compressor
TRANSCRIPT
Air or Gas Compressors: A steady-state, steady flow machine that is usedto compressed air or gas to final pressure exceeding 241.25 Kpa gage.Types of Compressor:
1. Centrifugal Compressors: For low pressure and high capacity applications.2. Rotary Compressors: For medium pressure and low capacity
application.3. Reciprocating Compressors: For high pressure and low capacity
application.Uses of compressed air:
1. Operation of small engines 2. Pneumatic tools 3. Air hoists 4. Industrial cleaning by air blast 5. Tire inflation 6. Paint Spraying
7. Air lifting of liquids8. Manufacture of plastics and other industrial products
9. To supply air in mine tunnels 10. Other specialized industrial applicationsAnalysis of Centrifugal and Rotary Type
1 Suction
2 Discharge
W (Work)
AssumptionKE = 0 PE = 0
For a compressor, work is done on the system W = h - Q 1. For Isentropic Compression: PVk = C Q = 0
W = h
P
V
P2
P1
PVk = C
Where:m – mass flow rate in kg/sec Cp – constant pressure specific heat in KJ/kg-C or KJ/kg-K
1kRk
Cp
111
k1k
1
211
k1k
1
2
1
2
12P
mRTVP
1PP
1kVkP
W
PP
TT
TTmCΔhW ; 0Q
2. Polytropic compression: PVn = C
111
n1n
1
211
Vn
n1n
1
2
1
2
12n12P
mRTVP where; 1PP
1nVnP
W
n1nk
CC ; PP
TT
TTmCQ ; TTmCh ; QΔhW
P
V
P2
P1
PVn = C
3. Isothermal Compression: PV = C
111
1
211
mRTVPPP
lnVPW
-QWtherefore 0h ; QΔhW
Analysis of Reciprocating Type Compressor (Piston-in-cylinder type):
piston
Valves
cylinder Piston rod
P
V
P2
P1
PV = C
Pressure-Volume Diagram (PV)
HE – head endCE – Crank endL – length of strokeP1 – suction pressureP2 – discharge pressureV1’ – volume flow rate at intakeVD – displacement volumeCVD – clearance volumeCVD = V3
L
HE CE
P
V1
23
4
P2
P1
V1’
VDCVD
VD
1. Isentropic Compression: PVk = C
11'1
k1k
1
21'1
k1k
1
2
1
2
12P
mRTVP
1PP
1kVkP
W
PP
TT
TTmCΔhW ; 0Q
Where:V1’ – volume flow rate at intake, m3/secm – mass flow rate corresponding V1’
P1 – suction pressure, KpaP2 – discharge pressure, KpaT1 – suction temperature, KT2 – discharge temperature, KW – work, KW
2. Polytropic Compression: PVn = C
n-1n-k
CCmRTVP1PP
1nVnP
WPP
TT
TTmCh ; TT mCQ Q;-ΔhW
vn11'1
n1n
1
21'1n
1n
1
2
1
2
12P12n
; ; ;
3. Isothermal Compression: PV = C
11'1
1
21'1
mRTVPPP
lnVPW
-QWtherefore 0h ; QΔhW
Percent Clearance: Ratio of the clearance volume to the displacement volume.
D3
D
3
CVV
100% xVV
C
Note: For compressor design values of C ranges from 3 to 10 percent.
Pressure Ratio: Ratio of the discharge pressure to suction pressure.
1
2p P
P=r
Volumetric Efficiency: Ratio of the volume flow rate at intake to the displacement volume.
% 100 xVV
=ηD
1'v
1. For Isentropic Compression and Expansion process: PVk = C
k1
1
2v P
PCC1η
2. For Polytropic Compression and Expansion process: PVn = C
n1
1
2v P
PCC1η
2. For Isothermal Compression and Expansion process: PV = C
1
2v P
PCC1η
Actual Volumetric Efficiency: Ratio of the actual volume of air drawn in by the compressor to the displacement volume.
100% xVV
ηD
ava
For an air compressor handling ambient air where pressure drop and heating of air occurs due to fluid friction and irreversibilities of fluid flow, less amount of air is being drawn by the cylinder. The actual volumetric efficiency is:
TT
PP
ηη1
O
O
1vva
Where:PO – ambient air pressure in KpaTO – ambient air temperature in K
Displacement Volume: Volume of air occupying the highest stroke L ofthe piston within the cylinder. The length of stroke L is the dis-tance from the HE (head end) to the CE (crank end).
1. For Single Acting: For single acting compressor, the piston works on one side (at head end only) of the cylinder.
secm
4(60)
Nn'LDV
32
Dπ
2. For Double Acting: For double acting compressor, the piston works on both sides (at head end & crank end) of the cylinder.
a. Without considering the volume of the piston rod.
secm
4(60)
Nn'LDV
32
D2π
b. Considering the volume of the piston rod.
secm
d-2D4(60)LNn'
V3
22D
π
Where:D – diameter of piston in metersd – diameter of piston rod in metersN – no. of RPMn’ – no. of cylinders
Piston Speed: It is the linear speed of the piston.
secm
602LN
PS
minm 2LNPS
Compressor Performance Factor:
1. Compression Efficiency: Ratio of Ideal Work to Indicated Work.
100% xWork Indicated
Work Idealηcn
2. Mechanical Efficiency: Ratio of Indicated Work to Brake or Shaft Work.
100% xWorkShaft or Brake
Work Indicatedηm
3. Compressor Efficiency: Ratio of Ideal Work to Brake or Shaft Work.
mcnc
c
η ηη
100% xWorkShaft or Brake
Work Idealη
MULTISTAGE COMPRESSION:Multi staging is simply the compression of air or gas in two or more cylinders in place of a single cylinder compressor. It is used in reciprocating compressors when pressure of 300 KPa and above are desired, in order to: 1) Save power 2) Limit the gas discharge temperature 3) Limit the pressure differential per cylinder 4) Prevent vaporization of lubricating oil and to prevent its ignition if the tem- perature becomes too high.It is a common practice for multi-staging to cool the air or gas between stages of compression in an intercooler, and it is this cooling that affects considerable saving in power.
