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186 Clean 2007, 35 (2), 186 – 192
Ahmet Baylar 1
Davut Hanbay 2
Emrah Ozpolat 1
1 Firat University, Civil Engineering
Department, Elazig, Turkey.
2 Firat University, Electronic and
Computer Science Department, Elazig,
Turkey.
1 Introduction
Research Article
Stepped cascade flows are characterized by the strong turbulent
mixing, the large residence time, and the substantial air bubble
entrainment. Stepped flows can be classified into skimming flow,
transition flow, and nappe flow. For narrow steps or larger discharges
such as the design discharge the water skims over the step
corners and recirculating zones develop in triangular niches
formed by the step faces and the pseudo-bottom, as shown in Fig. 1a.
In skimming flow the water flows as a coherent stream over the
pseudo-bottom formed by the step corners. For a range of intermediate
discharges, a transition flow regime takes place. The dominant
feature is stagnation on the horizontal step face associated with significant
splashing and a chaotic appearance (see Fig. 1b). For nappe
flow the steps act as a series of overfalls with the water plunging
from one step to another (see Fig. 1c). Generally speaking, the nappe
flow is found for low discharges and wide steps [1].
Self-aeration on stepped cascades is now recognized for its substantial
contribution to the air-water transfer of atmospheric gases
such as oxygen and nitrogen. Stepped cascades are very efficient
means of aeration because of the strong turbulent mixing, the large
residence time, and the substantial air bubble entrainment.
Stepped cascades are used in water treatment for re-oxygenation,
denitrification, or VOC removals. In the treatment of drinking
water, cascade aeration may be used to remove chlorine and to eliminate
or reduce offensive taste and odor [2].
Chanson and Toombes [3] conducted gas-liquid interface measurements
in a stepped cascade. Local void fractions, bubble count
rates, bubble size distributions, and gas-liquid interface areas were
measured simultaneously in the air-water flow region using resistivity
probes. However, they stated that future work is needed to compare
aeration efficiencies estimated with detailed interfacial area
data and based upon dissolved gas measurements. Recently, Baylar
Correspondence: Prof. A. Baylar (abaylar@firat.edu.tr), Firat University,
Civil Engineering Department, Elazig, Turkey.
Modeling Aeration Efficiency of Stepped Cascades
by Using ANFIS
The physical process of oxygen transfer or oxygen absorption from the atmosphere
acts to replenish the used oxygen, a process termed re-aeration or aeration. Aeration
enhancement by macro-roughness is well-known in water treatment and one form is
the aeration cascade. The macro-roughness of the steps significantly reduces the flow
velocities and leads to flow aeration along the stepped cascade. In this paper, the aeration
efficiency in stepped cascade aerators was modeled by using the Adaptive Network
Based Fuzzy Inference System (ANFIS). The obtained model was tested with experimental
data. Test results showed that ANFIS can be used to estimate the aeration
efficiency in stepped cascade aerators.
Keywords: ANFIS; Aeration efficiency; Modeling; Oxygen transfer;
Received: February 14, 2007; revised: March 9, 2007; accepted: March 12, 2007
DOI: 10.1002/clen.200700019
Figure 1. Flow regimes above stepped cascades: a) Skimming flow; b)
Transition flow; c) Nappe flow [22].
and Emiroglu [4], Emiroglu and Baylar [5], Baylar et al. [6], Emiroglu
and Baylar [7], and Baylar et al. [8 – 10] did some detailed experiments
on the aeration efficiency of stepped cascades. It was found
that water can trap a lot of air when passing through the steps and
that the oxygen content in the water body is increased. So stepped
cascades can be used as highly effective aerators in streams, rivers,
constructed channels, fish hatcheries, water treatment plants, etc.
Intelligent techniques are used in various areas of water-related
research [11 – 14]. Recently, Hanbay et al. [15,16] modeled the aeration
efficiency of weirs by using the Adaptive Network Based Fuzzy
Inference System (ANFIS) and by using wavelet and neural network.
