Recently, the concept of a vessel-shaped fish farm was proposed for open sea applications. The fish farm comprises a vessel-shaped floater, five fish cages, and a single-point mooring system. Such a system weathervanes, and this feature increases the spread area of fish waste. Still, the downstream cages may experience decreased exchange of water flow when the vessel heading is aligned with the current direction, and fish welfare may be jeopardized. To ameliorate the flow conditions, a dynamic positioning (DP) system may be required, and its power consumption should relate to the heading misalignment. This paper proposes an integrated method for predicting the heading misalignment between the vessel-shaped fish farm and the currents under combined waves and currents. A numerical model is first established for the fish farm system with flexible nets. Current reduction factors are included to address the reduction in flow velocity between net panels. The vessel heading is obtained by finding the equilibrium condition of the whole system under each combined wave and current condition. Then, the Kriging metamodel is applied to capture the relation between the misalignment angle and environmental variables, and the probability distribution of this misalignment angle is estimated for a reference site. Finally, the requirement for the DP system to improve the flow condition in the fish cages is discussed.

References

References
1.
Burnell
,
G.
, and
Geoff
,
A.
, eds.,
2009
,
New Technologies in Aquaculture: Improving Production Efficiency, Quality and Environmental Management
,
Elsevier
,
Cambridge, UK
, pp.
895
913
.
2.
SalMar Group
,
2016
, “
Offshore Fish Farming—A New Era in Fish Farming is on Its Way
,” Kverva, Trondheim, Norway, accessed Oct. 7, 2017, http://www.salmar.no/en/offshore-fish-farming-a-new-era
3.
Berge
,
A.
,
2017
, “
Today, ‘Ocean Farm 1’ comes to Froya
,” Frøya, Norway, accessed Oct. 20, 2017, http://salmonbusiness.com/today-ocean-farm-1-comes-to-froya/
4.
Li
,
L.
, and
Ong
,
M. C.
,
2017
, “
A Preliminary Study of a Rigid Semi-Submersible Fish Farm for Open Seas
,”
ASME
Paper No. OMAE2017-61520.
5.
Nordlaks, 2018, “
Havfarm
,” Nordlaks, Stokmarknes, Norway, accessed Feb. 10, 2018, http://www.nordlaks.no/Havfarmene
6.
Li
,
L.
,
Jiang
,
Z.
, and
Ong
,
M. C.
,
2017
, “
A Preliminary Study of a Vessel-Shaped Offshore Fish Farm Concept
,”
ASME
Paper No. OMAE2017-61665.
7.
Li
,
L.
,
Jiang
,
Z.
,
Høiland
,
A. V.
, and
Ong
,
M. C.
,
2018
, “
Numerical Analysis of a Vessel-Shaped Offshore Fish Farm
,”
ASME J. Offshore Mech. Arct. Eng.
,
140
(
4
), p.
041201
.
8.
Klebert
,
P.
,
Lader
,
P.
,
Gansel
,
L.
, and
Oppedal
,
F.
,
2013
, “
Hydrodynamic Interactions on Net Panel and Aquaculture Fish Cages: A Review
,”
Ocean Eng.
,
58
, pp.
260
274
.
9.
Klebert
,
P.
,
Patursson
,
Ø.
,
Endresen
,
P. C.
,
Rundtop
,
P.
,
Birkevold
,
J.
, and
Rasmussen
,
H. W.
,
2015
, “
Three-Dimensional Deformation of a Large Circular Flexible Sea Cage in High Currents: Field Experiment and Modeling
,”
Ocean Eng.
,
104
, pp.
511
520
.
10.
Gansel
,
L. C.
,
Rackebrandt
,
S.
,
Oppedal
,
F.
, and
McClimans
,
T. A.
,
2014
, “
Flow Fields Inside Stocked Fish Cages and the Near Environment
,”
ASME J. Offshore Mech. Arct. Eng.
,
136
(
3
), p.
031201
.
11.
Bi
,
C.-W.
,
Zhao
,
Y.-P.
,
Dong
,
G.-H.
,
Xu
,
T.-J.
, and
Gui
,
F.-K.
,
2013
, “
Experimental Investigation of the Reduction in Flow Velocity Downstream From a Fishing Net
,”
Aquacultural Eng.
,
57
, pp.
71
81
.
12.
Gansel
,
L. C.
,
McClimans
,
T. A.
, and
Myrhaug
,
D.
,
2012
, “
Flow Around the Free Bottom of Fish Cages in a Uniform Flow With and Without Fouling
,”
ASME J. Offshore Mech. Arct. Eng.
,
134
(
1
), p.
011501
.
13.
Moe-Føre
,
H.
,
Lader
,
P.
,
Lien
,
E.
, and
Hopperstad
,
O.
,
2016
, “
Structural Response of High Solidity Net Cage Models in Uniform Flow
,”
J. Fluids Struct.
,
65
, pp.
180
195
.
14.
MARINTEK
,
2015
, “
SIMO—Theory Manual Version 4.6
,”
Marintek
,
Trondheim, Norway
, pp.
6
126
.
15.
MARINTEK
,
2015
, “
RIFLEX Theory Manual Version 4.6
,”
Marintek
,
Trondheim, Norway
, pp.
3
107
.
16.
MARINTEK
,
2016
,
Modelling of Aquaculture Net Cages in SIMA
,
Marintek
,
Trondheim, Norway
, pp.
4
21
.
17.
DNV
,
2008
, “
Wadam Theory Manual
,”
Det Norske Veritas
,
Oslo, Norway
, pp.
7
79
.
18.
Tian
,
X.
,
Ong
,
M. C.
,
Yang
,
J.
, and
Myrhaug
,
D.
