A method for generating a static mixer structure parameter

Abstract

This invention relates to the field of electronic digital data processing technology and discloses a method for generating structural parameters of a static mixer. The method includes: selecting the inclination angle of the crossbars and the aspect ratio of the mixer as structural parameters to be optimized, with the optimization objectives being minimizing the relative standard deviation of the concentrations of each component at the outlet section and minimizing the pressure drop; constructing a three-dimensional geometric model of the static mixer based on the structural parameters and setting the inlet and outlet positions; solving the flow field based on the Navier-Stokes equations and the continuity equation, and solving the concentration field of each component based on the convection-diffusion equation; obtaining the concentration distribution and pressure drop data of each component at the mixer outlet section under different structural parameters through multiphysics simulation, and calculating the relative standard deviation of each component concentration; screening structural parameter combinations with relative standard deviations less than a threshold, and selecting the one with the smallest pressure drop as the optimal structural parameter. This method solves the problems of reliance on trial and error and long cycles, achieving the goals of high accuracy, high efficiency, and low cost.

Description

Technical Field

[0001] This invention relates to the field of electronic digital data processing technology, and in particular to a method for generating static mixer structural parameters. Background Technology

[0002] One of the key steps in the production of rigid polyurethane foam is the efficient mixing of various raw materials to prepare component A (commonly known as "white material"). This component then reacts with component B (isocyanate, commonly known as "black material") to ultimately form rigid polyurethane foam. Component A mainly includes high-viscosity polyols, volatile physical blowing agent cyclopentane, and a small amount of crucial chemical catalysts. This mixing process must be completed rapidly and uniformly under high pressure. The mixing quality of component A is the core factor determining the final foam quality, directly affecting three key properties: 1) the uniformity and closed-cell ratio of the cell structure, determining thermal insulation performance; 2) overall mechanical stability, including compressive and deformation resistance; and 3) long-term dimensional stability, ensuring the durability and reliability of the product in application. Currently, static mixers are commonly used in industrial production to achieve this continuous mixing process, with the SX-type static mixer being particularly widely used. This type of mixer contains a series of crossbars arranged at specific angles. As the fluid flows through the mixer, these bars continuously divide and recombine the fluid, thereby achieving the mixing purpose. In existing technologies, related research (the paper "Optimization Design and Experimental Verification of SX-type Static Mixer Structure") only simulates the internal flow field of the SX-type static mixer, without calculating the concentration distribution of each component in the mixing system. It only calculates the physical dispersion of the dispersed phase in the matrix, without considering the convective diffusion process between the components in the mixer, and therefore cannot accurately evaluate the mixing quality. This patent evaluates the mixing performance of the static mixer based on the dispersion coefficient of the concentration of each component at the outlet, and optimizes the structural parameters of the static mixer.

[0003] For example, Chinese patent CN117195428A discloses a method and system for optimizing the structure of a hydrogen-blended natural gas mixer based on numerical simulation. The method provides the following technical solution: establishing a parametric geometric model of the hydrogen-blended natural gas mixer, the structure of which includes a mixer shell; establishing a CFD model of the hydrogen-blended natural gas mixer based on the parametric geometric model; optimizing a first set of design variables, including the aspect ratio of the shell cross-section, the number of mixing units, and the spacing between adjacent mixing units, based on the numerical simulation of the CFD model of the hydrogen-blended natural gas mixer, with the goal of achieving optimal mixing uniformity at the flow channel outlet cross-section; and optimizing a second set of design variables, including the shell length and the torsion angle of the mixing units, based on the numerical simulation of the CFD model of the hydrogen-blended natural gas mixer, under the constraint of the optimal values ​​of the first set of design variables, with the goal of achieving optimal mixing uniformity at the flow channel outlet cross-section and minimizing the flow field pressure drop. This invention reduces computational workload and improves the efficiency and accuracy of the optimization design process. However, the aforementioned method and system for optimizing the structure of hydrogen-blended natural gas mixers based on numerical simulation does not address high-viscosity, multi-component systems, lacks detailed modeling of the diffusion behavior of specific materials, and does not involve concentration dispersion coefficient as the core evaluation index, making it difficult to directly apply to complex chemical mixing processes such as polyurethane. Summary of the Invention

[0004] This invention solves the problems of existing technologies, such as reliance on trial and error, high cost, long cycle, and inaccurate mixing evaluation. It proposes a method for generating static mixer structural parameters, achieving the goals of high accuracy, high efficiency, and low cost.

