An optimization design method of a spiral pipe heat exchanger

Abstract

This invention relates to the field of heat exchanger optimization design technology, specifically an optimization design method for a spiral tube heat exchanger. The method includes: obtaining the heat exchanger's process operating conditions and structural parameters; establishing a calculation model for heat transfer and flow resistance in the tube and shell sides; using a bisection method to iteratively calculate the outlet temperature of the tube and shell side medium; calculating the corresponding pressure drop; constructing a multi-sub-objective function that characterizes heat transfer performance, flow resistance, entropy production characteristics, and manufacturing cost; and using a differential evolution algorithm framework to optimize the system, conducting multiple iterations with structural parameters as variables. In each generation, modeling, temperature calculation, pressure drop calculation, and objective function evaluation are repeatedly performed for each candidate parameter combination within the population. After convergence, the optimal parameter combination is selected as the design scheme. This invention achieves coupled temperature calculation and full-process iterative optimization, adapting to multi-dimensional design requirements.

Description

Technical Field

[0001] This invention relates to the field of heat exchanger optimization design technology, and in particular to an optimization design method for a spiral tube heat exchanger. Background Technology

[0002] Existing designs for spiral tube heat exchangers often rely on a single heat transfer model to perform independent temperature calculations for the tube side or shell side. Pressure drop calculations depend on fixed structural parameters and empirical formulas. Optimization processes often employ single-objective or bi-objective functions and rely on conventional evolutionary algorithms to optimize parameters after a single modeling iteration. Some schemes use simple iterative methods to solve for temperature. During the optimization iteration process, only the structural parameters are numerically adjusted, without performing full-process model reconstruction and performance calculations for each candidate parameter combination.

[0003] The tube-side and shell-side temperature calculations lack a coupled iterative mechanism, leading to deviations in outlet temperature values ​​and consequently, a low degree of matching between the calculated pressure drop and actual operating conditions. The objective function fails to synchronously integrate heat transfer performance, flow resistance, entropy production characteristics, and manufacturing cost dimensions, resulting in missing optimization dimensions. Conventional optimization algorithms cannot repeatedly perform the entire process of modeling, temperature calculation, pressure drop calculation, and objective function evaluation for each generation of candidate structural parameter combinations, resulting in insufficient coupling between parameter optimization and actual operating conditions, and poor adaptability of the optimization results to practical applications.

[0004] It is necessary to achieve coupled iterative calculation of the tube-side and shell-side outlet temperatures to eliminate subsequent calculation errors caused by temperature value deviations. In each iteration of the differential evolution algorithm, the entire process of establishing a computational model, calculating the outlet temperature, calculating the pressure drop, and evaluating multiple sub-objective functions needs to be completed for each candidate structural parameter combination, and the synchronous optimization mechanism of multi-dimensional sub-objectives needs to be improved. Summary of the Invention

[0005] The purpose of this invention is to address the shortcomings of existing technologies by proposing an optimized design method for spiral tube heat exchangers.

[0006] To achieve the above objectives, the present invention adopts the following technical solution: an optimized design method for a spiral tube heat exchanger, comprising:

[0007] Obtain the process operating conditions and structural parameters of the heat exchanger, and establish a heat transfer calculation model and a flow resistance calculation model that includes the tube side and the shell side.

[0008] Based on the aforementioned heat transfer calculation model and process operating conditions, the outlet temperatures of the medium in the tube and shell sides are calculated iteratively using the bisection method.

[0009] Based on the flow resistance calculation model, process operating conditions, and calculated outlet temperature, the pressure drop between the tube side and the shell side is calculated.

[0010] Construct an objective function containing multiple sub-objectives, including sub-objectives characterizing heat transfer performance, sub-objectives characterizing flow resistance, sub-objectives characterizing entropy production characteristics, and sub-objectives characterizing manufacturing cost;

[0011] Using an optimization framework based on differential evolution algorithm, with the structural parameters as optimization variables and the objective function as the evaluation criterion, multi-generation search and iterative optimization are performed;

[0012] In each generation of multi-generation search and iterative optimization, a population containing multiple candidate structural parameter combinations is generated. For each candidate structural parameter combination in the population, the steps of establishing a computational model, calculating the outlet temperature, calculating the pressure drop, and evaluating the objective function are repeatedly executed.

[0013] After the multi-generation search and iterative optimization process converges, the candidate combination of structural parameters that makes the objective function numerically optimal is selected from the final generation population as the optimal design scheme for the spiral tube heat exchanger.

[0014] As a further aspect of the present invention, the establishment of a heat transfer calculation model including the tube side and the shell side includes the following steps:

[0015] The process operating conditions include the flow rate of the medium in the tube side and the shell side, the inlet temperature, the operating pressure, and the type of medium.

[0016] The structural parameters include the helix angle, helix diameter, pitch, tube spacing, interlayer spacing, and total tube length.

[0017] Based on the flow rate, inlet temperature, operating pressure, and medium type in the tube and shell sides, the physical properties of the medium are determined, including density, specific heat capacity, thermal conductivity, and dynamic viscosity.

[0018] Calculate the flow cross-sectional area, heat exchange area, equivalent diameter, and centerline length of the spiral tube based on the spiral angle, spiral diameter, pitch, tube spacing, interlayer spacing, and total tube length.

[0019] Based on the structural parameters of the shell side, including the shell inner diameter, tube bundle arrangement, tube spacing and layer spacing, calculate the flow cross-sectional area, equivalent diameter and effective length of fluid flow in the shell side;

[0020] Based on the flow conditions and geometric parameters of the tube side, the convective heat transfer coefficient of the tube side is calculated using a correlation formula.

[0021] Based on the flow conditions and geometric parameters of the shell side, the convective heat transfer coefficient of the shell side is calculated using a correlation formula.

[0022] Based on the convective heat transfer coefficients of the tube side and shell side and the thermal resistance of the tube wall, the overall heat transfer coefficient between the tube side and shell side is calculated, thus completing the establishment of the heat transfer calculation model.

[0023] As a further aspect of the present invention, a flow resistance calculation model including the tube side and the shell side is established, comprising the following steps:

[0024] Based on the flow rate, physical properties, and cross-sectional area of ​​the medium in the tube and shell sides, the flow velocity of the medium in the tube side is calculated.

[0025] Based on the flow rate, physical properties, and cross-sectional area of ​​the medium in the tube and shell sides, the flow velocity of the medium in the shell side is calculated.

[0026] Based on the flow velocity in the tube and the geometry of the helical tube, including the helix angle, helix diameter, pitch, and total tube length, the friction coefficient along the tube is calculated using the friction coefficient correlation applicable to helical tube flow.

[0027] Based on the flow velocity in the shell side, the tube bundle arrangement, the tube spacing and the layer spacing, the friction coefficient along the shell side is calculated using the friction coefficient correlation applicable to the flow across the tube bundle in the shell side.

[0028] Calculate the pressure drop in the tube side based on the friction coefficient along the tube, the flow velocity in the tube side, the total length of the tube, and the equivalent diameter.

[0029] The pressure drop in the shell side is calculated based on the friction coefficient along the shell side, the flow velocity in the shell side, the effective length of the fluid flow in the shell side, and the equivalent diameter.

[0030] As a further aspect of the present invention, the step of using the bisection method to iteratively calculate the outlet temperature of the medium in the tube side and the shell side includes the following steps:

[0031] An initial search range is set for the outlet temperature of the tube-side medium, where the lower bound of the initial search range is the inlet temperature of the shell-side medium, and the upper bound of the initial search range is the inlet temperature of the tube-side medium.

[0032] An initial search range is set for the outlet temperature of the shell-side medium, the lower bound of which is the inlet temperature of the tube-side medium, and the upper bound of which is the inlet temperature of the shell-side medium.

[0033] Within the search range of the tube-side medium outlet temperature, the midpoint temperature value is taken as the currently assumed tube-side outlet temperature.

[0034] Based on the energy conservation equation and the heat transfer calculation model, the corresponding shell-side outlet temperature is calculated using the currently assumed tube-side outlet temperature.

[0035] Determine whether the calculated shell-side outlet temperature is within the set search range of the shell-side medium outlet temperature. If not, adjust the search range of the tube-side outlet temperature according to the energy balance relationship, update the midpoint temperature value, and recalculate the corresponding shell-side outlet temperature.

[0036] Repeat the judgment and adjustment steps until the calculated shell-side outlet temperature stably falls within its search range, and the energy exchange between the tube side and the shell side meets the preset convergence accuracy. The temperature value obtained at this time is the final determined tube-side and shell-side outlet temperature.

[0037] As a further aspect of the present invention, the construction of the objective function comprising multiple sub-objectives includes the following steps:

[0038] Define sub-objectives characterizing heat transfer performance, which are calculated based on the overall heat transfer coefficient, heat transfer area, and the average logarithmic heat transfer temperature difference between the tube side and the shell side.

[0039] Define a sub-objective characterizing flow resistance, which is obtained by summing the calculated tube-side pressure drop and shell-side pressure drop;

[0040] Define a sub-objective characterizing entropy production characteristics. The sub-objective characterizing entropy production characteristics is obtained by summing the flow entropy production and heat transfer entropy production calculated separately based on the pressure drop, heat transfer, inlet and outlet temperatures, and ambient temperature of the tube and shell sides.

[0041] Define a sub-objective to characterize manufacturing cost. This sub-objective is calculated using a cost estimation model based on the total length of the spiral tube, spiral diameter, tube material usage, shell size, and material unit price.

[0042] The sub-objectives characterizing heat transfer performance, flow resistance, entropy production, and manufacturing cost are combined into the objective function through weighted summation or a multi-objective processing method based on the Pareto front.

[0043] As a further aspect of the present invention, the optimization framework based on differential evolution algorithm, using the structural parameters as optimization variables and the objective function as the evaluation criterion, performs multi-generational search and iterative optimization, including the following steps:

[0044] Initialize the parameters of the differential evolution algorithm, including population size, scaling factor, crossover probability, and maximum number of generations;

[0045] Within the allowed range of values ​​for the structural parameters, an initial population is randomly generated. The initial population consists of multiple individuals, each representing a specific set of values ​​for the structural parameters.

[0046] For each individual in the initial population, the values ​​of the structural parameters it represents are substituted into the calculation model, the steps of establishing the calculation model, calculating the outlet temperature, calculating the pressure drop and evaluating the objective function are performed to obtain the objective function value corresponding to each individual;

[0047] The iteration begins, and for each target individual in the current population, a mutation operation is performed. The mutation operation generates a test vector based on several different individuals randomly selected from the current population, according to the mutation strategy of the differential evolution algorithm.

[0048] A crossover operation is performed on the target individual and the test vector, and some parameter components of the target individual and the test vector are swapped according to the crossover probability to generate a new candidate individual;

[0049] Substitute the structural parameter values ​​of the new candidate individual into the calculation model, calculate the outlet temperature, calculate the pressure drop and evaluate the objective function again to obtain the objective function value corresponding to the new candidate individual;

[0050] The objective function value of the new candidate individual is compared with the objective function value of the target individual, and the one with the better objective function value is retained in the next generation population.

[0051] Repeat the mutation, crossover, evaluation, and selection operations until all individuals have been processed, thus completing the evolution of one generation of the population;

[0052] Repeat the evolutionary process of the population for multiple generations until the preset maximum number of generations is reached or the convergence condition is met.

[0053] As a further aspect of the present invention, in each generation of multi-generation search and iterative optimization, a population containing multiple candidate structural parameter combinations is generated. For each candidate structural parameter combination in the population, the steps of establishing a computational model, calculating the outlet temperature, calculating the pressure drop, and evaluating the objective function are repeatedly executed, including the following specific processes:

[0054] For a given combination of candidate structure parameters, i.e. an individual in the differential evolution algorithm, its specific values ​​correspond to a set of values ​​for helix angle, helix diameter, pitch, tube spacing, layer spacing and length.

[0055] Using the values ​​of helix angle, helix diameter, pitch, tube spacing, interlayer spacing, and length, the key geometric parameters of the heat exchanger are recalculated, including the flow cross-sectional area, heat transfer area, equivalent diameter, and centerline length of the helical tubes on the tube side, as well as the flow cross-sectional area, equivalent diameter, and effective length of fluid flow on the shell side.

[0056] Based on the recalculated geometric parameters, known process operating conditions, and physical property parameters, the convective heat transfer coefficients of the tube side and shell side, as well as the overall heat transfer coefficient, are recalculated.

[0057] Based on the recalculated geometric parameters and flow conditions, the frictional resistance coefficients and pressure drops along the tube and shell sides were recalculated.

[0058] The steps of using the bisection method to iteratively calculate the outlet temperature are invoked, and the outlet temperatures of the tube side and shell side are recalculated based on the current overall heat transfer coefficient and geometric parameters.

[0059] Substitute the recalculated total heat transfer coefficient, pressure drop, and outlet temperature into the calculation formulas for each sub-objective in the objective function;

[0060] The final objective function value corresponding to the candidate structure parameter combination is obtained by comprehensive calculation. The final objective function value is used for individual fitness comparison in the differential evolution algorithm.

[0061] As a further aspect of the present invention, it also includes a step of setting constraints before optimization, wherein the constraints include:

[0062] Set upper and lower limits for structural parameters to ensure that the helix angle, helix diameter, pitch, pipe spacing, layer spacing, and length are within the allowable range for engineering manufacturing and installation;

[0063] Set performance constraints, including limiting the maximum allowable pressure drop in the tube side and shell side, and limiting the minimum heat transfer efficiency of the heat exchanger;

[0064] In each generation of the differential evolution algorithm, for candidate structural parameter combinations that do not meet the constraints, their objective function values ​​will be given a very large penalty value to reduce their probability of being selected for the next generation.

[0065] As a further aspect of the present invention, the method is optimized for multi-layer spiral tube heat exchangers, wherein:

[0066] The spacing between the spiral tube layers in the structural parameters specifically refers to the radial distance between the central axes of two adjacent spiral tube layers in a multi-layer spiral tube structure.

[0067] When establishing the heat transfer calculation model, the thermal interference between the multi-layer spiral tubes needs to be considered, and the flow and heat transfer correlation of the shell-side fluid needs to be modified accordingly.

[0068] When establishing the flow resistance calculation model, it is necessary to consider the additional resistance caused by the multi-layer tube bundle to the shell-side fluid flow, and make corresponding corrections to the correlation of the shell-side friction resistance coefficient.

[0069] As a further aspect of the present invention, the method is optimized for a double-shell-pass multilayer spiral tube heat exchanger, wherein:

[0070] In the aforementioned process operating conditions, the shell-side medium is divided into two streams, which flow in two independent shell-side channels respectively. It is necessary to obtain the flow rate, inlet temperature, working pressure and medium type of the two shell-side media respectively.

[0071] When establishing the heat transfer calculation model and the flow resistance calculation model, it is necessary to establish independent heat transfer and pressure drop calculation sub-models for the two shell-side channels respectively.

[0072] The step of using the bisection method to iteratively calculate the outlet temperature requires simultaneously iteratively solving the tube-side medium outlet temperature, the first shell-side medium outlet temperature, and the second shell-side medium outlet temperature to ensure that the energy exchange between the three channels reaches a balance at the same time.

[0073] When constructing the objective function, the sub-objective characterizing flow resistance must include the pressure drop of both shell sides, and the sub-objective characterizing entropy production characteristics must include the contribution of both shell sides.

[0074] Compared with the prior art, the advantages and positive effects of the present invention are as follows:

[0075] The bisection method is adopted to iteratively calculate the outlet temperature of the medium based on the tube-side and shell-side coupled heat transfer calculation model and process operating conditions. The temperature parameters of the tube side and shell side form a bidirectional coupled feedback. The calculated outlet temperature results are close to the actual heat exchange conditions. The pressure drop calculation is carried out based on the accurate outlet temperature parameters. The parameter benchmark for flow resistance calculation is consistent with the actual heat exchange state, avoiding the parameter deviation caused by independent temperature calculation. The parameter matching of heat transfer and resistance calculation is improved. The coupled temperature values ​​can be directly used as input parameters for pressure drop calculation. The parameter transmission of each calculation link is close to the actual operating logic of the heat exchanger, and the correlation between temperature and pressure drop calculation is closer.

[0076] Within the optimization framework based on the differential evolution algorithm, each iteration generates multiple candidate structural parameter combinations to form a population. Each candidate structural parameter combination repeatedly executes the steps of establishing a computational model, calculating the outlet temperature, calculating the pressure drop, and evaluating multiple sub-objective functions. Four types of sub-objectives—heat transfer performance, flow resistance, entropy production characteristics, and manufacturing cost—are simultaneously incorporated into the evaluation system. Multi-dimensional performance indicators participate in the iterative optimization process simultaneously. The population iteration process is consistent with the actual design calculation process of the heat exchanger, and the closed-loop logic of the optimization iteration matches the actual design conditions. Finally, the parameter combinations output by the population have a higher degree of adaptability to multi-dimensional design requirements. The iterative optimization process fully covers the entire calculation process of heat exchanger design, and the evaluation process of candidate parameters is consistent with the actual design calculation process. Attached Figure Description

[0077] Figure 1 A flowchart of an optimized design method for a spiral tube heat exchanger according to the present invention;

[0078] Figure 2 A flowchart for establishing a flow resistance calculation model. Detailed Implementation

[0079] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0080] In the description of this invention, it should be understood that the terms "length," "width," "upper," "lower," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," and "outer," etc., indicating orientation or positional relationships, are based on the orientation or positional relationships shown in the accompanying drawings and are only for the convenience of describing the invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation of the invention. Furthermore, in the description of this invention, "a plurality of" means two or more, unless otherwise explicitly specified.

[0081] See Figure 1 This invention provides an optimized design method for a spiral tube heat exchanger, the specific method including:

[0082] The process operating conditions and structural parameters of the heat exchanger are obtained. The process operating conditions include medium flow rate, inlet temperature, operating pressure, and medium type. The structural parameters include helix angle, helix diameter, helix pitch, tube spacing, interlayer spacing, and total tube length. Based on these input parameters, a heat transfer calculation model and a flow resistance calculation model are established, encompassing both the tube side and shell side. Based on the established heat transfer calculation model and the known process operating conditions, the final outlet temperature of the medium in both the tube side and shell side is calculated using a bisection method iteratively. Based on the established flow resistance calculation model, process operating conditions, and the calculated outlet temperature, the pressure drop in both the tube side and shell side is calculated. Then, an objective function containing multiple sub-objectives is constructed. These sub-objectives include those characterizing heat transfer performance, flow resistance, entropy production characteristics, and manufacturing cost. Using an optimization framework based on differential evolution, with the aforementioned structural parameters as optimization variables and the constructed objective function as the evaluation criterion, multi-generational search and iterative optimization are performed. In each generation of the optimization process, the algorithm generates a population containing multiple candidate structural parameter combinations. For each candidate structural parameter combination in the population, the complete sequence of steps—establishing a computational model, calculating the outlet temperature, calculating the pressure drop, and evaluating the objective function—must be repeatedly executed. When the multi-generation search and iterative optimization process converges, the candidate structural parameter combination that achieves the optimal objective function value is selected from the final generation of the population. This combination is then determined as the optimal design scheme for the helical tube heat exchanger.

[0083] In one embodiment of the present invention, when establishing a heat transfer calculation model including the tube side and shell side, the required process operating conditions include the flow rate, inlet temperature, operating pressure, and medium type of the medium in both the tube side and shell side. The required structural parameters include the helix angle, helix diameter, pitch, tube spacing, interlayer spacing, and total tube length of the spiral tube. Based on the flow rate, inlet temperature, operating pressure, and medium type in both the tube side and shell side, the physical properties of the medium are determined, including density, specific heat capacity, thermal conductivity, and dynamic viscosity. Based on the helix angle, helix diameter, pitch, tube spacing, interlayer spacing, and total tube length of the spiral tube, the flow cross-sectional area, heat transfer area, equivalent diameter, and spiral tube centerline length of the tube side are calculated. Based on the structural parameters of the shell side, including the shell inner diameter, tube bundle arrangement, tube spacing, and interlayer spacing, the flow cross-sectional area, equivalent diameter, and effective length of fluid flow in the shell side are calculated. According to the flow conditions and geometric parameters of the tube side, an appropriate correlation equation is selected to calculate the convective heat transfer coefficient of the tube side. Based on the flow conditions and geometric parameters of the shell side, an appropriate correlation equation is selected to calculate the convective heat transfer coefficient of the shell side. Based on the calculated convective heat transfer coefficients of the tube side and shell side, as well as the thermal resistance of the tube wall, the overall heat transfer coefficient between the tube side and shell side is calculated, thus completing the establishment of the heat transfer calculation model.

[0084] In practical implementation, the step of establishing a heat transfer calculation model including both the tube side and shell side involves inputting the process operating conditions and structural parameters of the spiral tube heat exchanger. The process operating conditions explicitly include the flow rates of the medium in the tube side and shell side, the inlet temperature of the medium in the tube side, the inlet temperature of the medium in the shell side, the operating pressures of both the tube side and shell side, and the types of the medium in both sides. The structural parameters explicitly include the helix angle, helix diameter, helix pitch, tube spacing between spiral tubes, interlayer spacing of multi-layer spiral tubes, and the total length of the spiral tubes. In practical implementation, based on the known medium types, operating pressures, and inlet temperatures of the tube side and shell side media, the physical property parameters of the medium under corresponding conditions are obtained by retrieving data from a physical property database or by calculating through physical property equations. These physical property parameters include density, specific heat capacity, thermal conductivity, and dynamic viscosity.

[0085] In practical implementation, the geometric characteristics related to the tube pass are calculated based on the structural parameters of the helical tube. The helix angle is the angle between the centerline of the helical tube and a plane perpendicular to the helix axis; the helix diameter is the diameter of the centerline of the helical tube; and the pitch is the distance the helical tube travels in one revolution along the axis. Using the helix angle, helix diameter, pitch, tube spacing, layer spacing, and total tube length, the flow cross-sectional area of ​​the tube pass can be calculated. The calculation of the flow cross-sectional area considers the cross-sectional area of ​​a single helical tube and the total number of tubes in the tube pass. The heat exchange area is calculated based on the outer diameter of a single helical tube, the total length of the helical tube, and the total number of tubes in the tube pass. The equivalent diameter is calculated based on the equivalent hydraulic diameter formula for the flow cross-sectional area of ​​the tube pass. There is a geometric relationship between the length of the helical tube centerline and the total length of the helical tube, the helix diameter, and the pitch.

[0086] In practical implementation, the shell-side geometric characteristics are calculated based on the shell-side structural parameters. These parameters include the shell's inner diameter, tube bundle arrangement, tube spacing, and interlayer spacing. Based on these parameters, the flow cross-sectional area of ​​the shell is calculated, which is the cross-sectional area of ​​the shell cavity minus the cross-sectional area occupied by the tube bundle. The equivalent diameter of the shell is also calculated based on its flow cross-sectional area. The effective length of the shell-side fluid flow is determined by the axial length of the helical tube bundle within the shell. In practical implementation, the convective heat transfer coefficient of the tube side is calculated using correlations based on the flow conditions and geometric parameters of the tube side. The flow conditions include the flow rate and physical properties of the tube side medium, while the geometric parameters include the equivalent diameter of the tube side and the centerline length of the helical tube. The correlations used in the calculations are empirical formulas for forced convective heat transfer within the helical tube, such as the Dietus-Belth formula form including the Reynolds number and Prandtl number, and are corrected according to the curvature of the helical tube. The Nusselt number in the formula characterizes the strength of convective heat transfer.

[0087] In practice, the shell-side convective heat transfer coefficient is calculated using correlations based on the flow conditions and geometric parameters of the shell side. The flow conditions include the flow rate and physical properties of the shell-side medium, while the geometric parameters include the equivalent diameter of the shell, the tube bundle arrangement, and the tube spacing. The correlations used in the calculations are empirical formulas for convective heat transfer when the fluid flows across the tube bundle. For multi-layered helical tube bundles, correction factors that account for the mutual influence between tube bundles need to be introduced into the correlations.

[0088] Based on the calculated tube-side and shell-side convective heat transfer coefficients, and the thermal resistance of the tube wall, the overall heat transfer coefficient between the tube side and shell side is calculated using the principle of superposition of series thermal resistances. The thermal resistance of the tube wall is determined by the thermal conductivity of the tube wall material and the tube wall thickness. The formula for calculating the overall heat transfer coefficient K is:

[0089]

[0090] in: This represents the convective heat transfer coefficient of the tube side. This represents the shell-side convective heat transfer coefficient. This represents the thermal resistance of the pipe wall. The completion of the calculation of the overall heat transfer coefficient marks the establishment of the heat transfer calculation model.

[0091] In one embodiment of the present invention, when establishing a flow resistance calculation model including the tube side and shell side, the flow velocity of the medium in the tube side is calculated based on the flow rate and physical property parameters of the medium in the tube side and shell side, and the previously calculated tube side flow cross-sectional area. See also Figure 2 Based on the flow rate and physical properties of the medium in the tube and shell sides, and the previously calculated shell-side flow cross-sectional area, the flow velocity of the medium in the shell side is calculated. Based on the flow velocity in the tube side and the geometry of the helical tube, including the helix angle, helix diameter, pitch, and total tube length, the friction coefficient along the tube side is calculated using a friction coefficient correlation applicable to helical tube flow. Based on the flow velocity in the shell side, the tube bundle arrangement, tube spacing, and interlayer spacing, the friction coefficient along the shell side is calculated using a friction coefficient correlation applicable to shell-side flow across the tube bundle. Based on the friction coefficient along the tube side, the flow velocity in the tube side, the total tube length, and the equivalent diameter, the pressure drop in the tube side is calculated. Based on the friction coefficient along the shell side, the flow velocity in the shell side, the effective length of the shell-side fluid flow, and the equivalent diameter, the pressure drop in the shell side is calculated.

[0092] In practical implementation, the steps for establishing a flow resistance calculation model that includes both the tube side and shell side are based on previously determined process operating conditions, physical properties, and geometric parameters. First, based on the flow rate and density of the tube side medium, and the previously calculated tube flow cross-sectional area, the flow velocity of the medium in the tube side is calculated. The tube side flow velocity equals the tube side medium volumetric flow rate divided by the tube side flow cross-sectional area. Similarly, based on the flow rate and density of the shell side medium, and the previously calculated shell side flow cross-sectional area, the flow velocity of the medium in the shell side is calculated. The shell side flow velocity equals the shell side medium volumetric flow rate divided by the shell side flow cross-sectional area. In practical implementation, these two flow velocities are the basis for calculating fluid flow resistance.

[0093] In practical implementation, the friction coefficient along the tube side is calculated. Based on the calculated tube-side flow velocity and the geometry of the helical tube, including the helix angle, helix diameter, pitch, and total tube length, a friction coefficient correlation applicable to helical tube flow is used for calculation. The correlation typically includes the Reynolds number and Dean number; the Dean number reflects the relative magnitudes of centrifugal and viscous forces in the helical tube. It is understood that different friction coefficient correlations exist for laminar or turbulent flow within a helical tube. For example, an optional correlation form for turbulent flow is:

[0094]

[0095] in: This represents the frictional resistance coefficient along the pipe side. This represents the Reynolds number calculated based on the equivalent pipe diameter and the pipe flow velocity. The Dean number represents the ratio of the Reynolds number to the pipe's radius of curvature. , , , These are empirical coefficients for the correlation. In some embodiments, the specific form of the correlation and the empirical coefficients need to be selected from recognized literature or manuals based on the specific geometry and flow conditions of the helical tube. In a specific implementation, the frictional drag coefficient along the shell side is calculated. Based on the calculated shell-side flow velocity, tube bundle arrangement, tube spacing, and layer spacing, the frictional drag coefficient correlation applicable to shell-side flow across the tube bundle is used for calculation. It can be understood that the form of the correlation is closely related to the tube bundle arrangement, the ratio of tube spacing to tube diameter, and the shell-side Reynolds number. For example, for a square in-line or equilateral triangular staggered tube bundle arrangement, there are different frictional drag coefficient calculation charts or empirical formulas. An optional correlation form for staggered tube bundles is:

[0096]

[0097] in: This represents the frictional resistance coefficient along the shell side. This represents the shell-side Reynolds number calculated based on the shell-side equivalent diameter and shell-side flow velocity. Indicates the horizontal pipe spacing. Indicates the longitudinal pipe spacing. Indicates the outer diameter of the pipe. , , , This is an empirical coefficient related to the arrangement of the tube bundles. In some embodiments, for multi-layered helical tube bundles, a correction factor needs to be added to the basic correlation to account for the combined effect of multiple rows of tube bundles on flow resistance.

[0098] In practical implementation, the pressure drop in the tube side is calculated based on the calculated friction coefficient, flow velocity, total length of the helical tube, and equivalent diameter of the tube side. The pressure drop is calculated according to the Darcy-Weisbach formula, which includes the friction coefficient, the square of the flow velocity, the ratio of the total length of the helical tube to the equivalent diameter, and the density of the medium in the tube side. Local resistance losses within the helical tube must be considered during the calculation; optionally, these losses can be included in the total pressure drop using either the equivalent length method or the local resistance coefficient method. Similarly, the pressure drop in the shell side is calculated based on the calculated friction coefficient, flow velocity, effective length of the shell fluid flow, and equivalent diameter. The shell side pressure drop is also calculated using the Darcy-Weisbach formula, but the effective length and equivalent diameter of the shell side must be the values ​​previously calculated for the shell side. It is understandable that the shell-side pressure drop calculation also includes the inlet and outlet local resistances of the fluid entering and exiting the heat exchanger shell side. These local resistances are usually related to the square of the shell-side flow velocity through empirical coefficients and are superimposed on the pressure drop along the flow path.

[0099] In one embodiment of the present invention, when using the bisection method to iteratively calculate the outlet temperatures of the medium in the tube side and shell side, an initial search interval for the tube side medium outlet temperature is set. The lower bound of this initial search interval is set as the inlet temperature of the shell side medium, and the upper bound is set as the inlet temperature of the tube side medium. Similarly, an initial search interval for the shell side medium outlet temperature is set, with the lower bound set as the inlet temperature of the tube side medium and the upper bound set as the inlet temperature of the shell side medium. Within this search interval, the midpoint temperature is taken as the currently assumed tube side outlet temperature. Based on the energy conservation equation and the established heat transfer calculation model, the corresponding shell side outlet temperature is calculated using the currently assumed tube side outlet temperature. It is determined whether the calculated shell side outlet temperature falls within the set search interval for the shell side medium outlet temperature. If not, the search interval for the tube side outlet temperature is adjusted according to the energy balance relationship, the midpoint temperature value is updated, and the corresponding shell side outlet temperature is recalculated. Repeat the above judgment and adjustment steps until the calculated shell-side outlet temperature stably falls within its search range, and the energy exchange between the tube-side and shell-side meets the preset convergence accuracy. The temperature value obtained at this point is the final determined tube-side and shell-side outlet temperature. When constructing an objective function containing multiple sub-objectives, define a sub-objective characterizing heat transfer performance, calculated based on the overall heat transfer coefficient, heat transfer area, and the average logarithmic heat transfer temperature difference between the tube-side and shell-side. Define a sub-objective characterizing flow resistance, calculated by summing the calculated tube-side and shell-side pressure drops. Define a sub-objective characterizing entropy production characteristics, calculated by summing the flow entropy production and heat transfer entropy production based on the pressure drops, heat transfer, inlet and outlet temperatures, and ambient temperature of the tube-side and shell-side. Define a sub-objective characterizing manufacturing cost, calculated using a cost estimation model based on the total length of the helical tube, helical diameter, tube material usage, shell dimensions, and material unit price. The sub-objectives characterizing heat transfer performance, flow resistance, entropy production, and manufacturing cost are combined into a complete objective function through weighted summation or a multi-objective processing method based on the Pareto front.

[0100] In practical implementation, a bisection method is used to iteratively calculate the outlet temperatures of the medium in both the tube and shell sides. An initial search interval is set for the tube-side medium outlet temperature, with its lower bound being the known inlet temperature of the shell-side medium and its upper bound being the known inlet temperature of the tube-side medium. Simultaneously, an initial search interval is set for the shell-side medium outlet temperature, with its lower bound also being the known inlet temperature of the tube-side medium and its upper bound being the known inlet temperature of the shell-side medium. Within the current search interval for the tube-side medium outlet temperature, the midpoint temperature is taken as the currently assumed tube-side outlet temperature. Based on the energy conservation equation and the previously established heat transfer calculation model, the corresponding shell-side outlet temperature is calculated using the currently assumed tube-side outlet temperature. The calculations involve the overall heat transfer coefficient, heat transfer area, and logarithmic mean temperature difference of the heat exchanger. The system determines whether the calculated shell-side outlet temperature falls within the set search interval for the shell-side medium outlet temperature. If the calculated shell-side outlet temperature is lower than the lower bound of the search interval, it indicates that the currently assumed tube-side outlet temperature is too high, and the upper bound of the search interval needs to be updated to the currently assumed tube-side outlet temperature. If the calculated shell-side outlet temperature is higher than the upper bound of the search interval, it indicates that the currently assumed tube-side outlet temperature is too low, and the lower bound of the search interval needs to be updated to the currently assumed tube-side outlet temperature. It can be understood that after each update to the tube-side outlet temperature search interval, the midpoint of the interval needs to be recalculated as the new assumed tube-side outlet temperature, and the corresponding shell-side outlet temperature also needs to be recalculated. The process of repeatedly checking whether the shell-side outlet temperature is within the set range and adjusting the tube-side outlet temperature search range accordingly continues until the calculated shell-side outlet temperature stably falls within its initial search range, and the heat transfer and energy exchange between the tube-side and shell-side meet the preset convergence accuracy (e.g., the difference between the tube-side and shell-side outlet temperatures calculated in two consecutive iterations is less than 0.01 K). At this point, the iteration stops, and the obtained temperature values ​​are the finally determined tube-side and shell-side outlet temperatures. In practice, the convergence accuracy can be set to a smaller value to improve calculation accuracy.

[0101] In practical implementation, an objective function containing multiple sub-objectives is constructed. A sub-objective characterizing heat transfer performance is defined, calculated based on the overall heat transfer coefficient, heat transfer area, and the average logarithmic heat transfer temperature difference between the tube side and shell side. One possible expression is the product of the heat transfer coefficient and the heat transfer area, i.e., the overall heat transfer coefficient multiplied by the heat transfer area. A sub-objective characterizing flow resistance is defined, obtained by summing the calculated tube-side pressure drop and shell-side pressure drop, i.e., the tube-side pressure drop plus the shell-side pressure drop. A sub-objective characterizing entropy production characteristics is defined, obtained by summing the calculated flow entropy production and heat transfer entropy production based on the pressure drop, heat transfer, inlet and outlet temperatures, and ambient temperature of the tube and shell sides. The flow entropy production is caused by the pressure drop in the tube side and the pressure drop in the shell side, while the heat transfer entropy production is caused by the heat transfer due to the temperature difference between the tube and shell sides. A common formula for calculating entropy production is:

[0102]

[0103] in: Represents the total entropy productivity. Represents the fluid entropy productivity. Indicates the heat transfer entropy yield. and These represent the mass flow rates of the tube-side and shell-side media, respectively. and These represent the pressure drops in the tube side and the shell side, respectively. and These represent the average densities of the tube-side and shell-side media, respectively. and These represent the arithmetic mean temperatures of the tube-side and shell-side media, respectively. Indicates the total heat transfer. and These represent the outlet temperatures of the tube-side and shell-side media, respectively. A sub-objective characterizing manufacturing cost is defined, calculated using a cost estimation model based on the total length of the spiral tube, spiral diameter, tube material usage, shell dimensions, and material unit price. In practice, the cost estimation model can be a linear or polynomial model, summing the product of the material volume of the main components and the material cost per unit volume.

[0104] In practical implementation, weighted summation involves multiplying the sub-objectives representing heat transfer performance, flow resistance, entropy production, and manufacturing cost by their respective weight coefficients and then summing them. These weight coefficients reflect the importance of each sub-objective. The Pareto front-based multi-objective approach does not use weighting; instead, it directly compares the non-dominated relationships of individuals in the differential evolution algorithm to find a set of non-dominated solutions as the Pareto optimal set. Finally, a design scheme is selected from this set based on the decision-maker's preferences. See Table 1.

[0105] Table 1: Example Table of Weighting Coefficients for Sub-Objective Functions

[0106] Subtarget name Weighting coefficient Remark Sub-objectives characterizing heat transfer performance 0.4 The goal is to maximize, so before weighting, the algorithm needs to be normalized and unified into a minimization problem (e.g., taking the reciprocal). Sub-objectives characterizing flow resistance 0.3 The objective is to minimize the weighted average; therefore, normalization is required before weighting. Sub-objectives characterizing entropy production 0.2 The objective is to minimize the weighted average; therefore, normalization is required before weighting. Sub-objectives characterizing manufacturing costs 0.1 The objective is to minimize the weighted average; therefore, normalization is required before weighting.

[0107] In some embodiments, each sub-objective needs to be normalized before weighting to eliminate the influence of different physical dimensions and orders of magnitude. Normalization can be performed using the maximum, minimum, or average value of the sub-objective in the current population. It is understood that when using a Pareto front-based method, it is not necessary to define and set weight coefficients.

[0108] In one embodiment of the present invention, when performing multi-generational search and iterative optimization using an optimization framework based on differential evolution algorithm, the parameters of the differential evolution algorithm are initialized, including population size, scaling factor, crossover probability, and maximum number of generations. Within the allowable range of structural parameters, an initial population is randomly generated, consisting of multiple individuals, each representing a specific set of structural parameter values. For each individual in the initial population, its represented structural parameter value is substituted, and the steps of establishing a computational model, calculating the outlet temperature, calculating the pressure drop, and evaluating the objective function are executed to obtain the objective function value corresponding to each individual. Iteration begins, and for each target individual in the current population, a mutation operation is performed. The mutation operation generates a test vector based on several randomly selected different individuals in the current population, according to the mutation strategy of the differential evolution algorithm. A crossover operation is performed on the target individual and the test vector, exchanging some parameter components of the target individual and the test vector according to the crossover probability to generate a new candidate individual. The structural parameter values ​​of the new candidate individual are substituted, and the steps of establishing a computational model, calculating the outlet temperature, calculating the pressure drop, and evaluating the objective function are executed again to obtain the objective function value corresponding to the new candidate individual. The objective function values ​​of new candidate individuals are compared with those of the target individual, and the better one is retained in the next generation of the population. Mutation, crossover, evaluation, and selection operations are repeated until all individuals have been processed, thus completing the evolution of one generation of the population. This evolutionary process is repeated across multiple generations until the preset maximum number of generations is reached or the convergence condition is met. In each generation of multi-generational search and iterative optimization, for a given combination of candidate structural parameters (i.e., an individual in the differential evolution algorithm), its specific values ​​correspond to a set of values ​​for helix angle, helix diameter, pitch, tube spacing, interlayer spacing, and length. Using these values, the key geometric parameters of the heat exchanger are recalculated, including the flow cross-sectional area, heat transfer area, equivalent diameter, and helical tube centerline length of the tube side, and the flow cross-sectional area, equivalent diameter, and effective fluid flow length of the shell side. Based on the recalculated geometric parameters, known process operating conditions, and physical properties, the convective heat transfer coefficients of the tube side and shell side, as well as the overall heat transfer coefficient, are recalculated. Based on the recalculated geometric parameters and flow conditions, the friction drag coefficients and pressure drops along the tube and shell sides are recalculated. The step of iteratively calculating the outlet temperature using the bisection method is invoked, and the outlet temperatures of the tube and shell sides are recalculated based on the current overall heat transfer coefficient and geometric parameters. The recalculated overall heat transfer coefficient, pressure drop, and outlet temperature are substituted into the calculation formulas for each sub-objective in the objective function, and the final objective function value corresponding to the candidate structural parameter combination is obtained through comprehensive calculation. This final objective function value is used for individual fitness comparison in the differential evolution algorithm.

[0109] In practical implementation, a multi-generational search and iterative optimization framework based on the differential evolution algorithm is used. The control parameters of the differential evolution algorithm are initialized, including population size, scaling factor, crossover probability, and maximum number of generations. The population size determines the number of candidate solution individuals in each generation. The scaling factor controls the amplification ratio of the difference vector during mutation operations. The crossover probability determines the proportion of parameter components inherited by the experimental vector from the target individual. The maximum number of generations sets the upper limit of the algorithm's iterations. Within the allowed range of structural parameters, an initial population is randomly generated. The initial population consists of multiple individuals, each of which is a vector representing a specific set of structural parameters, including helix angle, helix diameter, pitch, tube spacing, layer spacing, and total helical tube length. For each individual in the initial population, the specific values ​​of the structural parameters it represents are substituted into the algorithm. A complete sequence of steps is executed: establishing heat transfer and flow resistance calculation models; iteratively calculating the tube-side and shell-side outlet temperatures using a bisection method; calculating the tube-side and shell-side pressure drops; and evaluating the objective function. This yields the objective function value for each individual in the initial population, also known as the fitness value in differential evolution algorithms. In practice, a smaller objective function value indicates a better solution represented by that individual, as sub-objectives are typically treated as minimization problems.

[0110] In practice, the iterative evolution process begins. For each target individual in the current population, a mutation operation is performed. The mutation operation is based on three randomly selected individuals from the current population: the base vector individual, the first difference vector individual, and the second difference vector individual. Following a basic mutation strategy in differential evolution algorithms, a trial vector is generated. The formula for generating the trial vector is:

[0111]

[0112] in: This represents the test vector generated for the target individual i in the Gth generation. This represents a basis vector individual randomly selected in the Gth generation. and This represents two other distinct individuals randomly selected in generation G. This represents the scaling factor. The three randomly selected individuals must be distinct from the target individual i. In practice, the scaling factor F is typically between 0.5 and 1.0. A crossover operation is performed on the target individual and the trial vector. This crossover operation increases population diversity. Crossover is performed on each parameter component of both the target individual vector and the trial vector according to a preset crossover probability.

[0113] In practice, the structural parameter values ​​of the newly generated candidate individuals are substituted into the algorithm, and the complete sequence of steps—establishing heat transfer and flow resistance calculation models, using the bisection method to iteratively calculate tube-side and shell-side outlet temperatures, calculating tube-side and shell-side pressure drops, and evaluating the objective function—is executed again to obtain the objective function value corresponding to this new candidate individual. The objective function value of the new candidate individual is compared with that of the target individual. If the objective function value of the new candidate individual is less than or equal to that of the target individual, the target individual is replaced by this new candidate individual in the next generation. If the objective function value of the new candidate individual is greater than that of the target individual, the original target individual is retained in the next generation. The mutation, crossover, evaluation, and selection operations are repeated until all individuals in the current population have been treated as target individuals, thus completing the evolution of one generation of the population. This evolutionary process is repeated for multiple generations until the algorithm iterates to the preset maximum number of generations, or until the objective function value of the best individual in the population no longer shows significant improvement over several consecutive generations, satisfying the convergence condition. In practical implementation, the convergence condition can be set as the change in the fitness of the optimal individual within 50 consecutive generations being less than a minimum threshold. The optimization framework of the differential evolution algorithm uses structural parameters as optimization variables and the objective function value as the evaluation criterion for multi-generational search throughout the entire process.

[0114] In practical implementation, in each generation of multi-generational search and iterative optimization, the calculation process needs to be re-executed for each candidate structural parameter combination in the differential evolution algorithm population. A candidate structural parameter combination corresponds to a specific set of values ​​for helix angle, helix diameter, pitch, tube spacing, layer spacing, and total helical tube length. Using the specific values ​​of helix angle, helix diameter, pitch, tube spacing, layer spacing, and total helical tube length, the key geometric parameters of the heat exchanger are recalculated. Key geometric parameters include the flow cross-sectional area, heat transfer area, equivalent diameter, and helical tube centerline length of the tube side, and the flow cross-sectional area, equivalent diameter, and effective flow length of the fluid in the shell side. Based on the recalculated geometric parameters, known process operating conditions (flow rate, inlet temperature, pressure, medium type), and physical properties, the convective heat transfer coefficients of the tube side and shell side are recalculated, and the overall heat transfer coefficient between the tube side and shell side is further calculated. Based on the recalculated geometric parameters and flow conditions, the frictional resistance coefficients along the tube side and shell side are recalculated, and then the pressure drop in the tube side and shell side are calculated. The process involves iteratively calculating the outlet temperature using a bisection method. Based on the currently calculated overall heat transfer coefficient and geometric parameters, the outlet temperatures of the tube-side and shell-side media are recalculated iteratively. The recalculated overall heat transfer coefficient, tube-side pressure drop, shell-side pressure drop, tube-side outlet temperature, and shell-side outlet temperature are then substituted into the various sub-objective calculation formulas of the objective function. These include sub-objectives characterizing heat transfer performance, flow resistance, entropy production, and manufacturing cost. The final objective function value corresponding to this candidate structural parameter combination is then calculated. This final objective function value is used for individual fitness comparison and selection operations in the differential evolution algorithm. See Table 2.

[0115] Table 2: Example Table of Parameters for Differential Evolution Algorithm

[0116] Parameter name Example values Population size 50 scaling factor F 0.8 Crossover probability CR 0.9 Maximum number of generations 500

[0117] In some embodiments, during the mutation operation, if a parameter component of the experimental vector exceeds the allowable range of the structural parameter, various boundary handling methods can be adopted, such as resetting it to an upper or lower bound, or regenerating a random value within the allowable range. When evaluating the objective function value, if a candidate combination of structural parameters violates preset constraints, its objective function value will be given a large penalty value to ensure it is at a disadvantage in the selection. After the optimization process is completed, the specific values ​​of the structural parameters represented by the individual with the smallest objective function value recorded by the algorithm are the optimal design scheme for the spiral tube heat exchanger.

[0118] In one embodiment of the present invention, constraints are set before optimization, including upper and lower limits for structural parameters and performance constraints. The upper and lower limits for structural parameters ensure that the helix angle, helix diameter, pitch, tube spacing, interlayer spacing, and length are within the allowable range for engineering manufacturing and installation. Performance constraints include limiting the maximum allowable pressure drop in the tube side and shell side, and limiting the minimum heat transfer efficiency of the heat exchanger. In each generation of the differential evolution algorithm, for candidate combinations of structural parameters that do not meet the constraints, their objective function values ​​are given a large penalty value to reduce their probability of being selected for the next generation. This method can be used to optimize multi-layer spiral tube heat exchangers, where the interlayer spacing of the spiral tubes in the structural parameters specifically refers to the radial distance between the central axes of two adjacent spiral tubes in the multi-layer spiral tube structure. When establishing the heat transfer calculation model, the thermal interference between the multi-layer spiral tubes needs to be considered, and the correlation between the flow and heat transfer of the shell-side fluid needs to be corrected accordingly. When establishing the flow resistance calculation model, the additional resistance caused by the multi-layer tube bundle to the shell-side fluid flow needs to be considered, and the correlation of the shell-side friction resistance coefficient needs to be corrected accordingly. This method can also be optimized for double-shell-pass multilayer spiral tube heat exchangers. Under the process operating conditions, the shell-side medium is divided into two streams, flowing in two independent shell-side channels. The flow rate, inlet temperature, operating pressure, and medium type of each shell-side medium need to be obtained separately. When establishing the heat transfer calculation model and the flow resistance calculation model, independent heat transfer and pressure drop calculation sub-models need to be established for each of the two shell-side channels. The step of using the bisection method to iteratively calculate the outlet temperature requires simultaneous iterative solutions for the tube-side medium outlet temperature, the first shell-side medium outlet temperature, and the second shell-side medium outlet temperature to ensure that the energy exchange between the three channels reaches equilibrium simultaneously. When constructing the objective function, the sub-objective characterizing the flow resistance must include the pressure drop of both shell-side channels, and the sub-objective characterizing the entropy production characteristics must include the contributions of both shell-side channels.

[0119] In practical implementation, the step of setting constraints before initiating the differential evolution algorithm optimization includes upper and lower limits for structural parameters and performance constraints. The upper and lower limits for structural parameters ensure that the helix angle, helix diameter, pitch, tube spacing, layer spacing, and total length of the helical tube are within the allowable range for engineering manufacturing and installation. For example, the helix angle can be set from 5 to 30 degrees, the helix diameter range is determined based on the shell size, the pitch must be greater than the outer diameter of the tube to prevent interference, and the layer spacing must ensure sufficient welding or installation space. Performance constraints include limiting the maximum allowable pressure drop in the tube side, limiting the maximum allowable pressure drop in the shell side, and limiting the minimum heat transfer efficiency of the heat exchanger. During each generation of evaluation in the differential evolution algorithm, for each candidate combination of structural parameters, it is checked whether it satisfies all constraints. If a candidate combination of structural parameters does not satisfy the constraints, its objective function value will be assigned a very large penalty value. The penalty value P can be calculated as follows:

[0120]

[0121] in: This represents the fitness value after applying a penalty. This represents the initial fitness value calculated from the objective function. Indicates something much larger than Penalty factor within the normal range of values. Indicates the degree of violation of the i-th inequality constraint (when the constraint is satisfied). When violated ), Represents a structure parameter vector. This represents the total number of constraints. The purpose of assigning a maximum penalty value is to significantly reduce the probability that candidate structural parameter combinations that do not meet the constraints will be selected by the differential evolution algorithm to enter the next generation.

[0122] In practical implementation, the method can be optimized for multi-layer spiral tube heat exchangers. In the optimization of multi-layer spiral tube heat exchangers, the spiral tube spacing in the structural parameters specifically refers to the radial distance between the central axes of two adjacent spiral tube layers in the multi-layer spiral tube structure. When establishing the heat transfer calculation model, the thermal interference between the multi-layer spiral tubes needs to be considered, and the flow and heat transfer correlation of the shell-side fluid needs to be corrected accordingly. It can be understood that the thermal interference correction is usually achieved by introducing a correction factor related to the number of tube rows, tube spacing, and layer spacing. This correction factor is used to multiply the shell-side convective heat transfer coefficient obtained from the basic single-row tube bundle heat transfer correlation. When establishing the flow resistance calculation model, the additional resistance caused by the multi-layer tube bundle to the shell-side fluid flow needs to be considered, and the shell-side frictional resistance coefficient correlation needs to be corrected accordingly. The additional resistance correction is also achieved through a correction factor related to the number of tube rows and their arrangement. This correction factor is used to multiply the basic single-row tube bundle flow resistance correlation.

[0123] In practical implementation, the method can also be optimized for double-shell-pass multilayer spiral tube heat exchangers. When optimizing a double-shell-pass multilayer spiral tube heat exchanger, under the process operating conditions, the shell-side medium is divided into two streams, flowing in two independent shell-side channels. It is necessary to obtain the flow rate, inlet temperature, operating pressure, and medium type of the first shell-side medium, as well as the flow rate, inlet temperature, operating pressure, and medium type of the second shell-side medium. When establishing the heat transfer calculation model and the flow resistance calculation model, independent heat transfer calculation sub-models and pressure drop calculation sub-models need to be established for the first and second shell-side channels respectively. The heat transfer calculation sub-model for each shell-side channel calculates its convective heat transfer coefficient based on its own flow conditions, geometric parameters, and medium properties. The pressure drop calculation sub-model for each shell-side channel calculates its frictional resistance coefficient and pressure drop based on its own flow conditions and geometric parameters. The step of using the bisection method to iteratively calculate the outlet temperature requires simultaneously iteratively solving for the tube-side medium outlet temperature, the first shell-side medium outlet temperature, and the second shell-side medium outlet temperature. The iterative process needs to ensure that energy exchange between the tube side and the first shell side, energy exchange between the tube side and the second shell side, and indirect thermal coupling between the first and second shell sides through the tube wall are simultaneously balanced. This usually requires an extended bisection method or a multivariate Newton-Raphson iterative method. When constructing the objective function, the sub-objective characterizing flow resistance should include the pressure drop in the tube side, the pressure drop in the first shell side, and the pressure drop in the second shell side, and these three are usually summed. The sub-objective characterizing entropy production characteristics should include the contributions of the tube side, the first shell side, and the second shell side. When calculating the total entropy production, the flow entropy production of the tube side, the first shell side, and the second shell side, as well as the heat transfer entropy production caused by all heat transfer temperature differences, need to be calculated separately and then summed.

[0124] The above are merely preferred embodiments of the present invention and are not intended to limit the present invention in any other way. Any person skilled in the art may make changes or modifications to the above-disclosed technical content to create equivalent embodiments that can be applied to other fields. However, any simple modifications, equivalent changes, and modifications made to the above embodiments based on the technical essence of the present invention without departing from the scope of the present invention shall still fall within the protection scope of the present invention.

Claims

1. An optimized design method for a spiral tube heat exchanger, characterized in that, The method includes the following steps: Obtain the process operating conditions and structural parameters of the heat exchanger, and establish a heat transfer calculation model and a flow resistance calculation model that includes the tube side and the shell side. Based on the aforementioned heat transfer calculation model and process operating conditions, the outlet temperatures of the medium in the tube and shell sides are calculated iteratively using the bisection method. Based on the flow resistance calculation model, process operating conditions, and calculated outlet temperature, the pressure drop between the tube side and the shell side is calculated. Construct an objective function containing multiple sub-objectives, including sub-objectives characterizing heat transfer performance, sub-objectives characterizing flow resistance, sub-objectives characterizing entropy production characteristics, and sub-objectives characterizing manufacturing cost; Using an optimization framework based on differential evolution algorithm, with the structural parameters as optimization variables and the objective function as the evaluation criterion, multi-generation search and iterative optimization are performed; In each generation of multi-generation search and iterative optimization, a population containing multiple candidate structural parameter combinations is generated. For each candidate structural parameter combination in the population, the steps of establishing a computational model, calculating the outlet temperature, calculating the pressure drop, and evaluating the objective function are repeatedly executed. After the multi-generation search and iterative optimization process converges, the candidate combination of structural parameters that makes the objective function numerically optimal is selected from the final generation population as the optimal design scheme for the spiral tube heat exchanger.

2. The optimized design method for a spiral tube heat exchanger as described in claim 1, characterized in that, The establishment of a heat transfer calculation model including the tube side and the shell side includes the following steps: The process operating conditions include the flow rate of the medium in the tube side and the shell side, the inlet temperature, the operating pressure, and the type of medium. The structural parameters include the helix angle, helix diameter, pitch, tube spacing, interlayer spacing, and total tube length. Based on the flow rate, inlet temperature, operating pressure, and medium type in the tube and shell sides, the physical properties of the medium are determined, including density, specific heat capacity, thermal conductivity, and dynamic viscosity. Calculate the flow cross-sectional area, heat exchange area, equivalent diameter, and centerline length of the spiral tube based on the spiral angle, spiral diameter, pitch, tube spacing, interlayer spacing, and total tube length. Based on the structural parameters of the shell side, including the shell inner diameter, tube bundle arrangement, tube spacing and layer spacing, calculate the flow cross-sectional area, equivalent diameter and effective length of fluid flow in the shell side; Based on the flow conditions and geometric parameters of the tube side, the convective heat transfer coefficient of the tube side is calculated using a correlation formula. Based on the flow conditions and geometric parameters of the shell side, the convective heat transfer coefficient of the shell side is calculated using a correlation formula. Based on the convective heat transfer coefficients of the tube side and shell side and the thermal resistance of the tube wall, the overall heat transfer coefficient between the tube side and shell side is calculated, thus completing the establishment of the heat transfer calculation model.

3. The optimized design method for a spiral tube heat exchanger as described in claim 2, characterized in that, Establishing a flow resistance calculation model that includes both the tube side and the shell side involves the following steps: Based on the flow rate, physical properties, and cross-sectional area of ​​the medium in the tube and shell sides, the flow velocity of the medium in the tube side is calculated. Based on the flow rate, physical properties, and cross-sectional area of ​​the medium in the tube and shell sides, the flow velocity of the medium in the shell side is calculated. Based on the flow velocity in the tube and the geometry of the helical tube, including the helix angle, helix diameter, pitch, and total tube length, the friction coefficient along the tube is calculated using the friction coefficient correlation applicable to helical tube flow. Based on the flow velocity in the shell side, the tube bundle arrangement, the tube spacing and the layer spacing, the friction coefficient along the shell side is calculated using the friction coefficient correlation applicable to the flow across the tube bundle in the shell side. Calculate the pressure drop in the tube side based on the friction coefficient along the tube, the flow velocity in the tube side, the total length of the tube, and the equivalent diameter. The pressure drop in the shell side is calculated based on the friction coefficient along the shell side, the flow velocity in the shell side, the effective length of the fluid flow in the shell side, and the equivalent diameter.

4. The optimized design method for a spiral tube heat exchanger as described in claim 3, characterized in that, The method of using the bisection method to iteratively calculate the outlet temperature of the medium in the tube and shell sides includes the following steps: An initial search range is set for the outlet temperature of the tube-side medium, where the lower bound of the initial search range is the inlet temperature of the shell-side medium, and the upper bound of the initial search range is the inlet temperature of the tube-side medium. An initial search range is set for the outlet temperature of the shell-side medium, the lower bound of which is the inlet temperature of the tube-side medium, and the upper bound of which is the inlet temperature of the shell-side medium. Within the search range of the tube-side medium outlet temperature, the midpoint temperature value is taken as the currently assumed tube-side outlet temperature. Based on the energy conservation equation and the heat transfer calculation model, the corresponding shell-side outlet temperature is calculated using the currently assumed tube-side outlet temperature. Determine whether the calculated shell-side outlet temperature is within the set search range of the shell-side medium outlet temperature. If not, adjust the search range of the tube-side outlet temperature according to the energy balance relationship, update the midpoint temperature value, and recalculate the corresponding shell-side outlet temperature. Repeat the judgment and adjustment steps until the calculated shell-side outlet temperature stably falls within its search range, and the energy exchange between the tube side and the shell side meets the preset convergence accuracy. The temperature value obtained at this time is the final determined tube-side and shell-side outlet temperature.

5. The optimized design method for a spiral tube heat exchanger as described in claim 4, characterized in that, The construction of the objective function containing multiple sub-objectives includes the following steps: Define sub-objectives characterizing heat transfer performance, which are calculated based on the overall heat transfer coefficient, heat transfer area, and the average logarithmic heat transfer temperature difference between the tube side and the shell side. Define a sub-objective characterizing flow resistance, which is obtained by summing the calculated tube-side pressure drop and shell-side pressure drop; Define a sub-objective characterizing entropy production characteristics. The sub-objective characterizing entropy production characteristics is obtained by summing the flow entropy production and heat transfer entropy production calculated separately based on the pressure drop, heat transfer, inlet and outlet temperatures, and ambient temperature of the tube and shell sides. Define a sub-objective to characterize manufacturing cost. This sub-objective is calculated using a cost estimation model based on the total length of the spiral tube, spiral diameter, tube material usage, shell size, and material unit price. The sub-objectives characterizing heat transfer performance, flow resistance, entropy production, and manufacturing cost are combined into the objective function through weighted summation or a multi-objective processing method based on the Pareto front.

6. The optimized design method for a spiral tube heat exchanger as described in claim 5, characterized in that, The optimization framework based on differential evolution algorithm, using the structural parameters as optimization variables and the objective function as the evaluation criterion, performs multi-generational search and iterative optimization, including the following steps: Initialize the parameters of the differential evolution algorithm, including population size, scaling factor, crossover probability, and maximum number of generations; Within the allowed range of values ​​for the structural parameters, an initial population is randomly generated. The initial population consists of multiple individuals, each representing a specific set of values ​​for the structural parameters. For each individual in the initial population, the values ​​of the structural parameters it represents are substituted into the calculation model, the steps of establishing the calculation model, calculating the outlet temperature, calculating the pressure drop and evaluating the objective function are performed to obtain the objective function value corresponding to each individual; The iteration begins, and for each target individual in the current population, a mutation operation is performed. The mutation operation generates a test vector based on several different individuals randomly selected from the current population, according to the mutation strategy of the differential evolution algorithm. A crossover operation is performed on the target individual and the test vector, and some parameter components of the target individual and the test vector are swapped according to the crossover probability to generate a new candidate individual; Substitute the structural parameter values ​​of the new candidate individual into the calculation model, calculate the outlet temperature, calculate the pressure drop and evaluate the objective function again to obtain the objective function value corresponding to the new candidate individual; The objective function value of the new candidate individual is compared with the objective function value of the target individual, and the one with the better objective function value is retained in the next generation population. Repeat the mutation, crossover, evaluation, and selection operations until all individuals have been processed, thus completing the evolution of one generation of the population; Repeat the evolutionary process of the population for multiple generations until the preset maximum number of generations is reached or the convergence condition is met.

7. The optimized design method for a spiral tube heat exchanger as described in claim 6, characterized in that, In each generation of multi-generation search and iterative optimization, a population containing multiple candidate structural parameter combinations is generated. For each candidate structural parameter combination in the population, the steps of establishing a computational model, calculating the outlet temperature, calculating the pressure drop, and evaluating the objective function are repeatedly executed, including the following specific processes: For a given combination of candidate structure parameters, i.e. an individual in the differential evolution algorithm, its specific values ​​correspond to a set of values ​​for helix angle, helix diameter, pitch, tube spacing, layer spacing and length. Using the values ​​of helix angle, helix diameter, pitch, tube spacing, interlayer spacing, and length, the key geometric parameters of the heat exchanger are recalculated, including the flow cross-sectional area, heat transfer area, equivalent diameter, and centerline length of the helical tubes on the tube side, as well as the flow cross-sectional area, equivalent diameter, and effective length of fluid flow on the shell side. Based on the recalculated geometric parameters, known process operating conditions, and physical property parameters, the convective heat transfer coefficients of the tube side and shell side, as well as the overall heat transfer coefficient, are recalculated. Based on the recalculated geometric parameters and flow conditions, the frictional resistance coefficients and pressure drops along the tube and shell sides were recalculated. The steps of using the bisection method to iteratively calculate the outlet temperature are invoked, and the outlet temperatures of the tube side and shell side are recalculated based on the current overall heat transfer coefficient and geometric parameters. Substitute the recalculated total heat transfer coefficient, pressure drop, and outlet temperature into the calculation formulas for each sub-objective in the objective function; The final objective function value corresponding to the candidate structure parameter combination is obtained by comprehensive calculation. The final objective function value is used for individual fitness comparison in the differential evolution algorithm.

8. The optimized design method for a spiral tube heat exchanger as described in claim 7, characterized in that, It also includes the step of setting constraints before optimization, the constraints including: Set upper and lower limits for structural parameters to ensure that the helix angle, helix diameter, pitch, pipe spacing, layer spacing, and length are within the allowable range for engineering manufacturing and installation; Set performance constraints, including limiting the maximum allowable pressure drop in the tube side and shell side, and limiting the minimum heat transfer efficiency of the heat exchanger; In each generation of the differential evolution algorithm, for candidate structural parameter combinations that do not meet the constraints, their objective function values ​​will be given a very large penalty value to reduce their probability of being selected for the next generation.

9. The optimized design method for a spiral tube heat exchanger as described in claim 8, characterized in that, The method is optimized for multi-layer spiral tube heat exchangers, wherein: The spacing between the spiral tube layers in the structural parameters specifically refers to the radial distance between the central axes of two adjacent spiral tube layers in a multi-layer spiral tube structure. When establishing the heat transfer calculation model, the thermal interference between the multi-layer spiral tubes needs to be considered, and the flow and heat transfer correlation of the shell-side fluid needs to be modified accordingly. When establishing the flow resistance calculation model, it is necessary to consider the additional resistance caused by the multi-layer tube bundle to the shell-side fluid flow, and make corresponding corrections to the correlation of the shell-side friction resistance coefficient.

10. The optimized design method for a spiral tube heat exchanger as described in claim 9, characterized in that, The method is optimized for double-shell multilayer spiral tube heat exchangers, wherein: In the aforementioned process operating conditions, the shell-side medium is divided into two streams, which flow in two independent shell-side channels respectively. It is necessary to obtain the flow rate, inlet temperature, working pressure and medium type of the two shell-side media respectively. When establishing the heat transfer calculation model and the flow resistance calculation model, it is necessary to establish independent heat transfer and pressure drop calculation sub-models for the two shell-side channels respectively. The step of using the bisection method to iteratively calculate the outlet temperature requires simultaneously iteratively solving the tube-side medium outlet temperature, the first shell-side medium outlet temperature, and the second shell-side medium outlet temperature to ensure that the energy exchange between the three channels reaches a balance at the same time. When constructing the objective function, the sub-objective characterizing flow resistance must include the pressure drop of both shell sides, and the sub-objective characterizing entropy production characteristics must include the contribution of both shell sides.

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