Reciprocating compressors Civil Engineering (CE) Notes | EduRev

Civil Engineering (CE) : Reciprocating compressors Civil Engineering (CE) Notes | EduRev

 Page 1


1
RECIPROCATING COMPRESSORS
There are various compressor designs:
Rotary vane; Centrifugal & Axial flow (typically used on gas
turbines); Lobe (Roots blowers), and Reciprocating .
The main advantages of the reciprocating compressor are that
it can achieve high pressure ratios (but at comparatively low
mass flow rates) and is relatively cheap.
It is a piston and cylinder device with (automatic) spring
controlled inlet and exhaust valves. Delivery is usually to a
receiver. The receiver is effectively a store of energy used to
drive (eg) compressed air tools.
Receiver
Delivery
TDC BDC
Inlet
Clearance vol.
¬   Swept vol.®
Page 2


1
RECIPROCATING COMPRESSORS
There are various compressor designs:
Rotary vane; Centrifugal & Axial flow (typically used on gas
turbines); Lobe (Roots blowers), and Reciprocating .
The main advantages of the reciprocating compressor are that
it can achieve high pressure ratios (but at comparatively low
mass flow rates) and is relatively cheap.
It is a piston and cylinder device with (automatic) spring
controlled inlet and exhaust valves. Delivery is usually to a
receiver. The receiver is effectively a store of energy used to
drive (eg) compressed air tools.
Receiver
Delivery
TDC BDC
Inlet
Clearance vol.
¬   Swept vol.®
2
Reciprocating compressors usually compress air but are also
used in refrigeration where they  compress a superheated
vapour (to which the gas laws strictly do not apply).
In order to be practical there is a clearance between the piston
crown and the top of the cylinder. Air 'trapped' in this clearance
volume is never delivered, it expands as the piston moves
back and limits the volume of fresh air which can  be induced
to a value less than the swept volume.
The induced volume flow is an important purchasing
parameter. It is called the  "Free Air Delivery" (FAD), and it
measures the capacity of a compressor in terms of the air flow
it can handle.  It is normally measured at standard sea level
(SSL) atmospheric conditions and allows the capacities (size)
of compressors to be compared.
N.B. The induced mass per cycle must equal the delivered
mass per cycle (continuity!), although the induced and
delivered volumes will be different.
Page 3


1
RECIPROCATING COMPRESSORS
There are various compressor designs:
Rotary vane; Centrifugal & Axial flow (typically used on gas
turbines); Lobe (Roots blowers), and Reciprocating .
The main advantages of the reciprocating compressor are that
it can achieve high pressure ratios (but at comparatively low
mass flow rates) and is relatively cheap.
It is a piston and cylinder device with (automatic) spring
controlled inlet and exhaust valves. Delivery is usually to a
receiver. The receiver is effectively a store of energy used to
drive (eg) compressed air tools.
Receiver
Delivery
TDC BDC
Inlet
Clearance vol.
¬   Swept vol.®
2
Reciprocating compressors usually compress air but are also
used in refrigeration where they  compress a superheated
vapour (to which the gas laws strictly do not apply).
In order to be practical there is a clearance between the piston
crown and the top of the cylinder. Air 'trapped' in this clearance
volume is never delivered, it expands as the piston moves
back and limits the volume of fresh air which can  be induced
to a value less than the swept volume.
The induced volume flow is an important purchasing
parameter. It is called the  "Free Air Delivery" (FAD), and it
measures the capacity of a compressor in terms of the air flow
it can handle.  It is normally measured at standard sea level
(SSL) atmospheric conditions and allows the capacities (size)
of compressors to be compared.
N.B. The induced mass per cycle must equal the delivered
mass per cycle (continuity!), although the induced and
delivered volumes will be different.
3
0
100
200
300
400
500
600
700
800
900
1000
0 0.2 0.4 0.6 0.8 1 1.2
4 ® 1                    Induction
1 ® 2                    Compression
2 ® 3                    Delivery
3 ® 4                    Expansion
Cycle Analysis
The cycle may be analysed as two non-flow (compression and
expansion) processes and two flow processes (delivery and
induction)
PROCESS      GROSS WORK
p 2 V 2 - p 1 V 1
n -1
p 2 (V 2 -V 3 )
p 4 V 4 - p 3 V 3
n-1
p 1 (V 4 -V 1 )
Note that we assume polytropic compression and expansion.
This is because some degree of cooling is usually attempted
for reasons we shall see later.
If no cooling were attempted n becomes g .
On p-V co-ordinates:
1
2 3
4
pressure (kPa)
Volume (litres)
Page 4


