Multi-objective optimization design method for multi-parameter balanced flowmeter based on matrix structure

Abstract

A multi-objective optimization design method for multi-parameter balanced flowmeters based on a matrix structure belongs to the field of flow detection technology. The method employs a variable concentric layer structure of up to five layers to construct an initial parameter variable matrix, parameterizing the orifice plate for CFD mesh generation. The CFD calculation module calculates the objective functions of permanent pressure loss and velocity uniformity at a given cross-section. An optimized orifice plate structure is generated through a multi-objective, multi-parameter optimizer, coupled with the CFD calculation module to achieve optimal loss reduction and flow field uniformity. The design module receives the optimal orifice shape and constructs the instrument coefficient correlation and initial values; the CFD calculation module performs variable Reynolds number calculations; based on the initial instrument coefficient correlation, the design module performs nonlinear regression to obtain an empirical correlation between the discharge coefficient and the Reynolds number and orifice shape, outputting the instrument coefficient and completing the optimization design. This design, through multi-objective structural optimization, achieves accurate output of the discharge coefficient and instrument coefficient for any multi-orifice flowmeter, improving the accuracy and adaptability of the balanced flowmeter in real-world conditions.

Description

Technical Field

[0001] This invention relates to the field of flow detection technology and provides a multi-objective optimization design method for a multi-parameter balanced flow meter based on a matrix structure. Background Technology

[0002] In industrial production, fluid measurement and management play a crucial role. Flow meters, as key equipment for achieving this goal, directly impact production efficiency, product quality, and energy consumption. However, commonly used flow meters, such as standard orifice plates, nozzles, and venturi flow meters, struggle to simultaneously meet high-performance requirements in terms of straight pipe length, accuracy, stability, and pressure loss. Therefore, there is an urgent need for a flow meter that can handle most operating conditions to a high standard without sacrificing the unique advantages of differential pressure flow meters. The balanced multi-orifice plate flow meter offers an excellent solution.

[0003] Patent CN118981969A provides a method for optimizing the design of a single-concentric orifice arrangement structure. To improve design efficiency, it employs a sparse sample method with discrete structural parameters, limiting its applicability. Patent CN119397952A, based on the optimization function of the commercial FLUENT computing platform, achieves multi-objective optimization design of orifice plates with a central and surrounding orifice arrangement, providing a design method for flow metering structures applicable only to low-temperature working fluid cavitation phase change scenarios. While both patents can achieve specific optimized structures and output constant discharge coefficients within the Reynolds number (Re) range, they fail to construct correlations for scenarios where the discharge coefficient varies with Re, thus limiting their application. Summary of the Invention

[0004] To address the problems existing in current technologies, this invention proposes a multi-objective optimization design method for a multi-parameter balanced flowmeter based on a matrix structure. This method innovatively constructs a matrix-based multi-parameter, multi-objective optimization framework. Through parametric modeling, a fluid equilibrium distribution structure with a five-layer annular array of orifices is designed, achieving multi-field synergistic optimization of momentum balance, energy balance, and mass balance. This invention aims to comprehensively improve key performance indicators such as flow measurement accuracy, reduce upstream and downstream pressure loss, and optimize the uniformity of flow field velocity distribution, seeking the optimal balance point among various objectives, thereby fully leveraging the potential advantages of porous orifice plate structures in fluid measurement.

[0005] The technical solution adopted in this invention is: a multi-objective optimization design method for a multi-parameter balanced flowmeter based on a matrix structure, comprising the following steps:

[0006] S100. Construct the initialization parameter variable matrix using a multi-layered structure. The parameter variable matrix is ​​constructed from the number of layers i, the diameter of the layers D, the number of holes N in each layer and the diameter of the holes d.

[0007] S200, the parameter variable matrix is ​​output to the balanced flow meter calculation module, the corresponding STL file is generated by parameterization, and the subsequent CFD mesh generation and numerical calculation analysis are completed by exporting; the CFD results are output and the two target physical field functions of fluid flow velocity uniformity in the pipeline and permanent pressure loss before and after the orifice are calculated.

[0008] S300: Set up a multi-objective, multi-parameter optimizer to control the multi-parameter variables to find optimal combinations under inequality constraints and threshold constraints, and update the parameter variables in a loop to generate an optimized orifice plate structure, thereby achieving the goals of reducing permanent pressure loss before and after the orifice plate and improving the uniformity of flow velocity in the flow channel.

[0009] S400: Set up the balanced flow meter design module, receive the optimal solution of the orifice plate structure from the calculation module, construct the outflow coefficient correlation, input the initial instrument coefficient for CFD calculation, complete the nonlinear regression based on the calculation results to obtain the coefficient value and perform a second CFD calculation; establish the empirical correlation of the outflow coefficient with respect to Reynolds number and orifice ratio and output the instrument coefficient.

[0010] Furthermore, in step S100, five concentric concentric circles—m, n, p, q, and r—are set from the inside out, with the corresponding number of circles determined according to different working conditions. Their structure follows a recursive principle: the first concentric circle structure contains only the m-th layer; the second concentric circle structure consists of m and n layers; the third concentric circle structure consists of m, n, and p layers; the fourth concentric circle structure consists of m, n, p, and q layers; and the fifth concentric circle structure includes all layers from m to r. The diameter parameters of the concentric circles are D. m D n D p D q D r Cylindrical holes are evenly distributed on each layer, with the number parameter N. m N n N p N q N r The diameter parameters of the holes in each layer are d. m d n d p d q d r .

