## Abstract

The standard *k*–*ε* model coupled with the mixture model was used to study two-phase flow in a large dissolved air flotation (DAF) unit. The numerical results can simulate fairly well the velocity vectors and air volume fraction distribution data of a DAF unit from the literature. The typical DAF structure parameters were analyzed in detail to investigate their predicted influences on the internal flow structure and removal effect. The simulations indicated that the short length of the separation zone was not conducive to the formation of a stratified flow pattern, and the turbulent kinetic energy at the bottom of the separation zone increased as the length decreased. With the increase in the height of the DAF tank, the horizontal flow structure in the separation zone would be disrupted, and the distribution range and the intensity of the turbulence kinetic energy increased. Further analysis showed that the formation of horizontal stratified flow facilitated the removal of bubbles, and the formation of stratified flow is related to the size of the DAF unit. Detailed analyses showed that the reduction of DAF height and the increase of separation zone length were beneficial to improve the bubble removal efficiency. Finally, a theoretical analysis was carried out to study the relationship between DAF parameters and the removal effect. The results revealed that when the horizontal flow structure was not destroyed and stratified flow occurred, the bubble removal efficiency was positively linearly related to the length of the separation zone. The removal efficiency increases as DAF height decreases.

## HIGHLIGHTS

The formation of horizontal stratified flow facilitated the removal of bubbles.

The stratified flow would be formed under the condition of appropriate structure parameters.

When the horizontal flow structure was not destroyed and stratified flow occurred, the bubble removal efficiency was positively linearly related to the length of the separation zone. And it changed in the opposite pattern when the DAF height varied.

## INTRODUCTION

Dissolved air flotation (DAF) is a fast and efficient water treatment technology, which is now widely used in the fields of wastewater treatment, seawater desalination, and potable water filtration (Edzwald 1995; Ding *et al.* 2014; Sancho *et al.* 2018). In the context of the current global shortage of freshwater resources and serious water pollution, DAF technology has a broad prospect in the field of water treatment. Similar to sedimentation basins, DAF tanks rely on the principle of gravity separation for particle removal (Viadero 2005); however, in sedimentation, particles are removed by sinking to the bottom of the tank, while in DAF tank, solid and semi-solid particles are removed by attaching to fine bubbles forming agglomerates that float to the surface. Sedimentation tanks are suitable for the removal of large and easily sinkable flocs, while DAF tanks are more advantageous for the removal of small, low-density flocs. In the DAF system, after the raw water is mixed and flocculated, it first enters the contact zone of the DAF tank, where a large number of bubbles adhere to the floc particles in the feed water, forming a floc-bubble aggregate with a small density relative to the surrounding liquid, which rises to the surface of the liquid in the separation zone.

Many experiments and numerical simulations have been carried out on the influence of the contact and separation zones of DAF tanks on the air flotation water purification process. Haarhoff & Vuuren (1995), after an experimental study of DAF, pointed out that the water purification effect of the air flotation process is inextricably related to its internal hydraulic structure characteristics. Since then, many experimental studies and measurements have focused on the internal fluid flow of the tank. Lundh *et al.* (2000) conducted an experimental study on the separation zone of rectangular DAF and found that stratified flow was presented at air–water two-phase flow conditions, while there was no stratified structure in the single-phase flow. Furthermore, by changing the air concentration entering the DAF tank, Lundh *et al.* (2001) found that the air fraction was an important factor affecting the formation of stratified flow in the DAF separation zone. Haarhoff & Edzwald (2004) continued their study of the contact and separation zones and concluded that factors such as coagulation pretreatment, bubble size, air volume fraction, and mean fluid residence time all have an effect on the performance of the contact and separation zones. Anderson Maia *et al.* (2015) found that the inlet velocity of the contact zone affects the degree of agitation which in turn affects the size of the flocs and the efficiency of the flotation process.

