## Abstract

The performance of the perforated tray aerator (PTA) was evaluated by conducting experiments in a tank of size 4 m × 4 m × 1.5 m. Based on the dimensional analysis, non-dimensional numbers related to geometric variables, viz. numbers of trays (*n*), ratio of consecutive width of tray to total height of aerator , ratio of perforation diameter to total height of aerator and ratio of the volume of water in the tank to total height of aerator were developed. Experiments were conducted with different numbers of trays (*n*): 1, 2, 3 and 4, keeping = 0.33, = 2.5 × 10^{−4}, = 2,500 and pump flow rate (*Q*) = 0.010 m^{3}/s as constants. The optimum number of perforated trays was found to be 3. Response surface methodology (RSM) and central composite rotatable design (CCRD) were used to further optimize the geometric variables with combinations of non-dimensional geometric variables , and . The flow rate (*Q*) of 0.013 m^{3}/s and number of trays (*n*) as 3 were kept as constants. The optimum performance of PTA was obtained at = 0.665, = 1.85 × 10^{−4} and = 312.50 with the maximum non-dimensional standard aeration efficiency (NDSAE) and standard aeration efficiency (SAE) of 35.58 × 10^{−3} and 1.45 kgO_{2}/kWh.

## INTRODUCTION

Water is one of the most important natural resources, an essential element for the existence of human and animal life. The increase in human population has necessitated the upgrading of existing technology and adoption of new practices to utilize natural resources including water in a justifiable manner (Haghiabi *et al.* 2018). Water is used for domestic and industrial purposes. Therefore, the maintenance of a water quality standard for domestic and industrial sectors is very much essential. Aeration is one of the means to maintain the water quality standard for various uses.

Dissolved oxygen (DO) is an important variable regulating post-aeration-system water treatment. DO refers to the mass of oxygen that is contained in water. The concentration of DO is an essential indicator of the water quality in a terrestrial or aquatic environment. As the DO concentration drops below 5.0 mg/L in water, aquatic life is put under stress and if the concentration remains below 1–2 mg/L for a few hours, the chances of mortality of the species is high (Baylar *et al.* 2008; Boyd & Hanson 2010). The intensive aquaculture system possesses very high stocking density. Therefore, in order to maintain the water quality with an appropriate level of dissolved oxygen, artificial aeration through aerators becomes essential. Aerators increase the DO level in the water body, thus enhancing the oxygen transfer rate and simultaneously providing water circulation which prevents stratification in the water body (Boyd & Martinson 1984).

Aeration systems such as paddle wheel aerators or diffused air aerators require high electrical energy input, and the components require frequent maintenance resulting in relatively high operating cost. Therefore, a need is felt for a more sustainable, easy-to-operate and economical aerator for fish culture. The perforated tray aerator (PTA) offers a more practical solution to this problem (Eltawil & ElSbaay 2016). The perforated tray aerator (PTA) is mainly used in water treatment plants as well as in aquaculture water treatment to increase DO content in pond water (Chesness & Stephens 1971; Boyd & Watten 1989).

The perforated tray aerator (PTA) is generally made up of a number of trays (*n*) arranged vertically one above the other with a constant vertical spacing (SP) between the trays. The tray is made from a flat sheet with a number of holes drilled on it. The variation in number of trays (*n*) and hole diameter (*d*) are important parameters which may affect the oxygen transfer rate and the aeration efficiency. Water is pumped over the topmost tray and it falls vertically through the perforations of the trays. The fall through the small-diameter holes helps the water-drops to form fine sprays. The fine spray increases the water–air surface contact area and thus helps to increase the aeration efficiency of the perforated tray aerators (El-Zahaby & El-Gendy 2016). When water is allowed to fall over consecutive trays (trays are square in shape), a large area to water volume ratio in contact with the air is obtained. According to Tchobanoglous *et al.* (2004) and Scott *et al.* (1955), this improves the oxygen transfer rate. The volume of the water in the tank also influences the oxygen transfer rate. Elliott (1969) suggested the aerator power to water volume ratio to be less than 0.1 kW/m^{3}, while APHA (1980) and Lawson & Merry (1993) mentioned that the above ratio should lie between 0.01 and 0.04 kW/m^{3}. However, there are no universally accepted standards that can be applied to all aerators and test equipment. Moreover, in the design of perforated tray aerators, researchers did not specify anything about the volume of water in which they carried out their aeration studies. Therefore, the present study was taken up for design of the dimensions of the perforated tray aerator for achieving the maximum aeration efficiency.

