Evaluation of a low profile cascade aerator

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Evaluation of a low profile cascade aerator Evaluation of a low profile cascade aerator

Chukwukelue Kenneth Monwuba

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EVALUATION OF A LOW PROFILE CASCADE AERATOR

By


A Thesis Submitted to the Faculty of Mississippi State University

in Partial Fulfillment of the Requirements for the Degree of Master of Science

in Civil Engineering in the Department of Civil and Environmental Engineering

Mississippi State, Mississippi

December, 2007

Copyright by


2007

EVALUATION OF A LOW PROFILE CASCADE AERATOR

By


Approved:

_________________________________ _________________________________ Dennis D. Truax James L. Martin Head and Professor of Civil and Professor and Graduate Coordinator Environmental Engineering of the Department of Civil and (Director of Thesis) Environmental Engineering (Committee Member) _________________________________ _________________________________ Benjamin S. Magbanua, Jr. . Roger L. King, Associate Professor of Civil and Associate Dean of Bagley College Environmental Engineering of Engineering (Committee Member)

Name: Chukwukelue Kenneth Monwuba Date of Degree: December 14 2007 Institution: Mississippi State University Major Field: Civil Engineering Major Professor: Dr. Dennis D. Truax Title of Study: EVALUATION OF A LOW PROFILE CASCADE AERATOR Pages in Study: 98 Candidate for Degree of Master of Science

The aeration potential of a low profile cascade aerator was studied under varying

operational conditions in accordance with the ASCE Standard for Measurement of

Oxygen Transfer in Clean Water [ASCE 2-06, 2007]. Operational parameters delved into

included the channel slope (2.50, 4.50 and 6.50); water flow rate (465.75 L/min.m (37.5

gpm/ft), 931.45 L/min.m (75 gpm/ft) and 1397.20 L/min.m (112.5 gpm/ft)); and weir

geometry (rectangular-shaped, inverted T-shaped, W-shaped and inverted Cross shaped

weir). The oxygen transfer coefficient, KLa, was derived by use of a FORTRAN-based

nonlinear regression analysis computer program and served to assess the effectiveness of

various combinations of operational parameters. Statistical tests (ANOVA analysis and

main plot, interactive plot) were performed on the results to determine the optimal

operating conditions. It was discovered that the combination of the inverted Cross shaped

weir and flow rates of 1397.20 L/min.m (112.5 gpm/ft) produced the highest reaeration

rates for all slope considered. On the other hand, the W-shaped weir produced better

reaeration values at lower flows of 465.75 L/min.m (37.5 gpm/ft) and 931.45 L/min.m

(75 gpm/ft) for the range of channel slopes examined.

These effects can be respectively attributed to the strong turbulent mixing

generated by the plunging nappe flow and recirculating air vortices, which apparently led

to substantial air entrainment in the water mass.

ii

DEDICATION

This project write up is whole-heartedly dedicated to the Almighty God, to my

parents, Mr. & Mrs. Monwuba for their moral, spiritual and financial support in the long

road leading to this day and also my brother, Nnamdi and sisters, Ada and Uche for being

there all the time through phone calls and emails despite the distance from home.

iii

ACKNOWLEDGMENTS

I would like to express my heart-felt gratitude to a number of people, who

contributed to the successful completion of this thesis.

Firstly, I am immensely grateful to Dr. Dennis D. Truax, my thesis director,

advisor and friend, for his priceless contributions, experience, directives that enabled me

to successfully carry out this project. My gratitude also goes to Mr. Joe Ivy, Ayan, Chris

and A.J for their technical support and encouraging words.

Furthermore, a warm thank you goes to Tom and Linda for providing the

experimental aerator model used for this research. I also owe my sincere appreciation to

my professors, family, friends and colleagues for various forms of assistance while

undertaking this degree.

Finally, to the BIG man behind all these, my unquantifiable gratitude goes to the

Almighty God, my reason for existence and without whose assistance nothing is possible.

iv

TABLE OF CONTENTS

Page

DEDICATION ............................................................................................................. ii

ACKNOWLEDGMENTS ........................................................................................... iii

LIST OF TABLES ....................................................................................................... vi

LIST OF FIGURES ..................................................................................................... vii

CHAPTER

I. INTRODUCTION ........................................................................................... 1

Brief History on Cascade Aerators ...................................................... 2 Focus of Research ................................................................................ 4

II. BACKGROUND ............................................................................................. 5

Review of Earlier Researches .............................................................. 5 Oxygen Transfer Process “Two-Film” Theory of Gas Absorption ..... 8 Flow Regimes in Cascade Aerators ..................................................... 13 Mechanisms of Entrainment of Air Bubbles in Cascade Aerators ...... 15 Air Entrainment in Nappe Flow Regime ............................................. 16 Air Entrainment in Skimming Flow Regime ....................................... 17 Aeration Equipment Performance ........................................................ 18 Measurement of Oxygen Transfer in Clean Water ............................. 19

III. METHODOLOGY .......................................................................................... 22

Objective of Study ............................................................................... 22 Description of Low Profile Cascade Aerator Model ........................... 22 Design Geometry for Weirs ................................................................. 25 Three Slope Variation .......................................................................... 27 Flow Rates Calibration ........................................................................ 27 Application of Sodium Sulphite and Cobalt Chloride ......................... 29 Water Quality ....................................................................................... 31 Dissolved Oxygen (DO) Measurements .............................................. 32 Test Procedure ..................................................................................... 34 KLa Estimation: Nonlinear Regression Method ................................... 34

v

IV. RESULTS AND DISCUSSION ...................................................................... 38

General Observations ........................................................................... 38 Channel Slope 2.50 ............................................................................... 39 Channel Slope 4.50 ............................................................................... 43 Channel Slope 6.50 ............................................................................... 44

Interaction between Channel Slope, Flow Rates, Weir Geometry and Oxygen Transfer Coefficient………. ...................................... 46

V. CONCLUSIONS AND RECOMMENDATIONS .......................................... 55

REFERENCES ............................................................................................................ 61

APPENDIX A DO PROFILE GRAPH ................................................................................... 63

B NON-LINEAR REGRESSION PARAMETER ESTIMATES ...................... 82

C MINITAB® OUTPUT .................................................................................... 89

vi

LIST OF TABLES TABLE Page 4.1 KLa Non-Linear Regression Estimates for Channel Slope 2.50 .................... 39 4.2 KLa Non-Linear Regression Estimates for Channel Slope 4.50 .................... 43 4.3 KLa Non-Linear Regression Estimates for Channel Slope 6.50 .................... 44 4.4 One-Way ANOVA ........................................................................................ 49 4.5 Two-Way ANOVA ....................................................................................... 51 4.6 Two-Way ANOVA for Weir Geometry ........................................................ 52

4.7 Balance (Three-Way) ANOVA ..................................................................... 53 B.1 Results for Evaluation of Channel Slope 2.50 ............................................... 83 B.2 Results for Evaluation of Channel Slope 2.50 ............................................... 85 B.3 Results for Evaluation of Channel Slope 2.50 ............................................... 87

vii

LIST OF FIGURES FIGURE Page 2.1 Elemental Control Volume ............................................................................ 8

2.2 Lewis and Witman’s “Two-Film Theory” .................................................... 10 2.3 Nappe Flow Regime with Fully-Developed Hydraulic Jump ....................... 14 2.4 Skimming Flow Regime with Stable Cavity Recirculation .......................... 15

2.5 Flow Aeration in Nappe Flow Regime with Fully-Developed Hydraulic jump… ..................................................................................... 16 2.6 Flow Aeration in Skimming Flow Regime ................................................... 18 3.1 Schematic Diagram of a Low Profile Cascade Aerator Model ..................... 23 3.2 Front View of Model Aerator with DO Probe (Channel Slope 4.50) ............ 24

3.3 Side View of Model Aerator with DO Probe ................................................ 25 3.4 Rectangular-shaped Weir .............................................................................. 26 3.5 Inverted T-shaped Weir ................................................................................. 26

3.6 W-shaped Weir .............................................................................................. 26 3.7 Inverted Cross shaped Weir ........................................................................... 26 3.8 Equally Spaced Velocity Measurements ....................................................... 28 3.9 Nessler Tube Test to Determine Level of Complete Mixing ........................ 31

viii

4.1 Schematic Front View of Flow over Cross Weir .......................................... 40 4.2 Schematic Front View of Flow over W Weir ................................................ 41 4.3 Schematic Front View of Single Layer Flow over Cross weir ...................... 41 4.4 Main Effect Plot (data means) for KLa .......................................................... 47 4.5 Interaction Plot (data means) for KLa ............................................................ 48 A.1 DO Profile: Rec. Weir, Flow 37.5 gpm/ft, Slope 2.5 deg. ............................ 64 A.2 DO Profile: T. Weir, Flow 37.5 gpm/ft, Slope 2.5 deg. ................................ 64

A.3 DO Profile: W. Weir, Flow 37.5 gpm/ft, Slope 2.5 deg. ............................... 65

A.4 DO Profile: Crs. Weir, Flow 37.5 gpm/ft, Slope 2.5 deg. ............................. 65

A.5 DO Profile: Rec. Weir, Flow 75 gpm/ft, Slope 2.5 deg. ............................... 66

A.6 DO Profile: T. Weir, Flow 75 gpm/ft, Slope 2.5 deg. ................................... 66

A.7 DO Profile: W. Weir, Flow 75 gpm/ft, Slope 2.5 deg. .................................. 67

A.8 DO Profile: Crs. Weir, Flow 75 gpm/ft, Slope 2.5 deg. ................................ 67

A.9 DO Profile: Rec. Weir, Flow 112.5 gpm/ft, Slope 2.5 deg. .......................... 68

A.10 DO Profile: T. Weir, Flow 112.5 gpm/ft, Slope 2.5 deg. .............................. 68

A.11 DO Profile: W. Weir, Flow 112.5 gpm/ft, Slope 2.5 deg. ............................. 69

A.12 DO Profile: Crs. Weir, Flow 112.5 gpm/ft, Slope 2.5 deg. ........................... 69

A.13 DO Profile: Rec. Weir, Flow 37.5 gpm/ft, Slope 4.5 deg. ............................ 70

A.14 DO Profile: T. Weir, Flow 37.5 gpm/ft, Slope 4.5 deg. ................................ 70





ix







A.25 DO Profile: Rec. Weir, Flow 37.5 gpm/ft, Slope 6.5 deg. ............................ 76

A.26 DO Profile: T. Weir, Flow 37.5 gpm/ft, Slope 6.5 deg. ................................ 76











C.1 Summary of KLa values for Slope 2.50. ......................................................... 96

C.2 Summary of KLa values for Slope 4.50. ......................................................... 97 C.3 Summary of KLa values for Slope 6.50. ......................................................... 98

1

CHAPTER I

INTRODUCTION

Water, water everywhere, not a drop to drink………… Samuel Coleridge.

Water quality and its enhancement are closely linked with the presence of

dissolved oxygen (DO) concentrations; basically serving as a prime indicator of water

quality both for human use and aquatic biota life. Typically low DO contents prevent the

development of aquatic life forms and also might indicate the presences of some form of

pollution associated with excessive wastewater inflows. In general the physical process

by which oxygen is transferred or absorbed from the atmosphere to serve as

replenishment for used up oxygen in water is termed rearation. It involves bringing into

contact the water or the wastewater with oxygen in air and thus dissolving the oxygen in

the water phase.

The most common use of aeration is in the biological treatment of wastewater, to

provide oxygen to aerobic microorganisms; due to the low solubility of oxygen additional

devices are applied to aid the natural aeration process. These aeration devices can be

broadly classified into two groups, diffused and mechanical surface systems, and these

are selected by treatment plants based on function to be performed, type and geometry of

the reactor and cost to install and operate the systems.

2

On the other hand, aeration is not limited to only to biological treatment of

wastewater treatment plants. With the ever increasing stringent requirements being

imposed by National Pollution Discharge Elimination Systems permits for certain

effluent standard and high dissolved oxygen levels, the need for postaeration was

developed. Final effluents from certain wastewater treatment plants need to be reaerated

to significant levels (6-8 mg/l) before being discharged to water-quality-limited stream

sections and to effluent dominated waters (Metcalf and Eddy, 2003). The regulatory

intent is to make sure that low dissolved oxygen levels in the treated wastewater do not

cause any form of depression in oxygen levels in waters of receiving streams.

Cascade aerators are one of the methods currently being used to achieve this

requirement. This is being propagated because of low installation, operational and

maintenance cost, especially if water flow is under gravity. Basically, the cascade

aerators increase dissolved oxygen levels by creating some form of turbulent conditions

where small air bubbles can be transferred into the bulk flow of water.

Brief History on Cascade Aerators

Cascade hydraulic structures or stepped wastewater ways were commonly used to

assist with energy dissipation of flow during the 19th and early 20th century (Chanson,

1995). The world’s oldest stepped spillways are presumably those of the Khosr River

dams (or Ajilah dams), in Iraq (Smith, 1971; Schnitter, 1994). Later the Romans,

Moslem and Spanish civil engineers also incorporated the stepped flow into their dams,

mainly to control flow of water (Chanson, 1994). These technology later spread to the

French and British engineers by the middle of the 17th century, in designing their dam,

3

which helped dissipate energy and prevent scouring. It is worth mentioning some

relatively ancient timber and crib dams with stepped overflows; the North-East part of

America benefited from the experience of Northern European settlers and timber dams

were reported as early as A.D 1600 (Chanson, 1994).

