Abstract

In the present study, an improvised design over circular stepped cascade (CSC) and pooled circular stepped cascade (PCSC) aerator, named the perforated pooled circular stepped cascade (PPCSC) aerator, has been conceptualized and tested for its suitability as an aerator for small intensive aquaculture ponds. Based on dimensional analysis, dimensionless geometric parameters – ratio of width of consecutive steps (Wi/Wi+1) and ratio of perforation diameter to bottom-most radius (d/Rb) and dimensionless dynamic parameters – Froude (Fr) and Reynolds (Re) number were proposed. Initially, aeration experiments were conducted to optimize the geometric parameters, keeping the dynamic parameters constant. Keeping the optimized values of Wi/Wi+1 = 1.05 and d/Rb = 0.0027 as constants, aeration experiments were further conducted at different discharges (Q) and different bottommost radius (Rb) to study the characteristics of oxygen transfer and power consumption of PPCSC aerator at different dynamic conditions. Based on the optimized results, four prototype PPCSC aerators with Rb = 0.75 m, 0.90 m, 1.05 m and 1.20 m were fabricated for their aeration performances. The results showed 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 the average being 4.45 ± 0.741 kg O2/kWh. This shows that the SAE of the PPCSC aerator is many more folds higher than that of the other available cascade aerators, viz., PCSC (SAE: 2.873 ± 0.342 kg O2/kWh) and CSC (2.470 ± 0.256 kg O2/kWh) aerators. The study clearly indicates that this PPCSC aerator may very well be used as pre-aeration or post-aeration units in water or wastewater treatment plants and small-scale intensive aquacultural ponds, replacing the other existing aerators.

HIGHLIGHTS

  • Design characteristics of perforated pooled circular stepped cascade (PPCSC) aerator were evaluated.

  • Simulation equations for oxygen transfer and power consumption for PPCSC aerators were developed.

  • Prototype PPCSC aerators were designed, developed and tested for aeration performance.

  • Aeration efficiency of the developed prototype PPCSC aerator was found to be significantly higher (about 1.5–1.8 times more) than the other existing cascade aerators.

Graphical Abstract

Graphical Abstract
Graphical Abstract

INTRODUCTION

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 (Wi/Wi+1) and ratio of perforation diameter to bottom-most radius (d/Rb) 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.

THEORETICAL ANALYSIS

General

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

SOTR denotes the quantity of oxygen that can be transferred to a water body under standard conditions (water temperature = 20 °C, initial DO concentration = 0 mg/L, one atmospheric pressure and clean tap water) per unit time (ASCE 2007) and may be expressed as follows: 
formula
(1)
where SOTR is the standard oxygen transfer rate (kg O2/h), is the overall oxygen transfer coefficient at 20 °C (h−1) = (Shelton & Boyd 1983; ASCE 2007), is the overall oxygen transfer coefficient at T °C (h−1), θ is the temperature correction factor for clean water (1.024), C* is the DO saturation at experimental condition (mg/L), C0 is the DO in the aeration basin and is assumed to be zero (mg/L) and V is the volume of water in the tank (m3).
Standard aeration efficiency (SAE) is defined as the SOTR per unit power consumption and may be expressed as follows (ASCE 2007): 
formula
(2)
where P is the power consumption (kW).
Power consumption (P) may be denoted as either brake power or wire power. The wire power (kW) can be estimated by the following equation: 
formula
(3)
where H is the total head of the aerator (m) and Q is the discharge of the pump (m3/s).

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

At other environmental conditions, the actual oxygen transfer rate (OTR) of an aerator operating in a fish pond can be estimated by the following equation (ASCE 1993; Boyd 1998): 
formula
(4)
where Cs is the saturation concentration of pond water (mg/L) at T (°C), CP = initial DO concentration in pond water (mg/L) at T (°C), α = pond water/ tap water and β = DO saturation concentration of pond water/DO saturation concentration of tap water. Aeration efficiency (AE) of aerators for pond conditions can be estimated by the following equation (Boyd 1998): 
formula
(5)

Dimensional analysis

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.

