computational modelling of large aerated lagoon hydraulics

8
Available at www.sciencedirect.com journal homepage: www.elsevier.com/locate/watres Computational modelling of large aerated lagoon hydraulics Konstantin Pougatch a , Martha Salcudean a, , Ian Gartshore a , Philip Pagoria b a Department of Mechanical Engineering, University of British Columbia, 2054-6050 Applied Science Lane, Vancouver, BC, Canada V6T 1Z4 b Environment, Health and Safety, Weyerhaeuser Company, 32901 Weyerhaeuser Way South, Federal Way, WA 98003, USA article info Article history: Received 29 July 2006 Received in revised form 7 February 2007 Accepted 12 February 2007 Available online 6 April 2007 Keywords: Aerated lagoons Surface aerators Computational fluid dynamics (CFD) Residence time distribution (RTD) abstract A good understanding of the hydraulic performance of aerated lagoons is required for their design and operation. A comprehensive numerical procedure has been developed for the three-dimensional computational modelling of the flow in large lagoons including high- speed floating mechanical surface aerators. This paper describes the procedure that consists of separate aerator modelling, then applying the obtained results as boundary data for a full lagoon model. A model application to an industrial aerated lagoon serves as an example of flow analysis. Post processing of the results by calculating the local average residence time (age of fluid) provides a powerful and intuitive technique to visualize and analyse the lagoon performance. The model has been verified by comparing the local average residence time predictions with measurements from a dye study. It is shown that the numerical modelling proposed is feasible and constitutes an effective new tool in improving the performance and design of industrial lagoons. & 2007 Elsevier Ltd. All rights reserved. 1. Introduction Very large aerated lagoons are commonly used in the pulp and paper industry for biological wastewater treatment. Atmospheric oxygen transferred at the water surface is not sufficient for the aerobic bacterial process and has to be supplemented by mechanical aeration. Mixing is necessary to maintain partial suspension of bacterial solids and ensure adequate contact with organic pollutants. Floating mechan- ical surface aerators provide simultaneously both mixing and oxygenation. Aerators are strategically placed to ensure a partially mixed flow regime that supports both biological reactions and staged solids settling. To improve lagoon performance a greater understanding of flow patterns is required. There are limited quantitative and qualitative means to characterize the mixing process in an aerated lagoon. A common procedure is to inject a tracer into the lagoon inlet, and by measuring its outlet concentration, obtain a residence time distribution (RTD) curve. The procedure is thoroughly described by NCASI (1983). The RTD curves can be analysed as functions or by central tendencies parameters, such as the mean, median, and peak residence time. These central tendencies can be compared with the theoretical residence time that equals the liquid volume of the lagoon divided by the flow rate. In addition to measuring the outlet tracer concentration, the measurements are sometimes done throughout the lagoon (NCASI, 1983; Schu- macher and Pagoria, 1997) in order to obtain the distribution of the tracer in the system, or the age distribution function. Tracer studies are labour intensive, expensive and do not permit predictive capabilities for engineering analysis of alternatives. Modelling could be utilized to understand the impact of aerator and baffle placement on lagoon perfor- mance. A complete model has to include computation of the fluid flow (hydraulic) coupled with biological reaction me- chanisms. However, based on the premise that biological ARTICLE IN PRESS 0043-1354/$ - see front matter & 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.watres.2007.02.019 Corresponding author. Tel.: +1 604 822 2732; fax: +1 604 822 2403. E-mail address: [email protected] (M. Salcudean). WATER RESEARCH 41 (2007) 2109– 2116

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Page 1: Computational modelling of large aerated lagoon hydraulics

ARTICLE IN PRESS

Available at www.sciencedirect.com

WAT E R R E S E A R C H 4 1 ( 2 0 0 7 ) 2 1 0 9 – 2 1 1 6

0043-1354/$ - see frodoi:10.1016/j.watres

�Corresponding auE-mail address:

journal homepage: www.elsevier.com/locate/watres

Computational modelling of large aerated lagoonhydraulics

Konstantin Pougatcha, Martha Salcudeana,�, Ian Gartshorea, Philip Pagoriab

aDepartment of Mechanical Engineering, University of British Columbia, 2054-6050 Applied Science Lane, Vancouver, BC, Canada V6T 1Z4bEnvironment, Health and Safety, Weyerhaeuser Company, 32901 Weyerhaeuser Way South, Federal Way, WA 98003, USA

a r t i c l e i n f o

Article history:

Received 29 July 2006

Received in revised form

7 February 2007

Accepted 12 February 2007

Available online 6 April 2007

Keywords:

Aerated lagoons

Surface aerators

Computational fluid dynamics (CFD)

Residence time distribution (RTD)

nt matter & 2007 Elsevie.2007.02.019

thor. Tel.: +1 604 822 2732;[email protected] (M. Sa

a b s t r a c t

A good understanding of the hydraulic performance of aerated lagoons is required for their

design and operation. A comprehensive numerical procedure has been developed for the

three-dimensional computational modelling of the flow in large lagoons including high-

speed floating mechanical surface aerators. This paper describes the procedure that

consists of separate aerator modelling, then applying the obtained results as boundary data

for a full lagoon model. A model application to an industrial aerated lagoon serves as an

example of flow analysis. Post processing of the results by calculating the local average

residence time (age of fluid) provides a powerful and intuitive technique to visualize and

analyse the lagoon performance. The model has been verified by comparing the local

average residence time predictions with measurements from a dye study. It is shown that

the numerical modelling proposed is feasible and constitutes an effective new tool in

improving the performance and design of industrial lagoons.

& 2007 Elsevier Ltd. All rights reserved.

1. Introduction

Very large aerated lagoons are commonly used in the pulp

and paper industry for biological wastewater treatment.

Atmospheric oxygen transferred at the water surface is not

sufficient for the aerobic bacterial process and has to be

supplemented by mechanical aeration. Mixing is necessary to

maintain partial suspension of bacterial solids and ensure

adequate contact with organic pollutants. Floating mechan-

ical surface aerators provide simultaneously both mixing and

oxygenation. Aerators are strategically placed to ensure a

partially mixed flow regime that supports both biological

reactions and staged solids settling. To improve lagoon

performance a greater understanding of flow patterns is

required. There are limited quantitative and qualitative

means to characterize the mixing process in an aerated

lagoon. A common procedure is to inject a tracer into the

lagoon inlet, and by measuring its outlet concentration,

r Ltd. All rights reserved.

fax: +1 604 822 2403.lcudean).

obtain a residence time distribution (RTD) curve. The

procedure is thoroughly described by NCASI (1983). The RTD

curves can be analysed as functions or by central tendencies

parameters, such as the mean, median, and peak residence

time. These central tendencies can be compared with the

theoretical residence time that equals the liquid volume of

the lagoon divided by the flow rate. In addition to measuring

the outlet tracer concentration, the measurements are

sometimes done throughout the lagoon (NCASI, 1983; Schu-

macher and Pagoria, 1997) in order to obtain the distribution

of the tracer in the system, or the age distribution function.

Tracer studies are labour intensive, expensive and do not

permit predictive capabilities for engineering analysis of

alternatives. Modelling could be utilized to understand the

impact of aerator and baffle placement on lagoon perfor-

mance. A complete model has to include computation of the

fluid flow (hydraulic) coupled with biological reaction me-

chanisms. However, based on the premise that biological

Page 2: Computational modelling of large aerated lagoon hydraulics

ARTICLE IN PRESS

Nomenclature

A age distribution function, s�1

C tracer concentration, kg m�3

Deff effective diffusivity (molecular+turbulent), m2 s�1

~r position vector, m

t time, s

U spray velocity, m s�1

~U water velocity (at the surface), m s�1

~V water velocity, m s�1

Greek symbols

e water volume fraction in a spray

y relative residence time

r density, kg m�3

t local average residence time, s

Subscripts

ex exit of the lagoon

n normal component

r radial component

w water

WAT E R R E S E A R C H 4 1 ( 2 0 0 7 ) 2 1 0 9 – 2 1 1 62110

processes have minimal impact on the fluid flow, these two

aspects of the lagoon operation usually are studied separately.

The initial models that connected lagoon geometry and the

number of aerators with the residence times and/or pollutant

removal were mostly algebraic. Most of them started with a

one-dimensional concentration transport equation (Murphy

and Wilson, 1974; Ferrara and Harleman, 1981). Depending on

the value of the diffusion coefficient, the model becomes a

plug flow model (the coefficient is zero), completely mixed

model (the coefficient is infinity), or an axial dispersion model

(finite non-zero value of the coefficient). Most of the

researchers followed Danckwerts (1953) in describing partial

mixing with a dispersion number, which is the inverse of the

Peclet number. A dispersion model proposed by Polprasert

and Bhattarai (1985) connected the pond’s length, depth,

width, and the flow rate with the dispersion number.