[0011] Furthermore, step S200 includes the following sub-steps:

[0012] S201. A large cylindrical plate and multiple small cylinders are created using a specific data structure; the position of the large cylindrical plate is determined, and the hole positions of the small cylinders are calculated and laid out. Based on five sets of hole parameters, the starting angles of each set of holes are designed to achieve an alternating arrangement.

[0013] The first group starts at 0 degrees; the initial angle of the second group is offset by half of the included angle of the first group of small cylinders, and subsequent groups are successively added by half of the included angle of the previous group. The angular gap between small cylinders in the same concentric circle is 360° / n; the center position of the small cylinders is accurately calculated using a polar coordinate algorithm. The final polar angle at the center of the cylinder:

[0014]

[0015]

[0016]

[0017] S202. After generating the coordinates of the small cylinder based on the parameters, the corresponding volume is subtracted from the position of the small cylinder through Boolean difference set operation, thereby processing holes in the main cylindrical plate to form a three-dimensional solid hole plate structure, which is output in STL format.

[0018] S203 and STL files are used for CFD mesh generation and numerical analysis, outputting calculation results and calculating two objective physical field functions: the uniformity of fluid flow velocity in the pipe and the permanent pressure loss before and after the orifice.

[0019] Furthermore, in step S203, the pressure tapping method adopts radial pressure tapping, flange pressure tapping, or corner pressure tapping.

[0020] Furthermore, the step S300 is characterized by comprising the following sub-steps:

[0021] S301. Set constraints on the key variables included in the parametric design of the perforated plate structure: number of layers i, layer diameter D, number of holes N in each layer, and hole diameter d;

[0022] For setting inequality constraints and threshold constraints for multiple parameters, the center distance between any two adjacent concentric holes must be greater than the sum of their radii, i.e., the basic condition must be met.

[0023] For any adjacent concentric layers i and i+1, the linear inequality constraint is:

[0024]

[0025] Among them, D i Let D be the diameter of layer i. i+1 Let d be the diameter of the i+1th layer. i Let d be the diameter of the cylindrical hole on layer i. i+1 Let be the diameter of the cylindrical hole on the i+1 layer;

[0026] The radial distance between the circles distributed on adjacent concentric circles. The minimum radial spacing required for the edges of the two concentric holes to overlap;

[0027] If this constraint is not met, holes in adjacent concentric layers will radially overlap or become tangent at their edges (this issue is not considered when the number of concentric layers is 1). Furthermore, to prevent the hole distribution from exceeding the range of the large cylindrical plate, when the number of concentric layers is ≥2, the length of the sum of the radius of the outermost concentric layer on the plate and the radius of the holes distributed on that layer should be less than the radius of the large cylindrical plate. If the number of concentric layers is 1, the length of the sum of the radius of that concentric layer and the radius of the holes distributed on that layer should also be less than the radius of the large cylindrical plate.

[0028]

[0029]

[0030]

[0031]

[0032] ;

[0033] Add another domain value constraint: ;

[0034] Among them, i, It is a positive integer. For discrete integer set variables, It is a continuous variable;

[0035] S302. Based on the multi-parameter constraint definition design space, the optimizer starts an iterative optimization loop and returns the combined parameters to the parameter variable matrix; the algorithm generates a parameter set in the constraint space, returns the calculation results, and evaluates the quality of the solution based on the multi-objective output; if the convergence criterion is not met, the next generation of parameters is generated iteratively based on the result of this generation, and the iteration continues; when the convergence condition is met, the algorithm terminates and outputs the global optimal solution.

[0036] Furthermore, in step 301, for a five-layer structure, five sets of inequality constraints must be satisfied simultaneously (for a 2-4 layer concentric structure, the number of constraint sets is reduced accordingly):

[0037]

[0038]

[0039]

[0040]

[0041] .

[0042] Furthermore, step S400 includes the following sub-steps:

[0043] S401. Obtain the optimal solution and determine the geometry of the orifice plate, including the orifice distribution and aperture ratio β on the orifice plate;

[0044] set up The instrument coefficient is used to establish a general correlation between the Reynolds number Re and the aperture ratio β:

[0045] It can degenerate into a correlation similar to that of the ISA1932 nozzle:

[0046] ;

[0047] S402. Input the initial coefficients of the above correlation into the calculation module to perform CFD calculation and analysis of the outflow coefficients under different Reynolds number ranges; based on the calculation results, complete the regression calculation of the instrument coefficients, and obtain the instrument coefficient values ​​after evaluating the quality of the regression.

[0048] After substituting the instrument coefficient values ​​into the degraded correlation, a second calculation is performed to obtain the final empirical correlation of the outflow coefficient with respect to the Reynolds number Re and the aperture ratio β.

[0049] S403. Write the empirical correlation formula into the flow meter's processing unit and output the instrument coefficient in real time during actual measurement.

[0050] Furthermore, step S201 specifically includes:

[0051] S2011. Based on the geometric structure, a script program is generated to read design parameter values ​​from the geometric matrix mapping configuration file, including key design variables such as the distribution diameter, aperture size, and number of holes of the five-layer annular array.

[0052] S2012 defines a specific data structure for a parameterized cylinder generator, specifically designed to create the basic geometric units for flow meter models. The volumes of both the main cylinder and smaller cylinders can be automatically generated using this data structure.

