## 4 Result and Discussion  
### Simulation of Energy Consumption  
In the cryogenic system, such as the controllable nuclear fusion [1], the expansion work of the turboexpander was usually consumed. Because the operation temperature is quite low, the total energy input of the system is much bigger than the expansion work. In these systems, reliability and adjustability needs to be guaranteed firstly. With the energy consumption, the flow process of the turboexpander becomes simple and the turboexpander is easy to regulate. There are several kinds of energy consumption methods, consisting of the oil brake, eddy brake and brake of a blower. The specific brake characteristics of these methods were somewhat different, but the approaches and goals are similar. The rotating speed of the turboexpander was regulated through changing the brake power, resulting in high expansion efficiency. Because the blower is easy to adjust, different brake characteristics could almost be simulated by a blower. In a cryogenic refrigerator, as the turboexpander with the brake of a blower, there are two commonly used methods: Certain brake pressure and certain expander efficiency. The method of certain brake pressure has advantages of reliability, stability, simple process and low economy cost. Whereas, with this method, the turboexpander is unable to adjust and can only adapt to change with the operation parameters of the cold end. With certain expander efficiency, additional devices are required, and the economy cost increases. For example, a brake circuit, which is composed of a buffer, control valve, pipes and coolers, is necessary, as shown in Figure 2. But the advantages are obvious, it means the cooling capacity and energy efficiency can be greater under varied conditions. Both the two conditions were simulated, and the cooling performance and energy efficiency are presented and compared. The simulations were conducted with heat exchanger inlet pressure of 0.400 MPa, atmospheric pressure and temperature of 0.100 MPa and 300.0 K.  
As shown in Figure 6, the dynamic cooling characteristics of the refrigerator under different operation modes are presented. In the beginning, the cooling speed of the refrigerator with optimal expander efficiency is significantly faster than those under certain brake pressure. As the cooling goes on, the cooling speeds of different conditions became similar, as shown in Figure 6b. The expander efficiency under brake pressure of 0.100 MPa increases first and then decreases, and it reaches the optimal value at the 18 th min. The expander efficiency under brake pressure of 0.118 MPa reaches the optimal value at the 36 th min. In most of the cooling period, the expander efficiency under brake pressure of 0.118 MPa is higher than the one under brake pressure of 0.100 MPa, and is closer to the optimal one. As shown in Figure 6d, the refrigerator with this brake pressure also has higher effectiveness of heat exchanger. More working conditions were simulated to evaluate the operation modes, as shown in Figure 7. The lowest ultimate refrigerating temperature is achieved under optimal expander efficiency, and the value is 109.7 K. With the increase of brake pressure, the ultimate temperature decreases first and then increases. It comes close to the lowest one in the brake pressure range of 0.112-0.124 MPa, as shown in Figure 7a. The ultimate temperature is 111.1 K at the brake pressure of 0.118 MPa. The highest ultimate temperature of the refrigerator is 113.0 k, which is obtained at the brake pressure of 0.100 MPa. The required times for the refrigerator to achieve this value were compared under different conditions, as shown in Figure 7b. When \(p_{B}\) = 0.100 MPa, it takes 148 min for the refrigerator to reach 113.0 K. Under optimal expander efficiency, the required time is 54 min shorter than the longest one. The shorter cooling time means the shorter energy and economy cost. When \(p_{B}\) is around 0.118 MPa, the cooling time is quite near the shortest one and the deviation is about 10 min.