In this study, the aeration efficiency in stepped cascade aerators is
modeled by using ANFIS. After reviewing some basic properties of
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Clean 2007, 35 (2), 186 – 192 Modeling of Aeration Efficiency 187
the oxygen transfer posses and the ANFIS, the effectiveness of the
proposed intelligent system is demonstrated.
2 Preliminaries
The oxygen transfer process and the theoretical foundations for the
intelligent system used in the presented study are given in the following
subsections.
2.1 Oxygen Transfer Process
The rate of oxygen mass transfer, i. e., from the gas (air bubbles) to
the liquid phase (water) is governed by the term described below:
dC
dt
¼ KL
A
V ðCs CÞ ð1Þ
Where C is the dissolved oxygen (DO) concentration, KL is the
liquid film coefficient for oxygen, A is the surface area associated
with the volume, V, over which the transfer occurs, Cs is the saturation
concentration, and t is the time. The term A/V is often called the
specific surface area, a, or surface area per unit volume.
Eq. (1) does not consider sources and sinks of oxygen in the water
body because their rates are relatively slow compared to the oxygen
transfer that occurs at most hydraulic structures due to the increase
in free-surface turbulence and the large quantity of air that is normally
entrained into the flow.
The predictive relations assume that Cs is constant and determined
by the water-atmosphere partitioning. If that assumption is
made, Cs is constant with respect to time, and the oxygen transfer
efficiency (aeration efficiency), E, may be defined as [17]:
E ¼ Cd Cu
Cs Cu
¼ 1
1
r
where u and d are subscripts indicating upstream and downstream
locations, respectively, and r is the oxygen deficit ratio:
[(Cs – Cu)/(Cs –Cd)]
A transfer efficiency value of 1.0 means that the full transfer up to
the saturation value has occurred at the structure surface. No transfer
would correspond to E = 0.0. The saturation concentration in distilled,
deionized water may be obtained from charts or equations
what is an approximation as the saturation DO concentration for
natural waters is often different from that of distilled, deionized
water due to the salinity affects.
Comparative evaluations of oxygen uptake at hydraulic structures
require that the aeration efficiency is corrected to a reference
temperature. To provide a uniform basis for comparison of measurement
results, the aeration efficiency is often normalized to a 208C
standard. Gulliver et al. [17] proposed the following equation to
describe the influence of the temperature:
1–E20 =(1–E) 1/f (3)
Where E is the transfer efficiency at the actual water temperature,
E20 is the transfer efficiency for 208C, and f is an exponent described
by:
f = 1.0 + 2.1610 –2 (T –20) + 8.26610 –5 (T–20) 2 (4)
ð2Þ
In this study, the aeration efficiency was normalized to 208C
using Eq. (3).
2.2 Adaptive Network Based Fuzzy Inference System
(ANFIS)
The architecture and learning rule of ANFIS have been described in
detail in [18]. ANFIS is a Multilayer feed forward network where
each node performs a particular function on incoming signals. Both
square and circle node symbols are used to represents different
properties of adaptive learning. To perform desired input-output
characteristics, adaptive learning parameters are updated based on
gradient learning rules [18 – 20]. The ANFIS architecture has six
inputs and one output. This architecture is formed by using five
layer and 64 if-then rules, a sample rule base is described in Eq. (5):
If (x is A1, y is B1, …, zz is F1)
then (f1 = p1x +q1y+… + pp1zz + ri) (5)
Where, x, y, …, zz, are inputs and p, q, r, …, pp, u are linear output
parameters. The node functions in the same layer are similar and
described as below:
Layer-1: Every node i in this layer is a square node with a node
function.
O 1 i ¼ lAiðxÞ ð6Þ
Where, x1, x2, …, x5, x6 are inputs to node i, and Ai, Bi, Ci, …, Hi are
linguistic labels associated with this node function. O1 i is the membership
function of Ai. Usually lAi(x) is chosen as a bell-shaped function
with a maximum value equal to 1 and a mininmum value equal
to 0.
