Effect of Fine-Pore Aeration Tube Layout on Dissolved Oxygen Distribution and Aeration Performance in Large-Scale Pond

Abstract

Dissolved oxygen (DO) is a crucial water quality characteristic in the cultivation of vannamei shrimp. Increasing the DO concentration in shrimp ponds can be carried out using the aeration method with a tool called an aerator. In this study, types of fine-pore aeration tubes are chosen. This aerator offers multiple benefits, such as superior aeration efficiency, effortless installation, and minimal clogging. In practice, fine-pore aeration tubes can be arranged according to needs, so the layout used can influence the resulting aeration performance. This research uses the computational fluid dynamics (CFD) method to analyze DO distribution, water circulation, and aeration performance ($K_L{a}_{20}$, SOTR, and SOTE) produced in various aerator layouts, namely straight-type, ring-type, and square-type, in a vannamei shrimp pond. The results show that the straight-type layout has the best DO distribution because it is spread throughout the pond area. The square-type layout has the best water circulation because it has the largest area with water velocities of less than 5 cm/s. The optimal aeration performance was achieved with the straight-type layout, which demonstrated a $K_L{a}_{20}$ value of 3.16 h⁻¹, SOTR value of 19.20 kg/h, and SOTE of 29.30%.

1. Introduction

Indonesia, with its extensive coastline of 108,000 km [1], is the world’s second-longest coastline [2]. This geographical feature greatly benefits coastal communities, particularly in shrimp cultivation [3]. The country’s long coastline, stable water temperatures, ample water supply, and natural mangrove habitats provide ideal conditions for shrimp farming [4].

The Indonesian Ministry of Research, Technology, and Higher Education, along with Diponegoro University (Undip), is working on developing the Marine Science Techno Park (MSTP) in Teluk Awur Village, Tahunan, Jepara Regency. MSTP-Undip is one of 18 Science Techno Parks (STPs) in Indonesia, aimed at supporting the national maritime vision and Nawacita program. Among the innovations at MSTP is a sustainable, supra-intensive vannamei shrimp cultivation technology [5].

Water quality is crucial in shrimp cultivation, as shrimp are aquatic organisms dependent on water quality from stocking to harvest [6]. Key water quality parameters include dissolved oxygen (DO), temperature, salinity, pH, and others, which influence shrimp health and productivity [7]. Monitoring and managing these parameters are essential to prevent stress and disease, which can otherwise impact shrimp growth and yield.

Dissolved oxygen (DO) is a critical factor for water quality and shrimp production [8]. DO levels indicate the amount of oxygen available to aquatic life [7] and are crucial for maintaining ecosystem health. Low DO levels can lead to anoxia, slow growth, and even death of shrimp [9]. While natural aeration through algae and phytoplankton is effective during the day [10], it becomes insufficient at night [11]. Factors like high fertilization and dense shrimp populations further inhibit DO production and DO consumption. To address this, artificial aeration methods are employed, such as fine-pore aeration tubes [12]. These aeration tubes are aerators placed at the bottom of the pond, which will then produce fine bubbles and come into contact with the surface between air and water [13]. Fine-pore aeration tubes have superior aeration efficiency, effortless installation, and minimal clogging [14].

Laboratory tests by Cheng et al. [14] examined fine-pore aeration tube efficiency. Under the identical conditions, the I-shaped diffuser has the highest aeration efficiency and the S-shaped diffuser the lowest. When mass transfer of air-free water surfaces is blocked, all diffusers lose efficiency, but the I-shaped diffuser performs best and the S-shaped diffuser the worst.

Li et al. [15] assessed the efficacy of a fine-bubble diffused aeration system in a cylindrical aeration tank using the fuzzy c-means method. The evaluation of fine-bubble diffused aeration systems revealed the aeration characteristic criterion (ACC) to be more sensitive than the volumetric oxygen transfer coefficient and specific standard oxygen transfer efficiency (SSOTE) in measuring oxygen transfer efficiency. Ring diffusers function best, followed by square, parallel line and cross diffusers. The fuzzy c-means technique enhances horizontal and vertical dissolved oxygen (DO) distribution analyses in cylindrical aeration tanks.

