Date June 2009
Author Kessel, J.L.F. van and F. Fathi Address
Deift University of Technology
Ship Hydromechanics Laboratory
Mekelweg 2, 2628 CD Delft
TUDeift
Deift University of Technology
Page /of 1/1
A comparison between CFD, potential theory
and model tests for oscillating aircushion
supported structures
by
J.L.F. van Kessel and F. Fathi
Report No. 1626-P
2009
Proceedings of the ASME 2009 28th International
Confe-rence on Ocean, Offshore and Arctic Engineering, OMAE
2009, May 31June 5, Honolulu, Hawaii, USA, ISBN:
OMAE2009:
Welcome from the Conference Chairs
Page 1 of
2WELCOME FROM THE CONFERENCE CHAIRS
file ://E:\data\chair-welcome.html
8-6-2009
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 pro or post conference enjoying the island of Oahu. 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
MESSAGE FROM THE TECHNICAL PROGRAM CHAIR
Welcome to the 28th International Conference on Ocean, Offshore and Arctic
p
'
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. Valentine
division 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. Mei 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
file://E:\data\chair-message.html
8-6-2009
OMAE2009: Message from the Tecimical 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 I
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 1. 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
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Proceedings of the ASME 2009 28th lnternationa Conference on Ocean, Offshore and Arctic Engineering
OMAE2009
May 31 - June 5, 2009, Honolulu, Hawaii, USA
ABSTRACT
This contribution presents a comparison between Computational Fluid Dynamics (CFD), potential theory and model tests for an oscillating aircushion supported structure.
The linear method was developed at DeIft University of Technology and uses a linear adiabatic law to describe the air pressure inside the cushion. In this method, the structure and the water surface within the aircushion are modelled by means of panel distributions representing oscillating sources.
The CFD solver is the commercial software CFX which solves the whole flow field using Reynolds Averaged Navier Stokes
Equations (RANSE). The free surface is modelled by a Volume of Fluid (VOF) approach.
The results in this paper show a good agreement between
experimental results and numerical results of both methods for aircushion pressure variations, added mass, damping and wave elevations inside the aircushion.
As such it is validated that the behaviour of an aircushiori
supported structure subjected to forced heave oscillations can be well predicted by both CFD and potential theory.
KEYWORDS
Aircushion supported structure, model tests, potential theory, CFD, forced oscillations, added mass, damping, air pressure variations, wave elevation.
INTRODUCTION
Aircushions can significantly influence the behaviour of large floating offshore structures in waves. Research in the past has shown that aircushions can be of particular interest for large floating offshore structures since wave bending moments and drift forces can both be significantly reduced at the same time.
OMAE2009-79766
A COMPARISON BETWEEN CFD, POTENTIAL THEORY AND MODEL TESTS FOR OSCILLATING
AIRCUSHION SUPPORTED STRUCTURES
).L.F. van Kessel
F. FathiOffshore Engineering Department, GustoMSC
Deift University of Technology, Schiedam, The Netherlands Deift, The Netherlands
The behaviour of large aircushion supported structures in waves was studied by Pinkster et. al. [12] - [15] and Van Kessel et. al. [21] - [25] at DeIft University of Technology. Tabeta carried out model tests in the towing tank of the Ship Hydrodynamics
Laboratory which served as a validation of the computational method [17]. In addition, Pinkster and Meevers Scholte [15], [20] performed model experiments of a large aircushion
supported Mobile Offshore Base (MOB) at the same facility in
1999.
Lee and Newman [10] carried out computations with respect to acoustic disturbances in an aircushion. Thiagarajan et. al. [181 investigated the wave-induced motions of air-supported offshore structures in shallow water by means of an analytical approach and model tests. Ikoma et. [2 - 9] al. investigated the behaviour of aircushions on floating structures at the College of Science and Technology at Nihon University, this research was mainly
aimed at investigating the effects of air chambers on the
hydroelastic response of floating structures. Tsubogo et. at. [19] used a different numerical approach to calculate the behaviour of an elastic aircushion supported structure. In his case the air
inside the cushion was also described by a potential formulation.