Considering the importance of fluid dynamics in DAF and the difficulty of DAF equipment design, computational fluid dynamics (CFD) becomes a promising option for the development of this field. Lakghomi *et al.* (2012) investigated the effect of stratified flow on the water purification effect of the DAF process using the CFD technique, and the calculation results showed that an increase in the air content was beneficial to the formation of stratified flow and improved the removal rate, but the hydraulic load exceeding the critical value would destroy the fluid stratified flow pattern. In addition, Lakghomi *et al.* (2015) carried out a modeling approach and the results demonstrated that the presence of stratified flow enhanced particle removal in the tank, and also found that higher air fractions were required to achieve the same removal efficiency at higher loading rates. Lee *et al.* (2020) investigated the variation of flow behavior at different operating parameters of DAF, such as microbubble size, volume fraction, and inlet velocity. The simulation results showed that excessive increase in the inlet volume fraction, diameter, and inlet flow velocity of microbubbles may not be effective in removing pollutants from wastewater due to the short interaction time between pollutants and microbubbles and the increased bouncy force.

In terms of optimization of structural parameters of DAF tank, Kwon *et al.* (2006) conducted a study, where they used CFD software to build a three-dimensional full-size air floatation cell for simulation, and the calculation results showed that the length/width ratio of DAF has a significant effect on its separation efficiency, and when the length/width ratio is greater than 2:1, the dead zone of DAF cell appears.

In the numerical simulation technique, the choice of model has a significant influence on the accuracy of the calculation results. Lots of investigations have been done to develop an effective CFD model to describe precisely the flow in a DAF tank. Hague *et al.* (2001) compared the results of two-phase simulations with different turbulence models. The results indicated that the *k*–*ε* turbulence model was better than the laminar flow model when comparing simulation results with experimental data. Bondelind *et al.* (2010) set up both a two-dimensional and a three-dimensional CFD model of a DAF tank, and the simulation results demonstrated that a stratified two-phase flow in the separation zone can be modeled well with a 2D model. Rodrigues & Béttega (2018) evaluated different approaches of the multiphase flow model, turbulence model, and drag model as well as different boundary conditions for simulating the DAF tank surface. The numerical simulation results were compared with data in the literature and the results showed that the Eulerian approach is feasible and the *k*–*ε* turbulence model is the most suitable model to describe the flow characteristics in the DAF tank.

As mentioned above, although many researchers have presented various experimental results and models of fine bubble and particle interactions, there is still a lack of understanding of the effect of DAF structural parameters on the internal flow structure of DAF tanks. Also, the relationship between the hydraulic flow of DAF and the bubble removal rate needs further insight. Consequently, a two-phase CFD model was developed in this paper to investigate the effect of variation in DAF height and separation zone length on hydraulic behavior. Additionally, the influence of structural parameters on bubble removal was analyzed.

## GOVERNING EQUATIONS AND NUMERICAL SETUP

### Multiphase flow model

Currently, the Eulerian–Eulerian method and the Eulerian–Lagrange method are the most widely studied methods for multiphase flow (Zhang & Jiao 2018; Zhang *et al.* 2019). The Eulerian–Lagrange method treats the primary phase as continuous and the secondary phase as discrete for calculation, which is only applicable to the case where the volume fraction of the secondary phase is low. The Eulerian–Eulerian methods, including VOF (Katopodes 2019), Mixture model (ANSYS 2014), and Eulerian method (Chen *et al.* 2016), treat both the primary phase and the secondary phase as continuous, and the different phases penetrate each other. Each model has its specific scope of application, of which the mixture model is a relatively simplified multiphase flow model. It is based on an assumption of local equilibrium on a short spatial scale and simulates multiphase flow with different velocities of each phase, which makes the phases strongly coupled to each other. Therefore, multiphase flow models are commonly used for the calculation of discrete phase mixtures, droplet, and particle loaded flows. It has obvious advantages for the calculation of the DAF model with a large range of water and air two-phase distribution and a high requirement of computational stability. The equation of the mixture model is described in ANSYS (2014) and Lee *et al.* (2020).

### Turbulence model

As previously mentioned, the standard *k*–*ε* model was used well to predict the recirculation zones and the stratification of the flow (Lakghomi *et al.* 2012, 2015). In addition, it can describe the characteristics of turbulence of the DAF tanks at an acceptable computational cost. Consequently, the standard *k*–*ε* model is used to model the turbulence flow of the DAF unit in this paper.

