Simulation And Optimization Of Helium Liquefaction Cycle Based On Equation Oriented Approach

For large-scale scientific facilities,the use of superconducting magnet technology is one of the most important means to enhance device performance,and the construction of large helium cryogenic systems is a prerequisite for the widespread application of superconducting magnets.The construction of large helium cryogenic systems requires a huge investment and incurs extremely high operating energy consumption.From the perspective of energy saving and cost control,simulating and optimizing the processes of large helium cryogenic systems is of great significance.In the future,China aims to construct a number of large-scale helium cryogenic systems with a cooling capacity of tens of kilowatts.This paper analyzes domestic and foreign large-scale helium cryogenic systems and identifies the following characteristics for 4K and 2K systems with cooling capacities above ten kilowatts:1)the number of precooling stages in the reverse Brayton cycle is usually greater than or equal to four;2)the pressurization system typically includes high,medium,and low pressure levels,and for 2K systems,there is an additional negative pressure level,making multi-stream heat exchangers very common in such systems;3)series configurations are commonly used for the turbines in the high-temperature region.These characteristics result in the large-scale helium cryogenic system design involving numerous variables and increase the difficulty of process simulation and optimization.A review of past research on steady-state simulation of helium liquefaction cycles reveals that existing work mainly focuses on parameter sensitivity analysis and optimization based on heuristic algorithms(e.g.,genetic algorithms),while research on process simulation methods and process optimization based on rigorous optimization algorithms is scarce.In order to establish reliable simulation models for large-scale helium cryogenic systems and obtain optimization results of engineering significance,this paper primarily undertakes the following work:(1)The equation-oriented approach based on pseudo-transient continuation is adopted to simulate the helium liquefaction cycle,and pseudo-transient models for common components in the helium liquefaction cycle are established,including two-stream counterflow heat exchangers,turbine expanders,non-throttling stage valves,throttling valves,and phase separators.By comparing the results with the simulations of the Collins helium liquefaction cycle based on the commercial software HYSYS in published literature,a difference of approximately 1%was found,verifying the accuracy of this method.By comparing the initial values and final solutions obtained from the model,it was observed that they differed by a factor of nearly 2-3,indicating a wide convergence range of this method.Using this method,parameter sensitivity analyses were conducted on the modified Claude helium liquefaction cycle from both energy and exergy perspectives.It was found that the expander bypass ratio and intermediate expansion pressure around 0.8 and 0.25,respectively,maximize the helium liquefaction efficiency and cryogenic exergy efficiency.(2)A new optimization framework for the helium liquefaction cycle was established,in which the optimization problem of the helium liquefaction cycle was formulated as a constrained nonlinear programming problem.The methods for calculating the cycle exergy efficiency as the objective function and the heat exchanger area and turbine speed as the constraint functions were analyzed.Taking the Collins cycle as the analysis target,comparisons were made with other optimization studies.Compared to parameter sensitivity analysis,this framework achieved a 10.367%increase in cycle exergy efficiency and a 6.098%increase in helium liquefaction rate,and compared to genetic algorithm,this framework achieved a 7.814%increase in helium liquefaction rate.Additionally,it was found that optimizing solely for helium liquefaction rate would result in lower cycle exergy efficiency,while optimizing solely for cycle exergy efficiency would result in lower helium liquefaction rate,highlighting the limitations of single-objective optimization.The impact of adding a constraint on turbine rotational speed to measure turbine operation stability on the optimization results of helium liquefaction rate and cycle exergy efficiency was analyzed using the parameter of wheel peripheral speed.It was found that as the upper limit of the wheel peripheral speed decreased from 450 m/s to 300 m/s,the helium liquefaction rate and cycle exergy efficiency decreased by 49.226%and 63.492%,respectively.This result demonstrates that the lack of consideration for turbine operation stability in system performance optimization has limited practical value.Finally,the Pareto optimal solution set was obtained by simultaneously optimizing for cycle exergy efficiency and helium liquefaction rate,and the final optimized solution was selected using the TOPSIS method.Compared to the results of single-objective optimization,the TOPSIS solution only decreased by 8.1623%and 10.821%in cycle exergy efficiency and helium liquefaction rate,respectively,effectively balancing both performance indicators.(3)A rigorous three-stream heat exchanger process simulation model was established,which seamlessly integrates with the process simulation methods and optimization framework described in the previous chapters.Taking the modified Claude helium liquefaction cycle with a three-stream heat exchanger as the analysis target,comparisons were made with the optimization results from other research papers.Compared to parameter sensitivity analysis,this framework achieved a 14.704%increase in helium liquefaction rate,and compared to genetic algorithm,it achieved a 9.759%increase in helium liquefaction rate.(4)Based on a 100 L/h helium liquefier,the simulation and optimization methods described above were validated.Under consistent liquefaction rates,a comparison was made between the optimized calculation results and the overall inlet mass flow rate and temperatures at various nodes under actual operating conditions.The mass flow rate differed by 12.57%,and the maximum relative deviation for each node’s temperature did not exceed 15%,indicating a good agreement between the optimized calculation results and the actual operating conditions.The process simulation and optimization framework proposed in this paper is not only applicable to helium liquefaction cycles but also effective for refrigeration cycles,providing designers of low-temperature systems with advanced process simulation and optimization methods,as well as innovative optimization ideas.