Du et al. [12] conducted a study on the impact of various arrangements of fine-pore aeration tubes on the accumulation of dirt and the process of aeration in rectangular water tanks. They came to the conclusion that the four-corner-type diffuser, with its good aeration and dirt collecting ability, is most suited for usage in shrimp ponds.

Nevertheless, their research has not addressed the distribution of dissolved oxygen (DO) at different depths inside the ponds. Therefore, in the present study, the discussion focuses on a larger-scale pond, the Marine Science Techno Park–Undip vannamei shrimp pond, to obtain a better selection of aeration tube layouts. Problem solving was carried out using the computational fluid dynamics (CFD) method via ANSYS Fluent 2023 R2. ANSYS Fluent 2023 R2 is a state-of-the-art CFD software known for its advanced simulation capabilities in modeling fluid flow and heat transfer released in 2023 with the second revised version in that year. By using CFD, it is hoped that it can provide a clearer representation of the distribution of dissolved oxygen at various depths and aerator layouts, so as to increase the efficiency of shrimp cultivation.

2. Materials and Methods

2.1. Governing Equations

This study employs two primary equations as the governing equations for fluid flow. Equation (1) represents the mass conservation equation, while Equation (2) denotes the momentum conservation equation. Both equations account for interactions between the gas phase and the liquid phase [12].

$$\nabla \left({\rho }_i{\alpha }_i{U}_i\right)=0$$

(1)

$${\displaystyle \frac{\partial \left({\alpha }_i{\rho }_i{U}_i\right)}{\partial t}}+\nabla \left({\alpha }_i{\rho }_i{U}_i{U}_i\right)=-\alpha \nabla P+\nabla \left({\alpha }_i{\tau }_i\right)\pm F_i+{\alpha }_i{\rho }_{i}g(i=g,l)$$

(2)

where ${\rho }_i$ represents the phase density, with the gas phase measured in g/L and the liquid phase in g/cm³; $a_i$ denotes the volume fraction of phase i; $U_i$ indicates the phase velocity; $P$ stands for pressure (Pa); ${\tau }_i$ represents the diffusion phase, shear stress (N/m³); and $F_i$ denotes the force between the phases. The Schiller–Naumann drag model, commonly employed in two-fluid models, is utilized for the drag function. For the lift force, the Moraga lift model, which is more suitable for spherical bubbles, is applied [16].

The k-ε turbulence model is one of the most common turbulence models used in CFD. This model consists of two equation models to express the turbulence properties of a flow. Generally, the k-ε turbulence model well represents the flow field properties of the liquid–gas phase. Equations (3) and (4) show the realizable k-ε turbulence model.

$${\displaystyle \frac{\partial \left({\alpha }_l{\rho }_{l}k\right)}{\partial t}}+{\displaystyle \frac{\partial \left({\alpha }_l{\rho }_{l}k{u}_i\right)}{\partial x_j}}={\displaystyle \frac{\partial }{\partial x_j}}\left[{\alpha }_l\left(\mu +{\displaystyle \frac{{\mu }_t}{{\sigma }_k}}\right){\displaystyle \frac{\partial k}{\partial x_j}}\right]+{\alpha }_l\left(G_k+G_b-{\rho }_lϵ\right)$$

(3)

$${\displaystyle \frac{\partial \left({\alpha }_l{\rho }_lϵ\right)}{\partial t}}+{\displaystyle \frac{\partial \left({\alpha }_l{\rho }_lϵu_j\right)}{\partial x_j}}={\displaystyle \frac{\partial }{\partial x_j}}\left[{\alpha }_l\left(\mu +{\displaystyle \frac{{\mu }_t}{{\sigma }_{ϵ}}}\right){\displaystyle \frac{\partial ϵ}{\partial x_j}}\right]+{\alpha }_l\left({\rho }_l{C}_2{\displaystyle \frac{{ϵ}^2}{k+\sqrt{{\nu }_lϵ}}}+C_{1ϵ}{\displaystyle \frac{ϵ}{k}}{C}_{3ϵ}{G}_b\right)$$

