Numerical simulation method for pressure and torque characteristics of vertical planetary kneader

Abstract

This application relates to the field of chemical safety technology and discloses a numerical simulation method for the pressure and torque characteristics of a vertical planetary kneader. The method includes: constructing a fluid domain model within a reactor; correcting the rotational speed of a dual-blade kneader in a non-revolutionary system based on the revolution speed in the planetary motion system, obtaining a corrected rotational speed value; constructing blade motion parameter equations based on the geometric coordinates of the dual blades, the corrected rotational speed value, and the revolution speed; configuring a dynamic mesh on the fluid domain model based on the blade motion parameter equations; obtaining a corrected Reynolds number based on the corrected rotational speed value and the revolution speed, and determining a flow model matching the corrected Reynolds number; and performing numerical simulation on the fluid domain model with the configured dynamic mesh based on the flow model to obtain the pressure and torque characteristics of the dual blades. Its advantage is that it achieves high-precision simulation.

Description

Technical Field

[0001] This application relates to the field of chemical safety technology, and in particular to a numerical simulation method for the pressure and torque characteristics of a vertical planetary kneader. Background Technology

[0002] Vertical planetary kneaders are crucial equipment for mixing high-viscosity, high-solids-content materials. However, the complex planetary motion of the internal blades results in an extremely complex flow field, making key parameters such as pressure and torque difficult to measure directly. This has led to a long-standing reliance on experience in industrial design, lacking a reliable forward design theory. To circumvent these technical obstacles, related numerical simulation methods commonly employ a significantly simplified method based on the pot wall motion. While this method offers computational stability, it results in distorted physical models, making it difficult to meet the demands of high-precision simulations. Summary of the Invention

[0003] This application provides a numerical simulation method for the pressure and torque characteristics of a vertical planetary kneader, which solves the technical problem that related technologies cannot accurately predict the pressure and torque characteristics of a kneader, and achieves the technical effect of high-precision simulation.

[0004] To achieve the above objectives, the main technical solutions adopted in this application include:

[0005] In a first aspect, embodiments of this application provide a numerical simulation method for the pressure and torque characteristics of a vertical planetary kneader. The method includes: constructing a fluid domain model within a reactor; correcting the rotational speed of a dual-blade kneader in a non-revolutionary system based on the revolution speed in the planetary motion system, obtaining a corrected rotational speed value; constructing blade motion parameter equations based on the geometric coordinates of the dual blades, the corrected rotational speed value, and the revolution speed; configuring a dynamic mesh on the fluid domain model based on the blade motion parameter equations; obtaining a corrected Reynolds number based on the corrected rotational speed value and the revolution speed, and determining a flow model matching the corrected Reynolds number; and performing numerical simulation on the fluid domain model with the configured dynamic mesh based on the flow model to obtain the pressure and torque characteristics of the dual blades.

[0006] The numerical simulation method for pressure and torque characteristics of a vertical planetary kneader provided in this application corrects the kneading rotation speed of the non-revolutionary system based on the revolution speed of the planetary motion system, eliminating the interference of revolution on the relative motion of the two blades and ensuring that the two blades maintain the correct kneading state in the combined motion of rotation and revolution. By integrating the geometric coordinates of the two blades, the correction value of the rotation speed, and the revolution speed, the blade motion parameter equation is constructed to accurately quantify the actual motion law of the two blades of the vertical planetary kneader. The blade motion parameter equation is used as the boundary driving condition of the moving mesh, so that the fluid domain mesh adjusts in real time with the motion of the two blades. The corrected Reynolds number adapted to the planetary motion flow field is obtained by using the correction value of the rotation speed and the revolution speed. The actual flow state of the flow field is determined based on the corrected Reynolds number, thereby selecting the appropriate flow model. The fluid domain model with the configured moving mesh is numerically solved by the flow model, and finally, the high-precision output of the pressure and torque characteristics of the two blades is achieved.

[0007] Optionally, the dual propeller blades include hollow blades and solid blades. Based on the revolution speed in the planetary motion system, the rotation speed of the dual propeller blades in a non-revolutionary system is corrected to obtain a correction value for the rotation speed. This includes: obtaining the helix angle ratio of the hollow blades and the solid blades; determining the second rotation speed required for the solid blades to achieve pinching in the non-revolutionary system based on the first rotation speed of the hollow blades in the non-revolutionary system and the helix angle ratio; correcting the first rotation speed based on the revolution speed to obtain the first correction value for the hollow blades' rotation speed in the planetary motion system; and correcting the second rotation speed based on the revolution speed to obtain the second correction value for the solid blades' rotation speed in the planetary motion system.

[0008] In order to maintain the optimal pinching relationship determined by the helix angle ratio in a real planetary motion system, the first and second rotation speeds in the non-revolutionary system were corrected by the revolution speed to accurately counteract the interference of the revolution motion on the relative motion of the two propeller blades. Finally, the corrected values ​​of the first and second rotation speeds in the planetary motion system were obtained, which provided a numerical basis for subsequent high-precision numerical simulation.

[0009] Optionally, the first rotation speed is corrected based on the revolution speed to obtain a first rotation speed correction value for the hollow blade in the planetary motion system; the second rotation speed is corrected based on the revolution speed to obtain a second rotation speed correction value for the solid blade in the planetary motion system, including: vector synthesis of the revolution speed and the first rotation speed to obtain the first rotation speed correction value; and vector synthesis of the revolution speed and the second rotation speed to obtain the second rotation speed correction value.

[0010] A vector synthesis method was adopted, performing vector calculations based on the revolution speed and the first and second rotation speeds respectively, to ensure that the corrected speed values ​​could be adapted to the combined motion requirements of the two propellers. The final corrected first and second rotation speed values ​​not only retained the optimal kneading speed ratio determined by the helix angle ratio in the non-revolutionary system, but also eliminated the relative motion disturbances caused by revolution. This ensured that the shear angle and extrusion force of the two propellers remained coordinated and matched to the material during planetary motion, further improving the realism of the kneading effect simulation.

[0011] Optionally, based on the geometric coordinates of the two blades, the rotational speed correction value, and the revolution speed, the blade motion parameter equation is constructed, including: for any blade, determining the eccentricity of the blade according to its geometric coordinates; determining the translational velocity component of the blade based on the eccentricity and the revolution speed; determining the rotational angular velocity component of the blade based on the rotational speed correction value; and constructing the blade motion parameter equation based on the translational velocity component and the rotational angular velocity component.

[0012] By constructing the propeller motion parameter equations through vector synthesis of two types of components, the true motion state of the two propellers at any time can be completely and accurately quantified. This provides accurate boundary driving conditions for subsequent dynamic meshing, while ensuring the consistency between the motion description and the physical laws of planetary motion, and avoiding motion distortion problems caused by simplified models.

[0013] Optionally, based on the blade motion parameter equation, configuring a dynamic mesh for the fluid domain model includes: setting the mesh interface in the fluid domain model that coincides with the surface of the dual blades as a rigid body motion boundary; generating real-time motion parameters of the rigid body motion boundary based on the blade motion parameter equation; and dynamically adjusting the displacement of the mesh nodes in the fluid domain model based on the real-time motion parameters.

[0014] By defining the mesh interface coinciding with the surface of the twin propeller blades in the fluid domain model as the rigid body motion boundary, a precise boundary carrier is provided for motion transmission. Real-time motion parameters generated based on the propeller motion parameter equations provide motion commands for the rigid body motion boundary, ensuring complete synchronization between the boundary motion and the actual planetary motion of the twin propeller blades. Based on these real-time motion parameters, the displacement of the fluid domain mesh nodes is dynamically adjusted, enabling the mesh to adapt in real time to the combined motion of the twin propeller blades' revolution and rotation, effectively avoiding problems such as mesh distortion, overlap, or negative volume.

[0015] Optionally, obtaining the corrected Reynolds number based on the rotational speed correction value and the revolution speed includes: calculating a characteristic speed based on the rotational speed correction value and the revolution speed; and calculating the corrected Reynolds number based on the characteristic speed.

[0016] The characteristic rotational speed, synthesized from the correction value of the rotational speed and the revolution speed, is the equivalent characteristic velocity tailored for this complex flow field. It integrates the driving contributions of both motions to the fluid, providing accurate and suitable core parameters for calculating the corrected Reynolds number. The corrected Reynolds number calculated based on this characteristic rotational speed can serve as a reliable criterion for judging the flow state of the flow field, ensuring that the flow model selected accordingly is based on correct fluid dynamics principles, thereby guaranteeing the physical authenticity of the entire numerical simulation process and results.

[0017] Optionally, based on the rotational speed correction value and the revolution speed, the characteristic speed is calculated, including: calculating a first product of the first rotational speed correction value and the diameter of the hollow blade; calculating a second product of the revolution speed and the revolution diameter of the planetary motion system; calculating the sum of the first product and the second product, and determining the sum as the characteristic speed.

