Characteristics of flow in the wake region of a bluff vertical cylinder in the presence of waves,currents and combined wave current flows 1

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.. iii Summary This stu

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

i Dedicated to my Late Father

ii

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

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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 = 1 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

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a single upstream cylinder, as well as tandem cylinders for the downstream cylinder locations x = 1 ½

D, y = 0 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 wave-current-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

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x xix xxi xxiii

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

1.2.4 Combined 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

1.2.8 Flow Parameters in Present Study

Chapter 2 Objectives of the Present Study

2.1 Questions leading to the objectives of this study

2.2 Objectives of this study

25

25

26

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Chapter 3 Experiments - Design, Construction and Implementation

3.1 Similitude, Scaling and Flow Regimes

3.4.3 Cable Train and Cabling

3.4.4 Model and Instrumentation frame

3.4.5 Structural Response of Tow Carriage

3.4.6 Ramp Up acceleration rates

3.4.7 Controls and Safety

3.8.2 PIV system overview

3.8.3 PIV Measurements in the Flume

Chapter 4 Experimental Study of Flow Field in the Wake of a Bluff Cylinder

4.1 Kinematics in the Wake of a Bluff Cylinder

61

61

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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 a Bluff Cylinder

4.3.1 Force Characteristics on a Downstream Slender Cylinder in Current Flows

4.3.2 Force Characteristics on a Downstream Slender Cylinder in Wave Only

Flows

4.3.3 Force Characteristics on a Downstream Slender Cylinder in Combined

Wave Current Flows

4.4 Flow Vector Visualization using PIV

4.4.1 Test Matrix

4.4.2 Visualization frame of reference

4.4.3 Flow Vector Characteristics in the Bluff Cylinder Wake

4.4.3.1 Typical Flow Vector Visualization Plot 4.4.3.2 Single Bluff Cylinder Wake Flow Characteristics, T = 0.7s 4.4.3.3 Bluff Cylinder Wake Characteristics with Slender Cylinder at x = 1 ½

D, y = 0 T = 0.7s 4.4.3.4 Bluff Cylinder Wake Characteristics with Slender Cylinder at x = 1 ½

Chapter 5 Computation Fluid Dynamics Modelling

5.1 Model and Meshing

5.2 Turbulence Modelling in STAR CCM+

5.3 Free Surface Modelling

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5.7 Mesh Convergence and Time Step Sensitivity Tests

5.8 Test Matrix and Data Monitoring on CFD Runs

104

107

Chapter 6 Results of Numerical Modelling

6.1 Wave Elevations at Locations in the Wave Tank

6.2 Flow Field in the Wake of the Bluff Cylinder

6.3 Forces on the Downstream Cylinder

6.4 Vector and Vorticity Plots

6.5 Iso – Surface Plots

6.5.1 Evolution of Iso – surface Patterns for T = 0.7s, C = 50 mm/s Flows

6.5.2 Periodicity of Distorted Iso – surface Patterns

6.6 Comparison of Results Obtained in Experiments and CFD Simulations

6.6.1 Kinematics in the Wake of the Bluff Upstream Cylinder

6.6.2 Forces on Downstream Cylinder in the Wake of a Bluff Cylinder

6.6.3 Flow Vector Visualization around Downstream Cylinder in PIV and CFD

6.7 Wake Flow Characteristics in Beat Phenomenon

6.7.1 Features of Flow around Slender Downstream cylinder at x = 1 ½ D, y = 0

6.7.2 Features of Flow around Slender Downstream cylinder at x = 1½ D, y= 0.6D

Chapter 7 Discussion on Beat Phenomenon in a Bluff Cylinder Wake

7.1 Origins of the Beat Phenomenon

7.2 Beat Periods in Combined Wave Current Flows

7.3 Drag Coefficients in the Bluff Cylinder Wake

7.4 Velocity Spectrum in Measured Flow Velocities at x = 1 ½ D Downstream

7.5 Effects of Beat Phenomenon on Simulated Motions of Downstream Cylinder

7.5.1 One Degree of Freedom Model

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7.5.2 Surge Responses of Downstream Cylinder

7.6 Vorticity patterns in Upstream Cylinder Wake, with Downstream Cylinder at x =

1 ½ D, y = 0

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8.1 Conclusions of this study

8.2 Recommendations for future work

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 I Deviation of Similarity Scale factors using Dimensional Analysis 399

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List of Figures

Figure 1 Photograph of a semi-submersible drill ship working alongside the Neptune SPAR

platform

Figure 2 A drawing of a typical TAD semi-submersible (left) and SPAR platform (right) moored

next to each other

Figure 3 Spectra density plot of SPAR and TAD responses in collinear waves and currents (in

red) and waves only (in blue), from Haslum (2006)

Figure 4 Plot of the relative motions 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 different Reynolds flow regimes Sumer &

Fredsoe (2006)

Figure 7 Graph of f / fn vs Vr illustrating the lock-in region where the vortex shedding

frequency is synchronized to the frequency of cylinder oscillation Feng (1968) Figure 8 Schematics showing plot of amplitude-diameter ratio (A/D) versus reduced velocity

(Vr) of a Truss SPAR system where high A/D response extend beyond Vr > 10 Irani & Finn (2004)

Figure 9 Flow characteristics around a smooth cylinder in oscillatory flows Sarpkaya (1986),

Williamson (1985)

