Computational fluid dynamics (CFD) models of dissolved air flotation (DAF) have shown formation of stratified flow (back and forth horizontal flow layers at the top of the separation zone) and its impact on improved DAF efficiency. However, there has been a lack of experimental validation of CFD predictions, especially in the presence of solid particles. In this work, for the first time, both two-phase (air–water) and three-phase (air–water–solid particles) CFD models were evaluated at pilot scale using measurements of residence time distribution, bubble layer position and bubble–particle contact efficiency. The pilot-scale results confirmed the accuracy of the CFD model for both two-phase and three-phase flows, but showed that the accuracy of the three-phase CFD model would partly depend on the estimation of bubble–particle attachment efficiency.

## INTRODUCTION

The dissolved air flotation (DAF) process is known for its efficiency in the removal of low-density particles from water. The performance of the system depends, in part, on the hydrodynamics of the flow. Both experimental measurements and mathematical models have been applied in the past to evaluate DAF hydrodynamics. Several studies have used direct velocity measurements including laser Doppler velocimetry and acoustic Doppler velocimetry to investigate the flow pattern in DAF (Hague *et al.* 2001; Lundh *et al.* 2001). These methods can be expensive, susceptible to errors due to the high concentration of bubbles, and have been limited to small pilot-scale units (Haarhoff 2008; Edzwald 2010). Despite their limitations, these techniques have helped to provide a better understanding of the major flow features and their significance in DAF systems. A study by Lundh *et al.* (2001) reported the presence of a stratified flow pattern in which water traveled in a horizontal layer in the top of the separation zone toward the far wall, and then traveled back to the baffle in a second horizontal layer underneath the first, in a small pilot-scale DAF tank under certain conditions. The concept of this stratified flow was used to qualitatively explain the feasibility of higher loading rates in DAF by some researchers (Edzwald 2007). The study by Lundh *et al.* (2001) was, however, limited to a pilot-scale shallow tank and could not be easily extended to full-scale DAF design. In addition, it focused on two-phase flow conditions in the absence of solid particles and coagulation.

In general, velocity measurement in an opaque solution in the presence of solid particles is very challenging (Edzwald 2010). Computational fluid dynamics (CFD) can be applied as an alternative approach to evaluate the effect of geometry and presence of solid particles, but would still require some means of validation. Lakghomi *et al.* (2015) developed a multiphase CFD model of a DAF system to account for the presence of solid particles and formation of bubble–particle aggregates. Their model was able to predict the formation of stratified flow and demonstrated that stratified flow can improve bubble and particle removal. The model of Lakghomi *et al.* (2015), however, was based on the same shallow DAF geometry used by Lundh *et al.* (2001) and was not compared to experimental data. Furthermore, a perfect attachment efficiency (*α* = 1) between bubbles and particles was assumed in their calculation of removal efficiency.

In this work, CFD model predictions of a pilot-scale DAF unit were compared to experimental results of a large-scale pilot DAF system for two-phase and three-phase flow conditions. First, an attachment efficiency (*α*) was obtained through bench-scale measurements as an input for the CFD model. The CFD predictions were then compared to the pilot system using measurements of residence time distribution (RTD), bubble layer position and bubble–particle contact efficiency. The effects of air, loading rate, solid particles and attachment efficiency on the flow pattern were evaluated. As will be demonstrated, the results of this study show that the model and experimental results are in good agreement; thus they experimentally confirm the previous theory with respect to formation and impact of stratified flow. The results also suggest that the CFD model can be used with a degree of confidence to further optimize DAF system design.

## METHODOLOGY

### DAF pilot plant

All the trials were performed using a DAF pilot system developed by Corix Water Systems, Canada (Figure 1). The pilot apparatus consisted of two-stage mechanical flocculation with vertical axis paddles and a rectangular flotation unit. The flotation unit was 2.74 m in depth, 1.3 m in length, and 0.3 m in width. Tap water was used for all of the experiments. For three-phase flow conditions, a bentonite suspension (Sigma-Aldrich) was spiked continuously in the influent pipe to generate a 40 mg bentonite/L suspension. Aluminum sulfate liquid solution (Chemtrade Chemicals Canada Ltd) was fed as the main coagulant to the influent pipe ahead of a static mixer to provide a concentration of 30 mg/L based on maximum turbidity removal in bench-scale jar tests. Polymer (Percol LT22S) was directly pumped into the first flocculator at a concentration of 0.1 mg/L as a flocculation aid. The first and second stage flocculator speeds were set to provide estimated *G*-values of 70 and 10 s^{−1}.

