computational investigation of forces around an …

Oil

& G

as T

echnolo

gy

Dep

artm

ent

of Com

puta

tional

M

echanic

sAal

borg

Univ

ersi

ty

COMPUTATIONAL INVESTIGATION OF COMPUTATIONAL INVESTIGATION OF FORCES AROUND AN OFFSHORE FORCES AROUND AN OFFSHORE

MONOPILE FOUNDATION.MONOPILE FOUNDATION.

COMPUTATIONAL INVESTIGATION OF FORCES AROUND AN

OFFSHORE MONOPILE FOUNDATION.

(X – SEMESTER)

A Thesis submitted in partial fulfilment for the degree of

Master of Science in Oil and Gas Technology

BY

G.S. RAVI SHANKAR

Thesis Submitted: Nov 2007. Degree Awarded : Y / N

Computational investigation of forces around an offshore monopile foundation. i

ACKNOWLEDGEMENT

I would like to acknowledge Professor Tron Solberg and Associate Professor Anders

Schmidt Kristensen, Department of Computational mechanics, for supervising the Thesis.

The guidance and contribution of their experiences is not only on this Thesis work but also

throughout my career is deeply appreciated.

This Thesis would not have been materialized without the help of Prof. Tron Solberg for his

training towards my work with computational simulations. My sincere thanks to Asc. Prof.

Anders Schmidt Kristensen for forwarding me to CFD track and giving consistent stress

relief therapy for progressing the work. I also thank Prof. Bjørn H. Hjertager for providing

class lectures in CFD and his supervision towards it.

I greatly thank Henrik Carstens, Rambøll for offering me a very interesting research

opportunity in the field of CFD to build my career and fulfil my Thesis work. I appreciate for

the meetings and discussion arranged at Rambøll together with Aalborg University Esbjerg.

I wish to express my gratitude to the staff of Aalborg University Esbjerg for very good

student support during my stay, especially Diana Bie and Kirsten Bisgaard Kirchner. Many

thanks to Rolf Hansen, PhD student for his technical support during the computational

simulations.

The Ministry and board of education, Denmark is greatly acknowledged for its economical

support towards my MSc. education in Aalborg University Esbjerg.

… to the memory of my parents.

Computational investigation of forces around an offshore monopile foundation. 1

TABLE OF CONTENTS

LIST OF FIGURES ...................................................................................................................... 2

LIST OF TABLES ......................................................................................................................... 2

LIST OF PLOTS ........................................................................................................................... 3

ABSTRACT ................................................................................................................................. 5

1. INTRODUCTION.................................................................................................................. 6 1.1 PROBLEM DEFINITION.......................................................................................................... 6 1.2 BACKGROUND ..................................................................................................................... 8 1.3 PROBLEM IDENTIFICATION................................................................................................. 10 1.3 LITERATURE REVIEWS ....................................................................................................... 12

2. COMPUTATIONAL HYDRODYNAMICS...................................................................... 15 2.1 INTRODUCTION.................................................................................................................. 15 2.2 GOVERNING EQUATIONS.................................................................................................... 15 2.3 DISCRETISATION................................................................................................................ 16 2.4 GEOMETRY........................................................................................................................ 17

2.4.1 Geometry 1 ................................................................................................................ 17 2.4.2 Geometry 2 ................................................................................................................ 18 2.4.3 Geometry alignment .................................................................................................. 19

2.5 NUMERICAL METHODOLOGY ............................................................................................. 19 2.6 BOUNDARY CONDITIONS ................................................................................................... 23

3. COMPUTATIONAL RESULTS ........................................................................................ 25 3.1 GRID INDEPENDENCY ........................................................................................................ 25 3.2 VALIDATION...................................................................................................................... 25

3.2.1 Center-line Velocity profile....................................................................................... 26 3.2.2 Visualization.............................................................................................................. 27 3.2.3 Vortex shedding......................................................................................................... 28 3.2.4 Drag coefficients ....................................................................................................... 29

3.3 RESULTS............................................................................................................................ 30 3.3.1 Lift and drag convergence (Plot 9 to Plot 16) .......................................................... 31 3.3.2 Drag coefficients (Plot 17 to Plot 21) ....................................................................... 31 3.3.3 Static pressure and velocity contours (Plot 22 to Plot 33) ....................................... 32

4. CONCLUSION..................................................................................................................... 37

5. FUTURE RESEARCH WORK .......................................................................................... 38

PLOTTING RESULTS................................................................................................................ 39

REFERENCES ........................................................................................................................... 59

APPENDIX-1............................................................................................................................. 61

APPENDIX-2............................................................................................................................. 63


List of Figures

Figure 1 Site location and picture of ‘Wave run-up’ on one of the foundations of the Horns Rev windmill farm. Hs = 2.5m, platform level = 9m above SWL, Elsam [1]........................... 6 Figure 2 Definition sketch......................................................................................................... 7 Figure 3 Moving through the separation point. ........................................................................ 9 Figure 4 Representation of Unit cell volume in 2D using FVM. ........................................... 16 Figure 5 Geometry1 Vs. Geometry2. ..................................................................................... 18 Figure 6 Alignment of offshore monopile wind turbine in a fixed horizontal flow direction. 19 Figure 7 Procedural steps of FLUENT simulation ................................................................. 20 Figure 9 Boundary conditions for CFD simulations. ............................................................. 23 Figure 10 Feasibility study for generating waves. Mesh (Left), Free surface wave (right). .. 24 Figure 11 Contour of Stream function at Re 20, D = 0.1m, laminar...................................... 25 Figure 12 Center-line Velocity profile in x-direction for a computational domain................ 26 Figure 13 Visualization plot of velocity magnitude at Re = 150, Flow time = 4000 seconds,27 Figure 14 Visualization plot of velocity magnitude at Re = 150, Flow time = 4000 seconds,27 Figure 15 Validation plots showing coefficient of drag and lift for unsteady state............... 28 Figure 16 Validation plot showing coefficient of drag against Reynolds number, D = 0.1m., laminar, Virtual, Unique domain. ........................................................................................... 29

List of Tables Table 1 Coordinates of three different domains and cylinder position................................... 18 Table 2 Summary of CFD problem setup................................................................................ 22 Table 3 Grid independent analysis, drag and lift coefficients. ............................................... 25 Table 4 Vortex shedding validation using Strouhal number.................................................. 28 Table 5 Validation of Cd Vs Re for Virtual unique model, D = 0.1m..................................... 30 Table 6 Combinations of plotting in ‘Ansys Fluent’. .............................................................. 30 Table 7 History of non-dimensional drag force values computed for both Virtual and Upscale models. (For all: Reynolds number corresponds to large cylinder) ...................................... 33


List of Plots

Plot 1 Geometry1 (left), Quadrilateral mesh (right).................................................................... 39 Plot 2 Geometry2 (left), Tri Paved mesh (right) .......................................................................... 39 Plot 3 Contour of velocity magnitude, Re 150, Flow time 4000 sec. (65 min.), laminar, unsteady......................................................................................................................................... 40 Plot 4 Contour of static pressure, Re 150, Flow time 4000 sec. (65 min.), laminar, unsteady. .. 40 Plot 5 Contour of velocity vector plot, Re 150, Flow time 4000 sec. (65 min.), laminar, unsteady......................................................................................................................................... 40 Plot 6 Contour of velocity magnitude, Re 500, Flow time 1200 sec. (20 min.), laminar, unsteady......................................................................................................................................... 41 Plot 7 Contour of static pressure, Re 500, Flow time 1200 sec. (20 min.), laminar, unsteady. .. 41 Plot 8 Contour of velocity vector plot, Re 500, Flow time 1200 sec. (20 min.), laminar, unsteady......................................................................................................................................... 41 Plot 9 Drag convergence history of Virtual domains in the laminar turbulent region................ 42 Plot 10 Lift convergence history of Virtual domains in the laminar turbulent region................. 42 Plot 11 Drag convergence history of Bottom aligned family for Virtual and Upscale domains. ........................................................................................................................................ 43 Plot 12 Lift convergence history of Bottom aligned family for Virtual and Upscale domains. ... 43 Plot 13 Drag convergence history of Left aligned family for Virtual and Upscale domains. ..... 44 Plot 14 Lift convergence history of Left aligned family for Virtual and Upscale domains. ........ 44 Plot 15 Drag convergence history of Right aligned family for Virtual and Upscale domains. ... 45 Plot 16 Lift convergence history of Right aligned family for Virtual and Upscale domains. ...... 45 Plot 17 Validation plot, Experimental Vs Virtual domains at various Re number, D=0.1m....... 46 Plot 18 Validation plot, Experimental Vs Upscale domains at various Re number, D=5m. ....... 46 Plot 19 Family of Drag coefficients for flow past vertical monopile foundation structure including Left aligned boat landing facility. ................................................................................. 47 Plot 20 Family of Drag coefficients for flow past vertical monopile foundation structure including Bottom aligned boat landing facility............................................................................. 47 Plot 21 Family of Drag coefficients for flow past vertical monopile foundation structure including Right aligned boat landing facility................................................................................ 48 Plot 22 Contour of velocity magnitude for Left aligned boat landing facility, Upscale model, .. 49 Plot 23 Contour of velocity magnitude for Bottom aligned boat landing facility, Upscale model, Re = 2.5E07, V= 5m/s. ...................................................................................................... 49 Plot 24 Contour of velocity magnitude for Right aligned boat landing facility, Upscale model, ............................................................................................................................................ 49 Plot 25 Contour of velocity magnitude for Left aligned boat landing facility, Upscale model, .. 50 Plot 26 Contour of velocity magnitude for Bottom aligned boat landing facility, Upscale model, Re = 5E07, V= 10m/s. ....................................................................................................... 50 Plot 27 Contour of velocity magnitude for Right aligned boat landing facility, Upscale model, ............................................................................................................................................ 50 Plot 28 Contour of static pressure for Left aligned boat landing facility, Upscale model, ......... 51 Plot 29 Contour of static pressure for Bottom aligned boat landing facility, Upscale model,.... 51 Plot 30 Contour of static pressure for Right aligned boat landing facility, Upscale model,....... 51 Plot 31 Contour of static pressure for Left aligned boat landing facility, Upscale model, ......... 52 Plot 32 Contour of static pressure for Bottom aligned boat landing facility, Upscale model,.... 52 Plot 33 Contour of static pressure for Right aligned boat landing facility, Upscale model,....... 52 Plot 34 Static pressure around vertical monopile foundation structure for Bottom aligned boat landing facility, Virtual scale, D=0.1m. ............................................................................... 53


