Experimental Setup
The experimental setup for the hydrocyclone mainly consists of a batching system including a stirrer, material tank, and a feed system comprising a centrifugal pump and material pipelines. The separation and testing system consist of various types of hydrocyclones and testing instruments. Under identical experimental conditions, separation experiments are conducted on different types of hydrocyclones. Overflow and underflow samples are collected three times and averaged to reduce experimental errors. Figure 3 illustrates the experimental equipment for the hydrocyclone separator, while Fig. 4 depicts the process flow diagram for the hydrocyclone separation experiments.
Experimental Method
The experiment utilized a mixture of 1% mass concentration of glass bead fine powder and water. The median particle size of the glass beads was measured as 41.52µm using an Eyetech laser particle size analyzer. The true density of the glass beads was determined to be \(2.6\text{g}/{\text{c}\text{m}}^{3}\). Figure 5 presents the particle size distribution of the glass bead experimental raw material.
To collect samples from the overflow and underflow outlets, the mixture was filtered and weighed. Subsequently, the collected samples were subjected to filtration, extraction, drying, and weighing processes.
During the experimental process, the overflow and underflow flow rates were measured using electromagnetic flowmeters. The inlet and outlet pressures were measured using pressure gauges, and the pressure drop across the hydrocyclone was calculated based on Eq. (1). The mass of the glass bead samples after drying was weighed, and the separation efficiency of the hydrocyclone was calculated using Eq. (2).
Pressure Drop Calculation Formula:
$$\varDelta \text{P}={\text{P}}_{\text{i}\text{n}}-{\text{P}}_{\text{o}\text{u}\text{t}}$$
1
In the equation, \({\text{P}}_{\text{i}\text{n}}\) represents the inlet pressure of the hydrocyclone, and \({\text{P}}_{\text{o}\text{u}\text{t}}\) represents the overflow outlet pressure of the hydrocyclone.
The efficiency calculation formula is as follows:
$$\eta =\frac{{M}_{\text{d}}}{{M}_{\text{i}\text{n}}}\times 100\text{%} (2)$$
Numerical Calculation Method
Calculation Model and Grid Generation
Numerical simulations were conducted to study the internal flow of the hydrocyclone, and the computational domain was established. Firstly, three-dimensional models of the three types of hydrocyclones were constructed using SolidWorks software. Subsequently, the constructed three-dimensional models were imported into CFD mesh software for grid generation.
To better represent the fluid motion, a tetrahedral structured grid was used as the fluid domain model for the hydrocyclone. During the grid generation process, refinement was applied to regions such as the tangential inlet of the hydrocyclone to capture the flow characteristics more accurately. Grid independence tests were also performed to reduce the influence of grid quantity on the numerical simulation results. Taking Type A conventional hydrocyclone as an example, since the fluid domain models had the same diameter and length before and after improvement, different grid numbers (approximately 200,000, 400,000, 600,000, and 900,000) were used for numerical simulation.
Through these numerical simulations, the influence of different grid quantities on the simulation results was evaluated, and an appropriate grid number was determined to obtain accurate and reliable simulation results. This exploration is crucial for further analyzing the performance of the hydrocyclone and the effects of improvements.
Numerical Calculation Method and Boundary Conditions
ANSYS Fluent software was used to conduct numerical simulations for different types of hydrocyclones. For the simulation, the Reynolds Stress Model (RSM) was chosen as the turbulence model for the fluid in the hydrocyclone, and standard wall functions were adopted [29]. The Reynolds Stress Model adequately accounts for the stress tensor induced by fluid rotation and is particularly suitable for high-intensity turbulent flow, making it a suitable option in this study.
The Volume of Fluid (VOF) model was employed for multiphase flow simulations. The VOF model can be used to simulate the interface between two or more immiscible fluids and track the movement of the phase interface by solving the continuity equation.
In the simulation of the hydrocyclone, the main phase was set as the mixture liquid, with a constant temperature, density of \({998.2\text{k}\text{g}/\text{m}}^{3}\), and viscosity of \(0.001\text{P}\text{a}\bullet \text{s}\). The air phase was considered as the second phase, with a density of \({1.293\text{k}\text{g}/\text{m}}^{3}\) and viscosity at room temperature. The overflow and underflow outlets were set as pressure outlets, and the air backflow rate was set to 1.
