Complex pipeline system layout optimization method based on multi-material interpolation model

Abstract

The invention relates to the technical field of pipeline layout, and discloses a complex pipeline system layout optimization method based on a multi-material interpolation model. The problems that in the prior art, multi-pipeline independent communication cannot be met, and the multi-inlet-outlet matching relation is difficult to specify can be solved to a certain extent. The method comprises the following steps: acquiring geometric information and pipeline information of a design domain, carrying out finite element mesh generation on the design domain, setting a pseudo-density variable field, filtering the pseudo-density variable field through a Helmholtz equation, carrying out projection through a black viezeldet equation, and establishing an interpolation model; the method comprises the following steps: setting laminar flow physics fields, giving inlet and outlet boundary conditions, respectively solving fluid control equations of the laminar flow physics fields, calculating to obtain fluid flow dissipated energy, fluid volume fraction and outlet flow variance in each pipeline, establishing a complex pipeline network system layout optimization problem model, and selecting a mathematical programming algorithm to carry out optimization design. And the optimized pipeline system layout is obtained.

Description

Technical Field

[0001] This invention relates to the field of pipeline layout technology, and relates to, but is not limited to, a method for optimizing the layout of complex pipeline systems based on a multi-material interpolation model. Background Technology

[0002] Piping systems are critical functional structures in aerospace vehicles. Fluid pipelines (such as fuel lines and lubricating oil lines) are used to transport liquid working fluids to designated locations (such as engine combustion chambers and hydraulic actuators) to perform tasks such as power supply and actuation control. Because aircraft need to perform complex and multi-tasking tasks, different liquid working fluids (such as fuel, coolant, and hydraulic oil) need to be transported separately through independent piping systems, resulting in piping systems exhibiting two main characteristics: The pipeline topology features complex connection relationships, such as one inlet and one outlet, one inlet and multiple outlets, multiple inlets and one outlet, and multiple inlets and multiple outlets.

[0003] Different pipelines must strictly maintain independent paths and isolation between fluid media to avoid functional failures caused by pipeline interference.

[0004] Traditional piping system design methods are based on empirical layout and segmented assembly processes. Due to the limitations of manufacturing processes on the manufacturability of complex geometries, they often adopt conservative straight / broken-line path planning, resulting in large redundant weight, high flow resistance loss, and low space utilization of the piping system, making it difficult to meet the requirements of lightweight and high performance of aircraft.

[0005] The development of additive manufacturing technology has improved the forming capability of complex piping systems, expanded their design space, and allowed the use of advanced topology optimization methods for piping layout design. However, existing flow channel layout optimization techniques based on density variable methods have the following key drawbacks: This approach cannot meet the requirement of independent connectivity for multiple pipelines. Existing methods use a single density variable field to characterize the distribution of the fluid and solid domains, and generate connected flow channels through optimization algorithms. However, this method can only generate a single connected flow channel and cannot distinguish the independent path requirements of different pipelines.

[0006] It is difficult to specify multiple import / export matching relationships.

[0007] Existing methods treat all inlets and outlets as global boundary conditions and drive the optimization process through a single flow field, which makes it impossible to specify directional connectivity between specific inlets and outlets. Summary of the Invention

[0008] In view of this, in order to solve the problems that the existing technology cannot meet the independent connection of multiple pipelines and the difficulty in specifying the matching relationship of multiple inlet and outlet, this application provides a layout optimization method for complex pipeline systems based on a multi-material interpolation model.

[0009] The specific technical solutions of this invention are as follows: The embodiment of the present application provides a complex pipeline system layout optimization method based on a multi-material interpolation model, comprising: obtaining geometric information and pipeline information of a design domain, and performing finite element mesh division on the design domain, wherein the pipeline information comprises a number of independent pipelines; setting a same number of pseudo-density variable fields as the number of independent pipelines, for defining the distribution of multiple fluid media and solid materials; filtering the pseudo-density variable fields through Helmholtz equation to obtain a filtering field; projecting the filtering field through Hodge equation to obtain a projection field; based on the multi-material interpolation model, combining the filtering field and the projection field to establish interpolation models of element flow resistance coefficients and element fluid volume ratios respectively; setting a same number of laminar flow physical fields as the number of independent pipelines, respectively solving fluid control equations of each laminar flow physical field, and calculating fluid flow dissipation energy, fluid volume ratios and outlet flow variances in each pipeline according to the interpolation models of the element flow resistance coefficients and the element fluid volume ratios respectively; taking the pseudo-density variable fields as design variables, taking the weighted results of the fluid flow dissipation energy in the pipelines as an objective function, constructing constraint functions by using the fluid volume ratios, the outlet flow variances and the upper and lower limits of the design variables, and establishing a complex pipeline network system layout optimization problem model; calculating the sensitivity of the objective function and the constraint functions with respect to the design variables, selecting a mathematical programming algorithm for optimization design, and obtaining an optimized pipeline system layout.

