Dynamic Response of Circular, Hexagonal and Rectangular Shaped

Floating Fish Cage in Waves

Yuni A. Wibowo

, and M. Romdhonul Hakim

Department of Marine Technology, Pangandaran Marine and Fisheries Polytechnic, 46396, Pangandaran, Indonesia

Keywords: Fish Cage, Circular, Hexagonal, Rectangular, RAO, Response Spectra

Abstract: A three dimension (3D) model of floating fish cage in both regular and irregular waves is investigated by

numerical simulations. The model vary in the geometry of circular, hexagonal and rectangular/square shaped.

Main purpose of this research is to develop a comparison of floating fish cage responses between the models.

Frequency domain analysis is performed to investigate the responses in both regular and irregular waves. The

fish cage model comprises floating collar with two concentric HDPE tubes and held together by the horizontal

and vertical braces. The benchmark model of circular fish cage is adopted from Shen [1], OD fish cage =

60m, then it is modified into hexagonal and rectangular shaped with nearly dimension from circular shaped.

The model was assumed in rigid state and excluding flexible nets in order to simplify the computation.

Dynamic analysis was performed in free-floating condition by calculating the hydrodynamic properties i.e.

added mass, damping and wave oscillation forces in three-dimensional diffraction theory. The corresponding

analysis reveal that the response of circular fish cage has the largest amplitude in heave and pitch motion than

hexagonal and rectangular model. The following condition is emerged in accordance of viscous damping of

each geometry.

1 INTRODUCTION

In recent years the development of marine

aquaculture located in offshore progressively

increases due to limited nearshore. The fish farms are

being moved by industry from nearshore to more

exposed sea region where waves and current are

stronger. Indonesia, which is 75% of it’s territory,

comprises of the seas, it contributes the huge

opportunity in marine culture/mariculture

development such as marine aquaculture as known

locally as Keramba Jaring Apung (KJA). The model

of KJA is in the form of floating cage in circular

shaped comprised of two concentric HDPE tube

commonly used nowadays.

A numerous research has been done to investigate

the dynamic responses of floating cage by model tests

and simulations. Endersen (2011) evaluate the loads

and responses of floating fish farm in circular collar.

The hydrodynamic behaviors of multiple net cages in

waves and current were investigated numerically by

Xu et al. (2012, 2013b). Shen et al. (2018) provide

numerical and experiment investigations on mooring

loads of a marine fish farm in waves and current.

This research is focused to investigate the motion

characterstics of floating collar fish cage in various

shapes : circular, hexagonal and rectangular/square.

The floating collar comprises with two concentric

tubes and were held together with both horizontal and

vertical braces. In order to simplify the calculation,

the model was simulated in rigid state and exclude the

modeling of flexible nets cage and mooring system.

Thus, in this paper we neglect the effect of

nonlinierity. Dynamic analysis was performed in

free-floating condition by calculating the

hydrodynamic properties i.e. added mass, damping

and wave oscillation forces in three-dimensional

diffraction theory.

The models were investigated in both regular and

irregular seas to obtain the comparison of the motion

characteristic of each model. JONSWAP wave

spectra is conducted to develop the dynamic analysis

in irregular seas, vary from wave height, H, 1.00 to

10.00 meters.

In summary, the present paper organized as

follows. First, a general description of methodology

used in this research, next a brief description model

simulation in three shapes : circular, hexagonal and

rectangular. Second chapter is elaboration of waves

configuration and analysis basic concept in regular

Wibowo, Y. and Hakim, M.

Dynamic Response of Circular, Hexagonal and Rectangular Shaped Floating Fish Cage in Waves.

DOI: 10.5220/0008544900200026

In Proceedings of the 3rd International Conference on Marine Technology (SENTA 2018), pages 20-26

ISBN: 978-989-758-436-7

 2020 by SCITEPRESS – Science and Technology Publications, Lda. All rights reser ved

and irregular waves. Next, generating the governing

equation of motion behaviour. And finally,

performing result and discussion, consist of motion

characteristic on regular wave, responses on irregular

waves and comparing statistical response of each

model.