It is only in the 21st century that stepped water overflows became more

pronounced as a means of reaerating oxygen-depleted water. In rivers artificial stepped

cascade and weirs have been introduced to enhance the dissolved oxygen of depleted

streams (Avery and Novak, 1978; Nakasone, 1987). A typical example is the Chatuge

weir built by the Tennessee Valley Authority, a cascade built downstream of the dam.

The series of five aeration step cascade built along the Calumet waterway in Chicago is

another example, assisting to re-oxygenate the polluted canal and also serve as landscape

for leisure parks, combining flow aeration and aesthetics.

Presently cascade aerators serve a wide range of uses, which includes

denitrification or removal of volatile organic compounds (VOCs), removal of chlorine in

treatment of drinking water, elimination or reduction of offensive taste and odour.

Generally stepped cascade aerators are known to be very efficient means of aeration

because of the strong turbulent mixing, the large residence time and the substantial air

bubble entrainment (Toombes and Chanson, 2000).

4

Focus of Research

This research is aimed at evaluating the various parameters that affect the

reaeration process of clean water using a low profile cascade aerator. Investigations will

be undertaken as to the efficiency of this aerator under varying combinations of

operational conditions; these conditions are flow rates from 465.75 L/min.m (37.5

gpm/ft) to 1397.20 L/min.m (112.5 gpm/ft); channel slopes from 2.50 to 6.50 and four

different weir geometries. Evaluations will be done in accordance with procedures

detailed in the ASCE Standards of Measurements of Oxygen Transfer in Clean Water,

(ASCE 2-06, 2007). This standard presents a general methodology for the unsteady-state

evaluation of both diffused-air and mechanical aeration systems.

This low profile cascade aeration system is being selected for investigation

because of high efficiency in entrainment of air bubbles by the simplistic use of natural

gravitational forces through controlled application of velocity, pressure differentials,

weirs, weir spacing, height, and controlled head over weirs, during the aeration process.

An optimal combination of flow, weir design and channel slope will be proposed at the

end of this study. Statistical test (ANOVA) will also be undertaken to determine which

parameters greatly influence aeration rates.

5

CHAPTER II

BACKGROUND

Aeration is simply the introduction of oxygen into a bulk liquid, this process may

occur through natural means, such surface diffusion or be propagated by use of

equipments such as (1) diffusers in a pipe or channel (2) cascading water and (3) surface

turbines or wheels that mix water at the top of basins. Regardless of the mechanism being

employed, the fundamental concepts of the aeration process remain the same. This

chapter will focus on such underlying principles involving oxygen transfer and

measurements.

Review of Earlier Researches

Little material could be found on researches which delved into matters pertaining

to the use of the low profile cascade aerator for postaeration of effluent water. Most of

the researches focused more on the conventional cascade aerator, which though different

from model being investigated, basically operates using the same underlying principle of

turbulent mixing of water while flowing under gravity.

Studies undertaken by Baylar and Emiroglu (2007) for flat and stepped cascade

aerators indicated that water can trap a lot of air when passing through steps, and then

increase oxygen content in the water body, and this advantage becomes more pronounced

in the nappe flow regime. Results further indicated that aeration efficiencies are strongly

6

affected by the type of flow regime, which in turn is a function of the step height, channel

slope and flow rate. Moreover it was demonstrated that aeration efficiency of stepped

aerators increased with increasing channel slope.

Likewise, Chanson (1994) performed a comparative analysis on the variability of

slope on aeration of water and came to the conclusion that aeration increases with

increasing channel slope between 150 and 450 and that an optimum aeration rate is

achieved at slope angles of between 450 and 600 . Any further increase in channel slope

will increase the mean velocity there by reducing the residence time needed for air

entrainment, hence reducing aeration efficiency.

Furthermore, Chanson and Toombes (1997) conducted gas-liquid interface

measurements in a stepped cascade aerator and came to the conclusion that stepped

cascade flows are highly aerated and they are characterized by substantial air-water gas

transfer potential. However these researchers stated that additional information is still

needed to predict more accurately the rate of energy dissipation, the rate of air-water gas

transfer and the re-oxygenation characteristics of stepped cascades.

In research conducted by Nakasone (1987) to show the correlation between

discharge and aeration efficiency, it was concluded that aeration efficiency increases with

increased discharge but eventually begins to decrease. The optimal point for aeration was

found to be at a q of about 235 m3/m.h (2529.5 ft3/ft.h) (where q = discharge per meter

(foot) width of weir). The researcher also confirmed that weir geometry affects aeration

efficiency, by splitting a nappe into separate narrow nappes proved to be more effective,

typically nappe width should be less than 1m (3.3 ft).

7

Further credence has also being lent to the reaerating potential of cascades plants

through experiments done by Aral and Gonullu, (1994). They have shown through a

cascade pilot plant aeration system established in the Fezzan Area of Turkey, a site

having hot climate for all seasons yielded an appreciable reaeration performance with

dissolved oxygen concentration nearing saturation values both for winter and summer

seasons, 6.4 mg/L and 5.6 mg/L respectively.

Pincince (1999) in his research on the “Effects of Multiple Compartments on

Oxygen Transfer in Postaeration Tanks” proposed the use of tanks with a high-length to

width ratio for postaeration, due to optimum efficiency obtained during aeration. Multiple

reareation tanks in series require a lower Standard Oxygen Transfer Rate (SOTR) than a

single reaeration tank. For compartmented tanks, the optimum geometry is obtained when

the SOTR for each tank is equal.

Though not typically in line of reaeration goals; research done by Boyden, et al

(1992), demonstrated that inclined cascade aeration was effective in removing 10

chlorinated volatile organic chemicals (VOCs) from drinking water at liquid loadings of 5

gpm/ft to 15 gpm/ft. Cascade angle of 600 was found most efficacious for compounds

with Henry’s law constant Hp values > 300 atm; compounds with Hp values < 300 atm

were most effectively stripped at yet steeper angles.

From the literature mentioned above, it was be observed that water mass

gravitating over weir or steps has some potential of aerating water due to the turbulence

mixing generated in this process which is also based on the operational conditions of the

particular type of cascade aerator used. As earlier mentioned the low profile aerator being

8

investigated in this study similarly functions through the basic underlining principle of a

traditional cascade aerator however in this case it uses an optimal sloping water-way

fitted with weirs, to achieve its rearation, hence it may not be far-fetched to purport that

the low profile cascade aerator also has the capabilities of aerating, which is the objective

of this paper.

Oxygen Transfer Process: “Two-Film” Theory of Gas Absorption.

Aeration can be described as a mass transfer process, whereby a gaseous

component is absorbed into a liquid phase. This transfer process can be portrayed in the

light of the advection-diffusion equation, which considers transportation by moving water

as well as dispersion through turbulence and molecular diffusion, and biological,

physical, and chemical reaction and interaction of the constituent within the elemental

volume (Kiely, 1997). However the aeration in “clean” water, it is assumed that no

biological, physical, or chemical reactions occur to alter the quantity of oxygen

transferred. Also at the elemental level, mass transfer due to advection and turbulent

diffusion is considered negligible.

Figure 2.1 Elemental Control Volume

9

The transfer of soluble gases into liquid is typically attributed to molecular

diffusion (Metcalf and Eddy, 2003) and as shown in the figure 2.1, applying the mass-

balance approach to the elemental control volume, the transfer of mass to a system can be

modeled as:

xCDr M δδ*−= (2.1)

where:

r = Rate of mass transfer per unit area per unit time, ML-2T-1

DM = Coefficient of molecular diffusion in the x direction, L2T-1

C = Concentration of constituents being transferred, ML-3

x = distance, L

This fundamental theory was first proposed by Lewis and Whitman in 1924

(Metcalf and Eddy, 2003). Based on the assumption that two films exist at the gas-liquid

interface, the rate of absorption of a gas into a liquid is related to the diffusivity across the

film established on each side of the gas-liquid interface. Gas transfer across the film is

proportional to the difference in partial pressure of the gas on either side of the gas film

and vice versa, see figure 2.2. It should also be noted that under steady state conditions,

the rate of mass transfer of gas through the gas film must be equal to the rate transfer

through the liquid film (Metcalf and Eddy, 2003).

10

Figure 2.2 Lewis and Whitman’s “Two-Film Theory”

When Fick’s first law of molecular diffusion is applied to this interface, this

equation is derived:

r = kG(PG – PI) = kL(CI - CL) (2.2)

where:

r = rate of mass transferred per unit area per unit time, ML-2T-1

kG = gas film mass transfer coefficient, T-1

PG = partial pressure of constituent in bulk gas phase, ML-2

PI = partial pressure of constituent at the interface in equilibrium with CI, ML-2

kL = liquid film mass transfer coefficient, L/T

CI = concentration of constituent at the interface in equilibrium with PI, ML-3

CL = concentration of constituent in the bulk liquid phase, ML-3

11

The driving force resulting in transfer in the gas and the liquid phase is the

concentration gradient that exist across the interface; (PG – PI) in gas and (CI-CL) in the

liquid, with coefficients kG and kL respectively. Due to difficulties in quantifying these

coefficients, it is generally appropriate to use the overall coefficients KG and KL,

depending on which films controls the mass transfer process (Metcalf and Eddy, 2003).

Furthermore, if it is assumed that the liquid film controls the mass transfer, based

on Henry’s Law equation 2.3 and 2.4.

PG = HCS (2.3)

PI = HCI (2.4)

where, H is the Henry’s Law constant for the constituent.

This Law states that the weight of any gas that will dissolve in a given volume of

liquid at a constant temperature is directly proportional to the pressure exerted by the gas.

Hence in absorption of a low solubility gas like oxygen in water, since the rate of

diffusion across the liquid film is much lower than that across the gas film, the bulk gas

phase is typically more saturated in comparison with the bulk liquid phase. Therefore it

will be appropriate to define that rate of mass transfer in terms of the overall liquid mass

transfer coefficient, thus:

r = KL(CS – CL) = kG(PG – PI) = kL(CI – CL) (2.5)

where, KL is the overall liquid mass transfer coefficient and CS is the concentration of

constituent at the interface in equilibrium with the partial pressure in the bulk gas phase.

12

Thus combining equations 2.3, 2.4 and 2.5 and assuming diffusion through the

liquid film controls the process, the overall driving force for the mass transfer can be

written as:

(CS – CL) = (CS – CI) + (CI – CL) (2.6)

Further substitution in equation 2.6 (Metcalf and Eddy, 2003) shows that a

relationship between overall liquid and gas phase transfer coefficient can be established

as thus:

CS-CL = r/KL (2.7)

= (CS-CI) + (CI-CL) (2.8)

= (PG-PI)/H + (CI-CL) (2.9)

= r/kGH + r/kL (2.10)

1/KL = 1/kGH + 1/kL (2.11)

When H is high, 1/KL >> 1/KGH and KL ~ kL

1/KL = 1/HKG (2.12)

where: KG = Overall gas mass transfer coefficient and r = KG(PG-PI)

Now in order to estimate the rate of diffusion of a gas into a liquid phase at a

particular time and when considering a unit volume, the rate of transfer r can be defined

as:

rv = KL A/V (CS-Ct) = KLa(CS-Ct) (2.13)

where:

rv = rate of mass transfer per unit volume per unit time, ML-3T-1

KL = volumetric mass transfer coefficient, L-3T-1

13

A = area through which mass is transferred in liquid phase, L2

V = volume in which mass is transferred in liquid phase, L3

a = interfacial area for mass transfer per unit volume (A/V), L-1

CS = concentration in equilibrium with gas as given by Henry’s law =PG/H, ML-3

Ct = concentration in bulk liquid, ML-3

Thus for absorption of gases the change in concentration can be defined in terms

of equation 2.14:

dC/dt = KLa(CS-Ct) (2.14)

Flow Regimes in Cascade Aerators

Air entrainment in cascade flow is greatly influenced by the type of regimes

present in the flow. Basically stepped flows can be classified into two distinct flows

regimes: nappe and skimming flow regimes. A third regime, transition phase is generally

not emphasized.

At low flow rates as water bounces from one step to the next one as a succession

of free-falling nappes; this is called a nappe regime. figure 2.3. In most cases such flows

are characterized by a hydraulic jump as the flow from each step hits the step below.

Generally speaking these flows are found in low discharge or wide steps.

14

Figure 2.3 Nappe Flow Regime with Fully-Developed Hydraulic Jump

On the other hand for narrow steps, steeper slopes or larger discharges, skimming

flows dominate, the water flows down the cascade as a coherent stream, the streamlines

being parallel to the pseudo-bottom formed by the step edges, figure 2.4. Beneath the

pseudo-bottom, recirculating vortices develop filling the zone between the main flow and

steps (Chanson, 1994). The recirculation is maintained through the transmission of shear

stress from the water flowing past the edge of the steps.

15

Figure 2.4 Skimming Flow Regime with Stable Cavity Recirculation

For a range of intermediate discharges, a transition flow regime occurs, easily

identified by stagnation on the horizontal face step, significant splashing and a chaotic

appearance (Baylar and Emiroglu, 2007).

