A multi-objective optimization design method for shell and tube heat exchangers based on non-dominated sorting differential evolution algorithm

Abstract

The present invention provides a method for multi-objective optimization design of a shell-and-tube heat exchanger based on a non-dominated sorting differential evolution algorithm. This method aims to better solve the multi-objective optimization design problem of a shell-and-tube heat exchanger and reduce the complexity of process calculations in heat exchanger design. Based on the design requirements, operating parameters, and physical parameters, the required heat load is calculated. The objective functions are to reduce the heat exchange area, reduce the shell-side pressure drop, and increase the number of heat transfer units. A single-baffle shell-and-tube heat exchanger is used as a structural model. Design variables are selected from the operating and structural parameters. Constraints are established according to national standards and empirical data tables. Based on process calculations, a multi-objective optimization design model for the shell-and-tube heat exchanger is established. The multi-objective optimization design model is solved using a non-dominated sorting differential evolution algorithm to obtain the optimal solution set for the three objective functions, thereby achieving the goal of designing a heat exchanger with low investment, low pressure drop, and high heat exchange capacity. Furthermore, the designer can select the optimal solution set from the generated solution set based on actual design requirements as the design solution.

Description

Technical Field

[0001] The patent of this invention relates to the technical field of heat exchanger optimization design, and in particular to a multi-objective optimization design method for shell and tube heat exchangers based on a non-dominated sorting differential evolution algorithm. Background Art

[0002] Heat exchangers, as chemical machinery that transfers heat between process materials, are widely used in industries such as chemical, petroleum, and electric power. Currently, shell-and-tube heat exchangers dominate the market due to their simple structure, low manufacturing costs, and wide adaptability. However, the current design of shell-and-tube heat exchangers often relies on empirical experience, resulting in low design efficiency and numerous repeated calculations, making it difficult to achieve the optimal design. This increases manufacturing costs, prevents the exchanger from achieving its maximum heat transfer capacity, and often results in excessive energy waste due to designs designed solely to meet heat load requirements.

[0003] The optimization design methods for shell and tube heat exchangers at home and abroad include single-objective optimization design and multi-objective optimization design. Single-objective optimization often only considers the optimality of this objective, which will cause the reduction of other performances; while multi-objective optimization design mostly optimizes from external factors such as cost, total entropy output value, etc., and does not reflect the optimization of the structural parameters of the shell and tube heat exchanger, and the optimization effect is not very good. At the same time, the use of traditional algorithms to solve problems often falls into some local optimal solutions, or has slow convergence speed, resulting in the optimization results not being able to achieve the optimal. The optimization process using commercial software such as HTRI is often complicated, and it needs to be adjusted based on the experience of the designer, and it is impossible to directly output the optimal result. In order to solve the above problems and to better optimize the shell and tube heat exchanger, the applicant proposed a multi-objective optimization design method for shell and tube heat exchangers based on a non-dominated sorting differential evolution algorithm. Summary of the Invention

[0004] The invention patent is to solve the optimization design problem of shell and tube heat exchangers, improve design efficiency, reduce costs, reduce pressure drop, improve heat transfer capacity, and solve the problem of falling into local optimal solutions and slow convergence during solution. A multi-objective optimization design method for shell and tube heat exchangers based on non-dominated sorting differential evolution algorithm is proposed. Taking a single-bow shell and tube heat exchanger as a structural model, according to the process calculation method, the heat transfer area, pressure drop, and heat transfer capacity are used as objective functions to establish a shell and tube heat exchanger optimization design model. Based on the non-dominated sorting differential evolution algorithm, while improving the convergence speed, the non-dominated sorting method of the elite strategy is adopted to calculate the individual crowding distance, generate the Pareto solution set, and obtain the optimal solution set according to the difference in individual crowding distance.

[0005] This patented method improves design efficiency, avoids design calculation complexity, and provides designers with multi-objective optimization design. The algorithm used achieves rapid computational convergence and avoids falling into local optima. Not only can the optimal solution set for all three objective functions be obtained, but designers can also obtain the optimal solution set for one or two of the objective functions based on actual design requirements.

