CFD Simulation of Modified Venturi-Type Gas Dispersers, Installed in a Laboratory Flotation Column

Column flotation is a separation method applied to recover mineral species of interest or to clean effluents contaminated with heavy metals or with organics; in these cases, control of gas dispersion characteristics (bubble diameter, gas volume, and bubble surface area) is important for flotation devices to operate efficiently. Mathematical modeling was carried out using Computational Fluid Dynamics (CFD), for 6 Venturi-type gas disperser designs, varying the diameter ratio (convergent and divergent diameter/vena contracta diameter), and for different air inlets to the disperser. The venturi was simulated and coupled to a laboratory flotation column. The simulation results show that with the diameter ratio in the Venturi equal to 3, the pressure drop values are more stable and represent more homogeneous dispersion characteristics. Regarding the number of air inlets to the disperser, it is concluded that 4 of them at 45° is the most efficient, because it maintains the laminar flow, and the pressure differential is sufficiently large. The feasibility of applying the simulation tool for the design of Venturi-type dispersers installed in a flotation column is shown, by predicting values of gas fractions of up to 18%, and bubble diameters of 0.5 to 2mm.

Keywords:Venturi-type disperser; Gas disperser; Gas holdup; Bubbles design; CFD simulation; Flotation columns

Bubble size and gas fraction (gas holdup) reflect the efficiency in a flotation process; these factors are in part defined by the type of gas disperser used, there is the advantage of mathematically simulating dispersion devices by applying Computational Fluid Dynamics (CFD) theory [1], changing the volumetric flows of liquid and gas fed to the gas dispersers. The results obtained from the mathematical simulation show a good correlation with the experimental results [2,3]. The control of the surface area flow of bubbles, on the other hand, guarantees the possibility of mass transport or transport of a certain species attached to the bubbles [4]. Due to the various applications of gas dispersion systems, the control of their size and concentration is important and has been the subject of various investigations for years [5,6]. Flotation systems using microbubbles with diameters less than 100μm tend to remove numerous contaminants (e.g., colloids, metal ions, microorganisms, proteins, oil emulsions, and fine and ultrafine particles), in wastewater treatment [7]; however, bubbles with diameters between 0.5 and 2mm are used to float larger or heavier particles, such as valuable mineral species [8,9]. The use of the Venturi as a bubble generator in gas-liquid systems generates a wide range of bubble sizes from microns to millimeters [5,10-12]. This disperser is divided into three sections: convergent, throat or vena contracta, and divergent section. As for the bubbles, they are generated by the increase in pressure in the section of the vena contracta, caused by the feeding of liquid and gas, which, when exiting through the divergent section of the venturi, transforms into bubbles [3]. Due to the advantages in their use, Venturi-type dispersers are currently seeing a certain rise in design studies, but all research agrees that the control of the characteristics of the dispersion they generate is the main factor of efficiency in their application [13-17].

Computational Fluid Dynamics (CFD) is a tool that emerged in recent years as an instrument to predict the hydrodynamics and performance of systems that involve fluid dynamics, such as flotation systems. This is due to the sensitivity of CFD programming to recalculate systems with changes in the design and operation of systems of different phases, this has helped to understand complex flow systems and allows the analysis of performance within a given system, saving the cost of physical experimentation [18]. For CFD models, a flotation system is discretized into finite volumes in which the local values of the system are determined. Understanding the physical phenomena in the system will be achieved by achieving maximum efficiencies in the processes simulated and then adapted or corrected. For example, in the case of the simulation of flotation in columns, the results help in the analysis of fluidbubble- particle interactions in a real system [2,19,20]. In most of these investigations, the efficiency of capturing solid particles with bubbles is modelled as three subprocesses involving collision, adhesion, and detachment. It should be taken into account that, in these investigations, the effect of the density of the particles attached to the bubbles is not considered.

The basis of CFD modelling is to solve the continuity equation, and the Navier-Stokes equations for incompressible Newtonian fluids, which are based on the conservation of mass (one equation), and momentum (three equations) at each point in the domain. The solution of these equations provides the pressure and velocity components at each of the points in the domain, and if high flow velocities are involved in this process, turbulent fluid flow must be incorporated into such models [3]. The objective of this research is to examine the effect of the design of the modified Venturi-type disperser, in terms of the air injection points and the diameter ratio (d₁/d₂), on the characteristics of the gas dispersion generated in a column of floatation.

