Design characteristics of showering aeration system

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 (r) of the SAS with different values, such as r 1⁄4 0, 5, 10, 15, and 20 mm, and maintain other geometric parameters, i.e. number of holes in the shower (n); 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 (r) 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 (n), the ratio of the height of water fall to the length of shower arm (H=l ); the ratio of the diameter of the hole to the length of shower arm (d=l) and the ratio of the volume of water to the cube of the length of shower arm (V=l3): 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 was obtained from the SAS performance at n1⁄4 80; H=l 1⁄4 2; d=l1⁄4 4 and V=l3 1⁄4 48.

• 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 Â 10 6 against the predicted NDSAE value of 17.70 Â 10 6 . NOMENCLATURE ANOVA analysis of variance u temperature correction factor C concentration of oxygen at time (ML À3 ) C* oxygen saturation at standard conditions (ML À3 ) C 0 dissolved oxygen concentration at time, t ¼ 0 (ML À3 ) DO dissolved oxygen Fr Froude number g acceleration due to gravity (LT À2 ) H height of water fall (L) K L a 20 standard oxygen transfer coefficient at 20°C (T À1 ) K L a T overall oxygen transfer coefficient at T°C (T À1 ) n number of holes in the shower NDSAE non-dimensional number characterizing SAE P power consumption (ML 2 T À3 ) Q pump discharge/water flow rate (L 3 T À1 ) Re Reynolds number SOTR standard oxygen transfer rate (MT À1 ) SAE standard aeration efficiency (L À2 T 2 ) T temperature (°C) V volume of water under aeration (L 3 ) W Weber number r a density of air (ML À3 ) r w density of water (ML À3 ) s w surface tension of water (MT À2 ) ν w kinematic viscosity of water (L 2 T À1 ) RSM Response Surface Methodology SAS showering aeration system BBD Box-Behnken Design FCR feed conversion ratio SGR specific growth rate RGR relative growth rate r radius of curvature (L) D distance between showers (L) d diameter of shower hole (L) 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(Roy et al. , 2021b(Roy et al. , 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(Roy et al. , 2020a(Roy et al. , 2020bRoy 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. 2002Moulick et al. , 2005Moulick et al. , 2010Roy et al. 2020aRoy et al. , 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 as 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 lesser 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.
The SOTR of an aeration system is defined as the mass of oxygen that the device can introduce into a body of water per unit time under standard circumstances of 20°C water temperature, 0 mg/L initial DO concentration, one atmospheric pressure and clear tap water (APHA 1980;ASCE 1997).
where SOTR is the standard oxygen transfer rate (kgO 2 /h), (k L a) 20 is the standard oxygen transfer coefficient at , 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 ). In most circumstances, larger aerators will transport more oxygen than smaller ones. So, the SAE, which is defined as the quantity of oxygen transported per unit of energy input, is a superior comparative parameter than SOTR (Lawson & Merry 1993). It is expressed as follows: where P is the power applied to the aerator (kW). Power (P) in kW was estimated using the following equation: H ¼ total head ¼ static head þ frictional head loss, 9.81 ¼ acceleration due to gravity (m/s 2 ), Q ¼ flow rate (m 3 /s), and η ¼ pump efficiency (42%).

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. 2020aRoy et al. , 2020bRoy et al. , 2021aRoy et al. , 2021bRoy et al. , 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 ¼ height of waterfall; n ¼ number of holes in shower; l ¼ length of shower arm; V ¼ volume of water; d ¼ diameter of the shower holes; D ¼ distance between showers. Process attributes: g ¼ acceleration due to gravity; Q ¼ discharge from the pump. Material attributes: ρ a ¼ mass density of air; ρ w ¼ mass density of water; υ w ¼ kinematic viscosity; σ w ¼ surface tension of water.
The principal parameter of the absorption method is the absorption rate coefficient (k L a) 20 Â V (Zlokarnik 1979). It is expressed as follows: Therefore, the variables that affect the oxygen transfer rate at 20°C can be expressed as the functional dependence of the aeration tank and the aeration system with a specific shape and design as follows: Lawson & Merry (1993) reported that SAE is a better comparative index than SOTR. So, SOTR is replaced by SAE. Also, the functional relation between SAE/ΔC and key variables can be expressed as follows: Using the Buckingham's π theorem, l, ρ w , g were chosen as the repeating variables and Equation (6) can be expressed as dimensionless as follows: Since the aeration tests were performed using only air and water, the r a =r w ratio remains same in all the cases. The existing literature (Schmidtke & Horváth 1978;Rao 1999;Moulick et al. 2005;Moulick & Mal 2009;Kumar et al. 2013;Roy et al. 2015Roy et al. , 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: AQUA -Water Infrastructure, Ecosystems and Society Vol 00 No 0, 4

Uncorrected Proof
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 (l) and distance between showers (D), so these variables are fixed as Q ¼ 0.0015 m 3 /s; l ¼ D ¼ 0.5 m.

