# Influence of Frost Growth and Migration in Cryogenic Heat Exchanger on Air Refrigerator
## 1 Introduction  
The heat transfer in reverse Brayton cycles has the characteristics of no phase change and the one between the cold and hot fluids in the cryogenic regenerator is gas-gas [1; 2]. As the gas-gas heat transfer coefficient is small, the cryogenic regenerator of the reverse Brayton refrigerator is required to have great heat transfer area. Due to high efficiency, great specific surface area, compactness and light weight, the plate-fin heat exchanger is widely used in the reverse Brayton refrigerator [3; 4]. The cryogenic heat exchanger is a very important equipment in low temperature equipment. It not only affects the economy of the cryogenic equipment, but also affects the possibility of process realization [5; 6; 7; 8]. Employing air as the working fluid has brought the reverse Brayton refrigerator many advantages. For example, the open cycle can be conducted and related equipment and losses are reduced. Meanwhile there are some downsides, of which the biggest one is the influence of air humidity. As the refrigerator runs, new air enters the system continuously. Although most of the water is removed by the precooling system, some of the water vapor still enters the system [7]. In the operation process of the cryogenic refrigerator, the temperature inside the heat exchanger might be below\(-100\)\({}^{\circ}\)C or even lower for a long time [3; 7]. The frosting will occur when the wet air flows through the heat exchanger, thus affecting the system performance. Frost formation on the surface of a heat exchanger raises the heat barrier and flow resistance, thus affecting the heat exchanger performance. Much research has been conducted on plate-fin heat exchanger both theoretically and experimentally. [PERSON] et al. [8] simulated the dynamic performance of a cryogenic heat exchanger under different energy utilization modes using the numerical method. [PERSON] and [PERSON] et al. [9] specialized in the experimental study of compact surface, and their famous literature contained the experimental data of 56 types of plate fin surface. [PERSON] et al. [10] performed numerical simulation of a cryogenic heat exchanger in nitrogen expansion cycle. With the application in gas separation and liquefaction plant, the research of plate-fin heat exchanger has been developed rapidly. [PERSON] [11] fitted the experimental correlations off factor and j factor respectively according to the experimental data of pressure loss and heat transfer of various fins. The heat transfer performance of the plate-fin heat exchanger in reverse Brayton refrigerator is usually calculated by numerical methods. [PERSON] et al. [12] performed the numerical solution of the plate-fin heat exchanger in methane gas liquefaction of inverse Brayton cycle, and optimized the size of the heat exchanger. [PERSON] et al. [13] studied the plate-fin heat exchanger for the reverse Brayton cycle of an LNG carrier. The finite difference method was used to solve the heat exchanger, and a dynamic model was established. To remove the water in air refrigerator, there are several methods to adopt. In the aircraft environmental control system (ECS), the high-pressure water separation is commonly used to reduce air humidity. For example, [PERSON] et al. [14] conducted a bootstrap air cycle refrigeration system, using a compressor to raise the pressure of air stream, and then cooled it down to the dew-point in a condenser. [PERSON] et al. [15] proposed the water injection subsystem (in the blue frame) for cabin humidity control. [PERSON] [16] conducted energy and exergy analyses of humidity control in the environmental control system of aircraft. In the model, the three-wheel bootstrap cycle was involved and evaluated. The prediction models for frosting in evaporator have been developed in the past several decades [17; 18; 19]. [PERSON] et al. [20] reviewed the most simulation models available in open literatures. [PERSON] et al. [21] proposed a semi-empirical frost density correlation, which was within a 20% error band.