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Effective swept volume of compressor

07/12/2021 Client: muhammad11 Deadline: 2 Day

PNEUMATIC AND HYDRAULIC EQUIPMENT

HYDRAULICS

TOPIC TITLE : PNEUMATIC AND HYDRAULIC EQUIPMENT

LESSON 1 : AIR COMPRESSION THEORY

APH - 2 - 1

Published by Teesside University Open Learning (Engineering)

School of Science & Engineering

Teesside University

Tees Valley, UK

TS1 3BA

+44 (0)1642 342740

retrieval system, or transmitted, in any form or by any means, electronic, mechanical,

photocopying, recording or otherwise without the prior permission

of the Copyright owner.

This book is sold subject to the condition that it shall not, by way of trade or

otherwise, be lent, re-sold, hired out or otherwise circulated without the publisher's

prior consent in any form of binding or cover other than that in which it is

published and without a similar condition including this

condition being imposed on the subsequent purchaser.

________________________________________________________________________________________

INTRODUCTION ________________________________________________________________________________________

For many years pneumatic equipment has been used to provide useful work

and to operate complex control systems. However, this would not have been

possible without a supply of compressed air of the correct quality with regard

to cleanliness, pressure level and flow rate.

In this lesson we deal with the theory of air compression, an understanding of

which is essential for the efficient operation and maintenance of compressed

air equipment for production plant.

________________________________________________________________________________________

YOUR AIMS ________________________________________________________________________________________

On completion of this lesson you should be able to:

• explain the difference between isothermal, adiabatic and polytropic

compression processes

• use a p – V diagram to explain the compression cycle of a

reciprocating piston compressor

• define volumetric efficiency in relation to air compressors

• explain the effect that clearance volume has on volumetric efficiency

• explain the effect of pressure on volumetric efficiency

Teesside University Open Learning (Engineering)

• appreciate the effect that pressure and temperature have on the

moisture-carrying capacity of air

• explain the reasons for multi-stage compression.

________________________________________________________________________________________

STUDY ADVICE ________________________________________________________________________________________

It would be advantageous for your understanding of this text if you review the

Gas laws prior to starting this lesson.

Teesside University Open Learning (Engineering)

________________________________________________________________________________________

AIR COMPRESSORS ________________________________________________________________________________________

The function of an air compressor is to take a definite quantity of air and

deliver it into a system at an increased pressure.

The most efficient machine is one which will accomplish this objective with a

minimal input of mechanical work.

The most common types of air compressors in use today are:

• reciprocating or piston compressors

• rotary screw compressors

• rotary sliding vane compressors

• centrifugal compressors

• axial flow compressors.

The last two types are roto-dynamic machines while the other designs are

positive displacement air compressors. In a pneumatic system, the type of

compressor used depends upon the system requirements in terms of pressure

and flowrate.

A general distinction can be made on the basis of performance. Positive-

displacement types have the characteristics of low mass flowrate and high

pressure ratios whilst roto-dynamic machines are usually associated with low

pressure ratios and high mass flow rates. However, pressures ranging from

atmospheric to 9 bar are common to most types.

Teesside University Open Learning (Engineering)

FIGURE 1 shows the broad pressure and capacity ranges over which the

various types of compressor normally operate. Note that the scales on both

axes of the diagram are not linear but logarithmic.

FIG. 1

10 100 1000 10 000 100 000 106 107 108

1 0

00 0

0 00

Reciprocating compressors

Centrifugal compressors

Axial flow compressors

Rotary compressors

G au

ge p

re ss

ur e

(b ar

)

Air flow rate (m3 h–1)

Teesside University Open Learning (Engineering)

________________________________________________________________________________________

AIR COMPRESSION THEORY ________________________________________________________________________________________

ISOTHERMAL AND ADIABATIC COMPRESSION

The compression of air requires an input of power to the compressing

elements. If we consider a simple single-cylinder reciprocating-piston

machine, most of the power supplied to drive the piston reappears as heat in

the air being compressed. This generated heat is an unwanted product of the

compression process.

The temperature increase of the air is due to the increase in velocity of the air

molecules, which bombard each other and the confining walls of the

compression space while the confined volume is being reduced. This causes a

conversion of some of the kinetic energy of the molecules into heat energy.

