Abstract

A porous-media-tuned liquid damper (PMTLD) can serve as an effective and economical dynamic vibration absorber. Placing porous media within a water tank can improve the capacity for energy dissipation and optimize the performance by varying its material properties. Two numerical models are adopted to simulate the sloshing problem in PMTLD and the dynamics of a floating platform in waves. Besides, the effectiveness of response mitigation can be verified numerically. The first potential-based approach employs a mixed-type boundary value problem (BVP) solver and a free-surface particle tracker. This approach not only simulates the inviscid water wave but also includes the nonlinear damping of the PMTLD via a quadratic Forchheimer term. Another equivalent mechanical model is used to reduce the degree-of-freedom of the PMTLD system. The Newmark method is incorporated to solve the rigid-body dynamics. The second viscous approach uses the finite element method (FEM) to spatially discretize the Navier–Stokes (NS) equations and handles the free surface via the volume of fluid (VOF) and the level set (LS) equations. The multiphase simulation is implemented by computational modeling toolkits, Proteus and Chrono, for the fluid and solid phases, respectively. The correlations between potential flow and two-phase NS models are presented. The PMTLD is designed by analogy with the tuned mass damper (TMD). Numerical results show that the PMTLD can effectively reduce the structure's dynamic response in terms of vibration amplitude around resonance. Such damping devices have great potential for offshore platforms and wind turbine design.

References

1.
Burger
,
W.
, and
Corbet
,
A. G.
,
1966
, “Chapter III—Anti-Rolling Devices in General,”
Ship Stabilizers: A Handbook for Merchant Navy Officers
,
Pergamon Press
,
Oxford, UK
, pp.
31
37
.
2.
Chen
,
Y. H.
, and
Ko
,
C. H.
,
2003
, “
Active Tuned Liquid Column Damper With Propellers
,”
Earthquake Eng. Struct. Dyn.
,
32
(
10
), pp.
1627
1638
.
3.
Yalla
,
S. K.
,
Kareem
,
A.
, and
Kantor
,
J. C.
,
2001
, “
Semi-Active Tuned Liquid Column Dampers for Vibration Control of Structures
,”
Eng. Struct.
,
23
(
11
), pp.
1469
1479
.
4.
Marzouk
,
O. A.
, and
Nayfeh
,
A. H.
,
2009
, “
Control of Ship Roll Using Passive and Active Anti-Roll Tanks
,”
Ocean Eng.
,
36
(
9–10
), pp.
661
671
.
5.
Gattulli
,
V.
, and
Ghanem
,
R.
,
1999
, “
Adaptive Control of Flow-Induced Oscillations Including Vortex Effects
,”
Int. J. Non Linear Mech.
,
34
(
5
), pp.
853
868
.
6.
Kawano
,
K.
,
1993
, “
Active Control Effects on Dynamic Response of Offshore Structures
,”
Proceedings of the 3rd International Offshore and Polar Engineering Conference
,
Singapore
,
June 6–11
, pp.
594
598
.
7.
Lee
,
H. H.
,
Wong
,
S. H.
, and
Lee
,
R. S.
,
2006
, “
Response Mitigation on the Offshore Floating Platform System With Tuned Liquid Column Damper
,”
Ocean Eng.
,
33
(
8–9
), pp.
1118
1142
.
8.
Bossanyi
,
E. A.
,
2000
, “
The Design of Closed Loop Controllers for Wind Turbines
,”
Wind Energy
,
3
(
3
), pp.
149
163
.
9.
Andersen
,
P. B.
,
Henriksen
,
L.
,
Gaunaa
,
M.
,
Bak
,
C.
, and
Buhl
,
T.
,
2010
, “
Deformable Trailing Edge Flaps for Modern Megawatt Wind Turbine Controllers Using Strain Gauge Sensors
,”
Wind Energy
,
13
(
2–3
), pp.
193
206
.
10.
Castaignet
,
D.
,
Barlas
,
T. K.
,
Buhl
,
T.
,
Poulsen
,
N. K.
,
Wedel-Heinen
,
J. J.
,
Olesen
,
N. A.
,
Bak
,
C.
, and
Kim
,
T.
,
2013
, “
Full-Scale Test of Trailing Edge Flaps on a Vestas V27 Wind Turbine: Active Load Reduction and System Identification
,”
Wind Energy
,
17
(
4
), pp.
549
564
.
11.
Rahman
,
M.
,
Ong
,
Z. C.
,
Chong
,
W. T.
,
Julai
,
S.