Agunwamba (1992) suggested a slightly different expression

for the dispersion number by using physical modelling and

connecting the model lagoon with the real one through some

dimensionless expressions. Length-to-width ratios were stu-

died by Arceivala (1983) who put forward optimal values by

studying empirical data. Dorego and Leduc (1996) evaluated

Polprasert and Bhattarai (1985) and Arceivala (1983) models by

applying them to the tracer study. A number of researchers

have done comparative studies on various hydraulic models.

Nameche and Vasel (1998) evaluated the models described

above plus a few other models by comparing them with a

number of tracer study results. They found that in most of the

cases the simple approaches produce the same results as

more complicated models.

Computational fluid dynamics (CFD) methods that involve

solving a full set of flow equations have been introduced to

lagoon modelling by Wood et al. (1995). They investigated the

influence of baffle placement in a hypothetical rectangular

pond. Even though they assumed flow uniformity in the

vertical direction (two-dimensionality of the problem) and

modelled an aerator as an arbitrary radial acceleration

around the circle, their work showed benefits that can be

obtained by applying numerical methods into the lagoon

analysis. Ta and Brignal (1998) applied a computational model

to an industrial reservoir. They calculated various inlet, outlet

and baffle arrangements and compared the RTD curves for

each case. It has to be noted that even though the geometry

they studied was three-dimensional, their lagoon configura-

tion did not have aerators. Another application of numerical

modelling to the non-aerated lagoon was presented by Baleo

et al. (2001). They introduced a post processing procedure that

allows determining the local age distribution function.

Peterson et al. (2000) used numerical modelling to assess

sedimentation quality in an aquaculture pond. The pond was

aerated by paddlewheels and propeller aspirators which were

modelled as a body force added to the momentum equation.

In their following work (Peterson et al., 2001) the researchers

applied CFD model to optimize the aerator placement. More

recent study done by Kretser et al. (2002) shows an application

of a CFD modelling approach to the simulation of an aerated

lagoon used to treat wastewater from a pulp and paper mill.

Unfortunately, their paper provides limited information about

the assumptions involved with the aerator modelling.

Despite the limitations of the referenced works it has

become clear that the application of the numerical methods

into lagoon analysis has great potential to improve and

optimize lagoon design by studying the velocity field in detail,

including investigation of possible back flow, short circuiting,

and dead zones.

The objective of this work is to establish a comprehensive

numerical model that accounts for the flow in and around

aerators and their effect on lagoon performance in order to

fully understand the resulting flow patterns. The method

accounts for both mass and momentum transfer resulting

from the action of aerators, because mass transfer plays a

significant role in high-speed floating mechanical surface

aerators and, therefore, cannot be ignored, as done in

previous work. In addition, the computational procedure

has to be feasible for very large-scale industrial lagoons, with

a significant number of aerators. These lagoons have surface

areas an order of magnitude larger than those previously

investigated.

2. Model description

2.1. Modelling approach

A hydraulic model can provide important knowledge for the

design of mechanically aerated lagoons and can also serve as

a base for further studies. Knowing the velocity and turbu-

lence field, residence time information can be obtained and

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WAT E R R E S E A R C H 41 (2007) 2109– 2116 2111

analysed. Moreover, the hydraulic model can be the basis for a

comprehensive lagoon model that includes complex biologi-

cal processes.

First of all, the model has to reflect three-dimensionality of

the velocity field in the lagoon. As aerators are the dominant

factor impacting the flow field, special care has to be taken to

simulate them correctly. The flow through an aerator is fairly

complex and multiphase involving liquid sprayed in the air.

Furthermore, there are typically multiple aerators throughout

a lagoon. To make the solution practical we propose to

decouple the aerator flow from the lagoon flow. This means

that an aerator is modelled separately and the modelling

results applied as boundary conditions in the lagoon model.

Also, it is reasonable to assume that each aerator of the same

type and size can be represented with similar boundary

conditions. As the difference in the water level at the

entrance and at the exit is relatively small, the model does

not include hydrostatic forces: the flow is driven by the

pressure gradients developing from the assigned inlet mass

flow rate. Finally, in order to avoid a computationally

expensive free surface modelling, a smooth frictionless

surface at the top of the lagoon is assumed (rigid lid

assumption).

