FUNDAMENTAL DEVELOPMENT AND THE DESIGN OF AN
EFFICIENT CASCADE AERATOR
A.D. Talib1, A. Yusoff2, A. Shahrir3 R. Roslina Aida4
1,4
Faculty of Mechanical Engineering,
Universiti Teknikal Malaysia Melaka
2,3
Faculty of Engineering,
National University of Malaysia
Email: talib@utem.edu.my
Abstract:Cascade aerators are normally used in water treatment for recreational lakes and fish
raring ponds and also in the post aeration of drinking water supply, which generally have
quite low efficiencies with dissolved oxygen serves as healthcare element in the human
body when consumed as drinking water. The objective of this research is to develop and
design an efficient cascade aerator for treated water based on the plunging water jet. The
development of the cascade aerator in the past since the industrial revolution is studied
and analyzed in order to identify the relationships between the properties of the cascade
aerator with the important parameters such as water potential energy, water flow-rate,
conditions of atmospheric air, diffusivity and dissolvability of air-water, saturation level
of dissolved oxygen, water temperature and water pressure. The geometrical parameters
involved are the height of plunging of water jet, angle of plunging water jet with respect
to horizontal plane, size of water jet nozzle pipe, height of cascading, depth of water in
lower tank and depth of water in upper tank. In the first stage, research is focused on
identifying the parameters that influence the performance of a cascade aerator by means
of theoretical study and by referring to the finding of the earlier research works. The
relationship equation between height of cascading H and the ratio of dissolved oxygen
deficit, R and also the other parameters consisting of temperature, T , water quality
coefficient, a, geometrical parameters coefficient, b for a 4 stage weir based cascade
aerator which had been developed by Barrett, relating height of cascading H which is
proportional to the ratio of Oxygen deficit and inversely proportional to the temperature,
is used as the basis for deriving the equations for the new design of cascade aerator
based on the plunging water jet. While the general aeration equation in term of dissolved
oxygen gradient proportional to the overall aeration coefficient value of the aerator, KLa
is used as the basis to determine the coefficient of oxygen mass transfer of the whole
cascade aerator. The following stage of research works is to determine the optimum
points of test parameters in an empirical experiment by collecting data from a single
stage, single nozzle model of cascade aerator based on the dissolved oxygen
concentration values for several nozzle pipe’s internal diameter,  of 10 mm, 14 mm,
18mm, 20 mm. While the angle of plunging jet is varied by changing the angular position
of the nozzle so as to produce angle of impact,  is tested at 30o, 45o, 60o, 75o and 90o.
The water jet plunging height, H is tested at several vertical distances of 170 mm, 280
mm, 330 mm, 400 mm, and 500 mm. The depth of water in the lower tank, dt is tested at
several depth of 145 mm, 175 mm, 200 mm, 245 mm and 280 mm. While the depth of
water in the upper tank, da is tested at several depth of 410 mm, 450 mm, 510 mm, 580
mm and 700 mm. The results of the experiment found that the optimum height of
plunging of the water jet, H is at 330 mm and the optimum angle of water jet,  and 
with respect to the horizontal plane are 50o at inception point and 56o at impact point at
the nozzle and at the lower tank water surface respectively. Optimum diameter of the
plunging jet  is 19 mm while the optimum depth of lower water tank is 190 mm and
finally the optimum depth of upper water in the upper tank is at 515 mm. The results
obtained in experimental study is then validated by using computer simulation program,
CFD (FLUENT) and test on the prototype based on the optimum parameters. The
optimum geometrical parameters obtained and validated above are used as the basis of the
new design of an efficient plunging water jet based cascade aerator for the post aeration
process of treated water supply.
Keywords: Cascade, Aerator, Dissolved Oxygen, Efficient oxygen transfer
1 Introduction
Since the last decade, water aerating system has been evolving in terms of the methods and
conventional technology, where the modifications are done to optimize the factors or parameters that
affect the efficiency of the system. Cascade aerator is usually used in the post treatment of drinking
water widely. It consisted by a series of waterfall on a concrete ladder using the potential energy of the
gravitational pull of the water at the water inlet of the system. The cascade aerating depends on the
early level of dissolved oxygen, the concentration of dissolved oxygen that is needed and the
temperature of the treated water.
More research has to be done cascade aerator to design a cascade aerator that is highly efficient to
benefit the powers of the gravity that is not only cheap, but also free and flexible. The factor that
makes the cascade aerator not so popular amongst it is the emergence of the mechanical aerator that has
a high SOTR (Standardized Oxygen Transfer Rate) and has made the technology of the cascade aerator
that is currently available not profitable to be improved in terms of incentive and innovatively (Koduri
& Barkdoll 2003). Other factors will be discussed in the following sections.
