Solution method and device for thermal system simulation, electronic equipment and medium

Abstract

The present disclosure provides a kind of thermal system simulation solving method, device, electronic equipment and medium, method includes: the control equation of thermal system is constructed, and the overall mathematical model of thermal system is constructed according to control equation;According to the characteristics of linear or nonlinear of control equation, the equivalent nonlinear programming problem of overall mathematical model is constructed;The initial value of the operating parameter of thermal system contained in nonlinear control equation is preset, the initial value is substituted into linear control equation to calculate the pressure distribution of thermal system and the temperature field distribution of sectional heat exchanger in thermal system;The thermal resistance value of sectional heat exchanger is calculated according to nonlinear control equation;Using generalized Benders decomposition method, the equivalent nonlinear programming problem is solved according to initial value, pressure distribution, temperature field distribution, thermal resistance value, and the operating parameter of each state point of thermal system is obtained.The method, device, electronic equipment and medium solve the problems of low accuracy, poor robustness, high dependence on initial value and low calculation efficiency of thermal system solving.

Description

Technical Field

[0001] This disclosure relates to the field of thermal technology, and in particular to a solution method, apparatus, electronic device and medium for simulating thermal systems. Background Technology

[0002] Thermal systems, as a crucial component of modern industrial society, are widely used in energy, aerospace, chemical engineering, and many other fields. High-efficiency thermal systems typically consist of multiple components, with various nonlinear physical processes such as working fluid transport, energy transfer and conversion coupled together. Changes in the working fluid's properties influence its flow and heat transfer patterns. Traditional modeling methods directly superimpose component models and introduce simplifications to establish a mathematical model of the system. Then, simultaneous equations, sequential modular methods, or simultaneous modular methods are used to solve the model and obtain relevant operating parameters of the thermal system. For complex thermal systems, this analytical strategy introduces numerous intermediate variables into the model, resulting in strong nonlinearity. Furthermore, simplifications can lead to low model accuracy, poor robustness, high dependence on initial conditions, and low computational efficiency during the solution process.

[0003] To address the aforementioned issues, the heat flow modeling method transfers the nonlinear factors of the driving potential in traditional models to the thermal resistance, obtaining a linear constitutive relationship between the driving potential of heat transport and the heat transfer. This is centered on constructing the overall constraint equations of the system, and system constraints with minimal intermediate variables are obtained through circuit principles and network topology analysis. Regarding model solving, based on the characteristic that the heat flow model can be separated into linear topological features and nonlinear explicit component features, researchers proposed a hierarchical-divide-conquer algorithm. This algorithm categorizes the control equations according to their mathematical properties: linear topological constraints are solved using matrix operations; explicit nonlinear constraints are calculated by direct substitution; implicit nonlinear constraints are solved using fixed-point iteration; and preset unknown variables are updated until convergence. Compared to traditional algorithms, the hierarchical-divide-conquer algorithm significantly improves convergence range and robustness while significantly reducing computation time. However, in solving implicit nonlinear constraints and updating unknown variables, it only uses simple fixed-point iteration without utilizing any variable gradient information, resulting in a relatively inefficient iterative update process. There is still significant room for improvement in computational efficiency and convergence. Furthermore, the iterative solution process of the hierarchical-divide-conquer algorithm lacks principles and relies on design experience, which can easily lead to unnecessary loss of computational efficiency. Summary of the Invention

[0004] In view of this, this disclosure provides a solution method, apparatus, electronic device and medium for thermal system simulation, which at least partially solves the problems of low accuracy, poor robustness, high dependence on initial values ​​and low computational efficiency in the prior art for thermal system solutions.

[0005] The first aspect of this disclosure provides a solution method for simulating a thermal system, comprising: constructing the control equations of the thermal system and constructing an overall mathematical model of the thermal system based on the control equations; constructing an equivalent nonlinear programming problem of the overall mathematical model based on the linear or nonlinear characteristics of the control equations; pre-setting initial values ​​of the operating parameters of the thermal system contained in the nonlinear control equations, substituting the initial values ​​into the linear control equations to calculate the pressure distribution of the thermal system and the temperature field distribution of the segmented heat exchangers in the thermal system; calculating the thermal resistance of the segmented heat exchangers based on the nonlinear control equations; and using the generalized Benders decomposition method to solve the equivalent nonlinear programming problem based on the initial values, pressure distribution, temperature field distribution, and thermal resistance to obtain the operating parameters of each state point of the thermal system.

[0006] According to embodiments of this disclosure, the governing equations of a thermodynamic system are constructed, specifically including: establishing an equivalent heat flow model of the thermodynamic system based on the heat flow method of overall thermodynamic system analysis; establishing the flow equation of the working component based on the functional relationship between the pressure difference before and after the working fluid flows through the working component and the mass flow rate of the working fluid; establishing the pressure distribution equation of the working fluid flow based on the pressure loss of the working fluid flow; establishing the heat-work conversion process equation and the working fluid mixing process equation based on the coupling relationship between the temperature and pressure of the working fluid; and constructing an overall mathematical model of the thermodynamic system based on the equivalent heat flow model, the flow equation, the pressure distribution equation, the heat-work conversion process equation, and the working fluid mixing process equation.

[0007] According to embodiments of this disclosure, the objective function of the equivalent nonlinear programming problem is the sum of squares of the residuals of the nonlinear control equations, and the constraint condition of the equivalent nonlinear programming problem is the linear control equations.

[0008] According to embodiments of this disclosure, the linear control equations include the equivalent heat flow model and pressure distribution equation of the thermodynamic system, and the nonlinear control equations include the flow equation, heat-work conversion process equation, and working fluid mixing process equation of the thermodynamic system.

[0009] According to embodiments of this disclosure, the thermodynamic system operating parameters included in the nonlinear control equations include temperature, pressure, mass flow rate, heat exchange, and work done.

[0010] According to embodiments of this disclosure, the thermal resistance value of a segmented heat exchanger is calculated based on nonlinear control equations, specifically including: after determining the pressure distribution of the thermal system and the temperature field distribution of the segmented heat exchanger in the thermal system, obtaining the physical property parameters of each segment of the segmented heat exchanger under variable physical property conditions; calculating the convective heat transfer coefficient and the heat transfer coefficient of the segmented heat exchanger based on the physical property parameters; and substituting the convective heat transfer coefficient and the heat transfer coefficient into the nonlinear control equations to calculate the thermal resistance value of the segmented heat exchanger.

[0011] According to embodiments of this disclosure, the convective heat transfer coefficient and the heat transfer coefficient are calculated using empirical correlations.

[0012] According to embodiments of this disclosure, the physical property parameters of each segment of the segmented heat exchanger are obtained by querying an open-source physical property parameter calculation library.

[0013] According to embodiments of this disclosure, a generalized Benders decomposition method is used to solve an equivalent nonlinear programming problem based on initial values, pressure distribution, temperature field distribution, and thermal resistance. Specifically, this includes: defining the equivalent nonlinear programming problem with fixed initial values, pressure distribution, temperature field distribution, and thermal resistance as a subproblem; solving for the values ​​of other unknown variables in the subproblem and the objective function of the equivalent nonlinear programming problem; calculating the Benders cut set based on the values ​​of the other unknown variables and the objective function, where the Benders cut set is a linear inequality composed of the generalized Lagrangian function values ​​of the subproblem and the gradient values ​​of the generalized Lagrangian function with respect to the operating parameters of the thermodynamic system contained in the nonlinear control equation; constructing a linear programming master problem using the Benders cut set as constraints; solving the linear programming master problem to obtain new values ​​of the operating parameters of the thermodynamic system contained in the nonlinear control equation and the objective function of the linear programming master problem; repeating the above steps for iterative calculation until the lower and upper boundaries of the equivalent nonlinear programming problem are approximated, and the value of the objective function of the equivalent nonlinear programming problem is less than a preset threshold, and the operating parameters of the thermodynamic system under this condition are taken as the final operating parameters.