[0018] As the main driving blade, the hollow blade's first rotational speed correction value can equivalently represent the shear driving effect of the dual-blade coordinated rotation on the fluid. The first product of the first rotational speed correction value and the hollow blade diameter accurately quantifies the contribution of the main driving blade's rotational motion, after correction for revolution interference, to the local shear velocity generated by the fluid. The second product of the revolution speed and the revolution diameter accurately quantifies the contribution of the macroscopic circulation velocity formed by the revolution motion of the dual blades. By summing these two values, the velocity characteristics of the composite flow field under the planetary motion system, which combines local high shear and macroscopic circulation, are integrated. The output characteristic speed can truly reflect the overall motion intensity of the flow field, solving the problem that traditional single velocity parameters cannot fully characterize composite flow fields.

[0019] Optionally, the flow model is determined as follows: if the corrected Reynolds number is less than or equal to a preset critical Reynolds number, the flow model is a laminar flow model; if the corrected Reynolds number is greater than the critical Reynolds number, the flow model is a turbulent flow model.

[0020] The modified Reynolds number, as a specific similarity criterion number adapted to complex planetary motion flow fields, is compared with the preset critical Reynolds number to determine whether the flow field is in a laminar or turbulent state. When the modified Reynolds number is less than or equal to the critical Reynolds number, it indicates that the flow field has low motion intensity, fluid viscosity dominates, and the flow field exhibits a stable laminar state. In this case, a laminar flow model is used for solution. When the modified Reynolds number is greater than the critical Reynolds number, it indicates that the flow field has high motion intensity, inertial forces dominate the flow field motion, accompanied by significant high shear disturbances, and the flow field exhibits a complex turbulent state. In this case, a turbulent flow model is used for calculation. This method of accurately matching the corresponding flow model based on the actual flow field state ensures that subsequent numerical simulations can accurately solve for key parameters such as velocity, pressure, and shear stress in the planetary motion flow field, thereby outputting high-precision pressure and torque characteristics results for the dual-blade flow.

[0021] Optionally, constructing a fluid domain model within the reactor includes: performing unstructured mesh generation on the fluid domain geometric model to obtain a fluid domain mesh; and constructing the fluid domain model based on the fluid domain mesh; wherein the discrete elements in the fluid domain mesh satisfy the following conditions: minimum orthogonal mass greater than 0.2, average orthogonal mass greater than 0.75, maximum skewness less than 0.8, and average skewness less than 0.25.

[0022] The motion of the impeller causes continuous and drastic changes in the shape of the fluid domain, resulting in extensive deformation and reconstruction of the mesh. Unstructured meshes, with their flexible node connections, are more robust than structured meshes when handling such large deformations and displacements. By employing unstructured meshes with strictly controlled quality, problems such as numerical diffusion, pressure oscillations, and even computational divergence caused by element distortion can be effectively avoided, ensuring the accuracy and convergence of the flow field solution. This allows for stable and accurate high-fidelity simulations based on the actual motion equations.

[0023] Optionally, the numerical simulation employs an adaptive time step, which is determined as follows: a Gaussian weighted model centered on the high shear phase is constructed; the time difference between the current periodic phase of the planetary motion system and the preset high shear center time is calculated; a weighting factor is calculated based on the time difference and the Gaussian weighted model; and the current time step is obtained by interpolation within a preset time step range based on the weighting factor.

[0024] By synchronizing the simulation time with the physical process through periodic phase mapping and using a high shear center as a reference, a control model was constructed using a Gaussian function to ensure that the time step continuously and smoothly varies with the intensity of the flow field. Small step sizes are used at critical kneading moments where the flow field changes drastically to ensure accuracy and convergence, while larger step sizes are used in non-critical stages where the flow field is relatively calm to improve computational speed. This fundamentally overcomes the technical obstacle of excessively high computational costs caused by traditional dynamic mesh simulations that are forced to use extremely small fixed step sizes throughout to ensure stability. While ensuring the capture of key transient physical phenomena, it significantly improves the overall simulation efficiency, breaks through the technical bias that high-precision planetary motion simulation is uneconomical, and provides an efficiency guarantee for achieving high-fidelity simulation.

[0025] Secondly, embodiments of this application provide a numerical simulation system for the pressure and torque characteristics of a vertical planetary kneader. The system includes: a construction module for constructing a fluid domain model within a reactor; a correction module for correcting the rotational speed of a dual-blade kneader in a non-revolutionary system based on the revolution speed in the planetary motion system, thereby obtaining a correction value for the rotational speed; a configuration module for constructing blade motion parameter equations based on the geometric coordinates of the dual blades, the correction value for the rotational speed, and the revolution speed; configuring a dynamic mesh for the fluid domain model based on the blade motion parameter equations; a determination module for obtaining a corrected Reynolds number based on the correction value for the rotational speed and the revolution speed, and determining a flow model matching the corrected Reynolds number; and a simulation module for performing numerical simulations on the fluid domain model with the configured dynamic mesh based on the flow model, thereby obtaining the pressure and torque characteristics of the dual blades.

[0026] Thirdly, embodiments of this application provide a computer device, including: a memory and a processor, wherein the memory and the processor are communicatively connected to each other, the memory stores computer instructions, and the processor executes the computer instructions to perform the above-mentioned numerical simulation method for pressure and torque characteristics of a vertical planetary kneader.

[0027] Fourthly, embodiments of this application provide a computer-readable storage medium storing computer instructions, which are used to cause a computer to execute the above-described numerical simulation method for the pressure and torque characteristics of a vertical planetary kneader.

[0028] Fifthly, embodiments of this application provide a computer program product, including computer instructions, which are used to cause a computer to execute the above-described numerical simulation method for the pressure and torque characteristics of a vertical planetary kneader. Attached Figure Description

[0029] To more clearly illustrate the technical solutions in the specific embodiments of this application or the prior art, the drawings used in the description of the specific embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of this application. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0030] Figure 1 A flowchart illustrating a numerical simulation method for the pressure and torque characteristics of a vertical planetary kneader, provided in an embodiment of this application;

[0031] Figure 2 This application provides graphs showing the variation in the number of meshes under different dynamic meshing methods in its embodiments.

[0032] Figure 3 Pressure change curves obtained from simulation and experimentation are provided for embodiments of this application;

[0033] Figure 4 Pressure change curves obtained from simulation and experimentation are provided for embodiments of this application;

[0034] Figure 5 This is a schematic diagram illustrating the unstructured discretization effect of the fluid domain provided in an embodiment of this application;

[0035] Figure 6 Torque curves under different grid division numbers provided in embodiments of this application;

[0036] Figure 7 Velocity distribution diagrams under different grid division numbers provided in embodiments of this application;

[0037] Figure 8 A schematic diagram of time step distribution provided for embodiments of this application;

[0038] Figure 9 A comparison chart of the maximum pressure variation curves between the blade motion method provided in the embodiments of this application and the traditional simplified method;

[0039] Figure 10 A comparison diagram of axial flow variation curves between the blade motion method provided in the embodiments of this application and the traditional simplified method;

[0040] Figure 11 A comparison diagram of torque variation curves between the blade motion method provided in this application embodiment and the traditional simplified method;

[0041] Figure 12 A graph showing the variation of maximum kneading pressure of the vertical planetary kneader provided in this application embodiment at different cross-sectional heights;

[0042] Figure 13The transient pressure cloud diagram of the cross section provided in the embodiments of this application;

[0043] Figure 14 The transient pressure cloud diagram of the cross section provided in the embodiments of this application;

[0044] Figure 15 The transient pressure cloud diagram of the cross section provided in the embodiments of this application;

[0045] Figure 16 The transient pressure cloud diagram of the cross section provided in the embodiments of this application;

[0046] Figure 17 A schematic diagram of the torque curve provided for an embodiment of this application;

[0047] Figure 18 This is a schematic diagram of the kneading stage of the kneading surface provided in an embodiment of this application;

[0048] Figure 19 This is a schematic diagram of the non-kneading surface kneading stage provided in an embodiment of this application;

[0049] Figure 20 A schematic diagram of a numerical simulation system for the pressure and torque characteristics of a vertical planetary kneader provided in this application embodiment;

[0050] Figure 21 This is a schematic diagram of the structure of a computer device provided in an embodiment of this application. Detailed Implementation

[0051] To make the objectives, technical solutions, and advantages of the embodiments of this application clearer, the technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0052] In chemical, pharmaceutical, food, and defense technology (such as solid propellant production) fields, the uniform mixing of high-viscosity, high-solids-content materials is a core process. Kneaders, which apply strong extrusion and shearing forces to materials through impellers, are key equipment for achieving efficient mixing of such materials. Among them, vertical planetary kneaders, due to their superior sealing and safety, have gradually replaced horizontal kneaders, which pose a risk of material leakage, and have become the industry mainstream. However, the mixing process of vertical planetary kneaders is extremely complex: its impellers rotate on their own axis while also revolving around the central axis of the reactor, forming a complex planetary motion. This complex kinematic characteristic leads to a highly unsteady flow field inside the reactor, and key parameters such as the pressure on the impellers and the driving torque are difficult to measure accurately through experimental means. Therefore, the industry has long relied mainly on experience for design, lacking reliable forward design theories and quantitative basis. Numerical simulation technology is considered an effective tool for revealing the internal flow mechanism of kneaders and predicting their performance. However, numerical simulations of vertical planetary kneaders face fundamental challenges and have led to widespread technical biases. Those skilled in the art generally believe that full-scale simulation of the composite planetary motion—formed by the superposition of revolution around a reference center and rotation around its own axis—is extremely difficult. Mainstream computational fluid dynamics (CFD) software's built-in conventional rotating reference frames and mesh topology strategies (including multiple reference frames, sliding meshes, and standard moving mesh methods) cannot directly define such composite rotational motions of multiple rigid bodies around different axes. Therefore, related numerical simulation methods typically employ a significantly simplified "boiler wall motion method," assuming the impeller system does not rotate but instead applies its revolution velocity in the opposite direction to the reactor wall. While this simplification avoids complex motion definitions, its physical model differs fundamentally from reality, resulting in severely distorted flow fields (especially axial flow, local pressure, and torque distribution) that fail to accurately reflect the true mechanism of planetary kneading. Furthermore, there is a widespread understanding in the industry that even if the definition of planetary motion could be achieved, the resulting dynamic mesh deformation would lead to a sharp deterioration in mesh quality, easily resulting in negative volumes and computational interruptions. Simultaneously, the extremely small time step necessary to maintain mesh stability would cause computational costs to skyrocket to unacceptable levels. This common perception of the high difficulty and cost of directly simulating planetary motion further solidifies the industry practice of using simplified strategies such as the "boiler wall motion method," hindering the development of high-precision simulation technology.