Mechanisms of Entrainment of Air Bubbles in Cascade Aerators

Typically, air entrainment in stepped chute flows are due to turbulent velocities

acting next to the air-water interface, flows are characterized by their strong turbulent

mixing, large residence time and substantial air bubble entrainment. Through this

interface, air is continuously trapped and released and entrainment occurs when both

surface tension and gravity effects can be overcome by the turbulent kinetic energy, that

16

is, this turbulent velocity must be able to subdue bubble rise velocity component and also

surface tension (Chanson, 1994).

Air Entrainment in Nappe Flow Regime

In a nappe flow regime air is entrained by two basic mechanisms. Firstly when the

falling nappe hits a receiving pool of water, air is entrained at the intersection between

the pool and the underside of the jet and this air is drawn from the air cavity beneath the

nappe, hence ventilation of the cavity between the nappe and the vertical step should be

ensured. This type of air entrainment is known as the plunging jet entrainment, figure 2.5,

and the effectiveness of this method is dependent on the jet velocities, with higher

velocities producing more qualitative entrainment process.

Figure 2.5 Flow Aeration in Nappe Flow Regime with Fully-Developed Hydraulic Jump

17

The second method of entrainment is due to the hydraulic jump which takes place

immediately downstream of the impact of the falling nappe, where additional air bubbles

are captured at the toe of the jump (figure 2.5).

Air Entrainment in Skimming Flow Regime

For a skimming flow down a cascade channel, the flow is highly turbulent and

this supports the conditions for free-surface aeration. Pockets of air are usually entrained

along the channel and the region where the free-surface aerated flow occurs is smooth

and glossy. Nevertheless, turbulence is created next to the boundary and as this boundary

layer grows, until it reaches the free surface, the turbulence initiates natural free surface

aeration (figure 2.6) (Chanson, 1994).

Flows in a skimming regime are generally categorized into three; point of

inception; downstream a gradual varied flow layer of both air and water and further

downstream a uniform equilibrium flow region.

18

Figure 2.6 Flow Aeration in Skimming Flow Regime

Aeration Equipment Performance

Generally, oxygen transfer rate measurements are used in comparing the

performance and energy efficiency of oxygenation devices in clean water. Although

slight difference in performance efficiency of the equipment when used in process water,

these differences are dependent on the equipment, how it is applied and nature of the

process water (ASCE 2-06, 2007). Research conducted by Barkdoll and Koduri (2003),

while applying twelve different predictive models for oxygen transfer efficiency to

cascade aerators in four wastewater treatment plants in and around Mississippi; showed

19

that none of the predictive models accurately predicted the oxygen transfer efficiencies of

all the treatment plants. This was attributed to the fact that these predictive equations are

only applicable to the particular hydraulic structure for which the models was developed

thereby accounting for the unique physical properties of the structure or the flow

conditions of application to estimate the oxygen transfer efficiencies. It was concluded

that there was a need for a new more comprehensive equation since existing models were

not developed for stepped cascade aerators.

For these and other reasons, a procedure by which aeration equipment

performance could be evaluated under a set of conditions and results of these evaluations

could be extrapolated with reasonable estimates for real life scenarios was developed by

the American Society of Civil Engineers (ASCE).

Measurement of Oxygen Transfer in Clean Water

Due to the need for a uniform evaluation of aeration devices, the American

Society of Civil Engineers (ASCE) created a committee in January 1977, saddled with

the responsibility of developing standard procedures for determining oxygen transfer

rates. Earlier works aimed at assessing existing aeration equipment and techniques

employed in deriving performances of such equipments in use (ASCE Oxygen Transfer

Standard Committee, 1983).

In 1984, the first standards were incorporated by ASCE based on work by the

1983 committee. Over a series of time these standards have been re-evaluated and

corrected for necessary updates, with the most recent being the ASCE STANDARD,

20

Measurement of Oxygen Transfer in Clean Water, ASCE 2-06, (2007); based on which

all procedures pertaining this research was adhered to.

This present test method is simply based on the removal of oxygen form water by

the means of sodium sulfite in the presence of a catalyst, cobalt chloride. Dissolved

oxygen concentration measurements are then collected periodically throughout the re-

oxygenation process. The data collected are then analyzed to derive the apparent mass

transfer coefficient, KLa and the steady-state DO saturation concentration C*∞; based on

equation 2.15:

C = C*∞ – (C*∞– C0) exp (-KLat) (2.15)

where:

C = DO concentration

C*∞ = determination point value of the steady-state DO saturation concentration

as time approaches infinity.

C0 = DO concentration at time zero

KLa = determination point value of apparent volumetric mass transfer coefficient,

t-1, defined so that

KLa = rate of mass transfer per unit volume / (C*∞– C)

By use of nonlinear regression analysis, equation 2.15 can be used to determine KLa and

C*∞ for each determination point (ASCE 2-06, 2007). The ASCE method of evaluation

has gained wide acceptance and is applicable to both field and laboratory evaluation, used

21

for tank volumes ranging from vessels of a few liters to large tanks over 1 million

gallons.

Specific aspects pertaining to the testing protocol, as detailed by the ASCE 2-06,

(2007) document with the potential to influence the reported output values of this

investigated cascade model, were stringently adhered to and will be further expounded in

succeeding chapter of this document.

22

CHAPTER III

METHODOLOGY

Objective of Study

As earlier stated, the aims and objective of this project is to investigate and

optimize the various factors that affect the reaeration potential of the cascade aerator

model being examined. Influential external factors that will be considered are the water

flow rates, the slope angles and the weir geometry and its effect on oxygen mass transfer

coefficients (KLa) will also be statistically examined using the analysis of variance test

(ANOVA).

The ASCE 2-06 (2007) offers a detailed protocol with respect to experimental

procedures, data collection and analysis, so that a standard uniform methodology could

be applied to all experiments pertaining to aeration in order to yield generally acceptable

results.

Description of Low Profile Cascade Aerator Model

The model being investigated is a cascade only in the sense that it is water

gravitating over stages of weirs. Contrary to traditional cascade models where water falls

steeply from step to step requiring great depth for effectiveness, this modified cascade

aerator simply utilizes optimum sloping waterways fitted with series of turbulence

23

control aeration weirs along the channel. A schematic of a model unit is illustrated as

figure 3.1.

Figure 3.1 Schematic Diagram of a Low Profile Cascade Aerator Model

The model aerator used for this study is made of a 165.1 cm (65 inches) long,

20.32 cm (8 inches wide) and 0.635 cm (¼ inches) thick transparent flexi-plastic inclined

at a fixed slope of 4.50. This channel bed was partitioned into three equal sections by the

three weirs which were placed along its length and was fittedly-enclosed in an open

prismatic Rectangular-shaped tank also made of ¼ inches of flexi-plastic, 152.4 cm (60

inches) long, 20.32 cm (8 inches) wide and 50.8 cm (20 inches) deep, with steel-framed

edges for additional support. All joints were tightly sealed with an acrylic solvent cement

24

sealant to ensure no leakages and this was constantly checked during the course of

experiments to ensure water tight connections. A constant water volume of 58 liters (15.3

gallons) was used for the study. Salinity and total dissolved solids effects were minimized

by using tap water and this was pumped by a ¾ HP centrifugal pump (Hayward® High

Performance pump), which firmly rested on steel plates attached underneath the tank,

(figure 3.2 and 3.3).

Figure 3.2 Front View of Model Aerator with DO Probe (Channel Slope 4.50)

25

Figure 3.3 Side View of Model Aerator with DO Probe.

Design Geometry for Weirs.

Four different types of weirs geometry were used for this study. These weirs were

constructed using 3.81 cm (1.5 inches) by 20.32 cm (8 inches) by 0.635 cm (¼ inch)

thick flexi-plastic strips. Three of each type of weir were constructed and placed at three

equal intervals along the channel bed; (at the tip upstream end of the channel bed, and

one-third and two-thirds the distance from the tip), in order to generate the turbulence

needed for aeration. The four geometries looked at are a Rectangular-shaped weir, an

inverted T-shaped weir, a W-shaped weir and an inverted Cross shaped weir, as

illustrated in figure 3.4 to 3.7. The spacing between the flexi strips in the W-shaped weir

and in the Cross-shaped weir were equal, in order to minimize errors that may arise due

to lack of uniformity.

26

Figure 3.4 Rectangular-shaped Weir

Figure 3.5 Inverted T-shaped Weir

Figure 3.6 W-shaped Weir

Figure 3.7 Inverted Cross shaped Weir

27

Three Slope Variation

Channel bed slopes of 2.50, 4.50 and 6.50 were examined. The fixed angle of the

channel bed was 4.50. The other two angles were determined by applying appropriate

increases in height to the ends of the tank. Needed additions were calculated using basic

Pythagoras theorem and further verified by using plumb lines and protractors. It was

eventually determined that an angle of 6.50 could be achieve by applying shims to give an

increase of 5.33 cm (2.1 inches) to the upstream end of the tank and likewise for an angle

of 2.50.

Flow Rates Calibration

The effects of three flow rates on the oxygen transfer coefficient were evaluated;

these three flow rates were selected based on the capacity of the pump. A maximum flow

of 1397.20 L/min (112.5 gpm/ft) could be obtained from the pump which then served as

the highest flow; the two other flow rates readings 465.75 L/min.m (37.5 gpm/ft) and

931.45 L/min.m (75 gpm/ft) are equally spaced flow rates lower than the highest flow.

The water discharge was calibrated with a FLO-MATETM Model 2000 portable

flowmeter. In order to achieve sufficient data for statistical analysis, it was initially

proposed that five flow rates should be evaluated, however due to the limitations in

acquiring five clearly distinct flow calibrations, through the flowmeter; hence flow rate

was limited to three.

Velocity measurements were taken at three equally spaced positions, figure 3.8

(V1, V2, and V3) across the width of the upstream water discharge unto the channel. An

28

average velocity (V) was then derived which was multiplied by the total flow area (A) to

derived the flow rate (Q).

Figure 3.8 Equally Spaced Velocity Measurements

V = (V1+ V2 + V3)/3 (3.1)

Q = V*A (3.2)

where:

V = average velocity calculated from by flowmeter measurements ft/s

A = water flow area ft2

Q = water discharge ft3/s

Initially it was proposed that flow rates be calculated for each weir geometry,

however upon close calculation and verification, it was concluded that it was unnecessary

because differences in flow velocities were considerably negligible. For instance, the

rectangular-shaped weir produced velocities of 0.202 m/s (0.6633 ft/s); inverted T-shaped

0.201 m/s (0.66 ft/s); W-shaped 0.206 m/s (0.675 ft/s) and inverted Cross shaped 0.207

m/s (0.68 ft/s),at mid flows 931.45 L/min.m (75 gpm/ft) hence flow velocity for the

rectangular weir was adopted for all weirs, since it gave more accurate values.

29

Na2SO3 + ½O2 Na2SO4

Co

The three flow rates, 465.75 L/min.m (37.5 gpm/ft), 931.45 L/min.m (75 gpm/ft)

and 1397.20 L/min.m (112.5 gpm/ft), were obtained by appropriately adjusting the valve

controlling the flow of water until a corresponding stable flow velocity was obtained on

the flowmeter. This was done for all flows to obtain accurate flows.

Application of Sodium Sulphite and Cobalt Chloride.

Sodium sulphite (Na2SO3) was limited to around 4.39 g per test run, in

accordance with ASCE 2-06, (2007) manual, which states that theoretically 7.88 mg/L of

sodium sulphite is needed per 1.0 mg/L of DO concentration. Reagent based sodium

sulphite was also used.

(3.3)

This quantity was sufficient to achieve the depressed DO level of 0.5 mg/L

initially needed before every run.

In order to limit the effect of total dissolved solids and salinity, municipally

supplied tap water was used and total runs were restricted to twelve, after which the test

water was then changed. By limiting total runs to twelve, an approximate total dissolved

solids mass of 52.68 g was ensured, this would result in a TDS concentration of about

908 mg/L in the test water, which is well below the 2,000 mg/L limit set by the ASCE 2-

06, (2007) standards. Such precaution were necessary because it has being reported that

theoretically for every 45.4 kg (100 lb) of sodium sulfite added, 53.1 kg (117 lbs) of

sodium sulphate is formed (USEPA, 1979).

30

ASCE 2-06 (2007) specifies that reagent or technical grade cobalt chloride

CoCl2.6H20 or cobalt sulfate, CoSO4 should be as a catalyst for the sulfite deoxygenation

to achieve a soluble cobalt concentration of between 0.1 mg/L to 0.50 mg/L in the test

water. To achieve this concentration approximately 17.4 mg of reagent based cobalt

chloride was used once for every 58 liters of water tested in this experimental procedure,

this was added prior to the beginning of the system operation.

Generally results from initial tests runs were discarded due to anomalies

associated with stabilization of water chemistry. It is recommended that pre-conditioning

of test water be carried out by mixing it first with sodium sulphite and then aerating to

saturation before starting the test program.

Furthermore in order to ensure adequate dispersion of chemicals in the tank, a

Nessler tube color analysis was carried out in the tank. An equivalent quantity of food

coloring was poured into the tank and then samples were taken every 30 seconds and

compared in 100 ml Nessler tubes in order to determine level of mixing necessary for

complete mixing to occur, see figure 3.9.

