## Abstract

The showering aeration system (SAS) was designed and its performance was evaluated by conducting the aeration experiments in a tank of dimension 2 × 4 × 1.5 m. Initially, the aeration experiments were conducted to optimize the radius of curvature of the SAS with different values, such as = 0, 5, 10, 15, and 20 mm, and maintain other geometric parameters, i.e. number of holes in the shower (); height of water fall (*H*); diameter of the shower hole (*d*); volume of water under aeration (*V*) and water flow rate (*Q*) as constants. The optimum radius of curvature () was found to be 10 mm. The aeration experiments were further conducted with four different non-dimensional geometric parameters such as the number of holes , the ratio of the height of water fall to the length of shower arm the ratio of the diameter of the hole to the length of shower arm and the ratio of the volume of water to the cube of the length of shower arm The Response Surface Methodology and Box–Behnken Design were used to optimize the non-dimensional geometric parameters of the SAS to maximize the Non-Dimensional Standard Aeration Efficiency. The result indicates that the maximum NDSAE of 16.98 × 10^{6} was obtained from the SAS performance at = 80; = 2; = 4 and = 48.

## HIGHLIGHT

The optimized non-dimensional geometric parameters (

*H*/*l*;*d*/*l*;*V*/*l*^{3};*n*) for the showering aeration system were experimentally validated, and the final NDSAE value was found to be 16.98 × 10^{6}against the predicted NDSAE value of 17.70 × 10^{6}.

## NOMENCLATURE

- ANOVA
analysis of variance

temperature correction factor

*C*concentration of oxygen at time (ML

^{−3})*C**oxygen saturation at standard conditions (ML

^{−3})*C*_{0}dissolved oxygen concentration at time,

*t*= 0 (ML^{−3})- DO
dissolved oxygen

- Fr
Froude number

*g*acceleration due to gravity (LT

^{−2})*H*height of water fall (L)

*K*_{L}*a*_{20}standard oxygen transfer coefficient at 20 °C (T

^{−1})*K*_{L}*a*_{T}overall oxygen transfer coefficient at

*T*°C (T^{−1})number of holes in the shower

- NDSAE
non-dimensional number characterizing SAE

*P*power consumption (ML

^{2}T^{−3})*Q*pump discharge/water flow rate (L

^{3}T^{−1})- Re
Reynolds number

- SOTR
standard oxygen transfer rate (MT

^{−1})- SAE
standard aeration efficiency (L

^{−2}T^{2})*T*temperature (°C)

*V*volume of water under aeration (L

^{3})- W
Weber number

density of air (ML

^{−3})density of water (ML

^{−3})surface tension of water (MT

^{−2})*ν*_{w}kinematic viscosity of water (L

^{2}T^{−1})- RSM
Response Surface Methodology

- SAS
showering aeration system

- BBD
Box–Behnken Design

- FCR
feed conversion ratio

- SGR
specific growth rate

- RGR
relative growth rate

radius of curvature (L)

*D*distance between showers (L)

*d*diameter of shower hole (L)

length of shower arm (L)

## INTRODUCTION

Dissolved oxygen (DO) is one of the most vital parameters in the aquaculture water body, and it has a direct influence on aquatic lives. Therefore, it is essential to maintain the desired oxygen level in such water bodies through an artificial aeration system. An artificial aeration system is one of the methods of maintaining required DO levels in aquaculture ponds and water treatment plants (Roy *et al.* 2021a, 2021b, 2021c). The oxygen deficiency in the pond will retard the growth, locomotion, feeding, excretion and biosynthetic processes in the culture organisms (Van Dam & Pauly 1995). The minimum concentration of DO to be maintained is 5 mg/L and it is adequate for the aquatic organisms to respire. If DO level falls below 1–2 mg/L, it causes a high risk to the culture organism which even leads to mortality (Baylar *et al.* 2008; Boyd & Hanson 2010). Such risk factors can be avoided by facilitating the body of water with artificial aeration through mechanical aerating devices (Roy *et al.* 2015, 2017, 2020a, 2020b; Roy *et al.* 2022). Aerators enhance the interfacial area between the air and water, thus increasing the oxygen transfer rate, providing a better water circulation, and also preventing stratification of DO and temperature in the water body (Rogers 1989).