*k*and the dissipation rate of the turbulent energy

*ε*are modeled aswhere the equation subscript ‘m’ represents the mixture phase,

*u*(m/s) is the velocity,

*i*represents three directional components of the velocity,

*k*(m

^{2}/s

^{2}) is the turbulence kinetic energy,

*μ*is the vortex viscosity coefficient,

*G*

_{k}is a generation of turbulence kinetic energy due to the mean velocity gradient,

*G*

_{b}represents the generic term of turbulence kinetic energy due to buoyancy,

*Y*

_{M}is the generation of pulsation expansion in compressible turbulent fluids,

*G*

_{b}and

*Y*

_{M}are zero for incompressible fluids.

*S*

_{k}is the user-defined source term.

### Numerical setup

#### Geometry model and calculation domain

For the simulation, the Ansys Fluent was used for fluid dynamics calculations and for analysis of the simulated results. Two-dimensional (2D) simulations of a DAF tank are sufficient to predict the stratified two-phase flow in the separation zone to a certain extent (Bondelind *et al.* 2010), so it is feasible to use the 2D model for simulation calculations. The details of the DAF tank geometry are shown in Table 1 and Figure 1.

Information . | Size (m) . |
---|---|

The height of water inlet (A) | 0.2 |

The length of water and air recycle inlet (B) | 0.07 |

The length of outlets (D) | 0.4 |

The height of baffle (E) | 3.5 |

The length of water inlet (F) | 1.2 |

The length of contact zone (G) | 0.8 |

The height of water and air recycle inlet (H) | 1.3 |

The length of separation zone (I) | 8, 9.5, 10, 11, 12, or 14 |

The height of DAF tank (J) | 3.8, 4.5, 5, 5.6, or 6.2 |

Information . | Size (m) . |
---|---|

The height of water inlet (A) | 0.2 |

The length of water and air recycle inlet (B) | 0.07 |

The length of outlets (D) | 0.4 |

The height of baffle (E) | 3.5 |

The length of water inlet (F) | 1.2 |

The length of contact zone (G) | 0.8 |

The height of water and air recycle inlet (H) | 1.3 |

The length of separation zone (I) | 8, 9.5, 10, 11, 12, or 14 |

The height of DAF tank (J) | 3.8, 4.5, 5, 5.6, or 6.2 |

#### Boundary conditions

Table 2 contains information about the conditions used in this study. The water surface of the separation zone is the water–air interface, and boundary conditions such as a wall, outflow, and outlet-vent were used to approximate the calculation step by step. The magnitude of gravity was set to 9.81 m/s^{2}, and the direction is along the negative direction of the *y*-axis. The flow and air volume fractions for the base case are based on data from a DAF tank provided by a water company in Shanghai. It should be noted that changes in both flow and air volume fraction affect the simulation results, so the same values are used for both flow rate and air volume fraction when discussing the effect of changes in height and separation zone length on the DAF tank, as shown in Table 2.

Variable . | Boundary condition . | Value . |
---|---|---|

Water inlet | Velocity inlet | 0.11 m/s |

Water and air recycle inlet | Velocity inlet | 0.041 m/s |

Air fraction of water and air recycle inlet | – | 0.4 |

Outlets | Pressure outlet | – |

Walls and baffle | Wall | – |

Surface of contact zone | Wall | – |

Surface of separation zone | Outlet-vent | – |

Variable . | Boundary condition . | Value . |
---|---|---|

Water inlet | Velocity inlet | 0.11 m/s |

Water and air recycle inlet | Velocity inlet | 0.041 m/s |

Air fraction of water and air recycle inlet | – | 0.4 |

Outlets | Pressure outlet | – |

Walls and baffle | Wall | – |

Surface of contact zone | Wall | – |

Surface of separation zone | Outlet-vent | – |

#### The grid independence

A geometric model with a separation zone length (I) of 11 m and a DAF tank height (J) of 5 m is selected for grid-independent verification. Three meshes with coarse, medium, and fine resolutions were generated. Comparing the simulation results, it can be verified that the predictions of the medium grid are not very different from those of the fine grid. Therefore, the mesh of 20,170 cells, as shown in Figure 2, was considered sufficient and would be employed for further simulations in this paper (Figure 3 and Table 3).

