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Lesson
10
Vapour Compression
Refrigeration Systems
1

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The specific objectives of the lesson:
This lesson discusses the most commonly used refrigeration system, i
...
Vapour
compression refrigeration system
...

2
...


The Carnot refrigeration cycle & its practical limitations (Section 10
...
4)
Analysis of Standard Vapour compression Refrigeration System (Section 10
...
Analyze and perform cyclic calculations for Carnot refrigeration cycle (Section
10
...
State the difficulties with Carnot refrigeration cycle (Section 10
...
Analyze and perform cyclic calculations for standard vapour compression
refrigeration systems (Section 10
...
Perform various cycle calculations for different types of refrigerants (Section
10
...
1
...
As
mentioned in the previous chapter, in a typical gas cycle, the working fluid (a gas) does
not undergo phase change, consequently the operating cycle will be away from the
vapour dome
...
In a vapour cycle the working fluid undergoes
phase change and refrigeration effect is due to the vaporization of refrigerant liquid
...
However, if a zeotropic mixture is used as a refrigerant, then there will
be a temperature glide during vaporization and condensation
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Hence, the required
mass flow rates for a given refrigeration capacity will be much smaller compared to a gas
cycle
...
Among these the vapour compression
refrigeration systems are predominant
...
2
...
As the name implies, these systems belong to the general
class of vapour cycles, wherein the working fluid (refrigerant) undergoes phase change at
least during one process
...
The input to the system is in
the form of mechanical energy required to run the compressor
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Vapour compression refrigeration

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systems are available to suit almost all applications with the refrigeration capacities
ranging from few Watts to few megawatts
...
The actual vapour compression
cycle is based on Evans-Perkins cycle, which is also called as reverse Rankine cycle
...
This limit is set by a completely reversible
cycle
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3
...
It is used as reference against which the real cycles are compared
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1
(a) and (b) show the schematic of a Carnot vapour compression refrigeration system and
the operating cycle on T-s diagram
...
10
...
Refrigeration effect (q41 = qe) is obtained at the evaporator as the refrigerant undergoes the process of
vaporization (process 4-1) and extracts the latent heat from the low temperature heat
source
...
The refrigerant pressure increases from Pe
to Pc during the compression process (process 1-2) and the exit vapour is saturated
...
The high pressure saturated liquid then flows through
the turbine and undergoes isentropic expansion (process 3-4)
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Since a saturated liquid is expanded in
the turbine, some amount of liquid flashes into vapour and the exit condition lies in the
two-phase region
...
Thus as shown in Fig
...
1(b), the cycle
involves two isothermal heat transfer processes (processes 4-1 and 2-3) and two
isentropic work transfer processes (processes 1-2 and 3-4)
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Work is supplied to the compressor during
the isentropic compression (1-2) of refrigerant vapour from evaporator pressure Pe to
condenser pressure Pc, and work is produced by the system as refrigerant liquid expands
isentropically in the turbine from condenser pressure Pc to evaporator pressure Pe
...
e
...

Applying first and second laws of thermodynamics to the Carnot refrigeration cycle,

∫ δq = ∫ δw
∫ δq = q 4 −1 − q 2 −3 = q e − q c
∫ δw = w 3− 4 − w 1− 2 = w T − w C = − w net

3

(10
...
10
...
10
...
ds = Tc (s 2 − s 3 )

(10
...
ds = Te (s 1 − s 4 )

(10
...
4)

the Coefficient of Performance (COP) is given by:

COPCarnot =

⎛ Te
q
Te (s1 − s 4 )
refrigeration effect
= e =
=⎜
net work input
w net Tc (s 2 − s 3 ) − Te (s1 − s 4 ) ⎜ Tc − Te
⎝

⎞
⎟
⎟
⎠

(10
...
This is the
reason why exactly the same expression was obtained for air cycle refrigeration systems
operating on Carnot cycle (Lesson 9)
...
From Carnot’s theorems, for the same heat source and sink
temperatures, no irreversible cycle can have COP higher than that of Carnot COP
...
10
...
Carnot refrigeration cycle represented in T-s plane

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It can be seen from the above expression that the COP of a Carnot refrigeration system
increases as the evaporator temperature increases and condenser temperature decreases
...
10
...
As shown
in the figure, COP is the ratio of area a-1-4-b to the area 1-2-3-4
...
Similarly for a fixed
evaporator temperature Te, as the condensing temperature Tc increases, the net work input
(area 1-2-3-4) increases, even though cooling output remains constant, as a result the
COP falls
...
3 shows the variation of Carnot COP with evaporator temperature
for different condenser temperatures
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COP reduces as
the condenser temperature increases, but the effect becomes marginal at low evaporator
temperatures
...