31

Figure 3.9 Nessler Tube Test to Determine Level of Complete Mixing

Water Quality

Test water quality must be equivalent to that of potable public water supply

(ASCE 2-06, 2007). This is done to provide some uniformity in source water quality.

However it is known that differences exist between water qualities from various

municipalities. Hence an alternative means of evaluating the oxygen transfer efficiencies

of different systems may be needed.

The use of correction factors α and β is widely accepted and used. The correction

factor, α is used to estimate the KLa in actual system and it is strongly influenced by the

mixing intensity and tank geometry, where:

α = (KLa)WW / (KLa)TW (3.4)

(KLa)WW = oxygen reaeration rate for wastewater

(KLa)TW = oxygen reaeration rate for tap water (reference water)

32

Likewise, the correction factor β is used for evaluating the oxygen transfer rate

based on differences that exist due to constituents such as salts, particulates and surface-

active substances (Metcalf and Eddy, 2003),

β = (CS) WW / (CS) TW (3.5)

(CS) WW = oxygen saturation concentration for wastewater

(CS) TW = oxygen saturation concentration for tap water

Generally the tap water referred to here, is the tap water located at the vicinity of

the wastewater treatment plant, however for water of more consistent characterization,

probably distilled water may be preferred.

Its being reported that values of α vary from 0.3 to 1.2 depending on the type of

aeration equipment while β values range from 0.7 to 0.98 (Metcalf and Eddy, 2003).

Dissolved Oxygen (DO) Measurements

The location of DO probes is in test tanks is generally based on type of aeration

device, size and geometry of the tank and mixing pattern of the tank (ASCE 2-06, 2007).

For this research the DO probe was placed downstream of the channel slope and firmly

secured to minimize movement due to flowing water currents.

DO measurements were taken with the use of a YSI 5010 BOD probe and

recorded with a YSI Model 5100 meter at regular intervals of 10 seconds or 20 seconds,

depending on which time intervals deemed appropriate for the reaeration process. The

probe was submerged at a depth well below the surface of the flowing water at the

downstream end of the channel, in order to achieve appropriate readings and readings

33

were electronically transferred to Excel spreadsheets. The DO meters were also calibrated

daily and, calibration procedures followed those recommended by the manufacturers.

All tests were continued long enough so that the last measured DO values were

equal or close to the 98% of the saturation oxygen value and more than 21 DO values

were recorded equally spaced at approximate equal time intervals from the first to the last

DO values.

Water temperature is known to affect the rate of oxygen transfer into liquid, low

temperatures slow the deoxygenation process and may introduce some error (ASCE 2-06,

2007). It is recommended that temperature that tests runs be carried out at water

temperatures of between “100C and 300C, and as close to 200C as possible”, temperature

outside this range are permissible if approved by engineer-owner-representative. In

addition to this, it is advised that a temperature correction factor, θ, of 1.024 be used to

adjust temperature taken outside stipulated range. During the course of this project

temperature typically varied from 220C to 340C.

It is worthy of note that aeration is not only affected by total dissolved solids and

temperature; alkalinity, chlorine residuals, pH, iron, manganese, total organic carbon,

chemical oxygen demand (COD) cobalt and various surfactants have being reported to

affect oxygen transfer rates, but no clear relationship have being determined to establish

the extent. These effects were not measured or taken into consideration while undertaking

this paper. In addition minute quantities of oil contaminants have also being known to

have effects on oxygen transfer rates.

34

Test Procedure

At the beginning of each test run, the tank was filled with tap water to a measured

volume of 58 liters (15.3 gal). Prior to starting to the flow in the channel, the DO probe is

set in place, centrally positioned above the downstream end of the channel, after which

already measured appropriate quantity of deoxygenating chemicals, cobalt chloride and

sodium sulphate concentration was added to the test water.

The desired flow rate is then started; while monitoring the DO meter, as soon as

the DO level is at or below 0.5 mg/L, measurements are then taken at periodic intervals.

This test is carried out three times for a particular flow rate, slope angle and weir

geometry. Results are attached in the appendix.

KLa Estimation: Nonlinear Regression Method

Recorded dissolved oxygen concentration and its corresponding time are used in

estimating mass transfer coefficient KLa, typically the characteristic plot of the obtained

data is a curvilinear graph, which may prove a little difficult in determination of data.

Hence numerical models are generally the preferred means of data estimation.

The general form of oxygen transfer is based on these equations:

W = dC / dt = KLa (C∞* - C) (3.6)

Where:

W = dC / dt = transfer rate per unit volume

KLa = volumetric mass transfer coefficient

C∞* = dissolved oxygen concentration in the liquid phase

C = dissolved oxygen concentration at time t

35

Integrating the above equation and equation initial time t = 0 and concentration C

as C0, further yields the logarithmic equation (3.7) and exponential equation (3.8) below:

ln (C∞* - C) = - ln (C∞* - C0) KLa (t – to) (3.7)

C = C∞* - (C∞* - C0) e - KLa (t – to) (3.8)

where,

C = dissolved oxygen concentration at time t

C∞* = dissolved oxygen concentration in the liquid phase

C0 = dissolved oxygen concentration at time = 0

KLa = volumetric mass transfer coefficient

t = time

Through various application of these equations, it was noticed that the KLa values

obtained from each of this equation differ from each other, therefore no specific model

has being lauded as producing accurate values. Three areas of concern are immediately

identified when trying to fit a mathematical model to a given set of data. The first is

whether the equation being proposed correctly models the system under study. The

second is selecting which bests estimates the parameters of the proposed model and the

third is precision of the selected model (USEPA, 1979).

Using equation 3.6 seems appropriate in analysizing data because no value of C∞*

is required and the model form is linear, however significant inconsistencies have being

observed (USEPA, 1983) even when the data set contains little “noise”. This method is

36

generally not recommended because of lack of accuracy and over shadowing effect of

even the minutest error.

Likewise the logarithmic form (log-deficit approach) of the equation (3.7) is

similar to the linear/differential form but requires the value of C∞* to be given for

analysis. This is seen as a limitation (Boyle et. al., 1974) because values of C∞* vary

depending on field measurements, published values, and assumption. Using this

approach, an increase in selected value of C∞* will invariably cause a decrease in KLa

value for a given data.

Equation 3.8 is typically evaluated using the non-linear regression analysis. The

best estimates of KLa, equilibrium oxygen concentration and initial oxygen concentration

are chosen which then drive the model equation through the prepared DO concentration-

versus-time data points with a minimum residual sum of squares (ASCE 2-06, 2007). The

difference in concentration between a measured DO value at a given time and the DO

value predicted by the model at the same time is known as the residual. This method is

largely preferred by ASCE because there is limited opportunity for bias to be introduced

into the equation, although a drawback is that it is an iterative process and would require

a computer program for such repetitive calculations.

In applying both the log-deficit and non-linear regression method it required that

data be collected over a specific period of time as outlined by the ASCE 2-06 (2007)

instruction manual. Here it is stated that the sulfite added shall depress the DO

concentration to less than 0.5 mg/L at all determination points. It was observed during the

course of the experiments that initial DO readings fluctuated due to the limits of the

37

membrane-based DO method used; hence we deemed it fit to eliminate all of this data as

being equivalent to zero. Therefore we only regressed data that showed a steady positive

increase in DO, which in a couple of cases were of a value greater than 0.5 mg/L,

however it was ensured that DO values greater than 30% of the saturation concentration

were not truncated as stated in the manual (ASCE 2-06, 2007).

38

CHAPTER IV

RESULTS AND DISCUSSIONS

General Observations

The experiments were run following a three-stage sequence starting from the

lowest slope of 2.50 to the highest of 6.50. We also began with lowest flow rates of

465.75 L/min.m (37.5 gpm/ft) and concluded with the highest of 1397.20 L/min.m (112.5

gpm/ft). Attaining an initially DO concentration of 0.5 mg/L for the high slope and high

flow rate conditions proved somewhat difficult because of the rather fast rate of

reaeration resulting from the extremely turbulent flows conditions that occurred in this

setup. It was found that DO values instantly rose as soon pump was started, hence a few

initial DO levels at this stages ranged between 0.5 mg/L to 1.0 mg/L.

On the other hand flows in the lower discharge regime tended to take longer

periods of time to attain the 98% saturation level as required by the ASCE manual, as a

result longer run periods had to be performed. Due to the longer run periods (20 minutes

to 30 minutes), there was an appreciable temperature increase, especially when three

repetitions were made on the same water sample. As earlier stated total dissolved solids

concentration were kept below limits 2000 mg/L by regularly changing water samples

after 12 runs. It was calculated that performing 12 tests would result in an equivalent

increase in the TDS of about 912 mg/L.

39

In all experimental procedures for all three slope stages were relatively consistent

with ASCE 2-06, (2007) manual. A nonlinear regression FORTRAN program developed

here at the department (Brown; 2005) was used to estimate the mass transfer coefficient

data. Appendix A shows the raw data in a graphical form of oxygen increase over time

for all 108 runs performed.

Channel Slope 2.50

It can be observed from the average KLa stated in Table 4.1 that at flow rates of

465.75 L/min.m (37.5 gpm/ft) the W-shaped weir seems to have most favourable

reareation rates (KLa). Likewise for discharges of 931.45 L/min.m (75 gpm/ft), the W-

shaped weir also appeared most advantageous when compared with the rest of the weirs

considered.

Table 4.1 KLa Non-Linear Regression Estimates for Channel Slope 2.50

Flow Rate (gpm/ft)

Average KLa (min-1) For the Specified Weir Geometry

Rec. T W Cross 37.5 0.177 0.195 0.224 0.198 75 0.334 0.354 0.418 0.354

112.5 0.616 0.615 0.812 1.381

On the other hand at flow rates of 1397.20 L/min.m (112.5 gpm/ft) the Cross weir

produced the better reaeration rates in comparison with the W-shaped weir. This higher

KLa can be traced to the additional turbulence generated as a result of increase in flow

rates. This generated an extra nappe plunging flow regime over the upper region of the

Cross weir, which when combined with the lower region flows greatly enhanced air

40

entrainment mechanism see figure 4.1. Similar results were obtained by Nakasone,

(1987) who narrowed the width of his nappe flow regimes invariably increasing

turbulence which then led to an increase in aeration efficiency. At flow rates lower than

283.9L/min (112.5 gpm/ft) this beneficial additional layer could not be generated because

flow rates lower than this are not high enough to drive the water over the upper region of

the Cross weir.

Figure 4.1 Schematic Front View of Flow over Cross Weir

At flow rates of 465.75 L/min.m (37.5 gpm/ft) and 931.45 L/min.m (75 gpm/ft)

for all of the channel slopes examined, the W-shaped weir produced better results. It was

obvserved that the turbulence generated by the more restricted “dual” passage of water

through the “prong” of W-shaped weir (see figure 4.2) exceeded the turbulence created

by the flow over the lower portions of the Cross weir. When compared to the Cross weir,

the W-shaped weir reduces the channel width by 55% in comparison to the Cross’s

reduction of 20%, this reduced flow area may have contributed to an increase in plunging

41

depth of the nappe flow over the weir, thus creating additional turbulence downstream of

the channel bed.

Figure 4.2 Schematic Front View of Flow over W Weir

At these flow rates discharges were not high enough to generate the double layer

plunging nappe flow needed by the Cross shaped weir (figure 4.3), hence the flow was

limited to the lower region of the Cross weir. The W-shaped weir therefore generated

more turbulence, thus its KLa were higher for flow rates of 465.75 L/min.m (37.5 gpm/ft)

and 931.45 L/min.m (75 gpm/ft).

Figure 4.3 Schematic Front View of Single Layer flow over Cross Weir

42

By the calculating the critical velocities for each channel slope, it can be shown

that the super critical velocities occurred on the downstream of the weir, White, (1999).

vc = (gyc)1/2 (4.1)

Where:

vc = critical velocity

g = acceleration due to gravity

yc = critical depth

The critical depth yc can be obtained from equation 4.2:

3/12

2

)(gb

Qyc = (4.2)

Where:

Q = flow rate

b. = width of channel

Critical velocity derived was determined to be 0.589m/s (1.933ft/s), which is

greater than the maximum velocity obtained during flow, hence turbulence occurred on

the downstream side. Furthermore this critical velocity generated a critical depth of about

1.9 cm (0.75 inches) this is less than the low head depth of all weirs which were all 3.8

cm (1.5 inches) in width further confirming that super critical flow was downstream.

The subcritical velocities built up on the upstream of the weir, generated

sufficient depth for the free falling nappe flows to generated large enough turbulence for

entrainment of oxygen in the body of water. As explained before this effect was more

pronounced at lower flow rates 465.75 L/min.m (37.5 gpm/ft) and 931.45 L/min.m (75

43

gpm/ft) for all channel slope, which is most probably why the W-shaped weir dominated

in this flow regimes, because its rather restricted passage water ways forced water depth

to build up on both end before falling down the water ways.

