Understanding Reciprocating Compressor Volumetric Efficiency

The volumetric efficiency ($\eta_v$) of a reciprocating compressor is a crucial parameter that measures its performance. It represents the ratio of the actual volume of gas delivered by the compressor during the suction stroke to the theoretical volume displaced by the piston, known as the swept volume ($V_s$).

A simplified formula often used to express volumetric efficiency, considering the effect of clearance volume ($V_c$) and pressure ratio ($r_p = P_d/P_s$), is:

$$ \eta_v = 1 + c - c \left( \frac{P_d}{P_s} \right)^{1/n} $$

Where:

• $c$ is the clearance ratio, defined as $c = V_c / V_s$.
• $P_d$ is the discharge pressure.
• $P_s$ is the suction pressure.
• $n$ is the polytropic index for the expansion of trapped gas.

Impact of Clearance Ratio on Volumetric Efficiency

The clearance ratio ($c$) refers to the ratio of the volume remaining in the cylinder after the piston reaches the top dead center (clearance volume, $V_c$) to the piston's swept volume ($V_s$).

• When the piston moves upwards, the gas trapped in the clearance volume expands. This expansion reduces the cylinder's volume available for fresh gas intake during the subsequent suction stroke.
• A higher clearance ratio means more gas is trapped, leading to greater re-expansion.
• As the clearance ratio ($c$) increases, the term $-c \left( \frac{P_d}{P_s} \right)^{1/n}$ in the formula becomes more negative.
• Therefore, the volumetric efficiency ($\eta_v$) decreases as the clearance ratio increases.

Impact of Pressure Ratio on Volumetric Efficiency

The pressure ratio ($r_p$) is the ratio of the discharge pressure ($P_d$) to the suction pressure ($P_s$).

• Higher pressure ratios require the compressor to work harder, compressing the gas to a greater extent.
• As the pressure ratio $(P_d/P_s)$ increases, the re-expansion volume of the trapped clearance gas also increases relative to the suction pressure. This means the clearance gas has to expand over a larger volume range before the suction pressure is reached and the suction valve opens.
• Looking at the formula, if the pressure ratio $(P_d/P_s)$ increases, the term $\left( \frac{P_d}{P_s} \right)^{1/n}$ increases.
• Consequently, the term $-c \left( \frac{P_d}{P_s} \right)^{1/n}$ becomes more negative.
• This results in a decrease in volumetric efficiency ($\eta_v$) as the pressure ratio increases.

Conclusion on Factors Affecting Volumetric Efficiency

Based on the analysis and the formula:

• Increasing the clearance ratio ($c$) reduces volumetric efficiency.
• Increasing the pressure ratio ($r_p$) also reduces volumetric efficiency.

Therefore, the volumetric efficiency of a reciprocating compressor decreases both with increasing clearance ratio and increasing pressure ratio.