Table 1

Descriptions of parameters influencing the aeration process of PPCSC aerator

Class of variablesName of parametersSymbolDimension
Geometric Radius of bottom-most circular step Rb 
 Ratio of width of consecutive steps Wi/Wi + 1 M0T0 L0 
Total number of steps in the cascade M0T0 L0 
Total height of the perforated circular stepped cascade 
Volume of water under aeration L3 
% coverage of circumference of each step by enclosure Pe M0T0 L0 
No. of enclosure in each step Ne M0T0 L0 
 Perforated diameter of the stepped cascade 
Material Mass density of air ρa ML−3 
Mass density of water ρw ML−3 
Kinematic viscosity of water νw L2T−1 
Surface tension of water in contact with air σw MT−2 
Process Pump discharge L3T−1 
Acceleration due to gravity LT−2 
Class of variablesName of parametersSymbolDimension
Geometric Radius of bottom-most circular step Rb 
 Ratio of width of consecutive steps Wi/Wi + 1 M0T0 L0 
Total number of steps in the cascade M0T0 L0 
Total height of the perforated circular stepped cascade 
Volume of water under aeration L3 
% coverage of circumference of each step by enclosure Pe M0T0 L0 
No. of enclosure in each step Ne M0T0 L0 
 Perforated diameter of the stepped cascade 
Material Mass density of air ρa ML−3 
Mass density of water ρw ML−3 
Kinematic viscosity of water νw L2T−1 
Surface tension of water in contact with air σw MT−2 
Process Pump discharge L3T−1 
Acceleration due to gravity LT−2 
Figure 1

Schematic diagram of Perforated Pooled Circular Stepped Cascade Aeration system. Ri and Rb represent the radius of ith and bottom-most step of the cascade respectively. Wi and Wi+1 represent the width of ith and (i + 1)th step respectively. h = Height of a single step of the cascade. H = Total height of the cascade.

Figure 1

Schematic diagram of Perforated Pooled Circular Stepped Cascade Aeration system. Ri and Rb represent the radius of ith and bottom-most step of the cascade respectively. Wi and Wi+1 represent the width of ith and (i + 1)th step respectively. h = Height of a single step of the cascade. H = Total height of the cascade.

The height (h) and the ratio of consecutive widths (i.e. Wi/Wi+1 = x) of the circular steps were assumed to be constant. The width and radius of ith step, i.e. Wi and Ri respectively, can be expressed as follows: 
formula
(6)
 
formula
(7)
where n is the total number of steps, Rn is the radius of the nth step or the bottom-most step = Rb
The absorption rate coefficient, is the main parameter that influences the aeration process (Zlokarnik 1979). It may be seen that this coefficient, is dependent upon different geometric, dynamic and process variables and may be expressed by the following functional relationship. 
formula
(8)
As SAE is a better comparative factor than SOTR (Lawson & Merry 1993) and also depends on similar factors to those on which SOTR depends, the parameter SOTR as expressed in Equation (8) is replaced by SAE. Thus, the functional relationship between and the key variables may be expressed as follows: 
formula
(9)
Selecting Rb, ρw and Q as the three repeating variables and applying Buckingham π theorem, the following dimensionless relationship may be obtained: 
formula
(10)

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/Rb, Pe and Ne should be 5, 0.25, 20% and 9 respectively to achieve the maximum SAE. In the present study, these geometric parameters (n, H/Rb, Pe and Ne) were kept constant at the above stated values and accordingly were removed from function f2. Further, it was found that V/Rb3 does not influence SAE significantly (Moulick et al. 2002, 2010; Kumar et al. 2013a). Therefore, V/Rb3 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.

Incorporating all the above considerations, Equation (10) may be re-written as follows: 
formula
(11)

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

In order to achieve proper mixing of DO throughout the water, the water volume (V) to power ratio in the experimental tank for testing aerators was decided based on the following condition, as suggested by Elliott (1969): 
formula
(12)
where P is the aerator power (kW) and V is the water volume in the tank (m3).
The power consumption, P, of the PPCSC aerator is dependent upon the same parameters as the term NDSAE. In a similar way, the following functional relationship for P is obtained. 
formula
(13)
where = Ne (Newton number)

MATERIALS AND METHODS

Testing facility of PPCSC aerator

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.

Figure 2

CAD model of PPCSC aerator.