In this study, the initial stage of the calculation used a mixture liquid calculation, and after convergence, it transitioned to two-phase calculation. The implicit transient pressure-velocity coupling method used the SIMPLEC method. To ensure computational stability, the pressure gradient was computed using the Green-Gauss Cell-Based method, the pressure discretization used the PRESTO! method, the momentum discretization used the Second Order Upwind method, and the turbulent kinetic energy and turbulent kinetic energy dissipation rate used the first-order upwind scheme. The convergence criterion was set at a residual tolerance of 1e-5, and the balance of mass flow rates at the inlet and outlet phases was used as the criterion for convergence judgment.
Overflow Pipe Slotted Structure Optimization
Impact of Overflow Pipe Slotted Structure on Hydrocyclone Separation Performance
In this study, solid-liquid separation experiments were conducted for the hydrocyclone. Firstly, based on the desired feed concentration and separation target, the concentration of the mixture liquid was adjusted to obtain a glass bead fine particle mass concentration of 1%. Subsequently, the mixture liquid was adequately covered by the stirrer, and the motor was adjusted to start the stirrer, initiating the mixing of the material and water.
Simultaneously, the centrifugal pump's rotational speed was controlled to achieve the experimentally preset initial reading of the electromagnetic flowmeter, which was set at an initial flow rate of 680 ml/s. During the experimental stage, after the mixture liquid was fully and uniformly mixed under the action of the stirrer, and the flow rates at the overflow and underflow outlets of the hydrocyclone stabilized, the beakers were quickly placed at the overflow and underflow outlets for sampling.
The collected samples were subjected to drying, and the dried samples were weighed using a precise balance. The mass data of the samples obtained from the experiment were recorded. Specifically, in the experiment, weighing equipment (as shown in Fig. 6) was used to ensure the accurate weighing of the samples, ensuring the accuracy and reliability of the data.
The separation performance of the hydrocyclone with a single-layer slotted conical overflow pipe Type B hydrocyclone and the conventional Type A hydrocyclone under equivalent operating conditions is illustrated in Fig. 7. The graph depicts the influence of different inlet flow rates on the separation efficiency (η) and pressure drop (ΔP) for both types of hydrocyclones. The x-axis represents the hydrocyclone inlet flow rate (Q), the left y-axis represents the separation efficiency (η) of the hydrocyclone, and the right y-axis represents the pressure drop (ΔP) across the hydrocyclone.
When the inlet flow rate is the same, the improved Type B hydrocyclone shows a slight decrease in separation efficiency compared to the conventional Type A hydrocyclone. However, it also achieves a certain degree of pressure drop reduction, resulting in energy-saving benefits. Under the operating conditions with inlet flow rates ranging from 680 ml/s to 920 ml/s, the improved Type B hydrocyclone exhibits a relatively small reduction in pressure drop. However, when the inlet flow rate exceeds 780 ml/s, the pressure drop reduction of the Type B hydrocyclone gradually increases, reaching its maximum at 860 ml/s. Compared to the conventional Type A hydrocyclone, the Type B hydrocyclone shows a pressure drop reduction of 6.8 units. The pressure drop for the conventional Type A hydrocyclone is 42.04kPa, while it is 39.18kPa for the Type B hydrocyclone.
Furthermore, after the slotted modification, the separation efficiency of the improved Type B hydrocyclone is slightly lower than that of the conventional hydrocyclone. When the inlet flow rate is greater than 760 ml/s, the separation efficiency of the Type B hydrocyclone approaches that of the conventional Type A hydrocyclone. At an inlet flow rate of 880 ml/s, the separation efficiency of the conventional Type A hydrocyclone is 97.96%, while the Type B hydrocyclone achieves a separation efficiency of 97.62%. Compared to the conventional Type A hydrocyclone, the separation efficiency of the Type B hydrocyclone decreases by 0.35 percentage points. Moreover, with the increase in inlet flow rate, the separation efficiency of the Type B hydrocyclone gradually approaches that of the conventional Type A hydrocyclone, while the pressure drop reduction increases.