2.2. Aerator model

A surface aerator is schematically shown in Fig. 1. The

impeller pushes the liquid upwards through the intake cone

and draft tube. After hitting a deflector plate, the liquid

atomizes and acquires a radial momentum. The water

Impeller

Flotationring

plate

Intakecone

Motor shaft

Drafttube

Water spray

Fig. 1 – Aerator schematic.

Fig. 2 – Water volume fraction

droplets then fly outwards before landing on the water

surface. The whole assembly is kept afloat by a flotation ring.

The approach to the aerator simulation is dictated by the

requirements of its implementation in the lagoon model. It is

necessary to obtain a correct mass and momentum transfer

from the aerator to the lagoon. The droplet size distribution,

interactions between sprays and the water surface, and other

small-scale details are of a lesser importance for a large-scale

flow in the lagoon. With these reasons in mind, the Eulerian

multiphase method was chosen to model the aerator flow. It

assumes that the two phases (air and water) are interpene-

trating and the separate mass and momentum conservation

equations are solved for each phase. The turbulence is limited

to the air phase with no influence from the droplets. Water

droplets are assumed to be spheres with a constant diameter

of 1 mm. To assess the solution dependency on the droplet

diameter, additional cases with a range of diameters from 0.5

to 5 mm were calculated and the results proved to be similar.

It is necessary to note that the atomization is a very complex

process and cannot be modelled accurately with this

approach; however, the method truthfully represents the

resulting momentum transfer to the lagoon.

A computer code solving the Eulerian set of equations in

curvilinear coordinates was developed at UBC (Pougatch et al.,

2005) based on Spalding (1980) IPSA procedure. Aqua-Aero-

bics’ 75 hp (55.9 kW) ‘‘Aqua-Jet’’ floating high-speed mechan-

ical surface aerators were chosen for modelling, as this is the

aerator used in the example industrial application. As the

aerator flow is axisymmetric, the model can be reduced to

two-dimensions. At the bottom of the draft tube, a known

water mass flow rate of 1.26 kg s�1 was imposed; the

secondary phase (air), which appears after the impeller due

to cavitation and the air entrainment, is assumed to have the

same velocity as the primary phase (water). The secondary

phase volume fraction is assumed to be 10% (it has been

observed that the influence of this parameter on the

momentum transfer to the lagoon is minimal).

The contours of the liquid volume fraction presented in Fig.

2 show the water flowing vertically in the draft tube, then

hitting the deflector plate, and being sprayed in a radial

pattern. The graph of the water volume fraction (Fig. 3) at the

surface illustrates the splashing pattern. The maximum

contours (dimensionless).

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WAT E R R E S E A R C H 4 1 ( 2 0 0 7 ) 2 1 0 9 – 2 1 1 62112

diameter of the simulated spray pattern (6.4 m) is lower than

the one provided by the manufacturer (9.1 m). This difference

is to be expected as the simulation does not account for the

droplet break-up and formation of secondary droplets.

2.3. Application of an aerator model to a small pond

In order to investigate the aerator sub-model application to

aerated lagoon modelling, a simple case of a round pond, 50 m

in diameter and 4 m in depth with a single aerator placed in

the centre was considered for modelling (Fig. 4). Reynolds

averaged Navier–Stokes equations are solved in a computa-

Fig. 3 – Water volume fraction along the surface.

R = 25m

H = 4m

Intake cone

Draft tube

Flotation ringWater

Water surface

Fig. 4 – Test pond schematic diagram.

Fig. 5 – Velocity vectors in a test pond. Shade indicates the ar

(mixing area).

tional domain together with the k-epsilon turbulence model.

The computer code used for these computations has also

been developed at UBC (Nowak and Salcudean, 1996). The

boundary conditions for this model take into account the

results of the aerator simulations. The only aerator compo-

nents that are explicitly included are the intake cone and the

draft tube, which are needed to provide a realistic outflow

condition from the pond into an aerator. The surface area

where the aerator spray lands corresponds to the inlet

condition or the splash zone for the pond model. It is a

ring-shaped surface extending from the outside edge of the

flotation ring to the farthermost point reached by the spray.

The normal velocity at the splashing zone can be easily

defined from mass conservation:

�wrw~Un ¼ rw

~~Un. (1)

The radial velocity can be determined from conservation of

the total momentum assuming that the entire momentum of

the droplets is transferred to the water.