[0053] S2013. The center of the bottom surface of the main cylindrical plate is located at the origin of the coordinate system (0, 0, 0), and the cylinder axis is along the Z-axis. The coordinates of the center of the small cylinder (hole) are accurately determined through polar coordinate transformation. For the i-th layer of the hole array (i=1,2,…,5), let its distribution layer diameter be D. i Number of holes N i The initial offset angle is θ 0,i Then the Kth hole (k=0,1,..,N) i-1 The angular position of in the polar coordinate system is:

[0054]

[0055] Where the initial offset angle θ 0,i Determined using an indexing staggered strategy:

[0056]

[0057]

[0058] This formula means that, starting from the second layer, the initial angle of each small cylinder is successively increased by half the included angle of the previous layer's small cylinder. Then, the three-dimensional coordinates of the center of the small cylinder are obtained through polar coordinate-Cartesian coordinate transformation:

[0059]

[0060]

[0061]

[0062] z here i,k =0 indicates that the center of all small cylinders is located on the flowmeter's mid-plane (i.e., the z=0 plane), ensuring that the orifice axis is parallel to the orifice plate thickness direction.

[0063] S2014, The geometric parameters of the cylinder are accepted from the parameter variable matrix, including the concentric circle diameter D. i Number of holes N i The aperture d on each layer i The numerical values ​​are used to generate their respective geometric volumes.

[0064] Furthermore, step S202 specifically includes:

[0065] S2021. Using Boolean difference operations, all array holes are precisely cut out from the generated solid cylinder. This process involves traversing five layers of hole position data, sequentially "subtracting" the small cylinder corresponding to each hole from the main model, ultimately forming a structurally complete flow meter plate with holes. After completing the geometric modeling, the system exports the final 3D solid model as a standard STL file.

[0066] S2022. Numerical analysis of the flow field characteristics of a balanced flowmeter is performed through a systematic CFD modeling and solution process. First, a cylindrical computational domain is constructed to completely cover the orifice plate structure. Boolean operations are used to extract the fluid region outside the orifice plate, forming a physical flow domain that matches the actual flow. Based on this flow domain, a regular mesh is generated.

[0067] S2023. In terms of numerical solution, the finite volume method is used for spatial discretization: the time term uses a steady-state scheme, the gradient term uses Gaussian linear interpolation, the convection term uses a bounded linear upwind scheme with a constraint to balance stability and accuracy, and the Laplace term and surface normal gradient use a modified scheme suitable for non-orthogonal grids. Pressure-velocity coupling is implemented using the SIMPLE algorithm, where the pressure Poisson equation is solved efficiently using Geometric Algebraic Multigrid (GAMG), and the velocity and turbulent transport equations are calculated iteratively using a smooth solver. Iterative stability is enhanced by appropriately setting field relaxation and equation relaxation factors. Relative tolerance is used in the initial stage to accelerate convergence, while absolute tolerance is used in the final iteration stage to ensure solution accuracy. Finally, CFD numerical simulations are completed, key physical field data are acquired and output, providing quantitative basis for multi-objective optimization.

[0068] Furthermore, S302 aims to reduce permanent pressure loss before and after the orifice plate and improve the uniformity of fluid flow velocity within the pipeline. Pressure sampling points are located at a radial distance of 1 pipe diameter upstream and 6 pipe diameter downstream. To evaluate velocity uniformity, the velocity standard deviation at the 6 pipe diameter downstream section is calculated. An iterative optimization loop is designed based on multi-parameter constraints. The algorithm generates a parameter set within the constraint space, drives geometric modeling and automatic CFD calculations, and evaluates the quality of the solution based on multi-objective outputs. If the optimal convergence criterion is not met, the next generation of parameters is updated and generated based on the previous result, and the iteration continues. The loop terminates when the convergence condition is met, outputting the global optimal solution.

[0069] Furthermore, step S302 specifically includes:

[0070] S3021. During the optimization process, all performance objectives must be quantified into numerical values ​​for calculation and optimization. Therefore, the permanent pressure loss is set as the pressure difference between the pressure taps before and after the orifice plate (the upstream pressure tap is set at a distance of 1D from the upstream end face of the orifice plate, and the downstream pressure tap is set at a distance of 6D from the downstream end face of the orifice plate); the flow field velocity uniformity is quantified through the physical field of the pipe section located at 6D from the downstream end face of the orifice plate. By extracting the three-dimensional velocity components u, v, and w of this section, their average value and standard deviation are calculated respectively.

[0071] S3022. The MOGA (NLPQL, SNOPT, NSGA-II, etc.) optimization method is used for the optimal design of a multi-orifice balanced flowmeter. By performing a global search in the design space composed of five orifice array parameters, multiple parameter combinations are generated and their values ​​are fed back to the design variables in the geometric parameter variable matrix in S100, continuously approaching the goals of minimizing pressure loss and improving flow field uniformity. Simultaneously, since the final result of multi-objective optimization is a non-dominant Pareto optimal solution, an optimization front reflecting different design trade-offs is formed.

[0072] This invention offers the following advantages: By developing a non-commercial, open-source, end-to-end modeling, calculation, and optimization process, the geometric parameters of the balanced flowmeter are matrixed, enabling efficient and automated multi-objective optimization design, including permanent pressure loss and velocity uniformity. The diameter D of the layered distribution of the multi-layered annular aperture array... i aperture d i Number of holes N i The parameter matrix is ​​structured so that each column represents a concentric circle and each row represents a geometric feature. Parameter values ​​are set using a combination of continuous and discrete variables, ensuring stable sample optimization space exploration and reliable structural sensitivity analysis. This method, capable of designing arbitrary orifice distribution geometries such as multi-layered concentric circles, equidistant patterns, and radial arrangements within five concentric circles, significantly improves the freedom and robustness of orifice plate structure optimization. It also offers significant advantages in computation and optimization: it integrates with optimization methods such as genetic algorithms, facilitating large-space optimization and computation of optimization variables. After structural optimization, variable Reynolds number CFD calculations are performed to establish the correlation between instrument coefficient regression and outflow coefficient with Reynolds number and orifice ratio, thus enabling productization.

