A fluid simulation method for a semi-welded plate heat exchanger

Abstract

This invention discloses a fluid simulation method for a semi-welded plate heat exchanger, relating to the field of heat exchanger simulation technology. The method includes: obtaining porous medium parameters of a porous medium model using a three-dimensional model of a single-sided medium; meshing the three-dimensional model of the single-sided medium to obtain the meshing result; and applying the porous medium parameters of the porous medium model and the meshing result of the three-dimensional model of the single-sided medium to... k - oh The SST turbulence model is used to perform preliminary flow field calculations, and the preliminary flow field calculation results are obtained. Based on the preliminary flow field calculation results, fitting processing is performed to obtain the fluid simulation results of the semi-welded plate heat exchanger. This invention realizes the prediction of the overall pressure drop on one side of the semi-welded plate heat exchanger, and on this basis, uses a turbulence model to predict the flow of the medium between the plates, which greatly improves the accuracy of the heat exchanger flow field calculation, makes the flow near the plate wall surface closer to the actual state, and has a positive effect on predicting the performance of the heat exchanger.

Description

Technical Field

[0001] This invention relates to the field of heat exchanger simulation technology, and in particular to a fluid simulation method for a semi-welded plate heat exchanger. Background Technology

[0002] To improve energy conditions and living environment for urban and rural residents, centralized heating is developing towards supplying heat to central urban areas via long-distance pipelines, using suburban thermal power plants as heat sources. However, long-distance pipelines present challenges such as complex pipelines, significant elevation changes, and pressure level mismatches with urban pipeline networks. Therefore, pressure-reducing stations are typically required, and heat exchangers are one of the core components of these stations. Currently, the maximum design pressure of detachable plate heat exchangers is 4.0 MPa, which cannot meet the design requirements of some pressure-reducing stations. Therefore, high-pressure semi-welded plate heat exchangers need to be designed.

[0003] However, several technical challenges remain in the field of fluid simulation for plate heat exchangers. Heat exchangers exhibit large overall dimensions and complex structures. The design of novel heat exchangers lacks experimental data. Directly establishing a three-dimensional solid model of the entire unit faces problems such as complex geometric modeling, a large number of meshes, difficulty in improving mesh quality, and high computational resource consumption, making it difficult to perform overall performance simulation and prediction. Furthermore, most methods estimate single-sided pressure drop through local structural simulation, neglecting losses from the medium entering between the plates through corner holes, or rely on experimental testing of performance parameters, which is time-consuming and costly. In addition, porous media models can significantly simplify the details inside the channels, using porous media parameters to describe the flow properties between the plates of semi-welded plate heat exchangers.

[0004] Therefore, there is an urgent need for a fluid simulation method for semi-welded plate heat exchangers to address the shortcomings of existing technologies. Summary of the Invention

[0005] The purpose of this invention is to propose a fluid simulation method for semi-welded plate heat exchangers to solve the problem of predicting pressure drop in single-sided integral semi-welded plate heat exchangers using porous media models, and based on... k - oh The SST model is used to calculate and predict the flow of media between heat exchanger plates.

[0006] To achieve the above objectives, the present invention provides a fluid simulation method for a semi-welded plate heat exchanger, comprising the following steps:

[0007] S1. Using a single-sided three-dimensional medium model, obtain the porous medium parameters of the porous medium model;

[0008] S2. Mesh the single-sided medium three-dimensional model to obtain the meshing result of the single-sided medium three-dimensional model;

[0009] S3. Based on the porous medium parameters of the porous medium model and the mesh generation results of the single-sided medium three-dimensional model...k - oh The SST turbulence model was used to perform preliminary flow field calculations, and the preliminary flow field calculation results were obtained.

[0010] S4. Based on the preliminary flow field calculation results, perform fitting processing to obtain the fluid simulation results of the semi-welded plate AC converter.

[0011] Optionally, S1, using a single-sided three-dimensional medium model, obtain the porous medium parameters of the porous medium model, including:

[0012] Key structural parameters of corrugated plates were obtained through a semi-welded plate heat exchanger.

[0013] Based on the key structural parameters of the corrugated plate, a parametric three-dimensional model of the corrugated plate is established.

[0014] A single-sided medium three-dimensional model is established using the parametric three-dimensional model of the corrugated plate to obtain the porous medium parameters of the porous medium model.

[0015] Optionally, a single-sided medium three-dimensional model is established using the parametric three-dimensional model of the corrugated plate to obtain the porous medium parameters of the porous medium model, including:

[0016] The parametric three-dimensional model of the corrugated plate is assembled to obtain the corrugated plate assembly.

[0017] Based on Boolean operations, the fluid physics computational domain is obtained from the assembly of the corrugated plates.

[0018] Geometric repair is performed based on the fluid physics computational domain to construct a three-dimensional model of a single-sided medium.

[0019] The geometric feature parameterization mapping of the three-dimensional model of the single-sided medium is performed to obtain the geometric feature parameters of the three-dimensional model of the single-sided medium, wherein the geometric feature parameters include the corner hole shrinkage ratio, the ripple disturbance angle, the equivalent hydraulic diameter and the porosity;

[0020] Based on the geometric feature parameters of the single-sided medium three-dimensional model, the drag coefficient of the porous medium model is obtained using a preset fitting coefficient. The drag coefficient of the porous medium model includes the inertial drag coefficient and the viscous drag coefficient of the porous medium model.

[0021] A porous media model is established using the resistance coefficient and porosity of the aforementioned porous media model.

[0022] Using the porous medium model and the corresponding solid model of the porous medium model, the one-sided pressure drop error of the porous medium model and the solid model is obtained;

[0023] Determine whether the one-sided pressure drop error between the porous medium model and the solid model meets the one-sided pressure drop error threshold. If yes, obtain the porosity, the inertial drag coefficient, the viscous drag coefficient, and the equivalent hydraulic diameter as the porous medium parameters of the porous medium model. Otherwise, adjust the preset fitting coefficient and return to execute the first operation.

[0024] The first operation is as follows: based on the geometric feature parameters of the three-dimensional model of the single-sided medium, the drag coefficient of the porous medium model is obtained using a preset fitting coefficient.

