# Influence of Frost Growth and Migration in Cryogenic Heat Exchanger on Air Refrigerator
## 4 Result and Discussion
### Experimental Study
#### 4.1.2 Experimental Verification  
To verify the frosting model of heat exchanger, the simulation results were compared with the test data. The simulation was conducted under the same operating conditions as test 1.  
The comparison of the heat exchanger characteristics between the simulation and test was illustrated in Figure 7. As shown in Figure 7a, the simulated non-steady cooling trend of the system under frosting condition agreed well with the experimental value. At the 120 th min, the numerical and experimental deviations at the hot fluid outlet and the cold fluid inlet of heat exchanger were 5.6 K and 3.6 K respectively. The relative deviations of the hot fluid outlet and the cold fluid inlet were 4.0% and 3.3%. The maximum relative deviations of the two in the cooling process were 9.3% and 10.8%, which occurred at about the 11 th min. As shown in Figure 7b, with certain spatial and temporal discretization, \(C_{FL}\) changed with the variations of the space position and the time. In the cold channel of the heat exchanger, \(C_{FL}\) was obvious greater than that in the hot side, which restricted the maximum value of \(C_{FL}\). That is because, the velocity of the cold fluid was higher than that of the hot fluid. In this simulated condition, the time and space steps were 0.5 ms and 4.0 mm, respectively. As shown in Figure 7c, the moisture content measured at the outlet of the heat exchanger was basically 0 after about 20 mins in the test. The simulation showed that the moisture content at the outlet of the hot side in heat exchanger was almost 0 after about 40 mins. It means that most of water vapor froze on the hot side of the heat exchanger. It once more proved the assumption of frost mainly occurring in  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Parameters**} & **Inlet Pressure/MPa** & **Outlet Pressure/MPa** & \multirow{2}{*}{**Inlet Temperature/K**} & **Inlet Moisture Content/g** \\  & **(abs.)** & & & **(kg- dry air)\({}^{-1}\)** \\ \hline Test 1 & 0.507–0.510 & 0.100 & 294.0–295.4 & 1.511–1.550 \\ Test 2 & 0.508–0.510 & 0.100–0.101 & 294.1–295.0 & \textless{}0.0075 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Operation parameters of the heat exchanger.  
Figure 6: Comparison of heat exchanger between dry and wet air: (**a**) Cooling characteristics; (**b**) Pressure loss.  
the hot side of heat exchanger. As shown in Figure 7d, the simulated and tested pressure loses in heat exchanger were in good agreement. The pressure loss in the heat exchanger was little, which showed that the assumption of ignoring the moment equation was reasonable. There was a loose-coupled level between the pressure and velocity. The frosting model is adequate to simulate the dynamic heat and mass transfer characteristic in the cryogenic heat exchanger of air refrigerator to some extent.  
Errors existed between the simulated and tested results. This was due to the simplifications and assumptions of both the models of the expander and heat exchanger. The heat exchanger was simulated using one-dimensional method, and the semiempirical correlations were introduced to describe the frosting, all of which caused the deviations. The models will be improved by adopting more accurate calculating of the heat exchanger and in-depth research of the frosting model. Also, the visible test apparatus were necessary for studying the frosting mechanism. The model in the present study, which combined the numerical heat transfer and the semi-empirical correlations of the Lewis analogy formula, could provide a basis and reference for related research.