(4)

where G_k represents the rate of kinetic energy generation due to the mean velocity gradients, $C_{1ϵ}=1.44$, $C_{2ϵ}=1.9$; $G_b$ is the rate of kinetic energy generation due to buoyancy; k denotes the turbulence kinetic energy (m²/s²); ${\mu }_t$ is the turbulent viscosity (kg/m·s); $\nu$ is the kinematic viscosity (m²/s); and $ϵ$ is the dissipation rate (m²·s).

2.2. Oxygen Transfer Model

Gas–liquid mass transfer refers to the movement of mass between the gas and liquid phases. This can happen by absorption (gas to liquid) or desorption (liquid to gas) [17]. This phenomenon takes place when there is contact between the gas and liquid phases, and there is a pressure or concentration gradient. This means that the concentrations in the two phases deviate from what is expected according to Henry’s law. Henry’s law states that the quantity of a specific gas dissolved in a particular liquid, at a consistent temperature, is directly proportional to the partial pressure of the gas in equilibrium with the liquid. The pressure gradient is specific to the gas phase, whereas the concentration gradient is specific to the liquid phase. Equation (5) represents the general concentration transfer equation in two-phase flow [18].

$${\displaystyle \frac{\partial \left({\alpha }_i{c}_i\right)}{\partial t}}+\overrightarrow{\nabla }·\left(a_i{c}_i{\overrightarrow{U}}_i\right)=-\overrightarrow{\nabla }\left({\alpha }_i\left({\overrightarrow{J}}_i+\overline{c_i^{\prime }{U}_i^{\prime }}\right)\right)+\overline{L_i}$$

(5)

where $\overline{L_i}$ denotes the interfacial transfer of concentration, ${\overrightarrow{J}}_i$ represents the flux due to the molecular diffusion, and $\overline{c_i^{\prime }{U}_i^{\prime }}$ denotes the turbulent diffusion of the concentration.

Equation (6) models the mass transfer of oxygen between the gas bubble and the liquid.

$$\overline{L_L}=k_{L}a(C_L^{*}-C_L)$$

(6)

where $a$ represents the interfacial area, $k_L$ denotes the local mass transfer coefficient, and $\left(C_L^{*}-C_L\right)$ is the driven force of the oxygen transfer.

The interfacial area is defined as the ratio of the total air bubble surface to the volume of liquid. For spherical bubbles having a bubble Sauter diameter $d_{bs}$, the interfacial area is expressed in Equation (7).

$$a={\displaystyle \frac{6}{d_{bs}}}{\displaystyle \frac{{\alpha }_g}{1-{\alpha }_g}}$$

(7)

Equation (8) represents the mathematical model for the local mass transfer coefficient.

$$k_L=2\sqrt{{\displaystyle \frac{D_L{V}_r}{\pi d_{bs}}}}$$

(8)

where $D_L$ represents the diffusion coefficient of the oxygen in water (at 20 °C) and $V_r$ is the relative velocity.

This oxygen transfer model is used to build a user-defined function (UDF). This is based on Wu et al. (2014). The value of the oxygen diffusion coefficient into water is 3.36 × 10⁻⁴ m²/s [19]. In addition, the saturated DO concentration was also defined in this UDF with a value of 8.1 mg/L by considering the temperature and salinity of the pond water in this study based on Lin and Tseng (2019) [20].