[0010] In a possible implementation manner, the number of independent pipelines is defined as n, the number of inlets corresponding to the i-th pipeline is m i , and the number of outlets is k i .

[0011] In a possible implementation manner, the number of pseudo-density variable fields is n, and the pseudo-density variable field is represented as γ i (i=1, 2,···, n), and any one element in the design domain is characterized by a vector (γ1, γ2,···,γ n ) representing a physical state, when one component in the vector takes a value of 1 and other components all take a value of 0, the vector represents the fluid medium in the i-th pipeline; and other value conditions represent solid materials.

[0012] In a possible implementation manner, the Helmholtz equation is represented as: ; wherein, is the filtering field, r h is a filtering radius.

[0013] In one possible implementation, the Heaviside equation is expressed as: ; in, Let β be the projection field, β be the sharpening parameter used to control the sharpness of the projection, and η be the threshold parameter that determines the boundary point of binarization.

[0014] In one possible implementation, the unit flow resistance coefficient α i The resistance of the element to the fluid in the i-th pipe is characterized by its interpolation model, which is expressed as: ; Where, α max It is the maximum flow resistance coefficient, characterizing the resistance coefficient of the solid region to flow, p α The penalty coefficient for the flow resistance interpolation model is a positive integer, and π represents the multiplication sign, which represents all... When performing a series of multiplications, k≠i.

[0015] In one possible implementation, the unit fluid volume percentage v i The volume fraction of the i-th fluid within the cell is represented by the interpolation model as follows: ; Where, p v The penalty coefficient for the fluid volume fraction interpolation model is a positive integer, and π represents the multiplication sign, which means that all fluid volumes are multiplied together. When performing a series of multiplications, k≠i.

[0016] In one possible implementation, the number of laminar physical fields is n, and the fluid control equation for the i-th laminar physical field is expressed as: ; Where, ρ i It is the density of the fluid in the i-th pipe, μ i U is the dynamic viscosity coefficient of the fluid in the i-th pipe. i and p i Let m be the flow velocity and pressure of the fluid in the i-th pipe, respectively. i The entry points are respectively ,but k of the i-th pipe i The exports are respectively ,but , yes At a given flow rate, yes The stress at the point is n, where n is the unit normal vector of the boundary.

[0017] In one possible implementation, the energy dissipation of fluid flow, the fluid volume fraction, and the variance of the outlet flow rate are calculated for each of the n pipelines, including: The energy dissipated by fluid flow in the i-th pipe is Ψ. i The calculation formula is: ; The fluid volume ratio V in the i-th pipeline i The calculation formula is: ; The i-th pipe k i The formula for calculating the variance of flow at each outlet is: ; Among them, Q i,j Let i be the flow rate at the j-th outlet of the i-th pipe. It is Q i,j The average value of Q i,j The calculation formula is: .

[0018] In one possible implementation, the model for the layout optimization problem of the complex pipeline network system is expressed as: Where Ψ is the objective function, w i Ψ is the weighting coefficient for the energy dissipation of fluid flow in the i-th pipeline. i Let i be the energy dissipated by the fluid flow in the i-th pipe. This represents the upper limit of the fluid volume fraction in the i-th pipeline. Let be the upper limit constraint on the variance of the outlet flow rate of the i-th pipeline. and These are design variables The upper and lower limits.

