1 Introduction

The stock of wild fish is decreasing due to overfishing; thus, marine aquaculture is growing rapidly to meet the demands of seafood production. However, land-based pollution, serious fish diseases, and the problem of coastline comprehensive utilization have also limited the development and output of nearshore aquaculture (Winthereig-Rasmussen et al., 2016; Chen and Christensen, 2017). So aquaculture needs to be expanded from nearshore to offshore sites. Several experimental and numerical studies have been conducted to investigate the hydrodynamic characteristics of net cages. Some researchers have studied the hydrodynamic characteristics of knotless netting with various solidity ratios and angles of inclination (normal, parallel, or inclined) with respect to the free stream (Zhou et al., 2015; Tang et al., 2017). Zhao et al. (2007) numerically investigated the effects of structure size ratio and mesh type on three-dimensional deformation of the fishing-net gravity cage in current. As biofouling is a big problem in aquaculture, series of studies have been conducted to assess the increase in drag force caused by biofouling on netting (Swift et al., 2006; Bi et al., 2015; Moe-Føre et al., 2016). Tsukrov et al. (2011) studied the drag resistance of copper alloy nets and found they exhibit significantly lower drag coefficients than similar nylon nets with comparable solidities. Recently, Huang et al. (2016) numerically studied the deformation and forces of a floating fish cage collar in waves. The effects of collar dimensions, such as collar circumference, pipe diameter in cross section, and pipe thickness, on the dynamic behavior of the floating collar were presented. Considering the mooring configuration, the applications of fixed multipoint (Loverich and Forster, 2000; DeCew et al., 2005), mooring and grid array (Celikkol et al., 2000; Fredriksson et al., 2007) as traditional mooring arrangements have since been investigated. Single-point mooring arrangements have attracted much attention because of its advantages, which include reduced mooring costs and benthic accumulation of waste products (Goudey et al., 2001).

Offshore sites exposed to a range of complex external disturbances (strong current, severe wave, and storm surge) may cause damage to the cages and severely stress the fish. Moreover, traditional fish cages lack the ability to withstand severe adverse offshore conditions, especially typhoon-related conditions. Submersible fish cages are especially designed to minimize structural damages, compared with floating cages at the same severe condition, by reducing external loads and movements. Recent research shows that submersible fish cage aquaculture may also help fishes avoid surface-related issues such as jellyfish infestation, unsuitable temperature, high pollutant level, oil spill, and many types of biofouling. Because of the advantageous characteristics, submersible fish cages are increasingly applied for offshore aquaculture. The submergence behavior of a small-volume fish cage in a single-point mooring system under the action of current has been investigated by a numerical model (DeCew et al., 2010). Furthermore, Kim et al. (2011) developed an automatic submersible fish cage system using air control and conducted a physical model test to examine the automatic submergence characteristics of the cage. In a subsequent study, Kim et al. (2012) developed a submersible fish cage system operated remotely by a tethered surface control station. Xu et al. (2013) analyzed the hydrodynamic characteristics of a submersible fish cage and mooring system in waves and current by a numerical method. Overall, the studies on the hydrodynamic characteristics of submersible net cage are limited; therefore, it is necessary to investigate the optimum submergence depth and the hydrodynamic behavior of the net cage at various submergence depths.

The submersible fish cage is different from the traditional structures in ocean engineering, such as floating oil boom (Shi et al., 2017), flexible plant (Yin et al., 2017), and perforated plate (Jin et al., 2017), and can be categorized as a floating-flexible-porous structure. A fish cage is mainly composed of a floating collar system, a netting system, a mooring system, and a weight system which is added to the net to help it retain its shape and volume. Because of the complex structure of the submersible fish cage, physical model experiments are used to investigate the hydrodynamic characteristics (mooring line tension and the movement of the floating collar) of the fish cage at different submergence depths to determine the optimum submergence depth. Determining the optimum submergence depth can guarantee optimum design and safety, as well as avoid the operation difficulty and unnecessary cost caused by excessive submergence. However, the basic research on submersible fish cages is limited, which results in the lack of a theoretical basis during design and model selection. In this paper, the hydrodynamic characteristics of a submersible fish cage at various submergence depths are reported and compared with those at the floating condition.

