## 1 Introduction  
The cryogenic turbo-based refrigerator, which consists of the reverse Brayton cycle, Claude cycle, and Kapitza cycle etc., is extensively applied in many areas, such as the controllable nuclear fusion [1], air separation and liquefaction [2], Zero Boil Off liquid hydrogen storage [3], low temperature environmental simulator [4], superconducting [5, 6], food industry [7, 8], and heat pump [9]. Because of the low operational temperature, the thermal capacity of system components, and so on, the cooling process of a cryogenic turbo-based refrigerator is quite long and complex [4, 7]. Moreover, the cryogenic refrigerator usually operates under varying conditions, which makes the dynamic performance more complex and unpredictable. Therefore, an efficient simulation and evaluation method is quite necessary for the turbo-based refrigerators, which can help evaluating, and optimizing, the cryogenic refrigerator; and improving the energy efficiency and energy economy. The turbo-based reverse Brayton refrigerator is a basic and important form of cryogenic turbo-based systems [10], it was chosen as the objective to research the dynamic cooling characteristics. Many experiments and simulations have been conducted to research the dynamic performances of turbo-based systems. [PERSON] et al. [11] tested an air refrigeration system employing a turboexpander compressor for road transport under several conditions. [PERSON] et al. [12] experimentally studied the dynamic performance of a gas bearing turboexpander for conditioner in aircraft, which achieved high efficiency. [PERSON] et al. [5,13] manufactured a neon reverse Brayton refrigerator for superconducting applications. They investigated the dynamic cooling characteristics under different conditions, but further analysis was relatively rare. [PERSON] et al. studied dynamic characteristics of the turboexpander with brake blower [4] and turboexpander compressor [14] respectively. Then they proposed a transient cooling model of the reverse Brayton refrigerator and analyzed the refrigerator cooling performance under several typical operational modes [15]. The matching analyses were separate, and the system efficiency and economy were not clarified. Some dynamic simulations of the turbo-based refrigerator were also done. The refrigerator mainly includes many components, which interact with each other mutually. Many working processes and dynamic characteristics of components are simplified for easy of calculation. In some models, the steady-state calculation of heat exchanger was adopted for dynamic simulation, resulting in great errors [16,17]. [PERSON] et al. [18] conducted thermal optimization of a cryogenic system using the genetic algorithm. In the research, the heat exchanger was researched in detail, but the performance of expander was simplified. [PERSON] et al. carried out costs and exergy analysis for cryogenic refrigerators [19,20]. In their research, the turboexpander efficiencies were set as constant. Through thermodynamic simplification, [PERSON] et al. [21] proposed a dynamic system model for the control of the TEALARC process. [PERSON] et al. [22] carried out a simulation of a cryogenic N2 expansion cycle. The calculation of heat exchanger was illustrated detailly, but the matching performance of turboexpander was simplified. In these works, the matching characteristics of turboexpander were usually simplified for easy simulation or specific to a certain type (e.g., a brake blower). Moreover, the dynamic calculation of energy efficiency and economic cost of different modes were rare, especially the quantitative evaluation method. The turboexpander is the main device that influences the refrigerator greatly. It is quite an efficient equipment to gain low temperature, and is one of the main advantages for turbo-based refrigerators. Thus, it is necessary to establish a dynamic simulation and evaluation method, which could evaluate the system energy efficiency accurately and consider the turboexpander matching characteristics completely.