�wrw~Un

~Un þ ~Ur

� �¼ rw

~~Un~~Un þ

~~Ur

� �. (2)

Such definitions ensure full conservation of mass and

momentum along the splash zone aerator boundary. Even

though the droplets have some tangential velocity due to a

rotational action of the impeller, this velocity is small

compared with the radial and the normal components and

it is neglected in the current model application. The point

values are calculated from the profiles of velocities and

volume fractions obtained from the aerator model. The

remaining portion of the top boundary representing the free

surface has a free slip condition. In order to analyse the

modelling results velocity vectors in the pond are plotted (Fig.

5). A strong recirculation area is formed around the aerator.

The diameter of the recirculation zone, defined as the area

where the average velocity value is higher than 0.01 m s�1,

equals 36 m and is in good agreement with the mixing zone

diameter �39.6 m—provided by the aerator manufacturer. In

addition to the case where the splash zone boundary is

defined with the use of the velocity profiles, another calcula-

tion was made that uses the average values of velocities

applied to a ring with the outer radius equalling 3 m in a way

that ensures the same total mass and momentum flow rates.

ea where the velocity magnitude is greater than 0.01 m s�1

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Fig. 6 – Radial velocity at the top of the pond for profile and

averaged spray boundary.

W = 315 m

L = 315.6 m

Fig. 7 – Lagoon schematic with aerator locations. An arrow

shows a called North location.

WAT E R R E S E A R C H 41 (2007) 2109– 2116 2113

The difference between the results for the two cases is limited

to a small area near the aerator centre; at the distances

greater than 4 m from the axis, the two solutions are

practically indistinguishable (Fig. 6). The recirculation zone

diameter for this case remains the same as for the previous

one. It is interesting to note that for other cases with averaged

boundary conditions calculated with different values of the

splash radius (R ¼ 2 and 5 m), the recirculation area diameter

still does not change much, whilst there are noticeable

variations in the velocity distribution near the boundary. In

further modelling a uniform boundary with a 3 m splashing

radius is used, assuming that the flow near the aerator axis

has little effect on the general flow pattern in the lagoon.

3. Analysis of the lagoon flow

3.1. Lagoon description and computational procedure

The described approach has been applied to a first cell of a 2-

cell aerated lagoon located at the Weyerhaeuser pulp mill in

Grande Prairie, Alberta. The first cell geometry together with

the aerator placement is schematically shown in Fig. 7. The

cell is almost square in shape with sides of 315.6 and 315.0 m,

respectively. The wastewater inlet is located near the upper

left corner and the effluent exit is at the right through the

midpoint channel. The cell has slanted walls all around and

its depth is 2.85 m, taking into account that 40% of the design

volume is lost to uniform sludge deposition. The cell contains

nineteen aerators, 55.9 kW each. The average influent waste-

water flow rate is 58,059 m3 day�1 that provides a theoretical

residence time for this cell of 4.88 days. A three-dimensional

structured curvilinear grid that contains about 1.6 million

computational cells arranged in 54 segments has been

developed to represent the lagoon geometry. It is highly

non-uniform: the grid is refined near the aerators to

accurately resolve the flow where the velocity gradients are

high and relatively coarse, far enough from the aerators to

keep the computational cost within practical limits. As a

result, the volume of the computational cell varies from

3�10�3 to 1.7 m3. The aerator boundary conditions are the

same as described for the small pond case. As all of the

aerators are the same, the aerator boundaries are also the

same throughout the lagoon. At the lagoon inlet the known

wastewater mass flow rate is imposed. After some prelimin-

ary studies that found the buoyancy is much less than the

forced convection due to a negligible surface to bottom

temperature gradient, the buoyancy force is ignored in the

computations. The presence of large differences of scales in

the velocity field (the velocity magnitude near the aerator is

about 1 m s�1 and far from it is about 1 mm s�1) makes the

convergence very slow and, therefore, needs extensive under-

relaxation of flow parameters. It takes about 10 days of

computational time on a PC with PIII at 1.2 GHz to obtain a

converged solution.

3.2. Lagoon characterization

The numerical solution provides us with the knowledge of the

pressure and the velocity field, as well as the turbulence

parameters in the entire lagoon. However, for better under-

standing and characterisation of the lagoon performance

some post processing is required. It has been customary in

industry to characterise the lagoon with an exit RTD curve.

