Compressor efficiency relative work

The recuperated Brayton cycle approaches Carnot efficiency in the ideal limit. As compressor and turbine work are reduced, the average temperatures for heat addition and rejection approach the cycle limit temperature. The limit is reached as compressor and turbine work (and cycle pressure ratio) approach zero and fluid mass flow per unit power output approaches infinity. It can be expected from this that practical recuperated Brayton cycles would operate at relatively low pressure ratios, but be very sensitive to pressure drop. With tire assumption of constant gas specific heat over the cycle temperature range, a good assumption for helium, the cycle efficiency of a recuperated Brayton cycle may be expressed ... 

Let us assume that a reciprocating compressor has two cylinders working in parallel. Each cylinder has both a crank-end section and a head-end suction, where gas is compressed. In effect, we have four small compressors working in parallel. The inlet and outlet pressures, and hence the compression ratio, for each of these four minicompressors, is the same. The relative efficiency for each minicompressor is then... 

The relative overall efficiency of the pumped LOX cycles vs. the LP cycle is a function of product pressure and the ef cienc y differences between the oxygen compressor and the air booster. Typically, the power consumption of both cycles is comparable. At higher pressures the pump work becomes more significant. The pumped LOX cycle is typically lower cost, due to the elimination of the oxygen compressor. 

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