39
1 Martti Veuro / Aki Valkeapää COOLING TECHNOLOGY Building services PART 1 MAMK / MUAS Mikkeli University of Applied Sciences
1
Martti Veuro / Aki Valkeapää
COOLING TECHNOLOGY
Building services
PART 1
MAMK / MUAS
Mikkeli University of Applied Sciences
2
CONTENT
1 Introduction (AkiV) ...................................................................................................................... 3
2 THERMODYNAMIC BASIC PRINCIPLES AND CONCEPTS ............................................... 5
3 HEAT ENGINE, HEAT PUMP AND COOLING MACHINE ................................................... 7
4 COEFFICIENT OF PERFORMANCE COP and EER (page 2:7) ............................................... 8
5 Coefficients of performance of the Carnot refrigerator and heat pump ..................................... 10
6 Refrigerants, diagrams and tables of properties (page 5:1 ...) .................................................... 12
7 A cooling machine and a heat pump in the vapour compression cycle ...................................... 17
8 Condensation and evaporation in log(p), h -diagram Virhe. Kirjanmerkkiä ei ole määritetty.
9 ISENTROPIC EFFICIENCY AND REAL COMPRESSION ................................................... 26
10 SUBCOOLING OF THE REFRIGERANT .......................................................................... 27
11 SUPERHEATING OF REFRIGERANT IN EVAPORATOR AND SUCTION LINE ......... 29
12 INTERNAL HEAT EXCHANGER ....................................................................................... 31
13 VOLUME FLOW RATE, VOLUMETRIC REFRIGERATING EFFECT ........................... 33
14 COOLING / REFRIGERATING CAPACITY (POWER) OF EVAPORATOR AND
COMPRESSOR UNDER THE CONDITIONS OF CALCULATIONS .......................................... 36
15 EER Energy efficiency ratio (total COP2t) .............................................................................. 36
16 REAL VAPOUR CYCLE ....................................................................................................... 38
3
1 Introduction
Cooling of supply air or operation of water chillers, ground source heat pumps, air to air heat pumps
and local split / cooling units bases on the vapour compression cycle.
In the following figure can be seen the vapour compression cycle of a cooling machine or a heat
pump, main components, sub processes and piping between main components.
1-2 compression in compressor
2-3 superheat removal in condenser
3-4 condensing in condenser
4-5 subcooling in condenser
5-6 pressure drop and expansion in expansion / throttling valve
6-7 evaporation of wet vapour in evaporator
7-1 superheating in evaporator and in suction line
Figure. Main components and vapour compression cycle (Kaappola 1996)
To be able to analyze the process and operation of cooling systems and heat pumps, you must
understand the compression vapour cycle. Domestic refrigerators, commercial cooling in retail
shops, storing of frozen products etc. are also based on the same process.
In the following chapter is discussed the thermodynamic principles of the cycle.
A Compressor
B Condenser
C Liquid tank
D Expansion valve
E Evaporator
F Pipings
a Suction line
b Discharge line
c Condense line
d Liquid line
a
c
d
b d
4
Figure. Cooling cycle and main components
Figure. Compressor cooling system (water chiller) with indirect condensing and cooling and
equipped with free cooling using outdoor air.
1. low pressure vapour
2. high pressure vapour
3. high pressure liquid
4. partly evaporated mixture
5
Figure. A heat pump equipped with two different heat exchangers. 16=desuperheater for highest
possible water temperature, utilising heat stratification in the tank.
2 THERMODYNAMIC BASIC PRINCIPLES AND CONCEPTS
A machine or a part of it can be inspected as a thermodynamic system. Around the system border is
the environment / surroundings. Between system and surroundings is “balance” boundary (control
boundary). Between system and surroundings can occur substance flow qm , mechanical work W or
heat transfer Q.
System is closed if there is no transferring of substance over the system border. In other cases the
system is open. In the open system substance and material is transferred over the border. The
system is adiabatic (thermally insulated) if there is no heat transfer over the system border (Q = 0).
When there is no interaction between system and surroundings then the system is isolated.
A stationary system does not depend on time. When state of system changes during time it is
nonstationary system. In a stationary system substance and energy flows in and out of system are
equal.
qm1
qm2 (=qm1)
balance boundary
system
environment/
surroundings
Φ
h1
h2
6
Figure. An open stationary system (cooling compressor)
Mechanical work (e.g. compressor shaft power needed to maintain refrigerating cycle) is
τ
WP = (1)
P mechanical power, kW (=kJ/s)
W mechanical work, kJ
τ time, s
Thermal power (e.g. thermal power extracted from condenser to the surroundings) is
τφ
Q= (2)
φ thermal power, kW (=kJ/s)
Q thermal energy, kJ
τ time, s
In cooling technology enthalpy and entropy are key (physical) thermo dynamical magnitudes.
Enthalpy is expressing energy (heat content). Unit is kJ/kg. The change of enthalpy is used when is
calculated cooling power of evaporator, heat power of condenser or compressor shaft power.
