A method and system for determining an optimal structure of a pipe based on energy loss difference

Abstract

The present application relates to the technical field of pipeline design, in particular to a method and system for determining the optimal structure of a pipeline based on energy loss difference, comprising the following: obtaining the total energy loss result according to the friction loss along the way, the local loss of the channel with varying cross-section, and the equivalent velocity; obtaining the cross-sectional area and initial velocity expression at the interface of the structure based on the parameter information of the 2-section structure and the 3-section ideal structure, and analyzing the calculation results of the friction loss along the way and the local pressure loss in combination with the total energy loss result and the expression; constructing the energy loss difference objective function of different pipeline structures according to the calculation results of the friction loss along the way and the local pressure loss; obtaining the optimization equation of the half cone angle and the straight channel length of the 3-section ideal structure based on the energy loss difference objective function, obtaining the expression of the horizontal length of the left tapered pipe in the 3-section ideal structure, and establishing the parameter equation group at the maximum value in combination with the optimization equation and the expression; and the present application efficiently determines the optimal structure of the pipeline based on the parameter equation group.

Description

Technical Field

[0001] This invention relates to the field of pipeline design technology, specifically to a method and system for determining the optimal pipeline structure based on energy loss difference. Background Technology

[0002] The structural design of pipes and jet orifices plays a crucial role in gas flow characteristics, energy utilization efficiency, and overall system performance. Among them, the jet orifice, as a key component for gas injection, directly affects the gas flow state and energy loss, thereby impacting the overall system's operational effectiveness and economic benefits.

[0003] Currently, most jet orifices adopt a single straight-channel design. When gas enters this straight channel from the right inlet, due to the lack of acceleration structures such as tapered tubes, the airflow can only decelerate continuously within the channel. This straight-channel design leads to significant energy loss during gas flow, causing the gas's kinetic energy within the channel to gradually convert into internal energy and other forms of energy, resulting in energy waste, reduced system energy utilization efficiency, and inability to meet the requirements for high-efficiency gas injection.

[0004] To address the energy loss issue inherent in straight-channel designs, existing technologies employ a combination of single straight channels and single-section-variable channels. The principle behind the tapered tube design is to gradually reduce the channel cross-section, causing gas compression during flow and thus increasing airflow velocity. This mitigates, to some extent, the energy loss caused by airflow deceleration in straight channels. While this design improves gas flow and increases jet velocity, it still has significant drawbacks in practical applications. Due to the large cone angle difference between the two channel walls, the airflow along the tapered tube wall collides violently with the airflow along the straight channel wall at the interface between the straight channel and the tapered tube. The larger the cone angle, the more pronounced the collision, equivalent to a sharp contraction of the channel cross-section at this point. This abrupt change in cross-section leads to abrupt changes in gas flow, resulting in substantial energy loss, including turbulence and impact losses. Although the tapered tube's initial design aims to increase airflow velocity by reducing the cross-section, the lack of sufficient consideration of the cone angle's impact on gas flow and energy loss at the structural interface prevents the existing design from achieving the expected energy-saving and high-efficiency jetting effects in practical applications.

[0005] In summary, existing jet orifice designs have significant shortcomings in energy loss control. Whether it's a single straight-channel design or a combination of a straight channel and a tapered tube without considering the cone angle, neither can effectively reduce energy loss while ensuring gas injection performance. Therefore, there is an urgent need for a method and system that can comprehensively consider gas flow characteristics and energy loss factors to accurately determine the optimal pipeline structure. This would address the problems in existing technologies, improve the energy utilization efficiency and overall performance of gas injection systems, and provide a scientific and effective solution for pipeline and jet orifice structural design. Summary of the Invention

[0006] To address the shortcomings of existing methods and their limitations in practical application, this invention provides a scientific, reliable, and highly practical solution for determining the optimal pipeline structure by comprehensively considering gas flow characteristics and energy loss factors. This aims to improve the energy utilization efficiency and overall operational performance of the gas injection system, and to provide a comprehensive consideration of pipeline and jet orifice structural design. Firstly, this invention provides a method for determining the optimal pipeline structure based on energy loss difference. The method includes the following steps: obtaining the friction loss along the straight channel and the local loss of the cross-section-changing channel; combining the equivalent velocity, the friction loss along the channel, and the local loss to obtain the total energy loss result; setting parameter information based on two-segment and three-segment ideal structures; obtaining the cross-sectional area and initial velocity expression at the structural interface based on the parameter information; combining the total energy loss result and the cross-sectional area and initial velocity expression to obtain the friction loss calculation result and the local pressure loss calculation result; establishing an energy loss difference expression based on the friction loss calculation result and the local pressure loss calculation result; setting the variable domain of the energy loss difference expression; constructing an energy loss difference objective function for different pipeline structures based on the energy loss difference expression and the variable domain; and calculating the partial angle of the energy loss difference objective function to obtain a half-cone angle. With the length of the three ideal structural straight channels The optimization equations, based on geometric constraints, height relationships, and variable coupling, yielded the horizontal length of the left tapering tube in the three ideal structures. Expression; combined with the optimization equation and the The expression establishes a set of parametric equations for the maximum value, and the optimal pipeline structure is determined by the set of parametric equations for the maximum value.

[0007] This invention optimizes the pipeline structure by minimizing the energy loss difference based on the objective function of energy loss difference for different pipeline structures. This effectively reduces the energy loss of gas during the flow process in the pipeline, improves the energy utilization efficiency of the gas, and enables the gas injection system to achieve the same working effect with lower energy consumption.

[0008] Optionally, obtaining the friction loss along the straight channel and the local loss of the cross-section-changing channel includes:

[0009] The friction coefficient is calculated based on the Reynolds number and pipe roughness; the friction coefficient is iteratively solved to obtain the friction loss along the straight channel; the local loss coefficient is analyzed based on the geometry and cone angle of the tapered converging pipe; and the local loss of the channel with changing cross-section is obtained based on the local loss coefficient.

[0010] The friction loss along the straight channel satisfies the following relationship:

[0011] ,

[0012] in, This represents the friction loss along the straight path. Indicates the coefficient of friction. Indicates the length of the straight channel. Indicates the pipe diameter. Indicates airflow velocity. Represents gravitational acceleration;

[0013] The local loss of the cross-sectional change channel satisfies the following relationship:

[0014] ,

[0015] in, This represents the local loss of the channel with varying cross-section. Represents the local loss coefficient. Indicates airflow velocity. It represents the acceleration due to gravity.

[0016] This invention combines friction loss along the straight channel with local loss in the channel with cross-sectional changes to obtain the total energy loss result, which directly reflects the energy loss of gas during the flow process in the pipeline. Based on the total energy loss result, the influence of different pipeline structural parameters on energy loss is further analyzed, providing a clear direction and goal for subsequent pipeline structure optimization design.

[0017] Optionally, obtaining the total energy loss result by combining the equivalent velocity, the friction loss along the pipe, and the local loss includes: obtaining the equivalent velocity based on the power-law velocity distribution; deriving the velocity relationship between the average velocity and the maximum velocity at the center of the pipe based on the equivalent velocity; and obtaining the total energy loss result by combining the velocity relationship, the friction loss along the pipe, and the local loss.

[0018] The total energy loss result satisfies the following relationship:

[0019] ,

[0020] in, Indicates total energy loss. Indicates air density, Indicates the coefficient of friction. Indicates the length of the straight channel. Indicates the pipe diameter. Indicates airflow velocity. Represents the local loss coefficient. This indicates the flow velocity at the inlet of the section where the cross-section changes.

[0021] This invention divides the energy loss during the flow process in a pipeline into two parts: friction loss along the flow path and local loss. It then uses mathematical expressions to link these losses with parameters such as gas velocity and density, which can more accurately reflect the energy lost by the gas during the flow process due to friction and cross-sectional changes, thus further ensuring the scientific validity and rationality of the calculation results.

