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Aquacultural Engineering 67 (2015) 24–31 Contents lists available at ScienceDirect Aquacultural Engineering journal homepage: www.elsevier.com/locate/aqua-online Experimental study on ﬂow velocity and mooring loads for multiple net cages in steady current Yun-Peng Zhao a,∗ , Chun-Wei Bi a,∗ , Chang-Ping Chen b , Yu-Cheng Li a , Guo-Hai Dong a a b State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology, Dalian 116024, China Civil Engineering, Dalian Ocean University, Dalian 116023, China a r t i c l e i n f o Article history: Received 14 February 2015 Received in revised form 7 May 2015 Accepted 18 May 2015 Available online 28 May 2015 Keywords: Net cage Multi-cage system Hydrodynamic characteristics Flow-velocity reduction a b s t r a c t To enable the optimum design and evaluation of ﬁsh farm and mooring performance in the energetic open ocean, a series of physical model experiments were conducted to investigate the hydrodynamic characteristics of a large ﬁsh farm containing 1 up to 8 net pens with the model scale of 1:40. In the physical model experiments, the main mooring line tension and ﬂow-velocity magnitude were measured when current ﬂowed through the multiple net cages. According to the experimental data, the upstream anchor lines of the cage will endure most of the current load acting on the multi-cage system. When the net cages are arranged in double columns, the tension force in the upstream anchor lines increases with increasing number of net cage. But this phenomenon is not obvious when the net cages are arranged in single column. There exists obvious ﬂow-velocity reduction inside net cages of the multi-cage conﬁgurations; however, there is no statistical difference in ﬂow velocity over varied conﬁgurations with different number of net cage. The appropriate multi-cage system in engineering practices should be determined through considering both the mooring line force and the ﬂow-velocity distribution. © 2015 Elsevier B.V. All rights reserved. 1. Introduction Marine aquaculture is expanding all over the world, and the net cage is becoming prevalent in the aquaculture industry. Large ﬁsh farms that include multiple-cages are becoming common in the aquaculture industry. In addition, the new mooring system allows auxiliary equipment, such as feeding platforms (Rice et al., 2003; Fullerton et al., 2004), to be installed at the site. The intent is to approach commercial level operations so that proper economic and environmental assessments can be initiated. In the meantime, increased activity is expected to force a move to less sheltered sites where loads in the mooring lines and ﬂow ﬁeld inside and around the cage are expected to become more important. From the engineering perspective, multi-cage systems need to be designed to cost-effectively withstand extreme conditions while providing a suitable growing environment. The study on open ocean ﬁsh cage and mooring system dynamics has focused primarily upon either the oscillatory response of components to waves or the steady drag of these structures to ocean currents (Kristiansen and Faltinsen, 2014; Kim et al., 2014). ∗ Corresponding authors. fax: +86 0411 84708526. E-mail addresses: Ypzhao@dlut.edu.cn (Y.-P. Zhao), bicw@mail.dlut.edu.cn (C.-W. Bi). http://dx.doi.org/10.1016/j.aquaeng.2015.05.005 0144-8609/© 2015 Elsevier B.V. All rights reserved. As to the multi-cage system in the open ocean, the ﬂuid will ﬂow through the adjacent side and bottom areas as it moves toward the sea cage. The motion of the ﬂow is a rather complicated process. The ﬁshing net is a kind of small-scale ﬂexible structure. The interaction between the ﬁshing net and the ﬂuid is very complicated. Though the hydrodynamics of the ﬁshing net have been studied extensively, the behaviors of ﬂuid ﬂowing around ﬁshing net and the velocity reduction downstream from a ﬁshing net are still a problem to be solved. Techniques used to investigate these mechanisms have typically included the use of scaled physical and numerical models, and where possible, ﬁeld measurements. In the past decades, a number of studies have been carried out to investigate dynamic loads acting on the net-cage system. To our knowledge, Kawakami (1964) proposed relative reliable semi-empirical formula to calculate the drag force acting on net. Aarsnes et al. (1990) further divided the external forces on net cage into drag force and lift force, considering the angle between normal direction of plane net and current velocity. Their work has laid a foundation for further study of the dynamic characteristics of net cage. Colbourne and Allen (2001) surveyed the motion and load responses of gravity cage with ﬁeld test, and compared the results of ﬁeld test and physical model test. Li et al. (2006a,b) investigated the dynamic behavior of gravity cage with numerical and physical model tests, and obtained a promising result. Lee et al. (2008) proposed a mathematical model Y.