The present contribution describes the use of a CFD method for aircushion supported structures. In addition a comparison with
potential theory and model tests will be given. First, both
numerical methods will be introduced, followed by a description
of the model tests program. Afterwards, the numerical and experimental results will be discussed and finally conclusions will be drawn.
THEORETICAL FORMULATION
Both CFD and potential computations were performed in order to compute the behaviour of an aircushion supported structure subjected to forced heave oscillations. CFD computations were performed with the program ANSYS-CFX version 11.0. First the basic theory underlying these computations will be discussed in this section. Next a description of the potential theory will be
given.
CFD METHOD
Computational Fluid Dynamics (CFD) simulates the viscous flow field in the whole domain. For each grid cell, the fluid velocity vector and the pressure scalar are computed at each time step. In this paper, the time dependent incompressible Navier-Stokes equations are solved in their statistical Reynolds averaged (URANS) formulation [261.
The CFD solver ANSYS-CFX [1] uses a finite volume
discretization on a collocated grid of the URANS equations to determine the time evolution of the flow field. The presence of both air and water in the simulation is modeled by the volume of fluid (VOF) method. Within each cell, the relative proportion of
each phase is given by the volume fraction 4. This scalar function comprised between 0 (grid cell full of air) and 1 (cell full of water) is used as a weighting function. A unique flow field is solved by the URANS equations where the relative
contribution of each phase is represented by for water and (1
- 4)) for air. The time evolution of is given by the transport
equation, Eq. (1). The free surface profile, generally defined as the iso-surface with constant 4=0.5 is sharpened using a specific compression algorithm as described in [1]. Both air and water are modeled as incompressible fluids. The fluid equations solved by the code are the following:
ax,
a a
--
r a (aP ai2,' 1+(Jv,)=--I--I-p,,I+I+R.y i+A
at ax, ax ax, ax, ax, )j
öt ox, p=tp. +(I-Ø)p,, m =Øu.,,.,. +(I-,)j,. = x,y,z in which: fr; p F R3= i component of the statistically averaged
velocity
= fluid mixture density = Buoyancy force
= Reynolds stress tensor
The UR.ANS formulation implies a closure modeling of the
averaged cross products of the fluctuating terms which are not solved by the averaged equations, known as Reynolds stresses R.
A classical 2-equation eddy viscosity model, Menter's Shear Stress Transport (SST) is employed in this respect [11].
Following Boussinesq's assumption, the Reynolds stresses are
considered proportional to the fluid shear stresses. a (ai a13'i 2
I?,, = -i,,
-+-, ax, ) 3in which:
k = turbulent kinetic energy Pt = turbulent viscosity
The turbulent viscosity is an anisotropic model for the added energy dissipation occurring in the fluid because of turbulence. Its effect is then taken into account by simply adding it to the
fluid viscosity p. p is determined locally by solving two more scalar equations corresponding to the fields of turbulent kinetic
energy k and turbulent dissipation frequency w. p is then retrieved using the dimensional relation it=pk/w. The complete formulation can be found in [11].
CFX uses a multi-grid accelerated algorithm [16] to solve both the continuity equation and the momentum equations in a single
system. Non-linearities of the system are treated using an iterative pseudo-transient approach.
3D POTENTIAL METHOD
The rigid part of the aircushion supported structure is modelled in the usual way by means of panels representing pulsating sources distributed over the mean wetted surface of the
construction. The free surface within the aircushion is modelled by panels representing oscillating source distributions laying in the mean free surface of the cushion.
All panels of the free surface within an aircushion are assumed to represent a body without material mass but having added mass, damping, hydrostatic restoring and aerostatic restoring
characteristics. Each free surface panel has one degree of
freedom being the vertical motion of panel n within cushion c. It will be clear that properties such as added mass coupling and damping coupling exist between all free surface panels and the rigid part of the construction. The total number of degrees of freedom (D.O.F.) therefore amounts to:
D.O.F.=6+N
in which:
N, = number of panels in cushion c
(2)
(3)
The number 6 represents the six degrees of freedom of the rigid part of the structure. The equations of motion for an aircushion supported structure can be written as:
DO F.