Additionally, an experimental setup for investigating the hydrodynamic characteristics of submersible fish cages is presented in Section 2. In Section 3, experimental results of the mooring line tension and the movement of floating collar for both floating and submersible conditions are provided. A detailed discussion is provided in Section 4. Finally, Section 5 presents the main conclusions.

2 Physical Model Experiment

To determine the optimum submergence depth of a submersible fish cage, a series of physical model experiments were conducted to observe the hydrodynamics of a submersible fish cage at various submergence depths. In the physical model experiment, the mooring line tension and the movement of the floating collar in waves were measured.

2.1 Physical Model

Considering the wave-current flume scale, experimental wave conditions, and actual fish cage dimensions, a model in a scale of 1:20 was selected to represent a fish cage with a circumference of 40 m and a net height of 7 m. The fish cage structures were modeled according to geometric and gravity similarities. In addition, the elasticity similarity was considered with respect to the mooring line. The net system was modeled according to the extended gravity simulation criteria that have been discussed and validated by Li et al. (2005). The net was mounted with diamond meshes in the same manner as the prototype.

2.1.1 Mooring system

The mooring system was composed of main mooring lines, grid lines, bridle lines, and buoy lines. Four grid lines each with a length of 1.25 m made up the square mooring grid, which was located 0.2 m below the water surface. The mooring grid was perpendicular to the wave direction. In addition, four foam buoys with a diameter of 8 cm were mounted on four nodes. By using these buoys, the cage system was maintained with no pre-tension in the mooring line. Eight load cells were mounted on the main mooring line to measure the tension. The mooring line in the model was 1.68 m long, corresponding to the prototype length of 33.6 m long.

The elasticity similarity is the main consideration in the mooring line. Polyethylene (PE) is usually used for mooring lines. As suggested by previous research (Gui, 2006), the elasticity relation of the polyethylene elastic under tension is close to linear. The calculated percentage elongations of the model mooring line under different loads are given in Table 1.

The elasticity of mooring line was simulated by rubber bands. Based on the elasticity test of selected rubber bands, two rubber bands were first connected to form a group, and then two groups were used in parallel. Compared with the elasticity provided by rubber bands, the elasticity of the mooring line can be neglected. Table 2 shows the relationship between percentage elongation and the tension of the mooring line (obtained by loading experiment). The results show that there is little difference between the calculated and experimental measured elasticity (see Fig. 1); therefore, the rubber bands could approximately simulate the elasticity of the mooring line.

2.1.2 Floating collar system

Fig. 2 shows the floating collar used in the experiment. The floating collar primarily consisted of internal and external floating pipes, guardrails, handrails, and jointing elements. According to the geometric similarity criterion, the specifications of the floating collar components in the experiment were calculated (Table 3). Based on the gravity similarity criterion, the weight of a unit length of the prototype floating tube was about 22 kg m⁻¹, corresponding to a length of 55.5 g m⁻¹ for the model. In this experiment, polyvinylchloride (PVC) tubes with a weight of 52 g m⁻¹ were selected to manufacture the floating tubes. The unit weight of the prototype guardrails and handrails was 3 kg m⁻¹, corresponding to a value of 7.5 g m⁻¹ for the model. Polyvinylchloride tubes with a diameter of 5.5 mm and unit weight of 7 g m⁻¹ were selected to make the guardrail and handrail models. The weight discrepancy between the model and the prototype was regulated by adjusting the weight of the connecting structure.

2.1.3 Netting system

In this experiment, the prototypical net was used to replace the model net according to the geometric similarity criterion. The stiffness and elasticity of the polyethylene net was too weak, and therefore, the elasticity similarity of net was not considered. In the equivalent process, it was necessary to ensure that the flow resistances of the equivalent and theoretical net were the same. The equivalent method used to simulate the net system will result in a weight difference between the equivalent net and the theoretical net; therefore, the weight of the equivalent net need to be corrected to satisfy the gravity similarity rule. According to a previous research (Gui, 2006), using the equivalent net makes the mass of the model net to increase by 15.8 g; therefore, the model can be made to conform to the gravity similarity criterion by subtracting 15.8 g from the mass of the sinker.