-P. Zhao et al. / Aquacultural Engineering 67 (2015) 24–31 for analyzing the performance of a ﬁsh-cage system inﬂuenced by currents and waves. DeCew et al. (2010) investigated the submergence behavior of a ﬁsh cage in a single-point mooring system under currents by a numerical model. Tsukrov et al. (2011) investigated the normal drag coefﬁcients of copper alloy netting used in marine aquaculture. Xu et al. (2012) studied numerically the hydrodynamic behavior of multiple net cages in waves. Kristiansen and Faltinsen (2014) investigated the mooring loads on an aquaculture net cage in current and waves by dedicated model tests and numerical simulations. Both from an engineering perspective and from an ecological perspective, the ﬂow ﬁeld of open-ocean aquaculture net-cages must be considered under the effect of steady ocean currents. Aarsnes et al. (1990) carried out a series of tests to study the velocity distribution within net cage systems, and velocity reduction formulae for the net cages were developed. Fredriksson (2001) studied the ﬂow velocity in an open ocean cage with ﬁeld measurements, and an approximate 10% velocity reduction was found. Lader et al. (2003) conducted a series of experiments to investigate the forces and geometry of a net cage in uniform ﬂow, and an average of 20% velocity reduction was measured inside the cage. Johansson et al. (2007) performed ﬁeld measurements at four farms in Norway, and major current reduction was measured in the current passing through the cages. The measured current reduction was between 33% and 64%. Gansel et al. (2011) conducted laboratory tests and ﬁeld measurements to study the effects of biofouling and ﬁsh behavior on the ﬂow ﬁeld inside and around stocked salmon ﬁsh cages. Recently, Bi et al. (2014) developed a numerical strategy to study the ﬂow inside and around ﬂexible ﬁsh cages by combining the porous-media ﬂuid model and the lumped-mass mechanical model based on their previous study of Zhao et al. (2013). Cornejo et al. (2014) developed a numerical model to describe the ﬂow velocity downstream of the salmon farm on an incident current with constant and semidiurnal variability. Rasmussen et al. (2015) conducted full-scale measurements to visualize the ﬂow ﬁeld in the wake of the salmon farm over the duration of two days in an oscillating tidal current. Herein, a series of physical experiments is conducted to investigate the hydrodynamic characteristics of a large ﬁsh farm containing 1 up to 8 net pens. In the physical model experiments, the main mooring line tension and ﬂow-velocity distribution are measured under different multi-cage conﬁgurations in currents. The objective of this paper is to describe the dynamics of the multi-grid mooring system and the ﬂow-velocity reduction of multiple cages. Understanding the hydrodynamic behavior would enable the multi-cage system to be used more effectively. This paper is organized as follows. In Section 2, a description of the physical model is introduced. Section 3 contains the results of the physical model experiments, which include two parts: Part 1 presents the mooring line tension of ﬁve different multi-cage conﬁgurations; and Part 2 presents the ﬂow-velocity reduction inside the net cages. Finally, in Section 4, the conclusions are presented. Fig. 1. The schedule of net cages in experiments. 2.1. Facilities and instruments The experiments were conducted in a wave-current basin (56 m long, 34 m wide and 1 m deep) at the State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology, China (see Fig. 1). The basin was equipped with current-producing system, acoustic Doppler velocimeter (ADV), data acquisition system, a tension sensor for measuring the forces under water and computers. 