The inflow water rate varied between 55 L/min (with mean hydraulic retention time of 19.4 minutes) and 110 L/min (with mean hydraulic retention time of 9.7 minutes). The recycle flow was treated water that was pumped to the vertical saturator and saturated with air at 520 kPa. The recycle water was then introduced into the bottom of the contact zone through two nozzles. The recycle rate could be controlled by opening one or two of the recycle valves. The recycle flow rate was set to 6.5–7.8 L/min by opening one recycle valve.

The front surface of the flotation unit was made of Plexiglas to allow visualization of the bubbles and tracer. The system was assumed to reach steady-state when the bubble layer location no longer changed with time. Tracer injection and sampling commenced after the system was assumed to be in steady-state.

### Tracer testing

A step input tracer experiment with rhodamine dye was used to evaluate the flow pattern in the contact and separation zones. A 0.3 g/L stock solution of rhodamine B was prepared in a separate feed tank and was supplied at a constant flow rate at the inlet of the contact zone using a peristaltic pump. An injector with uniform pores helped to ensure uniform distribution of the tracer along the width of the contact zone. The samples were collected at the outflow in 1 minute intervals for three retention times after the injection was started, and the tracer concentration was measured at the peak absorption wavelength of 543 nm using a UV–visible spectrophotometer (DR 3900 Hach). A step tracer input was used as it allowed uniform mixing of the tracer along the width of the contact zone. The tracer results are subsequently reported as residence time distributions (*E*-curves), which were obtained by numerically differentiating the cumulative tracer concentrations (i.e., the *F*-curves) recorded in the tests (Levenspiel 1999).

### Particle size measurement

*et al.*2001), particle–particle attachment was assumed to be negligible. As a result, the change in particle concentration for a given size range from inlet to the outflow would represent the number of particles of that size that have contacted with the bubbles and formed aggregates, and therefore, similar to Haarhoff & Edzwald (2004), the contact efficiency for that given particle size can be calculated as:

Size range (μm) | 2–5 | 5–10 | 10–15 | 15–25 | 25–50 | 50–75 | 75–100 | >100 |

Size range (μm) | 2–5 | 5–10 | 10–15 | 15–25 | 25–50 | 50–75 | 75–100 | >100 |

### Batch DAF jar test

The purpose of the batch jar tests was to obtain an optimum coagulation dose in the pilot plant based on turbidity reduction, and to estimate the average attachment efficiency as an input for the CFD model. A DBT6 batch DAF jar tester from EC Engineering was used for this work. The 1 L jars were filled with tap water and spiked with 40 mg/L of bentonite powder (Sigma-Aldrich). After addition of the coagulant, water was mixed at 150 rpm for 10 seconds (to simulate the static mixer in the pilot system), 60 rpm for 10 minutes (to simulate the first flocculator), followed by 30 rpm for 10 minutes (to simulate the second flocculator) to replicate the conditions of the pilot plant. Subsequently, the mixing was stopped, 100 mL of air-saturated water mixture (520 kPa) was injected, and the turbidity removal was measured after 5 minutes using a Hach 2100 turbidimeter. The tests were performed with aluminum sulfate doses between 10 and 50 mg/L, and Percol LT22S cationic polymer doses from 0.1 to 0.5 mg/L. Maximum turbidity removal of 38.1% at bench-scale was observed with 30 mg/L of aluminum sulfate and 0.1 mg/L polymer.

*et al.*2001). can be estimated as: where

*K*is the collision frequency obtained from the model of Kostoglou

*et al.*(2007) as a function of bubble and particle size, and are particle and bubble number concentrations, is the initial particle concentration, and represent bubble volume fraction and bubble diameter. The contact time,

*t*, in the batch jar tester is calculated as where

*l*is the height of the batch tester and

*v*

_{b}is the bubble rise velocity, equal to . and are bubble and water density, and is water viscosity. Bubble and particle sizes are assumed to be 40 μm and 7.5 μm, respectively, similar to those in the pilot plant.

