream cylinder in the PIV experiments are investigated, for downstream cylinder location x = ½ D, y = 0.6 D. As described earlier, the PIV is set up such that the flow images are captured in a different frame of reference. The image capture is stationary, while the current flows are simulated by towing the models past the image window. Thus, to compare these PIV flow visualization with CFD vector plots, the X velocity component in the flow visualization has to be vectorially compensated by the tow speed used. This is analyzed using a routine in Tecplot software, where each flow vector is resolved into its X and Y components, amending the X velocity vectors, and recalculating the resultant flow vectors. These calculated vectors are plotted in a color map that matched the CFD plots. Figure 116 below compares the flow visualization between PIV and CFD for combined waves and currents, C =50 mm/s, T = 0.7s, as the wave crest passes the upstream cylinder. These are plotted on the same scale and it should be noted that there blind zones in the PIV images near the cylinder boundary. The plots show that the features of the flow, the separation angle, and magnitude of the vectors compares well. Figure 116. Comparison of (a) PIV and (b) CFD flow visualization images for combined wave current flow as the wave crest traversed past the upstream cylinder. 163 The PIV flow visualization is sampled at 15 Hz, while the vector plots in CFD are recorded at time increments of 0.025 s, or 40 Hz. The images records are placed side by side to capture the equivalent time snapshots. Although the sampling rates in these two records are different, a close enough time-step snapshot comparison is possible. Figure 117 shows paired images for wave current combination of C = 50 mm/s, T = 0.7s, as the wave crest passes the downstream cylinder, over four consecutive wave periods. The images over the four successive wave periods show that: a. A differential between the flow over the top side and bottom side of the downstream cylinder exist at each wave period, b. The flow differential velocities varies over successive wave period, c. The angles are which the flow approached the downstream cylinder are very similar in both the PIV experiments and CFD simulations. As PIV images are available only for these four wave periods, it is not possible to accurately compare and quantify the statistics of these velocities over these four periods with those obtained in CFD. Longer experiment runs with more wave cycles are required to make a better assessment of the velocity field. Nevertheless, these images lend support to the flow characteristics around the downstream cylinder in describing the beat phenomenon. Comparison with paired images from another combined wave current run of C = 75 mm/s, T = 0.7s, in Figure 118 also show similar characteristics in flow differentials, angle of approaching flow, and flow velocity variation over three successive wave periods. 164 t=T (a) (b) t = 2T (a) (b) t = 3T (a) (b) t = 4T (a) Figure 117. (b) Flow images of wave crest passing the downstream cylinder for combined wave and current flows, T = 0.7s, C = 50 mm/s, for; (a) PIV, (b) CFD. 165 t=T (a) (b) t = 2T (a) (b) t = 3T (a) Figure 118. (b) Flow images of wave crest passing the downstream cylinder for combined wave and current flows, T = 0.7s, C = 75 mm/s, for; (a) PIV, (b) CFD. 166 6.7 Wake Flow Characteristics in Beat Phenomenon The beat phenomenon has been described in the kinematics, forces as well as wave heights in the wake of the upstream cylinder. Discussions earlier in this chapter show that differentials in the flow velocities that vary over each beat period give rise to the modulated features in the time series signatures. The beat phenomenon requires a transient period of time to evolve, both in experiments and CFD simulation before these features are fully brought out. This section describes the features of the flow in the initial ramp up phase, and its subsequent features in steady beating, using visualization plots obtained from CFD. 6.7.1 Features of Flow around Slender Downstream cylinder at x = ½ D, y = 0. Two different wave cycles of velocity vector plots are examined, at t = 14T’ and t = 88T’. Figure 119 shows the flow characteristics in the wake. It is observed that at t = 14T’ where the beat phenomenon have yet to kick