Enthalpy can be seen and read in refrigerant diagrams. When the refrigerant mass flow rate is
known then the power of evaporator, condenser or compressor can be calculated using the
following formula
kmk
lm
hm
hqP
hq
hq
∆⋅=
∆⋅=Φ
∆⋅=Φ
1
2
(3)
Φ2 cooling power of evaporator, kW
∆hh change of enthalpy in evaporator, kJ/kg
Φ1 heating power of condenser, kW
∆hl change of enthalpy in condenser, kJ/kg
Pk compressor shaft power, kW
∆hk change of enthalpy in condenser, kJ/kg
Entropy is a physical magnitude which expresses ”disorder” in a system. Unit is kJ/kg, K. Concept
of entropy is needed when the compression process is studied. When refrigerant is compressed in
P
7
the compressor so that there is no change of entropy then the compression is called isentropic
compression. Isentropic compression necessitates that there are no losses like friction or heat
transfer to surroundings. Isentropic compression is lossless reversible process. In a real compressor
(compression) there are always losses and heat transfer so the entropy changes / increases during
compression. A real process can never be isentropic or lossless. Isentropic compression is used as a
reference process for a real compression (isentropic efficiency of compressor).
Real processes are irreversible. Real processes can ”happen” by themselves only into one direction.
Some examples of irreversible processes where entropy changes because of actual compression and
compressor:
• mechanical work changes into heat because of friction (heat cannot change into mechanical
work by friction)
• heat transfer from the compressor outer surface to the surroundings (heat do not transfer
from surroundings to the compressor because tcompressor > tsurroundings.
3 HEAT ENGINE, HEAT PUMP AND COOLING MACHINE
Heat engine is a machine, which takes heat from one sink (source), converts it partly to work and
rejects rest of heat to another sink. So the heat engine is a machine in which heat is converted to
mechanical work. Heat is often got as a result of combustion process. E.g. in a steam boiler water is
vaporized with the heat of fuel / combustion, steam / vapour is lead as superheated into a turbine
and then cooled steam is lead through condenser back to the steam boiler as water.
T2 < T1
Figure. Heat engine
Heat pump is a reverse heat engine. It takes heat from one storage (e.g. ground) and transfers it with
the work of a compressor to another storage (e.g. hot water heating water).
T2 < T1
Figure. Heat pump.
W
T1 T2
W
T2 T1
8
A cooling machine operates like a heat pump, because with both machines heat is transferred from a
lower temperature source to a higher temperature sink (surroundings). When the removed heat
(”cold”) is utilized the machine is called a cooling machine and when the rejected / extracted heat is
utilized it is then called a heat pump. Sometimes these two are utilized at the same time like e.g.
skating hall ice – heating of other spaces like sports hall or a swimming pool. The machine can be
called ”refrigeration heat pump”.
4 COEFFICIENT OF PERFORMANCE COP and EER (page 2:7)
Some fundamentals (mostly based on Refrigerating engineering, Granryd et al, 2009)
Heat is transferred by itself from a higher temperature (heat source) to a lower temperature (heat
sink).
If you want create and maintain a system at a lower temperature than in its surroundings, heat must
be removed / pumped from the refrigerated space or substance (e.g. refrigerator, cooled storage
room etc.). This means that work must be done.
Also when spaces and rooms are cooled with air (tsupply air < troom) or with water (twater < troom) heat
must be removed / pumped from air or water so to say work must be done.
T1 > T2
According to the first law of thermodynamics, ”conservation of energy”, ”neither energy nor matter
can be destroyed”.
EQQ += 21
P+Φ=Φ 21
According to the second law of thermodynamics heat is never transferred from a lower temperature
source to a higher temperature sink without work (work must be done).
The amount of utilized cooling or heating power / capacity / energy is called either EER (standard
SFS-EN 14511-1, energy efficiency ratio, cooling, also COP2) or COP (coefficient of performance,
COP1, heating, heat pump).
Refrigeration process E (P)
T1
T2
Q2 ( Φ2 )
Q1 ( Φ1)
9
The momentary COP is
PCOPEER t
22
Φ==
units: kW / kW
and for a certain time period
E
QCOPEER t
22 ==
units: kJ / kJ
When the heat removed is utilized (heat pump) the momentary coefficient of performance COP1 is
PCOPt
11
Φ=
and for a certain time period (e.g. one year = annual coefficient of performance) is
E
QCOPt
11 =
If all the terms in the previous equation are divided with E we’ll get
122
11 +=+== COP
E
E
E
QCOP
E
Q
21
22
TT
TCOP C
−=
and respectively for heat pump
21
1
1TT
TCOP C
−=
Those two previous equations are only valid for ideal (lossless) process. Actual process includes
always losses.