2 Stage Compressor without pressure drop in the intercooler:
1 2 3 4Suction DischargeQx
Intercooler
1st stage 2nd stage
For an ideal multistage compressor, with perfect inter-cooling and minimum work, the cylinder were properly designed so that: a) the work at each stage are equal b) the air in the intercooler is cooled back to the initial temperature c) no pressure drop occurs in the intercooler
Work of 1st stage cylinder (W1): Assuming Polytropic compression on both stages.
11'1
n1n
1
21'11
mRTVP
1PP
1nVnP
W
Work of 2nd stage cylinder (W2): Assuming Polytropic compression on both stages.
33'3
n1n
3
43'32
mRTVP
1PP
1nVnP
W
P
V
P4
P1
Px
1
4
32
5
6
7
8
PVn = C
W1
W2
S
T
4
3
2
1
P4 Px P1
Qx
For perfect inter-cooling and minimum work:W1 = W2
T1 = T3
W = W1 + W2
W = 2W1
P2 = P3 = Px
thereforeP1V1’ = P3V3’
21
1
4
1
2
41x
32x3
4
1
2
PP
PP
PP P
then ; P P Pbut ; PP
PP
Where: Px – optimum intercooler pressure or interstage pressure
1PP
1nV2nP
W
1PP
1nV2nP
W
2n1n
1
41'1
n1n
1
21'1
Then the work W for an ideal 2-stage compressor is:
Heat losses calculation:1. Heat loss during compression at 1st stage cylinder
Q1 = mCn(T2 – T1)2. Heat loss during compression at 2nd stage cylinder
Q2 = mCn(T4 – T3)3. Heat loss in the intercooler
Qx = mCp(T2 – T3)
2 Stage Compressor with pressure drop in the intercooler:
1 2 3 4Suction DischargeQx
Intercooler
1st stage 2nd stage
With pressure drop in the intercooler:T1 T3 and P2 P3
W = W1 + W2
P1V1’ P3V3’
1PP
1nVnP
W
1PP
1nVnP
W
n1n
3
43'32
n1n
1
21'11
P
V
P4
P1
P3
1
4
32
5
6 7
8
PVn = C
W1
W2
S
T
4
3
2
1
P4 P1
Qx
P2
P2 P3
3 Stage Compressor without pressure drop in the intercooler:
1 2 3 4
Suction Discharge
Qx
LP Intercooler
1st stage 2nd stage 3rd stage
5 6Qy
HP Intercooler
S
T
4
3
2
1
P6 Px P1
Qx
P
V
P6
P1
Px
1
4
3
2
5
67
12
PVn = C
W1
W2
Py 9
10
11
8
W3
Py
5
6
Qy
For perfect inter-cooling and minimum work:T1 = T3 = T5 Px = P2 = P3 W1 = W2 = W3 Py = P4 = P5
W = 3W1P1V1’ = P3V3’ = P5V5’
mRT1 = mRT3 = mRT5
Therefore: rP1 = rP2 = rP3
Work for each stage:
1PP
1nVnP
Wn
1n
1
21'11
1st Stage:
1PP
1nVnP
Wn
1n
3
43'32
2nd Stage:
3rd Stage:
1PP
1nVnP
Wn
1n
5
65'53
3 261y
36
21x
y
6
x
y
1
x
5
6
3
4
1
2
PPP ; PPP
hence
PP
P
P
PP
or PP
PP
PP
Intercooler Pressures:
Total Work:
W = 3W1
11'1
3n1n
1
61'1
mRTVP
1PP
1nV3nP
W
Heat Losses during compression:Q1 = mCn(T2 – T1)Q2 = mCn(T4 – T3)Q3 = mCn(T6 – T5)
Heat loss in the LP and HP intercoolers:LP Intercooler
Qx = mCp(T2 – T3)HP Intercooler
Qy = mCp(T4 – T5)Note:1. For isentropic compression and expansion process, no heat loss during compression.2. For isothermal compression and expansion process, the loss during
compression is equivalent to the compression work, and no intercooleris required.
For multistage compression with minimum work and perfect inter-cooling and no pressure drop that occurs in the inter-coolers between stages, the following conditions apply: 1. the work at each stage are equal 2. the pressure ratio between stages are equal 3. the air temperature in the inter-coolers are cooled to the original temperature T1
4. the total work W is equal to
1PP
1nVSnP
W2S
1n
1
2S'
11Where: s – is the number of stages.
Note: For multistage compressor with pressure drop in the intercoolers the equation of W above cannot be applied. The total work is equal to the sum of the work for each stage that is computed separately.