[0006] To achieve the above purpose, the present invention adopts the following technical solutions:

[0007] A multi-objective optimization design method for a shell and tube heat exchanger based on a non-dominated sorting differential evolution algorithm is characterized by comprising the following steps:

[0008] (1) Calculate and determine the required heat load based on design requirements, operating parameters and physical properties;

[0009] (2) Establish the objective function of heat transfer area A =

[0010] (3) Establish the objective function of shell-side pressure drop ∆ P s =(∆ P 1 +∆ P 2 ) F s N s

[0011] (4) Establishing the objective function of heat transfer capacity ε = =

[0012] (5) Taking the single segmented baffle heat exchanger as the structural model, select design variables from the operating parameters and structural parameters, and establish constraint conditions based on national standards and empirical data tables;

[0013] (6) A multi-objective optimization model is established, and the optimal solution is the minimum of the three objective functions. The Pareto optimal solution of the established multi-objective optimization design model is performed based on the non-dominated sorting differential evolution algorithm to obtain the optimal solution set output result.

[0014] The step (1) calculates and determines the required heat load using the heat transfer equation according to the design requirements, operating parameters and physical parameters.

[0015] The total heat transfer coefficient of step (2) is K =[ + r s + + rt ] -1 .

[0016] The step (3) is the shell side pressure drop, and the tube side pressure drop can also be ∆ P t =(∆ P l +∆ P r ) F t N s n +∆ P n N s .

[0017] The design requirements are special requirements proposed based on actual conditions. The operating parameters and physical parameters are the inlet and outlet temperatures of the cold and hot fluids, the flow rates of the cold and hot fluids, thermal conductivity, density, viscosity, fouling thermal resistance, and Prandtl number.

[0018] The structural parameters can be selected as design variables from the structural parameters of the single-bow baffle heat exchanger, such as the outer diameter of the heat exchange tube, tube spacing, tube length, baffle spacing, baffle cutout center angle, number of tubes, cylinder inner diameter, etc.

[0019] The constraints mentioned are current national standards and data experience tables.

[0020] In order to ensure the accuracy of the solution in step (6), a complete multi-objective optimization design model of the shell and tube heat exchanger needs to be established before the solution based on the non-dominated sorting differential evolution algorithm can be performed to obtain the optimal solution set.

[0021] The non-dominated sorting differential evolution algorithm is used for solving the problem. The algorithm process goes through the process of population initialization, mutation operation, and crossover operation. On this basis, the elite strategy and non-dominated sorting method of the non-dominated sorting genetic algorithm are used to perform Pareto non-dominated sorting, calculate the individual crowding distance, and perform a selection operation based on the elite selection strategy to select the top N optimal individuals as the new parent generation. Iteration is performed until the number of iterations is completed to obtain the Pareto optimal solution set and output the final optimization design result.

[0022] Compared with the prior art, the advantages of the present invention are:

[0023] A multi-objective optimization design mathematical model for a shell-and-tube heat exchanger with a single segmented baffle was established. A non-dominated sorting differential evolution algorithm was used to solve the problem, resulting in a Pareto-optimal solution set. This multi-objective optimization of heat transfer area, pressure drop, and heat transfer capacity was achieved, thereby improving the performance of the designed shell-and-tube heat exchanger and reducing manufacturing costs.

[0024] Based on a non-dominated sorting differential evolution algorithm, it has fast convergence and, using an elite selection strategy, avoids the drawbacks of traditional algorithms that often fall into local optimal solutions. This algorithm solves the problem by obtaining a Pareto optimal solution set, eliminating the need for designers to perform conventional design trials and ensuring the accuracy of the calculation results and the optimal solution set.

[0025] Compared with the HTRI commercial design software, this method avoids the complex operations of the HTRI software optimization process while ensuring the accuracy of the optimization results. It is a method that is very suitable for the multi-objective optimization design of shell and tube heat exchangers. BRIEF DESCRIPTION OF THE DRAWINGS

[0026] Figure 1 This is the implementation flow chart of the patent of this invention, a multi-objective optimization design method for shell and tube heat exchangers based on non-dominated sorting differential evolution algorithm.

[0027] Figure 2 It is a method for obtaining the optimal solution set using the non-dominated sorting differential evolution algorithm.