From Equation (2), for 38.1% turbidity removal, attachment efficiency was calculated to be 0.16. For good coagulation conditions, a higher attachment efficiency between 0.5 and 1 was reported previously (Haarhoff & Edzwald 2004). The CFD model was repeated for *α* = 0.5 and *α* = 0.8 in addition to the estimated value from the bench-scale result (i.e., *α* = 0.16), to observe the impact of *α* on predicted DAF performance.

### CFD model

The single-phase, two-phase and three-phase CFD models were developed using ANSYS FLUENT (ANSYS 2013). The position of the bubble layer from two-dimensional and three-dimensional models for the loading rate of 12 m/hour differed by less than 3.5%; therefore, two-dimensional modeling was applied for the simulations. Two-phase and three-phase flow conditions were modeled using the FLUENT mixture model. For two-phase flow, bubbles and water were modeled as phases while bubble aggregation was included through a discrete population balance method. For three-phase flow, bubbles, water, and aggregates were modeled as phases and the particles were modeled as a user-defined passive scalar (UDS). Bubble–particle attachment and the formation of aggregates were modeled through user-defined mass source terms, and the collision frequency between bubbles and particles was calculated as a function of size and turbulence similar to Lakghomi *et al.* (2015). For modeling turbulence, the *k*-epsilon turbulence method (based on two empirical equations) was applied. More details of the modeling methodology can be found in Lakghomi *et al.* (2012, 2015).

The CFD simulation was limited to the DAF tank, with the flocculation step prior to DAF not included in the CFD model. The recycle stream was not modeled separately, and a blended air–water mixture with the same amount of air was introduced at the inlet. The geometry was divided into 160,136 structured elements. A mesh independence test was performed using 320,272 structured elements, which changed the position of the bubble layer by less than 2.7%. An inlet bubble size distribution of 0–160 μm with four different bins was assumed (Table 2) with an average bubble size of 40 μm, similar to Leppinen & Dalziel (2004).

Bubble size groups (bins) | 0–20 (μm) | 20–40 (μm) | 40–80 (μm) | 80–160 (μm) |
---|---|---|---|---|

% | 15 | 50 | 30 | 5 |

Bubble size groups (bins) | 0–20 (μm) | 20–40 (μm) | 40–80 (μm) | 80–160 (μm) |
---|---|---|---|---|

% | 15 | 50 | 30 | 5 |

For the single-phase flow (water only) a steady-state simulation was performed. For the two-phase and three-phase models a transient simulation of the conservation equations for water, air (bubble), and aggregate phases was conducted (Lakghomi *et al.* 2015). For each time step, 100 iterations were performed, and convergence was assumed to be achieved when the residuals decreased to less than . The simulation was continued for three retention times until a quasi-steady-state solution was obtained and the average bubble layer position in the separation zone (represented by air volume fraction of 0.0001) and mixture velocity at different points did not change. An overall system mass balance convergence criterion of less than was also implemented. Then, the tracer concentration was modeled as a UDS for the primary phase (water). The tracer concentration was initialized at the inlet, and it was recorded over time at the outflow to obtain the residence time distribution.

## RESULTS

In this work, pilot-scale measurements in a DAF tank were used to evaluate the accuracy of the CFD model previously presented in Lakghomi *et al.* (2012, 2015). First, the residence time distributions from CFD and pilot-scale measurements were compared. Evaluation of the CFD model was undertaken at different loading rates for single-phase (water), two-phase (water, air) and three-phase (water, air, and solid) conditions. Figure 2(a) shows the CFD and experimental RTD curves for single-, two- and three-phases at a loading rate of 12 m/hour. The measured tracer concentration is normalized by the nominal concentration *C*_{Tot,max}, defined as the total mass of the tracer over the total volume of the tank, and time is introduced in dimensionless form of *t*/*T* where *T* is the nominal residence time at the given loading rate. The comparison between CFD and tracer results in Figure 2(a) shows good general agreement between the model prediction and experimental RTDs. A two-sample Kolmogorov–Smirnov test was applied to compare the distributions of the values in the CFD and pilot RTDs. This test quantifies the distance between the empirical cumulative distribution functions of two samples. The satisfaction of the null hypothesis (*h* = 0) would demonstrate that the two data samples come from the same distribution. The comparison satisfied the null hypothesis (*h* = 0) at the 90% confidence interval for all of the two-phase and three-phase conditions (i.e., the CFD model accurately predicted the tracer test results).

