Date June 2009
Author Siegersma, H., R. Zoontjes and H. Ottens Address Deift University of Technology
Ship Hydromechanics Laboratory
Mekelweg 2, 2628 CD Delft
TUDeift
DeIft University of Technology
Using CFD to determine heave added mass and
damping of a suction pile
by
H. Siegersma, R. Zoontjes and H. Ottens
Report No. 1623-P
2009Proceedings of the ASME 2009 28th International Confe-rence on Ocean, Offshore and Arctic Engineering, OMAE 2009, May 31June 5, Honolulu, Hawaii, USA, ISBN: 978-0-7918-3844-0, OMAE2009-79373)
WELCOME FROM THE CONFERENCE CHAIRS
file ://E:\data\chair-welcome.htrn 1
8-6-2009
OMAE2009: Welcome from the Conference Chairs
Page 1 of2
R. Cengiz Ertekin H. Ronald Riggs Conference Co-Chair Conference Co-Chair
OMAE 2009 OMAE 2009
Aloha!
On behalf of the OMAE 2009 Organizing Committee, it is a pleasure to welcome you to Honolulu,
Hawaii for OMAE 2009, the 28th International Conference on Ocean, Offshore and Arctic
Engineering. This is the first conference with the new name, which reflects the expanded focus of the
OOAE Division and the conference.
OMAE 2009 is dedicated to the memory of Prof. Subrata Chakrabarti, an internationally known offshore
engineer, who passed away suddenly in January. Subrata was the Offshore Technology Symposium
coordinator, and he was also the Technical Program Chair for OMAE 2009. He was involved in the
development of the OMAE series of conferences from the beginning, and his absence will be sorely felt.
OMAE 2009 has set a new record for the number of submitted papers (725), despite an extremely
challenging economic environment. The conference showcases the exciting and challenging
developments occurring in the industry. Program highlights include a special symposium honoring the
important accomplishments of Professor Chiang C. Mei in the fields of wave mechanics and
hydrodynamics and a joint forum of 'Offshore Technology', 'Structures, Safety and Reliability' and
'Ocean Engineering' Symposia on Shallow Water Waves and Hydrodynamics. We believe the OMAE
2009 program will be one of the best ever. Coupled with our normal Symposia, we will also have
special symposia on:
Ocean Renewable Energy
Offshore Measurement and Data Interpretation
Offshore Geotechnics
Petroleum Technology
We want to acknowledge and thank our distinguished keynote speakers: Robert Ryan, Vice President
-Global Exploration for Chevron; Hawaii Rep. Cynthia Thielen, an environmental attorney who has a
special passion for ocean renewable energy; and John Murray, Director of Technology Development
with FIoaTEC, LLC.
A conference such as this cannot happen without a group of dedicated individuals giving their time and
talents to the conference. In addition to the regular symposia coordinators, the coordinators of the
special symposia deserve many thanks for their efforts to organize new areas for OMAE. We also want
to express our appreciation to Dan Valentine, who stepped into the Technical Program Chair position
OMAE2009: Welcome from the Conference Chairs
Page 2 of 2
on very short notice, following Subrata's passing. We also want to thank Ian Holliday and Carolina
Lopez of Sea to Sky Meeting Management, who have done a great job with the organization. Thanks
also go to Angeline Mendez from ASME for the tremendous job she has done handling the on-line
paper submission and review process.
Honolulu is one of the top destinations in the world. We hope that you and your family will be able to
spend some time pre or post conference enjoying the island of Qahu. Whether you're learning to surf in
legendary Waikiki, hiking through the rich rainforests of Waimea Valley, or watching the brilliant pastels
of dusk fade off of Sunset Beach, you'll find variety at every turn on Oahu.
Mahalo nui ba,
R. Cengiz Ertekin and H. Ronald Riggs, University of Hawaii
OMAE 2009 Conference Co-Chairmen
OMAE2009: Message from the Technical Program Chair
Page 1 of 2
MESSAGE FROM THE TECHNICAL PROGRAM CHAIR
Welcome to the 28th International Conference on Ocean, Offshore and Arctic
Engineering (OMAE 2009). This is the 28th conference in the OMAE series
guided by and influenced significantly by our friend and colleague, Subrata K.
Chakrabarti. It was a shock for me to learn that he had passed away so suddenly:
all involved with this conference express sincere condolence to his family, friends
and colleagues (the sentiments echoed by all of us are eloquently expressed in
the dedication included in this program). It is a great honor for me to have been
asked to continue his work on this conference. I and our community will miss his
leadership and friendship greatly. Although this series of conferences was
formally organized by ASME and the OOAE Division of the International
Petroleum Technology Institute (IPTI), it was Subrata's skill and dedication to this
Daniel T. Valentinedivision of ASME that made this series of conferences the success that it has
Technical Program ChairOMAE 2009
been and is today.
