1. Module 5
C H A P T E R
Reciprocating Air Compressor, Single stage compressor -
computation of work done,
isothermal efficiency, effect of clearance volume, volumetric efficiency, free air
delivery, Theoretical and actual indicator diagram.
Multistage compressors-Constructionaldetails ofmultistage compressors, Need of
multistage, Computation of work done, Volumetric efficiency, Condition for maximum
efficiency, Inter cooling and after cooling (numerical), Theoretical and actual indicator
diagram for multi stage compressors.
Rotary Air Compressors Classification, Difference between compressors and
blowers, Working and constructional details of roots blower, screw type and vane type
8.1 Definition ofa Compressor
Thecompressors are work absorbing devices. They can be defined as follows
Compressor: A compressor is a device which is used to increase the pressure ofafluid on the
expense of work energy supplied. Usually, the compressors are driven by motors, I.C. engines or
Air compressor: A compressor with workingfluid as air is called an air compressor.
Compressors can be classified in thefollowing ways:
Based on design and principle of operations : Based on the principle of operations
compressors can be classifiedas:
Positive displacement Compressors, and
i) Non-positive or Steady flow compressors
ositive displacementcompressors:These compressors are further divided into:
(a) Reciprocating compressors (b) Rotary compressors
2. Themodynamics (MU) 8-2
nt. Due to
displacement ofairby the piston in the cylinder, the air iscompressed and.
vessel called receiver.] These are capable of producing
The reciprocating compressors are considered as
ppen steady flow systems Tti
the rate of heat and work transfers are at uniform rate..
Reciprocating compressors may by single acting compressor or douhla
A reciprocating compressor uses the piston cylinder arrangement. De
large pressure ratios
A single acting reciprocating compressor hasonedeliverystrokeperrevolution
two delivery strokester
crankshaft, while the doubleacting reciprocatingcompressorhastwo deliverystrol
Inpositivedisplacementrotary compressor the positive displacement of air or fluid :.
to a rotating part causingcompression offluid. These compressors rotateat hiph
thereforethey can handldlarge volumeormassflowrate )butthe pressureratiosare
Examples of positive displacement rotary compressors are root blower, vane blowereto
Non-positive orsteadyflow compressors :
Non-positive displacement compressor
also called as
steady flow compressors e.g.lcentritugal compressors and axial
COnpresSOTS. Lnese are rotary compressors.
In these compressors, the fluid is not contained in a confined space (i.e. by so
boundaries like piston cylinder arrangement of a
reciprocating compressor), but t
moves at steady rate through the machine..
In rotary compressors the dynamic head imparted to a fluid of solid boundar
(e.g. impeller of centrifugal compressor ) causes the pressure rise of the fluid.
Based on number ofstages:Compressors based on number of stages are
) Single stage compressor
The Single stage compressors are either air cooled (small size) or water cooled
compressors (big sizes). Normally a single stage compressor is employed when the
pressure ratio is limited upto 5.
Multistagecompressorsareused to achieve higher pressure ratios exceeding the
compression ratio more than 5. Generally, the reciprocating compressors can deliver the
following maximum pressures
Keciprocatmg compressor aximum delivery pressures
Upto 5 bar
Single stage compressor
5 bar to 35 bar
Three stagecompressor 35 bar to 80 bar
Four stage compressor More than 80 bar
Depending uponthe discharge pressures, the compressors are also classified as
pressurecompressors:Delivery pressure upto 1.1 bar
Medium pressure compressors: Delivery pressure upto 7 bar
ii) High pressure compressors: Delivery pressure more than 7 bar.
3. Thermodynamics (MU)
Base on capacity of compressors
Low capacity compressors: Volume flow ratio upto 10 m/min or less
Medium capacity compressors:Volumeflow rates 10 m to 300 m per minute.
High capacity compressors: Volume flow rates above 300 m'/min.
8.2.1 Classification between Fan, Blower and Compressors
per American Society of Mechanical Engineers (ASME), the fans, blowers and compressors
a r e c l a s s i f i e c
fied according to pressure ratios achieved. These are as follows
Fans: Pressureratioupto 1.1
Blower: Pressure ratio from 1.1 to 2.5 A
Pressure ratio above 2.5
8.2.2 Air Pumps
Compressors used for creating vacuum are called air pumps or exhausters.