For an actual / real process / cycle is used the coefficient of performance of the Carnot refrigerator
21
22
TT
TCOP Ct
−×=η (cooling)
12
11
TT
TCOP Ct
−×=η (heat pump)
10
This coefficient of performance of the Carnot refrigerator depends on the process (in a vapour
process of the thermodynamic efficiency of the refrigerant) and the quality factor of the compressor
(efficiency).
See page 2:11 and Figure 2.16
5 Coefficients of performance of the Carnot refrigerator and heat pump
Carnot cycle is the ideal reference process for the cycle. Theoretically the best possible COP / EER
(Carnot efficiency, 2.13) depends only of temperatures T1 and T2 (absolute = thermodynamic
temperatures K) for cooling machine and heat pump. Coefficient of performance of Carnot cycle
depends only on evaporation and condensing temperatures.
Fig 1 shows the Carnot cycle on the area of wet vapour in T-s diagram.
Fig. 1. (see page 3:14 Fig. 3.16)
1-2 isentropic compression from T2 to T1
2-3 isothermal heat removal at temp T1
3-4 isentropic expansion to temp. T2
4-1 isothermal heat transfer at temp. T2
In Fig. 1. the net work input Wnetto to the process is the difference of the required work of
compression and the released work of expansion that is to say the difference area between temp.
curve and s-axis.
1432 −− −= QQWnetto
STSSTQ ∆=−=− 241214 )(
STSSTQ ∆=−=− 132123 )(
The coefficient of performance of the Carnot refrigeration cycle
21
min
2121211432
14142
)( TT
T
TT
T
STT
ST
STST
ST
Q
W
QCOP hhh
netto
C−
=−
=∆−
∆=
∆−∆
∆=
−==
−−
−−
11
and for a heat pump
21
1
21
1
21
1
21
1
1432
32141
)( TT
T
TT
T
STT
ST
STST
ST
Q
W
QCOP
netto
C−
=−
=∆−
∆=
∆−∆
∆=
−==
−−
−−
The coefficient of performance of the Carnot refrigeration / heat pump cycle is the theoretically best
achieved (but in practice impossible).
for cooling
21
2
2TT
TCOP C
−=
for heat pump
21
1
1TT
TCOPC
−=
In previous formulas the unit of temperature is Kelvin. COP of vapour cycle is got by multiplying
the COP of Carnot with the total Carnot efficiency ηCt .
21
22
TT
TCOP Ctt
−×= η (cooling machine)
12
11
TT
TCOP Ctt
−×= η (heat pump)
ηCt is the total Carnot efficiency
The total Carnot-efficiency depends on refrigerant and ”quality” of compressor.
Figure. Values of the total Carnot-efficiency ηCt of practical vapour compression systems
depending on temperature difference between evaporation and condensing (condensing temp.
t1≈35°C) and compressor motor power demand Pe (from mains). (Granryd 2009).
Pe
12
6 Refrigerants, diagrams and tables of properties
State diagrams present connections between values of substance. In cooling technology is used
log(p), h –diagrams and Mollier h, x -diagrams for moist air. In log(p), h –diagram the y-axis is
absolute pressure p and the scale is logarithmic. To the readings of normal (overpressure)
manometers must be added 1 bar (atmospheric pressure). In x-axis is shown enthalpy. Enthalpies of
sub cycles of the total process (evaporation, compression and condensation) can be read from the
diagram. Pressure remains constant in condenser and evaporator, in throttling (expansion valve)
enthalpy is constant.
Figure. Pure composition refrigerant or azeotropic mixture refrigerant log(p), h –diagram
(Aittomäki 2009).
Pure refrigerants (only one chemical compound) are homogenous by their composition. Evaporation
and condensing of pure refrigerants occur in constant temperature when pressure is constant.
Some mixtures like R502 are also Azeotropic.
Zeotropic refrigerants are mixtures of pure refrigerants. In refrigerant mixtures during evaporation
or condensing pure refrigerants components has different shares of vapour and liquid. Temperature
in zeotropic mixtures changes in constant pressure during evaporation or condensing. This change
critical point
13
of temperature is called temperature gliding. A commonly used zeotropic refrigerant mixture is
R407C, which is used in heat pumps and water chillers.
Figure. Azeotropic refrigerant, R134a, log(p), h –diagram.
14
Figure. Zeopropic refrigerant, R407C, log(p), h –diagram.
A certain temperature of the saturated liquid and vapour equals a certain pressure and vice versa ( a
certain pressure indicates a certain temp. etc)...
�the properties of the refrigerant can be expressed either as function of pressure or temperature.
The enthalpy difference between liquid and gaseous phase decreases when getting closer to the
critical point.
Over the critical point the change of phase (liquid or gas) does not occur anymore; no change of
volume � no specific heat of evaporation.
Figure. Vapour pressure curve (´´ saturated vapour, ´ saturated liquid).
pressure
(bar)
critical point
liqui
d
p’’, p’
vapour
t’’, t’
temperature
(°C)
15
Figure. Saturated vapour pressure versus temperature for some pure refrigerants. (Granryd et al.,
2009).