{_tv2(M +,)-i
=X,
n=I,2,...,D.O.F. (4)in which:
M, = mass coupling coefficient for the force in the n -mode due to acceleration in the
j
-mode. Zero for cushion panels.a,y = added mass coupling coefficient
b = damping coupling coefficient
= spring coupling coefficient
= mode of motion
X
= wave force in the ,, -modeIn the above equation 1=1,6 and n=1,6 represent motions and force modes respectively of the rigid part of the structure. The case of
j>6
and n.>6 represents the coupling between the panels of the free surfaces of the aircushions. The case of j-1,6 and n>6 represents the coupling between the rigid part of the construction and the vertical forces of the free surface panels in the cushions.j.>6
andn=6
represents the coupling between vertical motions of the free surface panels in the aircushions and the six force modes on the rigid part of the structure.The wave force X,, , the added mass and damping coupling coefficients a, and b,,1 are determined in the same way as is customary for a multi-body system. The contribution to the total potential due to the discrete pulsating source distributions over
the structure and the free surface of the aircushions can be expressed as:
;()=_±c()G(X, )As,
(5)= total number of panels of the structure and
free surfaces of all cushions = XJ,X2,X3= a field point
= A, A2, A. = location of a source
= Green's functJon of a source in A relative to
a field point X
= surface element of the body or the mean free surfaces in the aircushions
= strength of a source on surface element s due to motion mode!
= potential in
point A' due to j -mode of
motionThe unknown source strengths ci,, are determined based on boundary conditions placed on the normal velocity of the fluid at the centres of the panels:
_±.()+±
2 "
()--Gr,i)s =.-,
,n=1,2...N (6)4r,-,
" 3n 'The right hand side of the above equation depends on the case
to be solved.
Added mass and damping coupling coefficients are found by applying normal velocity requirements. For the six rigid body
motions (1=1,6) of the structure:
an
a.
=n,
j=1,6
(7)For this case the normal velocity components on all cushions
panels are equal to zero.
For the determination of the added mass and damping coupling arising from the normal motions of individual cushion panels the normal velocity boundary condition is zero except for one
cushion panel at a time for which the following value holds:
where the -1 follows from the fact that the free surface normal
is pointing in the negative X3-direction.
From the solutions of the source strengths for all these cases the total added mass a,, and damping coupling coefficients b,,1 can be obtained: a,,, =
Re[PØJk
1,,,k b,=_Im[PcoØj
k k-I 3 Copyright © 2009 by ASME in which:N = number of panels involved in the force in the n -mode. For the force on a cushion panelN,, = 1. For
the force on the structure N,, = N,
n,,k = generalised directional cosine of k -panel related to a-mode
area of k panel related to the force in the ,, -mode
ø.k = motion potential value on A -panel obtained from
Eq. (5)
The restoring coefficients c,, in general consist of two
contributions i.e. an aerostatic spring term and a hydrostatic spring term as described in [21]. The hydrostatic restoring term
is equal to the product of the waterline area, specific mass water and acceleration of gravity. This applies to both the
structure and the free surface panels. The aerostatic restoring terms are related to the change in air pressure in an aircushion due to, for instance, unit vertical displacement of a free surface panel. Conversely, displacing the structure in any of the three vertical modes of heave, roll or pitch may change the volume of an aircushion as well, thus inducing pressure changes resulting
in forces on all free surface panels and the structure. in which: N,
x
AG(X,A)
0,For the determination of the aerostatic part of the restoring
terms, use is made of a linearized adiabatic law as described in [21].
The motions of the cushion panels due to oscillations of the
structure are determined by solving the equation of motion for all individual panels. Use is made of added mass and damping
coupling coefficients, as well as spring coupling coefficients
based on the aerostatic restoring coefficients and the hydrostatic restoring coefficients of the cushion panels:
{nfa, ib, +ç}x, =X,,
n=7,D.O.F. (10)From the solution of the equation of motion of the cushion
panels the cushion pressure variations and the total added mass and damping coefficients for the aircushion supported structure
can be obtained.