[0019] The beneficial effects of the technical solutions provided by the embodiments of the present invention include at least the following: This application provides a method for optimizing the layout of complex pipeline systems based on a multi-material interpolation model. It uses multiple pseudo-density variable fields to characterize the fluid medium distribution within different pipelines, solving the pipeline cross-interference problem caused by traditional single-density field methods. This ensures the physical isolation of fluid media within different pipelines. Furthermore, based on the multi-material interpolation model, it achieves a spatially continuous mapping between the flow resistance coefficient and fluid volume fraction of each pipeline, enabling independent optimization of the flow channel morphology for different fluid characteristics. Additionally, by independently setting inlet / outlet boundary conditions for each pipeline and coupling multiple fluid control equations for solution, the optimization results satisfy a preset inlet / outlet matching relationship, overcoming the challenge of achieving directional flow channel connections that traditional methods cannot address. Attached Figure Description

[0020] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort, wherein: Figure 1 A flowchart illustrating a method for optimizing the layout of complex pipeline systems based on a multi-material interpolation model, provided in an embodiment of the present invention; Figure 2 The geometric model and fluid inlet / outlet diagram provided for embodiments of the present invention; Figure 3 This is a schematic diagram of the pipeline layout optimization results provided in an embodiment of the present invention. Detailed Implementation

[0021] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. The following embodiments are used to illustrate the present invention, but are not intended to limit the scope of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0022] In the following description, references are made to “some embodiments,” which describe a subset of all possible embodiments. However, it is understood that “some embodiments” may be the same subset or different subsets of all possible embodiments and may be combined with each other without conflict.

[0023] It should be noted that the terms "first, second, and third" used in the embodiments of the present invention are only used to distinguish similar objects and do not represent a specific ordering of objects. It is understood that "first, second, and third" can be interchanged in a specific order or sequence where permitted, so that the embodiments of the present invention described herein can be implemented in an order other than that illustrated or described herein.

[0024] It will be understood by those skilled in the art that, unless otherwise defined, all terms used herein (including technical and scientific terms) have the same meaning as commonly understood by one of ordinary skill in the art to which these embodiments of the invention pertain. It should also be understood that terms such as those defined in general dictionaries should be understood to have the same meaning as in the context of the prior art and should not be interpreted in an idealized or overly formal sense unless specifically defined as herein.

[0025] Figure 1 This is a flowchart illustrating a method for optimizing the layout of complex pipeline systems based on a multi-material interpolation model, as provided in an embodiment of the present invention. Figure 1 As shown, the method may include the following steps: Step 100: Obtain the geometric information and pipeline information of the design domain, and perform finite element meshing on the design domain. The pipeline information includes the number of independent pipelines, the inlet and outlet positions of the pipelines, and their matching relationships.

[0026] In one embodiment, the geometric information of the design domain includes its geometric dimensions and shape. The design domain is then meshed using finite element methods based on this geometric information. The number of independent pipes is defined as n, and the number of inlets corresponding to the i-th pipe is m. i The export quantity is k i .

[0027] It is possible to define the number of independent pipelines n and the number of inlets and outlets m. i and k i The matching relationship overcomes the shortcomings of traditional methods that cannot distinguish the independent paths of multiple pipelines. This embodiment lays the foundation for subsequent multi-physics field decoupling, ensuring that each pipeline can be optimized independently and avoiding system function failure caused by cross interference.

[0028] Step 200: Set up a pseudo-density variable field with the same number of independent pipelines to define the distribution of various fluid media and solid materials.

[0029] In one embodiment, by setting n pseudo-density variable fields γ i (i=1, 2,···, n), used to define the distribution of n types of fluid media and solid materials.

[0030] In this context, any element within the design domain is represented by a vector (γ1, γ2, ..., γ...). n To characterize its physical state, when component γ i When 1 is equal to 0 and all other components are 0, it represents the fluid medium in the i-th pipe; the rest represent solid materials.

[0031] It can achieve physical isolation between multi-pipe media and solid materials. Compared with the traditional single density field, this encoding method explicitly distinguishes n kinds of fluid media, ensuring the path independence of different pipelines during the optimization process and avoiding the "pseudo-connectivity" problem caused by the shared density field in the traditional method.

[0032] Step 300: Filter the pseudo-density variable field using the Helmholtz equation to obtain the filtered field.

[0033] In one embodiment, by analyzing n pseudo-density variable fields γ iThe Helmholtz equation is used for filtration to obtain the filtration field. .

[0034] The Helmholtz equation is expressed as: ; Where, r h Let r be the filtration radius. h The design needs to consider the geometric characteristics of the domain, the size of the mesh, and the physical properties of the fluid.