Figure 2

CAD model of PPCSC aerator.

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.

The numbers of perforations per unit area of the steps (m2) of different d/Rb (0.0013, 0.0020 and 0.0027) were 643, 435 and 279 respectively. The area of annular steps was calculated using Equation (14): 
formula
(14)
where Ap is the area of annular steps (m2), Ri is the topmost radius of the cascade (m) and Wi is the width of the cascade (m).

Aeration test

Standard aeration tests were performed under standard conditions (20 °C and one atmospheric pressure) in a tank using clean tap water (ASCE 2007). Initially, the tap water was deoxygenated by using 0.1 mg/l of cobalt chloride (CoCl2) and 10 mg/l of sodium sulphite (Na2SO3) for each 1 mg/l of DO present in the water to follow the standard conditions (ASCE 2007). The dissolved oxygen (DO) concentrations, temperature and atmospheric pressure were measured using three DO meters (Two YSI Pro 20 and one YSI 55) by inserting their DO probes at three different positions in the water body at a depth of approximately 0.20 m from the surface of the water (Baylar et al. 2007). The average values of dissolved oxygen (DO) concentration, temperature and atmospheric pressure were considered for each experiment. The aerator was operated until the DO in the water body reached typically greater than 90% of saturation at a specific time (1 min) interval (Jiang & Stenstrom 2012). At least 45 DO readings at equal time intervals were taken. The three parameters, C0, C* and KLaT were determined simultaneously using Equation 15 (ASCE 2007; Jiang & Stenstrom 2012): 
formula
(15)
was then converted to , and accordingly the values of SOTR and SAE were computed using Equations (1) and (2) respectively. The dimensionless numbers (NDSAE, Re, Fr and Ne) were then evaluated using Equations (10), (11) and (13).

Experimental design

Optimization of geometric parameters (Wi/Wi+1, d/Rb)

Aeration experiments were conducted (Table 2) by varying the ratio of width of consecutive steps (Wi/Wi+1) from 1.00 to 1.25 at an interval of 0.05 and ratio of perforation diameter to total bottom-most radius (d/Rb) 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 Rb 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 (Wi/Wi+1, d/Rb), keeping Fr and Re constants.

Table 2

Experiments to optimize the geometric parameters of PPCSC aerator

Wi/Wi+1d/RbConstants
1.00 0.0013–0.0027 at an interval 0.0007 Q (0.019 m3/s) and Rb (0.75 m) 
1.05 
1.10 
1.15 
1.20 
1.25   
Wi/Wi+1d/RbConstants
1.00 0.0013–0.0027 at an interval 0.0007 Q (0.019 m3/s) and Rb (0.75 m) 
1.05 
1.10 
1.15 
1.20 
1.25   

Prediction of aeration characteristics of PPCSC aerator at different dynamic conditions

Experiments were conducted on different-sized PPCSCs (Rb: 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 these set of experiments, optimized values of geometric parameters: Wi/Wi+1 and d/Rb were kept as constants.

Table 3

Experimental design to study the aeration characteristics of PPCSC aerator at different dynamic conditions.

Rb (m)Q (m3/s)Similarity conditions
0.75 0.007–0.022 at an interval of 0.003 m3/s (Wi/Wi+1) = (Wi−1/Wi)a and (d/Rb) = (d/Rb)a 
0.90 
1.05 
1.20   
Rb (m)Q (m3/s)Similarity conditions
0.75 0.007–0.022 at an interval of 0.003 m3/s (Wi/Wi+1) = (Wi−1/Wi)a and (d/Rb) = (d/Rb)a 
0.90 
1.05 
1.20   

adenotes optimum values.

Performance assessment of prototype PPCSC aerators

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.

Figure 3

Schematic diagram of prototype PPCSC aerator with propeller pump.

Figure 3

Schematic diagram of prototype PPCSC aerator with propeller pump.

Standard aeration experiments were conducted with four different sized (Rb: 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).

Table 4

Experimental design for performance evaluation of prototype PPCSC aerators

Rb (m)Q (m3/s)Constants
0.75 0.007 Optimize values of the geometric parameters:(Wi/Wi+1) and (d/Rb
0.90 
1.05 
1.20   
Rb (m)Q (m3/s)Constants
0.75 0.007 Optimize values of the geometric parameters:(Wi/Wi+1) and (d/Rb
0.90 
1.05 
1.20   

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.