NUMERICAL SETFINGS AND EXPERIMENTAL
SETUP
Results of model tests performed by Tabeta [17] will be used to
validate the results of the CFD and potential method. This
section describes the main particulars of the experimental model,
and numerical models used for CFD and potential computations. MODEL TESTS
Forced heave oscillation tests were performed by Tabeta [17] in towing tank No.1 of the Ship Hydrodynamics Laboratory of Delit University of Technology. This facility measures 140 m x 4.25 m x 2.5 m. It is equipped with a hydraulically operated, flap-type wave maker, by means of which regular or irregular waves can
be generated.
A simple rectangular barge model measuring 2.50 m x 0.70 m x 0.50 m was constructed out of wood. The model consisted of a horizontal deck surrounded by vertical side walls. The draft of
the barge measured to the lower edge of the side walls was
equal to 0.30 m. The thickness of the deck plate and the walls surrounding the aircushion was 2.0 cm. The main particulars of the model are presented in Table 1.
Table 1: Main 'articulars of the aircushion model
Length Breadth
Draught (structure) Draught (cushion) Area of Water Line
Displacement Oscillatin. Mass
I
2.50 0.70 0,30 0.15 1.75 0.2815 160Forced heave oscillations with amplitudes of 1 cm and 2 cm
were carried out in the basin. During these oscillations, the
heave added mass and damping coefficients were measured, as
well as the cushion pressure variations and the water elevation
inside the cushion.
Figure 1 shows the test set-up and location of the measuring devices. The cushion pressure variations are measured at locations l' and P. and the water elevation (h) is measured
at (x, y) = (0.1 m, 0.0 m).
070 m
0 fir
Fi'ure 1.' Setup of the model tests
CFD METHOD
Forced oscillation tests are simulated by imposing a harmonically periodic motion to the aircushion supported structure in still
water. In order to save computational resources, the problem is reduced to two dimensions. Only the transverse section of the cushion is modeled and 3D effects are neglected. A multi-block
body fitted structured mesh is generated using the software
ANSYS-ICEM as shown in Figure 2. Even if CFX makes use of unstructured grids only, the multi-block approach is preferable due to a better alignment with the flow of the grid cells when compared to the unstructured tetrahedral mesh generation. The
regularity of the cell distribution is also an advantage when
considering the mesh deformation caused by the cushion
displacement. Indeed, the cushion is modeled as an oscillating
solid wall boundary around which the mesh will deform
according to the cushion displacement. The near wall flow is captured by an 0-grid structure of the mesh around the cushion ensuring a good definition of the boundary layer. The resulting mesh size consists of 60,000 cells. Adequacy of the mesh has
been checked by performing a grid convergence study.
F2
-o)4 Copyright © 2009 by ASME
0.50 or 0.15m (aft cushion) - - -(tore cuohion( 2.50 m
f
Figure 2 Detail of CFD mesh around the cushion
The total domain width is 30 times the width of the cushion. The sideways external boundaries of the domain are modeled with a Neuman condition for the velocity, a fixed average value of 1
atm for the pressure and a fixed free surface profile
corresponding to the mean water elevation. In order to minimize the wave reflection phenomenon, a progressive coarsening of the grid cells in the spanwise direction away from the cushion is
performed. The ambient air is modeled as an opening with
constant pressure and the bottom of the basin as a non resisting
wall.
The advection terms are discretized with the High Resolution Scheme which is a local blending between a first order upwind
scheme and a second order central differencing.
The time discretization is second order accurate and the time step is chosen to be 1/100 of the oscillation period.
In order to ensure a significant reduction of the equation
residuals and a good resolution of the strong non-linearities, at least 10 outer-loop iterations are performed per time step. The results obtained with CFD are analogous to model tests and
consist of time dependent physical data. Therefore, the extraction of derived quantities such as added mass and damping requires the same type of treatment. In this paper,
they are computed using a least square fit of the filtered force
and pressure time traces. Effect of air compressibility
The compressibility of the aircushion (ci) is related to the height
of
the cushion and may be computed by
the followingexpression [21]:
pgk
(1)K P +
pg h
Where h is the height of the aircushion, K is the gas law
index (1.4 for air), and P is the air pressure inside the cushion. According to this formulation the compressibility is 2°/o and may
be neglected in the computations. In order to quantify more clearly the effect of compressibility on the simulations, a
numerical check is required. The following matrix of
computations is performed at an oscillation frequency of 5.86 rad/s:
Table 2: Comoutation matrix for air comaressibil/ty studj
Since the mesh convergence study has only been done using incompressible air, there could be an effect of the mesh size on the results. This is why a finer mesh was tested in combination
with compressible air.