[0053] In summary, the field has long been constrained by the aforementioned technical biases, which hold that high-fidelity simulation of the actual planetary motion of a vertical planetary kneader is unrealistic or uneconomical. Related technologies often oscillate between sacrificing solution accuracy for stability and being limited by mesh quality and computational efficiency, making it difficult to simultaneously achieve high-precision simulation and efficient solution for complex planetary motions. This has resulted in a persistent lack of a numerical simulation method capable of accurately and efficiently simulating the pressure and torque characteristics of a vertical planetary kneader. This has become a key technical bottleneck restricting the optimized design and performance improvement of this equipment.

[0054] This application provides a numerical simulation method for the pressure and torque characteristics of a vertical planetary kneader. It should be noted that the steps shown in the flowchart in the accompanying drawings can be executed in a computer system such as a set of computer-executable instructions. Furthermore, although a logical order is shown in the flowchart, in some cases, the steps shown or described may be executed in a different order than that shown here.

[0055] Please refer to Figure 1 , Figure 1 A flowchart illustrating a numerical simulation method for the pressure and torque characteristics of a vertical planetary kneader, as provided in this application embodiment, is shown below. Figure 1 As shown, the process includes the following steps:

[0056] Step S1: Construct a fluid domain model inside the reactor.

[0057] A reaction vessel is the container part of a vertical planetary kneader used to hold and mix materials (fluids). A fluid domain refers to the geometrical space region within the reaction vessel occupied by the fluid. A fluid domain model is a numerical model obtained by geometrically modeling and meshing the fluid domain. By performing numerical simulations on the fluid domain model, the flow state and related physical field information of the fluid within the vessel can be obtained.

[0058] Step S3: Based on the revolution speed in the planetary motion system, the rotation speed of the double-bladed paddlewheel system without revolution is corrected to obtain the rotation speed correction value.

[0059] The planetary motion system is used to describe the actual motion of the two blades in a vertical planetary kneader. In this system, each blade simultaneously performs two rotational motions: rotation around its own axis (rotation) and rotation around the central axis of the reactor (revolution). The revolution speed refers to the angular velocity of the two blades rotating together around the central axis of the reactor in the planetary motion system. This revolution speed is determined by the equipment design and is a known input parameter. The non-revolution system refers to the hypothetical state where the two blades only rotate on their own axes and do not revolve around the reactor. In this non-revolution system, to ensure proper kneading and extrusion of materials between the two blades, the individual rotation speed of each blade is defined as the kneading rotation speed.

[0060] In a real planetary motion system, the relative motion between the two propeller blades is affected by their orbital rotation speed, making proper pinching impossible. Therefore, correcting the rotational speed for pinching between the two propeller blades in a system without orbital rotation is fundamental to constructing a high-precision numerical simulation that reflects the true motion characteristics of the two propeller blades.

[0061] Step S5: Based on the geometric coordinates of the two blades, the rotation speed correction value, and the revolution speed, construct the blade motion parameter equations; based on the blade motion parameter equations, configure a dynamic mesh for the fluid domain model.

[0062] The geometric coordinates of the two blades are used to characterize their position within the reactor. Specifically, the geometric coordinates of the two blades refer to the spatial coordinates of their center of gravity in a coordinate system (i.e., the fluid domain coordinate system) with the center of the reactor bottom as the origin. In a planetary motion system, the absolute velocity of any point on the blade is the vector superposition of its rotational velocity and its revolution velocity. By combining the blade's geometric coordinates, the rotational speed correction value adapted to planetary motion, and the known revolution speed, the blade motion parameter equation can be constructed. This equation accurately describes the blade's true motion parameters at any given time. Dynamic meshing is a meshing technique in CFD numerical simulation where mesh nodes are dynamically adjusted according to boundary movement. In the practical application of numerical simulation of a vertical planetary kneader, the planetary motion of the two blades causes dynamic changes in the fluid domain boundary, leading to mesh deformation. Dynamic meshing technology determines the new positions of all mesh nodes within the fluid domain at each time step by solving the displacement field equilibrium equation, ensuring the continuity of mesh deformation and thus achieving accurate simulation of the planetary motion of the two blades. The blade motion parameter equations provide key boundary driving conditions for dynamic mesh technology and are the key basis for driving the dynamic adjustment of the mesh, ensuring that the adjustment rhythm of the fluid domain mesh is completely consistent with the planetary motion trajectory of the two blades.

[0063] By accurately quantifying the planetary motion of the dual-blade propeller using the equation of motion parameters, and combining this with dynamic meshing technology to allow the fluid domain mesh to adapt to the boundary motion in real time, the synergy of these two methods provides a foundation for high-precision numerical simulation of the actual motion state of the dual-blade propeller of the vertical planetary kneader, avoiding the physical field distortion problem caused by traditional simplified models.

[0064] Step S7: Based on the rotation speed correction value and the revolution speed, obtain the corrected Reynolds number and determine the flow model that matches the corrected Reynolds number.

[0065] Traditional Reynolds numbers are only applicable to single rotational motions. However, for the combined motion of revolution and rotation in a vertical planetary kneader-like flow, traditional Reynolds numbers cannot reflect the true velocity distribution of such complex flow fields. Directly using traditional Reynolds numbers can lead to misjudgments of the actual flow field, resulting in the selection of an incorrect flow model. The modified Reynolds number, by integrating the rotational speed correction value and the revolution speed, accurately matches the true characteristics of the complex flow field of planetary motion. It can accurately reflect the ratio of inertial forces to viscous forces in the flow field, providing an accurate basis for the selection of subsequent flow models and avoiding simulation distortions caused by incorrect judgments of the flow field state.

[0066] Step S9: Based on the flow model, perform numerical simulation on the fluid domain model with configured dynamic mesh to obtain the pressure and torque characteristics of the dual blades.

[0067] The fluid domain model with a dynamic mesh enables real-time dynamic adaptation of the mesh to the planetary motion of the two-bladed impeller, ensuring that the fluid domain boundary is completely consistent with the actual operating conditions of the vertical planetary kneader. The fluid domain model adapted to the corrected Reynolds number can accurately solve the fluid dynamics control equations. The obtained pressure and torque characteristics are key target parameters directly used to evaluate the kneader's workload and for structural design and optimization. In practical applications, pressure characteristics include core quantitative indicators such as the maximum pressure and peak-to-peak pressure at key cross-sections of the fluid inside the reactor. Torque characteristics include torque variation curves for hollow and solid impellers throughout their respective motion cycles, visually presenting the dynamic evolution of torque with the motion phase for both types of impellers. Numerical simulation of the fluid domain model with a dynamic mesh using the flow model provides a foundation for accurate simulation of the dynamic interaction between the two-bladed impeller driving the fluid and the fluid's reaction on the two impellers.

[0068] The numerical simulation method for pressure and torque characteristics of a vertical planetary kneader provided in this application corrects the kneading rotation speed of the non-revolutionary system based on the revolution speed of the planetary motion system, eliminating the interference of revolution on the relative motion of the two blades and ensuring that the two blades maintain the correct kneading state in the combined motion of rotation and revolution. By integrating the geometric coordinates of the two blades, the correction value of the rotation speed, and the revolution speed, the blade motion parameter equation is constructed to accurately quantify the actual motion law of the two blades of the vertical planetary kneader. The blade motion parameter equation is used as the boundary driving condition of the moving mesh, so that the fluid domain mesh adjusts in real time with the motion of the two blades. The corrected Reynolds number adapted to the planetary motion flow field is obtained by using the correction value of the rotation speed and the revolution speed. The actual flow state of the flow field is determined based on the corrected Reynolds number, thereby selecting the appropriate flow model. The fluid domain model with the configured moving mesh is numerically solved by the flow model, and finally, the high-precision output of the pressure and torque characteristics of the two blades is achieved.

