A horizontal screw centrifuge separation performance prediction method

Abstract

This invention relates to the field of centrifuge separation performance prediction technology, and proposes a method for predicting the separation performance of a horizontal screw centrifuge. The method involves establishing a single-phase fluid flow field model and flow field control equations; extracting flow field characteristic parameters; establishing a sedimentation separation criterion based on the preset condition that the parabolic trajectory of particles in the drum just falls on the drum wall, and calculating the particle settling velocity and settling threshold particle size; establishing a floating separation criterion based on the condition that particles are not carried out at the overflow port, and calculating the floating critical particle size; establishing a separation efficiency model based on the settling threshold particle size, floating critical particle size, and distribution function; and calculating the overall separation efficiency of the horizontal screw centrifuge based on the separation efficiency model. This invention establishes single-phase flow field models for centrifuges with different structural parameters and operating conditions, and uses thin-layer flow theory, sedimentation separation criteria, and floating separation criteria as theoretical foundations. The algorithm is simpler, the analysis results are more consistent with reality, and the theoretical basis is more sufficient.

Description

Technical Field

[0001] This invention relates to the field of centrifuge separation performance prediction technology, and in particular to a method for predicting the separation performance of a horizontal screw centrifuge. Background Technology

[0002] Horizontal screw discharge sedimentation centrifuges are widely used in petrochemical, fine chemical, environmental protection, and food industries. They offer advantages such as excellent separation performance, wide application range, large single-unit processing capacity, continuous automatic operation, and high adaptability to various material properties. Suitable for solid sedimentation and dewatering, liquid clarification, suspension thickening, solid classification, and separation of three-component systems, they can handle a wide range of materials (particle size 5μm~2000μm, solid content 2%~40%). They are a key piece of equipment in the production of synthetic plastics (e.g., polyvinyl chloride, polypropylene, polyethylene) and synthetic fibers (e.g., polyethylene terephthalate), and also have wide applications in calcium carbonate, talc, starch production, and wastewater treatment.

[0003] In actual industrial production applications, the centrifuge structure, operating conditions, and material properties are all key factors affecting the centrifuge separation effect.

[0004] Current research on centrifuge separation performance mainly relies on Σ theory or empirical formulas, or employs CFD (Computational Fluid Dynamics) or multiphase simulations such as the DPM (Discrete Phase Model) and Euler-Euler multiphase models. Σ theory is the classic theory for calculating centrifuge separation performance, estimating separation efficiency by simplifying assumptions (such as an ideal flow field). It is convenient for calculation but cannot reflect the true details of the flow field. Empirical formulas are merely theoretical formulas derived from a large amount of experimental data rather than rigorously derived from physical laws, lacking a theoretical foundation. CFD analysis can reproduce the flow field distribution with high accuracy, but it is a numerical simulation method and it is difficult to directly extract analytical theoretical mechanisms.

[0005] Therefore, existing research on centrifuge separation performance has the drawback of not being able to accurately predict centrifuge separation performance based on the actual structural parameters and operating conditions of the centrifuge. Summary of the Invention

[0006] The main objective of this invention is to provide a method for predicting the separation performance of a horizontal screw centrifuge that can accurately analyze the separation performance of centrifuges under different structural parameters and operating conditions.

[0007] To achieve the above objectives, the present invention provides a method for predicting the separation performance of a horizontal screw centrifuge, comprising the following steps: Based on the parameters of the horizontal screw centrifuge, a flow field model and flow field control equations for a single-phase fluid are established, and the flow field is solved. Based on the flow field model, characteristic parameters of the flow field are extracted, and the average axial velocity of the thin layer and the circumferential hysteresis of the liquid are calculated. Based on the preset condition that the parabolic trajectory of particles in the drum of a horizontal screw centrifuge can just fall on the drum wall, a sedimentation separation criterion is established. The sedimentation velocity of the particles is calculated according to the sedimentation separation criterion, and the sedimentation boundary particle size is calculated according to the sedimentation formula. Based on the condition that particles are not carried out at the overflow port of a horizontal screw centrifuge, a floating separation criterion is established, and the critical floating particle size is calculated. A separation efficiency model is established based on the settling threshold particle size, the floating threshold particle size, and the separation efficiency function. The overall separation efficiency of the horizontal screw centrifuge is calculated based on the separation efficiency model. The production capacity of the horizontal screw centrifuge is then calculated based on the overall separation efficiency. Finally, the separation performance of the horizontal screw centrifuge is analyzed based on the overall separation efficiency and production capacity.

[0008] Optionally, the steps of establishing a single-phase fluid flow field model and flow field control equations based on the parameters of the horizontal screw centrifuge, and solving the flow field, include: Establish a geometric model of a horizontal screw centrifuge, which includes the drum column section, screw, and overflow weir. Set material parameters and boundary parameters; among them, material parameters include mother liquor density and mother liquor viscosity; boundary parameters include inlet axial velocity, inlet circumferential velocity, screw blade speed and drum wall speed; The solution is obtained by calculating based on the flow field control equations; The flow field governing equations include: Continuity equation: ; NS equation: ; ; ; in, For operators, ; For the Laplace operator, ; The dynamic viscosity of the liquid phase; Let be the radial velocity of the particle. Let be the circumferential velocity of the particle. λ is the axial velocity of the particle; It is the density of the solid. The angular velocity of the free liquid surface; The radius of gyration in the radial direction of the particle; For fluid density; Circumferential coordinates For axial coordinates.