Mesh . | Air fraction of flotation tank surface (C) . | Air fraction of outlets (D) . |
---|---|---|

Coarse | 0.008393 | 0.001837 |

Medium | 0.007585 | 0.001150 |

Fine | 0.007743 | 0.001131 |

Mesh . | Air fraction of flotation tank surface (C) . | Air fraction of outlets (D) . |
---|---|---|

Coarse | 0.008393 | 0.001837 |

Medium | 0.007585 | 0.001150 |

Fine | 0.007743 | 0.001131 |

## RESULTS AND DISCUSSION

### Validation of numerical results

To investigate how accurately the above methodology can simulate the multiphase flow in DAF, classic experimental measurements of the flow field in a pilot DAF tank (Lundh *et al.* 2000, 2001) were adopted to validate the numerical results. In the simulation of the DAF process, many researchers have used these experimental data to verify the numerical simulation method (Ta *et al.* 2001; Lakghomi *et al.* 2012; Chen *et al.* 2016).

The DAF system model used to validate the calculation method is shown in Figure 4. The CFD results in Figure 5(a) showed the velocity vectors plot for the surface loading rate of 23.6 m/h (flow rate of 20 m^{3}/h) and the air volume fraction of 0.005. It can be observed that there is a clear stratified flow in the separation zone. Figure 5(b) plots the comparison of air content in the separation zone from the experimental and present models. The air volume fraction calculated from the CFD model showed that the air distribution is in relatively good agreement with the experimental results of Lundh *et al.* (2001). The above results showed that the flow of DAF calculated by the methodology used in this paper is reliable.

### Validation of the numerical model

In order to compare the difference between the two-dimensional calculation results and the three-dimensional calculation results of the air floatation tank, a three-dimensional model as shown in Figure 6 was established for simulation. Figure 7 shows contours of air volume fraction for different *Z*-axis cross-sections. By comparing the simulation results, it can be found that the air volume fraction distribution in the separation zone is similar in different cross-sections. The gas volume fraction distribution in the contact zone is slightly different due to the inlet pipe distribution. In the subsequent discussion of the effect of the variation of DAF tank height and separation zone length, the use of the two-dimensional model can greatly reduce the computational resource consumption while simulating the flow state in the DAF tank with acceptable accuracy, so the two-dimensional model will be used for simulation prediction in the subsequent discussion.

### Effect of DAF height (J) and separation zone length (I) on flow patterns

#### DAF separation zone length (I)

Initially, the different lengths of separation zone were simulated in order to understand their influence on the internal flow structure.

Figure 8 shows the simulation results of stream traces when separation zone length varies (8, 9.5, 10, 11, 12.5, and 14 m each). As can be seen, a top horizontal flow layer was present regardless of the length of the separation zone. As seen in Figure 8(a), fluids travel from left to right and circulate in the clockwise direction when it meets the right wall, with the center of circulation in the middle of the separation zone. As seen in Figure 8(b), it has a similar flow pattern to Figure 8(a), but the center of circulation is shifted a little bit to the right. On the other hand, all the other lengths showed somewhat different flow behaviors compared with the length of 8 and 9.5 m. In all other cases, a back horizontal flow layer that returned the water toward the baffle was formed underneath the top layer; however, there are also somewhat different from Figure 8(b)–8(e).