[0014] According to embodiments of this disclosure, the solution method for thermal system simulation further includes: normalizing the values ​​of thermal system operating parameters contained in the nonlinear control equations during the iterative calculation process.

[0015] According to embodiments of this disclosure, the solution method for thermal system simulation further includes: during the iterative calculation process, multiplying each term of the objective function of the equivalent nonlinear programming problem by a preset adaptive coefficient.

[0016] According to embodiments of this disclosure, the solution method for thermal system simulation further includes: adding the sum of squares of the residuals of the linear control equations to the objective function of the equivalent nonlinear programming problem, so that the number of terms in the objective function of the equivalent nonlinear programming problem is the same as the number of thermal system operating parameters contained in the nonlinear control equations.

[0017] According to embodiments of this disclosure, the solution method for thermal system simulation further includes: analyzing the operating characteristics of the thermal system based on the operating parameters of each state point of the thermal system to obtain analysis results; and running the thermal system to realize the corresponding thermodynamic process based on the analysis results.

[0018] The second aspect of this disclosure provides a solution device for simulating a thermal system, comprising: a construction module for constructing the control equations of the thermal system and constructing an overall mathematical model of the thermal system based on the control equations; a construction module for constructing an equivalent nonlinear programming problem of the overall mathematical model based on the linear or nonlinear characteristics of the control equations; a first calculation module for presetting initial values ​​of the operating parameters of the thermal system contained in the nonlinear control equations, substituting the initial values ​​into the linear control equations to calculate the pressure distribution of the thermal system and the temperature field distribution of the segmented heat exchangers in the thermal system; a second calculation module for calculating the thermal resistance of the segmented heat exchangers based on the nonlinear control equations; and a third calculation module for solving the equivalent nonlinear programming problem using the generalized Benders decomposition method based on the initial values, pressure distribution, temperature field distribution, and thermal resistance, to obtain the operating parameters of each state point of the thermal system.

[0019] A third aspect of this disclosure provides an electronic device, comprising: one or more processors; and a memory for storing one or more programs, wherein when the one or more programs are executed by the one or more processors, the one or more processors cause the one or more processors to implement the method described above.

[0020] A fourth aspect of this disclosure provides a computer-readable storage medium having executable instructions stored thereon, which, when executed by a processor, cause the processor to implement the method described in the claims.

[0021] The solution method, apparatus, electronic device, and medium for thermal systems provided in the embodiments of this disclosure have at least the following beneficial effects:

[0022] Based on the linear or nonlinear characteristics of the governing equations, the problem of solving complex thermodynamic systems is equivalently transformed into a simple nonlinear programming problem. Then, based on the initial values ​​of the operating parameters of the thermodynamic system, pressure distribution, temperature field distribution, and thermal resistance, the generalized Benders decomposition method is used to solve the nonlinear programming problem, which simplifies the complex problem and improves the robustness, accuracy, and computational efficiency of solving the thermodynamic system.

[0023] Furthermore, in solving nonlinear programming problems using the generalized Benders decomposition method, a linear inequality consisting of the generalized Lagrangian function values ​​of the subproblems and the gradient values ​​of the generalized Lagrangian function with respect to the thermodynamic system operating parameters contained in the nonlinear control equations is used as a constraint. The gradient information of the operating parameters is used for iterative solution, which points the direction for iterative updates, enabling the solution process to have a larger convergence range, further improving the robustness of the thermodynamic system solution, and achieving higher computational efficiency within a smaller convergence range.

[0024] Furthermore, during the iterative calculation process, the values ​​of the operating parameters of the thermodynamic system contained in the nonlinear control equation are normalized, and each term of the objective function of the equivalent nonlinear programming problem is multiplied by a preset adaptive coefficient, making the solution process easier to converge. Under the premise of ensuring the accuracy of the model, the efficient and stable solution of the thermodynamic system is further realized. Attached Figure Description

[0025] The above and other objects, features and advantages of this disclosure will become clearer from the following description of embodiments with reference to the accompanying drawings, in which:

[0026] Figure 1 A flowchart illustrating a solution method for thermal system simulation according to an embodiment of the present disclosure is shown.

[0027] Figure 2 A flowchart illustrating a method for constructing the governing equations of a thermal system according to an embodiment of the present disclosure is shown.

[0028] Figure 3 A flowchart illustrating a method for calculating the thermal resistance of a segmented heat exchanger according to an embodiment of the present disclosure is shown.

[0029] Figure 4 A flowchart illustrating a method for solving nonlinear programming problems based on generalized Benders decomposition according to an embodiment of the present disclosure is shown.

[0030] Figure 5 A schematic diagram of a supercritical carbon dioxide recompression Brayton cycle power generation system according to an embodiment of the present disclosure is shown.

[0031] Figure 6 A schematic diagram illustrating the overall heat flow model of a supercritical carbon dioxide recompression Brayton cycle power generation system according to an embodiment of the present disclosure is shown.

[0032] Figure 7A The schematic diagram illustrates the structure of a shell-and-tube countercurrent heat exchanger used in a supercritical carbon dioxide recompression Brayton cycle power generation system according to an embodiment of the present disclosure.

[0033] Figure 7B A segmented heat flow model diagram of a heat exchanger in a supercritical carbon dioxide recompression Brayton cycle power generation system according to an embodiment of the present disclosure is illustrated.

[0034] Figure 8 A flowchart illustrating the solution method for a supercritical carbon dioxide recompression Brayton cycle power generation system based on generalized Benders decomposition according to an embodiment of the present disclosure is shown.

[0035] Figure 9A block diagram of a solution apparatus for simulating a thermal system according to an embodiment of the present disclosure is shown schematically.

[0036] Figure 10 A block diagram of an electronic device suitable for implementing the methods described above, according to embodiments of the present disclosure, is illustrated schematically. Detailed Implementation

[0037] To make the objectives, technical solutions, and advantages of this disclosure clearer, the following detailed description is provided in conjunction with specific embodiments and accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of this disclosure. All other embodiments obtained by those skilled in the art based on the embodiments of this disclosure without inventive effort are within the scope of protection of this disclosure.

[0038] The terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit this disclosure. The terms “comprising,” “including,” etc., as used herein indicate the presence of the stated features, steps, operations, and / or components, but do not exclude the presence or addition of one or more other features, steps, operations, or components.

[0039] In this disclosure, unless otherwise expressly specified and limited, the terms "installation," "connection," "linking," "fixing," etc., should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral part; they can refer to a mechanical connection, an electrical connection, or a connection that allows communication between them; they can refer to a direct connection or an indirect connection through an intermediate medium; they can refer to the internal communication of two components or the interaction between two components. Those skilled in the art can understand the specific meaning of the above terms in this disclosure according to the specific circumstances.

[0040] In the description of this disclosure, it should be understood that the terms "longitudinal", "length", "circumferential", "front", "rear", "left", "right", "top", "bottom", "inner", "outer", etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings, and are only for the convenience of describing this disclosure and simplifying the description, and do not indicate or imply that the subsystem 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 this disclosure.

