Compressor

Air Compressors

COMPRESSOR – A device which takes a definite quantity of fluid ( usually gas, and

most often air ) and deliver it at a required pressure.

Air Compressor – 1) Takes in atmospheric air,

2) Compresses it, and

3) Delivers it to a storage vessel ( i.e. Reservoir ).

Compression requires Work to be done on the gas,

⇒ Compressor must be driven by some sort of Prime Mover ( i.e. Engine )

 Classification
Air Compressors

Reciprocating Rotary

Centrifugal

No. of Stages No. of Sides of Piston

for Compression in operation
Single – stage Single – acting
Multi - stage Double - Acting
 Reciprocating Compressor - Working

2. Principle of Operation
 Fig. shows single-acting piston actions in
the cylinder of a reciprocating compressor.

The piston is driven by a crank shaft via a
connecting rod.

At the top of the cylinder are a suction
valve and a discharge valve.

A reciprocating compressor usually has
two, three, four, or six cylinders in it.
Reciprocating Compressor - Working
 COMPRESSORS

POSTIVE ROTO--DYNAMIC
DISPLACEMENT

TURBO COMPRESSOR EJECTOR

RECIPROCATING ROTARY

RADIALFLOW MIXED AXIAL

(CENTRIFUGAL) FLOW FLOW
SINGLE STAGE MULTI STAGE

SINGLE ACTING DOUBLE ACTING

 Single stage reciprocating compressor with clearance:

 With clearance volume the cycle is represented on Fig.

 The work done for compression of air polytropically can be

given by the area enclosed in cycle 1-2-3-4.

 Clearance volume in compressors varies from 1.5% to 35%

depending upon type of compressor.

 In the cylinder of reciprocating compressor (V1-V4) shall be

the actual volume of air delivered per cycle.

 Vd = V1 – V4. This (V1 – V4) is actually the volume of air in

hated in the cycle and delivered subsequently.
 Equation for Work without clearance volume
Thus, comparison between the Isothermal Work and the Actual Work is important.
Isothermal Work
Isothermal Efficiency, ηiso =
Actual Work
Thus, more the Isothermal Efficiency, more the actual compression approaches to the
Isothermal Compression.
Actual Work = Wact = Area 4-1-2-3-4
3 2’ 2 2”
P2 PV = C Wact = Area (4-1) – Area (1-2) – Area (2-3)
(Isothermal)
2 2 − PV
PV
PV γ = C = 1 1
+ PV
2 2 − PV
1 1
(Adiabatic) n −1
PV n = C
4 1 (Polytropic)
 n 
÷ ( PV 1 1)
P1
Wiso =  2 2 − PV
 n −1 
V2 V1
 Equation for Work without clearance volume

n n
3 2’ 2 2” Now, P1V1 = P2V2
P2 PV = C 1/ n
(Isothermal) V2  P1 
⇒ =  
PV γ = C V1  P2 
(Adiabatic)
PV n = C
4 1 (Polytropic)  n  
 P2 
n −1/ n

P1 Wiso =  ÷ PV
1 1  ÷ − 1
 n −1   P1  
V2 V1
 n −1

 n   P2  n

Wiso = ÷ mRT1  ÷ − 1
Delivery Temperature,  n − 1  P
 1  
n −1  
 P2  n
T2 =T1 
P 

 1 
Minimum Compression work
Isentropic Compression
 γ−1

γ  p2  γ

W = p1V1  ÷, − 1
γ−1  p1  
 

polytropic compression
 n− 1

n  p  n

W = p1V1  2 ÷ −1
n −1  p1  
 
Isothermal compression
 p2 
W =RT1 ln  ÷
p
 1 

As Compressor is a work consuming device, every effort is desired to

reduce the work.

Work done = Area of P-V curve

⇒ 1 – 2” : Adiabatic Compression = Max. Work.

⇒ 1 – 2 : Polytropic Compression
⇒ 1 – 2’ : Isothermal Compression = Min. Work.
 Methods of cooling/ Methods of improving
isothermal efficiency
 Faster heat dissipation from inside of compressor to
outside by use of fins over cylinder. Fins facilitate quick
heat transfer from air being compressed to atmosphere
so that temperature rises during compression can be
minimized.

 Water jacket may be provided around compressor

cylinder so that heat can be picked by cooling water
circulating through water jacket. Cooling water circulation
around compressor regulates rise in temperature to
great extent.
 The water may also be injected at the end of
compression process in order to cool the air being
compressed. This water injection near the end of
compression process requires special arrangement in
compressor and also the air gets mixed with water
and needs to be separated out before being used.