[0022] Optionally, the step of setting parameter information based on the 2-segment structure and the 3-segment ideal structure, and obtaining the expression for the cross-sectional area and initial velocity at the structural interface based on the parameter information, includes: setting parameter information based on the 2-segment structure and the 3-segment ideal structure, wherein the parameter information includes the cross-sectional area at each structural interface, the initial velocity at the inlet of each structural interface, the pipe diameter, the straight channel length of the 2-segment structure, the straight channel length of the 3-segment ideal structure, the horizontal length of the entire effective structure, half the cone angle of the left converging tube in the 3-segment ideal structure, half the cone angle of the right converging tube in the 2-segment structure / 3-segment ideal structure, and the total gas flow rate at the jet inlet; and obtaining the expression for the cross-sectional area and initial velocity at the structural interface based on geometric relationships, flow rate related formulas, and the parameter information.

[0023] The cross-sectional area at the interface of the structure satisfies the following relationship with the initial velocity:

[0024] ,

[0025] in, This represents the cross-sectional area at the first interface. Represents pi (π). Indicates the pipe diameter. This indicates the horizontal length of the tapered tube in the two-segment structure. This represents half the cone angle of the right-hand tapered tube in a 2-segment / 3-segment ideal structure. This represents the initial velocity at the entrance of the first interface. This indicates the total gas flow rate at the jet inlet. This represents the radius of the cross-section of the tapered tube on the right in a 2-segment or 3-segment ideal structure. This represents the infinitesimal variable representing the radius of the cross-section of each structural segment in the integral expression. This represents the cross-sectional area at the second interface. This represents the horizontal length of the left tapering tube in the three-segment ideal structure. This represents half the cone angle of the left tapered tube in the ideal three-segment structure. This represents the initial velocity at the entrance of the second interface. Let represent the radius of the cross-section of the left-hand tapered tube in the three-segment ideal structure. This represents the cross-sectional area at the straight passage of each structure. This represents the radius of the cross-section of the straight channel in a 2-segment or 3-segment ideal structure. This represents the initial velocity at the entrance of each structural straight channel.

[0026] This invention can adapt to relatively complex pipe structures such as 2-section and 3-section ideal structures. It accurately describes the flow characteristics of gas in complex structures through parameters and derived expressions, and can meet the analysis needs of complex flow conditions in practical applications.

[0027] Optionally, the step of combining the total energy loss result and the expression for cross-sectional area and initial velocity to obtain the friction loss calculation result and the local pressure loss calculation result includes:

[0028] The calculated friction loss along the route satisfies the following relationship:

[0029] ,

[0030] in, This indicates the friction loss along the two sections. Indicates the length of the straight channel in the two-segment structure. Indicates the pipe diameter. This represents the initial velocity at the entrance of each structural straight channel. This represents the ideal friction loss along the three segments. This represents the length of the straight channel in the three ideal structures. This indicates the total gas flow rate at the jet inlet. Represents pi (π). The infinitesimal variable representing the radius of the straight channel in the integral expression;

[0031] The calculated results of the local pressure loss satisfy the following relationship:

[0032] ,

[0033] in, This indicates the local loss of the two-segment structure. This represents half the cone angle of the right-hand tapered tube in a 2-segment / 3-segment ideal structure. Represents gravitational acceleration. This indicates the horizontal length of the tapered tube in the two-segment structure. This represents the cross-sectional area at the straight passage of each structure. Represents pi (π). Let represent the infinitesimal variable representing the length of the two tapered tube segments in the integral equation. This indicates the total gas flow rate at the jet inlet. The infinitesimal variable representing the radius of the cross-section of each structural segment in the integral expression. This represents the local loss of the three-segment ideal structure. This represents the length of the right-hand tapered tube in the three-segment ideal structure. This represents the cross-sectional area at the second interface. This represents the horizontal length of the left tapering tube in the three-segment ideal structure. This represents half the cone angle of the left tapered tube in the ideal three-segment structure. The infinitesimal variable represents the length of the left-hand tapering tube of the three-segment ideal structure in the integral.

[0034] Optionally, the step of establishing an energy loss difference expression based on the friction loss calculation results and the local pressure loss calculation results, setting the variable domain of the energy loss difference expression, and constructing an objective function for the energy loss difference of different pipeline structures based on the energy loss difference expression and the variable domain includes: the energy loss difference expression satisfying the following relationship:

[0035] ,

[0036] in, This represents the energy loss difference between a 2-segment structure and a 3-segment ideal structure. This indicates two local losses. This indicates the friction loss along the two sections. This represents the ideal friction loss along the three segments. This represents three ideal local losses;

[0037] Based on the energy loss difference expression, the domain of different variables in the energy loss difference expression is set; based on the energy loss difference expression and the domain, an objective function for the energy loss difference is constructed.

[0038] The objective function for the energy loss difference satisfies the following relationship:

[0039] ,

[0040] in, This represents the energy loss difference between a 2-segment structure and a 3-segment ideal structure. This represents half the cone angle of the right-hand tapered tube in a 2-segment / 3-segment ideal structure. Represents gravitational acceleration. The factorless part representing the local loss of a two-segment tapered tube is shown. The factorless part represents the local loss of the right-hand tapered tube in the three-segment ideal structure. This represents half the cone angle of the left tapered tube in the ideal three-segment structure. The factorless part representing the local loss of the left-hand tapered tube in the three-segment ideal structure. This represents the difference in travel loss along the straight path between the 2-segment structure and the 3-segment ideal structure.

[0041] Optionally, the partial calculation of the objective function for the energy loss difference yields a half cone angle. With the length of the three ideal structural straight channels The optimization equations include: for the objective function of the energy loss difference Taking the partial derivative, we get Partial derivative analysis results; for the objective function of the energy loss difference Taking the partial derivative, we get Partial derivative analysis results; setting the... Partial derivative analysis results and the above The partial derivative analysis results are all zero, thus obtaining half the cone angle. With the length of the three ideal structural straight channels The optimization equation;

[0042] The optimization equation satisfies the following relationship:

[0043] ,

[0044] ,

[0045] in, This represents the length of the straight channel in the three ideal structures. This represents the initial velocity at the entrance of each structural straight channel. Indicates the pipe diameter. This represents half the cone angle of the right-hand tapered tube in a 2-segment / 3-segment ideal structure. The factorless part represents the local loss of the right-hand tapered tube in the three-segment ideal structure. This represents half the cone angle of the left tapered tube in the ideal three-segment structure. This represents the factorless portion of the local loss of the left-hand tapered tube in a three-segment ideal structure.

[0046] This invention transforms the pipeline structure optimization problem into an optimization equation solving problem, which simplifies the calculation process, reduces the number of calculation variables and complexity, and improves the solution efficiency.

[0047] Optionally, the horizontal length of the left tapering tube in the three ideal structures is obtained based on geometric constraints, height relationships, and variable coupling. The expressions include:

[0048] The The expression satisfies the following relationship:

[0049] ,

[0050] in, This represents the horizontal length of the left tapering tube in the three-segment ideal structure. This represents the length of the straight channel in the three ideal structures. Indicates the length of the straight channel in the two-segment structure. This represents half the cone angle of the right tapered tube in a 2-segment or 3-segment ideal structure.

[0051] Different piping systems have different manufacturing requirements. This invention uses expressions for calculation to ensure that the piping structure meets both geometric constraints and manufacturing requirements.

[0052] Optionally, the combination of the optimization equation and the The expression establishes a set of parametric equations for the maxima, and the optimal pipeline structure is determined by the set of parametric equations for the maxima, including:

[0053] The parametric equations at the maximum value satisfy the following relationship:

[0054] ,

[0055] in, This represents the horizontal length of the left tapering tube in the three-segment ideal structure. This represents the length of the straight channel in the three ideal structures. Indicates the length of the straight channel in the two-segment structure. This represents half the cone angle of the right-hand tapered tube in a 2-segment / 3-segment ideal structure. The factorless part represents the local loss of the right-hand tapered tube in the three-segment ideal structure. This represents half the cone angle of the left tapered tube in the ideal three-segment structure. The factorless part representing the local loss of the left-hand tapered tube in the three-segment ideal structure. This represents the maximum radius of the left converging tube in the three-segment ideal structure. This represents the initial velocity at the entrance of each structural straight channel. Indicates the pipe diameter.