[0073] This process achieves multi-objective structural optimization, possessing advantages unmatched by traditional optimization methods. By simultaneously addressing multiple conflicting performance indicators, it systematically explores the balance within the design space, rather than relying on limited evaluation criteria. It enables stable and accurate structural optimization of large geometric spaces and high degrees of freedom for equilibrium orifice plates under any conditions, media, and phases, unaffected by Reynolds numbers.

[0074] After determining the optimal orifice plate structure, nonlinear regression of the instrument coefficient was performed using CFD simulation and experimental data. The fitting ability of nonlinear regression was employed to capture the complex relationship between the instrument coefficient and measurement parameters, significantly improving the accuracy and adaptability of instrument measurements and avoiding the problem of large measurement errors in traditional constant instrument coefficients under wide ranges and complex operating conditions. A correlation formula for the outflow coefficient with respect to Reynolds number and orifice ratio was established:

[0075] The process involves outputting instrument coefficients to complete the productization of the balanced flow meter. This process improves the accuracy and reliability of the balanced flow meter under actual operating conditions. The final output instrument coefficients link structural parameters with flow characteristics, streamlining the calibration and performance prediction of orifice plates of different specifications. This calibration process, which combines experimental data and models, has significant engineering experience value.

[0076] In addition to the objectives, features, and advantages described above, the present invention has other objectives, features, and advantages. The invention will now be described in further detail with reference to the figures. Attached Figure Description

[0077] The above and other features of the present invention will become more apparent from the detailed description of the embodiments shown in conjunction with the accompanying drawings. In the accompanying drawings, the same reference numerals denote the same or similar elements. Obviously, the drawings described below are merely some embodiments of the present invention. For those skilled in the art, other drawings can be obtained from these drawings without any creative effort. In the drawings:

[0078] Figure 1 This is a flowchart of a multi-objective optimization design method for a multi-parameter balanced flow meter based on a matrix structure.

[0079] Figure 2 This is a 3D model illustration of a balanced flow meter orifice plate.

[0080] Figure 3 A schematic diagram of the installation structure for a balanced flow meter assembly.

[0081] The markings in the diagram are: 1. Raised face weld neck steel pipe flange, 2. Concave face weld neck steel pipe flange, 3. Balanced flow meter orifice plate, 4. Graphite gasket.

[0082] Figure 4 This is an example of the geometry generation for a partially selected combination of parameters for an orifice plate. Detailed Implementation

[0083] The embodiments of the present invention will be described in detail below with reference to the accompanying drawings. However, the present invention can be implemented in many different ways as defined and covered below.

[0084] The multi-objective optimization design method for a multi-parameter balanced flow meter based on a matrix structure in this embodiment includes the following steps:

[0085] S100. Construct the initialization parameter variable matrix, which uses a variable concentric structure with up to 5 layers and sets the corresponding number of layers according to different working conditions. From the inside out, a maximum of five concentric concentric layers can be set: m, n, p, q, and r. Their construction follows a recursive principle: the first concentric structure contains only m layers; the second concentric structure consists of m and n layers; the third concentric structure consists of m, n, and p layers; the fourth concentric structure consists of m, n, p, and q layers; and the fifth concentric structure includes all layers from m to r. The concentric diameter parameters are D... m D n D p D q D r A certain number of cylindrical holes are evenly distributed on each layer, with the quantity parameter N. m N n N p N q N r The diameter parameters of the holes in each layer are d.m d n d p d q d r ;

[0086] The S200 parameter variable matrix is ​​output to the balanced flowmeter calculation module. Using the received geometric parameters, a corresponding STL file is generated and exported to complete subsequent CFD mesh generation and numerical calculation analysis. The CFD results are output, and the two target physical field functions—fluid flow velocity uniformity within the pipe and permanent pressure loss before and after the orifice—are calculated.

[0087] S300: Set up a multi-objective, multi-parameter optimizer to control the multi-parameter variables to find optimal combinations under inequality constraints and threshold constraints, and update the parameter variables in a loop to generate an optimized orifice plate structure, thereby achieving the goals of reducing permanent pressure loss before and after the orifice plate and improving the uniformity of flow velocity in the flow channel.

[0088] S400, Configure the balanced flow meter design module and input the optimal orifice plate structure. The instrument coefficient is used to establish a general correlation between the Reynolds number Re and the aperture ratio β:

[0089] Input the initial instrument coefficients and perform CFD calculations. Based on the calculation results, perform nonlinear regression to obtain... The instrument coefficient values ​​are calculated and a secondary CFD is performed. An empirical correlation between the outflow coefficient and the Reynolds number and orifice ratio is established, and the instrument coefficient is output.

[0090] Specifically, step S100 sets an initialization parameter variable matrix, which uses a variable concentric structure with up to 5 layers and sets the corresponding number of layers according to different working conditions. From the inside out, a maximum of five concentric concentric layers can be set: m, n, p, q, and r. Their construction follows a recursive principle: the first concentric structure contains only m layers; the second concentric structure consists of m and n layers; the third concentric structure consists of m, n, and p layers; the fourth concentric structure consists of m, n, p, and q layers; and the fifth concentric structure includes all layers from m to r. The concentric diameter parameters are D... m D n D p D q D r A certain number of cylindrical holes are evenly distributed on each layer, with the quantity parameter N. m N n N p N q N r The diameter parameters of the holes in each layer are d. m d n d p d qd r .

[0091] When the process is started for the first time, the matrix reads the initial values ​​set in the file and assigns them to each parameter variable. In subsequent optimization calculations, it receives parameter values ​​that are continuously updated iteratively.