[0025] Optionally, S2, mesh the 3D model of the single-sided medium to obtain the meshing result of the 3D model of the single-sided medium, including:

[0026] Geometric preprocessing is performed on the single-sided medium three-dimensional model to obtain the preprocessed single-sided medium three-dimensional model and periodic boundary conditions;

[0027] Based on the periodic boundary conditions, the preprocessed one-sided medium three-dimensional model is divided into polyhedral meshes to obtain the mesh division result of the preprocessed one-sided medium three-dimensional model.

[0028] Quality control is performed based on the mesh generation results of the preprocessed one-sided medium three-dimensional model to obtain the mesh generation results of the one-sided medium three-dimensional model.

[0029] Optionally, quality control is performed based on the mesh generation results of the preprocessed 3D model of the single-sided medium to obtain the mesh generation results of the 3D model of the single-sided medium, including:

[0030] The distortion rate and aspect ratio of the mesh generation result are obtained from the mesh generation result of the preprocessed single-sided medium three-dimensional model.

[0031] Determine whether the distortion rate of the mesh generation result meets the preset distortion rate threshold. If yes, perform the second operation; otherwise, delete the mesh generation result that does not meet the preset distortion rate threshold according to the mesh generation result of the preprocessed single-sided medium 3D model, and perform the second operation.

[0032] The second operation is as follows: determine whether the aspect ratio of the mesh division result meets the preset aspect ratio threshold. If yes, obtain the mesh division result of the preprocessed single-sided medium 3D model as the mesh division result of the single-sided medium 3D model. Otherwise, delete the corresponding mesh division result that does not meet the preset aspect ratio threshold according to the mesh division result of the preprocessed single-sided medium 3D model, and obtain the mesh division result of the single-sided medium 3D model.

[0033] Optionally, S3, based on the porous medium parameters of the porous medium model and the mesh generation result of the single-sided medium three-dimensional model... k- oh Before obtaining the preliminary flow field calculation results for the SST turbulence model, the following steps are also included:

[0034] Set single-sided entry boundary conditions;

[0035] The Reynolds number is obtained based on the single-sided inlet boundary condition.

[0036] Optionally, S3, based on the porous medium parameters of the porous medium model and the mesh generation result of the single-sided medium three-dimensional model... k - oh The SST turbulence model was used to perform preliminary flow field calculations, and the preliminary flow field calculation results were obtained, including:

[0037] Based on the Reynolds number, the turbulence intensity within the channel is obtained;

[0038] Using the turbulence intensity within the channel to k - oh The SST turbulence model is initialized to obtain the initialization data. k - oh SST turbulence model;

[0039] The porous medium parameters of the porous medium model and the mesh generation results of the single-sided medium 3D model are input into the initialization process. k - oh The SST turbulence model was used to perform preliminary flow field calculations based on the single-sided inlet boundary conditions to obtain preliminary flow field calculation results.

[0040] Optionally, S4, based on the preliminary flow field calculation results, a fitting process is performed to obtain the fluid simulation results of the semi-welded plate AC converter, including:

[0041] Using the preliminary flow field calculation results, the pressure drop data of the welded plate heat exchanger was obtained;

[0042] The pressure drop data of the welded plate heat exchanger is fitted to obtain the fitting result of the pressure drop data.

[0043] The fitting results of the pressure drop data were verified to obtain the fluid simulation results of the semi-welded plate AC.

[0044] Optionally, the fitting results of the pressure drop data are verified to obtain the fluid simulation results of the semi-welded plate AC converter, including:

[0045] The predicted value of the fitting result is obtained by fitting the pressure drop data;

[0046] The predicted values ​​from the fitting results are compared point by point with the pressure drop data of the welded plate heat exchanger to obtain the comparison error.

[0047] Determine whether the comparison error meets the preset comparison error value. If yes, obtain the fluid simulation result of the semi-welded plate AC based on the fitting result of the pressure drop data. Otherwise, return to execute the third operation.

[0048] The third operation is as follows: performing fitting processing on the pressure drop data of the welded plate heat exchanger to obtain the fitting result of the pressure drop data.

[0049] Compared with the closest existing technology, the present invention has the following advantages:

[0050] This invention enables prediction of the overall pressure drop on one side of a semi-welded plate heat exchanger, and based on this, utilizes... k - oh The SST turbulence model predicts the flow of media between plates, greatly improving the accuracy of heat exchanger flow field calculations and making the flow near the plate wall closer to the actual state, which has a positive effect on predicting heat exchanger performance.

[0051] This invention is based on k - oh The SST turbulence model can more accurately simulate the flow state near the wall of the plate, increasing the simulation accuracy of fluid analysis; the present invention can effectively shorten the product design cycle and reduce the development cost of new products through periodic boundary conditions; the present invention uses a porous medium model to predict the pressure drop of the overall semi-welded plate heat exchanger, solving the problem that existing methods cannot predict the overall pressure drop on one side. Attached Figure Description

[0052] To more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the specific embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0053] Figure 1 This is a flowchart of a fluid simulation method for a semi-welded plate heat exchanger according to an embodiment of the present invention. Detailed Implementation

[0054] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions in the embodiments of this invention will be clearly and completely described below with reference to specific embodiments and corresponding drawings. Obviously, the described embodiments are only a part of the embodiments of this invention, and not all of them. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention.

[0055] The terminology used in the embodiments section of this invention is for the purpose of explaining specific embodiments of the invention only, and is not intended to limit the invention.

[0056] like Figure 1 As shown, this embodiment of the invention provides a fluid simulation method for a semi-welded plate heat exchanger, including:

[0057] S1. Using a single-sided three-dimensional medium model, obtain the porous medium parameters of the porous medium model;

[0058] A single-sided medium 3D model is a three-dimensional spatial model of a single fluid channel (such as only the cold or hot side medium) in a semi-welded plate heat exchanger, used to simulate the flow process of that medium from the inlet to the outlet. A porous medium model simplifies the inter-plate flow channels of a semi-welded plate heat exchanger with a complex internal structure into a virtual medium filled with pores. Using the single-sided medium 3D model, relevant parameters characterizing the porous medium's properties, such as porosity, can be obtained. e Inertial drag coefficient C 2. Viscous resistance coefficient 1 / α Equivalent hydraulic diameter D h These parameters are the foundation for subsequent simulation calculations, reflecting the influence of porous media on fluid flow and heat transfer.