[0035] Helmholtz filtering: via r h Local smoothing eliminates mesh dependency while preserving the 1mm×1mm local geometric features at the inlet and outlet, balancing computational efficiency and structural resolution.

[0036] Step 400: Project the filtered field using the Heaviside equation to obtain the projected field.

[0037] In one embodiment, the projected field is obtained by projecting the filter field using the Heaviside equations. field.

[0038] The Heaviside equation is expressed as: ; Where β is the sharpening parameter, used to control the sharpness of the projection; η is the threshold parameter, which determines the boundary point of binarization.

[0039] Blackside projection: A progressive sharpening strategy with doubling β parameter avoids getting trapped in local minima in the early optimization stage, and finally obtains clear binarized pipe boundaries to meet the geometric accuracy requirements of additive manufacturing.

[0040] Step 500: Based on the multi-material interpolation model, establish an interpolation model for the unit flow resistance coefficient and the unit fluid volume ratio by combining the filter field and the projection field.

[0041] In one embodiment, the unit flow resistance coefficient α i The resistance of the element to the fluid in the i-th pipe is characterized by its interpolation model: .

[0042] Where, α max It is the maximum flow resistance coefficient, characterizing the resistance coefficient of the solid region to flow, p α The penalty coefficient for the flow resistance interpolation model is usually a positive integer, and π represents the multiplication sign, which means that all... When performing a series of multiplications, k≠i.

[0043] This interpolation model shows that a unit is the i-th pipe if and only if ( When ), its flow resistance coefficient satisfies That is, the i-th fluid resistance is 0 and it can flow, while the j-th fluid resistance is very large and it is not easy to flow.

[0044] Unit fluid volume ratio v i The volume fraction of the i-th fluid within the cell is represented by the interpolation model: .

[0045] Where, p v The penalty coefficient for the fluid volume fraction interpolation model is usually a positive integer, and π represents the multiplication sign, which means that all fluid volumes are included in the multiplication model. When performing a series of multiplications, k≠i.

[0046] The interpolation model shows that the fluid volume ratio of a unit satisfies the following condition if and only if the unit is of the i-th fluid. .

[0047] The interpolation model for the unit flow resistance coefficient provided in some embodiments of this application ensures that non-target pipeline units generate great resistance to the fluid through a solid penalty mechanism of the maximum flow resistance coefficient, forcing the flow channel to be generated along the target path, thus solving the defect of traditional methods that cannot specify the inlet and outlet matching relationship.

[0048] The fluid volume fraction interpolation model provided in some embodiments of this application explicitly quantifies the volume fraction of the i-th fluid in the cell, providing a differentiable physical basis for subsequent constraints and avoiding system performance deviations caused by volume errors.

[0049] Step 600: Set up a laminar flow physical field with the same number of independent pipelines, give the inlet and outlet boundary conditions, and solve the fluid control equations for each laminar flow physical field. Calculate the fluid flow dissipation energy, fluid volume fraction, and outlet flow variance in each pipeline.

[0050] In one embodiment, firstly, by setting n laminar physical fields and giving inlet and outlet boundary conditions respectively, the fluid control equations are solved. The fluid control equation for the i-th laminar physical field is: .

[0051] Where, ρ i It is the density of the fluid in the i-th pipe, μ i U is the dynamic viscosity coefficient of the fluid in the i-th pipe. i and p i and represent the flow rate and pressure of the fluid in the i-th pipe, respectively.

[0052] m of the i-th pipe i One entry point is ,but .

[0053] k of the i-th pipe i One export is ,but .

[0054] yes At a given flow rate, yes The stress at the point is n, where n is the unit normal vector of the boundary.

[0055] Furthermore, the energy dissipation of fluid flow, fluid volume fraction, and variance of outlet flow rate within the n pipelines are calculated, which are as follows: The energy dissipated by fluid flow in the i-th pipe is Ψ. i The mathematical expression for is; ; The fluid volume ratio V in the i-th pipeline i The mathematical expression is: ; The i-th pipe k i The mathematical expression for the variance of the flow at each outlet is: ; Among them, Q i,j Let i be the flow rate at the j-th outlet of the i-th pipe. It is Q i,j The average value.

[0056] Q i,j The mathematical expression is: .

