Case Study of Central Outlet Cap Used in Flow-Through Aquaculture Systems by Using Computational Fluid Dynamics

Abstract

The consumption of aquaculture products and, in turn, the importance of the aquaculture industry are increasing with the depletion of global fishery resources. In the flow-through aquaculture systems used in Korea, olive flounders are overcrowded near the central outlet, causing stress, and the sharp central outlet hole injures the olive flounders. Therefore, in this study, we propose a central outlet cap that can prevent overcrowding and injuries in olive flounders near the central outlet in a flow-through aquaculture system. An L₂₇(3⁵) orthogonal array was constructed using five central outlet cap design variables, and computational fluid dynamics (CFD) analysis was performed for each experimental point. The pressure drop between the tank inlet and the central outlet was evaluated, and the experimental point with the highest pressure drop was identified. In addition, the internal fluid velocity of the experimental point with the highest pressure drop value was confirmed to be improved compared to the initial flow-through aquaculture system. The central outlet cap designed in this study is expected to be economically beneficial to aquaculture by reducing the overcrowding of olive flounder and preventing injury to olive flounder while improving the internal fluid velocity.

1. Introduction

According to the Food and Agriculture Organization (FAO) of the United Nations, fish consumption is increasing worldwide because of rising incomes and technological advances [1]. In 2020, global fish production stood at 178 million tons, of which 88 million tons originated from aquaculture-based production. According to Iber B and Kasan N [2], the aquaculture industry could curb the demand for wild fish and thereby halt overfishing. In addition, with the depletion of global fishery resources, strengthening of international fishery laws, and rising demand for aquaculture products, the aquaculture industry is gaining increasing importance, and fish-farming ecosystems are improving [3]. Therefore, the world is expected to rely primarily on aquaculture to meet the growing demand for fish [4]. Farmed fish are affected by several stressors including overcrowding, water temperature, dissolved oxygen concentration, stocking density, and various water quality parameters. These stressors can significantly affect the physiology and activity of farmed fish, leading to excessive energy consumption and adverse effects on their health and immunity and consequently increasing their mortality rates [5,6]. Stress also causes some components of the immune system to lose their function, making fish susceptible to infections and diseases [7], resulting in economic losses for fish farmers [5]. Therefore, fish stress management is a critical research issue facing the aquaculture industry, as the death of farmed fish can financially destabilize the aquaculture industry and seriously damage its foundation.

Olive flounder is currently farmed in approximately 30.5% of all farms in the aquaculture industry in Korea, making it the most widely farmed species [8]. A field survey of a flow-through aquaculture system for olive flounder farming confirmed that these fish were continuously overcrowded in the central outlet. According to Yin et al. [9], overcrowding is a stressor for farmed fish, and it can lead to increased mortality of olive flounder in a flow-through aquaculture system. In addition, the sharp edges of the central outlet cause injuries to overcrowded olive flounders.

Researchers have analyzed the flow characteristics of various aquaculture systems using computational fluid dynamics (CFD) to optimize them [10,11,12]. In addition, research on various structures, such as net-type structures in water and floating porous nets for aquaculture, has been conducted recently [13,14]. For example, Oca et al. [15] considered the design variables of a circular tank inlet and calculated the optimal values of parameters such as the flow rate, inlet diameter, and water level; further, they analyzed the flow rate inside the tank. An et al. [16] examined the water column diameter and outlet location to optimize the inlet topography according to the flow characteristics of the tank. Although various studies have investigated aquaculture systems, few have aimed to prevent the overcrowding of olive flounder by adding other structures in such systems. Therefore, the authors propose a central outlet cap that can reduce the degree of overcrowding of olive flounder at the central outlet and prevent their injury. We performed a CFD analysis of the flow-through aquaculture system to determine the optimal shape of the central outlet cap based on the pressure drop inside the system.