In flotation processes, the dispersion of gas in the form of bubbles in a liquid is carried out to have gas-liquid contact. To disperse a gas in a liquid it is possible when a liquid is volatile and can be vaporized, either by decreasing the pressure of the system or by increasing its temperature, also by a chemical reaction that produces a gas, or equally introducing the gas into the liquid through a disperser, although another way would be through the destruction of a large bubble or a gas current caused by turbulence in the liquid. The design of the gas dispersers used in flotation processes decisively influences the size distribution of the bubbles produced and, consequently, the fraction of gas retained, the interfacial area, and the flotation speed. Once the gas-liquid dispersion has been generated through a disperser installed at the base of the column, the cloud of bubbles enters the device from its base and rises until it exits at the top of the column [21].

In a Venturi-type disperser the system seeks its mechanical equilibrium and the reduction in diameter in the vena contracta of the disperser increases the energy within it. The flows of liquid and air through the venturi continue and as it passes through the expansion of the disperser, the released energy is converted into air bubbles; that is, by increasing the flow of liquid, as well as compressed air through the venturi, the number of bubbles increases, which represent more of the system’s capacity to capture and separate a certain species. Figure 1 shows the diagram of a Venturi-type disperser.

Figure 1:Scheme of a modified venturi-type disperser, with the three geometric characteristics: convergent diameter (d₁), vena contracta (d₂), and divergent diameter (d₃), with d₃=d₁.

According to Bernoulli, the mechanical balance in the disperser is indicated by equation 1.

Where Δp is the pressure drop between points 1 and 2 in centimeters of water column (cm H₂O), ρ is the density of the liquid in gr/cm³; V₁ and V₂ are the surface velocities at points 1 and 2, respectively in cm/s, and g is the acceleration due to gravity. On the other hand, the continuity equation is shown in equation (2).

A₁ and A₂ are the cross-sectional areas at points 1 and 2, respectively (cm²). The surface velocity of a fluid in cm/s is the relationship that exists between the flow rate Q in cm³/s, fed to the disperser, and the cross-sectional area of the section in cm², as indicated in equation (3).

The cross-sectional area of a circular section is defined with equation (4), where “d” is the diameter of the section.

The pressure differential depends on the diameter ratio in the venturi; that is, as the diameter of the vena contracta decreases, the velocity of the fluid at this point increases, as well as the pressure; conversely, when fluid passes from the vena contracta to the divergent section, fluid velocity, and pressure decrease. According to Bernoulli, and by the continuity equation, the above is expressed by equation (5).

On the other hand, the interaction of the gas-liquid system is defined by the way the gas is dispersed in the continuous phase; for instance, in a flotation column, the size of the bubbles and their distribution varies with height, due to coalescence and the expansive nature of the air [22]. The characteristics of gas dispersions are bubble size, fraction of retained gas, and bubble surface area; the main factors that determine the values of these characteristics are the type of disperser, the airflow, as well as the surface tension and viscosity of the liquid. In the case of the venturi-type disperser and according to what is shown by equation (5), the dispersion characteristics depend on the air and liquid flows, the density of the fluids, and the diameter ratio in the convergent section, and the vena contracta [23]. To fully describe the flow pattern of a fluid, it is necessary to know the properties of the system, such as density, pressure, and velocities in the three spatial directions of the system (u, v, w) corresponding to the axes (x, y, z). Because the system is made up of six unknowns, six equations are needed to find the solution to the three-dimensional flow, which are obtained from the five Navier-Stokes equations in conjunction with the ideal gas law [24,25]. For multiphase systems where the dispersed phases (particles, bubbles, or drops) are very small (on the order of micrometers), with CFD models it is possible to adequately simulate them. The accuracy of the simulations is limited not by computer speed or memory, but by the lack of good models to solve multiphase flow. In the case of the venturi in this study, the Volume of Fluid (VOF) model is applied for multiphase flows by tracking the interface between the different phases. This model is suitable for stratified flow, free surface flows, and movement of large bubbles in liquids, as is the case in flotation systems [23].