1
RECIPROCATING COMPRESSORS
There are various compressor designs:
Rotary vane; Centrifugal & Axial flow (typically used on gas
turbines); Lobe (Roots blowers), and Reciprocating .
The main advantages of the reciprocating compressor are that
it can achieve high pressure ratios (but at comparatively low
mass flow rates) and is relatively cheap.
It is a piston and cylinder device with (automatic) spring
controlled inlet and exhaust valves. Delivery is usually to a
receiver. The receiver is effectively a store of energy used to
drive (eg) compressed air tools.
Receiver
Delivery
TDC BDC
Inlet
Clearance vol.
¬   Swept vol.®
2
Reciprocating compressors usually compress air but are also
used in refrigeration where they  compress a superheated
vapour (to which the gas laws strictly do not apply).
In order to be practical there is a clearance between the piston
crown and the top of the cylinder. Air 'trapped' in this clearance
volume is never delivered, it expands as the piston moves
back and limits the volume of fresh air which can  be induced
to a value less than the swept volume.
The induced volume flow is an important purchasing
parameter. It is called the  "Free Air Delivery" (FAD), and it
measures the capacity of a compressor in terms of the air flow
it can handle.  It is normally measured at standard sea level
(SSL) atmospheric conditions and allows the capacities (size)
of compressors to be compared.
N.B. The induced mass per cycle must equal the delivered
mass per cycle (continuity!), although the induced and
delivered volumes will be different.
3
0
100
200
300
400
500
600
700
800
900
1000
0 0.2 0.4 0.6 0.8 1 1.2
4 ® 1                    Induction
1 ® 2                    Compression
2 ® 3                    Delivery
3 ® 4                    Expansion
Cycle Analysis
The cycle may be analysed as two non-flow (compression and
expansion) processes and two flow processes (delivery and
induction)
PROCESS      GROSS WORK
p 2 V 2 - p 1 V 1
n -1
p 2 (V 2 -V 3 )
p 4 V 4 - p 3 V 3
n-1
p 1 (V 4 -V 1 )
Note that we assume polytropic compression and expansion.
This is because some degree of cooling is usually attempted
for reasons we shall see later.
If no cooling were attempted n becomes g .
On p-V co-ordinates:
1
2 3
4
pressure (kPa)
Volume (litres)
4
The work per cycle is given by: å gross work
p 2 V 2 - p 1 V 1
n -1
p 2 (V 2 -V 3 )
p 4 V 4 - p 3 V 3
n-1
p 1 (V 4 -V 1 )
work per cycle =
+ + +
p 4 V 4 - p 1 V 1
n-1
p 2 V 2 - p 3 V 3
n-1
p 1 (V 4 -V 1 ) p 2 (V 2 -V 3 )
p 1 (V 4 -V 1 )
n-1
p 1 (V 4 -V 1 )
p 2 (V 2 -V 3 )
n -1
p 2 (V 2 -V 3 )
p 1 (V 4 -V 1 ) {1+  } + p 2 (V 2 -V 3 ){1+  }
 1
n -1
 1
n -1
but     mass delivered = mass induced
p 1 (V 1 -V 4 )
  RT 1
p 2 (V 2 -V 3 )
  RT 2
=
p 2 (V 2 -V 3 )
p 1 (V 1 -V 4 )
T 2
T 1
p 1 (V 1 -V 4 ) {  } [  -1]
 n
n-1
T 2
T 1
for a polytropic process :
T 2
T 1
p 2
p 1
n-1
 n
= (   ) = r p
n-1
 n
=
Noting that (V 1 -V 4 ) is the induced volume (V ind ), and p 1 is the
inlet pressure (p in ) we may re-arrange and write:
work per cycle =   p in V ind { r p  -1}
 n
n-1
n-1
 n
work per cycle =
+
+ +
=
but p 1 =p 4 & p 2 =p 3
work per cycle = + +
+
=
\
NB Power required = work per cycle x cycles per sec
Page 5