,
2014
, “
Large-Eddy Simulation of the Flow Normal to a Flat Plate Including Corner Effects at a High Reynolds Number
,”
J. Fluids Struct.
,
49
, pp.
149
169
.
19.
DNV
,
2010
, “
Environmental Conditions and Environmental Loads: Recommended Practice
,”
Det Norske Veritas
,
Oslo, Norway
, Standard No.
DNV-RP-C205
.https://www.dnvgl.com/oilgas/download/dnvgl-rp-c205-environmental-conditions-and-environmental-loads.html
20.
Løland
,
G.
,
1993
, “
Current Forces on, and Water Flow Through and Around, Floating Fish Farms
,”
Aquaculture Int.
,
1
(
1
), pp.
72
89
.
21.
Lader
,
P. F.
, and
Enerhaug
,
B.
,
2005
, “
Experimental Investigation of Forces and Geometry of a Net Cage in Uniform Flow
,”
IEEE J. Oceanic Eng.
,
30
(
1
), pp.
79
84
.
22.
Wang
,
G. G.
, and
Shan
,
S.
,
2007
, “
Review of Metamodeling Techniques in Support of Engineering Design Optimization
,”
ASME J. Mech. Des.
,
129
(
4
), pp.
370
380
.
23.
Jiang
,
Z.
, and
Gu
,
M.
,
2010
, “
Optimization of a Fender Structure for the Crashworthiness Design
,”
Mater. Des.
,
31
(
3
), pp.
1085
1095
.
24.
Li
,
L.
,
Jiang
,
Z.
, and
Ong
,
M. C.
,
2018
, “
Design Optimization of Mooring System: An Application to a Vessel-Shaped Offshore Fish Farm
,”
Eng. Struct.
(under review).
25.
Simpson
,
T. W.
,
Lin
,
D. K.
, and
Chen
,
W.
,
2001
, “
Sampling Strategies for Computer Experiments: Design and Analysis
,”
Int. J. Reliab. Appl.
,
2
(
3
), pp.
209
240
.http://www.personal.psu.edu/users/j/x/jxz203/lin/Lin_pub/2001_IJRA.pdf
26.
McKay
,
M. D.
,
Beckman
,
R. J.
, and
Conover
,
W. J.
,
2000
, “
A Comparison of Three Methods for Selecting Values of Input Variables in the Analysis of Output From a Computer Code
,”
Technometrics
,
42
(
1
), pp.
55
61
.
27.
Cressie
,
N.
,
1988
, “
Spatial Prediction and Ordinary Kriging
,”
Math. Geol.
,
20
(
4
), pp.
405
421
.
28.
Papadrakakis
,
M.
,
Lagaros
,
N. D.
, and
Tsompanakis
,
Y.
,
1998
, “
Structural Optimization Using Evolution Strategies and Neural Networks
,”
Comput. Methods Appl. Mech. Eng.
,
156
(
1–4
), pp.
309
333
.
29.
Dyn
,
N.
,
Levin
,
D.
, and
Rippa
,
S.
,
1986
, “
Numerical Procedures for Surface Fitting of Scattered Data by Radial Functions
,”
SIAM J. Sci. Stat. Comput.
,
7
(
2
), pp.
639
659
.
30.
De Boor
,
C.
, and
Ron
,
A.
,
1990
, “
On Multivariate Polynomial Interpolation
,”
Constructive Approximation
,
6
(
3
), pp.
287
302
.
31.
Wang
,
J.
,
Li
,
L.
,
Jakobsen
,
J. B.
, and
Haver
,
S. K.
,
2019
, “
Metocean Conditions in a Norwegian Fjord in Relation to the Floating Bridge Design
,”
ASME J. Offshore Mech. Arct. Eng.
,
141
(
2
), p.
021604
.
32.
Turner
,
A. A.
,
Jeans
,
T. L.
, and
Reid
,
G. K.
,
2016
, “
Experimental Investigation of Fish Farm Hydrodynamics on 1:15 Scale Model Square Aquaculture Cages
,”
ASME J. Offshore Mech. Arct. Eng.
,
138
(
6
), p.
061201
.
33.
DeCew
,
J.
,
Fredriksson
,
D.
,
Lader
,
P.
,
Chambers
,
M.
,
Howell
,
W.
,
Osienki
,
M.
,
Celikkol
,
B.
,
Frank
,
K.
, and
Høy
,
E.
,
2013
, “
Field Measurements of Cage Deformation Using Acoustic Sensors
,”
Aquacultural Eng.
,
57
, pp.
114
125
.
34.
Johansson
,
D.
,
Juell
,
J.-E.
,
Oppedal
,
F.
,
Stiansen
,
J.-E.
, and
Ruohonen
,
K.
,
2007
, “
The Influence of the Pycnocline and Cage Resistance on Current Flow, Oxygen Flux and Swimming Behaviour of Atlantic Salmon (Salmo Salar L.) in Production Cages
,”
Aquaculture
,
265
(
1–4
), pp.
271
287
.
35.
Solstorm
,
D.
,
Oldham
,
T.
,
Solstorm
,
F.
,
Klebert
,
P.
,
Stien
,
L. H.
,
Vågseth
,
T.
, and
Oppedal
,
F.
,
2018
, “
Dissolved Oxygen Variability in a Commercial Sea-Cage Exposes Farmed Atlantic Salmon to Growth Limiting Conditions
,”
Aquaculture
,
486
, pp.
122
129
.
36.
Remen
,
M.
,
Sievers
,
M.
,
Torgersen
,
T.
, and
Oppedal
,
F.
,
2016
, “
The Oxygen Threshold for Maximal Feed Intake of Atlantic Salmon Post-Smolts is Highly Temperature-Dependent
,”
Aquaculture
,
464
, pp.
582
592
.
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