Power Plant Engineering – DAY 10
Definitions:
Refrigeration - is the process of maintaining the space cooler than the
QR surrounding.
3
P
Condenser
P=C 2
S=C 3 2
P=C
h=C
C
Comp h=C
S=
m P=C 1
4
P=C WC
1
Evaporator h
4
P-h Diagram
QA=RE
Schematic Diagram
The Vapor Compression Cycle
1. Compressor Power (Wc) - is the power needed to compress the
refrigerant. h2
2
Wc = h2 - h1 , KJ/kg
h1 C Wc
Wc = m(h2 - h1), KW 1
where:
m = mass of refrigerant circulated
2. Heat Rejected (QR) - is the amount of heat rejected to the cooling
medium. t2
QR = h2 - h3 , KJ/kg
= m(h2 - h3), KW h3 QR
3
For cooling water:
2
QR = mw cP (t2 – t1), KW h2 t1
mW
3. Expansion Valve Process (h3 = h4)
h3 = h4 = hf4 + xhfg4
hfg4 = hg4 - hf4
where:
x = quality after expansion or weight of flash gas per
unit weight of refrigerant circulated
4. Refrigerating Effect (RE) - is the amount of heat gained from the
load.
RE = h1 - h4, KJ/kg = m(h1 - h4), KW
For chilling water:
RE = mw cP (t1 – t2), KW
5. Tons of refrigeration (TR)
TR =
TR =
where:
1 ton of refrigeration = 3.516 KW = 200 Btu/min
= 12,000 Btu/hr
Performance of Refrigeration System
1. Coefficient of Performance (COP) - is the ratio of
refrigerating effect and compression work.
COP =
COP =
2. Power Per Ton :
3. Energy Efficiency Ratio (EER) – the ratio of energy removed at the
evaporator (refrigerating effects) to the electrical energy consumed.
This shall conform with the standards set by the Department of
energy.
EER =
4. Volume Flow at Suction (V1)
V1 = mv1 , m3/sec
5. Volume Flow Per Ton :
6. Standard Refrigeration Cycle:
Evaporation Temperature = 5F(-15C)
Condenser Temperature = 86F(30C)
Chilling and Cooling Load
A. Chilled liquid in the evaporator:
1. Refrigerating effect = m(h1 - h4)
Heat loss from water = mL cp (t1 – t2)
Note:
Refrigerating Effect = Heat loss from water
2. Mass of liquid circulated (mL):
mL =
where:
m = mass flow of refrigerant
mL = mass of liquid circulated
CP = specific heat of liquid
= 4.187 KJ/kg-K for water
t1 = initial temperature of liquid
t2 = final temperature of liquid
B. Cooling water in the condenser:
1. Heat Rejected in the condenser (QR)
QR = m(h2 - h3)
QR = mw cP (t2 - t1)
2. Mass of cooling water required (mw):
mw =
3. Volume flow of cooling water required, Q:
VW =
where:
wH20 = density of water
(1 gallon = 3.785 li)
Motor and Compressor Performance
a. Efficiency of motor =
b. Efficiency of coupling =
c. Efficiency of compressor =
d. Over-all efficiency =
where: Pim = power input of motor
Pom = power output of motor
Pic = power input of compressor
Poc = power output of compressor
Reversed Carnot Refrigeration cycle:
a. QR = Heat Rejected in Condenser
= T2(S1 - S4) T QR
b. QA = Refrigerating Effect 3 2
= T1(S1 - S4) T=C
c. W = Net Work
= QR - QA = (T2 - T1)(S1 - S4) S=C S=C W
d. COP = T=C
4 1
QA
e. Tons of Refrigeration:
S
S4
S1
For a system operates in a Heat Pump:
For Carnot refrigerator:
COPC = COP cooling
COPC =
For Carnot Heat pump:
COPH =
COPH = COP heating or Performance factor
Relation of COP cooling and COP heating:
COPH = COPC + 1
Refrigeration Compressors
A. Compressor Output = m (h2 - h1)
B. Volume flow at suction,
V1 = m v1
C. Volume displacement, VD :
Single Acting Cylinder:
VD =
Double Acting Cylinder:
VD =
D. Volumetric efficiency, v :
E. Compression ratio
=
where: c = percent clearance
v1 = specific volume at suction
v2 = specific volume at discharge
D = bore = diameter
L = length of stroke
C = no. of cylinders
Degree Superheating and Degree Sub-cooling:
o
SC
3 2
1
4
o
SH
h
Where:
o
SH = degree superheat
o
SC = degree subcooled
Degree superheating
- is the difference between actual temperature entering the
compressor and the evaporator temperature.
SH = t1 - tevap
Degree subcooling
- is the difference between condenser temperature and the
actual temperature entering the expansion valve.
SC = tcon - t3
Where:
t1 = actual temperature entering the compressor
tevap = evaporator temperature
tcon = = condenser temperature
t3 = actual temperature entering the expansion valve
Cascade Refrigeration System:
7 6
condenser Note:
m2
TEV point 1-2: s=c
5 point 2-3: P=c
8 point 3-4: h=c
Compressor 2
2 point 4-1: P=c
3 Cascade m1 point 5-6: s=c
TEV
condenser point 6-7: P=c
1
point 7-8: h=c
evaporator
4 Compressor 1 point 8-5: P=c
P2=P3=P8=P5
Schematic Diagram
*
P-h Diagram
B. By heat balance in the cascade condenser:
8 5
3 2
m1(h2 - h3) = m2(h5 -h8)
where:
m1 = mass flow of refrigerant at low pressure loop
m2 = mass flow of refrigerant at high pressure loop
C. Total compressor power = WC1 + WC2
= m1(h2 - h1) + m2 (h6 - h5)
D. COP =
E. Refrigerating Effect
QA = RE = m1(h1 – h4)
F. Heat Rejected
m2(h6 – h7)
QR =
Product Load Calculations:
A. Load without freezing
Cooling Load: RE = mW cp (t1 – t2)
B. Load with freezing
Cooling Load =
Where:
T = time
C. Tons of Refrigerant, TR:
where:
m = mass of product
cP1 = specific heat above freezing
cP2 = specific heat below freezing
L = latent heat of fusion
t1 = initial temperature
tf = freezing temperature
t2 = final temperature
For Beef:
CP1 = 0.77 Btu/lb-R
CP2 = 0.41 Btu/lb-R
L = 100 Btu/lb