[0005] Furthermore, this invention aims to provide a simulation optimization design method for the structural parameters of an SX-type static mixer for polyol, cyclopentane, and catalyst systems. Through coupled simulation of flow field and mass transfer, and using the outlet concentration dispersion coefficient as the evaluation index, the structural parameters can be rapidly and accurately optimized, thereby shortening the R&D cycle, reducing experimental costs, and improving mixing performance.

[0006] To achieve the above objectives, the present invention adopts the following technical solution: A method for generating static mixer structure parameters, comprising: The inclination angle of the crossbar and the length-to-diameter ratio in the mixer are selected as the structural parameters to be optimized, and the optimization objectives are to minimize the relative standard deviation of the concentration of each component at the outlet section and to minimize the pressure drop. Construct a three-dimensional geometric model of the static mixer based on the structural parameters, and set the inlet and outlet positions; The flow field is solved based on the Navier-Stokes equations and the continuity equation, and the concentration field of each component is solved based on the convection-diffusion equation. Multiphysics simulation was used to obtain the concentration distribution and pressure drop data of each component at the mixer outlet section under different structural parameters, and the relative standard deviation of each component concentration was calculated. The combination of structural parameters with a relative standard deviation less than a threshold is selected, and the one with the smallest voltage drop is chosen as the optimal structural parameter.

[0007] By employing systematic parameter optimization and multiphysics simulation, compared to the traditional trial-and-error design approach, the accuracy of simulation results is significantly improved, R&D efficiency is increased, and R&D costs are reduced.

[0008] Preferably, the solution of the flow field based on the Navier-Stokes equations and the continuity equations includes: setting the fluid as an incompressible laminar flow, calculating the velocity field and pressure field using the governing equations under isothermal conditions, and the flow field boundary conditions including: no slippage on the wall, inputting the inlet according to the mass flow rate, setting the outlet to a fixed pressure, and inputting the dynamic viscosity and density parameters of each component.

[0009] This ensures the physical accuracy of fluid motion, provides a reliable basis for velocity and pressure distribution in concentration field calculations, and improves the reliability of the simulation model.

[0010] Preferably, the governing equation is that the inertial force per unit volume of a fluid element is equal to the divergence of the surface force acting on it, wherein the inertial force per unit volume of a fluid element is the fluid density multiplied by the convective acceleration term, and the divergence of the surface force is the resultant stress per unit volume, including the pressure stress component and the viscous stress component.

[0011] Preferably, the method of solving the concentration field of each component based on the convection-diffusion equation includes: establishing a convection-diffusion coupling equation according to the law of conservation of mass and Fick's first law; inputting the initial concentration, inlet concentration and diffusion coefficient of each component; setting the boundary condition to zero mass flux perpendicular to the boundary direction; and substituting the velocity field obtained from the flow field solution into the equation to calculate the concentration distribution of each component.

[0012] The simulation of component concentration evolution under convection and diffusion solves the problem of insufficient focus on the flow field and improves the accuracy of mixing quality assessment.

[0013] Preferably, the construction of the three-dimensional geometric model includes generating a static mixer flow channel structure based on the set crossbar tilt angle and length-to-diameter ratio, including an outlet position, an inlet position, and the arrangement of the blade units inside the mixer. The inlet position includes a positive inlet for inputting polyol in the positive direction, and two separate inlets on each side for inputting catalyst and cyclopentane, respectively.

[0014] Preferably, the multiphysics simulation includes obtaining the concentration distribution cloud map of each component in the static mixer through a multiphysics simulation solver, extracting the concentration data of polyol, cyclopentane and catalyst of all grid cells at the mixer outlet section, calculating the average concentration of each component at the outlet section, and calculating the standard deviation of the component concentration at the outlet section for each set of structural parameter schemes.

[0015] A quantitative assessment of mixing uniformity was achieved, and data support was provided through the concentration relative standard deviation index.

[0016] Preferably, the acquisition of the pressure drop data specifically includes: obtaining a pressure distribution cloud map inside the static mixer by solving the Navier-Stokes equation and the continuity equation; extracting the pressure data of the inlet section and calculating the average inlet pressure; and, combined with the set outlet pressure boundary conditions, determining that the mixer pressure drop is equal to the average inlet pressure minus the outlet boundary pressure, thereby quantitatively evaluating the mechanical energy loss when the fluid flows through the mixer.

[0017] Pressure drop calculations help optimize energy consumption and reduce operating costs while meeting hybrid requirements.