Channel Slope 4.50

In comparison with channel slope of 2.50, all KLa obtained were generally higher

for each respective corresponding flow rates, also linked to the increase in slope angle

which invariably leads to added turbulence to all the flow regimes. Likewise, average

KLa followed the same trends as discussed in channel slope of 2.50, better reaeration rates

were obtained for flow rates of 1397.20 L/min.m (112.5 gpm/ft) using the Cross shaped

weir geometry, see Table 4.2. This effect equally attributed to the extra nappe flow

turbulent regime generated over the upper region of the Cross weir.


Flow Rate (gpm/ft)


Rec. T W Cross 37.5 0.201 0.214 0.298 0.273 75 0.425 0.425 0.495 0.456

112.5 0.961 0.998 1.065 1.293

Similarly as in the case of channel slope of 2.50, at flow rates of 465.75 L/min.m

(37.5 gpm/ft) and 931.45 L/min.m (75 gpm/ft), it appeared that most favourable

reaeration rates for slope of 4.50 were also obtained from the W-shaped weir.

44

Channel Slope 6.50

Predictably, the highest KLa for all three channel slopes considered were obtained

at this channel slope for all corresponding flow rates. At a combination of this slope angle

and a flow rate of 1397.20 L/min.m (112.5 gpm/ft), using the Cross weir seemingly

appeared to achieve the most optimal reaeration rates for combination of all operational

parameters considered (Table 4.3). As before the W-shaped produced the best reaeration

values for both the 465.75 L/min.m (37.5 gpm/ft) and 931.45 L/min.m (75 gpm/ft) flow

rates.


Flow Rate (gpm/ft)


Rec. T W Cross 37.5 0.257 0.247 0.276 0.226 75 0.441 0.442 0.569 0.554

112.5 1.780 1.774 1.904 1.977

Based on the earlier discussions we should expect that the inverted T and Cross

weir produce similar KLa at flows of 465.75 L/min.m (37.5 gpm/ft) and 931.45 L/min.m

(75 gpm/ft), since flows here were limited to the lower region of the Cross weir, and

hence it acted as a T-shaped weir. This trend can be observed in their respective KLa for

channel slopes 2.50 and 4.50, though they are not all precisely similar possibly due to

human and experimental errors while running the experiment, they are of some what

roughly close proximity. However as would be seen in Table 4.3 this was not the case for

the flow rates of 931.45 L/min.m (75 gpm/ft) at the slope of 6.50, because at this stage

45

there were intermittent surges of water over the upper regions of the Cross weir, thus

creating additional turbulence in this setup.

As mentioned earlier, in comparison to the other two slope channels investigated,

it can be distinctly noticed that reaeration rates in the channel slope of 6.50 for all four

weir geometries for each respective flow rates are considerable higher than their

corresponding flow rates counterparts in the other two channel slopes. Hence it may be

advisable to operate the low profile cascade aerator at this slope or even a much higher

slope, because better reaeration values are seems to be obtained with increase in channel

slope. Though further analysis may need to be obtained to determine the most optimal

channel slope, because based on literature by Chanson, 1994 reareation process are still

achievable until slopes of between 450 to 600.

On the long run, it appears that the W-shaped weir may be overall the most

beneficial weir. This is because at the highest flow rates of 1397.20 L/min.m (112.5

gpm/ft) where the Cross weir had a distinctly higher reaeration rates in lower slopes; at

this channel slope of 6.50, the difference in KLa between the two weir geometries is rather

negligible and may probably have similar effects. This may be traced to the fact that an

increase in channel slope and flow rates combination may eventually reach a point where

the differences in weir geometry design may have no significant impact on air

entrainment. Therefore, a statistical analysis was under taken to determine if there was a

significant improvement in aeration when the Cross was used.

46

Interaction between Channel Slope, Flow Rates, Weir Geometry

and Oxygen Transfer Coefficient

As part of efforts to delineate which factors play significant roles in the reaeration

a main and interactive effect plot graph was performed on the mean KLa values derived

from one and a combination of the operational parameters.

Firstly a graphical plot of the main effects of the varied operational parameter on

KLa was conducted as displayed in figure 4.4. Isolating the effects of slope channel, it can

be seen that the highest mean oxygen transfer rates are obtained for channel slopes of

6.50, followed by slopes of 4.50, then 2.50, hence it may be safe to say the higher the

channel slope, the better the oxygen transfer rates. Furthermore, if the effects of flow

rates are singled out, from the plot displayed, it is observed that at flow rates of 1397.20

L/min.m (112.5 gpm/ft) highest aeration is achieved.

Finally, in considering the plot showing the effects of the various weir geometries

on the mass transfer coefficient, it is obvious that the Cross shaped weir produced higher

average reaeration rates. Despite this high rates it may be rather hasty to conclude that the

Cross shaped weir are the most influential of all weir type considered, because they are

found to produce better reaeration rates at flow rates of 112.5 gpm/ft, further analysis

may be needed. The rectangular and inverted T-shaped weir appears to produce the same

effect.

47

Mea

n of

KLa

6.54.52.5

1.2

0.9

0.6

0.3

112.575.037.5

WTRec.Crs.

1.2

0.9

0.6

0.3

Slope Flowrates

Weir Config.

Figure 4.4 Main Effects Plot (data means) for KLa

A more detailed analysis of the interactions between the varied parameters and

KLa can be seen in the interaction plot diagram, figure 4.5. Firstly, taking a look at the

slope angle, for all channel slopes the highest aeration rates are obtained for flow rates of

1397.20 L/min.m (112.5 gpm/ft), similarly the Cross shaped weir had the highest

reaeration rates for all channel slopes. It is worth noting that at channel slope of 6.50 and

flow rate of 1397.20 L/min.m (112.5 gpm/ft), aeration rate coefficient for all weir

geometries seem to converge at near equal values. As earlier explained, it may be derived

that at this flow rate and slope angle, difference in weir geometry has negligible impact

on the mass transfer coefficient.

48

Slope

2

1

0

Flowrates

Weir Config.

WTRec.C rs.

112.575.037.5

2

1

0

6.54.52.5

2

1

0

Slope

6.5

2.54.5

Flowrates

112.5

37.575.0

Weir

TW

Config.Crs.Rec.

Figure 4.5 Interaction Plot (data means) for KLa

Secondly, for flow rates of 1397.20 L/min.m (112.5 gpm/ft), KLa peak at channel

slopes of 6.50 and Cross weir geometry, verifying the previous relationship obtained.

Finally for the weir geometries, the Cross weir appeared to be better for flow rates of

1397.20 L/min.m (112.5 gpm/ft) and slope angle of 6.50.

These results indicate that aeration coefficient increases as the flow rates and

slope angle increases, with higher mass transfer coefficient being obtained at this

condition for the Cross shaped weir. The reason for this as discussed earlier, can be

traced to the additional turbulence generated as water flows over the upper and lower

portions of the Cross shaped weir which creates strong mixing of the free falling nappe

49

flow water regime. However it still leaves us in the dark as to which weir is most

influential when all three flow rates and slopes are taken into cognizance.

Further analysis was carried out on the three varied parameters using the One-

way, Two-way and Balanced analysis of variance (ANOVA) procedure of MINITAB®

Student Release 14 (1972-2003 MINITAB® Inc.). Here a 95% (α=0.05) confidence

interval serves as the basis for our computation and the probability (P) that any of the

operational parameters significantly affected reaeration (KLa) could be determined by

comparing both α and P. Here operational or a combination of operational parameters are

deemed as significantly affecting reaeration rates if the probabilities (P values) are less

than α and vice versa.

In the One-way analysis the effects of individual operational parameters were

singled out and examined, results (see Table 4.4) it appears that both flow rates and slope

significantly affects reaeration; because the P values( P=0.000; P=0.003) were less than

α=0.05, P=0.000; P=0.003 respectively. However it was observed that the weir

geometries reportedly had no considerably significant effects on KLa; α=0.05, P=0.635.

Table 4.4 One-Way ANOVA

Parameter F P α=0.05

Slope 6.190 0.003 Flow rates 120.07 0.000 Weir Geo. 0.57 0.635

This analysis clearly indicates that the most significant parameters controlling

aeration in a low profile cascaded aerator are the slope and the flow rate. It is understood

50

that steeper slopes provide better aeration. However, this is a constraint limited by the

desire to minimize this parameter while optimizing aeration. Flow rate is a major

parameter because higher rates of oxygen transfer are obtained as the rate of flow through

an area increases.

Regarding weir geometry, four types were considered and its relationship oxygen

transfer. Lumping them together in this analysis does not allow one to define if one

geometry is significantly better then the others or if there are opportunities to improve

oxygen transfer using different weirs. Therefore, though the above analysis suggests weir

geometry is not all that significant in the process, for a given slope and at a given flow

rate, the analysis is still inconclusive.

Analysis was further undertaken using the Two-way approach; this studied the

effects of the interactions (in pairs), of the three operational parameters considered. It was

identified that the interaction of pairs involving the weir geometry; that is the slope and

weir combinations and flow rates vs. weir combinations, seemingly had no noteworthy

effects on the reaeration rates; (Table 4.5) since P values (P=0.988, P=0.282 respectively)

were greater than α=0.05. Although when considered individually slope and flow rates

appear to influence the reaeration process, a combination with various weir geometries

seems to lessen this effect. On the other hand the combinations of slope and. flow rates

were played significantly greater roles in the reaeration process. (P=0.000). It can be

deduced that discharge and slope angle play a major role in re-aeration using the low

profile cascade aerators.

51

Table 4.5 Two-Way ANOVA


Weir Geo. 0.590 0.621 Slope 5.79 0.004

Interaction 0.07 0.988

Weir Geo. 1.940 0.128 Flow rates 125.11 0.000

Interaction 1.260 0.282

Slope 85.04 0.000 Flow rates 560.72 0.000

Interaction 55.32 0.000 There is a relationship, albeit marginal between the weir geometry and the flow

rate. This suggests that there is a significant difference in the aeration based on weir

geometry when different flow rates are being used. The previous data indicates

specifically that Cross is better at the highest flow studies while the W was better at the

others. However, this analysis could also be suggesting that the “W” and Cross are

simply better then “Rec.” and “T”. Therefore the results are not conclusive at this level.

As expected, flow rate and slope are very significant predictors of reaeration.

Based on the data observations, it can again be concluded that higher flow rates and

slopes are better for reaeration then lower values for either parameter.

Furthermore, in trying to ascertain the degree of influence a particular weir

geometry had over the reaeration rates, a two way ANOVA of on each weir was

52

undertaken. Both the single and combined effect of flow rates and channel slope as it

affects reaeration for a particular weir geometry was evaluated. Apparently the

interaction of the flow rates and channel slopes with the W-shaped weir has a greater

influence on reaeration rates in comparison with the rest of the weirs. This is indicated by

a higher F value (95.16) as detailed in table 4.6. Reaeration derived from the flow of the

Cross weir seems to be largely influenced by a higher flow rate as noticed from its rather

large F value, 2322. This further confirms our earlier discussion that higher flow rates

increases reaeration in Cross shaped weir. Performance by Cross shaped weir

significantly improves as the flow rates increases due to the double layer nappe flow

generated at such high flow rates setup (283.91L/min.m (112.5 gpm/ft) as portrayed in

KLa values obtained from experimental analysis.

Table 4.6 Two Way ANOVA for Weir Geometry

Weir Geo. Rec. T W Cross α=0.05

Parameter F P F P F P F P Slope 112.28 0.000 97.31 0.000 148.71 0.000 107.21 0.000

Flow rates 430.77 0.000 403.16 0.000 825.69 0.000 2322.03 0.000 Interaction 77.14 0.000 71.88 0.000 95.16 0.000 85.13 0.000

For the W-shaped weir it seems that steeper slopes improves reaeration

performance as seen in its high F value 148.71. This further clarifies the increase in KLa

results obtained as channel slope increases from 4.50 to 6.50 Both the rectangular and T-

shaped weir appear to have similar influences on reaeration rates on the low profile

53

cascade aerator model. However statistical analysis shows that there is little advantage to

rectangular weir when compared to the T weir.

An overall investigation was carried out using Balanced (Three) way analysis and

this showed that a combination of all three parameters significantly influence reaeration.

(P=0.000) see figure 4.7.

Table 4.7 Balanced (Three-Way) ANOVA


Slope 438.31 0.000 Flow rates 2890.08 0.000 Weir Geo. 44.92 0.000

Slope*Flow rates 285.12 0.000 Slope*Weir Geo. 5.64 0.000

Flow rates*Weir Geo. 29.18 0.000 Slope*Flow rates*Weir Geo. 7.890 0.000

However, the three-way analysis result may not be a precise representation of

effects, as observed in the unusually high F values, this can be traced to the some what

“limited” data obtained in the course of running this experiments. Typically, the norm for

this type of ANOVA analysis is to ensure that experimental data are derived from at least

six (6) repetitions of test runs, that is at least twice the number of operational

parameters/factors investigated (Montgomery et al, 2003), unless accuracy may be

compromised.

Nevertheless, based on the data obtained, the three-way ANOVA further

corroborates the findings of the two earlier ANOVA analysis and the results of

54

experiments by Baylar, Emiroglu., et al (2007), Chanson,(1994) and Nakasone.,(1987);

that the flow rates and channel slope angle seem to be major players in the aeration

process, since their F-ratios is well into the critical region.