[0056] This invention finds the parameter combination that minimizes energy loss in a pipeline system by solving the parametric equations at their maxima, thereby reducing energy loss, improving the energy utilization efficiency of the pipeline system, and further meeting diverse engineering application needs.

[0057] Secondly, the present invention also provides a system for determining the optimal pipeline structure based on energy loss difference, which can efficiently execute the method for determining the optimal pipeline structure based on energy loss difference provided by the present invention. The system includes an input device, a processor, an output device, and a memory, wherein the input device, processor, output device, and memory are interconnected. The memory includes a computer-readable storage medium as described in the first aspect of the present invention, and is used to store a computer program. The computer program includes program instructions, and the processor is configured to call the program instructions. The system for determining the optimal pipeline structure based on energy loss difference provided by the present invention has a compact structure, strong applicability, and greatly improves operating efficiency. Attached Figure Description

[0058] Figure 1 This is a flowchart of the method for determining the optimal pipeline structure based on energy loss difference according to the present invention;

[0059] Figure 2 This is a schematic diagram of a two-segment structure and a three-segment ideal structure in the method for determining the optimal pipeline structure based on energy loss difference in this invention;

[0060] Figure 3 This is a simulation diagram of the pipeline structure in the method for determining the optimal pipeline structure based on energy loss difference in this invention;

[0061] Figure 4 This is a schematic diagram of the system for determining the optimal pipeline structure based on energy loss difference according to the present invention. Detailed Implementation

[0062] Specific embodiments of the present invention will now be described in detail. It should be noted that the embodiments described herein are for illustrative purposes only and are not intended to limit the invention. In the following description, numerous specific details are set forth in order to provide a thorough understanding of the invention. However, it will be apparent to those skilled in the art that these specific details are not necessary to practice the invention. In other instances, well-known circuits, software, or methods have not been specifically described to avoid obscuring the invention.

[0063] Throughout this specification, references to "an embodiment," "an embodiment," "an example," or "an example" mean that a particular feature, structure, or characteristic described in connection with that embodiment or example is included in at least one embodiment of the invention. Therefore, the phrases "in an embodiment," "in an embodiment," "an example," or "an example" appearing in various places throughout the specification do not necessarily refer to the same embodiment or example. Furthermore, specific features, structures, or characteristics can be combined in one or more embodiments or examples in any suitable combination and / or sub-combination. Moreover, those skilled in the art will understand that the illustrations provided herein are for illustrative purposes and are not necessarily drawn to scale.

[0064] Please see Figure 1 To ensure that airflow passes through multiple tapered pipes in a decreasing cone angle order, effectively reducing the collision effect generated when airflow moves along the wall at the structural interface, minimizing energy loss and waste, and achieving a rational design of the multi-segment structure, thereby improving system performance and practical application, this invention provides a method for determining the optimal pipe structure based on energy loss difference. This method includes the following steps:

[0065] S1. Obtain the friction loss along the straight channel and the local loss of the channel with varying cross-section. Combine the equivalent velocity, friction loss along the straight channel, and local loss to obtain the total energy loss result. The implementation steps and specific details are as follows:

[0066] First, obtain the friction loss along the straight channel and the local loss of the channel with changing cross-section.

[0067] In an optional embodiment, the friction loss along the straight path is obtained, and the specific implementation steps are as follows:

[0068] The first step is to calculate the friction coefficient based on the Reynolds number and the pipe roughness.

[0069] In the field of fluid mechanics, the coefficient of friction is a key factor in calculating energy loss, especially for the flow characteristics of viscous fluids in straight channels. Based on Reynolds number And the roughness of the pipe is calculated.

[0070] Energy loss in straight channels primarily stems from viscous friction. The Darcy-Weisbach equation provides a scientifically universal method for calculating this type of energy loss. As a phenomenological equation in fluid mechanics, it precisely describes the gradual dissipation of energy—i.e., friction loss—caused by the continuous friction between the fluid and the pipe wall, and the viscous shear stress within the fluid, as the viscous fluid flows through a pipe. The Darcy-Weisbach equation has broad applicability and can cover computational needs at all Reynolds numbers.

[0071] In the process of investigating the fluid flow characteristics inside the jet orifice, the friction coefficient was accurately determined. This is an important part of analyzing fluid flow resistance mechanisms and calculating friction losses along the flow path. This embodiment is mainly based on fluid mechanics theory, when the Reynolds number inside the jet orifice... When the fluid exhibits turbulent flow, the Colbrook equation becomes the accurate formula for calculating the friction coefficient. Ideally, the Colbrook equation described above is presented in implicit form, and its mathematical expression is as follows:

[0072]

[0073] in, Indicates the coefficient of friction. This indicates the absolute roughness of the pipe (for pipes made of ceramic or coated metals, its absolute roughness is...). ), Indicates the pipe diameter. Represents the Reynolds number.

[0074] The Reynolds number is an important dimensionless number for measuring the state of fluid flow.

[0075] The second step is to iteratively solve for the friction coefficient to obtain the friction loss along the straight channel.

[0076] Because the above mathematical expression has implicit characteristics, iterative algorithms are needed to continuously adjust the friction coefficient. The initial guess value is used until it meets the preset convergence accuracy, thereby obtaining the friction coefficient. The exact solution.

[0077] The embodiment utilizes the Brassius formula for rapid estimation. The Brassius formula is specifically designed for the turbulent smooth region of smooth pipes. It exhibits extremely high computational accuracy within the Reynolds number range. Due to the Reynolds number in the embodiment... The range is in The conditions between these values ​​perfectly match the applicability of the Blasius formula, therefore the above formula can be used for calculation.

[0078] The specific form of the above Blasius formula is as follows:

[0079]

[0080] in, Indicates the coefficient of friction. Represents the Reynolds number.

[0081] By using the two methods described above, the friction coefficient f can be obtained comprehensively and accurately, thus providing a reliable basis for calculating friction loss along a straight channel.

[0082] Based on friction coefficient The friction loss along the straight path can then be obtained, and it satisfies the following relationship:

[0083]

[0084] in, This represents the friction loss along the straight path. Indicates the coefficient of friction. Indicates the length of the straight channel. Indicates the pipe diameter. Indicates airflow velocity. It represents the acceleration due to gravity.

[0085] In the calculation of energy loss in straight channels, scientific and accurate calculation methods are provided for different situations. When the Reynolds number... When the fluid is in a turbulent state, using the Colbrook equation and obtaining the solution of the friction coefficient through an iterative algorithm helps to accurately calculate the friction loss along the flow path.

[0086] Meanwhile, this embodiment sets a Reynolds number range, and the friction coefficient can be quickly and accurately estimated using the Blasius formula, providing a reliable basis for calculating friction loss along the path. Combined with the friction coefficient calculation method, it can comprehensively and accurately calculate the friction loss along the path of a straight channel.

[0087] In another alternative embodiment, the local loss of the cross-sectional change channel is obtained, and the specific implementation steps are as follows:

[0088] The first step is to analyze the local loss coefficient based on the geometry and cone angle of the tapered converging tube.

[0089] Since the geometry of the tapered tube has a significant impact on the local loss coefficient, and the cone angle is a key parameter describing its geometric characteristics, it is necessary to analyze the geometry and cone angle of the tapered tube in order to effectively determine the local loss coefficient.

[0090] This embodiment limits the cone angle range to [specific range]. Within this range, a representative typical tapered conical tube model can be used for calculation, and the local loss coefficient is then determined. The approximate formula can be expressed as:

[0091]

[0092] in, Represents the local loss coefficient. Indicates the taper angle of the converging tube. Indicates the cross-sectional area of ​​the outlet. This represents the inlet cross-sectional area. The aforementioned local loss coefficient is a dimensionless quantity, and its value is closely related to the geometry of the tapered converging tube and the flow state of the fluid within it.

