Design characteristics of perforated pooled circular stepped cascade (PPCSC) aeration system

Dissolved oxygen (DO) is a very important parameter in aquaculture water as it directly affects the growth and survival of aquatic species. It is therefore necessary to maintain the desired oxygen level in such waters through artificial aerators. Different types of aerators, viz., mechanical, diffused-air, gravity and so on have been developed over the years and are currently in use in aquacultural operations (Boyd 1998, 2009; Moulick et al. 2002, 2005; Moulick & Mal 2009; Jayraj et al. 2018; Cheng et al. 2019). The cascade aerator, a type of gravity aerator, is very popularly used in water treatment plants to remove iron and manganese or various dissolved gases or volatile organic compounds (Mahmad et al. 2015). In aquacultural ponds with water volume ≤1,000 m³, cascade aeration systems (circular stepped cascade aerator (Singh 2010) and pooled circular stepped cascade aerators (Kumar et al. 2013a)) were found to be the most economical ones (Kumar et al. 2013b).

In a circular stepped cascade (CSC) aerator, the setup consists of a CSC along with a pump. The pump lifts the water to the top of the CSC and allows the water to fall over the steps of the aerator. This arrangement creates turbulence in the water and thus breaks the air-water interface, which leads to aeration. The aeration efficiency depends on the flow rate of the water and the exposure time of the water over the steps. Singh (2010) found the standard aeration efficiency (SAE) of the CSC aerator to vary between 2.16 and 2.70 kg O₂/kWh. In pooled circular stepped cascade (PCSC) aerators, partial enclosures are attached at the boundary of each of the circular steps of the CSC aerator in a zigzag manner in order to increase the time of exposure of the water. Kumar et al. (2013a) found the SAE (2.43–3.23 kg O₂/kWh) of the PCSC aerator to be higher than the CSC aerator.

The idea of this present study is to further increase the aeration efficiency of the PCSC aerator by adopting some changes in its design. When water is allowed to fall over the steps, initially a larger step width is required for proper contact of the water layer with the steps. In the PCSC aerator, the width of the circular steps was kept the same. It was felt that by varying the step width in decreasing order from top to bottom of the setup, better aeration may be achieved. In addition, if holes or perforations are provided in the steps, it will allow a part of the flow to fall vertically through the holes in the form of fine spray. It is strongly believed that this modified design of PCSC aerator, hereafter named the perforated pooled circular stepped cascade (PPCSC) aerator, will have a better aeration efficiency than the other existing aerators and may have potential application in small intensive aquacultural ponds and also as pre-aeration or post-aeration units in water or wastewater treatment plants.

Based on the above discussion, the following objectives are taken up in the present study:

• I.

  Optimization of the geometric design parameters – ratio of width of consecutive steps (W_i/W_i+1) and ratio of perforation diameter to bottom-most radius (d/R_b) of the PPCSC aerator.

• II.

  Formulation of predictive model equations for evaluation of the aeration performances of the PPCSC aerator at different dynamic conditions.

• III.

  Development and performance assessment of prototype PPCSC aerators.

• IV.

  Comparison of the performance of the PPCSC aerator with the other existing cascade aerators.

The performances of aerators are mainly assessed in terms of standard oxygen transfer rate (SOTR) and standard aeration efficiency (SAE).

The brake power (kW) can be estimated by dividing the wire power by the overall efficiency (η) of the pump-motor assembly.

The experimental setup for testing of the PPCSC aerator is shown schematically in Figure 1. The various geometric, material and process variables affecting oxygen transfer for the PPCSC aerator are listed in Table 1.

Based on dimensional analysis, the non-dimensional SAE, i.e., NDSAE was expressed as a function of geometric and dynamic parameters.

Where, non-dimensional standard aeration efficiency (NDSAE) = ⁠;

• = Weber number, W;

• = Reynolds numbers, Re; and

• = Froude number, Fr.

The first seven dimensionless quantities in function f₂ represent geometric variables, the eighth and ninth one represent the material variables and finally the last two represent the process variables.