[0018] Preferably, the convection-diffusion coupling equation is specifically that the rate of increase in substance concentration is equal to the rate of increase in concentration caused by fluid flow plus the rate of increase in concentration caused by molecular diffusion.

[0019] Preferably, in the selection of the crossbar tilt angle and the length-to-diameter ratio in the mixer as structural parameters to be optimized, the crossbar tilt angle ranges from 60 degrees to 120 degrees, and the length-to-diameter ratio ranges from 2 to 10.

[0020] Preferably, the optimization objectives include minimizing the relative standard deviation of the concentration of each component at the outlet section and meeting the mixing uniformity standard, with the secondary objective being minimizing the pressure drop. The mixing uniformity standard is defined as a relative standard deviation of the concentration of each component of less than 1% indicating uniform mixing and less than 5% indicating good mixing.

[0021] Compared with the prior art, the beneficial effects of the present invention are as follows.

[0022] 1. This invention simulates the component concentration distribution within a static mixer by establishing a multi-field coupled model of flow field and mass transfer. Compared to traditional methods that only focus on the flow field, this invention uses the relative standard deviation of the outlet component concentration as the core evaluation index to quantitatively assess mixing uniformity, significantly improving the accuracy and reliability of the simulation results.

[0023] 2. This invention uses computer simulation to quickly evaluate the impact of different structural parameters on mixing effects and pressure drop, avoiding the traditional trial-and-error process. Designers can adjust the crossbar angle and length-to-diameter ratio in a virtual environment and obtain performance data in real time, thereby significantly shortening the R&D cycle, quickly identifying the optimal design solution, and significantly improving product development speed.

[0024] 3. This invention uses digital simulation to replace physical prototype testing, saving on the procurement costs of experimental materials such as polyols and cyclopentane, and eliminating the expenses of prototype manufacturing and scrapping. Simultaneously, by optimizing structural parameters, it can reduce pressure drop and equipment operating energy consumption while ensuring mixing quality, significantly lowering research and development and production costs. Attached Figure Description

[0025] Figure 1 This is an overall flowchart of a method for generating structural parameters of an SX-type static mixer according to the present invention.

[0026] Figure 2 is a geometric model of an SX-type static mixer with a crossbar tilt angle of 90° when L / D=10, based on the method for generating structural parameters of an SX-type static mixer according to the present invention.

[0027] Figure 3 is a geometric model of an SX-type static mixer with a crossbar tilt angle of 120° when L / D=10, based on the method for generating structural parameters of an SX-type static mixer according to the present invention.

[0028] Figure 4 is a geometric model of an SX-type static mixer with a crossbar tilt angle of 60° when L / D=10, based on the method for generating structural parameters of an SX-type static mixer according to the present invention.

[0029] Figure 5 This is a pressure distribution cloud map illustrating the method for generating structural parameters of an SX-type static mixer according to the present invention.

[0030] Figure 6 This is a velocity distribution cloud map illustrating the method for generating structural parameters of an SX-type static mixer according to the present invention.

[0031] Figure 7 This is an overall streamline diagram of the method for generating structural parameters of an SX-type static mixer according to the present invention.

[0032] Figure 8 shows the cyclopentane surface and cross-sectional concentration cloud map of the method for generating structural parameters of an SX-type static mixer according to the present invention.

[0033] Figure 9 shows the catalyst surface and cross-sectional concentration cloud map of the method for generating structural parameters of an SX-type static mixer according to the present invention.

[0034] Figure 10 shows the polyol surface and cross-sectional concentration cloud map of the method for generating structural parameters of an SX-type static mixer according to the present invention.

[0035] Figure 11 shows the relative standard deviation of component concentration and pressure drop at different aspect ratios when θ=90°, based on the method for generating structural parameters of an SX-type static mixer according to the present invention.

[0036] Figure 12 shows the relative standard deviation of component concentration and pressure drop at different aspect ratios when θ=60°, based on the method for generating structural parameters of an SX-type static mixer according to the present invention.