Figure 10 Plot of KC numbers versus Reynolds numbers, illustrating regimes of flow around a

cylinder in oscillatory flows, Sarpkaya (1986)

Figure 11 Graph of Stokes number versus Keulegan-Carpenter Number (Sarpkaya 2006), and

the domain where the present study encompass

Figure 12 Schematic of streaming around a cylinder in oscillatory unseparated flows

Figure 13 Force time series of a cylinder in a coexisting current-wave flow Sumer et al (1992) Figure 14 Variation of inline force coefficients CD and CM vs Uc/Uw , at different KC numbers

Plots extracted from Sumer (1992), Sarpkaya and Storm (1985) Dashed lines are asymptotic values for steady current case

Figure 15 Different instabilities observed at various cylinder separations Bokaian et al (1984)

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Figure 16 Discontinuous changes in pressure coefficients at critical cylinder spacing of 3.5D

Zdravkovich and Pridden (1977)

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 =100 Zhou et al (2000)

Figure 18 Vortex patterns in the wake of a cylinder in combined wave current flows at (a) KC =

3, Uc / Uw = 1, (b) KC = 4, Uw / Uc = 1 Zhou (2000)

Figure 19 Illustration of Kelvin waves from a moving point source from Soomere (2007)

Figure 20 Plot of Drag coefficient CD vs Reynolds Number Massey B S (2002)

Figure 21 Plot of Strouhal numbers vs Reynolds numbers Williamson (1989), Schewe (1983) Figure 22 Wave elevation signatures of calibrated (a) 0.7 s, (b) 0.85 s, (c) 1.0 s, (d) 2.0 s and (e)

3.6 s waves

Figure 23 Schematic of the isolated chassis and frame design of the tow carriage

Figure 24 Photograph of one of the four ROSTA elastomeric dampeners installed on the

carriage

Figure 25 Photograph showing details of the carriage drive system

Figure 26 Photograph showing details of the cable train system

Figure 27 Photograph of tow carriage with model and instrumentation

Figure 28 Photograph of dead weights on instrumentation frame

Figure 29 Velocimeter readings, for a carriage starting from rest, at ramp-up rates of (a) 150

mm/s2, and (b) 5 mm/s2 Figure 30 Photograph of (a) User control panel, (b) Wireless remote control

Figure 31 Schematics of the NORTEK Vectrino + Velocimeter used in this study

Figure 32 Photograph of the KENEK CHT-4 capacitance wave height meter

Figure 33 The Kyowa 50N range LSM-B-SA 1 force transducer

Figure 34 In-situ calibration charts of the Kyowa LSM-B-SA 1, in the (a) X and (b) Y direction Figure 35 Schematic of the dimensions of downstream cylinder for force measurements Figure 36 Schematics showing components of instrumented downstream cylinder

Figure 37 Photos of the instrumented downstream cylinder; (a) As constructed, (b) Installed

on the carriage together with the upstream cylinder

Figure 38 Raw signals from force transducer in the (a) X and (b) Y direction when tapped twice

in quick succession with a mallet

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Figure 39 Basic PIV measurement technique

Figure 40 Schematics of PIV Laser Set – Up

Figure 41 Schematic of the PIV set up in this study

Figure 42 Photograph showing laser light sheet and mirror reflected sheet

Figure 43 PIV raw images under different set up conditions

Figure 44 Locations in wake where kinematics are measured

Figure 45 X and Y velocity plots at the point x = 1 ½ D, y = 0 for currents only runs

Figure 46 Velocity and spectra plots in the X, Y and Z directions, at x = 1 ½ D, y = 0.6 D, for

wave only flow, T = 0.7 s

Figure 47 Velocity and spectra plots in the X, Y and Z directions, at x = 1 ½ D, y = 0.6 D, for

combined wave current flow, C = 125 mm/s, T = 0.7 s (Te = 0.688s)

Figure 48 Velocity and spectra plots in the X, Y and Z directions, at x = 1 ½ D, y = 0, for

combined wave current flow, C = 50 mm/s, T = 0.7 s (Te = 0.695s)

Figure 49 Velocity and spectra plots in the X, Y and Z directions, at x = 1 ½ D, y = 0.6 D, for

combined wave current flow, C = 50 mm/s, T = 0.7 s (Te = 0.695 s)

Figure 50 Wave elevation signatures and spectra measured alongside the upstream cylinder

for T = 0.7s, (a) C = 100 mm/s, (b) C = 75 mm/s, (c) C = 50 mm/s, (d) Waves only Figure 51 Forces on downstream cylinder placed at x = 1 ½ D, y = 0, for currents only flow, at

(a) C= 150 mm/s, (b) C= 125 mm/s, (c) C= 100 mm/s, (d) C= 75 mm/s, and (e) C= 50 mm/s

Figure 52 Forces on downstream cylinder placed at x = 1 ½ D, y = 0.6 D, for currents only flow,

at (a) C= 150 mm/s, (b) C= 125 mm/s, (c) C= 100 mm/s, (d) C= 75 mm/s, and (e) C=

150 mm/s, (b) C= 125 mm/s, (c) C= 100 mm/s, (d) C= 75 mm/s, and (e) C= 50 mm/s

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Figure 57 Forces on downstream cylinder placed at x = 1 ½ D, y = 0, for T = 0.85 s, and (a) C=

150 mm/s, (b) C= 125 mm/s, (c) C= 100 mm/s, (d) C= 75 mm/s, and (e) C= 50 mm/s Figure 58 Forces on downstream cylinder placed at x = 1 ½ D, y = 0.6 D, for T = 0.85 s, and (a)