2.3. Aeration Performance

The efficacy of an air diffuser in oxygen transfer is assessed by measuring the volumetric oxygen transfer coefficient ($K_L{a}_T$) in accordance with the oxygen mass transfer model outlined by ASCE (American Society of Civil Engineers) standards. Equation (9) represents the fundamental equation for oxygen mass transport [12].

$$C=C_{\infty ,T}^{*}-\left(C_{\infty ,T}^{*}-C_0\right)\exp \left(-K_L{a}_{T}t\right)$$

(9)

where $C_0$ denotes initial dissolved oxygen concentration before aeration begins, which is generally 0; C represents dissolved oxygen at a certain time (mg/L); $K_L{a}_T$ denotes the volumetric oxygen transfer coefficient at water temperature (s⁻¹); $C_{\infty ,T}^{*}$ is the saturation dissolved oxygen concentration at water temperature T (mg/L); and t is the aeration time (s).

If the water temperature does not show a value of 20 °C, then $K_L{a}_T$ correction is needed to calculate SOTR (standard oxygen transfer rate). The equation for correcting the $K_L{a}_T$ value is shown in Equation (10).

$$K_L{a}_{20}=K_L{a}_T·{\theta }^{T-20}$$

(10)

where $K_L{a}_{20}$ represents the standard volumetric oxygen transfer coefficient, $\theta$ denotes a constant that generally has a value of 1.024, and $T$ represents the water temperature (°C).

SOTR, the standard oxygen transfer rate, quantifies the amount of oxygen that is introduced into water by an aerator under specific conditions of temperature (20 °C) and pressure (1 atm). This SOTR value will then be used to calculate the SOTE (standard oxygen transfer efficiency) value. $SOTR$ can be calculated using Equation (11).

$$SOTR=K_L{a}_{20}{C}_{\infty }^{*}V\times {10}^{-3}$$

(11)

where SOTR denotes the standard oxygen transfer rate (kg/h); $C_{\infty }^{*}$ represents the dissolved oxygen saturation concentration at 20 °C (mg/L); and V is the volume of water in the pond (m³).

SOTE, or standard oxygen transfer efficiency, quantifies the ratio of oxygen that is introduced into the water to the overall oxygen intake during the process of aeration. SOTE can be calculated using Equation (12).

$$SOTE={\displaystyle \frac{SOTR}{0.21\times 1.3\times q}}\times 100\%$$

(12)

where SOTE represents standard oxygen transfer efficiency (%); 0.21 denotes the percentage of oxygen in the air; 1.3 represents the oxygen density (kg/m³); and q denotes the air flow rate (m³/h).

2.4. Computational Model

2.4.1. Geometric Model

Figure 1 illustrates the geometry of a shrimp pond at MSTP-Undip, providing a clear visual representation along with specific parameters essential for the pond’s design and subsequent analysis, helping to conceptualize the spatial layout necessary for the shrimp farming research. The table accompanying Figure 1,

Table 1. Parameters of Figure 1.

Parameter	Symbol	Value	Unit
Pond length	L	25	m
Pond depth	D	1.2	m

, lists the key parameters that describe this geometry. The pond has a length (L) of 25 m and a depth (D) of 1.2 m.

The total length of the aeration tubes is 80 m with three layout variations, namely a straight-type diffuser, ring-type diffuser, and square-type diffuser. Aeration tubes are arranged as the inlet and outlet are on the surface of the pond.

Figure 2 and

Table 2. Parameters of Figure 2.

Parameter	Symbol	Value	Unit
Distance between aerators horizontally	A1	3.57	m
Distance between aerators vertically	B1	1.67	m
Diffuser length	C1	1	m
Diffuser diameter	D1	16	mm

show the straight-type layout aeration tubes at the bottom of the pond. The dimensions of the pond are 25 m long, 25 m wide, and 1.2 m deep. Aeration tubes with a length of 1 m each, a diameter of 16 mm, and an arrangement of 8 × 10 are arranged in a distributed manner at the bottom of the pond.

Figure 3 and

Table 3. Parameters of Figure 3.