Plot 35 Static pressure around Bottom aligned boat landing facility for two small vertical cylinders, Virtual scale, D=7.112mm. .......................................................................................... 53 Plot 36 Static pressure around vertical monopile foundation structure for Bottom aligned boat landing facility, Upscale, D=5m. .......................................................................................... 53 Plot 37 Static pressure around Bottom aligned boat landing facility for two small vertical cylinders, Upscale, D=355.6mm................................................................................................... 54 Plot 38 Summary of static pressure for Bottom aligned monopile foundation structure for Virtual and Upscale domains. ....................................................................................................... 54 Plot 39 Static pressure around vertical monopile foundation structure for Left aligned boat landing facility, Virtual scale, D=0.1m......................................................................................... 55 Plot 40 Static pressure around Left aligned boat landing facility for two small vertical cylinders, Virtual scale, D=7.112mm. .......................................................................................... 55 Plot 41 Static pressure around vertical monopile foundation structure for Left aligned boat landing facility, Upscale, D=5m. .................................................................................................. 55 Plot 42 Static pressure around Left aligned boat landing facility for two small vertical cylinders, Upscale, D=355.6mm................................................................................................... 56 Plot 43 Summary of static pressure for Left aligned monopile foundation structure for Virtual and Upscale domains. ....................................................................................................... 56 Plot 44 Static pressure around vertical monopile foundation structure for Right aligned boat landing facility, Virtual scale, D=0.1m......................................................................................... 57 Plot 45 Static pressure around Right aligned boat landing facility for two small vertical cylinders, Virtual scale, D=7.112mm. .......................................................................................... 57 Plot 46 Static pressure around vertical monopile foundation structure for Right aligned boat landing facility, Upscale, D=5m. .................................................................................................. 57 Plot 47 Static pressure around Right aligned boat landing facility for two small vertical cylinders, Upscale, D=355.6mm................................................................................................... 58 Plot 48 Summary of static pressure for Right aligned monopile foundation structure for Virtual and Upscale domains. ....................................................................................................... 58 Plot 49 Separation points for Left, Bottom and Right aligned boatlanding facility for two small vertical cylinders, Virtual scale, D=7.112mm, Perimeter=0.22 m, Re = 20, 40, 150. ....... 64 Plot 50 Separation points for Left, Bottom and Right aligned boatlanding facility for two small vertical cylinders, Virtual scale, D=7.112mm, Perimeter=0.22 m, Re = 500, 1000, 5000. .............................................................................................................................................. 64 Plot 51 Separation points for Left, Bottom and Right aligned boatlanding facility for vertical monopile foundation structure, Virtual scale, D=0.1m, Perimeter= 0.314m, Re = 20, 40, 150.. 65 Plot 52 Separation points for Left, Bottom and Right aligned boatlanding facility for vertical monopile foundation structure, Virtual scale, D=0.1m, Perimeter=0.314m, Re = 500, 1000, 5000. .............................................................................................................................................. 65 Plot 53 Separation points for Left, Bottom and Right aligned boatlanding facility for two small vertical cylinders, Upscale, D=355.6mm, Perimeter=1.116m, Re = 1E06, 2.5E07, 5E07. ............................................................................................................................................. 66 Plot 54 Separation points for Left, Bottom and Right aligned boatlanding facility for vertical monopile foundation structure, Upscale, D=5m, Perimeter=15.7m, Re = 1E06, 2.5E07, 5E07. ............................................................................................................................................. 66


ABSTRACT

One of the classical problems in fluid mechanics is the determination of the flow field around

a bluff body represented by a circular cylinder. This is of great interest in many engineering

applications, such as hydrodynamic loading on ocean marine piles and offshore platform

risers and casing pipes etc. The hydrodynamic behavior of the complex flow field around the

three circular cylinders was investigated. Flow past three circular cylinders of different

diameters in two dimensional domain was simulated using commercial software Ansys Fluent

v6.3. Three different angle of attacks with 0, 90 and 180 degrees were used with two small

cylinders located at left, bottom and right side (three patterns) of the large cylinder

respectively. The diameter ratio of the large cylinder to the small one is 14 with constant

center-to-center distance. The segregated implicit solver approach was chosen with the

SIMPLE (Semi-Implicit Method for Pressure Linked Equation) method by Patankar (1981)

to achieve pressure-velocity coupling and the field variables are interpolated using the first

order upwind scheme. The second order pressure discretization was chosen for good

resolution during capturing of pressure field near cylinder. The residual factors for computing

continuity, x and y velocities were set to 1E06 to reach absolute convergence criteria. The

Ansys Fluent standards were used for most user interface input panels.

Validation experiments were conducted in five stages: Grid independency, visualization,

center-line velocity profile, vortex shedding lift profile and drag force prediction against

Reynolds number. Validation for higher turbulent region fails when a standard KE turbulence

model was used to predict the drag coefficients around cylinder resulting 25% error. The

simulations were carried though pointing this limitation governs and few techniques for

minimizing this error was identified and discussed as an hypothesis.

A total of 65 simulation runs were carried which include steady and unsteady state solutions.

Plotting is found to be the challenging and gaming tool in Ansys Fluent, once all simulation

data were stored. Various contour and x-y plots of static pressure, velocity magnitude, drag

coefficients, convergence etc. were computed using a clubbing technique for evaluation. A

couple of animations were also made in MPEG format at Re 150 for identifying vortex

behavior and demonstration purpose.


1. Introduction

1.1 Problem definition One of the world’s biggest wind farms, ‘Horns Rev’ is located off the west coast of Denmark

in the North Sea. Here the so-called "mono-pile" concept was used; single pile foundations of

5 m. diameter are driven into the seabed. Construction of these offshore wind turbines

encompasses building of large structures like foundation, pile and turbine together with boat

landing facility, ladder, platform and door. Recently, wave run-up and wave impacts caused

damage to existing platform and boat landing facilities. The Figure 1 below shows the site

location and description of wave run-up on one of the foundations of the Horns Rev wind

mill farm.

Figure 1 Site location and picture of ‘Wave run-up’ on one of the foundations of the Horns

Rev windmill farm. Hs = 2.5m, platform level = 9m above SWL, Elsam [1].

It is obvious that when such obstacles are placed in a free stream flow, the flow behavior is

disturbed and the energy of flow is transferred to these structures and thus arise problems.

Such problems are often encountered in offshore oil and gas and marine applications, few

reasons include, loss of material integrity due to corrosion and hydrodynamic forces, erosion

of sea bed due to high bottom velocities called scour etc. Hence the marine, wind and oil and

gas engineers always try to minimize the surface area exposed to the flow and mechanical

equipment. The type of flow behavior is dependent on the shape of the structure. Several non

dimensional quantities and parameters like Reynolds number, Drag coefficients, Morrison

forces etc. play important to define the hydrodynamic problem. In today’s computing world,

a clear picture of certain problems are being identified using coupled Mathematical-

SWL


Computational fluid dynamic technique, so called Computational Fluid Dynamics (CFD).

The given problem will be investigated using this technique which is cost and time effective,

and robust to predict the results.

The main objective of the project is to implement the problem numerically using commercial

CFD software Ansys Fluent v6.3 and investigate the flow physics for safe installation of boat

landing facility of an offshore wind turbine.

The major achievements of this thesis are summarized below:

1. To study and understand the concept of hydrodynamic behavior of offshore monopile

foundation and defining the specific problem,

2. To check the compatibility, simulate and examine the computational hydrodynamic

model,

3. To calculate the hydrodynamic drag forces for a steady current flow and validate the

numerical results with experimental data and up scaling to real conditions,

4. To investigate the interaction of flow behavior around offshore monopile foundation

including boatlanding facility,

5. To perform feasibility studies for numerical simulation of fluid-fluid (air-water)

interaction (not detailed in this thesis).

To accomplish the above goal, an efficient numerical model shall be created for numerical

simulation and further studies. For this, a drawing is provided from client ‘Rambøll A/s

Denmark’ as shown in Appendix-1 to investigate the flow field around the monopile for boat

landing installations in actual scale [14].

Figure 2 Definition sketch.

Upon clients interest three flow directions (α = 0, 90, 180) are assumed as defined in Figure 2

to study the flow behavior and force interaction between monopile (or large cylinder) and

boat landing facility (or two small cylinders). Where α is the angle of attack.

y

x

D d

θ

Inflow

α = 0 y

x

D d

θ

Inflow

α = 90 y

x

D d

θ

Main cylinder, monopile

Small cylinder, Boatlanding facility

Inflow

α = 180 A

B


1.2 Background Few applications and importance of performing CFD simulations for this Thesis work are

highlighted first and specific problem of interest is discussed later.

When the wind blows on a calm ocean, it first generates short ripples, which are affected by

surface tension as well as gravity. Of given time and distance offshore, longer waves become

dominant. These waves coming from different systems could build up into giant waves and

sometimes appear in the areas of extended storms or converging weather fronts. Several

offshore oil rigs get hit by such waves so called rogue waves. In 1984, the radar reports from

the Gorm oilfield in the central North Sea (Sand et al., 1990) show 466 rogue-wave

encounters in the last 12 years. These days oil rigs and ships are built to withstand waves of

15 meters (49 feet). [2]

During adverse harsh climatic conditions, the bottom velocities wash away the sediments

around offshore foundation structures at sea bed bottom, where as the free surface velocities

at SWL (Sea Water Level) frequently hit these foundations and run-up over the structures.

The former is called ‘Scour problem’ and later ‘Wave run-up problem’. Both problems were

extensively studied by Aalborg University as detailed in literature reviews later.

Flow past three cylinders in a tandem or side by side arrangement represents a complex flow

configuration. In most of the oil and gas applications we observe the phenomena of flow past

identical diameters. For example, risers, platform piles, wind turbine offshore parks, drill

pipes, pipelines, heat exchanger tube bundle, industrial boilers etc are all circular cylinders.

There are various phenomena associated with flow around cylinder; one of the most

important of these is the force acting on the body due to the fluid. The drag component of the

forces parallel to the direction and resisting the motion, is of concern in most external flows.

The component of force normal to the direction of motion, the lift, is also of obvious

importance in many flows. The fluid imposes the force on the body through the surface as

viscous shear forces and pressure forces. The drag components due to viscous forces and

pressure forces are called skin friction drag and form (pressure) drag respectively. Pressure

drag is a result of the net force on an object due to the static pressure distribution around the

object. Pressure drag is the major contribution to drag on blunt objects such as plates whose

surface is normal to the flow.


Separation is of particular interest when studying external flows. Separation occurs when the

main stream flow leaves the body and forms a free stream surface in the interior of the fluid.

The location of the separation point is strongly dependent upon the geometry of the body. An

abrupt change in the geometry, such as a backward facing step will cause the flow to

separate. The main stream may also separate from a body because of an adverse (positive)

pressure gradient. Basically the momentum of the fluid near the surface may be insufficient

to overcome the effect of the increasing pressure which exerts a net retarding force on the

fluid with backward flow as seen in Figure 3. The turbulent boundary layer will separate

farther down stream than a laminar boundary layer because the momentum is higher (due to

the higher velocities) near the surface for turbulent flow. Thus turbulent flow will be able to

overcome an adverse pressure gradient for a longer distance before it separates.

Figure 3 Moving through the separation point.

The separation point on the cylinder is not stationary but oscillates around its average

location, such as between A and B as shown in Figure 2. A vortex is generated as the

separation point moves form B to A, is then 'shed' from the cylinder and the separation

suddenly moves back to point B. This process continues with a shedding frequency ω and

results in oscillatory force acting on the cylinder. If w is near the natural frequency of the

cylinder, the resulting condition of resonance may be sufficient to cause structural damage- A

dramatic case of this phenomenon is the wind-driven oscillations which caused the collapse

of a suspension bridge near Tacoma, Washington. Power lines, TV antennas, and other

structures have also been damaged by this effect. Care must be taken in the design of

structures which exhibit this phenomenon so that their natural frequency is quite different

from that of the shedding vortices.

B. Mutlu Sumer and Jørgen Fredsøe (2002) [3], made extensive studies on flow past

cylinders exposed to marine environment. One of their implications in discussion is that the

vortex shedding occurs only when the two shear layers interact each other. If this interaction


is inhibited in one way or another, for example by putting a splitter plate or obstacle at the

downstream side of the cylinder between two shear layers, the shedding would be prevented

and therefore no vortex shedding would occur in this case. When such a cylinder is placed

close to the wall in case of marine pipelines, the vortex shedding is suppressed completely.

The main importance to study vortex shedding is to find the behavior of flow past cylinder

upon varying Reynolds number. In other words, vortex shedding causes enormous amount of

vibrations due to the action of negative atmospheric pressure creating vacuum. Two problems

are identified here. One, when vortex shedding frequency matches the cylinder material

natural frequency, the vibrations and noises occurs causing subsequent deflections on the

structure. Second, higher the velocity, the higher the vortex shedding length scales. For an oil

and gas platform, where foundation piles and casing pipes of un-identical diameters are

sitting close to each other, the study of vortex behavior is even more complex. Thus several

applications exist in extension to present Thesis work.

1.3 Problem identification Flow around two circular cylinders of different diameters is relevant to flow around two

pipelines in offshore oil and gas. Due to certain technical requirements and economical

considerations, a piggyback pipeline (could be OFC or electrical cable) is sometimes laid

together with the main pipeline. This pipeline is often of a different diameter from the main

pipeline. Laying the two pipelines together reduces installation costs. Ming Zhao, Liang

Cheng, Bin Teng and Dongfang Liang (2004) [4] from University of Western Australia,

extensively investigated for a two cylinder problem numerically using Finite element method

in two dimensions. This sort of studies will be extended in this Thesis work for numerical

investigation using finite volume method for a three cylinder problem.

