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FIGURE 1. Brayton cryocooler with counter-flow heat exchanger (HX2) for cooling liquid nitrogen (LN). IDEAL BRAYTON CYCLE Before the practical design, an ideal cycle is considered to examine the fundamental nature of Brayton refrigeration shown in FIGURE 1. A standard reverse-Brayton cycle is composed of two isentropic processes (compression and expansion) and two isobaric processes (heat exchangers). It is assumed that the refrigerant (helium or neon) is an ideal gas with constant specific heat. As the inlet (i) and exit (e) temperatures of LN are given and T3 is fixed at 300 K, there are seven unknowns to determine: pressure ratio (rP = PH/PL), flow rate of refrigerant ( m R ), and refrigerant temperature at 1, 2, 4, 5, and 6. It is noted that only the pressure ratio is counted in the ideal cycle, because a different choice of PH and PL with same pressure ratio results in exactly the same cycle. The energy balance equations for regenerative heat exchanger (HX1) and LN heat exchanger (HX2) are T −T =T −T (4) 1634 m R C P ( T 6 − T 5 ) = m L N C L N ( T i − T e ) ( 5 ) where CP is the specific heat at constant pressure of refrigerant. The isentropic relations for compressor and expander are T2 =T4 =r(k−1)/k (6) TTP 15 where k is the specific heat ratio of refrigerant, which is 1.667 for both helium and neon. The performance of heat exchanger is given as a value of effectiveness. For HX1 T −T εHX1= 1 6 (7) T3 −T6 as the capacity rate is identical for two streams. For HX2, however, εHX2 =Ti −Te (caseI) or εHX2 =T6 −T5 (caseII) (8) Ti −T5 Ti −T5 1666PDF Image | Thermodynamic design of 10 kW Brayton cryocooler for HTS cable
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