2.2. Net-cage model A model in scale 1:40 was used to represent a ﬁsh cage with a circumference of 50 m and net depth of 10 m. Circular polyethylene net cages with a circumference of 40–120 m and a depth of 6–30 m are most common in China today. The net cages are often arranged in mooring grids in single or double columns with typically space between them greater than 20 m. At most sites, the mooring grid is oriented perpendicular to the dominant current direction to maximize water ﬂow, oxygen supply and the removal of wastes from the net cages. As a result, the forces on the system and the net deformation have increased. According to the prototype dimensions of the gravity cage and the experimental conditions; the model scale of the experiments is set as 1:40. The net cage structures are modeled according to geometric and gravity similarities (see Table 1). In addition, elastic similarity should be considered when referring to the mooring line. The net system is modeled according to extended gravity simulation criteria that has been discussed and validated by Li et al. (2005). Table 1 Speciﬁcations of the prototype and model of the gravity cage. Component Parameter Prototype Model Floating collar Outer circle diameter Inner circle diameter Pipe diameter Density Material 16.92 m 15.92 m 250 mm 11.35 kg/m HDPE 0.423 m 0.398 m 6.25 mm 7.1 g/m PVC Cylindrical net Height Mesh size Twine diameter Material 10 m 40 mm 2.35 mm PE 0.25 m 23.4 mm 0.72 mm PE Sinker Unit mass Number of pieces 34.3 kg 10 0.54 g 10 Buoy Diameter Geometric shape 1.2 m Sphere 38 mm Sphere Mooring line Twine diameter Density Material 40 mm 953 kg/m3 PE 0.72 mm 953 kg/m3 PE 2. Experimental setup To enable the optimum design and evaluation of ﬁsh cage and mooring performance in the energetic open ocean, a series of physical model experiments was conducted to investigate the hydrodynamic characteristics of a large ﬁsh farm. In the physical model experiments, the main mooring line tension was measured under different multi-cage conﬁgurations in currents. Flow-velocity magnitude inside and downstream from the net cage was also measured. 25 26 Y.-P. Zhao et al. / Aquacultural Engineering 67 (2015) 24–31 Fig. 2. The single cage grid mooring system (unit: m). The net-cage model consists of a ﬂoating collar, a cylindrical net and ten sinkers attached to the bottom of the net. The net is mounted with diamond meshes as same as the prototype. The total number of the meshes in the circumferential direction is 92 and in the depth direction is 12. The speciﬁcations of the net-cage model are presented in Table 1. corresponding to the prototype velocities of 0.7 m/s and 0.9 m/s. Current measurements were made using ADV with a speciﬁed accuracy of 1 mm/s. The sampling rate was 50 Hz. The measurements were run three times to assess the repeatability of the measurements. Each measurement of current was conducted over a period of 30 s. The mean velocity at a measurement point is the averaged value of the three measurements. 2.3. Model arrangement The physical model experimental setup, taking a single cage as an example, is shown in Fig. 2. The grid mooring system consists of three types of mooring lines, which are bridle lines, grid lines and anchor lines. The square-mooring grid is located 0.1 m below the water surface and there is a buoy at each corner. The conﬁguration of the cage system is maintained using these buoys with no pre-tension in the mooring line. The tension in the mooring line is measured using a tension sensor mounted on the anchor line. The ﬂow velocities inside and downstream from the net cages are also measured. Fig. 3 shows the general setting of gauging points for each net cage. Sketch of ﬁve multi-cage conﬁgurations are shown in Fig. 4. The coordinate system for the model is a right-handed, 3D Cartesian coordinate system. In the coordinate system, x is positive toward the ﬂow direction, y is perpendicular to the ﬂow direction on the horizontal plane and z is negative toward the direction of the acceleration of gravity. 2.4. Current conditions The hydrodynamic characteristics of net cages were investigated at the prototype water depth of 20 m. According to the model scale of the laboratory experiment, the experimental water depth was 0.5 m. The velocity of incidence ﬂow is measured by a gauging point in front of the heading net cage (about 1.2 m). The designed velocity of incidence ﬂow is set as 0.111 m/s and 0.142 m/s, Fig. 3. The sketch of gauging points inside and around a net cage (unit: m). Y.-P. Zhao et al. / Aquacultural Engineering 67 (2015) 24–31 27 Fig. 4. Sketch of ﬁve multi-cage conﬁgurations. 3. Results and discussion The multi-cage conﬁguration was anchored to the bottom of the wave-current basin with the mooring grid system. At the end of the anchor lines, load cells were positioned to measure the anchor forces. ADV velocity instrument was used to measure the ﬂow ﬁeld in the net cylinders when current ﬂow through the net cages. There are ﬁve different kinds of net-cage arrangements (conﬁgurations A–E) when 2 up to 8 net pens are contained. 