[0092] The matrix parameter values ​​are then passed to the geometry in S200, generating the main cylindrical plate and multiple small cylinders. The coordinates of the small cylinders are generated based on the parameters, and Boolean difference operations are used to subtract the corresponding volume from the positions of the small cylinders, thus machining specific holes in the main cylindrical plate and forming an orifice plate structure STL file. Boolean operations are used to extract the fluid region outside the orifice plate, forming a physical flow domain that matches the actual flow. This flow domain is then meshed and CFD calculated to obtain two target physical field functions: the uniformity of fluid flow velocity within the pipe and the permanent pressure loss before and after the orifice plate.

[0093] In step S300, constraints are imposed on the parameter matrices of the defined five-layer aperture array, including the concentric circle radius, aperture diameter, and aperture number. A multi-objective optimization algorithm performs global optimization within this constraint space and feeds back the optimized parameter values ​​of each generation to the parameter matrix of S100, thereby driving the geometry generation and CFD simulation cycle until convergence to obtain the Pareto optimal solution set.

[0094] Subsequently, in step S400, the optimal parameter configuration is selected from the Pareto front based on actual working conditions, and the geometry is regenerated and CFD verification calculations are performed accordingly. The instrument coefficient is used to establish a general correlation between the Reynolds number Re and the aperture ratio β:

[0095] Input the initial instrument coefficients and perform CFD calculations. Based on the calculation results, perform nonlinear regression to obtain the coefficients. The instrument coefficient values ​​are calculated and a secondary CFD is performed. An empirical correlation between the outflow coefficient and the Reynolds number and orifice ratio is established, and the instrument coefficient is output.

[0096] In this embodiment, step S100 specifically includes:

[0097] S101. Construct the initialization parameter variable matrix, that is, adopt a variable concentric structure within a maximum of 5 layers and set the corresponding number of concentric layers according to different working conditions. The maximum number of layers can be set from the inside out as follows: Figure 2 The example shows five concentric circles: m, n, p, q, and r. Their construction follows a recursive principle: the first circle contains only the m-th circle; the second circle consists of m and n circles; the third circle consists of m, n, and p circles; the fourth circle consists of m, n, p, and q circles; and the fifth circle includes all circles from m to r. The diameter parameters of each circle are D. m D n Dp D q D r A certain number of cylindrical holes are evenly distributed on each layer, with the quantity parameter N. m N n N p N q N r The diameter parameters of the holes in each layer are d. m d n d p d q d r The parameter matrix initially acquires the initial parameter variable values, initiating the first optimization iteration.

[0098] S102. In the process of determining the optimal design or optimal deterministic calibration parameter set, the design parameter variables are evaluated for solution quality based on the multi-objective output after each CFD calculation. If the optimal convergence criterion is not met, the parameter variables will be adjusted and replaced. That is to say, the parameter values ​​will be in a dynamic process due to the feedback of spatial optimization combination until the optimal solution is found. During this process, the parameter variable matrix will continuously receive new parameter values ​​and pass them to the balanced flowmeter calculation module to generate geometry for subsequent calculations.

[0099] In this embodiment, step S200 specifically includes:

[0100] S201. The script uses object-oriented modeling to construct the basic geometry. A specific `bfmGenerator` class is defined specifically for generating parameterized cylinders. First, a solid large cylinder representing the basic circular plate is created; its radius and height are determined in the script. The cylinder's center is located at the origin, and the bottom surface uses a custom number of high-segmentation sections to ensure the model's smoothness. Then, the script performs hole calculation and layout. Based on five sets of hole parameters, the starting angles of each set of holes are designed to achieve an alternating arrangement: the first set (set m) starts from 0 degrees; the initial angle of the second set (set n) is offset by half the included angle of the first set of smaller cylinders (360° / (2×N)). m The goal is to ensure that the first group of holes fits precisely into the gap between the first group of small cylinders. Subsequent groups (p, q, r) are formed by adding half the included angle of the previous group, creating a staggered layout similar to a "pitch circle." The angular gap between the small cylinders in the same ring is 360° / n. The center position of the small cylinders is precisely calculated using a polar coordinate algorithm. The final polar angle at the center of the cylinder:

[0101]

[0102]

[0103]

[0104] S202. After generating the coordinates of the small cylinder based on the parameters, the corresponding volume is subtracted from the position of the small cylinder using Boolean difference operations, thereby machining specific holes in the main cylindrical plate to form a perforated plate structure. After Boolean operations, the final three-dimensional solid perforated plate with a complex hole array is obtained and output in STL format. This script can quickly generate a large number of perforated plate models of different specifications through dynamic updates of parameter variables, which can be directly used for CFD mesh generation and calculation.

[0105] S203. Set two target physical field functions: uniformity of fluid flow velocity in the pipeline and permanent pressure loss before and after the orifice plate. The function values ​​are calculated from the CFD physical field results.

[0106] In this embodiment, step S201 specifically includes:

[0107] S2011. Read the design parameter values ​​from the parameter variable matrix, including key design variables such as the distribution diameter, aperture size, and number of holes in the five-layer annular array.

[0108] S2012, based on CADQuery or OCCT functions, defines a specific data structure for bfmGenerator, a parameterized cylinder generator specifically used to create the basic geometric units for flow meter models. The volumes of both the main cylinder and smaller cylinders can be automatically generated using this data structure. This data structure stores the cylinder's geometric parameters, including cylinder coordinates, cylinder radius, cylinder height, and the number of segments on the cylinder's base profile.