[0009] Optionally, the step of setting material parameters and boundary parameters includes: Take the inlet suspension flow rate With the large end clear liquid outlet flow rate The arithmetic mean flow rate, i.e. ( + ) / 2, representing the volumetric flow rate of the inlet axial velocity; The inlet axial velocity is calculated based on the volumetric flow rate at the inlet axial velocity, using the following equation: ; in, It is the axial velocity of the inlet. It is the inner diameter of the drum in the drum column section. It is the outer diameter of the screw; The inlet circumferential velocity is calculated using the following equation: ; in, It is the import circumferential speed. It is the screw speed. The diameter is the inner diameter of the screw cylinder.

[0010] Optionally, the flow field characteristic parameters include the thin layer thickness, feed rate, overflow rate, and free surface radius; the extraction of flow field characteristic parameters includes the following steps: The thickness of the thin layer is determined by statistically analyzing cross sections at equal intervals along the radial direction in the axial direction of the drum, and taking the thickness of the region where the axial velocity reaches the maximum value as a preset proportion. The maximum negative radial velocity at the overflow outlet of the overflow weir was obtained by using time-averaged statistical values. The average axial velocity of the thin layer is calculated based on the flow field characteristic parameters, and the calculation equation is as follows: ; in, The average axial velocity of the thin layer, This is the arithmetic mean of the feed throughput and the overflow discharge rate. The radius of the free surface; For thin layer thickness; The circumferential hysteresis rate of the liquid is calculated based on the flow field characteristic parameters, and the calculation equation is as follows: ; in, This refers to the circumferential hysteresis of the liquid. The screw angular velocity, The average circumferential velocity of the free liquid surface.

[0011] Optionally, the step of establishing the sedimentation separation criterion includes: Based on the pre-set condition that the parabolic trajectory of the particles in the drum can just fall on the drum wall, a calculation equation is established to make the settling time of the particles from the free liquid surface to the drum wall equal to the residence time of the suspension in the drum. The calculation equation is the settling separation criterion. The particle settling velocity is calculated based on the settling time of the particles from the free liquid surface to the drum wall and the residence time of the suspension in the drum. Calculate the settling boundary particle size based on the particle settling motion equation.

[0012] Optionally, the method for calculating particle settling velocity includes the following steps: Based on the fact that the force acting on a particle in a centrifugal force field is the difference between inertial force and buoyancy, the equation for the sedimentation motion of the particle is established as follows: ; in, For particle mass, It is the radial settling velocity of the particles. For time, Particle size, = - , This is the fluid resistance coefficient. This refers to the free settling velocity of the particles. The free settling velocity of particles is calculated using the following formula: when When the velocity is less than 28.8, the particles are in the laminar flow region, and the corresponding settling formula is: ; When 28.8 < When the temperature is less than 57600, the particles are in the transition zone, and the corresponding sedimentation formula is: ; when When the temperature is >57600, the particles are in the turbulent region, and the corresponding sedimentation formula is: ; in, This is a flow pattern determination criterion used to assess particle motion before applying a settling formula, and then to apply the corresponding settling formula based on that motion. The formula for calculation is: ; in, Centrifugal acceleration, ; For the separating factors, , It is the acceleration due to gravity; According to Stokes's settling theorem, a correction factor is introduced to calculate the particle settling velocity. The calculation formula is as follows: ; in, It is a correction factor for the settlement velocity. , It is the volume concentration of solid particles in a suspension.

[0013] Optionally, the step of calculating the settling boundary particle size includes: Assume the particle size is constant; The flow pattern is determined based on the assumed particle size. The particle motion is determined by the flow pattern criterion, and the corresponding sedimentation formula is used based on the particle motion. Calculate the settling boundary particle size based on the corresponding settling formula and settling velocity; The flow pattern is verified and the criteria are determined based on the calculated settling boundary particle size. If the flow pattern determination criterion is still within the original flow region, then the settling boundary particle size meets the settling separation criterion. If the flow pattern determination criterion is not within the original flow region, then the settling boundary particle size does not meet the settling separation criterion. A different particle size is then assumed, and the settling boundary particle size is recalculated.

[0014] Optionally, the step of calculating the critical particle size for buoyancy includes: Assume the particle size is constant; The flow pattern is determined based on the assumed particle size. Based on the flow pattern, the corresponding settling formula is used to determine the criterion, and the critical particle size for floating is calculated based on the settling formula and the floating separation criterion. The flow pattern is verified and the criterion is determined based on the calculated critical particle size for buoyancy. If the flow pattern judgment criterion is still within the original flow region, then the critical floating particle size satisfies the floating separation criterion. If the flow pattern judgment criterion is not within the original flow region, then the critical floating particle size does not satisfy the floating separation criterion. A different particle size is then assumed, and the critical floating particle size is recalculated.

[0015] Optionally, the step of establishing the separation efficiency model includes: Based on the minimum settling threshold particle size, determine the critical particle size at which the particle will definitely float. ; Determine the critical particle size at which the particle will definitely settle based on the maximum floating critical particle size. ; A separation efficiency model is established based on the sedimentation separation criterion and the buoyancy separation criterion. The separation efficiency model is as follows: ; in, For the separation efficiency model, Let be the particle separation efficiency function. For the sedimentation boundary particle size, The critical particle size for buoyancy. For the minimum settling boundary particle size, This is the maximum critical particle size for upward floating.