[0057] Solve independent fluid control equations for each pipeline to decouple the densities ρ of different fluids. i With viscosity μ i The difference overcomes the limitations of the traditional single flow field assumption, and by specifying m i One entry point and k i The directional boundary conditions for each exit ensure that the optimization results strictly meet the preset conditions.

[0058] Step 700: Using the pseudo-density variable field as the design variable, the weighted average of the energy dissipated by the fluid flow in the pipeline as the objective function, and the fluid volume fraction in different pipelines, the variance of the pipeline outlet flow rate, and the upper and lower limits of the design variables as constraint functions, a model for the layout optimization problem of a complex pipeline network system is established.

[0059] In one embodiment, the mathematical expression for the layout optimization problem model of a complex pipeline network system is: Where Ψ is the objective function, wi Ψ is the weighting coefficient for the energy dissipation of fluid flow in the i-th pipeline. i Let i be the energy dissipated by the fluid flow in the i-th pipe. This represents the upper limit of the fluid volume fraction in the i-th pipeline. yes Stress at the point, and These are design variables The upper and lower limits.

[0060] Through weight w i Balancing the performance of multiple pipelines to achieve optimal system-level performance, rather than local optima for a single pipeline, fluid volume ratio. The upper limit is set to prevent a certain pipeline from excessively encroaching on the design domain space, ensuring lightweight structure, constraining the variance of outlet flow, forcing the uniformity of flow across multiple outlets, and avoiding flow imbalance caused by traditional empirical design.

[0061] Step 800: Calculate the sensitivity of the objective function and constraint functions to the design variables, select a mathematical programming algorithm for optimization design, and obtain the optimized pipeline system layout.

[0062] Furthermore, the specific steps include: Step 810: Calculate the sensitivity of the objective function and constraint functions to the design variables; In one embodiment, the discrete adjoint method can be used to calculate the sensitivity of the objective function and constraint functions to the design variables.

[0063] Step 820: Based on the analysis results, select a mathematical programming algorithm that is appropriate for the problem size and characteristics.

[0064] Step 830: Initialize the parameters of the optimization algorithm, including the number of iterations and convergence accuracy.

[0065] Step 840: Then perform optimization iteration, continuously adjusting the value of the pseudo-density variable field through iterative calculation.

[0066] Step 850: During each iteration, check whether the optimization process meets the convergence condition. If it does, stop the optimization; otherwise, continue the iteration.

[0067] Step 860: Using the output of the optimization algorithm, the optimized pipeline system layout is finally obtained, including the geometry and spatial distribution of each pipeline.

[0068] In one embodiment, the mathematical programming algorithm selects the GCMMA algorithm for optimization design, and then continuously adjusts the value of the pseudo-density variable field through iterative optimization to minimize the objective function while satisfying all constraints, thus obtaining the optimized pipeline system layout.

[0069] To verify this application, a pipeline layout optimization design based on given design domain geometry information and pipeline information is used as an example for illustration.

[0070] like Figure 2 As shown, the given design domain has a geometric dimension of 10mm×10mm×5mm. There are 4 independent pipes in the design domain, of which pipe 1 has one inlet and two outlets, and pipes 2, 3 and 4 each have one inlet and one outlet.

[0071] The fluid inlet and outlet positions are fixed, and the inlet and outlet dimensions are 1mm × 1mm.

[0072] The fluid medium is water, and its density is... Dynamic viscosity coefficient The fluid inlet normal velocity is The outlet static pressure is set to The maximum flow resistance coefficient of solid materials is .

[0073] The specific steps are as follows: Step 1: Discretize the design domain into a tetrahedral mesh with a side length of 0.4 mm.

[0074] Step 2: Set up 4 pseudo-density variable fields γ1, γ2, γ3, γ4 to define the distribution of 4 types of fluid media and solid materials.

[0075] In this design domain, any element is represented by a vector (γ1, γ2, γ3, γ4) to characterize its physical state: (1, 0, 0, 0) represents the fluid medium in the first pipe, (0, 1, 0, 0) represents the fluid medium in the second pipe, (0, 0, 1, 0) represents the fluid medium in the third pipe, (0, 0, 0, 1) represents the fluid medium in the fourth pipe, and the remaining combinations represent solid materials.

[0076] Step 3: Filter the pseudo-density variable fields γ1, γ2, γ3, γ4 using the Helmholtz equation to obtain the filtered field. .

