6.2 Compression Ratio and Volumetric Efficiency

Thermodynamic Principles of Compression

In a vapor-compression refrigeration cycle, the compressor elevates the pressure of the refrigerant vapor from the low-pressure side (evaporator) to the high-pressure side (condenser). This process requires mechanical work and increases the temperature of the gas due to the heat of compression. Two primary metrics define the performance of this compression process: the compression ratio and the volumetric efficiency. For industrial ammonia operators, understanding these variables is critical because they directly impact the compressor's capacity, power consumption, and thermal limits.

Calculating the Compression Ratio

The compression ratio ($R_c$) is a dimensionless ratio that compares the absolute discharge pressure to the absolute suction pressure.

The Compression Ratio Formula

To calculate the compression ratio, the absolute pressures must be used. Using gauge pressures (psig) will result in incorrect calculations, especially at low suction pressures or under vacuum conditions. The formula is:

$R_c = \frac{P_{\text{discharge, absolute}}}{P_{\text{suction, absolute}}}$

Where:

• $P_{\text{discharge, absolute}} = P_{\text{discharge, gauge}} + P_{\text{atmospheric}}$
• $P_{\text{suction, absolute}} = P_{\text{suction, gauge}} + P_{\text{atmospheric}}$
• Standard atmospheric pressure at sea level is 14.7 psi.

Worked Example 1: Standard High-Stage Operation

An ammonia compressor operates with a suction pressure of 20.0 psig and a discharge pressure of 185.0 psig. Calculate the compression ratio.

1. Convert gauge suction pressure to absolute pressure: $P_{\text{suction, absolute}} = 20.0 \text{ psig} + 14.7 \text{ psi} = 34.7 \text{ psia}$
2. Convert gauge discharge pressure to absolute pressure: $P_{\text{discharge, absolute}} = 185.0 \text{ psig} + 14.7 \text{ psi} = 199.7 \text{ psia}$
3. Calculate the compression ratio: $R_c = \frac{199.7 \text{ psia}}{34.7 \text{ psia}} \approx 5.76$

Worked Example 2: Booster Operation Under Vacuum

A low-temperature booster compressor operates with a suction pressure of 8.0 inches of mercury (in. Hg) vacuum and a discharge pressure of 30.0 psig. Calculate the compression ratio.

1. Convert inches of mercury vacuum to absolute pressure. Since $29.92 \text{ in. Hg} = 14.7 \text{ psi}$, each inch of mercury represents approximately $0.491 \text{ psi}$. The formula for vacuum is: $P_{\text{suction, absolute}} = 14.7 - (\text{Vacuum in. Hg} \times 0.491)$ $P_{\text{suction, absolute}} = 14.7 - (8.0 \times 0.491) = 14.7 - 3.928 = 10.77 \text{ psia}$
2. Convert gauge discharge pressure to absolute pressure: $P_{\text{discharge, absolute}} = 30.0 \text{ psig} + 14.7 \text{ psi} = 44.7 \text{ psia}$
3. Calculate the compression ratio: $R_c = \frac{44.7 \text{ psia}}{10.77 \text{ psia}} \approx 4.15$

Volumetric Efficiency and Clearance Volume

Volumetric efficiency ($\eta_v$) is the ratio of the actual volume of refrigerant vapor drawn into the cylinder to the theoretical displacement of the cylinder (the volume swept by the piston). It is expressed as a percentage.

The Role of Clearance Volume

In a reciprocating compressor, the piston cannot travel all the way to touch the valve plate at the top of its stroke (Top Dead Center, or TDC). A small gap must remain to prevent mechanical contact and allow space for the valves. This space is called the clearance volume.

• Re-Expansion of Clearance Gas: At the end of the discharge stroke, the clearance volume is filled with high-pressure refrigerant vapor at discharge pressure. As the piston begins its downward stroke, the suction valve cannot open immediately. First, this trapped high-pressure gas must expand until its pressure drops below the suction manifold pressure. Only then will the pressure differential push the suction valve open to draw in fresh vapor.
• Impact of Compression Ratio on Re-Expansion: If the compression ratio is high, the gas in the clearance volume is compressed to a higher pressure. Consequently, it must expand over a larger portion of the downward stroke before the pressure drops below suction pressure. This delays the opening of the suction valve, meaning less of the piston stroke is available to draw in fresh refrigerant vapor, which directly decreases the volumetric efficiency.
• Mathematical Relationship: $\eta_v = 1 - C \left[ \left(\frac{P_{\text{discharge, abs}}}{P_{\text{suction, abs}}}\right)^{1/k} - 1 \right]$ Where $C$ is the clearance volume expressed as a fraction of piston displacement, and $k$ is the specific heat ratio of the refrigerant (for ammonia, $k \approx 1.31$).

Clearance Pockets for Capacity Control

Adjustable clearance pockets are chambers connected to the cylinder head through a valve. Opening a clearance pocket artificially increases the clearance volume of the cylinder.

• Pumping Reduction: By increasing the clearance volume, the amount of gas that must re-expand is increased. This reduces the volumetric efficiency of that cylinder, decreasing the amount of fresh suction gas it can draw in.
• Application: Operators use manual or automatic clearance pockets to reduce compressor capacity during low-load conditions without cycle-stopping the compressor or using suction valve unloaders.

R_c Limits: Thermal Stress and Lubrication Breakdown

A high compression ratio has severe operational consequences beyond reducing volumetric efficiency:

1. Elevated Discharge Temperatures: The thermodynamic properties of ammonia (specifically its high specific heat ratio of 1.31) mean that it heats up rapidly during compression. The higher the compression ratio, the higher the final discharge temperature.
2. Oil Carbonization: Compressor lubricating oils are organic or synthetic hydrocarbons. If the discharge temperature exceeds 275°F (135°C), the oil begins to break down, vaporize, and form hard carbon deposits on the discharge valves. These carbon deposits cause the valves to leak, which allows hot gas to leak back into the cylinder (re-compression), driving the temperatures even higher.
3. Mechanical Failure: Operating above a compression ratio of 8:1 in a single-stage reciprocating compressor typically pushes discharge temperatures above the safe limit of 275°F, leading to lubrication failure, cylinder wall scoring, and piston seizure.
4. Multi-Stage Solutions: To prevent high discharge temperatures when operating with high pressure differentials (such as in low-temperature freezing systems), the compression process is split into two stages: a low-stage booster compressor and a high-stage compressor, with an intercooler in between to cool the booster discharge gas down to saturation before it enters the high-stage machine.

Safety and Preventive Guidelines

• Monitor Non-Condensables: Non-condensable gases (like air) accumulate in the condenser, raising the discharge pressure and artificially inflating the compression ratio. Regular purging is required to keep discharge pressure low.
• Keep Evaporators Defrosted: Heavy frost accumulation on evaporators acts as an insulator, forcing the system to operate at a lower suction pressure to maintain cooling, which increases the compression ratio.
• Clean Condenser Tubes: Scale or algae buildup on condenser tubes reduces heat transfer, raising discharge pressure and the compression ratio.