C= 150 mm/s, (b) C= 125 mm/s, (c) C= 100 mm/s, (d) C= 75 mm/s, and (e) C= 50 mm/s

Figure59 Beat periods of force signatures at various current and wave combinations for (a) X

forces, at x = 1 ½ D, y = 0, (b) Y forces, at x = 1 ½ D, y = 0, (c) X forces, at x = 1 ½ D, y

= 0.6 D, and (d) Y forces, at x = 1 ½ D, y = 0.6 D

Figure 60 Typical velocity flood image in this PIV study(C = 75 mm/s, T = 0.7 s)

Figure 61 PIV images of a single bluff cylinder in wave only flow T = 0.7 s, in time increments

of T / 10

Figure 62 PIV images of a single bluff cylinder in combined wave current flow T = 0.7 s, C = 50

mm/s, in time increments of T / 10

Figure 63 PIV images of bluff upstream cylinder, and downstream cylinder at x = 1 ½ D, y = 0,

in wave only flow T = 0.7s, in time increments of T / 10

Figure 64 PIV images of bluff upstream cylinder, and downstream cylinder at x = 1 ½ D, y = 0 in

currents only flow C = 50 mm/s, in time increments of T / 10

Figure 65 PIV images of bluff 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 only flow C = 50 mm/s, in time increments of T /10

Figure 68 PIV images of bluff upstream cylinder, and downstream cylinder at x = 1 ½ D, y = 0.6

D in combined wave current flow, T =0.7 s, C = 50 mm/s, in time increments of T/ 10 Figure 69: Mesh refinement in fluid region at: (a) wave elevation, (b) area around cylinders, (c)

wave height monitor region

Figure 70: Plan view of the wave tank showing location of cylinders and initial wave front Figure 71: Location of wave height monitoring on bare wave tank for mesh sensitivity tests Figure 72: Wave height signatures at: (a) cylinder location (x, y) = (0, 0), and (b) near end of

wave tank (x, y) = (9.24, 0) at final mesh size and trimmer mesh configuration

Figure 73: Comparison of wave height signatures for calibrated wave T = 0.7s, H = 25 mm

between CFD (in blue) and experiments (in red)

Figure 74: Volume mesh in this study for two cylinder runs

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Figure 75: Locations in red in the wave tank where (a) local wave elevations and forces on the

downstream cylinder are measured in the two cylinder runs, (b) local wave elevations and downstream kinematics are measured in the single cylinder runs, (c) Wave elevations along the wave tank

Figure 76 Locations where wave elevations were monitored in the CFD simulations

Figure 77 Surface elevation time histories in the wave tank at (a) x=-0.84 m, (b) x=+0.84 m, (c)

x=+9.24 m for wave only flow, for downstream cylinder located at x = 1 ½ D, y = 0

Figure 78 Surface elevation time histories in the wave tank at (a) x=-0.84 m, (b) x=+0.84 m, (c)

x=+9.24 m for combined wave current flow, C = 50 mm/s, T = 0.7s, for downstream cylinder located at x = 1 ½ D, y = 0

Figure 79 Surface elevation time histories in the wave tank at (a) x=-0.84 m, (b) x=+0.84 m, (c)

x=+9.24 m for wave only flow, for downstream cylinder located at x = 1 ½D, y = 0.6D Figure 80 Surface elevation time histories in the wave tank at (a) x=-0.84 m, (b) x=+0.84 m, (c)

x=+9.24 m for combined wave current flow, C = 50 mm/s, T = 0.7s, for downstream cylinder located at x = 1 ½ D, y = 0.6 D

Figure 81 Selected locations for study of flow kinematics

Figure 82 X direction velocities measured at y = 0.6 D offset, at (a) x = 1 ½ D, (b) x = 2 D, and (c)

x = 2 ½ D for waves only flow, T = 0.7 s

Figure 83 Y direction velocities measured at y = 0.6 D offset, at (a) x = 1 ½ D, (b) x = 2 D, and (c)

x = 2 ½ D for waves only flow, T = 0.7 s

Figure 84 X direction velocities measured at y = 0.6 D offset, at (a) x = 1 ½ D, (b) x = 2 D, and (c)

x = 2 ½ D for combined wave current flow, T = 0.7 s, H = 25 mm, C = 50 mm/s

Figure 85 Y direction velocities measured at y = 0.6 D offset, at (a) x = 1 ½ D, (b) x = 2 D, and (c)

x = 2 ½ D for combined wave current flow, T = 0.7 s, H = 25 mm, C = 50 mm/s

Figure 86 Velocity vector plots around bluff upstream cylinder in increments of T / 7, for wave

only flow (T = 0.7 s), at simulation time t = 14T to 15T

Figure 87 Velocity vector plots around bluff upstream cylinder in increments of T / 7, for wave

only flow (T = 0.7 s), at simulation time t = 57T to 58T

Figure 88 Velocity vector plots around bluff upstream cylinder in increments of Te / 7, for

combined wave current flow (T = 0.7 s, C = 50 mm/s), at time t = 14T to 15T

Figure 89 Velocity vector plots around bluff upstream cylinder in increments of Te / 7, for

combined wave current flow (T = 0.7 s, C = 50 mm/s), at time t = 57T to 58T

Figure 90 Velocity vector plots around bluff upstream cylinder in increments of Te / 7, for