Based on the experimental data, it can be observed that compared to the conventional Type A hydrocyclone, the slotted conical overflow pipe structure has a relatively minor impact on separation efficiency as the inlet flow rate increases. However, it has a significant effect on pressure drop reduction. The slots act as fluid passages, increasing the outlet area of the overflow pipe, reducing the axial velocity of the fluid inside the hydrocyclone, and thereby reducing the kinetic energy loss and pressure drop.
Optimization of Slotted Layer Number
In order to further reduce the energy consumption of the Type B hydrocyclone, an optimization design of the slotted layer number was conducted. The slotted layer number was set from 1 to 4, with a layer spacing of 6mm, slot angle of\(30^\circ\), and slot position size of 3mm. These were designated as Type B to Type E, and separation experiments were carried out for each design. The relationship curves between different slotted layer numbers, inlet flow rates, and the hydrocyclone's separation efficiency and pressure drop are shown in Fig. 8.
The separation efficiency of the five types of hydrocyclones is positively correlated with the inlet flow rate. With an increase in the number of slots, the overall trend of the separation efficiency in Type B to Type E hydrocyclones gradually decreases. Among them, Type B to Type D hydrocyclones (with 1 to 3 layers of slots) exhibit a slow decline in separation efficiency, with a small reduction. The Type E hydrocyclone (with 4 layers of slots) shows a relatively larger decrease in separation efficiency because the increased number of slots elevates the slot position, causing short-circuit flow in the overflow pipe region, leading to the entrainment of solid particles from the slots into the overflow pipe, thereby increasing the separation efficiency reduction.
Regarding the pressure drop, as the inlet flow rate increases, all five types of hydrocyclones show a gradual upward trend in pressure drop. With an increase in the number of slots, compared to the conventional Type A hydrocyclone, the pressure drop reduction in Type B to Type E hydrocyclones gradually increases. Type B and Type C hydrocyclones (with 1 to 2 layers of slots) experience minor changes in pressure drop reduction, while Type D and Type E hydrocyclones (with 3 to 4 layers of slots) demonstrate a significant increase in pressure drop reduction. The increase in the number of slots results in a larger slot area, which increases the flow rate entering the overflow pipe, reduces the local pressure at the bottom inlet of the overflow pipe, decreases the overall dynamic pressure of the internal swirling flow in the overflow pipe, and increases the outlet static pressure of the overflow pipe. According to fluid dynamics principles, the change in velocity has a significant impact on fluid kinetic energy, which is a key reason for the significant reduction in pressure drop after slot modification. Based on the analysis above, Type D hydrocyclone exhibits a remarkable pressure drop reduction while maintaining almost the same separation efficiency.
During the actual experimental process, at an inlet flow rate of 680 ml/s, the Type D hydrocyclone achieved a separation efficiency of 90.6% with a pressure drop of 36.31 kPa. Compared to the conventional Type A hydrocyclone, the separation efficiency of the Type D hydrocyclone decreased by 3.04%, and the pressure drop decreased by 1.83%.As the inlet flow rate reached the working condition of 900 ml/s, the Type D hydrocyclone showed a turning point in separation efficiency, reaching its maximum value. At this point, the separation efficiency and pressure drop for the conventional Type A hydrocyclone were 97.69% and 43.34 kPa, respectively, while for the Type D hydrocyclone, they were 97.53% and 38.65kPa, respectively. Compared to the conventional Type A hydrocyclone, the separation efficiency of the Type D hydrocyclone decreased by 0.16%, and the pressure drop decreased significantly by 10.28%. These results indicate that the Type D hydrocyclone is more suitable for separation operations under high inlet flow rate conditions.
Optimization of Slot Position and Angle
The different slot positions in the overflow pipe will have a certain impact on the separation efficiency and pressure drop of the hydrocyclone. An experiment was conducted to explore the effect of slot positions on the Type D hydrocyclone. The slot size "a" was set to 4 mm, 5 mm, and 6 mm, corresponding to Type T, Type Jj, and Type Zz, respectively. Figure 9 shows the flow rate-separation efficiency and flow rate-pressure drop curves for different types of hydrocyclones under inlet flow rates ranging from 680 ml/s to 920 ml/s.