55

CHAPTER V

CONCLUSIONS AND RECOMMENDATIONS

With the ever increasing stringent dissolved oxygen effluent standards and

permits imposed by the National Pollution Discharge Elimination System on various

wastewater treatment plants spread across the United States, there is a growing need for

post-aeration. Some research has been performed on a wide variety of post-aeration

options, but as of now, there has been no general consensus on a particular advantageous

method. Cascade aerators have been proved to be the least costly (Metcalf and Eddy,

2003) most especially if site constraints and hydraulic conditions permit gravity flow.

The purpose of this research was to simulate as closely as possible a full-scale

operation of a low profile cascade aerator, hence a model aerator was fabricated.

Investigation was carried out on three parameters that tend to affect aeration; flow rates

(465.75 L/min.m (37.5 gpm/ft), 931.45 L/min.m (75 gpm/ft), 1397.20 L/min.m (112.5

gpm/ft)), channel slope (2.50, 4.50 and 6.50) and weir geometry (four different geometry).

Evaluation was undertaken in accordance with protocols established in the ASCE

document; “Measurement of Oxygen Transfer in Clean Water (2007)”. This document

offers specific guidance for various aspects of the evaluation process such as de-

oxygenation methodology, data collection and analysis.

56

Based on the results of this investigation, it has been demonstrated that the low

profile cascade aerator is one of the promising avenue of increasing oxygen content in a

water body. As explained in preceding chapters, the nappe flow regime was predominant

in all flows and reaeration is associated with the strong turbulent mixing which occurs as

the water stream plunges downstream along the channel bed. In this flow regime, aeration

is typically linked to two reasons; (1) the effects of the plunging nappe on receiving water

which causes air bubbles to be entrained at the intersection of the jet with the receiving

pool, and (2) the effects of hydraulic jump which immediately takes place after the nappe

plunge at the downstream end of the flow (Chanson, 1994).

Certain observations and recommendations can be deduced from the

experimental analysis

• At a channel slope of 2.50 it appears that in general, the lowest reaeration rates

were obtained when compared to the rest of the slopes studied. Presently the low

cascade aerator is being operated at a channel slope of 4.50, however from results

obtained from this study it can be seen that higher reaeration rates were obtained

at slope of 6.50. Hence it is recommended that the low profile cascade channel

slope should be higher than 4.50 if a significant improvement in aeration operation

is desired. While Chanson (1994) details that reaeration achieves maximum

capability at slopes of 450 to 600, it is noted that the benefit of low profile aerators

would be lost if inclined to this level. Still, it is clear from this effort that minor

increases in slope provide notable increases in aeration and it is suggested that

aerator slopes be increased when specific applications allow.

57

• Similarly, higher reaeration rates are produced with increase in flow rates for all

channel slopes, with highest reaeration being obtained at flow rates of 1397.20

L/min.m (112.5 gpm/ft) for each channel slope. Therefore it may be safe to

recommend that flow rates should be equal to or higher than 1397.20 L/min.m

(112.5 gpm/ft) in order to achieve appreciable increases in reaeration rates.

Further research may be needed to be undertaken to establish an optimal flow

rates, where any increase may not significantly aid the reaeration.

• If the flow rates of 1397.20 L/min.m (112.5 gpm/ft) are to be used for operation

of the low profile cascade aerator for channel slopes of 2.50 and 4.50, it may be

advisable to use the Cross shaped weir, because better reaeration are generally

obtained when it is applied, for example when compared to the next closest

reaeration rates (W-shaped), there is a 70% and 21% increase respectively.

However a minimal increase of 3% for channel slope 6.50 may not

overwhelmingly necessitate a preference for the Cross shaped weir.

• On the other hand if flow rates of 931.45 L/min.m (75 gpm/ft) and 465.75

L/min.m (37.5 gpm/ft) are used, it is preferable to use the W-shaped weir for all

channel slope conditions investigated in this study. As explained in chapter 3

better reaeration are obtained for the W weirs at these flow rates, because flow

rates are not large enough to generate the additional plunging nappe flow over the

upper bar of the Cross weir, which other wise would given it extra turbulence and

hence better reaeration rates.

58

• Furthermore it can be observed that as the channel slope increases the difference

between the least and highest reaeration rates invariably reduces. For example

considering the flow rates of 1397.20 L/min.m (112.5 gpm/ft) for each slope, it

can be observed that the differences between these two values (lowest and highest

KLa values) for slopes of 2.50 and 6.50, reduces from 124% to 11%. As stated

earlier it appears that a combination of an optimal channel slope and flow rates

may exist where differences in weir geometry may have minimal impact on

reaeration rates.

On the long run a balance should be struck between opting for the Cross or the W-

shaped weir based on the operational conditions of the plant. For example if operating at

lower flow rates of 465.75 L/min.m (37.5 gpm/ft) and 931.45 L/min.m (75 gpm/ft) for

the three channel slope type, based on this findings it is recommended that W-shaped

weir be used because as it produces higher reaeration rates.

Additional investigations undertaken using statistical analysis displayed that

reaeration was strongly affected by flow rates and slope angles. The higher the two

parameters, the higher the aeration coefficient, which is in concurrence with findings by

Nakasone, (1987) and Baylar, Emiroglu,, et al (2007). Further investigation is

recommended to obtain an empirical model that could easily depict the relationships that

exist between all the operational parameters involved. This recommendation would serve

to provide results of equipment performance evaluations that are representative of the

practical operating conditions experienced in both pilot and field scale equipment.

59

Another area of recommendation is in this investigation of the effect of tank

geometry on the post-aeration capabilities of the low profile cascade aerator. In this study

no analysis was done to determine the effect of reactor geometry. This might play a role

in the aeration process, for example such as the length to width ratio. Pincince., (1999)

advocates the use of a tank with a high length-to-width ratio, divided into compartment

having the same standard oxygen transfer rate, however this he says is applicable to post-

aeration using mechanical aerators. The effects of side wall friction on flow rates of water

may also be taken in cognizance due to the dragging effect that might occur when

different materials are used.

Typically performance of this aerator will largely depend on the initial dissolved

oxygen, required discharge dissolved oxygen levels, air and water temperatures,

atmospheric humidity, and total dissolved solids concentrations. Other water quality

parameters such as pH, presence of oil, iron, manganese, residual chlorine, chemical

oxygen demand have also be know to affect aeration, though no definite limiting

relationship have been determined to date (ASCE 2-06, 2007). Additional study is

recommended on these influential parameters.

In addition an alternative method for providing the basis for a uniform

comparison of aerator performance may need to be addressed, the alpha and beta

correlation factors being proposed by ASCE seems slightly implausible. This is due to the

fact that differences exist in the drinking water standards used by many pubic water

suppliers. To use these factors in setting clean water evaluations it may be advisable to

60

use a reference water of more consistent characterization regardless of location, for

example distilled water.

Finally it is recommended that a comparative cost analysis be performed on the

various types of post-aeration devices currently in use in the industry; for example,

mechanical or diffused aerators. It might be advantageous to determine which best suits

demand in terms of design, manufacturing, operational and maintenance cost. Further,

the relatively low energy loss, moderate capital cost, and low maintenance cost of the low

profile aerator should position it to be a very competitive approach to aerating treated

wastewater prior to discharge to the environment.

61

REFERENCES American Society of Civil Engineers (ASCE); (2007). “Measurement of Oxygen Transfer

in Clean Water.” ASCE Standard [ASCE/EWRI 2-06] American Society of Civil Engineers, Reston Virginia.

Aral, N. and Gonullu, M.T.; (1994), “Aeration by Conventional Cascades in Arid Weather.” Journal of Environmental Science Health, A29 (9), 1749-59.H.

Baylar, A.; Bagatur, T.; and Emiroglu, M.E.; (2007). “Aeration Efficiency with Nappe Flow over Stepped Cascade.” Water Management 160 Issue WMI, Proceeding of the Institute of Civil Engineers, 43-50.

Barkdoll, D. and Koduri, S.; (2003). “Evaluation of Oxygen Transfer at Stepped Cascade Aerators.” World Water and Environmental Resources Congress June 23-26 2003, Philadelphia, Pennsylvania USA. ASCE Conference Proceedings.

Boyden, Brace H; Banh, Duong T.; Huckaboy, Houston K.; and Fernandes, Joseph B.; (1992). “Using Inclined Cascade Aeration to Strip Chlorinated VOCs From Drinking Water.” Journal of the American Water Works Association 8 (5) 62-69.

Boyle, W.C.; Berthouex, P.M.; and Rooney, T.C.; (1994). “Pitfalls in Parameter Estimation for Oxygen Transfer Data.” Journal of the Environmental Engineering Division, ASCE, 100 (EE2): 391-408, April 1974

Brown, Gregory A.; (2005). “Factors to Consider when Evaluating Horizontal Rotor Aerator Performance” Master of Science Thesis, Dept. of Civil and Environmental Engineering, Mississippi State University.

Chanson, H.; (1994). “Air-Water Interface Area in Self-Aerated Flows.” Water Research 28 (4) 923-929

Chason, H. and Toombes, L.; (1997). “Flow Aeration at Stepped Cascade.” Civil Engineering. Research Reports, Dept. of Civil Engineering, The University of Queensland, Brisbane Queensland 40742 Australia.

Chanson, H.; (1994). “Hydraulic Design of Stepped Cascades, Channels, Weirs and Spillways. “ 1st Edition. Elsevier Science Inc., New York, U.S.A.

Kiely, G.; (1997). “Environmental Engineering.” McGraw-Hill, London, England.

62

Metcalf and Eddy, Inc.; (2003). Edited by George Tchobanoglous, Franklin L. Burton, and H. David Stensel. “Wastewater Engineering, Treatment and Reuse.”McGraw-Hill, New York, NY.

Montgomery, Douglas C. and Runger, George C.; (2003). “Applied Statistics and Probability for Engineers.” 3rd Edition. John Wiley & Sons, Inc, New York, NY.

Nakasone, H.; (1987). “Study of Aeration at Weirs and Cascade.” Journal of Environmental Engineering 113 (1), ASCE Paper No. 21221.

Pincince, Albert B; (1999). “Effect of Multiple Compartments on Oxygen Transfer in Postaeration Tanks” Water Environment Research 71 (6) 1229-34

Tebbutt, T.H.Y.; Issery, I.T.S., and Rasaratnam, S.K.; (1977). “Reaeration Performance of Stepped Cascades.” Journal of the Institution of Water Engineers and Scientists, 31 (4) 285-97

Thacker, N.P.; Katkar, S.L.; and Rudra, A.; (2002). “Evaluation of Mass Transfer Coefficient of Free Fall-Cascade-Aerator.” Environmental Monitoring and Assessment 74 1-9.

United States Environmental Protection Agency (USEPA); (1979). “Proceedings: Workshop Toward an Oxygen Transfer Standard.” EPA-600/9-78-021

United States Environmental Protection Agency (USEPA); (1983). “ Development of Standard Procedures for Evaluating Oxygen Transfer Devices.” EPA-600/2-83-102.

White, F.M.; (1999). “Fluid Mechanics.” 4th Edition. McGraw-Hill United States o America.

63

APPENDIX A

DO PROFILE GRAPHS

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Figure A.1 DO Profile: Rec. Weir, Flow 37.5 gpm/ft, Slope 2.5 deg.

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Figure A.3 DO Profile: W. Weir, Flow 37.5 gpm/ft, Slope 2.5 deg.

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Figure A.4 DO Profile: Crs Weir, Flow 37.5 gpm/ft, Slope 2.5 deg.

Run 1 @ 29.01C Run 2 @ 30.55C Run 3 @ 31.8C

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Figure A.5 DO Profile: Rec. Weir, Flow 75 gpm/ft, Slope 2.5 deg.

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Figure A.7 DO Profile: W. Weir, Flow 75 gpm/ft, Slope 2.5 deg.

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Figure A.8 DO Profile: Crs. Weir, Flow 75 gpm/ft, Slope 2.5 deg.

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Figure A.10 DO Profile: T Weir, Flow 112.5 gpm/ft, Slope 2.5 deg.

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Figure A.11 DO Profile: W Weir, Flow 112.5 gpm/ft, Slope 2.5 deg.

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Figure A.12 DO Profile: Crs. Weir, Flow 112.5 gpm/ft, Slope 2.5 deg.

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Figure A.14 DO Profile: T. Weir, Flow 37.5 gpm/ft, Slope 4.5 deg.

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Figure A.18 DO Profile: T Weir, Flow 75 gpm/ft, Slope 4.5 deg.

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Figure A.19 DO Profile: W Weir, Flow 75 gpm/ft, Slope 4.5 deg.

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Figure A.30 DO Profile: T Weir, Flow 75 gpm/ft, Slope 6.5 deg.

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Figure A.31 DO Profile: W Weir, Flow 75 gpm/ft, Slope 6.5 deg.

