In Flotation Equipment, the operation takes place in a highly turbulent flow. Therefore, the modelling as well as the optimization of a flotation process necessitate the application of essential results of the statistical turbulence theory, where an extensive simplification of the complicated laws is typical for the application in processing. Three effects of turbulence are important in flotation: the turbulent transport phenomena (suspension of particles), the turbulent dispersion of air and the turbulent particle–bubble collisions. While the transport phenomena are mainly caused by the macroturbulence, the microturbulence controls the two last-named microprocesses. In the paper a brief introduction of the theoretical background is given as far as it is necessary for modelling. The effect of turbulence damping by fine particles is also discussed. Models of the microprocesses air dispersion and particle–bubble collisions are presented, and it is clearly demonstrated that the particle–bubble attachment almost exclusively occurs in the zone of high energy dissipation rates, i.e., in the impeller stream. Further on, it is shown that the entrainment of fine particles into the froth lamellae is a result of the suspension state and, therefore, can be influenced by the design of the turbulence generating system (impeller–stator system). Finally, it is demonstrated that there is no feasibility to achieve optimum hydrodynamics for all particle sizes simultaneously. For coarse particle flotation, the power input should be minimized (generation of coarser bubbles; stronger buoyancy and lower turbulent stresses acting on the particle–bubble agglomerates!). In contrast to this, fine particle flotation requires high turbulent collision rates, i.e., a higher power input.

Mineral flotation machines are classified into two main types; forced air and self-aerated machines. Wemco machines are widely used self-aerated machines where no air pumping mechanism is required, which simplifies flotation plant design and operation. The rate of air flow and power consumption of Wemco machines depend on the flow structure and the hydrodynamics within the pulp volume. For a given machine, rate of airflow depends on the rotor speed (RPM) among other operating conditions such as rotor blades and disperser design. Instantaneous airflow rate in a Wemco machine is not known a priori and depends on machine design and operating conditions. Therefore, computational fluid dynamics (CFD) simulation of a Wemco machine is a challenging problem because airflow rate cannot be specified but it has to be an outcome of the simulation. Moreover, rate of air flow may vary significantly with time to the extent that air is temporarily "exhaled" by the standpipe instead of being "inhaled". Computer simulations of such a machine should predict the time-history of the rate of air flow, and the average rate is an output. The unknown rate of air flow and the possibility of "breathing" require careful treatments of the standpipe and pulp–froth interface boundary conditions. Koh and Schwarz conducted CFD simulation of the self-aerated flotation machine Denver-Metso Minerals. In that machine, air flow rate depends on suction pressure created by the impeller, the hydrostatic head of the pulp, and the frictional losses along the delivery shaft from the inlet valve to the impeller. The air motion was not simulated in the standpipe. They predicted the air flow rate iteratively during the simulation by applying pressure loss formula to find the pressure drop in the standpipe. An empirical constant in the formula was adjusted for CFD simulations to match the experimental data.

Computational domains of flotation machines are large, and flow physics are complex involving multi-phase flow turbulence. Even two-phase flow simulations of flotation machines are time consuming and require large computational resources. Some approaches have been used to reduce computational costs for two-phase flow; see, for example, the approach by Tiitinen et al., where sector based simulations were used to reduce the number of grid nodes. Bubble size is one of the most important parameters that affect the air holdup of the pulp phase. A spectrum of bubble sizes exists in flotation machines depending on air flow rate and turbulence parameters. To predict such bubble size distribution, another set of equations that describes a population balance can be solved in the course of CFD simulation. This approach increases the computational demands where transport equation for each size group has to be implemented. A more feasible approach is to conduct a parametric study for different uniform bubble sizes to study their effects on air holdup and rate constant.

Theory for the upper limit of coarse particle Flotation Machine suggests that a quiescent flow field is necessary to prevent the particles from becoming detached from the bubbles. A liquid-fluidized bed provides a suitable environment. The flotation feed is introduced into the fluidized bed, and air bubbles are dispersed in the fluidizing water. Coarse particles attach to the bubbles rising through the bed and are lifted into the froth layer that is maintained on top of the cell in the usual way. Particles of galena up to 1 mm in diameter have been recovered in such a bed, while for particles of lower density such as quartz and coal, the upper limit for flotation has been extended to at least 2 mm and 5.6 mm respectively. The fluidized bed technology provides major advantages beyond the ability to recover coarse particles currently lost in existing operations. Thus, if the upper flotation limit can be extended, the top size for grinding can be raised, with significant reductions in energy costs. Liberation of the values is the key limitation. Also, a fluidized bed flotation cell can accept a feed with much higher percent solids, leading to significant reductions in water requirements.

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