, and
Khoo
,
S. Y.
,
2015
, “
Performance Enhancement of Wind Turbine Systems With Vibration Control: A Review
,”
Renewable Sustainable Energy Rev.
,
51
, pp.
43
54
.
12.
Stewart
,
G.
, and
Lackner
,
M.
,
2013
, “
Offshore Wind Turbine Load Reduction Employing Optimal Passive Tuned Mass Damping Systems
,”
IEEE Trans. Control Syst. Technol.
,
21
(
4
), pp.
1090
1104
.
13.
Si
,
Y.
,
Karimi
,
H. R.
, and
Gao
,
H.
,
2014
, “
Modelling and Optimization of a Passive Structural Control Design for a Spar-Type Floating Wind Turbine
,”
Eng. Struct.
,
69
, pp.
168
182
.
14.
Dinh
,
V. N.
, and
Basu
,
B.
,
2014
, “
Passive Control of Floating Offshore Wind Turbine Nacelle and Spar Vibrations by Multiple Tuned Mass Dampers
,”
Struct. Control Health Monit.
,
22
(
1
), pp.
152
176
.
15.
Colwell
,
S.
, and
Basu
,
B.
,
2009
, “
Tuned Liquid Column Dampers in Offshore Wind Turbines for Structural Control
,”
Eng. Struct.
,
31
(
2
), pp.
358
368
.
16.
Tong
,
X.
,
Zhao
,
X.
, and
Karcanias
,
A.
,
2018
, “
Passive Vibration Control of an Offshore Floating Hydrostatic Wind Turbine Model
,”
Wind Energy
,
21
(
9
), pp.
697
714
.
17.
Chen
,
J.
,
Zhan
,
G.
, and
Zhao
,
Y.
,
2016
, “
Application of Spherical Tuned Liquid Damper in Vibration Control of Wind Turbine due to Earthquake Excitations
,”
Struct. Des. Tall Special Build.
,
25
(
10
), pp.
431
443
.
18.
Martynowicz
,
P.
,
2015
, “
Vibration Control of Wind Turbine Tower-Nacelle Model With Magnetorheological Tuned Vibration Absorber
,”
J. Vib. Control
,
23
(
20
), pp.
3468
3489
.
19.
Martynowicz
,
P.
,
2017
, “
Control of a Magnetorheological Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined Force Tracking Algorithm
,”
J. Low Freq. Noise Vib. Act. Control
,
36
(
4
), pp.
339
353
.
20.
Staino
,
A.
,
Basu
,
B.
, and
Nielsen
,
S.
,
2012
, “
Actuator Control of Edgewise Vibrations in Wind Turbine Blades
,”
J. Sound Vib.
,
331
(
6
), pp.
1233
1256
.
21.
Chen
,
Y. H.
,
Hwang
,
W. S.
, and
Tsao
,
W. H.
,
2018
, “
Nonlinear Dynamic Characteristics of Rectangular and Cylindrical TLD’s
,”
J. Eng. Mech.
,
144
(
9
), p.
06018004
.
22.
Zahrai
,
S. M.
,
Abbasi
,
S.
,
Samali
,
B.
, and
Vrcelj
,
Z.
,
2012
, “
Experimental Investigation of Utilizing TLD With Baffles in a Scaled Down 5-Story Benchmark Building
,”
J. Fluids Struct.
,
28
, pp.
194
210
.
23.
Warnitchai
,
P.
, and
Pinkaew
,
T.
,
1998
, “
Modelling of Liquid Sloshing in Rectangular Tanks With Flow-Dampening Devices
,”
Eng. Struct.
,
20
(
7
), pp.
293
600
.
24.
Faltinsen
,
O. M.
,
Firoozkoohi
,
R.
, and
Timokha
,
A. N.
,
2011
, “
Analytical Modeling of Liquid Sloshing in a Two-Dimensional Rectangular Tank With a Slat Screen
,”
J. Eng. Math.
,
70
(
1–3
), pp.
93
109
.
25.
Hamelin
,
J. A.
,
Love
,
J. S.
,
Tait
,
M. J.
, and
Wison
,
J. C.
,
2013
, “
Tuned Liquid Dampers With a Keulegan-Carpenter Number-Dependent Screen Drag Coefficient
,”
J. Fluids Struct.
,
43
, pp.
271
286
.
26.
Tait
,
M. J.
,
2008
, “
Modelling and Preliminary Design of a Structure-TLD System
,”
Eng. Struct.
,
30
(
10
), pp.
2644
2655
.