[0069] In some specific embodiments, the dual propeller blades include hollow blades and solid blades. Based on the revolution speed in the planetary motion system, the rotation speed of the dual propeller blades in a non-revolutionary system is corrected to obtain a corrected rotation speed value. This includes: obtaining the helix angle ratio of the hollow blade and the solid blade; determining the second rotation speed required for the solid blade to achieve pinching in the non-revolutionary system based on the first rotation speed of the hollow blade in the non-revolutionary system and the helix angle ratio; correcting the first rotation speed based on the revolution speed to obtain the first corrected rotation speed value of the hollow blade in the planetary motion system; and correcting the second rotation speed based on the revolution speed to obtain the second corrected rotation speed value of the solid blade in the planetary motion system.

[0070] The helix angle ratio refers to the ratio of the tangent of the helix angle of the hollow blade to that of the solid blade. The helix angle ratio is a known, fixed equipment design parameter that determines the fixed proportional relationship that the rotational speeds of the two blades must satisfy in an ideal kneading state with only self-rotation and no revolution, ensuring the synergistic shearing and extrusion effect of the two blades on the material. Typically, the hollow blade is the main driving blade, and its first rotational speed is a known input parameter. By using the first rotational speed and the helix angle ratio, the second rotational speed required for the solid blade to achieve ideal kneading in a system without revolution can be obtained.

[0071] In order to maintain the optimal pinching relationship determined by the helix angle ratio in a real planetary motion system, the first and second rotation speeds in the non-revolutionary system were corrected by the revolution speed to accurately counteract the interference of the revolution motion on the relative motion of the two propeller blades. Finally, the corrected values ​​of the first and second rotation speeds in the planetary motion system were obtained, which provided a numerical basis for subsequent high-precision numerical simulation.

[0072] In practical applications, the rotational speed of a dual-blade kneading system without revolution is calculated from the ratio of the first rotational speed of the hollow blade to the helix angle. The specific calculation formula is as follows:

[0073]

[0074]

[0075] In the above formula, For solid blades, the helical lift angle is [not specified]. The helical lift angle is for hollow blades; The rotational speed ratio between hollow blades and solid blades; This is the first rotational speed of the hollow blade in a system without revolution; This is the second rotational speed of a solid blade in a system without revolution.

[0076] In some specific embodiments, the first rotation speed is corrected based on the revolution speed to obtain a first rotation speed correction value for the hollow blade in the planetary motion system; the second rotation speed is corrected based on the revolution speed to obtain a second rotation speed correction value for the solid blade in the planetary motion system, including: vector synthesis of the revolution speed and the first rotation speed to obtain the first rotation speed correction value; and vector synthesis of the revolution speed and the second rotation speed to obtain the second rotation speed correction value.

[0077] The interference of revolution on rotation is essentially a vector conflict between the direction of motion and velocity. A vector synthesis method is employed, performing vector calculations based on the revolution speed and the first and second rotation speeds respectively, ensuring that the corrected speed values ​​can adapt to the combined motion requirements of each of the two propeller blades. The final corrected first and second rotation speed values ​​retain the optimal kneading speed ratio determined by the helix angle ratio in a system without revolution, while eliminating the relative motion disturbances caused by revolution. This ensures that the shear angle and extrusion force of the two propeller blades maintain a consistent match during planetary motion, further enhancing the realism of the kneading effect simulation.

[0078] In practical applications, if the linear velocity vector of the hollow blade's rotational motion is in the same direction as its orbital motion, to counteract the orbital interference, the equivalent velocity component corresponding to the orbital speed needs to be subtracted from the vector composition of the rotational speeds to restore the effective rotational speed. Conversely, if the linear velocity vector of the solid blade's rotational motion is in the opposite direction to its orbital motion, to counteract the orbital interference, the equivalent velocity component corresponding to the orbital speed needs to be added to the vector composition of the rotational speeds to restore the effective rotational speed. The specific calculation formula is as follows:

[0079]

[0080]

[0081] In the above formula, This refers to the revolution speed; This is the correction value for the first rotational speed of the hollow blade; This is the second rotational speed correction value for solid blades.

[0082] In some specific embodiments, the blade motion parameter equations are constructed based on the geometric coordinates of the two blades, the rotational speed correction value, and the revolution speed. This includes: for any blade, determining the eccentricity of the blade based on its geometric coordinates; determining the translational velocity component of the blade based on the eccentricity and the revolution speed; determining the rotational angular velocity component of the blade based on the rotational speed correction value; and constructing the blade motion parameter equations based on the translational velocity component and the rotational angular velocity component.

[0083] Eccentricity refers to the distance between the blade axis and the central axis of the reactor. Revolutionary speed is the angular velocity of the blade rotating around the reactor's central axis. The product of eccentricity and revolutionary speed yields the translational velocity component generated by the blade's revolution, which accurately describes the overall translational movement of the blade along its revolution trajectory. The spin speed correction value, after offsetting revolution interference, is the effective angular velocity of the blade rotating around its own axis, adapted to the planetary motion system. It can be directly used as the rotational angular velocity component of the blade around its own axis, truly reflecting the intensity and direction of the blade's rotation. The translational velocity component determines the overall translational trajectory of the blade, while the rotational angular velocity component determines the blade's rotational state. By constructing the blade motion parameter equations through vector synthesis of these two types of components, the true motion state of the two blades at any given time can be completely and accurately quantified. This provides precise boundary driving conditions for subsequent dynamic meshing, while ensuring consistency between the motion description and the physical laws of planetary motion, avoiding motion distortion problems caused by simplified models.

[0084] In practical applications, based on the geometric coordinates of the two blades, the rotational speed correction value, and the revolution speed, the blade motion parameter equations are constructed, and the specific calculation formula is as follows:

[0085]

[0086]

[0087] In the above formula, This represents the initial phase of the hollow blade's center of gravity. The initial phase of the solid blade's center of gravity; The initial ordinate of the center of gravity of the hollow blade; is the initial x-coordinate of the centroid of the hollow blade; The initial ordinate of the center of gravity of the solid blade; Let x be the initial x-coordinate of the center of gravity of the solid blade.

[0088] The equations of motion for the hollow blade are as follows:

[0089]

[0090] In the above formula, , , This represents the real-time translational velocity component of the hollow blade. This indicates that the hollow blades only undergo planetary motion in the horizontal plane and have no vertical displacement. The eccentricity of the hollow blade is the distance from the axis of the hollow blade to the central axis of the reactor. t is the time variable, describing the dynamic evolution of the motion over time. The angular velocity component of the hollow blade about its own z-axis.

[0091] The equations of motion for the solid blades are as follows:

[0092]

[0093] In the above formula, , , This represents the real-time translational velocity component of the solid blade. This indicates that the solid blades only undergo planetary motion in the horizontal plane and have no vertical displacement. The eccentricity of the solid blade is the distance from the axis of the solid blade to the central axis of the reactor. The component of the rotational angular velocity of the solid blade about its own z-axis.

[0094] In some specific embodiments, configuring a dynamic mesh for the fluid domain model based on the blade motion parameter equations includes: setting the mesh interface in the fluid domain model that coincides with the surface of the dual blades as a rigid body motion boundary; generating real-time motion parameters of the rigid body motion boundary based on the blade motion parameter equations; and dynamically adjusting the displacement of the mesh nodes in the fluid domain model based on the real-time motion parameters.

[0095] By defining the mesh interface coinciding with the surface of the twin propeller blades in the fluid domain model as the rigid body motion boundary, a precise boundary carrier is provided for motion transmission. Real-time motion parameters generated based on the propeller motion parameter equations provide motion commands for the rigid body motion boundary, ensuring complete synchronization between the boundary motion and the actual planetary motion of the twin propeller blades. Based on these real-time motion parameters, the displacement of the fluid domain mesh nodes is dynamically adjusted, enabling the mesh to adapt in real time to the combined motion of the twin propeller blades' revolution and rotation, effectively avoiding problems such as mesh distortion, overlap, or negative volume.

[0096] In some specific implementations, the dynamic mesh employs a combination of spring smoothing and a unified mesh generation method. The spring smoothing method simulates the spring force between mesh nodes to achieve smooth mesh deformation; the unified mesh generation method re-meshes local areas when mesh deformation exceeds a threshold. The combination of the two can significantly reduce the frequency of mesh redrawing and reduce numerical interpolation errors.

[0097] In some specific implementations, the dynamic mesh employs a combination of diffusion smoothing and uniform mesh generation. The diffusion smoothing method controls the displacement of mesh nodes through diffusion equations, resulting in more uniform mesh deformation; the uniform mesh generation method ensures mesh quality in areas of high local deformation. This combination can also effectively maintain mesh morphology stability and improve simulation efficiency.

[0098] In some specific implementations, to evaluate the impact of different dynamic mesh smoothing methods on simulation accuracy and computational efficiency, this application selects two mainstream mesh smoothing methods and sets multiple sets of differentiated parameters. Specifically, in the diffusion smoothing method, the diffusion parameter is set to 2, and the maximum number of iterations is set to 100. In the spring smoothing method, four sets of parameters are set: a spring constant factor of 0.1, a convergence tolerance of 1×10⁻⁶, and a convergence tolerance of 1×10⁻⁶. −4 Maximum number of iterations: 500; spring constant factor: 0.1; convergence tolerance: 1×10⁻⁶. −5 Maximum number of iterations: 500; spring constant factor: 0.1; convergence tolerance: 1×10⁻⁶. −4 Maximum number of iterations: 100; spring constant factor: 0.1; convergence tolerance: 1×10⁻⁶. −5 Maximum number of iterations: 100.