[0037] Figure 13 shows the relative standard deviation of component concentration and pressure drop at different aspect ratios when θ=120°, based on the method for generating structural parameters of an SX-type static mixer according to the present invention. Detailed Implementation

[0038] See Figure 1-Figure 1 As shown in Figure 3, a method for generating static mixer structure parameters includes: The inclination angle of the crossbar and the length-to-diameter ratio in the mixer are selected as the structural parameters to be optimized, and the optimization objectives are to minimize the relative standard deviation of the concentration of each component at the outlet section and to minimize the pressure drop. Construct a three-dimensional geometric model of the SX-type static mixer based on the structural parameters, and set the inlet and outlet positions; The flow field is solved based on the Navier-Stokes equations and the continuity equation, and the concentration field of each component is solved based on the convection-diffusion equation. Multiphysics simulation was used to obtain the concentration distribution and pressure drop data of each component at the mixer outlet section under different structural parameters, and the relative standard deviation of each component concentration was calculated. The combination of structural parameters with a relative standard deviation less than a threshold is selected, and the one with the smallest voltage drop is chosen as the optimal structural parameter.

[0039] The purpose of this invention is to provide a highly efficient, low-cost, and precise simulation optimization design method for SX-type static mixers. This method can quickly determine the optimal structural parameters for polyol-cyclopentane-catalyst systems by simulating the impact of static mixer structural parameters on mixing performance and pressure drop, thereby shortening the development cycle, reducing costs, and improving mixer performance.

[0040] like Figure 1In one embodiment shown, the present invention relates to a method for generating structural parameters of an SX-type static mixer. The key dimensions of the mixer are optimized using numerical simulation to reduce energy consumption while ensuring mixing uniformity. First, the structural parameters to be optimized are defined as the crossbar tilt angle and the length-to-diameter ratio (the ratio of the mixer's length to its diameter). The angle typically ranges from 60° to 120°, and the length-to-diameter ratio ranges from 2 to 10. The optimization objectives include two aspects: the primary objective is to minimize the relative standard deviation of the concentration of each component at the outlet cross-section, typically requiring it to be below 1% to achieve uniform mixing; the secondary objective is to minimize the pressure drop as much as possible to reduce the mechanical energy loss of the fluid passing through the mixer.

[0041] During the model building phase, a three-dimensional geometric model of the static mixer is generated based on the set crossbar tilt angle and aspect ratio. The model includes an outlet position and a layout of a main inlet and two sub-inlets. The main inlet is used to input polyols, and the two sub-inlets are used to input catalysts and cyclopentane, respectively. At the same time, the arrangement of the internal blade units is determined.

[0042] Next, numerical calculations of the flow field and concentration field are performed. The incompressible laminar flow is solved based on the Navier-Stokes equations and the continuity equations. The wall is set as a no-slip boundary, the inlet is set according to the mass flow rate given by the process, and the outlet is set to a fixed pressure condition. The dynamic viscosity and density parameters of each component are input, and the balance between the inertial force and the surface force divergence per unit volume of the fluid micro-element is ensured by the control equations.

[0043] In the concentration field simulation, a convection-diffusion coupling equation is established based on the law of conservation of mass and Fick's first law. The initial concentration, inlet concentration, and diffusion coefficient of each component are input, and the boundary condition is set to zero flux perpendicular to the boundary. The velocity field obtained from the flow field solution is substituted into the equation to calculate the concentration distribution of each component. Through multiphysics coupling simulation, the flow and mixing conditions inside the mixer under different structural parameters can be obtained. The simulation output includes concentration and pressure distribution contour maps. The concentration data of each component in all grid cells of the outlet section are extracted from these maps, and their average and standard deviations are calculated to obtain the relative standard deviation of the concentration. Simultaneously, the average inlet pressure is extracted based on the pressure contour map and compared with the set outlet pressure to obtain pressure drop data for evaluating mechanical energy loss. Finally, among all structural parameter combinations that meet the mixing homogeneity requirement (i.e., the relative standard deviation is below a set threshold), the scheme with the smallest pressure drop is selected as the optimal structural parameter, thereby achieving comprehensive optimization of mixing effect and energy efficiency.

[0044] In another embodiment, this invention establishes a flow field-mass transfer coupling model based on the law of conservation of mass, Fick's law, and the convection-diffusion equation, coupled with the Navier-Stokes equations. The COMSOL finite element method is used to simulate the concentration field evolution process of each component within a static mixer, simulating the convection-diffusion coupling. The concentration distribution of each component at the mixer outlet is obtained for different structural parameters. The relative standard deviation (COV) of each component concentration is used as a quantitative evaluation index for mixing uniformity, and combined with the pressure drop (ΔP) index for comprehensive analysis, ultimately selecting the optimal structural parameter scheme. The specific implementation process is as follows: Design and optimization objectives for static mixer structural parameters: The crossbar tilt angle (θ) and length-to-diameter ratio (L / D) of the static mixer were selected as structural parameters for design. The crossbar tilt angle θ ranged from 60°, 90°, and 120°, as shown in Figures 2-4; the length-to-diameter ratio L / D ranged from 2, 4, 6, 8, and 10. The optimization objectives were divided into primary and secondary parts. The primary objective was to minimize the relative standard deviation of the concentration of each component at the outlet section, meeting industry standards (COV < 1% indicates uniform mixing, COV < 5% indicates good mixing). The secondary objective was to minimize pressure drop, reducing operating energy consumption (pressure drop reflects the mechanical energy loss of the fluid passing through the mixer) while maintaining uniform mixing.