[0016] Optionally, the steps of calculating the overall separation efficiency of the horizontal screw centrifuge based on the separation efficiency model, calculating the production capacity of the horizontal screw centrifuge based on the overall separation efficiency, and analyzing the separation performance of the horizontal screw centrifuge based on the overall separation efficiency and production capacity include: The overall separation efficiency of the horizontal screw centrifuge is calculated based on the separation efficiency model. The formula is as follows: ; in, The total separation efficiency of the horizontal screw centrifuge. Let be the particle separation efficiency function. For particle size Take the differential, The minimum settling boundary particle size; The production capacity of a horizontal screw centrifuge is calculated based on the overall separation efficiency using the following formula: ; in, For the production capacity of horizontal screw centrifuges, This refers to the feed throughput. This refers to the solids content of the feed. The separation performance of the horizontal screw centrifuge was analyzed based on the overall separation efficiency and production capacity.

[0017] In the technical solution of this invention, a centrifuge is modeled based on the parameters of a horizontal screw centrifuge to simulate the flow field of a single-phase fluid (mother liquor) within the drum. Characteristic parameters are extracted from the simulation results. Thin-layer flow theory is introduced, and sedimentation and flotation separation criteria are established. These criteria, combined with the sedimentation formula, are used to calculate the critical particle size for sedimentation and flotation. Based on the critical particle size for sedimentation and flotation, and the particle separation efficiency function, the total separation efficiency of the centrifuge is calculated, yielding the product production capacity. The method of this invention has the following advantages: First, this invention models a horizontal screw centrifuge using simulation software, simulating the flow field of a single-phase fluid (mother liquor) within the centrifuge. It calculates only single-phase flow, simplifying the calculation algorithm. Second, this invention introduces thin-layer flow theory, overflow port floating theory, sedimentation separation criteria, and floating separation criteria to analyze particle motion, providing a solid theoretical basis and greater reliability. Third, by combining the sedimentation formulas corresponding to different particle motion conditions with the sedimentation and floating separation criteria, the invention calculates the critical sedimentation and floating particle sizes. Finally, based on the particle separation efficiency function, the overall separation efficiency of the horizontal screw centrifuge is calculated, resulting in calculations that better reflect the actual operation of the particles.

[0018] Secondly, this invention establishes a flow field model on simulation software based on the basic parameters (structural parameters and operating parameters) of the centrifuge; it can effectively analyze the influence of the centrifuge structure on the flow field and predict the separation performance of the centrifuge under different operating conditions, thus providing important guidance for the improvement design of the centrifuge.

[0019] Third, the core separation process of the centrifuge in this invention conforms to the principles of fluid mechanics, making it suitable for application to computer software systems to predict centrifuge separation performance with high accuracy. Attached Figure Description

[0020] Figure 1 This is a flowchart of the first embodiment of the present invention; Figure 2 This is a schematic diagram of the horizontal screw centrifuge structure in specific embodiment 2 of the present invention; Figure 3 This is a schematic diagram of particle movement within the drum in specific embodiment 1 of the present invention; Figure 4 This is a schematic diagram of the separation efficiency of a horizontal spiral centrifuge according to a specific embodiment 2 of the present invention.

[0021] The objectives, features, and advantages of this invention will be further explained in conjunction with the embodiments and with reference to the accompanying drawings. Detailed Implementation

[0022] It should be understood that the specific embodiments described herein are for illustrative purposes only and are not intended to limit the scope of the invention.

[0023] In the following description, the use of suffixes such as "unit," "component," or "element" to denote elements is solely for the purpose of illustrative purposes and has no specific meaning in itself. Therefore, "unit," "component," or "element" may be used interchangeably.

[0024] Please see Figures 1 to 4 The first embodiment of the present invention provides a method for predicting the separation performance of a horizontal screw centrifuge, comprising the following steps: Step S10: Based on the parameters of the horizontal screw centrifuge, establish the flow field model and flow field control equations for a single-phase fluid, and solve the flow field. Step S20: Extract flow field characteristic parameters based on the flow field model, and calculate the thin-layer average axial velocity and liquid circumferential hysteresis of the flow field. Step S30: Based on the preset condition that the parabolic trajectory of the particles in the drum of the horizontal screw centrifuge can just fall on the drum wall, a sedimentation separation criterion is established, and the sedimentation velocity of the particles is calculated according to the sedimentation separation criterion. The sedimentation boundary particle size is calculated according to the sedimentation formula. Step S40: Based on the condition that the particles are not carried out at the overflow port of the horizontal screw centrifuge, establish the floating separation criterion and calculate the critical floating particle size. Step S50: Establish a separation efficiency model based on the settling threshold particle size, the floating threshold particle size, and the separation efficiency function. Step S60: Calculate the total separation efficiency of the horizontal screw centrifuge based on the separation efficiency model, calculate the production capacity of the horizontal screw centrifuge based on the total separation efficiency, and analyze the separation performance of the horizontal screw centrifuge based on the total separation efficiency and production capacity.

[0025] This embodiment models a horizontal screw centrifuge using simulation software, simulating the flow field of a single-phase fluid (mother liquor) within the centrifuge. It calculates only single-phase flow, simplifying the calculation algorithm. Furthermore, it introduces thin-layer flow theory, overflow port floating theory, sedimentation separation criteria, and floating separation criteria to analyze particle motion, providing a solid theoretical basis and greater reliability. By combining the sedimentation formulas corresponding to different particle motion conditions with the sedimentation and floating separation criteria, the settling threshold particle size and floating critical particle size are calculated. Finally, the overall separation efficiency of the horizontal screw centrifuge is calculated based on the particle separation efficiency function, resulting in calculations that better reflect the actual operating conditions of the particles.

