Chapter3 Compressor
Chapter3 Compressor
Chapter3 Compressor
COMPRESSOR
CONTENT
• Working Cycle and p-v Diagram
• Indicated Power and work
• Conditions for minimum work
• Mechanical Efficiency
• Isothermal Efficiency
• Clearance Volume
• Volumetric Efficiency
• Multistage Compressor 2
What is Compressor?
Compressors uses mechanical work to take an
amount of fluid and deliver it at a required
pressure
An efficient compressor increases pressure
with minimum work
The amount of fluid is limited by the volume
of the compressor cylinder which is fixed
The reciprocating compressor operates in a
cyclic manner
The properties of the working fluid at inlet
and outlet are average values 3
CLASSIFICATION
COMPRESSOR
(a – b): Compression v2 v1
Inlet valve closes p
Piston compresses air
Pressure rises until P2 at (b) c
p2 b
Temperature also increases
(b – c): Delivery
Delivery valve opens
High pressure air is delivered
Pressure and temperature is constant
during this process p1 d a
p2v 2 p1v 1
Win
1 n
where
n polytropic index of a gas
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WORK & INDICATED
POWER
Work input per cycle p
Win area abcd
cycle
P2 c b
area abef area bc0e area ad0f
p V p1Va p V p V
2 b 2 b 1 a
n 1
p V p1v a (n 1) p 2v b (n 1) p1v a
2 b
n 1 P1 d a
n
p 2Vb p1Va V
n 1 0 e f
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CONDITIONS FOR MINIMUM
WORK
We know that the work done is equal to the area under the
graph
The smaller the area the lesser the work and the better the
compressor
For reciprocating compressors, the pressure ratio is fixed, so the
height of p-v diagram is fixed
The volume of cylinder is also fixed so the line d-a is fixed
Therefore the area representing work depends the index n.
For n = 1,
pV = constant (Isothermal)
For n = ,
pV = constant (isentropic)
So, the process can be polytropic, isothermal or isentropic
12
CONDITIONS FOR MINIMUM
WORK
pV =constant (isothermal)
p
pV =constant (isentropic) b1 b b2
pVn =constant (polytropic) P2 c
pV = C
pVn = C
From here it can be seen
pV = C
that the isothermal process
is the best because it
requires minimum work P1 d a
13
CONDITIONS FOR MINIMUM
WORK
ISOTHERMAL WORK p
Work area ab1ef area b1c0e - area ad0f b1
P2 c
p1
p2Vb1 ln p1Vb1 p1Va
p2
pV = C
for isothermal process p1Va p2Vb
p1 p1
Win p2Vb1 ln p1Va ln
p2 p2
From pV mRT P1 d a
p
Win mRT ln 1
p2 0 e f
where T is the constant temperature V
p
Isothermal power m RT ln 2
p1
14
CONDITIONS FOR MINIMUM
WORK
ISOTHERMAL EFFICIENCY
Isothermal efficiency indicates isothermal work compared to the
indicated work.
Isothermal Work
Isothermal Efficiency ,isoth
Indicated Work
15
EXAMPLE
A single stage reciprocating compressor induce
1.23kg/min of air at pressure 1.023 bar and
temperature 23oC and delivers it at 8.5 bar. If its
polytropic index is 1.3, determine:
i. Indicated power
ii. Isothermal power
iii. Isothermal efficiency
16
MECHANICAL EFFICIENCY,
ηm
Because there are moving mechanical parts in the
compressor, it is likely that losses will occur due to
friction
Therefore power required to drive the compressor is
actually more higher than the indicated power
So there is need to measure the mechanical efficiency of
the cycle
Mechanical efficiency of the compressor is given by:
indicated power
m required power
17
MECHANICAL EFFICIENCY,
ηm
4.5kW
Shaft power 5.625kW
0.8
18
Example
A single stage reciprocating compressor operates by inducing 1m3/min
of air at 1.013 bar and 15oC and delivers it at 7bar. Assume the
compression process being polytropic and the polytropic index is 1.35.
The compressor is to be driven at 300 rev/min and is a single acting,
single cylinder machine, Calculate:
i. Mass of air delivered per minute
ii. Indicated power
iii. The cylinder bore required, assuming a stroke to bore
ratio of 1.5/1
iv. The power of the motor required to drive the compressor
if the mechanical efficiency of the compressor is 85% and
that of the motor transmission is 90%
19
CLEARANCE VOLUME (VC)
20
CLEARANCE VOLUME (VC)
Process P
After delivery at (c) (volume is VC, e c b
p2
pressure is p2 and temperature is
PVn = C
T2). So, there are some gas left in
the cylinder PVn = C
When piston moves downward, this
gas expands according to PVn = C
until p1 at (d). p1
f d a
Then induction begins (d – a)
Then gas is compressed according v
VC VS
to PVn = C
Finally there is the delivery (b – c) VC = Clearance volume
VS = Swept volume
21
Effect of VC
Because of the expansion of gas
remaining in the VC, induced P
volume is reduced from swept p2
e c b
volume VS to (Va – Vd) which is
PVn = C
the effective volume
PVn = C
V Va Vd or V Va Vd
Mass or air per unit time p1
f d a
m a m b and m c m d
VC VS v
Mass delivered per unit time =
mass induced per unit time
m
m b m
c m
a m
d
22
CLEARANCE VOLUME (VC)
INDICATED WORK & INDICATED POWER FOR
COMPRESSOR WITH CLEARANCE VOLUME
Work done per cycle
W area abcd area abef - area cefd
cycle
n n
Indicated power W ma R T 2 T 1 md R T 2 T 1
n 1 n 1
n
m a m d R T 2 T1
n 1
P
because m a m d m mass induc ed per unit time
e c b
n 1
p2
n n p n
W mR T 2 T 1
mRT 1 2
1
n 1 n 1 p PVn = C
1
kg
where m N m PVn = C
min
kg
or m N ma md
min
p1
We see here that the work done per cycle and f d a
indicated power per unit mass is the same whether
23 v
with or without clearance VC VS
Double-acting Compressors
A single-acting compressor completes one compression cycle with one
revolution of the crank
A double-acting compressor completes two compression cycles with one
revolution of the crank
So the mass induce per revolution is twice than a single acting where
kg kg
m 2 N m or m 2 N ma md
min min
Delivery Delivery
Induction Induction
24
EXAMPLE
A single stage, double-acting compressor is required to
deliver 8m3/min of air measured at pressure of 1.013 bar and
15oC. Delivery pressure is 6 bar and crank speed is 300rpm.