combined wave current flow (T = 0.7 s, C = 75 mm/s), at time t = 14T to 15T

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Figure 91 Velocity vector plots around bluff upstream cylinder in increments of Te / 7, for

combined wave current flow (T = 0.7 s, C = 75 mm/s), at time t = 57T to 58T

Figure 92 50 mm Slice of downstream cylinder at 80 mm below still water level where forces

were monitored

Figure 93 (a) X direction forces and (b) Y direction forces acting on a slice of downstream

cylinder placed at x = 1 ½ D, y = 0, for wave only flow T = 0.7 s, H = 25 mm

Figure 94 (a) X direction forces and (b) Y direction forces acting on a slice of downstream

cylinder placed at x = 1 ½ D, y = 0.6 D, for wave only flow T = 0.7 s, H = 25 mm Figure 95 (a) X direction forces and (b) Y direction forces acting on a slice of downstream

cylinder placed at x = 1 ½ D, y = 0, for combined wave current flow T = 0.7 s, H = 25

mm, C = 50 mm/s

Figure 96 (a) X direction forces and (b) Y direction forces acting on a slice of downstream

cylinder placed at x = 1 ½ D, y = 0.6 D, for combined wave current flow T = 0.7 s, H =

25 mm, C = 50 mm/s

Figure 97 Velocity vector plots at every T increment at steady state Wave only flow

Downstream Cylinder located at x = 1 ½ D, y = 0

Figure 98 Vorticity plots at every T increment at steady state Wave only flow Downstream

cylinder located at x = 1 ½ D, y = 0

Figure 99 Velocity vector plots at every 2Te increment at steady state beating C = 50 mm/s, T

= 0.7 s flow Downstream cylinder located at x = 1 ½ D, y = 0

Figure 100 Vorticity plots at every 2Te increment at steady state beating C = 50 mm/s, T = 0.7 s

flow Downstream cylinder located at x = 1 ½ D, y =0

Figure 101 Velocity vector plots at every 2Te increment at steady state Wave only flow

Downstream cylinder located at x = 1 ½ D, y = 0.6 D

Figure 102 Vorticity plots at every 2Te increment at steady state Wave only flow Downstream

cylinder located at x = 1 ½ D, y = 0.6 D

Figure 103 Velocity vector plots at every 2Te increment at steady state beating C = 50 mm/s, T

= 0.7 s flow Downstream Cylinder located at x = 1 ½ D, y = 0.6 D

Figure 104 Vorticity plots at every 2Te increment at steady state beating C = 50 mm/s, T = 0.7 s

flow Downstream cylinder located at x = 1 ½ D, y = 0.6 D

Figure 105 Iso surface over first 12 T of run Wave only flow, Downstream cylinder at x = 1 ½ D,

y = 0.6 D

Figure 106 Iso surface plots over first 12 T of run Combined wave current flow, Downstream

cylinder at x = 1 ½ D, y = 0.6 D

Figure 109 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 110 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 current only flow, C = 50mm/s

Figure 111 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 combined wave current flow,

T = 0.7 s, C = 50mm/s

Figure 112 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 combined wave current flow,

T = 0.7 s, C = 100mm/s

Figure 113 Comparison of experimental and CFD simulated Forces on slender downstream

cylinder placed 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 114 Comparison of experimental and CFD simulated Forces on slender downstream

cylinder placed at (a) x = 1 ½ D, y = 0, (b) x = 1 ½ D, y = 0.6 D, for combined wave current flow, T = 0.7 s, C = 50 mm/s

Figure 115 Comparison of experimental and CFD simulated Forces on slender downstream

cylinder placed at (a) x = 1 ½ D, y = 0, (b) x = 1 ½ D, y = 0.6 D, for combined wave current flow, T = 0.7 s, C = 100 mm/s

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

Figure 117 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 118 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 119 Velocity vector plots around cylinders, for downstream cylinder placed at x = 1 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) Steady beating, t = 88T’

Figure 120 Comparison of vorticity plots for slender downstream placed at x = 1 ½ D, y = 0, for

combined wave current flows, T = 0.7 s, C = 50 m, at (a) Transient, t = 14T’ and (b) Steady beating, t = 88T’

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Figure 121 Velocity vector plots around cylinders, for downstream cylinder placed at x = 1 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) Steady beating, t = 88T’

Figure 122: Velocity vector plots and corresponding local iso surface plots over two successive

wave periods T, for wave only flow, T = 0.7 s Downstream cylinder location at x = 1

½ D, y = 0

Figure 123: Velocity vector plots and corresponding local iso surface plots over two successive

encounter wave periods Te, for C = 50 mm/s, T = 0.7 s Downstream cylinder location

at x = 1 ½ D, y = 0

Figure 124: Velocity vector plots and corresponding local iso surface plots over two successive

encounter wave periods Te, for C = 75 mm/s, T = 0.7 s Downstream cylinder location

at x = 1 ½ D, y = 0

Figure 125: Velocity vector plots and corresponding local iso surface plots over each successive

encounter wave periods Te, for C = 100 mm/s, T = 0.7 s Downstream cylinder location at x = 1 ½ D, y = 0

Figure 126: Velocity vector plots and corresponding local iso surface plots over two successive

wave periods T, for wave only flow, T = 0.7 s Downstream cylinder location at x = 1