Figure 3 shows the filtered time traces of the pressure for the considered cases. The added mass and damping coefficients calculated for each configuration are reported in Table 3.
60 60 40 20 -20 -40 183 19.0 19.5 20.0 20.5 21.0 213 22.0 22.5 lime (sec)
- Standard Case - Compressible Air Refined Mesh - Refined Mesh & Comur. Air
Figure 3 Filtered Force time traces
Table 3: Pressure and phase differences for different cases of
the air comøressibilitv stud
The time traces and derived coefficients show that the combined effects of air compressibility and mesh refinement account for less than 2°h difference in the pressure amplitude and less than 1% for the phase angle. This is well within the precision of the
filtering and least square methods used to determine the coefficients.
The main difference when using compressible air modeling lies in the computational time. It takes significantly more time for the pressure to converge toward an established regime when
compressible air is used. This is due to high frequency
oscillations appearing at the beginning of the simulation as can be seen in Figure 4. It takes a relatively long time before these
5 Copyright © 2009 by ASME Case Standard case Compressible air Refined mesh Compressible air + Refined mesh Mesh size 60K 60K 110K 110K Compressible
air NO YES NO Yes
Standard
case Compressible air
Refined mesh compressible air + Refined mesh PolPal 59.442 61.230 60.094 61.328 c (rOd) -15.711 -16.531 -15.326 -14.925
peaks are damped. Since the accuracy gain is negligible and the computational time increased, the conclusion of this preliminary check IS to keep a fully incompressible model for both fluids for all the simulations.
2300 2100 1900 a, 0- 1700 a, 1500 a, a, 1300 a. 1100 900 700 Aircushlon Pressure - Incompressible alil Compressible air
F(gure 5: Panel model of the aircushion structure (upside down)
DISCUSSION OF RESULTS
Figure 6 to Figure 11 show the numerical and experimental results
of the
forced heave oscillationsof the
aircushion supported structure. Potential and CFD simulation wereperformed for a range of frequencies between 2.4 and 8.6 rod/s.
It
takes less than one second to compute one oscillatingfrequency with the present potential method. In general CFD computations are more time consuming. However the problem
was reduced to 2D. As a result the CFD simulations are relatively
fast and the same computation with the CFD software takes on
average 18 hours on a single 3 GHz processor.
The time trace of the aircushion pressure can be translated to a response amplitude operator (RAO) of the aircushion pressure variations as shown in Figure 6. Both Figure 6 and 7 indicate that numerical results are in good agreement with model tests. All data points are close together and the oscillation amplitude has no effect on the RAO of the pressure variations. In other words, there is a linear relation between air pressure variations and the oscillation amplitude.
Aircuehion Pressure Variations 45 40 35 -30 .25 a, 20-U, a, a, 15 a-10 0 1.00 o Exp:z0.01 Fm] >( Exp:z0.02]m]
CFO: z = 0.01 ]m] CaIc: 364+120 panels GaIc: 364+480 panels 3% Cushion damping
0 )0 2.00 3.00 4.00 5.00 9. o Exp z = 0.01 ml X Exp z = 0.02 rn] CFD: z = 0.01 rn] CaIc: 364+120 panels - CaIc: 364+480 panels 3% Cushion p!g Oscillating Frequency Irad/si
Fi'ure 7: Phase of aircush/on pressure variations
Contrary, the original potential formulation exhibits sharp
variation peaks around 5.90 rad/s and 7.50 rad/s. These peaks are not present in the experimental results and encouraged a further investigation into numerical effects happening around
these frequencies. For this reason CFD computations were
performed and the potential method was modified to take into
account additional damping of the cushion panels.