[0045] Geometric model construction: Building geometric models based on different structural parameters; Taking θ=90° and L / D=10 as an example, the inlet and outlet positions of the polyol, cyclopentane, and catalyst, as well as the geometric model of the mixer, are shown in Figure 2. The inlet position of the polyol is the one directly opposite to the left, the inlet position of the cyclopentane is to its left, and the inlet position of the catalyst is to its right. The inlet positions of the cyclopentane and the catalyst are symmetrical to each other, and the outlet position is located at the tail.

[0046] Flow field settings: Set the flow field physical equations, flow field boundary conditions, input the dynamic viscosity, density and other physical property parameters of each component, and input the mass flow rate and outlet pressure of each component according to the preset process parameters.

[0047] The flow field physics equations employ the Navier-Stokes equations and the continuity equation. The Navier-Stokes equations describe the conservation of fluid momentum, reflecting the relationship between velocity, pressure, viscosity, and density, and determining the velocity distribution and pressure gradient of the flow field. The continuity equation describes the conservation of fluid mass, ensuring that fluid mass is not created or destroyed during flow, and constraining the continuity of the velocity field.

[0048] The static mixer is maintained at a constant temperature (23±1℃). The polyol-cyclopentane-catalyst system flows in an incompressible laminar flow state within the mixer. The Navier-Stokes equations and the continuity equation are used to solve for the flow field and pressure field distribution. The specific governing equations are as follows: equal , Where μ is the dynamic viscosity (Pa·s); u is the velocity (m / s); ρ is the fluid density (kg / m³); p is the pressure (Pa); I is the pressure direction matrix (N / m²); and T is the transpose sign. The left side of the governing equations... The first term, convective acceleration, describes the change in momentum of a fluid element due to its motion in a spatially varying velocity field. Overall, it represents the inertial force per unit volume of the fluid element. The second term describes the surface stress acting on the fluid element. It is the Cauchy stress tensor, including -pI as the compressive stress component, and As a component of viscous stress.

[0049] The flow field boundary conditions are: At the wall boundary, the fluid velocity relative to the wall is zero (no slip boundary condition), that is, when the fluid is in close contact with the wall, it remains relatively stationary with the wall, i.e., u=0; Inlet boundary: Input the mass flow rate of each component to define the rate at which the fluid enters the mixer and the proportion of each component. Set the outlet boundary and outlet pressure to define the pressure reference when the fluid flows out of the mixer and balance the pressure distribution of the flow field.

[0050] Convection-diffusion setup: This involves setting the convection-diffusion physical equations, boundary conditions, and inputting the temperature, initial concentration, inlet concentration, and diffusion coefficient of each component based on process parameters. When components flow within the mixer, they are subjected to convection due to the segmentation effect of the blades inside the static mixer; simultaneously, driven by the concentration gradient, components diffuse from high-concentration areas to low-concentration areas. The entire convection-diffusion process is based on the law of conservation of mass; no chemical reaction occurs within the mixer, and the mass of each component is neither generated nor consumed. Spatial migration is achieved through both convection and diffusion. According to the law of conservation of mass, the cumulative rate of change of components per unit volume = net diffusion inflow rate - net convection outflow rate; convection is driven by the flow field velocity field *u*, and is a macroscopic migration process of components carried by fluid flow. Because the flow proceeds along the velocity direction, the vector dot product is used… Quantification, Concentration gradient (mol / m 4 Diffusion is a spontaneous migration process of components from a region of high concentration to a region of low concentration, following Fick's first law and expressed in the form of divergence. "Quantization, D is the component diffusion coefficient (m 2 / s). Based on the above mass conservation relationship and various quantitative expressions, the convection-diffusion equation is finally obtained as follows: Plus equal Where u is velocity, in m / s; D is diffusion coefficient, in m² / s; c is concentration, in mol / m³; and t is time, in s.