The papers published in this CD were presented at OMAE2009 in thirteen
symposia. They are:
SYMP-1: Offshore Technology
SYMP-2: Structures, Safety and Reliability
SYMP-3: Materials Technology
SYMP-4: Pipeline and Riser Technology
SYMP-5: Ocean Space Utilization
SYMP-6: Ocean Engineering
SYMP-7: Polar and Arctic Sciences and Technology
SYMP-8: CFD and VIV
SYMP-9: C.C. Mel Symposium on Wave Mechanics and Hydrodynamics
SYMP-lO: Ocean Renewable Energy
SYMP-1 1: Offshore Measurement and Data Interpretation
SYMP-12: Offshore Geotechnics
SYMP-13: Petroleum Technology
The first eight symposia are the traditional symposia organized by the eight
technical committees of the OOAE Division. The other symposia are specialty
symposia organized and encouraged by members of the technical committees to
focus on topics of current interest. The 9th symposium was organized to
recognize the contributions of Professor C. C. Mei. Symposia 10, 11, 12 and 13
offer papers in the areas of renewable energy, measurements and data
interpretation, geotechnical and petroleum technologies as they relate to ocean,
offshore and polar operations of industry, government and academia.
The first symposium, Symposium 1: Offshore Technology was always Subrata
Chakrabarti's project. It was typically the largest of the symposia at OMAE. His
exemplary work on this symposium provided the experience and guidance for
others to continue to develop the other symposia. Symposium 1 in conjunction
with the OMAE series of conferences is Subrata's legacy. The Executive
Committee has a most difficult yet honorable task of finding a successor to carry
on this important annual symposium in offshore engineering. We are all grateful
OMAE2009: Message from the Technical Program Chair
Page 2 of 2
for the inspiration and encouragement provided to all of us by Subrata.
Please enjoy the papers and presentations of OMAE2009.
Daniel T. Valentine, Clarkson University, Potsdam, New York
OMAE2009 Technical Program Chair
OMAE2009: International Advisory Committee
Page 1 of 1
INTERNATIONAL ADVISORY COMMITTEE
R.V. Ahilan, Noble Denton, UK
R. Basu, ABS Americas, USA
R. (Bob) F. Beck, University of Michigan, USA
Pierre Besse, Bureau Veritas, France
Richard J. Brown, Consultant, Houston, USA
Gang Chen, Shanghai Jiao Tong University, China
Jen-hwa Chen, Chevron Energy Technology Company, USA
Yoo Sang Choo, National University of Singapore, Singapore
Weicheng C. Cui, CSSRC, Wuxi, China
Jan Inge Dalane, Statoil, Norway
R.G. Dean, University of Florida, USA
Mario Dogliani, Registro Italiano Navale, Italy
R. Eatock-Taylor, Oxford University, UK
George Z. Forristall, Shell Global Solutions, USA
Peter K. Gorf, BP, UK
Boo Cheong (B.C.) Khoo, National University of Singapore, Singapore
Yoshiaki Kodama, National Maritime Research Institute, Japan
Chun Fai (Collin) Leung, National University of Singapore, Singapore
Sehyuk Lee, Samsung Heavy Industries, Japan
Eike Lehmann, TU Hamburg-Harburg, Germany
Henrik 0. Madsen, Det Norske Veritas, Norway
Adi Maimun Technology University of Malaysia, Malaysia
T. Miyazaki, Japan Marine Sci. & Tech Centre, Japan
T. Moan, Norwegian University of Science and Technology, Norway
G. Moe, Norwegian University of Science and Technology, Norway
A.D. Papanikolaou, National Technical University of Athens, Greece
Hans Georg Payer, Germanischer Lloyd, Germany
Preben T. Pedersen, Technical University of Demark, Denmark
George Rodenbusch, Shell IntI, USA
Joachim Schwarz, JS Consulting, Germany
Dennis Seidlitz, ConocoPhillips, USA
Kirsi Tikka, ABS Americas, USA
Chien Ming (CM) Wang, National University of Singapore, Singapore
Jaap-Harm Westhuis, Gusto!SBM Offshore, Netherlands
Ronald W, Yeung, University of California at Berkeley, USA
OMAE2009: Copyright Information
Page 1 of I
COPYRIGHT INFORMATION
Proceedings of the
ASME 2009 28th International Conference on Ocean, Offshore and Arctic
Engineering (OMAE2009)
May 31
- June 5, 2009. Honolulu, Hawaii, USA
Copyright © 2009 by ASME
All rights reserved.