8.3 Applications / Practicaluses of Compressed Air
MU May 12
Enumeratethevarioususes ofaircompressor (May12)
The compressed air finds its use in many industrial applications. Some of its uses are
To operate pneumatic tools like drill, hammers, riveting machine etc.
i) Driving a compressed air engine
() Spray painting
(iv) Refrigeration and air conditioning industry.
Gas turbine power plants
(vi) Supercharging of LC.
(V1) Conveying the materials like sand and concrete along a pipe line
Vii) Pumping of water.
ix) Driving mining machinery where fire risks are too many.
() In blast furnaces and boiler furnaces.
(xi) Cleaning the surfaces by air blast.
Basic Concept of Thermodynamic Cycle
for Compressors and Efficiencies
Representation of Thermodynamic cycle of compressors on (p-V)
and (T-S) diagrams for compressors
ueneral: Schematic representation ofa compressor is shown inFig. 8.4.1.
Heat loss to -
water) Work supplied, W
(Ether by motor
or IC engines)
Air in surroundings
Fig. 84.1: Schematie representatlon ofan alr compressor
As shown in Fig. 8.4.1, the air is taken into compressor from the surroundings
P. V, T). It is compressed to pressure p, upto state 2 (P, V2, T,) on the expense of work
During the compression, heat may be rejected cither to surrounding air in case of air cooled e
having fins or to cooling water in cylinder jacket in casc of watcr cooled compressors.
8.4.1 Representation of Compresslon Processes on (p-V) and (T-S)
Diagrams and Work Input
The theoretical air compression cycle is shown in Fig. 8.4.2 on (p-V) and (T-S) diagrams
representation ofwork and heat transfers. with
Delivery pressure T
a Suction pressure
a) (p-V) diagram (b) (T-S) diagram
(C)Work,W= area (a-1-2-b) (d) Heat transfer
Q area (c-1-2,d)
Fig. 8.4.2: Representation of compressionprocesses on
(p-V) and (1-S) diagram
with work and heat transfers
5. 7Themodynamics (MU)
lly the compressors are
high speed machines due to which the ratc of hcat transre
be negligible, thus the process is essentiallyfadiabaticl If friction is ncgccld
cess becomes reversible adiabatic or
isentropic andfollows the law pV=
shows the thermodynamic cycle involved in compression. In this (a-1) shows the
sess at constant pressure, followed by reversible adiabatic compression
suctoue Dressure and temperatures rise to P2» T2 due to work supplied from external source and finally
on process (1-2) during
w h i c h
elivered in process 2-b) at constant pressure, P2
8.4.2(c) represents the workdone required during the cycle on (p-V) diagram. In case the
in kinetic and potential energies are neglected then the work, W = [- V. dp. This work
c h a n g e s
bythearea under the
e p r e s
ented by the
Work done, W = V dp =
area (a- 1 -2-b)J
The heat transter dunng polytropic the process of a (1 -2) cooled compressor is shown in
s42(d) on (T-S) diagram. The area under the compression process curveon abscissa represenis the
heat transfer during the processi.e.area(1-2-c-d).
Based on the above discussion the work transfer and heat transfer in various processes can be
marized with the help of Fig. 8.4.2(a) and Fig. 8.4.2(b) respectively as follows:
Sr. No. ProcesSS Work transfer,W
Refer Fig.8.4.2a)1 Refer Fig,84.2(6]
1. Adiabatic process,p . V=C Area (a-1-2-b) Zero
2. Polytropic process,p V =C Area (a-1-2'-b) Area (1-2-d-c)
Isothermal process, p . Area (a-1-2"-b)Area (1-21 e - c)|
It is evident from above table that the work required is maximum with adiabaric process and
work required isminimum with isothermal process.
As a designer our aim issupply minimumenefgyinput during compression process.
Therefore, isothermal compression process is considered as an ideal process because the
work input required is minimum. Thus the best value of index of compression isn = 1. m
However, the isothermal compression is not possible in practice since the heat needs to be
dissipated corresponding to infinitesimal temperature rise during infinitesimal compression process.
