Dinc Ibrahim. Refrigeration systems and applications 2th edition

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Refrigeration Cycles and Systems 161

= 120 kPa

= s

= 0.3738 kJ/kg · K



= 92.98 kJ/kg

Turb,out

= h

− h

= 101.61 − 92.98 = 8.63 kJ/kg

net,in

= w

Comp,in

− w

Turb,out

= 73.54 − 8.63 = 64.91 k/kg

= h

− h

= 236.97 − 92.98 = 144.0kJ/kg

COP =

net,in

144.0kJ/kg

64.91 kJ/kg

= 2.21

The COP increases by 20.1% by replacing the expansion valve by a turbine. This replacement

makes thermodynamic sense since it decreases the work requirement and thus increases COP.

However, this is not practical for household refrigerators and most other refrigeration systems.

In natural gas liquefaction plants, the liqueﬁed natural gas is expanded by cryogenic turbines,

which is proven to be feasible.

(d) If the evaporator pressure is 160 kPa,

COP =

− h

241.12 − 101.61

310.51 − 241.12

= 2.01

Increasing evaporator pressure from 120 to 160 kPa (increasing evaporating temperature from

−22.3 to −15.6

◦

C) increases the COP from 1.84 to 2.01, an increase of 9.2%.

(e) If the condenser pressure is 800 kPa,

COP =

− h

236.97 − 95.47

311.92 − 236.97

= 1.89

Decreasing condenser pressure from 900 to 800 kPa (decreasing condensing temperature from

35.5 to 31.3

◦

C) increases the COP from 1.84 to 1.89, an increase of 2.7%.

4.4 Exergy Analysis of Vapor-Compression Refrigeration Cycle

Figure 4.2 is a schematic of a vapor-compression refrigeration cycle operating between a low-

temperature medium (T

) and a high-temperature medium (T

). The maximum COP of a refriger-

ation cycle operating between temperature limits of T

and T

based on the Carnot refrigeration

cycle was given in Chapter 1 as

COP

Carnot

− T

− 1

(4.8)

Practical refrigeration systems are not as efﬁcient as ideal models like the Carnot cycle, because

of the lower COP due to irreversibilities in the system. As a result of Equation 4.8, a smaller temper-

ature difference between the heat sink and the heat source (T

− T

) provides greater refrigeration

system efﬁciency (i.e., COP). The Carnot cycle has certain limitations, because it represents the

cycle of the maximum theoretical performance.

The aim in an exergy analysis is usually to determine the exergy destructions in each component

of the system and to determine exergy efﬁciencies. The components with greater exergy destructions

are also those with more potential for improvements. Exergy destruction in a component can be

determined from an exergy balance on the component. It can also be determined by ﬁrst calculating

the entropy generation and using

dest

= T

gen

(4.9)

162 Refrigeration Systems and Applications

where T

is the dead-state temperature or environment temperature. In a refrigerator, T

is usually

equal to the temperature of the high-temperature medium T

. Exergy destructions and exergy

efﬁciencies for major components of the cycle are as follows (state numbers refer to Figure 4.2):

Compressor:

−

out

−

dest,1– 2

= 0

dest,1– 2

−

out

(4.10)

dest,1– 2

W +

−

W − 

W −˙m

[

− h

− T

− s

)

]

W −

rev

dest,1– 2

= T

gen,1 – 2

=˙mT

− s

) (4.11)

ex,Comp

rev

= 1 −

dest,1– 2

(4.12)

Condenser:

dest,2–3

−

out

dest,2–3

= (

−

) −

(4.13)

=˙m

[

− h

− T

− s

)

]

−



1 −



dest,2– 3

= T

gen,2 – 3

=˙mT



− s



(4.14)

ex,Cond

−



1 −



˙m

[

− h

− T

− s

)

]

= 1 −

dest,2–3

−

(4.15)

Expansion valve:

dest,3– 4

−

out

dest,3– 4

−

=˙m

[

− h

− T

− s

)

]

(4.16)

dest,3– 4

= T

gen,3 – 4

=˙mT

− s

) (4.17)

ex,ExpValve

= 1 −

dest,3– 4

−

= 1 −

−

(4.18)

Evaporator:

dest,4–1

−

out

dest,4–1

=−

−

dest,4–1

= (

−

) −

(4.19)

=˙m

[

− h

− T

− s

)

]

−



−



1 −



Refrigeration Cycles and Systems 163

dest,4– 1

= T

gen,4 – 1

=˙mT



− s

−



(4.20)

ex,Evap

−



1 −



˙m

[

− h

− T

− s

)

]

= 1 −

dest,4– 1

−

(4.21)

The total exergy destruction in the cycle can be determined by adding exergy destructions in

each component:

dest,total

dest,1– 2

dest,2– 3

dest,3– 4

dest,4 – 1

(4.22)

It can be shown that the total exergy destruction in the cycle can also be expressed as the

difference between the exergy supplied (power input) and the exergy recovered (the exergy of the

heat transferred from the low-temperature medium):

dest,total

W −

(4.23)

where the exergy of the heat transferred from the low-temperature medium is given by

=−



1 −



(4.24)

The minus sign is needed to make the result positive. Note that the exergy of the heat transferred

from the low-temperature medium is in fact the minimum power input to accomplish the required

refrigeration load

min

(4.25)

The second-law efﬁciency (or exergy efﬁciency) of the cycle is deﬁned as

min

= 1 −

dest,total

(4.26)

Substituting

W =

COP

and

=−



1 −



into the second-law efﬁciency relation

(Equation 4.26)

−



1 −



COP

=−



1 −



COP

− T

COP

Carnot

(4.27)

since T

= T

. Thus, the second-law efﬁciency is also equal to the ratio of actual and maximum COPs

for the cycle. This second-law efﬁciency deﬁnition accounts for irreversibilities within the refrigerator

since heat transfers with the high- and low-temperature reservoirs are assumed to be reversible.