[0099] Please refer to Figure 2 , Figure 2 This is a graph showing the change in the number of meshes under different dynamic meshing methods provided in the embodiments of this application. Through the above parameter settings, such as… Figure 2 As shown, a total of 5 dynamic mesh smoothing schemes with gradient differences were obtained (denoted as group AE). Different schemes will cause dynamic changes in the number of meshes in the fluid domain.

[0100] Based on the mesh smoothing method for each group, dynamic mesh configuration and unstructured mesh generation were performed on the fluid domain model of the reactor, resulting in 5 corresponding dynamic mesh computational models. Subsequently, a complete numerical simulation was conducted on each group of models, outputting the core simulation results, including axial flow rate, impeller torque, and maximum kneading pressure within the reactor, as shown in Table 1 below.

[0101] Table 1

[0102]

[0103] As shown in the table above, the blade torque and maximum kneading pressure values ​​for each group tend to be consistent, indicating that the torque and maximum kneading pressure have achieved mesh independence, and different smoothing methods have minimal impact on the simulation accuracy of these two core indicators. The relative error of axial flow rate between group D and group E is as high as 10.7%, indicating that the mesh resolution of group E is insufficient and cannot accurately capture the axial flow characteristics of the flow field; while the axial flow rate values ​​of group AD are more convergent, with the results of group D combining accuracy and stability. Considering the balance between simulation accuracy and computational efficiency, the dynamic mesh smoothing method and mesh number corresponding to group D can be determined as the target dynamic mesh scheme. This scheme can accurately reproduce the flow field characteristics of axial flow rate while ensuring the accuracy of torque and maximum kneading pressure, and the mesh number is moderate, avoiding the waste of computational resources caused by excessive mesh refinement, providing the optimal dynamic mesh foundation for subsequent high-precision numerical simulation of the pressure and torque characteristics of the dual-blade vertical planetary kneader.

[0104] In some specific embodiments, to verify the prediction accuracy of the numerical simulation method for the pressure and torque characteristics of the vertical planetary kneader provided in this application, the prediction results of the numerical simulation are directly and quantitatively compared with the physical test measurement data under the same working conditions. The specific implementation steps are as follows:

[0105] 1) Obtain simulation and experimental comparison data. Based on the above target dynamic mesh scheme, after the simulation is completed, extract the pressure simulation results at a specific monitoring section inside the reactor, such as the pressure change curve over time within a complete motion cycle. Under the corresponding operating conditions (the same impeller speed, material properties, etc.), measure the pressure at the same cross-sectional location using sensors on an actual vertical planetary kneader test bench to obtain the experimental pressure results.

[0106] 2) Calculate the error between the pressure simulation results and the pressure test results. If the relative error between the simulated and experimental values ​​of key parameters, such as the peak-to-peak pressure, is less than the specified error, such as 10%, then the current target dynamic mesh scheme is determined to meet the accuracy requirements and can accurately reflect the real flow conditions.

[0107] For a detailed explanation of the verification results, please refer to [link / reference]. Figures 3-4 , Figure 3 and Figure 4 The pressure change curves obtained from simulation and experiment are provided for embodiments of this application. The rotational speed is set to 60 rpm (e.g., Figure 3 (as shown) and 80 rpm (as shown) Figure 4 Simulations and experiments were conducted under two typical operating conditions (as shown in the figure). Comparing the simulation and experimental results of the pressure peak-to-peak values ​​under both conditions, the relative error remained within 10%. This result fully demonstrates that the target dynamic mesh scheme provided in this application embodiment can accurately reproduce the transient pressure fluctuation characteristics within a real reactor.

[0108] In some specific implementations, the fluid domain structure of the vertical planetary kneader is specifically configured for the moving mesh region as follows: both hollow and solid blades are designated as rigid body motion regions. Since the blades are rigid structures, their geometry does not deform during movement. This configuration ensures that the mesh boundaries on the blade surface are completely synchronized with the blade movement, avoiding geometric distortion. The upper surface of the fluid domain is designated as a deformable region. This region dynamically deforms with the planetary motion of the two blades. Through the combined effect of smoothing and re-meshing methods, the continuity and regularity of the mesh in this region are ensured, avoiding mesh overlap or negative volume issues.

[0109] In some specific implementations, to ensure the stability of the dynamic mesh adjustment and the convergence of the numerical solution, the time step and the number of iterations are set as follows: Setting a reasonable adaptive time step strategy ensures that the angle through which the blades rotate within a single time step does not cause excessive mesh deformation, avoiding solution interruptions caused by excessive mesh distortion and improving computational efficiency. The number of iterations within each time step is set to 20. This number ensures that the flow field solution residuals within each time step meet the preset convergence criteria, ensuring the accuracy and reliability of the numerical simulation results.

[0110] Through the above-described dynamic mesh setup steps, a deep synergy between the dual-blade motion equations, dynamic mesh technology, and adaptive time step strategy was achieved. This not only provided accurate dynamic drive for the fluid domain mesh, but also ensured mesh quality and solution stability by optimizing the dynamic mesh method and parameter settings, laying the foundation for high-precision numerical simulation of the pressure and torque characteristics of the dual-blade vertical planetary kneader.

[0111] In some specific embodiments, obtaining the corrected Reynolds number based on the rotational speed correction value and the revolution speed includes: calculating a characteristic speed based on the rotational speed correction value and the revolution speed; and calculating the corrected Reynolds number based on the characteristic speed.

[0112] Traditional Reynolds number calculations only consider the rotational speed, neglecting the driving effect of revolution on the fluid flow field. Therefore, they cannot accurately characterize the true velocity intensity of the flow field under the combined revolution and rotation of a vertical planetary kneader's two-bladed propeller, necessitating targeted correction. The characteristic speed, synthesized from the corrected rotational speed and the revolutional speed, is a tailor-made equivalent characteristic velocity for this combined flow field. It integrates the driving contributions of both motions to the fluid, providing a precise and suitable core parameter for calculating the corrected Reynolds number. The corrected Reynolds number calculated based on this characteristic speed can serve as a reliable criterion for judging the flow state, ensuring that the subsequent flow model selected is based on correct fluid dynamics principles, thus guaranteeing the physical authenticity of the entire numerical simulation process and results.

[0113] In some specific implementations, in order to keep the dimensional analysis of the vertical planetary kneader consistent with the theoretical system of the classic single-shaft mixer, the characteristic rotational speed is defined as the ratio of the maximum speed at the tip of the hollow blade to Π, so as to ensure dimensional consistency and engineering comparability.

[0114] The tip velocity of a hollow blade is the superposition of its rotational and revolving linear velocities, and its maximum velocity is expressed as:

[0115]

[0116] In the above formula, This is the maximum speed of the hollow blade; d is the first rotational speed correction value for the hollow blade; d is the diameter of the hollow blade. This refers to the revolution speed; The diameter is the diameter of the revolution.

[0117] Characteristic speed The calculation formula is:

[0118]

[0119] Vertical planetary kneaders have multiple geometric length dimensions. To simplify the analysis and maintain consistency with classical mixing theory, this embodiment uses the revolution diameter. As a characteristic length (when the rotational speed of the two blades is 0, the system can be equivalent to a classic stirring system with the diameter of the impeller as the diameter of the revolution diameter).

[0120] Calculate the corrected Reynolds number based on the characteristic rotational speed and characteristic length. The calculation formula is:

[0121]

[0122] In the above formula, For fluid density, Characteristic rotational speed, This refers to dynamic viscosity.

[0123] The modified Reynolds number is a similarity criterion number specifically adapted to complex flow fields of planetary motion, and can accurately characterize the ratio of inertial force to viscous force in the flow field.

[0124] In some specific embodiments, the characteristic rotational speed is calculated based on the rotational speed correction value and the revolution speed, including: calculating a first product of the first rotational speed correction value and the diameter of the hollow blade; calculating a second product of the revolution speed and the revolution diameter of the planetary motion system; calculating the sum of the first product and the second product, and determining the sum as the characteristic rotational speed.

[0125] As the main driving blade, the hollow blade's first rotational speed correction value can equivalently represent the shear driving effect of the dual-blade coordinated rotation on the fluid. The first product of the first rotational speed correction value and the hollow blade diameter accurately quantifies the contribution of the main driving blade's rotational motion, after correction for revolution interference, to the local shear velocity generated by the fluid. The second product of the revolution speed and the revolution diameter accurately quantifies the contribution of the macroscopic circulation velocity formed by the revolution motion of the dual blades. By summing these two values, the velocity characteristics of the composite flow field under the planetary motion system, which combines local high shear and macroscopic circulation, are integrated. The output characteristic speed can truly reflect the overall motion intensity of the flow field, solving the problem that traditional single velocity parameters cannot fully characterize composite flow fields.

[0126] In some specific embodiments, the flow model is determined as follows: if the corrected Reynolds number is less than or equal to a preset critical Reynolds number, the flow model is a laminar flow model; if the corrected Reynolds number is greater than the critical Reynolds number, the flow model is a turbulent flow model.