Thermo physical data tables are made separately for saturated liquid / vapour and for superheated
vapour. Properties of refrigerants are given with a certain temperature or pressure intervals. There
are different ways to set the starting or fixed point for enthalpy. One common way is to set the
enthalpy to a value of 200 kJ/kg at the temperature of 0 °C of saturated liquid.
16
Figure. An example of data tables, refrigerant R134a. Values are given with temperature intervals
of 1 °C. Enthalpy of saturated liquid is set here as 200 kJ/kg and entropy s’ = 1 kJ/kg, K.
(Coolpack)
17
7 A cooling machine and a heat pump in the vapour compression cycle
Vapour cycle and main components
The main parts of a cooling machine or a heat pump are the following: evaporator, condenser,
compressor and throttling / expansion valve. Components are connected to each others with piping
(suction pipe, discharge pipe, liquid pipes). In the systems flows refrigerant. Refrigerant is as
vapour in suction and discharge lines and as liquid in liquid lines. Vaporizing occurs in expansion
valve and in evaporator, condensing in condenser and heat transfer from or to surroundings from
refrigerant.
In vapour cycle there are four main stages / sub processes:
1. Vaporizing of refrigerant from liquid to vapour at low temperature and pressure
2. Pressure rising and warming in compressor
3. Condensing of refrigerant from vapour to liquid in condenser at high temperature and pressure.
4. Pressure drop and cooling of refrigerant in throttling / expansion valve.
Figure. Main components of a cooling machine / heat pump. Paisuntaventtiili=expansion valve;
höyrystin = evaporator; lauhdutin = condenser.
18
Figure. An direct air conditioning system of a air handling unit
An evaporator is a heat exchanger where the refrigerant is boiling and vaporizing at low pressure
and it becomes vapour. Vaporization needs heat energy which the refrigerant takes from the
surroundings e.g. room air or supply air in AHU. In heat pumps heat is taken from a secondary fluid
flow circuit.
Figure. An evaporator with natural convection (Fincoil).
A compressor maintains the cycle of refrigerant in the system. The compressor sucks the low
pressure refrigerant vapour from the evaporator and compresses it to a higher pressure. At the
compression temperature of refrigerant vapour rises.
aircooled condenser in outdoor
air on the roof (direct
condensing) AHU with a direct cooling coil
(evaporator in air flow)
cooling compressor
19
Figure. Scroll-compressor (Danfoss).
A condenser is a heat exchanger where the high pressure and temperature refrigerant condenses
(becomes liquid) and extracts heat to its surroundings. After this refrigerant becomes warm liquid.
In heat pumps this heat is transferred to a heating system like circulated water in hot water heating.
Figure. An air cooled liquid cooler (indirect condensing) (Fincoil)
Refrigerant flows through an expansion valve which keeps the pressure difference as desired
between low and high pressure sides of the system.
20
Figure. An expansion valve (Danfoss).
Condensing and evaporation
In the following figure is shown the evaporation and condensing of refrigerant in a log(p), h –
diagram.
Figure. Pure refrigerant log(p),h -diagram
a’ � b’’ : evaporation of refrigerant, saturated liquid becomes saturated vapour as pressure remains
constant � volume changes (liquid to gaseous phase), enthalpy changes, entropy changes
c’’ � d’ : condensation of refrigerant, saturated vapour becomes saturated liquid as pressure
remains constant, volume + enthalpy + entropy changes
In the previous figure the change of enthalpy hb’’ – ha’ is the heat of evaporation. In a cooling
machine / heat pump the flow of refrigerant to the evaporator is a mixture of gas and liquid.
because part of the refrigerant evaporates already in the expansion valve. So the point a’ moves to
the area of moist vapour (mixture of gas and liquid). Respectively on the condensing side of the
saturated vapour saturated liquid
neste
d’ c’’
log p
(bar)
liquid and gas liquid
a’ b’’
vapour
h (kJ/kg)
21
system the superheated vapour is first cooled down as gas (actually the point c’’ is on the area of
superheated vapour). After that the refrigerant starts to condense and it can also be subcooled as
liquid in the condenser. If it is subcooled then the point d’’ moves to the area of subcooled liquid.
Compression in compressor
In isentropic compression (lossless compression) entropy is constant which means that compression
process goes along the constant entropy curve in the diagram. In a real case entropy increases
because of losses like friction and heat transfer from compressor to surroundings.
First is inspected the case where the suction vapour is saturated (following figure).
Figure. Isentropic (b’’ � cis) and real (b’’ �c) compression, when suction vapour is saturated.