From studies and library research at Aalborg University, it is understood that research exist

for identical cylinders in uniform or random aligned arrangement [16]. Where as for

problems involved with un-identical cylinders in a typical or random pattern is still a new

concept to many researchers. The part of the Thesis work identifies this problem to open

gateway to similar problems in several oil and gas applications.

In our problem as shown in Figure 2, two small cylinders are placed around large cylinder in

three different locations of respective three independent domains. How vortex shedding does

influence when an additional two small cylinders are installed at various locations around a


5m. monopile? Further, there will be frequent shifts in the separation points at the rear side of

the cylinder in the direction parallel to the flow. To investigate this, feasibility studies are

performed modeling a unique domain first which consist of only large cylinder, and checking

for the compatibility of FLUENT solver by validating with experiments performed by B.

Mutlu Sumer and Jørgen Fredsøe (2002). In other words, a mesh or grid independent analysis

will be made to fulfill this criterion.

Before, few assumptions are highlighted to simplify the problem and avoid complications

during simulations. These are chosen case-by-case upon experiencing problems during

simulations.

1. Flow is two dimensional and steady current.

2. Vortex shedding results are ideally satisfied in two dimensional for validation.

This does not in real case, where vortices distribute energy in cross flow direction to

the sea floor. For a three dimensional flow past vertical cylinder, assuming the

domain is made up of a several slices in two dimensions, the separation points around

cylinder for every slice varies due to uneven distribution and negative pressure actions

behind wake. Since identification of separation points are not of specific interest and

assuming it doesn’t vary much for steady current flow, this assumption fulfils our

criteria. (There is opportunity to study in future extruding existing 2d meshes to 3d

and simulate for vortex shedding as a part of research.)

3. All cylinders and solid walls in the computational domain are smooth surfaced.

The affect of surface roughness is ignored during simulations for time being. (There is

opportunity to study in future modifying all solid boundary conditions from saved

simulation data found in CDROM for further research.)

4. The force values obtained around cylinder does not experience out bounded range

when applied standard turbulence model, trusting FLUENT solver capability.

All the solid bodies consist of very thin laminar boundary layer (in other words, a

molecular viscous layer) region, into which the turbulence eddies enter and disturb the

viscous layer and thus affecting the force values. This is not true when coming to real

situation. The CFD numerics are necessarily be given some special treatment to avoid

such problems which gives totally wrong results. Several ways exist although, SKE an

industrially approved model with enhanced wall treatment and pressure gradients was

chosen, which suppress those eddies near boundary layer region. (There is


opportunity to study in future specifying user defined log of the wall and molecular

viscosity, near walls.)

1.3 Literature reviews Ming Zhao, Liang Cheng, Bin Teng and Dongfang Liang (2004) [4], have made an extensive

studies for flow around a large cylinder with a single small cylinder next to it. The abstract is

as follows. Viscous flow past two circular cylinders of different diameters is simulated by

using a finite element method. The diameter ratio between the small cylinder and the large

one is 0.25. The Reynolds number based on the diameter of the cylinders is 500 for the large

cylinder and 125 for the small cylinder. The gap between the small cylinder and the large

cylinder ranges from 0.05 to 1.0 times the diameter of the large cylinder. The position angle

of the small cylinder relative to the flow direction ranges from 0 to π. The effects of the gap

ratio between the two cylinders and the position angle of the small cylinder on drag and lift

coefficients, pressure distributions around the cylinders, the vortex shedding frequencies from

the two cylinders and flow characteristics are investigated. The magnitudes and frequencies

of the fluctuating forces acting on the two cylinders are compared with those on a single

cylinder of an equivalent diameter.

H. K. Virahsawmy, L. Chen, J. Tu and Y. Zhou (2005) [5], performed simulations for

unstable flows of three side-by-side cylinders unequally and equally spaced in a uniform

cross flow (Re = 300)/ the simulations were carried out using Ansys Flotran 7.0. A mesh

independent study was conducted on a single cylinder at Re = 100. The Strouhal number and

wake flow characteristics compare well with experimental results. Simulation of three side-

by-side cylinders in uniform cross flow has revealed that the gap flows are unstable and

constantly re-orientating, which has the effect of reconstructing the wake flows behind the

cylinders. They had good agreement with the visualization of Wang et al. (2002) in which the

gap flow and wake flow are constantly in transition.

Flow around cylinder has been studied extensively. It exhibits different behavior as the

Reynolds number increases from zero to large values based on the free stream velocity,

cylinder diameter and kinematic viscosity. In current investigation, we are interested in the

problem of flow interface when three cylinders are placed in a steady current. Williamson [6],

observed that when more than one body is placed in a fluid flow, the resulting forces and


vortex shedding pattern may be completely different from those found at the same Reynolds

number. Kim Durbin (1988) [7], identified a variety of flow patterns which characterize the

behavior of the wake region depending upon the arrangement of the circular cylinders.

Recently, Peter Frigård (2006) [1, 8], has conducted wave run-up physical tests in Aalborg

University Denmark in the shallow wave flume for both regular and irregular waves for two

different shaped pile foundations, cylindrical and conical. They observed that water depth to

pile diameter ratio and the wave height to water depth ratio has only a small influence on the

run up factor which applies to the velocity head where as wave run-up is influenced by wave

steepness is noticed. Wave run-up on offshore wind turbine foundations is much higher than

often predicted by linear wave theory, causing problems to access facilities. He recommended

the designers of offshore foundations to take the wave forces from up running waves into

consideration. The wave behavior on offshore structures and wave run-up is well explained

by Chakrabarthi (1991) and James F. Wilson (1993) [9, 10].

Theresa Kleefsman [11], made an extensive studies during his PhD work on Water impact

loading on offshore structures like FPSO using a simulation program called COMFLOW. Her

studies include design and implementation of wave generation. She also investigated the free

surface flows using Volume of Fluid method with extensively modified boundary conditions

for pressure damping and at free surface with geometric reconstruction. The validation is

made at different stages for wave propagation, water entry and impact of water on the

structure. The results show very good agreement when compared with laboratory

experiments. This Thesis will be a good representation for marine investigators for problems

with free surface flows. A part of the Thesis was studied here for exercising in Ansys Fluent

for generating free surface using linear wave theory in two dimensional domain.

To describe the wave run up over a cylinder and hydrodynamic forces, it is necessary to

understand the hydrodynamic behavior around the vertical cylindrical pile when placed in

marine environment. This is well described by B. Mutlu Sumer and Jørgen Fredsøe (1997) [3,

12]. Sumer et al (2002) used a finite volume hydrodynamic model with KE turbulence

modeling to simulate the 3D flow around a pile. Conditions for simulation were diameter of

pile = 10cm, depth of flow = 20 cm and velocity = 1.6. He was able to capture all the main

features of the scour process and scour depth with fair agreement with measurements but this


model was made impractical for which simulation of this model was approximated to several

weeks.

Tron Solberg, Bjørn Hjertager and Stefano Bove (2006) [13], used FLUENT to predict the

three dimensional flow field around circular cylinder for rigid beds. They implemented the

CFD model developed by Brørs (1998) for scour below pipelines to test for scour around

circular piles. They observed no transient large scale flow structures and recommended LES

rather than KE turbulence model to capture the dynamics of the large scale flow structures.

The predictions for scour depth are significantly smaller than the empirical relation found in

literature. For better predictions they recommend a lattice gas model rather than a CFD model

for predictions of scour formation.

Computational Fluid Dynamics became a very popular technique after the arrival of personal

computers. The numerical solutions for aerodynamic and hydrodynamic flows like flow

around airfoil or cylinder and for simple fluid mechanic flows like flow in an open

channel were accurately modeled and solved. This success motivated wind engineers to try

and numerically simulate the flow around offshore structures. In spite of being a young field

of research, a lot of development occurred in terms of predicting the behavior of flow around

bluff bodies. Accurate turbulence modeling being the key for wind engineering flows,

modifications in the existing turbulence models have been suggested, as well as many new

models were proposed. The computational wind engineers are constantly testing, analyzing

and validating turbulence models, in order to achieve accuracy in estimation of correct

pressures and wind loads on the offshore wind farms in Denmark [15].


2. Computational Hydrodynamics

2.1 Introduction In marine CFD, we are concerned with problems in hydrodynamics. Here we frequently

calculate global pressures, fluid velocity components and forces in a 2D and 3D space

surrounding the submerged portion of the offshore structures. We make assumptions

regarding the behavior of the flow depending upon the nature of the problem, whether steady

or unsteady. Here the computational method for the simulation of fluid flow is explained and

various complications and problems during simulation are evaluated.

2.2 Governing equations The numerical solution of any fluid mechanics problem requires the solution of the general

equations of viscous fluid motion i.e. the continuity equation and the Navier-Stokes equation.

These equations are a set of nonlinear partial equations with appropriate boundary conditions.

The continuity equation (1) and the general form of the Navier-Stokes equations (2), in tensor

notation, are given by:

( ) 0ii

ut xρ ρ∂ ∂+ =

∂ ∂ (1)

( ) ( ) jii i j

j i j j i

uuPu u u Ft x x x x xρ ρ μ

⎡ ⎤⎛ ⎞∂∂∂ ∂ ∂ ∂+ = − + + +⎢ ⎥⎜ ⎟⎜ ⎟∂ ∂ ∂ ∂ ∂ ∂⎢ ⎥⎝ ⎠⎣ ⎦

(2)

The left most term in equation (1) is the instantaneous acceleration term; the next one is the

convection term. The first term on the right hand side is the pressure gradient term followed

by the viscous dissipation term. F denotes the body forces. For incompressible flows ρ is

constant and the equations are simplified. All these equations can be represented in a general

transport equation form as,

( ) ( )i ii i i

u St x x x φ

φρφ ρφ⎡ ⎤∂ ∂ ∂ ∂

+ = Γ +⎢ ⎥∂ ∂ ∂ ∂⎣ ⎦ (3)

Where φ is the property which may take variable, u, v, w, T or h i.e. velocities, temperature

or enthalpy respectively. When φ =1 the equation (3) converts to continuity equation (1). The

term Sφ is the source which can be body force or buoyancy etc. The boundary conditions near

wall region enters into the source term of equation (3) and introducing a large source term at

a node [18].


The standard KE turbulent model used is according to Ansys Fluent v6.3 and one may refer to

the user guide.

The coefficient of drag CD for flow over a cylinder is a measure of the pressure distribution

around surface of the cylinder. The force in the x direction is given by,

, , ,D x w x surf xsurface surface

F dA P dAτ= +∫ ∫ (4)

Neglecting shear stress reduces to, 2

,0

cos( )D x xF P Lrdπ

θ θ= ∫ (5)

The drag coefficient obtained from dimensionless analysis is defined as, 2

02

cos( )

0.5

x

D

P LrdC

Av

π

θ θ

ρ∞ ∞

=∫

(6)

Where, v∞ and ρ∞ are the free stream velocity and density, A is the characteristic area, ,w xτ is

the x-direction wall shear stress, and ,surf xP is the static pressure around the cylinder surface.

Similarly, lift coefficient LF is defined as,

20.5L

LFC

Avρ∞ ∞

= (7)

2.3 Discretisation The discrete system is a large set of coupled algebraic equations in the discrete variables.

Solving these using such as TDMA (Tri Diagonal Matrix Algorithm) involves a very large

number of repetitive calculations for all ‘n’ number of cells to satisfy continuity equation.

The spatial and time discretisation procedure for steady and unsteady state using FVM (Finite

Volume Method) is explained in my previous semester project K8O. The similar techniques

apply for solving the problem here or one may refer Ansys Fluent v6.3 manual.

Figure 4 Representation of Unit cell volume in 2D using FVM.