[0059] S2. Mesh the single-sided medium three-dimensional model to obtain the meshing result of the single-sided medium three-dimensional model;

[0060] The 3D model of the single-sided medium is meshed to obtain the corresponding meshing results. Due to the special plate structure of the semi-welded plate heat exchanger, with small plate spacing and many irregular areas such as small gaps, slits, and sharp corners, a polyhedral mesh is adopted, combined with local densification and automatic node movement. This reduces meshing time, controls the number of meshes, and ensures mesh quality, thus meeting the requirements of engineering applications.

[0061] S3. Based on the porous medium parameters of the porous medium model and the mesh generation results of the single-sided medium three-dimensional model... k - oh The SST turbulence model was used to perform preliminary flow field calculations, and the preliminary flow field calculation results were obtained.

[0062] Based on the obtained porous media parameters and mesh generation results, k - oh The SST turbulence model was used to perform preliminary flow field calculations. This model can accurately simulate the near-wall flow state by solving for turbulent energy. k Turbulent dissipation rate oh Turbulent viscosity m tWe obtain flow field calculation results such as velocity field and pressure field to provide data support for subsequent fitting.

[0063] S4. Based on the preliminary flow field calculation results, perform fitting processing to obtain the fluid simulation results of the semi-welded plate AC converter.

[0064] The preliminary flow field calculation results are fitted. By fitting the relationship between the pressure drop and flow velocity on the hot and cold sides of the porous medium model, the fluid simulation results of the semi-welded plate heat exchanger are finally obtained, including the prediction of the overall pressure drop on one side and the flow field distribution characteristics. This allows for a deeper understanding of the fluid flow and pressure drop characteristics within the heat exchanger, which is helpful for guiding the performance evaluation and design optimization of the heat exchanger.

[0065] In summary, steps S1 to S4 obtain the porous medium parameters of the porous medium model using the 3D model of the single-sided medium. Then, the 3D model of the single-sided medium is meshed. Finally, based on the obtained parameters and the meshing results, the porous medium parameters are obtained using... k - oh The SST turbulence model is used to perform preliminary flow field calculations, and the results are then fitted to obtain the fluid simulation results for the semi-welded plate AC converter. This series of operations can accurately simulate the fluid flow conditions inside the semi-welded plate AC converter, effectively improving the accuracy and reliability of fluid simulation. It provides scientific and accurate data support for optimizing the structural design and performance parameters of the semi-welded plate AC converter, reducing R&D costs and time.

[0066] As one possible implementation, in the above embodiments, step S1 may specifically include the following steps:

[0067] S1-1. Obtain the key structural parameters of the corrugated plate through a semi-welded plate heat exchanger;

[0068] Extract key structural parameters of the corrugated plates from the design drawings or physical samples of semi-welded plate heat exchangers, such as plate length. L , board width W , plate thickness d Spacing between boards d ripple angle i , wave height h Law Section t , corrugation angle α Corner hole diameter f The physical object is precisely measured using a coordinate measuring machine or laser scanning technology to ensure parameter errors are <0.1mm. For design drawings, parametric definitions are directly read from CAD software to establish a parameter database. This step provides a precise data foundation for subsequent modeling, avoids simulation errors caused by parameter deviations, and ensures geometric consistency between the model and the actual product.

[0069] S1-2. Based on the key structural parameters of the corrugated plate, establish a parametric three-dimensional model of the corrugated plate;

[0070] Using parametric CAD software such as SolidWorks, the key structural parameters of the corrugated plates obtained above are set as variables. Mathematical expressions for the corrugated surfaces (such as sine functions) are generated through dimension-driven methods, constructing a fully parametric 3D model. Parameter relationships are established to ensure automatic model updates when any parameter is modified. Simultaneously, the corrugation meshing state of adjacent plates is checked to eliminate interference areas (e.g., corrugation peak-valley misalignment ≤ 0.05mm). This model supports one-click generation of different plate types, achieving design standardization and automation, and shortening model update time compared to traditional methods.

[0071] S1-3. Use the parametric three-dimensional model of the corrugated plate to establish a three-dimensional model of the single-sided medium and obtain the porous medium parameters of the porous medium model.

[0072] By utilizing a parametric 3D model of a corrugated plate, a 3D model of a single-sided medium is constructed. Porosity, drag coefficient, and other porous medium parameters are derived through volumetric statistics and dimensional analysis, achieving accurate acquisition of these parameters. This operation, through parametric modeling and geometric calculations, ensures the geometric consistency between the porous medium model and the actual flow channel, reducing porosity calculation errors and providing reliable physical parameters for subsequent flow field simulations. This effectively improves the agreement between simulation results and actual operating conditions.

[0073] In summary, steps S1-1 to S1-3 obtain the key structural parameters of the corrugated plates using a semi-welded plate heat exchanger. Based on these parameters, a parametric 3D model of the corrugated plates is built using software such as SolidWorks, enabling rapid generation and modification of the model under parameter-driven conditions. Then, based on this 3D model, a 3D model of the medium on one side is obtained through operations such as assembling adjacent plates and Boolean operations. Data such as fluid domain volume and equivalent hydraulic diameter are then extracted from this model to calculate the porous medium parameters. This process improves design flexibility and modeling efficiency through parametric modeling, enabling the rapid generation of different plate types and accurate extraction of porous medium parameters. The porous medium model effectively reflects the flow characteristics of the actual flow channel. Compared with solid flow channel simulation, the pressure drop prediction error is reduced, while the number of meshes is decreased, significantly improving computational efficiency. This provides an accurate and efficient foundation for the fluid simulation and optimization design of semi-welded plate heat exchangers.

[0074] As one possible implementation, in the above embodiments, steps S1-3 may specifically include the following steps:

[0075] S1-3-1. Assemble the parametric three-dimensional model of the corrugated plate to obtain the assembly of the corrugated plate.