In the case of the PCSC aerator, Kumar et al. (2013a) established that the dimensionless geometric parameters: n, H/R_b, P_e and N_e should be 5, 0.25, 20% and 9 respectively to achieve the maximum SAE. In the present study, these geometric parameters (n, H/R_b, P_e and N_e) were kept constant at the above stated values and accordingly were removed from function f₂. Further, it was found that V/R_b³ does not influence SAE significantly (Moulick et al. 2002, 2010; Kumar et al. 2013a). Therefore, V/R_b³ was also omitted from the function f₂.

The dimensionless material variables – – remained constant as all the experiments were carried out involving air and water only. Therefore, these two dimensionless material variables were also excluded from the function f₂.

Studies conducted by several investigators (Schmidtke & Horvath 1977; Rao 1999; Moulick et al. 2005, 2010; Moulick & Mal 2009; Kumar et al. 2013a; Roy et al. 2017) showed that Froude (Fr) and Reynolds (Re) number mainly affect the aeration process. Accordingly the Weber number, W was neglected.

In the above equation, the first two dimensionless quantities (W_i/W_i+1 and d/R_b) represent the geometric similarity and the last two (Fr and Re) represent the dynamic similarity.

A testing facility for the PPCSC aerator was developed as shown in Figure 2. The testing facility includes a reinforced cement concrete tank of dimension 4 m × 4 m × 1.5 m for conducting the aeration tests, open well submersible pump set (5 HP) with a control valve for pumping and discharging water at the top of the cascade setups and different setups of PPCSC aerator with metallic stand as per the experimental design. An Electromagnetic Flow Meter (Full Bore) (Make: Manas; Series: SROAT 1000; Liner: PTFE; Meter size: DN 100; Flow rate: 0–40 L/s) was used to measure the discharge.

Different PPCSC setups were fabricated locally using 0.64 mm thick galvanized iron (G.I.) sheets consisting of perforations of different diameters (d). A funnel with top diameter equal to twice the diameter of the topmost step and bottom diameter equal to 100 mm was fabricated using the same G.I. sheet for each cascade setup. One side of the funnel was welded with the topmost step and the other end with one 100 mm pipe piece having threads at the other end to facilitate its joining with the control valve of the pump.

Aeration experiments were conducted (Table 2) by varying the ratio of width of consecutive steps (W_i/W_i+1) from 1.00 to 1.25 at an interval of 0.05 and ratio of perforation diameter to total bottom-most radius (d/R_b) from 0.0013 to 0.0027 at an interval of 0.0007. A full factorial design was considered with a total of 54 experiments (first input with 6 levels × second input with 3 levels × 3 repetitions = 54 experiments) to evaluate the performance of the PPCSC aerator for an optimal solution. Keeping Q and R_b as 0.019 m³/s and 0.75 m respectively, experiments were conducted such that the dimensionless dynamic parameters (Fr = 0.0124 and Re = 30864) remained constants. The commercial statistical software package Design Expert (Stat-Ease, 2008 and version-7.1.6) was used for FFD (full factorial design), analysis of variance (ANOVA) and regression analysis. ‘Numerical Optimization’ process was adopted to optimize the geometric parameters (W_i/W_i+1, d/R_b), keeping Fr and Re constants.

Experiments were conducted on different-sized PPCSCs (R_b: 0.75 to 1.20) and at different discharges (Q: 0.007 to 0.022 m³/s) to assess the effect of dynamic conditions on aeration characteristics (Table 3). In this set of experiments, optimized values of geometric parameters: W_i/W_i+1 and d/R_b were kept as constants.

Prototype PPCSC setup was fabricated by attaching the cascade setup to a propeller pump (0.18 kW; Make – Kirloskar Electric Co. Ltd, India) along with the motor assembly (Figure 3). The outlet of the propeller pump was kept above the top surface of the PPCSC setup to allow the discharge of water to fall all over the cascade.

Standard aeration experiments were conducted with four different sized (R_b: 0.75, 0.90, 1.05 and 1.20 m) prototype PPCSC setups, keeping the water flow rate (Q) at 0.007 m³/s (Table 4).