2.4 Geometry Several modifications have been done for generating mesh of interest. Two geometries are

quantified using Gambit, geometry1 and geometry2. Each geometry consists of four

independent domains (unique, right, bottom, left aligned) so as to distinguish the quality of

solution while plotting. In other words, a grid independent analysis is performed and results

are shown in the following chapter. Geometry1 is generated according to laboratory

experimental setup where the dimensions and grid capability were found unsuitable during

plotting after simulations. Hence geometry2 (modified geometry) is created due to problems

experienced with validation due to unseen vortex shedding profiles. It is observed that Tri

paved mesh with proper node spacing is showing very good quality of results compared to

quadrilateral mesh with good vortex profiles. Further geometry2 is initialized and extended to

three different domains for angle of attacks 0, 90, 180 respectively as shown in Figure 2.

2.4.1 Geometry 1

Geometry1 of the flow field for numerical simulation is generated according to the laboratory

experimental setup for wave run up, conducted at Aalborg University [1]. The entire zone is

rectangular with a pile sitting in the center of the computational domain. The domain is

chosen to be 30 pile diameters long in the stream flow direction and 12 diameters in the cross

stream wise direction.

The grids near the cylinder are generated more densely because the flow in this region is

more complex with boundary layer separation. To achieve this goal, a multi block grid

generation technique is used. The grid is divided into combination of structured and

unstructured mesh. In Plot1 the blocks 1 to 8 surrounding cylinder are structured with coarse

mesh and block 9 is unstructured with fine mesh. The similar is extended to 3D along water

depth. This combination effect in creating mesh is giving good capture during plotting

results. However the geometry1 is found unsuitable for simulating vortex shedding in the

laminar region. Two reasons are identified. One, quality and type of mesh; second, stream

flow and cross stream flow lengths are insufficient to allow vortex shedding where the flow is

suppressed. Hence modified Tri-paved mesh with closer spacing giving high resolution is

generated, expanding linearly and laterally to allow the flow to develop the vortex profile in

the wake region.


2.4.2 Geometry 2

To ensure that the pile is far enough from the influences due to flow into and out of the

computational domain, the mesh was expanded by 20 diameters in the stream wise direction

both upstream and down stream as shown in Plot 2. Similarly 15 diameters in the cross

stream direction on both sides. Geometry2 pertaining to four domains of our interest will be

created as shown in Figure 6 and Plot 2.

Table 1 Coordinates of three different domains and cylinder position.

Coordinates Position of cylinder Position of fixed faces Name m. Main Cylinder1 Cylinder2 Vertices X Y

X 0 0.07 0.07 A -2 -1.5 Right aligned

Y 0 0.018 -0.018 B 2 -1.5

X 0 -0.018 0.018 C 2 1.5 Bottom aligned

Y 0 -0.07 -0.07 D -2 1.5

X 0 -0.07 -0.07 E 2 -0.15 Left aligned

Y 0 0.018 -0.018 F 2 0.15

Diameter, m. D, d 0.1 0.007112 0.007112 G 0 0

Upscale, 1:50 m. 5 0.3556 0.3556

The major disadvantage of modifying the geometry is that, Geometry2 consists of 19494 cells

in contrast to Geometry1 consisting of 3800 cells as highlighted in Figure 5.

Grid featuresGeometry1(Quad) Vs. Geometry2(Tri)

0

10000

20000

30000

40000Cells

Faces

Nodes

Cells 3800 4758 5605 4015 19494 19878 19590 19484

Faces 7752 9726 11406 8194 29623 30193 29761 29602

Nodes 3952 4966 5799 4177 10129 10313 10169 10116

Unaligned Right alignedBottom aligneLeft aligned Unaligned Right alignedBottom aligneLeft aligned

Geometry1, Quarilateral mesh (Ignored) Modified Geometry2, Tri paved mesh

Figure 5 Geometry1 Vs. Geometry2.

In pertaining to number of cells, the discretisation equations are primarily to solve around

each cell which means to compute for 19,494 number of cells for current 2D simulations. If


the similar is extended to 3D would potentially increase CPU effort and time which needs to

solve nearly 100,000 number of cells. For this reason, the thesis work is limited to follow up

simulations in two dimensional for numerical investigation.

2.4.3 Geometry alignment

Of given specific problem as shown in Figure 2, three flow directions are varied if structure

i.e. here domain is fixed, or three domains are created rotating structure if flow direction is

fixed. In other words, the angle of attack in three flow directions with fixed mesh is obtained.

Former is found unsuitable since the domain is not meant for all purpose to specify boundary

conditions. Later option is chosen, creating four different domains keeping flow direction

fixed as shown in Figure 6 below.

Unique Right aligned, α =180

Bottom aligned, α = 90 Left aligned, α = 0

Figure 6 Alignment of offshore monopile wind turbine in a fixed horizontal flow direction. large cylinder (monopile), small cylinders (boatlanding facility)

2.5 Numerical methodology ‘Ansys Fluent v.6.3’ is a state-of-art computer program for modeling fluid flow and heat

transfer in complex geometries which enables to analyze complex flows. It applies computer

simulation methods to analyze and solve practical design problems based on fundamental


principles of computational fluid dynamics such as the conservation of mass, momentum and

energy. The 3D model solves full Navier Stokes equations in actual scale. A general CFD

template can be seen in Figure 8. The basic procedural steps of Fluent simulations will be

according to Figure 7.

The physical models, fluid/material properties, and boundary conditions that describe the

problem to be modeled are added to the grid information and stored in Case-File that is a

record of all the inputs for problem definition. The results of the calculations were stored in

Data file.

Fluent is a two part program consist of a pre-processor called Gambit, and a main module -

Fluent. Gambit is used to define the geometry and a structured grid of the problem to be

modeled. The grid information was then imported from Gambit to Fluent. Gambit’s mesh

options include both structured and unstructured meshes in two and three dimensions, as well

as tools for checking mesh quality. Gambit was used in the current study to construct the

computational domain for the three circular cylinder problem.

START

STEP 3: Import the Grid

STEP 1: Create the model Geometry and Grid

STEP 5: Select the Solver

STEP 6: Choose the basic equations to be solved

STEP 4: Check the Grid

STEP 7: Specify material properties

STEP 9: Adjust the solution control parameters

STEP 10: Initialize the flow filed

STEP 8: Specify boundary conditions

STEP 11: Calculate a solution

STEP 12: Examine and save the results

STEP 13: Consider revisions to the numerical model

parameters

STOP

Figure 7 Procedural steps of FLUENT simulation


Pre-

proc

essi

ng

Mes

h

Phy

sics

Sol

ver

Rep

ort

Def

ine

Geo

met

ry

Post

-pr

oces

sing

Auto

mat

ic

Stru

ctur

ed

Uns

truct

ured

Mod

elG

eom

etry

Hea

t tra

nsfe

r?

Com

pres

sibl

e?

Flow

pro

perti

es

Visc

ous

mod

els

Boun

dary

co

nditi

ons

Initi

al c

ondi

tions

(p

ress

ure,

ve

loci

ties,

tu

rbul

ant

quan

titie

s)

Lam

inar

Man

ual

Coa

rse

Med

ium

Fine

Use

r def

ined

S

paci

ng

Inte

rval

s

Firs

t len

gth

Turb

ulan

t

Invi

scid

Inle

t

Out

let

Wal

l

Sym

met

ry

etc.

Den

sity

, vis

cosi

ty, s

peci

fic

heat

, the

rmal

con

duct

ivity

Dom

ain

para

met

ers

One

Eq.

Two

Eq.

K-e

, k-w

LES

Stea

dy/

Uns

tead

y

Itera

tions

/ Tim

e st

eps

Tim

e st

ep s

ize

Con

verg

ence

lim

it

Num

eric

al

sche

mes

1st o

rder

up

win

d

2nd o

rder

up

win

d

Qui

ck

Lift/

Dra

g C

oeff.

Fric

tion

fact

or

Pres

sure

dro

p

XY p

lot

Verif

icat

ion/

V

alid

atio

n

Res

idua

ls

Cen

terli

ne v

eloc

ity

dist

ribut

ion

Cen

terli

ne p

ress

ure

dist

ribut

ion

Cen

terli

ne te

mpe

ratu

re

Prof

iles

of a

xial

vel

ocity

She

ar s

tress

Pre

ssur

e co

effic

ient

Ski

n fri

ctio

n

Turb

ulan

t kin

etic

ene

rgy

Wal

l tem

pera

ture

di

strib

utio

ns

Con

tour

s

Vec

tors

Stre

amlin

es

Anim

atio

ns

Mai

n M

odul

e

Fig

ure

8 G

ener

al C

FD T

empl

ate.


Fluent solves the hydrodynamic equations (for u, v, w, p) as a single system. This solution

approach uses a fully implicit discretisation of the equations at any given time step. For

steady state problems, the time-step behaves like an ‘acceleration parameter’ to reach the

converged solution, thus reducing the number of iterations. The user interface updates based

upon whether the steady or unsteady solver selected. The time step size, the number of

iterations per time step and the total number of time steps is to be specified if the unsteady

solver is used. The total number of iterations and the convergence limit shall be specified if

the steady solver is used. Proper flow physics shall be defined with appropriate solver

settings. Fluent has in built plotting tool for generating wide variety of reports. Several plots

like contour and vector plots together with animations can be created to describe the

consistency of the final solution.

Domain 1 2 3 4

Angle of attack Unique Right aligned Bottom aligned Left aligned

Four cases will be simulated in two dimensions. Prior to the analysis of aligned cylinders, a

mesh independent study will be carried at Re 150 based on cylinder diameter. The segregated

implicit solver approach is chosen with the SIMPLE method by Patankar (1981) [19] to

achieve pressure-velocity coupling. The discretisation of the transport equation is under

assumption that flow field is known and need to satisfy the fundamental properties, which are

conservativeness, boundedness and transportiveness [18, 20]. The first order upwind

differencing scheme is used to obtain the face fluxes for all cells. This scheme widely

satisfies all the fundamental properties to find for neighboring coefficients in the discretised

flow field. The second order pressure discretization is chosen for good resolution during

capturing of pressure field near cylinder. Based on assessment findings as reported by Fluent

India Pvt. Ltd [21] and Prof. Tron Solberg, Aalborg University, the two equation SKE

turbulence model with enhanced wall treatment is chosen to resolve the near wall viscous

layer for Reynolds number greater than and equal to 5000. To ensure this, the computational

flow field shall reach a stable condition before subjecting it to unsteady analysis. The

simulation is initially processed in steady state condition and then switched over to transient

computation. The more details of computation can be seen in Table 2 next page.

Table 2 Summary of CFD problem setup.


2.6 Boundary conditions Fluent offers a variety of boundary condition options such as velocity inlet, pressure outlet,

walls etc. The boundary conditions enter the discretised equations via source terms. It is very

important to specify the proper boundary conditions in order to have a well-defined problem.

A single wrong boundary condition shall give a totally wrong result which is observed during

performing simulations. For example, proper care is to be given in specifying reference

values and boundary conditions for finding drag forces.

The top and bottom boundaries are treated as solid walls with free slip condition i.e. zero

shear, which means the velocity near wall is equal to the free stream velocity of fluid near

wall. All solid cylinders are treated as smooth surfaced with no slip condition i.e. zero

velocity at wall. The boundary conditions and fluid properties are specified according to

Figure 9 and Table 2.

Figure 9 Boundary conditions for CFD simulations.

Simulation of free surface flows usually requires defining boundary and initial conditions to

set up appropriate pressure and volume fraction fields. The VOF (volume of fluid) model

described by Hirt and Nicholas (1981) is used to solve such free surface problems. For

pressure-specified outlet boundary, the pressure above the free surface is constant and the

pressure below the free surface is a hydrostatic distribution. Near the fluid-fluid interface

region, the cells require special treatment to find for volume fractions. At this region single

coupled momentum equation is used to solve for volume fractions and pressure correction is

made according to local height function technique. An experiment is made as a part of

feasibility studies using VOF model for generating waves in two dimensional domain, half

filled with water (red) and half with atmospheric air (blue) as shown in Figure 10.

u = U v = 0

u = v = 0u = free v = free

u = U, v = 0

u = U, v = 0


Figure 10 Feasibility study for generating waves. Mesh (Left), Free surface wave (right).