Parameter	Symbol	Value	Unit
Distance between aerators	A2	5	m
Diffuser diameter	B2	16	mm
Diffuser length	C2	5	m

show the ring-type layout aeration tubes at the bottom of the pond. The dimensions of the pond are 25 m long, 25 m wide, and 1.2 m deep. Aeration tubes with a length of 5 m each, a diameter of 16 mm, and an arrangement of 4 × 4 are arranged in a distributed manner at the bottom of the pond.

Figure 4 and

Table 4. Parameters of Figure 4.

Parameter	Symbol	Value	Unit
Distance between aerators	A3	6.65	m
Diffuser diameter	B3	16	mm
Diffuser side length	C3	1.25	m

show the ring-type layout aeration tubes at the bottom of the pond. The dimensions of the pond are 25 m long, 25 m wide, and 1.2 m deep. Aeration tubes with a length of 5 m each, a diameter of 16 mm, and an arrangement of 4 × 4 are arranged in a distributed manner at the bottom of the pond.

2.4.2. Independent Mesh

After creating the geometry, the meshing process is carried out using the geometry that has been created. Meshing is the division of a geometry into small elements that are interconnected between points or nodes that will be calculated numerically. In this simulation, the meshing process is carried out using the Fluent Meshing tool with the element size of 100 mm and Polyhedral element types. The selection of the element size of 100 mm is based on the grid independence carried out. Figure 5 shows that the change in DO concentration does not change significantly between an element size of 100 mm and an element size of 50 mm. The results of the meshing model are shown in Figure 6.

2.4.3. Boundary Conditions

Through the implementation of various approaches, boundary conditions for the numerical simulation are established once the grid is generated, as detailed in

Table 5. Boundary conditions and material properties.

Parameter	Symbol	Value	Unit
Pond
Water density	${\rho }_l$	1015	kg/m3
Water viscosity	${\mu }_l$	1.030 × 10−3	kg/ms
Salinity	S	20	psu
Volume	V	750	m3
Temperature	T	20	°C
Initial DO concentration	$C_0$	0	mg/L
Saturated DO concentration	$C_{\infty }^{*}$	8.1	mg/L
Air
Air density	${\rho }_g$	1.225	kg/m3
Air viscosity	${\mu }_g$	1.789 × 10−5	kg/ms
Bubble diameter	d	0.5–2	mm
Inlet volume fraction	$\alpha$	1	[-]
Oxygen mass fraction	wt%	0.21	[-]

. Specifically, at the inlet section designated as a velocity inlet, air is introduced into the water domain at a velocity of 0.0166 m/s, corresponding to an airflow rate of 240 m³/h. The outlet is arranged as a degassing where air can be released while the water remains in the fluid domain. No-slip boundary conditions with standard wall functions are applied to the pond walls.

2.5. Solution Set-Up

The pressure–velocity coupling scheme used is Phase Coupled SIMPLE. The gradient is discretized using the Least Square Cell-Based approach, the pressure is discretized using PRESTO!, and the volume fraction is discretized using Modified HRIC. The second-order upwind approach is employed for the calculation of the momentum, turbulent kinetic energy, turbulent dissipation rate, interfacial area concentration, and user scalar 0.

Table 6. Solution method used in this study.

Solution Method
Pressure–Velocity Coupling
Scheme	Phase Coupled SIMPLE
Spatial Discretization
Gradient	Least Square Cell-Based
Pressure	PRESTO!
Momentum	Second-Order Upwind
Volume Fraction	Modified HRIC
Turbulent Kinetic Energy	Second-Order Upwind
Turbulent Dissipation Rate	Second-Order Upwind
Interfacial Area Concentration	Second-Order Upwind
User Scalar 0	Second-Order Upwind

displays the employed solution methodology. The convergence threshold for all variables is set at 10⁻³, except for uds-0, which is set at 1. The initialization approach employed is the typical initialization technique, which involves a computational simulation procedure that encompasses all zones. The time step used is 1 s with the number of time steps of 5000, and the maximum iterations/time step is 20.

