Compressor Isentropic Efficiency

Compressing a gas from one pressure to another takes a certain minimum amount of work, and that minimum is the compression that generates no entropy at all: the isentropic one. Draw it on a pressure–enthalpy diagram and it is the line from the suction state straight up to the discharge pressure along a constant-entropy curve, ending at $h_{2s}$. A real compressor never lands there. Friction in the bearings and rings, throttling losses across the valve plate on every stroke, and — in a hermetic — heat picked up from the motor windings all add entropy, and entropy added at a fixed discharge pressure moves the end point to the RIGHT on the chart, which is to say to a higher enthalpy. So the real discharge $h_2$ is always above the ideal $h_{2s}$, and the isentropic efficiency is the ideal rise divided by the real one.

Note carefully which way up that is, because the turbine page in this catalog puts the same three enthalpies the other way round. A turbine takes work OUT, so the isentropic expansion is the MOST you can get and the ratio is actual-over-ideal. A compressor puts work IN, so the isentropic compression is the LEAST you can spend and the ratio is ideal-over-actual. In both cases the ideal is on the favourable side and the fraction comes out below one; write either equation with the other's numerator and a perfectly ordinary machine reports 125 %. A worked case: suction vapour at 400 kJ/kg, an isentropic discharge at 436 and a measured discharge at 445 gives (436 − 400)/(445 − 400) = 36/45 = 80 %.

Typical numbers, so you know when to be suspicious. A hermetic reciprocating compressor runs 60 to 75 %, a scroll 65 to 80 %, and a well-matched screw 70 to 85 %, all at their design pressure ratio; efficiency falls away on both sides of that ratio, which is why a machine picked for a chiller behaves badly on a low-ambient day. Anything under about 45 % is a broken or leaking valve reed, worn rings, or a pressure ratio far outside the design. Anything over 100 % is not a machine at all, it is a measurement: usually $h_{2s}$ read at the suction pressure instead of the discharge pressure, or a discharge temperature taken downstream of the muffler where the gas has already given heat back to the shell.

Three efficiencies share a compressor and only one of them is this one. Isentropic efficiency compares the actual enthalpy rise with the ideal one. VOLUMETRIC efficiency is a different question entirely — what fraction of the swept volume actually gets drawn in, which the clearance volume re-expanding at the start of each stroke eats into, and which sets capacity rather than power. MOTOR efficiency is a third, and on a hermetic it is tangled with the first because the winding losses land in the refrigerant and show up as extra discharge enthalpy, so a hermetic's apparent isentropic efficiency is depressed by the motor sitting inside the gas stream. And one genuine exception to the whole model: an oil-flooded screw injects so much oil that the compression is meaningfully cooled as it happens, which is no longer adiabatic, and comparing it against an adiabatic ideal is comparing two different processes.