The clearance volume is 5% of swept volume and the
compression index is 1.3. Calculate
i. Swept volume, VS
ii. Delivery temperature, T2
iii. Indicated power
25
EXAMPLE
A single stage, single-acting compressor running at 1000
rev/min deliver air at 25 bar. For this purpose the induction
and free air conditions can be taken as 1.013 bar and 15oC,
and the FAD as 0.25m3/min. The clearance volume is 3% of
swept volume and the compression index is 1.3. and the
stroke/bore ratio is 1.2/1. Calculate
i. Bore and stroke size
ii. Volumetric efficiency
26
VOLUMETRIC EFFICIENCY, ηv
27
VOLUMETRIC EFFICIENCY, ηv
So by first definition,
P
P1 Va Vd e c b
RT 1 P V Vd RT 0 p2
v 1 a
P0V s RT 1 P0V s PVn = C
RT 0
PVn = C
v
Va Vd P1 T 0
Vs P0 T1
p1
If assume P1 Po and T 1 T o , v
V Vd
a
f d a
Vs
VC VS v
V s Vc V d V s Vc V d
v
Vs Vs Vs Vs
V V V V
v 1 c 1 d 1 c d 1 (1)
V s Vc V s V c
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VOLUMETRIC EFFICIENCY, ηv
n n
Since P1Vd P2Vc
1
n
Vd P Vd P2 n
2 and therefore
V c P1 Vc P1
29
VOLUMETRIC EFFICIENCY, ηv
2nd definition:
The ratio of the actual volume (Vactual) in the cylinder that is
measured at free air condition with swept volume (Vs)
30
VOLUMETRIC EFFICIENCY, ηv
Combining the two mathematical definition, we get
Po Vactual P1 V a Vd
RT o RT 1
P1 T 0
Vactual Va Vd (1)
P0 T 1
v
Va Vd P1 T 0
Vs P0 T1
Note that the equation above is the same the one in the first
definition.
31
Example
A single stage, double-acting air compressor has a
FAD of 14 m3/min measured at pressure of 1.013 bar
and 15°C. The pressure and temperature in the
cylincer during induction are 0.95 bar and 32°C. The
delivery pressure is 7 bar and the index of
compression and expansion is 1.3. The clearance
volume is 5% of swept volume. Calculate:
i. Indicated power
ii. Volumetric efficiency
iii. Swept volume
32
MULTI-STAGING COMPRESSOR
• When delivery pressure is
increased to a higher value,
P
several weaknesses were
found: p4 c” b”
p1
• To overcome those matter, d d’ d” a
multi-staging compressor is
V
introduced VC VS
33
MULTI-STAGING COMPRESSOR
Coolant in Coolant out
Intercooler
LP Compressor HP Compressor
It consist of more than one compressor where the air passes through
an intercooler before entering the next compressor.
The size of the next compressor is smaller to compromise Vs.
In the intercooler, heat is transferred to the surrounding and
temperature will decreased. It will be brought back to its inlet
temperature (before induction process).
It is assumed that all compressors will have the same polytropic
34
index.
MULTI-STAGING COMPRESSOR
a-b : PVn=C compression p
g
b-e : Q from air to surrounding P2 f
Te=Ta CPMPRESSOR
V
Vc Vs
***NOTES:
a. Since no mass is allow to escape during its travel, mLP = mHP
b. If pressure ratio and the ratio of Vc/Vs is the same, volumetric efficiency
for both compressor is the same. 35
EXAMPLE
In a single acting, two-stage reciprocating air compressor, 4.5 kg/min of
air is compressed from 1.013 bar and 15oC surrounding conditions through
a pressure ratio of 9 to 1. Both stages have the same pressure ratio, and
the law of compression and expansion in both stages is PV1.3=C. The
clearance volume of both stages are 5% of their respective swept volumes
and it runs at 300 rpm. If inter cooling is complete, calculate:
i. Indicated power
ii. Volumetric efficiency
iii. Cylinder swept volumes required.
iv. Shows the power saving on p -v diagram and get the value in
percentage.
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