2.1.4 Weight system

The prototype sinker weighed 502.4 kg, and the model sinker weighed 62.8 g according to the model scale. In addition, the quality difference of 15.8 g caused by the equivalent net was considered. A stainless steel ring with a diameter of 62 cm and a weight of 47 g was used as sinker. The specifications of the submersible fish cage model are presented in Table 3.

2.2 Experimental Setup

The experiments were conducted in a wave-current flume at the State Key Laboratory of Costal and Offshore Engineering, Dalian University of Technology, Dalian, China. The wave-current flume was 60 m long, 4 m wide, and 2.5 m deep with a working water depth of 0.2–2.0 m and a wave period range of 0.5–5.0 s. A hydraulic servo wave maker was equipped to generate regular and irregular waves in the flume. In this study, only regular waves were generated. At the other end of the flume, wave absorbers were installed to mitigate wave reflection (see Fig. 3).

Fig. 4 shows the top and front views of the experimental setup. In this study, the submersible fish cage was anchored in 1.2 m deep water by eight anchor points, corresponding to a prototype depth of 24 m. The coordinate system for the model was a right-handed 3D Cartesian coordinate system. In the coordinate system, x was positive toward the wave direction, y was perpendicular to the wave direction on the horizontal plane, and z was negative toward the direction of the acceleration of gravity.

The water surface elevations were recorded by capacitance-type wave gauges with an absolute accuracy of ±1 mm arranged along the center line of the wave flume. A charge-coupled device camera (Fig. 5) was used to track the motion of the floating collar (two diodes were arranged in the front and at the back of the floating collar as the trace points). A self-developed software DUT-FlexSim (Gui et al., 2006) was used to calculate the motion responses of the floating collar. In this experiment, a hydraulic data acquisition system (Fig. 6A), load cells (Fig. 6B), and other auxiliary equipment were also used to measure the tension in the mooring lines.

2.3 Experimental Conditions

The wave parameters used in the physical model experiment as well as the corresponding prototype values are presented in Table 4. The wave heights of the regular wave were 0.06, 0.12, and 0.18 m, and the wave periods ranged from 1.0 to 1.8 s. The experimental water depth was 1.2 m, corresponding to the prototype water depth of 24 m. Waves were generated parallel to the flume in the x direction.

In this study, the submerged level of the fish cage is described by submergence depth, which is the distance from the center of the float collar to the still water surface. The hydrodynamic characteristics of the submersible fish cage was investigated under five working conditions: 1) floating on the water surface, 2) submergence depth of 1/6 of water depth (20 cm in the model experiment), 3) submergence depth of 1/4 of water depth (30 cm in the model experiment), 4) submergence depth of 1/3 of water depth (40 cm in the model experiment), and 5) submergence depth of 1/2 of water depth (60 cm in the model experiment). The target submergence depth of the fish cage was mainly controlled by the submergence depth of the squared grid, which consisted of four grid lines, and the target submergence depth could be reached by adjusting the length of buoy and bridle lines. The submergence depth of the fish cage, taking the float collar as reference, was approximately twice the submergence depth of the squared grid. The positions of the anchors were fixed for various submergence depths.

2.4 Data Analysis Method

Before initiating any measurements, the wave gauges were examined for soundness, cleaned if necessary, and then calibrated. A multi-channel computer control system developed by Beijing Hydraulic Research Institute was used for collecting the data of free surface elevations. In the experiments, two wave gauges with a spacing of 0.3 m were fixed 1 m upstream of the net cage. The time series of wave elevation at each measurement point was recorded with a sampling rate of 50 Hz. A stable data for a period of 30 s was chosen for data analysis, and the wave height at a measurement point was the average value of the corresponding time series.

Water-resistant load cells with a capacity of 1.0 N were used to measure the forces on the mooring lines. The specified accuracy of the load cell was 0.01 N. Each measurement was run three times to diminish the impact of random and bias errors. Data sampling was conducted over a period of 30 s. The final experimental data were the average value of the three measurements.

3 Results

For the movement of the floating collar, the heave, pitch, and surge were analyzed for both floating and submerged configurations. Load cells were used to measure the force acting on mooring lines. In this study, the mooring line system was divided into four parts: windward, intermediate windward, intermediate leeward, and leeward mooring lines. In this section, the tension in the mooring line and the movement of the floating collar are discussed in details.