This heat transfer will require sufficient time. In other words, an air compressor needs to be run at an
extremely slow speed to achieve approximately an isothermal process. It will reduce the mass flow rate
of air which can be compressed. Whereas, the practical requirement is to compress the air with high
mass flow rate.
Generally, compressors run at sufficient high speed to obtain sufficient mass flow rate of
compressed air, the process of compression will be nearly adiabatic with index n = y.
However toapproachtheisothermalcompressionprocess,theairorwatercoolingisdone during
pression processorcoldwateris sprayedduringcompression,so thatthe adiabaticcompression
gesto polytropic compression withindex n <y.Thevalueofindexn varies between 1.25 to1.35.
Due to continuous cooling of compressed air, it's specific volume reduces. It results in decrease
d work input which equals to area (1 -2-2)asshown in Fig. 8.4.2(a) and Fig. 84.2(b) in
polytropic process and area (1 - 2-2") in case of isothermal process.
6. Themodynamics (MU) 8-6
The actual work supplied at the shaft called shaft work or motor work will he.
compression work if the mechanical friction is considered.
be more than
8.4.2 Isothermal, Polytroplc and Isentroplc Efflclencles
Isothermal eficiency,Tr Actual work input
Polytr pic workinput
Polytropic efficiency, n, Actual workinput 842)
Adiabatic or Isentropic efficiency, n,= Actual work input .(843
In case of uncooled rotary compressors, the ideal T
process is isentropic process (1 -
2) and actual process is
represented by polytropic compression process (1 -
index n >y after considering the fluid friction. Thermodynamic
cycle is represented in Fig. 8.5.1 on (T-S) diagram.
Note that cooling of rotary compressors cannot be
carried out due to inherent practical difficulties. The additional
work needs to be supplied to overcome the friction. Since
friction work converts into heat, as a result the specific volume
during compression process increases.
The additional work required in uncooled compression will be the sum of -V dp workequalto
area (1 2 2) due to increased specific
(c 1-2 -d)
volume of air and the frictional work equal to area
Ideal or Isentropic efficiency, n Actual work done ...(8.5.1)
Syllabus Topic: Reciprocating Air Compressor- Single Stage Compressor
and Computation of Workdone, Isothermal Efficiency
8.6 ReciprocatingAir Compressor
(1) Mechanicalefficiency (2) Indicatedpower
Explain construction and working of single-state, double-actingreciprocatingair compressor
7. Themoaynamics (MU)
D e s c r i p t i o n
6.1 shows the sketch of a
I- intet Vat
consists of a piston
D Ootvery Vatre
r e c i p r o c a t e s
in a cylinder and it
d n v e
through the connecting rod
a n d c r a n k
The rankshaft is driven
h a prime mover. The inlet
the delivery valve (D) are
nted in the cylinder head. The
F a / T e s a
are plate type and spring loaded
called presure differential type i.e. Crank
the valves are automatically opened
ciosed depending upon the
diiference across the valves
c e n
outside and cylinder
P T e s s u r e s .
Foliowing are the assumptionsmade in consideing the cycle of operation:
6) There is no clearance.
) Working fluid is a perfectgas.
(i) There are no friction losses.
iv) There are no wire-drawing effects in the valvesorpipe line.
(v) The cylinder is well insulated.
An ideal (p-V) diagram for a single stage reciprocating aircompressoris shown in Fig. 8.62
Fig. 8.6.2: (p-V) and(T-S) diagrams for single stage air compressor
The air is sucked inside the cylinder at pressure p When the inlet valve
conditions as represented by the process (a-b).
The air is then compressed adiabatically and reversibly upto pressure pa
Curve (b-c), thelawofcompression beingp V= Constant.
Now the dclivery valve opens and the compressed air
of the cylinder is dischar a
at constant pressure, p, represented by the process (c -
The anca (a be d) ropresents the work required to compress the air from pregeq
discharged to a
pressure p, to
cquals to -V dp work.
(d) Calculations for work of compresslon and efficlencles
6) Reversible adiabatic work
Workdone on the air per cycle,
PVPp, V, =(T V,-P, V)
W Area (a bcd)= Area(odce)+Area(ec b)-Area(o a bf
But, PV =
p2 V, ,
- ( or,
From Equations (i) and (i) we get,
W "- 8.6.1)
Also, p V, = mRT,
mR 1 gan .8.6.)