## THEORETICAL ANALYSIS

_{2}/h);

*K*

_{L}

*a*

_{20}= overall oxygen transfer coefficient at 20 °C (h

^{−1}); ; = overall oxygen transfer coefficient at

*T*°C;

*θ*= temperature correction factor = 1.024 for clean water;

*C** = saturation value of DO under test conditions (mg/L);

*C*

^{0}= initial DO concentration (mg/L); 9.07 = saturated DO concentration of clean water (mg/L) at 20 °C and standard atmospheric pressure;

*V*= volume of water (m

^{3}) and 10

^{−3}= factor for converting g to kg.

*P*= power input (kW).

As the height of the aerator increases, the head (*H*) also increases resulting in higher power requirement. As may be seen from Equation (3), *P* is directly proportional to *H*. Considering the practical aspects of aeration and the power requirement, a total height of 1.0 m was selected for the perforated tray aerator.

### Dimensional analysis

A laboratory-scale setup was used to conduct aeration experiments. The results obtained from laboratory-scale experiments were interpreted and geometric dimensions were scaled up for use of the aerator in the actual pond. The installation of PTA in the field requires a geometrical similarity condition, i.e., it should be built following a definite geometric ratio with the corresponding dimensions of the laboratory-scale setup (Rao & Kumar 2007).

*H*= total height of perforated tray aerator,

*n*= number of trays,

*W*= width of the trays,

*d*= perforated diameter of each tray,

*V*= volume of water in tank,

*ρ*

_{a}= mass density of air,

*ρ*

_{w}= mass density of water,

*g*= acceleration due to gravity,

*Q*= pump discharge,

*ν*

_{w}= kinematic viscosity of water and

*σ*

_{w}= surface tension of water.

*π*theorem, selecting

*H*,

*ρ*

_{w},

*g*as the three repeating variables, Equation (5) may be expressed as follows in the dimensionless form: where NDSAE = non-dimensional SAE = ×

= Froude number, Fr

= Reynolds number, Re

= Weber number, We

*et al.*2002, 2005, 2010; Kumar

*et al.*2013; Roy

*et al.*2017) gave more importance to the Froude (Fr) and Reynolds (Re) numbers than the Weber number (We) for the purpose of scale-up. This may be due to the fact that the Froude (Fr) and Reynolds (Re) numbers have more influence under the turbulent flow condition than surface tension. Hence, the Weber number, We, may also be omitted. Thus, Equation (6) may be re-expressed as:

In the above equation, the first four dimensionless quantities govern the geometric similarity of the system and the last two dimensionless quantities govern the dynamic similarity. In the study, dynamic similarities were maintained due to the fact that the Froude (Fr) and Reynolds (Re) numbers are directly proportional to *Q* and inversely proportional to *H*. Considering the above fact, *Q* and *H* were fixed at 0.0013 m^{3}/s and 1.0 m respectively.

## METHODOLOGY

### Experimental setup

The perforated tray aerator (Figure 1) consists of an open submersible pump of 3.7 kW (5 hp) (make: Kirloskar Brothers Limited, Kolkata, India) with a control valve and a structure to support the trays. The water discharge through the outlet of the pump was measured using an electromagnetic flow meter.

### Aeration test

*et al.*2007). Finally was estimated using Equation (8) by determining the three parameters,

*C*

_{0},

*C** and simultaneously using a nonlinear method (ASCE 1997; Jiang & Stenstrom 2012):

Finally was converted to a value at a standard temperature of 20 °C as , and the values of SOTR and SAE were computed using Equations (1) and (2) respectively.

## EXPERIMENTAL DESIGN AND STATISTICAL ANALYSIS

Aeration tests were conducted on a perforated tray aerator attached with different numbers of trays (*n*): 4, 2, 3 and 1; keeping = 0.33, = 2,500, = 2.5 × 10^{−4} and pump discharge (*Q*) at 0.010 m^{3}/s to maintain a constant dynamic condition and to obtain the optimum value of *n*.