If a means could be devised to remove this heat from the air as fast as it is

generated then the temperature of the air would remain constant throughout the

compression cycle.

The instant removal of this heat is impossible to achieve in practice but the

condition can be approached in machines running at very low speeds. Under

these conditions, the theoretical concept of compression at a constant

temperature is termed isothermal and represents the ultimate in compression

efficiency.

At the other extreme, compression occurring quickly without time for heat

extraction is known as adiabatic or isentropic. During this process of

compression the temperature rises rapidly and progressively. Since the air is

confined in a cylinder and cannot expand, the effect is to increase the rate at

which the pressure rises. This in turn calls for an increased power input to the

piston.

Teesside University Open Learning (Engineering)

In practical reciprocating compressors running at moderate speeds, the mode

of compression lies between these two extremes, with some of the heat of

compression being extracted by means of a compressor cooling system.

Alternatively, or in addition, the compression may be carried out in a number

of stages. Each stage of compression is followed by a cooling process to

reduce the temperature of the gas.

Why is it not possible to achieve in practice isothermal or adiabatic compression?

...................................................................................................................................................

________________________________________________________________________________________

To achieve isothermal compression would require perfect cooling and to achieve adiabatic

compression would require perfect insulation. However, as it is impossible to obtain perfect

cooling or perfect insulation it is therefore impossible to achieve adiabatic or isothermal

compression.

The theoretical power required for isothermal compression is, however, only about 36% of

that required for adiabatic compression, which is why designers strive to produce

compressors that operate as close to isothermal conditions as possible.

Teesside University Open Learning (Engineering)

PRESSURE – VOLUME DIAGRAMS

The cycle of events of the reciprocating compressor may be illustrated using a

pressure-volume diagram, which will aid your understanding of the

compression process.

A pressure-volume diagram is a graph which illustrates the pressure-volume

relationship within a compression process. Volume is plotted on the horizontal

axis and the corresponding pressure on the vertical axis.

FIGURE 2 illustrates an ideal single-cylinder compressor and its p – V

diagram.

FIG. 2(a) Reciprocating Compressor Layout

Stroke length

Air out

Air in

where

Swept volume = length of stroke × area of piston

Piston

Piston area

Teesside University Open Learning (Engineering)

where swept volume = stroke length × piston area.

FIG. 2(b) Pressure – Volume (p – V) Diagram for Reciprocating Compressor

Assume that the cycle starts with the piston at its top dead centre (TDC),

position A. Line AB represents the suction stroke where air is being drawn

through the inlet valve into the cylinder by the action of the piston being

withdrawn. This will occur at a constant pressure with a gradual increase in

volume.

Line BC represents the compression stroke where the piston is advancing to

reduce the volume of the air with a corresponding increase in pressure.

Line CD represents discharge of air from the cylinder through the delivery

valve at constant pressure.

FIGURE 2 (b) neglects to show the effect on the p – V diagram of the

clearance space between the piston and cylinder head at TDC.

0 V

W.D.

Swept volume

A – B B – C C – D W.D.

= = = =

Induction Compression Delivery Work Done

where

Atmospheric pressure

Absolute pressure

Teesside University Open Learning (Engineering)

How do you think the plate valves controlling the flow of air in and out of the

compression chamber are activated?

...................................................................................................................................................

________________________________________________________________________________________

Both the inlet and outlet valves are usually spring-loaded and are made to open and close

automatically by a pressure differential across each valve. The strength of the springs and

the area of valve plate exposed to the pressure differential control the opening and closing

pressures.

Teesside University Open Learning (Engineering)

________________________________________________________________________________________

THE EFFECT OF CLEARANCE VOLUME ________________________________________________________________________________________

Prior to the inlet valve opening and air entering the cylinder, pressure within

the cylinder must be less than atmospheric. In reciprocating compressors it is

necessary to have a gap between the top of the piston and the cylinder head at

TDC. This will result in a clearance volume in which will be held a small

amount of high pressure gas. This gas must be re-expanded to below

atmospheric pressure before induction of a fresh charge of air can take place.

FIGURE 3 shows the actual sequence of events as they would occur in a

compressor with a clearance volume (CV).

(a) p – V diagram with clearance volume

(b) Actual reciprocating compressor layout

FIG. 3

0 V

W.D.