[0051] Based on the process parameters, input a temperature of 23℃ to ensure that the diffusion coefficient D of each component is constant; input the initial concentration of each component as 0 mol / m³. 3 Since there was no pre-stored fluid in the mixer at the initial moment, there was no component residue; according to the process formula and physical property data, the inlet concentration of each component was entered (polyol 1642 mol / m). 3 Cyclopentane 10694 mol / m 3 Catalyst 3833 mol / m 3 ) and corresponding diffusion coefficient (polyol 1×10 -12 m 2 / s, cyclopentane 8×10 -10 m 2 / s, catalyst 6×10 -11 m 2 / s).

[0052] A convection-diffusion boundary is set such that the mass flux perpendicular to the boundary direction is zero at the boundary. =0; where n is the unit of the surface normal vector. Substitute the velocity field obtained from the flow field calculation into the convection-diffusion equation to calculate the concentration distribution of each component, so as to accurately reflect the influence of actual flow on the convection and diffusion of matter.

[0053] The concentration distribution contour maps of each component within the static mixer were obtained using the COMSOL multiphysics simulation solver. Further, concentration data at the outlet section were extracted, including the concentration data of polyols, cyclopentane, and catalyst in all grid cells at that section, and the average concentration of each component at that outlet section was calculated. For each set of structural parameter schemes, a set of relative standard deviations (COV) for each component's concentration was obtained. The COV is calculated as follows: COV equals the standard deviation of the component concentration at the outlet section (mol / m³) divided by the average concentration of the component at the outlet section (mol / m³) multiplied by 100%.

[0054] Based on the Navier-Stokes equations and the continuity equation, a pressure distribution contour map of the static mixer is obtained. Inlet cross-sectional pressure data is extracted from this contour map, and the average inlet pressure is calculated. Combined with the set outlet pressure boundary conditions, the mixer pressure drop is obtained by subtracting the outlet boundary pressure from the average inlet pressure. This pressure drop is used to quantitatively assess the mechanical energy loss of fluid flowing through the mixer. Simultaneously, pressure distribution contour maps, velocity distribution contour maps, streamline diagrams, and concentration contour maps are output to visually display the internal mixing state. Through multiphysics coupling simulation, replacing difficult-to-implement experimental observations, data on flow field and concentration are obtained, clearly revealing the mixing mechanism.

[0055] To determine the optimal structural parameters, we screen out parameter schemes that meet the mixing uniformity standard (COV < 1%), and then select the scheme with the smallest pressure drop (ΔP) from this range, which is the optimal structural parameter.

[0056] The cloud map of the calculation results with θ=90° and L / D=10 is shown below. Figures 5-7 As shown, Figure 5 The pressure distribution inside the mixer is shown. The pressure gradually decreases along the flow direction. The pressure drop mainly comes from the local resistance of the blade units to the flow. Its magnitude is related to the blade geometry (number and angle), arrangement, and fluid properties. Figure 6 The axial velocity distribution inside the mixer is shown, revealing a distinct periodicity in the flow field. The blade structure causes a periodic variation in the effective flow cross-section of the channel; the fluid velocity increases as it flows through narrow regions and decreases as it enters open regions. This periodic variation not only enhances fluid shearing but also increases the frequency of fluid segmentation and recombination, thereby improving mixing efficiency. Figure 7 The streamline diagram illustrates how the blades guide the fluid to form a three-dimensional spiral and cross-flow, with the streamlines exhibiting a complex, interwoven pattern. Each time the fluid passes through a set of blade units, it undergoes a "splitting-recombining" process: the blades cut the fluid into multiple sub-flows, which then re-converge in the downstream channel before entering the next set of blade units for repeated splitting. This process shortens the diffusion path of component molecules and improves mixing efficiency.

[0057] The surface concentration cloud maps and cross-sectional concentration cloud maps of cyclopentane, catalyst, and polyol are shown in Figures 8-10. When the three components first enter the mixer, the concentration distribution is extremely uneven, and the color difference in the cloud maps is significant. After flowing into the mixer, they are rapidly divided by the blades and diffuse radially. After passing through 9-10 blade units, the concentration distribution tends to be uniform, and the color difference between the surface and cross-sectional concentration cloud maps decreases significantly.

[0058] In another embodiment, an example is taken of optimizing an SX-type static mixer for a three-component mixing process of polyether polyol, cyclopentane, and catalyst.