The domain consists of ten wave lengths with specified amplitude. A linear wave theory

written in C language by Prof. Tron Solberg, Aalborg University is used to hook up the user

defined functions in Fluent. Unsatisfactory results were obtained to distinguish formation of

waves. Due to lack of time, this problem of simulation was stopped to avoid complications.

No. I Prepare Update Rev. PagesII AAUE 16.10.2007 3 2III RAVI SHANKAR

Row Col. 1 2 3 4 5 6 7 8 912 Virtual Model 1:13 Steady4 Main cylinder 1 Cyl. Run1 Run2 Run3 Run4 Run5 Run6 Run7 - -5 Right aligned 3 Cyl. Run8 Run9 Run10 Run11 Run12 Run13 Run14 - -6 Bottom aligned 3 Cyl. Run15 Run16 Run17 Run18 Run19 Run20 Run21 - -7 Left aligned 3 Cyl. Run22 Run23 Run24 Run25 Run26 Run27 Run28 - -8 Unsteady9 Main cylinder 1 Cyl. - - Run57 Run58 - - - - -

10 Right aligned 3 Cyl. - - - - - - - - -11 Bottom aligned 3 Cyl. - - - - - - - - -12 Left aligned 3 Cyl. - - - - - - - - -13 Animations MPEG - - Run 59 Run60 - - - - -14 Upscale model 1:5015 Steady16 Main cylinder 1 Cyl. - - Run29 Run30 Run31 Run32 Run33 Run34 Run3517 Right aligned 3 Cyl. - - Run36 Run37 Run38 Run39 Run40 Run41 Run4218 Bottom aligned 3 Cyl. - - Run43 Run44 Run45 Run46 Run47 Run48 Run4919 Left aligned 3 Cyl. - - Run50 Run51 Run52 Run53 Run54 Run55 Run5620 Unsteady21 Main cylinder 1 Cyl. - - - - - - - -22 Right aligned 3 Cyl. - - Run61 - - - - - -23 Bottom aligned 3 Cyl. - - Run62 - - - - - -24 Left aligned 3 Cyl. - - Run63 - - - - - -25 Animations MPEG - - - - - - - Run64 Run652627 Fluid Water Water Water Water Water Water Water Water Water28 Density Kg/m3 998.2 998.2 998.2 998.2 998.2 998.2 998.2 998.2 998.229 Viscosity Kg/ms 0.001003 0.001003 0.001003 0.001003 0.001003 0.001003 0.001003 0.001003 0.001003303132 Only for Virtual model33 Diameter m 0.1 0.1 0.1 0.1 0.1 0.1 0.1 - -34 Velocity inlet, X m/s 0.000200962 0.000401923 0.001507213 0.005024043 0.010048087 0.050240433 1.004808656 - -35 Velocity inlet, Y m/s 0 0 0 0 0 0 0 - -36 Reynolds number Re.no. 20 40 150 500 1000 5000 1.00E+06 - -37 Only for Upscale model38 Diameter m - - 5 5 5 5 5 5 539 Velocity inlet, X m/s - - 3.01443E-05 0.000100481 0.000200962 0.001004809 0.200961731 5 1040 Velocity inlet, Y m/s - - 0 0 0 0 0 0 041 Reynolds number Re.no. - - 150 500 1000 5000 1.00E+06 24880358.92 49760717.8542 For all43 Interior Fluid Water Water Water Water Water Water Water Water Water44 Pressure outlet Pa 0 0 0 0 0 0 0 0 045 Outer walls Pa No slip No slip Zero shear Zero shear Zero shear Zero shear Zero shear Zero shear Zero shear46 Main cylinder m/s No slip No slip No slip No slip No slip No slip No slip No slip No slip47 Small cylinders m/s No slip No slip No slip No slip No slip No slip No slip No slip No slip48 Roughness m - - - - - - - - -495051 Fluent defaults Null 0 0 0 0 0 0 0 - -525354 Model SKE SKE SKE SKE55 Coefficients Cmu Laminar Laminar Laminar Laminar Laminar 0.09 0.09 0.09 0.0956 C1e Laminar Laminar Laminar Laminar Laminar 1.44 1.44 1.44 1.4457 C2e Laminar Laminar Laminar Laminar Laminar 1.92 1.92 1.92 1.9258 TKE Laminar Laminar Laminar Laminar Laminar 1 1 1 159 TDR Laminar Laminar Laminar Laminar Laminar 1.3 1.3 1.3 1.3606162 Area, virtual (upscale) m2 0.1 (5) 0.1 (5) 0.1 (5) 0.1 (5) 0.1 (5) 0.1 (5) 0.1 (5) 0.1 (5) 0.1 (5)63 Density Kg/m3 998.2 998.2 998.2 998.2 998.2 998.2 998.2 998.2 998.264 Depth m 1 1 1 1 1 1 1 1 165 Length, virtual (upscale) m 0.1 (5) 0.1 (5) 0.1 (5) 0.1 (5) 0.1 (5) 0.1 (5) 0.1 (5) 0.1 (5) 0.1 (5)66 Pressure Pa 0 0 0 0 0 0 0 0 067 Velocity m/s68 Viscosity Kg/ms 0.001003 0.001003 0.001003 0.001003 0.001003 0.001003 0.001003 0.001003 0.001003697071 XY72 Static pressure Y Y Y Y Y Y Y Y Y73 X-wallshear stress Y Y Y Y Y Y Y Y Y74 Coeff of drag Y Y Y Y Y Y Y Y Y75 Coeff of lift Y Y Y Y Y Y Y Y Y76 Convergence Y Y Y Y Y Y Y Y Y77 Surface N N N Y N N N N N78 Contour Y Y Y Y Y Y Y Y Y79 Vel magnitude Y Y Y Y Y Y Y Y Y80 Static pressure Y Y Y Y Y Y Y Y Y81 Vector velocity Y Y Y Y Y Y Y Y Y8283 Graphs84 Cd - Re85 Cl - Re - - - - - - - - -868788 The Case and Data simulation files can be accessed in Ansys Fluent v6.3, available in CDROM.89 All mentioned plots and animations are available in CDROM to visualize.

Simulations

Table.2 Summary of CFD Problem SetupComputational investigation of forces around an offshore monopile foundation.

Aalborg University Esbjerg.

AAUE AAUEVerify Approve

Rambøll DenmarkClient

Boundary conditions

HENRIK CARSTENS

::: Combined Plot of Drag Convergence :::

TRON SOLBERGANDERS

(See Boundary conditions for corresponding Re.no.and Velocity)

(See Boundary conditions for corresponding Re.no.and Velocity)

(Same as in Boundary conditions above, Virtual and Upscale models)

Plots

Material properties

NOTES:

Reference values for forces

Viscous model

Initial conditions

Computational investigation of forces around an offshore monopile foundation. 22.1


3. Computational results

3.1 Grid independency A grid independent analysis is conducted using three meshes with varying geometrical

dimensions build of quadrilateral and tri paved cells. Each mesh is processed using SKE

viscous model at a free stream velocity corresponding to Re 1E06.

Table 3 Grid independent analysis, drag and lift coefficients.

Cell type Cells Lift coefficient Drag coefficient

Experimental 0.28 0.45

Unstructured No. Computed Error (%) Computed Error (%)

Geometry 0 Quadrilateral 1971 0.01 -96.4 1.56 246.6

Geometry 1 Quadrilateral 3800 0.12 -57.1 1.22 171.1

Geometry 2 Tri, paved 19494 0.30 7.1 0.52 15.5 Geometry 0 and 1 shows an out bounded error in computing drag and lift coefficients during

simulation. The lift coefficients obtained has high negative error where as drag coefficients

with high positive error. The observation and causes of this error reveals improper boundary

layer near solid walls. Hence further improvements are made followed by Geometry 2. The

error in obtaining the force values are with in acceptable range showing 7.1% for lift and

15.5% for drag coefficients. This is presumably accepted when compared to many previous

researches in numerical simulation [22].

3.2 Validation The formation of two wakes at Re 20 in a steady current flow can be seen in Figure 11. For

Re>40, the boundary layer over the cylinder surface will separate due to adverse pressure

gradient imposed by the divergent geometry of the flow environment at the rear side of the

cylinder. As a result, a shear layer is formed downstream of the separation point and causes

the layer to roll up into a vortex.

Figure 11 Contour of Stream function at Re 20, D = 0.1m, laminar.


The validation parameters for this study are:

1. Center-line velocity profile,

2. Visualization,

3. Strouhal number (St) and

4. Reynolds number (Re),

The Reynolds number is defined as the ratio of viscous force to the inertial force. The

Strouhal number is defined as the relationship between the dominant frequency of vortex

stretching sf , the free stream velocity U and the cylinder diameter D.

Re UDρμ

= , sf DStU

=

3.2.1 Center-line Velocity profile

If a horizontal line is drawn in the domain crossing center of the large cylinder sitting at

centre (0,0), the x-velocity profile along this line - upstream, at cylinder and downstream is

shown below for validation of flow behavior.

Figure 12 Center-line Velocity profile in x-direction for a computational domain.

The x-direction velocity profile is computed at Re 150 with steady current velocity 0.0015

m/s as shown in Figure 12. The upstream velocity gradually drops to zero as the flow

approaching near cylinder. The velocity around the cylinder of diameter 0.1m is zero. The

further drop near cylinder is due to adverse negative pressure effect. Due this effect, the flow

is reversed behind showing velocity in the negative region. Later as flow approaches in

downstream, the velocity raises again.

Stagnation point

Stagnation point


3.2.2 Visualization

The Strouhal number experiences four major changes with respect to Reynolds number, at

subcritical range, critical range, super critical range and Upper transition region. The vortex

shedding first appears at Re 40 and corresponding St is 0.1. St then gradually increases as Re

is increased and attains a value of 0.2 at Re 300 at the lower end of the subcritical flow

regime and is constant through this region. The St frequency experiences sudden jump at Re

3.5 x 10E5 in the critical Re range where St increases 0.2 to 0.45. This is maintained through

and again shifts at Re 1.5 x 10E6 at super critical region, where the boundary layer at one side

of the cylinder is fully turbulent and other end partly laminar and turbulent, which creates the

asymmetric Lee wake vortices. The regular vortex shedding is established when Re is

increased higher than 4.5 x 10E6 where St number takes value of 0.25 - 0.3.

Figure 13 Visualization plot of velocity magnitude at Re = 150, Flow time = 4000 seconds,

laminar, Positive photo (left), Negative photo (right), ANSYS FlowLab Inc.,[17]

Figure 13 and Figure 14 represents velocity contours at a Reynolds number of 150, showing

a time dependent solution. Here a unique domain (consist of only single cylinder) is used for

simulations and validation purposes initially; and specific problem using right, bottom and

left aligned domains (three cylinder problem) are used in the later stage.

Figure 14 Visualization plot of velocity magnitude at Re = 150, Flow time = 4000 seconds,

laminar, Positive photo (left), Negative photo (right), ANSYS Fluent v.6.3, computed simulation.


The visualization gives good agreement between computed Ansys Fluent simulations and plot

provided by Ansys Flowlab. The flow of vortices behind cylinder resembles similar behavior

showing symmetry. Further, validation is proceeded to check for Strouhal number.

3.2.3 Vortex shedding

The lift and drag convergence is computed for unsteady state condition as shown in Figure

15. The current simulation results from Ansys Fluent v6.3 are compared against Ansys

Flowlab v1.3 simulations provided by Fluent Inc. with similar conditions.

Figure 15 Validation plots showing coefficient of drag and lift for unsteady state.

Strouhal number verification has been performed for a Reynolds number of 150 with a

cylinder diameter 0.1 m and an inlet velocity of 0.0015 m/s as shown in Table 4. For a

Reynolds number of 150, the experimentally determined value of the Strouhal number is

approximately 0.172 [3]. The time period of the flow oscillation provided by FlowLab and

predicted by Fluent are 385 and 390 seconds respectively, which is evaluated by plotting the

lift history over the cylinder.

The numerically predicted values of Strouhal number are 0.173 and 0.170, which differs by

0.64% and (-) 0.63% respectively from the experimentally determined value. Here a negative

error is observed due to drop down of lift force during simulations as compared to the

Flowlab simulations.

