Layered optimization method for marine gas turbine waste heat driven supercritical carbon dioxide cycle

Abstract

This invention relates to the field of marine propulsion technology and discloses a hierarchical optimization method for supercritical carbon dioxide cycle driven by waste heat from a marine gas turbine. The method includes: acquiring exhaust heat source parameters of the marine gas turbine; establishing a supercritical carbon dioxide working fluid property library; constructing mass, energy, entropy, and uranium balance equations for two types of cycles: simple regeneration and recompression; coupling one-dimensional control equations for the heat exchanger, turbomachinery, and printed circuit board heat exchanger; conducting multi-objective optimization at the cycle level with output power, uranium efficiency, and levelized cost of electricity as objectives; generating a Pareto front and selecting decision points; and then, using the cycle decision point parameters as boundaries, performing structural optimization of the regenerator volume, pressure drop, and cost at the component level, ultimately outputting the synergistic optimization results of the cycle operating conditions and component structure. This invention significantly improves the overall performance of supercritical carbon dioxide cycle driven by waste heat from a marine gas turbine.

Description

Technical Field

[0001] This invention relates to the field of marine power plant technology, and more specifically, to a stratified optimization method for supercritical carbon dioxide cycle driven by waste heat from a marine gas turbine. Background Technology

[0002] Supercritical carbon dioxide Brayton cycle is a novel power cycle technology that uses supercritical carbon dioxide as the working fluid. It boasts advantages such as high thermal efficiency, compact structure, wide applicability to various heat sources, and low noise, and is considered one of the most promising next-generation energy conversion devices, with broad application prospects in the field of marine waste heat recovery. Marine gas turbine exhaust temperatures typically exceed 450°C, still containing a significant amount of usable heat energy. Deep recovery of this heat energy through supercritical carbon dioxide cycle technology can achieve cascaded energy utilization, further enhancing the overall performance of marine power plants.

[0003] In the design and optimization of supercritical carbon dioxide cycles, the degree of matching between cycle performance and component structure is a key factor affecting its overall performance. However, in traditional supercritical carbon dioxide cycle design methods, cycle performance and component geometric parameters are often disconnected. While simplified modeling methods using given component performance indicators offer fast computation speeds, the optimization results lack component selection verification, fail to reflect the mutual influence between components, and are difficult to conduct performance analysis under non-design conditions. Using fully coupled component modeling methods improves computational accuracy but significantly increases computational complexity, and since component geometric parameters are often directly given, there is a lack of systematic optimization of component structural parameters, limiting further improvement in overall cycle performance. It is difficult to simultaneously achieve joint optimization at the cycle and component levels, making it difficult to balance computational efficiency and optimization accuracy.

[0004] Therefore, it is necessary to design a hierarchical optimization method for supercritical carbon dioxide cycle driven by waste heat from marine gas turbines to solve the problems of disconnect between cycle performance and component structure, single optimization dimension, and difficulty in balancing computational efficiency and optimization accuracy in traditional supercritical carbon dioxide cycle design. Summary of the Invention

[0005] In view of this, the present invention proposes a hierarchical optimization method for supercritical carbon dioxide cycle driven by waste heat of marine gas turbine, which aims to solve the problems of disconnect between cycle performance and component structure, single optimization dimension, and difficulty in balancing computational efficiency and optimization accuracy in traditional supercritical carbon dioxide cycle design.

[0006] This invention proposes a stratified optimization method for supercritical carbon dioxide cycle driven by waste heat from marine gas turbines, comprising: The exhaust flow rate, temperature, and pressure heat source parameters of marine gas turbines are obtained, and a supercritical carbon dioxide working fluid property parameter library is established. Based on the pressure heat source parameters and the supercritical carbon dioxide working fluid property parameter library, the mass conservation, energy conservation, entropy balance, and sludge balance equations for simple regenerative cycles and recompression cycles are constructed sequentially. The heat transfer equations of heat exchangers, the energy equations of compressors and turbines, and the mass, momentum, and energy conservation control equations of hot and cold channels and metal substrates of printed circuit board heat exchangers are coupled and established. Based on the control equations at the cyclic level, a multi-objective function is constructed for output power, efficiency, and levelized cost of electricity. Iterative optimization is carried out on working fluid flow rate, high and low operating pressure, minimum operating temperature, split ratio, heat exchanger effectiveness, and adiabatic internal efficiency to generate a cyclic non-dominated solution set and Pareto front. The cyclic decision point is selected by positive and negative ideal points and proximity calculations, and the inlet and outlet thermal parameters of each component are extracted. Using the extracted inlet and outlet thermal parameters of the component as boundary conditions, the effectiveness and heat exchange constraints of the regenerator are set. At the component level, objective functions of volume, pressure drop, and cost are constructed. Iterative optimization is carried out on channel length, single channel flow rate, and channel diameter to generate non-dominated solution set and Pareto front of the component. The component decision point is selected through proximity calculation, and the results of collaborative optimization of cycle conditions and component structure are output.

[0007] Furthermore, when constructing the conservation equations for the two types of cycles based on the heat source parameters and the supercritical carbon dioxide working fluid property parameter library, the following are included: A first and a second threshold for determining the critical state of carbon dioxide are preset, with the first threshold being less than the second threshold. The operating pressure and operating temperature parameters of each node in the two types of cycles are then used to determine the state partitions, which include the supercritical stable region, the near-critical abrupt change region, and the subcritical region. When both the node's operating pressure and operating temperature are greater than the second judgment threshold, it is determined to be in the supercritical stable region. The working fluid property parameters of the corresponding interval in the supercritical carbon dioxide working fluid property parameter library are called to participate in the calculation and solution of each conservation equation. When the node's operating pressure is greater than the second judgment threshold and the operating temperature is between the first judgment threshold and the second judgment threshold, it is judged as a near-critical mutation zone. After the step size of the encrypted physical property parameters is called and the continuity of the parameters is verified segment by segment, the parameters are substituted into each conservation equation to complete the calculation. When either the node's operating pressure or operating temperature is less than or equal to the first determination threshold, it is determined to be in the subcritical interval. The system then switches to the working fluid property calculation logic corresponding to the subcritical interval to complete the solution of each conservation equation.

[0008] Furthermore, when conducting iterative optimization at the loop level, it includes: A first flow threshold and a second flow threshold are preset, with the first flow threshold being less than the second flow threshold. At the same time, the upper and lower limits of the values ​​of each optimization variable and the threshold of the single iteration step size are preset. The optimization variables include working fluid flow rate, high and low operating pressure, minimum operating temperature, split ratio, heat exchanger effectiveness, and adiabatic internal efficiency. When the working fluid flow rate in a single iteration is less than or equal to the first flow threshold, it is determined to be a low flow condition. The maximum operating temperature parameter of the fixed cycle remains unchanged, and the heat exchange calculation logic corresponding to the low flow condition is matched to complete the solution of this iteration. When the working fluid flow rate in a single iteration is between the first flow threshold and the second flow threshold, it is determined to be a normal flow condition, and the benchmark calculation logic is directly used to complete the solution of this iteration. When the working fluid flow rate in a single iteration is greater than or equal to the second flow threshold, it is determined to be a high flow condition. The decrease in the highest operating temperature of the cycle is verified, and the heat absorption calculation logic corresponding to the high flow condition is corrected simultaneously to complete the solution of this iteration. When the iterative value of any optimization variable exceeds the pre-set upper and lower limit range, the variable value is automatically truncated to the corresponding interval boundary value, and the iteration result is marked as the boundary condition solution and included in the candidate solution set.

[0009] Furthermore, in generating the cyclic non-dominated solution set and the Pareto front, the following is included: Pre-set the dominance relationship determination rules and the crowding distance threshold, and perform fast non-dominated sorting on all iteratively generated work condition solutions; When any one working condition solution is better than another working condition solution on all objective functions, and at least one objective function is better, the former is determined to dominate the latter and the latter is removed from the candidate solution set; After determining and sorting the dominance relationships of all working condition solutions, the first set of non-dominated solutions with the highest sorting level is extracted as the initial Pareto front. For all solutions within the initial Pareto front, calculate the crowding distance between adjacent solutions; When the crowding distance between adjacent solutions is less than the crowding distance threshold, the solutions are determined to be overlapping and the solutions with high repetition are removed. When the crowding distance between adjacent solutions is greater than or equal to the crowding distance threshold, it is determined to be a valid distribution solution and is retained. After the screening is completed, a uniformly distributed final cyclic nondominated solution set and Pareto front are formed.

