The main purpose of the study is to investigate the breaking wave interaction with a group of four circular cylinders. The physical process of wave breaking involves many parameters, and an accurate numerical modeling of breaking waves and the interaction with a structure remain a challenge. In the present study, the open-source computational fluid dynamics (CFD) model REEF3D is used to simulate the breaking wave interaction with multiple cylinders. The numerical model is based on the incompressible Reynolds-averaged Navier–Stokes (RANS) equations, the level set method for the free surface, and the k–ω model for turbulence. The numerical model is validated with experimental data of large-scale experiments for the free surface elevation and the breaking wave force on a single cylinder. A good agreement is obtained between the numerical results and experimental data. Two different configurations with four cylinders are examined: in-line square configuration and diamond square configuration. For both configurations, three different tank widths and four different spacings between the cylinders are investigated. The breaking wave forces on each cylinder in the group are computed for each case for the two configurations, and the results are compared with the breaking wave force on a single isolated cylinder. Furthermore, the study investigates the water surface elevations and the free surface flow features around the cylinders. For the closely spaced cylinders in a relatively narrower tank, the cylinders in both configurations experience the maximum forces lower than the maximum force on a single cylinder. But for the widely spaced cylinder in a relatively wider tank, the forces are higher and lower for the upstream cylinders and downstream cylinders, respectively, than the maximum force on a single isolated cylinder. The results of the present study show that the interference effects from the neighboring cylinders in a group strongly influence the kinematics around and the breaking wave forces on them.

References

References
1.
Sparboom
,
U.
,
Oumeraci
,
H.
,
Schmidt-Koppenhagen
,
R.
, and
Grüne
,
J.
,
2005
, “
Large-Scale Model Study on Cylinder Groups Subject to Breaking and Nonbreaking Waves
,”
Proceedings of the 5th International Symposium on Ocean Waves Measurement and Analysis
,
Madrid, Spain
,
July 3–7
, Paper No 106.
2.
Alagan Chella
,
M.
,
Tørum
,
A.
, and
Myrhaug
,
D.
,
2012
, “
An Overview of Wave Impact Forces on Offshore Wind Turbine Substructures
,”
Energy Procedia
,
20
, pp.
217
226
.
3.
Goda
,
Y.
,
Haranaka
,
S.
, and
Kitahata
,
M.
,
1966
, “
Study of Impulsive Breaking Wave Forces on Piles. Tech. Rep.
,”
Port and Harbor Research Institute, Ministry of Transport
.
4.
Sawaragi
,
T.
, and
Nochino
,
M.
,
1984
, “
Impact Forces of Nearly Breaking Waves on a Vertical Circular Cylinder
,”
Coast. Eng. J.
,
27
(
1
), pp.
249
263
.
5.
Wienke
,
J.
, and
Oumeraci
,
H.
,
2005
, “
Breaking Wave Impact Force on a Vertical and Inclined Slender Pile-Theoretical and Large-Scale Model Investigations
,”
Coast. Eng.
,
52
(
5
), pp.
435
462
.
6.
Morison
,
J. R.
,
Johnson
,
J. W.
, and
Schaaf
,
S. A.
,
1950
, “
The Force Exerted by Surface Waves on Piles
,”
J. Petrol. Technol.
,
2
(
5
), pp.
149
154
.
7.
Longuet-Higgins
,
M. S.
, and
Cokelet
,
E. D.
,
1976
, “
The Deformation of Steep Surface Waves on Water I—A Numerical Method of Computation
,”
Proc. R. Soc. Lond. Ser. A: Math. Phys. Sci.
,
350
(
1660
), pp.
1
26
.
8.
Vinje
,
T.
, and
Brevig
,
P.
,
1981
, “
Numerical Simulation of Breaking Waves
,”
Adv. Water Resour.
,
4
(
2
), pp.
77
82
.
9.
Lemos
,
C. M.
,
1992
, “
A Simple Numerical Technique for Turbulent Flows With Free Surfaces
,”
Int. J. Numer. Methods Fluids
,
15
(
2
), pp.
127
146
.
10.
Lin
,
P.
, and
Liu
,
P. L.-F.
,
1998
, “
A Numerical Study of Breaking Waves in the Surf Zone
,”
J. Fluid Mech.
,
359
, pp.
239
264
.
11.
Zhao
,
Q.
,
Armfield
,
S.
, and
Tanimoto
,
K.
,
2004
, “
Numerical Simulation of Breaking Waves by a Multi-Scale Turbulence Model
,”
Coast. Eng.
,
51
(
1
), pp.
53
80
.
12.
Xie
,
Z.
,
2013
, “
Two-Phase Flow Modelling of Spilling and Plunging Breaking Waves
,”
Appl. Math. Model.
,
37
(
6
), pp.
3698
3713
.
13.
Alagan Chella
,
M.
,
Bihs
,
H.
,
Myrhaug
,
D.
, and
Muskulus
,
M.
,
2015
, “
Breaking Characteristics and Geometric Properties of Spilling Breakers Over Slopes
,”
Coast. Eng.