Different types of aeration devices have been developed to maintain desired levels of DO concentration in aquaculture operations in an effort to improve the aeration efficiency (Boyd 1998; Moulick *et al.* 2002, 2005, 2010; Roy *et al.* 2020a, 2022). The paddlewheel and the diffuser aeration systems are widely used in ponds and tank-based aquaculture systems, respectively. Ahmad & Boyd (1988) evaluated the performance of the paddle wheel aerator and found the Standard Aeration Efficiency (SAE) as 2.25 kgO_{2}/kWh. Roy *et al.* (2017) conducted a study in a different design of a paddle wheel aerator called a spiral aerator. The results showed that the maximum SAE is attained when the optimal number of handles per shaft and the rotational speed are 13 and 220 rpm, respectively. These aerators require significantly high energy input and also require constant maintenance, resulting in relatively higher running costs (Tanveer *et al.* 2018). Therefore, there is a need for a more environment-friendly, simple-to-operate, and economic aerator for aquaculture. It is firmly believed that the implementation of the SAS will reduce the cost of operation and maintenance while also potentially resolve the problems of low DO content, high concentration of volatile organic components, high accumulation of nitrogenous compounds and stratification.

The showering aeration system (SAS) is a splashing aerator that limits its usage to tank-based operations. A SAS consists of a required number of showers positioned in a horizontal pattern of polyvinyl chloride (UPVC) pipelines above the water surface to an average height of 1.0 m to distribute the water. The centrifugal pump is one of the primary components of SAS. It lifts the water to the desired height and it is dispersed into fine droplets of spray from the shower, which efficiently takes in oxygen from the atmosphere through adsorption. This flow creates a larger water surface area in contact with air, allowing the water to get oxygenated before falling into the tank (El-Zahaby & El-Gendy 2016). The efficiency of aeration depends on the surface area of the water droplet in contact with air, which is controlled primarily by the size of the shower opening and the dispersion of the water molecules. Studies suggest that the volume of water also influences the oxygen transfer rates. Elliott (1969) stated that the aerator power to water volume ratio should be less than 0.1 kW/m^{3}. These showers were designed and fabricated to enable the complete mixing of water in order to achieve DO destratification in the water column.

Studies were carried out in the area of showering aeration, which mainly focused on operating with a single shower in small capacity fiber-reinforced plastic (FRP) tanks. Salim *et al.* (2016) conducted the study with Nile tilapia in the SAS and obtained a satisfactory outcome in terms of feed conversion ratio, relative growth rate, specific growth rate and dissolved oxygen (DO) with the lowest energy consumption and higher net profit compared to the other aeration systems.

The present study attempted to develop a SAS with several showers in conjunction with a centrifugal pump as a primary aeration unit for usage in tank-based aquaculture and water treatment operations. The main features of the SAS are: it requires a small installation area, very minimum contact between the system and water, large specific area, thin film aeration, and requires minimum energy. It is believed that the implementation of such an aerator will reduce the cost of operation and manpower while also potentially resolving the problems in existing aeration systems like foam formation due to nutrient denaturation, clogging of nanopores in the aeration tubes, hypoxia and stratification. Therefore, in the present study, it was attempted to optimize the geometric parameters of SAS and evaluate its performance.

## THEORETICAL ANALYSIS

The performance evaluation of aerators is mainly carried out in terms of standard oxygen transfer rate (SOTR) and the SAE.