Results of the potential method show that the intensity and
position of the peaks is affected by the mesh resolution which indicates that they are originated by cushion panel resonance. For high frequency oscillations larger than 7.40 rad/s, the potential calculations tend to underestimate the amplitude of the
air pressure variations.
6 Copyright © 2009 by ASME
2.00 3.00 4.00 5.00 6.00 700 8.00 9 00 Oscillating Frequency [radlsl
Fi'ure 6: RAO of aircushion pressure variations
Phase of Aircushion Pressure Variations
0 5 10 15 20 25
Time [seci
Fi'ure 4: Time
trace of the internal pressure
inside theaircush/on computed by CFD for heave oscillations of 1 cm at a frequency of 5.8 rad/s
3D POTENTIAL METHOD
Both the structure and the free surface inside each aircushion are modelled by panels. Two different panel models are constructed to show the influence of the panel size on the
results. In both cases the structure is modelled by 364 panels,
while the number of panels on the free surface inside the
cushion is either equal to 120 or 480 panels. Figure 5 shows the model with 120 cushion panels.
A third potential computation was performed in which 3% of the critical damping was added to the cushion panels. In this case the structure and cushion were modeled by 364 and 120 panels
respectively. 10 201 -50 a, -80 C, in -110
r
a. -140 -170 -200The introduction of additional damping to the cushion panels, being equal to 3% of the critical damping, does not affect the general trends while the peaks are filtered out. This leads to a better agreement with model tests. Although computed
oscillation phase is in good agreement with model test data, the pressure amplitude is nevertheless still underestimated at high
frequencies.
CFD results on the other hand are in good agreement with the experimental data over the total range of frequencies, both for
phase and amplitudes of aircushion pressure variations.
Remarkably, the reduction to a 2D model does not lead to major discrepancies with the experimental results.
Added mass and damping may be retrieved from the amplitudes and phase differences of the total pressure on the structure. The total pressure on the structure is almost equal to the pressure
inside the cushion since the major part of the buoyancy is provided by the aircushion. Added mass and damping are
presented in Figure 8 and Figure 9. It can be seen that these values are sensible to the differences in phase angles as was presented in Figure 7. During post-processing of the CFD results it was seen that a small difference in the raw data may lead to an important divergence in damping and added mass values.
This explains why the agreement between experiments and computations is in some cases less good than the direct
comparison of the amplitude and phase.
As a result, the general conclusions with respect to added mass
and damping are the same as for the cushion pressure
variations. Unphysical peaks predicted by the potential
calculations are suppressed by additional damping but relatively
larger discrepancies in the results still exist at high frequencies.
CFD predictions are relatively accurate over the whole frequency range, but damping is under predicted at a frequency of 5.80
rad/s.
Heave Added Mass
2.0 1.5 1,0-z C 0. 0.0 1)0 5 04 E C
0'
0 0 Heave Damping 0 2.00 3.00 4.00 5.00 6.00 7.00 8. Ii 9)0 o Exp z 0.01 ]m) x Exp z = 0.02 [ml CFD. z = 0.01 Em) -Calc; 364+120 panels Cab: 364+440 panels - 3% Cushion damping 0 o 0 705 1.00 2.00 3.00 4.00 5.00 6.00Oscillating Frequency Irad/si
Figure 10: £40 of wave elevations inside the cushion
at(x = 0.1, y = 0.0) 0 0 7.00 8.00 9.00 7 Copyright © 2009 by ASME -0.5 OE.np;z0.0l (ml XExp:z0,02)mf1 CFD: z = 0.01 [m] -CaIc: 364+120 panels
1.0 - Cslc; 364+480 panels -3% Cushion damping Oscillating Frequency Irad/si
Figure 9: /?jQ of heave damping
It will be clear that air pressure variations inside the cushion are
the result of the motion of the structure and water motions
inside the aircushion. During model tests, wave elevations were
also measured inside the aircushion near the centre of the structure. Figure 1 showed the location of these measurements. The RAO5 of the wave elevations underneath the structure
arising from the forced heave oscillations of the structure are presented in Figure 10. Figure 11 shows the corresponding phase differences. Experimental results show relatively high
wave elevations around 6.00 and 7.50 rad/s, which are closely related to the increase of heave damping as indicated in Figure
9.