2 Research Objectives
The objective of this research is to develop a cascade aerator that will be represented by a group of
equations or general formula to design a universal cascade aerator that is efficient. This will be done in
all aspects that include theoretical research and also laboratory research and a compatibility comparison
will be done on the findings of the previous research. The optimization research is done on the first
geometry cascade fall ladder only. While the geometry of the subsequent cascade falls are repetitions
of the optimal first ladder cascade fall geometry where the efficiency has been optimized.
3 Problem Statement
Issues and problem that contribute to the extended research on the cascade aerator:
3.1 The Need to Supply Oxygen to Water to Support the Life of Water
Treating Microorganism
The adding of oxygen supply to the water mass is needed to promote the activity of microorganism
such as bacteria and algae where it changes the colloid and other undissolved carbon based organic
materials into gases and other vaporizing material and other tissues.
3.2 The use of High Power in other Aerating Systems
Other aerating system is actually not highly efficient in terms of cost if compared to the value of energy
cost that is used. A cascade aerator that is proposed in this research will ensure that maximum
efficiency in all aspects such as cost, aerating rate and space.
3.3 High Operational Cost and Maintenance Cost of other Types of
Aerating System other than Cascade Aerator
For the water that already has the potential energy like in the rivers and multi level lakes or positioned
in a higher level, the cost of this collapses into zero because the water is no longer needed to be
pumped onto a higher level. While the operational cost of a cascade aerator is only on the cost of
ensuring the aerating equipment functioning normally without any waste or floating solids from the
water that has been stuck on the cascade dam that may affect the transfer of oxygen into the water mass
compared to other aerator that needs spare parts and also high expertise for maintenance.
3.4 The Need to Generate Bubbles or Air Balls without Cavitation to the
Aerator
The increase in the space of the interphase between the air and the water will increase the rate of
oxygen transfer to the water mass (Robert & Oscar 2002). Therefore, the increase in bubbles and air
balls in the water will increase the oxygen transfer rate in the interphase region and will be one of the
main criterias that is needed to be analyzed and studied comprehensively to ensure the optimization of
the physical design on the cascade aerator.
3.5 Cavitation and Air Entrapment
The presence of air bubbles in the water flow will give an impact to the explosive cavitation ball
mechanism, diverting the water hammer jet away from the surface of the solid. As an awareness to the
dangers that is caused by the activities of cavitation, this research has to take into account the effects of
cavitation in the process of developing and designing so that the geometry of the cascade aerator that
will be designed does not allow the unexpected process of cavitation to happen.
4 METHODOLOGY
4.1 Formula and design of an efficient cascade aerator based on optimal
values
The design of a cascade aerator based on a efficient cascade water jet plunge is governed by the
optimum level that has been predefined from laboratory test and the restrictions or rules that has been
found by early researchers. The velocity of the impact or the velocity of the colliding water jet to the
surface of the receiving water tank to give out a formula of the rate of water flow into the cascade
aerator.
Figure 1: Schematic cross section of the water flow cascade.
With reference to Figure 1 and using the kinetic hydraulic fall formula, the velocity of the impact to the
lower water tank surface can be calculated .The velocity of the water jet as soon as it exits the nozzle is
Vo (Refer figure 1 di above). While the velocity of the water jet velocity during the impact onto the
surface of the receiving water is given by the equation below:
V1 sin = Vo sin + gt
Thus
V1 =
V0 sin   gt
sin 
(1)
(2)
With g (gravitational acceleration,ms-2), t ( time taken for the water jet to reach the surface of the
water, s), θ ( angle of the water jet with respect to the horizontal plane during impact, unit degrees),  (
angle of the water jet with the projection as it exits the nozzle, unit degrees).
Velocity Vo can be obtained from the equation below:
Velocity of Nozzle Exit, Vn = Cv  (2gh )
(3)
with Cv as coefficient of velocity of jet at nozzle = Cc / Cd (coefficient of contraction / coefficient of
exit ), Coefficient of contraction = d12 /d22 (inner diameter of nozzle tube / outer diameter of nozzle
tube) with the height of the cascade H and the initial jet velocity Vo , the kinetic water cascade
equation is,
H = Vo sin t + ½ gt2
(4)
On the optimal jet cascade, as soon as it exits the nozzle is  , and H know thus the time taken t taken
to reach the surface os the lower surface of the water tank is the solver to the quadratic equation above.
Knowing the value of Vo , a rate of the water flow through the nozzle can be determined using one
given by the water flow equation as below:
Qn = V o x A n
(5)
With An ( the size of the inner diameter of the cascade nozzle) and Qn = the rate of water in a nozzle
jet cascade.