Layer-2: Every node in this layer is a circle node labeled P which
multiplies the incoming signals and sends the product out. For
instance:
wi = lAi(x)*lBi(y)*lCi(z)*lDi(xx)*lEi(yy)*lEi(yy)
i =1,2,3,…, 64 (7)
Each node output represents the firing strength of a rule.
Layer-3: Every node in this layer is a circle node labeled N. The i th
node calculates the ratio of the i th rules firing strength to the sum of
all rule's firing strengths.
wi ¼
wi
w1 þ w2:::w64
i ¼ 1; 2; 3; :::; 64 ð8Þ
Layer-4: Every node i in this layer is a square node with a node
function:
O 4 i ¼ wifi ¼ wiðpix þ qiy þ :::: þ riÞ i ¼ 1; 2; 3; :::; 64 ð9Þ
Where, wi is the output of layer 3 and {pi, qi, ri, …, ppi, ui} is the
parameter set. Parameters in this layer will be referred to as consequent
parameters.
Layer-5: The single node in this layer is a circle node labeled S that
computes the overall output of ANFIS as the summation of all
incoming signals.
X
O 5 i
¼ overall output ¼ X
i 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim www.clean-journal.com
i
wifi ¼
i
X
i
wifi
wi
ð10Þ

188 A. Baylar et al. Clean 2007, 35 (2), 186 – 192
Figure 2. Experimental arrangement for the stepped cascade model.
Figure 3. ANFIS model structure.
3 Experimental Results and Application
3.1 Experimental Arrangement
The data used in this study were taken from studies conducted by
Baylar et al. [4, 6] on a large model of a stepped cascade. Schematic
representation of the experimental setup used in these studies is
shown in Fig. 2. All experiments were conducted in a prismatic rectangular
channel with 0.30 m width and 0.50 m deepth. The side
walls were made of transparent methacrylate to follow the flow
regime. Water was pumped from the storage tank to the stilling
tank, from which it entered the stepped channel through an
approach channel.
The discharge was measured by means of a flow meter installed
in the supply line. All experimental runs were carried out in unit
discharges ranging between 16.67 and 166.67 L/s m. For the stepped
channel, the downstream channel was 3.0 m long, 0.35 m wide, and
Figure 4. Training performance of the ANFIS model.
Figure 5. Test performance of the ANFIS model.
0.45 m deep. The slopes of the stepped channel were varied: 14.488,
18.748, 22.558, 308, 408, and 508. For all slopes tested, steps with a
height, h, of 5, 10, and 15 cm were used.
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Clean 2007, 35 (2), 186 – 192 Modeling of Aeration Efficiency 189
Table 1. Data of stepped cascade for h = 0.05 m.
q
(m 2 /s610 –3 )
h
(m)
a
(deg.)