[0076] For the parametric 3D model of the corrugated plates, the assembly state of two adjacent plates is simulated according to the actual spacing, thereby obtaining the assembly. This ensures that there is no interference in the corrugation meshing of adjacent plates (e.g., the corrugation peak-valley misalignment is ≤0.1mm). The corrugated plate assembly refers to the combination of two corrugated plates precisely aligned and fixed according to the design spacing (e.g., 2-3mm), simulating the assembly state of plates in an actual heat exchanger. This ensures that the fluid domain geometry is consistent with the actual flow channel and is the basis for extracting the single-sided medium model.

[0077] S1-3-2. Based on Boolean operations, obtain the fluid physics calculation domain according to the assembly of the corrugated plates;

[0078] The single-sided medium space is extracted from the assembly using Boolean operations (difference), inlet corner holes, outlet surfaces, and sealing boundaries are added, all curved surfaces are stitched together, and a fluid physics computational domain is generated. This ensures that the fluid domain topology matches the actual flow channel, reducing errors from manual modeling. In this embodiment, the fluid physics computational domain is composed of two corrugated plates stacked together, forming a complex three-dimensional flow channel.

[0079] S1-3-3. Based on the fluid physics computational domain, perform geometric repair and construct a three-dimensional model of a single-sided medium;

[0080] Curvature analysis is used to mark geometric defects such as corrugated tips and slits, and CAD software is used for monitoring. Geometric defects such as tiny gaps and overlapping surfaces in the fluid physics computation domain are repaired to ensure that the corrugated plate surface is smooth and to avoid tiny gaps or overlapping surfaces. Different boundary condition labels are assigned to the inlet corner holes, outlet surface and wall surface to facilitate subsequent computational fluid dynamics (CFD) settings and ensure the reliability of flow field calculation.

[0081] S1-3-4. Perform geometric feature parameterization mapping on the three-dimensional model of the single-sided medium to obtain the geometric feature parameters of the three-dimensional model of the single-sided medium, wherein the geometric feature parameters include the corner hole shrinkage ratio, the ripple disturbance angle, the equivalent hydraulic diameter and the porosity.

[0082] First, when performing geometric feature parameterization mapping on the 3D model of a single-sided medium, the corner hole diameter, a key structural parameter of the corrugated plate, is used as the starting point. f Spacing between boards d Calculate the corner hole shrinkage ratio β ,Right now β = f / d First, to quantify the degree of flow contraction at the inlet section; second, based on the corrugation angle. α Extracting the ripple disturbance angle Δ i , that is, Δ i =2 aThis is used to evaluate the disturbance intensity of the ripples on the fluid; secondly, the flow channel cross-section is selected, and the cross-sectional area is used to assess this disturbance. A With wetted perimeter P Calculate the equivalent hydraulic diameter D h ,Right now D h =4 A / P This provides a basis for Reynolds number calculation; finally, the fluid domain volume is obtained using the software's volume statistics function. V f With plate solid volume V s Calculate the porosity, i.e. e = V f / ( V f + V s This process achieves precise conversion from physical geometry to physical parameters, reduces the deviation between parameters such as the corner hole shrinkage ratio and the ripple disturbance angle and the actual measurements, as well as the calculation error of the equivalent hydraulic diameter, and lays a high-precision data foundation for the subsequent derivation of the drag coefficient of the porous media model, effectively ensuring the accuracy and reliability of the flow field simulation.

[0083] S1-3-5. Based on the geometric feature parameters of the three-dimensional model of the single-sided medium, the drag coefficient of the porous medium model is obtained using a preset fitting coefficient, wherein the drag coefficient of the porous medium model includes the inertial drag coefficient and the viscous drag coefficient of the porous medium model.

[0084] Geometric characteristic parameters such as orifice shrinkage ratio, corrugation angle, equivalent hydraulic diameter, and porosity extracted from a 3D model of a single-sided medium were used to obtain the inertial drag coefficient through dimensional analysis and CFD pre-calculation data, and fitted using the least squares method. C 2, that is C 2= k 1· i · β + k 2; Simultaneously, based on Darcy's law, the viscous drag coefficient 1 / α Spacing between boards d Porosity e The relation is 1 / α = k 3· d -1 · e -2 The viscous drag coefficient 1 / α .in, k 1. k 2 represents the preset fitting coefficient. k3 is the material coefficient (for stainless steel corrugated plates). k 3 = 3.6 × 10 -3 This method improves the efficiency of parameter extraction compared to traditional local simulation, and reduces the number of grids in the calculation of porous media models, thus shortening the time required for a single simulation. It provides high-precision and high-efficiency parameter support for predicting the overall pressure drop on one side of a semi-welded plate heat exchanger.

[0085] S1-3-6. Using the resistance coefficient and porosity of the porous medium model, establish a porous medium model;

[0086] Based on the obtained inertial drag coefficient C 2、 Viscous resistance coefficient 1 / α With porosity e Substituting it into the Darcy-Fochheimer equation to construct a porous medium model, this model simplifies the complex three-dimensional corrugated flow channel into a porous medium abstract model, reducing the number of meshes and shortening the computation time. It effectively solves the problems of complex overall modeling and high computational resource consumption of semi-welded plate heat exchangers, and provides a practical engineering tool for rapid performance evaluation and plate optimization of heat exchangers.

[0087] S1-3-7. Using the porous medium model and the corresponding solid model of the porous medium model, obtain the one-sided pressure drop error of the porous medium model and the solid model.

[0088] The porous media model and its corresponding solid model were imported into simulation software such as Fluent, and flow field calculations were performed under the same boundary conditions (e.g., inlet velocity 1.5 m / s, outlet pressure 0 Pa) to calculate the one-sided pressure drop error. The solid model used a 300,000-element polyhedral mesh with local refinement, while the porous media model was calculated using a simplified drag coefficient formula. This process quantifies the accuracy of the porous media model, saves verification costs compared to traditional physical experiments, and ensures that the flow characteristics of the porous media model and the solid flow channel are consistent through an error feedback mechanism.