Additional comparisons between the predicted and measured RTD results were then performed using three methods: (i) an *R*^{2} value; (ii) the number of conceptual continuous stirred tank reactors (CSTRs) best representing the flow (*N*); and (iii) log normal distribution parameters ( and ). The coefficient of determination, , was calculated based on the variance of the difference between experimental and CFD predictions of C/C_{Tot,max} at each t/T . *R*^{2} values of higher than 0.70 and 0.68 were observed for all two-phase and three-phase flow conditions (Table 3), demonstrating good agreement between CFD predictions and experimental measurements. The CFD and experimental RTDs were then fit to the conceptual CSTRs-in-series model, . The number of conceptual CSTRs (*N*) represents the degree of mixing in the tank, and as *N* increases, the flow pattern changes from a completely mixed reactor toward a plug flow reactor. The *N* values showed good agreement between the RTDs for CFD predictions and experimental measurements (Table 3), and also showed similar trends with the addition of particles and an increase in the loading rate. The results were also fit to a log normal distribution, , where λ and σ are location and scale parameters of the distribution. The fitted log normal distributions from CFD were also in agreement with the experimental distributions (Table 3), showing that σ increases with an increase in loading rate and addition of particles.

Loading rate (m/hour) | 12 | 18 | 24 | |||
---|---|---|---|---|---|---|

One-phase | ||||||

R^{2} | 0.824 | |||||

Two-phase | ||||||

CFD | EXP | CFD | EXP | CFD | EXP | |

N | 25 | 29 | 15 | 21 | 9 | 10 |

−0.069 | −0.083 | −0.134 | −0.151 | −0.181 | −0.199 | |

0.183 | 0.174 | 0.238 | 0.251 | 0.298 | 0.277 | |

R^{2} | 0.938 | 0.709 | 0.870 | |||

Three-phase, α = 0.16 | ||||||

CFD | EXP | CFD | EXP | CFD | EXP | |

N | 19 | 16 | 14 | 10 | 9 | 6 |

−0.148 | −0.108 | −0.158 | −0.169 | −0.185 | −0.174 | |

0.199 | 0.234 | 0.263 | 0.274 | 0.344 | 0.328 | |

R^{2} | 0.774 | 0.723 | 0.684 |

Loading rate (m/hour) | 12 | 18 | 24 | |||
---|---|---|---|---|---|---|

One-phase | ||||||

R^{2} | 0.824 | |||||

Two-phase | ||||||

CFD | EXP | CFD | EXP | CFD | EXP | |

N | 25 | 29 | 15 | 21 | 9 | 10 |

−0.069 | −0.083 | −0.134 | −0.151 | −0.181 | −0.199 | |

0.183 | 0.174 | 0.238 | 0.251 | 0.298 | 0.277 | |

R^{2} | 0.938 | 0.709 | 0.870 | |||

Three-phase, α = 0.16 | ||||||

CFD | EXP | CFD | EXP | CFD | EXP | |

N | 19 | 16 | 14 | 10 | 9 | 6 |

−0.148 | −0.108 | −0.158 | −0.169 | −0.185 | −0.174 | |

0.199 | 0.234 | 0.263 | 0.274 | 0.344 | 0.328 | |

R^{2} | 0.774 | 0.723 | 0.684 |

An additional verification of the two-phase CFD predictions on the effect of loading rate was performed by comparison of the bubble layer position from CFD predictions and measurement through the Plexiglas wall in the pilot plant. Both CFD and observations at the pilot plant showed that the position of bubble layer moved down in the tank and reached the collection system at the loading rate of 18 m/hour (Figure 3). Experimental data were only available at three loading rates (i.e., 12, 18, and 24 m/hour), but CFD simulations were performed at two additional loading rates (i.e., 6 and 15 m/hour) to provide a better understanding of the change in bubble layer position with increase in loading rate.