For a particular dynamic condition (combined in the three parameters, Fr, Re and We), a specific set of values of the three non-dimensional geometric variables, the ratio of the consecutive width of tray to total height of aerator , the ratio of the volume of water in the tank to total height of aerator and the ratio of perforation diameter to total height of aerator that maximizes NDSAE can be found out. Hence, keeping *Q* and *n* as constants, which makes Fr, Re and We invariant, a design of experiment using central composite rotatable design (CCRD) was adopted considering , and as key variables. A central composite rotatable design with eight factorial points, six axial points and six central points was used to develop the experimental design. The CCRD was selected in the study due its efficiency with respect to the number of runs required for ﬁtting a second-order response surface model. The range of the three independent variables, (0.33–1.00), (2,500–312.50) and (1.2 × 10^{−4}–2.5 × 10^{−4}), was selected based on preliminary trials.

## RESULTS

### Optimum numbers of trays (n ) of PTA

*n*(4, 3, 2 and 1). A typical plot showing the variation of NDSAE with

*n*is shown in Figure 2. It can be seen that all the points can be well fitted by the following second-order polynomial:

At = 0, *n* = 2.55 and = −0.0173 (<0)

Therefore, SAE attains its maximum value at *n* = 3.

At *n* = 3, *Q* was kept constant, and NDSAE becomes directly proportional to SAE. Therefore, the optimum value of *n* corresponds to the maximum SAE. In the study, the decreasing rate of NDSAE might be due to less width (area) of trays due to which water did not fall uniformly over the tray and improper air–water contact over the trays took place. From the relationship developed by using the experimental data, it may be concluded that the optimum number of trays for efficient aeration is 3.

### Optimum values of geometric parameters , and

The experiments were conducted keeping the number of trays at the optimum (*n* = 3) and under particular dynamic conditions to determine the optimum geometric variables of the perforated tray aerator (optimum number of trays (*n*) of the PTA). These experiments were designed using RSM of CCRD to study the effect of the three independent variables, i.e., , and on the NDSAE (non-dimensional SAE) of the perforated tray aerator. The experimental results are presented in Table 1. It is seen from Table 1 that the variation of NDSAE was from 5.8 × 10^{−3} to 35.58 × 10^{−3}. The corresponding SAE values were 0.236 and 1.451 kg O_{2}/kWh respectively.

RUN . | . | . | × 10^{4}
. | SOTR (kgO_{2}/h)
. | SAE (kgO_{2}/kWh)
. | NDSAE × 10^{3}
. |
---|---|---|---|---|---|---|