L
(m)
Tap water was used throughout the present experiments. The
water was changed for each experiment. The water in the tank was
deoxygenated by the sodium sulfite method. Theoretically, 7.9 g/m 3
of sodium sulfite is required to remove 1 g/m 3 of DO. Based on the
DO of the test tap water, the approximate sodium sulfite requirements
are estimated (a 10 – 20% excess is used). Usually, addition of
cobalt(II) chloride is required at a dosage of 3.3 g/m 3 as a catalyst for
the deoxygenation reaction. In this study, 70 g/m 3 of sodium sulfite
and 3.3 g/m 3 of cobalt(II) chloride were added. The salt content of
the tap water used for all of the experiments reported in this paper
was low and monitored constantly during the experiments to
ensure no significant buildup of residues caused by deoxygenation
of the chemicals added to the water. Therefore, it is unlikely that
N E20
(–)
Flow Regime
16.67 0.05 14.48 5.00 25 0.60 Nappe
33.33 0.05 14.48 5.00 25 0.58 Transition
50.00 0.05 14.48 5.00 25 0.55 Skimming
66.67 0.05 14.48 5.00 25 0.45 Skimming
100.00 0.05 14.48 5.00 25 0.30 Skimming
133.33 0.05 14.48 5.00 25 0.26 Skimming
166.67 0.05 14.48 5.00 25 0.23 Skimming
16.67 0.05 30.00 5.00 50 0.81 Nappe
33.33 0.05 30.00 5.00 50 0.82 Skimming
50.00 0.05 30.00 5.00 50 0.74 Skimming
66.67 0.05 30.00 5.00 50 0.70 Skimming
100.00 0.05 30.00 5.00 50 0.62 Skimming
133.33 0.05 30.00 5.00 50 0.59 Skimming
166.67 0.05 30.00 5.00 50 0.57 Skimming
16.67 0.05 18.74 3.89 25 0.60 Nappe
33.33 0.05 18.74 3.89 25 0.57 Transition
50.00 0.05 18.74 3.89 25 0.52 Skimming
66.67 0.05 18.74 3.89 25 0.44 Skimming
100.00 0.05 18.74 3.89 25 0.28 Skimming
133.33 0.05 18.74 3.89 25 0.22 Skimming
166.67 0.05 18.74 3.89 25 0.16 Skimming
16.67 0.05 40.00 3.89 50 0.74 Transition
33.33 0.05 40.00 3.89 50 0.75 Skimming
50.00 0.05 40.00 3.89 50 0.72 Skimming
66.67 0.05 40.00 3.89 50 0.70 Skimming
100.00 0.05 40.00 3.89 50 0.63 Skimming
133.33 0.05 40.00 3.89 50 0.59 Skimming
166.67 0.05 40.00 3.89 50 0.56 Skimming
16.67 0.05 22.55 3.26 25 0.68 Nappe
33.33 0.05 22.55 3.26 25 0.61 Transition
50.00 0.05 22.55 3.26 25 0.53 Skimming
66.67 0.05 22.55 3.26 25 0.42 Skimming
100.00 0.05 22.55 3.26 25 0.32 Skimming
133.33 0.05 22.55 3.26 25 0.29 Skimming
166.67 0.05 22.55 3.26 25 0.24 Skimming
16.67 0.05 50.00 3.26 50 0.79 Transition
33.33 0.05 50.00 3.26 50 0.77 Skimming
50.00 0.05 50.00 3.26 50 0.75 Skimming
66.67 0.05 50.00 3.26 50 0.74 Skimming
100.00 0.05 50.00 3.26 50 0.72 Skimming
133.33 0.05 50.00 3.26 50 0.66 Skimming
166.67 0.05 50.00 3.26 50 0.64 Skimming
the results were measurably affected by the presence of chemicals
or pollutants.
Each experiment was started by filling the storage tank with
water by adding Na2SO3 and CoCl2 for chemical deoxygenation. During
the experiments, DO measurements upstream and downstream
of the stepped cascade were taken using calibrated portable HANNA
Model HI 9142 oxygen meters at the locations identified in Fig. 2.
Measurements were made by submersing the probe to a depth of
approximately 0.20 m at the sampling points. The DO meters were
calibrated daily according to local atmospheric pressure, prior to
use, by the air calibration method. Calibration procedures followed
those recommended by the manufacturer. The calibration was performed
in humid air under ambient conditions. In this study, the
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190 A. Baylar et al. Clean 2007, 35 (2), 186 – 192
Table 2. Data of stepped cascade for h = 0.10 m.
q
(m 2 /s610 –3 )
saturation concentrations were determined by the chart of McGhee
[21].
3.2 Modeling
h
(m)
a
(deg.)
L
(m)
The experimental results for the aeration efficiency in the stepped
cascade aerators are given in Tabs. 1 – 3.