Thus the rate of water flow for a nozzle is given by the equation below:
Qn = Vo x  do2
4
(6)
While the rate of water flow intake for the whole aerator dam is given by the equation as shown:
Qov = N x Vo x  do2
4
(7)
with, Qov ( Rate of water flow for the whole cascade aerator) and N ( The no. of nozzle on the
circumfrence of the first cascade tank).
5 RESULTS AND DISCUSSION
Based on empirical data through experimentation, a simplified result obtained were value for depth of
lower water tank, 190.75 mm , inner diameter of the cascade jet nozzle, 18.62 mm, height of cascade ,
327.5 mm, angle of water cascade (Incident angle of water surface), 55.5, depth of upper water tank ,
515 mm.
The optimal values above are again verified with a computational simulation study to ensure that the
validaty of the empirical results compared to the theoretical values. When it has been verified both
research, the optimal levels above can be made as a baseline to designa cascade aerator based on an
efficient cascade water jet.
5.1 Computer simulation results for optimal parameter values that is
obtained from the graphical verification from the optimization curve
The optimal value that was obtained from the curve that is the depth of the reservoir water tank is
190mm, Inner diameter of the cascade jet nozzle 19mm, height of the cascade 330mm, water cascade
angle 50 ° and depth of the upper water tank 515mm, is tested again by using simulation. The results
that were obtained are as figure below:
Figure 2 : Graphical Computer Simulation of the Water Jet Cascade on The
Depth of the Water Tank Below optimum levels which is at 190mm
Figure 3 : Graphical Computer Simulation of the Water Jet Cascade on the Inner
Diameter Optimal Cascade Jet which is at 19 mm
Figure 4 : Graphical Computer Simulation of the Water Jet Cascade at the
Optimal Height of Water Jet Cascade which is at 330 mm
Figure 5 : Graphical Computer Simulation of a Cascade Water Jet at the Optimal
Cascade Water Jet Angle of 50°
Figure 6 : Graphical Computer Simulation of the Water Jet Cascade at the
Optimal Water Tank Depth which is at 515mm
5.2 Optimal cascade aerator design based on the cascade water jet
Figure 7 : Schematic of a Single Ladder Cascade Aerator
Figure 7 above is drawn based on the optimization results of multiple design paratemers. The velocity
of the water exiting the optimum nozzle which is at an inner diameter of 19mm is 2.063 m/s. Other
geometrical dimensions of the tank such as the depthm the angle of the cascade and the height of the
tanks will be the baseline for the new deisgn of the cascade aerator based on the water jet cascade. One
of the features of this new finding that proves to be very useful is that the difference between a typical
cascade aerator with this new cascade aerator is the induction plate positioned at dt. This induction
plate will act as an inducer to the creation of air bubbles. Although this feature looks simple but has
never been designed before in terms of the compressed to achieve the goal of optimizing space.context
of a cascade aerator.
6 CONCLUSION
From the results and the discussions that were done on the Empirical Research, Computer Simulation
Research and Validity Test on the Prototype, a few conclusions that be made as follows:
6.1 Optimal Geometrical Parameter Values for the Cascade Aerator based
on the Water Jet Plunge
There are optimal values that have been obtained from the laboratory tests. These optimum values are
either value that can generate the maximum dissolved oxygen content or is the optimization between
the levels of dissolved oxygen with the space efficiency that balances the need for the dissolved
oxygen. The level of optimization is told as below:
(a) Depth of the Lower Tank Water, d
(b) Nozzle Pipe Internal Diameter, 
(c) Height of the Cascading Jet, H
(d) Angle of the Water Jet, 
dan 
(e) Depth of the Upper Tank Water, da
=
=
=
=
=
190 mm
19.0mm
330 mm
56o dan 50o
515 mm
6.2 Formula for the Design of the Cascade Aerator based on Water Jet
Cascade
6.2.1 Design Equation for the Height of the Cascade, H
The design formulafor determining the height of the cascade water jet is given by the equation below:
H = 0.0082 ( R – 1 ) + 0.06 ( in unit m)
(8)
Where by, R = (Cs – Co) / (Cs – C) . The rules for the equation above can be used for the test range
from 170mm  H  550mm.
6.2.2 Equation for the Design of the Depth of the Upper Water Tank, da
The design formula for determining the depth of the Upper Water Tank is given by the equation
below:
da = 0.004R +0.356
( in unit m)
(9)
Where by,
R = (Cs – Co) / (Cs – C) . The rules for the equation above can be used for the test range
from 410mm  da  700mm.