However, such an approach treats the lagoon essentially as a

black box, because the RTD curve does not provide informa-

tion about the local features of the flow necessary for

improvements and optimizations. We believe that the best

lagoon characterization can be achieved with the description

of the local residence times. In addition, such a description is

also more suitable for the numerical modelling.

3.3. Mean average residence time calculation and modelvalidation

It was chosen to solve an additional differential equation for

the mean average residence time that was obtained by

Sandberg (1981) and used by Baleo and Le Cloirec (2000) for

a non-aerated lagoon. This technique has its roots from the

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WAT E R R E S E A R C H 4 1 ( 2 0 0 7 ) 2 1 0 9 – 2 1 1 62114

tracer experiments when a pulse of dye is injected at the inlet.

The age distribution function is defined as

Að~r; tÞ ¼Cð~r; tÞR1

0 Cð~r; tÞdt. (3)

It shows the normalized tracer concentration at any point

and at any time. The local average residence time can be

obtained by multiplication by time and integration of the age

distribution function:

t ¼Z 1

0Að~r; tÞt dt ¼

R10 Cð~r; tÞt dtR10 Cð~r; tÞdt

. (4)

The propagation of tracer in the lagoon is governed by a

concentration transport equation:

qCqtþr ~VC

� �¼ rðDeffrCÞ. (5)

It can be multiplied by time (t) and integrated from zero to

infinity. After a few transformations one can obtain the

equation for the local residence time:

r ~Vt� �

¼ rðDeffrtÞ þ 1. (6)

Boundary conditions for this equation can be obtained from

boundary conditions of a concentration transport equation by

a similar multiplication-integration operation. Zero value of

the residence time at the inlet, zero flux through the walls

and free surface, and zero gradient at the exit complete the

problem description. Flow parameters, such as pressure,

velocity and turbulence are obtained from the flow solution

and assumed constant during the solution of the local

residence time equation. It is also assumed that the flow

inside an aerator is well mixed as it goes up through the

impeller, resulting in the uniform distribution of concentra-

tion throughout the top aerator boundary.

The first test to confirm the validity of the model is to

ensure the computational results are consistent with the

established analytical relationships. The mean average resi-

dence time at the exit, obtained by averaging across the cross-

section, should equal the theoretical residence time for

steady incompressible flows (Spalding, 1958). Our modelling

results show the exit value of 5.08 days, this is within 4% error

margin of the theoretical value of 4.88 days. In order to further

verify the model performance, we compare the predicted

values of the local average residence time at the corners of

the lagoon (except one corner near the inlet, where the value

Table 1 – Comparison of measured and predicted valuesof local average residence time at three corner points

Measuredtime, days

Calculatedtime, days

Difference,%

SW

corner

4.72 4.93 +4.4

NE

corner

5.54 5.28 �4.7

SE

corner

5.25 5.13 �2.3

Directions are as noted in Fig. 7.

is almost zero) and the measured ones obtained by Schuma-

cher and Pagoria (1997). The comparison presented in Table 1

confirms the model capability to represent the actual lagoon

conditions; the simulation results are within 5% of the

experimentally measured values. Considering the complexity

of the problem, the experimental uncertainties, and a number

of simplifications, such as an assumption of the flat sludge

bottom profile and an isolation of the first cell of the lagoon,

the agreement is remarkably good and indicates the robust-

ness of the model.

3.4. Flow analysis and discussion

For further analysis we plot the contours of the relative local

residence time, which is defined as the local residence time

divided by its value at the exit of the lagoon (Fig. 8).

y ¼ttex

. (7)

If the lagoon was operated as an ideal mix reactor, the value

of the relative local average residence time (age of fluid)

would be unity throughout the domain. However, we can see

an area at the left and the lower side of the plot where the

liquid spends less time than average. This area can be

interpreted as the counter-clockwise bypass flow from the

entrance to the exit. In order to improve mixing there the

addition of some aerators would be beneficial. On the other

hand, the relative residence time is more than unity in an

area in the upper right part of the cell. It is likely that there is

more internal recirculation and less interchange with the

surrounding areas. Some changes in the aerator positioning

may be beneficial to promote flow in this area. Another

means to quantify lagoon mixing performance, is to plot the

graph showing the distribution of the lagoon volume (normal-

ized) that falls within certain intervals of the local average

residence times (Fig. 9). The dispersion value of this distribu-

tion characterizes the deviation of the lagoon from the ideally

mixed reactor, for which the dispersion equals zero.