[0010] Furthermore, when selecting cyclic decision points through positive and negative ideal points and proximity calculations, the following steps are included: Two objective weighting modes are pre-defined: an entropy weighting mode based on the degree of data dispersion and a critical weighting mode based on the conflict of indicators. For all non-dominated solutions on the Pareto front, calculate the Euclidean distance of each solution relative to the positive and negative ideal points, and preliminarily calculate the original relative proximity of each solution based on the Euclidean distance; When using the entropy weighting mode, corresponding weights are assigned according to the data dispersion of each objective function. The objective function with higher dispersion is assigned a higher weight. After weighting and correcting the relative closeness of each solution, the solution with the highest closeness is output as the candidate entropy weight decision point. When the critical weighting mode is adopted, the corresponding weights are assigned by comprehensively considering the comparative strength of each objective function and the conflict between indicators. After weighting and correcting the relative closeness of each solution, the solution with the highest closeness is output as the final loop decision point. Extract the inlet and outlet thermal parameters of each component corresponding to the final loop decision point, and use them as boundary conditions for subsequent component-level optimization.

[0011] Furthermore, when extracting the inlet and outlet thermal parameters of each component as boundary conditions at the component level, the following are included: A first verification threshold and a second verification threshold are preset for the performance of the regenerator, and the first verification threshold is less than the second verification threshold; From the operating parameters corresponding to the final cycle decision point, the inlet and outlet temperatures, pressures, and mass flow parameters of the five core components—heater, regenerator, cooler, compressor, and turbine—are extracted respectively, and the theoretical heat exchange and theoretical effectiveness of the regenerator are calculated simultaneously. The theoretical calculation values ​​of the regenerator are compared with the iterative calculation values ​​of the circulation layer to identify the discrepancies. When the comparison deviation is less than or equal to the first verification threshold, all extracted parameters are determined to be valid and are directly used as the input boundary conditions for component-level optimization. When the comparison deviation is greater than the first verification threshold and less than the second verification threshold, the parameter is determined to be corrected, and the deviation verification is re-executed after the performance parameters of the regenerator are locally calibrated. When the comparison deviation is greater than or equal to the second verification threshold, the parameter is deemed invalid, and the process returns to the loop level to iterate and correct the relevant performance parameters of the regenerator until the deviation meets the verification requirements.

[0012] Furthermore, when setting the constraints on the effectiveness and heat exchange of the regenerator, the following are included: The minimum constraint thresholds for the effectiveness of the regenerator and the minimum constraint thresholds for the heat exchange of the regenerator are pre-set. Both types of thresholds are taken from the corresponding performance parameters output by the cycle decision point and serve as hard constraints for component structure iteration. Constraint verification is performed on the regenerator performance parameters output from a single structural iteration; When the effectiveness of the regenerator in a single iteration is greater than or equal to the minimum effectiveness constraint threshold, and the heat exchange is also greater than or equal to the minimum heat exchange constraint threshold, the structural scheme is determined to meet the performance constraints and is included in the candidate solution set for component optimization. When the regenerator effectiveness in a single iteration is less than the minimum effectiveness constraint threshold, but the heat exchange meets the constraint requirements, the scheme is judged as an effectiveness constraint violation, and is directly eliminated and the subsequent objective function calculation is skipped. When the heat exchange of the regenerator in a single iteration is less than the minimum constraint threshold for heat exchange and the effectiveness meets the constraint requirements, the scheme is judged as a heat exchange constraint violation, and is directly eliminated and the constraint violation type is marked simultaneously. When the effectiveness of the regenerator and the heat exchange rate in a single iteration do not meet the constraints, the scheme is judged as a double constraint violation, and is directly eliminated and all violation types are marked.

[0013] Furthermore, when selecting component decision points at the component level through proximity calculations, the following are included: Three target weight allocation modes are pre-defined: compression reduction priority mode, compact and low cost priority mode, and comprehensive balance mode. At the same time, the corresponding weight rules of volume, compression reduction and cost optimization targets are pre-defined for each mode. For all non-dominated solutions on the Pareto front of the component layer, calculate the relative proximity of each solution. When the pressure reduction priority mode is adopted, the allocation weight of the pressure reduction target is increased, and after weighted correction of the relative closeness of each solution, the solution with the highest closeness and closest to the optimal pressure reduction extreme point is selected as the low resistance candidate decision point. When adopting the compact and low-cost priority mode, the weight of volume and cost objectives is increased, and the relative closeness of each solution is adjusted by weighting. The solution with the highest closeness and closest to the optimal extreme point of volume and cost is selected as the compact alternative decision point. When the comprehensive equilibrium mode is adopted, the equilibrium weights of the three types of objectives are equally distributed. After the relative closeness of each solution is corrected by weighting, the solution with the highest closeness near the Pareto front inflection point is selected as the final component decision point. Extract the channel length, single-channel flow rate, and channel diameter structural parameters corresponding to the final component decision point as components of the collaborative optimization results.

[0014] Furthermore, before outputting the results of the co-optimization of the cyclic operating conditions and component structure, the following steps are included: A first verification threshold and a second verification threshold are pre-set for the loop component to match, and the first verification threshold is less than the second verification threshold; Substitute the actual pressure drop parameters corresponding to the component decision points into the thermodynamic control model at the cycle level, and recalculate the overall output power, efficiency and levelized cost of electricity performance index of the cycle. The recalculated cycle performance index is compared with the corresponding index of the original cycle decision point to identify the deviation. When the performance deviation is less than or equal to the first verification threshold, the cyclic operating condition and component structure are deemed to be in good match, and the collaborative optimization result can be directly output. When the performance deviation is greater than the first verification threshold and less than the second verification threshold, the matching degree is determined to be in need of optimization. After locally correcting the voltage drop boundary parameters at the loop level, the performance index is recalculated. When the performance deviation is greater than or equal to the second verification threshold, the matching is deemed unqualified, and the actual pressure drop of the component is returned to the loop level as a new constraint to start the loop multi-objective optimization iteration again. Repeatedly perform bidirectional iterative verification of the loop component until the performance deviation meets the threshold requirement.

[0015] Furthermore, when outputting the collaborative optimization results, the following are included: Three types of cycle selection modes are preset: power economy priority mode, energy efficiency priority mode, and comprehensive balance mode. At the same time, the performance selection judgment rules for simple regenerative cycle and recompression cycle are preset. Output complete collaborative optimization schemes after the simple regenerative cycle and recompression cycle have passed the matching verification. The schemes include cycle operation parameters and corresponding component structural parameters. When adopting the power economy priority mode, the output power and levelized cost of electricity of the two types of cycles are compared, and the simple regenerative cycle scheme with superior overall performance is selected as the final output result. When adopting the energy efficiency priority mode, the recompression cycle scheme with superior overall performance is selected as the final output by comparing the efficiency and energy utilization rate of the two types of cycles. When using the comprehensive equilibrium mode, the comprehensive closeness score of the two types of cyclic schemes is calculated separately, and the cyclic scheme with the highest comprehensive closeness score is selected as the final output result.

[0016] Compared with the prior art, the beneficial effects of the present invention are as follows: By adopting a hierarchical architecture of "cycle-level optimization → component-level optimization", the optimal operating parameters and performance indicators are first determined at the cycle level. Then, the regenerator structure is optimized using the component inlet and outlet thermal parameters at the cycle decision point as boundary conditions. This achieves bidirectional matching between cycle operating parameters and component geometric parameters, avoiding the defects of cycle optimization and component design being independent and parameter mismatch in traditional methods, and ensuring the consistency between cycle performance indicators and actual component structure.

[0017] A two-layer, multi-objective optimization system was constructed. At the cycle level, three objectives—output power, efficiency, and levelized cost of electricity—were simultaneously optimized, balancing dynamic performance, thermodynamic performance, and economic efficiency. At the component level, three objectives—regenerator volume, pressure drop, and cost—were simultaneously optimized, balancing compactness, flow performance, and economic efficiency. By employing the Pareto front and multi-objective decision-making methods, multiple mutually constraining objective functions were effectively balanced, avoiding the problem of rapid deterioration of other performance aspects due to optimization of a single indicator, and achieving comprehensive performance improvement across multiple dimensions.

[0018] A hierarchical optimization strategy is adopted. At the cyclic level, a system-level model is used for wide-range parameter optimization to ensure computational efficiency. At the component level, the parameter range is narrowed based on the cyclic optimization results, and then a refined one-dimensional flow and heat transfer model is performed to ensure design accuracy. This approach avoids the problems of excessive computational load and difficulty in performing wide-range parameter optimization in fully coupled modeling, while overcoming the shortcomings of simplified modeling, such as lack of component structure verification and difficulty in implementing optimization results. It achieves the best balance between computational efficiency and optimization accuracy.