[0109] S2013. The center of the bottom surface of the main cylindrical plate is located at the origin of the coordinate system (0, 0, 0), and the cylinder axis is along the Z-axis. The coordinates of the center of the small cylinder (hole) are accurately determined through polar coordinate transformation. For the i-th layer of the hole array (i=1,2,…,5), let its distribution layer diameter be D. i Number of holes N i The initial offset angle is θ 0,i Then the Kth small cylinder (k=0,1..,N) i-1 The angular position of in the polar coordinate system is:

[0110]

[0111] Where the initial offset angle θ 0,i Determined using an indexing staggered strategy:

[0112]

[0113]

[0114] This formula means that, starting from the second layer, the initial angle of each small cylinder is successively increased by half the included angle between the small cylinders in the previous layer. Then, the three-dimensional coordinates of the center of the small cylinder are obtained through polar coordinate-Cartesian coordinate transformation:

[0115]

[0116]

[0117]

[0118] z here i,k =0 indicates that the center of all small cylinders is located on the flowmeter's mid-plane (i.e., the z=0 plane), ensuring that the orifice axis is parallel to the orifice plate thickness direction.

[0119] S2014, The geometric parameters of the cylinder are accepted from the parameter variable matrix, including the concentric circle diameter D. i Number of holes N i The aperture d on each layer i The numerical values ​​are used to generate their respective geometric volumes.

[0120] In this embodiment, step S202 specifically includes:

[0121] S2021. Using Boolean difference operations, all array holes are precisely cut out from the generated solid cylinder. This process involves traversing five layers of hole position data, sequentially "subtracting" the cylinder corresponding to each hole from the main model, ultimately forming a structurally complete flow meter plate with holes. This Boolean operation based on solid modeling ensures the geometric accuracy of the hole edges. After completing the geometric modeling, the system exports the final 3D solid model as a standard STL file.

[0122] S2022. Numerical analysis of the flow field characteristics of a balanced flowmeter is performed through a systematic CFD modeling and solution process. First, a cylindrical computational domain is constructed to fully cover the orifice plate structure. Boolean operations are used to extract the fluid region outside the orifice plate, forming a physical flow domain that matches the actual flow. Based on this flow domain, a high-quality hexahedral-dominated mesh is generated. Through a three-stage strategy of "background cutting - surface adsorption - boundary layer generation," geometric features are accurately captured while progressively denser prismatic meshes are constructed in the wall region to analyze the boundary layer flow.

[0123] S2023. In terms of numerical solution, the finite volume method is used for spatial discretization: the time term uses a steady-state scheme, the gradient term uses Gaussian linear interpolation, the convection term uses a bounded linear upwind scheme with a constraint to balance stability and accuracy, and the Laplace term and surface normal gradient use a modified scheme suitable for non-orthogonal grids to ensure discretization accuracy under complex geometric conditions. Regarding solver configuration, pressure-velocity coupling is implemented using the SIMPLE algorithm, where the pressure Poisson equation is solved efficiently using a geometric algebraic multigrid (GAMG) approach, while the velocity and turbulent transport equations are calculated iteratively using a smooth solver. Iterative stability is enhanced by appropriately setting field relaxation and equation relaxation factors. Relative tolerance is used in the initial stage to accelerate convergence, while absolute tolerance is enabled in the final iteration stage to ensure solution accuracy, achieving a synergistic optimization of computational efficiency and numerical accuracy. Finally, CFD numerical simulations are completed, key physical field data are acquired and output, providing quantitative basis for multi-objective optimization.

[0124] In this embodiment, step S300 specifically includes:

[0125] S301. The key variables included in the parametric design system of the perforated plate structure are: the diameter parameters D of the five concentric rings, the hole diameter d parameter, and the number of holes N arranged on each concentric ring. Considering the characteristics of multi-concentric arrangement, a group of hole diameter variables is defined layer by layer, including the innermost hole diameter d. m The diameter d of the second layer hole n The diameter d of the third layer hole p The diameter d of the fourth layer hole q The fifth layer hole diameter d r Individual parameters are set to ensure that the aperture size of each layer can be controlled independently. The layer diameter parameter, including the diameter D of the first layer, is also set. m The diameter of the second concentric ring, D n The diameter of the third concentric circle, D p The diameter of the fourth concentric circle, D q The fifth concentric circle diameter D r This is used to regulate the radial distribution of each concentric circle. Therefore, linear inequality constraints and threshold constraints are set for multiple parameters. It is required that the center distance between any two adjacent concentric circle holes must be greater than the sum of their radii, i.e., the basic condition must be met.

[0126] For any two adjacent concentric circles i and i+1, let:

[0127] D i : i-th layer diameter, D i+1 : diameter of layer i+1, d i : the diameter of the small holes (diameter of the small cylinders) on the i-th layer, d i+1 If the aperture of the small hole on the i+1 layer is given, then the linear inequality constraint is:

[0128] (i=1, 2, 3, 4)

[0129] Physical meaning:

[0130] Left side : Radial distance between circles distributed on adjacent concentric layers

[0131] right side If the minimum radial spacing required for the overlap of the edges of two concentric holes is not met, the holes in adjacent concentric layers will radially overlap or have tangent edges (this issue is not considered when the number of concentric layers is 1). Additionally, to prevent the hole distribution from exceeding the range of the large cylindrical plate, when the number of concentric layers is ≥2, the length of the sum of the radius of the outermost concentric layer on the plate and the radius of the holes distributed on that layer should be less than the radius of the large cylindrical plate. If the number of concentric layers is 1, the length of the sum of the radius of that concentric layer and the radius of the holes distributed on that layer should also be less than the radius of the large cylindrical plate.

[0132] Therefore, a five-layer structure must simultaneously satisfy five sets of inequality constraints (the number of constraint sets is reduced accordingly for 2-4 layer structures):

[0133]

[0134]

[0135]

[0136]

[0137]

[0138] In addition, add field value constraints: Integer constraint i, It is a positive integer. For discrete integer set variables, It is a continuous variable.