in, the flow behind the upstream cylinder are generally symmetrical about the horizontal centerline of the cylinder over the entire wave cycle. Symmetrical vortices are observed where the flow around the cylinder met the wake region. Over subsequent wave cycles, asymmetry gradually appears in the flow patterns in the wake. This in turn alters the flow symmetry over the downstream cylinder. At stable beating, t = 88T’, a clear differential in the flows past the top and bottom half of the downstream cylinder is observed. Over this wave cycle, some remnants of flow from the upstream cylinder is seen to be trapped around the front face of the downstream cylinder, leading to unequal flow patterns when the wave crest passes the downstream cylinder. The transition from symmetrical flow in the wake to varying unequal flow during beating can be attributed to the vortices forming past the upstream cylinder. Figure 120 shows the vorticity plots at the two wave cycles investigated. It is clearly recognizable that in the early transient phase of the flow, the vortices behind the upstream cylinder are symmetrical. At stable beating, the vortices shed in an asymmetrical manner, which contribute to the differential flow characteristics over the downstream cylinder. 167 t = 14 T’ t = 14 T’ + 1/6 T’ t = 14 T’ + 2/6 T’ t = 14 T’ + 3/6 T’ t = 14 T’ + 4/6 T’ t = 14 T’ + 5/6 T’ (a) t = 88 T’ t = 88 T’ + 1/6 T’ t = 88 T’ + 2/6 T’ t = 88 T’ + 3/6 T’ t = 88 T’ + 4/6 T’ t = 88 T’ + 5/6 T’ (b) Figure 119. Velocity vector plots around cylinders, for downstream cylinder placed at x = ½ D, y = 0, for combined wave current flows, T = 0.7 s, C = 50 mm/s over one wave cycle, at (a) Transient, t = 14T’ and (b) Stable beating, t = 88T’. 168 t = 14 T’ (a) t = 88 T’ (b) Figure 120. Comparison of vorticity plots for slender downstream placed at x = ½ D, y = 0, for combined wave current flows, T = 0.7 s, C = 50 m, at (a) Transient, t = 14T’ and (b) Stable beating, t = 88T’. 169 6.7.2 Features of Flow around Slender Downstream cylinder at x = ½ D, y = 0.6 D. Similar velocity vector plots at transient phase and stable beating are investigated for downstream cylinder placed at y = 0.6 D offset, presented in Figure 121. At transient, it is observed that both upstream and downstream cylinders had distinct separate wakes. While the presence of the downstream cylinder did partially obstructed the flow in the upstream cylinder’s wake, the features in the wake retain near symmetrical characteristics. Wave flow reversal around the upstream cylinder can clearly be seen. At stable beating, the wake region had fully developed to a configuration where both cylinder wakes had merged together, which is most evident at wave phases where the wave zero crossing passed the downstream cylinder. This combined wake now interacted as a whole, and as a result, the reverse flow on the upstream cylinder over each wave cycle is greatly reduced. Some of the flow past the top half of the upstream cylinder that impinges on the downstream cylinder are partially trapped over the frontal face of the downstream cylinder. These interferes with the wake flow over each wave cycle, and contributes to assymmetrical flow features around the downstream cylinder. The assymetry characteristics changes over successive wave cycles resulting in a gradual change in the flow differentials over the top and bottom sides of the downstream cylinder. This change is observed to be cyclic over one beat period. This behaviour is also seen in the vorticity plots presented in Figure 104. 170 t = 14 T’ t = 14 T’ + 1/6 T’ t = 14 T’ + 2/6 T’ t = 14 T’ + 3/6 T’ t = 14 T’ + 4/6 T’ t = 14 T’ + 5/6 T’ t = 88 T’ t = 88 T’ + 1/6 T’ t = 88 T’ + 2/6 T’ t = 88 T’ + 3/6 T’ t = 88 T’ + 4/6 T’ t = 88 T’ + 5/6 T’ (a) (b) Figure 121. Velocity vector plots around cylinders, for downstream cylinder placed at x = ½ D, y = 0.6 D, for combined wave current flows, T = 0.7 s, C = 50 mm/s over one wave cycle, at (a) Transient, t = 14T’ and (b) Stable beating, t = 88T’. 171 [...]