[0127] The modified Reynolds number, as a specific similarity criterion number adapted to complex planetary motion flow fields, is compared with the preset critical Reynolds number to determine whether the flow field is in a laminar or turbulent state. When the modified Reynolds number is less than or equal to the critical Reynolds number, it indicates that the flow field has low motion intensity, fluid viscosity dominates, and the flow field exhibits a stable laminar state. In this case, a laminar flow model is used for solution. When the modified Reynolds number is greater than the critical Reynolds number, it indicates that the flow field has high motion intensity, inertial forces dominate the flow field motion, accompanied by significant high shear disturbances, and the flow field exhibits a complex turbulent state. In this case, a turbulent flow model is used for calculation. This method of accurately matching the corresponding flow model based on the actual flow field state ensures that subsequent numerical simulations can accurately solve for key parameters such as velocity, pressure, and shear stress in the planetary motion flow field, thereby outputting high-precision pressure and torque characteristics results for the dual-blade flow.

[0128] In some specific embodiments, constructing a fluid domain model within the reactor includes: dividing the fluid domain geometric model into an unstructured mesh to obtain a fluid domain mesh; and constructing the fluid domain model based on the fluid domain mesh; wherein the discrete elements in the fluid domain mesh satisfy the following conditions: minimum orthogonal mass greater than 0.2, average orthogonal mass greater than 0.75, maximum skewness less than 0.8, and average skewness less than 0.25.

[0129] Please refer to Figure 5 , Figure 5This diagram illustrates the unstructured discretization effect of the fluid domain provided in this embodiment. Unstructured meshing of the fluid domain geometric model refers to meshing with tetrahedrons as the main component. In practical applications, 3D modeling software can be used to construct the geometric model of the reactor. Orthogonality mass is a core indicator for measuring the perpendicularity of mesh element edges. Setting a minimum orthogonality mass greater than 0.2 and an average orthogonality mass greater than 0.75 ensures that mesh elements are not excessively elongated or skewed, preventing a sharp increase in discretization errors during numerical solutions. Skewness is a key parameter characterizing the degree of distortion in the shape of mesh elements. Setting a maximum skewness less than 0.8 and an average skewness less than 0.25 prevents extreme distortion or deformities in mesh elements. Both of these indicators represent stringent thresholds for ensuring mesh quality in numerical simulation, effectively preventing mesh overlap, negative volume, and other failures during subsequent dynamic mesh adjustments, preventing numerical solution interruptions or divergences, and ensuring the stability of the entire simulation process.

[0130] The motion of the impeller causes continuous and drastic changes in the shape of the fluid domain, resulting in extensive deformation and reconstruction of the mesh. Unstructured meshes, with their flexible node connections, are more robust than structured meshes when handling such large deformations and displacements. By employing unstructured meshes with strictly controlled quality, problems such as numerical diffusion, pressure oscillations, and even computational divergence caused by element distortion can be effectively avoided, ensuring the accuracy and convergence of the flow field solution. This allows for stable and accurate high-fidelity simulations based on the actual motion equations.

[0131] In some specific embodiments, the method further includes: obtaining multiple different grid numbers, wherein the maximum grid number is 3-4 times the minimum grid number; performing unstructured grid division on the fluid domain geometric model based on each grid number to obtain the corresponding fluid domain model; obtaining the corresponding pressure and torque characteristic results of the dual blades based on each fluid domain model; identifying the target results that meet the preset criteria among the pressure and torque characteristic results of each dual blade, and determining the grid number corresponding to the target result as the target grid number; and constructing the target fluid domain model based on the target grid number.

[0132] For example, obtain multiple different grid numbers: 310,000 (Scheme 1), 480,000 (Scheme 2), 710,000 (Scheme 3), 1,040,000 (Scheme 4), and 1,260,000 (Scheme 5). Please refer to [the relevant documentation / reference]. Figure 6 , Figure 6 Torque curves under different mesh division numbers provided in the embodiments of this application. Please refer to... Figure 7 , Figure 7 Velocity distribution diagrams under different grid division numbers provided in the embodiments of this application.

[0133] like Figure 6 and Figure 7 As shown, the calculation error of the hollow blade torque gradually decreases and tends to stabilize as the number of grids increases. Comparing partitioning scheme 1 (310,000), partitioning scheme 2 (480,000), and partitioning scheme 3 (710,000) and partitioning scheme 5 (1,260,000), the torque calculation error is less than 1%, indicating that the grid density of partitioning scheme 3 is sufficient to ensure the calculation accuracy of torque characteristics and achieve grid independence. As the number of grids increases, the accuracy of the fluid velocity distribution description gradually improves. Among them, partitioning scheme 2 (480,000) cannot accurately describe the velocity distribution at a height of 0.02-0.04 meters above the bottom, while the velocity distribution accuracy of the other partitioning schemes is relatively high, further verifying the reliability of the grid density of partitioning scheme 3 and above. Based on the verification results of torque and velocity distribution, partitioning scheme 3 (710,000 grids) is determined to be the target grid number that meets the preset accuracy standard.

[0134] In some specific embodiments, the numerical simulation employs an adaptive time step, which is determined as follows: a Gaussian weighted model centered on a high-shear phase is constructed; the time difference between the current periodic phase of the planetary motion system and the preset high-shear center time is calculated; a weighting factor is calculated based on the time difference and the Gaussian weighted model; and the current time step is obtained by interpolation within a preset time step range based on the weighting factor.

[0135] The high-shear phase refers to the time period within a complete planetary orbital period when the two blades are closest to each other, resulting in intense compression and shearing of the material. The current period phase refers to the position of the current point in the planetary orbital period at a specific moment in the numerical simulation. For example, if the orbital period is 1 second, and the simulation reaches 3.25 seconds, the current period phase is 0.25 seconds. The preset high-shear center moment refers to the specific moment when the flow field shearing reaches its absolute peak within one orbital period.

[0136] By synchronizing the simulation time with the physical process through periodic phase mapping and using a high shear center as a reference, a control model was constructed using a Gaussian function to ensure that the time step continuously and smoothly varies with the intensity of the flow field. Small step sizes are used at critical kneading moments where the flow field changes drastically to ensure accuracy and convergence, while larger step sizes are used in non-critical stages where the flow field is relatively calm to improve computational speed. This fundamentally overcomes the technical obstacle of excessively high computational costs caused by traditional dynamic mesh simulations that are forced to use extremely small fixed step sizes throughout to ensure stability. While ensuring the capture of key transient physical phenomena, it significantly improves the overall simulation efficiency, breaks through the technical bias that high-precision planetary motion simulation is uneconomical, and provides an efficiency guarantee for achieving high-fidelity simulation.

[0137] In some specific implementations, an adaptive time step control method based on a Gaussian modulation function is adopted, the specific implementation steps of which include:

[0138] 1) Initial Startup Transition. To address the unstable flow field at startup of the vertical planetary kneader, an initialization phase is implemented. Specifically, the first 0.04 seconds after the simulation begins are designated as a warm-up period, during which the minimum time step is enforced. The initial time step is set to 0.001s to prevent divergence in the initial calculation phase. Subsequently, a linear transition period is set between 0.04s and 0.14s to adjust the time step from... The value is smoothly and gradually changed to the value calculated by the subsequent adaptive algorithm, thereby avoiding numerical oscillations caused by abrupt changes in the time step.

[0139] 2) Periodic Phase Mapping. Based on the periodicity of the planetary motion in the vertical planetary kneader, its physical rotation period T (e.g., 1 s) is first determined. At each moment of the simulation, the currently accumulated physical simulation time t is mapped to the phase time t_cycle within a single cycle through a modulo operation. This operation ensures that the time step adjustment strategy can be automatically repeated within each rotation cycle, synchronized with the physical process.

[0140] 3) High-shear phase center location. Based on the torque characteristic curve of the vertical planetary kneader, identify the moment when the flow field changes most drastically, i.e., when the kneading effect of the two blades is strongest, and define this as the high-shear center moment t_center. This moment usually corresponds to the peak point of the torque curve. Calculate the absolute time difference between the current phase time t_cycle and the center moment t_center. .

[0141] 4) Construction of Gaussian weighting factor. A Gaussian kernel function is introduced to construct a smooth weighting factor W( This factor, along with The increase in amplitude leads to a smooth decay, thereby achieving smooth modulation of the time step. The calculation formula is:

[0142]

[0143] In the above formula, The bandwidth parameter of the Gaussian function is set to 0.11 in this embodiment. This value means that within a range of approximately 0.11 seconds before and after the high shear center time t_center, the weighting factor W( This will have a significant impact on the time step.

[0144] 5) Adaptive time step calculation. Using the calculated weighting factor W( Within the preset global maximum time step and minimum time step Linear interpolation is performed between the values ​​to determine the current time step. The calculation formula is as follows:

[0145]

[0146] In the above formula, Set to 0.004 seconds. The time was set to 0.001 seconds. These two preset values ​​ensure that even at the maximum step size, the distance swept by the blade within one time step is less than half the minimum mesh size of the fluid domain, which is a basic requirement for satisfying the stability of the dynamic mesh algorithm.