2 RESEARCH METHODOLOGY

2.1 General

This research began with determining the fixed

variable of fish cage principal dimension. Based on

model generated by Shen (Shen & Faltinsen, 2018),

we kept the dimension of Outer Diameter = 60 m for

circular model, then adopted the OD into the diagonal

length with the exact dimension to the other model.

With this fixed dimension, we generate the model of

fish cage into circular, hexagonal and rectangular

shaped (Figure 2). The model generated in 3D surface

model, based on 3D diffraction concept. Next, finding

the equilibrium position of each model and

computing the dynamic analysis in regular wave to

obtain the motion characteristic of each model and

presented into Response Amplitude Operator (RAO)

graph, then investigating the motion in irregular

waves by tabulating the squared RAO and multiply

by wave spectra to obtain the response spectra.

Finally, stochastic analysis is performed to generate

the statistical responses and compared the response to

each model. (Show Figure 1)

Figure 1: Research methodology used in this paper.

Figure 1: Research methodology used in this paper. (next)

2.2 Model Simulation

The floating collar composed of two concentric

HDPE tubes with outer cross sectional diameter,

odtube = 0.44 m, and wall thickness, wttube = 0.04

m. The diameter of the center line of the outer tube,

ODouter = 60 m. The inner tube was positioned with

the distance, l = 2.22 m inside the outermost, leading

to the center line diameter, Odinner = 55.56 m. The

tubes were held together by both horizontal and

vertical braces with the length of lhorbrace = 2.22 m

and lverbrace = 2.78 m. Those braces has cross

sectional diameter, odbrace = 0.25 m and wall

thickness, wtbrace = 0.02 m. Material properties of

HDPE tube used in this present paper is given in

Table 1.

The model of circular fish cage is adopted from

Shen (Shen & Faltinsen, 2018), Figure 2 (top-left),

then it is modified into hexagonal and

rectangular/square shaped with the near-dimension

from circular model, see Figure 2. The model was

simplified in rigid state and excluding flexible nets in

order to simplify the computation. Dynamic analysis

was performed in free-floating condition by

calculating the hydrodynamic properties i.e. added

mass, damping and wave oscillation forces in three-

dimensional diffraction theory.

Dynamic Response of Circular, Hexagonal and Rectangular Shaped Floating Fish Cage in Waves

Table 1: Material properties of HDPE.

Figure 2: Floating fish cage geometry : isometric view (top-

left); top view : circular, hexagonal and rectange shaped.

2.3 Waves Configuration and Analysis

The responses of floating fish cage in both regular and

irregular waves are to be evaluated. Linear theory is

adopted to compute the regular wave. According to

Djatmiko (Djatmiko, 2012), the floating structure

exposed to the external force, such as wave excitation

force, then the structure moves with the steady

amplitude and frequency, as known as steady state

oscillation. This state can be performed in the

equation 1.

= z

sin (wt - e

)

(1)

Where z

denotes oscillating motion amplitude

and e

is the phase degree between motion and the

propagating wave force. The function of Equation 1

gives the oscilating sinusoidal graph with x-axis of

time (s), and y-axis of wave elevation (z

The wave excitation forces are the diffraction

force due to added mass and water particle

acceleration and the Froude-Kriloff pressure force

due to the undisturbed dynamic pressure over the

wetted surface of the structure. The diffraction force

will be calculated according to linear theory.

Besides, an irregular waves simulation is

evaluated by computing JONSWAP wave spectra,

suggested by DNV (DNV, 2010), as follows :

&'(

)

./0

2345'

787

:'7

(2)

where,

= Pierson-Moskowitz spectrum

'4$

4EFG

;

(3)

= significant wave height

= 2p/Tp (angular spectral peak frequency)

= non-dimensional peakedness parameter

= spectral width parameter

s =0.07

for v < v

s =0.09 for v > v

= 1- 0.287 ln(

) as the normalizing factor

Spectral response analysis is conducted by

computation on the basis of H

intensities for the

long-term occurence varying from 1.00 to 10.00 m.

The responses of floating fish cage are obtained by

multiplying the square of RAO and wave spectrum

considered in this analysis. The stokhastic parameter

can be generated using the varians of the statistical

method, as follows:

''''''''''''''''''''''''J

(4)

where

denotes varian n

and

is the

wave spectra.

