General Drag Correlations for Particle-Fluid System

Particle-fluid flows are commonly encountered in industrial applications. It is of great importance to understand the fundamentals governing the behavior of such a flow system for better process design, control, and optimization. Generally, the particle-fluid flow behavior is strongly influenced by the interaction forces between fluid and particles. Among the various kinds of particle-fluid interaction forces, the drag force is the most essential. This chapter reviews the modeling of drag force for particle-fluid systems: from single particle to multiple particles, monosize to multisize, spherical to nonspherical, and Newtonian fluid to non-Newtonian fluid. Typical drag correlations in the literature are compared and assessed in terms of physical meaning, consistency, and generality

Numerical simulation of the in-line pressure jig unit in coal preparation

This paper presents a numerical study of the multiphase flow in an in-line pressure jig (IPJ), which is a high yield and high recovery gravity separation device widely used in ore processing but may have potential in coal preparation. The mathematical model is developed by use of the combined approach of computational fluid dynamics (CFD) for liquid flow and discrete element method (DEM) for particle flow. It is qualitatively verified by comparing the calculated and measured results under similar conditions. The effects of a few key variables, such as vibration frequency and amplitude, and the size and density of ragging particles, on the flow and separation performance of the IPJ are studied by conducting a series of simulations. The results are analyzed in terms of velocity field, porosity distribution and forces on particles. The findings would be helpful in the design, control and optimisation of an IPJ unit

Computational investigation of the effect of particle density on the multiphase flows and performance of hydrocyclone

Hydrocyclones are widely used to separate coal fines by size in the coal industry. They, however often face the problem associated with the misplacement of particles at the outlets due to the presence of a wide particle density range. This paper presents a numerical study of the multiphase flows and performance of hydrocyclone by means of two-fluid model, with special reference to particle density effect. The application of the model is firstly examined by comparing the measured and calculated results in terms of water velocities and particle partition curves. It is then used to investigate the behaviors of coal particles with different sizes and densities under different operational and geometrical conditions. The numerical results show that the separation efficiency of particles decreases with the decrease of particle density, and light coarse particles tend to be misplaced at the overflow outlet while ultrafine particles by-pass the separation in proportion to the water split. These results are in line with the experimental observations. This misplacement problem is attributed to the significant accumulation of particles and weakened swirling flow in the spigot area. Based on these findings, the modifications on the standard hydrocyclone by either lengthening conical section or using a convex cone are proposed to improve the performance of cyclones used to handle different sized particles with a wide density range. The results show that both modifications are useful to reduce the amount of light coarse particles misplaced at the overflow outlet

CFD study of the multiphase flow in classifying hydrocyclone : effect of cone geometry

This paper presents a numerical study of the gas–liquid– solid flow in hydrocyclones by a recently developed continuum-based multiphase flow model. The applicability of the model has been verified by a good agreement between the calculated and measured flow fields and separation efficiency (Kuang et al., 2012), and is used here to study the effect of cone length from a feed solids concentration of 4 to 30% (by volume). The numerical results show that for a standard design of cone section, decreasing cone length leads to the decrease of separation efficiency and the increase of inlet pressure drop for a given feed solids concentration. It is also shown that the performance of the cyclone with a short cone section is very sensitive to feed solids concentration

Numerical analysis of hydrocyclones with different conical section designs

Hydrocyclones generally follow a conventional design and may have some limitations on separation performance. This paper presents a numerical study of hydrocyclones with different conical configurations by a recently developed computational fluid dynamics method. The feed solids concentration considered is up to 30% (by volume), which is well beyond the range reported before. The numerical results show that the cyclone performance is sensitive to both the length and shape of the conical section, as well as the feed solids concentration. A longer conical section length leads to decreased inlet pressure drop, cut size d50, and Ecart probable Ep, and at the same time, an increased water split (thus larger by-pass effect). When conical shape varies from the concave to convex styles gradually, a compromised optimum performance is observed for the cyclone with a convex cone, resulting in a minimum Ep and relatively small inlet pressure drop and water split. Almost all these effects are pronounced with increasing feed solids concentration. Based on the numerical experiments, a new hydrocyclone featured with a long convex cone is proposed. It can improve the performance of the conventional cyclone at all the feed solids concentrations considered

Computational study of the multiphase flow and performance of hydrocyclones : effects of cyclone size and spigot diameter

This paper presents a numerical study of multiphase flow in hydrocyclones with different configurations of cyclone size and spigot diameter. This is done by a recently developed mixture multiphase flow model. In the model, the strong swirling flow of the cyclone is modeled using the Reynolds stress model. The interface between liquid and air core and the particle flow are both modeled using the so-called mixture model. The solid properties are described by the kinetic theory. The applicability of the proposed model has been verified by the good agreement between the measured and predicted results in a previous study. It is here used to study the effects of cyclone size and spigot diameter when feed solids concentration is up to 30% (by volume), which is well beyond the range reported before. The flow features predicted are examined in terms of the flow field, pressure drop, and amount of water split to underflow, separation efficiency and underflow discharge type. The simulation results show that the multiphase flow in a hydrocyclone varies with cyclone size or spigot diameter, leading to a different performance. A smaller cyclone results in an increased cut size, a decreased pressure drop and a sharper separation, and, at the same time, an increased water split (thus worse bypass effect) and a more possibly unstable operation associated with rope discharge, particularly at relatively high feed solids concentrations. Both large and small spigot diameters may lead to poor separation performance. Accordingly, an optimum spigot diameter can be identified depending on feed solids concentration. It is also shown that for all the considered hydrocyclones, a better separation performance and a smoother running state can be achieved by the operation at a lower feed solid concentration

Numerical analysis of hydrocyclones with different vortex finder configurations

This paper presents a numerical study of the multiphase flow and performance of hydrocyclone by means of two-fluid model, with special reference to the effects of diameter, length and shape of vortex finder at a wide range of feed solids concentrations. The considered shapes include the conventional cylindrical style and the new conical and inverse conical styles. The simulation results are analysed with respect to cyclone flow and performance in term of cut size d50, water split, Ecart probable Ep and inlet pressure drop. It is shown that when vortex finder diameter or shape varies, a compromised optimum performance can be identified, resulting in relatively small inlet pressure drop, Ep, and water split. Both d50 and Ep are more sensitive to feed solids concentration than inlet pressure drop and water split. Overall, the effect of vortex finder length on the separation efficiency of particles is much less significant than diameter and shape, which shows opposite trends at low and high feed solids concentrations. All these results can be well explained using the predicted tangential and axial velocities and solid volume fraction