two and three-phase simulations of an ill-functioning

Two and Three-Phase Simulations of an Ill-Functioning Dissolved Air Flotation Tank V. Emmanouil, T. D. Karapantsios* and K. A. MatisDivision of Chemical Technology, Department of Chemistry, Univ. Box 116, Aristotle University of Thessaloniki, 541 24 Thessaloniki, Greece E-mail: [email protected], E-mail: [email protected], E-mail: [email protected] *corresponding author

ABSTRACT: Computational Fluid Dynamics (CFD) simulations were employed to examine the performance of

a large scale Dissolved-Air flotation (DAF) tank. The tank was ill-functioning as it was operated with bubbles

much larger than originally designed for. Different multiphase models, turbulence models and boundary

conditions for the free surface of the tank were tested in 2D simulations. The simulation results were assessed

through comparisons of the predicted spatial distributions of water velocity as well as volume fraction of air

bubbles, solid particles and bubble/particles aggregates inside the tank. Although the predicted global features

were similar among the different multiphase models, there were also discrepancies at a local scale suggesting

that local characteristics must be viewed with reservation. Two well known turbulence models, the standard

k-ε and standard k-ω, were cross examined in three-phase simulations yielding similar results for the flow

field and phase distributions but different for the solid recovery at the surface of the tank. Furthermore, the

boundary condition of considering the free surface of the tank as a sink for bubble/particles aggregates proved

advantageous with respect to computational convenience without loosing any goodness in prediction.

KEYWORDS: Computational Fluid Dynamics (CFD); Dissolved Air Flotation (DAF); large bubbles; zeolites;

multiphase models

Biographical Notes: Vasiliki A. Emmanouil obtained a Diploma in Chemical Engineering from the Aristotle University of Thessaloniki, Greece, in 2000. She also holds an MSc degree from the Chemistry Department of the Aristotle University of Thessaloniki. Her research interest is in the area of computational fluid dynamics. Thodoris D. Karapantsios obtained an honors Diploma in Chemical Engineering (1986) and a Ph.D. degree (1993) from the Aristotle University of Thessaloniki. He also holds a M.S. degree from the University of Rochester, USA, (1989). He is currently an assistant professor at the department of Chemistry of the Aristotle University of Thessaloniki. His main research interests are in the field of multiphase dynamics. He has published more than 50 articles in refereed journals, participated in more than 40 scientific meetings and has received one European patent. He has coordinated or participated in more than 20 national and international research programs.

V. Emmanouil, T.D. Karapantsios and K.A Matis, PAGE 2

Kostas A. Matis obtained his first degree in Chemistry (1973) from the same Department in Aristotle University that he has been serving since 1980. He was awarded his MSc by research (1975) and his PhD (1977) from the then Chemical Engineering Department of the University of Newcastle-upon-Tyne, UK. He became a Professor of Chemical Technology, in 1995. He has published more than 120 papers in refereed journals (which have attracted around 600 citations) and participated in more than 50 scientific meetings. He is the editor of three books, mainly on flotation and has received two patents. His main specialisation is in separation science and technology, and also in wastewater treatment, environmental biotechnology, inorganic materials and mineral processing.

1 INTRODUCTION

Flotation technology is frequently applied in water and wastewater treatment. A flotation tank

can be thought of as consisting of two basic regions: a “noisy” reaction zone and a “quiet”

flotation zone. In the reaction zone, released bubbles are brought vividly in contact with

incoming contaminated water. Particles and bubbles attach in this region. In the flotation zone,

bubble/particles aggregates are allowed to rise, thus separating the pollutants from the main

water stream. A properly operating flotation tank warrants that no single particles settling occurs

in both zones.

During the last decade, several investigators have employed numerical simulations to

examine large scale hydrodynamic aspects of flotation processes. Due to the large

computational burden, most of them refer to two-phase (gas-liquid) systems and a 2D-

structure grid and only a few attempts were made with three coexisting phases (gas-liquid-

solid). Fawcett (1997) studied the two-phase hydraulics of a DAF tank (average bubble size

70 μm) in a 2D frame of reference using the CFX 4 code. Among the examined parameters

(tank dimensions, internal baffle arrangements, water flow rate and air flow rate) he found

that the injected air-to-water flow momentum ratio was the most critical design parameter

dictating the effective mixing of air with the main liquid stream.

