Volumetric efficiency trend with compression ratio in reciprocating compressors: which statement best describes the relationship?

Introduction / Context:
Volumetric efficiency (eta_v) is the ratio of the actual intake volume (converted to suction conditions) to the swept volume. It captures how clearance gas re-expansion, valve drops, heating, and leakage reduce the fresh charge admitted during the suction stroke. Its variation with compression ratio is central to compressor sizing.

Given Data / Assumptions:

• Fixed machine geometry and clearance ratio.
• Comparison across different pressure (compression) ratios.
• Similar suction conditions, valve characteristics, and speeds.

Concept / Approach:
At higher compression ratios, the residual gas in the clearance volume is left at a higher discharge pressure and temperature. During the subsequent suction stroke, it expands more, occupying a larger fraction of the swept volume before cylinder pressure drops below suction pressure. Hence less fresh air is taken in, reducing eta_v. Conversely, lowering the compression ratio reduces this effect, increasing eta_v.

Step-by-Step Solution:
Recognize clearance gas at end of delivery has p ≈ p_discharge.Higher compression ratio → higher p_discharge → greater re-expansion volume.Greater re-expansion → less swept volume left for fresh intake → lower eta_v.Therefore, eta_v increases when compression ratio decreases.

Verification / Alternative check:
Simplified correlations show eta_v ≈ 1 + C - C*(p_dis/p_suc)^(1/n), demonstrating a drop with increasing ratio for given clearance C and polytropic index n.

Why Other Options Are Wrong:

• Options (b) and (c) invert the observed trend.
• (d) is partially true but incomplete without stating the opposite condition; option (a) states the positive direction clearly.
• (e) ignores strong dependence on pressure ratio and clearance.

Common Pitfalls:
Neglecting valve pressure losses and heating, which further depress volumetric efficiency at high ratios.

Final Answer:
Increases with decrease in compression ratio