2.6. Determination of Aeration Performance

After carrying out numerical simulations, a plot of DO concentration against aeration duration is used to determine aeration performance. The plot needs to be adjusted first using a process called curve fitting. Curve fitting is the process of creating a curve or a mathematical function that best suits the data obtained from research results. In this research, curve fitting is useful for determining the standard volumetric oxygen transfer value ($K_L{a}_{20}$), which is based on Equation (9). After curve fitting is carried out and the $K_L{a}_{20}$ value is obtained, calculations of other aeration performance parameters can be carried out sequentially, starting from SOTR and then SOTE.

3. Results and Discussion

3.1. Calculation

The process began with a comprehensive literature review to understand the existing knowledge base and methodology related to shrimp pond design and aeration technology. After that, specific data were collected regarding the geometry of shrimp ponds at MSTP-Undip, which served as a basic data collection for this study.

The next step involves creating the pond geometry based on the model proposed by Du et al. (2020) [12]. This model is then used to carry out case simulations, incorporating a user-defined function (UDF) to describe the oxygen transfer model. The results of this simulation are plotted and a grid independence test is carried out to ensure the consistency and reliability of the simulation results. If test results are inconsistent, adjustments are made until consistent results are achieved.

After the simulation results were verified, a comparison was made between the results of the present study and those of Du et al. (2020), ensuring that the difference is within a 10% margin. If the results are satisfactory, then the research will continue by creating specific geometries for MSTP-Undip shrimp ponds, including straight-type, ring-type, and square-type layouts.

Each of these geometries underwent research case simulations, evaluating key parameters such as dissolved oxygen concentration and water circulation. The performance of each aeration layout is then determined. The final stage includes a thorough analysis and presentation of the results, followed by drawing conclusions based on the findings. This process culminates in a comprehensive summary of the research results, which effectively concludes this study.

3.2. Validation

To confirm that the method is valid, the validation of the method with previous research is needed. Validation was carried out by comparing the average DO concentration over a certain time period based on experimental research conducted by Du et al. (2020) [12]. Figure 7 and

Table 7. Parameters of Figure 7.

Parameter	Symbol	Value	Unit
Pond width	A4	3.2	m
Pond length	B4	6.3	m
Pond depth	C4	1.4	m
Diffuser length	D4	1	m
Diffuser length	E4	1.5	m
Diffuser length	F4	2.5	m

show the geometry of the pond model with a four-corner-type diffuser layout used by Du et al. (2020) in their experiments.

Figure 8 shows the change in DO concentration in water with time (in seconds) during the validation process, with a comparison between studies conducted by Du et al. (2020) and the present study. The error value between the two studies has the highest value of 2.7% and the lowest value of 0.2%, indicating that the difference between the two studies is relatively small. This graph indicates that the results of the present study have good accuracy and are in line with previous research. These validation results confirm the reliability of the method used in the present study.

3.3. Water Velocity

The analysis related to water velocity in the shrimp pond can be used to determine good water circulation for shrimp. Water velocity is analyzed at each pond depth. Water velocity is analyzed for each pond depth at the 5000th second.

Figure 9 shows the water velocity contours on the straight-type layout at several depth levels. The water velocity range in this layout is between 0 m/s and 2.972 × 10⁻¹ m/s. On the surface of the pond, it can be seen that the water velocity pattern on the sides of the pond has the highest value, reaching around 2.9 × 10⁻¹ m/s, while in the middle, the water velocity is lower. At various depth levels of 0.3–0.9 m, the water velocity has a pattern similar to the surface of the pond but with lower values. At the bottom of the pond, the water velocity pattern is not visible at all, with values close to zero.

Figure 10 shows the water velocity contours on the ring-type layout at several depth levels. The water velocity range in this layout is between 0 m/s and 1.616 × 10⁻¹ m/s. The water velocity pattern is only visible around the aerator. At various depth levels of 0.3–0.9 m, the water velocity has the same pattern as the pond surface but with lower values. At the bottom of the pond, the water velocity pattern is not visible at all with values close to zero.