 In case of multistage compression in different

compressors operating serially, the air leaving one
compressor may be cooled up to ambient state or
somewhat high temperature before being injected
into subsequent compressor. This cooling of fluid
being compressed between two consecutive
compressors is called intercooling and is frequently
used in case of multistage compressors.
 Equation for Work with clearance volume
Clearance Volume :

6 3 2
P2 Volume that remains inside the cylinder
after the piston reaches the end of its
inward stroke.
PV = Cn

5 4 1
P1 Thus, Effective Stroke Volume = V1 – V4
V3 V4 V1

Effective Swept Volume, V1-V4

Clearance Volume,
V3=Vc Swept Volume, V1-V3=Vs Actual Work = Wact = Area 1-2-3-4
Total Volume, V1 Wact = Area (5-1-2-6) – Area (5-4-3-6)
 Equation for Work with clearance volume
 n −1
  n −1

n  P2  n  n  P3  n 
Wact = PV
1 1  ÷ − 1 − PV
4 4  ÷ − 1
6 3 2 n −1 P
 1   n − 1 P
 4  
P2    

But, P4 = P1 and P3 = P2
 n −1

PV = Cn
n 
 P2  n

⇒ Wact = PV
1 1  ÷ − 1 
5 4
n −1 P
 1  
P1
1  
V3 V4 V1  n −1

n 
 P2  n

− PV
1 4  ÷ − 1
Effective Swept Volume, V1-V4 n −1 P
 1  
Clearance Volume,  
V3=Vc Swept Volume, V1-V3=Vs

 n   
 P2 
n −1/ n

÷ P1 ( V1 − V4 )  ÷
Total Volume, V1
Wact = − 1
 n − 1  P
 1  
 Volumetric Efficiency
Volumetric Efficiency :
Ratio of free air delivered to the displacement of the compressor.
6 3 2 Ratio of Effective Swept Volume to Swept Volume.
P2
Presence of Clearance Volume
⇒ Volumetric Efficiency less than 1. ( 60 – 85 % )
PV n = C
Effective Swept Volume
Volumetric Efficiency =
5 4 1 Swept Volume
P1
V1 – V4
V3 V4 V1
=
V1 – V3
Effective Swept Volume, V1-V4
Clearance Volume, Clearance Volume
V3=Vc Swept Volume, V1-V3=Vs Clearance Ratio =
Swept Volume
Total Volume, V1
Vc
= = γ ( 4 – 10 % )
Vs
 Volumetric Efficiency
V1 − V4
ηvol =
V1 − V3
⇒

6 3 2
⇒

=
( V1 − V3 ) + (V3 − V4 )
=1+
V3
−
V4
P2 (V1 − V3 ) (V1 − V3 ) (V1 − V3 )
V3 V4 V3
=1+ − •
(V1 − V3 ) (V1 − V3 ) V3
V3 V3 V4
=1+ − •
5 4 1 (V1 − V3 ) (V1 − V3 ) V3
P1
V3 V4 V1
Effective Swept Volume,
V1-V4
Clearance Volume,
V3=Vc Swept Volume, V1-V3=Vs

Total Volume, V1
 Reciprocating Compressor – Volumetric Efficiency

6 3 2
P2 V3  V3 
ηvol = 1+ 1 − 
V1 −V3  V4 
V3  V3 
ηvol = 1−  − 1
V1 −V3  V4 
5 4 1
P1 
V3   P3 
1/ n

V3 V4 V1 ηvol = 1−   − 1
V1 −V3   P4  
Effective Swept Volume,  
V1-V4
Clearance Volume,   P 1 / n 
V3=Vc Swept Volume, V -V =V ηvol = 1 − γ •   3  − 1
  P4  
1 3 s

Total Volume, V1  
 Reciprocating Compressor – Actual P-V Diagram
Receiver Pressure 1-2-3-4-1 : Theoretical P-V Diagram.

3 2 At 4, inlet valve does not open due to :

P2
1. There must be a pressure difference across the valve to open.
2. Inlet valve inertia.
Pr. Drop continues till sufficient level
Atmospheric Pressure for valve to force its seat.
Intake Depression
4 Some valve bounce is set (wavy line).
1
P1 Eventually, the pressure sets down at a level lower
Valve Bounce than atmospheric pressure. This negative pressure
difference is known as Intake Depression.
Similar situation appears at 2, i.e. at the start of the delivery.