27.
Tsao
,
W. H.
, and
Hwang
,
W. S.
,
2018
, “
Tuned Liquid Dampers With Porous Media
,”
Ocean Eng.
,
167
, pp.
55
64
.
28.
Tsao
,
W. H.
, and
Hwang
,
W. S.
,
2019
, “
Dynamic Characteristics of Liquid Sloshing in Cylindrical Tanks Filled With Porous Media
,”
IOP Conf. Ser. Earth Environ. Sci.
,
351
, p.
012007
.
29.
Tsao
,
W. H.
, and
Chang
,
T. J.
,
2020
, “
Sloshing Phenomenon in Rectangular and Cylindrical Tanks Filled With Porous Media: Supplementary Solution and Impulsive-Excitation Experiment
,”
J. Eng. Mech.
,
146
(
12
), p.
04020139
.
30.
Tsao
,
W. H.
, and
Huang
,
Y. L.
,
2021
, “
Sloshing Force in a Rectangular Tank With Porous Media
,”
Results Eng.
,
11
, p.
100250
.
31.
Tsao
,
W. H.
,
Huang
,
L. H.
, and
Hwang
,
W. S.
,
2021
, “
An Equivalent Mechanical Model With Nonlinear Damping for Sloshing Rectangular Tank With Porous Media
,”
Ocean Eng.
,
242
, p.
110145
.
32.
Grilli
,
S. T.
,
Skourup
,
J.
, and
Svendsen
,
I. A.
,
1989
, “
An Efficient Boundary Element Method for Nonlinear Water Waves
,”
Eng. Anal. Boundary Elem.
,
6
(
2
), pp.
97
107
.
33.
Grilli
,
S. T.
, and
Horrillo
,
J.
,
1997
, “
Numerical Generation and Absorption of Fully Nonlinear Periodic Waves
,”
J. Eng. Mech.
,
123
(
10
), pp.
1060
1069
.
34.
Chen
,
Y. H.
,
Hwang
,
W. S.
, and
Tsao
,
W. H.
,
2017
, “
Nonlinear Sloshing Analysis by Regularized Boundary Integral Method
,”
J. Eng. Mech.
,
143
(
8
), p.
040170046
.
35.
Sen
,
D.
,
1993
, “
Numerical Simulation of Motions of Two-Dimensional Floating Bodies
,”
J. Ship Res.
,
37
(
4
), pp.
307
330
.
36.
Van Daalen
,
E. F. G.
,
1993
, “
Numerical and Theoretical Studies of Water Waves and Floating Bodies
,”
Ph.D. thesis
,
Universiteit Twente
,
The Netherlands
.
37.
Tanizawa
,
K.
,
1995
, “
A Nonlinear Simulation Method of 3D Body Motions in Waves
,”
J. Soc. Nav. Archit. Jpn.
,
178
, pp.
179
191
.
38.
Hermans
,
A. J.
,
2000
, “
A Boundary Element Method for the Interaction of Free-Surface Waves With a Very Large Floating Flexible Platform
,”
J. Fluids Struct.
,
14
(
7
), pp.
943
956
.
39.
Koo
,
W.
, and
Kim
,
M. H.
,
2004
, “
Freely Floating-Body Simulation by a 2D Fully Nonlinear Numerical Wave Tank
,”
Ocean Eng.
,
31
(
16
), pp.
2011
2046
.
40.
Jung
,
K. H.
,
Chang
,
K. A.
, and
Jo
,
H. J.
,
2006
, “
Viscous Effect on the Roll Motion of a Rectangular Structure
,”
J. Eng. Mech.
,
132
(
2
), pp.
190
200
.
41.
Kim
,
Y.
,
Nam
,
B. W.
,
Kim
,
D. W.
, and
Kim
,
Y. S.
,
2007
, “
Study on Coupling Effects of Ship Motion and Sloshing
,”
Ocean Eng.
,
34
(
16
), pp.
2176
2187
.
42.
Guerber
,
E.
,
Benoit
,
M.
,
Grilli
,
S. T.
, and
Buvat
,
C.
,
2012
, “
A Fully Nonlinear Implicit Model for Wave Interactions With Submerged Structures in Forced or Free Motion
,”
Eng. Anal. Boundary Elem.
,
36
(
7
), pp.
1151
1163
.
43.
Dombre
,
E.
,
Benoit
,
M.
,
Violeau
,
D.
,
Peyrard
,
C.