_{2}/h), (

*k*

_{L}

*a*)

_{20}is the standard oxygen transfer coefficient at 20 °C (h

^{−1}), (

*k*

_{L}

*a*)

_{20}= (

*k*

_{L}

*a*)

*/*

_{T}*θ*

^{T}^{−20}, (

*k*

_{L}

*a*)

*is the overall oxygen transfer coefficient at*

_{T}*T*°C (h

^{−1}),

*θ*is the temperature correction factor of 1.024 for clean water,

*C** is the saturation value of DO at test condition (mg/L),

*C*

_{0}is the initial DO concentration (mg/L),

*V*is the volume of water under aeration (m

^{3}).

*P*is the power applied to the aerator (kW).

### Dimensional analysis

A laboratory-scale setup was used to conduct the aeration experiments. The results obtained from laboratory-scale experiments were interpreted and geometric dimensions were scaled up for the use of the aerator in an actual pond. The installation of SAS in the field requires a geometrical similarity condition, i.e., it should be built by following a definite geometric ratio with the corresponding dimensions of the laboratory-scale setup (Rao & Kumar 2007; Roy *et al.*2020a, 2020b, 2021a, 2021b, 2021c). This geometric similarity is established with the corresponding dimensions of the laboratory system to achieve similar results of oxygen transfer rates in the field conditions. Generally, the oxygen transfer rate in water is determined by the size of the air bubbles and their distribution per unit volume. Also, the oxygen transfer rate is determined by the physical characteristics of the water and air, flow parameters as well as the geometric parameters of the developed aeration system (Maise 1970). It may be categorized into three groups for convenience:

*Geometric attributes: H* = height of waterfall; = number of holes in shower; = length of shower arm; *V* = volume of water; *d* = diameter of the shower holes; *D* = distance between showers.

*Process attributes: g* = acceleration due to gravity; *Q* = discharge from the pump.

*Material attributes: ρ*_{a} = mass density of air; *ρ*_{w} = mass density of water; *υ*_{w} = kinematic viscosity; *σ*_{w} = surface tension of water.

*k*

_{L}

*a*)

_{20}×

*V*(Zlokarnik 1979). It is expressed as follows:

*C*and key variables can be expressed as follows:

*l*,

*ρ*

_{w},

*g*were chosen as the repeating variables and Equation (6) can be expressed as dimensionless as follows:where

= Froude Number (Fr); (Roy

*et al.*2017, 2020a)= Reynolds Number (Re); (Roy

*et al.*2017, 2020a)= Weber Number (W).

*et al.*2005; Moulick & Mal 2009; Kumar

*et al.*2013; Roy

*et al.*2015, 2017) shows that researchers needs to pay more attention to the Froude (Fr) and Reynolds (Re) numbers instead of Weber number (W) when evaluating the performance of aerators. Therefore, the Weber number (W) can be ignored and Equation (7) can be rewritten as follows:In the above formula, the first five dimensionless quantities determine the geometric similarity of the system, and the latter two dimensionless quantities determine the dynamic similarity. In the study, since the Froude (Fr) and Reynolds (Re) numbers are proportional to

*Q*and inversely proportional to the length of shower arm and distance between showers (

*D*), so these variables are fixed as

*Q*= 0.0015 m

^{3}/s; =

*D*= 0.5 m.

## MATERIALS AND METHODOLOGY

### Experimental setup

A cemented concrete rectangular tank of dimensions 2 × 4 × 1.5 m was used to evaluate the performance of the developed aeration system. A line sketch diagram of the aeration setup showing the sectional view (side and top views) is presented in Figure 1. The SAS was developed using various materials and fabricated as per the specifications furnished in Table 1. The system was operated with the centrifugal pump (1 HP), which was manufactured by Texmo Industries Pvt., Ltd. A control valve was provided to manage the flow of water, and the flow rate of water was measured using an electromagnetic flow meter. The system consists of the arrangement of pipes and showers at an average height of 1.0 m from the water surface. Initially, shower plates were designed and experiments were carried out to optimize the radius of curvature () (Figure 2). The radius of curvature () has a significant effect on the water spread area. The radius of curvature (*r*) at a particular point is defined as the radius of the approximating circle. After optimizing the radius of curvature (), nine types of showers (8 nos. in each type) were fabricated with a combination of geometric parameters namely = 60, 80, 100 and = 1.5 mm, 2 mm, 2.5 mm as shown in Figure 3. The showers were assembled in an alternate pattern and are equally spaced as shown in the schematic diagram given below.

