# Piston Displacement, Compressor Capacity, Clearance Volume of Compressor

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## Introduction

This article describes some important terms related to the refrigeration and air conditioning compressors. These are compression ratio, capacity and volumetric efficiency of the compressor.

## Piston Displacement or Compressor Capacity

The capacity of the compressor is very important parameter, since the capacity of whole refrigeration or the air conditioning plant depends on it. The capacity of the reciprocating compressor depends on the diameter of the cylinder bore, the length of the piston stroke inside the cylinder, number of cylinders in the compressor and the speed of rotation of the crankshaft. Piston displacement of the reciprocating compressor is the volume swept by the piston inside the cylinder in unit time and it is same as the capacity of the compressor. The piston displacement or the capacity of the compressor can be expressed in cubic meter per min (m3/min), cubic meter per sec (m3/sec), cubic feet per minute (cfm) or liters per second (lps).

In general the capacity of the compressor is given by the formula:

Capacity = Π * D2 * L * N * n/4

Where: D is the diameter of the bore of the bore of cylinder

- L is the stroke of the piston inside the cylinder, which can also be the length of the bore.

- n is the number of cylinders in the compressor

- N is the speed of the rotation of the crankshaft that can be expressed in rotations per minute (rpm) or rotations per second (rps)

## Clearance Volume of the Compressor

When the piston reaches top dead center (TDC) position inside the cylinder, it cannot go and touch the extreme end of the cylinder. The piston stroke is performed only till certain length inside the cylinder and small volume inside the cylinder towards its extreme top end remains empty. This volume is called as the clearance volume. The space left between the TDC position of the piston and the discharge valve is called as the clearance volume of the cylinder or compressor. The clearance volume limits the stroke of the piston; hence it reduces the capacity of the compressor as well as its volumetric efficiency.

## Compression Ratio of the Reciprocating Compressor

The compression ratio, R, of the reciprocating compressor is defined as the ratio of the suction pressure of the refrigerant to the discharge pressure of the refrigerant. Thus,

R = Absolute suction pressure of the refrigerant/ absolute discharge pressure of the refrigerant

## Volumetric Efficiency of the Reciprocating Compressor

The actual volume of gas inducted inside the cylinder for compression is less than the theoretical calculated volume because of the clearance volume. When the gas is compressed, and is delivered by the discharge valve, not all the gas is discharged since some volume of the gas remains inside the clearance volume at high discharge pressure. When the piston starts moving downwards, the suction valve does not opens immediately because of this high pressure gas. As the piston moves downwards the pressure of the gas in the clearance volume starts reducing due to expansion. Only when the pressure of this gas reaches to certain minimum level, the suction valve opens. Thus the portion of the suction stroke of the piston goes unused and during this certain volume of the refrigerant is not sucked. This reduces the volume of the refrigerant that can be sucked by the cylinder or the compressor.

Thus the actual amount of refrigerant sucked by the cylinder is less than the theoretical amount of gas that it could have sucked based on the diameter of the bore and its length. The volumetric efficiency (V) of the compressor is defined as the ratio of the actual volume of gas sucked by it to the theoretical volume that it could have sucked if clearance volume was not present.

V = Actual volume of gas sucked by the compressor/ Theoretical volume of the compressor

It is clear from the above discussion that more is the clearance volume, less is the volumetric efficiency of the compressor. The volumetric efficiency of the compressor also affects the capacity of the compressor since the capacity is directly dependent on the piston displacement inside the cylinder. Lesser the volumetric efficiency less is the capacity of the compressor.

The volumetric efficiency of the compressor also depends on the compressor ratio. If the difference between the suction and the discharge pressure is higher, the refrigerant will remain trapped inside the clearance volume for longer time and prevent the opening of the suction valve. Thus as the compression ratio of the compressor increases, its volumetric efficiency and the capacity reduces.

## This post is part of the series: Refrigeration and Air Conditioning Compressors

This is the series of articles that describes the difference between the refrigeration compressors and air compressors, types of refrigeration compressors, principle of working of the reciprocating compressors and parts of the reciprocating compressors.