Ta and co-workers made decisive steps in CFD application to DAF tanks. In particular,

Hague et al (2000) compared simulations using a k-ε turbulence model against laminar flow

simulations and, furthermore, against laser Doppler velocimetry data for single and two-phase

flow (average bubble size 50 μm) using FLUENT 4.5 code. Strangely, at the quiescent

flotation zone of the tank, the turbulent model gave closer agreement with the measured

horizontal velocities than the laminar model, a peculiarity which could be attributed to the

small size of the employed lab scale tank, which did not allow vortices from the reaction zone

to sufficiently decay before entering the flotation zone. In another study, Ta (2000) recognised


that the water flow would dominate the motion of air bubbles inside the tank when bubbles

are small (20-100 μm) and the air volume fraction is below 10%. In a more advanced effort,

Ta et al. (2000) simulated a large scale DAF tank (average bubble size 50 μm) incorporating

three phases and a 3D structure grid. Air/water flow was described by a Eulerian-Eulerian

model whereas particles were tracked using a disperse Lagrangian model. No bubble/particle

collision was considered. CFD results were compared with visual information from an

underwater camera and an acoustic Doppler velocimetry technique. Overall, the agreement

between measurements and predictions was only qualitative with CFD being unable to predict

unsteady flow features such as lateral dispersion of bubble clouds.

Working with a dispersed air flotation tank of special design, the so-called Bubble

Accelerated Flotation (BAF) tank, Desam et al. (2000) undertook a detailed CFD study where

the model was validated against measurements from a dye tracing and a photographic

technique. The FLUENT 5.0 code was used to simulate the flotation zone in 3 dimensions.

The effect of bubble diameter as well as the inlet/outlet position and inlet velocity of the

air/water mixture in the separation tank, were examined and found to be significant on the

separation efficiency. Bubbles 250, 500 and 1000 μm were used (one size at a time) in the

calculations. A message from their work is that by proper selection of the system geometrical

details and further adjustment of the bubble/liquid flow rates it is possible to achieve

appreciable mixing of phases and bubble recovery at the tank surface even under reduced

shear conditions. This is the case of a DAF tank where the only shearing action is imposed by

the liquid flow as it moves through the reaction zone and mixes with the injected bubbles.

To our knowledge, the first time that flotation kinetic concepts such as collision,

attachment and detachment efficiencies were used in CFD studies was by Koh and co-workers

(2000, 2003, 2005). CFD simulations in 3 dimensions were performed on a Denver-type

dispersed air flotation tank using the CFX 4.1 code and incorporating a turbulent collision

model. It must be stressed though that in dispersed air flotation tanks the effect of turbulence

is far more important than in ordinary DAF tanks.

In real situations, it is sometimes the case that due to a malfunction a DAF tank is supplied

with bubbles larger than 50-100 μm (which is the range for ordinary performance). Such

irregularity may occur due to a defective gas compressor or air-injection pressure reducing

needle valve, partially blocked air-injection nozzles or even a viscosity increase of the

continuous phase (O’Neill et al. 1997; Matis 1981). The aforementioned causes can slow


down the de-pressurisation process of the injected gas-saturated stream which, in turn, may

slow down bubble nucleation and growth eventually leading to fewer and larger bubbles in

the tank. Recent simulations from this lab (Emmanouil et al. 2007) showed that in such ill-

functioning DAF tanks it is still possible to attain reasonable performance by properly

adjusting a few operational parameters. The location for air injection, the inclination of the

internal baffle of the tank and the liquid mass flow rate were proposed as such. Yet, the above

were found from two phase simulations where bubble/solids interactions were neglected.

Recent systematic theoretical analyses clearly depicted the various hydrodynamic and

physicochemical parameters that dictate flotation performance (King 2001, Nguyen & Schulze

2004). The extensive interrelationships between parameters acting on different length scales

make such models exceedingly complicated to evaluate and new multiscale generalization

concepts have been recently developed to cope with this issue (Kostoglou et al., 2006). Among

these parameters, the large scale hydrodynamic features inside a flotation tank have a profound

effect on the overall performance of the process.