[0147] By employing the aforementioned adaptive time step control method based on Gaussian modulation function, this application achieves control in the high shear stage where the flow field changes drastically ( Smaller, W( (Approaching 1), automatically adopt the approach. Small step sizes are used to accurately capture transient characteristics and ensure convergence. This is particularly important during the low-shear phase where the flow field is relatively flat. Larger, W( (Approaching 0), automatically adopt the approach value. A large step size is used to accelerate the calculation process. This effectively avoids pressure field oscillations caused by sudden changes in step size, maximizing the overall calculation speed while strictly ensuring the analytical accuracy of key physical processes. Actual calculations show that the above-mentioned adaptive time step control method based on Gaussian modulation function is effective. Please refer to [reference needed]. Figure 8 , Figure 8 A schematic diagram of the time step distribution provided for embodiments of this application, such as... Figure 8 As shown, in the 2-second physical time of the simulation, the total number of calculation steps is only 815. Compared with the scheme that uses a fixed minimum step size of 0.001s (requiring 2000 steps) throughout the process, the amount of computation is reduced by about 59.25%, overcoming the obstacle of excessively high computational cost in high-precision planetary motion simulation.

[0148] In some specific embodiments, the numerical simulation method for the pressure and torque characteristics of a vertical planetary kneader provided in this application is used to simulate the kneading process of high-viscosity polybutene material. This material is a typical high-viscosity Newtonian fluid. Therefore, when constructing the fluid domain model, the fluid inside the reactor is set as a single-phase Newtonian fluid reaction system. Considering the flow characteristics of high-viscosity polybutene material, where the viscous force of the high-viscosity fluid is dominant and the corrected Reynolds number is less than the preset critical Reynolds number, a laminar flow model is selected. Simultaneously, the SIMPLE algorithm and a second-order discretization scheme are employed to improve the solution accuracy of the fluid domain model.

[0149] In some specific embodiments, in order to verify and highlight the accuracy and superiority of the method provided in the embodiments of this application, it can be compared and analyzed with the traditional numerical simulation method of vertical planetary kneader.

[0150] Traditional numerical simulation methods typically employ the "boiler wall motion method" to simplify calculations. The basic principle of this method is to ignore the actual revolution of the impeller system and instead apply the velocity vector of that revolution in the opposite direction to the inner wall of the reactor, causing the vessel wall to rotate around its central axis in the opposite direction to the rotation of the hollow impeller. While this simplified model avoids defining complex composite motions, it leads to physical distortions.

[0151] The planetary motion method proposed in this application strictly follows the actual physical process: first, the planetary motion of the propeller blade is decomposed into two components: revolution and rotation; then, the theoretical rotation speed is kinematically corrected according to the revolution speed to obtain a rotation speed correction value that matches the actual planetary motion; finally, by constructing accurate propeller blade motion parameter equations and implementing them in a moving mesh, the composite planetary motion of revolution and rotation is completely and realistically reproduced.

[0152] To quantify the differences between the two methods, numerical simulations were performed using both methods under the same operating conditions, and the key results were compared. Please refer to [reference needed]. Figures 9-11 , Figure 9 This is a comparison chart of the maximum pressure variation curves between the blade motion method provided in the embodiments of this application and the traditional simplified method. Figure 10 This is a comparison chart of the axial flow variation curves between the blade motion method provided in this application embodiment and the traditional simplified method. Figure 11 A comparison chart of torque variation curves between the blade motion method provided in this application embodiment and the traditional simplified method. The comparison results show that:

[0153] 1) For the instantaneous hollow blade torque variation curve over time, the average error of the results obtained by the two methods is about 2.88%, which is relatively small.

[0154] 2) For the curve of the maximum kneading pressure between the two blades as a function of time, the average relative error of the results obtained by the two methods is about 2.10%, and the difference is not significant.

[0155] Therefore, in the key areas where the blades and the vessel wall, and between blades, kneading occurs, the relative motion speeds defined by the two methods are basically consistent, which is the main reason why their predicted torque and pressure results are relatively close.

[0156] However, for the change of instantaneous axial volumetric flow rate over time at a certain monitoring section within the reactor, the two methods show significant differences (e.g., Figure 10(As shown). The fundamental reason is that the rotational motion of the vessel wall in the vessel wall motion method not only changes the local flow field near the impeller (leading to a lower relative fluid velocity), but also causes a global disturbance to the flow field structure in the entire reactor region far from the impeller, resulting in severe distortion of the axial flow prediction. In contrast, the planetary motion method provided in this application accurately captures the transport characteristics of the fluid inside the reactor, especially the axial flow, because it realistically reproduces the impeller motion.

[0157] In summary, while traditional methods based on the motion of the boiler wall may provide approximate trends in predicting certain local mechanical parameters (such as torque and kneading pressure), they have fundamental shortcomings in revealing overall flow characteristics (such as axial mixing and conveying capacity). The numerical simulation method provided in this application demonstrates superior overall accuracy in both the global flow field and key process parameters.

[0158] In some specific embodiments, the method further includes detailed monitoring and analysis of key physical fields within the vertical planetary kneader to reveal its internal flow and mechanisms of action. The specific implementation process is as follows:

[0159] 1) Analysis of pressure characteristic evolution. Please refer to... Figure 12 , Figure 12 The graph shows the maximum kneading pressure variation curves of the vertical planetary kneader provided in this application embodiment at different cross-sectional heights. By setting multiple axial monitoring cross-sections (e.g., heights of 21.1 mm, 31.1 mm, and 41.1 mm respectively), the system obtains the transient maximum pressure variation curves at each cross-section (see...). Figure 12 ).like Figure 12 As shown, under the same operating parameters, the pressure curves at different heights exhibit consistent amplitude and waveform, with phase shifts occurring only along the time axis. This indicates that in planetary systems, the main form of pressure pulsation is transmitted consistently along the axial direction, and the choice of section height does not affect the analysis of the essential laws governing pressure changes, further verifying the physical self-consistency of this simulation method in the spatial dimension.

[0160] For example, regarding the pressure change at a specific cross-section (e.g., a height of 31.1 mm), please refer to... Figures 13-16 , Figures 13-16 The transient pressure contour plot of the cross section provided in the embodiments of this application is shown below. Figures 13-16As shown, a complete cycle can be divided into four consecutive stages: the first stage, the impeller-vessel wall kneading stage, where local pressure peaks; the second stage, the impellers approaching each other without kneading, where pressure is at a transitional low level; the third stage, the impeller-to-impeller kneading stage, where the gap between the two impellers is smallest, the shearing effect is strongest, and the pressure reaches the global peak, which is the key stage determining the mixing effect; and the fourth stage, the impellers moving away from each other, where pressure gradually decreases. The above analysis fully reveals the dynamic details of pressure evolution and the peak generation mechanism during the kneading process.

[0161] 2) Torque characteristics and power consumption analysis. Please refer to [reference needed]. Figure 17 , Figure 17 This is a schematic diagram of the torque curve provided in the embodiments of this application, such as... Figure 17 As shown, the transient torque changes of the driven propeller blades are monitored synchronously. The torque changes exhibit a clear two-stage characteristic: Please refer to... Figure 18 , Figure 18 This is a schematic diagram of the kneading stage of the kneading surface provided in the embodiments of this application, as shown below. Figure 18 As shown, the torque reaches its global peak during the period when the main kneading surfaces of the blades participate in intense shearing; this stage is the period of concentrated power consumption. Please refer to... Figure 19 , Figure 19 This is a schematic diagram of the non-kneading surface kneading stage provided in an embodiment of this application, as shown below. Figure 19 As shown, during the period when the non-primary kneading surfaces of the blades are involved, the torque exhibits a local peak, while the power consumption is relatively low. This result clarifies the key distribution phase of torque and power consumption, providing a direct basis for optimizing equipment energy efficiency.

[0162] The numerical simulation method provided in this application can not only more accurately simulate the transient flow field in a planetary kneader, but also make high-fidelity predictions of key process parameters such as pressure and torque, providing reliable technical support for improving equipment efficiency and reducing production energy consumption.

[0163] Accordingly, please refer to Figure 20 , Figure 20 A schematic diagram of a numerical simulation system for the pressure and torque characteristics of a vertical planetary kneader provided in this application embodiment is shown below. Figure 20As shown, the system includes: a construction module for constructing a fluid domain model within the reactor; a correction module for correcting the rotational speed of the dual-blade kneading system without revolution based on the revolution speed in the planetary motion system, to obtain a correction value for the rotational speed; a configuration module for constructing blade motion parameter equations based on the geometric coordinates of the dual blades, the correction value for the rotational speed, and the revolution speed; configuring a dynamic mesh for the fluid domain model based on the blade motion parameter equations; a determination module for obtaining a corrected Reynolds number based on the correction value for the rotational speed and the revolution speed, and determining a flow model that matches the corrected Reynolds number; and a simulation module for performing numerical simulations on the fluid domain model with the configured dynamic mesh based on the flow model, to obtain the pressure and torque characteristics of the dual blades.

[0164] Further functional descriptions of the above modules and units are the same as those in the corresponding embodiments described above, and will not be repeated here.

[0165] The numerical simulation system for the pressure and torque characteristics of the vertical planetary kneader in this embodiment is presented in the form of functional units. Here, a unit refers to an ASIC (Application Specific Integrated Circuit) circuit, a processor and memory that execute one or more software or fixed programs, and / or other devices that can provide the above functions.