3.1 Tension in the Mooring Line

Because of the symmetry of the net cage model and the mooring lines, the average value of the tension in the mooring lines at symmetrical position was used for force analysis. The force analysis results of the mooring lines under floating and four submergence conditions with nine wave conditions are presented in Fig. 7. The tensions in the windward, intermediate windward, intermediate leeward, and leeward mooring lines were compared. The force acting on the windward mooring lines was the largest, followed by those acting on the intermediate windward, intermediate leeward, and leeward mooring lines. The changes of mooring line tensions for the windward, intermediate windward, and intermediate leeward systems were uniform. Under the same wave height, the mooring line tension was positively correlated with the wave period, which means that the windward mooring line tension increased with increasing wave periods. However, there was no obvious trend in the change of the leeward mooring line tension.

Fig. 8 illustrates the mooring tension of each line when the wave period was 1.8 s and wave height was 0.18 m. It can be observed that the windward mooring lines of the fish cage was subjected to great force, and the tensions in the intermediate windward and intermediate leeward mooring lines were smaller than that in the windward mooring line. As the submergence depth increased, the tension acting on each mooring line decreased.

The tension force in the mooring line exhibited noticeable attenuation effect with increasing submergence depth. To clearly present the attenuation effect of tension force in different mooring lines, a ratio R_T is defined as follows:

$ R_{T}=\frac{\text { Tension under submersible condition }}{\text { Tension under floating condition }} \times 100 \%. $

When the wave period was 1.4 s and wave height was 12 cm, the corresponding R_T was taken as an example, and the obtained values are given in Table 5. Excluding the leeward mooring line tension, the mooring line tensions of the other systems were significantly reduced at submergence depths with 1/6, 1/4, and 1/3 of water depths; however, as the submergence depth continued to increase, the reduction tendency of the line tensions gradually weakened (Fig. 9). The line tensions became stable when the cage was submerged to a certain depth. The line tension showed similar values at submergence depths with 1/2 and 1/3 of water depths under the studied wave conditions. Thus, from a perspective of external loads, a submergence depth with 1/3 of water depth is considered as the optimal one of the fish cage.

3.2 Motion Response of the Floating Collar

Extreme violent motion of the floating collar is not conducive for the safety of fish cages and aquaculture and will cause serious destruction. Therefore, it's important to study the motion of the floating collar at different submergence depths to ensure the safety of fish cages. In this study, the motion of the fish cage could be obtained by tracking the motion of two markers set on the floating collar.

The surge (displacement in the direction of the wave incident), pitch (sum of the maximum counterclockwise angle and maximum counterclockwise angle), and heave (displacement along the wave height) for the floating and submerged configurations were compared (Fig. 10). The surge, heave, and pitch values of the floating collar all decreased with increasing submergence depth. When the submergence depth reached 1/6 of water depth, the pitch, and heave of the floating collar decreased rapidly.

Herein, R_S/P/T is defined to show the attenuation effect in movement as follows:

$ {R_{S/P/T}} = \\ \frac{{{\text{ Surge (pitch, heave) under submersible condition }}}}{{{\text{ Surge (pitch, heave) under floating condition }}}} \times 100\% . $

Table 6 provides the R_S/P/T value under the wave height of 12 cm and wave period of 1.4 s. The R_S/P/T increased with increasing submergence depth. When the submergence depth was 1/6, 1/4, and 1/3 of water depth, the difference between the values of the ratio was much more than that for the 1/2 of water depth. The difference between the values for submergence depths of 1/3 and 1/2 of water depth was small. This means that the movement of the net cage will become stable when the net cage is submerged to a certain depth, which is consistent with the trend of mooring line tension.

4 Discussion

To overcome the devastating loads caused by the wind and waves, fish cages can be submerged below the water surface, which can reduce the motion of fish cages and prevent the damage of mooring lines. The mooring line tension is considered as the key parameter for the structural design and safety check of mooring systems, and the movement of net cages is directly related to the facility safety and the fish welfare. According to the results of the present experiment, both the mooring line tension and movement of the net cage significantly reduced with increasing submergence depth.