CV ESV

Teesside University Open Learning (Engineering)

The inlet valve opens at point A, when the pressure in the cylinder is below

atmospheric, and air is drawn into the cylinder. Line AB now represents the

effective swept volume (ESV) which can be seen as being less than the total

swept volume (SV).

At point B the piston reverses direction and compression takes place up to

point C.

At point C the pressure in the cylinder has risen to delivery pressure and the

discharge valve opens. Line C to D represents the delivery volume at a

constant pressure.

At point D (TDC) the piston reverses direction, the delivery valve closes and

the clearance gas is re-expanded down to point A where the inlet valve opens

and the cycle recommences.

It can be seen that induction of air does not take place until the pressure inside

the cylinder is lower than atmospheric, which requires the clearance volume to

be expanded. This will have the effect of delaying the opening of the inlet

valve hence reducing the volume of air drawn into the cylinder during

induction, resulting in a reduction in volumetric efficiency.

Why do you think it necessary for a reciprocating piston compressor to have a

clearance space between the piston and the cylinder head at top dead centre?

...................................................................................................................................................

________________________________________________________________________________________

The reason for a clearance space at top dead centre on a single-acting compressor (and a

clearance space at bottom dead centre also for double acting machines) is to prevent the

compressor internal components (piston, rod and valves etc.) from mechanical damage due

to the piston striking the cylinder head during operation.

Teesside University Open Learning (Engineering)

________________________________________________________________________________________

VOLUMETRIC EFFICIENCY ________________________________________________________________________________________

For the purpose of this text and to aid your understanding of the effect

clearance volume has on the operation of a reciprocating compressor, we will

treat volumetric efficiency as:

Theoretically, the compressor will draw in its swept volume of air per stroke,

which is equal to the area of the piston × the stroke length, but in practice the stroke length can only be considered from the point that the inlet valve opens.

Therefore, the volumetric efficiency becomes:

From this it can be seen that if the effective swept volume reduces, so too does

the volumetric efficiency.

Consider now the effect of increasing the clearance volume: this will result in a

greater volume of high-pressure air trapped in the clearance space which must

be re-expanded to below atmospheric pressure to allow the inlet valve to open;

this means that the piston must travel further down its induction stroke before

the inlet valve opens. This will give a reduction in the effective swept volume

and hence volumetric efficiency. In simple terms, the compressor will be

passing less air through the system per cycle. FIGURE 4 illustrates this effect.

effective swept volume total swept volume

volumetric efficiency = actual volume drawn inn per stroke

theoretical volume drawn in perr stroke

Teesside University Open Learning (Engineering)

FIG. 4 Effect of Changing the Clearance Volume

W.D.

ESV

0 V

W.D.

CV ESV

Teesside University Open Learning (Engineering)

How do you think clearance volumes are set and what do you think would be the effect

of an incorrectly set clearance volume on the operation of a reciprocating piston

compressor?

...................................................................................................................................................

________________________________________________________________________________________

On single-acting machines, clearance volumes are usually factory set and not adjustable.

However, machining the cylinder head or altering its gasket thickness will affect the

clearance volume.

On double-acting machines clearance volumes will usually be adjustable and be set to a

predetermined value supplied by the machine manufacturer. The degree of adjustment is

usually achieved by screwing the piston rod in or out of the crosshead.

If the clearance volume is incorrectly set at a higher value than that recommended by the

manufacturer this will usually result in a loss of volumetric efficiency leading to a reduction

in compressor performance. If the value is set at a level lower than recommended then this

will increase the risk of mechanical damage occurring due to contact between the piston and

cylinder head.

Teesside University Open Learning (Engineering)

________________________________________________________________________________________

EFFECT OF PRESSURE ON VOLUMETRIC EFFICIENCY ________________________________________________________________________________________

Another factor which will affect the opening of the inlet valve and hence the

effective swept volume is the pressure of the air in the cylinder. If the pressure

is low, only a small increase in its volume will be necessary to achieve the

required pressure reduction, but if it is high then a greater increase in its

volume will be required to allow the inlet valve to open.

FIGURE 5 illustrates this effect for three different pressures.