3.1. Mooring line tension The anchor line tension is a key parameter of common concerns. Herein, the tension in the anchor lines of the single cage system and the ﬁve multi-cage conﬁgurations are analyzed to obtain the loads distribution throughout the net cage system. In this section, all quantities are provided in prototype scale, which equal the corresponding model-scale force divided by the third power of model scale 1/40. 3.1.1. Mooring line tension of the single cage Considering the symmetry of the cage system, we focused on the anchor lines deployed at one side of the cage and the anchor lines are numbered as Fig. 5. The tension in each anchor line is the Fig. 5. Sketch of the single cage model with numbered anchor lines. Table 2 The tension in the anchor lines in two current cases (unit: kN). u (m/s) 0.7 0.9 Anchor line no. 1 2 3 4 8.93 12.4 6.39 7.72 4.83 5.75 0.09 0.31 average value of the two anchor lines in the symmetric position. Table 2 shows the average values of tension in the anchor lines of the single cage system in two current cases. As shown in Table 2, the tension in the anchor line 1 is larger than that in other anchor lines and the anchor line 3 loads slight tension. It is apparent that the anchor lines upstream of the net cage are most loaded. The side anchor lines endure certain external forces which is smaller than that in upstream corner anchor lines. The tension in the anchor lines on the lee-side is slight. Therefore, in a current, the external forces on each cage mainly contain two parts: one is transferred to upstream corner anchor line (anchor line 1); the other is transferred to the side anchor line (anchor line 2). In the laboratory experiment, the setback of the cage system is not noticeable which is difﬁcult to be measured. Alternatively, the deformation of the cage system corresponding to prototype velocity of 0.7 m/s is calculated using the lumped-mass method (Zhao et al., 2007; Xu et al., 2012) (see Fig. 6). As a result, the calculated setback of the mooring grid is approximately 5% of the cage diameter. There is no pre-tension in the cage system; however, line 4 in the single cage model does not go slack in the two current cases. The tension force in line 4 under the 0.9 m/s current is larger than that under the 0.7 m/s current, although the tension forces are quite small. This is probably due to the fact that incidence ﬂow makes the ﬂoating collar pitch in a small angle, thus the downstream lines are tensioned. In addition, larger velocity intuitively creates larger pitch angle which leads to more tension force in line 4. The tension in each anchor line increases with increasing current velocity and it presents the similar trend under different current cases. For simplicity, the anchor line tensions of each cage conﬁguration are analyzed when u0 = 0.7 m/s in the following section. 28 Y.-P. Zhao et al. / Aquacultural Engineering 67 (2015) 24–31 Fig. 6. The setback of the cage system corresponding to prototype velocity of 0.7 m/s calculated using the lumped-mass method. The blue dashed line describes the original position of the cage system and the red solid line describes the deformed system. (For interpretation of the references to color in ﬁgure legend, the reader is referred to the web version of the article.) 3.1.2. Mooring line tension of multi-cage conﬁguration As shown in Fig. 7, the anchor lines upstream of the multi-cage conﬁgurations endure great force and the tension in side anchor lines is smaller than that in upstream anchor lines. It is indicated that the anchor lines upstream of the cages endure most of the external forces acting on the multi-cage system. However, there is no signiﬁcant difference in the tension in side anchor lines among the ﬁve conﬁgurations. For conﬁgurations A and E, the tension forces in the anchor line upstream of the two conﬁgurations are almost equal (see Fig. 7). The forces are 24.32 kN and 24.0 kN, respectively. It illustrates that the increase in the number of net cage has little effect on the tension in the anchor lines upstream of the net-cage system when the net cages are laid out in single column. For conﬁgurations B–D, net cages are laid out in double columns. The maximum tension force in the anchor lines upstream of the conﬁgurations increases with increasing number of net cage (see Fig. 7). The forces are 15.36 kN for conﬁguration B, 18.88 kN for conﬁguration C and 24.64 kN for conﬁguration D. The comparison shows that the tension force in the upstream anchor lines is not proportional to the number of net cage. Despite the number of net cage multiplied, the tension force only increased by 22.9% and 30.5% for conﬁgurations C and D respectively. It