Turbulent kinetic energy for the various separation zone lengths is shown in Figure 9. The magnitude of the turbulent kinetic energy can characterize the degree of fluid mixing, the higher turbulent kinetic energy indicates a higher degree of fluid mixing. And the generation of the vortex will increase the intensity of turbulence in this region. By comparing both results in Figure 9, the maximum turbulent kinetic energy is distributed in the upper part of the contact zone, which is due to the mixing of bubbles and water there. On the other hand, the simulation predicts that the distribution of turbulent kinetic energy in the separation zone varies significantly with the growth of the length. When the length of the separation zone is 8 m, the turbulent kinetic energy has a larger value at the right wall, which is due to the short length of the separation zone and, there is still a large flow velocity when the fluid develops to the right wall. Combined with Figure 8(a), there is a large vortex in the right region of the separation, which enhances the intensity of turbulence here. When the length of the separation zone is 9 m, the vortex shifts to the right, and the turbulence intensity decreases. Observing Figures 8(c) and 9(c), it can be found that tiny vortices appear at the right wall of the separation zone and the turbulence intensity at the right wall is enhanced. As the length of the separation zone increases, the vortex range at the right region becomes larger and the turbulence intensity at the right wall decreases, the effect of the vortex on the upper bubble layer of the separation zone decreases.

Figure 10 shows the simulation results of volume fraction contours when separation zone length varies (8, 9.5, 10, 11, 12.5, and 14 m each). It can be observed that the bubble layer formed in the contact zone has a certain thickness, but it becomes thinner and thinner as it flows through the contact zone. By comparing both results, it can be observed that the air mainly accumulates at the top of the separation zone, but the volume fraction distribution of microbubbles is more chaotic in the middle and bottom of the separation zone when the length is 8 and 9.5 m. As seen in Figure 10(c) and 10(d), the air volume fraction gradually decreases from top to bottom, and there is a clear stratified distribution. When the length of the separation zone is 12.5 and 14 m, the volume fraction of microbubbles at the bottom in the separation zone is significantly reduced compared to Figure 10(c) and 10(d). As the lengths of the separation zone increase, the water surface outlet backflow areas increase because the thinning of the bubble layer near the right part of the separation zone makes the buoyancy force decrease and the fluid flows downward by gravity.

#### DAF height

The different heights of the separation zone were simulated in order to understand their influence of them on the internal flow structure. It should be noted that in the model used in the simulation, the baffle height is kept constant. Therefore, as the height of the DAF tank increases, the distance between the top of the baffle and the surface of the DAF tank also increases, which will affect the internal flow structure of the DAF tank.

The CFD results in Figure 11 showed that stream traces varies with the increasing height of the DAF system. As seen in Figure 11(a), the result showed a distinct rotational movement in the entire separation zone. After leaving the contact zone, although the bubble layer at the top of the separation zone is thin, the high air volume fraction allows sufficient buoyancy of the fluid to flow horizontally to the right wall. And then fluids returned toward the baffle along the bottom. The baffle forces flow upward to rejoin the horizontal flow beneath the surface. As shown in Figure 11(b), the top of the separation zone also has a horizontal surface flow to the right wall, and there is a horizontal flow toward the baffle beneath the horizontal surface flow in the separation zone. The horizontal surface flow still continues to flow to the right wall and then forms a horizontal flow back to the baffle. As can be observed in Figure 11(c)–11(e), rotating flow appeared above the baffle in the contact zone, and the range of rotating flow expanded with the increase of the DAF height. In the separation zone, it can be observed that rotational flow occurs on the right side of the separation zone near the wall when the height of DAF is 5 m, and the rotational flow area expands when the height of DAF increases to 5.6 m. By comparing the simulation prediction results, it can be found that the change of DAF tank height will cause the change of distance from the top of the baffle to the surface of the DAF, which makes the inlet size of the separation zone change, and then affects the flow layer distribution in the separation zone.

Turbulent kinetic energy for the various separation zone heights is shown in Figure 12. It can be observed from Figure 12 that the turbulence intensity in the contact zone increases when the height of the DAF is higher. As can be seen from Figure 11, the location of the vortex appearance in the contact zone does not change with the change in the height of the air floatation cell, but an appropriate increase in the height of the DAF can make the vortex development more adequate and can enhance the mixing of fluid and bubbles in the contact zone. In the separation zone, it can be observed from Figure 12(a) that the turbulence intensity in the separation zone is low when the height is 3.8 m. When the height of the air floatation tank is 4.5 m, the turbulence intensity increases in the upper area of the separation zone and near the right wall as shown in Figure 12(b). As shown in Figure 12(c)–12(e), the turbulence intensity in the separation zone near the right side wall was further enhanced when the DAF height was 5 m, but the turbulence intensity in this region weakened when the DAF height was 5.6 and 6.2 m. Combined with Figure 11, when the height of the DAF is 5 m, there are micro vortexes in the right side of the separation area near the wall, and they enhance the turbulence intensity in this area, when the height of the DAF is 5.6 and 6 m, the vortex becomes larger and the turbulence intensity in the area decreases, and the distribution range of turbulence energy increases.

