Introduction

In Korea, the coastal harvesting of wild abalone has increased from 2,062 MT in 2005 to 6,228 MT in 2010 to meet the demand for abalone meat (FAO, 2012). Abalone is also cultured in southern Korea, particularly in the coastal waters of Jeonnam province where Haliotis discus hannai is the most common species. However, the coastal waters of Korea have been polluted by many anthropogenic sources that have affected the dissolved oxygen (DO) levels (Kim et al., 2014a). For instance, Choi et al. (2013) showed that the DO levels within a near-shore abalone farm could be as low as 40% saturation (4.0 mg/L).

Low DO levels limit the production of many aquaculture species (Boyd and Watten, 1989) because DO is a limiting factor for growth, even though it does not act directly on growth in the manner that many toxins do, because it limits the scope of aerobic metabolism (Fry, 1971; Brett, 1979). As farming intensity increases, the DO level and its impact on abalone growth will become more important for farmers. The specific growth rate (SGR) is significantly affected by hypoxia, whether it is measured on a length or whole weight basis (Harris et al., 1999). According to Harris et al. (1999), significant reductions in survival occur at the lowest DO concentrations (4.9–4.2 mg DO L^-1) and a significant reduction in food consumption occurs at 5.6 mg DO L^-1 (73% oxygen saturation), which approximates to the beginning of the range at which reductions in SGR occur.

Therefore, one option to expand abalone aquaculture operations is to consider more exposed, under-utilized sites where the exchange of dissolved respiratory gas is better. Kim et al. (2014a) developed a submersible abalone cage grow-out system for commercial use that consists of a modu-lar box structure. The abalone containment structure contains 16 boxes (each with 16 plastic plate shelters in a box) filled with abalone and kelp (in each individual caged container).

Computational fluid dynamics (CFD) modeling has been used to analyze the flow or DO characteristics of marine aquaculture structures. Helsley and Kim (2005) performed CFD simulations using the FLOW3D finite difference software to analyze the downstream diffusion of a bi-conical rigid cage system. Fredriksson et al. (2008) used CFD (FLUENT software) to analyze closely spaced solid cylinders. Shim et al. (2009) used CFD to investigate the flow through and around a fish cage by calculating the drag and the flow velocity distribution around cylinders with different porosities. Patursson et al. (2010) used the FLUENT software package to apply a porous media model for the flow through net panels. Zhao et al. (2013) performed a numerical simulation of the flow field inside and around gravity cages. Bi et al. (2014) used a numerical approach to simulate the interaction between flow and flexible nets in a steady current. Kim et al. (2014b) investigated the flow characteristics and DO exchange within two potential co-culture cage systems designed for the grow-out of juvenile abalone, Haliotis discus hannai, with juvenile sea cucumber, Apostichopus japonicas (Selenka), using CFD analysis.

Because abalone is contained in densely-packed box structures, the availability of dissolved oxygen is a substantial design issue that needs to be considered. In this study, numerical modeling analyses based on flow characteristics were performed with CFD to determine the DO concentration distribution through a container. The flow characteristics in the abalone cage system were investigated previously by Kim et al. (2014a).

Materials and Methods

System description

The submersible abalone cage grow-out system for commercial use consists of a modular box structure (Fig. 1). The entire abalone containment structure contains 16 boxes (with 16 plastic plate shelters per box) filled with abalone and kelp (in each individual caged container). The containers are organized with a symmetric 4 × 4 geometry within the framed structure. The individual containers have dimensions of 2.4 × 2.4 × 3 m³, and the spacing between the containers is 0.9 m (Fig. 1). The submersible abalone cage consists of 16 containers and 16 plastic shelters which were installed within each container (Kim et al., 2014a). The upper, lower, and side parts of the container were all surrounded with nylon netting (Td 210 × 60, mesh size: 30 mm, twine diameter: 2 mm). Each abalone shelter also consists of six sheets of polyethylene plate (thickness: 2.4 mm; space of plate: 132 mm) with an outer frame (PP pipe diameter: 32 mm). The size of the shelter is 950 × 865 × 480 mm (L×B×D), as shown in Fig. 2.