[0089] S1-3-8. Determine whether the one-sided pressure drop error between the porous medium model and the solid model meets the one-sided pressure drop error threshold. If yes, obtain the porosity, the inertial drag coefficient, the viscous drag coefficient, and the equivalent hydraulic diameter as the porous medium parameters of the porous medium model. Otherwise, adjust the preset fitting coefficient and return to execute S1-3-5.

[0090] The one-sided pressure drop error of the porous media model and the solid model is compared with a preset one-sided pressure drop error threshold (e.g., 8%). If the error is within the threshold range (≤8%), the initial porous media parameters of the current porous media model (including porosity, inertial drag coefficient, viscous drag coefficient, equivalent hydraulic diameter, etc.) are considered to meet the accuracy requirements and are directly used as the final porous media parameters. If the error exceeds the threshold (>8%), the preset fitting coefficients are adjusted according to the rules (e.g., the fitting coefficients are adjusted to the original value × (1 + error / 10), and the geometric feature parameters (e.g., corrugation angle, corner pore shrinkage ratio, etc.) based on the one-sided media 3D model and the adjusted fitting coefficients are returned to re-derive the drag coefficient of the porous media model. This process, through error judgment and iterative correction, can achieve automatic optimization of porous media model parameters, ensure that the simulation accuracy meets engineering requirements, improve design efficiency, and reduce R&D costs.

[0091] In summary, steps S1-3-1 to S1-3-8 revolve around obtaining parameters for the porous media model. First, the parametric 3D model of the corrugated plate is assembled to obtain an assembly. Boolean operations are then used to obtain the fluid physics computational domain. Next, a 3D model of the medium on one side is constructed through geometric repair. Then, its geometric features are parametrically mapped. Based on the obtained parameters and preset fitting coefficients, the drag coefficient of the porous media model is obtained. After establishing the model, the 1 / 2-sided pressure drop error is compared with that of the solid model. Parameters are determined or adjusted based on whether the error meets a threshold. This scheme can accurately construct a porous media model that conforms to actual working conditions, effectively improving the accuracy of porous media parameter acquisition. This provides a more reliable data foundation for subsequent fluid simulation of semi-welded plate AC converters based on these parameters, thereby enhancing the guiding value of simulation results for product design optimization and performance evaluation.

[0092] As one possible implementation, in the above embodiments, step S2 may specifically include the following steps:

[0093] S2-1. Perform geometric preprocessing on the single-sided medium three-dimensional model to obtain the preprocessed single-sided medium three-dimensional model and periodic boundary conditions;

[0094] When performing geometric preprocessing on a 3D model of a single-sided medium, the following steps are taken: First, eliminate geometric defects such as micro-gaps and overlapping surfaces. Round off sharp corners of the corrugated structure and remove secondary features that do not affect the main flow field to simplify the channel topology, resulting in a preprocessed model. Second, clearly define boundary regions such as the inlet, outlet, and wall, and mark high-gradient regions with complex flow states. Finally, extract periodic elements containing complete wave-trough pairs from the preprocessed 3D model of the single-sided medium, and set periodic boundary conditions on both sides of the elements to make the flow field characteristics repeat periodically at the boundaries. This process effectively improves the geometric quality of the model, reduces invalid computation regions, provides a regular geometric basis for subsequent mesh generation, and significantly reduces the computational scale through periodic modeling.

[0095] S2-2. Based on the periodic boundary conditions, perform polyhedral meshing on the preprocessed one-sided medium three-dimensional model to obtain the meshing result of the preprocessed one-sided medium three-dimensional model;

[0096] The unique structure of semi-welded plate heat exchangers results in very small plate spacing, leading to numerous small gaps, slits, sharp corners, and other irregularly shaped areas during mesh discretization. To reduce mesh generation time, control the number of meshes, and ensure mesh quality for engineering applications, a polyhedral mesh is employed. Specifically:

[0097] Based on periodic boundary conditions, a hybrid mesh strategy is adopted for the preprocessed model: a polyhedral mesh is used for the main flow channel to adapt to the complex geometry; multiple prismatic boundary layers are generated on the plate walls to accurately resolve near-wall flow; and local mesh refinement is applied to key areas such as the inlet contraction section and corrugated transition points. This meshing method utilizes the geometric adaptability of the polyhedral mesh to reduce the number of meshes, and the local refinement strategy ensures the computational accuracy of key areas. While balancing computational efficiency and accuracy, it ensures that the mesh meets the solution requirements of the turbulence model.

[0098] S2-3. Perform quality control based on the mesh generation results of the preprocessed one-sided medium three-dimensional model, and obtain the mesh generation results of the one-sided medium three-dimensional model;

[0099] Quality control is performed on the mesh generation results. The quality-controlled mesh can accurately capture the velocity gradient and flow separation phenomenon in the flow field, avoiding calculation errors or solution failures caused by mesh defects. This provides a reliable mesh basis for subsequent flow field calculations and ensures that the simulation results can truly reflect the actual flow state inside the heat exchanger.

[0100] In summary, steps S2-1 to S2-3 first perform geometric preprocessing on the 3D model of the single-sided medium, which not only yields the preprocessed 3D model of the single-sided medium but also determines the periodic boundary conditions, laying the foundation for subsequent calculations. Next, based on the periodic boundary conditions, a polyhedral mesh is generated from the preprocessed model to better fit its complex geometry, obtaining preliminary meshing results. Finally, quality control is used to optimize the preliminary results, yielding the final meshing result for the 3D model of the single-sided medium. This approach effectively improves the accuracy and quality of mesh generation, precisely captures the geometric features and flow characteristics of the model, reduces calculation errors, and enhances the accuracy and stability of flow field calculations and fluid simulations based on this mesh generation. This provides a reliable mesh foundation for the performance analysis and optimization design of semi-welded plate AC converters.

[0101] As one possible implementation, in the above embodiments, step S2-3 may specifically include the following steps:

[0102] S2-3-1. Obtain the distortion rate and aspect ratio of the mesh generation result from the preprocessed single-sided medium three-dimensional model.

[0103] S2-3-2. Determine whether the distortion rate of the mesh division result meets the preset distortion rate threshold. If yes, execute the second operation. Otherwise, delete the corresponding mesh division result that does not meet the preset distortion rate threshold according to the mesh division result of the preprocessed single-sided medium three-dimensional model, and execute S2-3-3.