ISBN 978-0-791 8-3844-0
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Proceedings of the ASME 2009 28th International Conference on Ocean, Offshore and Arctic Engineering OMAE2009 May 31 - June 5, 2009, Honolulu, Hawaii, USA
OMAE2009-79373
USING CFD TO DETERMINE HEAVE ADDED MASS AND DAMPING
OF A SUCTION PILE
Richard Zoontjes
Heerema Marine Contractors Leiden, Netherlands ABSTRACT
This paper presents results of a research project within Heerema Marine Contractors to determine added mass and damping coefficients of suction piles using CFD. Analyses have been performed for suction piles which are fully closed and with open hatches. The results are compared with model tests presented at the OMAE by Ireland et al. (2007) and Roe et al. (2008).
Two modeling approaches have been used. The
firstapproach is simulating a forced oscillation by oscillating the flow around a fixed body. The second approach is by using a Dynamic Fluid Body Interaction (DFBI) model simulating a decay test. The DFBI model allows the (fluid induced) motion of an object to be predicted in six degrees of freedom.
The oscillating flow method gives very good results for both closed and open hatch conditions. The computational costs for this method are very low. The niain drawback is the inability to model oscillations close to a floor. The DFBI model gives the opportunity to quantify floor effects. At a floor clearance of h/D = 0.40 damping and added mass are accurately predicted. For a floor clearance of h/D = 0.20 added mass as well as damping is slightly overestimated.
No major deviations have been noticed when comparing the results of model-scale to fI.ill-scale simulations. Apparently, Froude scaling is applicable for this particular geometry and scaling.
INTRODUCTION
Oil exploration is expanding to ever deeper water. In 2008, Heerenia Marine Contractors' Deepwater Construction Vessel (DCV) Balder installed the Perdido Spar in the Gulf of Mexico in a record setting water depth of 2,400 m. For the permanent mooring, suction anchors where installed in water depths of up to 2,600 m. Future developments show exploration in ultra deep water of over 3,000 m deep. Installation contractors now face
Harm Siegersma Deift University of Technology
Delft, Netherlands
Harald Ottens Heerema Marine Contractors
Leiden, Netherlands
the challenges of installing structures in these water depths.
This requires stretching the limits, not only regarding the
capabilities of the installation equipment, but also regarding the analytical methods to arrive at an efficient and safe installation procedure.
Figure 1. HMC's DCV Balder installing the Perdido Spar For water depths up to 1,000 m, experience shows that the structures often move niore or less with the crane without experiencing significant dynamic amplification due to resonance. However, when the water depth increases, resonance effects start to play a major role in the dynamic behavior. This can have an adverse effect on load fluctuations in the hoisting wires, which may result in an overload of the cranes or slack in the hoisting arrangement. Other criteria may impose additional restrictions on the environmental limits of installing stnictures on the seafloor. For suction piles, usually a maximum set-down velocity is defined to guarantee that the pile can penetrate in the soil without washing the soil away hence reducing holding capacity. A less obvious, but very practical limit is the heave motion of the pile prior to set-down. If the motion is too large the ROV (Remotely Operated Vehicle), which monitors the stabbing operation, may not be able to keep track of the pile. Since the pile needs to be oriented correctly before set-down, this significantly complicates the operation.
During preparations
of the
project execution phase, hydrodynamic analysesare performed to
demonstrate the feasibility of installing these stnctures, to establish specifications for the lifting equipment including possible heave compensation systems, and to assess limiting environmental conditions for the operation. In addition, these analyses can be used to optimize the shape of the stnicture, e.g. for suction piles to determine optimal valve size. In any case, the accuracy of the analysis can have a direct effect on the design and installation sequence of the stnictures, hence influence the overall costs.The dynamic behavior is usually analyzed using a non-linear time domain finite element program. Accurate modeling of the hoisting arrangenlent is required in terms of stiffness and damping properties, but also the mass of the hoisting wires
which can be large in comparison with the structure to be
lowered, in particular in ultra deep water.
The stnicture itself is characterized by mass, added mass and damping. The latter two are a function of the Keulegan-Carpenter number, which is a measure of the intensity of the oscillation relative to the size of the stnicture. Just before set-down, the vicinity of the floor has an influence on the added mass and damping, hence on the dynamic behavior. Traditional analysis methods like diffraction theory have limitations in assessing the added mass and, in particular, the damping. In many cases, model tests are performed to establish coefficients, which are included in the dynamic lowering analyses. As an alternative, CFD has the potential to assess these coefficients in a numerical manner. However, CFD is not yet a proven method,
and validation of the results
is required to reach generalacceptance of this method.
This paper presents results of a research project within Heerema Marine Contractors to determine added mass and damping coefficients of suction piles using CFD. Analyses have been performed for suction piles which are fully closed and with open hatches. The results are compared with model tests presented at the OMAE by Ireland et al. (2007) and Roe et al. (2008).