At an inlet flow rate of 680 ml/s, the separation efficiency of the Type Jj hydrocyclone is 90.72%, with a pressure drop of 26.0 kPa. Compared to the conventional Type A hydrocyclone, the separation efficiency of the Type Jj hydrocyclone decreases by 1.91%, and the pressure drop decreases by 2.99%.
When the inlet flow rate reaches the working condition of 900 ml/s, the Type Jj hydrocyclone achieves its highest separation efficiency at 97.84%, with a pressure drop of 37.87 kPa. Compared to the conventional Type A hydrocyclone, the separation efficiency of the Type Jj hydrocyclone increases by 0.15%, and the pressure drop decreases by 12.62%.Regarding the other three types of hydrocyclones with different slot positions, the relationship between efficiency, pressure drop, and slot position changes is not very pronounced. However, for the Type Zz hydrocyclone, a relatively significant decrease in separation efficiency is observed. This is because the top slot position is close to the short-circuit flow region, allowing some particles to enter the overflow pipe through the slots along with the fluid motion, resulting in a reduction in the hydrocyclone's separation efficiency. On the other hand, the variation in the slot position below the short-circuit flow has little effect on the hydrocyclone's separation performance.
To achieve continuous analysis of different levels of various factors within the experimental conditions and obtain a more accurate optimal solution, the response surface optimization method was utilized. In this approach, the inlet flow rate (Q) and the slot size (a) were selected as the influencing factors. The ranges of these two factors were determined, and the experimental data corresponding to these two factors' levels were input into the Design-Expert design software. By employing central composite design, specific values for the three levels of each factor were obtained (as shown in Table 3). The three levels are lower limit, center point, and upper limit, respectively.
Table 3
Factors and Levels Setting for Optimization of Slotted Structure in Hydrocyclone
Horizontal | Factor |
Q(ml/s) | a(mm) |
\({\text{X}}_{1}\) | \({\text{X}}_{2}\) |
Lower Limit | 680 | 3 |
Center Point | 800 | 4.5 |
Upper Limit | 920 | 6 |
Regarding the experimental data, a response surface optimization design method was employed to conduct multivariate regression analysis. The experimental data was input into the Design-Expert software to establish the quadratic polynomial response surface regression equations for the target functions, separation efficiency (\({\text{Y}}_{\text{e}}\)) and pressure drop (\({\text{Y}}_{\text{p}}\)), with respect to the variables X1 and X2, as shown in Equations (3) and (4):
$$\begin{array}{c}{Y}_{e}=220.85963-0.66914{\text{X}}_{1}-0.39914{\text{X}}_{2}-0.012242{\text{X}}_{1}{\text{X}}_{2}+1.07257\times {10}^{-3}{\text{X}}_{1}^{2}+\\ 1.44434{\text{X}}_{2}^{2}+3.55769\times {10}^{-6}{\text{X}}_{1}^{2}{\text{X}}_{2}+8.24863\times {10}^{-4}{\text{X}}_{1}{\text{X}}_{2}^{2}-5.20469\times {10}^{-7}{\text{X}}_{1}^{3}-0.17974{\text{X}}_{2}^{3}(3)\end{array}$$
$$\begin{array}{c} {Y}_{p}=581.15828-2.32640{\text{X}}_{1}+19.96128{\text{X}}_{2}-8.3460\times {10}^{-3}{\text{X}}_{1}{\text{X}}_{2}+3.05799\times {10}^{-3}{\text{X}}_{1}^{2}-\\ 4.1517{\text{X}}_{2}^{2}+4.86014\times {10}^{-6}{\text{X}}_{1}^{2}{\text{X}}_{2}+2.47253\times {10}^{-5}{\text{X}}_{1}{\text{X}}_{2}^{2}-1.29826\times {10}^{-6}{\text{X}}_{1}^{3}+0.32974{\text{X}}_{2}^{3}(4)\end{array}$$
Figure 10(a) and (b) illustrate the interaction effects of inlet flow rate and orifice size on the objective functions \({\text{Y}}_{\text{e}}\) and \({\text{Y}}_{\text{p}}\). With other parameters kept constant, an increase in the inlet flow rate leads to higher pressure drop and separation efficiency. In this simulation, while maintaining the other dimensions of the hydrocyclone unchanged, increasing the orifice size initially enhances the separation efficiency but then causes a decrease, and the pressure drop shows a decreasing trend followed by an increasing trend. When the orifice size is set to 5.3mm, a better balance between separation efficiency and pressure drop can be achieved.