[0026] In the first embodiment of the method for predicting the separation performance of a horizontal screw centrifuge according to the present invention, and in the second embodiment of the method for predicting the separation performance of a horizontal screw centrifuge according to the present invention, step S10, which involves establishing a flow field model and flow field control equations based on the parameters of the horizontal screw centrifuge, and solving the flow field, includes: Step S11: Establish the geometric model of the horizontal screw centrifuge, wherein the geometric model of the horizontal screw centrifuge includes the drum column section, the screw, and the overflow weir; Step S12: Set material parameters and boundary parameters; wherein, the material parameters include mother liquor density and mother liquor viscosity; the boundary parameters include inlet axial velocity, inlet circumferential velocity, screw blade speed and drum wall speed. Step S13: Calculate and solve the flow field control equations; The flow field governing equations include: Continuity equation: ; NS equation: ; ; ; in, For operators, ; For the Laplace operator, ; The dynamic viscosity of the liquid phase; Let be the radial velocity of the particle. Let be the circumferential velocity of the particle. λ is the axial velocity of the particle; It is the density of the solid. The angular velocity of the free liquid surface; The radius of gyration in the radial direction of the particle; For fluid density; Circumferential coordinates For axial coordinates.

[0027] In this embodiment, based on the parameters of the horizontal screw centrifuge, a flow field model and flow field control equations are established. The steps for solving the flow field also include using a quadrilateral mesh structure, refining the mesh on the drum and screw blade walls near the wall along a direction perpendicular to the wall; refining the mesh at the inlet and outlet and near the free liquid surface; setting material parameters and boundary parameters, including feed flow rate, solid content, and solid density; in the CFD software model, the flow field solution can be performed using a pressure-based approach under steady-state conditions; the pressure-velocity coupling can use the SIMPLE algorithm; the pressure discretization scheme can use PRESTO!, which is suitable for calculating high-speed rotating fluids; momentum, circumferential velocity, and turbulent kinetic energy can use a second-order upwind discretization scheme; and the convergence criteria (Absolute Criteria) are set to a minimum of 10 for all calculated variables. -6 Furthermore, in the control window of the CFD software model, the circumferential velocity at the free surface, the pressure value at the free surface, and the radial velocity value at the overflow port are turned on. When all these values ​​reach a stable state and hardly change during the calculation, the calculation is ended and the final calculation result is output.

[0028] In the second embodiment of the horizontal screw centrifuge separation performance prediction method of the present invention, and in the third embodiment of the horizontal screw centrifuge separation performance prediction method of the present invention, step S12, setting material parameters and boundary parameters includes the following steps: Step S121, take the inlet suspension flow rate With the large end clear liquid outlet flow rate The arithmetic mean flow rate, i.e. ( + ) / 2, representing the volumetric flow rate of the inlet axial velocity; Step S122: Calculate the inlet axial velocity based on the volumetric flow rate of the inlet axial velocity. The calculation equation is as follows: ; in, It is the axial velocity of the inlet. It is the inner diameter of the drum in the drum column model. The screw model shows the outer diameter of the screw; Step S123, calculate the inlet circumferential velocity. The calculation equation is as follows: ; in, It is the import circumferential speed. The screw speed is... The diameter of the inner cylinder of the screw conveyor.

[0029] In this embodiment, the inlet axial velocity and inlet circumferential velocity are calculated based on the basic parameters of the centrifuge, and then used as the boundary conditions of the constrained flow field model.

[0030] In the first embodiment of the method for predicting the separation performance of a horizontal screw centrifuge according to the present invention, and in the fourth embodiment of the method for predicting the separation performance of a horizontal screw centrifuge according to the present invention, in step S20, the flow field characteristic parameters include thin layer thickness, feed throughput, overflow discharge rate, and free liquid surface radius; the extraction of flow field characteristic parameters includes the following steps: Step S21: Statistically analyze the cross-sections along the radial direction at equal intervals in the axial direction of the drum, and take the thickness of the area where the axial velocity reaches the maximum value as the thickness of the thin layer. Step S22: Obtain the maximum negative radial velocity of the overflow outlet of the overflow weir using time-averaged statistical values; Step S23: Calculate the average axial velocity of the thin layer based on the flow field characteristic parameters. The calculation equation is as follows: ; in, It is the average axial velocity of the thin layer. It is the arithmetic mean of the feed throughput and the overflow discharge rate; It is the radius of the free surface; It refers to the thickness of the thin layer; Step S24: Calculate the circumferential hysteresis rate of the liquid based on the flow field characteristic parameters. The calculation equation is as follows: ; in, This refers to the circumferential hysteresis of the liquid. The screw angular velocity, The average circumferential velocity of the free liquid surface.

[0031] In this embodiment, the thickness of the thin layer in the flow field model is taken as the thickness of the region where the axial velocity reaches a preset proportion of the maximum value. The preset proportion is taken within a reasonable range based on the actual situation, and can be 90%. The flow field characteristic parameters also include the maximum negative radial velocity of the overflow outlet. u r,min and the effective settlement radius, where the effective settlement radius is .

[0032] In the first embodiment of the horizontal screw centrifuge separation performance prediction method of the present invention, and in the fifth embodiment of the horizontal screw centrifuge separation performance prediction method of the present invention, step S30, establishing sedimentation separation criteria, includes the following steps: Step S31: Based on the preset condition that the parabolic trajectory of the particles in the drum can just fall on the drum wall, establish a calculation equation that the settling time of the particles from the free liquid surface to the drum wall is equal to the residence time of the suspension in the drum. The calculation equation is the settling separation criterion. Step S32: Calculate the particle settling velocity based on the settling time of the particles from the free liquid surface to the drum wall and the residence time of the suspension in the drum. Step S33: Calculate the settling boundary particle size based on the particle settling motion equation.