Pressure ratio of compressor is π = p1 / p2 .
log p
(bar)
h (kJ/kg)
cis
b’’
s = constant
p1
p2
c
phase of refrigerant at
compressor outlet
phase of refrigerant at
compressor inlet
22
Expansion in expansion / throttling valve
After the condenser the high pressure refrigerant liquid is flowing through the expansion valve back
to the evaporator (there is also often a tank, liquid receiver, between condenser and expansion
valve). In the expansion valve / device pressure and temperature of liquid refrigerant decreases and
part of the refrigerant vaporizes before evaporator. Enthalpy does not change (adiabatic expansion),
but entropy changes.
Figure. Expansion of refrigerant in three cases; d’ → a2, refrigerant is saturated liquid in point d’;
d1 → a1 , refrigerant is subcooled liquid before expansion valve; d2 → a’, refrigerant is saturated
liquid after expansion valve.
Vapour content of refrigerant
( )( )'''
'1
ab
aa
hh
hhx
−
−=
Vapour content in point a’ is 0 and in point b’’ is 1.
Ideal vapour cycle
In this context ideal means that suction vapour is saturated vapour, compression is isentropic and
liquid before expansion valve is saturated. In addition to this there are no pressure and heat transfer
in the system. So ideal in this case does not mean totally lossless cycle and the pressure loss in
expansion / throttling causes losses which increase entropy (isenthalpic expansion).
log p
(bar)
h (kJ/kg)
d2
td1
p1
p2
refrigerant liquid subcooling td’-td2
pressure drop in expansion
valve
d1 d’
a2 a1 a’
td’
x1
x2
b’’
23
Figure. Ideal vapour cycle of a cooling machine / heat pump in log(p), h- diagram. - isobaric evaporation and condensing (pressure is constant during change of phase)
- refrigerant vapour is saturated after evaporator compressor
- compression is isentropic in compressor (lossless compression, entropy does not change)
- refrigerant liquid is saturated before expansion valve
- flow of refrigerant is adiabatic through expansion valve (enthalpy does not change during expansion)
- there are no pressure losses in evaporator or condenser
- there are no pressure or heat losses in piping and equipments
Figure. Simple cooling system.
log p
(bar)
h (kJ/kg)
p1
p2
d’
a
xa
b’’
s = constant cis
cis
low pressure side
high pressure side
a
d b
P
Φ1
Φ2
hcis hd’=ha hb’’
tcis
24
Fig. 3.22. The basic cycle in log p-h diagram. (E Granryd et al., 2009)
With the remarks of figure 3.22 the cooling capacity / power is
( )abm hhq −=Φ2 ( )skm hhq −=Φ 22
Φ2 cooling power of evaporator, kJ/s , kW
qm mass flow rate of refrigerant, kg/s
hb enthalpy in compressor inlet, kJ/kg
ha enthalpy before evaporator, kJ/kg
and condensing capacity
( )dcism hhq −=Φ1 ( )dkism hhq −=Φ 11
Φ1 condensing capacity / power kW
qm mass flow rate of refrigerant, kg/s
hcis enthalpy in compressor inlet, kJ/kg
hd enthalpy before evaporator, kJ/kg
The shaft power of the compressor (to maintain the cycle without losses of power transmission or
motor) is
( )bcismcis hhqP −=
( )kkcismcis hhqP 21 −=
Pcis shaft power of compressor, kW
The coefficient of performance of the refrigerant in the refrigeration cycle is (?an ideal vapour
compression process is?)
ciskkis
sk
dPhh
hhCOP 2
21
2
2
Φ=
−
−=
hkis hh
25
The COP of an ideal vapour process depends on evaporation temp. t2, condensation temp. t1 and the
properties of the refrigerant (values seen in log(p),h –diagram.
The Carnot efficiency of a refrigerant is ηCd is (page 3:19 Equation 3.24)
c
d
CdCOP
COP
2
2=η
where Carnot –process coefficient of performance COP2C is calculated according to Eq (3.24)
21
22
TT
TCOP C
−=
Figure.(3.25)The Carnot efficiency of the refrigerant ηCd in a basic cycle as a function of the
evaporating temperature t2 and the condensing temperature t1 . (Granryd 2009)
26
8 ISENTROPIC EFFICIENCY AND REAL COMPRESSION
The actual / real compression process is neither isentropic nor isothermal. Because the isentropic
compression / process defines / represents better the actual compression in the compressor it is used
as an ideal referring process to the actual process.
Isentropic efficiency
The ratio between enthalpy change in isentropic compression and in actual compression is called
(total) isentropic efficiency i.e. the ratio between theoretical compression work and actual
compression work.
Figure. Isentropic (here subscript cis, b’’→cis) and actual (here subscript c, b’’→c) compression in
p,h diagram; the suction vapour is saturated before compressor inlet.
The isentropic efficiency of the compressor is ηkis
k
kis
bc
bcis
kish
h
hh
hh
∆
∆=
−
−=
''
''η (19)
∆hkis the change of enthalpy in compressor in isentropic compression, kJ/kg
∆hk the change of enthalpy in compressor in real compression, kJ/kg
In this equation the isentropic efficiency ���� contains compression and pressure losses (leakage
losses, pressure drops in conduits and other parts in compressor) and heat losses from the
compressor to the surroundings.