, and
Grilli
,
S. T.
,
2015
, “
Simulation of Floating Structure Dynamics in Waves by Implicit Coupling of a Fully Non-Linear Potential Flow Model and a Rigid Body Motion Approach
,”
J. Ocean Eng. Mar. Energy
,
1
(
1
), pp.
55
76
.
44.
Vinje
,
T.
, and
Brevig
,
P.
,
1981
, “
Nonlinear, Two-Dimensional Ship Motions
,” Technical Report of the Norwegian Institute of Technology, R-112.81.
45.
Belibassakis
,
K. A.
,
2008
, “
A Boundary Element Method for the Hydrodynamic Analysis of Floating Bodies in Variable Bathymetry Regions
,”
Eng. Anal. Boundary Elem.
,
32
(
10
), pp.
796
810
.
46.
Wu
,
G. X.
, and
Eatock-Taylor
,
R.
,
1996
, “
Transient Motion of a Floating Body in Steep Water Waves
,”
Proceedings of the 11th International Workshop on Water Waves and Floating Bodies
,
Hamburg, Germany
,
Mar. 17–20
.
47.
Piperno
,
S.
,
Farhat
,
C.
, and
Larrouturou
,
B.
,
1995
, “
Partitioned Procedures for the Transient Solution of Coupled Aeroelastic Problems Part I: Model Problem, Theory and Two-Dimensional Application
,”
Comput. Methods Appl. Mech. Eng.
,
124
(
1–2
), pp.
79
112
.
48.
Farhat
,
C.
, and
Lesoinne
,
M.
,
2000
, “
Two Efficient Staggered Algorithms for the Serial and Parallel Solution of Three-Dimensional Nonlinear Transient Aeroelastic Problems
,”
Comput. Methods Appl. Mech. Eng.
,
182
(
3–4
), pp.
499
515
.
49.
Guermond
,
J. L.
,
Minev
,
P.
, and
Shen
,
J.
,
2006
, “
An Overview of Projection Methods for Incompressible Flows
,”
Comput. Methods Appl. Mech. Eng.
,
195
(
44–47
), pp.
6011
6045
.
50.
Matthies
,
H. G.
,
Niekamp
,
R.
, and
Steindorf
,
J.
,
2006
, “
Algorithms for Strong Coupling Procedures
,”
Comput. Methods Appl. Mech. Eng.
,
195
(
17–18
), pp.
2028
2049
.
51.
Rodrigues
,
M. V.
,
Correa
,
F. N.
, and
Jacob
,
B. P.
,
2007
, “
Implicit Domain Decomposition Methods for Coupled Analysis of Offshore Platforms
,”
Commun. Numer. Methods Eng.
,
23
(
6
), pp.
599
621
.
52.
Palm
,
J.
,
Eskilsson
,
C.
,
Paredes
,
G. M.
, and
Bergdahl
,
L.
,
2016
, “
Coupled Mooring Analysis of Floating Wave Energy Converters Using CFD: Formulation and Validation
,”
Int. J. Mar. Energy
,
16
, pp.
83
99
.
53.
Tezduyar
,
T. E.
,
2001
, “
Finite Element Methods for Flow Problems With Moving Boundaries and Interfaces
,”
Comput. Meth. Eng.
,
8
(
2
), pp.
83
130
.
54.
Karimirad
,
M.
,
Michailides
,
C.
, and
Nematbakhsh
,
A.
,
2018
,
Offshore Mechanics: Structural and Fluid Dynamics for Recent Applications
,
Wiley
,
UK
.
55.
Osher
,
S.
, and
Sethian
,
J. A.
,
1988
, “
Fronts Propagating With Curvature-Dependent Speed: Algorithms Based on Hamilton-Jacobi Formulations
,”
J. Comput. Phys.
,
79
(
1
), pp.
12
49
.
56.
Osher
,
S.
, and
Fedkiw
,
R.
,
2003
,
Level Set Methods and Dynamic Implicit Surfaces: Applied Mathematical Sciences
, Vol.
153
.
Springer-Verlag
,
New York
.
57.
Mittal
,
R.
, and
Iaccarino
,
G.
,
2005
, “
Immersed Boundary Methods
,”
Annu. Rev. Fluid Mech.
,
37
(
1
), pp.
239
261
.
58.
Molin
,
B.
,
2011
, “
Hydrodynamic Modeling of Perforated Structures
,”
Appl. Ocean Res.
,
33
(
1
), pp.
1
11
.
59.
Mackay
,
E.
,
Liang
,
H.
, and
Johanning
,
L.