In this study, the pressure drop is the average total pressure displacement between the tank inlet and the central outlet. Previous studies have shown that the pressure drop increases with increasing fluid velocity [17,18]. Therefore, in a flow-through aquaculture system, the pressure drop caused by friction between the fluid and the central outlet cap is used as a proxy for the fluid velocity. The dissolved oxygen concentration in the tank, which is closely related to the mortality of farmed fish, affects the growth rate of the fish. A low dissolved oxygen concentration can lead to decreased food intake, poor response to stimulation, and lethargy in farmed fish [19]. According to Pastore et al. [20], because dissolved oxygen increases as the current velocity increases, increasing the fluid velocity inside the flow-through aquaculture system can have a positive effect on the tank.

In this study, we attempt to derive a central outlet cap shape that can reduce the overcrowding of olive flounder near the central outlet of a flow-through aquaculture system and prevent the surfacing of olive flounder. The flow chart of this study is shown in Figure 1. Five central outlet cap design variables were selected, and an orthogonal array was created according to the design variables and levels using Minitab 21.4.1 software. CFD analysis was performed for each experimental point of the orthogonal array to derive an experimental point with a high-pressure drop.

2. Model Design and Methods for Numerical Analysis and Simulation

2.1. Geometric Model and Boundary Conditions

KWON I and KIM T [21] determined the optimal shape of the flow-through aquaculture system used in Korea. The present study utilized this optimal shape, as shown in Figure 2. The flow-through aquaculture system has a diameter of 5000 mm, a wall height of 1000 mm, a water depth of 400 mm, and a bottom inclined at 3°. It has four tank inlets, and each tank inlet has six inlet holes. Further, it has one outlet with 10 holes at its center. Water flows into the tank at a flow rate of 4.167 kg/s through the four tank inlets, and atmospheric pressure conditions are created at the central outlet [21]. The tank inlet, central outlet, and central outlet cap are made of polyvinyl chloride (PVC), and the rest of the tank is made of concrete. As shown in Figure 3, the central outlet cap is installed on the central outlet.

2.2. Numerical Model Set Up

ANSYS Fluent 2023 R2 software, based on the finite volume method (FVM), was used to analyze the pressure drop in the flow-through aquaculture system using CFD [22]. The continuity equation and Reynolds-averaged Navier–Stokes (RANS) equation were solved using ANSYS Fluent to calculate the fluid flow in the flow-through aquaculture system, and the governing equations were discretized using the FVM. The steady-state condition was considered, and the shear stress transfer $k-\omega$ (SST $k-\omega$) model developed by Menter [23] was used to effectively combine the robust and accurate $k-\omega$ formulation in the near-wall region with the free-flow independence of the $k-\epsilon$ formulation in the far-field region [24]. The SST $k-\omega$ turbulence model has been used to perform CFD analyses in various aquaculture studies [25,26,27,28,29]. The turbulent kinetic energy ($k$) and specific dissipation rate ($\omega$) of SST $k-\omega$ are expressed in Equations (1) and (2), respectively.

$${\displaystyle \frac{\partial }{\partial t}}\left(\rho k\right)+{\displaystyle \frac{\partial }{\partial x_i}}\left(\rho k{u}_i\right)={\displaystyle \frac{\partial }{\partial x_j}}\left[{\mathsf{\Gamma }}_k{\displaystyle \frac{\partial k}{\partial x_j}}\right]+G_k-Y_k+S_k$$

(1)

$${\displaystyle \frac{\partial }{\partial t}}\left(\rho \omega \right)+{\displaystyle \frac{\partial }{\partial x_i}}\left(\rho \omega u_i\right)={\displaystyle \frac{\partial }{\partial x_j}}\left[{\mathsf{\Gamma }}_{\omega }{\displaystyle \frac{\partial \omega }{\partial x_j}}\right]+G_{\omega }-Y_{\omega }+D_{\omega }+S_{\omega }$$

(2)

where $t$ is the time, $\rho$ is the fluid density, and $u$ is the fluid velocity. $G_k$ denotes the production of turbulence kinetic energy and $G_{\omega }$ represents the generation of $\omega$. The calculated values $Y_k$ and $Y_{\omega }$ represent the dissipation of $k$ and $\omega$, respectively, because of turbulence. $D_{\omega }$ is the cross-diffusion term, and $S_k$ and $S_{\omega }$ are user-defined source terms. Here, the effective diffusivities of $k$ and $\omega$ are expressed in Equations (3) and (4), respectively.