From the above it is apparent that the application of CFD codes to simulate large scale

flotation processes offers distinct advantages in investigating the relative significance of

various design and operating parameters. At present, the computer load when many phases are

solved simultaneously is large and even simple 2D problems take several hours to converge.

With this in mind, this paper uses the FLUENT 6.1 code to describe the hydrodynamics inside

a large-scale DAF tank that is ill-functioning because it is supplied with bubbles larger than

50-100 μm (which is the bubble size range for nominal performance). Given that there is no

net flow across the tank and in order to reduce the computational effort, a 2D frame of

reference is employed. Three multiphase models (DPM, Eulerian and Mixture) and two

turbulence models (standard k-ε and standard k-ω) are cross-examined in two and three phase

simulations. Furthermore, the results of the turbulence models are also assessed in three-phase

simulations where bubble/solids attachment is accounted for by an appropriate kinetic model.

In addition, the effect of applying two different boundary conditions for the free surface of the

tank is examined.

2 NUMERICAL MODEL

To model the flow in the present flotation tank, the code FLUENT 6.1 was used. Since the

dispersed phase (bubbles) is dilute in the continuous aqueous phase, a Eulerian-Langrangian


model (Discrete Phase model, DPM) was selected for the continuous-dispersed phase,

respectively. In DPM, the dispersed phase is represented by bubbles that are continually

introduced at a given mass flow rate and are carried along by the main flow. The interaction

between phases is accounted for by adding a momentum source term in the Eulerian

conservation equation of the continuous phase. The same simulations were also performed

using two Eulerian-Eulerian models, the so-called Mixture and Eulerian models (FLUENT

User Guide 2003).

For DPM, only two distinct phases were considered in the simulations: air bubbles

interacting with the main aqueous stream. For the Eulerian model, again only two phases

were considered at a time: either air bubbles or solid particles interacting with the main

aqueous stream. The addition of a third phase made the calculations by this model

exceedingly cumbersome and time consuming. For the Mixture model, four distinct phases

were always accounted for: air bubbles, water, solid particles and bubble/particles aggregates.

The Eulerian model is the most accurate one but it is demanding in terms of computational effort

as it solves the continuity and momentum equations for each phase separately. The Mixture

model is a time-saving compromise to the Eulerian model that solves the continuity and

momentum equations assuming that all phases behave as a mixture and then uses the concept of

drift and slip velocities to describe the dispersed phases. In order to appraise the suitability of

using the multiphase models for different applications, certain criteria were proposed based on

particle loading and Stokes number (FLUENT User Guide 2003). According to these criteria,

the Mixture model is appropriate for the present simulations (Emmanouil, 2004).

The geometrical details of the flotation tank are shown in Figure 1. There were two vertical

baffles near the entry of the tank to control the fluid flow in the tank. Due to the baffles’

arrangement, the liquid which enters the tank was forced to travel through a downflow section

first and an upflow section afterwards. This was where the contaminated with solid particles

incoming water mixed with bubbles.

Inspired by a real application where heavy metals are initially absorbed on minute zeolite

particles which are then removed by flotation (Matis et al. 2004; Zaboulis et al. 2004), the

solids chosen for the present simulations were zeolites. Solid particles 3 μm in diameter and

density 2000 kg/m3 (zeolites) were entering the tank together (well-mixed) with the main

liquid flow. The concentration was 1 kg solids per m3 of water yielding a volumetric fraction

at the entrance equal to 5 × 10-4.


Given the relatively heavy zeolite particles that have a strong tendency to sink in the tank,

the liquid and gas flow rates must be selected high enough to provide sufficient turbulence to

mix phases and also warrant an adequate amount of bubble/particle collisions but yet not too

high to avoid disintegration of bubble/particles aggregates. For this reason it was decided the

present flotation runs to be performed with an inlet liquid velocity of 0.26 m/s (0.09 kg/s).

This corresponds to a hydraulic load of approx. 45 m/h which is above the normal conditions

for DAF operation but for this particular tank design has also been successfully employed in

the past (Fawcett, 1997).