[0019] Using the regenerator as the core component, a one-dimensional flow heat transfer model of a semi-circular straight-channel printed circuit board heat exchanger was established. The geometric parameters such as channel length, single-channel flow rate, and channel diameter were systematically optimized for multiple objectives. This replaced the traditional approach of directly giving component parameters based on experience, fully explored the performance improvement potential at the component level, and further improved the overall comprehensive performance of the circulation system. Attached Figure Description

[0020] Various other advantages and benefits will become apparent to those skilled in the art upon reading the following detailed description of preferred embodiments. The accompanying drawings are for illustrative purposes only and are not intended to limit the invention. Furthermore, the same reference numerals denote the same parts throughout the drawings. In the drawings: Figure 1 A flowchart illustrating the stratified optimization method for supercritical carbon dioxide cycle driven by waste heat from marine gas turbines, provided in an embodiment of the present invention.

[0021] Figure 2 The SSBC and RSBC cyclic Ts diagrams provided in this embodiment of the invention; Figure 3 Stacked graph showing the construction cost of the SSBC circulation device as a function of the working fluid flow rate, provided in an embodiment of the present invention; Figure 4 Stacked graph showing the construction cost of the RSBC circulation device as a function of the working fluid flow rate, as provided in the embodiments of the present invention. Detailed Implementation

[0022] Exemplary embodiments of the present disclosure will now be described in more detail with reference to the accompanying drawings. While exemplary embodiments of the present disclosure are shown in the drawings, it should be understood that the present disclosure may be implemented in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided to enable a more thorough understanding of the present disclosure and to fully convey the scope of the disclosure to those skilled in the art. It should be noted that, unless otherwise specified, embodiments and features in the embodiments of the present invention can be combined with each other. The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0023] Reference Figure 1 In some embodiments of this application, a stratified optimization method for supercritical carbon dioxide cycle driven by waste heat from a marine gas turbine includes the following steps: Step S100: Obtain the exhaust flow rate, temperature, and pressure heat source parameters of the marine gas turbine, match and establish a supercritical carbon dioxide working fluid property parameter library, and construct the mass conservation, energy conservation, entropy balance, and sludge balance equations for simple regenerative cycle and recompression cycle based on the pressure heat source parameters and the supercritical carbon dioxide working fluid property parameter library. Couple and establish the heat transfer equation of the heat exchanger, the energy equation of the compressor and turbine, and the mass, momentum, and energy conservation control equations of the hot and cold channels of the printed circuit board heat exchanger and the metal substrate. Step S200: Based on the control equations at the loop level, construct a multi-objective function for output power, efficiency, and levelized cost of electricity. Iteratively optimize the working fluid flow rate, high and low operating pressure, minimum operating temperature, split ratio, heat exchanger effectiveness, and adiabatic internal efficiency to generate a loop non-dominated solution set and Pareto front. Select the loop decision point through positive and negative ideal points and proximity calculations, and extract the inlet and outlet thermal parameters of each component. Step S300: Using the extracted component inlet and outlet thermal parameters as boundary conditions, set the regenerator effectiveness and heat exchange constraints, construct volume, pressure drop, and cost objective functions at the component level, perform iterative optimization on channel length, single channel flow rate, and channel diameter, generate component non-dominated solution set and Pareto front, select component decision points through proximity calculation, and output the cyclic operating condition and component structure co-optimization results.

[0024] The above embodiments, through a hierarchical architecture of "cycle-level optimization → component-level optimization", first determine the optimal operating parameters and performance indicators at the cycle level, and then carry out regenerator structure optimization with the component inlet and outlet thermal parameters at the cycle decision point as boundary conditions. This achieves bidirectional matching between cycle operating parameters and component geometric parameters, avoiding the defects of cycle optimization and component design being independent and parameter mismatch in traditional methods, and ensuring the consistency between cycle performance indicators and actual component structure.

[0025] The above embodiments construct a two-layer multi-objective optimization system. At the cycle level, it simultaneously optimizes three objectives: output power, efficiency, and levelized cost of electricity (LCOE), balancing dynamic performance, thermodynamic performance, and economic efficiency. At the component level, it simultaneously optimizes three objectives: regenerator volume, pressure drop, and cost, balancing compactness, flow performance, and economic efficiency. By employing the Pareto front and multi-objective decision-making methods, it effectively balances multiple mutually constraining objective functions, avoiding the problem of rapid deterioration of other performance aspects due to optimization of a single indicator, and achieving a comprehensive performance improvement across multiple dimensions.

[0026] The above embodiments employ a hierarchical and progressive optimization strategy. At the cyclic level, a system-level model is used for wide-range parameter optimization, ensuring computational efficiency. At the component level, the parameter range is narrowed based on the cyclic optimization results, and then a refined one-dimensional flow and heat transfer model is performed, ensuring design accuracy. This approach avoids the problems of excessive computational load and difficulty in performing wide-range parameter optimization associated with fully coupled modeling, while overcoming the shortcomings of simplified modeling, such as lack of component structure verification and difficulty in implementing optimization results. It achieves the best balance between computational efficiency and optimization accuracy.

[0027] The above embodiments establish a one-dimensional flow heat transfer model for a semi-circular straight-channel printed circuit board heat exchanger with the regenerator as the core component. The geometric parameters such as channel length, single-channel flow rate, and channel diameter are systematically optimized in a multi-objective manner, replacing the traditional approach of directly giving component parameters based on experience. This fully explores the performance improvement potential at the component level and further enhances the overall comprehensive performance of the circulation system.

[0028] Specifically, when constructing the conservation equations for two types of cycles based on the heat source parameters and the supercritical carbon dioxide working fluid property parameter library, the following are included: A first and a second threshold for determining the critical state of carbon dioxide are pre-set, with the first threshold being less than the second threshold. The operating pressure and operating temperature parameters of each node in the two types of cycles are then used to determine the state by partitioning. The state partitions include the supercritical stable region, the near-critical abrupt change region, and the subcritical region. When both the node's operating pressure and operating temperature exceed the second judgment threshold, it is determined to be in the supercritical stable region. The corresponding range of working fluid properties in the supercritical carbon dioxide working fluid property parameter library are then called to participate in the calculation and solution of various conservation equations. When the node's operating pressure is greater than the second judgment threshold and the operating temperature is between the first judgment threshold and the second judgment threshold, it is judged to be in the near-critical mutation zone. After the step size of the encrypted physical property parameters is called and the continuity of the parameters is verified segment by segment, the parameters are substituted into each conservation equation to complete the calculation. When either the node's operating pressure or operating temperature is less than or equal to the first judgment threshold, it is determined to be in the subcritical interval. The system then switches to the working fluid property calculation logic corresponding to the subcritical interval to complete the solution of each conservation equation.

[0029] Specifically, this step is the adaptive property calling step for working fluid state partitioning. Based on the characteristic of drastic changes in the physical parameters of supercritical carbon dioxide near the critical region, it sets two levels of judgment thresholds. The first judgment threshold corresponds to the critical parameters of carbon dioxide (critical temperature 304.2K, critical pressure 7.38MPa), and the second judgment threshold corresponds to the threshold where the physical property changes tend to be gradual (temperature 323.2K, pressure 8.0MPa). In this way, the operating pressure and temperature parameters of each state node in the simple regenerative cycle and recompression cycle are judged into three zones: supercritical stable region, near-critical abrupt change region, and subcritical region. When both node temperature and pressure are above the second threshold, the system is classified as a supercritical stable region with gentle property fluctuations. Data from the corresponding interval of the supercritical carbon dioxide working fluid property parameter library built on the CoolProp open-source library is directly called and substituted into equations for mass conservation and energy conservation, balancing computational efficiency and accuracy. When node pressure is above the second threshold and temperature is between the two thresholds, the system is classified as a near-critical abrupt change region with drastic property changes. In this region, the compressibility factor, density, viscosity, and thermal conductivity of the working fluid change significantly with temperature and pressure. The step size for calling property parameters needs to be encrypted, and the continuity of parameters needs to be verified segment by segment before being substituted into the equations for calculation, avoiding divergence and result deviations caused by property abrupt changes. When either node temperature or pressure is less than or equal to the first threshold, the system is classified as a subcritical region. The system switches to the property calculation logic corresponding to the subcritical region to complete the conservation equation solution, ensuring the stability and accuracy of the cyclic simulation calculation across the entire operating range.