NOM EN C LATU RE
Dimensionless equivalent damping
Dimensionless linear and quadratic damping Amplitude of motion Added mass coefficient Hatch diameter Pile diameter Distance floor to pile Pile height
Applied spring stiffness
KC=
R m mA M = m + mA R S T [-] Keulegan-Carpenter number[kg] Structural mass in air [kg] Hydrodynamic added mass [kg] Total mass
[m] Pile radius
[s] Time
[m2] Top plate area [s] Period of oscillation
2 Copyright © 2009 by ASME
v=
[ms]
Wall friction velocityp
yo [m] Wall distance
[-] Dimensionless wall distance
,L1
Vmax
[ms']
Maximum occurring pile velocityAt [s] Time step
APile [kg Pile displacement
1.1 [Pas] Dynamic viscosity
p [kgm3] Density
tw [Pa] Wall shear
(I)
[s']
FrequencyCASE DESCRIPTION
Motivated by the lack of information on the hydrodynamic properties of suction piles, Ireland conducted tests with a scaled model. Since this study did not include the effect of proximity of the seafloor, Roe performed further model tests to quantif' this effect. In these tests,
the added mass and damping
coefficients of a 6-meter diameter suction pile have been
determined by testing a 1: 10
model. At several
heave frequencies, free decay tests were conducted. To study the influence of floor clearance four clearances of the model from the seafloor were investigated ranging from a distance of 1.20 to 0.20 times the diameter of the pile. For each clearance, the influence of perforation of the suction pile top was examined. The comparison of the results from Roe and those from Ireland showed that the floor effect for a clearance of 1.20 times the diameter is negligibly small. In this study, this clearance is treated as the "deep water" condition.Table 1 and Figure 2 show the details for the full-scale suction pile as well as the model suction pile. The mass of the suction pile has been assumed to be 31 .0 kg for the scaled suction pile. This mass was not directly delivered from the available papers but had to be derived from data delivered by Ireland. BE [-I B1 ,B, [-1 C [mj CA [-] d [mj D [m] h [m] H [m] K [Nm
Table 1. Geometry of full-scale and model suction uile
Figure 2. Geometry of suction pile Table 2. Summary of model test uroeram
(2)
3 Copyright © 2009 by ASME
Description Full-scale Model - Units
Diameter D 6.000 0.600 m
Radius R 3.000 0.300 m
1-leight H 6.000 0.600 m
Top plate area S 28.27 0.283
Hatch pair #1 diameter d 0.380 0.038 m
Hatch pair #2 diameter d2 0.537 0.054 m
Hatch pair #3 diameter d 0.658 0.066 ni
Height of hatches - 0.500 0.050 rn Wall thickness - 0.020 0.002 m Water density p 1025 1000 kg/rn3 Mass m
3l.8l0
31.0 kg Description Parameter #1 3407.3 N/ni #2 2329.8 N/rn Spring stiflhess #3 1641.6 N/rn #4 1227.6 N/rn #5 824.3 N/rn Hatch conditions All hatches closedHatches #2 open 720 mm (h/D = 1.20) Floor clearance 240 mm (h/D 0.40) 120 nini (h/D = 0.20) Hydrodynamic properties
Hydrodynamic coefficients have been determined following the procedure of Roe et al. (2008). The properties of interest are heave added mass and damping. The damping includes linear and quadratic damping as a function of the Keulegan-Carpenter number:
KC=
R (1)
The total mass "M" of the system including added mass can be found from the period of oscillation and applied spring stiffliess. The added mass coefficient is then defined as follows:
CA
pirR2H
Mm
Following the formulation in
Roe et
al. (2008) adescription of the dimensionless linear and quadratic damping coefficients can be found.
ab - 2pSR
BE=
B+B2
.,KC
(3)irc
3.irM
Here a, b and c denote absolute heave displacements at peaks, troughs and the average of those two, respectively, in the heave time history.
SETUP OF THE CFD ANALYSES
Two modeling methods have been applied
to obtainhydrodynamic properties from the CFD analyses.
The first approach is to simulate a forced oscillation test by fixing the position of the suction pile and oscillating the flow around it, instead of moving the suction pile itself. In this paper this method is referred to as "oscillating flow method". Added mass and damping can be derived from the forces on the body during oscillation. By oscillating the flow, simulation of a forced oscillation test is relatively easy at very low computational costs. The main drawback of this approach is the inability to take floor effects into account.
The second approach is to simulate a decay test by using a Dynamic Fluid Body Interaction (DFBI) model. The body is vertically fixed to
a spring and after giving
it an initial displacement, the body starts to oscillate with decreasing amplitude. The response period of the heave motion can be used to derive the (added) mass properties; the decay of the heave motion in time can be used to calculate the damping. The DFBI model allows the fluid induced motion of an object to be predicted in six degrees of freedom. External forces applied on the body result in movement of the grid through the fluid. This way six degrees of freedom movement of a body (and grid) can be modeled.The CFD calculations have been performed with the
STAR-CCM+ R.ANS code, using dual quad core 3.0 GHz 64 bit
Intel processors with 32.0 GB of RAM. The CPU times
presented in this paper have been scaled to a CPU time using five CPUs.