The ANFIS model used in this study is shown in Fig. 3. The parameters
considered in the study are unit discharge (q), step height (h),
channel slope (a), channel length (L), total number of steps (N), flow
regime information and aeration efficiency at 208C(E20). The parameters,
q, h, a, L, N, and the flow regime information were used as
inputs to the ANFIS model for the estimation of E20. In the seventh
column, the numbers 1, 2, and 3 used to represent the flow regimes,
nappe, transition, and skimming, respectively. 100 of 126 experimental
data sets were used to train the ANFIS model and 26 experimental
data sets were used for the validation test. The 26 test data
were randomly selected among the whole data.
Before training and testing, the training input and output values
were normalized using Eq. (11):
xi ¼ xi xmin
xmax xmin
N E20
(–)
Flow Regime
16.67 0.10 14.48 5.00 12 0.55 Nappe
33.33 0.10 14.48 5.00 12 0.54 Nappe
50.00 0.10 14.48 5.00 12 0.54 Nappe
66.67 0.10 14.48 5.00 12 0.52 Transition
100.00 0.10 14.48 5.00 12 0.44 Transition
133.33 0.10 14.48 5.00 12 0.41 Skimming
166.67 0.10 14.48 5.00 12 0.34 Skimming
16.67 0.10 30.00 5.00 25 0.80 Nappe
33.33 0.10 30.00 5.00 25 0.79 Nappe
50.00 0.10 30.00 5.00 25 0.77 Nappe
66.67 0.10 30.00 5.00 25 0.75 Transition
100.00 0.10 30.00 5.00 25 0.72 Skimming
133.33 0.10 30.00 5.00 25 0.67 Skimming
166.67 0.10 30.00 5.00 25 0.60 Skimming
16.67 0.10 18.74 3.89 12 0.58 Nappe
33.33 0.10 18.74 3.89 12 0.58 Nappe
50.00 0.10 18.74 3.89 12 0.55 Nappe
66.67 0.10 18.74 3.89 12 0.55 Transition
100.00 0.10 18.74 3.89 12 0.47 Transition
133.33 0.10 18.74 3.89 12 0.41 Skimming
166.67 0.10 18.74 3.89 12 0.37 Skimming
16.67 0.10 40.00 3.89 25 0.74 Nappe
33.33 0.10 40.00 3.89 25 0.76 Nappe
50.00 0.10 40.00 3.89 25 0.77 Transition
66.67 0.10 40.00 3.89 25 0.76 Transition
100.00 0.10 40.00 3.89 25 0.70 Skimming
133.33 0.10 40.00 3.89 25 0.66 Skimming
166.67 0.10 40.00 3.89 25 0.63 Skimming
16.67 0.10 22.55 3.26 12 0.62 Nappe
33.33 0.10 22.55 3.26 12 0.59 Nappe
50.00 0.10 22.55 3.26 12 0.57 Nappe
66.67 0.10 22.55 3.26 12 0.55 Transition
100.00 0.10 22.55 3.26 12 0.46 Skimming
133.33 0.10 22.55 3.26 12 0.39 Skimming
166.67 0.10 22.55 3.26 12 0.30 Skimming
16.67 0.10 50.00 3.26 25 0.77 Nappe
33.33 0.10 50.00 3.26 25 0.74 Transition
50.00 0.10 50.00 3.26 25 0.74 Transition
66.67 0.10 50.00 3.26 25 0.73 Transition
100.00 0.10 50.00 3.26 25 0.71 Skimming
133.33 0.10 50.00 3.26 25 0.68 Skimming
166.67 0.10 50.00 3.26 25 0.65 Skimming
ð11Þ
Where xmin and xmax denote the minimum and maximum of the
stage and discharge data. Each input has two bell-shaped membership
functions. The desired sum squared error value was selected as
0.0001. The ANFIS model performed this value at 300 epochs.
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Clean 2007, 35 (2), 186 – 192 Modeling of Aeration Efficiency 191
Table 3. Data of stepped cascade for h = 0.15 m.
q
(m 2 /s610 –3 )
h
(m)
The training performance of the ANFIS model is graphically
showed in Fig. 4. Moreover, the test performance of the ANFIS model
is graphically presented in Fig. 5. As it can be seen from Fig. 5, the
ANFIS model estimates the measured values with a high accuracy.