[0030] Understandably, the working principle of this state partitioning determination is based on the characteristic that the compressibility factor, density, viscosity, and thermal conductivity of supercritical carbon dioxide change drastically with temperature and pressure near the critical temperature, and cannot be uniformly described by the ideal gas law. By presetting the first and second level of determination thresholds, the operating conditions of each node of the two types of cycles are divided into three categories: supercritical stable region, near-critical abrupt change region, and subcritical region. For the supercritical stable region where the property changes are gradual, the corresponding parameters of the working fluid property library are directly called to participate in the solution of the conservation equation. For the near-critical abrupt change region where the property changes nonlinearly, the numerical oscillation is weakened by encrypting the property call step size and verifying the continuity of parameters segment by segment. For the subcritical region, the appropriate property calculation logic is switched. In this way, while taking into account the computational efficiency, the accuracy and numerical stability of the mass conservation, energy conservation, entropy balance, and sludge balance equations under different operating conditions are ensured.

[0031] Specifically, when conducting iterative optimization at the loop level, it includes: A first flow threshold and a second flow threshold are preset, with the first flow threshold being less than the second flow threshold. At the same time, the upper and lower limits of the values ​​of each optimization variable and the threshold of the step size of a single iteration are preset. The optimization variables include working fluid flow rate, high and low operating pressure, minimum operating temperature, split ratio, heat exchanger effectiveness, and adiabatic internal efficiency. When the working fluid flow rate in a single iteration is less than or equal to the first flow threshold, it is determined to be a low flow condition. The maximum operating temperature parameter of the fixed cycle remains unchanged, and the heat exchange calculation logic corresponding to the low flow condition is matched to complete the solution of this iteration. When the working fluid flow rate in a single iteration is between the first flow rate threshold and the second flow rate threshold, it is determined to be a normal flow rate condition, and the benchmark calculation logic is directly used to complete the solution of this iteration. When the working fluid flow rate in a single iteration is greater than or equal to the second flow threshold, it is determined to be a high flow condition. The decrease in the highest operating temperature of the cycle is verified, and the heat absorption calculation logic corresponding to the high flow condition is corrected simultaneously to complete the solution of this iteration. When the iterative value of any optimization variable exceeds the pre-set upper and lower limit range, the variable value is automatically truncated to the corresponding interval boundary value, and the iteration result is marked as the boundary condition solution and included in the candidate solution set.

[0032] Specifically, in the iterative optimization process at the loop level, the optimization variables include the working fluid flow rate ( ), highest circulating pressure ( The value range is 15.0–30.0 MPa), and the minimum circulating pressure is ( The value range is 7.6–8.4 MPa), and the minimum operating temperature is ( (range 305.15–323.15K), split ratio ( (Limited to 0.5–0.9), heat exchanger effectiveness ( 0.75–0.95) and the internal adiabatic efficiency of the impeller machinery ( (0.75–0.90). Each optimization variable has pre-set upper and lower limits for its value and a single iteration step size threshold (where the working fluid flow rate step size is 5 kg / s, the maximum pressure step size is 0.5 MPa, the split ratio step size is 0.02, and the heat exchanger effectiveness and adiabatic internal efficiency step size are both 0.01) to control the precision of the search process and the computational burden.

[0033] Specifically, regarding the key variable of the working fluid flow rate, the iterative process divides the operating conditions into three intervals based on a preset first flow rate threshold (60 kg / s) and a second flow rate threshold (90 kg / s and 110 kg / s correspond to the peak output power points of SSBC and RSBC, respectively). When the working fluid flow rate in a single iteration is less than or equal to 60 kg / s, it is determined to be a low-flow operating condition, at which point the heat capacity flow rate on the S-CO2 side of the heater ( ˙ The heat exchanger efficiency is constrained by the S-CO2 side, which is relatively small compared to the gas exhaust side. Increasing the working fluid flow rate increases the heat absorption, but the maximum operating temperature of the cycle remains unchanged. Therefore, this temperature parameter is fixed, and the corresponding heat absorption calculation logic is matched to complete the iterative solution. When the working fluid flow rate is between 60 kg / s and the corresponding peak output power flow rate of the cycle (SSBC is 90 kg / s, RSBC is 110 kg / s), it is determined to be a normal flow rate condition. Within this range, the cycle thermal efficiency remains basically unchanged, and the output power increases approximately linearly with the flow rate. The baseline calculation logic is directly used to complete the solution. When the working fluid flow rate is greater than or equal to the above peak flow rate (i.e., the second flow rate threshold), it is determined to be a high flow rate condition. At this time, the heat capacity flow rate of the S-CO2 side exceeds that of the gas exhaust side. Continuing to increase the flow rate will cause the maximum cycle temperature to decrease, and the cycle thermal efficiency to decrease. Therefore, it is necessary to verify the magnitude of the decrease in the maximum cycle temperature and simultaneously correct the heat absorption calculation logic to complete the iterative solution.

[0034] Specifically, for all optimization variables, when the iterative value exceeds the pre-defined upper and lower limits, the algorithm automatically truncates the variable to the nearest boundary value and marks this set of solutions as boundary condition solutions, including them in the candidate solution set to ensure population diversity and the stability of the search process. This strategy is fully embedded in a multi-objective optimization framework based on the NSGA-II genetic algorithm, with a population size of 120, 100 generations, and parallel computation to shorten the solution time.

[0035] Understandably, in the iterative optimization at the loop level, the NSGA-II algorithm (population size 120, generation number 100, parallel computing) is used to search for variables such as working fluid flow rate (5–160 kg / s, step size 5 kg / s), maximum loop pressure (15–30 MPa, step size 0.5 MPa), minimum pressure (7.6–8.4 MPa), minimum temperature (305.15–323.15 K), split ratio (0.5–0.9, step size 0.02), heat exchanger effectiveness (0.75–0.95, step size 0.01), and adiabatic internal efficiency (0.75–0.90, step size 0.01). When the working fluid flow rate is ≤60kg / s (small flow rate, the heat capacity flow rate on the S-CO2 side is small, and the effectiveness is limited to this side), the highest circulating temperature is fixed and the corresponding heat absorption logic is matched; when the flow rate is between 60kg / s and the second threshold (SSBC is 90kg / s, RSBC is 110kg / s, i.e. their respective output power peak points), the baseline calculation logic is used; when the flow rate is ≥ the peak threshold (large flow rate, the heat capacity flow rate on the S-CO2 side exceeds that on the gas exhaust side), the temperature drop is checked and the heat absorption logic is corrected; if any variable goes out of bounds, it is truncated to the boundary value and marked as the boundary condition solution and included in the candidate set, thereby completing the multi-objective iterative solution.

[0036] Specifically, in generating the cyclic non-dominated solution set and the Pareto front, the following is included: Pre-set the dominance relationship determination rules and the crowding distance threshold, and perform fast non-dominated sorting on all iteratively generated work condition solutions; When any one working condition solution is better than another working condition solution on all objective functions, and at least one objective function is better, the former is determined to dominate the latter and the latter is removed from the candidate solution set; After determining and sorting the dominance relationships of all working condition solutions, the first set of non-dominated solutions with the highest sorting level is extracted as the initial Pareto front. Calculate the crowding distance between adjacent solutions for all solutions within the initial Pareto front; When the crowding distance between adjacent solutions is less than the crowding distance threshold, the solutions are judged to be overlapping and the solutions with high repetition are removed. When the crowding distance between adjacent solutions is greater than or equal to the crowding distance threshold, it is determined to be a valid distribution solution and is retained. After the screening is completed, a uniformly distributed final cyclic nondominated solution set and Pareto front are formed.

[0037] Specifically, in the multi-objective optimization process at the iterative level, the NSGA-II genetic algorithm (population size 120, evolutionary generations 100, parallel computing) is used to perform fast non-dominated sorting and crowding distance calculation on all iteratively generated operating condition solutions. The core mechanism of this algorithm is: when any operating condition solution is not inferior to another operating condition solution in all three objective functions (maximizing output power, maximizing efficiency, and minimizing levelized cost of electricity), and at least one objective function is strictly superior to the other, then the former is determined to dominate the latter, and the dominated solution is removed from the candidate solution set. After completing the dominance relationship determination and hierarchical sorting of all operating condition solutions, the first-level non-dominated solution set with the highest sorting level is extracted to form the initial Pareto front—this front is distributed in an approximately concave triangular surface in the three-dimensional target space, with the vertices corresponding to the extreme points of each single performance index. To further ensure the uniform distribution of the front solutions, the crowding distance of adjacent solutions is calculated for all solutions within the front. When the distance is less than a preset threshold, it is determined to be an overlapping solution and is removed; when the distance is greater than or equal to the threshold, it is determined to be a valid distributed solution and is retained. Ultimately, through an elite strategy, superior individuals from the parent generation are preserved, resulting in a uniformly distributed cyclic non-dominated solution set and a Pareto front.