Moreover, the tension in each mooring line increased with increasing wave periods, and a similar trend was observed under different wave heights. This is mainly due to the transmission of the wave force on the net. As observed in the experiment, the horizontal motion amplitude was positively related to the wave period; therefore, in a larger wave period, the wave force on the net transferred to the mooring line via the floating collar became greater with sharp movement. However, there was a significant phase difference between the wave propagation and the wave force on the net cage.

It is difficult to determine the relationship between wave period and wave force on net cages with various sizes. It is apparent that windward mooring lines are most subjected to tension. The intermediate windward and intermediate leeward mooring lines are subjected to certain external forces, which are much smaller than those in windward mooring lines. The tensions in leeward mooring lines are quite slight; this indicates that external forces acting on the line are mainly transferred to the windward and intermediate mooring lines. Submerged fish cages can effectively alleviate loads distribution throughout the fish cage. However, when the fish cage is submerged to a certain depth, the attenuation effect becomes imperfect, since the wave action weakens with increasing water depth. For example, in this experiment, there was no significant difference in the mooring line tension when the submergence depth of the fish cage was at 1/3 and 1/2 of water depth.

According to the results of the floating collar motion, the movement had a downward trend with increasing submergence depth. Considering the surge, heave and pitch, much difference existed among them at submergence depths of 1/6, 1/4, and 1/3 of water depth; however, there is no statistical difference in movement between the above three submergence depths and the submergence depth of 1/2 of water depth. This means that movement will be stable when the cage is submerged to a certain depth.

A suitable submergence depth of fish cages needs to be chosen. The water particle velocity was the largest at the water surface and decreased in amplitude with increasing depth in waves. In general, the motion of float collar in the submergence condition is expected to be significantly smaller than that in the floating condition, which results in low mooring line tension response. As shown in the experimental study, 1/3 of water depth was the critical submergence depth for both the motion of floating collar and the mooring line tension in waves. More submergence depth showed no significant advantage for the hydrodynamic characteristics of the fish cage. Considering the additional cost on practical operation for the unnecessary submergence depth, 1/3 of water depth is suggested as the optimal submergence depth of the fish cage.

As studied by Xu et al. (2013), there is no significant advantage when the submersible net cage is subjected to a relatively larger current. Therefore, the hydrodynamic characteristics of the submersible fish cage in different submergence depths subjected to a regular wave were studied, which provides some scientific basis for the design and selection. The results can be used to validate the numerical model of the submersible fish cage. However, the hydrodynamic characteristics of the submersible fish cage are quite complicated, and there are still many important features that need to be further studied. The interaction of the hydrodynamic characteristics of the fish cage at different submergence depths with irregular waves or reverse wave and current should be studied in the future. In addition, the submersible device and the hydrodynamic characteristics of the fish cage under the submergence process need to be given more attention.

5 Conclusions

The interactions of the hydrodynamic characteristics of the submersible fish cage at different submergence depths with regular waves were studied by a physical model test. The experiment includes nine wave conditions and five working conditions of the fish cage (floating condition and four submerged conditions: submergence depths with 1/6, 1/4, 1/3 and 1/2 of water depth). The results are summarized as follows:

1) The windward mooring lines were most subjected to external forces. The force acting on the leeward mooring line was much smaller than that acting on the other mooring lines; therefore, the force had little impact on the leeward mooring lines and the safety of the submersible fish cage. The forces acting on the windward and the intermediate mooring lines exhibited good attenuation effect after submergence; however, when the submergence reached a certain value, the attenuation effect was not obvious with increasing submergence depth. This means that when the cage is submerged to a critical depth, the effect of the wave action acting on mooring lines will gradually become stable.

2) The movement of the floating collar, including surge, heave, and pitch, exhibited a significant attenuation effect with increasing submergence depth of the fish cage. However, the motion of the floating collar became stable when the submergence depth was between 1/3 and 1/2 of water depth.

3) According to this study, 1/3 of water depth is suggested as the optimal submergence depth of the fish cage. Deeper submergence depth showed no significant advantage when considering the reduction in external loads and the movement of the fish cage in waves.

Acknowledgements

This work was financially supported by the National Natural Science Foundation of China (Nos. 51579037, 51609035, 51822901, 31872610), China Postdoctoral Science Foundation (Nos. 2017T100176, 2016M590224), and the Science and Technology Development Plan Project of Shandong Province (No. 2014GHY115023).