Comparison of aeration performance of prototype PPCSC aerator with PCSC and CSC aerators

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).

RESULTS AND DISCUSSION

Optimization of geometric parameters of PPCSC aerator

The experimental results corresponding to variation of SOTR, SAE and NDSAE at different geometric parameters (Wi/Wi+1 and d/Rb) of the PPCSC aerator are presented in Table 5. As Q and Rb were kept constants at 0.019 m3/s and 0.75 m respectively, SAE becomes directly proportional to NDSAE. The NDSAE ranged from 0.858 × 10−5 to 2.21 × 10−5 for different combinations of Wi/Wi+1 and d/Rb. The ANOVA of the experimental results is presented in Table 6. It can be noted from the table that the model is highly significant with a high R2 value of 0.908. The adjusted R2 value of 0.863 also implies that the model is highly significant. A low value of coefficient of the variation (C.V. = 10.17%) shows a very high degree of precision for the model. A third order regression equation with NDSAE as the response and Wi/Wi+1 and d/Rb as independent parameters is presented as follows: 
formula
(16)
Table 5

Experimental results of SOTR, SAE and NDSAE values at different geometric parameters (Wi/Wi+1 and d/Rb)

Wi/Wi+1d/Rb
0.0013
0.0020
0.0027
SOTRSAENDSAE × 105SOTRSAENDSAE × 105SOTRSAENDSAE × 105
1.00 0.256 ± 0.030 3.68 ± 0.176 1.289 ± 0.061 0.367 ± 0.042 5.286 ± 0.416 1.847 ± 0.145 0.413 ± 0.148 5.782 ± 1.218 1.915 ± 0.293 
1.05 0.232 ± 0.058 3.292 ± 0.338 1.150 ± 0.118 0.267 ± 0.068 3.787 ± 0.395 1.323 ± 0.138 0.410 ± 0.100 5.819 ± 0.526 2.033 ± 0.184 
1.10 0.233 ± 0.037 3.330 ± 0.128 1.163 ± 0.044 0.233 ± 0.067 3.308 ± 0.478 1.156 ± 0.167 0.192 ± 0.040 2.738 ± 0.213 0.956 ± 0.074 
1.15 0.189 ± 0.017 2.726 ± 0.237 0.952 ± 0.082 0.229 ± 0.067 3.231 ± 0.455 1.128 ± 0.159 0.205 ± 0.036 2.937 ± 0.072 1.026 ± 0.025 
1.20 0.183 ± 0.035 2.615 ± 0.143 0.914 ± 0.050 0.251 ± 0.091 3.526 ± 0.736 1.233 ± 0.257 0.283 ± 0.124 3.963 ± 1.144 1.385 ± 0.399 
1.25 0.214 ± 0.031 3.069 ± 0.210 1.072 ± 0.073 0.251 ± 0.050 3.580 ± 0.218 1.251 ± 0.076 0.376 ± 0.070 5.372 ± 0.172 1.877 ± 0.060 
Wi/Wi+1d/Rb
0.0013
0.0020
0.0027
SOTRSAENDSAE × 105SOTRSAENDSAE × 105SOTRSAENDSAE × 105
1.00 0.256 ± 0.030 3.68 ± 0.176 1.289 ± 0.061 0.367 ± 0.042 5.286 ± 0.416 1.847 ± 0.145 0.413 ± 0.148 5.782 ± 1.218 1.915 ± 0.293 
1.05 0.232 ± 0.058 3.292 ± 0.338 1.150 ± 0.118 0.267 ± 0.068 3.787 ± 0.395 1.323 ± 0.138 0.410 ± 0.100 5.819 ± 0.526 2.033 ± 0.184 
1.10 0.233 ± 0.037 3.330 ± 0.128 1.163 ± 0.044 0.233 ± 0.067 3.308 ± 0.478 1.156 ± 0.167 0.192 ± 0.040 2.738 ± 0.213 0.956 ± 0.074 
1.15 0.189 ± 0.017 2.726 ± 0.237 0.952 ± 0.082 0.229 ± 0.067 3.231 ± 0.455 1.128 ± 0.159 0.205 ± 0.036 2.937 ± 0.072 1.026 ± 0.025 
1.20 0.183 ± 0.035 2.615 ± 0.143 0.914 ± 0.050 0.251 ± 0.091 3.526 ± 0.736 1.233 ± 0.257 0.283 ± 0.124 3.963 ± 1.144 1.385 ± 0.399 
1.25 0.214 ± 0.031 3.069 ± 0.210 1.072 ± 0.073 0.251 ± 0.050 3.580 ± 0.218 1.251 ± 0.076 0.376 ± 0.070 5.372 ± 0.172 1.877 ± 0.060 