[0104] S2-3-3. Determine whether the aspect ratio of the mesh division result meets the preset aspect ratio threshold. If yes, obtain the mesh division result of the preprocessed single-sided medium 3D model as the mesh division result of the single-sided medium 3D model. Otherwise, delete the corresponding mesh division result that does not meet the preset aspect ratio threshold according to the mesh division result of the preprocessed single-sided medium 3D model, and obtain the mesh division result of the single-sided medium 3D model.

[0105] In summary, steps S2-3-1 to S2-3-3 obtain the distortion rate and aspect ratio of the preprocessed single-sided medium 3D model mesh generation results. First, it determines whether the distortion rate meets the preset distortion rate threshold. If not, the corresponding mesh is deleted. Then, it determines whether the aspect ratio meets the preset aspect ratio threshold (≤15). If it does, it is determined as the final mesh result. This process improves the mesh quality compliance rate, reduces near-wall flow simulation errors, and ensures the stability and accuracy of flow field calculations. In this embodiment, the preset distortion rate threshold is set to ≤0.9, and the preset aspect ratio threshold is set to ≤15.

[0106] As one possible implementation, in the above embodiment, the following steps are included before performing step S3:

[0107] Set single-sided entry boundary conditions;

[0108] The Reynolds number is obtained based on the single-sided inlet boundary condition.

[0109] Before conducting preliminary flow field calculations, it is necessary to set single-sided inlet boundary conditions based on the calculation sheets for the design conditions. This assumes that the medium is uniformly distributed within the corner orifice, calculates the inlet conditions for the single-sided channel, and assumes free outflow at the outlet, with the rest being wall-based. Then, the Reynolds number is calculated based on the single-sided inlet boundary conditions. Re The calculation formula is as follows:

[0110]

[0111] in, r For fluid density, v For flow velocity, D For feature size, m This refers to the fluid dynamic viscosity.

[0112] In summary, the above process is as follows: k - oh The SST turbulence model provides key input parameters, including the Reynolds number which guides the selection of the turbulence model and parameter initialization, and the inlet conditions which directly constrain the flow state in the computational domain. Specifically, this results in reduced pressure drop prediction error, improved accuracy in capturing turbulent boundary layers, faster computational convergence, and ensures that the flow field calculation results conform to both physical laws and engineering reliability.

[0113] As one possible implementation, in the above embodiments, step S3 may specifically include the following steps:

[0114] S3-1. Based on the Reynolds number, obtain the turbulence intensity within the channel;

[0115] Through Reynolds number ( Re The ratio of inertial force to viscous force in the fluid is quantified to determine the flow state (laminar or turbulent). The turbulence intensity within the channel is further calculated based on the Reynolds number. I ,Right now I =0.16( Re D ) -1 / 8 This parameter characterizes the intensity of fluid pulsation. This process, through the correlation between the Reynolds number and the turbulence intensity within the channel, provides a key input to the turbulence model that reflects the actual flow characteristics, enabling the model to accurately capture turbulent disturbances between heat exchanger plates caused by changes in flow velocity, fluid properties, and channel dimensions, such as under high Reynolds number conditions (…). Re >10 4 This allows for accurate assessment of the impact of turbulence intensity on flow separation and eddy formation, laying the foundation for subsequent flow field calculations.

[0116] S3-2, Utilizing the turbulence intensity within the channel to... k - oh The SST turbulence model is initialized to obtain the initialization data. k - oh SST turbulence model;

[0117] The calculated turbulence intensity inside the channel I The core parameters of the k-ω SST turbulence model are initialized by quantifying the fluid pulsation characteristics. Specifically: First, the turbulent kinetic energy is calculated from the turbulence intensity and flow velocity within the channel. k This parameter characterizes the energy magnitude of fluid turbulent fluctuations; then, the turbulence scale... l With model intrinsic constants C μ =0.09, solve for the turbulent dissipation rate ( oh This reflects the rate of energy dissipation in turbulence; finally, the calculated... kand oh As initial conditions, the parameters of the k-ωSST model are initialized. This process initializes the model through turbulence intensity, which can improve the simulation accuracy of the k-ωSST model for adverse pressure gradient flows (such as flow separation and reattachment phenomena) at the corrugations of heat exchanger plates. Compared with the standard k-ε model, it can more accurately predict the distribution of turbulence intensity in complex regions such as slits and sharp corners, avoid the distortion of flow field calculations caused by deviations in model parameter settings, and provide reliable turbulence characteristic inputs for subsequent flow field trials.

[0118] S3-3, Input the porous medium parameters of the porous medium model and the mesh generation results of the single-sided medium three-dimensional model into the initialization... k - oh The SST turbulence model is used to perform preliminary flow field calculations based on the single-sided inlet boundary conditions to obtain preliminary flow field calculation results.

[0119] The porous medium parameters and a high-quality mesh (the mesh generation result of the 3D model of the single-sided medium) are imported into the initialized model. Preliminary flow field calculations are then performed using the single-sided inlet boundary conditions to obtain the velocity field, pressure field, and turbulence parameters. This coupling of the porous medium parameters and the turbulence model allows for direct calculation of the drag effect of fluid passing through the plate structure, reducing the deviation between the pressure drop calculation and actual operating conditions. The synergy between the high-quality mesh and the model ensures the analytical accuracy of near-wall turbulence while improving the calculation convergence speed, providing reliable flow field data support for subsequent calculations and achieving efficient transformation from numerical simulation to engineering applications.

[0120] k - oh The SST turbulence model is defined as follows:

[0121] Turbulent energy k equation:

[0122]

[0123] Turbulent dissipation rate oh equation:

[0124]

[0125] Turbulent viscosity m t equation:

[0126]

[0127] in, k For turbulent kinetic energy, r For fluid density, t For time, u i For fluid in ivelocity components in the direction, x i for i Directional spatial coordinates, t ij For stress tensor, u j For fluid in j velocity components in the direction, β * As a model constant, this embodiment sets β * =0.09, oh For turbulent dissipation rate, m For fluid dynamic viscosity, s k The turbulent kinetic energy diffusion coefficient is... m t For turbulent viscosity, c These are model constants. v t Kinematic viscosity, P For the turbulent kinetic energy generation term, β These are model constants. s ω The diffusion coefficient represents the turbulent dissipation rate. F 1 is the main mixed function (a function whose value is between 0 and 1). s ω2 These are model constants. a * These are model constants. S For strain rate, F 2 is a submixed function (a function whose value is between 0 and 1). a 1 is a model constant.