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82

APPENDIX B

NON-LINEAR REGRESSION PARAMETER ESTIMATES

83

Table B.1 Results for Evaluation of Channel Slope 2.50

Run #

Average Non-Linear Regression Absolute Percent

Water Parameter Estimates Standard Deviation Standard Deviation

Temp, 0C Cs, mg/L Co. mg/L KLa, min-1 Cs, mg/L Co. mg/L KLa, min-1 Cs Co KLa

37.5 gpm/ft Flow Rate

R1 28.45 7.434 0.150 0.182 0.027 0.057 0.003 0.359 37.792 1.637

R2 27.35 7.277 -0.513 0.171 0.007 0.017 0.001 0.092 -3.333 0.423

R3 2.05 6.913 -0.029 0.177 0.009 0.025 0.001 0.128 -87.775 0.668

Average 7.208 -0.131 0.177 0.014 0.033 0.002 7.208 -17.772 7.208

T1 29.85 6.818 -0.076 0.201 0.043 0.128 0.007 0.633 -168.677 3.349

T2 29.7 6.917 0.366 0.184 0.075 0.227 0.011 1.084 61.928 6.209

T3 30.85 6.719 -0.355 0.200 0.028 0.095 0.005 0.415 -26.839 2.298

Average 6.818 -0.022 0.195 0.049 0.150 0.008 7.208 -44.529 7.208

W1 32.25 6.221 -0.008 0.236 0.038 0.187 0.012 0.610 -2499.34 4.464

W2 29.7 7.157 -0.528 0.228 0.008 0.021 0.001 0.115 -4.031 0.532

W3 27.5 7.573 -1.325 0.207 0.202 0.357 0.015 2.671 -26.939 9.143

Average 6.984 -0.620 0.224 0.083 0.189 0.010 7.208 -843.437 7.208

Cross1 29.005 6.797 -1.973 0.192 0.043 0.283 0.013 0.631 -14.364 4.431

Cross2 30.55 6.628 -0.626 0.186 0.033 0.107 0.005 0.500 -17.068 2.576

Cross3 31.8 6.344 -0.737 0.189 0.010 0.036 0.002 0.160 -4.903 0.859

Average 6.590 -1.112 0.189 0.029 0.142 0.006 7.208 -12.112 7.208

75 gpm/ft Flow Rate

R1 27.1 7.704 -0.245 0.372 0.018 0.053 0.005 0.231 -21.673 1.216

R2 27.55 7.261 -0.537 0.322 0.049 0.195 0.013 0.674 -36.279 4.039

R3 29.45 7.021 -0.797 0.309 0.070 0.261 0.017 0.993 -32.781 5.525

Average 7.329 -0.526 0.334 0.045 0.170 0.012 0.633 7.208 3.593

T1 30.45 6.716 -1.680 0.395 0.069 0.364 0.025 1.030 -21.657 6.361

T2 31.7 6.453 -0.936 0.350 0.065 0.325 0.023 1.013 -34.716 6.607

T3 33.3 6.154 -2.361 0.318 0.056 0.415 0.033 0.905 -17.562 6.398

Average 6.441 -1.659 0.354 0.063 0.368 0.027 0.983 0.421 6.455

W1 25.85 8.016 -0.218 0.438 0.017 0.048 0.006 0.218 -21.921 1.085

W2 27.95 7.092 0.052 0.415 0.010 0.033 0.004 0.135 64.084 0.893

W3 29.65 6.801 -1.651 0.401 0.010 0.056 0.004 0.145 -3.368 0.944

Average 7.303 -0.606 0.418 0.012 0.046 0.004 0.166 6.590 6.128

Cross1 31.1 6.449 -0.091 0.343 0.084 0.506 0.042 1.298 -556.436 10.737

Cross2 32.65 6.175 0.064 0.355 0.014 0.078 0.007 0.222 122.973 1.844

Cross3 32.55 6.130 -0.109 0.364 0.034 0.133 0.009 0.561 -121.895 3.499

Average 6.251 -0.045 0.354 0.044 0.239 0.019 0.694 6.590 5.360

84

Table B 1 continued.