½ D, y = 0.6 D

Figure 127: Velocity vector plots and corresponding local iso surface plots over two successive

encounter wave periods Te, for C = 50 mm/s, T = 0.7s Downstream cylinder location

at x = 1 ½ D, y = 0.6 D

Figure 128: Velocity vector plots and corresponding local iso surface plots over two successive

encounter wave periods Te, for C = 75 mm/s, T = 0.7s Downstream cylinder location

at x = 1 ½ D, y = 0.6 D

Figure 129: Velocity vector plots and corresponding local iso surface plots over each successive

encounter wave periods Te, for C = 100 mm/s, T = 0.7s Downstream cylinder location at x = 1 ½ D, y = 0.6 D

Figure 130 Normalized plot of ratio of beat to wave frequency vs Uc / Uw for downstream

cylinder placed at x = 1 ½ D, (a) y = 0, (b) y = 0.6 D

Figure 131 Comparison of beat frequencies between experiments and CFD simulations for

downstream cylinder placed at (a) y = 0, (b) y = 0.6 D

Figure 132 Comparison of experiment CD coefficients with plot from Price (1984)

Figure 133 Schematic of 1-DOF model used in this analysis

Figure 134 Comparison of simulated surge motions for downstream cylinder located at x = 1 ½

D, y = 0, from linear theory, experiments and CFD for:

(a) Wave only flow, T = 0.7s, fn = 0.5, (b)Wave current flow, T=0.7s, C=50mm/s, fn=0.5,

xviii

(c) Wave only flow, T = 0.7s, fn=0.108, (d) Wave current flow, T=0.7s, C=50mm/s, fn=0.108

Figure 135 Comparison of simulated surge motions for downstream cylinder located at x = 1 ½

D, y = 0.6 D, from linear theory, experiments and CFD for:

(b)Wave current flow, T=0.7s, C=50mm/s, fn=0.5, (c) Wave only flow, T = 0.7s, fn=0.108,

(d) Wave current flow, T=0.7s, C=50mm/s, fn=0.108

Figure 136 Vorticity plots showing vortex formation in the wake of the upstream cylinder for (a)

current only flow, C = 50 mm/s, (b) wave only flow, T = 0.7s, (c) combined wave current flow, C = 50 mm/s T = 0.7s (Red circles show vortex formation)

xix

List of Tables

Table 1 Force coefficients at oscillatory non-separated flow, using Wang (1968) formulae Table 2 Dimensions of cylinder model

Table 3 Range of parameters in this study

Table 4 Undisturbed flow normalized characteristics in this study

Table 5 Reflection coefficients Kr of the wave periods in this study

Table 6 Vectrino settings for this study

Table 7 Specifications of Wave Height Meter used in this study

Table 8 Properties of the glass bead seedlings used in PIV measurements

Table 9 PIV Timing Setup factors in this study

Table 10 Test matrix of kinematics measurements in the wake of upstream cylinder

Table 11 Comparison of experimental and calculated Strouhal frequencies (St = 0.2)

Table 12 X and Y velocity signatures and spectra frequencies at various measured locations,

for T = 0.7 s, C = 50 mm/s

Table 13 Test matrix of forces acting on a downstream cylinder

Table 14 Comparison of experimental force spectra and calculated Strouhal frequencies (St =

0.2)

Table 15 Test Matrix of PIV experiments

Table 16 Mesh refinements at selected locations of the wave tank

Table 17 Monitored wave heights as a percentage of original wave height for various mesh

sizes

Table 18 Comparison of inline forces and transverse forces on downstream cylinder, and

wave elevations at x=0.84m, for various prism layers around cylinders

Table 19 Test matrix of runs carried out in CFD model

Table 20 Spectra of the wave heights for all cylinder configurations at locations x=-0.84 and

+0.84m

Table 21 Table of Y force spectra, and dominant beat period (Windowed FFT are used in y = 0

offset cases.)

xx

Table 22 Waves used in this study, and corresponding modified Keulegan Carpenter number

KC’

Table 23 Spectra of kinematics in the wake of the upstream cylinder, measured at x = 1 ½ D, y

= 0 and 0.6 D offsets, for (a) Current only flow, (b) combined wave current flow at KC’ = 0.25, (c) combined wave current flow at KC’ = 0.35

Table 24 Standard deviation of surge responses of downstream cylinder at different natural

frequencies, and locations for waves only runs

Table 25 Standard deviation of surge responses of downstream cylinder at different natural

frequencies, and locations for combined waves and currents runs

KC’

KC number related to the hall line

Modified KC number, at a specified water depth

xxii

xxiii

List of Abbreviations

ADV Acoustic Doppler Velocimeter

ALE Arbitrary Lagrangian-Eulerian method

AVR Asymmetric vortex reversal

CFD Computational Fluid Dynamics

DC Direct current

DES Detached eddy simulation

DVR Detached vortex reversal

FFT Fast Fourier transform

GUI Graphical user interface

LES Large eddy simulation

PIV Particle Image Velocimetry

QVS Quasi – Vortex Shedding

RAM Random access memory

RANS Reynolds Averaged Navier-Stokes simulation

SEMI Semi-Submersible offshore floating structure

SPAR SPAR offshore floating platform

SVR Symmetrical vortex reversal

TAD Tender assisted drilling unit

VOF Volume of fluid simulation

1

Chapter 1 Introduction

In many offshore operations, there are many instances where two floating structures are positioned

in close vicinity to one other Some examples of these include a Tender assisted drilling submersible drilling a well alongside a SPAR platform, a derrick barge lifting modules onto a semi-submersible and a Tension leg platform (TLP) offloading crude petroleum onto a tanker, amongst others Figure 1 below shows an example of a drilling semi-submersible alongside a SPAR production platform

semi-Figure 1 Photograph of a semi-submersible drill ship working alongside the Neptune SPAR platform