The location for an effective bubble injection in the tank is a serious matter of concern that

has been dealt with in a previous study (Emmanouil et al. 2007). Among the several tested

configurations the most efficient one was to introduce air through a series of nozzles at the

left bottom corner of the tank i.e., just below the liquid entry region (Figure 1). Air was

introduced as individual bubbles of certain size. In this work, only 500 μm bubbles were

considered. Gas flow rate was set at 0.1 kg/m3s (4.9 10-3 kg/s), a value warranting that the

local air volume fraction was always below ~10% inside the tank as recommended for the

application of DPM (FLUENT User Guide, 2003).

Figure 1: Flotation tank geometry.

The modeling procedure involved two steps. The first step involved building the grid using

GAMBIT pre-processor and imposing the boundary conditions on the model. All the model

and solution parameters were fixed to obtain a solution using FLUENT solver in the second

step. A total number of 29071 cells were used to discretise the computational domain being

denser in regions of more intense activity, Figure 2.

Figure 2: Grid of flotation tank

The boundary condition for the tank inlet was the prescribed inlet water velocity with 10%

turbulence intensity. The boundary condition for the outlet was the pressure at the exit of the

tank with 10% backflow turbulence intensity and reference pressure the hydrostatic value. In

the case of DPM, the free surface of the tank was modeled as a wall with zero shear (trap

type). In the Eulerian model the free surface was considered as simply in contact with the air

phase. In the Mixture Model the free surface was modeled either as a wall acting as a sink for


the gas phase (closed tank) or as a wall in direct contact with air (open tank). The open tank

configuration consists of a gas space of equal size with the tank being in contact with the free

surface of the tank and which is further connected to the atmospheric air through a small

opening (0.5 m) at the middle top of it. The boundary condition was the exit pressure with

reference to the ambient pressure value.

The standard k-ε and k-ω turbulence models were used to describe the turbulence inside

the tank. The implicit segregated model was employed to solve the governing equations

whereas the pressure-velocity coupling is discretised by the SIMPLE algorithm. Convergence

was assumed accomplished if continuity was better than 10-5 to 10-6.

To describe the bubble/particles collisions and attachment the kinetic model proposed by

Koh et al. (2000) and Koh & Schwarz, (2003) was employed. The micro-kinetics of a

flotation system can be described by the rate of removal of the number of particles in a given

volume:

where Pc, Pa and Ps are the probabilities of particle-bubble collision, adhesion and

stabilisation against external forces and Zpb is the particle-bubble collision rate in turbulence

flow dependent on the size of the bubble and the hydrodynamics of the flotation pulp. The

collision equation which is applicable for fine particles and bubbles confined within eddies in

the low turbulent dissipation regions, is given by the equation of Saffman & Turner (1956):

where dp and db are the particle and bubble diameter respectively, Np and Nb are the particle

and bubble number concentrations, ε is the turbulent dissipation rate and ν is the kinematic

viscosity.

The probability of particle-bubble collision for the case of intermediate flows (0<Re<300)

could be estimated by the following equation (Yoon & Luttrell 1989):

2bd

2pd72.0

bRe1545.1cP ⎟

⎠⎞

⎜⎝⎛ += (3)

2/1

νε

3

2bdpd

bNpN15π8

pbZ ⎟⎠⎞

⎜⎝⎛

⎟⎟⎠

⎞⎜⎜⎝

⎛ += (2)

sPaPcPpbZdt

pdN−= (1)


where the Reynolds number refers to the bubble. The assumptions that have been made for

this equation are that the particles are much smaller than the bubbles, have no inertia and,

therefore, are subjected to streamflow. In this work, the probabilities of particle-bubble

adhesion and stabilisation were assumed as unity. This was done on the grounds that for a

successful flotation system where the appropriate surfactants are added as collectors and froth

stabilizers these probabilities are indeed close to unity. Unfortunately, there is no available

experimental evidence to justify this.

In flotation column experiments in our lab it was found that for the particular system at

hand (particles plus surfactants), large bubbles were covered with particles at roughly 5-10 %

of their surface and the achieved solid recovery at the froth was above 80-85% of the inlet

concentration (Zamoulis et al. 2004). Based on this, it was decided to assume a bubble

coverage of 7% for all present bubbles which corresponds to 6250 close-packed particles per

bubble. Details on the implementation of the collision/attachment kinetic model to the CFD

code are given elsewhere (Emmanouil, 2004).