S. No. . | Components . | Raw materials . |
---|---|---|

1 | Showers | Made of SS 304 |

2 | Support frame | Made of MS |

3 | Bolt and nut | Made of MS |

4 | Pipes | UPVC (1/4″) |

5 | Pump | One HP, three phase |

S. No. . | Components . | Raw materials . |
---|---|---|

1 | Showers | Made of SS 304 |

2 | Support frame | Made of MS |

3 | Bolt and nut | Made of MS |

4 | Pipes | UPVC (1/4″) |

5 | Pump | One HP, three phase |

### Aeration test

*et al.*2007). After each measurement, the oxygen deficit (OD) or DO deficit was calculated. The oxygen transfer coefficient was determined using the slope of the best fit line obtained by graphing natural logarithms of DO deficits on the

*Y*-axis against the period of aeration on the

*X*-axis at the test water temperature. It is expressed as follows:

Using the above values, SOTR and SAE can be computed with Equation (1).

### Experimental design

#### Effect of the radius of curvature (*r*) of the shower plate of SAS on oxygen transfer

A series of preliminary trials were carried out to optimize the radius of curvature (). Initially, five showers were fabricated with five different radiuses of curvature (): 0, 5, 10, 15 and 20 mm. A testing setup was developed in an FRP tank of capacity 1 m^{3} to conduct the experiments. The operating parameters as well as the other geometric parameters and their values are given in Table 2. Aeration tests were performed with constant discharge, = 0.0015 m^{3}/s, to achieve a dynamic flow condition. In all the trials, the testing water was exchanged, deoxygenated, and then re-aerated according to the standard procedures (ASCE 1997) to compute the SAE.

S. No. . | Varying geometric parameters . | Constant geometric parameters . | ||
---|---|---|---|---|

Variable . | Values (mm) . | Variable . | Values . | |

1 | Radius of curvature (r) | 0 | 80 | |

2 | 5 | 0.5 m | ||

3 | 10 | 1 m | ||

4 | 15 | 2 mm | ||

5 | 20 | 0.8 m^{3} |

S. No. . | Varying geometric parameters . | Constant geometric parameters . | ||
---|---|---|---|---|

Variable . | Values (mm) . | Variable . | Values . | |

1 | Radius of curvature (r) | 0 | 80 | |

2 | 5 | 0.5 m | ||

3 | 10 | 1 m | ||

4 | 15 | 2 mm | ||

5 | 20 | 0.8 m^{3} |

#### Effect of the non-dimensional geometric ratios on oxygen transfer

For a specific dynamic condition (combined in the three parameters, Fr, Re and We), a particular set of values of the four non-dimensional geometric variables: the ratio of height of water fall to the length of shower arm (); the ratio of diameter of shower holes to the length of shower arm (; the ratio of volume of water to the cube of the length of the shower arm (); the number of holes of the shower plate () that magnifies NDSAE can be found out. Hence, discharge , radius of curvature (*r*) and distance between showers (*D*) were kept as a constant, which make Fr, Re and W invariants. A design of experiments based on Response Surface Methodology (RSM) was adopted considering,, and as key variables. A Box–Behnken design (BBD) with six central points was used to develop the experimental design. The BBD was chosen for the evaluation because of its efficiency in terms of the number of runs necessary to find the second-order response surface model. The ranges of four independent variables = 1, 2, 3; = 3, 4, 5; = 32, 40, 48; = 60, 80, 100 were selected on the basis of preliminary trials.