In the presence of waves and currents, the dynamics of two bluff bodies close to each other can be complicated The wake of the upstream structure is scattered, diffracted and probably turbulent, and these become the incident flow on the downstream structure The motions of the structures further complicate the responses of the two structures The wave-current-structure interaction is non-linear and time dependent, and the response frequencies in these combined flows can lend to amplified motion for some cases

Public Domain Image from www.fugrochance.com/

Figure 2 A drawing of a typical TAD semi-submersible (left) and SPAR platform (right) moored

next to each other

The beat phenomenon was particularly obvious in the motions in the surge direction, as the tether lines between the two structures were subjected to higher than predicted loads due to the large relative motions of the two structures Sliders placed between the two structures meant for personnel movement were consequently subjected to high displacements

These tests in a model basin with combined wave and current flows acting on an upstream SPAR and downstream TAD placed in a collinear configuration had verified the existence of the beat phenomenon Figure 3, extracted from Haslum et al (2006) shows an example of the SPAR and TAD surge response spectra density plot in the model test, when beat phenomenon was observed

3

Figure 3 Spectra density plot of SPAR and TAD responses in collinear waves and currents (in

red) and waves only (in blue), from Haslum (2006)

The results of the model tests also revealed that the relative motions between the SPAR and TAD semi-submersible were significantly larger when current and waves were in a collinear direction, with the SPAR being upstream These motions differed very significantly when compared to currents and waves acting in opposing direction To illustrate this, Figure 4, from Haslum (2006) shows the time series plots of the relative motions between the SPAR and TAD in collinear wave current flows, and waves and currents in opposite directions, while Figure 5 shows the schematic of the SPAR and TAD arrangement and the direction of the current and wave flows

4

Figure 4 Plot of the relative motions between SPAR and TAD model when subjected to collinear

wave and current flow (blue) and opposing 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)

SPAR

TAD

Waves

Current direction from TAD

Current direction from SPAR Relative Motion

-15 -10 -5 0 5 10 15 20

5

When the beat phenomenon occurs, the mooring lines and the connecting systems between these two structures will be subjected to excessively large stresses On site modifications and rectifications to ensure the integrity of the system can be an expensive exercise In addition, the increased motions and relative displacements of these structures can have safety implications to personnel and operations

How the beat phenomenon occurs is not well understood and present literature had not reported the existence of the beat phenomenon in combined wave current flows around bluff structures This is an interesting problem in offshore engineering that deserves to be elucidated as similar combinations of collinear wave current flows had been reported in the offshore field This thesis is focused on a combination of experiments and numerical study to better understand this phenomenon

1.2 Review of Past Research

The beat phenomenon was observed between a SPAR, a single column floater, and a TAD, a multi – column floater Fundamentally, the flow interaction between the bluff column of the SPAR and one

of the columns of the TAD can be represented by two interacting cylinders in waves and currents The upstream cylinder would be one that is a bluff body where diffraction effects 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 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 = 103 to 105, and the Keulegan carpenter numbers are in the range of 0 < KC < 1 The physics of the flow around cylinders are discussed primarily within these ranges in the following paragraphs

6

1.2.1 Cylinders in Uniform Flow

The regime of flow around a bluff cylinder is dependent primarily on the Reynolds number, as well

as surface roughness, cross sectional shape of the cylinder, turbulence in the incipient free stream flow before the cylinder, as well as shear in the incoming current flow Unless the flow is in the very low Reynolds number regime (Re ≤ 40), separation and vortex shedding would be present in the flow past the bluff cylinder As shown in figure 6, various vortex shedding regimes are possible depending on the Reynolds number

Creeping Flow

Re < 5

(A) Laminar boundary layer separation

300 < Re < 300K Subcritical Regime

(B) Turbulent boundary layer separation but boundary layer is laminar

300K < Re <350K Critical Regime (Lower transition)

The boundary layer is part laminar, part turbulent

350K < Re <1500K Supercritical Regime

at one side of cylinder

1500K < Re < 4000K Critical Regime (Upper transition)

over two sides of cylinder

4000K < Re Transcritical Regime

Figure 6 Schematics of flow past a cylinder at different Reynolds flow regimes Sumer &

Fredsoe (2006)

Present Study

Industry Model Testing

Prototype

Vortex – induced vibration is a phenomenon when the Von Karman vortex streets generated by flow past a cylinder creates oscillatory forces on the cylinder in the direction perpendicular to both the flow and the structure

Some literature have used the concept of reduced velocity as a normalizing function relating the flow velocity, cylinder diameter and the natural frequency of the vibrating system, where:

(1.1)

