# Influence of Frost Growth and Migration in Cryogenic Heat Exchanger on Air Refrigerator
## 4 Result and Discussion
### Growth and Migration of Frost Layer  
To clarify the characteristics of the growth and migration of frost layer, simulations were conducted under the heat exchanger inlet temperature and pressure of 295.0 K and 0.510 MPa, outlet pressure of 0.100 MPa, inlet moisture content of 0.75 g (kg\(\cdot\)dry air)\({}^{-1}\), and expansion efficiency of 0.60.  
As shown in Figure 8a, the cooling performance of wet air was not very different from that in the case of dry air. Under the frosting condition, temperatures of the hot fluid outlet and the cold fluid inlet are 2.0 K and 1.5 K higher than those under the non-frosting condition at the 120 th min. As shown in Figure 8b, the heat exchanger effectiveness changed stably under the dry air condition. Variations of the effectiveness under the frosting condition was quite complex. As the cooling went on, the heat  
Figure 7: Verification of the frosting model: (**a**) Cooling trend; (**b**) Courant–Friedrichs–Lewy (CFL) number; (**c**) moisture content; (**d**) pressure loss.  
exchanger of frosting condition gradually had a higher effectiveness and then tended to another one. That was because, the cooling rate slowed down and the decline of effectiveness became slower when the frosting occurred. Then with the growth of frost layer, it gradually had a great impact on the heat transfer performance and the effectiveness began to decline obviously.  
Figure 9 shows the growth of frost layer. The simulations showed that the frosting began at the 3.0 th min, indicating that the moisture in the air quickly began to condense into frost under the rapid cooling effect of the refrigerator. As shown in Figure 9a, the frosting first occurred at the cold end of the heat exchanger, and gradually expanded to the hot end over time. That is because as the cooling went on, the area near the hot end of heat exchanger began to meet the frosting conditions. The moisture in the air was mainly frozen in the middle and hot end, while the moisture content in the wet air reaching the cold end gradually decreased. As shown in Figure 9b, after the refrigerator run for 40 min, the outlet moisture content was very low. At this time, more than half of the hot side of the heat exchanger had frosted, as shown in Figure 9a.  
It also can be seen that the frost surface was not smooth. As the temperature decreased, the frost density increased. Although frost deposits continued, the increase in height was not stable especially in the hot end, as shown in Figure 9c. Because the moisture content reaching the area, the surface temperature, and the air velocity were all changing during the cooling process, resulting in such a distribution pattern. As shown in Figure 9c, the frost growth pattern was different in different areas. At the cold end, frosting occurred early and the frost layer grew gently. After running for a certain period, the physical properties of the frost layer at the cold end were relatively stable and no longer grew. Near the hot zone, the frost layer grew more rapidly. This was due to the continuous entry of moisture, which first froze at the hot end. As shown in Figure 9d, the temperature difference was smaller in the middle area, which was corresponding to a thicker frost layer.  
Figure 8: Cooling characteristics under two moisture contents: (**a**) Cooling trend; (**b**) effectiveness.