,
95
, pp.
4
19
.
14.
Alagan Chella
,
M.
,
Bihs
,
H.
, and
Myrhaug
,
D.
,
2015
, “
Characteristics and Profile Asymmetry Properties of Waves Breaking Over an Impermeable Submerged Reef
,”
Coast. Eng.
,
100
, pp.
26
36
.
15.
Alagan Chella
,
M.
,
Bihs
,
H.
,
Myrhaug
,
D.
, and
Muskulus
,
M.
,
2015
, “
Hydrodynamic Characteristics and Geometric Properties of Plunging and Spilling Breakers Over Impermeable Slopes
,”
Ocean Model.
,
103
, pp.
53
72
.
16.
Bredmose
,
H.
, and
Jacobsen
,
N. G.
,
2010
, “
Breaking Wave Impacts on Offshore Wind Turbine Foundations: Focused Wave Groups and CFD
,”
Proceedings of the 29th International Conference on Ocean, Offshore and Arctic Engineering
,
Shanghai, China
,
June 6–11
.
17.
Mo
,
W.
,
Jensen
,
A.
, and
Liu
,
P. L.-F.
,
2013
, “
Plunging Solitary Wave and Its Interaction With a Slender Cylinder on a Sloping Beach
,”
Ocean Eng.
,
74
, pp.
48
60
.
18.
Choi
,
S.
,
Lee
,
K.
, and
Gudmestad
,
O.
,
2015
, “
The Effect of Dynamic Amplification Due to a Structures Vibration on Breaking Wave Impact
,”
Ocean Eng.
,
96
, pp.
8
20
.
19.
Bihs
,
H.
,
Kamath
,
A.
,
Alagan Chella
,
M.
, and
Arntsen
,
Ø. A.
,
2016
, “
Breaking Wave Interaction With Tandem Cylinders Under Different Impact Scenarios
,”
J. Waterw. Port Coast. Ocean Eng.
,
142
(
5
), p.
04016005
.
20.
Kamath
,
A.
,
Alagan Chella
,
M.
,
Bihs
,
H.
, and
Arntsen
,
Ø. A.
,
2015
, “
Evaluating Wave Forces on Groups of Three and Nine Cylinders Using a 3D Numerical Wave Tank
,”
Eng. Appl. Comput. Fluid Mech.
9
(
1
), pp.
343
354
.
21.
Kamath
,
A.
,
Bihs
,
H.
,
Alagan Chella
,
M.
, and
Arntsen
,
Ø. A.
,
2016
, “
Upstream-Cylinder and Downstream-Cylinder Influence on the Hydrodynamics of a Four-Cylinder Group
,”
J. Waterw. Port Coast. Ocean Eng.
,
142
(
4
), p.
04016002
.
22.
Mo
,
W.
,
Irschik
,
K.
,
Oumeraci
,
H.
, and
Liu
,
P. L. F.
,
2007
, “
A 3D Numerical Model for Computing Non-Breaking Wave Forces on Slender Piles
,”
J. Eng. Math.
,
58
(
1–4
), pp.
19
30
.
23.
Linton
,
C. M.
, and
Evans
,
D. V.
,
1990
, “
The Interaction of Waves With Arrays of Vertical Circular Cylinders
,”
J. Fluid Mech.
,
215
, pp.
549
569
.
24.
Apelt
,
C. J.
, and
Piorewicz
,
J.
,
1986
, “
Interference Effects on Breaking Wave Forces on Rows of Vertical Cylinders
,”
Proceedings of the 1st Australasian Port, Harbour and Offshore Engineering Conference
,
Institution of Engineers, Australia
,
Aug. 29–Sept. 2
, Paper No. 191.
25.
Irschik
,
K.
,
Sparboom
,
U.
, and
Oumeraci
,
H.
,
2002
, “
Breaking Wave Characteristics for the Loading of a Slender Pile
,”
Proceedings of the 28th Conference on Coastal Engineering
,
Cardiff, Wales
,
July 7–12
, pp.
1341
1352
.
26.
Kamath
,
A.
,
Alagan Chella
,
M.
,
Bihs
,
H.
, and
Arntsen
,
Ø. A.
,
2015
, “
CFD Investigations of Wave Interaction With a Pair of Large Tandem Cylinders
,”
Ocean Eng.
,
108
, pp.
734
748
.
27.
Alagan Chella
,
M.
,
Bihs
,
H.
,
Myrhaug
,
D.
, and
Muskulus
,
M.
,
2017
, “
Breaking Solitary Waves and Breaking Wave Forces on a Vertically Mounted Slender Cylinder Over an Impermeable Sloping Seabed
,”
J. Ocean Eng. Marine Energy
,
3
(
1
), pp.
1
19
.
28.
Alagan Chella
,
M.
,
Bihs
,
H.
, and
Myrhaug
,
D.
,
2019
, “
Wave Impact Pressure and Kinematics Due to Breaking Wave Impingement on a Monopile
,”
J. Fluids Struct.
,
86
, pp.