To investigate the influence of orifice angle on the separation efficiency and pressure drop of the hydrocyclone, four different angles, namely\(30^\circ\),\(45^\circ\),\(60^\circ\), and\(75^\circ\), were designed, corresponding to the models Type Jj, Type Nn, Type Rr, and Type Vv, respectively. These models were compared with the conventional Type A hydrocyclone under the same inlet flow rate condition. The flow rate-separation efficiency and pressure drop curves of the five hydrocyclone models are shown in Fig. 11.
Type Jj, Type Nn, and Type Rr hydrocyclones exhibit similar separation efficiencies, while Type Vv hydrocyclone experiences a more significant decrease in separation efficiency.The pressure drop reduction follows the order from the largest to the smallest: Type Vv, Type Rr, Type Nn, and Type Jj hydrocyclones.
As the orifice angle increases, the overflow flow rate gradually increases, leading to a decrease in the kinetic energy loss of the internal fluid. When solid particles are carried into the orifice, they need to change direction to enter the overflow pipe. Part of the particles experiences inertial impact with the pipe wall and undergo secondary separation. With the increase in orifice angle, the fraction of particles being impacted and re-separated decreases gradually, which significantly reduces the separation efficiency of the hydrocyclone. Among them, the Type Rr hydrocyclone experiences a substantial decrease in pressure drop while maintaining the separation efficiency nearly constant.
At an inlet flow rate of 900ml/s, the Type Rr hydrocyclone achieves the highest separation efficiency of 97.75% and a pressure drop of 31.56KPa.Compared to the conventional Type A hydrocyclone, the separation efficiency increased by 0.06%, and the pressure drop decreased by 24.85%.
Figure 12 (a) and (b) represent the interaction between inlet flow rate and orifice angle on the objective functions \({\text{Y}}_{\text{e}}\) and \({\text{Y}}_{\text{p}}\), respectively. When other parameters remain constant, an increase in the inlet flow rate leads to a rise in both separation efficiency and pressure drop. In this simulation, with the hydrocyclone's other dimensions unchanged, increasing the orifice angle initially enhances the separation efficiency and subsequently decreases it, while the pressure drop exhibits a gradual decline. An orifice angle of \(58^\circ\)appears to strike a balance between separation efficiency and pressure drop, providing better performance for the hydrocyclone.
To further investigate the optimization scheme with three orifice layers, a 5.3mm orifice size, and a\(58^\circ\)orifice angle, experimental research is conducted with an initial inlet flow rate of 800ml/s. The results are compared with the conventional Type A hydrocyclone, as shown in Fig. 13, illustrating the contrast in pressure drop and separation efficiency.
Figure 14 illustrates the comparison of particle size efficiency between the optimized and conventional hydrocyclones at an inlet flow rate of 900ml/s. Based on the results from Fig. 13 and the comparative chart in Fig. 14, it can be concluded that within the range of inlet flow rates from 900ml/s to 920ml/s, the optimized hydrocyclone exhibits higher separation efficiency compared to the conventional type. However, as the inlet flow rate increases, the improvement in separation efficiency gradually diminishes, while the pressure drop also increases. At an inlet flow rate of 900ml/s, the optimized hydrocyclone achieves the highest separation efficiency, reaching 97.77%, representing a 0.26% improvement compared to the conventional hydrocyclone. The corresponding pressure drop is 32.98KPa, resulting in a reduction of 24.88%.Within the particle size range larger than \(30{\mu }\text{m}\), the optimized hydrocyclone's particle size efficiency remains essentially unchanged compared to the conventional hydrocyclone.
These results indicate that the optimized hydrocyclone can achieve higher separation efficiency and relatively smaller pressure drop within a certain range of inlet flow rates. This is of great significance for improving the hydrocyclone's performance and efficiency.