1 | 0.466(−1) | 755.90(−1) | 2.23(1) | 0.058 | 0.236 | 5.800 |

2 | 0.665(0) | 1,406.25(0) | 1.85(0) | 0.231 | 0.931 | 22.828 |

3 | 0.665(0) | 1,406.25(0) | 1.20(−1.68) | 0.284 | 1.145 | 28.066 |

4 | 0.665(0) | 1,406.25(0) | 1.85(0) | 0.239 | 0.963 | 23.619 |

5 | 0.466(−1) | 2,056.59(1) | 1.46(−1) | 0.271 | 1.092 | 26.781 |

6 | 0.665(0) | 1,406.25(0) | 1.85(0) | 0.233 | 0.939 | 23.026 |

7 | 0.864(1) | 2,056.59(1) | 1.46(−1) | 0.283 | 1.141 | 27.967 |

8 | 0.665(0) | 1,406.25(0) | 1.85(0) | 0.246 | 0.991 | 24.311 |

9 | 1.0(1.68) | 1,406.25(0) | 1.85(0) | 0.320 | 1.290 | 31.624 |

10 | 0.665(0) | 312.5(−1.68) | 1.85(0) | 0.360 | 1.451 | 35.577 |

11 | 0.330(−1.68) | 1,406.25(0) | 1.85(0) | 0.298 | 1.201 | 29.450 |

12 | 0.665(0) | 1,406.25(0) | 2.50(1.68) | 0.317 | 1.281 | 31.407 |

13 | 0.864(1) | 2,056.598(1) | 2.23(1) | 0.345 | 1.391 | 34.095 |

14 | 0.864(1) | 755.90(−1) | 2.23(1) | 0.349 | 1.407 | 34.490 |

15 | 0.665(0) | 2,500.00(1.68) | 1.85(0) | 0.169 | 0.681 | 16.701 |

16 | 0.466(−1) | 755.90(−1) | 1.46(−1) | 0.188 | 0.758 | 18.579 |

17 | 0.466(−1) | 2,056.59(1) | 2.23(1) | 0.320 | 1.290 | 31.624 |

18 | 0.665(0) | 1,406.25(0) | 1.85(0) | 0.279 | 1.125 | 27.572 |

19 | 0.864(1) | 755.90(−1) | 1.46(−1) | 0.239 | 0.963 | 23.619 |

20 | 0.665(0) | 1,406.25(0) | 1.85(0) | 0.252 | 1.016 | 24.910 |

RUN . | . | . | × 10^{4}
. | SOTR (kgO_{2}/h)
. | SAE (kgO_{2}/kWh)
. | NDSAE × 10^{3}
. |
---|---|---|---|---|---|---|