Isothermal and polytropic work ofcompression
However the slope of an isothermal compression curve is less than the adiabatic curve. Theretor
in case the air is compressed isothermally it would follow curve (be"). The area (a b c" d woad
represent the work of compression which is less than the reversible adiabatic compression workbya
amount equal to the area (bc c'). In other words the isothermal process would be themostd
process but such a process is difficult to achieve in practice because it would need the compressor
run at an extremely slow speed consequently reducing the massflow-rate ofthe air compressed
In order to save the work of compression, the practice is to reduce the index ofcompression
high speeds by coolingthe cylinder. This is done either by spraying water on it or by waterjacketing
cylinder in case of single stage compressors so that the law of compression becomes,
Where the value of index 'n' is less than . It is represented by the curve (bc). In
work of compression per cycle with the help of Equation (8.6.1) can be written as,
9. 8-9 Cornpressors
Polytropic work, W,= .v. ..(8.5
i s o t h e r m a
isothermal compression the work ofcompression reauired per cycle would be gv y
1sathermal work, WP Vlog. v PV,logmRT,log.D |
Isothermal work, ...(8.6.4)
asairpower.required to drive the compressor i5
Thereforethe indicated power (L.P.), also known a
e q u a t i o n ,
W KW 8.6.5)
n Number of strokes/min. completedby the compressor
N Speed of compressor in r.p.m.
n N, for single acting compressor
n 2N,for double acting compressor
Actual work input
Isothermalefficiency, n .(8.6.6)
Itis defined as the ratio of polytropic work to actual work input.
Polytropicefficiency, n Polytropic work input ..8.6.6(A))
Actual work input
Note: InEquations (8.6.6 and(8.6.6(A),theactualworkinputmaybetakenasisentropicworkinput
casetheactualworkinputisnotgivenina problem a
() Mechanical efficiency: It is defined as the ratio ofindicatedpower to the power required torun
the compressor)The power required to drive the compressor is called the brake power(B.P.)
shaft power or the motor power which, in case of compressors, is more than the indicated
power (1.P.) because of the extra power requiredto overcome the friction and other losses of the
Mechanical efficiency B.P. 8.6.7)
Adiabatic efficiency = o
86.1 Methods of Improving Isothermal Efficiency T A
Use of fins over cylinder for faster heat dissipation from inside ofcompressor to outside.
0By providing waterjacket around compressor cylinder and cireulating the cooling water through
waler jacket. Thus it cools the air during compression.
By spraying water at the end of injection process.
However this method is not used since
) Alr gets mixed with water which has to be separated before use.
) It contaminates the lubricant film on cylinder surface which may cause corosion.
un Special arrangements need to be made in compressor.
10. gpThermodynamics (MU) 8-14
0.88 0.885.8305 kw
Isothermal powe 0.7103 or 71.03%
Actual power, P 5.1309
Actual power5.8305 U.7103or71.03%
(it) Cylinder dimensions (D and L)
V, = V, xN =% D'LN;
D x 1.8
0.1434 m and L= 1.8 D =
(iii) Raiing of drive =
Actual power =
Syllabus Topic : Effect of Clearance Volume, Volumetric Efficie
Air Delivery (F.A.D)
Define following termsforreciprocatingcompressors
(1)Volunmetricefficiency (2) Free AirDelivery
Practically speaking, a
certain amount of clearance has to be
provided between the piston nd
cylinder so that the piston does not strike with the cylinder head. Also, a certain space between nit
and cylinder has to be provided to accommodate valves.
The ideal (p- V) diagram for a
single stage air compressor is shown in Fig. 8.7.1 with clearance
A small quantity of air in clearance at
delivery pressure P2 of volume V. expands
polytropically along the curve (3-4) till its
pressure becomes equal to the suction P2
At point-4 the inlet valve opens and the air is
drawn into cylinder at
represented by the process (4-1). Therefore,
the volunme of air drawn (V, -
V) is less than,
the stroke volume(V,-V).
It follows that the handling capacity of the
compressor is reduced due to the clearance
space between the piston and cylinder head.