2.4 Motion Behaviour of Floating Fish

Cage

In the first stage, the analysis of floating fish cage

motions is conducted in the numerical model based

on frequency domain. The formulation of the

dynamic for the equation of floating structure motion,

in vertical axis may be written as follows (Endersen,

2011):

Q#RST%

V'W

ZS[

V\]

Q#RST%

ZS[

cdd.d' ecRR

dce0fKg

(5)

SENTA 2018 - The 3rd International Conference on Marine Technology

The vertical velocity and acceleration is

PQ#RST%

and

Q#RST%

. The unit for each term in the equation is N/m.

is the mass of the floater per unit length.

is not

varying in space and is therefore a constant.

is the

general hydrodynamic restoring coefficient. EI is the

bending stiffness.

ZS[

and

ZS[

are the

diffraction and Froude-Kriloff force.

cdd.d' ecRR

the added mass force because of vertical acceleration

of the floater section.

dce0fKg

is the damping force,

and contains contributions from potential damping,

skin friction, vortex shedding and structural damping.

Output of the analysis is presented in the form of

RAO curves which exhibit fluctuation of the ratio of

the motion amplitude and the wave amplitude as a

function of wave frequency increment from 0.1 up to

4.0 rad/s. In this analysis a comparison is performed

between the motion behaviors of circular, hexagonal

and rectangular shaped inheave and pitch motion.

Analysis of the motion behaviors in random waves is

obtained from the computation of the squared RAO

multiplied by the wave spectra, which yields the

stochastic data of significant motion responses as the

output.

3 RESULT AND DISCUSSION

3.1 Motion Characteristic on Regular

Wave

In the following section, we present results from the

numerical simulation in the form of RAO curve in

heave and pitch motion (Figure 4 and Figure 5). The

floating fish cage is exposed with the regular wave in

head seas direction (180 deg).

Figure 3: Comparison of heave motion RAO between

models.

Figure 4: Comparison of pitch motion RAO between

models.

According to Figure 4 the resonance of heave

motion for circular model occurs several times at 0.9,

1.3, 1.9 and 2.7 rad/s with the highest magnification

of heave amplitude through wave amplitude is 2.7

times. The resonance of hexagonal model can be

found at 1.5, 2.5 and 3.5 rad/s. While the rectangular

model gave the resonance at 1.7, 2.3 and 3.3 rad/s.

Observing the graph, we find the first resonance of

circular model occurs at 0.9 rad/s with the wave

(JONSWAP) occurence probability is 14% at the

same frequency. This condition will generate the high

response of heave at irregular wave.

Meanwhile the pitch motion of each model shown

at Figure 5 yields the highest RAO at wave frequency

2.0 rad/s, 2.7 rad/s and 2.3 rad/s for circular,

hexagonal and rectangular respectively.

3.2 Fish Cage Response on Regular Wave

Having accomplished analysis of the motions in

regular waves, the next stage is directed towards the

examination of floating fish cage motions in irregular

waves. In this regards the fish cage motions is

estimated by performing the spectral analysis using

the JONSWAP spectrum as shown in Figure 5. The

peak curve occurs at wave frequency, w = 0.95 rad/s.

The spectrum is derived for the wave height, H from

1.00 to 10.10 m. Results of the spectral analysis of

each model presented in Figure 6 to Figure 11, then

the stochastic analysis yields significant response and

compared to each other as given in Figure 12 and

Figure 13 for heave and pitch motion respectively.

Dynamic Response of Circular, Hexagonal and Rectangular Shaped Floating Fish Cage in Waves

Figure 5: JONSWAP wave spectrum from H = 1.00 to

10.00 m.

3.2.1 Circular Shaped

Based on Figure 6 and Figure 7, the density of circular

floating cage responses of heave and pitch has several

peaks, first at w = 0.90 rad/s that is caused by the

superposition of first resonance of motion and by

wave excitation. Then at w = 1.30 rad/s and w = 1.90

rad/s are caused by the superposition with second and

third resonance of motion.

3.2.2 Hexagonal Shaped

According to the Figure 8 and Figure 9, the peak

spectra response of heave motion found at w = 0.95

and 1.50 rad/s, while in pitch motion found at w =

0.90 and 1.50 rad/s, The first peak is generated from

wave excitation for heave, and superposition of both

motion and wave excitation for pitch.