Fig
...
3
...
During process 1-2, a mixture consisting of liquid and vapour have to be compressed
isentropically in the compressor
...
In practice, wet compression is very difficult especially with
reciprocating compressors
...
Even though some types of compressors can tolerate the presence of liquid in

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vapour, since reciprocating compressors are most widely is refrigeration, traditionally dry
compression (compression of vapour only) is preferred to wet compression
...
The second practical difficulty with Carnot cycle is that using a turbine and extracting
work from the system during the isentropic expansion of liquid refrigerant is not
economically feasible, particularly in case of small capacity systems
...
dP

(10
...
In
addition, if one considers the inefficiencies of the turbine, then the net output will be
further reduced
...

One way of achieving dry compression in Carnot refrigeration cycle is to have two
compressors – one isentropic and one isothermal as shown in Fig
...
4
...
10
...
Carnot refrigeration system with dry compression
As shown in Fig
...
4, the Carnot refrigeration system with dry compression consists of
one isentropic compression process (1-2) from evaporator pressure Pe to an intermediate
pressure Pi and temperature Tc, followed by an isothermal compression process (2-3)
from the intermediate pressure Pi to the condenser pressure Pc
...
In addition, use of two compressors in place of one is not
economically justified
...


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From the above discussion, it is clear that from practical considerations, the Carnot
refrigeration system need to be modified
...
Similarly, the isentropic expansion process can be replaced by an isenthalpic
throttling process
...
This is the theoretical cycle on which
the actual vapour compression refrigeration systems are based
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Device

C

wc

4

Evaporator

1

qe

Pc

T

2

Tc
Te

Pe

2'

3

4

1

S

Fig
...
5
...
4
...
5 shows the schematic of a standard, saturated, single stage (SSS) vapour
compression refrigeration system and the operating cycle on a T s diagram
...
As a result, one would expect the theoretical COP of standard cycle to be smaller than
that of a Carnot system for the same heat source and sink temperatures
...
This can be explained easily with the help of the cycle diagrams on T s
charts
...
6(a) shows comparison between Carnot and standard VCRS in terms of
refrigeration effect
...
10
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Comparison between Carnot and standard VCRS
The heat extraction (evaporation) process is reversible for both the Carnot cycle and
VCRS cycle
...
ds = Te (s 1 − s 4' ) = area e − 1 − 4'−c − e

(10
...
ds = Te (s 1 − s 4 ) = area e − 1 − 4 − d − e

(10
...
The throttling loss
is equal to the enthalpy difference between state points 3 and 4’, i
...
9)

It is easy to show that the loss in refrigeration effect increases as the evaporator
temperature decreases and/or condenser temperature increases
...

The heat rejection in case of VCRS cycle also increases when compared to Carnot cycle
...
10
...
Comparative evaluation of heat rejection rate of VCRS and Carnot cycle
As shown in Fig
...
6(b), the heat rejection in case of Carnot cycle (1-2’’-3-4’) is given
by:
3

q c,Carnot = − q 2''−3 = − ∫ T
...
10)

2 ''

In case of VCRS cycle, the heat rejection rate is given by:
3

q c,VCRS = − q 2−3 = − ∫ T
...
11)

2

Hence the increase in heat rejection rate of VCRS compared to Carnot cycle is equal to
the area 2’’-2-2’ (area A1)
...

Since the heat rejection increases and refrigeration effect reduces when the Carnot cycle
is modified to standard VCRS cycle, the net work input to the VCRS increases compared
to Carnot cycle
...
12)
(10
...
10
...
14)
T

A1
2
3

2'

2’’

4'

1

4

A2
c

e

d

S

Fig
...
6(c)
...
15)

w net , VCRS = w net ,Carnot + area A 1 + area A 2

(10
...
17)

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If we define the cycle efficiency, ηR as the ratio of COP of VCRS cycle to the COP of
Carnot cycle, then:
⎡
⎤
⎛ area A 2 ⎞
⎟
1− ⎜
⎢
⎥
⎟
⎜q
COPVCRS ⎢
⎥
⎝ e,Carnot ⎠
(10
...
Unlike Carnot COP, the cycle
efficiency depends very much on the shape of T s diagram, which in turn depends on the
nature of the working fluid
...
19)

Fig
...
7
...
10
...
20)

2

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f

and, (h 1 − h f ) = ∫ Tds = area e − 1 − f − g − e

(10
...
Now comparing this with the earlier
expression for work input (area 1-2-3-4’-c-d-4-1), we conclude that area A2 is equal to
area A3
...
The shape of the saturation curves depends on the nature of refrigerant
...
8 shows T s diagrams for three different types of refrigerants
...
10
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T-s diagrams for three different types of refrigerants
Refrigerants such as ammonia, carbon di-oxide and water belong to Type 1
...
That means deviation of
VCRS cycle from Carnot cycle could be significant when these refrigerants are used as
working fluids
...