[0139] At the same time, it should be noted that even if the parameters are violated, the orifice geometry can still be generated and CFD calculations can be performed for optimization, but the model is physically unrealizable and will not be considered.

[0140] S302 aims to reduce permanent pressure loss before and after the orifice plate and improve the uniformity of fluid flow velocity within the pipeline. Pressure sampling points are located at a radial distance of 1 pipe diameter upstream and 6 pipe diameter downstream. To evaluate velocity uniformity, the velocity standard deviation at the 6 pipe diameter downstream section is calculated. An iterative optimization loop is designed based on multi-parameter constraints. The algorithm generates a parameter set within the constraint space, drives geometric modeling and automatic CFD calculations, and evaluates the quality of the solution based on multi-objective outputs. If the optimal convergence criterion is not met, the next generation of parameters is updated and generated based on the previous result, and the iteration continues. The loop terminates when the convergence condition is met, outputting the global optimal solution.

[0141] In this embodiment, step S302 specifically includes:

[0142] S3021. During the optimization process, all performance targets must be quantified into numerical values ​​for calculation and optimization. Therefore, the permanent pressure loss is set as the pressure difference between the pressure taps before and after the orifice plate (the upstream pressure tap is set at a distance of 1D from the upstream end face of the orifice plate, and the downstream pressure tap is set at a distance of 6D from the downstream end face of the orifice plate); the flow field velocity uniformity is quantified through the physical field of the pipe section located at 6D from the downstream end face of the orifice plate. By extracting the three-dimensional velocity components u, v, and w of this section, their average value and standard deviation are calculated respectively. The average value of the axial velocity w reflects the mainstream intensity, and the average values ​​of the transverse components u and v characterize the transverse flow characteristics. The standard deviation of the three directional velocities quantitatively describes the uniformity of the velocity distribution; the smaller the value, the more stable the flow field. This statistic directly reflects the rectification effect of the flowmeter on the fluid and is a key indicator for evaluating the equilibrium performance of the porous structure.

[0143] S3022. The MOGA (NLPQL, SNOPT, NSGA-II, etc.) optimization method is used for the optimal design of a multi-orifice balanced flowmeter. By performing a global search in the design space composed of five orifice array parameters, multiple parameter combinations are generated and their values ​​are fed back to the design variables in the geometric parameter variable matrix in S100, continuously approaching the goals of minimizing pressure loss and improving flow field uniformity. Simultaneously, since the final result of multi-objective optimization is a non-dominant Pareto optimal solution, an optimization front reflecting different design trade-offs is formed. This multi-solution set characteristic allows designers to flexibly weigh performance indicators and select the most suitable structural parameter configuration according to actual application requirements.

[0144] In this embodiment, step S400 specifically includes:

[0145] S401. Construct the balanced flow meter design module, input the optimal orifice plate structure, and set... The instrument coefficient is used to establish a general correlation between the Reynolds number Re and the aperture ratio β:

[0146] It can degenerate into a correlation similar to that of the ISA1932 nozzle:

[0147] ;

[0148] S402. Input the initial instrument coefficients, reconstruct the geometry, and perform CFD calculations. Establish a relationship model between the geometric physical properties β and Reynolds number Re and the outflow coefficient C. Based on the CFD calculation results corresponding to the optimal solution, the program performs nonlinear least squares optimization using the Trust-Region Reflective algorithm with boundary constraints, searching for the optimal solution of the empirical correlation coefficient of the outflow coefficient within the set feasible region of parameters. Multiple numerical constraints are added during the calculation process: threshold protection is set for β when it is close to zero to avoid abnormal exponentiation, division by zero error is prevented when taking the reciprocal of Re, and large values ​​are truncated to avoid floating-point overflow. The program systematically evaluates the regression quality. Calculate the coefficient of determination R. 2 The model explains a proportion of variance, outputs the root mean square error (RMSE) to quantify prediction accuracy, generates a scatter plot comparing predicted and actual values ​​to demonstrate the fit, and plots the residual distribution to verify the rationality of the model assumptions. Finally, the optimized parameters, statistical indicators, and prediction results are saved to a file. This allows for the generation of outflow coefficients that are only related to the β value and Reynolds number in subsequent calculations. Based on the calculation results, a nonlinear regression is performed to obtain the instrument coefficient. The value is then used for secondary CFD calculations.

[0149] S403. Based on the results of the second-order CFD calculation, establish an empirical correlation between the outflow coefficient and the Reynolds number and the aperture ratio, and output the core algorithm of the instrument coefficient. The core algorithm is written into the processing unit of the flow meter, and the instrument coefficient is output in real time during actual measurement.

Claims

1. A multi-objective optimization design method for a multi-parameter balanced flowmeter based on a matrix structure, characterized in that, Includes the following steps: S100. Construct the initialization parameter variable matrix using a multi-layered structure. The parameter variable matrix is ​​constructed from the number of layers i, the diameter of the layers D, the number of holes N in each layer and the diameter of the holes d. S200, the parameter variable matrix is ​​output to the balanced flow meter calculation module, the corresponding STL file is generated by parameterization, and the subsequent CFD mesh generation and numerical calculation analysis are completed by exporting; the CFD results are output and the two target physical field functions of flow velocity uniformity in the pipe and permanent pressure loss before and after the orifice are calculated. S300: Set up a multi-objective, multi-parameter optimizer to control the multi-parameter variables to find optimal combinations under inequality constraints and threshold constraints, and update the parameter variables in a loop to generate an optimized orifice plate structure, thereby achieving the goals of reducing permanent pressure loss before and after the orifice plate and improving the uniformity of flow velocity in the flow channel. S400: Set up the balanced flow meter design module, receive the optimal solution of the orifice plate structure from the calculation module, construct the outflow coefficient correlation, input the initial instrument coefficient for CFD calculation, complete the nonlinear regression based on the calculation results to obtain the coefficient value and perform a second CFD calculation; establish the empirical correlation of the outflow coefficient with respect to Reynolds number and orifice ratio and output the instrument coefficient.