It can be seen in Figure 10 and 11 that there
is a goodagreement between both numerical methods and experimental
results at low frequencies up to 5.00 rad/s. Although the
potential method shows approximately the same trend as the
measurements at higher frequencies, there is a significant
difference in wave heights. CFD results on the other hand are fairly constant and in phase with the motion of the structure.
The peaks in the amplitude of the wave elevations are not reproduced by CFD data.
Wave Elevations Inside tile Aircushion
at (x = 0.1, y 0.0)
1.00 2 00 3.00 4.00 5.00 6.00 7.00 8 00 9.00
Oscillating Frequency Iradls]
Figure 8. RAO of heave added mass
1.4 1.2
.
0.6.
Pr
V < 0.4 0o Exp:z0.01 Imi x Exp:z=0.021m1
0.2 CFO: z = 0.01 rn] -CaIc; 364+120 panels 0.0 - CaIc. 364+480 panels -3% Cushion damping
300 240 180 07 a v 120 60 = 0 0 -60 -120
Phase of Wave Elevations Inside the Aircushlon
at (x 0.1, y = 0.0) o Exp z = 001 [ni) x Exp z = 002 (ni] CFD: z 001 [m) -CaIc; 364+120 panels -CaIc: 364+480 panels 3% Cushion dampin9
-0
0 2.00Oscillating Frequency [rad/s]
Figure 11: Phase of wave elevations inside the cushion
at(x= 0.1, y= 0.0)
The wave height in the centre of the structure is dominated by the length of the cushion. Since only two dimensional transverse sections are taken into account in the CFD computations, it is impossible to accurately predict the wave height underneath the structure in case of relatively short waves. Figure 12 shows the vertical motions of the cushion panels which are the result of the potential calculations. This figure clearly illustrates that the wave heights underneath the structure are mainly influenced by the length of the cushion, rather than the width. Due to peaks in the wave elevation in the air chamber, the radiation damping is relatively high at 5.80 and 7.40 red/s as was shown in Figure 9.
CusNon pansi motions Occiltetion mol'
Oectjlatto,i i,au-,+o1 3 +.++ ,edln
Onc011etton 9mplitede 0.01 e
RAO of vertical moto,n
-1-
III
.27 .24 .21 .11 .18 .12 .08 .88 .03 00 03 26 09 13 15 II 21 24 27 30 Figure 12: Vertical motions of cushion pane/s at 6.00 rad/s
CONCLUSION
The presented results show that the behaviour of an aircushion supported structure subjected to forced heave oscillations can be well predicted by both CFD and potential theory.
There is a good agreement between the numerical methods and experimental results for the aircushion pressure variation, added mass, damping and wave elevations inside the cushion. It was also shown that a linear relation between these quantities and the oscillation amplitude of the structure is justified.
In case of the potential method it was indicated that resonance effects of cushion panels may occur, which may efficiently be suppressed by additional damping. For aircushion supported
structures, improved potential calculations are an excellent tool to predict general trends and to obtain accurate results except
at high oscillation frequencies.
In spite of strong modelling assumptions of a 2D incompressible problem, CFD results are in good agreement with model tests. It shows that CFD can be used confidently within the complete range of oscillation frequencies. The only discrepancies with
model tests occur in the wave elevations underneath the
structure. Potential calculations show that these are dominated
by the cushion length which is not modelled in the 2D calculations. Therefore CFD emerges as a robust method allowing accurate simulations of forced heave oscillation of an
air cushion supported structure, especially for high frequencies.
The difference in computational time between CFD and the presented potential method is significant. It takes less than one
second to compute one oscillating frequency with in case
potential theory is used. Conversely an average of 18 hours of computation time is needed before a statistical significant number of periods are computed with CFD.
This shows that the choice between CFD and potential modeling is a trade-off between accuracy and computational requirements,
especially at high frequencies. Both methods are complementary
having their respective advantages and drawbacks and may be
used at different stages of the design process.
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