[0033] In this embodiment, when the parabolic trajectory of the particle in the drum just falls on the drum wall, mathematically it is expressed as the settling time of the particle from the free liquid surface to the drum wall being equal to the residence time of the suspension in the drum. The particle settling time is calculated using the following formula: ; in, For particle settling time, It is the particle settling velocity. It is the radius of the drum; The residence time of particles inside the drum is calculated using the following formula: ; in, The residence time of the particles inside the drum. It is the length of the drum column section. It is the average axial velocity of the thin layer; Residence time and settling time inside the rotating drum Calculate the average settlement velocity The calculation formula is as follows: .

[0034] In the fifth embodiment of the horizontal screw centrifuge separation performance prediction method of the present invention, and in the sixth embodiment of the horizontal screw centrifuge separation performance prediction method of the present invention, the calculation method for particle settling velocity in step S30 includes the following steps: Step S34: Based on the fact that the force acting on the particle in the centrifugal force field is the difference between inertial force and buoyancy, the sedimentation motion equation of the particle is established as follows: ; in, For particle mass, It is the radial settling velocity of the particles. For time, Particle size, = - , This is the fluid resistance coefficient. This refers to the free settling velocity of the particles. Step S35: Calculate the free settling velocity of the particles. The settling formula is as follows: when When the velocity is less than 28.8, the particles are in the laminar flow region, and the corresponding settling formula is: ; When 28.8 < When the temperature is less than 57600, the particles are in the transition zone, and the corresponding sedimentation formula is: ; when When the temperature is >57600, the particles are in the turbulent region, and the corresponding sedimentation formula is: ; in, This is a flow pattern determination criterion used to assess particle motion before applying a settling formula, and then to apply the corresponding settling formula based on that motion. The formula for calculation is: ; in, Centrifugal acceleration, ; For the separating factors, , It is the acceleration due to gravity; Step S36: According to Stokes' sedimentation theorem, the free settling velocity of a single particle in the liquid is taken as the particle settling velocity. A correction factor is introduced to calculate the particle settling velocity. The calculation formula is: ; in, It is a correction factor for the settlement velocity. , It is the volume concentration of solid particles in a suspension.

[0035] In this embodiment, the particle settling velocity is derived using the model of a single particle freely settling in a liquid, which is Stokes' sedimentation theorem. Based on the fact that the force acting on a particle in a centrifugal force field is the difference between inertial force and buoyancy, the particle's settling motion equation is established. Furthermore, other forces affecting particle motion can be considered in the actual particle motion, and these other actual forces are introduced to establish the particle's settling motion equation. When calculating the settling velocity... To account for the hindering effect of solid concentration on particle settling, the Richardson formula, simplified using experimental data by Sun Qicai et al., is used to approximate the settling velocity. The corresponding settling formula is adopted according to the particle's location in the laminar, transition, and turbulent regions. This study is based on experimental data from Reynolds and Lessenko.

[0036] In the fifth embodiment of the horizontal screw centrifuge separation performance prediction method of the present invention, and in the seventh embodiment of the horizontal screw centrifuge separation performance prediction method of the present invention, step S33, calculating the settling boundary particle size of the particles, includes the following steps: Step S331, assuming the particle size is constant; Step S332: Calculate the flow pattern judgment criterion based on the assumed particle size; Step S333: Determine the particle motion status based on the flow pattern judgment criterion, and use the corresponding sedimentation formula based on the particle motion status. Step S334: Calculate the settling boundary particle size according to the corresponding settling formula and settling velocity; Step S335: Verify the flow pattern judgment criterion based on the calculated settling boundary particle size; Step S336: If the flow pattern judgment criterion is still in the original flow region, then the settling boundary particle size meets the settling separation criterion. If the flow pattern judgment criterion is not in the original flow region, then the settling boundary particle size does not meet the settling separation criterion. A different particle size is assumed and the settling boundary particle size is recalculated.

[0037] In this embodiment, the particle size is assumed to be... =32um (can be assumed arbitrarily within the particle size range), calculate the flow pattern judgment criterion. =0.26; Use the corresponding settlement formulas (laminar, transitional, turbulent): By transforming the variables, the sedimentation boundary particle size can be obtained. The calculation formula (taking laminar flow as an example): ; in, The average centrifugal acceleration over the entire settling radius. .

[0038] Solving the boundary particle size of sedimentation =21μm, then calculate the flow pattern criterion. =2.2, if the flow pattern criterion is still within the laminar flow region. Therefore, the particle size... =21μm is the critical particle size that satisfies the sedimentation separation criterion; if the flow pattern judgment criterion is not in the laminar flow region, then the sedimentation separation criterion is not satisfied, and the particle size is re-assumed as transitional flow or turbulent flow, and the calculation is recalculated. Based on the transition zone settling formula, by transforming the variables, the boundary particle size of the transition flow settling zone is obtained. The calculation formula is: ; Based on the turbulent settling formula, by transforming the variables, the boundary particle size of the turbulent settling particles is obtained. The calculation formula is: .

[0039] In the first embodiment of the method for predicting the separation performance of a horizontal screw centrifuge according to the present invention, and in the eighth embodiment of the method for predicting the separation performance of a horizontal screw centrifuge according to the present invention, step S40, calculating the critical particle size for upward flotation, includes the following steps: Step S41, assuming the particle size is constant; Step S42: Calculate the flow pattern judgment criterion based on the assumed particle size; Step S43: Based on the flow pattern, use the corresponding settling formula to determine the critical particle size for floating. Calculate the critical particle size for floating based on the settling formula and the floating separation criterion. Step S44: Verify the flow pattern judgment criterion based on the calculated critical floating particle size; Step S45: If the flow pattern judgment criterion is still in the original flow region, then the critical floating particle size meets the floating separation criterion. If the flow pattern judgment criterion is not in the original flow region, then the critical floating particle size does not meet the floating separation criterion. A different particle size is assumed and the critical floating particle size is recalculated.