2. The multi-objective optimization design method for a multi-parameter balanced flowmeter based on a matrix structure according to claim 1, characterized in that, In step S100, the corresponding number of concentric circles is set according to different working conditions. From the inside out, a maximum of five concentric circles are set: m, n, p, q, and r. The diameter parameters of the concentric circles are D. m D n D p D q D r Cylindrical holes are evenly distributed on each layer, with the number parameter N. m N n N p N q N r The diameter parameters of the holes in each layer are d. m d n d p d q d r .

3. The multi-objective optimization design method for a multi-parameter balanced flowmeter based on a matrix structure according to claim 2, characterized in that, Step S200 includes the following sub-steps: S201. After receiving the parameter variable matrix data, create a large cylindrical plate and several small cylinders; the position of the large cylindrical plate is determined, and the small cylinders perform hole position calculation and layout. Based on the five sets of hole parameters, the starting angle of each set of holes is designed to achieve an alternating arrangement: The first group starts at 0 degrees; the initial angle of the second group of small cylinders is offset by half of the included angle of the first group, and subsequent groups are successively increased by half of the included angle of the previous group. The angular gap between small cylinders in the same concentric circle is 360° / n; the center position of the small cylinders is accurately calculated using a polar coordinate algorithm. The final polar angle at the center of the cylinder: ； ； ； S202. After generating the coordinates of the small cylinder based on the parameters, the corresponding volume is subtracted from the position of the small cylinder through Boolean difference set operation, thereby processing holes in the main cylindrical plate to form a three-dimensional solid hole plate structure, which is output in STL format. S203 and STL files are used for CFD mesh generation and numerical analysis, outputting calculation results and calculating two objective physical field functions: the uniformity of fluid flow velocity in the pipe and the permanent pressure loss before and after the orifice.

4. The multi-objective optimization design method for a multi-parameter balanced flowmeter based on a matrix structure according to claim 3, characterized in that, In step S203, the pressure tapping method is radial tapping, flange tapping, or corner tapping.

5. The multi-objective optimization design method for a multi-parameter balanced flowmeter based on a matrix structure according to claim 1, characterized in that, Step S300 includes the following sub-steps: S301. Set constraints on the key variables included in the parametric design of the perforated plate structure: number of layers i, layer diameter D, number of holes N in each layer, and hole diameter d; For setting inequality constraints and threshold constraints for multiple parameters, the center distance between any two adjacent concentric holes must be greater than the sum of their radii, i.e., the basic condition must be met. For any adjacent concentric layers i and i+1, the linear inequality constraint is: （i=1,2,3,4）； Among them, D i Let D be the diameter of layer i. i+1 Let d be the diameter of the i+1th layer. i Let d be the diameter of the cylindrical hole on layer i. i+1 Let be the diameter of the cylindrical hole on the i+1 layer; The radial distance between the circles distributed on adjacent concentric circles. The minimum radial spacing required for the edges of the two concentric holes to overlap; If the number of concentric circles is 1, then the radius of the concentric circle plus the radius of the holes distributed on the concentric circle should be less than the radius of the large cylindrical plate. When the number of concentric circles is greater than or equal to 2, the length of the outermost concentric circle on the perforated plate plus the radius of the holes distributed on that concentric circle should be less than the radius of the large cylindrical plate. And there are: ； ； ； ； ； Add a domain value constraint: ; Among them, i, It is a positive integer. For discrete integer set variables, It is a continuous variable; S302. Based on the multi-parameter constraint definition design space, the optimizer starts an iterative optimization loop and returns the combined parameters to the parameter variable matrix; the algorithm generates a parameter set in the constraint space, returns the calculation results, and evaluates the quality of the solution based on the multi-objective output; if the convergence criterion is not met, the next generation of parameters is generated iteratively based on the result of this generation, and the iteration continues; when the convergence condition is met, the algorithm terminates and outputs the global optimal solution.

6. The multi-objective optimization design method for a multi-parameter balanced flowmeter based on a matrix structure according to claim 5, characterized in that, In step 301, the five-layer structure must simultaneously satisfy five sets of inequality constraints: ； ； ； ； 。 7. The multi-objective optimization design method for a multi-parameter balanced flowmeter based on a matrix structure according to claim 6, characterized in that, Step S400 includes the following sub-steps: S401. Obtain the optimal solution and determine the geometry of the orifice plate, including the orifice distribution and aperture ratio β on the orifice plate; set up Instrument coefficients, among which, Establish a general correlation between the Reynolds number Re and the aperture ratio β: It degenerates into the following relation: ； S402. Input the initial instrument coefficients of the above correlation into the design module to perform CFD calculation and analysis of the outflow coefficients under different Reynolds number Re ranges; based on the calculation results, complete the regression calculation of the instrument coefficients, and obtain the instrument coefficient values ​​after evaluating the quality of the regression. Substitute the instrument coefficient value into the degraded correlation for a second calculation to obtain the final empirical correlation of the outflow coefficient with respect to the Reynolds number Re and the aperture ratio β. S403. Write the empirical correlation formula into the flow meter's processing unit and output the instrument coefficient in real time during actual measurement.

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