## RESULTS AND DISCUSSION

### Evaluation of radius of curvature (*r*) of the shower plate of SAS

*r*is shown in Figure 4.

Assume, = 0, we get *r* = 11.02–10 mm.

The maximum SAE was obtained at = 10 mm. The SAE decreases as the radius of curvature () increases. This is because the water spreads out of the tank when *r* is higher. At the same time, when *r* is less than 10 mm, then there is no uniform distribution of the oxygenated water throughout the tank which eventually reduces the aeration efficiency.

### Evaluation of optimum geometric parameters (*H*/*l*; *d*/*l*; *V*/*l*^{3}; *n*)

Further experiments were conducted under particular dynamic conditions and keeping the radius of curvature (): 10 mm to determine the optimum non-dimensional geometric variables of the SAS. These experiments were designed using the RSM of BBD to study the effect of the four independent variables ** =**1, 2, 3; ** =**3, 4, 5; ** =**32, 40, 48; = 60, 80, 100 on the NDSAE (Non-Dimensional SAE) of the SAS. The experimental results obtained are presented in Table 3. It is seen from Table 3 that the variation of NDSAE was from 7.597 × 10^{6} to 15.914 × 10^{6}, and the corresponding SAE values are 0.6888 and 1.4429 kgO_{2}/kWh, respectively.

Run . | . | . | . | . | SOTR (kgO_{2}/h)
. | SAE (kgO_{2}/kWh)
. | NDSAE × 10^{6}
. |
---|---|---|---|---|---|---|---|

1 | 80 | 1 | 4 | 32 | 0.0554 | 1.1087 | 12.228 |

2 | 80 | 3 | 5 | 40 | 0.0554 | 1.1087 | 12.228 |

3 | 80 | 2 | 5 | 32 | 0.0537 | 1.0732 | 11.836 |

4 | 80 | 1 | 4 | 48 | 0.0660 | 1.3198 | 14.556 |

5 | 100 | 2 | 4 | 48 | 0.0677 | 1.3537 | 14.93 |

6 | 100 | 2 | 5 | 40 | 0.0425 | 0.8497 | 9.371 |

7 | 100 | 2 | 3 | 40 | 0.0501 | 1.0021 | 11.052 |

8 | 60 | 1 | 4 | 40 | 0.0359 | 0.7187 | 7.927 |

9 | 100 | 2 | 4 | 32 | 0.0584 | 1.1678 | 12.88 |

10 | 60 | 2 | 5 | 40 | 0.0344 | 0.6888 | 7.597 |

11 | 80 | 1 | 3 | 40 | 0.046 | 0.9196 | 10.142 |

12 | 80 | 2 | 4 | 40 | 0.0706 | 1.4123 | 15.576 |

13 | 80 | 2 | 5 | 48 | 0.0642 | 1.2834 | 14.155 |

14 | 80 | 3 | 4 | 48 | 0.0721 | 1.4429 | 15.914 |

15 | 60 | 2 | 4 | 32 | 0.0494 | 0.9873 | 10.889 |

16 | 80 | 1 | 5 | 40 | 0.0377 | 0.754 | 8.316 |

17 | 80 | 2 | 3 | 32 | 0.0595 | 1.1894 | 13.118 |

18 | 100 | 1 | 4 | 40 | 0.0437 | 0.8746 | 9.646 |

19 | 80 | 3 | 3 | 40 | 0.057 | 1.1399 | 12.572 |

20 | 60 | 3 | 4 | 40 | 0.0407 | 0.8132 | 8.969 |

21 | 60 | 2 | 4 | 48 | 0.0626 | 1.2525 | 13.814 |

22 | 60 | 2 | 3 | 40 | 0.0393 | 0.7865 | 8.674 |

23 | 80 | 2 | 3 | 48 | 0.0691 | 1.3816 | 15.238 |

24 | 80 | 3 | 4 | 32 | 0.0613 | 1.2265 | 13.527 |

25 | 100 | 3 | 4 | 40 | 0.0512 | 1.0247 | 11.301 |

Run . | . | . | . | . | SOTR (kgO_{2}/h)
. | SAE (kgO_{2}/kWh)
. | NDSAE × 10^{6}
. |
---|---|---|---|---|---|---|---|