1.2.2 The Phenomenon of Lock-In for flows past cylinders

Experiments by Feng (1968) at sub-critical flow regimes showed that, for flows past free – oscillating

cylinders, a lock – in phenomenon is observed over a range of reduced velocities Vr For low flow

velocities, the vortex shedding frequency corresponds to that of a fixed cylinder, and the Strouhal number of the cylinder system dictates this frequency At higher flow velocities, the shedding frequency switches to the vibration frequency of the cylinder In these instances, the vortex shedding frequency is no longer related to the Strouhal number, but becomes ‘locked’ in to the

frequency of oscillation of the cylinder This lock – in occurs for a certain range of Vr, beyond which

the shedding frequency unlocks from the natural frequency of the cylinder, to follow the Strouhal vortex shedding frequency again An illustration of this phenomenon based on the analysis by Feng (1968) for the cross flow response of a flexibly mounted cylinder in steady air currents is shown in Figure 7 The plot showed that the locked in phenomenon occurred for a reduced velocity range from 4 to 7 Subsequent studies by Anand (1985) revealed that lock-in phenomenon exists at a similar reduced velocity range for hydrodynamic current flows past cylinders

In extreme cases where the locked in vortex shedding frequency, the natural frequency of the cylinder, and the vibration frequency coincide, the body motions of the cylinder in the lift direction can reach very large amplitudes as the shedding and therefore the lift force resonates with cylinder motion

n Df U

Vr=

8

Figure 7 Graph of f / f n vs Vr illustrating the lock-in region where the vortex shedding

frequency is synchronized to the frequency of cylinder oscillation Feng (1968)

The range of reduced velocities where lock – in occur is dependent on the vibration amplitude of the cylinder Typically, large vibration amplitudes would result in a wider lock – in range This is because larger vibration amplitudes of the cylinder which stem from smaller structural damping would require a higher shedding frequency to unlock itself from vibrating at the cylinder’s natural frequency to Strouhal frequency A higher shedding frequency in turn means a higher flow velocity and hence higher reduced velocity

For the case of oscillating cylinders in currents, the motion of the cylinder can initiate the instability mechanism that leads to vortex shedding The periodic movement of the cylinder gives a way of synchronizing the moment of vortex shedding along its length Bearman (1984) have shown that when this happens, the vortex shedding correlation length, a measure of the mean distance between vortex shedding cells, is increased The amplitude of the oscillation play a role in determining the range of reduced velocities where the vortex shedding frequency coincides with the cylinder’s natural frequency Larger oscillation amplitudes of the cylinder result in a wider range of frequency where synchronization occurs

Another important parameter influencing the lock - in phenomenon in flexibly supported cylinders is

the structure – fluid density ratio m* of the cylinders, where

9

(1.2)

m = Cylinder mass per unit length,

ρ = Density of the fluid,

D = Cylinder diameter

The vortex shedding frequency of systems with high m* is constrained by the structural frequency, while for systems with low m*, the fluid oscillation dictates the vortex shedding frequency A

consequence of this is that the range of lock-in is much narrower for small mass ratios (e.g cylinders

in air) compared to large mass ratios (e.g neutrally buoyancy cylinders in water.)

SPARs and other neutrally buoyant cylindrical structures have an extended lock-in range, as results from Irani (2004) showed Figure 8 shows typical VIV response of a SPAR illustrating that its

responses can extend beyond a reduced velocity of Vr > 10

Figure 8 Schematics showing plot of amplitude-diameter ratio (A/D) versus reduced velocity

(V r ) of a Truss SPAR system where high A/D response extend beyond V r > 10 Irani & Finn (2004)

2

*

D

m m

ρ

=

Range of our interest is below the “lock-in range”

A D

T U

For cylinders free to oscillate in both inline and transverse directions to the current flow, research by Sarpkaya (1978) have shown that due to the pattern of vortex shedding from flow past a cylinder, the alternating forces acting on the cylinder have a constructive effect on transverse oscillations When this transverse amplitude increases, it was determined that the mean in-line force on a cylinder undergoing lock –in increases

1.2.3 Cylinder in Waves

The characteristics of oscillatory flow past a cylinder depends primarily on the Reynolds number (Re), and the Keulegan Carpenter Number (KC), where:

(1.3)

Small KC numbers mean that the orbital motion of the water particles is small compared to the size

of the cylindrical structure Separation of flow behind a cylinder does not occur in oscillatory flows with very small KC numbers (less than 1.1)

Flow characteristics corresponding to low KC numbers and Reynolds flow in the sub-critical regime, (Re = 103), according to Sarpkaya (1986) and Williamson (1985) are summarized in Figure 9

Using flow visualization, Williamson (1985) had elucidated the key features associated with Re and

KC in the range of Re < 2.5 x 104 and 0 < KC < 35 respectively, including the formation, growth, shedding and reversal of vortices around a vertical cylinder in waves In particular, three categories

of wave flow regimes were identified

Where: U w = maximum particle velocity

T = Wave Period

D = Diameter of cylinder

11

Figure 9 Flow characteristics around a smooth cylinder in oscillatory flows Sarpkaya (1986),

Williamson (1985)

The first regime is known as the Symmetric / Asymmetric vortex reversal (SVR / AVR) and this occurs

at Keulegan-Carpenter numbers of between 3 and 8 In this regime, symmetric or asymmetric vortex pairs are formed in each half-wave cycle, but are not fully developed at the end of each half cycle

At higher KC numbers between the range of 8 to 25, detached vortex reversals are observed In this

”detached vortex reversal” (DVR) flow regime, fully grown and detached vortices reverse to form a sidewise vortex street These are formed for both the half cycles

For KC number higher than 25, the wake at each half cycle resembles a limited length Karman Vortex Street, and this vortex street effects the new vortex street formed at the next half cycle This regime

is known as Quasi – Vortex Shedding (QVS)