[0059] S1: Structural Parameter Design and Optimization Objectives: The inclination angle and length-to-diameter ratio of the crossbars of the static mixer are selected as structural parameters for design. In this embodiment, three sets of structural parameter design schemes are designed, maintaining consistent process parameters and a fixed mixer diameter of 30mm, as detailed below: Option 1: The inclination angle θ of the crossbar is 60°, and the length-to-diameter ratio L / D ranges from 2, 4, 6, 8, to 10. Option 2: The inclination angle θ of the crossbar is 90°, and the length-to-diameter ratio L / D ranges from 2, 4, 6, 8, to 10. Option 3: The inclination angle θ of the crossbar is 120°, and the length-to-diameter ratio L / D ranges from 2, 4, 6, 8, to 10. The optimization objectives are divided into two parts: primary and secondary. The primary objective is to minimize the relative standard deviation of the concentration of each component at the outlet section, which must meet the industry evaluation standards—COV < 1% indicates uniform mixing, and COV < 5% indicates good mixing. The secondary objective is to minimize the system pressure drop ΔP and reduce operating energy consumption while meeting the above requirements for uniform mixing.

[0060] S2: Geometric Model Construction: Design and build geometric models based on different structural parameters, such as... Figure 1 As shown in Figure 2; S3: Flow field settings: Set the flow field physical equations, flow field boundary conditions, input the dynamic viscosity, density and other physical property parameters of each component, and input the inlet mass flow rate and outlet pressure of each component according to the process parameters.

[0061] The static mixer is kept at a constant temperature (23±1℃). The polyol-cyclopentane-catalyst system flows in an incompressible laminar flow state within the mixer. The flow field and pressure field distribution are solved using the Navier-Stokes equations and the continuity equation.

[0062] The specific flow field settings are shown in Table 1: Table 1 S4: Convection-Diffusion Settings: Set the convection-diffusion physical equations, convection-diffusion boundary conditions, and input the temperature, initial concentration of each component, inlet concentration, and diffusion coefficient based on process parameters.

[0063] Based on the law of conservation of mass, and considering the convection and diffusion behavior of each component in a static mixer, a convection-diffusion equation is established to describe the mass transfer process. The convection-diffusion boundary is set to have zero mass flux in the direction perpendicular to the boundary.

[0064] The specific convection-diffusion settings are shown in Table 2: Table 2 Substitute the velocity field obtained from the flow field calculation into the convection-diffusion equation to calculate the concentration distribution of each component.

[0065] S5: Post-processing and calculation of relative standard deviation and pressure drop: The COMSOL multiphysics simulation solver is used to solve the concentration data of each component under different structural parameter schemes, and the relative standard deviation (COV) of each component concentration is calculated.

[0066] The pressure drop is calculated based on the pressure difference between the inlet and outlet, and is used to assess the mechanical energy loss of fluid as it passes through the mixer. Figures 5 to 7 Figures 11-13 show the pressure, velocity, streamline, and concentration contour maps when the crossbar tilt angle θ = 90°, visually illustrating the internal mixing state. Multiphysics coupling simulation replaces difficult-to-implement experimental observations, acquiring flow field and concentration data to clearly reveal the mixing mechanism. The relative standard deviations of component concentrations and pressure drop data for the three structural parameter design schemes are shown in Figures 11-13.

[0067] S6: Determination of Optimal Structural Parameters: Based on the optimization objective, the optimal structural parameters for this embodiment were determined, as shown in Tables 3-5. When θ = 120°, the relative standard deviation of each component is greater than 1%, and the mixing homogeneity does not meet the requirements. When θ = 60° and 90°, the COV values ​​of each component are less than 1%, meeting the mixing homogeneity requirements. However, at the same aspect ratio, the pressure drop of the θ = 90° scheme is 24.7% lower than that of θ = 60°, indicating better performance. As the aspect ratio L / D decreases, the system pressure drop decreases, but the relative standard deviation of each component increases. When θ = 90° and L / D = 8, the COV of each component is still less than 1%, with the relative standard deviation of the polyol being 0.085%, cyclopentane 0.645%, and catalyst 0.771%, and the system pressure drop being only 0.176 MPa. Specific data are shown in Tables 3-5. Table 3 Table 4 Table 5 Table 3 shows the COV and pressure drop at different angles when the length-to-diameter ratio L / D = 10; Table 4 shows the COV and pressure drop at different angles when the length-to-diameter ratio L / D = 8; and Table 5 shows the COV and pressure drop at different angles when the length-to-diameter ratio L / D = 6.

[0068] Based on comprehensive comparison, the optimal structural parameters determined by this invention are θ=90° and L / D=8. This scheme, while ensuring mixing uniformity, shortens the static mixer length by 20% compared to the conventional L / D=10 scheme, and reduces the pressure drop by approximately 19.6%, achieving simultaneous optimization of structural compactness and energy efficiency.