The wire power (0.14 kW) was recorded using MECO 3 phase 4 wire power analyser. The power consumption without any load was determined as 0.09 kW. Therefore, the brake power was calculated as (0.14–0.09) kW = 0.05 kW. The SAE in each case was reported on the basis of wire power as well as brake power.

The aeration performance, in terms of brake power SAE, of the prototype PPCSC aerator was compared with PCSC and CSC aerators (Singh 2010; Kumar et al. 2013a).

Optimization of the dimensionless geometric parameters (W_i/W_i+1 and d/R_b) was carried out using ‘Numerical Optimization’ technique with the Design Expert software. The optimum values of the dimensionless geometric parameters at which the maximum SAE can be achieved for the PPCSC aerator are presented in Table 7.

Aeration experiments were conducted at different discharges (Q = 0.007 to 0.022 m³/s) and different sizes of PPCSC (R_b = 0.75 to 1.20 m). Based on the experimental results, simulation equations for prediction of oxygen transfer and power consumption were formulated.

It can be observed from Figure 4 that NDSAE increases with increase in Re as a power function and NDSAE values for all cascade setups can be fitted by the above single function. As the Reynolds number is the ratio of inertial and viscous forces and transfer of oxygen takes place under a turbulent condition due to comparatively high inertial force, the Reynolds number significantly influences the phenomenon. A reasonably good coefficient of determination (R²) of 0.816 is obtained for the developed relationship. The uncertainty in the experimental results is represented in Figure 4 by the error bars corresponding to plus or minus one standard deviation (STD) with a 95% confidence limit.

From Figure 5, it is clear that the NDSAE increases with the increase in the values of Fr. A very high value of coefficient of determination (R²) of 0.989 shows that the relationship is highly significant. In Figure 5, the uncertainty of the analysis is shown by plotting the data points using error bars with one plus or minus STD at 95% confidence limit. It may be noted that the overall fitting for the data is good and most of the experimental data lie within the domain of the model.

It may be observed that Equation (18) provides better correlation than Equation (17). This is due to the fact that the flow, in the case of the cascade aerator, occurs primarily due to gravity forces. Therefore Fr plays a dominant role under such conditions. Many researchers also found the Froude criterion to be the most influencing factor in the analysis of stepped cascade systems (Toombes & Chanson 2005; Kumar et al. 2013a; Bayon-Barrachina & Lopez-Jimenez 2015; Rathinakumar et al. 2017). Hence in this study, Equation (18) (Fr criterion) was regarded as the simulation equation depicting oxygen transfer.

It can be noted from Figure 6 that, particularly at low values of Re, the data points representing Ne values are much away from the plotted curve. This clearly explains the fact that as the flow pattern is dependent mostly on gravity force, the effect of viscous force may not be significant. The experimental data are represented by error bars corresponding to plus or minus one standard deviation (STD) with the 95% confidence limit.

It can be seen from Figure 7 that all the points are located either on the predicted curve (Equation (20)) or are very close to it. Therefore, Equation (20) may be regarded as the simulation equation for power consumption of the PPCSC aerator. The experimental data represented in Figure 7 is plotted using error bars corresponding to plus or minus one standard deviation (STD) with the 95% confidence limit.

The simulation equations depicting oxygen transfer (Equation (18)) and power consumption (Equation (20)) can be readily used for estimation of SAE, P and SOTR for different sizes (R_b) of PPCSC aerator and pump discharge (Q).

Four prototype PPCSC aerators of different sizes (R_b: 0.75, 0.90, 1.05 and 1.20 m) were fabricated and evaluated for their aeration performance at a particular flow rate of the propeller pump (Q: 0.007 m³/s). The aeration performances of the prototype PPCSC aerators are shown in Table 8. It can be seen from the table that the SOTR as well as the SAE increases with the increase in size of the aerator as the power consumption in all the cases was nearly equal because of having the same pump discharge. It is clear from the result that, with the increase in the size of the aerator, more water will be exposed to atmosphere over the surface of the aerator, leading to higher oxygen transfer. However, a large size of aerator is not recommended as it may lead to maintenance and transport problems.