[0038] Understandably, in cyclic multi-objective optimization, the NSGA-II algorithm (population size 120, generation 100) performs fast non-dominated sorting on all iteratively generated solutions: dominance is determined based on three objective functions (maximizing output power, maximizing efficiency, and minimizing LCOE). If a solution is not inferior to another solution in all objectives and is strictly superior in at least one objective, then the former is determined to dominate the latter and is removed from the candidate solution set. After completing the full determination and hierarchical sorting, the highest level (first layer) non-dominated solutions are extracted as the initial Pareto front (distributed as a three-dimensional concave triangular surface, with vertices corresponding to the extreme points of each single objective). Then, the crowding distance between adjacent solutions is calculated for all solutions within the front. Overlapping solutions with a distance less than the threshold are removed, and effective solutions with a distance greater than or equal to the threshold are retained. Finally, an elite strategy is combined to form a uniformly distributed cyclic non-dominated solution set and a Pareto front.

[0039] Specifically, when selecting cyclic decision points through positive and negative ideal points and proximity calculations, the following are included: Two objective weighting modes are pre-defined: an entropy weighting mode based on the degree of data dispersion and a critical weighting mode based on the conflict of indicators. For all non-dominated solutions on the Pareto front, calculate the Euclidean distance of each solution relative to the positive and negative ideal points, and preliminarily calculate the original relative proximity of each solution based on the Euclidean distance; When using the entropy weighting mode, corresponding weights are assigned according to the data dispersion of each objective function. The objective function with higher dispersion is assigned a higher weight. After weighting and correcting the relative closeness of each solution, the solution with the highest closeness is output as the candidate entropy weight decision point. When the critical weighting mode is adopted, the corresponding weights are assigned by comprehensively considering the comparative strength of each objective function and the conflict between indicators. After weighting and correcting the relative closeness of each solution, the solution with the highest closeness is output as the final loop decision point. Extract the inlet and outlet thermal parameters of each component corresponding to the final loop decision point, and use them as boundary conditions for subsequent component-level optimization.

[0040] Specifically, this step is the core of the TOPSIS multi-attribute decision-making process for selecting the optimal operating condition after cyclic multi-objective optimization. The cyclic optimization objectives in this paper include three mutually constraining indices: output power, efficiency, and levelized cost of electricity (LCOE). Two objective weighting schemes without subjective human intervention—the entropy weight method and the Critic critical weight method—are pre-configured. For all non-dominated optimal solutions of the cyclic Pareto front obtained by the NSGA-II algorithm, positive and negative ideal reference points are constructed in the three-dimensional objective space. The Euclidean distance from each feasible solution to the two types of reference points is calculated, and the original proximity without weight correction is obtained based on the distance ratio. When using the entropy weight mode, the target datasets are used... Information entropy quantifies the degree of dispersion. The LCOE index data has the largest dispersion and higher information entropy, so it is assigned a larger weight to complete the proximity weight correction, and the peak proximity solution is selected as the entropy weight candidate decision point. When adopting the Critic critical weight mode, the weight is assigned while taking into account the contrast intensity of each target and the conflict relationship between the indicators. The balance between power, efficiency, and cost is comprehensively considered. The operating condition corresponding to the maximum proximity value after correction is set as the cyclic optimal decision point. Finally, the inlet and outlet temperatures, pressures, and working fluid flow thermodynamic parameters of all equipment such as heater, regenerator, cooler, compressor, and turbine under this decision point are extracted and fixed as the input boundary constraints for the structural optimization of printed circuit board regenerator components.

[0041] Understandably, this step relies on the TOPSIS multi-attribute decision-making principle to construct positive and negative ideal points for the Pareto non-dominated solution set of the cyclic three-objective problem obtained by NSGA-II. The original proximity is calculated by Euclidean distance, and the proximity is corrected by weighting the entropy weight method (which reflects the dispersion of the objective) and the Critic objective weighting method (which takes into account the intensity of comparison and conflict of the indicators). The optimal decision point of the cyclic equilibrium is selected, and the thermal parameters of all equipment inlet and outlet under this working condition are extracted to provide fixed boundary conditions for the structural optimization of the regenerator components.

[0042] Specifically, when extracting the inlet and outlet thermal parameters of each component as boundary conditions at the component level, the following are included: A first verification threshold and a second verification threshold are preset for the performance of the regenerator, and the first verification threshold is less than the second verification threshold; From the operating parameters corresponding to the final cycle decision point, the inlet and outlet temperatures, pressures, and mass flow parameters of the five core components—heater, regenerator, cooler, compressor, and turbine—are extracted respectively, and the theoretical heat exchange and theoretical effectiveness of the regenerator are calculated simultaneously. The theoretical calculation values ​​of the regenerator are compared with the iterative calculation values ​​of the circulation layer to identify the discrepancies. When the comparison deviation is less than or equal to the first verification threshold, all extracted parameters are deemed valid and directly used as the input boundary conditions for component-level optimization. When the comparison deviation is greater than the first verification threshold and less than the second verification threshold, the parameter is determined to be corrected. After the performance parameters of the regenerator are locally calibrated, the deviation verification is re-executed. When the comparison deviation is greater than or equal to the second verification threshold, the parameter is deemed invalid, and the process returns to the loop level to iterate and correct the relevant performance parameters of the regenerator until the deviation meets the verification requirements.

[0043] Specifically, after completing the multi-objective optimization at the cyclic level and determining the TOPSISCritic decision point, the inlet and outlet thermodynamic parameters of each component corresponding to that decision point are extracted as input boundary conditions for subsequent regenerator structure optimization. Specifically, from... Figure 2 From the listed TOPSISCritic decision point operating parameters, parameters such as temperature, pressure, and working fluid mass flow rate at each key node of the cycle are extracted to determine the inlet and outlet states of the hot and cold sides of the regenerator. Simultaneously, based on the effectiveness (0.959 for the SSBC regenerator, 0.951 for the RSBC high-temperature regenerator, and 0.943 for the low-temperature regenerator) and heat transfer (approximately 19.96 kW for the SSBC regenerator, approximately 17.19 kW for the RSBC high-temperature regenerator, and approximately 5.20 kW for the low-temperature regenerator) determined at this decision point, such as... Figure 3 , 4 The performance constraint parameters shown are used as performance constraints for the regenerator design. These are directly substituted into the multi-objective optimization problem shown in equation (20) (the constraint conditions are...). and ≥ The entire boundary condition extraction process is a one-time direct mapping.

[0044] Specifically, when setting the constraints on the effectiveness and heat exchange capacity of the regenerator, the following should be included: The minimum constraint thresholds for the effectiveness of the regenerator and the minimum constraint thresholds for the heat exchange of the regenerator are pre-set. Both types of thresholds are taken from the corresponding performance parameters output by the cycle decision point and serve as hard constraints for component structure iteration. Constraint verification is performed on the regenerator performance parameters output from a single structural iteration; When the effectiveness of the regenerator in a single iteration is greater than or equal to the minimum effectiveness constraint threshold, and the heat exchange is also greater than or equal to the minimum heat exchange constraint threshold, the structural scheme is determined to meet the performance constraints and is included in the candidate solution set for component optimization. When the regenerator effectiveness in a single iteration is less than the minimum effectiveness constraint threshold, but the heat exchange meets the constraint requirements, the scheme is judged as an effectiveness constraint violation, and is directly eliminated and the subsequent objective function calculation is skipped. When the heat exchange of the regenerator in a single iteration is less than the minimum constraint threshold for heat exchange and the effectiveness meets the constraint requirements, the scheme is judged as a heat exchange constraint violation, and is directly eliminated and the constraint violation type is marked simultaneously. When the effectiveness of the regenerator and the heat exchange rate in a single iteration do not meet the constraints, the scheme is judged as a double constraint violation, and is directly eliminated and all violation types are marked.