1 | 0.466(−1) | 755.90(−1) | 2.23(1) | 0.058 | 0.236 | 5.800 |

2 | 0.665(0) | 1,406.25(0) | 1.85(0) | 0.231 | 0.931 | 22.828 |

3 | 0.665(0) | 1,406.25(0) | 1.20(−1.68) | 0.284 | 1.145 | 28.066 |

4 | 0.665(0) | 1,406.25(0) | 1.85(0) | 0.239 | 0.963 | 23.619 |

5 | 0.466(−1) | 2,056.59(1) | 1.46(−1) | 0.271 | 1.092 | 26.781 |

6 | 0.665(0) | 1,406.25(0) | 1.85(0) | 0.233 | 0.939 | 23.026 |

7 | 0.864(1) | 2,056.59(1) | 1.46(−1) | 0.283 | 1.141 | 27.967 |

8 | 0.665(0) | 1,406.25(0) | 1.85(0) | 0.246 | 0.991 | 24.311 |

9 | 1.0(1.68) | 1,406.25(0) | 1.85(0) | 0.320 | 1.290 | 31.624 |

10 | 0.665(0) | 312.5(−1.68) | 1.85(0) | 0.360 | 1.451 | 35.577 |

11 | 0.330(−1.68) | 1,406.25(0) | 1.85(0) | 0.298 | 1.201 | 29.450 |

12 | 0.665(0) | 1,406.25(0) | 2.50(1.68) | 0.317 | 1.281 | 31.407 |

13 | 0.864(1) | 2,056.598(1) | 2.23(1) | 0.345 | 1.391 | 34.095 |

14 | 0.864(1) | 755.90(−1) | 2.23(1) | 0.349 | 1.407 | 34.490 |

15 | 0.665(0) | 2,500.00(1.68) | 1.85(0) | 0.169 | 0.681 | 16.701 |

16 | 0.466(−1) | 755.90(−1) | 1.46(−1) | 0.188 | 0.758 | 18.579 |

17 | 0.466(−1) | 2,056.59(1) | 2.23(1) | 0.320 | 1.290 | 31.624 |

18 | 0.665(0) | 1,406.25(0) | 1.85(0) | 0.279 | 1.125 | 27.572 |

19 | 0.864(1) | 755.90(−1) | 1.46(−1) | 0.239 | 0.963 | 23.619 |

20 | 0.665(0) | 1,406.25(0) | 1.85(0) | 0.252 | 1.016 | 24.910 |

### Model fitting and statistical analysis of the results

Term . | Coefficient . | SE Coefficient . | T
. | P
. |
---|---|---|---|---|

Constant | 0.0244 | 0.0029 | 8.242 | 0.000 |

0.0050 | 0.0033 | 1.524 | 0.039 | |

0.0007 | 0.0033 | 0.232 | 0.022 | |

0.0018 | 0.0033 | 0.545 | 0.008 | |

0.0039 | 0.0054 | 0.728 | 0.033 | |

−0.0004 | 0.0054 | −0.082 | 0.036 | |

0.0031 | 0.0054 | 0.580 | 0.005 | |

−0.0106 | 0.0072 | −1.459 | 0.175 | |

0.0088 | 0.0072 | 1.210 | 0.254 | |

0.0045 | 0.0072 | 0.625 | 0.546 |

Term . | Coefficient . | SE Coefficient . | T
. | P
. |
---|---|---|---|---|

Constant | 0.0244 | 0.0029 | 8.242 | 0.000 |

0.0050 | 0.0033 | 1.524 | 0.039 | |

0.0007 | 0.0033 | 0.232 | 0.022 | |

0.0018 | 0.0033 | 0.545 | 0.008 | |

0.0039 | 0.0054 | 0.728 | 0.033 | |

−0.0004 | 0.0054 | −0.082 | 0.036 | |

0.0031 | 0.0054 | 0.580 | 0.005 | |

−0.0106 | 0.0072 | −1.459 | 0.175 | |

0.0088 | 0.0072 | 1.210 | 0.254 | |

0.0045 | 0.0072 | 0.625 | 0.546 |

At the 95% confidence level of significance, *R*^{2} = 85% and adjusted *R*^{2} = 90%.

*R*

^{2}) and

*p*-values are 0.850 and 0.000 respectively. The statistical analysis (Table 2) reveals that the model terms , and and quadratic model term , and are significant at 95% confidence level. The interactive model terms × , × , × are not significant (

*p*> 0.05). Hence, these insignificant coefficients were removed and a new regression equation was obtained to better describe the response surface of the NDSAE:

The predicted value of NDSAE varies from 5.8 × 10^{−3} to 35.58 × 10^{−3}. The coefficient of determination (*R*^{2} = 0.917) shows the satisfactory correlation between the actual and predicted values for NDSAE (Figure 3).

The ANOVA of the fitted model (Table 3) indicates that the regression is highly significant (*p* = 0.000), while the lack of fit is not significant (*p* > 0.05). Hence, it is inferred that the design model adequately fits the experimental data (Montgomery 1991).

Source . | DF . | Seq SS . | Adj SS . | Adj MS . | F . | P
. |
---|---|---|---|---|---|---|

Regression | 9 | 0.000398 | 0.000398 | 0.000044 | 0.83 | 0.000 |

Linear | 3 | 0.000142 | 0.000142 | 0.000047 | 0.89 | 0.479 |

Quadratic | 3 | 0.000044 | 0.000044 | 0.000015 | 0.28 | 0.000 |

Interaction | 3 | 0.000212 | 0.000212 | 0.000071 | 1.33 | 0.320 |

Residual Error | 10 | 0.000531 | 0.000531 | 0.000053 | ||

Lack-of-Fit | 5 | 0.000516 | 0.000516 | 0.000103 | 33.72 | 0.078 |

Pure Error | 5 | 0.000015 | 0.000015 | 0.000003 | ||

Total | 19 | 0.000929 |

Source . | DF . | Seq SS . | Adj SS . | Adj MS . | F . | P
. |
---|---|---|---|---|---|---|

Regression | 9 | 0.000398 | 0.000398 | 0.000044 | 0.83 | 0.000 |

Linear | 3 | 0.000142 | 0.000142 | 0.000047 | 0.89 | 0.479 |

Quadratic | 3 | 0.000044 | 0.000044 | 0.000015 | 0.28 | 0.000 |

Interaction | 3 | 0.000212 | 0.000212 | 0.000071 | 1.33 | 0.320 |

Residual Error | 10 | 0.000531 | 0.000531 | 0.000053 | ||

Lack-of-Fit | 5 | 0.000516 | 0.000516 | 0.000103 | 33.72 | 0.078 |

Pure Error | 5 | 0.000015 | 0.000015 | 0.000003 | ||

Total | 19 | 0.000929 |

### Effect of geometric variables , and on NDSAE

From Figure 4, it can be observed that the NDSAE increases gradually with an increase in the ratio of the consecutive width of tray to total height of aerator at 0.864 to 0.665. Thereafter NDSAE starts declining with further increase in. This may be due to the fact that with some specific widths of the successive trays and with higher discharge, the residence time of the water on the trays increases. This causes uniform distribution of water over the trays resulting in better aeration (El-Zahaby & El-Gendy 2016). A higher range of aeration of the developed aerator takes place with the ratio in the range of 0.665 to 0.864. Further increase in above 0.864 reduces the NDSAE. This may be due to the fact that non-uniform distribution of water over the trays takes place with further increase in . This phenomenon decreases the air–water contact period and comparatively less oxygen transfer takes place, which finally reduces the NDSAE.