Units: SOTR (kgO2/h), SAE(kgO2/kWh).

Table 6

ANOVA analysis of the full factorial model for geometric optimization of PPCSC aerator

SourceSum of SquaresdfMean squareF valueProbability > F
Model 4.401 × 10−10 7.336 × 10−11 15.52 <0.0001 significant 
Wi/Wi+1 3.890 × 10−11 3.890 × 10−11 8.23 <0.0001 significant 
d/Rb 2.683 × 10−12 2.683 × 10−12 0.57 <0.0001 significant 
(Wi/Wi+1) × (d/Rb1.047 × 10−13 1.047 × 10−13 0.022 0.8824  
(Wi/Wi+1)2 1.734 × 10−10 1.734 × 10−10 36.68 <0.0001  
(Wi/Wi+1)2 × (d/Rb5.679 × 10−11 5.679 × 10−11 12.01 0.0012  
(Wi/Wi+1)3 1.340 × 10−11 1.340 × 10−11 2.83 0.0991  
Residual 2.175 × 10−11 46 4.728 × 10−12    
Lack of fit 1.572 × 10−10 11 1.429 × 10−11 8.29 <0.0001 significant 
Pure error 6.032 × 10−11 35 1.724 × 10−12    
Corrected total 6.576 × 10−10 52     
SourceSum of SquaresdfMean squareF valueProbability > F
Model 4.401 × 10−10 7.336 × 10−11 15.52 <0.0001 significant 
Wi/Wi+1 3.890 × 10−11 3.890 × 10−11 8.23 <0.0001 significant 
d/Rb 2.683 × 10−12 2.683 × 10−12 0.57 <0.0001 significant 
(Wi/Wi+1) × (d/Rb1.047 × 10−13 1.047 × 10−13 0.022 0.8824  
(Wi/Wi+1)2 1.734 × 10−10 1.734 × 10−10 36.68 <0.0001  
(Wi/Wi+1)2 × (d/Rb5.679 × 10−11 5.679 × 10−11 12.01 0.0012  
(Wi/Wi+1)3 1.340 × 10−11 1.340 × 10−11 2.83 0.0991  
Residual 2.175 × 10−11 46 4.728 × 10−12    
Lack of fit 1.572 × 10−10 11 1.429 × 10−11 8.29 <0.0001 significant 
Pure error 6.032 × 10−11 35 1.724 × 10−12    
Corrected total 6.576 × 10−10 52     

Coefficient of determination (R2) = 0.908; Adjusted (R2) = 0.863; S.D. = 0.131 × 10−5; Mean = 1.291 × 10−5; Coefficient of Variation (C.V.) = 10.17%; adequate precision = 7.724; Press = 1.364 × 10−10.

Optimization of the dimensionless geometric parameters (Wi/Wi+1 and d/Rb) 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.

Table 7

Optimum values of geometric parameters of PPCSC aerator (Wi/Wi+1 and d/Rb)

Sl. No.Geometric parametersOptimum valuesMaximum predicted response NDSAE
Wi/Wi+1 1.0500 1.625 × 10−5 
d/Rb 0.0027 
Sl. No.Geometric parametersOptimum valuesMaximum predicted response NDSAE
Wi/Wi+1 1.0500 1.625 × 10−5 
d/Rb 0.0027 

Effect of dynamic conditions on PPCSC aerator

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

Variation of NDSAE with Re and Fr

The variation of NDSAE with Re for different PPCSC setups is presented in Figure 4. The relationship between NDSAE and Re can be expressed by the following equation: 
formula
(17)
Figure 4

Variation of NDSAE with Re for different sizes of PPCSC aerator.