The isentropic efficiency of an actual /real compressor depends on the compressor type,
compression ratio (between inlet and outlet) and rotation speed. It is usually between 0,6…0,8.
p
hc hcis
p2
hb’’
s = constant
p1
h
c cis
b’’
27
When the supplied work of compression is multiplied with the mass flow of refrigerant then the
shaft power demand of compressor is got. For an isentropic compressor the shaft power is
( ) kismbcismkis hqhhqP ∆=−= ''
For an actual compressor
( )kis
bcis
mkmbcmk
hhqhqhhqP
η''
''
−=∆=−=
Because of compression, pressure drop and heat losses Pk > Pkis .
The enthalpy of the hot compressed gas is got from the equation
( )kis
bcis
bbcbc
hhhhhhh
η''
''''''
−+=−+=
The coefficient of performance for cooling COP2 defined with isentropic efficiency
dkisCOPCOP 22 η=
The isentropic efficiency defined with coefficients of performance for cooling COP2
d
kisCOP
COP
2
2=η
and the shaft power of the compressor respectively
dkis
kCOP
P2
2
η
φ=
COP2d is calculated with the equation
kisbcis
ab
dPhh
hhCOP 2
''
''
2
Φ=
−
−=
9 SUBCOOLING OF THE REFRIGERANT
Subcooled refrigerant is liquid refrigerant where temperature is lower than temperature of saturated
liquid at that pressure. When refrigerant is subcooled the enthalpy of refrigerant goes left in log p, h
–diagram (area of subcooled refrigerant liquid). So the change of enthalpy in evaporator increases
and with the same mass flow rate of refrigerant is got a higher cooling power in the evaporator.
Vapour content of refrigerant is lower in the beginning of evaporator than in the case of saturated
liquid. Because subcooling of refrigerant does not affect on the power demand of compressor, COP
becomes better.
28
Figure. Subcooling of the refrigerant
Refrigerant remains liquid as long as its temperature is lower or equal than temperature saturated
liquid at that pressure. If refrigerant is only slightly subcooled and there are too much pressure
losses before expansion valve, refrigerant starts to evaporate before the expansion valve. This
means that flowing refrigerant contains bubbles and operation of expansion valve is disturbed. The
pressure losses in liquid line are due to friction and local pressure losses and difference of elevation
between liquid receiver and expansion valve.
Figure. Subcooling of refrigerant with an additional circulation of refrigerant through a
subcooling part of the condenser / separated heat exchanger. (Seppälä 2004).
A subcooling heat exchanger can be added also to heat pumps. This kind of heat exchanger can
be used for low temperature heating purposes like e.g. heating of swimming pool water. The
power of subcooling heat exchanger is only 5…10 % of the total heating power of the heat pump
which means that utilization target cannot be big. Utilization of subcooling can be nevertheless
efficient because it do not increase power demand of compressor.
p (bar) 45°C
h40
∆pmax
h (kJ/kg)
p1
p2
h45
40°C
45°C
40°C
x40
x45
p’(40°C)
φ2
liquid line
discharge line
suction line
liquid line
29
Figure. The total possible power of a heat pump when the heat pump is equipped with three heat
exchangers; desuperheating, condensing and subcooling.
10 SUPERHEATING OF REFRIGERANT IN EVAPORATOR AND SUCTION LINE
Vapour entering through the suction line to the compressor in cooling machine or heat pump must
be dry. There must be no liquid drops. Because of this requirement suction vapour is superheated at
the end of evaporator. Suction vapour can be superheated also in the suction pipe line if the suction
line is long and poorly thermally insulated and the evaporation temperature is low. Expansion valve
requires also sufficient superheating to be able to operate correctly.
Superheated refrigerant vapour is defined as vapour with higher temperature than saturation
temperature of that gas at that pressure. Superheating of refrigerant before compressor moves point
b’’ in the following figure to the right and at the same time point c moves to the right.
Figure. Superheating of refrigerant vapour (∆t) in evaporator and in suction line.
p
thot gas
p2
p1
h
condensing power
superheating power subcooling power
t’’
t’
p
tc
+5°
p2
hb’’
p1
h
hb,superheated suction vapour
superheating in evaporator and in suction line
+15°
∆t t2=+5°
hb hc
c
b’’
30
Refrigerant is superheated in evaporator 4…10 K (useful superheating) and in suction line 1…20 K
(useless superheating) depending on the length, insulation and evaporation temperature of suction
line before compressor.
Figure. Superheating of refrigerant in a direct evaporation system in evaporator (∆tevaporator) and
in suction line (∆t suction line).
The temperature of suction vapour affects almost to all operating values of compressor. Density of
refrigerant vapour decreases and specific volume increases when refrigerant vapour is superheated.