Table 4 Vortex shedding validation using Strouhal number. Simulation Time Strouhal number

Seconds Computed Error, %

Experimental - 0.172 -

Ansys Fluent 390 0.170 - 0.63

Ansys Flow Lab. 385 0.173 0.64


The forces obtained by numerical simulation around cylinder are mainly influenced by the

boundary layer creation during grid formation. In Fluent simulations, a boundary condition

with enhanced wall treatment is applied near cylindrical wall to minimize the disturbances

near molecular region as explained before. Flowlab simulation is performed on an extremely

engineered grid consist of 30,000 quadrilateral cells and generating periodic log walls either

side, top and bottom symmetrical, with mesh densely at central longitudinal axis and at outer

walls. Further the results obtained in Table 4 are showing acceptable range +/-0.63% error

with a good agreement in obtaining force values near wall cylinder region and proceeded to

check for Reynolds number validation. One may visit Flowlab homepage [17] for open

source to compare current simulations run by Ansys Fluent v6.3. For information, both

commercial software’s uses Fluent solver in common.

3.2.4 Drag coefficients

The steady state drag forces are evaluated using a unique model for a single cylinder of

diameter 0.1m. The computed drag values clubbed together with experimental values are

plotted against Reynolds number for evaluation. The viscous models defined at

corresponding Reynolds number are as shown below.

Re < 1000 Laminar flow 1000 <Re <5000 Laminar flow

Re >= 5000 SKE model

Figure 16 Validation plot showing coefficient of drag against Reynolds number, D = 0.1m., laminar, Virtual, Unique domain.


The Figure 16 shows very good agreement in laminar and transition regions and over

estimates in turbulent regions with a significant error as shown in Table 5. The error still

prolongs to nearly 25-30% higher when compared to the experimental values which is

considered as a limitation in this thesis. A fully engineered grid with highly dense mesh near

walls and proper boundary conditions may minimize this error as explained above.

Table 5 Validation of Cd Vs Re for Virtual unique model, D = 0.1m. Solver

Velocity

Reynolds Number

Computed Drag Coefficient

Experimental Results [3]

% Error

Laminar 1.0E-05 1 10 9.89 1.1 Laminar 2.0E-04 20 2.52 2.55 -1.2 Laminar 4.0E-04 40 1.82 1.8 1.1 Laminar 1.5E-03 150 1.4 1.5 -6.7 Laminar 5.0E-03 500 0.98 1.05 -6.7 Laminar 1.0E-02 1000 0.854 0.9 -5.1

Laminar, SKE 5.0E-02 5000 0.8 0.94 -14.9 SKE 3.0E+00 3.0E+05 0.5 0.4 25.0 SKE 1.0E+01 1.0E+06 0.58 0.45 28.9

3.3 Results Several contours and vector plots of static pressure, velocity magnitudes etc. are available in

Fluent. All sort of plots can be animated if the time dependent solver is used to converge a

solution. One may not confuse here with terminology of plotting. The Table 6 below explains

how plotting is made with combinations of alignment, scale and selector. Virtual domain

which is not real, corresponds to scale 1:1 and Up scaled domain which is considered real and

actual, corresponds to scale 1:50.

Table 6 Combinations of plotting in ‘Ansys Fluent’.

Practically both cases scales may have to show the similar flow behavior since large to small

diameter D/d ratio is constant. However, here the motivation is to predict the correct results


and understand that the simulations are running properly. Secondly, it is easier to upscale the

virtual domains to any scale for desired diameter of the cylinder keeping D/d ratio constant.

For this reason both cases are considered and plotted for evaluation, which means simulating

twice for flow behavior. The virtual and upscale plots shall be clubbed for any deviations,

and discussion continues below only for upscale models, i.e. large cylinder of diameter 5m.

3.3.1 Lift and drag convergence (Plot 9 to Plot 16)

The drag and lift forces in a steady current flow for left, bottom and right aligned boat

landing facility are evaluated. Respective common drag and lift convergence history is

plotted for analyzing. The steady drag convergence history explains the non dimensional drag

force variations with varying inlet velocities. The steady drag and lift convergence for

laminar region can be seen in Plot 9 and Plot 10 and for turbulent region from Plot 11 to Plot

16. Although it is steady state solution irrespective to time, the laminar region can be

assumed to be similar to the unsteady state condition since flow in laminar region is treated as

steady in the form of layers with no disturbances.

The lift convergence history explains the formation of wake and vortices with non linear

waving action from zero level in laminar region. Plot 16, for a right aligned boat landing

facility, the lift is even for turbulent region. This is obvious when two small cylinders are

placed to the left or bottom of the large cylinder, which may disturb the flow behavior greatly

in a typical fashion.

The plots showing steady state drag convergence history has least importance to study other

than to understand simulations run good converged leaving residual error of 1E06 with out

any divergence.

3.3.2 Drag coefficients (Plot 17 to Plot 21)

The non dimensionless drag coefficients for all cylinders are computed and plotted against

Reynolds number for validation and evaluation. The corresponding drag coefficients

computed are shown in Table 7. Plot 17 and Plot 18 are validation plots for all large or main

cylinders in virtual (D=0.1m) and upscale (D=5m). The drag coefficients vary in small

magnitudes due the additional small cylinders in the flow field. Plot 19, Plot 20 and Plot 21

shows the families of drag coefficients for flow past vertical monopile foundation including

boat landing facility for left, bottom and right aligned respectively. These plots show very

good approximations for assessing the drag coefficients. The drag coefficients in Plot 19,


Plot 20 and Plot 21 shows a large error at Re 105 region when compared to experimental

data. Although the behavior of virtual and upscale domains is similar, the combined plots are

made finding for any deviations which means simulating twice for every angle of attack.

When looking at small cylinder curves lying bottom of the main cylinder curves, Plot 19

shows very good clubbing of both cylinder 1 and cylinder 2 one over another. In other words,

the flow behavior is similar for both small cylinders one and two. The influence of drag

coefficients for large cylinder is not much affected by small cylinders in this case. However

in section 3.2.4 above, the validation shows 25% error in computing drag values for turbulent

region has to be considered for all cases. Similarly when compared to Plot 19, in Plot 20 for

bottom aligned, there is a shift in the flow behavior, the drag values varies in small amounts

for cylinder 1 and cylinder 2. The drag coefficients of small cylinder 1 raises to three times

the small cylinder 2 with an angle of attack of 90 degrees are observed. In Plot 21, the curves

for both small cylinders are found disappeared which is of interest here. In this case, both

small cylinders are sitting behind the cylinder in the wake region with an angle of attack of

180 degrees. The drag forces obtained are negative due to reversed flow regime at this region.

The influence of drag coefficients for large cylinder is not much affected by small cylinders

in this case. The results shows very good agreement for boat landing when aligned right or

with an angle of attack of 180 degrees.

3.3.3 Static pressure and velocity contours (Plot 22 to Plot 33)

The corresponding flow behavior showing velocity magnitude and static pressure can be seen

from Plot 22 to Plot 33 for steady current higher velocities of 5 m/s and 10 m/s.

During simulations, it is observed that drag forces obtained are mainly due to the influence of

pressure forces with negligible viscous effects. The static pressures and velocity magnitudes

in the computational domain consist of three cylinders with different angle of attack, with

varying Reynolds number are evaluated. From obtained plots one can identify and conclude

that the boat landing facility (or two small cylinders) sitting in low pressure region shall be

least affected by the hydrodynamic forces with a steady current velocity. It is obvious to say

that boat landing facility when aligned right shall induce least forces as a rule of thumb.

However the overall idea shall be also to study the behavior of flow around three cylinders

with different angle of attack.

Secondly, the separation points are evaluated finding for x-direction wall shear stress around

three cylinders for all flow directions for both virtual and upscale domains with varying

Reynolds number.


Table 7 History of non-dimensional drag force values computed for both Virtual and Upscale models. (For all: Reynolds number corresponds to large cylinder)

VIRTUAL SCALE

Run Reynolds Number

Computed Drag Coefficient (Not aligned, Unique) Run

Reynolds Number

Computed Drag Coefficient (Right aligned)

Cylinder

main Cylinder1 Cylinder2 Cylinder

main Cylinder1 Cylinder2 1 20 2.52 - - 8 20 2.39 -0.0118 -0.01192 40 1.82 - - 9 40 1.69 -0.0114 -0.01153 150 1.4 - - 10 150 1.075 -0.0075 -0.00744 500 0.98 - - 11 500 0.867 -0.0038 -0.00375 1000 0.854 - - 12 1000 0.814 -0.0032 -0.00316 5000 0.8 - - 13 5000 0.798 -0.0028 -0.00487 1.00E+06 0.52 - - 14 1.00E+06 0.992 -0.0055 -0.0067

Run Reynolds Number

Computed Drag Coefficient (Bottom aligned) Run

Reynolds Number

Computed Drag Coefficient (Left aligned)

Cylinder


main Cylinder1 Cylinder2

15 20 2.094 0.365 0.127 22 20 1.767 0.215 0.21616 40 1.686 0.275 0.0861 23 40 1.355 0.157 0.15717 150 1.223 0.21 0.095 24 150 0.9 0.095 0.09618 500 0.965 0.181 0.101 25 500 0.798 0.066 0.067419 1000 0.884 0.165 0.097 26 1000 0.7646 0.0566 0.057720 5000 0.789 0.147 0.089 27 5000 0.721 0.0455 0.04621 1.00E+06 1.03 0.19 0.084 28 1.00E+06 0.743 0.0727 0.0744

UP SCALE

Run Reynolds Number

Computed Drag Coefficient (Not aligned, Unique) Run

Reynolds Number

Computed Drag Coefficient (Right aligned)

Cylinder



29 150 1.23 - - 36 150 1.075 -0.00745 -0.0074230 500 0.985 - - 37 500 0.865 -0.00411 -0.0037331 1000 0.867 - - 38 1000 0.816 -0.00296 -0.0031332 5000 0.802 - - 39 5000 0.797 -0.00286 -0.0048633 1.00E+06 0.724 - - 40 1.00E+06 0.716 -0.00298 -0.0062734 2.49E+07 0.612 - - 41 2.49E+07 0.538 -0.00512 -0.005635 4.98E+07 0.735 - - 42 4.98E+07 0.556 -0.00408 -0.00324

Run Reynolds Number

Computed Drag Coefficient (Bottom aligned) Run

Reynolds Number

Computed Drag Coefficient (Left aligned)

Cylinder



43 150 1.22 0.21 0.0988 50 150 0.893 0.0942 0.095444 500 0.957 0.182 0.0961 51 500 0.798 0.066 0.06745 1000 0.879 0.167 0.0977 52 1000 0.774 0.056 0.05746 5000 0.805 0.146 0.0884 53 5000 0.723 0.0451 0.046347 1.00E+06 0.697 0.145 0.0638 54 1.00E+06 0.457 0.0424 0.043148 2.49E+07 0.699 0.151 0.0683 55 2.49E+07 0.452 0.0461 0.04749 4.98E+07 0.67 0.143 0.0626 56 4.98E+07 0.436 0.0445 0.0452


Left aligned: Plot 22, Plot 25 and Plot 28, Plot 31 corresponds to velocity magnitude and

static pressure with velocities 5m/s and 10m/s respectively. A conical wake is observed

behind the cylinder with an angle of attack of 0 degrees. The change in the hydrodynamic

field is due the influence of small cylinders to the left of the large cylinder. Low velocities

and high pressures are observed near the stagnation region which may reduce the life of boat

landing facility exposed to repetitive wave loadings.

Bottom aligned: Plot 23, Plot 26 and Plot 29, Plot 32 corresponds to velocity magnitude and

static pressure with velocities 5m/s and 10m/s respectively. A wake of type bull horn shape,

with shift in the wake position extending from small cylinder 2 is observed. This type of

pattern shows a very typical change in the hydrodynamic behavior as compared to the flow

over single cylinder. A zero velocity with high pressure is observed near stagnation region

showing higher drag forces induced in case of cylinder1.