Pressure rise, followed by valve bounce and then pressure settles at a level higher than
the delivery pressure level.

Air delivery to a tank / receiver, hence, generally known as Receiver Pressure.

 Reciprocating Compressor – F.A.D.
Free Air Delivery (F.A.D.) : If the volume of the air compressor is reduced to atmospheric
temperature and pressure, this volume of air is called FAD (m3/min)
Delivered mass of air = intake mass of air
PtVt P1 (V1 −V4 ) P2 (V2 −V3 )
= =
Tt T1 T2
If clearance volume is neglected

PtVt P1V1 P2V2

= =
Tt T1 T2
Where

Pt = 101.325KN / m 2

Tt = 15 C = 288 K
0
Limitation of single stage compression

Advantages of multi stage compression

 Reciprocating Compressor – Multistage

High Pressure required by Single – Stage :

⇒ 1. Requires heavy working parts.

2. Has to accommodate high pressure ratios.
3. Increased balancing problems.
4. High Torque fluctuations.
5. Requires heavy Flywheel installations.

This demands for MULTI – STAGING…!!

 Reciprocating Compressor – Multistage
Series arrangement of cylinders, in which the compressed air from earlier cylinder
(i.e. discharge) becomes the intake air for the next cylinder (i.e. inlet).

L.P. = Low Pressure

Intercooler I.P. = Intermediate

Air Delivery
Pressure
H.P. = High Pressure

L.P. I.P. H.P. Intercooler :

Cylinder Cylinder Cylinder
Compressed air is cooled
between cylinders.

Intercooler

Air Intake
 Reciprocating Compressor – Multistage
Delivery Pr. 6 9 3 5 Overall Pr. Range : P1 – P3
Perfect Intercooling
P3 or Pd
Single – stage cycle : 8-1-5-6
Without Intercooling
H.P. Without Intercooling :
PV = C
n
L.P. : 8-1-4-7
Intermediate Pr. 7 4
P2 2 H.P. : 7-4-5-6
PV = C
L.P. With Intercooling :
Intake Pr. 8 1 L.P. : 8-1-4-7
P1 or Ps
H.P. : 7-2-3-6
Volume
Perfect Intercooling : After initial compression in L.P. cylinder, air is cooled in the
Intercooler to its original temperature, before entering H.P. cylinder
i.e. T2 = T1 OR
Points 1 and 2 are on SAME Isothermal line.
 Reciprocating Compressor – Multistage
Ideal Conditions for Multi – Stage Compressors :

A. Single – Stage Compressor :

6 9 3 5 Single – stage cycle : 8-1-5-6

 n −1

n  P5  n
H.P. W= P1 V1  ÷ − 1

n −1   P1  
7 PV n = C  
4
2 PV = C Delivery Temperature,
L.P. n −1
8 1  P5  n
T5 =T1 
P 

 1 
 Reciprocating Compressor – Multistage
B. Two – Stage Compressor (Without Intercooling) :
Without Intercooling :
6 9 3 5 L.P. : 8-1-4-7
H.P. : 7-4-5-6

H.P.  n −1

n  P4  n

PV n = C W = P1 V1  ÷ −1

7 4 n −1  P1  

 

2 PV = C
L.P.  n −1

n  P5  n
8 1 + P4 V4  ÷ −1

n −1  P4  

 


Without Intercooling ⇒Delivery Temperature also remains SAME.

This is SAME as that of Work done in Single – Stage.
 Reciprocating Compressor – Multistage
C. Two – Stage Compressor (With Perfect Intercooling) :

With Intercooling :
6 9 3 5 L.P. : 8-1-4-7-8
H.P. : 7-2-3-6-7
 n −1

n  P  n
W = P1 V1  4 ÷ −1
H.P. n −1  P1  

 

7 PV n = C
4  n −1

n  P  n
2 PV = C + P2 V2  3 ÷ −1
L.P. n −1  P2  
8

 

1
Delivery Temperature,
n −1 n −1
 P3  n  P3  n
T3 = T2   = T1   , as T2 = T1
 P2   P2 
 Reciprocating Compressor – Multistage
C. Two – Stage Compressor (With Perfect Intercooling) :
6 9 3 5
With Intercooling :
L.P. : 8-1-4-7-8
H.P. H.P. : 7-2-3-6-7

7 PV n = C Now, T2 = T 1
4
2 PV = C P2V2 = P1V1
L.P.
8 1
Also P 4 = P2
 n −1 n −1

n  P2  n  P3  n
W = P1 V1  ÷ +  ÷ − 2 

n −1  P1   P2  

 

