An optimization design method of a spiral wound heat exchanger

Abstract

The application provides an optimization design method of a spiral wound tube heat exchanger, which divides heat exchange of a tube side and a shell side into at most five sections according to whether phase change occurs in the tube side and the shell side. In each section, micro elements are divided to calculate heat transfer and pressure drop, and final heat transfer coefficients, heat exchange areas and pressure drops of the spiral wound tube heat exchanger are obtained by collecting all micro element data. According to an optimization target and structure parameters to be optimized, multi-objective optimization is carried out on the spiral wound tube heat exchanger, and the best structure parameters of the spiral wound tube heat exchanger are finally obtained through continuous iteration optimization of an algorithm. The optimization design method of the spiral wound tube heat exchanger has the characteristics of high flexibility, high calculation precision, wide application range and the like, and has high commercial value and market promotion value.

Description

Technical Field

[0001] This invention relates to an optimized design method for a wound tube heat exchanger, belonging to the field of enhanced heat transfer technology. Background Technology

[0002] Spiral coil heat exchangers, with their compact structure, high heat exchange efficiency, small temperature difference, high operating pressure, and ability to exchange heat with multiple media simultaneously, have become the main equipment for natural gas liquefaction. They are also widely used in industrial fields such as low-temperature methanol washing, large-scale air separation, and low-temperature liquid nitrogen processes.

[0003] Due to the unique structure of wound tube heat exchangers, the calculation of heat transfer and pressure drop is quite complex. For the phase change heat transfer processes involving the shell and tube sides, the relevant calculation methods are limited and cannot be applied to general situations. Current optimization calculations for wound tube heat exchangers involve relatively few structural parameters, failing to provide a holistic optimization of the entire device and thus unable to meet the various specific requirements of practical engineering. Therefore, developing a highly flexible and widely applicable optimization design method for wound tube heat exchangers is of significant importance for engineering design and the localization of equipment production. Summary of the Invention

[0004] Therefore, the technical problem to be solved by the present invention is to provide an optimized design method for a wound tube heat exchanger. Its advantages are that the structural parameters to be optimized can be selected according to the actual situation, and a complete set of process calculations for wound tube heat exchangers is designed. It is applicable to processes with and without phase change, has high calculation accuracy, and the optimization method is flexible.

[0005] The technical solution of the present invention is an optimization design method for a wound tube heat exchanger, which uses the heat exchange area and heat exchange margin of the wound tube heat exchanger as objective functions and uses a multi-objective optimization algorithm to optimize the structural parameters of the wound tube heat exchanger.

[0006] All potential optimization parameters are listed as optimization variables; if the value of the optimization variable is continuous, the upper and lower bounds are defined by inequalities; if the optimization variable is discrete, the range of values ​​is defined by sets; first, add inequality constraints to all optimization variables; if the optimization parameter is determined, make the upper and lower bounds of the inequality equal, otherwise determine the upper and lower bounds of the inequality according to the actual range of values ​​of the variable.

[0007] The design method flow is as follows: First, initialize the population; randomly generate an initial population, where each individual represents a candidate solution; the population size is a constant N given before the algorithm begins. population At this point, the number of iterations is 0;

[0008] The second step is to generate offspring. Random crossover and mutation operations are performed on the current population to generate a new population of the same size as the initial population, called the offspring. The initial population is called the parent population. The parent and offspring populations are then merged into a new population of size 2N. population A new population;

[0009] The third step is non-dominated sorting and fitness calculation. Based on the concept of dominance, each individual in the new population is sorted and assigned a non-dominated level. Solutions with lower levels dominate solutions with higher levels. The fitness of each individual in the population can be calculated through the non-dominated levels. The fitness of all solutions in the new population is calculated based on a set reference point. Solutions closer to the reference point have higher fitness, and solutions farther from the reference point have lower fitness. Solutions with higher fitness have higher priority when selected.

[0010] The fourth step is to generate the next generation population; from the new population, sequentially select the solution set with the lowest non-dominant level until the number of solution sets is greater than or equal to the population size N. population If the number of solutions selected from all non-dominant levels exceeds the population size N; population Then, based on fitness, several solution sets are removed until the size of the solution set equals the population size. If the size of all solution sets selected for the current non-dominant level is exactly equal to the population size, no operation is required. The selected solution set at this point becomes the next generation population, and the iteration count is increased by 1.

[0011] Fifth, repeat steps two, three, and four until the number of iterations reaches the maximum value. At this point, every solution in the population is the optimal solution.

[0012] According to the optimization design method of the wound tube heat exchanger of the present invention, preferably, for the wound tube heat exchanger, all potential optimization variables are: shell inner diameter D. s Core diameter D core outer diameter d of the spiral wound tube o Inner diameter d of the spiral wound tube i , winding angle θ, radial spacing S t axial spacing S l , Shell length L.

[0013] According to the optimization design method of the wound tube heat exchanger of the present invention, preferably, the objective function value of the optimization process is obtained by dividing the wound tube heat exchanger into segments based on the state changes of the tube side and shell side properties, and each segment is calculated using the infinitesimal method. Finally, the heat exchange area, area margin, tube side pressure drop, shell side pressure drop and other performance parameters of the wound tube heat exchanger are obtained by summarizing the data.

[0014] According to an optimization design method for a wound tube heat exchanger of the present invention, preferably, the optimization design method further includes a calculation method for the tube bundle structure of the wound tube heat exchanger.

[0015] According to the optimization design method of the wound tube heat exchanger of the present invention, preferably, the tube bundle structure calculation method of the wound tube heat exchanger is as follows: the structure of the wound tube heat exchanger mainly involves the following parameters: core diameter D core Used to support the wound tube bundle; the inner diameter d of the wound tube i With outer diameter d o , used to determine the specifications of the wound tube; winding angle θ, used to control the inclination angle of the heat transfer tube winding; radial spacing S t Used to control the spacing between different layers of wound tubes; axial spacing S l These parameters are used to control the spacing between the wound tubes in the same layer; based on these parameters, the structure of the entire wound tube bundle can be determined.

[0016] The following mathematical form is adopted:

[0017]

[0018] In the formula, x i The variables to be optimized are represented by n variables. The superscripts L and U represent the upper and lower boundaries of the optimized variables, respectively. The set of optimized variables is called the sample space, and n optimized variables mean that the sample space is n-dimensional. g(x) and h(x) both represent the constraints of the optimized variables. The values ​​of the optimized variables must satisfy the constraints. The difference is that g(x) represents inequality constraints, while h(x) represents equality constraints. There are J inequality constraints and K equality constraints. In special cases, the values ​​of J and K can be 0, that is, there are no constraints. f(x) represents the objective function in the optimization problem. There are M optimization objectives. When M is 1, it is a single-objective optimization problem. When M is greater than 1, it is a multi-objective optimization problem. The final goal of optimization is to maximize or minimize these objective functions. The result of multi-objective optimization is generally not one, but a solution set.

[0019] Each structural parameter of the wound tube heat exchanger corresponds to an 'x', where the outer diameter D of the core tube is... core Inner diameter of the shell D s , shell length L, winding angle θ, radial spacing S t and axial spacing S l The inner diameter d of the wound tube is a continuous variable. i With outer diameter d o These are discrete variables; each of these variables can be considered as one of x, but they are expressed in different ways. The range of continuous variables is: 0.075m ≤ D. core ≤0.8m, 5°≤θ≤20°, 10mm≤S t ≤34mm, 10mm≤S l ≤34mm; the range of values ​​for the discrete variable is: do ∈[9, 10, 12, 15, 19], d i ∈[7, 8, 10, 13, 15], in mm.

[0020] In the calculation method for the tube bundle structure of a wound tube heat exchanger, further, in order to determine the number of layers and length of the wound tubes, it is also necessary to know the inner diameter D of the shell. s The length L of the tube shell. In the above formula (2), the range of values ​​for the continuous variable is: 0.15m≤D s ≤3m, 1m≤L≤10m.

[0021] According to the optimization design method of the spiral wound tube heat exchanger of the present invention, preferably, for a process in which neither the tube side nor the shell side undergoes a phase change, the calculation of the spiral wound tube heat exchanger is divided into 1 segment; when a phase change occurs on one side of the tube side or the shell side, the calculation of the spiral wound tube heat exchanger is divided into a maximum of 3 segments based on the start or end of the phase change point; when both the tube side and the shell side undergo phase changes simultaneously, the calculation of the spiral wound tube heat exchanger is divided into a maximum of 5 segments based on the respective phase change points of the tube side and the shell side.

[0022] According to the optimized design method of the wound tube heat exchanger of the present invention, preferably, when neither the tube side nor the shell side undergoes a phase change, the tube side fluid and the shell side fluid flow in countercurrent, and the inlet and outlet temperatures of the tube side and the shell side are respectively T tube,in T tube,out T shell,in T shell,out The calculation methods for heat transfer and pressure drop are both non-phase change calculations, and the entire calculation process is divided into a whole segment.

[0023] When a phase change occurs on either the tube side or the shell side, taking the tube-side hot fluid undergoing a phase change as an example, the initial inlet temperature of the tube-side fluid is T. tube,in When the temperature reaches the first phase transition temperature T tube,b1 At this time, the fluid in the tube side begins to condense, corresponding to the shell side temperature T. shell,s1 The fluid in the tube side continues to condense until the second phase transition temperature T. tube,b2 At this point, the tube-side fluid completely condenses into condensate, corresponding to a shell-side temperature T. shell,s2 The fluid temperature in the tube continues to decrease until it reaches the outlet temperature T. tube,out At this time, the corresponding shell-side inlet temperature T shell,in The calculation of the entire heat exchanger is divided into three main sections: from top to bottom, the first section is single-phase tube side and single-phase shell side; the second section is tube side condensation and single-phase shell side; the third section is single-phase tube side and single-phase shell side. Each section requires the selection of the corresponding calculation method. The temperature segmentation method is similar when the shell side undergoes a phase change but the tube side does not.

[0024] When phase change occurs simultaneously on both sides, taking the tube-side heat transfer fluid as an example, the tube-side inlet temperature is T.tube,in The corresponding shell-side outlet temperature T shell,out When the tube-side temperature drops to the first phase transition temperature T tube,b1 At this time, the corresponding shell-side temperature T shell,s1 Condensation begins in the tube side, and the temperature continues to drop to T. tube,s1 At that time, the first phase transition point T in the shell side corresponds to shell,b1 Evaporation begins in the shell side; the tube side temperature reaches the second phase transition point T. tube,b2 At this point, the tube-side condensation ends, and the corresponding shell-side temperature is T. shell,s2 It is still evaporating; the temperature of the condensate in the tube side continues to drop until T. tube,s2 This corresponds to the second temperature phase transition point T in the shell side. shell,b2 This refers to the point where the shell side begins to undergo evaporation and phase transition; finally, the tube side reaches the outlet temperature T. tube,out The shell side reaches the inlet temperature T. shell,in At this point, the calculation of the entire heat exchanger is divided into five sections, from top to bottom: Section 1, tube side single phase, shell side single phase; Section 2, tube side condensation, shell side single phase; Section 3, tube side condensation, shell side evaporation; Section 4, tube side single phase, shell side evaporation; Section 5, tube side single phase, shell side single phase.

[0025] According to the optimization design method of a wound tube heat exchanger of the present invention, in the micro-element method calculation, the heat transfer of each micro-element is equal. Starting from the left or right side of the segment, the inlet and outlet temperatures of the tube side and shell side of the current micro-element are calculated, and the calculated temperature is used as the inlet and outlet temperature of the next micro-element segment. The inlet and outlet temperatures of all micro-element segments within the segment are calculated sequentially. By controlling the temperature difference between the inlet and outlet, the magnitude of the change in physical properties at the inlet and outlet temperatures of the micro-element is controlled. The arithmetic mean can be used to represent the physical property parameters within the entire micro-element. If a segment is divided into n micro-elements, the total heat transfer of the segment is Q. section Then the heat exchange dQ of each microelement element for Since the phase states on both sides of the infinitesimal element are fixed and will not change, the tube-side heat transfer coefficient h of the infinitesimal element can be calculated by selecting the corresponding heat transfer coefficient calculation method. t Heat transfer coefficient h of shell side s The overall heat transfer coefficient U of the micro-element element The calculation formula is

[0026] In the formula, r s With r t These are the fouling thermal resistances of the shell side and tube side, respectively; λ tube This refers to the thermal conductivity of the pipe material; based on the temperatures at the inlet and outlet on both sides of the infinitesimal element, the logarithmic mean temperature difference ΔT can be calculated. LMTD According to the heat exchange calculation formula dQ element =Uelement dA require ΔT LMTD The required heat transfer area dA of the infinitesimal element can be calculated. require And so on, the required heat exchange area A for this section section The total heat transfer coefficient U is the sum of the heat transfer areas required by all infinitesimal elements. section This represents the average of the total heat transfer coefficients of all micro-elements. Simultaneously, the pressure drop between the tube and shell sides of each micro-element can be calculated, and the pressure drops on both sides of the segment are the sum of the corresponding pressure drops of all micro-elements. Small temperature differences result in small changes in physical properties.

[0027] According to the optimization design method of a wound tube heat exchanger of the present invention, the specific segment location is determined by the uniqueness of the enthalpy value, thereby determining the temperature point of the segment. Then, the enthalpy value corresponding to the other side is calculated based on the heat balance to determine the specific segment temperature point.

[0028] According to the optimization design method of the wound tube heat exchanger of the present invention, preferably, after reading the physical property parameters, the enthalpy values ​​of the start and end of the phase change can be determined based on the position of the phase change point in the physical property parameters, thereby determining the phase change temperature, that is, determining the phase change temperature point T. tube,b1 T tube,b2 T shell,b1 T shell,b2 The temperature point T corresponding to the segment. tube,s1 T tube,s2 T shell,s1 T shell,s2 It is mainly obtained through heat exchange balance calculations. The physical property parameters refer to the fluid temperature, enthalpy, density, viscosity, specific heat, surface tension, etc., which need to be known in the "input tube side and shell side physical properties" step in the flow chart.

[0029] Beneficial effects:

[0030] This invention provides an optimized design method for wound tube heat exchangers. This method offers a general calculation method for heat transfer and pressure drop in wound tube heat exchangers. It segments the calculation of the wound tube heat exchanger according to the phase change section and improves calculation accuracy by using a micro-element method. Secondly, it determines the necessary structural parameters of the wound tube heat exchanger and proposes a specific calculation method for the tube arrangement. Using the structural parameters of the wound tube heat exchanger as optimization variables and area margin and heat transfer area as optimization objectives, it proposes an optimization strategy for wound tube heat exchangers. By changing the upper and lower bounds of the optimization variables, the specific optimization parameters can be controlled. This allows for overall optimization design of wound tube heat exchangers without any structural parameters, as well as optimization for industrial production scenarios where structural parameters are fixed and only other parameters need to be optimized. It is more flexible and better suited to practical engineering applications, thus completing the optimized design of wound tube heat exchangers. This optimized design method for wound tube heat exchangers features high flexibility, high calculation accuracy, and wide applicability. It provides theoretical support for the development of wound tube heat exchanger design software and has high commercial and market promotion value. Attached Figure Description

[0031] Figure 1 This is a schematic diagram showing the segmentation of the temperature range without phase change.

[0032] Figure 2 This is a schematic diagram of the single-sided phase transition temperature segmentation.

[0033] Figure 3 This is a schematic diagram of the temperature segmentation of the two-sided phase transition.

[0034] Figure 4 This is a schematic diagram of the micro-element partitioning.

[0035] Figure 5a This is a schematic cross-sectional view of a wound tube heat exchanger. Figure 5b This is a schematic diagram of the horizontal sweep of the wound tube bundle.

[0036] Figure 6 This is a schematic diagram of a wound tube structure.

[0037] Figure 7 Flowchart for design calculations of wound tube heat exchangers.

[0038] Figure 8 Flowchart for optimizing the design of wound tube heat exchangers. Detailed Implementation

[0039] The calculation method for heat transfer and pressure drop of the wound tube heat exchanger is determined. Based on the structural parameters to be optimized, the specific structure of the wound tube heat exchanger is calculated to obtain the corresponding objective function. By optimizing and iterating the structural parameters, the optimal structure of the wound tube heat exchanger is obtained, and the design is completed.

[0040] Depending on the tube-side and shell-side conditions of the wound tube heat exchanger, heat transfer and pressure drop calculations can be divided into three cases. The first case is where neither the tube-side nor the shell-side undergoes a phase change, such as... Figure 1 The tube-side fluid and shell-side fluid flow counter-currently, and the inlet and outlet temperatures of the tube-side and shell-side fluids are respectively T. tube,in T tube,out T shell,in T shell,out The calculation methods for heat transfer and pressure drop are both non-phase change calculations, and the entire calculation process is divided into a whole segment by the green line.

[0041] The second scenario involves a phase change occurring on one side. Taking a phase change in the tube-side heat transfer fluid as an example... Figure 2 The initial inlet temperature of the fluid in the tube is T. tube,in When the temperature reaches the first phase transition temperature T tube,b1 At this time, the fluid in the tube side begins to condense, corresponding to the shell side temperature T. shell,s1 The fluid in the tube side continues to condense until the second phase transition temperature T. tube,b2 At this point, the tube-side fluid completely condenses into condensate, corresponding to a shell-side temperature T. shell,s2 The fluid temperature in the tube continues to decrease until it reaches the outlet temperature T. tube,out At this time, the corresponding shell-side inlet temperature T shell,in The calculation of the entire heat exchanger is divided into three main sections by the green dividing line. From top to bottom, the first section is single-phase in both the tube side and shell side; the second section is tube-side condensation and shell-side single-phase; the third section is tube-side single-phase and shell-side single-phase. Each section requires the selection of a corresponding calculation method. The temperature segmentation method is similar when a phase change occurs in the shell side but not in the tube side.

[0042] The third scenario involves simultaneous phase transitions on both sides. Taking the tube-side heat transfer fluid as an example, such as... Figure 3 The tube inlet temperature is T. tube,in The corresponding shell-side outlet temperature T shell,out When the tube-side temperature drops to the first phase transition temperature T tube,b1 At this time, the corresponding shell-side temperature T shell,s1 Condensation begins in the tube side, and the temperature continues to drop to T. tube,s1 At that time, the first phase transition point T in the shell side corresponds to shell,b1 Evaporation begins in the shell side; the tube side temperature reaches the second phase transition point T. tube,b2 At this point, the tube-side condensation ends, and the corresponding shell-side temperature is T. shell,s2 It is still evaporating; the temperature of the condensate in the tube side continues to drop until T. tube,s2 This corresponds to the second temperature phase transition point T in the shell side. shell,b2 This refers to the point where the shell side begins to undergo evaporation and phase transition; finally, the tube side reaches the outlet temperature T. tube,out The shell side reaches the inlet temperature T. shell,inAt this point, the calculation of the entire heat exchanger is divided into five sections, from top to bottom: Section 1, tube side single-phase, shell side single-phase; Section 2, tube side condensation, shell side single-phase; Section 3, tube side condensation, shell side evaporation; Section 4, tube side single-phase, shell side evaporation; Section 5, tube side single-phase, shell side single-phase.

[0043] It should be noted that the temperature segmentation diagrams for single-sided and double-sided phase changes represent the theoretical maximum number of segments; in practice, the actual number of segments may not reach this figure. This is because situations may arise where evaporation or condensation is incomplete, or the inlet state may already be a mixture of gas and liquid phases, in which case the number of temperature segments will not reach the theoretical maximum.

[0044] Furthermore, the temperature of a fluid generally remains constant from the start to the end of a phase transition. In practical segmentation, the enthalpy is used as the reference for segmentation because it is unique throughout the entire physical property. Temperature and physical property parameters can be determined through enthalpy. After reading the physical property parameters, the enthalpy values ​​at the start and end of the phase transition can be determined based on the location of the phase transition point, thus determining the phase transition temperature, specifically the phase transition temperature T. tube,b1 T tube,b2 T shell,b1 T shell,b2 The temperature point T corresponding to the segment. tube,s1 T tube,s2 T shell,s1 T shell,s2 This is mainly derived through heat exchange balance calculations. Figure 3 In this configuration, the heat exchange between the tube side and the shell side is equal for each section. Taking the top section as an example, then T... shell,s1 The following equation must be satisfied:

[0045]

[0046] In the formula, H shell,out With H shell,s1 These are the enthalpy values ​​at the inlet and outlet of the shell side for this small segment; H tube,in With H tube,b1 These are the enthalpy values ​​at the inlet and outlet of the tube section, respectively. and These are the shell-side and tube-side mass flow rates, respectively. Only H... shell,s1 It is an unknown quantity, which can be calculated according to equation (3). The corresponding temperature point T can be obtained from the enthalpy value. shell,s1 By analogy, the unknown temperature points T during the segmentation process can be calculated sequentially. tube,s1 T shell,s2 With T tube,s2 .

[0047] After determining the segments of the wound tube heat exchanger, the accuracy can be improved by using the method of infinitesimal element division for each segment. Figure 4 The inlet and outlet temperatures of the tube side and shell side within each segment are known, allowing the calculation of the total heat transfer for the entire segment. The segment is divided into several micro-elements based on the heat transfer, with each micro-element having an equal heat transfer capacity. Starting from the left or right side of the segment, the inlet and outlet temperatures of the tube side and shell side of the current micro-element are calculated, and these calculated temperatures are used as the inlet and outlet temperatures for the next micro-element. This process is repeated for all micro-elements within the segment. Dividing the segment into micro-elements allows control over the temperature difference between the inlet and outlet, resulting in minimal changes in physical properties at the inlet and outlet temperatures of each micro-element. The arithmetic mean of these temperatures can then be used to represent the physical properties within the entire micro-element. Assuming a segment is divided into n micro-elements, and the total heat transfer of the segment is Q... section Then the heat exchange dQ of each microelement element for Since the phase states on both sides of the infinitesimal element are fixed and will not change, the tube-side heat transfer coefficient h of the infinitesimal element can be calculated by selecting the corresponding heat transfer coefficient calculation method. t Heat transfer coefficient h of shell side s The overall heat transfer coefficient U of the micro-element element The calculation formula is

[0048] In the formula, r s With r t These are the fouling thermal resistances of the shell side and tube side, respectively; λ tube This refers to the thermal conductivity of the pipe material. Based on the temperatures at the inlet and outlet on both sides of the micro-element, the logarithmic mean temperature difference ΔT can be calculated. LMTD According to the heat exchange calculation formula dQ element =U element dA require ΔT LMTD The required heat transfer area dA of the infinitesimal element can be calculated. require And so on, the required heat exchange area A for this section section The total heat transfer coefficient U is the sum of the heat transfer areas required by all infinitesimal elements. section This represents the average of the overall heat transfer coefficients of all micro-elements. Simultaneously, the pressure drop between the tube side and shell side within each micro-element can be calculated, and the pressure drops on both sides of the segment are the sum of the corresponding pressure drops of all micro-elements.

[0049] In this invention, the calculation method for shell-side heat transfer without phase change and pressure drop is the Gilli formula, the calculation method for boiling heat transfer is the Ren formula, the calculation method for condensation heat transfer is the McAdams formula, and the calculation method for two-phase flow pressure drop is the phase-separated flow model.

[0050] The calculation methods for heat transfer and pressure drop without phase change in the tube side are the Manlapaz and Beigzadeh formulas, the calculation method for boiling heat transfer is the Guo formula, the calculation method for condensation heat transfer is the Boyko formula, and the calculation method for pressure drop in two-phase flow is the phase-separated flow model.

[0051] To achieve optimized design of the wound tube heat exchanger, it is necessary to determine the structural calculation method for the wound tube heat exchanger. A schematic diagram of the structural parameters of the wound tube heat exchanger is shown in Figure 5. The main structural parameters involved in the wound tube heat exchanger are as follows: core diameter D. core Used to support the wound tube bundle; the inner diameter d of the wound tube i With outer diameter d o The θ is used to determine the specifications of the wound tube; the winding angle θ is used to control the inclination angle of the heat transfer tube winding. In the sweep view, the major axis of the ellipse of the wound tube cross-section is d. o / cosθ; radial spacing S t Used to control the spacing between different layers of wound tubes; axial spacing S l This is used to control the spacing between the wound tubes in the same layer. Furthermore, to determine the number of layers and the length of the wound tube, the inner diameter D of the shell is also required. s The length L of the tube shell. Based on the above parameters, the structure of the entire wound tube bundle can be determined.

[0052] In general, any optimization problem can be described in the following mathematical form:

[0053]

[0054] In the formula, x i The variables to be optimized are represented by n variables. The superscripts L and U represent the upper and lower boundaries of the optimized variables, respectively. The set of optimized variables is called the sample space, and n optimized variables mean that the sample space is n-dimensional. g(x) and h(x) both represent the constraints of the optimized variables. The values ​​of the optimized variables must satisfy the constraints. The difference is that g(x) represents inequality constraints, while h(x) represents equality constraints. There are a total of J inequality constraints and K equality constraints. In special cases, the values ​​of J and K can be 0, that is, there are no constraints. f(x) represents the objective function in the optimization problem. There are a total of M optimization objectives. When M is 1, it is a single-objective optimization problem. When M is greater than 1, it is a multi-objective optimization problem. The final goal of optimization is to maximize or minimize these objective functions. The result of multi-objective optimization is generally not one, but a solution set.

[0055] This invention uses the heat transfer area and heat transfer margin of the wound tube heat exchanger as objective functions, and employs a multi-objective optimization algorithm to optimize the structural parameters of the wound tube heat exchanger. The core idea of ​​this invention is to list all potential optimization parameters as optimization variables, defined as x. i Suppose there are n such variables. If we optimize variable x... i If the value of x is continuous, then x is defined by the inequality. i The upper and lower bounds; if the optimization variable x iIf the variables are discrete, their range of values ​​is defined using sets. While equality constraints can solve the problem of determining the values ​​of optimization parameters, they lack general applicability to specific optimization problems. Therefore, inequality constraints are first added to all n optimization variables. If the optimization parameter is determined, the upper and lower bounds of the inequality are made equal; otherwise, the upper and lower bounds of the inequality are determined according to the actual range of values ​​of the variables.

[0056] Using this optimization approach, the sample space for the optimization process can be determined. The optimization algorithm chosen is the Non-dominated Sorting Genetic Algorithm III (NSGA3). Its main idea is as follows: A certain number of initial populations are generated within the sample space. Based on the design calculation method for the wound tube heat exchanger according to this invention, the structure, heat transfer, and pressure drop of the wound tube heat exchanger are calculated. The priority of each individual is determined based on the objective function value and a defined reference point. The next generation population is generated through crossover, mutation, and selection operations. The parent and child populations are merged, and the new generation population is selected through sorting. This process is repeated until the maximum number of iterations is reached. The final population obtained represents the optimal structure of the wound tube heat exchanger. The specific optimization process is as follows: Figure 8 .

[0057] The specific steps are as follows:

[0058] Based on the characteristics of the coiled tube heat exchanger, the arrangement method of the coiled tubes in the coiled tube heat exchanger can be calculated. The structural parameters involved include: core diameter D. core Inner diameter d of the spiral wound tube i With outer diameter d o , winding angle θ, radial spacing S t axial spacing S l Inner diameter of the shell D s And the shell length L. The specific calculation method is as follows:

[0059] The constraint condition for the number of layers m of the spiral wound tube is:

[0060]

[0061] Because the number of layers is an integer, the decimal part must be rounded down based on the calculation result. The rounded-down length will be evenly distributed across two distances: the distance between the outer wall of the innermost winding tube and the core cylinder; and the distance between the outer wall of the outermost winding tube and the shell. The sum of these two distances is denoted as d. t Then the winding diameter D of the i-th layer of the winding tube is... i for:

[0062] D i =D core +2(i-1)S t +2d t +do (i=1,2,…,m) (6)

[0063] According to the winding diameter D i axial spacing S l And the winding angle θ, and the number of winding tubes n in the i-th layer. i The following constraints need to be met:

[0064]

[0065] In the formula, the number of wound tubes n i If we select the largest integer that satisfies the condition, then the heat transfer area of ​​the i-th layer is:

[0066] A i =n i πd o L tube (8)

[0067] The length L of the winding tube tube for:

[0068]

[0069] The pitch P of the i-th layer of wound tube i for:

[0070]

[0071] Total number of wound tubes N tubes And the total heat exchange area A is:

[0072] N tubes =n1+n2+…+n m (11)

[0073] A = A1 + A2 + ... + A m (12)

[0074] According to equations (5) to (12), the overall structure of a wound tube heat exchanger can be determined, and the number of layers of the wound tubes, the number of each layer, the winding diameter, and the overall heat exchange area can be calculated.

[0075] After determining the structure of the wound tube heat exchanger, it is necessary to determine the methods for calculating heat transfer and pressure drop in the tube side and shell side. The shell side has no phase change heat coefficient h. s With pressure drop ΔP s The calculation formula is:

[0076]

[0077]

[0078]

[0079] In the formula, F a F i With F n These are the correction factors for the arrangement of wound tubes, the tilt of wound tubes, and the number of tube rows for shell-side heat transfer, respectively; C a C i With C n These are the correction factors for the shell-side pressure drop: the winding tube arrangement correction factor, the winding tube tilt correction factor, and the number of tube rows correction factor; ρ is the density of the shell-side fluid; λ is the thermal conductivity of the shell-side fluid; n tubes The number of tube banks in the flow direction; Pr is the Prandtl number of the shell fluid; G eff Re represents the effective mass flow rate of the shell side. eff The effective Reynolds number; ρ is the mass flow rate of the shell-side fluid; μ is the dynamic viscosity of the shell-side fluid; c p A represents the specific heat capacity of the shell-side fluid. flow The flow area is the shell side.

[0080] In phase change calculations, the formula for calculating the shell-side boiling heat transfer coefficient is:

[0081]

[0082] When Re g <1000, Re l <1000 hours:

[0083]

[0084] When Re g >2000, Re l <1000 hours:

[0085]

[0086] When Re g <2000, Re l >2000:

[0087]

[0088] When Re g >2000, Re l >2000:

[0089]

[0090] In the formula, h l,sThe heat transfer coefficient is denoted by when only liquid phase flows in the shell side; X is the Martinelli number; x is the dryness fraction; the subscripts g and l represent gas and liquid, respectively. The formula for calculating shell-side condensation heat transfer is:

[0091]

[0092]

[0093] In the formula, Γ is the mass flow rate per unit length; X tube The total tube length is perpendicular to the flow direction; all other physical properties represent the shell-side liquid phase. The two-phase flow pressure drop ΔP in the shell side of the wound tube heat exchanger. tp,s The calculation formula is:

[0094] ΔP tp,s =ΔP tp,f +ΔP tp,a +ΔP tp,g (twenty three)

[0095]

[0096]

[0097]

[0098]

[0099] ΔP tp,g =ρ tp gL (28)

[0100] ρ tp =γ·ρ g +(1-γ)·ρ l (29)

[0101] In the formula, ΔP tp,f ΔP tp,a ΔP tp,g These represent frictional pressure drop, acceleration pressure drop, and gravitational pressure drop, respectively; γ represents the cavitation fraction; ΔP l,s ρ is the pressure drop without phase change when the shell side is entirely liquid; g is the acceleration due to gravity; tp The density is the two-phase flow density.

[0102] The structural diagram of the spiral tube is as follows: Figure 6 When the flow state inside the tube is laminar, the calculation method for heat transfer and pressure drop without phase change in the tube side of the wound tube heat exchanger is as follows:

[0103]

[0104]

[0105]

[0106]

[0107] Where P is the pitch of the spiral wound tube, D is the winding diameter of the spiral wound tube; Dn is the Dean number, and I is an empirical coefficient, with values ​​of 2, 1, and 0 for Dn < 20, 20 ≤ Dn ≤ 40, and Dn > 40, respectively; u t The flow rate is the tube side velocity. The mass flow rate of the tube side is given; when the flow state inside the tube is turbulent, the formulas for calculating the Nusselt number and the friction coefficient are:

[0108] Nu t =0.023Re 0.85 Pr 0.33 (d i / D) 0.1 (34)

[0109] f t =2.32Re -0.311 (d i / D) 0.467 (P / πD) -0.074 (35)

[0110] The boiling heat transfer coefficient h inside the wound tube tp,t The calculation formula is:

[0111]

[0112]

[0113] In the formula, p in With p crit These are the inlet pressure of the tube and the critical pressure of the fluid, respectively; h l,t Let be the heat transfer coefficient of the entire liquid phase inside the coiled tube. The formula for calculating the boiling pressure drop in the tube side is:

[0114] ΔP tp,t =Φ 2 ΔP l,t (38)

[0115]

[0116]

[0117] In the formula, ΔP l,t The tube-side single-phase pressure drop when the two-phase mass flow rate inside the tube is converted to a completely liquid phase; ψ1 is an empirical coefficient reflecting the characteristics of the wound tube; ψ is a semi-theoretical coefficient; G t Let be the mass flow rate in the tube side. The formulas for calculating tube-side condensation heat transfer and pressure drop are:

[0118]

[0119]

[0120] In the formula, h l,t The heat transfer coefficient ΔP is calculated when the flow in the tube is entirely liquid. l,t This refers to the frictional pressure drop during full-phase turbulent flow.

[0121] According to the segmented calculation method mentioned in the above invention, the calculation of the wound tube heat exchanger is first segmented. The heat transfer of each segment of the wound tube heat exchanger is calculated. Based on the uniform division of the heat transfer capacity into micro-elements, the heat transfer within each micro-element is ensured to be equal, and the inlet and outlet temperature difference is small. The average value of the inlet and outlet physical properties is used to represent the physical parameters within the micro-element for heat transfer and pressure drop calculations. Based on the above heat transfer and pressure drop calculation formulas, the heat transfer coefficients of the tube side and shell side, pressure drop, overall heat transfer coefficient, and required heat transfer area dA within each micro-element can be calculated. require The pressure drop across the tube side and shell side. The final required heat transfer area A of the wound tube heat exchanger can be obtained by summing the required heat transfer areas within all infinitesimal elements. require Then the area margin ζ is:

[0122]

[0123] In the formula, A actual This represents the actual heat exchange area of ​​the spiral wound tube heat exchanger. The specific calculation process for the spiral wound tube heat exchanger is as follows: Figure 7 .

[0124] Based on the core idea of ​​optimization, the first step is to determine all potential optimization parameters. According to the calculation method for wound tube heat exchanger structures, the optimization parameters include: shell inner diameter D. s Core diameter D core outer diameter d of the spiral wound tube o Inner diameter d of the spiral wound tube i , winding angle θ, radial spacing S t axial spacing S l , Shell length L.

[0125] After determining all optimization parameters, it is also necessary to determine the range of values ​​for each parameter. (Shell inner diameter D) s The dimensions of a wound tube heat exchanger are determined by the shell length L and the shell inner diameter D. s The diameter of the casing ranges from over 100mm to around 3m, therefore the inner diameter D of the casing is set accordingly. s The upper and lower limits are 0.1m and 3m respectively. Core outer diameter D core With the inner diameter D of the shell sA suitable core cylinder outer diameter is required, but an excessively large outer diameter will occupy most of the internal space of the shell, thus reducing the amount of tubing. Therefore, a range of 0.05m to 1m is chosen. The shell length L generally needs to exceed the shell inner diameter; considering the range of the shell inner diameter, a range of 1m to 15m is chosen. The specifications of the spiral wound tube, i.e., the outer diameter d of the spiral wound tube... o With inner diameter d i In engineering design, most spiral wound tubes are manufactured according to relevant standards. Commonly used spiral wound tube specifications include: Φ9×1, Φ10×1, Φ12×1, Φ15×1, and Φ19×2. Therefore, the outer diameter d of the spiral wound tube... o The set of values ​​for is 9, 10, 12, 15, and 19, while the inner diameter d of the spiral wound tube is... i The possible values ​​for are 7, 8, 10, 13, and 15. It should be noted that this is related to the inner diameter D of the shell. s Core outer diameter D core These parameters are different; the outer diameter d of the spiral wound tube o With inner diameter d i These are discrete variables, not continuous variables. The winding angle θ and the radial spacing S are examples. t axial spacing S l These parameters collectively determine the arrangement of the wound tubes. Typically, the winding angle θ of a wound tube heat exchanger is between 5° and 20°, and the radial spacing S... t Generally, the diameter is 1 to 15 mm larger than the outer diameter of the pipe, while the axial spacing S l The radial spacing S should be 1 to 15 millimeters larger than the major axis of the spiral wound tube cross-section. Considering the range of possible outer diameters for the spiral wound tube, the radial spacing S... t With axial spacing S l The upper and lower bounds are set to 10mm and 34mm, respectively. A summary of all input structural parameters and the default optimization range is shown in Table 1.

[0126] Table 1 Optimization parameters and default ranges

[0127]

[0128] Although the default range for each optimization parameter is determined, allowing for the calculation of the structure of the wound tube heat exchanger, it is clear that a series of structural parameters randomly generated during the optimization process may not be effective. For example, in a generated set of structural parameters, the core outer diameter D... core Compared to the outer diameter D of the shell s Large outer diameter d of the spiral wound tube o Specific inner diameter d iSuch a structure is impossible. While each structural parameter has its own default upper and lower bounds and they don't affect each other, in reality, there are often constraints between these parameters. Furthermore, the results of the objective function calculation also have certain requirements. When the area margin ζ is negative, it indicates that the heat exchanger's heat exchange capacity does not reach its rated capacity. In general industrial design, the area margin ζ of the heat exchanger is required to be around 10% to 30%. The pressure drop between the tube side and the shell side cannot exceed their respective allowable pressure drops; otherwise, this design must be rejected outright.

[0129] To ensure the rationality of the structural parameters of the wound tube heat exchanger, prevent errors during the calculation process, and ensure that the final optimization result does not contain any solutions that do not meet the actual requirements, it is necessary to add corresponding constraints to the randomly generated structural parameters and objective function:

[0130] (1) Inner diameter of the shell D s First, ensure that the outer diameter D of the core tube is greater than that of the core tube. core Big, that is, D s >D core Secondly, to ensure that at least one layer of wound tube can be arranged between the core cylinder and the shell, i.e., the number of wound tube layers m ≥ 1, according to the calculation of the number of wound tube layers m, it is necessary to satisfy D. s -D core ≥2S t Otherwise, the number of pipes might be zero, leading to a calculation error. Therefore, during the optimization process, a stronger inequality constraint D is added. s -D core ≥2S t .

[0131] (2) Inner diameter d of the winding tube i It must be greater than the outer diameter d o Small, and with the corresponding outer diameter d o To prevent unreasonable situations such as an outer diameter of 19mm and an inner diameter of 7mm, a mapping method is used in actual processing because these two parameters are discrete variables. This involves randomly selecting from the list of available pipe outer diameters and mapping the corresponding inner diameter to the outer diameter using a dictionary.

[0132] (3) Radial spacing S of the winding tube t Compared to the outer diameter d of the wound tube o Larger than 1-15mm, i.e., 1mm ≤ S t -d o ≤15mm; Axial spacing S l The longer axis d of the winding tube cross-section must be greater than that of the winding tube. o / cosθ is greater than 1 to 15 mm, that is, 1 mm ≤ S l -d o / cosθ≤15mm, add the above two inequality constraints.

[0133] (4) The length-to-diameter ratio of the spiral wound tube heat exchanger should be reasonable and not too small. Considering that the heat exchange tubes of the spiral wound tube heat exchanger have a transition section, the actual length-to-diameter ratio will be slightly larger. Based on the length-to-diameter ratio range of 4 to 10 for shell-and-tube heat exchangers, the length-to-diameter ratio of the spiral wound tube heat exchanger should be at least 2, i.e., 2D. s If ≤L, add the inequality constraint.

[0134] (5) The area margin of the spiral wound tube heat exchanger generally needs to reach 10% to 30%, that is, 10 ≤ ζ ≤ 30; the calculated tube-side pressure drop ΔP t With shell-side pressure drop ΔP s It must not exceed the allowable voltage drop, i.e., ΔP t ≤ΔP t,allow ΔP s ≤ΔP s,allow Add the above three inequality constraints.

[0135] By adding the above constraints, solutions that do not meet the requirements or cannot be calculated at all can be directly filtered out.

[0136] In this invention, NSGA-III is selected as the multi-objective optimization algorithm. The process of the NSGA-III optimization algorithm can be summarized as follows:

[0137] (1) Initialize the population. Randomly generate an initial population, where each individual represents a candidate solution. The population size is a constant N given before the algorithm begins. population At this point, the number of iterations is 0.

[0138] (2) Generating offspring. Randomly perform crossover and mutation operations on the current population to generate a new population of the same size as the initial population, called the offspring. The initial population is called the parent population. Merge the parent and offspring populations into a new population of size 2N. population A new population.

[0139] (3) Non-dominated ranking and fitness calculation. Based on the concept of dominance, each individual in the new population is ranked and assigned a non-dominated rank. Solutions with lower ranks dominate solutions with higher ranks. The fitness of each individual in the population can be calculated using the non-dominated rank. The fitness of all solutions in the new population is calculated based on a set reference point. Solutions closer to the reference point have higher fitness, and solutions farther from the reference point have lower fitness. Solutions with higher fitness have higher priority during selection.

[0140] (4) Generate the next generation population. From the new population, sequentially select the solution set with the lowest non-dominant level until the number of solution sets is greater than or equal to the population size N. population If selecting all solutions from the current non-dominant level exceeds the population size N. populationThen, based on fitness, several solution sets are removed until the size of the solution set equals the population size. If the size of all solution sets selected for the current non-dominant level is exactly equal to the population size, no further action is needed. The selected solution set at this point becomes the next generation population, and the iteration count is increased by 1.

[0141] (5) Repeat steps 2, 3, and 4 until the number of iterations reaches the maximum value. At this point, every solution in the population is the optimal solution.

[0142] The process conditions, physical property parameters, and optimization parameters of the wound tube heat exchanger can be input through programming; the structure, heat transfer, and pressure drop of the wound tube heat exchanger can be calculated, and the NSGA-III optimization algorithm can be applied. Taking a lean methanol cooler as an example, the specific process conditions are shown in Table 2.

[0143] Table 2 Process conditions for lean methanol cooler

[0144]

[0145] The relevant pressure drop constraints are set the same as those for the original wound tube heat exchanger, with a population size of 10,000 and a maximum number of iterations of 100. The final optimization results are shown in Table 3.

[0146] Table 3 Optimization results without restrictions on structural parameters

[0147]

[0148] If the specifications of the spiral wound tubes are set to be the same, that is, control d o With d i The values ​​are 15 and 13 mm respectively, and the optimization results are shown in Table 4.

[0149] Table 4 Optimization results of limiting pipe specifications

[0150]

[0151] If the size of the wound tube heat exchangers is set to be the same, that is, control D s D core The upper and lower bounds of variables L are 1.38m, 0.6m, and 11.63m, respectively. The optimization results are shown in Table 5.

[0152] Table 5 shows the optimization results for limiting the size of the spiral wound tube shell.

[0153]

[0154]

Claims

1. An optimized design method for a wound tube heat exchanger, characterized in that: Using the heat exchange area and area margin of the wound tube heat exchanger as the objective function, a multi-objective optimization algorithm is used to optimize the structural parameters of the wound tube heat exchanger. All potential optimization parameters are listed as optimization variables; if the values ​​of the optimization variables are continuous, upper and lower bounds are defined using inequalities. If the optimization variable is a discrete variable, its range is defined using a set. First, add inequality constraints to all optimization variables. If the optimization parameter is determined, make the upper and lower bounds of the inequality equal; otherwise, determine the upper and lower bounds of the inequality according to the actual range of values ​​of the variable. For a wound tube heat exchanger, all potential optimization variables are: shell inner diameter D. s Core diameter D core outer diameter d of the spiral wound tube o Inner diameter d of the spiral wound tube i , winding angle θ, radial spacing S t axial spacing S l , Shell length L; For processes where no phase change occurs in either the tube side or the shell side, the calculation of the wound tube heat exchanger is divided into 1 segment; when a phase change occurs on one side of the tube side or the shell side, the calculation of the wound tube heat exchanger is divided into a maximum of 3 segments based on the start or end of the phase change point; when both the tube side and the shell side undergo phase changes simultaneously, the calculation of the wound tube heat exchanger is divided into a maximum of 5 segments based on the respective phase change points of the tube side and the shell side. The objective function value of the optimization process is obtained by dividing the wound tube heat exchanger into segments based on the state changes of the tube-side and shell-side physical properties. Each segment is calculated using the infinitesimal element method. Finally, the heat exchange area, area margin, tube-side pressure drop, and shell-side pressure drop performance parameters of the wound tube heat exchanger are obtained by summarizing the data. In the micro-element method calculation, the heat transfer of each micro-element is equal. Starting from the left or right side of the segment, the inlet and outlet temperatures of the tube side and shell side of the current micro-element are calculated, and the calculated temperature is used as the inlet and outlet temperatures of the next micro-element segment. This process is repeated to calculate the inlet and outlet temperatures of all micro-element segments within the segment. By controlling the temperature difference between the inlet and outlet, the magnitude of the property changes at the inlet and outlet temperatures of the micro-element is controlled. The arithmetic mean can be used to represent the property parameters within the entire micro-element. If a segment is divided into n micro-elements, the total heat transfer of the segment is Q. section Then the heat exchange dQ of each microelement element for Since the phase states on both sides of the infinitesimal element are fixed and will not change, the tube-side heat transfer coefficient h of the infinitesimal element can be calculated by selecting the corresponding heat transfer coefficient calculation method. t Heat transfer coefficient h of shell side s The overall heat transfer coefficient U of the micro-element element The calculation formula is , In the formula, r s With r t These are the fouling thermal resistances of the shell side and tube side, respectively; λ tube This refers to the thermal conductivity of the pipe material; based on the temperatures at the inlet and outlet on both sides of the infinitesimal element, the logarithmic mean temperature difference ΔT can be calculated. LMTD； According to the heat exchange calculation formula dQ element =U element dA require ΔT LMTD The required heat transfer area dA of the infinitesimal element can be calculated. require And so on, the required heat exchange area A for this section section The total heat transfer coefficient U is the sum of the heat transfer areas required by all infinitesimal elements. section This is the average value of the total heat transfer coefficient of all micro-elements; at the same time, the pressure drop in the tube side and shell side of each micro-element can be calculated, and the pressure drop on both sides of the segment is the sum of the corresponding pressure drops of all micro-elements; The design method flow is as follows: First, initialize the population; randomly generate an initial population, where each individual represents a candidate solution; the population size is a constant N given before the algorithm begins. population At this point, the number of iterations is 0; The second step is to generate offspring. Random crossover and mutation operations are performed on the current population to generate a new population of the same size as the initial population, called the offspring. The initial population is called the parent population. The parent and offspring populations are then merged into a new population of size 2N. population A new population; The third step is non-dominated sorting and fitness calculation. Based on the concept of dominance, each individual in the new population is sorted and assigned a non-dominated level. Solutions with lower levels dominate solutions with higher levels. The fitness of each individual in the population can be calculated through the non-dominated levels. The fitness of all solutions in the new population is calculated based on a set reference point. Solutions closer to the reference point have higher fitness, and solutions farther from the reference point have lower fitness. Solutions with higher fitness have higher priority when selected. The fourth step is to generate the next generation population; from the new population, select the solution set with the lowest non-dominant level in turn, until the number of solution sets is greater than or equal to the population size N. population If the number of solutions selected from all non-dominant levels exceeds the population size N; population Then, based on fitness, several solution sets are removed until the size of the solution set equals the population size. If the size of all solution sets selected for the current non-dominant level is exactly equal to the population size, no operation is required. The selected solution set at this point becomes the next generation population, and the iteration count is increased by 1. Fifth, repeat steps two, three, and four until the number of iterations reaches the maximum value. At this point, every solution in the population is the optimal solution.

2. The optimized design method for a wound tube heat exchanger according to any one of claims 1, characterized in that, The optimization design method also includes a calculation method for the tube bundle structure of the wound tube heat exchanger.

3. The optimized design method for a wound tube heat exchanger according to claim 2, characterized in that, The calculation method for the tube bundle structure of a wound tube heat exchanger is as follows: The structure of a wound tube heat exchanger involves the following parameters: core diameter D core Used to support the wound tube bundle; the inner diameter d of the wound tube i With outer diameter d o , used to determine the specifications of the wound tube; winding angle θ, used to control the inclination angle of the heat transfer tube winding; radial spacing S t Used to control the spacing between different layers of wound tubes; axial spacing S l These parameters are used to control the spacing between the wound tubes in the same layer; based on these parameters, the structure of the entire wound tube bundle can be determined. The following mathematical form is adopted: In the formula, x i The variables to be optimized are represented by n variables. The superscripts L and U represent the upper and lower boundaries of the optimized variables, respectively. The set of optimized variables is called the sample space, and n optimized variables mean that the sample space is n-dimensional. g(x) and h(x) both represent the constraints of the optimized variables. The values ​​of the optimized variables must satisfy the constraints. The difference is that g(x) represents inequality constraints, while h(x) represents equality constraints. There are J inequality constraints and K equality constraints. In special cases, the values ​​of J and K can be 0, that is, there are no constraints. f(x) represents the objective function in the optimization problem. There are M optimization objectives. When M is 1, it is a single-objective optimization problem. When M is greater than 1, it is a multi-objective optimization problem. The final goal of the optimization is to maximize or minimize these objective functions. Each structural parameter of the wound tube heat exchanger corresponds to an 'x', where the outer diameter D of the core tube is... core Inner diameter of the shell D s , shell length L, winding angle θ, radial spacing S t and axial spacing S l The inner diameter d of the wound tube is a continuous variable. i With outer diameter d o These are discrete variables; each of these variables can be considered as one of x, but they are expressed in different ways. The range of continuous variables is: 0.075m ≤ D. core ≤0.8m, 5°≤θ≤20°, 10mm≤S t ≤34mm, 10mm≤S l ≤34mm; the range of values ​​for the discrete variable is: d o ∈[9, 10, 12, 15, 19], d i ∈[7, 8, 10, 13, 15], in mm.

4. The optimized design method for a wound tube heat exchanger according to claim 3, characterized in that, When no phase change occurs in either the tube side or the shell side, the tube-side fluid and the shell-side fluid flow in countercurrent, and the inlet and outlet temperatures of the tube side and shell side are respectively T. tube,in T tube,out T shell,in T shell,out The calculation methods for heat transfer and pressure drop are both non-phase change calculations, and the entire calculation process is divided into a whole segment. When a phase change occurs on either the tube side or the shell side, taking the tube-side hot fluid undergoing a phase change as an example, the initial inlet temperature of the tube-side fluid is T. tube,in When the temperature reaches the first phase transition temperature T tube,b1 At this time, the fluid in the tube side begins to condense, corresponding to the shell side temperature T. shell,s1 The fluid in the tube side continues to condense until the second phase transition temperature T. tube,b2 At this point, the tube-side fluid is completely condensed into condensate, corresponding to a shell-side temperature T. shell,s2 The fluid temperature in the tube continues to decrease until it reaches the outlet temperature T. tube,out At this time, the corresponding shell-side inlet temperature T shell,in The calculation of the entire heat exchanger is divided into three main sections. From top to bottom, the first section is single-phase tube side and single-phase shell side; the second section is tube side condensation and single-phase shell side; the third section is single-phase tube side and single-phase shell side. Each section requires the selection of the corresponding calculation method. The temperature segmentation method is similar when the shell side undergoes a phase change but the tube side does not. When phase change occurs simultaneously on both sides, taking the tube-side heat transfer fluid as an example, the tube-side inlet temperature is T. tube,in The corresponding shell-side outlet temperature T shell,out When the tube-side temperature drops to the first phase transition temperature T tube,b1 At this time, the corresponding shell-side temperature T shell,s1 Condensation begins in the tube side, and the temperature continues to drop to T. tube,s1 At that time, the first phase transition point T in the shell side corresponds to shell,b1 Evaporation begins in the shell side; the tube side temperature reaches the second phase transition point T. tube,b2 At this point, the tube-side condensation ends, and the corresponding shell-side temperature is T. shell,s2 It is still evaporating; the temperature of the condensate in the tube side continues to drop until T. tube,s2 This corresponds to the second temperature phase transition point T in the shell side. shell,b2 This refers to the point where the shell side begins to undergo evaporation and phase transition; finally, the tube side reaches the outlet temperature T. tube,out The shell side reaches the inlet temperature T. shell,in At this point, the calculation of the entire heat exchanger is divided into five sections, from top to bottom: Section 1, tube side single phase, shell side single phase; Section 2, tube side condensation, shell side single phase; Section 3, tube side condensation, shell side evaporation; Section 4, tube side single phase, shell side evaporation; Section 5, tube side single phase, shell side single phase.

5. An optimized design method for a wound tube heat exchanger according to claim 1 or 4, characterized in that, The specific segment location is determined by the uniqueness of the enthalpy value, thereby determining the temperature point of the segment. Then, the corresponding enthalpy value on the other side is calculated based on the heat balance, and the specific segment temperature point is determined.

6. The optimized design method for a wound tube heat exchanger according to claim 1 or 4, characterized in that, After reading the physical property parameters, the enthalpy values ​​for the start and end of the phase transition are determined based on the location of the phase transition point in the physical property parameters, thereby determining the phase transition temperature, and thus determining the phase transition temperature point T. tube,b1 T tube,b2 T shell,b1 T shell,b2 The temperature point T corresponding to the segmentation tube,s1 T tube,s2 T shell,s1 T shell,s2 It is derived through heat balance calculations.

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