[0069] All data collection and extraction in this invention are carried out under compliant and legal conditions.

Claims

1. A method of generating a static mixer structure parameter, characterized by, include: The inclination angle of the crossbar and the length-to-diameter ratio in the mixer are selected as the structural parameters to be optimized, and the optimization objectives are to minimize the relative standard deviation of the concentration of each component at the outlet section and to minimize the pressure drop. Construct a three-dimensional geometric model of the static mixer based on the structural parameters, and set the inlet and outlet positions; The flow field is solved based on the Navier-Stokes equations and the continuity equation, and the concentration field of each component is solved based on the convection-diffusion equation. Multiphysics simulation was used to obtain the concentration distribution and pressure drop data of each component at the mixer outlet section under different structural parameters, and the relative standard deviation of each component concentration was calculated. The combination of structural parameters with a relative standard deviation less than a threshold is selected, and the one with the smallest voltage drop is chosen as the optimal structural parameter.

2. The method for generating structure parameters of a static mixer according to claim 1, wherein, The solution of the flow field based on the Navier-Stokes equations and the continuity equation includes: The fluid is set as an incompressible laminar flow. Under isothermal conditions, the velocity and pressure fields are calculated using governing equations. The flow field boundary conditions include: no slip on the wall, inlet input based on mass flow rate, outlet set to fixed pressure, and input of the dynamic viscosity and density parameters of each component.

3. The method of claim 2, wherein, The governing equation is specifically that the inertial force per unit volume of a fluid element is equal to the divergence of the surface force acting on it, where the inertial force per unit volume of a fluid element is the fluid density multiplied by the convective acceleration term, and the divergence of the surface force is the resultant stress per unit volume, including the compressive stress component and the viscous stress component.

4. The method of claim 3, wherein, The method of solving the concentration field of each component based on the convection-diffusion equation includes: establishing a convection-diffusion coupling equation according to the law of conservation of mass and Fick's first law; inputting the initial concentration, inlet concentration and diffusion coefficient of each component; setting the boundary condition to zero mass flux perpendicular to the boundary direction; and substituting the velocity field obtained from the flow field solution into the equation to calculate the concentration distribution of each component.

5. The method of claim 1, wherein The construction of the three-dimensional geometric model includes generating a static mixer flow channel structure based on the set crossbar tilt angle and length-to-diameter ratio, including an outlet position, an inlet position, and the arrangement of the blade units inside the mixer. The inlet position includes a positive inlet for inputting polyol in the positive direction, and two separate inlets on each side for inputting catalyst and cyclopentane, respectively.

6. The method of claim 4, wherein, The multiphysics simulation includes obtaining the concentration distribution cloud map of each component in the static mixer through a multiphysics simulation solver, extracting the concentration data of polyol, cyclopentane and catalyst of all grid cells at the mixer outlet section, calculating the average concentration of each component at the outlet section, and calculating the standard deviation of the component concentration at the outlet section for each set of structural parameter schemes.

7. A method of generating a static mixer structure parameter according to claim 5 or 6, characterized in that, The acquisition of the pressure drop data specifically includes obtaining a pressure distribution cloud map inside the static mixer by solving the Navier-Stokes equation and the continuity equation, extracting the pressure data of the inlet section and calculating the average inlet pressure, and combining the set outlet pressure boundary conditions. The pressure drop of the mixer is equal to the average inlet pressure minus the outlet boundary pressure, and the mechanical energy loss when the fluid flows through the mixer is quantitatively evaluated.

8. The method of claim 4, wherein, The specific convection-diffusion coupling equation states that the rate of increase in substance concentration equals the rate of increase in concentration caused by fluid flow plus the rate of increase in concentration caused by molecular diffusion.

9. The method of claim 1, wherein, In the selection of the crossbar tilt angle and length-to-diameter ratio in the mixer as structural parameters to be optimized, the crossbar tilt angle ranges from 60 degrees to 120 degrees, and the length-to-diameter ratio ranges from 2 to 10.

10. The method of claim 9, wherein, The optimization objectives include minimizing the relative standard deviation of the concentration of each component at the outlet section and meeting the mixing uniformity standard. The secondary objective is to minimize the pressure drop. The mixing uniformity standard is defined as a relative standard deviation of the concentration of each component of less than 1% for uniform mixing and less than 5% for good mixing.

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