An overview of the different wake formation regimes presented by Sarpkaya (1986) is conceived in Figure 10

Flow Regime KC range (Re = 10 3 )

(a)

Creeping Flow Laminar Flow KC < 1.1

(b)

Separation with Honji vortices 1.1 < KC < 1.6 (c)

A pair of symmetric vortices 1.6 < KC < 2.1 (d)

A pair of symmetric vortices with turbulence over cylinder surface 2.1 < KC < 4.0 (e)

A pair of asymmetric vortices 4.0 < KC < 7.0

(f)

Vortex shedding KC > 7.0

12

Figure 10 Plot of KC numbers versus Reynolds numbers, illustrating regimes of flow around a

cylinder in oscillatory flows, Sarpkaya (1986)

For oscillatory flows at low KC numbers, whether the flow will be unseparated, in the unstable transition region, or in the regime undergoing chaotic interactions leading to turbulence, depends on both the KC numbers and Stoke’s parameter (β), where β is the ratio of Reynolds number to KC number As shown in Figure 11, Sarpkaya (2002, 2006) used two lines, KCcr and KCh to demarcate these regions, KCcr is the line that separates the region of no observable structures in the wake, and the inception of mushroom shaped (Honji) coherent structures On the other hand, KCh (the Hall line) is the boundary that separates the unstable region to the chaotic region where the coherent structures in the wake undergoes complex interactions leading to separation and turbulence

Separation with Honji vortices

Separation with Honji vortices

No separation but

A pair of symmetrical vortices

A pair of symmetrical vortices with

turbulence in b.l

turbulence

KC

Re x 103 Creeping Flow

13

Figure 11 Graph of Stokes number versus Keulegan-Carpenter Number (Sarpkaya 2006), and

the domain where the present study encompass

Sarpkaya (2006) demonstrated that the characteristic coherent structures can be formed at low KC oscillatory flows They generate and break up at KC < 2, and this flow motion repeats itself from cycle to cycle with regularity

In the case where the flow is unseparated around the cylinder at low KC and Re numbers (creeping flow), research by Schlichting (1979) and Wang (1968) have shown that streaming effects can happen and a constant secondary flow in the form of recirculating cells will appear around the periphery of the cylinder as shown in Figure 12 The cause of streaming can be explained as follows:

i The flow velocity at any location close to the periphery of the cylinder surface is not

symmetric with respect to the two half periods of the oscillating flow,

ii This velocity is larger when the flow is in the direction of converging cylinder surface,

then when the flow is in the opposite direction,

iii Due to this difference in the velocity in each period cycle, the flow has a non zero mean

velocity around each quarter of the cylinder surface, leading to a recirculating flow pattern

Sarpkaya Experiments

Present Study

Chaotic

14

Recent numerical studies involving the solution of Navier Stokes equation at Rewave =103 and KC = 2

by Badr et al (1995) shows that streaming effects can exist even in separated flows

Figure 12 Schematic of streaming around a cylinder in oscillatory unseparated flows

1.2.4 Combined waves and currents on a cylinder

When currents and waves coexist, the presence of one flow would interfere with the kinematics of the other To quantify the dominance of either currents or waves in the wave current field on a cylinder, the ratio of the current flow (Uc) to the maximum particle (Uw) in the oscillatory flow, Uc /

Uw is used

Sumer et al (1992) investigated the forces on an oscillating cylinder in a recirculating constant current flume, at a sub-critical regime Reynolds number of Re = 3 x 104 By varying the ratio of Uc /

Uw, from 0 to 1, it was ascertained that:

a The forces on the in-line direction of the cylinder varies in a same manner as the flow

velocity, for the range of Uc / Uw ,

b Transverse force signatures were absent at Uc / Uw = 1 over every other half period of

each oscillatory flow cycle, as highlighted in Figure 13 This suggests that no shedding

Oscillatory flow direction

15

characteristics were observed The reason for this is the cancelling effects of the current velocity and wave particle velocities when the oscillatory flow is in the reversed half of the oscillatory cycle,

c In combined wave current flows, the Strouhal frequency relationship is still satisfied,

with a modified equation defined by:

(1.4)

Figure 13 Force time series of a cylinder in a coexisting current-wave flow Sumer et al (1992)

The variation of force coefficients for coexisting current and wave flows was investigated by Sumer (1992) and Sarpkaya and Storm (1985) for various ratios of Uc / Uw < 2 Their studies were conducted

at two sub-critical Reynolds regime of Re = 3 x 104 and Re = 1.8 x 104 respectively The variations of

CD and CM are presented in Figure 14

w c

v t

U U

D f S

16

D

T V

1=

D

T V

2 =

Figure 14 Variation of inline force coefficients C D and C M vs U c /U w , at different KC numbers

Plots extracted from Sumer (1992), Sarpkaya and Storm (1985) Dashed lines are asymptotic values for steady current case

These plots show that the drag coefficient generally decreases with the increase in Uc / Uw, and approaches an asymptotic value as Uc / Uw approaches 2, which would be similar to the drag coefficient obtained for a steady current only case

The inertia coefficient is relatively independent of the changes in Uc / Uw except in the case at low KC numbers, where CM decreases with increase in Uc / Uw

Zdravkovich (1995) has proposed modified Keulegan Carpenter numbers KC1 and KC2 to take into account the relative effects of waves and current contributions, where KC1 and KC2 are defined by: