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The first issue is the selection of refrigerant from helium and neon. In FIGURE 4, the solid and dashed curves are the plots for helium and neon, respectively, and the maximum FOM points are again indicated by dots. The thermodynamic performance of two gases is almost the same at low PH, because both gases behave like an ideal gas. As PH increases, however, helium is more efficient than neon, due to the real-gas behavior (especially, the pressure-dependence of enthalpy). In addition, helium has a higher thermal conductivity and a smaller viscosity than neon over the temperature range. In order to reach a high FOM (over 20%), helium is selected as refrigerant, and the operating pressures are determined such that the pressure ratio should be around 2~3 and the high pressure should be greater than 1 MPa. Within the range of operating pressure, the required flow rate of helium is 0.14~0.40 kg/s. This compression can be carried out with a single-stage volumetric (reciprocating or screw type) compressor or with two-stage centrifugal (turbo type) compressors. FIGURE 5 compares FOM with single-stage and two-stage compressions. In two-stage compression, an inter-cooler is located between two compressors and the intermediate pressure is determined to minimize the total compressor work. Due to the nature of multi-stage compression with inter-cooling, two-stage cooling is more efficient over entire range of rP. However, the merit of two-stage compression is small when rP is less than 2, but becomes notably greater as rP increases over 2. Even though the theoretical optimum of rP (indicated by dots) for two-stage compression is as large as 3.0~3.5 at PH = 1~2 MPa, the pressure ratio may be determined at 2.0~2.5 without any significant loss in FOM. Taking into consideration the heavy flow rate of refrigerant, two-stage compression with centrifugal compressors is more suitable under this system. In addition, the multi-stage compression allows us an option of directly using the output power from expander to cover one stage of compression with so-called a “compander.” Another factor considered in determining the operating pressure is the possibility of freezing of liquid nitrogen. Since the required Te of liquid nitrogen (65 K) is close to its freezing temperature (63.2 K), liquid may be frozen near the exit wall of HX2 if T5 is less than 63.2 K. The solid nitrogen would result in an added thermal resistance in HX2. Recalling that the optimal rP is in the region of case II ( m LN CLN > m RCP ) and T5 may drop well below 63.2 K, as demonstrated in FIGURE 2. A design constraint to avoid the freezing of liquid nitrogen is imposed such that the wall temperature at the cold end should be greater than 63.2 K. FIGURE 5. FOM as a function of pressure ratio to compare single-stage and two-stage compressions. 1669PDF Image | Thermodynamic design of 10 kW Brayton cryocooler for HTS cable
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