Decreasing of density reduces the mass flow rate of refrigerant which goes through the compressor
and so the cooling power decreases too. Superheating increases also the condensing power
demand(area of the heat exchanger). When the temperature of suction vapour increases, all
temperatures in compressor increases e.g. the hot gas temperature after compressor. Suction line
must be insulated well, because heat transferring from surroundings to vapour in suction line
outside the refrigerated space is useless heat transfer and cooling power.
φsurrounding
φcooled space
∆tsuction line ∆tevaporation
compressor evaporator
t
x
31
11 INTERNAL HEAT EXCHANGER
Liquid refrigerant can be subcooled also with an internal heat exchanger.
Figure. Heat exchanger which is installed between compressor (cold) suction line after
evaporator and (hot) liquid line after condenser. (Danfoss, Automation of Commercial
Refrigeration Plant)
This heat exchanger is installed between cold suction line and hot liquid line (Figure). The
purpose of this HE is to cool down the hot liquid refrigerant going to the expansion valve with
the cold refrigerant vapour coming from the evaporator. The subcooling of the refrigerant
reduces the number of bubbles in liquid line before expansion valve and improves the function
of the expansion valve. At the same time the vapour flowing to the compressor is dryer and more
superheated.
Figure. The internal heat exchanger between liquid line and suction line (Granryd 2009, p. 3:35).
This heat exchanger can be used also in heat pumps to rise the temp. of the vapour after
compressor. Thus the hot domestic water production is more efficient (higher temp. and more
volume of HDW).
suction gas
inlet
liquid outlet
liquid inlet
suction gas
outlet
32
Because the mass flow refrigerant vapour in suction line is equal to the mass flow of liquid
refrigerant in liquid line through heat exchanger the change of enthalpy is
1212 hhnn hhhh −=−
The equation can be presented also with temperatures
( ) ( )1,2,,12, hhhpnnnp ttcttc −=−
Usually cp,n > cp,h thereby the change of temp. in suction gas (th2-th1) in the heat exchanger is
greater than the change of temp. in liquid line (tn2-tn1)
With real gases like refrigerants the specific heat capacity is a function of temp. and pressure so
when temp. of gas or liquid changes the specific heat capacities also change.
compressor
Heating supply and
return
heat exchanger
ground heat
source circuit in
and out
expansion valve
33
Figure. Heat transfer in an internal heat exchanger.
12 VOLUME FLOW RATE, VOLUMETRIC REFRIGERATING EFFECT
When inspecting a vapour compression part of the cycle where occurs subcooling and
superheating with the remarks of the following figure.
Figure. Subcooling and superheating (point b’’ = no superheating, b1 = refrigerant is superheated
in the evaporator and b2 in the suction line (compressor inlet)
The refrigerating effect (kylmän tuotto) is the the enthalpy difference between refriger. vapour
coming out from the evaporator and liquid refriger. going into the evaporator. When the refriger.
is neither subcooled nor superheated the refrigerating effect of the refriger. is (kJ/kg)
( )''0 ab hhq −= (28a)
p
p2
p1
h
ha1 ha
hb1
vb1
(m³/kg)
vb (m³/kg)
t2
t1 hc,is hc1 hc1,is
hb’’ hb2
vb2
(m³/kg)
∆th ∆ti
hc2,is hc hc2
p
tcompressed vapour
p2
p1
h
power of
superheating
increasing of power of
superheating subcooling
superheating and drying
of suction vapour in heat
exchanger
hn2 hn1 hh2 hh1
b’’
34
If the refriger. is subcooled before expansion valve then
( )10 ab hhq −= (28b)
If the refriger. is superheated in the evaporator but do not subcool then
( )ab hhq −= 10 (28c)
If the refriger. is both superheated in the evaporator and is subcooled before expansion valve
then
( )110 ab hhq −= (28d)
If the refriger. is both superheated in the evaporator and is subcooled before expansion valve and
is superheated also in the suction line then
( )110 ab hhq −= (28e)
The refrigerating capacity is got by multiplying the change of enthalpy in the evaporator with the
mass flow rate of the refriger. , e.g. for the basic compression cycle (no subcooling or
superheating)
)(2 abm hhq −=φ (29)
The cooling process / cycle has been discussed so far using the mass flow rate of the refrigerant
in the calculations (refrigerating capacity/power, condensing power, compressor power demand).
The cooling cycle and system function can be discussed and based also on suction volume flow
rate. The volume flow rate (m3/s, m
3/h) at the compressor inlet is got by multiplying the mass
flow rate (kg/s) with the specific volume (m3/kg) of the refrigerant at the compressor inlet.
bmi vqV ⋅=
.
(30)
If the eq. (29) and (30) are divided then is got the volumetric refrigerating effect of the
refrigerant (kJ/m3). Without subcooling or superheating for the isentropic compression (basic
cycle) the volumetric refrigerating effect is then
b
ab
i
vv
hh
V
q)(
.