[0041] Throughout the accompanying drawings, identical elements are represented by the same or similar reference numerals. Conventional structures or configurations have been omitted where they may cause confusion in understanding this disclosure. Furthermore, the shapes, dimensions, and positional relationships of the components in the drawings do not reflect their actual size, scale, or actual positional relationships. Additionally, any reference symbols enclosed in parentheses should not be construed as limiting this disclosure.

[0042] Similarly, to simplify this disclosure and aid in understanding one or more of the various aspects of the disclosure, in the above description of exemplary embodiments of the present disclosure, various features of the present disclosure are sometimes grouped together in a single embodiment, figure, or description thereof. The use of terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., refers to a specific feature, structure, material, or characteristic described in connection with that embodiment or example, which is included in at least one embodiment or example of the present disclosure. In this specification, illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples.

[0043] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Therefore, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of this disclosure, "multiple" means at least two, such as two, three, etc., unless otherwise explicitly specified.

[0044] Figure 1 A flowchart illustrating a solution method for thermal system simulation according to an embodiment of the present disclosure is shown.

[0045] like Figure 1 As shown, the solution method for the simulation of this thermal system may include, for example, operations S101 to S105.

[0046] In operation S101, the control equations of the thermodynamic system are constructed, and the overall mathematical model of the thermodynamic system is constructed based on the control equations.

[0047] In operation S102, based on the linear or nonlinear characteristics of the control equations, an equivalent nonlinear programming problem is constructed to form the overall mathematical model.

[0048] In operation S103, the initial values ​​of the operating parameters of the thermodynamic system contained in the nonlinear control equation are preset, and the initial values ​​are substituted into the linear control equation to calculate the pressure distribution of the thermodynamic system and the temperature field distribution of the segmented heat exchanger in the thermodynamic system.

[0049] In operation S104, the thermal resistance of the segmented heat exchanger is calculated based on the nonlinear control equation.

[0050] In operation S105, the generalized Benders decomposition method is used to solve the equivalent nonlinear programming problem based on the initial value, pressure distribution, temperature field distribution, and thermal resistance value, so as to obtain the operating parameters of each state point of the thermodynamic system.

[0051] In this embodiment of the disclosure, the operating parameters of the thermodynamic system included in the nonlinear control equation may include, for example, temperature, pressure, mass flow rate, heat exchange, and work done. These operating parameters are independent variables in the nonlinear control equation, and all independent variables in the nonlinear control equation can be determined as complex variables.

[0052] based on Figure 1 The solution method for the simulation of the thermal system shown can solve the overall mathematical model of the thermal system under certain boundary conditions, such as the known temperature and mass flow rate of the cold source and heat source of the system. This allows us to obtain the values ​​of operating parameters such as temperature, pressure, mass flow rate, heat exchange, and work done at each state point in the system.

[0053] Figure 2 A flowchart illustrating a method for constructing the governing equations of a thermal system according to an embodiment of the present disclosure is shown.

[0054] like Figure 2 As shown, the construction method may include, for example, operations S201 to S205.

[0055] In operation S201, based on the heat flow method of overall thermal system analysis, an equivalent heat flow model of the thermal system is established.

[0056] Specifically, for heat exchange processes under conditions of drastic changes in physical properties, a segmented heat flow model of a segmented heat exchanger can be constructed. Furthermore, the overall system heat flow control equation reflecting the laws of heat transfer and conversion can be derived based on Kirchhoff's laws in circuit theory.

[0057] In operation S202, the flow equation of the working component is established based on the functional relationship between the pressure difference before and after the working fluid flows through the working component and the mass flow rate of the working fluid.

[0058] In operation S203, the pressure distribution equation of the working fluid flow is established based on the pressure loss of the working fluid flow.

[0059] This pressure loss can be the pressure loss of the working fluid flowing through pipes, heat exchange components, etc.

[0060] In operation S204, based on the coupling relationship between the temperature and pressure of the working fluid, the heat-work conversion process equation and the working fluid mixing process equation are established.

[0061] In operation S205, an overall mathematical model of the thermodynamic system is constructed based on the equivalent heat flow model, flow equation, pressure distribution equation, heat-work conversion process equation, and working fluid mixing process equation.

[0062] based on Figure 2The overall mathematical model constructed by the method shown, which establishes the governing equations, is transformed into an equivalent nonlinear programming problem by classifying it according to its mathematical properties, such as linearity and (explicit / implicit) nonlinearity. The objective function of the equivalent nonlinear programming problem is the sum of squares of the residuals of the nonlinear governing equations, and the constraints of the equivalent nonlinear programming problem are the linear governing equations. The linear governing equations can include the equivalent heat flow model and pressure distribution equation of the thermodynamic system, while the nonlinear governing equations can include the flow equations, heat-work conversion process equations, and working fluid mixing process equations of the thermodynamic system.

[0063] After converting the problem of solving a complex thermodynamic system into a simple nonlinear programming problem, in order to make the nonlinear programming problem easier to solve, given the initial values ​​of the complex variables, we can substitute the initial values ​​into the linear control equations to calculate the pressure distribution of the thermodynamic system and the temperature field distribution of the segmented heat exchanger in the thermodynamic system.

[0064] After determining the pressure and temperature field distribution of the thermal system, the thermal resistance of the segmented heat exchanger can be calculated based on the nonlinear control equations.

[0065] Figure 3 A flowchart illustrating a method for calculating the thermal resistance of a segmented heat exchanger according to an embodiment of the present disclosure is shown.

[0066] like Figure 3 As shown, the method for calculating the thermal resistance of the segmented heat exchanger may include, for example, operations S301 to S303.

[0067] In operation S301, the physical property parameters of each section of the segmented heat exchanger are obtained under varying physical property conditions.

[0068] In this embodiment of the disclosure, the physical properties of each section of the segmented heat exchanger can be obtained by querying an open-source physical property parameter calculation library. This open-source physical property parameter calculation library could be, for example, the CoolProp physical property library.

[0069] In operation S302, the convective heat transfer coefficient and heat transfer coefficient of the segmented heat exchanger are calculated based on the physical property parameters.

[0070] In the embodiments of this disclosure, the convective heat transfer coefficient and the heat transfer coefficient can be calculated using empirical correlation formulas.

[0071] In operation S303, the convective heat transfer coefficient and the heat transfer coefficient are substituted into the nonlinear control equation to calculate the thermal resistance of the segmented heat exchanger.

[0072] In this embodiment of the disclosure, after obtaining the physical properties and heat transfer coefficient of the working fluid, the thermal resistance of each section of the segmented heat exchanger based on the inlet temperature difference can be obtained by directly substituting the nonlinear explicit control equation.

[0073] Based on the above operations, given the initial values ​​of complex variables and the calculated values ​​of pressure, temperature, and thermal resistance, the original equivalent nonlinear programming problem can be transformed into a more easily solvable nonlinear programming problem. The solution process of the original equivalent nonlinear programming problem is an iterative solution process.

[0074] Figure 4 A flowchart illustrating a method for solving nonlinear programming problems based on generalized Benders decomposition according to an embodiment of the present disclosure is shown.

[0075] like Figure 4 As shown, the method for solving nonlinear programming problems based on generalized Benders decomposition may include, for example, operations S401 to S405.

[0076] In operation S401, the equivalent nonlinear programming problem with fixed initial values, pressure distribution, temperature field distribution, and thermal resistance is defined as a subproblem.