[0077] ; Wherein, the filtration radius r h =0.3mm, in this embodiment, the filter radius r h The grid size (close to the minimum requirement) and design domain characteristics (inlet and outlet dimensions) were taken into account.

[0078] Step 4: Project using the Heaviside equation to obtain the projected field. .

[0079] ; The sharpening parameter β is initially set to 4, and doubles every 30 iterations until it reaches 128.

[0080] Step 5: Based on the multi-material interpolation model, establish an interpolation model for the flow resistance coefficient and the volume ratio of the unit fluid.

[0081] The interpolation model for the element flow resistance coefficient is as follows: ; Wherein, the maximum flow resistance coefficient α max =5.05×10 6 .

[0082] The interpolation model for the volume percentage of a single fluid element is as follows: .

[0083] Step 6: Set up 4 laminar flow physical fields, give the inlet and outlet boundary conditions respectively, and solve the fluid control equations.

[0084] The fluid governing equations for the first laminar physical field are: ; The fluid control equations for the second laminar physical field are: ; The fluid control equation for the third laminar physical field is: ; The fluid control equation for the fourth laminar physical field is: .

[0085] Step 7: Calculate the energy dissipation of fluid flow, fluid volume fraction, and variance of outlet flow rate in each of the four pipelines.

[0086] The energy dissipation of fluid flow in the four pipelines is calculated as follows: ; The fluid volume fractions in the four pipelines are calculated as follows: ; The variance of the flow rate at the first pipe outlet is calculated as follows: .

[0087] Step 8: Using the pseudo-density variable fields γ1, γ2, γ3, and γ4 as design variables, the weighted sum of the energy dissipated by the fluid flow in the pipeline as the objective function, and the fluid volume fraction in different pipelines, the variance of the pipeline outlet flow rate, and the upper and lower limits of the design variables as constraint functions, a model for the layout optimization problem of a complex pipeline network system is established.

[0088] The mathematical expression for the optimization problem model is: .

[0089] Step 9: Calculate the sensitivity of the objective function and constraint functions to the design variables, select the GCMMA algorithm for optimization design, and obtain the following results: Figure 3 The optimized piping system layout is shown.

[0090] It should be understood that the phrase "one embodiment" or "an embodiment" throughout the specification means that a specific feature, structure, or characteristic related to the embodiment is included in at least one embodiment of the invention. Therefore, "in one embodiment" or "in an embodiment" appearing throughout the specification does not necessarily refer to the same embodiment. Furthermore, these specific features, structures, or characteristics can be combined in any suitable manner in one or more embodiments. It should be understood that in the various embodiments of the invention, the sequence numbers of the above-described processes do not imply a sequential order of execution; the execution order of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiments of the invention. The sequence numbers of the above-described embodiments of the invention are merely descriptive and do not represent the superiority or inferiority of the embodiments.

[0091] It should be noted that, in this document, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Unless otherwise specified, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes that element.

[0092] In the several embodiments provided by this invention, it should be understood that the disclosed methods can be implemented in other ways. The methods disclosed in the several method embodiments provided by this invention can be arbitrarily combined without conflict to obtain new method embodiments. The features disclosed in the several method embodiments provided by this invention can be arbitrarily combined without conflict to obtain new method embodiments.

[0093] The above description is merely an embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A method for optimizing the layout of complex pipeline systems based on a multi-material interpolation model, characterized in that, include: Obtain the geometric and piping information of the design domain, and perform finite element meshing on the design domain. The piping information includes the number of independent pipes. Set up pseudo-density variable fields with the same number of independent pipelines to define the distribution of various fluid media and solid materials; The pseudo-density variable field is filtered using the Helmholtz equation to obtain the filtered field; The filtered field is projected using the Heaviside equation to obtain the projected field; Based on the multi-material interpolation model, interpolation models for the unit flow resistance coefficient and the unit fluid volume ratio are established by combining the filter field and the projection field. Set up laminar flow physical fields with the same number of independent pipelines, solve the fluid control equations for each laminar flow physical field, and calculate the fluid flow dissipation energy, fluid volume fraction, and outlet flow variance in each pipeline based on the interpolation models of the unit flow resistance coefficient and the unit fluid volume ratio. Using the pseudo-density variable field as the design variable, the weighted result of the energy dissipated by the fluid flow in the pipeline as the objective function, and the fluid volume fraction in different pipelines, the variance of the pipeline outlet flow rate, and the upper and lower limits of the design variables as constraint functions, a model for the layout optimization problem of complex pipeline network system is established. Calculate the sensitivity of the objective function and constraint functions to the design variables, select a mathematical programming algorithm for optimization design, and obtain the optimized pipeline system layout.