... shows the schematic of the SPAR and TAD arrangement and the direction of the current and wave flows 3 Collinear 10 yWWC currents waves and Opposite 10 yWW-Ccurrents waves and NonCol 20 15 Rel Distance (ft) 10 5 0 -5 -10 -15 15 00 Figure 4 16 00 17 00 18 00 Time [sec] 19 00 2000 Plot of the relative motions between SPAR and TAD model when subjected to collinear wave and current flow (blue) and opposing wave and. .. between the SPAR and TAD models when subjected to collinear wave and current flow (blue) and opposite wave and current flow (red), Haslum (2006) Figure 5 Schematic showing the SPAR and TAD configuration and the direction of current and wave flows when subjected to collinear wave and current flow (blue) and opposing wave and current flow (red), Haslum (2006) Figure 6 Schematics of flow past a cylinder at... following characteristics are discussed a Current flows past a cylinder, b Wave flows past a cylinder, c Combined current and waves past a cylinder, d Spacing between tandem cylinders, in relation to the above flows As this study would involve small scale physical experimentation in a flume, the scaled Reynolds numbers are in the subcritical regime of Re = 10 3 to 10 5, and the Keulegan carpenter numbers are... significant, while the downstream cylinder is a slender cylinder The area of interest is in the flow characteristics around and in the wake of a bluff upstream cylinder, where the focus is on the presence of beat phenomenon To investigate the physics of these wake flows, the hydrodynamics around cylindrical structures are first examined to ascertain their relevance to the present study In particular, the. .. surface at intervals of Te at steady state Combined wave current flow, C=75 mm/s, Downstream cylinder at x = 1 ½ D, y = 0.6 D Figure 10 9 Comparison of experimental and CFD simulated Kinematics in the upstream cylinder wake at (a) x = 1 ½ D, y = 0, (b) x = 1 ½ D, y = 0.6 D, for wave only flow, T = 0.7 s Figure 11 0 Comparison of experimental and CFD simulated Kinematics in the upstream cylinder wake at... upstream cylinder Figure 11 7 Flow images of wave crest passing the downstream cylinder for combined wave and current flows, T = 0.7s, C = 50 mm/s, for; (a) PIV, (b) CFD Figure 11 8 Flow images of wave crest passing the downstream cylinder for combined wave and current flows, T = 0.7s, C = 75 mm/s, for; (a) PIV, (b) CFD Figure 11 9 Velocity vector plots around cylinders, for downstream cylinder placed at... numbers and Reynolds flow in the sub-critical regime, (Re = 10 3), according to Sarpkaya (19 86) and Williamson (19 85) are summarized in Figure 9 Using flow visualization, Williamson (19 85) had elucidated the key features associated with Re and KC in the range of Re < 2.5 x 10 4 and 0 < KC < 35 respectively, including the formation, growth, shedding and reversal of vortices around a vertical cylinder in waves... at various cylinder separations Bokaian et al (19 84) x Figure 16 Discontinuous changes in pressure coefficients at critical cylinder spacing of 3.5D Zdravkovich and Pridden (19 77) Figure 17 Comparison of currents only and combined waves and currents flow lift force time histories at KC = 0.5, Uw / Uc = 1. 0, Re =10 0 Zhou et al (2000) Figure 18 Vortex patterns in the wake of a cylinder in combined wave. .. upstream cylinder, and downstream cylinder at x = 1 ½ D, y = 0 in combined wave current flow, T = 0.7 s, C = 50 mm/s, in time increments of T / 10 Figure 66 PIV images of bluff upstream cylinder, and downstream cylinder at x = 1 ½ D, y = 0.6 D in wave only flow T = 0.7s, in time increments of T / 10 Figure 67 PIV images of bluff upstream cylinder, and downstream cylinder at x = 1 ½ D, y = 0.6 D in currents... and current flow (red), Haslum (2006) Current direction from SPAR Relative Motion Current direction from TAD Waves TAD SPAR Figure 5 Schematic showing the SPAR and TAD configuration and the direction of current and wave flows when subjected to collinear wave and current flow (blue) and opposing wave and current flow (red), Haslum (2006) 4 When the beat phenomenon occurs, the mooring lines and the connecting . Experimental Study of Flow Field in the Wake of a Bluff Cylinder 4 .1 Kinematics in the Wake of a Bluff Cylinder 61 61 vii 4 .1. 1 Wake Characteristics in Current Flows 4 .1. 2 Wake Characteristics. in Wave Flows 4 .1. 3 Wake Characteristics in Combined Wave and Current Flows 4.2 Wave Surface Elevations Alongside Bluff Cylinder 4.3 Forces Acting on a Slender Cylinder in the Wake of. Waves and Currents on a Cylinder 1. 2.5 Tandem Cylinders in Current Flows 1. 2.6 Kinematics Characteristics in Cylinder Near Wake 1. 2.7 Kelvin Waves Estimation in Bluff Cylinder Wake