[0077] After fixing the initial values ​​of the complex variables, pressure distribution, temperature field distribution, and thermal resistance, the constraints in the subproblem are all linearly independent overall heat flow control equations of the thermodynamic system. Therefore, after fixing the complex variables, the equations have a unique solution.

[0078] In operation S402, the values ​​of other unknown variables in the subproblem and the objective function of the equivalent nonlinear programming problem are solved.

[0079] Since the system of equations has a unique solution corresponding to the values ​​of the other unknown variables and the objective function of the equivalent nonlinear programming problem, solving the system of equations will yield the values ​​of the other unknown variables and the objective function.

[0080] In operation S403, the Benders cut set is calculated based on the values ​​of other unknown variables and the value of the objective function.

[0081] In this embodiment of the disclosure, the calculated Benders cut set can be a linear inequality consisting of the values ​​of the generalized Lagrange function of the subproblem and the gradient values ​​of the generalized Lagrange function with respect to the thermodynamic system operating parameters contained in the nonlinear control equation. That is, the Benders cut set contains gradient information of the defined complex variables.

[0082] In operation S404, the main linear programming problem is constructed with Benders cut sets as constraints.

[0083] In this embodiment of the disclosure, the objective function of the linear programming master problem can be an introduced relaxation factor, and its constraint condition is the set of Benders cut sets obtained by solving the subproblems in each iteration.

[0084] By operating S405, the main linear programming problem is solved, and new values ​​of the operating parameters of the thermodynamic system contained in the nonlinear control equations and the value of the objective function of the main linear programming problem are obtained.

[0085] It should be noted that the iterative process can be as follows: after each time the initial value of the complex variable is redefined and the pressure distribution, temperature field distribution and thermal resistance value are calculated, operations S401 to S405 are repeated to solve for the value of the new complex variable and the value of the objective function of the linear programming main problem.

[0086] It should be noted that since the solution to the subproblem is a feasible solution to the original equivalent nonlinear programming problem, and the optimal solution to the original problem will be smaller than this feasible solution, the upper boundary of the optimal solution to the original nonlinear programming problem is the smaller value between the objective function value of the current subproblem and the upper boundary value of the previous iteration.

[0087] It should be noted that since the main problem is equivalent to a relaxed primal nonlinear programming problem, the optimal solution to the main problem is always less than the optimal solution to the primal problem. Therefore, the lower boundary of the main problem can be updated using the primal problem's optimal solution. The lower boundary is the larger of the current objective function value of the main problem and the lower boundary value from the previous iteration.

[0088] Through the above iterative solution process, until the lower and upper boundaries of the equivalent nonlinear programming problem are approached and the value of the objective function of the equivalent nonlinear programming problem is less than the preset threshold, the operating parameters of the thermal system under this condition are taken as the final operating parameters.

[0089] Based on the above embodiments, the solution method for the thermal system may further include, for example, normalizing the values ​​of the thermal system operating parameters contained in the nonlinear control equations during the iterative calculation process.

[0090] During the calculation process, the values ​​of the operating parameters (variables) of the thermal system may differ significantly in magnitude. To reduce the complexity of the calculation, a baseline value for the variables can be set to normalize all variables in the iteration.

[0091] Based on the above embodiments, the solution method for thermal systems may further include, for example, multiplying each term of the objective function of the equivalent nonlinear programming problem by a preset adaptive coefficient during the iterative calculation process.

[0092] During the calculation process, since the different terms of the objective function of the equivalent nonlinear programming problem may have large differences in magnitude during the iteration process, multiplying each term by an adaptive coefficient can make the iterative solution process more likely to converge.

[0093] Based on the above embodiments, the solution method for thermal systems may further include, for example, adding the sum of squares of the residuals of the linear governing equations to the objective function of the equivalent nonlinear programming problem to avoid overdetermining of subproblems when constructing the equivalent nonlinear programming problem. This ensures that the number of terms in the objective function of the equivalent nonlinear programming problem is the same as the number of thermal system operating parameters included in the nonlinear governing equations. Furthermore, during iterative calculations, for nonconvex optimization problems, when the calculation result gets stuck in a local optimum, a restart strategy of adding a Benders cut set back to the main problem is adopted at the current point to allow the solution process to continue until the global optimum is found.

[0094] Based on the above embodiments, the solution method for the thermal system may further include, for example, analyzing the operating characteristics of the thermal system based on the operating parameters at each state point of the thermal system to obtain analysis results. Then, the thermal system is operated according to the analysis results to realize the corresponding thermodynamic process. Because the solution for the thermal system is more robust and accurate, the obtained operating parameters at each state point are more accurate and closer to reality, thus better meeting the application needs of multiple fields such as energy, power, aerospace, and chemical engineering.

[0095] The solution method for thermal system simulation provided in this disclosure not only has the advantage of classifying and processing the control equations according to mathematical properties proposed by the hierarchical-divide-conquer algorithm, which converts the solution problem of complex thermal systems into a nonlinear programming problem, but also adopts the framework of the generalized Benders decomposition algorithm to decompose the nonlinear programming problem into subproblems that are easier to solve and the main problem in the form of linear programming. By using gradient information to accelerate iterative updates, the robustness of the algorithm can be significantly improved, the convergence range of the algorithm can be expanded, and higher computational efficiency can be achieved within a smaller convergence range.

[0096] To further illustrate the solution method for the thermal system provided in the embodiments of this disclosure, a supercritical carbon dioxide recompression Brayton cycle power generation system is used as a specific example for explanation below.

[0097] Figure 5 A schematic diagram of a supercritical carbon dioxide recompression Brayton cycle power generation system according to an embodiment of the present disclosure is shown.

[0098] like Figure 5 As shown, a supercritical carbon dioxide (sCO2) recompression Brayton cycle power generation system may include, for example, a precooler (PRC), a main compressor (MC), a low-temperature regenerator (LTR), a high-temperature regenerator (HTR), a main heat exchanger (HTX), and a turbine (T), wherein the sCO2 cycle process is as follows: Figure 5 As indicated by the middle arrow. The specific solution process is as follows:

[0099] First, an equivalent heat flow model for a supercritical carbon dioxide recompression Brayton cycle power generation system is established. Specifically, for the heat exchange process under varying physical property conditions, a segmented heat flow model of the heat exchanger is constructed.

[0100] Figure 6 A schematic diagram illustrating the overall heat flow model of a supercritical carbon dioxide recompression Brayton cycle power generation system according to an embodiment of the present disclosure is shown. Figure 7A The schematic diagram illustrates the structure of a shell-and-tube countercurrent heat exchanger used in a supercritical carbon dioxide recompression Brayton cycle power generation system according to an embodiment of the present disclosure. Figure 7B A segmented heat flow model diagram of a heat exchanger in a supercritical carbon dioxide recompression Brayton cycle power generation system according to an embodiment of the present disclosure is illustrated.