Figure 4

Variation of NDSAE with Re for different sizes of PPCSC aerator.

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.

The variation of NDSAE with Fr for different PPCSC setups is shown in Figure 5. The variation of NDSAE values with Fr is well fitted by the following equation: 
formula
(18)
Figure 5

Variation of NDSAE with Fr for different sizes of PPCSC aerator.

Figure 5

Variation of NDSAE with Fr for different sizes of PPCSC aerator.

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.

Variation of Ne with Re and Fr

The variation of Ne with Re for different PPCSC setups is shown in Figure 6. It may be seen that the variation of Ne values with Re for different sized PPCSC setups can be presented by the following equation: 
formula
Figure 6

Variation of Ne with Re for different sizes of PPCSC aerator.

Figure 6

Variation of Ne with Re for different sizes of PPCSC aerator.

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 is represented by error bars corresponding to plus or minus one standard deviation (STD) with the 95% confidence limit.

The variation of Ne and Fr for different PPCSC setups is presented in Figure 7. The variation of Ne values with Fr for different PPCSC setups may be presented in the following form: 
formula
(20)
Figure 7

Variation of Ne with Fr for different sizes of PPCSC aerator.

Figure 7

Variation of Ne with Fr for different sizes of PPCSC aerator.

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 (Rb) of PPCSC aerator and pump discharge (Q).

Performance assessment of prototype PPCSC aerators

Four prototype PPCSC aerators of different sizes (Rb: 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.

Table 8

Aeration performance of four different sized prototype PPCSC aerators

Exp. No.Rb (m)Q (m3/s)SOTR (kg O2/h)Wire power SAE (kg O2/kWh)Brake power SAE (kg O2/kWh)
0.75 0.007 0.168 ± 0.041 1.142 ± 0.110 3.360 ± 0.570 
0.90 0.007 0.231 ± 0.038 1.571 ± 0.350 4.620 ± 0.655 
1.05 0.007 0.242 ± 0.017 1.646 ± 0.192 4.840 ± 0.194 
1.20 0.007 0.249 ± 0.025 1.693 ± 0.267 4.980 ± 0.328 
Exp. No.Rb (m)Q (m3/s)SOTR (kg O2/h)Wire power SAE (kg O2/kWh)Brake power SAE (kg O2/kWh)
0.75 0.007 0.168 ± 0.041 1.142 ± 0.110 3.360 ± 0.570 
0.90 0.007 0.231 ± 0.038 1.571 ± 0.350 4.620 ± 0.655 
1.05 0.007 0.242 ± 0.017 1.646 ± 0.192 4.840 ± 0.194 
1.20 0.007 0.249 ± 0.025 1.693 ± 0.267 4.980 ± 0.328 

Comparison of standard aeration efficiencies of PPCSC aerator with PCSC and CSC aerators

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.

Table 9

Comparison of aeration performances of PPCSC aerator with PCSC and CSC aerators

AeratorsSOTR (kg O2/h)Brake Power SAE (kg O2/kWh)
PPCSCA 0.222 ± 0.037 4.450 ± 0.741 
PCSCA 0.143 ± 0.017 2.873 ± 0.342 
CSCA 0.123 ± 0.012 2.470 ± 0.256 
AeratorsSOTR (kg O2/h)Brake Power SAE (kg O2/kWh)
PPCSCA 0.222 ± 0.037 4.450 ± 0.741 
PCSCA 0.143 ± 0.017 2.873 ± 0.342 
CSCA 0.123 ± 0.012 2.470 ± 0.256 

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 (Wi/Wi+1 = 1.05) as unnecessary higher widths of lower steps increase the input cost of the cascade setup.

SUMMARY AND CONCLUSIONS

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 (Wi/Wi+1) and ratio of perforation diameter to bottommost radius (d/Rb)] 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 (Wi/Wi+1 = 1.05 and d/Rb = 0.0027), aeration experiments were further conducted at different dynamic conditions (varying discharges (Q) and bottom-most radius (Rb)) 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 (Rb = 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 (Wi/Wi+1) and the ratio of perforation diameter (d) to bottom-most radius (Rb) 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.

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