Numerical Simulation Analysis
Numerical simulation analysis is conducted on the optimized hydrocyclone, referred to as TypeⅠ, with three orifice layers, an orifice size of 5.3mm, and an orifice angle of \(58^\circ\). Numerical simulations are performed at an inlet flow rate of 900ml/s and compared with the conventional Type A hydrocyclone. By comparing the two hydrocyclones in terms of fluid axial velocity, tangential velocity, pressure distribution, and other aspects, this numerical simulation analysis provides deeper insights into the improvement achieved by TypeⅠ hydrocyclone, thereby serving as a reference for further research and optimization.
Grid Independence and Numerical Method Validation
By examining the average tangential velocity at different sections of the hydrocyclone, it was observed that the average tangential velocity remained relatively constant when the grid size increased to approximately 600,000 cells. To validate the numerical simulation of the Type A hydrocyclone, the tangential velocities at various cross-sections were compared with experimental values. The results from the numerical simulations were found to be in close agreement with the experimental values, indicating that the numerical model used in this study can reasonably predict the solid-liquid separation performance of the hydrocyclone. Therefore, the grids for Type A and TypeⅠ hydrocyclones were set to similar orders of magnitude, with 643,541 and 674,512 cells, respectively.
Pressure Analysis
Based on the pressure distribution analysis, it was observed that as both types of hydrocyclones approached the center radially, the pressure gradually decreased, forming negative pressure regions. Figures 15 and 16 illustrate the pressure distribution at different cross-sectional positions. Compared to the Type A hydrocyclone, the modified hydrocyclone exhibited significantly reduced overall pressure, with an increased diameter of the air column and a noticeable decrease in pressure drop along the column. This indicates that the modified overflow pipe had a significant impact on the pressure distribution along the hydrocyclone column. The improved overflow pipe possessed a larger equivalent diameter, resulting in increased fluid discharge within the overflow pipe, thereby reducing the internal pressure of the hydrocyclone.
Based on the pressure distribution curves at different axial cross-sections in the hydrocyclone, as shown in Fig. 17, it can be observed that the overall pressure trend exhibits an approximate "V" shape, and the negative pressure region at the axis of both hydrocyclones shows similar pressure values. The pressure is positively correlated with the radial position. Compared to the Type A hydrocyclone, the improved TypeⅠ hydrocyclone shows a gentler pressure curve in the external region of the overflow pipe, resulting in a significant overall pressure reduction.
Furthermore, the pressure of both hydrocyclone types is negatively correlated with the axial position. Specifically, in the axial positions ranging from the Y=-0.015m cross-section to the Y=-0.04m cross-section, the pressure variation in the TypeⅠ hydrocyclone is greater than that in the Type A hydrocyclone. Additionally, the pressure at the column cross-section located at Y = 0.01m is higher than the pressure at the overflow pipe cross-section. The improved design of the overflow pipe in the TypeⅠ hydrocyclone reduces internal frictional resistance, leading to a notably lower pressure at the overflow pipe cross-section compared to the column cross-section. However, the TypeⅠ hydrocyclone adopts a tapered slotted design, resulting in a rapid increase in fluid velocity as it enters the overflow pipe, leading to localized turbulence and increased energy loss. As a consequence, the TypeⅠ hydrocyclone exhibits a slightly higher pressure drop compared to the TypeA hydrocyclone.
In summary, the optimization of the hydrocyclone's overflow pipe design in the TypeⅠ hydrocyclone reduces the overall pressure and improves the pressure distribution compared to the conventional Type A hydrocyclone.However, due to the introduction of the tapered slotted structure, the TypeⅠ hydrocyclone experiences a slightly higher pressure drop, indicating a trade-off between pressure reduction and energy loss in the design optimization.
The changes in the internal pressure distribution of the hydrocyclone before and after the optimization of the slotted structure are jointly presented in Figs. 15 to 17.The results demonstrate that the pressure distribution of the optimized hydrocyclone is more reasonable and symmetrical in multiple cross-sections and axial profiles compared to the original hydrocyclone, and the pressure level is noticeably reduced. Specifically, the slotted structure leads to a reduction in pressure in the region near the outlet, a gradual decrease in the axial pressure gradient, and an overall pressure reduction across the hydrocyclone. The combined information from the three figures indicates that the introduction of the slotted structure significantly improves the internal pressure distribution of the hydrocyclone, which explains the observed phenomenon of reduced pressure drop from the perspective of the flow field. Therefore, the regulatory effect of the slotted structure on the internal pressure field is one of the key reasons for achieving the optimization of the hydrocyclone's performance.