,
2021
, “
A BEM Model for Wave Forces on Structures With Thin Porous Elements
,”
J. Fluids Struct.
,
102
, p.
103246
.
60.
Liang
,
H.
,
Zheng
,
S.
,
Magee
,
A.
, and
Greaves
,
D.
,
2022
, “
Water Wave Interactions With Perforated Elastic Disks: Quadratic Pressure Discharge Condition
,”
Phys. Rev. Fluids
,
7
(
5
), p.
054802
.
61.
Proteus: Computational Methods and Simulation Toolkit
,” http://proteustoolkit.org.
62.
Tasora
,
A.
,
Serban
,
R.
,
Mazhar
,
H.
,
Pazouki
,
A.
,
Melanz
,
D.
,
Fleischmann
,
J.
,
Taylor
,
M.
,
Sugiyama
,
H.
, and
Negrut
,
D.
,
2016
,
Chrono: An Open Source Multi-Physics Dynamics Engine, High Performance Computing in Science and Engineering—Lecture Notes in Computer Science
,
Springer
,
New York
.
63.
Nield
,
A. D.
, and
Bejan
,
A.
,
2013
,
Convection in Porous Media
, 4th ed.,
Springer
,
New York
.
64.
Beavers
,
G. S.
, and
Joseph
,
D. D.
,
1967
, “
Boundary Conditions at a Naturally Permeable Wall
,”
J. Fluid Mech.
,
30
(
1
), pp.
197
207
.
65.
Steiros
,
K.
,
Kokmanian
,
K.
,
Bempedelis
,
N.
, and
Hultmark
,
M.
,
2020
, “
The Effect of Porosity on the Drag of Cylinders
,”
J. Fluid Mech.
,
901
, p.
R2
.
66.
Xu
,
Y. P.
,
Liu
,
J. Y.
,
Chai
,
X. W.
, and
Shi
,
S. S.
,
2022
, “
Experimental Study on Measurement of Drag Coefficient of Sandy Soil Nonlinear Vadose
,”
Adv. Civil Eng.
,
2022
, p.
8104842
.
67.
Clément
,
A.
,
1996
, “
Coupling of Two Absorbing Boundary Conditions for 2D Time-Domain Simulations of Free Surface Gravity Waves
,”
J. Comput. Phys.
,
126
(
1
), pp.
139
151
.
68.
Bazilevs
,
Y.
,
Calo
,
V. M.
,
Cottrel
,
J. A.
,
Hughes
,
T. J. R.
,
Reali
,
A.
, and
Scovazzi
,
G.
,
2007
, “
Variational Multiscale Residual-Based Turbulence Modeling for Large Eddy Simulation of Incompressible Flows
,”
Comput. Methods Appl. Mech. Eng.
,
197
(
1–4
), pp.
173
201
.
69.
Kees
,
C. E.
,
Akkerman
,
I.
,
Farthing
,
M. W.
, and
Bazilevs
,
Y.
,
2011
, “
A Conservative Level Set Method Suitable for Variable-Order Approximations and Unstructured Meshes
,”
J. Comput. Phys.
,
230
(
12
), pp.
4536
4558
.
70.
Peskin
,
C. S.
,
1977
, “
Numerical Analysis of Blood Flow in the Heart
,”
J. Comput. Phys.
,
25
(
3
), pp.
220
252
.
71.
Ursell
,
F.
,
Dean
,
R. G.
, and
Yu
,
Y. S.
,
1960
, “
Forced Small-Amplitude Water Waves: A Comparison of Theory and Experiment
,”
J. Fluid Mech.
,
7
(
1
), pp.
33
52
.
72.
Jacobsen
,
N. G.
,
Fuhrman
,
D. R.
, and
Fredsøe
,
J.
,
2012
, “
A Wave Generation Toolbox for the Open-Source CFD Library: OpenFoam
,”
Int. J. Numer. Methods Fluids
,
70
(
9
), pp.
1073
1088
.
73.
Dimakopoulos
,
A. S.
,
de Lataillade
,
T.
, and
Kees
,
C. E.
,
2019
, “
Fast Random Wave Generation in Numerical Tanks
,”
Eng. Comput. Mech.
,
172
(
1
), pp.
1
11
.
74.
Den Hartog
,
J. P.
,
1956
,
Mechanical Vibrations
, 4th ed.,
McGraw-Hill
,
New York
.
75.
Soong
,
T. T.
, and
Dargush
,
G. F.
,
1997
,
Passive Energy Dissipation Systems in Structural Engineering
,
Wiley
,
New York
.
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