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How to Use the Two-Stage Compression Calculator
Select the refrigerant, then choose the temperature, pressure and capacity units. Cold storage and blast freezer work is usually done in degrees Celsius and kW.
Type the evaporating and condensing dew-point temperatures, the capacity, the superheat at the low-stage suction and any condenser subcooling.
Enter the isentropic efficiency of each stage and of the single-stage comparison, pick a flash tank or a closed intercooler, and choose the geometric mean, a search for the lowest power, or your own intermediate pressure.
Check the stage pressure ratios, the compressor power, the discharge temperatures and the saving against single stage. Add the project details, then use PDF, CSV, Copy or Print.
Two-stage compression from real refrigerant properties
A two-stage system splits one large pressure lift into two smaller ones, with an intercooler between them that removes the heat of the first compression and the flash gas from the liquid. This calculator solves the full cycle from CoolProp 8 enthalpy and entropy data. It finds the low-stage discharge from the isentropic efficiency, balances the energy of the intercooler to get the high-stage mass flow, and compares the total power with a single stage working between the same temperatures.
When the pressure ratio calls for a second stage
The first example is R-404A at -35°C evaporating and 40°C condensing, which is 1.6 bar absolute against 18.1 bar absolute, an overall ratio of 11.1. If your gauges read psig or kPa, the pressure converter turns them into the absolute pressures that the ratio needs. With 70% isentropic efficiency in every compressor, a single stage needs 39.2 kW for 50 kW of cooling and a two-stage flash-tank cycle needs 31.0 kW, a saving of 21.0%. The saving grows with the ratio: 13.6% at -10°C evaporating, 16.5% at -20°C, 19.5% at -30°C and 24.1% at -45°C. Part of that gain comes from the liquid, which is cooled to the intermediate temperature before it expands, and part comes from compressing in two smaller steps. The model gives all compressors the same efficiency by default. A single stage working at a ratio of 11.1 usually runs less efficiently, so lower the single-stage figure when the compressor data say so. At 62% it raises the saving to 30.0%.
Where the intermediate pressure should sit
The textbook choice is the geometric mean of the absolute suction and discharge pressures, which gives equal pressure ratios on the two stages. In the first example that is 5.45 bar, a -3.0°C dew point, and a ratio of 3.33 on each stage. The page also searches for the intermediate pressure with the lowest total power. For this case it lands at 6.2°C and 7.29 bar, where the stage ratios are 4.46 and 2.49 and the total is 30.5 kW, which is 1.6% below the geometric mean result. Across the nine refrigerants at -30°C and 40°C the gap is between 0.4% and 1.4%, so the optimum is flat and a nearby pressure that suits the compressors costs little. A study of six published expressions for the optimum intermediate condition found that the pressure-based expressions deviate from the optimum by as much as 18.4% and the temperature-based ones by at most 6.7%, and that the expressions cannot be used for all refrigerants.
Flash tank or closed intercooler
A flash tank takes the condenser liquid and the low-stage discharge gas into one vessel at the intermediate pressure. The vapour that leaves goes to the high-stage suction, and the saturated liquid goes to the evaporator. A closed intercooler passes the evaporator liquid through a coil inside the vessel, so that liquid leaves warmer than the vessel liquid by the approach temperature. With a 5 K approach the first example saves 19.2%, against 21.0% for the flash tank, because the refrigerating effect falls from 155.5 to 148.5 kJ/kg. The closed type keeps the evaporator liquid at condenser pressure, which some designs prefer. In both types the high stage handles about 1.82 times the low-stage mass flow, because the intercooler adds the flash gas and the vapour that cools the low-stage discharge.
Compressor sizing and discharge temperature
The high-stage compressor draws denser gas, so it needs less swept volume than the low stage. In the first example the low stage moves 138 m³/h of suction gas and the high stage 76 m³/h, a ratio of 0.55. The page reports those volumes at 100% volumetric efficiency, so divide by the efficiency from the compressor data to get displacement. Discharge temperature is the other reason to split the lift. For R-22 at -40°C and 35°C condensing, the model puts a single-stage discharge at 136°C, against 47°C and 69°C on the two stages. The Emerson low-temperature scroll data sheet gives a discharge line temperature control target of 110°C or less and a compressor shutdown above 125°C for its ZF*KQE series, so check the limits for the compressors you plan to use.
What the saving is worth, and what the model leaves out
In the first example the two-stage cycle saves 8.2 kW. Run for a full year at that load, which no real system does, it would be about 72,032 kWh, and the annual energy cost calculator turns a figure like that into dollars at your electricity rate. The calculation treats each refrigerant as a fixed composition. It ignores pressure drops, heat gain in the lines and part-load behaviour, and it assumes dry saturated vapour leaving the intercooler. Use it for design and for comparing options, and take final selections from the compressor manufacturer's software.
Frequently Asked Questions
There is no single threshold, but the saving grows with the pressure ratio. For R-404A at 40°C condensing with 70% efficiency in every compressor, the model gives a 13.6% power saving at -10°C evaporating, 16.5% at -20°C, 19.5% at -30°C and 22.5% at -40°C, where the overall ratio is 13.9. The saving is larger when the single-stage compressor loses efficiency at high ratio, since the same case at 62% single-stage efficiency saves 30.0% against 21.0% at 70%. Weigh the saving against the added compressor, vessel and controls, and against the discharge temperature limit.
The usual starting point is the geometric mean of the absolute suction and discharge pressures. In the R-404A example, 1.6 bar absolute and 18.1 bar absolute give 5.45 bar, a -3.0°C dew point and a ratio of 3.33 on each stage. With the stated efficiencies, the lowest total power in the model is at 6.2°C and 7.29 bar, where the total is 30.5 kW against 31.0 kW, a gap of 1.6%. Across the nine refrigerants at -30°C and 40°C the geometric mean costs between 0.4% and 1.4% more power than the lowest, so it is a sound first choice.
A flash tank receives the condenser liquid and the low-stage discharge gas directly, and feeds the evaporator with liquid at the intermediate saturation temperature. A closed intercooler passes the liquid through a coil, so the evaporator liquid is warmer by the approach temperature you set. In the R-404A example the flash tank saves 21.0% against single stage, and a closed intercooler with a 5 K approach saves 19.2%. The high stage handles 1.82 times the low-stage mass flow with a flash tank, because the flash gas and the desuperheating vapour join the high-stage suction.
Yes, but that is a cascade system and not a two-stage system. The two circuits have separate refrigerants, compressors and expansion devices, joined by a cascade heat exchanger. This calculator models one refrigerant through both stages, so use the cascade system calculator when the low-stage evaporating temperature is below what a single refrigerant can handle.