For this reason in case ofcompressors the
clearance volunme is kept asSmall-as
The measure of handling capacity in case of compressors, is defined as the
Fig. 8.7.1: Air compressor cycle with clearance
J s a d d
ctually compressedand deliveredattheinletpressureandtemperature
of Piston displacement
A.D) represents the rate of volume of surrounding airwhich is sucked by
N o t o :
c o m p r e s s o r and deliveredatdischargeepre
Mass ofactuallycompressedairand delivered air
ed that the workdone on the air delivered is not affected by the cleararnce
worke q u i r e
from point 4 to point 1.
noted that t
c o m p r e s s
of air in clearance volume is theoretically regained during its
87.1 alculations for
Eauation (8.7.1), the volumetric efficiency is given by, (Vs +Vo)
the stroke volumeand V.represents the clearance volume.
For ihe polytropic process (3-4) we have,
PaxV = P4x V or, V,= Vs
Also,PPa PP1 and V= Ve (Refer Fig. 8.7.1)
Substituting for V, from Equation (ii) in Equation (i),
v- Pi -
Let C =
Clearance volume ratio =V ()
TheEquation (8.7.3) can be rewritten as:
1, = 1-IG,-11C
P e seen from the Equation (8.7.4) that thevolunetricefficiency reduceswiththeincrease
Sure ratio, T, and the clearance volume ratio, C.
odvallg onnrebd on
8.7.2 Other Factors Affecting the Reduction in Volumetric Efficieney
Apart from reduction in volumetric efficiency due to increased pressure ratio.
volume ratio, C, other factors affecting the reduction in volumetric efficiency eeclea
Increase in temperature of free air drawn from atmosphere due to the heat transter
Pressure drop in the inlet passages and across the inlet valve.
cylinder walls. Due to this heating the specific volume of air increases, hence,them
actually present in the cylinder compared to the conditions of free air is reduced,
Leakage through the valves or past the piston because this decreases the mass of air delive.
(d) Inertia effects in opening the inlet valves.
8.7.3 Volumetric Efficiency Referred to Surrounding Conditions or on Frea
Sincethe condition of air at point-1 does not represent the conditions of free air delivered FA n
(at atmospheric pressure and temperature) due to heat transfer between the cylinder walls andD
and due to pressure drop past the valves, it is necessary to apply the correction factor in theexpr
ofvolumetricefficiency as follows
Let, Vo= Volume offree air delivered at surrounding pressure po and temperatureT
Mass of free air delivered,
Since mass of air sucked remains constant, it implies from above,
Hence the volumetric efficiency of Equation () expression referred to surrounding conditions can
be modified as,
Substituting the value of from Equation (8.7.4) in Equation (iv), the modified
expression for volumetric efficiency based on free air delivered becomes:
Note: Expression given byEquation (8.7.5) should not be used forcalculatingthedimenslons or
cylinder Only the expression of volumetric efficiency given by Equation (1.74 bas
suctionconditionsshouldbe used for calculation ofcylinderdimensions.
13. Themodynamics (MU) 8-17 Compressors
Workdone per cycle,
W Area (1 -2-3-4) = Area (a-1-2- b) - Area (3-4-a-b)
() ) -J-()»v
In case the index of expansion and compression is same.
For a single stage single acting reciprocating air compressor, actual volume of air
taken in is 10 m/min. Initial intake pressure is 1.013 bar and initial temperature is
27 C. Final pressure is 900 kPa clearance is 6% of stroke.
Compressor runs at 400 rpm.
Assume: LD = 1.25 and index ofcompression 1.3
Determine: (1) Volumetric efficiency
(2) Cylinder dimensions
(3) Indicated power
Solution: Refer Fig. P. 8.7.1
(V-V.) = 10m/min,
P 1013 bar= 101.3 kPa
T = 27°C = 300 K, P2 900 kPa
C 0.06=V -1.25, P1P
n = 1.3, N= 400 rpm
Fig. P. 8.7.1
) Volumetric efficiency, n»
1=1-0.06T01.3 1|=0.738or73.8% Ans.
i) Cylinder dimensions, D and L
V, = V, x N
D = 0.3256 m Ans.
L = 1.25 x D = 1.25 x 0.3256 = 0.407 m ..Ans.
ndicated power (L. P.)