OSCILLATING FLOW METHOD Nwnerical method
The setup of the domain is shown in Figure 3. By using
symmetry, only one sixth of the pile has to be modeled.
Axisymmetric modeling is also a possibility, but the hatches on the top plate could lead to an extra fraction of added mass. The velocity at the inlets at the bottom and side of the domain is varied to model the oscillation of the pile. The top and bottom
boundaries are positioned at a distance of 20 diameters from the pile. The velocity inlet at the side of the domain is positioned 10 diameters from the pile.
The available model tests only describe the hydrodynamic coefficients for the situation where hatches #2 are open. This means the use of symmetry planes has to be adjusted when open hatches are taken into account. Half of the pile is modeled for this case.
Figure 3. Overview of the domain
The mesh consists of hexahedral cells. This provides an efficient and robust meshing method. A prism layer mesh is used to capture the boundary layer at the pile. A grid density variation of the complete region is shown in Table 3. For this sensitivity study a time step At = 0.05 seconds was used. This results in about 35 steps per oscillation period of 1.75 seconds
and about 40 steps within a reference period
OfTRef=H
=2.ls.
max
A Menter SST model with an all-y wall treatment was used. This wall treatment is a hybrid treatment that attempts to use a low-y treatment where the viscous sub layer is properly resolved and attempts to use a high-y treatment where the near-wall cell lies within the logarithmic region of the boundary layer. This wall treatment is very useful for complex geometries when it is difficult to satisfy y<l for the whole geometry.
For all grids a near wall cell spacing y0 corresponding to a y+ in the order of one was kept. Except for the boundary layer all grid size properties were related to a base size.
From Table 3 it can be concluded
that good grid
convergence was achieved. The results for 34,000 cells differ less than one percent with the finer mesh with 69,000 cells. A coarser mesh resulted in invalid faces, which required major adjustments to the mesh. Therefore, the mesh with 34,000 cells was adopted for further investigation.
Table 3. Influence of grid spacing in complete domain, with time step At = O.05s
I
Within each time step inner iterations are performed. The amount of inner iterations depends on the monitored residuals.
These residuals are based on the average of the standard
deviations of all cells. After a sensitivity study two orders of magnitude was assumed sufficiently accurate. Figure 4 gives a typical picture of the residuals for oscillating flow. For this setup, 25 inner iterations were sufficient to achieve enough accuracy.
Figure 4. Residuals for oscillating flow, 25 inner iterations
Figure 5. Plot of vertical force on pile for 100 iterations, i.e. 4 time steps
4 Copyright © 2009 by ASME
Number of ce/is C4 CPU [hJ
34,000 1.62 0.039 1.7 69,000 1.62 0.039 4.5 481,000 1.62 0.036 23.8 3,524,000 1.61 0.038 203.7
iiiiiiiiiiàii
IIIII
liii VII1Ik1IIiI \
Figure 6. Overview of the unstructured mesh of 69,000 cells. The right part zooms in to the suction pile.
The influence of the grid spacing in the region around open hatches has been studied as well. The relative numerical error is about 1 percent when no additional refinement in this region is used, except for boundary layer adjustments at the open hatch. This is assumed to be sufficiently accurate.
The flow is governed by a relatively low frequency
excitation. An implicit time stepping scheme is
thereforeappropriate. Table 4 shows a time step variation study using a grid with 69,000 cells.
A time step of At = 0.05 seconds results in a relative
numerical error of about 1 percent compared to the results with a time step of 0.01 seconds. This is assumed to be sufficient. Therefore At = 0.05 is adopted for further simulations.
Table 4. Time step variation with 69.000 cells
For this setup, the influence of the turbulence models on the hydrodynamic coefficients is studied. A comparison of the k-c and the Menter SST model is given in Table 5. It can be noticed that the turbulence model only has very small influence on the hydrodynarnic coefficients. The added mass coefficient obtained using the Menter SST turbulence model improves very slightly. The theoretical extra computational costs are hardly noticeable. The Menter SST turbulence model was therefore selected for the rest of this study.
Table 5. Comparison of hydrodynamic coefficients for two turbulence models
Calculation of &vdrodynarnic coefficients
When imposing a harmonic heave displacement z(t)=ccos(o)t), hydrodynamic coefficients can be obtained by applying Fourier analysis to
the force time
history. The dimensionless coefficientsfor added mass and equivalent
damping can now be determined with: mA 1
JF(t)Sjfl(wt)dt_A
(4) JTC(O 0 II)2c
I
Oscillating flow results
Nine simulations have been nm over the same range of KC as the model tests. The deteniined hydrodynamic coefficients for a closed pile are shown in Figure 7, Many of the data points obtained from model tests are in the low range of KC numbers. Due to the low damping in this region, the decay tests result in relatively many samples for the smaller KC values. In addition, the spreading of the results in this region is relatively large,
possibly caused by the accuracy of the measurements in
proportion to the motion amplitudes or other effects. The
chosen distribution of the results from the simulated forced oscillation tests over the KC numbers is much more uniform. Due to this, a comparison of the averages and trends, which are derived in the same way as Ireland and Roe, may show some deviations. From the model test results can be observed that the added mass is actually slightly dependent on KC. The added mass coefficients obtained from the CFD agree with this trend. The determined damping agrees very well with model test results.