Standard aeration efficiencies based on brake power for the CSC, PCSC and PPCSC aerators are presented in Table 9. The results clearly indicate that the SAE of the PPCSC aerator is approximately 1.55 times and 1.80 times higher than the PCSC aerator and CSC aerator respectively.

In the existing cascade aerators (CSC and PCSC), the oxygen transfer occurs because of increase in interfacial area of air-water due to breaking of the water surface while falling over the circular steps. However, in the case of the PPCSC aerator, the oxygen transfer takes place not only due to breaking of the water surface over the steps, but also due to free fall of water droplets through the perorated holes in the PPCSC setup. This free fall of water droplets allows the atmospheric oxygen to enter into the water at a very fast rate as the air-water interfacial area becomes very high (El-Zahaby & El-Gendy 2016).

In the cascade aerator, the maximum turbulence is created in the top-most step and thereafter it decreases as it falls through the remaining steps. Due to this high turbulence, the air-water interfacial area increases and aeration takes place. At high flow rate, it may happen that the water flow may bypass the top-most steps without breaking the water droplets. In that case, effective aeration may not take place even through the water flows at high velocity. In PPCSC, such a phenomenon may not occur as the width of the top-most step is increased. As a result, at higher flow velocity also, breaking of water drops and resultant increase in air-water interfacial area takes place in the top-most step. The widths of the remaining steps are decreased following a constant ratio (W_i/W_i+1 = 1.05) as unnecessary higher widths of lower steps increase the input cost of the cascade setup.

In the present study, a new type of cascade aerator, namely the perforated pooled circular stepped cascade (PPCSC) aerator, has been developed by modifying some design features of the existing cascade aerators; that is, the circular stepped cascade aerator and pooled circular stepped cascade aerator. The modification was made in two aspects – (1) varying the step width with a decreasing rate starting from the topmost step and (2) adding perforations on the horizontal portion of the steps. The parameters affecting the aeration efficiency were non-dimensionalised and categorized as geometric [ratio of width of consecutive steps (W_i/W_i+1) and ratio of perforation diameter to bottommost radius (d/R_b)] and dynamic [Froude (Fr) and Reynolds (Re) number] based on Buckingham π theorem. Keeping the dynamic parameters constant, experiments were conducted to optimize the geometric parameters based on full factorial experimental design. Further, maintaining the optimized geometric parameters (W_i/W_i+1 = 1.05 and d/R_b = 0.0027), aeration experiments were further conducted at different dynamic conditions (varying discharges (Q) and bottom-most radius (R_b)) to study the aeration characteristics of the PPCSC aerator. Based on the experimental results, simulation equations could be formulated to predict SOTR, SAE and P for PPCSC aerators subject to 0.00141≤ Fr ≤0.01441. Four prototype PPCSC aerators with different sizes (R_b = 0.75 m, 0.90 m, 1.05 m and 1.20 m) were fabricated and evaluated for their aeration performances. It was found that the standard aeration efficiency (SAE) values of the prototype PPCSC aerators based on brake power ranged between 3.36 and 4.98 kg O₂/kWh, with an average of 4.45 ± 0.741 kg O₂/kWh. This clearly shows that the SAE of the PPCSC aerator is much higher than that of the other available cascade aerators; that is, PCSC (SAE: 2.873 ± 0.342 kg O₂/kWh) and CSC (2.470 ± 0.256 kg O₂/kWh) aerators.

The specific conclusions of the study are presented as follows:

• 1.

  The ratio of consecutive widths of steps (W_i/W_i+1) and the ratio of perforation diameter (d) to bottom-most radius (R_b) of the PPCSC should be kept at 1.05 and 0.0027 respectively for achieving the maximum aeration efficiency.

• 2.

  Simulation equations for prediction of aeration efficiency and power characteristics of the PPCSC aerator were formulated based on Froude (Fr) criterion, subject to 0.00141≤ Fr ≤0.01441.

• 3.

  The comparative aeration performance of cascade aerators reveals that the SAE of the PPCSC aerator is at least 150% more than that of the other available cascade aerators.