[0040] In this embodiment, the negative radial velocity with the maximum absolute value at the overflow outlet is obtained from the CFD calculation results as u. r,min=-0.15m / s, then = - u r,min =0.15m / s; Assuming the overflow outlet is located in the transitional flow region (laminar, transitional, and turbulent flow can all be assumed), the transitional flow settlement formula is as follows: ; The solid concentration at the overflow outlet is very low, so the influence of particles does not need to be considered. By changing the variables, the critical particle size for buoyancy can be obtained. The calculation formula is as follows: ; in, The centrifugal acceleration at the radius of the overflow outlet. , The radius of the overflow outlet; Will = - u r,min Substituting 0.15 m / s into the equation, we can solve for the critical particle size for buoyancy. =74μm, then calculate the flow pattern determination criterion. =96, if the flow pattern judgment criterion is still within the transition flow region, then the particle size =74μm is the critical particle size that satisfies the floating separation criterion; if the flow pattern judgment criterion is not in the transition flow region, then the floating separation criterion is not satisfied, and the overflow outlet is re-assumed to be in the laminar or turbulent region, and the calculation is recalculated. Based on the laminar settling formula, by transforming the variables, the critical particle size for laminar float is obtained. The calculation formula is: ; Based on the turbulent settling formula, by transforming the variables, the critical particle size for turbulent buoyancy is obtained. The calculation formula is: .

[0041] In the first embodiment of the horizontal spiral centrifuge separation performance prediction method of the present invention, and in the ninth embodiment of the horizontal spiral centrifuge separation performance prediction method of the present invention, step S50, establishing a separation efficiency model, includes the following steps: Step S51: Determine the critical particle size at which the particle will definitely float based on the minimum settling threshold particle size; ; Step S52: Determine the critical particle size at which the particle will definitely settle based on the maximum buoyancy critical particle size; ; Step S53: Establish a separation efficiency model based on the settling separation criterion and the floating separation criterion; The model is: ; in, For the separation efficiency model, Let be the particle separation efficiency function. For the sedimentation boundary particle size, The critical particle size for buoyancy. For the minimum settling boundary particle size, This is the maximum critical particle size for upward floating.

[0042] In this embodiment, in the separation efficiency model, when hour, =0 means that when the particle size is smaller than the predicted minimum settling boundary particle size, i.e., the particle size is smaller than all settling boundary particle sizes, according to the sedimentation separation criterion, this particle will definitely float. =0; In the separation efficiency model, when hour, =1 means that when the particle size is larger than the predicted maximum critical floating particle size, that is, when the particle size is larger than all critical floating particle sizes, according to the floating separation criterion, the particle will definitely settle. =1; In the separation efficiency model hour, = The meaning of this expression is that when the particle size is not less than the minimum settling threshold particle size and not greater than the maximum floating threshold particle size, the particle motion state only satisfies the settling separation criterion or only satisfies the floating separation criterion.

[0043] In the first embodiment of the horizontal screw centrifuge separation performance prediction method of the present invention, and in the tenth embodiment of the horizontal screw centrifuge separation performance prediction method of the present invention, step S60, calculating the total separation efficiency of particles according to the separation efficiency model, calculating the production capacity of the horizontal screw centrifuge according to the total separation efficiency of particles, and analyzing the separation performance of the horizontal screw centrifuge based on the total separation efficiency and production capacity, includes the following steps: Step S61, the formula for calculating the overall particle separation efficiency is: ; in, The total separation efficiency of the horizontal screw centrifuge. Let be the particle separation efficiency function. For particle size Take the differential, The minimum settling boundary particle size; Step S62, the production capacity calculation formula is: ; in, This refers to the production capacity of the horizontal screw centrifuge. It refers to the feed throughput. It is the solids content of the feed; The separation performance of a horizontal screw centrifuge is analyzed based on its production capacity.

[0044] In this embodiment, This means that when the particle size is not less than the minimum settling threshold particle size, a separation function is applied to all particles. The feed throughput, solids content, and solids density of a horizontal screw centrifuge can be determined based on the specific materials being processed by different horizontal screw centrifuges, as different horizontal screw centrifuges can handle different ranges of materials.

[0045] The following provides a specific embodiment of the horizontal spiral centrifuge separation performance prediction method of the present invention: Specific Implementation Example 1: A certain model of horizontal screw centrifuge has a feed flow rate of 33m³ / h. 3 Prediction of the separation performance of a suspension of HDPE particles with a solid content of 30% mixed with hexane solvent under the condition of / h.

[0046] In this embodiment, the centrifuge structural parameters and operating parameters are as follows: CFD simulations yielded a thin layer thickness δ of 8.5 mm and an average axial velocity within the thin layer. The maximum negative radial velocity at the overflow outlet is 0.344 m / s. u r,min The circumferential lag rate is -0.39 m / s. ε The sedimentation rate is 90.8%. Based on the sedimentation separation criterion and the floating separation criterion, the boundary particle size of the sediment is calculated. The critical particle size for buoyancy is 29.5 μm. With a particle size of 47µm, based on the particle size distribution map, the particle size recovery distribution efficiency is interpolated in the particle size distribution map, and the total separation efficiency of the material is ET = 96.7%, and the production capacity of HDPE solid product dry weight is 9.19t / h. Specific Implementation Example 2: A certain model of horizontal screw centrifuge has a feed flow rate of 200m³ / h. 3 Prediction of PX particle separation performance in mother liquor at a concentration of 17.66% solids per hour. In this embodiment, the centrifuge structural and operating parameters are as follows: In this embodiment, the centrifuge structural parameters and operating parameters are as follows: CFD simulations were used to determine the average axial velocity within a thin layer with a thickness δ of 75 mm. The maximum negative radial velocity at the overflow outlet is 0.23 m / s. u r,min The circumferential lag rate is -0.15 m / s. ε The sedimentation rate is 93%. Based on the sedimentation separation criterion and the flotation separation criterion, the boundary particle size of the sediment is calculated. The critical particle size for buoyancy is 21 μm. With a particle size of 74 μm, based on the normal distribution of particle size, the particle size recovery distribution efficiency is interpolated in the particle size distribution function, and the total separation efficiency of the material is ET = 83%, and the production capacity of PX solid product dry weight is 32 t / h.