FIG. 5 Effect of Delivery Pressure on Swept Volume

It can be seen from the diagram that, as maximum system pressure increases,

there is a delay in the opening of the inlet valve resulting in a decrease in the

effective swept volume.

pATM A1 A2 A3 B

D3 C3

Teesside University Open Learning (Engineering)

With reference to FIGURE 5 the lowest pressure cycle (p1) is the most efficient

in terms of volume (A1–B–C1–D1).

p2 is less efficient (A2–B–C2–D2).

p3 is the least efficient (A3–B–C3–D3).

What effect would a defective delivery valve have on the volumetric efficiency of the

machine?

...................................................................................................................................................

________________________________________________________________________________________

If the valve had springs which had become weak or broken due to fatigue failure, it would

open at a lower than desired pressure difference: this would improve volumetric efficiency,

but reduce the effective pressure of the air being delivered into the system. If for any reason

the valve was prevented from opening at the desired pressure differential then this would

put a higher effective pressure into the system but would reduce the volumetric efficiency of

the machine.

Teesside University Open Learning (Engineering)

________________________________________________________________________________________

ISOTHERMAL AND ADIABATIC COMPRESSION ________________________________________________________________________________________

The compression of air with all the heat of compression removed (isothermal)

and with "none" of the heat of compression removed (adiabatic) was outlined

earlier in the text. We will now consider the effect on the input power to the

compressor for each process. The p – V diagram will again be used to explain

these effects.

ADIABATIC COMPRESSION

If none of the heat generated during the compression process is allowed to

escape, the rate of pressure rise within the cylinder will be extremely high due

to the expansion of the gas during the process.

ISOTHERMAL COMPRESSION

If all the heat generated during the compression process is removed as it is

generated this will result in a slow rate of pressure rise within the cylinder

solely due to the reduction in volume.

Both processes are illustrated in the p – V diagram, FIGURE 6.

Teesside University Open Learning (Engineering)

FIG. 6

FIGURE 6 shows that during isothermal compression work done will be at a

minimum where the area inside the p – V loop is a minimum: this is the ideal

situation. The compressor designer aims to approach this mode of

compression.

The adiabatic curve is the worst situation showing work done in compressing

the gas is at a maximum where the area of the diagram is maximum. This is a

situation that designers try to avoid.

In practice, the mode of compression falls some way between the two and is

known as polytropic. It is shown on the diagram as a broken line.

Thus it is important to note that the extraction of heat of compression is an

important factor in compressor efficiency.

Polytropic

Adiabatic

Isothermal

Teesside University Open Learning (Engineering)

________________________________________________________________________________________

MOISTURE CONTENT IN AIR ________________________________________________________________________________________

Atmospheric air will always contain some moisture and under certain

conditions the amount can be considerable. This moisture, if allowed to enter

compressed air systems, can have a detrimental effect, therefore its removal is

critical.

The amount of moisture that can be supported by air is dependent on various

factors, two of the most important are:

• as temperature rises more water can be held

• as pressure rises less water can be held.

Since compressors both raise the temperature and the pressure of the air there

is some balancing of water retention capabilities. If we assume that air leaving

a compressor is just able to support its moisture content, any reduction in

temperature would result in the moisture being condensed and deposited into

the system with adverse effects. It is therefore desirable that the air is cooled

immediately after compression to remove moisture before it can enter the

pipework system.

Teesside University Open Learning (Engineering)

________________________________________________________________________________________

MULTI-STAGE COMPRESSION ________________________________________________________________________________________

It can be recognised now that there are limitations to the use of single-stage

compressors:

• there is a limited maximum pressure due to the problem of re-expansion

of the clearance gases

• it is difficult to remove all the heat generated during the compression

process quickly enough to achieve a process approaching isothermal.

A common method employed to help overcome the above two problems is the

use of a multi-stage compressor where air is cooled between each stage. This

method of compressing air has several advantages which are outlined briefly

below.

• Less work is done on the gas during the compression process, hence

greater efficiency is achieved.

• Higher pressures can be achieved due to reducing the problems of

clearance-space expansion.

• Moisture present in the air can be removed between stages.

FIGURE 7 illustrates the compression of air in two stages with cooling

between the stages. This cooling is known as inter-cooling.

The operation of the compressor plant in FIGURE 7 is as follows.

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