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FIGURE 6. FOM as a function of pressure ratio for various values of high pressure with helium, two-stage compression, and wall-temperature constraint to avoid freezing of liquid nitrogen. The wall temperature, Tw, between e and 5 is estimated by a thermal resistance model, neglecting the wall-conduction resistance and fouling factors hLN (Te − Tw ) = hR (Tw − T5 ) (9) where hLN and hR are the convective heat transfer coefficient of liquid nitrogen and refrigerant, respectively. The detailed heat exchanger design is beyond the scope of this study, but a rough estimation for the coefficients is made for typical plate-fin exchanger in a similar process described in [9]. FIGURE 6 is again a similar FOM plot for helium as the refrigerant and with two-stage compression, including a curve of Tw = 63 K. To make sure that liquid nitrogen should not be frozen in HX2, the operating condition is determined in left region of the curve. Under this constraint, the operating pressure is finally determined as rP = 2.5 and PH = 1.25 MPa, as indicated by a star in FIGURE 6. The complete thermodynamic properties of helium are listed in TABLE 1, and the corresponding temperature-entropy diagram is shown in FIGURE 7. The net power input is 157.9 kW, and the expected FOM is 21.4%. TABLE 1. Thermodynamic properties of helium for designed cycle 1 2a 2b 2c 3 4 5 6 FIGURE 7. Designed Brayton-cycle cryocooler on temperature-entropy diagram of helium. P (MPa) 0.506 0.801 0.791 1.25 1.24 1.19 0.576 0.556 Helium, 0.2091 kg/s T (K) h (J/g) 295.0 -16.86 374.0 393.9 300.0 9.07 380.4 426.9 300.0 8.78 75.80 -1159.5 61.38 -1232.9 70.50 -1185.1 s (J/g-K) 17.61 17.89 16.77 17.06 15.84 8.750 9.165 9.964 1670PDF Image | Thermodynamic design of 10 kW Brayton cryocooler for HTS cable
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