1 | 80 | 1 | 4 | 32 | 0.0554 | 1.1087 | 12.228 |

2 | 80 | 3 | 5 | 40 | 0.0554 | 1.1087 | 12.228 |

3 | 80 | 2 | 5 | 32 | 0.0537 | 1.0732 | 11.836 |

4 | 80 | 1 | 4 | 48 | 0.0660 | 1.3198 | 14.556 |

5 | 100 | 2 | 4 | 48 | 0.0677 | 1.3537 | 14.93 |

6 | 100 | 2 | 5 | 40 | 0.0425 | 0.8497 | 9.371 |

7 | 100 | 2 | 3 | 40 | 0.0501 | 1.0021 | 11.052 |

8 | 60 | 1 | 4 | 40 | 0.0359 | 0.7187 | 7.927 |

9 | 100 | 2 | 4 | 32 | 0.0584 | 1.1678 | 12.88 |

10 | 60 | 2 | 5 | 40 | 0.0344 | 0.6888 | 7.597 |

11 | 80 | 1 | 3 | 40 | 0.046 | 0.9196 | 10.142 |

12 | 80 | 2 | 4 | 40 | 0.0706 | 1.4123 | 15.576 |

13 | 80 | 2 | 5 | 48 | 0.0642 | 1.2834 | 14.155 |

14 | 80 | 3 | 4 | 48 | 0.0721 | 1.4429 | 15.914 |

15 | 60 | 2 | 4 | 32 | 0.0494 | 0.9873 | 10.889 |

16 | 80 | 1 | 5 | 40 | 0.0377 | 0.754 | 8.316 |

17 | 80 | 2 | 3 | 32 | 0.0595 | 1.1894 | 13.118 |

18 | 100 | 1 | 4 | 40 | 0.0437 | 0.8746 | 9.646 |

19 | 80 | 3 | 3 | 40 | 0.057 | 1.1399 | 12.572 |

20 | 60 | 3 | 4 | 40 | 0.0407 | 0.8132 | 8.969 |

21 | 60 | 2 | 4 | 48 | 0.0626 | 1.2525 | 13.814 |

22 | 60 | 2 | 3 | 40 | 0.0393 | 0.7865 | 8.674 |

23 | 80 | 2 | 3 | 48 | 0.0691 | 1.3816 | 15.238 |

24 | 80 | 3 | 4 | 32 | 0.0613 | 1.2265 | 13.527 |

25 | 100 | 3 | 4 | 40 | 0.0512 | 1.0247 | 11.301 |

### Model fitting and statistical analysis of the results

*A*is the number of holes (),

*B*is the ratio of height of water fall to the length of shower arm (),

*C*is the ratio of diameter of holes to the length of shower arm , and

*D*is the ratio of volume of water to the cube of the length of shower arm .

*p*< 0.05) and the interactive models are not significant (

*p*> 0.05). Therefore, the coefficient of the interactive model is withdrawn and the new regression equation was obtained to precisely describe the response surface of NDSAE (Equation (14)).where the coefficients are the same as for Equation (13).