$${\mathsf{\Gamma }}_k=\mu +{\displaystyle \frac{{\mu }_t}{{\sigma }_k}},$$

(3)

$${\mathsf{\Gamma }}_{\omega }=\mu +{\displaystyle \frac{{\mu }_t}{{\sigma }_{\omega }}}$$

(4)

where ${\sigma }_k$ and ${\sigma }_{\omega }$ denote the Prandtl numbers of $k$ and $\omega$, and they are expressed in Equations (5) and (6), respectively.

$${\sigma }_k={\displaystyle \frac{1}{\frac{F_1}{{\sigma }_{k,1}}+\frac{(1-F_1)}{{\sigma }_{k,2}}}},$$

(5)

$${\sigma }_{\omega }={\displaystyle \frac{1}{\frac{F_1}{{\sigma }_{\omega ,1}}+\frac{(1-F_1)}{{\sigma }_{\omega ,2}}}}$$

(6)

The turbulent viscosity is expressed in Equation (7), where $S$ is the magnitude of the strain rate. The low number correction coefficient ($\alpha *$) is expressed in Equation (8), where ${Re}_t$ and ${\alpha }_0^{*}$ are expressed in Equations (9) and (10), respectively. Here, ${\beta }_i$ = 0.072.

$${\mu }_t={\displaystyle \frac{\rho k}{\omega }}{\displaystyle \frac{1}{max\left[\frac{1}{\alpha *},\frac{S{F}_2)}{{\alpha }_1\omega }\right]}},$$

(7)

$$\alpha *={\alpha }_{\infty }^{*}\left({\displaystyle \frac{{\alpha }_0^{*}+\frac{R{e}_t}{R_k}}{1+\frac{R{e}_t}{R_k}}}\right)$$

(8)

$${Re}_t={\displaystyle \frac{\rho k}{\mu \omega }}$$

(9)

$${\alpha }_0^{*}={\displaystyle \frac{{\beta }_i}{x}}$$

(10)

The blending functions $F_1$ and $F_2$ are given by Equations (11) and (12), respectively:

$$F_1=\mathit{tanh}⌈{\left[min\left(max\left({\displaystyle \frac{\sqrt{k}}{0.09\omega y}},{\displaystyle \frac{500\mu }{\rho \omega y^2}}\right)\right),{\displaystyle \frac{4\rho k}{{\sigma }_{\omega ,2}{D}_{\omega }^{+}{y}^2}}\right]}^4⌉,$$

(11)

$$F_2=\tanh \left[{\left(max\left[{\displaystyle \frac{2\sqrt{k}}{0.09\omega y}},{\displaystyle \frac{500\mu }{\rho \omega y^2}}\right]\right)}^2\right]$$

(12)

where $y$ is the distance to the next surface, and $D_{\omega }^{+}$, expressed in Equation (13), is the positive portion of the cross-diffusion term.

$$D_{\omega }^{+}=max\left[{\displaystyle \frac{2\rho }{{\sigma }_{\omega ,2}\omega }}{\displaystyle \frac{\partial \omega }{\partial x_j}},{10}^{-10}\right]$$

(13)

The constants of the SST $k-\omega$ model used in this study are as follows: ${\sigma }_{k,1}=1.176,{\sigma }_{k,2}=1,{\sigma }_{\omega ,1}=2,\mathrm{a}\mathrm{n}\mathrm{d}{\sigma }_{\omega ,2}=1.168$.

The CFD analysis performed in this study used a coupled method within the pressure–velocity coupling algorithm that is easy to analyze in the steady state and can solve the momentum- and pressure-based continuity equations simultaneously [24].

2.3. Definition of Orthogonal Array

To determine the optimal shape of the central outlet cap, five design variables were selected as follows: vertical length ($x_1$) [mm], horizontal length ($x_2$) [mm], upper angle ($x_3$) [°], number of upper line holes ($x_4$) [number], and hole width ($x_5$) [mm]. Figure 4a depicts $x_1$, $x_2$, $x_3$, and $x_5$ of the central outlet cap, and Figure 4b shows the shapes of the central outlet cap according to the number of upper line holes. In addition, eight holes were created on the side of the central outlet cap for solid discharge in the flow-through aquaculture system.