The results for the perforated pile are shown in Figure 8. Similar to Figure 7 the damping shows relatively large
deviations for low values of KC due to the spreading and
distribution of the model test results as explained above. When looking at the individual samples, for KC values larger than 0. 1 damping is predicted very well. Similar to model tests the
dependency of added mass on the KC number becomes
apparent.
Copyright © 2009 by ASME
SST k-e A'Iodel tests
CA 1.62 1.62 1.57
BE 0.039 0.039 0.038
CPU time [hi 0.32 0.31
-fine step[s] CA
0.01 1.59 0.039
0.05 1.62 0.039
0.20 1.83 0.063
0.15 0.05 1.8 16 0.2 0.15 .1 05 Bl-c1212007[.J.B2-01d3.791-],51-nt 12011 [-L B2-r,12 3.60f-]
S...-.
...-01 03 04 05 08 KC(-JFigure 7. l-Iydrodynamc coefficients obtained by oscillating the flow. All hatches closed.
Ce-old 1.521-I.Ce-nt 1.45(-1
Ca-old P.an-cld Ca-ni Be-cId Treed-old Be-nt Trend-nt C Ce-old l.BOOld C Be-old - Trend-old Be-nt Treed-nd
Gf =(a.vg)j
(6) Within STAR-CCM+ there is no explicit way to implement a spring on a body. By using a JAVA-macro, an external force on the body can be related to the translation of the body. For each time step this external force is extrapolated from previous translations. A second degree Lagrange polynomial is used to extrapolate haIfa time step ahead.15 10 3
L(x)=-j-Y11 ---y,1 +-y,
(7) A decaying pile in "deep water" can now be modeled. However, modeling the effect of the floor is more complicated. Because the grid is moving and the floor is fixed, the volume mesh, in particular adjacent to the floor, should be able to deform or "morph". This option was not yet available in STAR-CCM+ and only became available just before delivery of this paper. Therefore, another option has been applied. The analyses have been performed using a fixed mesh, modeling the solid floor as a very dense and viscous fluid. Since motion of the pile may result in waves on the interface between the two phases, the density and viscosity of the "floor fluid" have to be as high as possible to limit the effect. However, too high values for these properties leadto divergence of the
solution. The following values are used:Pfloor = 1.0-lO6kg/m3
floor = 1.0
Pa-s
An increased sensitivity to the time step is likely due to the spring implementation and the DFBI model. Table 6 shows the results of a time step variation study over a limited KC range. The added mass seems to converge very well. From the given linear and quadratic damping terms it is hard to see which time step gives the best results. Therefore also the standard deviation to the trend line of the model test is given.
A time step smaller than At = 0.002s leads to excessive computational times in the order of weeks. This is considered to be impractical. Besides that, the given standard deviations for a time step of At = 0.0 Is and 0.002s are already in the same order of magnitude as the standard deviations of the model tests. The given results for this setup have been determined with a time step of At 0.002s.
Table 6. Comparison of hydrodynarnic properties for three different amounts of time ste
41 0.05s Al O.Ols At = O.002s Model tests
CA 1.63 1.60 1.60 1.57 -0.040 -0004 0.003 0.01 I B. 3.80 4,33 4.54 3.60 0Ca 0.086 0.037 0.036 0.038 Be 0.051 0.012 0.005 0.010 1.4 12 0.1 02 04 Os OS 0.1 08 0.8 61-old 0.032 (-I. B2-efd = 3.62H.61-nd 0.051 (-I, 02-nt 2.71 (-I
6 Copyright © 2009 by ASME
0 01 02 03 0.4 05 09
KG 1-I
Figure 8. Hydrodynamic coefficients obtained by oscillating the flow. Two hatches open.
DYNAMIC FLUID BODY INTERACTION MODEL
Numerical method
To model the decay test of a pile close to a floor, instead of moving the fluid, the motion of the pile has been simulated with a DFBI model. External forces on the body result in movement of the body and hence the grid through the fluid. This way six degrees of freedom movement of a body (and grid) can be modeled. Movement of the body results in an additional mass flux at each face in the domain:
Ce-old 1.82 t-i, Ce-ni = 1.57 (-1
01 02 03 04 05 08 0.7 08 06 2 1.6 16 14 12
First, this simulation of a decay test is checked without floor effects, i.e. "free decay". Since the geometry of the pile and the domain is identical to the "oscilJating flow" approach, no difference in grid sensitivity is assumed.