Shaded Area 2-4-5-3-2 : Work Saving due to Intercooler…!!
Condition for Min. Work :

6 9 3 5
⇒ There is an Optimum P 2 for which Area 2-4-5-3-2
is maximum,
H.P.
i.e. Work is minimum…!!
7 PV n = C 
 
n −1
 
n −1

4 n P n P n
W= P1 V1   2 ÷ +  3 ÷ − 2 
2 PV = C n −1   P1   P2  
L.P.  
For min. Work,
8 1
 n −1 n −1

 P  n  P  n
d  2 ÷ +  3 ÷ − 2 
 P1   P2  
dW 
 
 = 0
=
dP2 dP2
 Reciprocating Compressor – Multistage
Condition for Min. Work :  n −1 n −1

 P  n  P  n
d  2 ÷ +  3 ÷ − 2 
 P1   P2  
dW  
=  = 0
dP2 dP2

1  n −1  n −1   n −1    n −1  n −1  
 ( P2 )  n  + ( P3 )  n   ( P2 )  n   = 0
  −1   −  −1
n −1
• • − 
( P1 ) n  n    n  
6 9 3 5
( P2 ) −1/ n = ( P1 P )
 n −1 

 n 

 − 2 n +1  3
H.P. ( P2 )  n 
PV n = C
7
2
4
PV = C ( P2 ) 2 = ( P1 P3 )
L.P.
8 P2 P
1 P2 = P1 P3 OR = 3
P1 P2
 Reciprocating Compressor – Multistage
P2 obtained with this condition (Pr. Ratio per stage is equal) is the Ideal Intermediate
Pr. Which, with Perfect Intercooling, gives Minimum Work, Wmin.
⇒
 Reciprocating Compressor – Efficiency

Isothermal work done / cycle = Area of P – V Diagram

= P1V1 loge(P2/P1)

Isothermal Power = P1V1 loge(P2/P1) N kW

60 X 1000

Indicated Power : Power obtained from the actual indicator card taken during a
test on the compressor.

Compressor Efficiency = Isothermal Power

Indicated Power

Isothermal Efficiency = Isothermal Power

Shaft Power
NOTE : Shaft Power = Brake Power required to drive the Compressor.
 Reciprocating Compressor – Efficiency

Adiabatic Efficiency : Ratio of Power required to drive the Compressor; compared

with the area of the hypothetical Indicator Diagram; assuming
Adiabatic Compression.

 γ −1

γ  P  γ
P1 V1 1 −  2  
γ −1   P1  
 
η adiabatic =
Brake Power required to drive the Compressor

Mechanical Efficiency : Ratio of mechanical output to mechanical input.

Mechanical Efficiency, ηmech = Indicated Power

Shaft Power
 Reciprocating Compressor – Efficiency
How to Increase Isothermal Efficiency ?

A. Spray Injection : Assimilation of water into the compressor cylinder towards the
compression stroke.
Object is to cool the air for next operation.

Demerits : 1. Requires special gear for injection.

2. Injected water interferes with the cylinder lubrication.
3. Damage to cylinder walls and valves.
4. Water must be separated before delivery of air.

B. Water Jacketing : Circulating water around the cylinder to help for cooling the
air during compression.
 Reciprocating Compressor – Efficiency
How to Increase Isothermal Efficiency ?

C. Inter – Cooling : For high speed and high Pr. Ratio compressors.
Compressed air from earlier stage is cooled to its original
temperature before passing it to the next stage.

D. External Fins : For small capacity compressors, fins on external surfaces are useful.

E. Cylinder Proportions : Short stroke and large bore provides much greater surface
for cooling.
Cylinder head surface is far more effective than barrel
surface.
 Reciprocating Compressor – Efficiency
Clearance Volume : Consists of two spaces.
1. Space between cylinder end & the piston to allow for wear.
2. Space for reception of valves.

High – class H.P. compressors : Clearance Vol. = 3 % of Swept Vol.

: Lead (Pb) fuse wire used to measure the gap
between
cylinder end
Low – grade L.P. compressors : Clearance and
Vol. = 6piston.
% of Swept Vol.
: Flattened ball of putty used to measure the gap
between cylinder end and piston.
Effect of Clearance Vol. :
Vol. taken in per stroke < Swept Vol. ⇒ ↑ Size of compressor
↑ Power to drive compressor.