Turbulence is defined as the state of movement of a fluid in which the relevant variables, such as pressure and velocity, fluctuate disorderly. In turbulent flow, molecules move chaotically along complex irregular paths. This chaotic movement causes the different layers of the fluid to mix intensely. Due to the greater exchange of momentum and energy between molecules and solid walls, turbulent flow causes greater surface friction and heat transfer compared to laminar flow. Although the chaotic fluctuations of flow variables are deterministic, the simulation of turbulent flows still presents a major problem [26]. The equations proposed to model turbulence are similar to the Navier-Stokes equations in the sense that they have a derivative concerning time in addition to convective terms, diffusive terms, and source terms. Several ways have been proposed to solve this problem using different approaches; for example, Direct Numerical Simulation (DNS), Large Eddy Simulation (LES), Reynolds-Averaged Navier- Stokes Models (RANS), among which are the k-ε model, and the Reynolds Stress Model (RSM), which take viscosity into account. All these approximations are considered in the CFD models to be solved with the support of a computer. In closed ducts, where pressure drops are experienced, the laminar regime occurs for Reynolds numbers less than 3000; although Re numbers less than 5,500 are considered transitional before turbulence [27].

For the construction of the volume and geometry of the disperser, AutoCad® software was used, and then this geometry was exported to the ANSYS® system. The venturi model was made in 3 dimensions according to the location and number of air inlets in the vena contracta. For the meshing that determines the control volumes required by the software, the Meshing sub-application within the Fluent application was used (specially designed for fluid dynamics analysis). In the first stage of modeling, 6 Venturi geometries were designed, with a single air inlet at 45° concerning the flow line in the vena contracta (Figure 2), with the diameter relationships in the venturi shown in Table 1. Only water entry was considered at flows of 1 to 6 L/min, while the air that entered the Venturi was what the system allows naturally, according to Bernoulli’s principle. At this stage, no compressed air was supplied to the disperser to avoid the turbulent flow regime in the vena contracta.

Figure 2:Design and meshing of the venturi with 1 air inlet at 45° concerning the fluid flow in the vena contracta.

Table 1:Diameter ratio for the first simulation stage of the venturi disperser with water flow rates of 1, 2, 3, 4, 5, and 6L/min.

Table 2:Venturi simulation parameters, with a duration of 10 seconds.

Based on the results of pressure drop in the venture, and choosing those where laminar flow or transient state occurs, the second simulation stage was established, resulting in 1 disperser with a diameter ratio equal to 3 (d1 0.381m, and d2 0.127m). This disperser was now simulated by varying the compressed air entry points in the vena contracta at 45° by 1, 2, 4, and 8, and an additional venturi simulation with an air entry at 90°. During the simulation, the Cartesian coordinate system was considered, the fluid within the system was Newtonian, constant thermophysical properties as there were no temperature changes, no friction on the walls that contain the fluid, constant water and air flow rates (4.71, and 3.86L/min, respectively), the force of gravity acting vertically (about the Z axis), the dimensions of the scatterer and the column remain constant during each simulation. Table 2 shows the parameters considered in the simulation of the 5 Venturi dispersers for 10 seconds.

In the third part of the simulation, the Venturi with 4 and 8 inlets were selected, with a duration of 60 seconds, installed in the laboratory flotation column of 0.1m in diameter and 2.65m in height. The water and air flows correspond to a surface velocity of 0.01m/s, which, according to reports on the operation of flotation columns, at this value, the change from laminar to turbulent regime occurs and corresponds to the 0.1m column in diameter [27]. Table 3 shows the simulation parameters of this stage. As can be seen in Figure 3, for the Venturi disperser with more than one inlet, a circular tubular air distributor was considered to ensure a homogeneous supply of air to the Venturi.

Table 3:Simulation parameters during the third stage with a duration of 60 seconds.

Figure 3:Design and meshing of the venturi with 4 air inlets at 45° concerning the flow axis in the vena contracta.