From Figure 5, it is observed that there is an initial increasing trend of NDSAE with the increased values of and . This may be due to the fact that the water-bubble size with specific surface area enhances the air–water interaction and increases the residence time of the water, allowing a better oxygen transfer rate and producing more aeration in the water body (Navisa *et al.* 2014).

From Figure 6, it can be observed that the NDSAE increases with the increase in . As there is more volume of water in the tank, the residence time of water becomes longer, which increases the oxygen transfer (Al-Ahmady 2006). Thus the NDSAE is increased as the aeration efficiency is proportional to the oxygen transfer rate (Equation (2)).

After knowing the possible direction to maximize the NDSAE, optimization was carried out using the ‘Point Optimization’ technique of Design Expert software. The optimum conditions of different variables for maximum NDSAE are presented in Table 4. A maximum NDSAE of 25.408 × 10^{−3} was predicted at = 0.665, = 312.50 and = 0.000185. The NDSAE is equal to , where Δ*C* is saturation DO concentration at the 20 °C temperature of water used in the test. The values Δ*C* = 9.07 mg/L, *Q* = 0.013 m^{3}/s, water density *ρ*_{w} = 1,000 kg/m^{3} and *n* = 3 were assumed to be constant throughout the experiments. Therefore, for the maximum value of NDSAE, the SAE will also attain the maximum value. The maximum predicted SAE was found to be 1.451 kgO_{2}/kWh under the same geometric conditions as given in Table 4.

Variables . | Optimum value obtained . | Maximum predicted response NDSAE . |
---|---|---|

0.665 | 25.408 × 10^{−3} | |

312.50 | ||

1.85 × 10^{−4} |

Variables . | Optimum value obtained . | Maximum predicted response NDSAE . |
---|---|---|

0.665 | 25.408 × 10^{−3} | |

312.50 | ||

1.85 × 10^{−4} |

### Model validation

The optimized geometric variables were validated with an additional three sets of experiments to re-check the model. The predicted value of NDSAE was 25.40 × 10^{−3} as suggested by the RSM model. The mean value of NDSAE was found to be 27.47 × 10^{−3}. The difference between the experimental and predicted value (Table 5) was found to be ±2.07, thus confirming the adequacy of the model. Hence, the results of the validation parameters were satisfactory.

Experimental NDSAE × 10^{−3}
. | Predicted NDSAE × 10^{−3}
. |
---|---|

27.47 ± 2.70 | 25.40 ± 2.92 |

Experimental NDSAE × 10^{−3}
. | Predicted NDSAE × 10^{−3}
. |
---|---|

27.47 ± 2.70 | 25.40 ± 2.92 |

## SUMMARY AND CONCLUSIONS

The present study explores how the aeration characteristics of the perforated tray aerator depend on different geometric variables. In order to increase the efficiency of the perforated tray aerator, optimization of the geometric variables was performed.

To evaluate the optimum *n*, experiments were conducted with different geometric variables , and using response surface methodology. The results showed that SAE and NDSAE attained the maximum values at = 0.665, = 312.50 and = 1.85 × 10^{−4}. The optimum values of SAE and NDSAE were 1.451 kgO_{2}/kWh and 35.58 × 10^{−3} respectively. Optimum geometric variables using CCRD/RSM were validated and confirmed from the experimental results.

Based on the above results the following conclusions are drawn.

- (a)
The optimum number of trays in a perforated tray aerator should be 3 to achieve the maximum SAE.

- (b)
The maximum SAE and NDSAE can be obtained at = 0.665, = 312.50 and = 1.85 × 10

^{−4}. - (c)
Response surface graphs can be used to describe the effect of the geometric variables on the performance of a perforated tray aerator.

- (d)
The predicted NDSAE and SAE for the designed aerator are 25.40 × 10

^{−3}and 1.451 kgO_{2}/kWh respectively under the optimum geometric conditions. - (e)
The optimized parameters , and for the perforated tray aerator were experimentally validated and the final NDSAE value was found to be (27.47 ± 2.70) × 10

^{−3}against the predicted value of (25.40 ± 2.92) × 10^{−3}.

Finally, it may be said that the developed RSM/CCRD model is an effective tool for predicting the optimized geometric variables of a perforated tray aerator.