[0101] like Figure 6 , Figure 7A and Figure 7B As shown, based on Kirchhoff's laws in circuit theory, the overall heat flow control equation reflecting the heat transfer and conversion laws is derived as follows:

[0102] Q HTR，i R HTR，i +Q HTR，i+1 / (mc p ) HTR，c，i+1 -Q HTR，i+1 R HTR，i+1 -Q HTR，i / (mc p ) HTR，h，i =0, i=1, ...,N HTR -1 (1)

[0103] Q LTR，i R LTR，i +Q LTR，i+1 / (mC p ) LTR，c，i+1 -Q LTR，i+1 R LTR，i+1 -Q LTR，i / (mc p ) LTR，h，i =0, i=1,...,N LTR -1 (2)

[0104] Q PRC，i / (mc p ) PRC，h，i -Q PRC，i R PRC，i -Q PRC，i-1 / (mc p ) PRC，c，i-1 +Q PRC，i-1 R PRC，i-1 =0, i=2, ...,N PRC (3)

[0105] Q HTX / (mc p ) c，HTX -ε T -Q HTR，1 R HTR，1 +Q HTR，1 / (mc p ) c，1，HTR =0 (4)

[0106] Q HTR，N R HTR，N +ε 4，3 +Q LTR，1 / (mc p ) LTR，c，1 -Q LTR，1 R LTR，1 -Q HTR，N / (mc p ) HTR，h，N =0 (5)

[0107]

[0108]

[0109]

[0110] T6 = T hs，in -O HTX R HTX (9)

[0111]

[0112] T1 = T cs，in +Q PRC，1 R PRC，1 -Q PRC，1 / (mc p ) PRC，h，1 (11)

[0113] T7 = T hs，in -Q HTx R HTX +Q HTX / (mc p ) HTX，c (12)

[0114]

[0115] Among them, according to the heat flow model, the thermal resistance R is defined based on the inlet temperature difference. HTR，i R LTR，i R PRC，iAll have the form shown in equation (14). The heat transfer coefficient of the heat exchanger is calculated using an empirical correlation formula. The CO2 thermophysical properties at different temperatures and pressures are obtained by querying a property library, such as the CoolProp property library.

[0116]

[0117]

[0118] Equations (1) to (4) represent Kirchhoff's Voltage Law (KVL) for adjacent heat exchange units within the three heat exchanger models, respectively; equations (5) to (7) represent the KVL equations between different heat exchange components and heat-work conversion components. The above N... HTR +N LTR +N PRC +1 governing equations reflect the overall heat transfer constraints of the system; equations (8) to (13) represent the temperatures of other intermediate state points obtained from KVL or energy conservation equations.

[0119] Considering the functional relationship between the pressure difference and the mass flow rate of the working fluid before and after passing through the working component, the flow equation of the working component is established; considering the pressure loss of the working fluid through pipes, heat exchange components, etc., the pressure distribution equation of the working fluid flow is established.

[0120] The relationship between the pressure difference before and after sCO2 flows through the turbine and its mass flow rate is described by the Vlugel formula:

[0121]

[0122] The pressure loss of the working fluid during the heating or cooling process in the main heat exchanger (HTX), HTR, LTR, and PRC is linearly distributed, and the pressure loss Δp flowing through the heat exchanger is... 1oss If the pressure is proportional to the inlet pressure, then the pressure at any position z inside the heat exchanger can be expressed as p. z :

[0123] Δp loss =p in -p out =p in f P (17)

[0124] p z =p in -z·Δp loss / L (18)

[0125] The pressure at all state points of the system can be represented by the pressure at point 1 and point 7:

[0126]

[0127] For the main compressor (MC) and the refrigerant compressor (RC), the requirements for working fluid pressure changes and mass flow rate through the compressor can be met by directly adjusting the shaft speed.

[0128] Considering the coupling relationship between the working fluid temperature and pressure, equations for the heat-work conversion process and the working fluid mixing process are established.

[0129] sCO2 undergoes adiabatic expansion in a turbine with constant isentropic efficiency. Its governing equation is:

[0130] s8 = s(T7, p7) (20)

[0131] h8 = h(T7, p7) - η T [h(T7, p7) - h(s8, p8)] (21)

[0132] W T =m[h(T7, p7) - h8] (22)

[0133] In the heat flow model, the temperature change during the heat-work conversion of the working fluid is also represented by thermodynamic potential:

[0134] ε T =T7-T8=T7-T(h8, p8) (23)

[0135] Similarly, the governing equations for the adiabatic compression process of the working fluid in MC and RC are:

[0136] s2=s(T1,p1) (24)

[0137] h2=h(T1,p1)+[h(s2,p2)-h(T1,p1)] / η MC (25)

[0138] W MC =m(1-x)[h2-h1(T1, p1)] (26)

[0139] ε MC =T2-T1=T(h2,p2)-T1 (27)

[0140] s5=s(T 10 p 10 (28)

[0141] h5=h(T 10 p 10 )+[h(s5,p5)-h(T 10 p 10 )] / η RC (29)

[0142] W RC=mx[h5-h 10 (T 10 p 10 (30)

[0143] ε RC =T5-T 10 =T(h5, p5)-T 10 (31)

[0144] The sCO2 splits into two streams at point 10, and then the main flow at point 3 and the recompression flow at point 5 mix at point 4. The thermodynamic equation for this ideal mixing process is:

[0145] h4=(1-x)h(T3,P3)+xh5 (32)

[0146] In the heat flow model, the temperature change during the mixing process is represented by the thermodynamic potential as follows:

[0147] ε 4，3 =T4-T3=T(h4,p4)-T3 (33)

[0148] ε 5，4 =T5-T4=T5-T(h4,p4) (34)

[0149] By combining the above-mentioned overall system heat flow model control equations (1) to (13), working fluid flow equations (16) to (19), and flow-heat transfer coupling equations (20) to (34), the overall mathematical model of the supercritical carbon dioxide recompression Brayton cycle power generation system is constituted. The meanings of each variable are as follows:

[0150] Q – Heat exchange capacity of the heat exchanger, in W;

[0151] R—thermal resistance of the heat exchanger, K / W;

[0152] m—mass flow rate, kg / s;

[0153] c p Specific heat capacity at constant pressure, J / kg / K;

[0154] ε—Thermodynamic potential, K;

[0155] T – Temperature, K;

[0156] K – Heat transfer coefficient of the heat exchanger, W / K / m 2 ;

[0157] A – Heat exchange area of ​​the heat exchanger, in meters (m²) 2 ;

[0158] s — specific entropy, J / K;

[0159] h—specific enthalpy, J / kg;

[0160] p – Pressure, Pa;

[0161] k t —Characteristic flow coefficient of the turbine, s·m·K 0.5

[0162] W—Power of the working component, W;

[0163] N—Number of sections in the heat exchanger;

[0164] η—Isoentropy efficiency;

[0165] x — the mass fraction of the fluid that flows directly to the recompressor;

[0166] f p —Pressure loss coefficient.

[0167] The subscripts HTR, LTR, PRC, HTX, T, MC, and RC represent the high-temperature regenerator, low-temperature regenerator, precooler, main heat exchanger, turbine, main compressor, and recompressor, respectively. The subscript i represents the i-th segment of the segmented heat exchanger. The subscripts h and c represent the hot fluid and cold fluid, respectively. The subscripts hs and cs represent the system's heat source and cold source, respectively. The subscripts in and out represent the inlet and outlet, respectively. The numbers in the subscripts correspond to... Figure 5 The state point number in the system.

[0168] For a practical supercritical carbon dioxide recompression Brayton cycle power generation system, the inlet temperatures of the cold and heat source fluids and the mass flow rate of the heat source fluid are known quantities. The minimum circulation pressure, i.e., the inlet pressure of MC, is also given as a boundary condition. The adjustable variables during system operation are the shaft speeds of MC and RC, and the frequency of the cold source pump. Accordingly, the mass flow rate m of the circulating working fluid and the mass flow rate m of the cold source are selected. cs The boundary conditions and the mass fraction of the recompressed fluid, x, are the operating variables. Given the above boundary conditions and operating variables, solving the above system control equations can determine all unknown variables of the system, obtain the operating parameters under the corresponding operating conditions, and realize the performance analysis of the supercritical carbon dioxide recompression Brayton cycle power generation system.