Run #





R1 27.1 7.183 -0.758 0.618 0.079 0.296 0.038 1.098 -39.006 6.121

R2 28.3 6.985 -1.364 0.625 0.076 0.384 0.053 1.087 -28.168 6.804

R3 29.45 6.810 -1.078 0.606 0.046 0.196 0.025 0.670 -18.155 3.893

Average 6.993 -1.067 0.616 0.067 0.292 0.039 0.952 -28.443 5.606

T1 28.35 7.049 -0.466 0.626 0.077 0.264 0.033 1.096 -56.733 6.000

T2 29.65 6.796 -0.465 0.616 0.048 0.209 0.029 0.708 -44.962 4.504

T3 30.65 6.589 -0.747 0.604 0.030 0.129 0.017 0.452 -17.327 2.769

Average 6.811 -0.559 0.615 0.052 0.201 0.026 0.752 -39.674 4.424

W1 25.5 7.701 -0.234 0.803 0.032 0.125 0.020 0.414 -53.406 2.523

W2 26.65 7.437 -0.701 0.833 0.063 0.328 0.052 0.853 -46.747 5.867

W3 27.45 7.267 -0.677 0.799 0.055 0.242 0.037 0.751 -35.722 4.683

Average 7.468 -0.537 0.812 0.050 0.231 0.036 0.673 -45.292 4.357

Cross1 24.7 8.091 -2.248 1.321 0.097 0.418 0.072 1.200 -18.611 6.395

Cross2 25.5 7.838 -2.027 1.396 0.049 0.272 0.056 0.621 -13.441 4.006

Cross3 26.25 7.622 -1.058 1.426 0.025 0.145 0.034 0.331 -13.709 2.406

Average 7.850 -1.778 1.381 0.057 0.279 0.054 0.717 -15.253 4.269

85


Run #





R1 26.9 7.828 -0.214 0.204 0.030 0.044 0.003 0.377 -20.367 1.401

R2 26.5 10.898 -0.235 0.185 0.930 0.220 0.023 8.534 -93.606 15.674

R3 27.45 8.683 -1.524 0.214 0.576 0.648 0.058 6.639 -42.490 18.367

Average 9.136 -0.658 0.201 0.512 0.304 0.028 5.183 -52.154 11.814

T1 25.35 8.146 -0.195 0.220 0.008 0.014 0.001 0.099 -7.127 0.384

T2 28.1 7.805 -0.207 0.206 0.022 0.029 0.002 0.284 -14.036 0.987

T3 29.8 7.967 0.112 0.218 0.161 0.135 0.013 2.020 120.272 5.882

Average 7.972 -0.096 0.214 0.064 0.059 0.005 0.801 33.036 2.418

W1 30.65 7.228 0.367 0.288 0.061 0.114 0.011 0.844 30.983 3.715

W2 26.35 7.761 0.138 0.295 0.049 0.104 0.009 0.637 75.133 2.890

W3 27.3 7.535 0.074 0.312 0.035 0.089 0.007 0.465 120.188 2.320

Average 7.508 0.193 0.298 0.048 0.102 0.009 0.649 75.435 2.975

Cross1 30.35 7.352 -0.165 0.281 0.068 0.146 0.011 0.922 -88.320 4.075

Cross2 31.05 6.975 0.359 0.265 0.118 0.227 0.021 1.698 63.139 7.791

Cross3 31.6 6.558 -0.396 0.271 0.065 0.224 0.026 0.994 -56.574 5.529

Average 6.962 -0.067 0.273 0.084 0.199 0.019 1.205 -27.252 5.798

75 gpm/ft Flow Rate

R1 28.2 7.728 -0.310 0.408 0.316 0.337 0.026 4.092 -108.766 12.729

R2 31.2 6.107 -0.324 0.420 0.165 0.681 0.111 2.694 -210.147 18.759

R3 31.95 6.534 -0.281 0.446 0.007 0.029 0.003 0.106 -10.503 0.691

Average 6.790 -0.305 0.425 0.163 0.349 0.047 2.298 -109.805 10.727

T1 31.95 6.558 -0.134 0.401 0.012 0.031 0.004 0.189 -23.174 0.952

T2 33.9 6.326 -0.212 0.442 0.029 0.068 0.010 0.459 -31.955 2.186

T3 34 6.165 -0.117 0.432 0.009 0.027 0.004 0.139 -23.006 0.810

Average 6.350 -0.154 0.425 0.017 0.042 0.006 0.262 -26.045 1.316

W1 23.45 8.321 1.871 0.501 0.013 0.055 0.007 0.150 2.937 1.345

W2 25.05 8.005 -1.100 0.478 0.026 0.116 0.010 0.325 -10.524 2.004

W3 26.15 7.689 0.236 0.507 0.012 0.051 0.005 0.150 21.771 1.081

Average 8.005 0.335 0.495 0.017 0.074 0.007 0.209 4.728 1.477

Cross1 27.4 7.397 -0.382 0.450 0.006 0.022 0.002 0.078 -5.844 0.474

Cross2 28.7 7.183 -0.182 0.453 0.013 0.051 0.005 0.182 -27.961 1.139

Cross3 29.8 6.981 -0.439 0.464 0.019 0.074 0.008 0.266 -16.908 1.633

Average 7.187 -0.334 0.456 0.012 0.049 0.005 0.176 -16.904 1.082

86

Table B.2 continued

Run #





R1 30.8 6.842 -0.266 0.947 0.025 0.076 0.016 0.366 -28.480 2.086

R2 31 6.767 -1.118 0.903 0.064 0.380 0.061 0.946 -33.961 6.748

R3 31.95 6.701 -1.065 1.033 0.059 0.427 0.075 0.881 -40.083 7.264

Average 6.770 -0.816 0.961 0.049 0.294 0.051 0.731 -34.175 5.366

T1 32.2 6.639 -1.687 0.812 0.078 0.414 0.052 1.174 -24.509 7.296

T2 33.55 6.521 0.023 0.883 0.101 0.495 0.068 1.552 2141.931 11.577

T3 33.2 6.352 -0.262 0.915 0.037 0.153 0.039 0.583 -58.510 4.240

Average 6.504 -0.642 0.870 0.072 0.354 0.053 1.103 686.304 7.704

W1 30.2 7.306 -3.367 0.998 0.068 0.589 0.089 0.929 -17.503 6.820

W2 33.4 6.369 -0.405 1.124 0.045 0.182 0.062 0.709 -44.940 5.100

W3 27.3 8.042 0.767 1.072 0.038 0.174 0.050 0.469 22.746 3.670

Average 7.239 -1.001 1.065 0.050 0.315 0.067 0.702 -13.232 5.197

Cross1 26.3 7.824 0.456 1.270 0.059 0.245 0.067 0.749 53.732 5.274

Cross2 25.8 7.971 -24.396 1.244 0.038 2.988 0.257 0.476 -12.248 6.054

Cross3 27.1 8.067 -1.191 1.366 0.046 0.213 0.048 0.575 -17.914 3.536

Average 7.954 -8.377 1.293 0.048 1.149 0.124 0.600 7.856 4.955

87


Run #





R1 28.1 7.655 -0.240 0.229 0.049 0.071 0.005 0.635 -29.637 2.347

R2 30.55 7.165 -0.179 0.288 0.013 0.032 0.002 0.180 -17.594 0.851

R3 29.4 7.339 -0.697 0.255 0.025 0.059 0.004 0.337 -8.444 1.451

Average 7.386 -0.372 0.257 0.029 0.054 0.004 0.384 -18.558 1.550

T1 28.7 7.055 -0.153 0.233 0.017 0.037 0.003 0.244 -24.456 1.116

T2 30.05 6.918 0.112 0.240 0.021 0.046 0.003 0.298 41.342 1.404

T3 30.3 7.242 0.305 0.270 0.013 0.026 0.002 0.180 8.670 0.811

Average 7.072 0.088 0.247 0.017 0.037 0.003 0.241 8.519 1.111

W1 31.6 6.498 -0.371 0.275 0.029 0.092 0.006 0.450 -24.783 2.366

W2 32.3 6.364 -0.673 0.278 0.035 0.111 0.008 0.545 -16.562 2.778

W3 32.85 6.270 -0.647 0.275 0.025 0.097 0.006 0.406 -15.061 2.316

Average 6.377 -0.564 0.276 0.030 0.100 0.007 0.467 -18.802 2.487

Cross1 33.4 6.138 -0.564 0.257 0.012 0.037 0.003 0.195 -6.601 0.987

Cross2 28.45 7.309 -0.637 0.208 0.080 0.212 0.011 1.089 -33.274 5.073

Cross3 29.8 7.037 -1.080 0.214 0.067 0.156 0.008 0.954 -14.480 3.878

Average 6.828 -0.761 0.226 0.053 0.135 0.007 0.746 -18.118 3.313

75 gpm/ft Flow Rate

R1 29.25 7.698 -0.808 0.440 0.122 0.157 0.022 1.588 -19.484 4.896

R2 26.75 7.645 -0.042 0.431 0.034 0.123 0.012 0.441 -291.964 2.693

R3 28 7.414 -1.191 0.450 0.030 0.126 0.011 0.409 -10.564 2.359

Average 7.586 -0.680 0.441 0.062 0.135 0.015 0.813 -107.337 3.316

T1 28.95 7.434 -1.421 0.427 0.070 0.195 0.017 0.946 -13.753 4.129

T2 29.95 7.099 -1.003 0.432 0.078 0.236 0.023 1.095 -23.537 5.253

T3 30.35 6.948 -0.934 0.468 0.031 0.121 0.013 0.447 -12.944 2.513

Average 7.160 -1.119 0.442 0.060 0.184 0.017 0.829 -16.744 3.965

W1 25.55 7.243 0.098 0.572 0.050 0.256 0.031 0.689 262.053 5.375

W2 28.6 7.713 -0.825 0.578 0.045 0.116 0.018 0.590 -14.054 2.629

W3 30.7 6.987 -1.135 0.558 0.072 0.361 0.038 1.037 -31.793 6.731

Average 7.314 -0.621 0.569 0.056 0.244 0.029 0.772 72.068 4.912

Cross1 31.4 6.788 -0.958 0.542 0.033 0.162 0.017 0.485 -16.904 3.182

Cross2 32.05 6.731 -1.009 0.470 0.062 0.258 0.025 0.921 -25.582 5.365

Cross3 32.65 6.597 -1.762 0.650 0.057 0.345 0.038 0.869 -19.563 5.913

Average 6.705 -1.243 0.554 0.051 0.255 0.027 0.758 -20.683 4.820

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Table B.3 continued

Run #





R1 28.6 7.415 -9.005 1.885 0.105 2.573 0.323 1.410 -28.578 15.512

R2 29.4 7.227 -7.923 1.744 0.097 2.316 0.312 1.343 -29.233 15.261

R3 30.8 7.028 -6.642 1.712 0.081 1.508 0.202 1.159 -22.700 11.811

Average 7.223 -7.856 1.780 0.094 2.132 0.279 1.304 -26.837 14.195

T1 24.55 8.442 -7.485 1.729 0.082 1.536 0.178 0.970 -20.521 10.291

T2 26.1 8.073 -8.059 1.982 0.069 1.574 0.196 0.855 -19.536 9.868

T3 27.55 7.733 -6.022 1.611 0.072 1.237 0.159 0.937 -20.532 9.840

Average 8.082 -7.189 1.774 0.074 1.449 0.177 0.921 -20.196 10.000

W1 26.2 7.506 -7.835 1.989 0.062 1.670 0.217 0.828 -21.312 10.918

W2 27.8 7.986 -1.357 1.736 0.043 0.268 0.069 0.541 -19.722 3.988

W3 26.3 8.304 -1.306 1.987 0.016 0.119 0.033 0.197 -9.118 1.643

Average 7.932 -3.499 1.904 0.041 0.686 0.106 0.522 -16.717 5.516

Cross1 28.15 7.861 -1.464 1.946 0.014 0.101 0.028 0.181 -6.893 1.446

Cross2 25.3 8.514 -2.472 1.971 0.069 0.497 0.119 0.811 -20.125 6.022

Cross3 25.8 8.335 -1.762 2.013 0.013 0.096 0.025 0.155 -5.423 1.249

Average 8.236 -1.899 1.977 0.032 0.231 0.057 0.382 -10.813 2.906

89

APPENDIX C

MINITAB ® OUTPUT

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————— 7/29/2007 9:45:28 PM ———————————————————— Worksheet size: 10000 cells. Welcome to Minitab, press F1 for help. ————— 7/29/2007 9:47:30 PM ———————————————————— Worksheet size: 10000 cells. Welcome to Minitab, press F1 for help. Retrieving project from file: 'C:\Program Files\MINITAB 14 Student\Studnt14\Evaluation of Low Profile Cascade Aerator (Truncated KLa).MPJ' ————— 7/29/2007 9:54:27 PM ———————————————————— Worksheet size: 10000 cells. Welcome to Minitab, press F1 for help. Retrieving project from file: 'C:\Program Files\MINITAB 14 Student\Studnt14\Evaluation of Low Profile Cascade Aerator (Truncated KLa).MPJ' Main Effects Plot (data means) for KLa Interaction Plot (data means) for KLa ————— 7/29/2007 10:37:51 PM ———————————————————— Worksheet size: 10000 cells. Welcome to Minitab, press F1 for help. Retrieving project from file: 'C:\Program Files\MINITAB 14 Student\Studnt14\Evaluation of Low Profile Cascade Aerator (Truncated KLa).MPJ' ANOVA: KLa versus Slope, Flowrates, Weir Geo. Factor Type Levels Values Slope fixed 3 2.5, 4.5, 6.5 Flowrates fixed 3 25, 50, 75 Weir Geo. fixed 4 Cross, Rec., T, W Analysis of Variance for KLa Source DF SS MS F P Slope 2 3.28413 1.64206 438.31 0.000 Flowrates 2 21.65431 10.82716 2890.08 0.000 Weir Geo. 3 0.50481 0.16827 44.92 0.000 Slope*Flowrates 4 4.27262 1.06816 285.12 0.000 Slope*Weir Geo. 6 0.12674 0.02112 5.64 0.000

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Flowrates*Weir Geo. 6 0.65582 0.10930 29.18 0.000 Slope*Flowrates*Weir Geo. 12 0.35454 0.02954 7.89 0.000 Error 72 0.26973 0.00375 Total 107 31.12270 S = 0.0612071 R-Sq = 99.13% R-Sq(adj) = 98.71% Results for: Worksheet 2 One-way ANOVA: KLa versus Slope Source DF SS MS F P Slope 2 3.284 1.642 6.19 0.003 Error 105 27.839 0.265 Total 107 31.123 S = 0.5149 R-Sq = 10.55% R-Sq(adj) = 8.85% Individual 95% CIs For Mean Based on Pooled StDev Level N Mean StDev -----+---------+---------+---------+---- 2.5 36 0.4724 0.3393 (--------*-------) 4.5 36 0.5814 0.3593 (-------*--------) 6.5 36 0.8846 0.7424 (-------*--------) -----+---------+---------+---------+---- 0.40 0.60 0.80 1.00 Pooled StDev = 0.5149 Results for: Worksheet 3 One-way ANOVA: KLa versus Flowrates Source DF SS MS F P Flowrates 2 21.6543 10.8272 120.07 0.000 Error 105 9.4684 0.0902 Total 107 31.1227 S = 0.3003 R-Sq = 69.58% R-Sq(adj) = 69.00% Individual 95% CIs For Mean Based on Pooled StDev Level N Mean StDev ------+---------+---------+---------+--- 25 36 0.2315 0.0397 (--*-) 50 36 0.4389 0.0767 (--*-) 75 36 1.2679 0.5129 (--*--) ------+---------+---------+---------+--- 0.35 0.70 1.05 1.40 Pooled StDev = 0.3003 Results for: Worksheet 4

92

One-way ANOVA: KLa versus Weir Geo. Source DF SS MS F P Weir Geo. 3 0.505 0.168 0.57 0.635 Error 104 30.618 0.294 Total 107 31.123 S = 0.5426 R-Sq = 1.62% R-Sq(adj) = 0.00% Individual 95% CIs For Mean Based on Pooled StDev Level N Mean StDev ------+---------+---------+---------+--- Cross 27 0.7447 0.6178 (-------------*------------) Rec. 27 0.5954 0.5435 (-------------*-------------) T 27 0.5709 0.4833 (-------------*-------------) W 27 0.6735 0.5166 (-------------*-------------) ------+---------+---------+---------+--- 0.45 0.60 0.75 0.90 Pooled StDev = 0.5426 Results for: Worksheet 5 Two-way ANOVA: KLa versus Slope, Flowrates Source DF SS MS F P Slope 2 3.2841 1.6421 85.04 0.000 Flowrates 2 21.6543 10.8272 560.72 0.000 Interaction 4 4.2726 1.0682 55.32 0.000 Error 99 1.9116 0.0193 Total 107 31.1227 S = 0.1390 R-Sq = 93.86% R-Sq(adj) = 93.36% ————— 7/29/2007 11:16:40 PM ———————————————————— Worksheet size: 10000 cells. Welcome to Minitab, press F1 for help. Results for: Worksheet 2 Two-way ANOVA: KLa versus Slope, Weir Geo. Source DF SS MS F P Slope 2 3.2841 1.64206 5.79 0.004 Weir Geo. 3 0.5048 0.16827 0.59 0.621 Interaction 6 0.1267 0.02112 0.07 0.998 Error 96 27.2070 0.28341 Total 107 31.1227 S = 0.5324 R-Sq = 12.58% R-Sq(adj) = 2.56% Results for: Worksheet 3

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Two-way ANOVA: KLa versus Flowrates, Weir Geo. Source DF SS MS F P Flowrates 2 21.6543 10.8272 125.11 0.000 Weir Geo. 3 0.5048 0.1683 1.94 0.128 Interaction 6 0.6558 0.1093 1.26 0.282 Error 96 8.3078 0.0865 Total 107 31.1227 S = 0.2942 R-Sq = 73.31% R-Sq(adj) = 70.25%

————— 8/6/2007 9:38:12 AM ———————————————————— Worksheet size: 10000 cells. Welcome to Minitab, press F1 for help. ————— 8/6/2007 9:44:05 AM ———————————————————— Worksheet size: 10000 cells. Welcome to Minitab, press F1 for help. Retrieving project from file: 'C:\Program Files\MINITAB 14 Student\Studnt14\Evaluation of Low Profile Cascade Aerator (Individual Weir).MPJ' Results for: Worksheet 5 (Crs.) Two-way ANOVA: KLa versus Slope, Flowrates Source DF SS MS F P Slope 2 0.41501 0.20751 107.21 0.000 Flowrates 2 8.98904 4.49452 2322.03 0.000 Interaction 4 0.48521 0.12130 85.13 0.000 Error 18 0.03484 0.00194 Total 26 9.92411 S = 0.04400 R-Sq = 99.65% R-Sq(adj) = 99.49% Results for: Worksheet 4 Two-way ANOVA: KLa versus Slope, Flowrates (W) Source DF SS MS F P Slope 2 0.87927 0.43964 148.71 0.000 Flowrates 2 4.88190 2.44095 825.69 0.000 Interaction 4 1.12527 0.28132 95.16 0.000 Error 18 0.05321 0.00296 Total 26 6.93965

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S = 0.05437 R-Sq = 99.23% R-Sq(adj) = 98.89% Results for: Worksheet 2 Two-way ANOVA: KLa versus Slope, Flowrates (Rec) Source DF SS MS F P Slope 2 1.21177 0.60589 111.28 0.000 Flowrates 2 4.69063 2.34532 430.77 0.000 Interaction 4 1.67997 0.41999 77.14 0.000 Error 18 0.09800 0.00544 Total 26 7.68037 S = 0.07379 R-Sq = 98.72% R-Sq(adj) = 98.16% Individual 95% CIs For Mean Based on Pooled StDev Slope Mean +---------+---------+---------+--------- 2.5 0.375701 (--*---) 4.5 0.528950 (--*--) 6.5 0.881683 (--*--) +---------+---------+---------+--------- 0.32 0.48 0.64 0.80 Individual 95% CIs For Mean Based on Pooled StDev Flowrates Mean -----+---------+---------+---------+---- 37.5 0.21166 (-*-) 75.0 0.39988 (*-) 112.5 1.17479 (-*-) -----+---------+---------+---------+---- 0.30 0.60 0.90 1.20 Results for: Worksheet 3 Two-way ANOVA: KLa versus Slope, Flowrates (T) Source DF SS MS F P Slope 2 0.90481 0.45240 97.31 0.000 Flowrates 2 3.74855 1.87428 403.16 0.000 Interaction 4 1.33671 0.33418 71.88 0.000 Error 18 0.08368 0.00465 Total 26 6.07376 S = 0.06818 R-Sq = 98.62% R-Sq(adj) = 98.01% Individual 95% CIs For Mean Based on Pooled StDev Slope Mean -------+---------+---------+---------+-- 2.5 0.388274 (--*--)

95

4.5 0.503220 (---*--) 6.5 0.821103 (--*--) -------+---------+---------+---------+-- 0.45 0.60 0.75 0.90 Individual 95% CIs For Mean Based on Pooled StDev Flowrates Mean ---+---------+---------+---------+------ 37.5 0.21892 (-*-) 75.0 0.40720 (-*-) 112.5 1.08648 (*-) ---+---------+---------+---------+------ 0.25 0.50 0.75 1.00

96

1.41.21.00.80.60.40.2

Median

Mean

0.600.550.500.450.400.350.30

A nderson-Darling Normality Test

V ariance 0.11510Skewness 1.64491Kurtosis 2.32912N 36

Minimum 0.17102

A -Squared

1st Q uartile 0.20245Median 0.359233rd Q uartile 0.61707Maximum 1.42594

95% C onfidence Interv al for Mean

0.35761

2.42

0.58719

95% C onfidence Interv al for Median

0.28952 0.48204

95% C onfidence Interv al for StDev

0.27517 0.44255

P-V alue < 0.005

Mean 0.47240StDev 0.33927

95% Confidence Intervals

Figure C1 Summary of KLa Values for Slope 2.50

97

1.20.90.60.3

Median

Mean

0.700.650.600.550.500.450.40


V ariance 0.12911Skewness 0.782488Kurtosis -0.763302N 36

Minimum 0.18507

A -Squared



0.45981

2.00

0.70296


0.37775 0.58755


0.29144 0.46871

P-V alue < 0.005

Mean 0.58138StDev 0.35932



98

2.01.51.00.5

Median

Mean

1.21.00.80.60.4


V ariance 0.55117Skewness 0.70850Kurtosis -1.42012N 36

Minimum 0.20815

A -Squared



0.63337

4.09

1.13576


0.38992 0.90452


0.60215 0.96843

P-V alue < 0.005

Mean 0.88457StDev 0.74241



Evaluation of a low profile cascade aerator

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