[0048] Through the above description of the embodiments, those skilled in the art can clearly understand that the methods of the above embodiments can be implemented by means of software plus necessary general-purpose hardware platforms. Of course, they can also be implemented by hardware, but in many cases the former is a better implementation method. Based on this understanding, the technical solution of the present invention, or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product is stored in a computer-readable storage medium (such as ROM / RAM, magnetic disk, optical disk) as described above, and includes several instructions to cause a terminal device to enter the methods described in the various embodiments of the present invention.

[0049] In the description of this specification, references to terms such as "one embodiment," "another embodiment," "other embodiments," or "first embodiment to Xth embodiment," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the present invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, method steps, or characteristics described may be combined in any suitable manner in one or more embodiments or examples.

[0050] It should be noted that, in this document, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or system that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or system. Unless otherwise specified, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or system that includes that element.

[0051] The sequence numbers of the above embodiments of the present invention are for descriptive purposes only and do not represent the superiority or inferiority of the embodiments.

[0052] The above are merely preferred embodiments of the present invention and do not limit the scope of the patent. Any equivalent structural or procedural transformations made based on the description and drawings of the present invention, or direct or indirect applications in other related technical fields, are similarly included within the scope of patent protection of the present invention.

Claims

1. A method for predicting the separation performance of a horizontal screw centrifuge, characterized in that, Includes the following steps: Based on the parameters of the horizontal screw centrifuge, a flow field model and flow field control equations for a single-phase fluid are established, and the flow field is solved. Based on the flow field model, characteristic parameters of the flow field are extracted, and the average axial velocity of the thin layer and the circumferential hysteresis of the liquid are calculated. Based on the preset condition that the parabolic trajectory of particles in the drum of a horizontal screw centrifuge can just fall on the drum wall, a sedimentation separation criterion is established. The sedimentation velocity of the particles is calculated according to the sedimentation separation criterion, and the sedimentation boundary particle size is calculated according to the sedimentation formula. Based on the condition that particles are not carried out at the overflow port of a horizontal screw centrifuge, a floating separation criterion is established, and the critical floating particle size is calculated. A separation efficiency model is established based on the settling threshold particle size, the floating threshold particle size, and the separation efficiency function. The overall separation efficiency of the horizontal screw centrifuge is calculated based on the separation efficiency model. The production capacity of the horizontal screw centrifuge is then calculated based on the overall separation efficiency. Finally, the separation performance of the horizontal screw centrifuge is analyzed based on the overall separation efficiency and production capacity.

2. The method for predicting the separation performance of a horizontal screw centrifuge according to claim 1, characterized in that, The steps for establishing a single-phase fluid flow field model and flow field control equations based on the parameters of the horizontal screw centrifuge, and solving the flow field, include: Establish a geometric model of a horizontal screw centrifuge, which includes the drum column section, screw, and overflow weir. Set material parameters and boundary parameters; among them, material parameters include mother liquor density and mother liquor viscosity; boundary parameters include inlet axial velocity, inlet circumferential velocity, screw blade speed and drum wall speed; The solution is obtained by calculating based on the flow field control equations; The flow field governing equations include: Continuity equation: ； NS equation: ； ； ； in, For operators, ; For the Laplace operator, ; The dynamic viscosity of the liquid phase; Let be the radial velocity of the particle. Let be the circumferential velocity of the particle. λ is the axial velocity of the particle; It is the density of the solid. The angular velocity of the free liquid surface; The radius of gyration in the radial direction of the particle; For fluid density; Circumferential coordinates For axial coordinates.

3. The method for predicting the separation performance of a horizontal screw centrifuge according to claim 2, characterized in that, The steps for setting material parameters and boundary parameters include: Take the inlet suspension flow rate With the large end clear liquid outlet flow rate The arithmetic mean flow rate, i.e. ( + ) / 2, representing the volumetric flow rate of the inlet axial velocity; The inlet axial velocity is calculated based on the volumetric flow rate at the inlet axial velocity, using the following equation: ； in, It is the axial velocity of the inlet. It is the inner diameter of the drum in the drum column section. It is the outer diameter of the screw; The inlet circumferential velocity is calculated using the following equation: ； in, It is the import circumferential speed. It is the screw speed. The diameter is the inner diameter of the screw cylinder.