[0093] The second step is to obtain the local loss of the cross-sectional change channel based on the local loss coefficient.

[0094] After determining the local loss coefficient Next, the local losses in the cross-sectional change channel can be calculated. The energy loss caused by the cross-sectional change mainly stems from flow separation and velocity distribution distortion. This energy loss caused by flow separation, vortex generation, or velocity redistribution due to abrupt changes in pipe geometry (such as elbows, valves, expansion / contraction sections, etc.) can be collectively referred to as local losses.

[0095] Local loss of the aforementioned cross-sectional change channel The following relationship must be satisfied:

[0096]

[0097] in, This represents the local loss of the channel with varying cross-section. Represents the local loss coefficient. Indicates airflow velocity. It represents the acceleration due to gravity.

[0098] For channels with varying cross-sections, the local loss coefficient is analyzed based on the geometry and cone angle of the tapered converging tube. By limiting the cone angle range, the local loss coefficient is calculated using a typical tapered converging tube model and approximate formulas. These coefficients are closely related to the geometry and flow state. By combining the relationship between local loss and local loss coefficient, airflow velocity, and gravitational acceleration, the local loss of the channel with varying cross-sections can be reasonably calculated, providing a reference and data foundation for determining the optimal pipe structure.

[0099] Then, the total energy loss is obtained by combining the equivalent velocity, friction loss along the path, and local loss.

[0100] The first step is to obtain the equivalent velocity based on the power-law velocity distribution.

[0101] When Reynolds number The range is in In the laminar flow region, the velocity distribution characteristics of turbulent flow differ significantly from those of laminar flow, exhibiting a flatter velocity distribution. Specifically, the velocity gradient is smaller in the central region of the pipe, while the velocity changes drastically near the pipe wall. In the field of turbulence research, the power-law velocity distribution is a commonly used empirical formula, and the mathematical expression for this equivalent velocity is as follows:

[0102]

[0103] in, Indicates equivalent velocity. This indicates the maximum speed at the center of the pipe. This represents the radial distance from the center of the pipe to a certain point. Indicates the pipe radius. This indicates an index related to the Reynolds number.

[0104] Regarding the Reynolds number in This specific range can be adopted The power-law distribution is approximated by letting... In practical engineering, this index will fluctuate slightly with changes in the Reynolds number, but Power laws already possess sufficient accuracy in most engineering applications.

[0105] Therefore, the equivalent velocity expression can be simplified to:

[0106]

[0107] The second step is to derive the velocity relationship between the average velocity and the maximum velocity at the center of the pipeline based on the equivalent velocity.

[0108] Under turbulent conditions, the maximum velocity at the center of the pipe It cannot be obtained directly by dividing the flow rate Q by the cross-sectional area S, because... This represents the average velocity inside the pipe. .

[0109] To derive the average speed With maximum speed The relationship between the two is explained in the embodiment by calculating the flow rate Q using integration, based on the flow rate definition. Furthermore, by combining this with the power-law velocity distribution formula, the average velocity can be derived. and The relationship between them satisfies the following:

[0110]

[0111] Therefore, the maximum speed in this embodiment satisfies the following relationship: .

[0112] By calculating the flow rate through integration and deriving the relationship between the average velocity and the maximum velocity using the power-law velocity distribution formula, the maximum velocity can be easily obtained when the average velocity is known based on parameters such as flow rate and pipe size. This facilitates a comprehensive analysis of the velocity at different locations within the pipe, helps to gain a deeper understanding of the fluid flow characteristics within the pipe, and ultimately enables a more accurate assessment of the energy loss of the structural pipe.

[0113] Finally, the total energy loss is obtained by combining the velocity relationship, friction loss along the path, and local loss.

[0114] The above total energy loss results strictly satisfy the following mathematical relationship:

[0115]

[0116] in, Indicates total energy loss. Indicates air density, Indicates the coefficient of friction. Indicates the length of the straight channel. Indicates the pipe diameter. Indicates airflow velocity. Represents the local loss coefficient. This indicates the flow velocity at the inlet of the section where the cross-section changes.

[0117] In order to compare the performance difference between a two-segment structure and a multi-segment structure, this embodiment introduces the above-mentioned energy loss formula. Based on this, it can be seen that the energy loss of airflow in the pipeline mainly includes two parts: friction loss along the path (straight channel) and local loss (cross-sectional change channel), and the total energy loss is the sum of the two.

[0118] The above formula for total energy loss comprehensively considers two main factors: friction loss along the pipe and local losses. Friction loss along the pipe is related to the pipe's friction coefficient, length, diameter, and airflow velocity, reflecting the energy loss caused by friction between the fluid and the pipe wall during flow. Local losses are related to the local loss coefficient and the flow velocity at the inlet of sections with cross-sectional changes, taking into account energy losses caused by fluid eddies and impacts due to changes in pipe cross-section. These analytical steps make the calculation of total energy loss more accurate and reliable, truly reflecting the actual energy loss of the fluid within the pipeline system.

[0119] Accurate calculation of total energy loss provides a clear understanding of the impact of different pipeline structural parameters on energy loss. Changing the pipeline diameter affects both frictional losses and the velocity term in local losses, thus altering the total energy loss. Different cone angle structures lead to variations in the local loss coefficient, also resulting in different total energy losses. Based on these calculations, the energy loss under different pipeline structural schemes can be compared, allowing for the selection of the optimal pipeline structure with the lowest energy loss. This contributes to achieving energy conservation, emission reduction, and efficient operation of the pipeline system.

[0120] S2. Based on the parameter information of the 2-segment and 3-segment ideal structures, the cross-sectional area and initial velocity expressions at the structural interfaces are obtained according to the parameter information. Combining the total energy loss results and the cross-sectional area and initial velocity expressions, the friction loss calculation results and local pressure loss calculation results can be obtained. The specific steps and implementation content are as follows:

[0121] First, parameter information is set based on the 2-segment structure and the ideal 3-segment structure.

[0122] To accurately analyze the energy loss difference between the two-segment structure and the three-segment ideal structure, schematic diagrams of the two-segment and three-segment ideal structures were drawn. Please refer to [link / reference needed]. Figure 2 ,in It has a two-part structure. It is a 3-segment ideal structure.

[0123] based on Figure 2 The two-segment and three-segment ideal structure settings parameters in the embodiment mainly include the cross-sectional area at the interface of each structure. Initial velocity at the entrance of each structural interface Pipe diameter D, straight channel length of the two-section structure Length of straight channel in 3 ideal structures The horizontal length H of the entire effective structure, and the horizontal length of the left tapering tube in the three ideal structures. Horizontal length of the tapered tube in the 2-section structure Half the cone angle of the left tapered tube in the ideal three-segment structure Half the cone angle of the right tapered tube in a 2-segment / 3-segment ideal structure and the total gas flow rate Q at the jet inlet;

[0124] Then, based on geometric relationships, flow-related formulas, and parameter information, the expressions for the cross-sectional area and initial velocity at the structural interface are obtained.

[0125] The cross-sectional area at the interface of the above structures and the initial velocity satisfy the following relationship:

[0126]

[0127] in, This represents the cross-sectional area at the first interface. Represents pi (π). Indicates the pipe diameter. This indicates the horizontal length of the tapered tube in the two-segment structure. This represents half the cone angle of the right-hand tapered tube in a 2-segment / 3-segment ideal structure. This represents the initial velocity at the entrance of the first interface. This indicates the total gas flow rate at the jet inlet. This represents the radius of the cross-section of the tapered tube on the right in a 2-segment or 3-segment ideal structure. This represents the infinitesimal variable representing the radius of the cross-section of each structural segment in the integral expression. This represents the cross-sectional area at the second interface. This represents the horizontal length of the left tapering tube in the three-segment ideal structure. This represents half the cone angle of the left tapered tube in the ideal three-segment structure. This represents the initial velocity at the entrance of the second interface. This represents the radius of the cross-section of the left-hand tapering tube in the three-segment ideal structure. This represents the cross-sectional area at the straight passage of each structure. This represents the radius of the cross-section of the straight channel in a 2-segment or 3-segment ideal structure. This represents the initial velocity at the entrance of each structural straight channel.

[0128] Next, by combining the above total energy loss results and the expression for cross-sectional area and initial velocity, the results of friction loss calculation and local pressure loss calculation are obtained.

[0129] After completing the preliminary analysis of total energy loss and clarifying the expressions for cross-sectional area and initial velocity, further in-depth calculations of friction loss and local pressure loss are needed.

[0130] First, set the inlet pressure of the jet nozzle to be... This data can be referenced from numerical simulations and experimental studies on the motion characteristics of high-speed rotating airflow-fiber coupling.

[0131] In fluid mechanics, the Reynolds number It is an important parameter for determining the fluid flow state, and its calculation formula is as follows: ,in This represents air density, which takes the value of [value missing] under standard conditions. , This represents the initial velocity of the gas at the pipe inlet. Indicates the pipe diameter. express The dynamic viscosity of air, where the value is... .

[0132] Because the inner diameter of the straight channel is extremely small and the residence time of the airflow within the channel is short, the Blasius formula is selected based on the above flow conditions. To calculate the coefficient of friction This formula has high accuracy in the case of turbulent flow in a smooth straight pipe and can fit the current airflow characteristics well.

[0133] According to the Darcy-Weisbach formula The friction loss along the straight section can be derived. After further analysis and simplification, the friction loss calculation results satisfy the following specific relationship:

[0134]

[0135] in, This indicates the friction loss along the two sections. Indicates the length of the straight channel in the two-segment structure. Indicates the pipe diameter. This represents the initial velocity at the entrance of each structural straight channel. This represents the ideal friction loss along the three segments. This represents the length of the straight channel in the three ideal structures. This indicates the total gas flow rate at the jet inlet. Represents pi (π). The infinitesimal variable representing the radius of the straight channel in the integral expression;

[0136] By following the above calculation process and defining the parameters clearly, the calculation results of friction loss can be obtained accurately.

[0137] Furthermore, the calculated local pressure loss results for the 2-segment and 3-segment structures satisfy the following relationships:

[0138]

[0139] in, This indicates the local loss of the two-segment structure. This represents half the cone angle of the right-hand tapered tube in a 2-segment / 3-segment ideal structure. Represents gravitational acceleration. This indicates the horizontal length of the tapered tube in the two-segment structure. This represents the cross-sectional area at the straight passage of each structure. Represents pi (π). Let represent the infinitesimal variable representing the length of the two tapered tube segments in the integral equation. This indicates the total gas flow rate at the jet inlet. This represents the infinitesimal variable representing the radius of the cross-section of each structural segment in the integral expression. This represents the local loss of the three-segment ideal structure. This represents the length of the right-hand tapered tube in the three-segment ideal structure. This represents the cross-sectional area at the second interface. This represents the horizontal length of the left tapering tube in the three-segment ideal structure. This represents half the cone angle of the left tapered tube in the ideal three-segment structure. The infinitesimal variable represents the length of the left-hand tapering tube of the three-segment ideal structure in the integral.

[0140] In this embodiment, the friction coefficient is calculated based on the Darcy-Weisbach formula and combined with the Blasius formula. After further analysis and simplification, a specific relationship is obtained for the calculation results of friction loss along the flow path. This can accurately quantify the energy loss of airflow along the flow path in a straight channel, which helps to understand the energy consumption of straight channels with different structures. This allows for the rational planning of parameters such as the length and diameter of straight channels in pipeline design, avoiding unnecessary energy waste and achieving optimal energy allocation.

[0141] The local pressure loss analysis considers various factors such as the cone angle, horizontal length, cross-sectional area variation of the converging pipe, and airflow velocity distribution. Through multiple integrations, the local pressure loss is accurately calculated, precisely capturing energy loss at points of pipe structural change (such as converging pipes), thus providing a basis for optimizing pipelines.

[0142] The structure provides a basis for reducing local energy loss and helps to further improve energy efficiency.

[0143] S3. Based on the above calculation results of friction loss and local pressure loss, establish an expression for energy loss difference and set the domain of variables for the energy loss difference expression. Based on the above energy loss difference expression and domain of variables, construct an objective function for the energy loss difference of different pipeline structures. The specific steps and implementation content are as follows:

[0144] First, an expression for the energy loss difference is established based on the calculation results of friction loss and local pressure loss.

[0145] set up Let be the energy loss difference between the 2-segment structure and the 3-segment ideal structure. The expression for this energy loss difference satisfies the following relationship:

[0146]

[0147] in, This represents the energy loss difference between a 2-segment structure and a 3-segment ideal structure. This indicates two local losses. This indicates the friction loss along the two sections. This represents the ideal friction loss along the three segments. This represents three ideal local losses;

[0148] Then, the domain of different variables in the energy loss difference expression is set based on the energy loss difference expression.

[0149] After constructing the expression for the energy loss difference, it is necessary to further clarify the domain of each variable in the expression. This embodiment requires... Solve the inequality and find the difference. The expression is a combination of multiple parameters (D, H, h, ... , The positive or negative sign of an expression composed of (etc.) depends on the nonlinear superposition effect of each parameter on the positive and negative terms.

[0150] When solving for W>0, each variable needs to satisfy the following domain conditions:

[0151]

[0152] The explanations for the above variables are as follows:

[0153] This represents half the cone angle of the right tapered tube in a 2-segment or 3-segment ideal structure.

[0154] This represents half the cone angle of the left tapered tube in the ideal three-segment structure;

[0155] Indicates the pipe diameter;

[0156] Indicates the horizontal length of the entire effective structure;

[0157] This represents the horizontal length of the left tapering tube in the three-segment ideal structure;

[0158] This indicates the horizontal length of the tapered tube in the two-segment structure;

[0159] This indicates the length of the right-hand tapering tube in the three-segment ideal structure.

[0160] Indicates the length of the straight channel in the two-segment structure;

[0161] Indicates the length of the straight channel in the three ideal structures;

[0162] This represents the cross-sectional area at the first interface;

[0163] This represents the cross-sectional area at the straight passage of each structure;

[0164] This represents the initial velocity at the entrance of the first structural interface;

[0165] Finally, an objective function for the energy loss difference is constructed based on the expression for the energy loss difference and the domain.

[0166] After constructing the expression for the energy loss difference and defining the domain of variables, it is necessary to construct the objective function for the energy loss difference. The core task of this embodiment is to obtain the difference between the two-segment structure and the three-segment ideal structure. The maximum value of .

[0167] The specific operating procedure is as follows:

[0168] Determine parameters based on the two referenced structures. The specific values ​​were then adjusted based on relevant parameters to obtain the three ideal structures.

[0169] The overall idea is to use the difference Find the derivative, locate its extreme points, and then construct a set of conditions that satisfy the extreme point conditions. .

[0170] To facilitate subsequent analysis and calculation, the objective function is adjusted to The form is given, and a detailed analysis of the relationships between the various formulas is provided:

[0171]

[0172] in, Let represent the infinitesimal variable representing the cross-sectional radius of the right-hand tapered tube in the two-segment structure of the integral expression. Let represent the infinitesimal variable representing the radius of the right-hand tapered tube of the three ideal structures in the integral equation. The infinitesimal variable represents the radius of the cross-section of the left-hand tapered tube in the three-segment ideal structure of the integral expression.

[0173] Further analysis of the difference After simplification, the objective function for the energy loss difference of different pipeline structures is obtained, which satisfies the following relationship:

[0174]

[0175] in, This represents the energy loss difference between a 2-segment structure and a 3-segment ideal structure. This represents half the cone angle of the right-hand tapered tube in a 2-segment / 3-segment ideal structure. Represents gravitational acceleration. The factorless part representing the local loss of a two-segment tapered tube is shown. The factorless part represents the local loss of the right-hand tapered tube in the three-segment ideal structure. This represents half the cone angle of the left tapered tube in the ideal three-segment structure. The factorless part representing the local loss of the left-hand tapered tube in the three-segment ideal structure. This represents the difference in travel loss along the straight path between the 2-segment structure and the 3-segment ideal structure.

[0176] The parameter values ​​of the two-segment structure can be referenced, and then adjusted based on the relevant parameters to obtain the three-segment ideal structure. Therefore, it can be seen that the method in this embodiment, starting from the known structure and gradually deriving and constructing the ideal structure, makes the entire process repeatable and operable, facilitating the practical application and implementation of the method in actual engineering.

[0177] By differentiating the difference, we can find its extreme points, and then construct the pipe structure parameters that satisfy the extreme point conditions. Meanwhile, using mathematical differentiation to find extreme points is a scientific and rigorous optimization method that can ensure that the structural parameters found reach the optimal state in terms of energy loss difference.

[0178] S4. Obtain half the cone angle by partial calculation of the objective function for energy loss difference. With the length of the three ideal structural straight channels The optimization equations, based on geometric constraints, height relationships, and variable coupling, yielded the horizontal length of the left tapering tube in the three ideal structures. The expression, its specific steps, and related content are as follows:

[0179] In the process of pipeline structure optimization, a variable was defined. and bivariate function Its expression is:

[0180]

[0181] In an optional embodiment, half the cone angle is obtained. With the length of the three ideal structural straight channels The optimization equation.

[0182] For the objective function of energy loss difference Taking the partial derivative, we get Partial derivative analysis results.

[0183] right Partial derivatives, The partial derivative analysis results satisfy the following relationship:

[0184]

[0185] in:

[0186]

[0187] For the objective function of energy loss difference Find the partial derivative to obtain Partial derivative analysis results.

[0188] right Partial derivatives, The partial derivative analysis results satisfy the following relationship:

[0189]

[0190] in:

[0191]

[0192] Next, set Partial derivative analysis results and The partial derivative analysis results are all zero, thus obtaining half the cone angle. With the length of the three ideal structural straight channels The optimization equation.

[0193] In the example, setting the partial derivative to zero, we can obtain the following about and The optimization equation, and thus the maximum value, must satisfy the following condition:

[0194]

[0195] Among them Optimize:

[0196]

[0197] Simplifying, we get:

[0198]

[0199] right Optimize:

[0200]

[0201] Simplifying, we get:

[0202]

[0203] in, This represents the length of the straight channel in the three ideal structures. This represents the initial velocity at the entrance of each structural straight channel. Indicates the pipe diameter. This represents half the cone angle of the right-hand tapered tube in a 2-segment / 3-segment ideal structure. The factorless part represents the local loss of the right-hand tapered tube in the three-segment ideal structure. This represents half the cone angle of the left tapered tube in the ideal three-segment structure. This represents the factorless portion of the local loss of the left-hand tapered tube in a three-segment ideal structure.

[0204] In the process of finding partial derivatives, each intermediate variable (such as...) was analyzed in detail. , , (etc.) and , The complex relationships between them. In this example, the chain rule is used for calculation. , and At that time, I considered right and The rate of change, and , right The rate of change of other related parameters further reveals the intrinsic relationship between variables in the pipeline structure, which helps to more comprehensively understand the energy loss mechanism of the pipeline system.

[0205] In another alternative embodiment, the horizontal length of the left tapering tube in the three-segment ideal structure is obtained. expression.

[0206] In the structural design and analysis of the pipeline system, for three ideal structures, in order to accurately determine the horizontal length of the left converging pipe... This requires comprehensive consideration of geometric constraints, height relationships, and the coupling characteristics between variables. The specific derivation process is as follows:

[0207] First, based on the geometric constraints, the following geometric constraint equations exist in the pipeline structure:

[0208]

[0209] This equation reflects the geometric relationship between the horizontal length and cone angle of different tapered tubes.

[0210] Secondly, the height relationship is as follows:

[0211]

[0212] The above height relationship clarifies the relationship between the length of each segment and the total height. The quantitative relationship between them.

[0213] Finally, and Substituting the expression into the inverted geometric constraint equation, and after a series of algebraic operations and simplifications, we can obtain... For expressions with other known parameters, The expression satisfies the following relationship:

[0214]

[0215] in, This represents the horizontal length of the left tapering tube in the three-segment ideal structure. This represents the length of the straight channel in the three ideal structures. Indicates the length of the straight channel in the two-segment structure. This represents half the cone angle of the right tapered tube in a 2-segment or 3-segment ideal structure.

[0216] The above The expression is to follow The optimization analysis provides a mathematical reference, and the clear variable relationships help to deeply understand the coupling characteristics between various parameters in the pipeline structure. It can grasp the geometric characteristics of the pipeline system as a whole and provides a clear idea for further research on the interaction between energy loss and parameters.

[0217] In a method for determining the optimal pipeline structure based on energy loss difference, the geometric dimensions of each part of the pipeline are one of the key factors affecting energy loss. The derivation of the expression adds important geometric relationships to the entire theoretical system, making the analysis from geometric structure to energy loss more complete and systematic. It connects the geometry of the pipe (such as the taper angle and straight-channel length of a converging pipe) with specific dimensional parameters. This lays a solid theoretical foundation for further in-depth analysis of the relationship between energy loss and pipeline structure.

[0218] S5. Combining the above optimization equations and The expression establishes a set of parametric equations for the maxima, and the optimal pipeline structure is determined through this set of parametric equations for the maxima. The specific steps and related content are as follows:

[0219] In the process of optimizing the design of pipeline systems, in order to accurately determine the optimal pipeline structure, it is necessary to combine the optimization equations with the previously derived results. The expression is used to construct a system of parametric equations for the maximum value case, and the optimal structure parameters are determined by solving this system of equations. The specific steps and related content are as follows:

[0220] Because the equations involved are highly nonlinear, it is difficult to obtain an exact solution directly using conventional analytical methods. Therefore, it is necessary to comprehensively utilize the geometric relationships of the pipeline system, the energy loss characteristics, and the coupling relationships between various parameters to construct a set of parametric equations when the energy loss reaches a maximum value (which, from an optimization perspective, may be a local maximum used to find the optimal structural point). This set of equations serves as the basis for solving for the optimal structural parameters.

[0221] The parametric equations at the above maxima satisfy the following relationship:

[0222]

[0223] in, This represents the horizontal length of the left tapering tube in the three-segment ideal structure. This represents the length of the straight channel in the three ideal structures. Indicates the length of the straight channel in the two-segment structure. This represents half the cone angle of the right-hand tapered tube in a 2-segment / 3-segment ideal structure. The factorless part represents the local loss of the right-hand tapered tube in the three-segment ideal structure. This represents half the cone angle of the left tapered tube in the ideal three-segment structure. The factorless part representing the local loss of the left-hand tapered tube in the three-segment ideal structure. This represents the maximum radius of the left converging tube in the three-segment ideal structure. This represents the initial velocity at the entrance of each structural straight channel. Indicates the pipe diameter.

[0224] expression The horizontal length of the left tapering tube in the three-segment ideal structure is clearly defined. The length of the straight channel of the three ideal structures Length of straight channel in 2-section structure and tapered tube angle and The quantitative relationship between them is the fundamental geometric parameter expression for solving the subsequent system of equations.

[0225] Partial derivative equations related to energy loss s The factorless portion of the local loss of the right-side tapered tube in the three ideal structures is comprehensively considered. Factorless portion of local loss in the left-side tapered tube And the maximum radius of the tapered tube on the left With cone angle The relationship between the parameters, and the partial derivative calculations with respect to the parameters, reflect the energy loss as a function of the cone angle. The variation of is one of the key equations in the system of equations that describes the characteristics of energy loss.

[0226] Equation of relationship between velocity and geometric parameters The fluid velocity inside the pipe (the initial velocity at the inlet of each straight channel in the structure) ) and the geometric parameters of the pipe (cone angle) and pipe diameter This connection further demonstrates the interaction between fluid dynamics characteristics and pipeline geometry, which is of great significance for determining the optimal pipeline structure under specific fluid conditions.

[0227] By solving the parametric equations for the maximum value, the optimal parameter values ​​can be obtained, which is the optimal half-cone angle of the left converging tube. The optimal length of the three ideal structural straight channels After obtaining and Afterwards, according to The expression calculates the optimal horizontal length of the left converging tube. Then, by combining geometric relationships, the optimal half-cone angle of the right tapered tube can be further determined. The specific solution process can be achieved using numerical calculation methods, such as the Newton-Raphson method and genetic algorithms, which iteratively approximate the solution to the system of equations to determine the optimal structural parameters of the pipeline.

[0228] A method for determining the optimal pipeline structure based on energy loss difference also includes further verifying that the 3-segment structure is the structure with the least energy loss.

[0229] In addition to constructing and solving a system of equations with specific parameters to determine the pipe structure parameters, the above method can also further verify whether the obtained three-section structure is the structure with the least energy loss. The following is the relevant content of the verification process.

[0230] The parameters of the given two-segment structure are as follows:

[0231]

[0232] Based on the above parameters, the following results were obtained:

[0233]

[0234] Under this two-segment structure, the difference is calculated. The maximum value is 2273. Simultaneously, based on the pressure drop formula, the pressure loss difference between the two-section structure and the ideal three-section structure can be calculated. The value is 26730.48 Pa.

[0235] Theoretical analysis comparing three-segment structures with multi-segment structures;

[0236] To further investigate whether a 3-segment structure has less energy loss compared to 4-segment, 5-segment, or other multi-segment structures, we hypothesize the existence of a... Pressure loss difference function of segment Through the by Taking the partial derivative with respect to the parameter, we find that when hour To obtain an extreme value, that is It is the extreme point of the function.

[0237] To further verify this conclusion theoretically, a sequence formula was introduced for analysis. The expression:

[0238]

[0239] By observing the above expression, we can see that, excluding the first and last terms, the number of negative terms in the middle part increases with... The increase is due to the increase in [something]. In order to [do something] The key to achieving the maximum value lies in minimizing the number of negative terms.

[0240] In the extreme case, when there are no negative terms, i.e., only two structural segments exist, the calculation of the pressure loss difference becomes meaningless because there is no comparison with other multi-segment structures. However, when the number of negative terms is minimized, it is only when... When the condition is met, there is only one negative term, thus making It can reach the maximum value.

[0241] Based on the above theoretical analysis and the specific calculation results of the two-segment structure, a clear conclusion can be drawn: in a method for determining the optimal pipeline structure based on energy loss difference, the three-segment structure is the structure with the least energy loss. The method of this invention is not only strongly supported by theoretical function extremum analysis and sequence formula derivation, but also matches the actual calculation data of the two-segment structure, further verifying the superiority of the three-segment structure in reducing energy loss.

[0242] A method for determining the optimal pipeline structure based on energy loss difference also includes a simulation step.

[0243] In this embodiment, SolidWorks modeling and Ansys Fluent simulation analysis were used. After completing the theoretical verification that the three-segment structure is the structure with the least energy loss, the next step is to proceed to the simulation stage.

[0244] Based on the structural parameters determined in the above embodiments, fluid domain modeling will be performed using SolidWorks software, and the completed model will be imported into Ansys Fluent software for simulation analysis. This will primarily involve... cross section Velocity analysis was used to further verify the theoretical calculation results. A simulation diagram of the pipeline structure can be found in the provided text. Figure 3 .

[0245] From simulation results Figure 3 It can be clearly observed that The speed of the segment is significantly greater than The speed of the segment, specific data shows Section Duan Da This result is in high agreement with the energy loss results obtained from previous theoretical calculations, which fully demonstrates that the simulation data can accurately reflect the characteristics expected by the theoretical calculations, and further verifies the correctness and reliability of the theoretical model.

[0246] The vortex tube, a key component in this study, has a total of four jet holes. Simulation results show that the performance of each jet hole is significantly improved compared to previous versions, with an improvement rate reaching [percentage missing]. In the spinning process, the performance of the vortex tube jet orifice directly affects yarn quality and production efficiency. Improved jet orifice performance means a more stable and stronger airflow for the yarn, which helps to better control the yarn's trajectory, reduce yarn breakage and hairiness, and thus improve yarn quality and uniformity. Simultaneously, a stable airflow also improves the operational stability of spinning equipment, reduces the failure rate, and further increases production efficiency. Therefore, it can be expected that the optimized three-section pipe structure and the improved vortex tube jet orifice, based on this research, will have a positive and significant effect on the spinning process, bringing greater economic benefits and improved product quality to the textile industry.

[0247] Please see Figure 4 In an optional embodiment, the present invention also provides a system for determining the optimal structure of a pipeline based on energy loss difference. The system includes a processor, an input device, an output device, and a memory, which are interconnected. The memory stores a computer program, which includes program instructions. The processor is configured to call the program instructions and execute the specific steps of the method and related embodiments for determining the optimal structure of a pipeline based on energy loss difference provided by the present invention. The system for determining the optimal structure of a pipeline based on energy loss difference of the present invention is structurally complete, objective, and stable.

[0248] 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 them. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features therein. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention, and they should all be covered within the scope of the claims and specification of the present invention.

Claims

1. A method for determining the optimal pipeline structure based on energy loss difference, characterized in that, Includes the following steps: The friction loss along the straight channel and the local loss of the channel with changing cross-section are obtained. The total energy loss result is obtained by combining the equivalent velocity, the friction loss along the straight channel and the local loss. Based on the parameter information of the 2-segment structure and the 3-segment ideal structure, the cross-sectional area and initial velocity expression at the structural interface are obtained according to the parameter information. Combined with the total energy loss result and the cross-sectional area and initial velocity expression, the friction loss calculation result and the local pressure loss calculation result are obtained. An energy loss difference expression is established based on the friction loss calculation results and the local pressure loss calculation results. The domain of variables in the energy loss difference expression is set. An objective function for the energy loss difference of different pipeline structures is constructed based on the energy loss difference expression and the domain of variables. The partial cone angle is obtained by performing a partial calculation on the objective function of the energy loss difference. With the length of the three ideal structural straight channels The optimization equations, based on geometric constraints, height relationships, and variable coupling, yielded the horizontal length of the left tapering tube in the three ideal structures. expression; Combining the optimization equation and the The expression establishes a set of parametric equations at the maximum value, and the optimal pipeline structure is determined by the set of parametric equations at the maximum value. The step of establishing an energy loss difference expression based on the friction loss calculation results and the local pressure loss calculation results, setting the variable domain of the energy loss difference expression, and constructing an objective function for the energy loss difference of different pipeline structures based on the energy loss difference expression and the variable domain includes: The expression for the energy loss difference satisfies the following relationship: ， in, This represents the energy loss difference between a 2-segment structure and a 3-segment ideal structure. This indicates two local losses. This indicates the friction loss along the two sections. This represents the ideal friction loss along the three segments. This represents three ideal local losses; Based on the energy loss difference expression, the domain of different variables in the energy loss difference expression is set; Based on the energy loss difference expression and the domain, construct objective functions for energy loss difference of different pipeline structures; The objective function for the energy loss difference satisfies the following relationship: ， in, This represents the difference between a 2-segment structure and a 3-segment ideal structure. This represents half the cone angle of the right-hand tapered tube in a 2-segment / 3-segment ideal structure. Represents gravitational acceleration. The factorless part representing the local loss of a two-segment tapered tube is shown. The factorless part represents the local loss of the right-hand tapered tube in the three-segment ideal structure. This represents half the cone angle of the left tapered tube in the ideal three-segment structure. The factorless part representing the local loss of the left-hand tapered tube in the three-segment ideal structure. This represents the difference in friction loss along the straight path between the 2-segment structure and the ideal 3-segment structure. The partial cone angle is obtained by calculating the objective function of the energy loss difference. With the length of the three ideal structural straight channels The optimization equations include: For the objective function of the energy loss difference Taking the partial derivative, we get Partial derivative analysis results; For the objective function of the energy loss difference Taking the partial derivative, we get Partial derivative analysis results; Set the Partial derivative analysis results and the above The partial derivative analysis results are all zero, thus obtaining half the cone angle. With the length of the three ideal structural straight channels The optimization equation; The optimization equation satisfies the following relationship: ， ， in, This represents the length of the straight channel in the three ideal structures. This represents the initial velocity at the entrance of each structural straight channel. Diameter of the channel This represents half the cone angle of the right-hand tapered tube in a 2-segment / 3-segment ideal structure. The factorless part represents the local loss of the right-hand tapered tube in the three-segment ideal structure. This represents half the cone angle of the left tapered tube in the ideal three-segment structure. The factorless part represents the local loss of the left-side tapered tube of the three-segment ideal structure; The horizontal length of the left tapering tube in the three-segment ideal structure is obtained based on geometric constraints, height relationships, and variable coupling. The expressions include: The The expression satisfies the following relationship: ， in, This represents the horizontal length of the left tapering tube in the three-segment ideal structure. This represents the length of the straight channel in the three ideal structures. Indicates the length of the straight channel in the two-segment structure. This represents half the cone angle of the right tapered tube in a 2-segment or 3-segment ideal structure. The combination of the optimization equation and the The expression establishes a set of parametric equations for the maxima, and the optimal pipeline structure is determined by the set of parametric equations for the maxima, including: The parametric equations at the maximum value satisfy the following relationship: ， in, This represents the horizontal length of the left tapering tube in the three-segment ideal structure. This represents the length of the straight channel in the three ideal structures. Indicates the length of the straight channel in the two-segment structure. This represents half the cone angle of the right-hand tapered tube in a 2-segment / 3-segment ideal structure. The factorless part represents the local loss of the right-hand tapered tube in the three-segment ideal structure. This represents half the cone angle of the left tapered tube in the ideal three-segment structure. The factorless part representing the local loss of the left-hand tapered tube in the three-segment ideal structure. This represents the maximum radius of the left converging tube in the three-segment ideal structure. This represents the initial velocity at the entrance of each structural straight channel. Indicates the pipe diameter.