94
123
.
29.
Jiang
,
G. S.
, and
Shu
,
C. W.
,
1996
, “
Efficient Implementation of Weighted ENO Schemes
,”
J. Comput. Phys.
,
126
(
1
), pp.
202
228
.
30.
Shu
,
C. W.
, and
Osher
,
S.
,
1988
, “
Efficient Implementation of Essentially Non-Oscillatory Shock Capturing Schemes
,”
J. Comput. Phys.
,
77
(
2
), pp.
439
471
.
31.
Griebel
,
M.
,
Dornseifer
,
T.
, and
Neunhoeffer
,
T.
,
1998
,
Numerical Simulation in Fluid Dynamics: A Practical Introduction
, Vol.
3
,
SIAM
, pp.
21
48
.
32.
van der Vorst
,
H.
,
1992
, “
Bi-CGSTAB: A Fast and Smoothly Converging Variant of Bi-CG for the Solution of Nonsymmetric Linear Systems
,”
SIAM J. Sci. Stat. Comput.
,
13
pp.
631
644
.
33.
Chorin
,
A.
,
1968
, “
Numerical Solution of the Navier–Stokes Equations
,”
Math. Comput.
,
22
(
104
), pp.
745
762
.
34.
Sussman
,
M.
,
Smereka
,
P.
, and
Osher
,
S.
,
1994
, “
A Level Set Approach for Computing Solutions to Incompressible Two-Phase Flow
,”
J. Comput. Phys.
,
114
(
1
), pp.
146
159
.
35.
Peng
,
D.
,
Merriman
,
B.
,
Osher
,
S.
,
Zhao
,
H.
, and
Kang
,
M.
,
1999
, “
A PDE-Based Fast Local Level Set Method
,”
J. Comput. Phys.
,
155
(
2
), pp.
410
438
.
36.
Durbin
,
P. A.
,
2009
, “
Limiters and Wall Treatments in Applied Turbulence Modeling
,”
Fluid Dyn. Res.
,
41
(
1
), pp.
1
18
.
37.
Naot
,
D.
, and
Rodi
,
W.
,
1982
, “
Calculation of Secondary Currents in Channel Flow
,”
J. Hydraul. Div. ASCE
,
108
(
8
), pp.
948
968
.
38.
Larsen
,
J.
, and
Dancy
,
H.
,
1983
, “
Open Boundaries in Short Wave Simulations—A New Approach
,”
Coast. Eng.
,
7
(
3
), pp.
285
297
.
39.
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
.
40.
Miquel
,
A. M.
,
Kamath
,
A.
,
Alagan Chella
,
M.
, and
Bihs
,
H.
,
2018
, “
Analysis of Different Methods for Wave Generation and Absorption in a CFD-Based Numerical Wave Tank
,”
J. Marine Sci. Eng.
,
6
(
2
), pp.
1
21
.
41.
Kamath
,
A.
,
Alagan Chella
,
M.
,
Bihs
,
H.
, and
Arntsen
,
Ø. A.
,
2016
, “
Breaking Wave Interaction With a Vertical Cylinder and the Effect of Breaker Location
,”
Ocean Eng.
,
128
, pp.
105
115
.
42.
Alagan Chella
,
M.
,
Bihs
,
H.
,
Myrhaug
,
D.
, and
Muskulus
,
M.
,
2017
, “
Breaking Solitary Waves and Breaking Wave Forces on a Vertically Mounted Slender Cylinder Over an Impermeable Sloping Seabed
,”
J. Ocean Eng. Marine Energy
,
3
(
1
), pp.
1
19
.
43.
Schäffer
,
H. A.
, and
Klopman
,
G.
,
2000
, “
Review of Multidirectional Active Wave Absorption Methods
,”
J. Waterw. Port Coast. Ocean Eng.
,
126
(
2
), pp.
88
97
.
44.
Berthelsen
,
P. A.
, and
Faltinsen
,
O. M.
,
2008
, “
A Local Directional Ghost Cell Approach for Incompressible Viscous Flow Problems With Irregular Boundaries
,”
J. Comput. Phys.
,
227
(
9
), pp.
4354
4397
.
45.
NOTUR
,
2015
, “
The Norwegian Metacenter for Computational Science
,” http://www.notur.no/hardware/vilje
46.
Fenton
,
J.
,
1985
, “
A Fifth-Order Stokes Theory for Steady Waves
,”
J. Waterw. Port Coast. Ocean Eng.
,
111
(
2
), pp.
216
234
.
47.
Hildebrandt
,
A.
,
Sparboom
,
U.
, and
Oumeraci
,
H.
,
2008
, “
Wave Forces on Groups of Slender Cylinders in Comparison to an Isolated Cylinder Due to Non-Breaking Waves
,”
Proceedings of the 31st Conference on Coastal Engineering
,
Hamburg, Germany
,
Aug. 31–Sept. 5
, pp.
3770
3781
.
You do not currently have access to this content.