[0128] In summary, steps S3-1 to S3-3 determine the turbulence intensity within the channel based on the Reynolds number, and use this as a basis for... k - oh The SST turbulence model was initialized to obtain an initialization that better reflects actual working conditions. k - oh The SST turbulence model is then used. The porous medium parameters of the porous medium model and the mesh generation results of the 3D model of the single-sided medium are input into the model, and preliminary flow field calculations are performed based on the single-sided inlet boundary conditions to obtain preliminary flow field calculation results. This process effectively improves the fit between the turbulence model and the actual flow state. With accurate parameters and mesh data, it precisely simulates the turbulent flow within the channel, reduces calculation errors, and provides scientifically reliable calculation results for the flow field analysis of semi-welded plate AC converters. This helps optimize the internal flow channel design of the equipment, improve fluid transmission efficiency, and enhance the overall performance of the equipment.

[0129] As one possible implementation, in the above embodiments, step S4 may specifically include the following steps:

[0130] S4-1. Using the preliminary flow field calculation results, obtain the pressure drop data of the welded plate heat exchanger;

[0131] The pressure values ​​at the inlet and outlet sections are extracted from the preliminary flow field calculations. By calculating the difference between the inlet and outlet pressures, the pressure drop data of the heat exchanger under different flow velocity conditions is obtained. This step directly obtains the raw pressure drop data through numerical calculation, providing quantitative support for subsequent fitting processing, ensuring the accuracy and reliability of the data source, and laying the foundation for the resistance characteristic analysis of the heat exchanger.

[0132] S4-2. Perform fitting processing on the pressure drop data of the welded plate heat exchanger to obtain the fitting result of the pressure drop data;

[0133] Based on multiple sets of flow velocity and corresponding pressure drop data, it is assumed that the pressure drop and flow velocity satisfy a quadratic function relationship, i.e., Δ p = αv ²+ bv Regression analysis was used to solve for the function coefficients, resulting in a mathematical expression describing the relationship between pressure drop and flow velocity. α = C 2 r △ n / 2, b = m △ n / α , △ n Δ represents the thickness of the porous medium region along this direction. p The pressure drop of a semi-welded plate heat exchanger is the pressure difference between the inlet and outlet when fluid passes through the heat exchanger, used to measure the resistance to fluid flow. v The flow velocity of the fluid within the channels between the heat exchanger plates is a core variable affecting pressure drop, reflecting the speed of fluid flow. This process, through fitting, transforms discrete simulation data into continuous engineering formulas, enabling rapid prediction of pressure drop at arbitrary flow velocities. This enhances the engineering application value of the data and provides a convenient computational tool for heat exchanger performance evaluation.

[0134] S4-3. Verify the fitting results of the pressure drop data and obtain the fluid simulation results of the semi-welded plate AC converter;

[0135] The accuracy of the fitting formula was ensured by verifying the fitting results of the pressure drop data, so that the fluid simulation results can truly reflect the actual flow resistance characteristics of the heat exchanger. This provides a reliable basis for structural optimization and energy consumption assessment in engineering design, and enhances the engineering applicability of the simulation method.

[0136] In summary, steps S4-1 to S4-3, starting from the preliminary flow field calculation results, first extract the pressure drop data of the welded plate heat exchanger, a key indicator for evaluating heat exchanger performance. Next, the pressure drop data is fitted using mathematical methods to uncover patterns and obtain more representative fitting results. Finally, the fitting results are verified to obtain the fluid simulation results for the semi-welded plate heat exchanger. This process effectively integrates the preliminary calculation data and, through scientific data processing and verification, significantly improves the accuracy and reliability of the pressure drop data in the fluid simulation results. It provides a precise basis for evaluating the fluid transmission performance of the semi-welded plate heat exchanger and optimizing equipment structural design, helping engineers quickly identify potential equipment problems, reduce unnecessary experimental testing, accelerate product development iteration, and lower R&D costs.

[0137] As one possible implementation, in the above embodiments, step S4-3 may specifically include the following steps:

[0138] S4-3-1. Obtain the predicted value of the fitting result based on the fitting result of the pressure drop data;

[0139] S4-3-2. Compare the predicted value of the fitting result with the pressure drop data of the welded plate heat exchanger point by point to obtain the comparison error;

[0140] S4-3-3. Determine whether the comparison error meets the preset comparison error value. If yes, obtain the fluid simulation result of the semi-welded plate AC based on the fitting result of the pressure drop data. Otherwise, return to S4-2.

[0141] In summary, steps S4-3-1 to S4-3-3 calculate the predicted value based on the fitting results of the pressure drop data, compare it point by point with the pressure drop data of the semi-welded plate heat exchanger, obtain the comparison error, and determine whether the error meets the preset value. If it does, the fitting result is used as the fluid simulation result of the semi-welded plate heat exchanger; if it does not, the pressure drop data is re-fitted until a fitting result that meets the error requirements is obtained. This process, by quantitatively comparing the fitted predicted value with the actual pressure drop data, ensures the accuracy and reliability of the fitting model, effectively avoids engineering design errors caused by model deviations, provides accurate quantitative basis for heat exchanger structural optimization, pump power matching, etc., and enhances the guiding value of simulation results for practical engineering applications. At the same time, through a closed-loop correction mechanism, the fitting model is continuously optimized, enhancing the practicality and accuracy of the entire simulation method.

[0142] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0143] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure one One or more processes and / or boxes Figure one A device that provides the functions specified in one or more boxes.

[0144] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure one One or more processes and / or boxes Figure one The function specified in one or more boxes.

[0145] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure one One or more processes and / or boxes Figure one The steps of the function specified in one or more boxes.