2. The method for determining the optimal pipeline structure based on energy loss difference according to claim 1, characterized in that, The method for obtaining the friction loss along the straight channel and the local loss of the cross-sectional variation channel includes: The friction coefficient is calculated based on the Reynolds number and pipe roughness. The friction coefficient is iteratively solved to obtain the friction loss along the straight channel; Local loss coefficients are analyzed based on the geometry and cone angle of the tapered converging tube; The local loss of the cross-sectional change channel is obtained based on the local loss coefficient. The friction loss along the straight channel satisfies the following relationship: ， in, This represents the friction loss along the straight path. Indicates the coefficient of friction. Indicates the length of the straight channel. Indicates the pipe diameter. Indicates airflow velocity. Represents gravitational acceleration; The local loss of the cross-sectional change channel satisfies the following relationship: ， in, This represents the local loss of the channel with varying cross-section. Represents the local loss coefficient. Indicates airflow velocity. It represents the acceleration due to gravity.

3. The method for determining the optimal pipeline structure based on energy loss difference according to claim 1, characterized in that, The method of combining the equivalent velocity, the friction loss along the path, and the local loss to obtain the total energy loss result includes: The equivalent velocity is obtained based on the power-law velocity distribution; Based on the equivalent velocity, the velocity relationship between the average velocity and the maximum velocity at the center of the pipe is derived. The total energy loss result is obtained by combining the velocity relationship, the friction loss along the path, and the local loss. The total energy loss result satisfies the following relationship: ， in, Indicates total energy loss. Indicates air density, Indicates the coefficient of friction. Indicates the length of the straight channel. Indicates the pipe diameter. Indicates airflow velocity. Represents the local loss coefficient. This indicates the flow velocity at the inlet of the section where the cross-section changes.

4. The method for determining the optimal pipeline structure based on energy loss difference according to claim 1, characterized in that, The parameter settings based on the 2-segment and 3-segment ideal structures, and the expressions for the cross-sectional area and initial velocity at the structural interface obtained based on the parameter information, include: Based on the parameter information set for the 2-segment structure and the 3-segment ideal structure, the parameter information includes the cross-sectional area at the interface of each structure, the initial velocity at the inlet of each interface, the pipe diameter, the straight channel length of the 2-segment structure, the straight channel length of the 3-segment ideal structure, the horizontal length of the entire effective structure, the horizontal length of the left converging tube in the 3-segment ideal structure, the horizontal length of the converging tube in the 2-segment structure, half the cone angle of the left converging tube in the 3-segment ideal structure, half the cone angle of the right converging tube in the 2-segment structure / 3-segment ideal structure, and the total gas flow rate at the jet inlet. Based on geometric relationships, flow-related formulas, and the parameter information, the expressions for the cross-sectional area and initial velocity at the interface of the structure are obtained. The cross-sectional area at the interface of the structure satisfies the following relationship with the initial velocity: ， in, This represents the cross-sectional area at the first interface. Represents pi (π). Indicates the pipe diameter. This indicates the horizontal length of the tapered tube in the two-segment structure. This represents half the cone angle of the right-hand tapered tube in a 2-segment / 3-segment ideal structure. This represents the initial velocity at the entrance of the first interface. This indicates the total gas flow rate at the jet inlet. This represents the radius of the cross-section of the tapered tube on the right in a 2-segment or 3-segment ideal structure. This represents the infinitesimal variable representing the radius of the cross-section of each structural segment in the integral expression. This represents the cross-sectional area at the second interface. This represents the horizontal length of the left tapering tube in the three-segment ideal structure. This represents half the cone angle of the left tapered tube in the ideal three-segment structure. This represents the initial velocity at the entrance of the second interface. This represents the radius of the cross-section of the left-hand tapering tube in the three-segment ideal structure. This represents the cross-sectional area at the straight passage of each structure. This represents the radius of the cross-section of the straight channel in a 2-segment or 3-segment ideal structure. This represents the initial velocity at the entrance of each structural straight channel.

5. The method for determining the optimal pipeline structure based on energy loss difference according to claim 1, characterized in that, The process of combining the total energy loss result and the expression for cross-sectional area and initial velocity to obtain the friction loss calculation result and the local pressure loss calculation result includes: The calculated friction loss along the route satisfies the following relationship: ， in, This indicates the friction loss along the two sections. Indicates the length of the straight channel in the two-segment structure. Indicates the pipe diameter. This represents the initial velocity at the entrance of each structural straight channel. This represents the ideal friction loss along the three segments. This represents the length of the straight channel in the three ideal structures. This indicates the total gas flow rate at the jet inlet. Represents pi (π). The infinitesimal variable representing the radius of the straight channel in the integral expression; The calculated results of the local pressure loss satisfy the following relationship: ， in, This indicates the local loss of the two-segment structure. This represents half the cone angle of the right-hand tapered tube in a 2-segment / 3-segment ideal structure. Represents gravitational acceleration. This indicates the horizontal length of the tapered tube in the two-segment structure. This represents the cross-sectional area at the straight passage of each structure. Represents pi (π). Let represent the infinitesimal variable representing the length of the two tapered tube segments in the integral equation. This indicates the total gas flow rate at the jet inlet. This represents the infinitesimal variable representing the radius of the cross-section of each structural segment in the integral expression. This represents the local loss of the three-segment ideal structure. This represents the length of the right-hand tapered tube in the three-segment ideal structure. This represents the cross-sectional area at the second interface. This represents the horizontal length of the left tapering tube in the three-segment ideal structure. This represents half the cone angle of the left tapered tube in the ideal three-segment structure. The infinitesimal variable represents the length of the left-hand tapering tube of the three-segment ideal structure in the integral.

6. A system for determining the optimal pipeline structure based on energy loss difference, characterized in that, The system includes a processor, an input device, an output device, and a memory, which are interconnected. The memory stores a computer program, which includes program instructions. The processor is configured to invoke the program instructions to execute the method for determining the optimal pipeline structure based on energy loss difference as described in any one of claims 1-5.

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