[0169] Secondly, after establishing the overall model of the supercritical carbon dioxide recompression Brayton cycle power generation system, an equivalent nonlinear programming problem for system simulation is constructed based on the linear / nonlinear mathematical properties of the constraint equations.

[0170] Choose all independent variables (operating parameters) of the nonlinear control equation as complex variables y: y = {p7, T1, T2, T3, T5, T7, T8, T...} 10Let v be the other variables. Furthermore, to avoid overdetermining of subproblems, linear equation constraints need to be added to the objective function so that the number of terms in the objective function is the same as the number of complex variables. Finally, the constructed nonlinear programming problem is shown in the following equation:

[0171]

[0172]

[0173] The calculation formulas for T2'T4'T5'T8' are shown in equation (36). The specific enthalpy of the state point in each equation is obtained from the heat-work conversion process equations and the fluid mixing energy conservation equations in equations (20) to (32):

[0174]

[0175] Finally, after the complex variables are determined, the solution is obtained based on the generalized Benders decomposition method.

[0176] Figure 8 A flowchart illustrating the solution method for a supercritical carbon dioxide recompression Brayton cycle power generation system based on generalized Benders decomposition according to an embodiment of the present disclosure is shown.

[0177] like Figure 8 As shown, the solution process can be as follows:

[0178] When operating S801, preset the initial values ​​of complex variables.

[0179] For example, given the value of a complex variable: Let y = y k .

[0180] In operation S802, the initial values ​​of the preset complex variables are substituted into the pressure distribution equation of the working fluid flow, and the initial temperature field distribution of the heat exchanger is obtained.

[0181] For example, the initial values ​​of the preset complex variables are linearly substituted into the solution equation (19), and the initial temperature field distribution of the heat exchanger is obtained by combining the coupling relationship between temperature and pressure.

[0182] In operation S803, the CoolProp property library is queried to obtain the property parameters of each section of the segmented heat exchanger, and the convective heat transfer coefficient and heat transfer coefficient of the heat transfer process are calculated using empirical correlation formulas.

[0183] In operating S804, by directly substituting the convective heat transfer coefficient and the heat transfer coefficient into the nonlinear explicit equation, the thermal resistance values ​​of each section of the segmented heat exchanger based on the inlet temperature difference are obtained.

[0184] For example, after obtaining the physical properties and heat transfer coefficient of the working fluid, equations (14) and (15) are solved to obtain the thermal resistance values ​​of each section of the segmented heat exchanger based on the inlet temperature difference.

[0185] Fixed y = y k After directly substituting the operating parameters such as pressure and thermal resistance obtained from the solution, the subproblem becomes a nonlinear programming problem with some variables fixed, and its form is still Equation (35).

[0186] Using S805, solve the subproblem.

[0187] That is, given the value of a complex variable y = y k Under the given conditions, solve the nonlinear programming problem (35). Since the constraint equation system g in this problem are all linearly independent equality constraints, given y = y k Afterwards, g has a unique solution, meaning that every subproblem has a feasible solution. Let the solution be denoted as v = v k Find the current f. Since the solution to the subproblem is a feasible solution to the original equivalent nonlinear programming problem, and the optimal solution to the original problem will be smaller than this feasible solution, update the upper bound UB of the original problem:

[0188] UB k =min(UB) k-1 f) (37)

[0189] In operation S806, based on the solution to the current subproblem, the Benders cut set (Optimality cut) is computed. Specifically:

[0190]

[0191] Where z is the introduced slack variable, and L is the generalized Lagrange function for the nonlinear programming problem. Let L be the gradient of the complex variable y, and u be the Lagrange multiplier vector:

[0192]

[0193] Construct / update the main linear programming problem with objective function z and constraints consisting of the optimal cut set obtained by solving each subproblem:

[0194]

[0195] By operating S807, the main linear programming problem is solved, and the updated complex variable y is obtained.

[0196] Since the main problem is equivalent to a relaxed primal problem, the optimal solution to the main problem is always less than the optimal solution to the primal problem. Therefore, the lower bound (LB) between the main problem and the optimal solution to the primal problem can be updated using the main problem:

[0197] LB k =max(LB) k-1 ,z) (41)

[0198] When operating S808, determine whether the convergence condition is met.

[0199] The convergence criterion can be chosen as |UB-LB|<δ (δ>0) and each term f(i) of the objective function is less than a given threshold ε. i (ε i >0)

[0200] If the conditions are not met, repeat operations S801 to S807 for iterative calculation. Generally, for non-convex optimization problems, when |UB-LB| < δ (δ > 0) and the variable does not change much between two adjacent iterations, the iteration can be considered convergent.

[0201] For non-convex optimization problems, when the computational result gets stuck in a local optimum, a restart strategy is adopted at the current point, which involves adding a Benders cut set back to the main problem to allow the solution process to continue until the global optimum is found. Since the variables in the system model vary greatly in magnitude, data normalization is used to enhance the algorithm's convergence. T is selected. n p n m n c pn As the baseline values ​​for various variables, all variables in the iteration are normalized, as shown in equation (42). During normalization, the specific values ​​of the baseline values ​​only need to be of the same order of magnitude as the corresponding variables. Furthermore, different terms of the objective function in the subproblems may have significantly different orders of magnitude during the iteration process. Therefore, multiplying each term by an adaptive coefficient makes the problem easier to converge.

[0202]

[0203] This concludes the detailed explanation of the thermodynamic system solution method provided in the embodiments of this disclosure based on a supercritical carbon dioxide recompression Brayton cycle power generation system.

[0204] Figure 9 A block diagram of a solution apparatus for simulating a thermal system according to an embodiment of the present disclosure is shown schematically.

[0205] like Figure 9 As shown, the solution device 900 for thermal system simulation may include, for example, a construction module 910, a construction module 920, a first calculation module 930, a second calculation module 940, and a third calculation module 950.

[0206] Module 910 is used to construct the governing equations of the thermodynamic system and to construct the overall mathematical model of the thermodynamic system based on the governing equations.

[0207] Module 920 is used to construct an equivalent nonlinear programming problem of the overall mathematical model based on the linear or nonlinear characteristics of the governing equations.

[0208] The first calculation module 930 is used to preset the initial values ​​of the operating parameters of the thermodynamic system contained in the nonlinear control equation, and substitute the initial values ​​into the linear control equation to calculate the pressure distribution of the thermodynamic system and the temperature field distribution of the segmented heat exchanger in the thermodynamic system.

[0209] The second calculation module 940 is used to calculate the thermal resistance of the segmented heat exchanger based on the nonlinear control equation.

[0210] The third calculation module 950 is used to solve the equivalent nonlinear programming problem using the generalized Benders decomposition method based on the initial value, pressure distribution, temperature field distribution, and thermal resistance value, so as to obtain the operating parameters of each state point of the thermodynamic system.