3.2.3 Rectangular Shaped

Observing to the Figure 10 – 11, the density of

rectangular floating cage responses of heave motion,

has several peaks at w = 0.90, 1.30, 1.70 and 2.30

rad/s. The first peak is affected by wave excitation

while the second, third and forth peak are generatef

from resonance of heave motion. The peak of pitch

responce located at w = 0.90, 1.70 and 2.30 rad/s, the

first peak is generated from superposition of wave

excitation and motion, while the other two is

influenced by its motion.

3.2.4 Significant Responses Comparison

The stochastic number i.e. significant responses can

be derived from the computation of spectral response

accomplished before by identifying the variant of data

analysis. Significant responses of each motion are

shown at Figure 12 and Figure 13. According to the

graphs, the responses of floating cylinder on irregular

wave with the circular shaped has the largest

amplitude than the hexagonal and rectangular shaped

in vertical motion. The following condition is

emerged in accordance of viscous damping of each

geometry. The circular model has a smallest viscous

damping than hexagonal and rectangular model. Thus

the response of circular shaped yields larger than

other model.

The difference of heave responses of circular

shaped yields 1.26 times larger than hexagonal, and

1.71 times larger than rectangular shaped. While in

pitch, the circular responce significantly escalated 2.1

times larger than hexagonal and 2.34 times larger than

rectangular. The pitch response between hexagonal

and rectangular shaped remain the same.

Figure 6: Spectra response of heave : circular shaped fish

cage.

Figure 7: Spectra response of pitch : circular shaped fish

cage.

SENTA 2018 - The 3rd International Conference on Marine Technology

Figure 8: Spectra response of heave : hexagonal shaped fish

cage.

Figure 9: Spectra response of pitch : hexagonal shaped fish

cage.

Figure 10: Spectra response of heave : rectangular shaped

fish cage.

Figure 11: Spectra response of pitch : rectangular shaped

fish cage.

Figure 12: Significant response of heave on irregular

waves, Hs = 1.0 to 10 m.

Figure 13: Significant amplitude of pitch on irregular

waves, Hs = 1.0 to 10 m.

Dynamic Response of Circular, Hexagonal and Rectangular Shaped Floating Fish Cage in Waves

4 CONCLUSIONS

A numerical simulation has been performed to

investigate the responses of floating fish cage in

circular, hexagonal and rectangular/square shaped.

The simulation conducted in both regular and

irregular waves. This analysis yields some

conclusions as follows:

• The motion characteristic on regular wave of

circular shaped has the peak RAO curve in the

wave frequency appear in accordance to the peak

of irregular wave frequency. The following

condition will generate a resonance.

• The responses of circular model on irregular wave

has the largest amplitude than the hexagonal and

rectangular shaped in vertical motion. The

following condition is emerged in accordance of

viscous damping of each geometry. The circular

model has a smallest viscous damping than

hexagonal and rectangular model. Thus the

response of circular shaped yields larger than

other model.

The difference of heave responses of circular

shaped yields 1.26 times larger than hexagonal, and

1.71 times larger than rectangular shaped. While in

pitch, the circular responce significantly escalated 2.1

times larger than hexagonal and 2.34 times larger than

rectangular. The pitch response between hexagonal

and rectangular shaped remain the same.

REFERENCES

Djatmiko, E. B., 2012. Perilaku dan Operabilitas

Bangunan Laut di Atas Gelombang Acak. ITS Press,

Surabaya.

DNV, 2010. Global Performance Analysis of Deepwater

Floating Structures. DNV-RP-F205 ed. Norway: s.n.

Endersen, P. C., 2011. Vertical Wave Loads and Response

of a Floating Fish Farm. Master Thesis ed. NTNU,

Norway.

Shen, Y. & Faltinsen, O. M., 2018. Numerical and

Experiment investigations on mooring loads of a

marine fish farm in waves and current. Journal of Fluid

and Structures, Volume 79, pp. 115-136.

Xu, T. -J. et al., 2012. Analysis of hydrodynamic

behaviours of gravity net cage in regular waves. Ocean

Engineering, Volume 38, pp. 1545-1554.

SENTA 2018 - The 3rd International Conference on Marine Technology