The values of each design variable of the central outlet cap by level are shown in

Table 1. Magnitudes and levels of design variables of central outlet cap.

Level	${\mathit{x}}_1$ [mm]	${\mathit{x}}_2$ [mm]	${\mathit{x}}_3$ [°]	${\mathit{x}}_4$	${\mathit{x}}_5$ [mm]
1	50	400	0	0	3
2	125	800	7.5	1	6
3	200	1200	15	2	9

. When the number of design variables is 5 and the number of levels of each design variable is 3, the total number of treatment combinations in the full-factorial design (3⁵) is 243, which is very large. Therefore, we reduced the analysis time by using an orthogonal array that can efficiently analyze the central outlet cap without testing all combinations of design variables. An orthogonal array is a numerical matrix in which each row represents a level and each column represents a design variable. This array is called an orthogonal one because each column can be evaluated independently of the other columns [30]. This experimental design considered the interaction effects between $x_2$ and $x_3$ and those between $x_2$ and $x_4$ based on preliminary information; the results of the orthogonal array analysis are summarized in

Table 2. L₂₇(3⁵) orthogonal array.

Experimental Number	Variables Column
	${\mathit{x}}_1$	${\mathit{x}}_2$	${\mathit{x}}_3$	${\mathit{x}}_4$	${\mathit{x}}_5$
1	50 mm	400 mm	0°	0	3 mm
2	50 mm	400 mm	7.5°	1	6 mm
3	50 mm	400 mm	15°	2	9 mm
4	50 mm	800 mm	0°	1	6 mm
5	50 mm	800 mm	7.5°	2	9 mm
6	50 mm	800 mm	15°	0	3 mm
7	50 mm	1200 mm	0°	2	9 mm
8	50 mm	1200 mm	7.5°	0	3 mm
9	50 mm	1200 mm	15°	1	6 mm
10	125 mm	400 mm	0°	0	6 mm
11	125 mm	400 mm	7.5°	1	9 mm
12	125 mm	400 mm	15°	2	3 mm
13	125 mm	800 mm	0°	1	9 mm
14	125 mm	800 mm	7.5°	2	3 mm
15	125 mm	800 mm	15°	0	6 mm
16	125 mm	1200 mm	0°	2	3 mm
17	125 mm	1200 mm	7.5°	0	6 mm
18	125 mm	1200 mm	15°	1	9 mm
19	200 mm	400 mm	0°	0	9 mm
20	200 mm	400 mm	7.5°	1	3 mm
21	200 mm	400 mm	15°	2	6 mm
22	200 mm	800 mm	0°	1	3 mm
23	200 mm	800 mm	7.5°	2	6 mm
24	200 mm	800 mm	15°	0	9 mm
25	200 mm	1200 mm	0°	2	6 mm
26	200 mm	1200 mm	7.5°	0	9 mm
27	200 mm	1200 mm	15°	1	3 mm

. Various optimization studies have used orthogonal arrays to efficiently determine and analyze the combination of factor levels to be used in each experimental run [31,32,33].

2.4. Grid Models

We attempted to create a poly-hexacore grid model of the flow-through aquaculture system and the central outlet cap using ANSYS Fluentmesh to perform CFD analysis. To determine the mesh size of the analysis model, a mesh independence test was performed on experimental number 1, and the results are shown in Figure 5. The mesh independence tests were conducted using coarse (cell count = 1,873,547), medium (cell count = 3,877,453), and fine (cell count = 8,218,916) mesh types. While the pressure drop values of the medium and fine meshes are similar, that of the coarse mesh differs from those of the other two mesh types. In addition, the analysis time efficiency of the fine mesh was low due to the excessively long CFD analysis time compared to those for the coarse and medium meshes. Therefore, in this study, a grid model was created for each experimental point by using the medium mesh to achieve a balance between the mesh accuracy of the central outlet cap and analysis time efficiency. As shown in Figure 6, the tank inlet, central outlet, and central outlet cap were set to cell sizes of 0.5 to 8 mm to obtain accurate analysis results. The number of cells in the experimental points ranges from 2 million to 12 million and varies greatly depending on the shape of the central outlet cap.