Figure 13 gives the simulation results of volume fraction contours when separation zone height varies (3.8, 4.5, 5, 5.6, and 6.2 m each). In the contact zone, the gas bubbles mainly accumulate in the upper part, while the distribution of air volume fraction in the upper right side of the contact zone decreases significantly with the increase of the DAF height. In the separation zone, the gas bubbles mainly collect at the top, the thickness of the bubble layer is about 0.3 m, and basically, no gas is distributed at the bottom and middle when the height of DAF is 3.8 m. When the height of the DAF is 4.5 m, the gas is still mainly distributed at the top of the separation zone, the thickness of the bubble layer increases to about 0.7 m, and the air distribution increases in the middle and bottom compared with the simulation result of the height of 3.8 m. It can be observed that the bubble layer thickness increases to about 1 m when the height increases to 5 m and the air gradually decreases in a stratified distribution from top to bottom; however, when the height is 5.6 m, the volume fraction of air in the top bubble layer decreases significantly and the air distributed in the middle and lower part of the separation zone increases. When the height is 6.2 m, no obvious bubble layer appeared in the separation zone of the DAF.

By comparing the predicted simulation results, it can be seen that changes in both the length of the separation zone and the height of the DAF tank affect the flow structure within the separation zone and change the air volume fraction distribution. As the length of the separation zone increases, the thickness of the bubble layer on the surface of the separation zone increases, and a stratified flow structure is formed. The horizontal flow structure at the top of the separation zone is disrupted as the height of the DAF tank increases. Both the formation of the stratified flow structure and the disruption of the horizontal flow structure affect the performance of the DAF tank.

### Effect of DAF parameters on bubble removal efficiency

Figures 14 and 15 show the bubble removal efficiency at different separation zone lengths and heights. It can be observed that the change in DAF height and separation zone affects the bubble removal efficiency; however, Equation (4) is commonly used in traditional engineering applications to calculate the bubble removal efficiency, which is established by comparing the air volume fraction in water before and after air flotation treatment. The bubble removal efficiency calculated by this formula is macroscopic and cannot show the influence of structure parameters. Therefore, further theoretical derivation is needed to understand the relationship between structural parameters and bubble removal efficiency.

As Lakghomi *et al.* (2012) reported, the presence of the stratified flow pattern increased the area for clarification and the residence time of bubbles in the separation zone. The increase in residence time made the bubble-bubble contact time increase appropriately, and the mixing of bubbles and particles was more adequate, which was conducive to improving the bubble removal efficiency.

*S*is the thickness of the vertical plug flow layer. The vertical plug flow layer is a flow structure located at the bottom of the separation zone and flows vertically toward the outlet under the action of gravity. The calculation of bubble removal efficiency can be done in a similar way to the calculation of particle removal in sedimentation basins (Edzwald 2010; Crittenden 2012) based on Hazen (1904).where

*L*represents the length of the separation zone,

*U*is the horizontal velocity, and

*v*is the bubble rise velocity.

_{b}For the liquids entering the separation zone, the horizontal travel time in the first horizontal flow layer is . For any bubble, the vertical travel time in the first layer is . If the length of the separation zone increases, the first layer's horizontal travel time will increase and more bubbles will rise to the surface of the water column. When the length of the separation zone is certain, if the thickness of the first layer increases, the vertical path of the bubble rising to the top layer will increase. In addition, the thicker the first horizontal flow layer is, the more bubbles can not rise to the surface and will be brought down to the second layer by liquid.