1
RECIPROCATING COMPRESSORS
There are various compressor designs:
Rotary vane; Centrifugal & Axial flow (typically used on gas
turbines); Lobe (Roots blowers), and Reciprocating .
The main advantages of the reciprocating compressor are that
it can achieve high pressure ratios (but at comparatively low
mass flow rates) and is relatively cheap.
It is a piston and cylinder device with (automatic) spring
controlled inlet and exhaust valves. Delivery is usually to a
receiver. The receiver is effectively a store of energy used to
drive (eg) compressed air tools.
Receiver
Delivery
TDC BDC
Inlet
Clearance vol.
¬   Swept vol.®
2
Reciprocating compressors usually compress air but are also
used in refrigeration where they  compress a superheated
vapour (to which the gas laws strictly do not apply).
In order to be practical there is a clearance between the piston
crown and the top of the cylinder. Air 'trapped' in this clearance
volume is never delivered, it expands as the piston moves
back and limits the volume of fresh air which can  be induced
to a value less than the swept volume.
The induced volume flow is an important purchasing
parameter. It is called the  "Free Air Delivery" (FAD), and it
measures the capacity of a compressor in terms of the air flow
it can handle.  It is normally measured at standard sea level
(SSL) atmospheric conditions and allows the capacities (size)
of compressors to be compared.
N.B. The induced mass per cycle must equal the delivered
mass per cycle (continuity!), although the induced and
delivered volumes will be different.
3
0
100
200
300
400
500
600
700
800
900
1000
0 0.2 0.4 0.6 0.8 1 1.2
4 ® 1                    Induction
1 ® 2                    Compression
2 ® 3                    Delivery
3 ® 4                    Expansion
Cycle Analysis
The cycle may be analysed as two non-flow (compression and
expansion) processes and two flow processes (delivery and
induction)
PROCESS      GROSS WORK
p 2 V 2 - p 1 V 1
n -1
p 2 (V 2 -V 3 )
p 4 V 4 - p 3 V 3
n-1
p 1 (V 4 -V 1 )
Note that we assume polytropic compression and expansion.
This is because some degree of cooling is usually attempted
for reasons we shall see later.
If no cooling were attempted n becomes g .
On p-V co-ordinates:
1
2 3
4
pressure (kPa)
Volume (litres)
4
The work per cycle is given by: å gross work
p 2 V 2 - p 1 V 1
n -1
p 2 (V 2 -V 3 )
p 4 V 4 - p 3 V 3
n-1
p 1 (V 4 -V 1 )
work per cycle =
+ + +
p 4 V 4 - p 1 V 1
n-1
p 2 V 2 - p 3 V 3
n-1
p 1 (V 4 -V 1 ) p 2 (V 2 -V 3 )
p 1 (V 4 -V 1 )
n-1
p 1 (V 4 -V 1 )
p 2 (V 2 -V 3 )
n -1
p 2 (V 2 -V 3 )
p 1 (V 4 -V 1 ) {1+  } + p 2 (V 2 -V 3 ){1+  }
 1
n -1
 1
n -1
but     mass delivered = mass induced
p 1 (V 1 -V 4 )
  RT 1
p 2 (V 2 -V 3 )
  RT 2
=
p 2 (V 2 -V 3 )
p 1 (V 1 -V 4 )
T 2
T 1
p 1 (V 1 -V 4 ) {  } [  -1]
 n
n-1
T 2
T 1
for a polytropic process :
T 2
T 1
p 2
p 1
n-1
 n
= (   ) = r p
n-1
 n
=
Noting that (V 1 -V 4 ) is the induced volume (V ind ), and p 1 is the
inlet pressure (p in ) we may re-arrange and write:
work per cycle =   p in V ind { r p  -1}
 n
n-1
n-1
 n
work per cycle =
+
+ +
=
but p 1 =p 4 & p 2 =p 3
work per cycle = + +
+
=
\
NB Power required = work per cycle x cycles per sec
5
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 10 20 30 40 50
Volumetric Efficiency
The reference conditions (p & T) at which the volumetric
efficiency is measured should always be quoted (it would
normally be SSL conditions).
[The concept of h vol applies also to reciprocating engines.]
We have already noted that the induced volume is less than
the swept volume. To enable this effect to be evaluated we
define volumetric efficiency ( h vol ) as:
h vol =
Induced volume
Swept volume
V 1 -V 4
  V s
=
but  p 3 V 3 = p 4 V 4
n n
\ V 4 = V 3 r p
1
n
V 3 is the clearance volume (V c ), and V 1 = V c + V s
h vol =
V c + V s - V c r p
   V s
1
n
\
h vol = 1 -    ( r p  - 1 )
V c
V s
1
n
h vol
r p
= 0.05
n = 1.27
Vc
Vs
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