[0045] Specifically, this step belongs to the constraint verification process before multi-objective optimization of the printed circuit board type semi-circular straight-channel regenerator component. Based on the regenerator performance indicators output by the TOPSISCritic decision point in the circulation layer, the corresponding effectiveness and heat transfer values ​​are extracted as the minimum constraint thresholds for regenerator effectiveness and heat transfer, respectively. In the paper, the SSBC regenerator effectiveness is approximately 0.959 and heat transfer is 19.80MW, the RSBC high-temperature regenerator effectiveness is approximately 0.951 and heat transfer is 17.19MW, and the RSBC low-temperature regenerator effectiveness is approximately 0.943 and heat transfer is 5.20MW. These values ​​are used as the hard performance lower limit for the iterative solution of the component structure. After each round of iterative solution of channel length, single-channel flow rate, and channel diameter to obtain the regenerator performance parameters, a dual-channel optimization is immediately performed. For indicator constraint verification, if the regenerator effectiveness is greater than or equal to the corresponding minimum threshold and the heat exchange is greater than or equal to the corresponding minimum threshold in the iteration results, it indicates that the geometry can match the thermal requirements of the cycle level. The scheme is then included in the candidate solution set for component optimization for subsequent calculations of volume, pressure drop, and cost targets. If only the effectiveness is lower than the threshold and the heat exchange meets the target, it is judged as an effectiveness constraint violation, and the structure is directly discarded and the objective function solution step is skipped. If only the heat exchange is lower than the threshold and the effectiveness meets the target, it is judged as a heat exchange constraint violation, and the scheme is eliminated while marking the violation category for subsequent parameter tuning. If both the effectiveness and heat exchange parameters are lower than the set threshold, it is judged as a double constraint violation, and the scheme is directly eliminated while simultaneously marking both types of violation information. This significantly reduces the computational workload of invalid schemes and ensures that all regenerator structures participating in multi-objective optimization can meet the heat exchange requirements of the cycle operation.

[0046] Understandably, this step uses the regenerator effectiveness and heat exchange output from the cyclic optimal decision point as the lower limit hard constraint for component iteration. After each round of regenerator structural parameter iteration, the heat exchange performance is checked. Only when the effectiveness and heat exchange meet the standards simultaneously is the structure retained for multi-objective solution of volume, pressure drop, and cost. If any one or two indicators fail to meet the standards, the corresponding scheme is directly eliminated and the violation type is marked, and subsequent objective calculations are skipped to reduce invalid calculations and ensure that the selected regenerator structures can match the cyclic thermal requirements.

[0047] Specifically, when selecting component decision points at the component level based on proximity calculations, the following are included: Three target weight allocation modes are pre-defined: compression reduction priority mode, compact and low cost priority mode, and comprehensive balance mode. At the same time, the corresponding weight rules of volume, compression reduction and cost optimization targets are pre-defined for each mode. For all non-dominated solutions on the Pareto front of the component layer, calculate the relative proximity of each solution. When the pressure reduction priority mode is adopted, the allocation weight of the pressure reduction target is increased, and after weighted correction of the relative closeness of each solution, the solution with the highest closeness and closest to the optimal pressure reduction extreme point is selected as the low resistance candidate decision point. When adopting the compact and low-cost priority mode, the weight of volume and cost objectives is increased, and the relative closeness of each solution is adjusted by weighting. The solution with the highest closeness and closest to the optimal extreme point of volume and cost is selected as the compact alternative decision point. When the comprehensive equilibrium mode is adopted, the equilibrium weights of the three types of objectives are equally distributed. After the relative closeness of each solution is corrected by weighting, the solution with the highest closeness near the Pareto front inflection point is selected as the final component decision point. Extract the channel length, single-channel flow rate, and channel diameter structural parameters corresponding to the final component decision point as components of the collaborative optimization results.

[0048] Specifically, this step is a TOPSIS decision-making and screening process for a semi-circular straight-channel printed circuit board regenerator component after multi-objective optimization. The component optimization uses three conflicting optimization objectives: regenerator volume, flow pressure drop, and manufacturing cost. Optimization variables include channel length, single-channel flow rate on the hot and cold sides, and channel diameter. The generated Pareto front exhibits an L-shaped distribution, with the optimal extreme points for volume and cost coinciding, and the optimal extreme points for pressure drop distributed on both sides of the inflection point at the two ends of the curve. Three weight allocation modes are pre-set: pressure drop priority, compact low-cost priority, and comprehensive equilibrium, each with differentiated weight rules. The comprehensive equilibrium mode allocates weights equally to the three objectives of volume, pressure drop, and cost. All non-dominated solutions of the component's Pareto front are traversed, and the relative proximity of each solution is calculated. When the pressure drop priority mode is selected, the weight of the pressure drop objective is increased, and the solution with the highest proximity and closest pressure drop is selected. The scheme with the minimum value is used as a low-resistance candidate. When the compact and low-cost priority mode is selected, the weights of the volume and cost objectives are increased, and the compact candidate is selected that is close to the minimum value of volume and cost. When the comprehensive equilibrium mode is selected, the three types of objectives are equally weighted, and the solution with the maximum proximity at the inflection point of the L-shaped Pareto front is selected as the final component decision point. In the paper, the channel length of the SSBC regenerator comprehensive equilibrium TOPSISCritic decision point is 523.5 mm, and the diameters of the hot and cold channels are 2.1 mm and 2.2 mm, respectively. The channel length of the RSBC high-temperature regenerator is 508.5 mm, and the diameters of the hot and cold channels are 2.6 mm and 2.9 mm. The channel length of the RSBC low-temperature regenerator is 503.7 mm, and the diameters of the hot and cold channels are 2.0 mm and 2.0 mm. The geometric parameters of this set are extracted as the component structure output parameters of the cycle-component co-optimization results.

[0049] Understandably, this step uses the TOPSIS decision-making method to screen the Pareto front solution set obtained from the optimization of the regenerator components. It pre-sets three weight allocation rules: pressure drop priority, compact and low cost priority, and comprehensive balance, which respectively focus on pressure drop, volume and cost, and the balance of the three types of objectives. The relative closeness of each non-dominated solution is calculated by weighting the solutions with different weights, and the corresponding optimal alternative is selected according to the requirements. The comprehensive balance mode selects the optimal solution at the Pareto front inflection point as the final component solution, and extracts the channel length, single channel flow rate, and channel diameter geometric parameters of the solution as the result of the co-optimization of the cycle and the component.

[0050] Specifically, before outputting the results of the collaborative optimization of the cyclic operating conditions and component structure, the following are included: The loop component is pre-set to match a first verification threshold and a second verification threshold, wherein the first verification threshold is less than the second verification threshold; Substitute the actual pressure drop parameters corresponding to the component decision points into the thermodynamic control model at the cycle level, and recalculate the overall output power, efficiency and levelized cost of electricity performance index of the cycle. The recalculated cycle performance index is compared with the corresponding index of the original cycle decision point to identify the deviation. When the performance deviation is less than or equal to the first verification threshold, the cyclic operating condition and component structure are deemed to be in good match, and the collaborative optimization result can be directly output. When the performance deviation is greater than the first verification threshold but less than the second verification threshold, the matching degree is determined to be in need of optimization. After locally correcting the voltage drop boundary parameters at the loop level, the performance index is recalculated. When the performance deviation is greater than or equal to the second verification threshold, the matching is deemed unqualified, and the actual pressure drop of the component is returned to the loop level as a new constraint to start the loop multi-objective optimization iteration again. Repeatedly perform bidirectional iterative verification of the loop component until the performance deviation meets the threshold requirement.

[0051] Specifically, this step involves a bidirectional iterative verification process for the coordinated matching of the cyclic operating conditions and the printed circuit board regenerator structure. This compensates for the original paper's unidirectional layered optimization, which failed to consider the reverse impact of actual pressure drop on cyclic performance. Two levels of performance deviation judgment thresholds are pre-set, with the first and second verification thresholds progressively widening the allowable deviation range. The actual channel flow pressure drop corresponding to the component's TOPSISCritic decision point is substituted into the global thermodynamic conservation control equations of the SSBC and RSBC cycles. The three core indicators—system output power, efficiency, and levelized cost of electricity (LCOE)—are recalculated and compared with the performance values ​​of the original decision point in the previous cyclic layer, which did not account for actual pressure drop. If the deviation between the old and new performance indicators is less than or equal to the first verification threshold... The first verification threshold indicates that the pressure drop of the regenerator structure has minimal impact on the cycle performance, and the cycle and components are properly matched, allowing for the direct output of the complete collaborative optimization scheme. If the deviation is between the two thresholds, the matching effect is deemed insufficient, and the performance is recalculated after only minor adjustments to the regenerator pressure drop boundary parameters within the cycle model. If the deviation is greater than or equal to the second verification threshold, it indicates that the component pressure drop deviates significantly from the cycle's preset ideal value, resulting in a matching failure. The actual component pressure drop is then used as a hard constraint and returned to the cycle optimization layer to re-perform NSGA-II multi-objective optimization. This process is repeated iteratively until the performance deviation falls within the first threshold range, ensuring that the cycle operating parameters are fully adapted to the regenerator geometry and avoiding the problems of parameter fragmentation between upper and lower layers in hierarchical optimization and distortion of optimization results.