Right aligned: Plot 24, Plot 27 and Plot 30, Plot 33 corresponds to velocity magnitude and

static pressure with velocities 5m/s and 10m/s respectively. A wake with vortex stretching

pattern is observed even at higher steady current velocities. The formation of vortices is due

to the flow disturbances due to the influence of two small cylinders in the wake region. A

zero velocity with high pressure is observed near stagnation region and negatively induced

drag forces for both small cylinders.

From above it can be said that, with an angle of attack of 180 degrees, the boat landing

facility is protected in the low pressure region with low velocities. Larger negative forces are

also a problem due to vortex formation giving vibrations sometimes. At such higher

velocities sometimes at very low pressure region, there is possibility of formation of vortices

and it is unsafe for a boat to land at this region which may suck into the sea floor. Other way

is to avoid reaching offshore locations during harsh weather conditions.

3.3.4 Static pressure around cylinder (Plot 34 to Plot 48)

For description of static pressures around cylinder, let us consider the curves in every plot

consist of a head and two legs. The tip of the head always lies at 180 degree location which is

a stagnation point and above zero pressure and the two legs walks above and below zero

static pressure line. Plot 34 to Plot 38, Plot 39 to Plot 43 and Plot 44 to Plot 48 are a set of


families for bottom, left and right aligned boat landing facility for lower and higher Reynolds

number describing static pressures.

Plot 34, Plot 39 and Plot 44 shows that the laminar region has influence of very low or near

zero pressures where as at Re 1E06 the static pressures varies as +/- 0.6 to 0.8 bar around the

cylinder of diameter 0.1 m. Here the tip of the curve head cuts at 180 degrees for all three

flow directions showing curve length of value 0.157 m, where as both legs standing at

negative pressure region. In Plot 39, the static pressure varies at stagnation region as a

peculiar conical shape with the tip of the head i.e. stagnation point at 180 degrees lying at

0.62 bar. This peculiar pressure profile is due to the influence of neighbour two identical

small cylinders in a symmetrical pattern. (Plot 36, Plot 41 and Plot 46 show similar

hydrodynamic behavior for upscale domains of large cylinder diameter 5 m at higher steady

current velocities of 5 and 10 m/s.)

Plot 35, Plot 40 and Plot 45 shows the static pressures around small cylinders for lower and

higher Reynolds number with varying velocities for a diameter of 7.112mm, for bottom, left

and right aligned respectively. All results of static pressures around small cylinders varying

from Re 20 to Re 1E06 are clubbed for analysis. Of them, only two curves pertaining to Re

1E06 are shown up. In Plot 35, the two curves lie in a manner hug each other, half lying in

positive pressure and half in negative pressure region with its extremities +/- 1 bar. In Plot

40, the two curves or cylinders completely lie in positive pressure region with maximum of

+0.9 bar. Where as in Plot 45, the two curves or cylinders lie completely in negative pressure

region with minimum -0.2 bar. (Plot 37, Plot 42 and Plot 47 show similar hydrodynamic

behavior for upscale domains of small cylinder diameter 355.6 mm at higher steady current

velocities of 5 and 10 m/s.)

Plot 38, Plot 43 and Plot 48 shows the location of static pressures of large and small cylinders

for all three flow directions, i.e. angle of attack 0, 90 and 180 degrees over standard perimeter

length of the cylinder. From this summary plot, one may identify for corresponding static

pressure over cylindrical length and compare virtual and upscale domains. Keeping Reynolds

number constant for virtual domain of diameter 0.1m and upscale domain of diameter 5m

(Change in diameter implies change in inlet velocities for computing Re), the hydrodynamic

behavior may have to exhibit similar characteristics. But from these deviation plots, it is

understood that, choosing constant Re 1E06 for virtual and upscale domain for all three flow


directions, the location of static pressure around cylinders are transformed and not lying in

the same line. This implies that, for constant Reynolds number of a given diameter of the

cylinder, the static pressures are not constant.

3.3.5 Separation points (Plot 49 to Plot 54)

Discussion on this topic is out of scope of the Thesis work. For the purpose during

simulations, one may save time to generate additional plots. Thus few plots which define

shifts in separation points with change in Re are plotted as shown from Plot 49 to Plot 54 in

Appendix-2. It is understood that flow separates from the cylindrical wall where x-direction

wall shear stress equal to zero. Further explanation and discussion of this topic is left to the

reader.

Re 40

Re 150

Re 500

Re 1000

Re 5000

Re 1E06

Unique domain Right aligned Bottom aligned Left alignedFigure 14.1 NOTES


4. Conclusion

The present numerical simulation at lower and higher Reynolds number has revealed may of

the features characterizing the flow around three unidentical cylinders in tandem

arrangements. Flow past an offshore monopile including boat landing facility with three

different angles of attack 0, 90 and 180 degrees was studied using a commercial package

Ansys Fluent v6.3. The diameter ratio of the large cylinder to the small one is 14 with

constant center-to-center spacing. The two dimensional Navier-Stokes equations were solved

by using Finite volume method.

Code validation was undertaken on three different geometries. Geometry3 which consist of

19494 cells with a very fine Tripaved mesh shows a good agreement to proceed for

computing coefficient of drag. A standard KE turbulence model with enhanced wall

treatment and standard industrial constants was used. But still when higher turbulence was

applied, Reynolds number validation fails showing 25% error during computation of drag

forces in molecular viscous region around cylinder. A fully engineered grid with periodic

boundary condition specifying law of the wall and further increase in the mesh density from

19494 to 35000 cells may reduce this error. However to achieve this the computational time

increases potentially for transient simulations with increase in number of cells. Further

Strouhal number validation for vortex shedding gives very good agreement with an error +/-

0.63%, which is acceptable. A centre-line velocity profile shows very good agreement which

confirm flow computations are running correctly.

The hydrodynamic flow filed of upscale models for higher velocities 5 m/s and 10 m/s for all

three different angles of attack were studied. Keeping the limitation of drag force validation

inactive, the results showing several plots gives good agreement for predicting the flow

behavior for three cylinder problem. This was achieved in analogous with the flow over a

single cylinder and finding for anomalies. At higher Reynolds number region, double the

velocity, the length of the wake extending quarter length was observed. The wake formed

was shielded originating from the vicinity of the cylinder. For an angle of attack of 90

degrees, the drag forces computed were higher on one of the two small cylinders. The affect

of drag forces for large cylinder due to small cylinders shows no variations and of no

significant importance. But surprisingly the results reported a change in hydrodynamic field

around wake region showing shift of wake towards small cylinder and a wake of conical

shape. The numerical work has been limited for further investigation of this kind of behavior.


5. Future research work In present study, the flow around circular cylindrical pattern of different diameter is of

interest. For chosen flow direction around a monopile with boat landing facility, for existing

or future offshore wind parks in a pattern (say 50 offshore foundations) as shown in Figure 2

can be studied. This shall presumably to identify the influences and interaction of flow from

one pile to other with varying diameter.

In addition several external flow applications include for offshore oil and gas industry like

flow around platform piles, casing or drill pipes, pipelines, heat exchanger tube bundles etc.

The problem can be extended to 3D for vortex behaviour. Further, a free surface can be

generated in air-water flow field validating to wave tank laboratory experiments conducted

by Aalborg University. The existing numerical simulation for formation of scour around an

offshore wind turbine (conducted by Tron Solberg, Bjørn H. Hjertager and Stefano Bove,

Aalborg University Esbjerg) can be extended by implementing free surface flows for

investigation of wave run up and forces. Few trials have been made to generate surface waves

using FLUENT in 2D grid as a part of feasibility studies during the present Thesis work as an

exercise.

Using existing 2D modeling work, several factors like surface roughness for marine growth,

turbulence models, mesh formulation, scaling, boundary conditions, flow models and solver

settings can be altered for further predictions and complications. In section 1.3 Problem

identification, few assumptions with possible future modifications are highlighted.

One may use existing simulation data included in CDROM, for additional features and

complications as explained above.


Plotting results

Plot 1 Geometry1 (left), Quadrilateral mesh (right).

Plot 2 Geometry2 (left), Tri Paved mesh (right)


Plot 3 Contour of velocity magnitude, Re 150, Flow time 4000 sec. (65 min.), laminar, unsteady.

Plot 4 Contour of static pressure, Re 150, Flow time 4000 sec. (65 min.), laminar, unsteady.

Plot 5 Contour of velocity vector plot, Re 150, Flow time 4000 sec. (65 min.), laminar, unsteady.


Plot 6 Contour of velocity magnitude, Re 500, Flow time 1200 sec. (20 min.), laminar, unsteady.

Plot 7 Contour of static pressure, Re 500, Flow time 1200 sec. (20 min.), laminar, unsteady.

Plot 8 Contour of velocity vector plot, Re 500, Flow time 1200 sec. (20 min.), laminar, unsteady.


Plot 9 Drag convergence history of Virtual domains in the laminar turbulent region.

Plot 10 Lift convergence history of Virtual domains in the laminar turbulent region.


Plot 11 Drag convergence history of Bottom aligned family for Virtual and Upscale domains.

Plot 12 Lift convergence history of Bottom aligned family for Virtual and Upscale domains.


Plot 13 Drag convergence history of Left aligned family for Virtual and Upscale domains.

Plot 14 Lift convergence history of Left aligned family for Virtual and Upscale domains.


Plot 15 Drag convergence history of Right aligned family for Virtual and Upscale domains.

Plot 16 Lift convergence history of Right aligned family for Virtual and Upscale domains.


Plot 17 Validation plot, Experimental Vs Virtual domains at various Re number, D=0.1m.

Plot 18 Validation plot, Experimental Vs Upscale domains at various Re number, D=5m.


Plot 19 Family of Drag coefficients for flow past vertical monopile foundation structure including Left aligned boat landing facility.

Plot 20 Family of Drag coefficients for flow past vertical monopile foundation structure including Bottom aligned boat landing facility.


Plot 21 Family of Drag coefficients for flow past vertical monopile foundation structure including Right aligned boat landing facility.


Plot 22 Contour of velocity magnitude for Left aligned boat landing facility, Upscale model, Re = 2.5E07, V= 5m/s.

Plot 23 Contour of velocity magnitude for Bottom aligned boat landing facility, Upscale model, Re = 2.5E07, V= 5m/s.

Plot 24 Contour of velocity magnitude for Right aligned boat landing facility, Upscale model, Re = 2.5E07, V= 5m/s.


Plot 25 Contour of velocity magnitude for Left aligned boat landing facility, Upscale model, Re =5E07, V= 10m/s.

Plot 26 Contour of velocity magnitude for Bottom aligned boat landing facility, Upscale model, Re = 5E07, V= 10m/s.

Plot 27 Contour of velocity magnitude for Right aligned boat landing facility, Upscale model, Re = 5E07, V= 10m/s.


Plot 28 Contour of static pressure for Left aligned boat landing facility, Upscale model, Re = 2.5E07, V= 5m/s.

Plot 29 Contour of static pressure for Bottom aligned boat landing facility, Upscale model, Re = 2.5E07, V= 5m/s.

Plot 30 Contour of static pressure for Right aligned boat landing facility, Upscale model, Re = 2.5E07, V= 5m/s.


Plot 31 Contour of static pressure for Left aligned boat landing facility, Upscale model, Re = 5E07, V= 10m/s.

Plot 32 Contour of static pressure for Bottom aligned boat landing facility, Upscale model,

Re = 5E07, V= 10m/s.

Plot 33 Contour of static pressure for Right aligned boat landing facility, Upscale model, Re = 5E07, V= 10m/s.


Plot 34 Static pressure around vertical monopile foundation structure for Bottom aligned boat landing facility, Virtual scale, D=0.1m.

Plot 35 Static pressure around Bottom aligned boat landing facility for two small vertical cylinders, Virtual scale, D=7.112mm.

Plot 36 Static pressure around vertical monopile foundation structure for Bottom aligned boat landing facility, Upscale, D=5m.

* Re number corresponds to main cylinder.




Plot 37 Static pressure around Bottom aligned boat landing facility for two small vertical cylinders, Upscale, D=355.6mm.