is considered that most of the increased loads are distributed to the side anchor lines. For multi-cage conﬁgurations contain the same number of net cages, the arrangement type of the net cages will affect the distribution of the load in anchor lines. Taking as example for conﬁgurations C and E, four cages are arranged in double columns and single column respectively. The maximum tension force in the anchor line is 18.88 kN for conﬁguration C and 24.00 kN for conﬁguration E. According to the experimental results, the anchor lines upstream of conﬁguration E endure greater force than that of conﬁguration C. It can be interpreted that conﬁguration C can distribute the total force of the multi-cage system to each anchor line better than conﬁguration E. The tension force in the anchor lines decreases with the net cages arranged in double columns. Similar phenomenon occurs in the tension in each anchor line when comparing conﬁgurations A and B. 3.1.3. Practical implication In this study, the material of mooring line is polyethylene (PE) for both scale and prototype model. Increment in both tension force and amount of mooring line will intuitively lead to increased costs. Compared with single-column conﬁguration, double-column one can effectively reduce the number of mooring line with no signiﬁcant increment in tension force. Therefore, double-column Fig. 7. The tension in the anchor lines of each multi-cage conﬁguration (unit: kN). The maximum tension forces are highlighted in bold. Y.-P. Zhao et al. / Aquacultural Engineering 67 (2015) 24–31 29 Table 3 The ﬂow-velocity reduction factor inside and downstream from the single cage. Incidence velocity u0 (m/s) Velocity inside u1 (m/s) Velocity downstream u2 (m/s) Reduction factor u1 /u0 Reduction factor u2 /u0 0.1350 0.1543 0.1205 0.1342 0.0913 0.1052 0.89 0.87 0.68 0.68 Fig. 8. The ﬂow-velocity reduction factor inside the cage. conﬁguration is considered as more cost effective. Other than the tension-force difference, the 2 × 4 conﬁguration (conﬁguration D) is recommended over the ﬁve conﬁgurations from a perspective of economizing cost. 3.2. Flow velocity reduction 3.2.1. Flow through single gravity cage As there is no signiﬁcant difference between the values of ﬁve measurement points inside the net cage, their averaged value is considered as the ﬂow velocity in cage denoted by u1 . The value of the gauging point downstream from the net cage is considered as the ﬂow velocity downstream from cage denoted by u2 . The corresponding ﬂow-velocity-reduction factor can be obtained by comparing with the incidence velocity u0 . The ﬂow velocities and the ﬂow-velocity-reduction factors inside and downstream from the single cage in two current cases are presented in Table 3. There exists an obvious ﬂow-velocity reduction inside the cage while there is a larger velocity reduction downstream from the cage (see Table 3). It is indicated that the incidence ﬂow can be attenuated when passing the ﬁshing net and the reduction in ﬂow velocity increases with increasing number of ﬁshing net. As the free stream ﬂows through two nets before reaching the gauging point downstream from the net cage, the ﬂow-velocity reduction is larger than that inside the net cage which is attenuated only by the upstream net. 3.2.2. Flow through multi-cage conﬁguration The ﬂow-velocity-reduction factors present the similar trend under different current cases inside and downstream from the net cage. For ﬂow through multi-cage conﬁgurations, the ﬂowvelocity-reduction factor inside the cage is the average value of the reduction factors inside the same cage in the two current cases. Considering the symmetry of the cage system in double columns, we focused on the reduction factor inside the net cages deployed at one side of the cage system. The reduction factor is the average value of the two cages in the symmetric position. Obvious ﬂow-velocity reduction exists inside net cages of the multi-cage conﬁgurations, and the ﬂow-velocity reduction increases with increasing cage number (see Fig. 8). The net cages inﬂuence the ﬂow-velocity distribution inside themselves and also have noticeable inﬂuence on the ﬂow ﬁeld inside the net cages around them. Comparing the experimental results of conﬁgurations A and E, the ﬂow-velocity-reduction trends of the two conﬁgurations are consistent and there is no statistically difference (see Fig. 9). It illustrates that the increment in the number of downstream cage has no noticeable effect on increasing the ﬂow-velocity reduction inside the net cages. In conﬁgurations B–D, net cages are laid out in double Fig. 9. Comparisons of the ﬂow-velocity reduction factor inside the net cages between conﬁgurations A and E. 30 Y.