The regression coefficient (R 2 ) was calculated as R 2 = 0.999 for a training
performance of the ANFIS model and R 2 = 0.985 for a test performance
of the model.
4 Conclusions
a
(deg.)
L
(m)
Hydraulic structures can increase dissolved oxygen levels by creating
turbulent conditions where small air bubbles are carried into
the bulk of the flow. Stepped chute aeration is a particular instance
of this. In this study, an ANFIS model was used in estimation of the
aeration efficiency of stepped cascade aerators. There was a good
agreement between the measured aeration efficiencies and the
values computed from the ANFIS model. This is evidenced by a very
high regression coefficient, R 2 = 0.985. Therefore, ANFIS can be used
to estimate the aeration efficiency in stepped cascade aerators.
References
N E20
(–)
Flow Regime
16.67 0.15 14.48 5.00 8 0.49 Nappe
33.33 0.15 14.48 5.00 8 0.50 Nappe
50.00 0.15 14.48 5.00 8 0.48 Nappe
66.67 0.15 14.48 5.00 8 0.46 Nappe
100.00 0.15 14.48 5.00 8 0.43 Nappe
133.33 0.15 14.48 5.00 8 0.40 Transition
166.67 0.15 14.48 5.00 8 0.40 Transition
16.67 0.15 30.00 5.00 16 0.78 Nappe
33.33 0.15 30.00 5.00 16 0.76 Nappe
50.00 0.15 30.00 5.00 16 0.75 Nappe
66.67 0.15 30.00 5.00 16 0.75 Nappe
100.00 0.15 30.00 5.00 16 0.73 Nappe
133.33 0.15 30.00 5.00 16 0.72 Transition
166.67 0.15 30.00 5.00 16 0.71 Skimming
16.67 0.15 18.74 3.89 8 0.57 Nappe
33.33 0.15 18.74 3.89 8 0.58 Nappe
50.00 0.15 18.74 3.89 8 0.53 Nappe
66.67 0.15 18.74 3.89 8 0.52 Nappe
100.00 0.15 18.74 3.89 8 0.47 Nappe
133.33 0.15 18.74 3.89 8 0.43 Transition
166.67 0.15 18.74 3.89 8 0.39 Transition
16.67 0.15 40.00 3.89 16 0.76 Nappe
33.33 0.15 40.00 3.89 16 0.76 Nappe
50.00 0.15 40.00 3.89 16 0.77 Nappe
66.67 0.15 40.00 3.89 16 0.76 Nappe
100.00 0.15 40.00 3.89 16 0.71 Transition
133.33 0.15 40.00 3.89 16 0.69 Transition
166.67 0.15 40.00 3.89 16 0.68 Skimming
16.67 0.15 22.55 3.26 8 0.56 Nappe
33.33 0.15 22.55 3.26 8 0.56 Nappe
50.00 0.15 22.55 3.26 8 0.53 Nappe
66.67 0.15 22.55 3.26 8 0.52 Nappe
100.00 0.15 22.55 3.26 8 0.51 Nappe
133.33 0.15 22.55 3.26 8 0.47 Transition
166.67 0.15 22.55 3.26 8 0.41 Transition
16.67 0.15 50.00 3.26 16 0.77 Nappe
33.33 0.15 50.00 3.26 16 0.75 Nappe
50.00 0.15 50.00 3.26 16 0.74 Nappe
66.67 0.15 50.00 3.26 16 0.74 Transition
100.00 0.15 50.00 3.26 16 0.72 Transition
133.33 0.15 50.00 3.26 16 0.70 Skimming
166.67 0.15 50.00 3.26 16 0.69 Skimming
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Green Chemistry and
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