3. Result

CFD analysis was performed to investigate the flow in the flow-through aquaculture system. This numerical analysis was performed to determine the pressure drop difference between the inlet and outlet caused by pressure drop and to compare the fluid velocities. The pressure drop values derived using the CFD analysis for the experimental points in Table 2 are summarized in

Table 3. Pressure drop of flow-through aquaculture system.

Experimental Number	Pressure Drop [Pa]	Experimental Number	Pressure Drop [Pa]	Experimental Number	Pressure Drop [Pa]
1	1325.41523	10	659.465	19	594.73348
2	637.13841	11	596.37012	20	691.30139
3	584.4903	12	668.34447	21	597.20498
4	589.94417	13	585.31235	22	630.69791
5	577.98958	14	614.01653	23	587.17231
6	751.99647	15	606.39196	24	589.71031
7	580.17279	16	597.2357	25	583.21357
8	661.75538	17	594.46629	26	587.89079
9	585.91797	18	582.54783	27	611.24046

. The pressure drop of the initial flow-through aquaculture system was 579.46232 Pa; this is the second lowest value when compared to all experimental points. Experimental number 5 had the lowest pressure drop value among the 27 experimental points. By contrast, experimental number 1 produced the highest pressure drop among all experimental points. As shown in Figure 7, experimental number 1 showed a pressure drop value 128.73% higher than that of the initial flow-through aquaculture system. This is because the design variable levels of experimental number 1 are lowest, causing a large flow disturbance and high pressure loss.

4. Discussion

After performing CFD analysis, the fluid velocity inside the flow-through aquaculture system was evaluated. Figure 8 shows a comparison of the fluid velocity contours of the initial flow-through aquaculture system and experimental number 1. Figure 8a shows the initial flow-through aquaculture system, and Figure 8b shows the flow-through aquaculture system with the optimally shaped central outlet cap. Due to the effect of the high pressure drop value, the overall fluid velocity was higher in experimental number 1 than in the initial flow-through aquaculture system, confirming an improvement in the internal fluid velocity. Also, in both flow-through aquaculture systems, the flow velocity generally decreases toward the tank center. In experimental number 1, the fluid velocity appears to be improved mainly near the center of the tank. This is thought to be because the fluid velocity is high, as fluid moves only to the sideline holes of the central outlet cap.

Additionally, there is a problem where various solids, such as olive flounder feed and excrement, are continuously generated inside the flow-through aquaculture system. The accumulation of solids inside the aquaculture tank can create an environment favorable for the survival of fish pathogens [34]. Solids existing in the internal fluid of the tank are deposited at the bottom of the tank, and the deposition is promoted when the flow velocity is low [35]. In this respect, the improved internal fluid velocity of experimental number 1 is expected to be helpful in preventing solid deposition.

5. Conclusions

This study proposes the optimal shape of a central outlet cap that can be used in a flow-through aquaculture system using CFD. The design variables of the central outlet cap were selected to form an orthogonal array, and the pressure drop was evaluated by performing CFD simulations on the experimental points of the orthogonal array. The numerical results between the experimental points were compared, and the pressure drop of experimental number 1 was highest. Also, the internal fluid velocity was improved in experimental number 1 compared to the initial flow-through aquaculture system. Therefore, the design variables of the central outlet cap were derived as follows: level 1 of vertical length, level 1 of horizontal length, level 1 of upper angle, level 1 of the number of upper line holes, and level 1 of hole width.

The case study of the central outlet cap derived in this study is expected to reduce the overcrowding of olive flounder in a flow-through aquaculture system and provide various advantages at higher fluid velocities. In the future, we will conduct an optimal design to determine a more accurate shape of the central outlet cap along with a study on the comparison between the results of CFD simulations and additional experimental results on the lab scale.