-P. Zhao et al. / Aquacultural Engineering 67 (2015) 24–31 signiﬁcant. What is more, this phenomenon becomes more noticeable for the downstream net cage where the interaction between the paratactic net cages in different columns is considered reaches the maximum performance. In engineering practices, water motion helps to maintain the water quality in a net cage and that sufﬁcient water exchange is important for the health and growth of the caged ﬁsh. From this perspective, the 2 × 1 conﬁguration (conﬁguration B) is recommended for less reduction in ﬂow velocity inside the net cage. The experimental data have been compared with the numerical results of Bi et al. (2014) and the results of Løland’s formula (Løland, 1991; Aarsnes et al., 1990) (see Fig. 11). Løland combined theoretical work with experimental work to derive formulas for ﬂow-velocity reduction of the cage nets: u = u0 nc ri (1) i=1 where ri is given by Fig. 10. Comparisons of the ﬂow-velocity reduction factor inside the net cages among conﬁgurations B–D. columns and the number of the net cage doubles. Similarly, there is no signiﬁcant difference in ﬂow-velocity reduction between the three conﬁgurations (see Fig. 10). For ﬁsh farms containing the same number of net cages, the arrangement of the net cage can inﬂuence the ﬂow-velocity distribution. In conﬁguration B, the two net cages inﬂuence the ﬂow-velocity distribution inside each other. As a result, the ﬂowvelocity-reduction factor in conﬁguration B is a little greater than that of the upstream net cage in conﬁguration A, although it is not statistically signiﬁcant. Similar phenomenon occurs when comparing conﬁgurations E and C. Due to the water blockage of the ﬁshing net, the ﬂow velocity increases at the ﬂanks of the net cage. Therefore, the net cages deployed in double columns have less reduction in ﬂow velocity inside than the net cages in single column. Fig. 11 shows the comparisons of ﬂow-velocity-reduction factor between conﬁgurations D and E. The ﬂow-velocity-reduction factor inside the net cage of conﬁguration D is consistently greater than that of the corresponding net cage of conﬁguration E, although it is not statistically Fig. 11. Flow-velocity reduction factor inside the net cages from conﬁgurations D and E (present study), the numerical results of Bi et al. (2014) and the results of Løland’s formula (Løland, 1991). ri = 1.0 − 0.46Cd (2) where ri is the ﬂow velocity reduction factor, nc is the number of upstream crossings of other plane nets before the current hits the actual plane net, and Cd is the drag coefﬁcient of the net calculated using empirical formulas proposed by Balash et al. (2009): cyl Cd = Cd (8.03Sn2 − 0.74Sn + 0.12) cyl (3) −2/3 . where Cd = 1 + 10Ren The comparison shows that the present results are in good agreement with the numerical results of Bi et al. (2014). However, Løland’s formula seems to overestimate the ﬂow velocity inside downstream cages. This discrepancy is attributed to the difference in the deformation of ﬁshing net. Løland’s formula may apply to net cages with limited deformation as it shows good agreement with the numerical results of net cages with no deformation (Zhao et al., 2013). 4. Conclusions According to the experimental results, the following conclusions can be drawn: • The upstream anchor lines endure most of the external forces acting on the multi-cage system. The tension force in the upstream anchor lines increases with increasing number of net cage for double-column conﬁgurations while the increment in net cage has no noticeable effect on the line tension. For conﬁgurations consisting of the same number of net cage, the tension in each anchor line of the double-column conﬁguration is smaller than that of single-column one. Increment in both tension force and amount of mooring line will intuitively lead to increased costs. Other than the tension-force difference, the 2 × 4 conﬁguration is recommended from a perspective of economizing cost. • Obvious ﬂow-velocity reduction exists inside net cages of the multi-cage conﬁgurations and the ﬂow-velocity reduction increases with increasing cage number. However, there is no statistical difference in ﬂow velocity for varied conﬁgurations. In general, the net cages arranged in double columns have less reduction in inside than the net cages in single column. From the perspective of water exchange, the 2 × 1 conﬁguration is recommended. • The experimental results provide the basis for the optimum design of a ﬁsh farm. 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