Although this theory is based on the uniform horizontal velocity and uniform mixing of bubbles in each layer, this equation still shows that variations in DAF height, the baffle height, and separation zone length all have an impact on bubble removal efficiency.

Combined with the theoretical analysis above and the numerical results, it can be observed in Figure 14 that the increase in DAF length is positively correlated with the bubble separation efficiency. When the length of the separation zone is short, more bubbles are distributed at the bottom of the separation zone. As the length of the separation zone increases, the top bubble layer density increases, which is beneficial to bubble removal. The length increases to a certain value and still continues to increase its length, which will lead to a decrease in the density of the top bubble layer, but the bubble removal efficiency still tends to increase because the bubbles at the bottom of the separation zone are significantly reduced.

When the height of the DAF tank is short, the thickness of the area between the top of the baffle and the top of the DAF tank is narrow. According to Equation (6), this makes the bubble removal more efficient. As the height of the DAF tank increases, the number of bubbles on the surface of the separation zone decreases, the number of bubbles at the bottom increases, and the bubble removal efficiency decrease. As shown in Figure 15, the bubble removal efficiency is linearly and negatively correlated with the DAF tank height within a certain variation range. When the height of the DAF tank is too high or too short, the stratified flow is disrupted and the bubble removal efficiency deviates more from the trend line.

Since the derived formula in Equation (6) is built based on assumptions such as uniform horizontal velocity, and uniform mixing of bubbles in each layer. The linear relationship between DAF structure parameters and removal efficiency no longer exists significantly when the structure changes beyond a certain range and leads to the destruction of the layered flow structure; however, the comparison between the above relationship Equation (6) and numerical simulation results, when the top horizontal flow is not destroyed, can reveal the relationship between the effect of the variation of DAF tank height and separation zone length on the bubble removal efficiency.

## CONCLUSION

In the present study, CFD simulations were performed to investigate the expected impact of a DAF tank's separation zone length and depth on the flow patterns within the DAF unit. To achieve this, six different lengths and five different heights were adopted in flow analyses. After comparing analysis results of the air volume fraction, internal flow velocity vectors, turbulence kinetic energy, and stream trace, combined with the bubble removal efficiency, the following conclusions can be drawn.

There is definitely a relationship between the separation zone length and flow structure. In the case of short separation zone length, the surface bubble layer thickness of the separation zone is thin, showing the top water advection layer structure, and the right region of the separation zone has high turbulent kinetic energy. As the length of the separation zone increases, the thickness of the surface bubble layer of the separation zone increases. The back horizontal flow appears under the top layer, forming a layered flow structure, and the turbulence intensity in the near-wall area on the right side of the separation zone is further enhanced. As the length continues to increase, the flow pattern does not change much, and the bubble layer thickness at the top of the separation zone remains unchanged but the bubble density decreases significantly.

Changes in the height of the DAF tank can also affect the internal flow. When the height of DAF is short, the thickness of the bubble layer at the top of the separation zone is thin but the bubble density is high, there is obvious rotational motion in the separation zone, and the turbulence intensity in the DAF is low. With the increase in DAF tank height, the bubble layer thickness increases, the bubble density decreases, and the turbulence intensity of fluid in the whole tank increases. As the height of the air floatation cell continues to increase, the top horizontal flow structure is destroyed and there is no obvious bubble layer distribution in the upper part of the separation zone.

Air bubble removal efficiency is influenced by the length of the separation zone and the height of the DAF tank. A derived formula equation for calculating the bubble separation efficiency including the separation zone length and DAF height is proposed, which was developed based on the gravity separation principle to assist in the analysis of the relationship between bubble separation efficiency and DAF structure. The analysis of the combined theoretical and numerical simulation results shows that when the horizontal flow structure at the top of the separation zone of the DAF tank is not destroyed and stratified flow occurs, the bubble removal rate efficiency is proportional to the length of the separation zone and inversely proportional to the difference between the height of the DAF and the height of the baffle.

## DATA AVAILABILITY STATEMENT

All relevant data are included in the paper or its Supplementary Information.

## CONFLICTS OF INTEREST STATEMENT

The authors declare there is no conflict.

## REFERENCES

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