[0028] Figure 3 It is the distribution of the Pareto optimal solution set of the three objective functions. DETAILED DESCRIPTION

[0029] In order to make the present invention more clear, the following is a detailed description of a multi-objective optimization design method for a shell and tube heat exchanger based on a non-dominated differential evolution algorithm in conjunction with the accompanying drawings. The specific embodiments described herein are only used to explain the present invention, facilitate the understanding of the present invention by those skilled in the art, reflect the optimization effect of the present invention, and are not used to limit the present invention.

[0030] like Figure 1 As shown, the patent of this invention provides a multi-objective optimization design method for shell and tube heat exchangers based on a non-dominated differential evolution algorithm, which mainly includes two parts: the left half of the flow chart, the establishment of a multi-objective optimization mathematical model of the shell and tube heat exchanger and the right half of the flow chart, the solution of the Pareto optimal solution set of the non-dominated sorting differential evolution algorithm.

[0031] 1. A multi-objective optimization mathematical model for a shell and tube heat exchanger is established with a single segmented baffle heat exchanger as the structural model, including the following steps:

[0032] (1) Calculate the required heat load and determine the heat load based on the design requirements, operating parameters, and physical properties. Design requirements are specific requirements based on actual conditions. Operating parameters and physical properties are the inlet and outlet temperatures of the cold and hot fluids, the flow rates of the cold and hot fluids, thermal conductivity, density, viscosity, fouling resistance, and Prandtl number. Table 1 shows the operating parameters and physical properties of the shell and tube heat exchanger to be designed.

[0033] Table 1 Operating parameters and physical properties

[0034]

[0035] (2) Establish the heat transfer area objective function:

[0036] A = (1)

[0037] In formula (1) A is the heat exchange area, m²; Q is the heat load, kW; K is the total heat transfer coefficient, W / (m²·℃); is the average temperature difference, ℃

[0038] (3) Establish the shell-side pressure drop objective function:

[0039] f 2 ( x ) = ∆ Ps =(∆ P 1+∆ P 2) F s N s (3)

[0040] Wherein, is the shell-side pressure drop, Pa; is the pressure drop of the fluid across the tube bundle, Pa; is the pressure drop of the fluid through the baffle gap, Pa; is the scaling correction factor for the shell-side pressure drop, dimensionless, which can be 1.15 for liquids and 1.0 for gases; is the number of shell passes;

[0041] (4) Establish the objective function of heat transfer capacity:

[0042] ε = = (4)

[0043] In formula (4), the heat capacity of the fluid with smaller heat capacity among the two heat exchange fluids is expressed as follows;

[0044] (5) Taking the single-bow baffle heat exchanger as the structural model, design variables are selected from the operating parameters and structural parameters, and constraints are established based on national standards and empirical data tables; Table 2 shows the selected design variables, and Table 3 shows the constraints.

[0045] Table 2 Design variables

[0046] .

[0047] Table 3 Process and structural constraints

[0048] .

[0049] 2. After establishing a multi-objective optimization mathematical model for a shell-and-tube heat exchanger, a non-dominated differential evolution algorithm is used to obtain the Pareto optimal solution set and the design result. This includes the following steps:

[0050] (1) Establish an initial population and perform crossover, selection, and mutation operations based on the non-dominated differential evolution algorithm;

[0051] (2) The population size is set to 80. After 1000 iterations, the mutation probability is 0.4 and the crossover probability is 0.8. Figure 2 As shown in the figure, Pareto non-dominated sorting is performed, the crowding distance of individuals is calculated, and the elite selection strategy is used to select the top N individuals as new parents according to the size of the crowding distance. The next iteration is performed until the iteration ends and the optimal solution set is output.

[0052] In summary, the embodiment of the present invention provides a multi-objective optimization design method for a shell and tube heat exchanger based on a non-dominated differential evolution algorithm. With heat exchange area, shell-side pressure drop, and heat transfer capacity as objective functions, a multi-objective optimization model for a shell and tube heat exchanger is established. The solution is solved based on the non-dominated sorting differential evolution algorithm. The distribution of the Pareto optimal solution set is obtained by minimizing the three objective functions. Figure 3 The optimization of these three objective functions is realized to obtain the optimal design solution, which is also helpful for those skilled in the art to select the optimization of the required objective function according to the actual situation and obtain the required design solution.

[0053] The above description is merely a preferred embodiment of the present invention and does not limit the present invention in any way. Any person skilled in the art who, without departing from the scope of the present invention, makes any equivalent substitution, modification, or other changes to the technical solution and technical content disclosed in the present invention shall be deemed to be within the scope of the present invention and still fall within the scope of protection of the present invention.