[0052] Understandably, this step employs a two-way verification and matching mechanism between the cycle and components, sets two levels of performance deviation verification thresholds, substitutes the actual pressure drop obtained from component optimization into the cycle thermodynamic model to recalculate power, efficiency, and levelized cost of electricity, compares the deviations between the recalculated indicators and the original cycle decision point indicators, and performs three processing methods based on the threshold range of the deviation: direct output, local correction of pressure drop parameters, and adding pressure drop constraints to return to cycle optimization. The two-way iterative verification is repeated until the performance deviation meets the first-level threshold standard, ensuring that the cycle operating conditions and the regenerator component structure are mutually compatible and unified.

[0053] Specifically, when outputting the collaborative optimization results, the following are included: Three types of cycle selection modes are preset: power economy priority mode, energy efficiency priority mode, and comprehensive balance mode. At the same time, the performance selection judgment rules for simple regenerative cycle and recompression cycle are preset. Output complete collaborative optimization schemes after the simple regenerative cycle and recompression cycle have passed the matching verification. The schemes include cycle operation parameters and corresponding component structural parameters. When adopting the power economy priority mode, the output power and levelized cost of electricity of the two types of cycles are compared, and the simple regenerative cycle scheme with superior overall performance is selected as the final output result. When adopting the energy efficiency priority mode, the recompression cycle scheme with superior overall performance is selected as the final output by comparing the efficiency and energy utilization rate of the two types of cycles. When using the comprehensive equilibrium mode, the comprehensive closeness score of the two types of cyclic schemes is calculated separately, and the cyclic scheme with the highest comprehensive closeness score is selected as the final output result.

[0054] Specifically, this step involves the final scheme selection output stage after completing the bidirectional matching verification of the cycle and components. Based on the inherent performance differences between the two types of S-CO2 systems (Simple Regenerative Cycle SSBC and Recompression Cycle RSBC) described in the paper, three sets of selection logic are set up. Three selection modes—power economy priority, energy efficiency priority, and comprehensive balance—are pre-configured with corresponding indicator judgment standards. After successful bidirectional iterative verification, two complete schemes are generated. Each scheme includes cycle thermodynamic parameters such as working fluid flow rate, high and low pressure, and split ratio, as well as PCHE regenerator structural parameters such as channel diameter, channel length, and single-channel flow rate. The two schemes are compared under the power economy priority mode. In terms of output power and levelized cost of electricity (LCOE), the paper shows that the SSBC has higher output power and lower LCOE, so the SSBC scheme is preferred. In the energy efficiency priority mode, comparing heat exchange efficiency and energy utilization rate, the RSBC heat exchange efficiency is about 2.1% higher than the SSBC, and its heat exchange and energy utilization level are better, so the RSBC scheme is selected. The comprehensive balance mode adopts the TOPSIS comprehensive closeness scoring mechanism, which calculates the comprehensive score of the two systems by simultaneously weighting power, heat exchange efficiency and cost. The cyclic scheme with the higher comprehensive closeness value is selected as the final optimization result for output, which can adapt to the system selection requirements under different ship operation needs.

[0055] Understandably, this step pre-sets three cycle selection modes—power economy priority, energy efficiency priority, and comprehensive balance—and corresponding judgment rules. It first outputs two complete optimized schemes: a simple regeneration cycle and a recompression cycle, which have passed bidirectional matching verification and include cycle thermodynamic parameters and regenerator structural parameters. The power economy mode compares power and levelized cost of electricity to select the simple regeneration cycle, while the energy efficiency mode compares efficiency and energy utilization rate to select the recompression cycle. The comprehensive balance mode calculates the comprehensive closeness score of the two schemes and outputs the final collaborative optimization scheme that adapts to different design requirements of the ship.

[0056] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program goods. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program goods embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0057] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program goods according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0058] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0059] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0060] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the specific implementation of the present invention. Any modifications or equivalent substitutions that do not depart from the spirit and scope of the present invention should be covered within the scope of protection of the claims of the present invention.

Claims

1. A stratified optimization method for supercritical carbon dioxide cycle driven by waste heat from marine gas turbines, characterized in that, include: The exhaust flow rate, temperature, and pressure heat source parameters of marine gas turbines are obtained, and a supercritical carbon dioxide working fluid property parameter library is established. Based on the pressure heat source parameters and the supercritical carbon dioxide working fluid property parameter library, the mass conservation, energy conservation, entropy balance, and sludge balance equations for simple regenerative cycles and recompression cycles are constructed sequentially. The heat transfer equations of heat exchangers, the energy equations of compressors and turbines, and the mass, momentum, and energy conservation control equations of hot and cold channels and metal substrates of printed circuit board heat exchangers are coupled and established. Based on the control equations at the cyclic level, a multi-objective function is constructed for output power, efficiency, and levelized cost of electricity. Iterative optimization is carried out on working fluid flow rate, high and low operating pressure, minimum operating temperature, split ratio, heat exchanger effectiveness, and adiabatic internal efficiency to generate a cyclic non-dominated solution set and Pareto front. The cyclic decision point is selected by positive and negative ideal points and proximity calculations, and the inlet and outlet thermal parameters of each component are extracted. Using the extracted inlet and outlet thermal parameters of the component as boundary conditions, the effectiveness and heat exchange constraints of the regenerator are set. At the component level, objective functions of volume, pressure drop, and cost are constructed. Iterative optimization is carried out on channel length, single channel flow rate, and channel diameter to generate non-dominated solution set and Pareto front of the component. The component decision point is selected through proximity calculation, and the results of collaborative optimization of cycle conditions and component structure are output.

2. The stratified optimization method for supercritical carbon dioxide cycle driven by waste heat from marine gas turbines according to claim 1, characterized in that, When constructing conservation equations for two types of cycles based on heat source parameters and a database of supercritical carbon dioxide working fluid properties, the following are included: A first and a second threshold for determining the critical state of carbon dioxide are preset, with the first threshold being less than the second threshold. The operating pressure and operating temperature parameters of each node in the two types of cycles are then used to determine the state partitions, which include the supercritical stable region, the near-critical abrupt change region, and the subcritical region. When both the node's operating pressure and operating temperature are greater than the second judgment threshold, it is determined to be in the supercritical stable region. The working fluid property parameters of the corresponding interval in the supercritical carbon dioxide working fluid property parameter library are called to participate in the calculation and solution of each conservation equation. When the node's operating pressure is greater than the second judgment threshold and the operating temperature is between the first judgment threshold and the second judgment threshold, it is judged as a near-critical mutation zone. After the step size of the encrypted physical property parameters is called and the continuity of the parameters is verified segment by segment, the parameters are substituted into each conservation equation to complete the calculation. When either the node's operating pressure or operating temperature is less than or equal to the first determination threshold, it is determined to be in the subcritical interval. The system then switches to the working fluid property calculation logic corresponding to the subcritical interval to complete the solution of each conservation equation.

3. The stratified optimization method for supercritical carbon dioxide cycle driven by waste heat from marine gas turbines according to claim 2, characterized in that, When performing iterative optimization at the loop level, it includes: A first flow threshold and a second flow threshold are preset, with the first flow threshold being less than the second flow threshold. At the same time, the upper and lower limits of the values ​​of each optimization variable and the threshold of the single iteration step size are preset. The optimization variables include working fluid flow rate, high and low operating pressure, minimum operating temperature, split ratio, heat exchanger effectiveness, and adiabatic internal efficiency. When the working fluid flow rate in a single iteration is less than or equal to the first flow threshold, it is determined to be a low flow condition. The maximum operating temperature parameter of the fixed cycle remains unchanged, and the heat exchange calculation logic corresponding to the low flow condition is matched to complete the solution of this iteration. When the working fluid flow rate in a single iteration is between the first flow threshold and the second flow threshold, it is determined to be a normal flow condition, and the benchmark calculation logic is directly used to complete the solution of this iteration. When the working fluid flow rate in a single iteration is greater than or equal to the second flow threshold, it is determined to be a high flow condition. The decrease in the highest operating temperature of the cycle is verified, and the heat absorption calculation logic corresponding to the high flow condition is corrected simultaneously to complete the solution of this iteration. When the iterative value of any optimization variable exceeds the pre-set upper and lower limit range, the variable value is automatically truncated to the corresponding interval boundary value, and the iteration result is marked as the boundary condition solution and included in the candidate solution set.