From the first series of simulations, the pressure differentials generated for the different diameter ratios of the venturi disperser were analysed. Considering that the formation of bubbles and their performance in the flotation column must be under a laminar flow regime, appropriate diameter relationships were established that do not result in turbulent regimes that favour bubble coalescence. Taking the transition Re value as a reference, diameter ratios were chosen whose Re is less than 5500, but with the highest liquid flow, which means higher pressure drops that transform into bubbles when leaving the disperser. The venturi with Re less than 5500 corresponds to a diameter ratio equal to 3, and a water flow rate of 6L/min. Table 4 presents the simulation results of this stage. In the simulation results shown in Figure 4-8, the behavior of the water and air interfaces can be seen, at fully developed flow, after 10 seconds of simulation. As shown in Figure 9, four points were established inside the venturi to monitor the variables of interest, such as partial pressure, total pressure, velocity in its 3 components, turbulent kinetic energy, dissipation, and viscosity. With this simulation, the data necessary to calculate the gas fraction in the column was obtained, and the average bubble diameters generated were estimated through the Drift Flux model. Table 5 shows the values of the monitored variables.

Figure 4:Interface in the venturi disperser of 1 air inlet of 6mm at 90°.

Figure 5:Interface in the venturi disperser with 1 air inlet of 6mm at 45°.

Figure 6:Interface in the venturi disperser with 2 air inlets of 6mm at 45°.

Figure 7:Interface in the venturi disperser with 4 air inlets of 6mm at 45°.

Figure 8:Interface in the venturi disperser with 8 air inlets of 6mm at 45°.

Figure 9:Control points or measurement of variables inside the venturi, for all simulations.

Table 4:Pressure differentials and Reynolds numbers, according to the different diameter ratios and for the proposed flow rates. First experimental stage.

Table 5:Values of the variables monitored during the operation simulation of the different venturi disperser models.

From the previous table, a certain stability in the pressure drop is observed for the case of the venturi with an air inlet at 45°, which ensures that the bubbles generated will be of a homogeneous diameter, compared to the gas dispersion that will be generated with the disperser that has the air inlet at 90°. Regarding the pressure drop in the venturi where the number of air supply inlets was varied, the pressure drop increases with the number of inlets, until this pressure decreases drastically, perhaps caused by the bubble coalescence phenomenon in the vena contract, which decreases the density of the liquid-gas system and therefore results in a decrease in pressure. The previously established is supported by what is observed in Figure 10, which corresponds to the results of the simulation of dispersers with 4 and 8 air inlets, installed in the flotation column of 0.1m in diameter, but for 60 seconds. For their part, Figure 11 & 12 graphically show the evolution of the characteristics of the gas dispersions during the simulation.

Figure 10:The behavior of interfaces in the venturi with 4, and 8 air inlets in the simulation with a column for 60 seconds.

Figure 11:Bubble diameter for venturi with 4 and 8 air inlets; simulation with the column up to 60 seconds

Figure 12:Gas fractions are calculated from pressure drop values. Simulation for 60 seconds of venturi with 4 and 8 air inlets, installed in the column.

From the mathematical simulation of venturi-type dispersers with different diameter ratios and several air inlets, installed in a laboratory flotation column, the following conclusions are derived: Compared to the venturi with a 90° air inlet, the 45° one observes more stable pressure drops, even regardless of the number of air inlets to the vena contracta. The venturi with 4 air inlets reaches pressure drop values of the order of 260cm H2O [28]. With 8 air inlets, the pressure decreases due to the transition to a turbulent regime that causes the coalescence of bubbles, and therefore a decrease in the volume of gas, and surface area of bubbles. By predicting values of gas fractions of up to 18% and bubble diameters of 0.5 to 2mm, the results demonstrate the feasibility of applying the simulation tool for the design of venturi-type dispersers installed in a flotation column, for example, to separate valuable mineral species during mineral processing, or even in non-mineral applications, such as cleaning effluents contaminated with grease or organic species.

The financial support for this work is from the Consejo Nacional de Ciencia Humanidades y Tecnología (CONAHCyT), from Mexico. José Guadalupe González Valencia deeply thanks CONAHCyT for the scholarship during his Ph.D. studies through the grant (902631).

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