Claims

1. A multi-objective optimization design method for shell and tube heat exchangers based on non-dominated sorting differential evolution algorithm, characterized in that: The following steps are involved: (1) Calculate and determine the required heat load based on design requirements, operating parameters and physical properties; (2) Establish the objective function of heat exchange area Where: A——heat exchange area, m 2 Q——heat load, kW K——total heat transfer coefficient, W / (m 2 ℃) Δt m ——Average temperature difference, ℃ (3) Establish the target function ΔP of shell-side pressure drop s =(ΔP1+ΔP2)F s N s Where: ΔP s ——Shell side pressure drop, Pa ΔP I ——Pressure drop of fluid across the tube bundle, Pa ΔP2——pressure drop of fluid passing through the baffle gap, Pa F s —Fouling correction factor for shell-side pressure drop, dimensionless, 1.15 for liquids and 1.0 for gases N s ——Number of shell passes (4) Establishing the objective function of heat transfer capacity In the formula W min ——The heat capacity of the fluid with smaller heat capacity among the two heat exchange fluids NTU - Number of heat transfer units (5) Taking the single-bend baffle heat exchanger as the structural model, the design variables are selected from the operating parameters and structural parameters, and the constraints are established according to national standards and empirical data tables; (6) Establish a multi-objective optimization model, take the minimum of the three objective functions as the optimal solution, generate an initial population based on the non-dominated sorting differential evolution algorithm, perform Pareto non-dominated sorting after the mutation and crossover selection operations of the differential evolution algorithm, calculate the individual crowding distance, and select the top N individuals as the new parent generation according to the elite selection strategy. Iterate until the number of iterations is completed, obtain the Pareto optimal solution set, and output the result; Based on the non-dominated sorting differential evolution algorithm, the convergence speed is improved while the non-dominated sorting method of the elite strategy is adopted to calculate the individual crowding distance and generate the Pareto solution set. According to the difference in individual crowding distance, the optimal solution set is obtained.

2. The multi-objective optimization design method for a shell and tube heat exchanger based on a non-dominated sorting differential evolution algorithm according to claim 1 is characterized by: Step (1) Calculate and determine the required heat load using the heat transfer equation based on design requirements, operating parameters and physical parameters.

3. The multi-objective optimization design method for a shell and tube heat exchanger based on a non-dominated sorting differential evolution algorithm according to claim 1, characterized in that: The design requirements are special requirements proposed based on actual conditions. The operating parameters and physical parameters are the inlet and outlet temperatures of the cold and hot fluids, the flow rates of the cold and hot fluids, thermal conductivity, density, viscosity, fouling thermal resistance, and Prandtl number.

4. The multi-objective optimization design method for a shell and tube heat exchanger based on a non-dominated sorting differential evolution algorithm according to claim 1 is characterized by: The structural parameters can be selected from the structural parameters of the single-bow baffle heat exchanger as design variables; the structural parameters include the outer diameter of the heat exchange tube, tube spacing, tube length, baffle spacing, baffle cutout center angle, number of tubes, and cylinder inner diameter.

5. The multi-objective optimization design method for shell and tube heat exchangers based on non-dominated sorting differential evolution algorithm according to claim 1 is characterized in that In steps (2), (3), and (4) ΔP s =(ΔP1+ΔP2)F s N s 、 These three objective functions need to be calculated using the Kern method or the Bell-Delaware method based on relevant parameters to establish a mathematical model for multi-objective optimization design of a single-bow baffle heat exchanger.

6. The multi-objective optimization design method for shell and tube heat exchangers based on non-dominated sorting differential evolution algorithm according to claim 1 is characterized in that In step (5), the single-bow baffle heat exchanger is used as the structural model, and design variables are selected from the operating parameters and structural parameters. Constraints need to be established according to national standards and empirical data tables to constrain the objective function.

7. The multi-objective optimization design method for shell and tube heat exchangers based on non-dominated sorting differential evolution algorithm according to claim 1 is characterized in that Step (3) ΔP s =(ΔP l +ΔP2)F s N s The shell side pressure drop can be used as the objective function, or the tube side pressure drop can be used as the objective function.

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