It is evident that the flow information provided by the

numerical model not only helps uncover the undesirable flow

patterns in the lagoon, it is also points to potential reasons

why they appear, thus paving the way for improvements. The

numerical model can be used during the lagoon design stage

as well as during its operation to optimize aerator placement.

The computational modelling opens a black box, the aerated

lagoons or other complex engineering systems used to be, by

allowing the analyst to look inside it. The discovered flow

patterns are often not obvious, because they depend on an

interaction of a variety of factors, such as lagoon geometry,

aerator placements, and inlet and outlet locations. Even

though there are analytical and one-dimensional models that

can predict exit RTD, the engineers still have to rely on their

intuition to guess what causes the undesirable lagoon

behaviour. The industry standard dye propagation experi-

ments also have only an exit RTD curve as a result most of the

time. Measuring the dye concentration throughout the lagoon

during a long time interval, necessary to obtain the local age

of fluid, is very costly and rarely done. When it is done the

number of measurement points is limited and some flow

features may be lost. This is not to say that the dye

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Fig. 8 – Relative local average residence time contours (dimensionless). Aerator locations are shown with dots in the plot.

Fig. 9 – Distribution of relative local average residence time

throughout the lagoon.

WAT E R R E S E A R C H 41 (2007) 2109– 2116 2115

experiments or the analytical models become obsolete. On

the contrary, they all may grow to be the parts of an integral

method of the lagoon design and optimization. Dye tracer

studies can provide the CFD model with data for its

verification or tuning, which might be necessary. The

analytical model can use the computational results to make

the understanding of the flow easier and provide quick

evaluations of some proposed modifications.

Further, numerical model simplifications involving the

neglect of the recirculatory flow around an aerator is not a

viable option. Suffice it to say that the lagoon inlet flow rate is

about one half of a single aerator flow. Moreover, what is more

important is that the amount of wastewater that recirculates

in the mixing zone surrounding an aerator is about ten times

more than the flow going through the aerator itself. Clearly,

the lagoon flow would be very different without the aerators

and there is no practical value in trying to resolve it.

Application of the current model to other industrial aerated

lagoons with high-speed mechanical surface aeration re-

quires only an accurate description of lagoon geometry and

aerator placement.

4. Conclusions

The velocity field in an aerated lagoon is determined by

geometry of the liquid volume, inlet and exit locations, and

most of all, by aerators. The proposed modelling method

allows for the determination of velocity field and local

average residence times by applying a three-step method. In

the first step the aerator is simulated in a stand-alone model,

in the second step the resulting boundary conditions are

applied to simulate the flow in the lagoon, and in the third

step the local average time distribution is obtained by solving

the corresponding equation.

The most important condition to obtain a correct repre-

sentation of the aerator is to ensure the mass and momentum

conservation from the aerator to the lagoon. The numerical

model accurately represents an aerator mixing diameter that

remains practically unchanged for various boundary condi-

tions implementations as long as the mass and momentum

flow rates are kept constant.

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ARTICLE IN PRESS

WAT E R R E S E A R C H 4 1 ( 2 0 0 7 ) 2 1 0 9 – 2 1 1 62116

Application of the model to an industrial lagoon predicts

the flow behaviour and provides an engineering tool for

analysing impacts of aerator placement and lagoon design. A

post processing done by solving an extra differential equation

provides visual and quantitative information to describe

internal lagoon mixing characteristics. The aerated lagoon

numerical model has been verified by comparing its predic-

tions with experimental data. Knowing the flow patterns and

average local residence time distribution helps to modify or

optimize lagoon hydraulics to better achieve desired perfor-

mance. To the best of our knowledge this is the first

time a CFD model that includes the mass transfer due to

the action of aerators has been applied to a large industrial

wastewater treatment lagoon with high-speed floating

mechanical aerators.

Acknowledgement

The financial contribution from Natural Sciences and En-

gineering Research Council of Canada (NSERC) and Weyer-

haeuser is greatly acknowledged. The cooperation and

support led by Dave Lincoln of the Weyerhaeuser Grande

Prairie operations is also gratefully acknowledged. Curtis

Bryant and William Barkley of Weyerhaeuser Environment,

Health and Safety contributed technical review and insights

in aerated lagoon design and operation. In addition, the

authors appreciate the encouragement provided by Dr Eric

Hall from UBC.

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