Plot 38 Summary of static pressure for Bottom aligned monopile foundation structure for Virtual and Upscale domains.

cyl1, cyl2

Upscale cyl1, cyl2

Main cyl.

Upscale, Main cyl




Plot 39 Static pressure around vertical monopile foundation structure for Left aligned boat landing facility, Virtual scale, D=0.1m.

Plot 40 Static pressure around Left aligned boat landing facility for two small vertical cylinders, Virtual scale, D=7.112mm.

Plot 41 Static pressure around vertical monopile foundation structure for Left aligned boat landing facility, Upscale, D=5m.





Plot 42 Static pressure around Left aligned boat landing facility for two small vertical cylinders, Upscale, D=355.6mm.

Plot 43 Summary of static pressure for Left aligned monopile foundation structure for Virtual and Upscale domains.

cyl1, cyl2

Upscale cyl1, cyl2

Main cyl.

Upscale, Main cyl




Plot 44 Static pressure around vertical monopile foundation structure for Right aligned boat landing facility, Virtual scale, D=0.1m.

Plot 45 Static pressure around Right aligned boat landing facility for two small vertical cylinders, Virtual scale, D=7.112mm.

Plot 46 Static pressure around vertical monopile foundation structure for Right aligned boat landing facility, Upscale, D=5m.





Plot 47 Static pressure around Right aligned boat landing facility for two small vertical cylinders, Upscale, D=355.6mm.

Plot 48 Summary of static pressure for Right aligned monopile foundation structure for Virtual and Upscale domains.

cyl1, cyl2

Upscale cyl1, cyl2

Main cyl.

Upscale, Main cyl




References [1] Leen De Vos, Peter Frigård, Julien De Rouck, Wave run-up on cylindrical and cone shaped foundations for offshore wind turbines, Aalborg University and Ghent University, 2006. [2] Peter Muller, Chris Garrett and Al Osborne, Rogue Waves, Oceanography, Volume 18, The Oceanography society, PO Box 1031, Rockville, MD 20849-1931, USA. (For free video source: Visit BBC homepage, search for Rogue waves). [3] B. Mutlu Sumer & Jørgen Fredsøe, Hydrodynamics around cylindrical structures, Advanced series on Ocean engineering – Vol. 12, World scientific publishing, ISBN: 981-02-2898-8, 1997. [4] Ming Zhao, Liang Cheng, Bin Teng and Dongfang Liang, Numerical simulation of viscous flow past two circular cylinders of different diameters, University of Western Australia, 6 Oct 2004. [5] H.K. Virahsawmy, L. Chen, J. Tu, Y. Zhou, I.R. MacGillivray, Computation of flow behind three side-by-side cylinders of unequal/equal spacing, Maritime Platforms Division DSTO Melbourne, RMIT University, Australia. ISSN: 1446-8735, 25 July 2005. [6] Williamson CHK., Evolution of a single wake behind a pair of bluff bodies, Journal of Fluid Mechanics, 1985;159: Pg. 1–18. [7] Kim H J, Durbin PA., Investigation of the flow between a pair of cylinders in the flopping regime, Journal of Fluid Mechanics, 1988;196:431–48. [8] Authors of Offshore Center Denmark, Rambøll and Aalborg University, Offshore wind turbines situated in areas with strong currents, Pg. 1-127, Doc. No. 6004RE01ER1, Feb 2006. The report is accessible via: www.offshorecenter.dk/log/filer/6004RE01ER4.pdf [Last visited: 22-06-2007] [9] James F. Wilson, Dynamics of offshore structures, John Wiley & Sons Inc., ISBN: 0-471-26467-9, 2nd edition, 1993. [10] Chakrabarti, S.K., Hydrodynamics of Offshore Structures, WIT Press, ISBN 0-905451-66-X, 1991. [11] Theresa Kleefsman, A Numerical study on Water impact loading on offshore structures, PhD Thesis, The report is accessible via: http://www.math.rug.nl/~veldman/comflo/comflo.html [Last visited: -11-06-2007] [12] Andreas Roulund, B. Mutlu Sumer, Jørgen Fredsøe and Jess Michelsen, Numerical and experimental investigation of flow and scour around a circular pile, Pg. 351-401, Technical University of Denmark, DTU, Revised 6th Dec 2004.


[13] Tron Solberg, Bjørn H. Hjertager and Stefano Bove, Aalborg University Esbjerg, CFD modeling of Scour around offshore wind turbines in areas with strong currents, Pg. 128-155, Doc. No. 6004RE01ER1, Feb 2006. [14] Henrik Carstens, Rambøll A/s, Denmark, www.ramboll.dk, May 2007. [15] Wilcox D.C., Turbulence Modeling for CFD, DCW Industries, Inc., Second Edition, (2002). [16] Z. Huang, J.A. Olson, R.J. Kerekes, S.I. Green, Numerical simulation of the flow around rows of cylinders, 15 March 2005, University of British Columbia, Canada. [17] Ansys Fluent 6.3, Users Guide, Fluent Inc., (2007) http://www.ansys.com/products/flowlab/exercise/pdfs/cylinder.pdf, [Last visited: -19-10-2007] [18] Versteeg H.K., Malalasekera W., An Introduction to Computational fluid dynamics, The Finite Volume Method, Prentice Hall, (1995). [19] Suhas V. Patankar, Numerical heat transfer and fluid flow, Taylor & Franci, 1st edition, ISBN: 0891165223, 1980. [20] Bjørn H. Hjertager, Computational fluid dynamics and turbulence modeling, Class lecture notes, Aalborg University Esbjerg, 2005. [21] Ansys Fluent 6.3, Users Guide, Fluent India Pvt. Ltd, (2007). [22] Wikipedia, www.wikipedia.org, A web based free content encyclopedia, A free documentation License, Copyrights USA, 2000.


APPENDIX-1

(Drawing of a monopile foundation with boatlanding facility) (Copyrights2007, Rambøll Denmark)

2. REST PLATFORM AND EXTERNAL LADDER OMITTED FOR CLARITY. SEE DRWG. NO. RF-SS-03-0001 AND RF-SS-04-0001 RESPECTIVELY.

0 07.08.17 NKV ISSUED FOR INFORMATIONJPPC HEC

1 07.09.25 CK ISSUED FOR CONSTRUCTIONJPPC HEC

Rev Date Drawn Chkd Appr Description

NOTES6

A

54

RF-SS-02-0001Scale Size

Title

Drawing no. Rev.

Drawing no. Reference dwgs.

1

C

D

1. FOR GENERAL NOTES SEE DRWG. NO. RF-SS-00-0001.

B

C

D

654A1

KEY-PLAN

BOAT LANDING

RAMBØLL

MTH

RHYL FLATS OFFSHORE WIND FARM

NOTED 1

753409Job No.

GENERAL ARRANGEMENT

32Drawing no.

1

A

RF-SS-02-0001

B

32

772FOR INFO ONLY

TYP.

TYP.

200

306 90 521

CHS355.6X14.2TYP.

CHS177.8X12.5TYP.

325

CHS88.9X3.2

CHS355.6X16.0TYP.

CHS355.6X14.2TYP.

275

375

325

1800

NORTH

110

C - C. 1:20

E

E

RF-SS-02-0002

B

B

A

A

A - A. 1:50

DETAIL 3RF-SS-02-0002



D DRF-SS-02-0002

C C

-1.000-1.000-0.400

-0.335

NOTE 2

+13.600+13.400

+11.500

B - B. 1:50

-0.632

+4.000

+10.900


+22.820

+23.000

+19.220

+15.620

+12.220

+9.120

+6.320

+3.570

+1.070

-1.500

-0.100

+2.400

+5.400

+11.400

+8.100

NORTH

CENTERLINEBOAT LANDING

CENTERLINEACCESS PLATFORM

45

65


APPENDIX-2

(Separation points: Plot 49 to Plot 54)


Plot 49 Plot 50

Plot 49 Separation points for Left, Bottom and Right aligned boatlanding facility for two small vertical cylinders, Virtual scale, D=7.112mm, Perimeter=0.22 m, Re = 20, 40, 150.

Plot 50 Separation points for Left, Bottom and Right aligned boatlanding facility for two small vertical cylinders, Virtual scale, D=7.112mm, Perimeter=0.22 m, Re = 500, 1000, 5000.



Plot 51 Plot 52

Plot 51 Separation points for Left, Bottom and Right aligned boatlanding facility for vertical monopile foundation structure, Virtual scale, D=0.1m, Perimeter= 0.314m, Re = 20, 40, 150.

Plot 52 Separation points for Left, Bottom and Right aligned boatlanding facility for vertical monopile foundation structure, Virtual scale, D=0.1m, Perimeter=0.314m, Re = 500, 1000, 5000.



Plot 53 Plot 54

Plot 53 Separation points for Left, Bottom and Right aligned boatlanding facility for two small vertical cylinders, Upscale, D=355.6mm, Perimeter=1.116m, Re = 1E06, 2.5E07, 5E07.

Plot 54 Separation points for Left, Bottom and Right aligned boatlanding facility for vertical monopile foundation structure, Upscale, D=5m, Perimeter=15.7m, Re = 1E06, 2.5E07, 5E07.


ID Task Name Duration

40 10th Semester 138 days?

41 Initiation Phase 136 days?42 Project Objectives and Definition 4 days43 Ansys Fluent V.6.3 Practise 18 days?44 GAMBIT, Post processing, UDF 12 days?45 Excercies, Tutorials 15 days46 Computational Hydrodynamics and Reviews 6 days47 Planning and Preparation Phase 62 days?48 Articles, Literature reviews 13 days?49 Ansys Fluent models 37 days?50 2d, 3d Grid generation in GAMBIT 10 days51 Wave generation trials, 2d 6 days?52 Flow around cylinder, 2d 21 days?53 Summer holiday 24 days54 Execution Phase 43 days?55 Report Writing, Feasibility Studies 43 days?56 Ansys Fluent Simulations 20 days57 Grid modification 2 days58 Flow around monopile, 2d 10 days59 Grid Validation, Re, Kc, St, Cd, Cl 7 days60 Plotting and revision 1 day61 Re/simulations, validation reviews, Troubleshooting 6 days62 Animation and Graphics 2 days63 Ramboll, Decommissioning Conference Meeting 1 day64 Close out Phase 35 days?65 Report and Simulations 25 days?66 Grid modification, Re/simulations 2d, 3d, New 3 cylind 4.5 days67 Post processing, Validation, Finalize 16 days68 References, Figures, Close out 17 days69 Approve 1 day?70 Project Review 6 days?71 Hydrodynamics, CFD, Plots, Results, Validation agree 1 day?72 Conclusion 1 day?73 Finalize 1 day?74 10th Semester Project Submission 1 day?75 10th Semester End-of-Final Thesis 1 day?

Project Objectives and Definition

GAMBIT,Post processing,UDFExcercies,TutorialsComputational Hydrodynamics and Reviews

Article,Literature reviews

2d,3d Grid generation in GAMBITWave generation trials,2d

Flow around cylinder,2dSummer holiday

Report Writing

Grid modificationFlow around monopile,2d

Grid Validation,Re,Kc,St,Cd,ClPlotting and revision

Re/simulations,validation reviews,TroubleshootingAnimation and Graphics

Decommissioning seminar,Ramboll

Grid modification,Re/simulations 2d,New 3 cylinder concePost processing,Validation,Finalize

References,Figures,Close outApprove

Hydrodynamics,CFD,Plots,Results,Validation agConclusionFinalize10th Semester Project Submission

10th Semester End-of-Final Thesis

Mar Apr May Jun Jul Aug Sep Oct Nov Dec Jan Feb Mar Apr2nd Quarter 3rd Quarter 4th Quarter 1st Quarter 2nd Qu

Task

Split

Progress

Milestone

Summary

Project Summary

External Tasks

External Milestone

Deadline

Project Schedule, 2007Ravi Shankar - K10O

Aalborg University Esbjerg

Numerical simulation and feasibility study of Wave run up around offshore cylindrical piles. Page 2

Project: Ravi Thesis Schedule 2007Date: Mon 11/12/07

computational investigation of forces around an …

Documents