Governing equations

The three-dimensional (3D) flow pattern and the concentration of the dissolved oxygen inside and around the containers were analyzed using the FLUENT 14.0 CFD program (ANSYS Inc.), as described in FLUENT (2011). Steady state conditions were assumed for the flow calculations with the standard k-ε applied as the turbulence model. Continuity and Reynolds-averaged Navier-Stokes (RANS) formulations were used for the analysis. The turbulent eddy viscosity (μ_t) can be determined by applying the turbulence in the standard k-ε model:

where C_μ=0.09 represents a model constant. In Equation (1), the turbulent kinetic energy (k) and the turbulent kinetic energy dissipation rate (ε) were simulated with two transport equations. The transport equations for k-ε are

and

respectively, where t is time, P_k is the turbulent kinetic energy generated by the average velocity gradient, P_b is the kinetic energy of the turbulence generated as a result of the buoyancy, and Y_M is the contribution of the fluctuating dilatation in the compressible turbulence to the overall dissipation rate such that P_b = 0 and Y_M = 0 . S _k and S _ε are source terms that can be defined by the user, and σ_k and σ_ε are turbulent Prandtl numbers. The model constants for the realizable k-ε turbulence model are σ_ε = 1.2, C_1ε = 1.44, C_2ε = 1.92, σ_k = 1.0, and C_3ε =tanhu p u v , where u_p and u_v are the velocity components that are parallel and normal to gravity, respectively.

Along with the governing equations for the flow field characteristics inside and around the abalone cage, the distribution DO was also determined within the control volume domain. The transport equations of the pollutants were interpreted using the FLUENT software with a CFD model as,

In Equation (4), Y _i represents the mass fraction of each pollutant, J _j is a diffusion term of the turbulence, x_j is the coordinate of the component and S_i is the source term of each pollutant. The diffusion term for the turbulence is expressed as

where D _i,m represents the mass diffusion coefficient of each pollutant, μ_t is the turbulent eddy viscosity coefficient, and S _Ct=0.7 is the turbulent Schmidt number.

Porous model

Because the permeable walls of the cage (mesh-like structure) were modeled as porous materials, the nettings were represented using the porous media model proposed by Patursson et al. (2010). The flow resistance of the cage walls was introduced into the governing equations as an external force as

where D_ijμu_j and C _ij(EQ)ρuu_j are the viscous loss term and inertial loss term, respectively. D_ij and C _ij are the prescribed matrices consisting of porous media resistance coefficients,

where D_n represents a normal viscous resistance coefficient, D_t is a tangential viscous coefficient, C _n is the normal inertial resistance coefficient, and C _t is the tangential inertial resistance coefficient.

The normal inertial resistance coefficient can be calculated for the pressure loss by using a perforated plate with holes with an empirical equation to derive porous media inputs for the turbulent flow through a perforated plate or net. The relationship between the mass flow rate (^·m ) through the porous material and the pressure drop (Perry and Gree, 1997) is described as,

In Equation (8), A_f and A_p represent the free area or total area of the holes and the area of the netting (solid and holes), respectively, and C=0.98 is an experimental coefficient, as described in Smith and Winkle (1958).

Because m . = ρ u A p , Equation (8) can be rewritten as

In the case of the netting, most of the falling pressure occurs in the inertial loss term, and thus, C₂ is represented as,

where T is the thickness of the material.