Source . | d.f. . | Adj. SS . | Adj. MS . | F-Value
. | P-Value
. |
---|---|---|---|---|---|

Model | 14 | 154.795 | 11.0568 | 83.51 | 0.000 |

Linear | 4 | 42.344 | 10.5859 | 79.96 | 0.000 |

A | 1 | 10.660 | 10.6597 | 80.51 | 0.000 |

B | 1 | 8.125 | 8.1247 | 61.37 | 0.000 |

C | 1 | 6.924 | 6.9236 | 52.29 | 0.000 |

D | 1 | 16.636 | 16.6357 | 125.65 | 0.000 |

Square | 4 | 112.035 | 28.0088 | 211.55 | 0.000 |

A*A | 1 | 35.267 | 35.2668 | 266.37 | 0.000 |

B*B | 1 | 17.330 | 17.3297 | 130.89 | 0.000 |

C*C | 1 | 23.027 | 23.0274 | 173.93 | 0.000 |

D*D | 1 | 2.658 | 2.6578 | 20.07 | 0.001 |

Two-way Interaction | 6 | 0.416 | 0.0694 | 0.52 | 0.779 |

A*B | 1 | 0.094 | 0.0939 | 0.71 | 0.419 |

A*C | 1 | 0.091 | 0.0912 | 0.69 | 0.426 |

A*D | 1 | 0.191 | 0.1914 | 1.45 | 0.257 |

B*C | 1 | 0.029 | 0.0289 | 0.22 | 0.650 |

B*D | 1 | 0.001 | 0.0009 | 0.01 | 0.937 |

C*D | 1 | 0.010 | 0.0099 | 0.07 | 0.790 |

Error | 10 | 1.324 | 0.1324 | ||

Total | 24 | 156.119 |

Source . | d.f. . | Adj. SS . | Adj. MS . | F-Value
. | P-Value
. |
---|---|---|---|---|---|

Model | 14 | 154.795 | 11.0568 | 83.51 | 0.000 |

Linear | 4 | 42.344 | 10.5859 | 79.96 | 0.000 |

A | 1 | 10.660 | 10.6597 | 80.51 | 0.000 |

B | 1 | 8.125 | 8.1247 | 61.37 | 0.000 |

C | 1 | 6.924 | 6.9236 | 52.29 | 0.000 |

D | 1 | 16.636 | 16.6357 | 125.65 | 0.000 |

Square | 4 | 112.035 | 28.0088 | 211.55 | 0.000 |

A*A | 1 | 35.267 | 35.2668 | 266.37 | 0.000 |

B*B | 1 | 17.330 | 17.3297 | 130.89 | 0.000 |

C*C | 1 | 23.027 | 23.0274 | 173.93 | 0.000 |

D*D | 1 | 2.658 | 2.6578 | 20.07 | 0.001 |

Two-way Interaction | 6 | 0.416 | 0.0694 | 0.52 | 0.779 |

A*B | 1 | 0.094 | 0.0939 | 0.71 | 0.419 |

A*C | 1 | 0.091 | 0.0912 | 0.69 | 0.426 |

A*D | 1 | 0.191 | 0.1914 | 1.45 | 0.257 |

B*C | 1 | 0.029 | 0.0289 | 0.22 | 0.650 |

B*D | 1 | 0.001 | 0.0009 | 0.01 | 0.937 |

C*D | 1 | 0.010 | 0.0099 | 0.07 | 0.790 |

Error | 10 | 1.324 | 0.1324 | ||

Total | 24 | 156.119 |

@95% Confidence level of significance, *R*^{2} = 99%, *R*^{2} (adjusted) = 97%.

The obtained quadratic equation implies that the model might be well fitted for the experimental design. The coefficient of regression (*R*^{2}) and *p*-values are 0.99 and 0.000, respectively. The ANOVA of the fitted model indicates that the regression is significant; hence, it is inferred that adequacy of the designed model is satisfactory for the experimental data (Montgomery 2017).

### Effect of geometric parameters on NDSAE

NDSAE is linearly proportional to the number of holes () and reaches a maximum when = 80, as shown in Figure 5. This is due to the fact that flow of water to fall vertically through the holes in the form of fine spray, which creates a large number of air bubbles in the water body. These air bubbles enhance the oxygen transfer, which finally increases the aeration efficiency. Following that, NDSAE begins to decline as exceeds 80. This is due to the fact that as the number of holes increases, there is non-uniform distribution of water. This phenomenon decreases the air–water contact period and comparatively less oxygen transfer takes place, which finally reduces the NDSAE.