High molecular weight refrigerants such as CFC113, CFC114, CFC115, iso-butane
belonging to Type 3, do not have any superheat losses, i
...
, when the compression inlet
condition is saturated (point 1), then the exit condition will be in the 2-phase region, as a
result it is not necessary to superheat the refrigerant
...
Since the compressor exit condition of Type 3
refrigerants may fall in the two-phase region, there is a danger of wet compression
leading to compressor damage
...
This
implies that the refrigerant at the inlet to the compressor should be superheated, the
extent of which depends on the refrigerant
...
The superheat loss increases only the work input to the
compressor, it does not effect the refrigeration effect
...
However, the process of throttling is
inherently irreversible, and it increases the work input and also reduces the refrigeration
effect
...
5
...
The steady flow energy
equation is applied to each of the four components
...


Evaporator: Heat transfer rate at evaporator or refrigeration capacity, Q e is given by:

...


Q e = m r (h 1 − h 4 )

(10
...


where m r is the refrigerant mass flow rate in kg/s, h1 and h4 are the specific enthalpies
(kJ/kg) at the exit and inlet to the evaporator, respectively
...
The evaporator pressure Pe is the saturation
pressure corresponding to evaporator temperature Te, i
...
,
Pe = Psat (Te )

(10
...


Compressor: Power input to the compressor, W c is given by:

...


W c = m r (h 2 − h 1 )

(10
...
(h 2 − h 1 ) is known as specific work of compression or simply work of
compression, which is equal to the work input to the compressor per kilogram of
refrigerant
...


Condenser: Heat transfer rate at condenser, Q c is given by:

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...


Q c = m r (h 2 − h 3 )
(10
...

The condenser pressure Pc is the saturation pressure corresponding to evaporator
temperature Tc, i
...
,
Pc = Psat (Tc )
(10
...
27)
The exit condition of the expansion device lies in the two-phase region, hence applying
the definition of quality (or dryness fraction), we can write:
h 4 = (1 − x 4 ) h f ,e + x 4 h g ,e = h f + x 4 h fg

(10
...

The COP of the system is given by:
⎛
...
e ⎟ = ⎜
...
29)


...
e
...



...
30)

v

applying this equation to the inlet condition of the compressor,

...


mr =

V1

v1

(10
...


where V1 is the volumetric flow rate at compressor inlet and v1 is the specific volume at

...
At a given compressor speed, V1 is an indication of the size of the
compressor
...


...
⎛h −h
4
Q e = m r (h 1 − h 4 ) = V 1 ⎜ 1
⎜ v
1
⎝

⎛ h −h4
where ⎜ 1
⎜ v
1
⎝

⎞
⎟
⎟
⎠

(10
...

⎟
⎠

Generally, the type of refrigerant, required refrigeration capacity, evaporator temperature
and condenser temperature are known
...
Since the exit condition of the
compressor is in the superheated region, two independent properties are required to fix
the state of refrigerant at this point
...
Since the compression process is isentropic,
the entropy at the exit to the compressor is same as the entropy at the inlet, s1 which is the
saturated vapour entropy at evaporator pressure (known)
...
e
...
33)
s1 = s 2
The quality of refrigerant at the inlet to the evaporator (x4) could be obtained from the
known values of h3, hf,e and hg,e
...

Use of Pressure-enthalpy (P-h) charts:

Te

Tc

Pc

3

2'

2

P
Pe

4

1

h3 = h4

h1

h2

h

Fig
...
9
...
The use of these charts was first suggested by Richard Mollier
...
9
shows the standard vapour compression refrigeration cycle on a P-h chart
...
The
isotherms are almost vertical in the subcooled region, horizontal in the two-phase region
(for pure refrigerants) and slightly curved in the superheated region at high pressures, and
again become almost vertical at low pressures
...
Using P-h charts one can easily find various performance parameters from known
values of evaporator and condenser pressures
...


Questions:
1
...

Determine the work of compression and cooling effect produced by the cycle
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An ideal refrigeration cycle operates with R134a as the working fluid
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The mass flow rate of refrigerant is 0
...
Determine the cooling
capacity and COP of the plant
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A R-12 plant has to produce 10 tons of refrigeration
...
Determine
a)
b)
c)
d)
e)
f)

Refrigerant flow rate
Volume flow rate of the compressor
Operating pressure ratio
Power required to drive the compressor
Flash gas percentage after throtting
COP (Solution)

4
...
The cycle
operates between 25ºC and -15ºC
...

If the COP is 50% of theoretical COP, calculate the power required to drive the
compressor
...
In a refrigerator the power rating impressed on the compressor is 1
...
The
circulating wire in evaporator is 5 kW and the cooling water took away 10 kW from
condenser coil
...
Find the actual COP of the system (2) relative COP, assuming
the vapour is just dry and saturated at the end of the compression
...
A water cooler using R12 refrigerant works between 30ºC to 9ºC
...
7 kJ/kg K (Solution)
The properties of F12 at 30ºC and 2ºC are:
Temp ºC

30
5

Pressure (Bar)

7
...
626

Liquid
hf (kJ/kg)
Sf
(kJ/kg K)
64
...
2399
40
...
1587

18

hg
(kJ/kg)
199
...
7

Vapour
Sg
(kJ/kg K)
0
...
6942

vs
m3/kg
0
...
0475

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