2 −==
φ (31)
”The volumetric refrigerating effect is the refrigerating effect per unit of swept volume”. (Granryd et al. 2009)
35
When the refrigerant is superheated only in the evaporator, the enthalpy and specific volume are
values at point b1 (Figure 18). If there is also superheating in the suction line then in equation
(31) is used enthalpy at point b1 and specific volume at point b2 (Figure 18).
In Figure 19 there is as an example of the volumetric refrigerating effect of R134a; t2
evaporation temp., ts liquid temp. before exp. valve, ∆t in superheating either 0 °C or 18 °C.
(Granryd et al, Fig. 3.30). It can be seen in Fig. 19 that when evaporation temp. decreases the
volumetric refrigerating effect reduces. (Figure 3.30 a-d, Granryd et al. 2009)
Fig 19 Volumetric refrigerating effect qv for R134a depending on evaporation temp. t2 , liquid temp.
ts before expansion valve and superheating in evaporator (either 0 °C, saturated vapour or 18 °C
superheated vapour) (Granryd et al. 2009 Fig. 3.30 a)
36
13 COOLING / REFRIGERATING CAPACITY (POWER) OF EVAPORATOR AND
COMPRESSOR UNDER THE CONDITIONS OF CALCULATIONS
If the refrigerant do not warm (superheat) between evaporator and compressor inlet then the
compressor cooling capacity is equal with the cooling capacity of the evaporator. If the
refrigerant is superheated in suction line according to the heat transfer from surroundings to the
refriger. vapour and this heat transfer increases the cooling capacity of the compressor. In that
case and with the remarks of Fig. 18 the cooling capacity of the evaporator under these
conditions is
)( 112 abm hhq −=φ (32)
but the cooling capacity of the compressor is
)( 122 abm hhq −=φ (33)
14 EER Energy efficiency ratio (total COP2t)
The shaft power of the compressor with a straight / direct coupling
kis
kis
k
PP
η= (34)
and with belt drive / transmission
mtkis
kis
k
PP
ηη ⋅= (35)
where ηkis is the isentropic efficiency of the compressor and ηmt the efficiency of the belt drive.
The electricity power demand of the motor from the electricity network is eP
elm
k
elmmtkis
kise
PPP
ηηηη=
⋅⋅= (36)
where ηelm is the efficiency of the electric motor.
37
Figure. Typical values of efficiencies of belt transmission, ηmt and electric motors, ηelm , versus the
motor shaft power. (Granryd et al., 2009, page. 3:21).
The total coefficient of performance of the refrigeration cycle is
e
tP
COP 2
2
φ= (37)
or
delmmtkist COPCOP 22 ⋅⋅⋅= ηηη (38)
or
CelmmtkisCdt COPCOP 22 ⋅⋅⋅⋅= ηηηη (39)
By combining in equation (39) all the efficiencies is got
CCtt COPCOP 22 ⋅=η (40)
where
elmmtkisCdCt ηηηηη ⋅⋅⋅= (41)
In equation (41) the efficiency combined of different efficiencies is ηCt , the total Carnot efficiency.
The total coefficient of performance of refrigerator cycle expressed with the total Carnot efficiency
is then (42),
CCt
tCOP
COP2
2
2⋅
=η
φ (42)
where COP2C = T2/(T1-T2)
When calculating COP2t in indirect cooling systems of air conditioning the electricity used by
different circulation pumps, fans etc. must be taken into account. In heat pump systems the
circulation pumps of heat source loop must also be taken into account. In air to air heat pumps
electricity is needed also for melting ice in the outdoor unit from time to time and the fans consume
electricity also.
Pk
38
COP2C Carnot-process
ηCd (Carnot efficiency of the refrigerant)
COP2d Ideal cycle / process Pkis
ηkis (isentropic efficiency of compressor)
COP2 Cycle with a real compressor Pk
ηmt
ηelm
(pressure losses)
COP2t Cooling machine / heat pump Pe
total coefficient of performance
• liquid pumps
• circulation pumps (cooling, heating distribution)
• condenser or liquid cooler fans
• automation, melting of ice etc.
• heat losses tanks, pipings etc
COP2j Cooling or heat pump system total coefficient of performance Pej
15 REAL VAPOUR CYCLE
In a real vapour cycle there are pressure losses due to flowing refrigerant in pipes, evaporator,
condenser and in equipments. There are also pressure losses in compressor e.g. in inlet and outlet
valves of piston compressor. In real compressioncompressor sucks warmer refrigerant vapour and
respectively compresses vapour to a higher pressure than condensing pressure (otherwise the
desired condensing pressure is not achieved). There are also small pressure losses in evaporator and
condenser and thus the condensing and evaporation do not occur in a precisely constant pressure.
Pipe dimensioning is made so that pressure losses in pipe lines are low, because increasing of
pressure losses rises pressure ratio of the compressor and energy consumption. Pipes are
dimensioned generally so, that pressure losses are in pipe sections 0,5…1 K.
39
Figure. Real compression cycle (Kaappola 2011).