Figure 11 shows water velocity contours in the square-type layout at several depth levels. The water velocity range in this layout is between 0 m/s and 4.038 × 10⁻¹ m/s. On the surface of the pond, it can be seen that the water velocity pattern on the sides of the pond has the highest value, reaching around 3.1 × 10⁻¹ m/s, while in the middle, the water velocity is lower. At various depth levels of 0.3–0.9 m, the water velocity has the same pattern as the pond surface but with lower values. At the bottom of the pond, the water velocity pattern is not visible at all, with values close to zero.

The water velocity is analyzed as a vector quantity that depends on space and time. Although the water velocity theoretically varies at each point and time, the simulation results show that after reaching a steady state, there is no significant difference in the distribution of water velocities at various points in the pool. Therefore, the water velocity is only shown at time 5000 s, when the system has reached stability and significant changes in velocity no longer occur.

All three water velocity patterns demonstrate the occurrence of water circulation around the bubble. Due to the buoyancy effect, water velocity tends to be high at the pool’s surface. Air injected into water forms bubbles, which tend to rise to the surface due to the density difference between water and air. Shrimp tend to gather at water velocities below 5 cm/s [21]. As a result, a square-type layout with water circulation is the best choice because many areas have water velocities below 5 cm/s.

3.4. Dissolved Oxygen Distribution (DO)

The analysis related to DO distribution in shrimp ponds can be used to determine zones with good DO concentrations for shrimp. Additionally, dead zones can be determined through this analysis. The DO distribution was analyzed for each pond depth at the 5000th second.

Figure 12 shows the DO distribution of the straight-type layout. The DO concentration range in this layout is between 8.056 mg/L and 8.079 mg/L. DO with high concentrations is located on the sides of the pond, while those with low concentrations tend to be found in the middle area of the pond, especially at the bottom of the pond. Even though the concentration is relatively low in the middle of the pond, DO is suitable to support the life of shrimp because shrimp require a minimum DO concentration of 5 mg/L to live according to Boyd (2003) [22].

Figure 13 shows the DO concentration distribution in the ring-type layout. The DO concentration range in this layout is between 1.410 mg/L and 8.098 mg/L. DO with relatively high concentrations is located throughout the pond area, except in the corners of the pond. In the corners of the pond, the DO concentration is relatively low, only around 1.4 mg/L, where shrimp are not suitable for living in that area. Areas with low DO concentrations (below 2 mg/L) are usually called dead zones [23]. Even though it is not suitable for supporting shrimp life, this area is suitable for use as a sedimentation or waste collection area because of the low water circulation.

Figure 14 shows the DO distribution of the square-type layout. The DO concentration range in this layout is between 3.786 mg/L and 8.087 mg/L. DO with high concentrations is in all areas of the pond except in the middle. In the middle of the pool, DO concentrations tend to be low with a value of 3.78 mg/L. Even though it is low, this area still cannot be called a dead zone because the value is already above 2 mg/L.

It is evident from the three distribution patterns of the DO concentration that after 5000 s, the DO concentration has achieved the ideal level to sustain the life of vannamei shrimp. The straight-type DO distribution is optimal as it ensures a high concentration of dissolved oxygen (DO) throughout the entire pond area, leading to a uniform and stable environment for the shrimp. This uniformity is crucial for preventing hypoxic conditions that can stress or harm the shrimp. On the other hand, the ring-type method resulted in the most unfavorable dissolved oxygen distribution, with four areas of low oxygen concentration located in the corners of the pond. These low-oxygen zones can create dead zones where shrimp cannot thrive, potentially impacting overall pond productivity.