Figure 6 illustrates that, as the ratio of the height of the fall to the length of the shower arm rises, NDSAE also increases simultaneously. This is because as the height of the fall increases, the water's residence time in the air increases (Navisa *et al.* 2014). The SAE, which corresponds to the maximum NDSAE, ultimately increases as a result of the increase in residence time. A higher range of aeration is attained at = 2.

Figure 7 illustrates that the ratio of volume to the cube of the length of shower arm is directly proportional to NDSAE. The phenomenon behind the process is that when the water volume is higher, the oxygenated water has a longer residence time in the body of water and tends to mix and circulate for a longer period of time (Al-Ahmady 2006). This results in an increase in oxygen transfer that eventually elevates the levels of SAE and NDSAE as well.

Figure 8 interprets that initially the NDSAE increases with the ratio of diameter of the holes to the length of shower arm and it also reaches its peak when = 4. Beyond that the NDSAE progressively decreases as the value increases. This is due to the fact that when the diameter of the pores increases, it may be unable to break down the water particles into smaller droplets, failing to create more air–water contact area resulting in improper oxygenation.

## MODEL VALIDATION

The optimization of non-dimensional geometric variables was performed using ‘Response optimization’ in the Minitab 19 software. The obtained optimum values of non-dimensional geometric variables are listed in Table 5. Further, these geometric parameters were validated to re-assess the designed model, and the predicted and experimental results are given in Table 5. The predicted and experimented values of NDSAE were nearly similar with the standard deviation of ±0.51. Hence, the result of the model validation was satisfactory and thus justifying the adequacy of the model.

Variable . | Optimum values . | Predicted response value, NDSAE × 10^{6}
. | Actual value . | |
---|---|---|---|---|

SAE (kgO_{2}/kW h)
. | NDSAE × 10^{6}
. | |||

80 | 17.70 | 1.54 | 16.98 | |

2 | ||||

4 | ||||

48 |

Variable . | Optimum values . | Predicted response value, NDSAE × 10^{6}
. | Actual value . | |
---|---|---|---|---|

SAE (kgO_{2}/kW h)
. | NDSAE × 10^{6}
. | |||

80 | 17.70 | 1.54 | 16.98 | |

2 | ||||

4 | ||||

48 |

## SUMMARY AND CONCLUSION

The current study investigates how the different geometric factors affect the aeration characteristics of the SAS. The geometric variables were optimized in order to improve the efficiency of the SAS. The maximum SAE and NDSAE obtained from experimental trials were 1.4429 kgO_{2}/kWh and 15.914 × 10^{6}, respectively. To determine the optimum geometric parameters, the experimental results were validated using the RSM.

The major conclusions drawn from the obtained results are as follows:

The optimum radius of curvature (

*r*) should be 10 mm to attain maximum SAE that corresponds to the maximum NDSAE.Response surface graphs can be used to describe the effect of the geometric variables on the performance of the SAS.

For achieving the maximum NDSAE, ,, and are 2, 4, 48 and 80, respectively.

The predicted NDSAE and SAE values obtained from the developed model at the optimum geometric variables were found to be 17.70 × 10

^{6}and 1.54 kgO_{2}/kWh, respectively.The optimized non-dimensional geometric parameters for the SAS were experimentally validated, and the final NDSAE value was found to be 16.98 × 10

^{6}against the predicted NDSAE value of 17.70 × 10^{6}.

Finally, it may be said that the developed RSM/BBD model is an effective tool for predicting the optimized geometric variables of the SAS.

## ACKNOWLEDGEMENT

The authors are thankful to the College of Fisheries Engineering, Tamil Nadu Dr J. Jayalalithaa Fisheries University for providing support and motivation to conduct the study.

## DATA AVAILABILITY STATEMENT

All relevant data are included in the paper or its Supplementary Information.

Techniques for Modern Aquaculture, p. 511