4. The stratified optimization method for supercritical carbon dioxide cycle driven by waste heat from marine gas turbines according to claim 3, characterized in that, In generating the cyclic non-dominated solution set and the Pareto front, the following are included: Pre-set the dominance relationship determination rules and the crowding distance threshold, and perform fast non-dominated sorting on all iteratively generated work condition solutions; When any one working condition solution is better than another working condition solution on all objective functions, and at least one objective function is better, the former is determined to dominate the latter and the latter is removed from the candidate solution set; After determining and sorting the dominance relationships of all working condition solutions, the first set of non-dominated solutions with the highest sorting level is extracted as the initial Pareto front. For all solutions within the initial Pareto front, calculate the crowding distance between adjacent solutions; When the crowding distance between adjacent solutions is less than the crowding distance threshold, the solutions are determined to be overlapping and the solutions with high repetition are removed. When the crowding distance between adjacent solutions is greater than or equal to the crowding distance threshold, it is determined to be a valid distribution solution and is retained. After the screening is completed, a uniformly distributed final cyclic nondominated solution set and Pareto front are formed.

5. The stratified optimization method for supercritical carbon dioxide cycle driven by waste heat from marine gas turbines according to claim 4, characterized in that, When selecting cyclic decision points using positive and negative ideal points and proximity calculations, the following steps are included: Two objective weighting modes are pre-defined: an entropy weighting mode based on the degree of data dispersion and a critical weighting mode based on the conflict of indicators. For all non-dominated solutions on the Pareto front, calculate the Euclidean distance of each solution relative to the positive and negative ideal points, and preliminarily calculate the original relative proximity of each solution based on the Euclidean distance; When using the entropy weighting mode, corresponding weights are assigned according to the data dispersion of each objective function. The objective function with higher dispersion is assigned a higher weight. After weighting and correcting the relative closeness of each solution, the solution with the highest closeness is output as the candidate entropy weight decision point. When the critical weighting mode is adopted, the corresponding weights are assigned by comprehensively considering the comparative strength of each objective function and the conflict between indicators. After weighting and correcting the relative closeness of each solution, the solution with the highest closeness is output as the final loop decision point. Extract the inlet and outlet thermal parameters of each component corresponding to the final loop decision point, and use them as boundary conditions for subsequent component-level optimization.

6. The stratified optimization method for supercritical carbon dioxide cycle driven by waste heat from marine gas turbines according to claim 5, characterized in that, When extracting the inlet and outlet thermal parameters of each component as boundary conditions at the component level, the following are included: A first verification threshold and a second verification threshold are preset for the performance of the regenerator, and the first verification threshold is less than the second verification threshold; From the operating parameters corresponding to the final cycle decision point, the inlet and outlet temperatures, pressures, and mass flow parameters of the five core components—heater, regenerator, cooler, compressor, and turbine—are extracted respectively, and the theoretical heat exchange and theoretical effectiveness of the regenerator are calculated simultaneously. The theoretical calculation values ​​of the regenerator are compared with the iterative calculation values ​​of the circulation layer to identify the discrepancies. When the comparison deviation is less than or equal to the first verification threshold, all extracted parameters are determined to be valid and are directly used as the input boundary conditions for component-level optimization. When the comparison deviation is greater than the first verification threshold and less than the second verification threshold, the parameter is determined to be corrected, and the deviation verification is re-executed after the performance parameters of the regenerator are locally calibrated. When the comparison deviation is greater than or equal to the second verification threshold, the parameter is deemed invalid, and the process returns to the loop level to iterate and correct the relevant performance parameters of the regenerator until the deviation meets the verification requirements.

7. The stratified optimization method for supercritical carbon dioxide cycle driven by waste heat from marine gas turbines according to claim 6, characterized in that, When setting the effectiveness and heat exchange constraints of the regenerator, the following should be included: The minimum constraint thresholds for the effectiveness of the regenerator and the minimum constraint thresholds for the heat exchange of the regenerator are pre-set. Both types of thresholds are taken from the corresponding performance parameters output by the cycle decision point and serve as hard constraints for component structure iteration. Constraint verification is performed on the regenerator performance parameters output from a single structural iteration; When the effectiveness of the regenerator in a single iteration is greater than or equal to the minimum effectiveness constraint threshold, and the heat exchange is also greater than or equal to the minimum heat exchange constraint threshold, the structural scheme is determined to meet the performance constraints and is included in the candidate solution set for component optimization. When the regenerator effectiveness in a single iteration is less than the minimum effectiveness constraint threshold, but the heat exchange meets the constraint requirements, the scheme is judged as an effectiveness constraint violation, and is directly eliminated and the subsequent objective function calculation is skipped. When the heat exchange of the regenerator in a single iteration is less than the minimum constraint threshold for heat exchange and the effectiveness meets the constraint requirements, the scheme is judged as a heat exchange constraint violation, and is directly eliminated and the constraint violation type is marked simultaneously. When the effectiveness of the regenerator and the heat exchange rate in a single iteration do not meet the constraints, the scheme is judged as a double constraint violation, and is directly eliminated and all violation types are marked.

8. The stratified optimization method for supercritical carbon dioxide cycle driven by waste heat from marine gas turbines according to claim 7, characterized in that, When selecting component decision points at the component level using proximity calculations, the following are included: Three target weight allocation modes are pre-defined: compression reduction priority mode, compact and low cost priority mode, and comprehensive balance mode. At the same time, the corresponding weight rules of volume, compression reduction and cost optimization targets are pre-defined for each mode. For all non-dominated solutions on the Pareto front of the component layer, calculate the relative proximity of each solution. When the pressure reduction priority mode is adopted, the allocation weight of the pressure reduction target is increased, and after weighted correction of the relative closeness of each solution, the solution with the highest closeness and closest to the optimal pressure reduction extreme point is selected as the low resistance candidate decision point. When adopting the compact and low-cost priority mode, the weight of volume and cost objectives is increased, and the relative closeness of each solution is adjusted by weighting. The solution with the highest closeness and closest to the optimal extreme point of volume and cost is selected as the compact alternative decision point. When the comprehensive equilibrium mode is adopted, the equilibrium weights of the three types of objectives are equally distributed. After the relative closeness of each solution is corrected by weighting, the solution with the highest closeness near the Pareto front inflection point is selected as the final component decision point. Extract the channel length, single-channel flow rate, and channel diameter structural parameters corresponding to the final component decision point as components of the collaborative optimization results.

9. The stratified optimization method for supercritical carbon dioxide cycle driven by waste heat from marine gas turbines according to claim 8, characterized in that, Before outputting the results of the collaborative optimization of the cyclic operating conditions and component structure, the following are included: A first verification threshold and a second verification threshold are pre-set for the loop component to match, and the first verification threshold is less than the second verification threshold; Substitute the actual pressure drop parameters corresponding to the component decision points into the thermodynamic control model at the cycle level, and recalculate the overall output power, efficiency and levelized cost of electricity performance index of the cycle. The recalculated cycle performance index is compared with the corresponding index of the original cycle decision point to identify the deviation. When the performance deviation is less than or equal to the first verification threshold, the cyclic operating condition and component structure are deemed to be in good match, and the collaborative optimization result can be directly output. When the performance deviation is greater than the first verification threshold and less than the second verification threshold, the matching degree is determined to be in need of optimization. After locally correcting the voltage drop boundary parameters at the loop level, the performance index is recalculated. When the performance deviation is greater than or equal to the second verification threshold, the matching is deemed unqualified, and the actual pressure drop of the component is returned to the loop level as a new constraint to start the loop multi-objective optimization iteration again. Repeatedly perform bidirectional iterative verification of the loop component until the performance deviation meets the threshold requirement.

10. The stratified optimization method for supercritical carbon dioxide cycle driven by waste heat from marine gas turbines according to claim 9, characterized in that, When outputting the collaborative optimization results, the following should be included: Three types of cycle selection modes are preset: power economy priority mode, energy efficiency priority mode, and comprehensive balance mode. At the same time, the performance selection judgment rules for simple regenerative cycle and recompression cycle are preset. Output complete collaborative optimization schemes after the simple regenerative cycle and recompression cycle have passed the matching verification. The schemes include cycle operation parameters and corresponding component structural parameters. When adopting the power economy priority mode, the output power and levelized cost of electricity of the two types of cycles are compared, and the simple regenerative cycle scheme with superior overall performance is selected as the final output result. When adopting the energy efficiency priority mode, the recompression cycle scheme with superior overall performance is selected as the final output by comparing the efficiency and energy utilization rate of the two types of cycles. When using the comprehensive equilibrium mode, the comprehensive closeness score of the two types of cyclic schemes is calculated separately, and the cyclic scheme with the highest comprehensive closeness score is selected as the final output result.

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