Comparisons were made under two-phase and three-phase conditions where solid particles

were fed in the tank along with the water inlet. In the simulations involving bubble/particles

aggregates the evaluation of the different conditions was made directly with respect to the

achieved solid solids recovery, that is, the percentage of the fed solids that were removed as

aggregates from the tank. In order to allow comparisons in reasonable time, simulations were

performed in two dimensions, which still provide meaningful information.

3 RESULTS

3.1 Comparison of multiphase models

In the absence of field measurements, one way to indirectly judge on the adequacy of

multiphase models is to compare results among different modeling schemes in the case of two

phase simulations (solids follow the water streamlines). As different approximations are

involved in each model it is not obvious that they would be all able to describe the behavior of

the different phases. The most stringent comparison is between the DPM and the rigorous

Eulerian model. It must be noted that in our case the Eulerian and the Mixture models

produced virtually the same results. This verifies the multiphase model selection criteria

suggested by FLUENT, which clearly indicated that the Mixture model was as suitable as the

Eulerian model for our applications. With the Eulerian and Mixture models it proved


imperative to have the inlet and outlet of the flow not directly imposed to the tank but instead

use a phantom entrance and exit pipeline (diameter 0.3 m, length 1.7 m) to overcome the

abrupt disturbance of the velocity profile at these points.

The comparison between DPM, Eulerian model and Mixture model is presented in Figures

3 and 4 with respect to the distribution of water velocity and air volume fraction inside the

tank. From all plots, it is evident that a long flotation zone was necessary to avoid

bubble/solid aggregates carry over towards the tank outlet. This is so despite the employed

heavy particles and large bubbles that rapidly tend to settle down and rise, respectively.

Figure 3: Velocity magnitude (m/s) contours of water with bubbles 500 μm (a) DPM, (b) Eulerian Model and (c) Mixture Model.

Figure 4: Air volume fraction contours with bubbles 500 μm (a) DPM, (b) Eulerian Model and (c) Mixture Model.

As regards the velocity magnitude in Figure 3, the Eulerian and Mixture Models predicted

alike water velocity results, clearly different from the DPM results. A prominent difference

between DPM and the two other models was observed in the shape of the internal flow loop at

the right-hand side shaft of the flotation zone. The discrepancy reflects the inadequacy of

DPM to describe bubbles that circulate inside iterative local flow loops especially if the

volume fraction of air approaches 10%. This was also the case with bubbles of 200 μm but the

situation was markedly better with 1000 μm bubbles where buoyancy drives the bubbles out

of such closed loops (Emmanouil et al. 2005). To this end, it appears that the results of DPM

must be viewed with caution.

The above is supported further by comparisons among the predicted air volume fractions in

Figure 4. DPM gave considerably broader distributions in the reaction zone. Judging from the

shape of the air distribution patterns and also the bubble trajectories in these region (not

presented), one can argue that the additional spread of bubbles predicted by DPM might be a

computational artifact due to the inability of DPM to correctly describe bubbles that are

trapped in iterative flow loops (FLUENT, User Guide 2003). It was shown elsewhere

(Emmanouil et al. 2007) that the situation improves significantly as the size of the bubbles

increases or when bubbles of different sizes coexist in the tank.


Apparently, there are also small differences between the Eulerian model and the Mixture

model predictions especially in the value of local fractions and also the shape of air

distribution inside the reaction zone. Yet, the two models give quite similar results and for this

reason the less time-consuming Mixture model will be used henceforth to appraise other

calculation parameters.

3.2 Comparison of turbulence models

Figure 5 displays the three-phase predictions of the Mixture Model obtained with the standard

k-ε and k-ω turbulence models, respectively. With the exception of some small differences in

the estimated volume fractions, it appears that both models give comparable results.

Interestingly, the water velocity and air volume fraction contours are essentially the same with

those predicted from two phase simulations (without solids) (Emmanouil et al. 2005).

However, the estimated solids recovery (percentage of the entry solids that are removed as

bubble/particles aggregates from the surface of the tank) is distinctly different between models

as can be seen in Table 1.