6.3 The Value of KLa Cascade Aeration Tool Based on the Cascade Water
Jet and the Correction Factor
From the coefficient of oxygen mass transfer KLa below, the specific values for the geometrical
cascade aeration parameters can be calculated.
KL a =
ln C s  C1   ln C s  C2 
t 2  t1
(10)
Correction KLa for the geometrical Cascade Height and the Depth of the Upper Water Tank is not
accounted for because there is an optimal inner point in the values of the dissolved oxygen in the height
of the cascade parameters and the depth of the upper water tank. The optimization is instead done
taking into account of the efficiency of space.
From the KLa value above, thus the values of OTR, the cascade aerator is calculated as below:
OTRf = SOTR
 KLa*
(11)
Where by, SOTR is the Standard Oxygen Transfer Rate aeration to the zero value of the dissolved
oxygen
*- KLa is the coefficient of the overall oxygen mass transfer that needs to be
corrected
References
[1] Koduri, S. & Barkdoll B.D., 2003. Evaluation of Oxygen Transfer at Stepped
Cascade Aerator. Conference Proceeding at World Water and Environmental
Resources Congress, ASCE. Philadelphia, Pennysyvania, USA. Jilid 118. pg
257.
[2] Robert D.Z. & Oscar B., 2002, Fundamental of Gas Dynamics. Ed. Ke2.
California U.S.A. John Willey & Sons Inc.
[3] ASCE 1992. Measurement of Oxygen Transfer in Clean water ANSI/ASCE
2- 91. New York: American Society of Civil Engineers.
[4] Bagatur, T & Sekerdag, N. 2003. Air Entrainment Charcteristics In a
Plunging Water Jet System Using Rectangular Nozzles with Rounded Ends.
African Journal Online , Water SA 28. Vol 29 (1), 35 – 38.
[5] Bagatur, T et al, 2002. The Effect of Nozzle Typeon Air Entrainment by
Plunging Water Jets. Water Quality Research Journal of Canada, 37(3): 599612.
[6] Benson, B.B. & Krause, D. 1984. The Concentration and Isotropic
Fractionation of Oxygen Dissolved in Fresh water and Seawater in
Equilibrium with Atmosphere. Journal of Limnol Oceanogr. 29 : 620-632
[7] Bin, A.K. 1993. Gas Entrainment by Plunging Liquid Jets. Journal of
Chemical Engineering Science, .48 (21): 3585-3630
[8] Boyd, C.E. & Watten, B.J. 1989. Aeration System in Aquaculture. Journal of
Applied Aquaculture 1 : 425 – 472
[9] Brackbill, J.U. et al 1992. Continum Method for Modeling Surface Tension.
Journal of Computer Physics., 100 : 335-354
[10] Chanson, H. 1996. Air Bubble Entrainment in Free-Surface Turbulent Shear
Flow. Elsevier, Queensland, Australia. ACADEMIC PRESS. ISBN – 13:
978-0-12-168110-4.
[11] Chanson, H. 2004. Hydraulics of Rectangular Dropshafts. Journal of
Irrigation and Drainage Engineering.ASCE 130 (6): 523-529.
[12] Chanson, H. & Toombes, L. 2002. Energy Dissipation and Air Entrainment
in Stepped Storm Waterway: Experimental Study. Journal Of Irrigation
and Drainage Engineering, ASCE. 128(5) : 305-315.
[13] Cummings, P.D. & Chanson, H. 1997. Air Entrainment in The Development
Flow Region of Plunging Jet – Part 2: Experimental ( Data Bank
Contribution).Journal of Fluids Engineering, Transaction of ASME.
119:603-608.
[14] Cummings, P.D. & Chanson, H. 1999. Experimental Study of Individual
Air Bubble Entrainment at a planar plunging jet. Journal of Institute of
Chemical Engineers, Trans IChemE, 77(A): 159-164
[15] Emiroglu, M.E. & Baylar, A. 2005. Influence of Included Angle and Sill
Slope on Air Entrainment of Triangular Planform Labyrinth Weirs. Journal
of Hdraulic Engineering, ASCE. 131(3): 184-189
[16] Ferziger, J.H., 1999. Computational Methods for Fluid Dynamics. 2nd Ed. ,
Springer, USA.
[17] Knut, A. & Parviz, M. 1996. Large-Eddy Simulation of Turbulence
Confined Coannular Jets. Journal of Fluid Mechanics Digital Archive, 315,
387-411.
[18] Metcalf & Eddy 2004, George, T. Franklin, L. B. & David, H.S., (pnyt.).
Wastewater Engineering; Treatment and Reuse. Ed. Ke-4. Semak.Singapore
:Metcalf & Eddy, INC., McGraw-Hill International Edition 2004, Civil
Engineering Series.