[0211] Any one or more of the modules, submodules, units, and subunits according to embodiments of the present disclosure, or at least part of the functions of any one or more of them, can be implemented in one module. Any one or more of the modules, submodules, units, and subunits according to embodiments of the present disclosure can be implemented by dividing them into multiple modules. Any one or more of the modules, submodules, units, and subunits according to embodiments of the present disclosure can be at least partially implemented as hardware circuitry, such as Field Programmable Gate Arrays (FPGAs), Programmable Logic Arrays (PLAs), Systems-on-Chip, Systems-on-Substrate, Systems-on-Package, Application-Specific Integrated Circuits (ASICs), or implemented in hardware or firmware by any other reasonable means of integrating or packaging circuitry, or implemented in software, hardware, or firmware, or in any suitable combination of any of these three implementation methods. Alternatively, one or more of the modules, submodules, units, and subunits according to embodiments of the present disclosure can be at least partially implemented as computer program modules, which, when run, can perform corresponding functions.

[0212] For example, any plurality of the building module 910, construction module 920, first computing module 930, second computing module 940, and third computing module 950 can be combined into one module / unit / subunit, or any one of these modules / units / subunits can be split into multiple modules / units / subunits. Alternatively, at least part of the functionality of one or more of these modules / units / subunits can be combined with at least part of the functionality of other modules / units / subunits and implemented in one module / unit / subunit. According to embodiments of the present disclosure, at least one of the building module 910, construction module 920, first computing module 930, second computing module 940, and third computing module 950 can be at least partially implemented as hardware circuitry, such as a field-programmable gate array (FPGA), a programmable logic array (PLA), a system-on-a-chip, a system-on-a-substrate, a system-on-package, an application-specific integrated circuit (ASIC), or implemented in hardware or firmware by any other reasonable means of integrating or packaging the circuitry, or implemented in software, hardware, or firmware, or in any suitable combination of any of these three implementation methods. Alternatively, at least one of the building module 910, the construction module 920, the first calculation module 930, the second calculation module 940, and the third calculation module 950 may be implemented at least partially as a computer program module, which can perform corresponding functions when the computer program module is run.

[0213] It should be noted that the solution device part of the thermal system in the embodiments of this disclosure corresponds to the solution method part of the thermal system in the embodiments of this disclosure, and their specific implementation details and the resulting technical effects are the same, which will not be repeated here.

[0214] Figure 10 A block diagram of an electronic device suitable for implementing the methods described above, according to embodiments of the present disclosure, is illustrated schematically. Figure 10 The electronic device shown is merely an example and should not be construed as limiting the functionality and scope of the embodiments disclosed herein.

[0215] like Figure 10As shown, an electronic device 1000 according to an embodiment of the present disclosure includes a processor 1001, which can perform various appropriate actions and processes according to a program stored in a read-only memory (ROM) 1002 or a program loaded from a storage portion 1008 into a random access memory (RAM) 1003. The processor 1001 may include, for example, a general-purpose microprocessor (e.g., a CPU), an instruction set processor and / or an associated chipset and / or a special-purpose microprocessor (e.g., an application-specific integrated circuit (ASIC)), etc. The processor 1001 may also include onboard memory for caching purposes. The processor 1001 may include a single processing unit or multiple processing units for performing different actions of the method flow according to an embodiment of the present disclosure.

[0216] RAM 1003 stores various programs and data required for the operation of electronic device 1000. Processor 1001, ROM 1002, and RAM 1003 are interconnected via bus 1004. Processor 1001 performs various operations of the method flow according to embodiments of the present disclosure by executing programs in ROM 1002 and / or RAM 1003. It should be noted that the programs may also be stored in one or more memories other than ROM 1002 and RAM 1003. Processor 1001 may also perform various operations of the method flow according to embodiments of the present disclosure by executing programs stored in said one or more memories.

[0217] According to embodiments of this disclosure, the electronic device 1000 may further include an input / output (I / O) interface 1005, which is also connected to a bus 1004. The electronic device 1000 may also include one or more of the following components connected to the I / O interface 1005: an input section 1006 including a keyboard, mouse, etc.; an output section 1007 including a cathode ray tube (CRT), liquid crystal display (LCD), etc., and a speaker, etc.; a storage section 1008 including a hard disk, etc.; and a communication section 1009 including a network interface card such as a LAN card, modem, etc. The communication section 1009 performs communication processing via a network such as the Internet. A drive 1010 is also connected to the I / O interface 1005 as needed. A removable medium 1011, such as a disk, optical disk, magneto-optical disk, semiconductor memory, etc., is installed on the drive 1010 as needed so that computer programs read from it can be installed into the storage section 1008 as needed.

[0218] According to embodiments of this disclosure, the method flow according to embodiments of this disclosure can be implemented as a computer software program. For example, embodiments of this disclosure include a computer program product comprising a computer program carried on a computer-readable storage medium, the computer program containing program code for performing the methods shown in the flowchart. In such embodiments, the computer program can be downloaded and installed from a network via communication section 1009, and / or installed from removable medium 1011. When the computer program is executed by processor 1001, it performs the functions defined in the system of embodiments of this disclosure. According to embodiments of this disclosure, the systems, devices, apparatuses, modules, units, etc., described above can be implemented by computer program modules.

[0219] This disclosure also provides a computer-readable storage medium, which may be included in the device / apparatus / system described in the above embodiments; or it may exist independently and not assembled into the device / apparatus / system. The computer-readable storage medium carries one or more programs that, when executed, implement the method according to the embodiments of this disclosure.

[0220] According to embodiments of this disclosure, the computer-readable storage medium can be a non-volatile computer-readable storage medium. Examples include, but are not limited to: portable computer disks, hard disks, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), portable compact disk read-only memory (CD-ROM), optical storage devices, magnetic storage devices, or any suitable combination thereof. In this disclosure, the computer-readable storage medium can be any tangible medium that contains or stores a program that can be used by or in conjunction with an instruction execution system, apparatus, or device.

[0221] For example, according to embodiments of this disclosure, a computer-readable storage medium may include one or more memories other than ROM 1002 and / or RAM 1003 described above.

[0222] The flowcharts and block diagrams in the accompanying drawings illustrate the architecture, functionality, and operation of possible implementations of systems, methods, and computer program products according to various embodiments of the present disclosure. In this regard, each block in a flowchart or block diagram may represent a module, segment, or portion of code containing one or more executable instructions for implementing a specified logical function. It should also be noted that in some alternative implementations, the functions indicated in the blocks may occur in a different order than those indicated in the drawings. For example, two consecutively indicated blocks may actually be executed substantially in parallel, and they may sometimes be executed in reverse order, depending on the functions involved. It should also be noted that each block in a block diagram or flowchart, and combinations of blocks in a block diagram or flowchart, may be implemented using a dedicated hardware-based system that performs the specified function or operation, or using a combination of dedicated hardware and computer instructions. Those skilled in the art will understand that the features recited in the various embodiments and / or claims of this disclosure can be combined and / or combined in various ways, even if such combinations or combinations are not expressly described in this disclosure. In particular, the features described in the various embodiments and / or claims of this disclosure may be combined and / or combined in various ways without departing from the spirit and teachings of this disclosure. All such combinations and / or combinations fall within the scope of this disclosure.