Table 1: Bubble/particles aggregates solids recovery.

Τhe higher values given by the standard k-ω model are closer to industrial practice and

also agree with the bubble flotation experiments with the same physicochemical system in our

lab (Matis et al. 2004; Zamboulis et al. 2004). This implies that it is not the spatial distribution

of phases in the tank that determines the degree of the recovery but rather parameters such as

the probability of bubble/particle collisions and the collision rate which depend directly on the

local turbulence dissipation rate, and hence are influenced by the employed turbulence model

(Koh & Schwarz 2003, Emmanouil 2004). The effectiveness of the standard k-ω model is not

surprising as it is meant to describe better low Reynolds numbers flows such as the one inside

our DAF tank (Wilcox 1998).

Figure 5: Bubbles 500 μm; (a) Velocity magnitude (m/s) contours of water with k-ε turbulence model, (b) Velocity magnitude (m/s) contours of water with k-ω turbulence model, (c) Air volume fraction with k-ε turbulence model (d) Air volume fraction with k-ω turbulence model, (e) Bubble/particles aggregates volume fraction with k-ε turbulence model and (f) Bubble/particles aggregates volume fraction with k-ω turbulence model.


3.3 Comparison of boundary conditions

Figures 6-9 display contours of velocity and volume fractions of water, air bubbles, solids and

bubble/particles aggregates produced by the Mixture Model under the employed two different

boundary conditions for the free surface of the tank.

Figure 6: Velocity magnitude (m/s) contours of water (a) open tank and (b) closed tank.

Figure 7: Air volume fraction contours with 500μm bubbles, (a) open tank and (b) closed

tank. The white area in the air space above the free surface of the tank is artifact due to

scaling.

Figure 8: Solids volume fraction contours (a) open tank and (b) closed tank.

Figure 9: Bubble/particles aggregates volume fraction contours (a) open tank and (b) closed

tank.

On physical grounds, the “open” tank is a more realistic representation of the tank.

However, there are not significant discrepancies between the plots of the different boundary

conditions. Some deviations are only met in the vicinity of the free surface because for the

“open” tank bubble/particles aggregates have to rise slightly above the gas/liquid interface to

be removed whereas for the “closed” tank they are removed as soon as they arrive at the

interface. Furthermore, the estimated value of the overall solids recovery is virtually the same

between the two cases (open tank: 81.7 % and closed Tank: 80.6 %).

The above results have a great merit because they allow the flotation tank to be modeled as

a closed tank, a configuration which reduces drastically the computational effort.


4 CONCLUSIONS

Testing different multiphase and turbulence models in CFD simulations (FLUENT) was a

valuable tool for appraising the operation of an ill-functioning DAF tank. The Discrete Phase

Model gave different predictions (and rather in error) than the Eulerian and the Mixture

models with respect to water velocity and air volume fraction as the 500 micron bubbles seem

to get trapped in iterative flow loops. Regarding the employed turbulence models, the

standard k-ω and standard k-ε models produced comparable results in terms of the water

velocity and air volume fraction but predicted considerably different bubble/particles

aggregates recoveries. This is an indication that it is rather the local features of

bubble/particles encounters (probability of bubble/particle collisions and collision rate) and

not the macroscopic phase distributions in the tank that determines the flotation rate. Finally,

it was seen that considering the free surface of the tank as a wall acting as a sink for

bubble/particles aggregates was a sufficient boundary condition to produce acceptable results

at a reasonable computation time.

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FLUENT 6.1 User’s Guide, 2003, Fluent Inc.


Hague, J., Ta, C. T., Biggs, M. J. and Sattary, J. A. (2000) Small scale model for CFD validation in DAF application, In: The 4th International Conference Flotation in Water and Waste Water Treatment, Helsinki 11-14 September, Session 6.

King, R. P. (2001) Modelling and simulation of mineral processing systems, Butterworth-

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flotation for the separation of metal-loaded zeolites’, Chemosphere, Vol. 55, pp. 65-72. Nguyen, A. V. and Schulze, H. J. (2004) Colloidal Science of Flotation, Marcel Dekker Inc.,

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List of Tables Table 1: Bubble/particles aggregates solids recovery.


