A two-stage compressor splits the compression into two equal pressure ratios and cools the air between them, which saves 14.7% of the shaft power at 8 bar absolute and 19.5% at 16 bar absolute, and cuts the first-stage discharge from 374 °C to 162 °C at 15 bar gauge. The second cylinder’s bore is the first’s divided by the square root of the stage ratio, 50% for 15 bar gauge and 59.5% for 7 bar gauge, and for a 235.6 L/min machine the intercooler has to shed about 482 W.
Part of Piston Compressor
Two-stage compression adds a smaller second cylinder and a cooler between the stages, giving higher pressure, lower temperatures and better efficiency than one cylinder can.
Equal Stage Ratios Minimise the Work
For a total absolute pressure ratio r the work is least when each stage compresses by the same ratio, r^½, with the air cooled back to its inlet temperature between stages. The intermediate absolute pressure is then the square root of inlet times final. Working in the units of Gas Laws in Practice:
| Final pressure | Stage ratio | Intermediate pressure | Single-stage outlet | First-stage outlet | Power saved |
|---|---|---|---|---|---|
| 8 bar absolute (7 gauge) | 2.83 | 2.83 bar absolute | 258 °C | 121 °C | 14.7% |
| 16 bar absolute (15 gauge) | 4 | 4 bar absolute | 374 °C | 162 °C | 19.5% |
The carrier’s “15-20% less power” is right at 15 bar gauge and slightly generous at 7. The corpus’s compressed-air article gives 3-4 bar for the intermediate pressure on a 25-30 bar machine; the equal-ratio rule would put it at the square root of 25-30, about 5-5.5 bar, so that split is not the minimum-work one. This article sizes to the carrier’s 15 bar gauge. Whatever you choose, the receiver, pipe and relief valve must all be rated for the final pressure; corpus wrought-iron pipe made from strip is rated at only 3-8 bar (Metal Pipes), which would not do.
The Second Cylinder Is Smaller by a Square Root
The second stage takes in air already compressed by the first, so it needs only 1 / (stage ratio) of the first stage’s swept volume. With the same stroke the area, and so the bore squared, shrinks by the same factor:
Bore ratio = (stage ratio)^-½
- 7 bar gauge: stage ratio 2.83, bore ratio = 1 / √2.83 = 0.595, so a 100 mm first stage pairs with a second stage of about 60 mm (59.5%). This matches the carrier’s “roughly 60%“.
- 15 bar gauge: stage ratio 4, bore ratio = 1 / √4 = 0.5, so 100 mm pairs with 50 mm.
The carrier’s 60% therefore applies to the lower pressure; at 15 bar gauge the ratio is 50%.
The Intercooler Has a Real Heat Load
Between the stages the air drops from the first-stage outlet temperature back toward the inlet temperature. For a 100 mm x 100 mm first stage at 300 RPM and 7 bar gauge:
- Free-air flow = 0.003927 m³/s (235.6 L/min); mass flow = 0.003927 m³/s x 1.204 kg/m³ = 0.00473 kg/s (air density recalled)
- Temperature drop = 121.4 - 20 = 101.4 K
- Heat = 0.00473 x 1,005 J/(kg K) x 101.4 K = 482 W, using 1,005 J/(kg K) for air (recalled)
That equals the first stage’s work, as it should. A coil in a 20 L water bath absorbing 482 W warms the water by 482 x 3,600 / (20 x 4,186) = 21 K in an hour, using 4,186 J/(kg K) for water (recalled). So a still bath of a few tens of litres is only good for short runs; a larger bath or a stream of fresh water is needed for continuous running.
Better delivery too. With 5% clearance (an assumed value; see Single-Stage Design) a first stage at ratio 2.83 has a volumetric efficiency of 1 - 0.05 x (2.83^(1/1.3) - 1) = 0.94, against 0.80 for one cylinder compressing straight to 8:1. The same first cylinder delivers about 17% more air in a two-stage machine.
What You Need
- Two cylinders, the second at the bore ratio above, with its own piston, rings and valves
- An intercooler, a coil of copper tube in a water bath or finned pipe in a stream, with a drain for condensate at its lowest point
- A relief valve on the intercooler, set below the intercooler’s own rating and above the intermediate pressure
- A check valve on the second-stage outlet and the usual receiver fittings
Method: Plumb the Stages
Step 1: First stage to intercooler Run the first-stage outlet to the top of the coil and slope the coil so condensed water drains to the low point.
Step 2: Intercooler to second stage Feed the second-stage inlet from the cooled end. A leaking second-stage inlet valve lets full pressure back into the intercooler, which is the case the relief valve exists for.
Step 3: Test the intermediate pressure With the gauge on the intercooler, the pressure should settle near the intermediate value in the table. A reading far above it means the second cylinder is too small, a stuck valve or a blocked coil.
Common Mistakes
- No relief valve on the intercooler. The coil is the weakest, lightest part of the system and it sees second-stage pressure if a valve leaks back.
- Uncooled intercooler. If the water bath is hot, the second stage works on warm air and the saving disappears.
- Forgetting the drain. Water condenses in the intercooler and must be let out; see Moisture Removal.
Safety
The intercooler is a pressure vessel with thin walls
The intercooler coil holds intermediate-pressure air and the second-stage cylinder holds the final pressure. Fit a relief valve on the intercooler, test the coil with water before use, and never plug the relief outlet. First-stage and second-stage cylinders and the connecting pipe run hot enough to burn; guard them.
What’s Next
- Learn next: Receiver Tank Construction — the tank sized for the final pressure
- Combine with: Safety Devices — relief valves, gauges and drains