Boundary and initial conditions

The simulations were performed without abalone or macro- algae inside the container or fouling on the external structure. The CFD analysis was conducted for two cases. For Case 1, the incoming flow acts perpendicular to the plates, and for Case 2, the direction of flow acts along the six sheets of the polyethylene plate (Fig. 3). The computational model domain size for each simulation was 20 × 20 × 10 m³ with boundary conditions as described by Kim et al. (2014a). The coordinate system of the model domain was set with Z as the vertical direction. The least absolute normalized error (LANE) approach was applied in order to determine the friction coefficient of the netting, as described in the viscous loss term in Equation (3). The values for the friction coefficients of the porous media, as described in Equation (7), were set to the same values as those reported by Patursson et al. (2010): D_n=51,730 m^-2, D _t =26,379 m^-2, C _n=5.0980 m^-1, C _t =1.6984 m^-1. To estimate the concentration of DO within the abalone grow-out volume, the inverse of the respiratory CO₂ production was modeled as a constituent. To simulate the spatial distribution of the relative concentration, the DO inside the cage was assumed to have been converted into CO₂ by the abalone (Kim et al., 2014b). This approach was taken because it was difficult to perform a direct simulation of the exact emission quantity of a given pollutant. Therefore, the abalone was considered to be the pollutant source as opposed to a sink for the DO inside the cage system. In this case, the low pollutant levels indicated high levels of DO because an effective exchange took place. In this CFD model, the chemical reactions of the substance inside the cage were not considered, but the flow equation and the scalar transport equation of a substance (concentration, temperature, etc. of the substance) were taken into consideration. For the scalar transport equation, the normalized concentration of DO was assumed to be 1 upstream and 0 inside of the abalone cage. In other words, the boundary condition for the relative concentration of DO at the surface inside the cage was set to 0 in the simulation. Then, the upstream flow with a relative concentration of 1 (relative concentration of oxygen is assumed to be 100%), in which all of the dissolved oxygen in the seawater would still be available, passes through the cages, and the flow inside the cages changes to have a relative concentration value of 0 (0%) because all DO had been depleted by the abalone. The computational domain was discretized into 32,190,562 tetrahedral cells with 65,906,511 faces.

Results and Discussion

The distribution of DO in the containment structures was examined through CFD simulation (as representative slices in the X-Y plane) for Cases 1 and 2 (Fig. 4; blue color: high oxygen concentration, red color: low oxygen concentration). Because the abalone was assumed to use all of the oxygen in the cages, a relative concentration value of 1 was denoted to be the condition in which all of the dissolved oxygen in the water would still be available, whereas a relative concentration value of 0 would represent a situation in which all of the dissolved oxygen had been depleted. In Case 1, with an external flow perpendicular to the six sheets of polyethylene plates, a substantial amount of shadowing was evident and the oxygen replenishment rate was poor. For Case 2, in which the direction of the flow was parallel to the plates in the abalone shelter, the dissolved oxygen replenishment rate was better.

The relative concentration of DO in the X-Y plane, where Z = -2.2 for each case, is shown in Fig. 5. The DO concentration changes at Z = -1.6, -2.2, -2.8 and -3.4 m inside the container for Cases 1 and 2 is depicted in Figs. 5a and b. In Fig. 5, the dotted lines indicate the average oxygen concentration within the container for each height (Z), and a solid line indicates the average concentration according to the average flow velocity at the given height. The relative oxygen concentration within the container decreased to a level of approximately 10% in the wake streams for Case 1 (in which the flow acts perpendicular to the plates).

More than 60% of the relative oxygen concentration was maintained for Case 2 (in which the flow acts parallel to the plates). The changes in concentration through two sets of containers were then estimated for each case (Fig. 6). To estimate these values, the pattern of change in oxygen concentration was assumed to remain the same within a container, and then the procedure was applied to the second container in the series. The change was more drastic for Case 1 because the flow was much more restricted and had been reduced to less than 10% in the wake streams due to the flow colliding with the shelters (Fig. 6a). For Case 2 (Fig. 6b), the oxygen concentration decreases to 60, 40 and 30% as the flow is reduced through the series of container. These results clearly indicate that the abalone plate shelters should be placed parallel to the flow.

The CFD analysis revealed that more than 60% of the relative oxygen concentration in a container and 30% in two containers was maintained for Case 2 (where the flow acts parallel to the plates). In terms of the flow rate, Choi et al. (2013) reported that the flow rate within the containment changed from 0.11-0.19 m/s to 0.009-0.011 m/s and was reduced by more than 90% in a conventional abalone cage, in which the flow acts perpendicular to the plates. Taken together, it is clear from these results that the abalone plate shelters should be placed parallel to the flow.

Because the container structures and shelters for abalone grow-out used in the CFD modeling were very intricate, combining several types of structural members, it was very difficult to simulate the oxygen consumption and carbon dioxide produced by the animals when considering the addition of a comprehensive marine carbonate model. The next step involves modeling the oxygen consumption of the abalone and the foul organisms to take into account the addition of a comprehensive marine carbonate model.