List of Figures Figure 1: Flotation tank geometry. Figure 2: Grid of flotation tank Figure 3: Velocity magnitude (m/s) contours of water with bubbles 500 μm (a) DPM, (b)

Eulerian Model and (c) Mixture Model.

Figure 4: Air volume fraction contours with bubbles 500 μm (a) DPM, (b) Eulerian Model and (c) Mixture Model.

Figure 5: Bubbles 500 μm; (a) Velocity magnitude (m/s) contours of water with k-ε turbulence model, (b) Velocity magnitude (m/s) contours of water with k-ω turbulence model, (c) Air volume fraction with k-ε turbulence model (d) Air volume fraction with k-ω turbulence model, (e) Bubble/particles aggregates volume fraction with k-ε turbulence model and (f) Bubble/particles aggregates volume fraction with k-ω turbulence model.

Figure 6: Velocity magnitude (m/s) contours of water (a) open tank and (b) closed tank.

Figure 7: Air volume fraction contours with 500μm bubbles, (a) open tank and (b) closed

tank. The white area in the air space above the free surface of the tank is artifact

due to scaling.

Figure 8: Solids volume fraction contours (a) open tank and (b) closed tank.

Figure 9: Bubble/particles aggregates volume fraction contours (a) open tank and (b) closed

tank.


Table 1: Bubble/particles aggregates solids recovery.

Bubble size

(μm)

Turbulence

Model

Solids

Recovery %

500 standard k-ε 50.0

500 standard k-ω 80.6


Figure 1: Flotation tank geometry

Water inlet

Water outlet

7.45 m

0.3 m

1.9 m

0.7 m

1.5 m

0.3 m 60 o

0.65 m

Free surface collection of froth

Bubble Injection

Water inlet

Water outlet

7.45 m

0.3 m

1.9 m

0.7 m

1.5 m

0.3 m 60 o

0.65 m

Free surface collection of frothWater inlet

Water outlet

7.45 m

0.3 m

1.9 m

0.7 m

1.5 m

0.3 m 60 o

0.65 m

Water inlet

Water outlet

7.45 m

0.3 m

1.9 m

0.7 m

1.5 m

0.3 m 60 o

Water inlet

Water outlet

Water inlet Water inlet

Water outlet

7.45 m7.45 m

0.3 m

1.9 m1.9 m

0.7 m 0.7 m

1.5 m 1.5 m

0.3 m

0.65 m 0.65 m

Free surface collection of froth

Bubble Injection Bubble Injection


Figure 2: Grid of flotation tank

Free surface Velocity inlet

Pressure outlet

Velocity inlet

Pressure outlet

Velocity inlet

Pressure outlet Baffles


Figure 3: Velocity magnitude (m/s) contours of water with bubbles 500 μm (a) DPM, (b) Eulerian Model and (c) Mixture Model

(a)

(c)

(b)


Figure 4: Air volume fraction contours with bubbles 500 μm (a) DPM, (b) Eulerian Model and (c) Mixture Model

(a)

(c)

(b)


Figure 5: Bubbles 500 μm; (a) Velocity magnitude (m/s) contours of water with k-ε turbulence model, (b) Velocity magnitude (m/s) contours of water with k-ω turbulence model, (c) Air volume fraction with k-ε turbulence model (d) Air volume fraction with k-ω turbulence model, (e) Bubble/particles aggregates volume fraction with k-ε turbulence model and (f) Bubble/particles aggregates volume fraction with k-ω turbulence model

(a)

(b)

(d)

(c)

(f)

(e)


Figure 6: Velocity magnitude (m/s) contours of water (a) open tank and (b) closed tank

(a)

(b)


Figure 7: Air volume fraction contours with 500μm bubbles, (a) open tank and (b) closed tank. The white area in the air space above the free surface of the tank is artifact due to scaling.

(b)

(a)


Figure 8: Solids volume fraction contours (a) open tank and (b) closed tank

(b)

(a)


Figure 9: Bubble/particles aggregates volume fraction contours (a) open tank and (b) closed tank

(a)

(b)

two and three-phase simulations of an ill-functioning

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