4. The method for predicting the separation performance of a horizontal screw centrifuge according to claim 3, characterized in that, The flow field characteristic parameters include the thin layer thickness, feed rate, overflow rate, and free surface radius; the extraction of flow field characteristic parameters includes the following steps: The thickness of the thin layer is determined by statistically analyzing cross sections at equal intervals along the radial direction in the axial direction of the drum, and taking the thickness of the region where the axial velocity reaches the maximum value as a preset proportion. The maximum negative radial velocity at the overflow outlet of the overflow weir was obtained by using time-averaged statistical values. The average axial velocity of the thin layer is calculated based on the flow field characteristic parameters, and the calculation equation is as follows: ； in, The average axial velocity of the thin layer, This is the arithmetic mean of the feed throughput and the overflow discharge rate. The radius of the free surface; For thin layer thickness; The circumferential hysteresis rate of the liquid is calculated based on the flow field characteristic parameters, and the calculation equation is as follows: ； in, This refers to the circumferential hysteresis of the liquid. The screw angular velocity, The average circumferential velocity of the free liquid surface.

5. The method for predicting the separation performance of a horizontal screw centrifuge according to claim 4, characterized in that, The steps for establishing the sedimentation separation criterion include: Based on the pre-set condition that the parabolic trajectory of the particles in the drum can just fall on the drum wall, a calculation equation is established to make the settling time of the particles from the free liquid surface to the drum wall equal to the residence time of the suspension in the drum. The calculation equation is the settling separation criterion. The particle settling velocity is calculated based on the settling time of the particles from the free liquid surface to the drum wall and the residence time of the suspension in the drum. Calculate the settling boundary particle size based on the particle settling motion equation.

6. The method for predicting the separation performance of a horizontal screw centrifuge according to claim 5, characterized in that, The calculation method for particle settling velocity includes the following steps: Based on the fact that the force acting on a particle in a centrifugal force field is the difference between inertial force and buoyancy, the equation for the sedimentation motion of the particle is established as follows: ； in, For particle mass, It is the radial settling velocity of the particles. For time, Particle size, = - , This is the fluid resistance coefficient. This refers to the free settling velocity of the particles. The free settling velocity of the particles is calculated using the following formula: when When the velocity is less than 28.8, the particles are in the laminar flow region, and the corresponding settling formula is: ； When 28.8 < When the temperature is less than 57600, the particles are in the transition zone, and the corresponding sedimentation formula is: ； when When the temperature is >57600, the particles are in the turbulent region, and the corresponding sedimentation formula is: ； in, This is a flow pattern determination criterion used to assess particle motion before applying a settling formula, and then to apply the corresponding settling formula based on that motion. The formula for calculation is: ； in, Centrifugal acceleration, ; For the separating factors, , It is the acceleration due to gravity; According to Stokes's settling theorem, a correction factor is introduced to calculate the particle settling velocity. The calculation formula is as follows: ； in, It is a correction factor for the settlement velocity. , It is the volume concentration of solid particles in a suspension.

7. The method for predicting the separation performance of a horizontal screw centrifuge according to claim 6, characterized in that, The step of calculating the settling boundary particle size includes: Assume the particle size is constant; The flow pattern is determined based on the assumed particle size. The particle motion is determined by the flow pattern criterion, and the corresponding sedimentation formula is used based on the particle motion. Calculate the settling boundary particle size based on the corresponding settling formula and settling velocity; The flow pattern is verified and the criteria are determined based on the calculated settling boundary particle size. If the flow pattern determination criterion is still within the original flow region, then the settling boundary particle size meets the settling separation criterion. If the flow pattern determination criterion is not within the original flow region, then the settling boundary particle size does not meet the settling separation criterion. A different particle size is then assumed, and the settling boundary particle size is recalculated.

8. The method for predicting the separation performance of a horizontal screw centrifuge according to claim 7, characterized in that, The step of calculating the critical particle size for buoyancy includes: Assume the particle size is constant; The flow pattern is determined based on the assumed particle size. Based on the flow pattern, the corresponding settling formula is used to determine the criterion, and the critical particle size for floating is calculated based on the settling formula and the floating separation criterion. The flow pattern is verified and the criterion is determined based on the calculated critical particle size for buoyancy. If the flow pattern judgment criterion is still within the original flow region, then the critical floating particle size satisfies the floating separation criterion. If the flow pattern judgment criterion is not within the original flow region, then the critical floating particle size does not satisfy the floating separation criterion. A different particle size is then assumed, and the critical floating particle size is recalculated.

9. The method for predicting the separation performance of a horizontal screw centrifuge according to claim 8, characterized in that, The steps for establishing the separation efficiency model include: Based on the minimum settling threshold particle size, determine the critical particle size at which the particle will definitely float. ； Determine the critical particle size at which the particle will definitely settle based on the maximum floating critical particle size. ； A separation efficiency model is established based on the sedimentation separation criterion and the buoyancy separation criterion. The separation efficiency model is as follows: ； in, For the separation efficiency model, Let be the particle separation efficiency function. For the sedimentation boundary particle size, The critical particle size for buoyancy. For the minimum settling boundary particle size, This is the maximum critical particle size for upward floating.

10. The method for predicting the separation performance of a horizontal screw centrifuge according to claim 9, characterized in that, The steps of calculating the overall separation efficiency of the horizontal screw centrifuge based on the separation efficiency model, calculating the production capacity of the horizontal screw centrifuge based on the overall separation efficiency, and analyzing the separation performance of the horizontal screw centrifuge based on the overall separation efficiency and production capacity include: The overall separation efficiency of the horizontal screw centrifuge is calculated based on the separation efficiency model. The formula is as follows: ； in, The total separation efficiency of the horizontal screw centrifuge. Let be the particle separation efficiency function. For particle size Take the differential, The minimum settling boundary particle size; The production capacity of a horizontal screw centrifuge is calculated based on the overall separation efficiency using the following formula: ； in, For the production capacity of horizontal screw centrifuges, This refers to the feed throughput. This refers to the solids content of the feed. The separation performance of the horizontal screw centrifuge was analyzed based on the overall separation efficiency and production capacity.

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