Axial Velocity Analysis
In the analysis of axial velocity, detailed distribution simulations of the axial velocity were conducted at axial cross-section positions (Y = 0.04m and 0.08m) for both hydrocyclone types, and the results are presented in Fig. 18.By observing the axial velocity distribution of the two hydrocyclone types, it can be seen that the velocity gradually increases from the wall to the axis and sharply rises to its maximum value in the central region, presenting a generally symmetrical profile.
The improved symmetry in the pressure and velocity distributions of the optimized hydrocyclone compared to the original hydrocyclone confirms the effectiveness of the slotted structure optimization in achieving a more balanced and stable flow field inside the hydrocyclone. The changes in pressure and velocity distributions provide valuable insights into the flow behavior, contributing to the understanding of the improved separation performance and reduced pressure drop observed in the experimental results.
It is noteworthy that, compared to the Type A hydrocyclone, the TypeⅠ hydrocyclone exhibits a slight decrease in its axial velocity. In the TypeⅠ hydrocyclone, the reduction in axial velocity is more pronounced in the inner swirling region than in the outer swirling region. The optimized hydrocyclone with overflow slits shows a significant decrease in axial velocity in the inner swirling region near the overflow outlet. Specifically, at the Y = 0.04m section, the maximum axial velocity of the prototype hydrocyclone is approximately 3.2m/s, while the optimized version only reaches 2.8m/s. Similarly, at the Y = 0.08m section, the maximum axial velocity decreases from 2.9m/s to 2.6m/s. This reduction in axial velocity is attributed to the enlargement of the outlet area by the overflow slits, which weakens the intensity of the inner swirling vortex flow, leading to a decrease in the axial velocity of the vortex flow.
The increase in the number of overflow slits will further expand the outlet area and cause a further decrease in the axial velocity of the inner swirling flow. However, excessive slit numbers may lead to a saturation effect. Additionally, the opening angle of the slits affects the outlet flow rate, where too large an angle can result in excessively low axial velocities. On the other hand, the height of the slit controls its range of influence and directly determines the distribution pattern of the axial velocity field.
Figure 19 provides a visual representation of the X-direction velocity (axial velocity component) distribution in the axial section of the two hydrocyclones. From the figure, it is evident that the optimized hydrocyclone with overflow slits exhibits a more uniform and symmetric axial velocity distribution within its interior, especially in the region near the overflow outlet, where the velocity field distribution appears more reasonable. Specifically, after the slit optimization, the maximum axial velocity near the overflow outlet reduces significantly from the original 3.2m/s to 2.8m/s. This indicates that the introduction of the overflow slits weakens the intensity of the vortex flow in the overflow tube region, leading to a notable reduction in the axial velocity component.
The TypeⅠ hydrocyclone can effectively control the distribution of axial velocity to match the tangential velocity field, thereby achieving the goal of improving the hydrocyclone's separation efficiency. The axial velocity distribution plays a crucial role in optimizing the hydrocyclone's performance.
In addition, after introducing the overflow slit in the hydrocyclone, the axial velocity of the outer swirling region near the hydrocyclone wall shows a slight decrease, although this effect is relatively minor. However, as the radial position moves towards the axis, the axial velocity in the inner swirling region experiences a significant reduction, with the impact of the overflow slit becoming more pronounced. This phenomenon can be explained by the fact that, under the same inlet flow conditions, the overflow slit structure enlarges the equivalent diameter of the overflow outlet. As a result, the rotational speed of the fluid around the central axis decreases, causing the zero-velocity envelope surface to move inward. This process increases the time for medium and large particles in the outer swirling region to participate in the separation, resulting in a more thorough separation effect. Additionally, the overflow slit structure also reduces the likelihood of coarse particles in the outer swirling region re-entering the inner swirling flow. Therefore, the influence of the overflow slit on hydrocyclone performance is mainly manifested in the reduction of axial velocity in the inner swirling region and the enhancement of solid-liquid separation efficiency. The optimized combination of the overflow slit parameters in TypeⅠ hydrocyclone satisfies the separation requirements of the axial velocity field, thereby improving the overall separation performance of the hydrocyclone.