3.5. Aeration Performance

The performance of aeration systems is assessed to identify the most effective configuration of fine-pore aeration tubes for enhancing dissolved oxygen (DO) concentration in the pond. Aeration performance parameters are divided into three categories: the standard volumetric oxygen transfer coefficient ($K_L{a}_{20}$), standard oxygen transfer rate (SOTR), and standard oxygen transfer efficiency (SOTE).

Figure 15 shows the change in average DO concentration against aeration time as a result of the simulation, while Figure 16 shows the change in average DO concentration against aeration time as a result of curve fitting. Both graphs show a similar pattern of increasing DO concentration. The straight-type layout appeared to increase the average DO concentration more quickly than the other two layouts in the pond. This can be caused by the fact that this layout is evenly distributed at the bottom of the pond. Meanwhile, the ring-type layout seems very slow to increase the average DO concentration in the pond. This could be because this layout is not placed on the sides of the pond, so the DO distribution in that area tends to be low.

Figure 15 and Figure 16 show graphs of the average DO concentration over time, which depict the change in DO concentration over time across the entire analyzed space. In contrast, Figure 12, Figure 13 and Figure 14 show contours of the local DO distribution, depicting the variation in DO concentration at different points in space at a given time. This difference shows that DO concentration can vary across space at a given time, whereas the average graph provides a general picture of the change in DO concentration over time. Both provide complementary information about the distribution and dynamics of DO in the system.

Figure 17 presents a comparison of the standard volumetric oxygen transfer coefficient ($K_L{a}_{20}$) values for various layout types. This value is determined through curve fitting as shown in Figure 15, based on Equation (9). The $K_L{a}_{20}$ value reflects the efficiency of the aeration system and the capacity of the aerator to dissolve oxygen into the water. The straight-type layout exhibited the highest $K_L{a}_{20}$ value of 3.16 h⁻¹, while the ring-type layout displayed the lowest $K_L{a}_{20}$ value of 1.68 h⁻¹.

Figure 18 illustrates a comparison of standard oxygen transfer rate (SOTR) values across different layout types, calculated using Equation (11). The SOTR value indicates the mass transfer rate of oxygen from the gas phase to the liquid phase under standard conditions. The straight-type layout achieved the highest SOTR value of 19.20 kg/h, whereas the ring-type layout recorded the lowest SOTR value of 10.21 kg/h.

Figure 19 presents a comparison of standard oxygen transfer efficiency (SOTE) values for different layout types, derived from calculations using Equation (12). The SOTE value quantifies the percentage of oxygen transferred from the gas phase to the liquid phase relative to the total oxygen supplied to the system under standard conditions. The straight-type layout achieved the highest SOTE value of 29.30%, whereas the ring-type layout yielded the lowest SOTE value of 15.58%.

The straight-type layout has the best aeration performance, which is superior in various aeration performance parameters. This is because the aeration tubes are placed evenly at the bottom of the pond so that the DO distribution occurs more evenly. The uniform placement allows for optimal mixing and oxygen transfer throughout the pond. Meanwhile, the ring-type layout has the worst aeration performance, which is weak in various aeration performance parameters. This is because the aeration tubes are only placed in the middle area of the pond, leading to insufficient coverage and poor oxygen distribution in the outer areas.

4. Conclusions

The conclusions collected from this study on the impact of fine-pore aeration tube layouts on aeration performance are as follows:

• The variations in the layout of the fine-pore aeration tubes in the large pond can impact the efficiency of aeration due to the differing outcomes of each configuration. Layouts that exhibit even distribution, such as the straight-type layout, demonstrate superior aeration performance in comparison to a concentrated layout, such as the ring-type layout.
• The square-type layout best depicts water circulation because many regions have velocities of less than 5 cm/s.
• The most efficient aeration performance is attained by employing a straight-type layout, which ensures the even distribution of diffusers along the pond’s bottom. The straight-type layout has an aeration performance with a $K_L{a}_{20}$ value of 3.16 h⁻¹, SOTR value of 19.20 kg/h, and SOTE value of 29.30%.