Experimental setup
A cemented concrete rectangular tank of dimensions 2 Â 4 Â 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 (r) (Figure 2). The radius of curvature (r) 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 (r), nine types of showers (8 nos. in each type) were fabricated with a combination of geometric parameters namely n ¼ 60, 80, 100 and d ¼ 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.

Aeration test
Unsteady state aeration tests were carried out in a concrete tank following the standard procedures with clean tap water (ASCE 1997). First, the tap water was deoxidized with 0.1 mg/L cobalt chloride and 10 mg/L sodium sulfite for each mg/L DO in the water (Boyd 1998). DO measurements were taken with YSI Professional 20 DO meters positioned at different points underneath the water surface (one at shallow depth and another at the middle of the water column). At least 20 DO measurements were carried out at equal time intervals till DO increases from 0% to 80% saturation (Baylar 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: (K L a)T ¼ ( ln OD 10 À ln OD 80 ) 4 (t 80 À t 10 ) To compute SOTR, the oxygen transfer coefficient was adjusted to 20°C using a temperature correction factor. It is given as follows: (K L a) 20 ¼ (K L a) T 4 1:024 (T À20) Using the above values, SOTR and SAE can be computed with Equation (1).

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 (r). Initially, five showers were fabricated with five different radiuses of curvature (r): 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, Q ¼ 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.

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 nondimensional geometric variables: the ratio of height of water fall to the length of shower arm (H=l); the ratio of diameter of shower holes to the length of shower arm (d=l); the ratio of volume of water to the cube of the length of the shower arm (V=l 3 ); the number of holes of the shower plate (n) that magnifies NDSAE can be found out. Hence, discharge(Q), 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 H=l, d=l, V=l 3 and n 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 secondorder response surface model. The ranges of four independent variables H=l ¼ 1, 2, 3; d=l ¼ 3, 4, 5; V=l 3 ¼ 32, 40, 48; n ¼ 60, 80, 100 were selected on the basis of preliminary trials. Assume, d(SAE) d(n) ¼ 0, we get r ¼ 11.02-10 mm. The maximum SAE was obtained at r ¼ 10 mm. The SAE decreases as the radius of curvature (r) 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 (r): 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 H=l ¼ 1, 2, 3; d=l ¼ 3, 4, 5; V=l 3 ¼ 32, 40, 48; n ¼ 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 Â 10 6 to 15.914 Â 10 6 , and the corresponding SAE values are 0.6888 and 1.4429 kgO 2 /kWh, respectively. The experimental data were analyzed in Minitab 19 software using the RSM to determine the optimum geometric variables. From the analysis, it is obtained that a second-order polynomial (quadratic) was found to be fit. where A is the number of holes (n), B is the ratio of height of water fall to the length of shower arm (H=l), C is the ratio of diameter of holes to the length of shower arm (d=l), and D is the ratio of volume of water to the cube of the length of shower arm (V=l 3 ). It is evident from Table 4 that the linear and quadratic models are highly significant with (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     (14)).
NDSAE ¼ À80:6 þ 1:4608 A þ 10:733 B þ 22:09 C À 1:066 D À 0:008835A Ã A À 2:477 B Ã B À 2:856 C Ã C þ 0:01516 D Ã D where the coefficients are the same as for Equation (13). 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
The effects of the NDSAE over the four geometric variables are given in Figures 5-8, respectively.
NDSAE is linearly proportional to the number of holes (n) and reaches a maximum when n ¼ 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 n 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(H=l) 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 H=l ¼ 2. AQUA -Water Infrastructure, Ecosystems and Society Vol 00 No 0, 11 Uncorrected Proof Figure 7 illustrates that the ratio of volume to the cube of the length of shower arm (V=l 3 )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 d=l and it also reaches its peak when d=l ¼ 4. Beyond that the NDSAE progressively decreases as the d=l 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.