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Interactive effects between feed flow rate and feed size distribution (FSD) are numerically investigated. The results show that, for too large or too small feed flow rate, when the FSD increases, the content of solid particles misplaced to the overflow or underflow increases, leading to a decrease in separation sharpness. These results can be explained by the multiphase flow pattern and solid particle spatial distribution. What's more, when the feed flow rate too small, the differences between the equilibrium radiuses of different sized particles are small, resulting in low separation sharpness. When the feed flow rate is too large, the regular distribution of different sized particles in the radial direction is severely destroyed. Based on the results from this study, in order to achieve the desired separation performance and the precise particle separation, it is recommended to adapt to changes in the FSD by appropriately increasing the feed flow rate.

The interaction effect between feed size distribution (FSD) and underflow orifice diameter (Du) is crucial for the adjustment of the hydrocyclone in plant but not clearly understood. This paper presents a numerical study on effects of FSD on separation performances of hydrocyclones at a wide range of Du. The numerical results show that both small or large Du will cause numerous particles being misplaced to the overflow or underflow products, resulting in poor separation performance. These results can be well explained using the predicted water flow pattern and particle distribution. Moreover, there are intense interaction effects between the Du and the FSD. It is pointed out that for an extremely small Du, the cut size explodes, and the separation efficiency and separation sharpness deteriorate rapidly with the increase of feed median size (d0.5). These behaviors are mainly due to the increase in the coarse particle content as d0.5 increases, resulting in an increase in the extent of particle accumulation near the spigot. Such accumulation causes a decrease in the tangential velocity and a break in the air core, which in turn leads to a decrease in the flow field stability. Thereby, regular distribution of the particle equilibrium radius along the radial direction is destroyed. As Du increases, the separation performance of the hydrocyclone is no longer affected by fluctuations in the FSD. Based on results from this study, it is recommended a moderate increase in Du is competent to mitigate the adverse effects caused by fluctuations in the FSD, to achieve the expected cut size, and relatively high separation precise for particles.

Interactions between feed size distribution and separation performance for hydrocyclones with different vortex finder diameters (Do) are crucial for hydrocyclone designs but not clearly understood. In this work, the optimum range of Do is numerically confirmed for a 50 mm diameter hydrocyclone using computational fluid dynamics. Furthermore, effects of feed size distribution (FSD) on separation performance for hydrocyclones with different Do are discussed. For a given FSD, the lower limit of Do can be determined from the flow stability characterized by lower turbulence intensity and larger tangential velocity. Below the lower limit, a large proportion of fine particles report to the underflow. The upper limit can be determined from separation performance. Above the upper limit recovery to the underflow for coarse particles decreases drastically, which is caused by an outward shift of the locus of zero vertical velocity (LZVV) and an inward shift of particles equilibrium radius. For a given Do, FSD has no significant effects on partition curves when Do is in the optimum range. When Do is above the optimum range, both recovery to underflow for coarse particles and separation sharpness are decreased as the feed median size increases. In summary, when Do is in the optimum range, the hydrocyclone can adapt to different FSD to obtain the expected cut size by self-adjusting the LZVV and particles equilibrium radius. This method for determining the optimum range of Do is based on flow pattern characteristics and can be used as a universal tool for hydrocyclone design.

Existing design equations can hardly provide reliable guidance in hydrocyclone designs and give explanations for the selected optimum range. Therefore, a new method combined flow patterns and equation models (FP-EM) for hydrocyclone designs is proposed in this paper. The feed flow rate is used as a parameter to evaluate the FP-EM method. Results show that under a lower feed flow rate, the inner flow field is extremely unsteady, which is characterized by higher turbulence intensity and an unsteady air core. When the flowrate becomes extremely large, the value of the exponent n for the tangential velocity inside the free vortex region decreases. Furthermore, before flow field achieving stability, the separation accuracy is extremely low. In the optimum range, the separation efficiency and the accuracy increases with the increase of the feed flow rate, while the cut size decreases. Thus, for the φ50 mm hydrocyclone used in this study, the lower limit (15 L/min) can be determined by the flow field stability and the upper limit (55 L/min) is largely ascertained by energy consumption. Three power-type fitting equations are deduced in the optimum range to quantify the relationships between separation indexes (split ratio, pressure drop and cut size) and the flowrate. Correlation coefficients ( R 2 > 0.97) of three equations verify that equation models can predict the separation performance successfully. Therefore, all above results confirm that the FP-EM method is capable of providing an optimum range, quantifying the relationships between separation indexes and the feed parameter, and predicting separation performances.

An appropriate design of the inlet type has been proved to be an effective approach to improve the performance of a hydrocyclone. Until now, there is still no detail analysis on the mechanism underlying the flow control by the inlet type. In this paper, numerical simulation was conducted to investigate effects of curvature radius on the separation performance of the hydrocyclone with a tangent-circle inlet. The validity of the approach was verified by the reasonably good agreement between the predicted and measured results in terms of water velocities and particle partition curves. The simulating results were further analyzed in aspects of the flow field, pressure drop and separation performance. Results showed that a smaller curvature radius could increase the tangential velocity and the pressure gradient. Besides, the turbulence kinetic energy in the inlet section and the annular section are reduced by decreasing the curvature radius. Meanwhile, the symmetry of the inner flow field was improved by reducing the curvature radius. All these factors enhanced the radial regular distribution of particles in the inlet section and reduced influences of the short circuit flow on relatively coarse particles. Therefore, the classification precision was improved when using a tangent-circle inlet with a smaller curvature radius compared with base hydrocyclone.

Based on the evolutionary theory of U-Pb isotopic system, we have studied the genetic model for a uranium deposit occurring in carbonate-silicolite-pelite. The data show that the U-deposit is characterized by a multi-stage evolution with respect to its U-Pb isotopic system, and the mechanism of its genesis can be explained by later repeated superimposition of mine-ralization which took place at about 200±10m. y., 100±10m. y., 60±10m. y. and 11±1m. y. ago. These mineralization stages are closely related to regional tectonic activities.