Tangential Velocity Analysis
In this study, the tangential velocity of the fluid in the hydrocyclone with an inlet flow rate of 900 ml/s was analyzed. The comparison of the tangential velocity distribution curves at different cross-sectional positions for both hydrocyclone types is shown in Fig. 20.Overall, the tangential velocity distribution curve exhibits an "S"-shaped trend. As the distance from the hydrocyclone wall decreases, the tangential velocity increases with decreasing radius. It reaches its maximum value near the hydrocyclone wall and then gradually decreases with further reduction in radius. When approaching the vicinity of the air core, the tangential velocity drops sharply, eventually becoming zero at the central axis.
The design of overflow slit in the hydrocyclone reduces the internal fluid velocity, causing small-sized solid particles to lack sufficient centrifugal force to enter the outer swirling region for separation. Instead, they are eventually discharged through the overflow outlet, leading to a decrease in the hydrocyclone's particle size efficiency for small particles. However, large-sized particles, due to their larger volume and mass, can still overcome the reduced centrifugal force and enter the outer swirling region, thus their particle size efficiency remains unaffected. Compared to Type A hydrocyclone, the overall tangential velocity in TypeⅠ hydrocyclone slightly decreases, resulting in a reduction of the centrifugal force experienced by solid particles.
Additionally, when observing the tangential velocity above the overflow slit (Y=-0.04m) in Fig. 21, it is evident that the decrease in tangential velocity above the overflow slit is more significant compared to the cylinder and cone sections, with the cone section experiencing a larger reduction than the cylinder section. This phenomenon is attributed to the greater influence of diameter size on the tangential velocity, and the impact of the overflow slit structure becomes more pronounced above the overflow slit level.
As a result, the overflow slit design in the hydrocyclone has selective effects on particle size efficiency. It reduces the separation efficiency for small-sized particles due to reduced centrifugal force, while having limited impact on the efficiency of large-sized particles. Moreover, the influence of the overflow slit structure on tangential velocity is more evident above the overflow slit level, especially in the cone section.
Based on the combined analysis of the axial velocity distribution in Fig. 20 and the tangential velocity distribution in Fig. 21 at different axial cross-sections, it is evident that the TypeⅠ hydrocyclone, after optimization with the slotted structure, exhibits a more symmetrical and stable tangential velocity distribution compared to the Type A hydrocyclone. Specifically, at multiple cross-sections in Fig. 20, the tangential velocity near the hydrocyclone wall is reduced by 0.2–0.4 m/s in the optimized hydrocyclone compared to the Type A hydrocyclone, and the negative tangential velocity in the central region is also decreased. In Fig. 21, the tangential velocity distribution above the slotted structure shows an overall reduction of 0.3–0.5 m/s, with a smaller slope in the curve. This indicates that the introduction of the slotted structure weakens the internal vortex, resulting in a decrease in the tangential velocity component. Moderating the tangential velocity can contribute to achieving a more stable separation performance. Therefore, the regulation of the tangential velocity field through the slotted structure is one of the significant factors in optimizing the hydrocyclone's performance.
Furthermore, the proportion between axial and tangential velocities directly influences the hydrocyclone's separation efficiency. According to the above analysis, the velocity matching between the two components needs to be adjusted according to the particle size of different materials. For fine or low-density particles, increasing the axial velocity is necessary to rapidly remove them from the hydrocyclone wall and prevent excessive fine particles from entering the underflow. At the same time, providing a higher tangential velocity allows light particles to obtain sufficient centrifugal force to enter the overflow outlet. For coarse or high-density particles, reducing the axial velocity appropriately can increase their residence time inside the hydrocyclone for adequate separation. The tangential velocity can also be adjusted accordingly to reduce turbulence losses inside the hydrocyclone. For materials with a wide particle size distribution, a moderate combination of axial and tangential velocities should be chosen to achieve good separation performance for particles of different sizes. The axial velocity should not be too high or too low, and the tangential velocity needs to be controlled within an appropriate range. By adjusting the proportion between these two velocities when the operating conditions change, customized separation of materials can be achieved, thus expanding the hydrocyclone's applicability range.