The CFD model and the pilot experiments can be used to evaluate the effect of different parameters on the RTD. The presence of air is, in general, known to lead to the formation of stratified flow in the separation zone (Lundh *et al.* 2001; Lakghomi *et al.* 2012). Both experimental measurements and CFD demonstrated that with the addition of air, the concentration peak was observed closer to the average residence time and at a higher value (Figure 2(a)). From the RTD measurements, the concentration peak increased by 93% and was observed 0.43 T closer to the average retention time in the presence of air. Similarly, CFD showed the peak 0.35 T closer to the average retention time and with a 119% increase in the peak value when air was added. A higher concentration peak that is closer to the average residence time implies that the presence of air reduces dispersion and leads to more plug-flow-like conditions. For single-phase flow, the experimental RTD also shows the presence of additional small concentration peaks in the tail region. Multiple decaying peaks can indicate strong internal recirculation (Levenspiel 1999). Here, it is hypothesized that these smaller peaks are associated with the internal recirculation of the flow in the whole separation zone for single-phase flow. With addition of air and the formation of stratified flow, the tracer is mixed within the stratified layer at the top of the separation zone, which leads to the disappearance of the smaller peaks in the tail region.

CFD and tracer tests were also utilized to evaluate the effect of loading rate on the RTD in the presence of air. Both CFD and tracer tests showed that with an increase in the loading rate, the concentration peak had a lower value and was observed at a smaller *t*/*T*. With an increase in the loading rate from 12 to 24 m/hour, the concentration peak decreased by 25% as predicted by CFD and 21% in tracer measurements (Figure 2(b)). With an increase in loading rate from 12 to 24 m/hour, the flow moved away from stratified flow (Lakghomi *et al.* 2012) toward internal recirculation, which may explain the quick transport of the tracer to the outflow without mixing within the whole volume of the separation zone (Lundh & Jonsson 2005).

The RTD curves were also used to evaluate the effect of the presence of particles on the flow pattern. In the presence of solid particles, the concentration peak decreased showing that the flow pattern was moving away from plug flow with the addition of the particles. Figure 2(a) shows that with the addition of bentonite particles (40 mg/L), for a loading rate of 12 m/hour, there was a 19% decrease in the concentration peak from the tracer measurements and an 8% decrease as predicted by the CFD model. With the formation of particle–bubble aggregates that have a smaller rise velocity than bubbles alone, the flow moves away from the stratified pattern, leading to higher dispersion and a lower concentration peak.

The effect of particle–bubble attachment efficiency on the predicted RTDs was also tested. The CFD model with *α* = 0.16 shows less agreement with three-phase experimental RTDs compared to two-phase (Figure 2(a)). Therefore, the three-phase CFD simulations were repeated with two additional attachment efficiencies (i.e., *α* = 0.5 and 0.8) for a loading rate of 12 m/hour (Figure 2(c)). A better agreement between the three-phase CFD predictions and the experimental measurements was obtained with *α* = 0.5 providing an *R*^{2} value of 0.85. The results, therefore, show that the accuracy of the three-phase CFD RTDs depends on the estimated attachment efficiency.

Bubble–particle contact efficiency was also compared between CFD predictions and pilot measurements. The contact efficiency represents the ratio of the particles that are converted to aggregates to the number of particles entering the system. CFD simulations were performed for *α* = 0.16 (from bench-scale estimations) and *α* = 0.5 (representing the best fit to the experimental RTD). Particle counts showed that there is a general increase in contact efficiency with an increase in particle size up to 37.5 μm, which is in agreement with the CFD model predictions (Figure 4). CFD predictions with *α* = 0.5 provided a better agreement with the experimental contact efficiency, compared to the case when a value of *α* = 0.16, based on bench-scale tests, was used in the CFD model, which led to less attachment and an underestimate of the overall contact efficiency. Therefore, similar to three-phase RTDs, the accuracy of three-phase CFD predictions was shown to depend on the estimated attachment efficiency in the model.

## CONCLUSIONS

For the first time, both two-phase and three-phase CFD model predictions for a DAF system have been experimentally validated, with good agreement observed based on comparison of RTDs, bubble layer position, and bubble–particle contact efficiency. The experimental RTDs showed that the addition of air enhanced flow stratification, whereas with the addition of particles and an increase in loading rate, the flow pattern moved away from stratified flow. The pilot-scale results confirmed the accuracy of the CFD model for both two-phase and three-phase flows (the comparison satisfied the null hypothesis (*h* = 0) at the 90% confidence interval for all conditions), but showed that the accuracy of the three-phase CFD model would partly depend on the estimation of attachment efficiency. Overall, the study showed that the developed CFD model can predict formation of stratified flow under different conditions and can be applied with confidence for further optimization of DAF in the future.