Claims

1. A solution method for simulating a thermodynamic system, characterized in that, include: Construct the governing equations of the thermodynamic system, and build an overall mathematical model of the thermodynamic system based on the governing equations; Based on the linear and nonlinear characteristics of the control equations, construct the equivalent nonlinear programming problem of the overall mathematical model; The initial values ​​of the operating parameters of the thermodynamic system contained in the nonlinear control equation are preset, and the initial values ​​are substituted into the linear control equation to calculate the pressure distribution of the thermodynamic system and the temperature field distribution of the segmented heat exchanger in the thermodynamic system. Calculate the thermal resistance of the segmented heat exchanger based on the nonlinear control equation. The generalized Benders decomposition method is used to solve the equivalent nonlinear programming problem based on the initial values, pressure distribution, temperature field distribution, and thermal resistance, to obtain the operating parameters of the thermodynamic system at each state point. This includes: defining the equivalent nonlinear programming problem with fixed initial values, pressure distribution, temperature field distribution, and thermal resistance as a subproblem; solving for the values ​​of other unknown variables in the subproblem and the objective function of the equivalent nonlinear programming problem; and calculating the Benders cut set based on the values ​​of the other unknown variables and the objective function, wherein the Benders cut set is a generalized decomposition of the subproblem. A linear inequality is formed by the Lagrange function value and the gradient value of the generalized Lagrange function with respect to the operating parameters of the thermodynamic system contained in the nonlinear control equation. A linear programming master problem is constructed using the Benders cut set as constraints. The master problem is solved to obtain new values ​​of the operating parameters of the thermodynamic system contained in the nonlinear control equation and the value of the objective function of the master problem. The above process is repeated iteratively until the lower and upper boundaries of the equivalent nonlinear programming problem are approximated, and the value of the objective function of the equivalent nonlinear programming problem is less than a preset threshold. The operating parameters of the thermodynamic system under this condition are then taken as the final operating parameters.

2. The solution method for simulating a thermodynamic system according to claim 1, characterized in that, The governing equations for constructing the thermodynamic system specifically include: Based on the heat flow method of the overall analysis of the thermal system, an equivalent heat flow model of the thermal system is established. Based on the functional relationship between the pressure difference before and after the working fluid flows through the working component and the mass flow rate of the working fluid, the flow equation of the working component is established. Based on the pressure loss of the working fluid flow, establish the pressure distribution equation of the working fluid flow; Based on the coupling relationship between the temperature and pressure of the working fluid, the equations for the heat-work conversion process and the working fluid mixing process are established. The overall mathematical model of the thermodynamic system is constructed based on the equivalent heat flow model, the flow equation, the pressure distribution equation, the heat-work conversion process equation, and the working fluid mixing process equation.

3. The solution method for simulating a thermodynamic system according to claim 2, characterized in that, The objective function of the equivalent nonlinear programming problem is the sum of squares of the residuals of the nonlinear control equations, and the constraint condition of the equivalent nonlinear programming problem is the linear control equations.

4. The solution method for simulating a thermodynamic system according to claim 2 or 3, characterized in that, The linear control equations include the equivalent heat flow model and the pressure distribution equation of the thermodynamic system, while the nonlinear control equations include the flow equation, the heat-work conversion process equation, and the working fluid mixing process equation of the thermodynamic system.

5. The solution method for simulating a thermodynamic system according to claim 1, characterized in that, The operating parameters of the thermodynamic system included in the nonlinear control equations are temperature, pressure, mass flow rate, heat exchange, and work done.

6. The solution method for simulating a thermodynamic system according to claim 1, characterized in that, The calculation of the thermal resistance value of the segmented heat exchanger based on the nonlinear control equation specifically includes: After the pressure distribution of the thermal system and the temperature field distribution of the segmented heat exchanger in the thermal system are determined, the physical property parameters of each segment of the segmented heat exchanger under the variable physical property conditions are obtained. Calculate the convective heat transfer coefficient and the heat transfer coefficient of the segmented heat exchanger based on the aforementioned physical property parameters; The thermal resistance of the segmented heat exchanger is calculated by substituting the convective heat transfer coefficient and the heat transfer coefficient into the nonlinear control equation.

7. The solution method for simulating a thermodynamic system according to claim 6, characterized in that, The convective heat transfer coefficient and the heat transfer coefficient are calculated using empirical correlations.

8. The solution method for simulating a thermodynamic system according to claim 6, characterized in that, The physical property parameters of each section of the segmented heat exchanger are obtained by querying an open-source physical property parameter calculation library.

9. The solution method for simulating a thermodynamic system according to claim 1, characterized in that, The solution method for the thermodynamic system also includes: During the iterative calculation process, the values ​​of the thermodynamic system operating parameters contained in the nonlinear control equations are normalized.

10. The solution method for simulating a thermodynamic system according to claim 1, characterized in that, The solution method for the thermodynamic system also includes: During the iterative calculation process, each term of the objective function of the equivalent nonlinear programming problem is multiplied by a preset adaptive coefficient.

11. The solution method for simulating a thermodynamic system according to claim 3, characterized in that, The solution method for the thermodynamic system also includes: Add the sum of squares of the residuals of the linear control equations to the objective function of the equivalent nonlinear programming problem, so that the number of terms in the objective function of the equivalent nonlinear programming problem is the same as the number of thermodynamic system operating parameters contained in the nonlinear control equations.

12. The solution method for simulating a thermodynamic system according to claim 1, characterized in that, The solution method for the thermodynamic system also includes: The operating characteristics of the thermal system are analyzed based on the operating parameters at each state point of the thermal system, and the analysis results are obtained. The thermal system is run according to the analysis results to realize the corresponding thermodynamic process.

13. A solution device for simulating a thermodynamic system, characterized in that, include: A construction module is used to construct the governing equations of the thermodynamic system and, based on the governing equations, construct the overall mathematical model of the thermodynamic system. A construction module is used to construct an equivalent nonlinear programming problem of the overall mathematical model based on the linear and nonlinear characteristics of the control equations. The first calculation module is used to preset the initial values ​​of the operating parameters of the thermodynamic system contained in the nonlinear control equation, and substitute the initial values ​​into the linear control equation to calculate the pressure distribution of the thermodynamic system and the temperature field distribution of the segmented heat exchanger in the thermodynamic system. The second calculation module is used to calculate the thermal resistance value of the segmented heat exchanger according to the nonlinear control equation. The third calculation module is used to solve the equivalent nonlinear programming problem using the generalized Benders decomposition method, based on the initial values, pressure distribution, temperature field distribution, and thermal resistance, to obtain the operating parameters of each state point of the thermodynamic system. This includes: defining the equivalent nonlinear programming problem with fixed initial values, pressure distribution, temperature field distribution, and thermal resistance as a subproblem; solving for the values ​​of other unknown variables in the subproblem and the objective function of the equivalent nonlinear programming problem; and calculating the Benders cut set based on the values ​​of the other unknown variables and the objective function, wherein the Benders cut set is formed by the subproblem... The linear inequality is formed by the generalized Lagrangian function value and the gradient value of the generalized Lagrangian function with respect to the operating parameters of the thermodynamic system contained in the nonlinear control equation. Using the Benders cut set as constraints, a linear programming master problem is constructed. The master problem is solved to obtain new values ​​of the operating parameters of the thermodynamic system contained in the nonlinear control equation and the value of the objective function of the master problem. The above process is repeated iteratively until the lower and upper boundaries of the equivalent nonlinear programming problem are approximated, and the value of the objective function of the equivalent nonlinear programming problem is less than a preset threshold. The operating parameters of the thermodynamic system under this condition are then taken as the final operating parameters.

14. An electronic device, characterized in that, include: One or more processors; Memory, used to store one or more programs. Wherein, when the one or more programs are executed by the one or more processors, the one or more processors implement the method of any one of claims 1 to 12.

15. A computer-readable storage medium, characterized in that, It stores executable instructions that, when executed by a processor, cause the processor to implement the method of any one of claims 1 to 12.

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