[0146] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the specific implementation of the present invention. Any modifications or equivalent substitutions that do not depart from the spirit and scope of the present invention should be covered within the scope of protection of the claims of the present invention.

Claims

1. A fluid simulation method for a semi-welded plate heat exchanger, characterized in that, include: S1. Using a single-sided 3D model of the medium, obtain the porous medium parameters of the porous medium model, including: Key structural parameters of corrugated plates were obtained through a semi-welded plate heat exchanger. Based on the key structural parameters of the corrugated plate, a parametric three-dimensional model of the corrugated plate is established. A single-sided medium 3D model is established using the parametric 3D model of the corrugated plate, and the porous medium parameters of the porous medium model are obtained, including: The parametric three-dimensional model of the corrugated plate is assembled to obtain the corrugated plate assembly. Based on Boolean operations, the fluid physics computational domain is obtained from the assembly of the corrugated plates. Geometric repair is performed based on the fluid physics computational domain to construct a three-dimensional model of a single-sided medium. The geometric feature parameterization mapping of the three-dimensional model of the single-sided medium is performed to obtain the geometric feature parameters of the three-dimensional model of the single-sided medium, wherein the geometric feature parameters include the corner hole shrinkage ratio, the ripple disturbance angle, the equivalent hydraulic diameter and the porosity; Based on the geometric feature parameters of the single-sided medium three-dimensional model, the drag coefficient of the porous medium model is obtained using a preset fitting coefficient. The drag coefficient of the porous medium model includes the inertial drag coefficient and the viscous drag coefficient of the porous medium model. A porous media model is established using the resistance coefficient and porosity of the aforementioned porous media model. Using the porous medium model and the corresponding solid model of the porous medium model, the one-sided pressure drop error of the porous medium model and the solid model is obtained; Determine whether the one-sided pressure drop error between the porous medium model and the solid model meets the one-sided pressure drop error threshold. If yes, obtain the porosity, the inertial drag coefficient, the viscous drag coefficient, and the equivalent hydraulic diameter as the porous medium parameters of the porous medium model. Otherwise, adjust the preset fitting coefficient and return to execute the first operation. The first operation is: obtaining the drag coefficient of the porous medium model based on the geometric feature parameters of the three-dimensional model of the single-sided medium using a preset fitting coefficient; S2. Mesh the single-sided medium three-dimensional model to obtain the meshing result of the single-sided medium three-dimensional model; S3. Based on the porous medium parameters of the porous medium model and the mesh generation results of the single-sided medium three-dimensional model... k - ω The SST turbulence model was used to perform preliminary flow field calculations, and the preliminary flow field calculation results were obtained, including: Set single-sided entry boundary conditions; Based on the single-sided inlet boundary conditions, the Reynolds number is obtained; Based on the Reynolds number, the turbulence intensity within the channel is obtained; Using the turbulence intensity within the channel to k - ω The SST turbulence model is initialized to obtain the initialization data. k - ω SST turbulence model; The porous medium parameters of the porous medium model and the mesh generation results of the single-sided medium 3D model are input into the initialization process. k - ω The SST turbulence model is used to perform preliminary flow field calculations based on the single-sided inlet boundary conditions to obtain preliminary flow field calculation results. S4. Based on the preliminary flow field calculation results, perform fitting processing to obtain the fluid simulation results of the semi-welded plate AC converter, including: Using the preliminary flow field calculation results, the pressure drop data of the welded plate heat exchanger was obtained; The pressure drop data of the welded plate heat exchanger is fitted to obtain the fitting result of the pressure drop data. The fitting results of the pressure drop data were verified to obtain the fluid simulation results of the semi-welded plate AC.

2. The fluid simulation method for a semi-welded plate heat exchanger according to claim 1, characterized in that, S2. Mesh the single-sided medium 3D model and obtain the meshing result of the single-sided medium 3D model, including: Geometric preprocessing is performed on the single-sided medium three-dimensional model to obtain the preprocessed single-sided medium three-dimensional model and periodic boundary conditions; Based on the periodic boundary conditions, the preprocessed one-sided medium three-dimensional model is divided into polyhedral meshes to obtain the mesh division result of the preprocessed one-sided medium three-dimensional model. Quality control is performed based on the mesh generation results of the preprocessed one-sided medium three-dimensional model to obtain the mesh generation results of the one-sided medium three-dimensional model.

3. The fluid simulation method for a semi-welded plate heat exchanger according to claim 2, characterized in that, Quality control is performed based on the mesh generation results of the preprocessed 3D model of the single-sided medium. The mesh generation results of the 3D model of the single-sided medium are obtained, including: The distortion rate and aspect ratio of the mesh generation result are obtained from the mesh generation result of the preprocessed single-sided medium three-dimensional model. Determine whether the distortion rate of the mesh generation result meets the preset distortion rate threshold. If yes, perform the second operation; otherwise, delete the mesh generation result that does not meet the preset distortion rate threshold according to the mesh generation result of the preprocessed single-sided medium 3D model, and perform the second operation. The second operation is as follows: determine whether the aspect ratio of the mesh division result meets the preset aspect ratio threshold. If yes, obtain the mesh division result of the preprocessed single-sided medium 3D model as the mesh division result of the single-sided medium 3D model. Otherwise, delete the corresponding mesh division result that does not meet the preset aspect ratio threshold according to the mesh division result of the preprocessed single-sided medium 3D model, and obtain the mesh division result of the single-sided medium 3D model.

4. The fluid simulation method for a semi-welded plate heat exchanger according to claim 1, characterized in that, The fitting results of the pressure drop data are verified to obtain the fluid simulation results of the semi-welded plate AC converter, including: The predicted value of the fitting result is obtained by fitting the pressure drop data; The predicted values ​​from the fitting results are compared point by point with the pressure drop data of the welded plate heat exchanger to obtain the comparison error. Determine whether the comparison error meets the preset comparison error value. If yes, obtain the fluid simulation result of the semi-welded plate AC based on the fitting result of the pressure drop data. Otherwise, return to execute the third operation. The third operation is as follows: performing fitting processing on the pressure drop data of the welded plate heat exchanger to obtain the fitting result of the pressure drop data.

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