The above is valid for "free decay". When a viscous floor is taken into account this is not the case. The grid spacing around the interface of the two phases can be expected to be sensitive to a refinement. A grid density variation results in a total amount of 370,000 cells, Figure 9. The average cell size at the interface is about 10 mm. The required amount of cells is much larger for this setup, leading to computational times of 3 to 4 days.
Figure 9. Mesh refinement at the interface resulting in a total amount of 370,000 cells
Results forfree decay
To capture a wide KC range with one simulation a nm
of
about 100 seconds real time is required. To decrease this total required computational time three different initial displacements are used for the "all hatches closed" case. The determined hydrodynamic coefficients are shown in Figure 10.
A good prediction of the added mass is given for both hatch conditions. The added mass is in good agreement with the performed model tests. The prediction of damping is very good for both hatch conditions and for KC larger than 0.1.
0.2 0.15 0.1 0.05 2 1.8 T 1.6 0 1.4 12 0.2 0.15 0.1 0.05 01 Bl.cfd=0.003 H. B2.cfd =4.441-1, Bi-nI =0.01 .19.ni360[.1
U..
I...-
....-.
01 Bl.cfdo.0241.l,82-cfd5.02[-},B1.n10.051(.J82.M2.7 (-I 0.2 02 Cafd 1.59Fl.ca-ni = 1.57H 0.3 0.4 Cacfd = 1.44 H. ca-in = 1,451.1 03 0.4 05 0.5 06 06 0.7 0,7 08 06 09 09 Ca.cfd Average-cfd Ca.rrt Average-ni o Ca-cf an-cfd Ca-ni Be-cf Tnend.cfd Be-ni Trend.rr Be-cf d Trend-cfd Be-ni Trend.rre 7 Copyright © 2009 by ASMEUIUUL..
-
---1.2 --N---0 01 02 03 0.4 0.5 06 07 08 09 KC[-jFigure 10. 1-lydrodynamic coefficients obtained with DFBI model, At = 0.002s and all hatches closed.
0 01 02 03 04 05 06 07 08 09
(C
Figure 11. Hydrodynamic coefficients with DFBI model, At = 0.002s and two hatches open.
Figure 12 shows the velocity profile at four phases within one period. The picture on the upper left shows the pile at its highest position. At the bottom left, the pile has moved to its lowest position and starts to move up again.
2
1.6
T 1.6
cot = 3it/2 Figure 12. Velocity field at four phases in one period Results for decay close to floor
Figure 13 and Figure 14 show the results for decay at a distance of h/D = 0.40 and h/D = 0.20, respectively. From both figures can be observed that the predicted added mass is in very good agreement with model test values.
For hID = 0.40 predicted damping is in good agreement with model tests. The shown damping coefficients for hID = 0.20 are also in good agreement with model tests. Although for lower KC, damping is slightly under-estimated.
1.6 T 1.6 C C) IA
Il
0.2 0.15 0.1 8.05 Ca-cid 1 68[-, (.nt = 1.65 [-1Bi-cfd = 0.007 H ctd 7.92 1-). B1-ni 0.025 [-I, B2-n1 5.581-]
-U...
-a...-..
KC (-1
Figure 13. Hydrodynamic coefficients for decay tests with a closed pile at hID = 0.40, dt = 0.002 seconds
Ca.cld kan-cfd Ca-ni lan-nt o Be-cfd Trend-cf d Be-ni Trend-ITI 8 Copyright © 2009 by ASME 1.8 16 ° 1.4 1.2 0.2 0.15 0.1
I
0.05 Ca-cid = 1.591-1, Ca.nl = 1.49 .1----.- o
ca-cld an-c1d Ca-nt Mean-ni-.--...--
01 02 03 04 05 06 07 08 .9 81-eli =0.048 [-1. 62-cfd 6.3/(.J. 61-nt =0.072 1-] 82-n1 3.03 o Be-cf Trend.cfd Be-nt Trend-nt cot 0wt=it/2
01 02 03 04 05 0.9 0.7 08 09Figure 14. Hydrodynamic coefficients for decay tests with a closed pile at h/D = 0.20, dt = 0.002 seconds
SUMMARY OF RESULTS
Table 7 to Table 10 provide a summary of the obtained
results. The real time length of the decay test runs was
dependent on the range of KC covered. For consistency, the CPU time given in the tables below is normalized for a run of
30 seconds, which was sufficient for all cases.
