The hydrocyclone finds application across a wide range of industries such as mineral, chemical and pharmaceutical industries. The design and operational conditions are drastically different depending on the type of application. In this work, the application of hydrocyclone in the mineral processing is studied. In a typical plant, a bank of twelve hydrocyclones, each of size 500-mm handless 500 tph of solids slurried typically in water. In this context, the aim of modeling is to predict the flow split (between overflow and underflow), air-core dimensions and size classification. A successful model, especially based on computational fluid dynamics, would be a useful tool for studying design dimensions. More importantly, alternative geometries can be examined swiftly.

### 1. Modeling of the hydrocyclone

The hydrocyclone is widely used in industry with the classic configuration shown in Figure 1.1. It consist of a cylindrical upper body with a central tube called vortex finder and a conical lower body with a discharge tube called spigot.

Figure 1.1 Hydrocyclone configuration

This configuration has been used during the last eighty years. However, no one has studied if this geometry leads to a optimum classification efficiency. The hydrocyclone modeling allows the optimization of this device at a very low cost compared to investigating by actual experimentation.The dynamics of the flow is complex. The slurry is fed into the tangential inlet which creates a swirling flow, thus generating a high centrifugal field in the cylindrical section. The conical section restricts the flow downward, causing part of the flow to reverse and exit through the vortex finder. The high centrifugal field accelerates the coarse particles towards the wall. In turn these particles get trapped in the downward flow thus discharging the coarse particles through the spigot. The finer particles remain in the central column of upward flow which carries these particles to discharge through the vortex finder. Since the discharge outlets are open to the atmosphere, a low-pressure air-core forms along the central axis. The dynamics of this swirling flow and the presence of three phases make modeling a challenging task. In the early 70s, empirical models were used in the modeling. However, with development of computing power and fluid dynamics solver codes it is possible to directly solve the rigorous flow problem.

### 1.1 Empirical models

In the past thirty years, many empirical models have been developed, especially in the mining and mineral processing industry. These models quantify the misclassification of particles and predict the operational characteristics. These models are easy to apply to a specific operation. The empirical models use the dimensions of the hydrocyclone and constants related to the characteristics of the slurry to predict the size classification. Usually, the data collected under a variety of operating conditions is correlated with empirical expressions using the multiple linear regression method.The main disadvantage with this kind of model is, when the constants of the model are calibrated for a specific operating condition, the same model cannot be used to predict conditions far from the calibrated conditions. Furthermore, these models do not explain why some fine particles report to the coarse stream outlet and why some of the feed particles directly report to the fine stream outlet. The dynamics of fluid and particles motion are essential to improve the performance of the device and empirical models are not capable of providing such information.

### 1.2 Models based on fluid dynamics

Since empirical models could not explain the internal mechanics of fluid flow, models based on the physics of flow were sought. Fluid dynamics models have three main parts, the mass balance, momentum balance, and turbulence effect. The mass balance is described with the continuity equation, the momentum balance with the Navier-Stokes equations, and the turbulence effect with a turbulence-closure model. The continuity equation and Navier-Stokes equations are nonlinear partial differential equations in three dimensions, hence require great computational effort. The solution of these equations falls under the discipline called computational fluid dynamics (CFD).

In the past, the application of CFD to the hydrocyclone problem has been studied by a few researchers. These studies shed some light on the nature of turbulence encountered in this problem. Rajamani and Devulapalli (1994) applied the Prandtl mixing-length model for turbulence closure. The two-dimensional computations were successful in predicting velocities and size classification. However, the Prandtl mixing length defined in a different manner for the axial and tangential direction is not an accepted standard in the CFD literature. Nor is there a way to prove conclusively that this hypothesis is correct.

Dyakowsky and Williams (1992), Malhotra et al. (1994) and He et al. (1999) applied the k-ε model for turbulent closure. These researchers applied a modification of the definition of ε to compensate for the deviation in the predicted velocities and size classification. However, there is no conclusive proof that such a turbulence closure predicts the turbulence in hydrocyclones. It was clear that a better turbulence model was still needed. Cullivan et al. (2003) introduced the higher order turbulence model called Reynolds stress model (RSM), and the velocity profiles were well predicted. However, this model could not capture the free interface formed in the air/water boundary called air-core. If the air-core dimension is not arrived at accurately in CFD computations it introduces incorrect area for out flow in the discharge streams, and hence the mass split is incorrectly computed. Mass split is very basic to modeling the size classification in simulations. In summary Cullivan’s (2003) study points out that a higher order turbulence model is needed to describe the turbulence.

De Souza and Silveira (2002) also applied a high order turbulent model called large eddy simulation (LES), In this study the velocity profiles were successfully predicted, but the study was limited to small hydrocyclones, and there was no consideration of air core dimensions in this study.

### 1.3 CFD modeling for 75- and 250-mm diameter hydrocyclones

In this section the dynamics of the flow for 75-mm diameter hydrocyclone is evaluated with experimental results of operational conditions, velocity profiles, velocity fluctuations, air-core description and classification of particles for different concentrations. (Enter this page)In this section the dynamics of the flow for 250-mm diameter hydrocyclone is evaluated with experimental results of operational conditions, velocity profiles, velocity fluctuations, air-core description and classification of particles for different concentrations. (Enter this page).