2. The method for optimizing the layout of complex pipeline systems based on a multi-material interpolation model according to claim 1, characterized in that, Let n be the number of independent pipelines, and m be the number of inlets corresponding to the i-th pipeline. i The export quantity is k i .

3. The method for optimizing the layout of complex pipeline systems based on a multi-material interpolation model according to claim 2, characterized in that, The number of pseudo-density variable fields is n, and the pseudo-density variable field is represented as γ. i (i=1, 2, ..., n), any element within the design domain is represented by the vector (γ1, γ2, ..., γ). n The vector represents the physical state. When one component of the vector is 1 and the other components are 0, the vector represents the fluid medium in the i-th pipe; the other values ​​represent solid materials.

4. The method for optimizing the layout of complex pipeline systems based on a multi-material interpolation model according to claim 3, characterized in that, The Helmholtz equation is expressed as: ； in, For the filtering field, r h The filter radius is [value].

5. The method for optimizing the layout of complex pipeline systems based on a multi-material interpolation model according to claim 4, characterized in that, The Heaviside equation is expressed as: ； in, Let β be the projection field, β be the sharpening parameter used to control the sharpness of the projection, and η be the threshold parameter that determines the boundary point of binarization.

6. The method for optimizing the layout of complex pipeline systems based on a multi-material interpolation model according to claim 5, characterized in that, Unit flow resistance coefficient α i The resistance of the element to the fluid in the i-th pipe is characterized by its interpolation model, which is expressed as: ； Where, α max It is the maximum flow resistance coefficient, characterizing the resistance coefficient of the solid region to flow, p α The penalty coefficient for the flow resistance interpolation model is a positive integer, and π represents the multiplication sign, which represents all... When performing a series of multiplications, k≠i.

7. The method for optimizing the layout of complex pipeline systems based on a multi-material interpolation model according to claim 6, characterized in that, Unit fluid volume ratio v i The volume fraction of the i-th fluid within the cell is represented by the interpolation model as follows: ； Where, p v The penalty coefficient for the fluid volume fraction interpolation model is a positive integer, and π represents the multiplication sign, which means that all fluid volumes are multiplied together. When performing a series of multiplications, k≠i.

8. The method for optimizing the layout of complex pipeline systems based on a multi-material interpolation model according to claim 7, characterized in that, The number of laminar physical fields is n, and the fluid control equation for the i-th laminar physical field is expressed as: ； Where, ρ i It is the density of the fluid in the i-th pipe, μ i U is the dynamic viscosity coefficient of the fluid in the i-th pipe. i and p i Let m be the flow velocity and pressure of the fluid in the i-th pipe, respectively. i The entry points are respectively ,but k of the i-th pipe i The exports are respectively ,but , yes At a given flow rate, yes The stress at the point is n, where n is the unit normal vector of the boundary.

9. The method for optimizing the layout of complex pipeline systems based on a multi-material interpolation model according to claim 8, characterized in that, Calculate the energy dissipation, fluid volume fraction, and outlet flow variance for each of the n pipelines, including: The energy dissipated by fluid flow in the i-th pipe is Ψ. i The calculation formula is: ； The fluid volume ratio V in the i-th pipeline i The calculation formula is: ； The i-th pipe k i The formula for calculating the variance of flow at each outlet is: ； Among them, Q i,j Let i be the flow rate at the j-th outlet of the i-th pipe. It is Q i,j The average value of Q i,j The calculation formula is: 。 10. The method for optimizing the layout of complex pipeline systems based on a multi-material interpolation model according to claim 9, characterized in that, The model for the layout optimization problem of the complex pipeline network system is expressed as follows: Where Ψ is the objective function, w i Ψ is the weighting coefficient for the energy dissipation of fluid flow in the i-th pipeline. i Let i be the energy dissipated by the fluid flow in the i-th pipe. This represents the upper limit of the fluid volume fraction in the i-th pipeline. yes Stress at the point, and These are design variables The upper and lower limits.

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