[0166] Please see Figure 21 , Figure 21 This is a schematic diagram of the structure of a computer device provided in an embodiment of this application, such as... Figure 21 As shown, the computer device includes one or more processors 10, memory 20, and interfaces for connecting the components, including high-speed interfaces and low-speed interfaces. The components communicate with each other via different buses and can be mounted on a common motherboard or otherwise installed as needed. The processors can process instructions executed within the computer device, including instructions stored in or on memory to display graphical information of a GUI on external input / output devices (such as display devices coupled to the interfaces). In some alternative implementations, multiple processors and / or multiple buses can be used with multiple memories and multiple memory modules, if desired. Similarly, multiple computer devices can be connected, each providing some of the necessary operations (e.g., as a server array, a group of blade servers, or a multiprocessor system). Figure 21 Take a processor 10 as an example.

[0167] Processor 10 may be a central processing unit, a network processor, or a combination thereof. Processor 10 may further include a hardware chip. The hardware chip may be an application-specific integrated circuit (ASIC), a programmable logic device (PLD), or a combination thereof. The programmable logic device may be a complex programmable logic device (CAMP), a field-programmable gate array (FPGA), a general-purpose array logic (GDA), or any combination thereof.

[0168] The memory 20 stores instructions executable by at least one processor 10 to cause the at least one processor 10 to perform the method shown in the above embodiments.

[0169] The memory 20 may include a program storage area and a data storage area. The program storage area may store the operating system and applications required for at least one function; the data storage area may store data created based on the use of the computer device. Furthermore, the memory 20 may include high-speed random access memory and may also include non-transitory memory, such as at least one disk storage device, flash memory device, or other non-transitory solid-state storage device. In some alternative embodiments, the memory 20 may optionally include memory remotely located relative to the processor 10, and these remote memories may be connected to the computer device via a network. Examples of such networks include, but are not limited to, the Internet, intranets, local area networks, mobile communication networks, and combinations thereof.

[0170] The memory 20 may include volatile memory, such as random access memory; the memory may also include non-volatile memory, such as flash memory, hard disk or solid-state drive; the memory 20 may also include a combination of the above types of memory.

[0171] The computer device also includes a communication interface 30 for communicating with other devices or communication networks.

[0172] This application also provides a computer-readable storage medium. The methods described in this application can be implemented in hardware or firmware, or implemented as recordable on a storage medium, or implemented as computer code downloaded over a network and originally stored on a remote storage medium or a non-transitory machine-readable storage medium and subsequently stored on a local storage medium. Thus, the methods described herein can be processed by software stored on a storage medium using a general-purpose computer, a dedicated processor, or programmable or dedicated hardware. The storage medium can be a magnetic disk, optical disk, read-only memory, random access memory, flash memory, hard disk, or solid-state drive, etc.; further, the storage medium can also include combinations of the above types of memory. It is understood that computers, processors, microprocessor controllers, or programmable hardware include storage components capable of storing or receiving software or computer code. When the software or computer code is accessed and executed by the computer, processor, or hardware, the methods shown in the above embodiments are implemented.

[0173] This application provides a computer program product including computer instructions stored in a computer-readable storage medium. A processor of a computer device reads the computer instructions from the computer-readable storage medium and executes the computer instructions, causing the computer device to perform the method of any embodiment of this application.

[0174] The systems, modules, or units described in the above embodiments can be implemented by computer chips or entities, or by products with certain functions. A typical implementation device is a computer. Specifically, a computer can be, for example, a personal computer, laptop computer, cellular phone, camera phone, smartphone, personal digital assistant, media player, navigation device, email device, game console, tablet computer, wearable device, or any combination of these devices.

[0175] For ease of description, the above devices are described separately by function as various units. Of course, in implementing this application, the functions of each unit can be implemented in one or more software and / or hardware.

[0176] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0177] This application is described with reference to flowchart illustrations and / or block diagrams of methods, systems, and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0178] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0179] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0180] It should also be noted that the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0181] The various embodiments in this specification are described in a progressive manner. Similar or identical parts between embodiments can be referred to mutually. Each embodiment focuses on its differences from other embodiments. In particular, the system embodiments are basically similar to the method embodiments, so the description is relatively simple; relevant parts can be referred to the descriptions of the method embodiments.

[0182] The above description is merely an embodiment of this application and is not intended to limit this application. Various modifications and variations can be made to this application by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principle of this application should be included within the scope of the claims of this application.

[0183] Although embodiments of this application have been described in conjunction with the accompanying drawings, those skilled in the art can make various modifications and variations without departing from the spirit and scope of this application, and such modifications and variations all fall within the scope defined by the appended claims.

Claims

1. A numerical simulation method for the pressure and torque characteristics of a vertical planetary kneader, characterized in that, The method includes: Construct a fluid domain model within the reactor; Based on the revolution speed in a planetary motion system, the rotation speed of the dual-blade paddlewheel in a non-revolutionary system is corrected to obtain a corrected rotation speed value. The dual blades include hollow blades and solid blades. The correction includes: obtaining the helix angle ratio of the hollow blade and the solid blade; determining the second rotation speed required for the solid blade to achieve paddlewheel action in the non-revolutionary system based on the first rotation speed of the hollow blade in the non-revolutionary system and the helix angle ratio; correcting the first rotation speed based on the revolution speed to obtain the first corrected rotation speed value of the hollow blade in the planetary motion system; and correcting the second rotation speed based on the revolution speed to obtain the second corrected rotation speed value of the solid blade in the planetary motion system. Based on the geometric coordinates of the two blades, the rotational speed correction value, and the revolution speed, the blade motion parameter equations are constructed; based on the blade motion parameter equations, a dynamic mesh is configured for the fluid domain model; Based on the rotation speed correction value and the revolution speed, the corrected Reynolds number is obtained, and a flow model matching the corrected Reynolds number is determined; Numerical simulations were performed on the fluid domain model with a configured dynamic mesh based on the flow model to obtain the pressure and torque characteristics of the dual blades.

2. The method according to claim 1, characterized in that, Based on the revolution speed, the first rotation speed is corrected to obtain the first rotation speed correction value of the hollow blade in the planetary motion system; based on the revolution speed, the second rotation speed is corrected to obtain the second rotation speed correction value of the solid blade in the planetary motion system, including: The orbital speed and the first rotational speed are vector-synthesized to obtain a correction value for the first rotational speed. The orbital speed and the second rotational speed are vector-synthesized to obtain the correction value of the second rotational speed.

3. The method according to claim 1, characterized in that, Based on the geometric coordinates of the two blades, the rotational speed correction value, and the revolution speed, the blade motion parameter equations are constructed, including: For any blade, the eccentricity of the blade is determined based on its geometric coordinates. Based on the eccentricity and the revolution speed, the translational velocity component of the blade is determined; Based on the rotational speed correction value of the blade, the rotational angular velocity component of the blade is determined; Based on the translational velocity component and the rotational angular velocity component, the equations of motion parameters for the blade are constructed.

4. The method according to claim 1, characterized in that, Based on the blade motion parameter equations, a dynamic mesh is configured for the fluid domain model, including: The mesh interface that coincides with the surface of the twin propeller blades in the fluid domain model is set as the rigid body motion boundary. Based on the blade motion parameter equation, the real-time motion parameters of the rigid body motion boundary are generated. Based on the real-time motion parameters, the displacement of the grid nodes in the fluid domain model is dynamically adjusted.

5. The method according to claim 1, characterized in that, Based on the rotational speed correction value and the revolution speed, the corrected Reynolds number is obtained, including: The characteristic rotational speed is calculated based on the rotational speed correction value and the revolution speed; The corrected Reynolds number is calculated based on the characteristic rotational speed.

6. The method according to claim 5, characterized in that, Based on the rotational speed correction value and the revolution speed, the characteristic speed is calculated, including: Calculate the first product of the first rotation speed correction value and the diameter of the hollow blade; Calculate the second product of the orbital speed and the orbital diameter of the planetary system; Calculate the sum of the first product and the second product, and determine the sum as the characteristic rotational speed.

7. The method according to claim 1, characterized in that, The flow model is determined as follows: If the modified Reynolds number is less than or equal to the preset critical Reynolds number, then the flow model is a laminar flow model; If the modified Reynolds number is greater than the critical Reynolds number, then the flow model is a turbulent flow model.

8. The method according to claim 1, characterized in that, Constructing a fluid domain model within the reactor includes: The fluid domain geometric model is divided into an unstructured mesh to obtain the fluid domain mesh; Based on the fluid domain mesh, the fluid domain model is constructed; The discrete elements in the fluid domain mesh satisfy the following conditions: minimum orthogonal mass greater than 0.2, average orthogonal mass greater than 0.75, maximum skewness less than 0.8, and average skewness less than 0.

25.

9. The method according to claim 1, characterized in that, The numerical simulation employs an adaptive time step, which is determined as follows: Construct a Gaussian weighted model centered on the high shear phase; Calculate the time difference between the current periodic phase of the planetary motion system and the preset high shear center moment; Calculate the weighting factor based on the time difference and the Gaussian distribution weighting model; Based on the weighting factor, interpolation is performed within a preset time step range to obtain the current time step.

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