As noted before, the damping prediction for very low numbers of KC shows relatively large deviations due to the spreading of the model test results. For the given comparison the linearized damping coefficients only cover KC numbers larger than 0.1. For the added mass coefficients, the complete range of KC is considered. The distribution of data points has
an effect on the derivation of the tabled added mass and
Of 0.2 03 04 05 06 0.7 08 09
linearized damping coefficients. This should be kept in mind when looking at the results below. Especially the averaged added mass cocfficient from the oscillating flow method seems slightly higher, but this is mainly caused by the concentration of model test results in the low KC range. This is shown in Figure 7 and Figure 8. A valid comparison can be made by comparing the standard deviation with model test trend lines Ca and 0Be
Table 7. All hatches closed. deeu water
Table 8. Two hatches open, deep water
Table 9. All hatches c osed, hID = 0.40
Table 10. All hatches closed, hID = 0.20
SCALE EFFECTS
Due to the geometry of the structure, changing fluid
pressure governs the hydrodynamic forces, while shear forces play a minor role. At the sharp edges, separation takes place for the Reynolds numbers of interest. Based on these considerations
the flow is assumed independent of Reynolds number. Obtained results can be applied to full-scale stnictures.
The above is valid for the case where all hatches are
closed. However, the effect of open hatches is related to viscous effects. Roe et al. (2008) already noted that this flow might be dependent on Reynolds number. Due to scaling the Reynolds number decreases from 7.0.106 full-scale to 2.2l0 model-scale. Therefore, Froude scaling may not be appropriate.
Using the numerical methods discussed in this study, a full-scale simulation can easily be performed. This is done for a pile in "deep water" and open hatches using the oscillating flow method. Numerical results for the full-scale geometry can be compared to the results obtained with the model-scale geometry. This way the effect of scaling can be quantified.
The full-scale mesh is a scaled version of the mesh used before except for the mesh in the boundary region. The number of prism layers in the boundary region is increased to achieve a y of the same order of magnitude, i.e. a y in the order of one.
Table 11 shows the determined hydrodynamic properties for model-scale and full-scale simulations. No significant deviations are noticed. Apparently, the applied Froude scaling is valid for this particular geometry and scaling.
Table 11. Comparison of hydrodynamic properties for a scaled and a full-scale nile
CONCLUSIONS
The oscillating flow method gives very good results for both closed and open hatch conditions. Both model tests as well as CFD simulations show a dependency of added mass on the KC number. Damping is predicted accurately for KC numbers larger than 0.1. For low KC numbers, the model test results show some spreading. The computational costs for this method are very low. The main drawback is the inability to model oscillations close to a floor.
The DFBI model to simulate a decay test gives the
opportunity to quantify the floor effect. At a floor clearance of hID 0.40 damping and added mass are accurately predicted. For a floor clearance of h/D = 0.20 added mass as well as damping is slightly overestimated.
9 Copyright © 2009 by ASME
Osc. flow Decay DUfraction Model tests
CA 1.62 1.63 1.56 1.57 B1 0.009 0.003 - 0.011
B,
3.62 4.50 - 3.60 GCa 0.059 0.064 - 0.038 Be 0.003 0.006 - 0.010 CPU [hi 5.7 148 --Osc. flow Decay Diffraction Model tests
CA 1.52 1.44 1.16 1.45 B1 0.045 0.038 - 0.051
B,
2.57 3.69 - 2.71 Ca 0.105 0.083 - 0.090 Be 0.009 0.022 - 0.009 CPU [h] 6.1 219 - -Scaled Full-scale CA 1.54 1.55 B1 0.045 0.044 B2 2.57 2.62 BE (KC = 0.45) 0.068 0.067 CPU [h} 6.1 12.4Osc. flow Decay Diffraction Model tests
CA - 1.72 1.61 1.65 B1 - 0.008 - 0.025
B,
- 7.97 - 5.08 0Ca - 0.079 - 0.042 013e - 0.012 - 0.012 CPU[hi - 182 --Osc. flow Decay Dit/raction Model tests
CA - 1.92 1.70 1.75 B1 - 0.037 - 0.023 B., - 12.52 - 10.92 Ca - 0.182 - 0.053 - 0.019 - 0.014 CPU[hI - 237 -
-No major deviations to model-scale are noticed for full-scale simulations. Apparently, Froude scaling is applicable for this particular geometry and scaling.
REFERENCES
CD-adapco, User Guide STAR-CCM+, version 3.06.006, Londen, 2008
Det Norske Veritas (2000) Environmental conditions and environmental loads. Classification Notes No, 30.5.
freland, J. Macfarlane G., Drobyshevski 1. (2007)
Investigation into the sensitivity of the dynamic hook load during subsea deployment of a suction pile. Proceedings of
OMAEO726thInternational Conference on Offshore Mechanics and Arctic Engineering, June 10-15, San Diego, USA, OMAE2007-29244
Roe T.F., Macfarlane G., Drobyshevski 1. (2008) Heave added mass and damping of a suction pile in proximity to the
sea floor. Proceedings of OMAEO8 27th International
Conference on Offshore Mechanics and Arctic Engineering, June 15-20, Estoril, Portugal, OMAE2008-57559
White F.M. (1991) Viscous fluid flow, Second edition. McGraw-Hill