Example 4.2

A refrigerator using R-134a as the refrigerant is used to keep a space at −10

◦

C by rejecting heat

to ambient air at 22

◦

C. R-134a enters the compressor at 140 kPa at a ﬂow rate of 375 L/min

as a saturated vapor. The isentropic efﬁciency of the compressor is 80%. The refrigerant leaves

the condenser at 46.3

◦

C as a saturated liquid. Determine (a) the rate of cooling provided by the

system, (b) the COP, (c) the exergy destruction in each component of the cycle, (d) the second-law

efﬁciency of the cycle, and (e) the total exergy destruction in the cycle.

164 Refrigeration Systems and Applications

Solution

Temperature–entropy diagram of the cycle is given in Figure 4.4.

140 kPa

46.3 °C

Figure 4.4 Temperature–entropy diagram of vapor-compression refrigeration cycle considered in Example 4.2.

(a) The properties of R-134a are (from Tables B.4 and B.5)

= 140 kPa

= 1



= 239.17 kJ/kg

= 0.9446 kJ/kg · K

= 0.1402 m

/kg

= P

sat@46.3

◦

= 1200 kPa

= s

= 0.9446 kJ/kg · K



= 284.09 kJ/kg

= 1200 kPa

= 0



= 117.77 kJ/kg

= 0.4244 kJ/kg · K

= h

= 117.77 kJ/kg

= 140 kPa

= 117.77 kJ/kg



= 0.4674 kJ/kg · K

− h

0.80 =

284.09 − 239.17

− 239.17

−−−→ h

= 295.32 kJ/kg

= 1200 kPa

= 295.32 kJ/kg



= 0.9783 kJ/kg · K

The mass ﬂow rate of the refrigerant is

˙m =

(0.375/60) m

0.1402 m

/kg

= 0.04458 kg/s

Refrigeration Cycles and Systems 165

The refrigeration load, the rate of heat rejected, and the power input are

=˙m(h

− h

) = (0.04458 kg/s)(239.17 − 117.77) kJ/kg = 5.41 kW

=˙m(h

− h

) = (0.04458 kg/s)(295.32 − 117.77) kJ/kg = 7.92 kW

W =˙m(h

− h

) = (0.04458 kg/s)(295.32 − 239.17) kJ/kg = 2.50 kW

(b) The COP of the cycle is

COP =

5.41 kW

2.50 kW

= 2.16

= T

= 295 K, the exergy destruction in each

component of the cycle is determined as follows:

Compressor:

gen,1−2

=˙m(s

− s

) = (0.04458 kg/s)(0.9783 − 0.9446) kJ/kg · K = 0.001502 kW/K

dest,1– 2

= T

gen,1 – 2

= (295 K)(0.001502 kW/K) = 0.4432 kW

Condenser:

gen,2−3

=˙m(s

− s

) +

= (0.04458 kg/s)(0.4244 − 0.9783) kJ/kg · K +

7.92 kW

295 K

= 0.002138 kW/K

dest,2– 3

= T

gen,2– 3

= (295 K)(0.002138 kJ/kg · K) = 0.6308 kW

Expansion valve:

gen,3 – 4

=˙m(s

− s

) = (0.04458 kg/s)(0.4674 − 0.4244) kJ/kg · K = 0.001916 kW/K

dest,3– 4

= T

gen,3 – 4

= (295 K)(0.001916 kJ/kg · K) = 0.5651 kW

Evaporator:

gen,4– 1

=˙m(s

− s

) −

= (0.04458 kg/s)(0.9446 − 0.4674) kJ/kg · K −

5.41 kW

263 K

= 0.0006964 kW/K

dest,4– 1

= T

gen,4– 1

= (295 K)(0.0006964 kW/K) = 0.2054 kW

(d) The exergy of the heat transferred from the low-temperature medium is

=−



1 −



=−(5.41 kW)



1 −

295

263



= 0.6585 kW

This is also the minimum power input for the cycle. The second-law efﬁciency of the cycle is

0.6585

2.503

= 0.263 = 26.3%

166 Refrigeration Systems and Applications

This efﬁciency may also be determined from

COP

Carnot

where

COP

Carnot

− T

(−10 + 273) K

[

22 − (−10)

]

= 8.22

Substituting,

COP

Carnot

2.16

8.22

= 0.263 = 26.3%

The results are identical as expected.

(e) The total exergy destruction in the cycle is the difference between the exergy supplied (power

input) and the exergy recovered (the exergy of the heat transferred from the low-temperature

medium):

dest,total

W −

= 2.503 − 0.6585 = 1.845 kW

The total exergy destruction can also be determined by adding exergy destructions in each

component:

dest,total

dest,1– 2

dest,2– 3

dest,3– 4

dest,4– 1

= 0.4432 + 0.6308 + 0.5651 + 0.2054 = 1.845 kW

The results are identical as expected.

4.5 Practical Vapor-Compression Refrigeration Cycle

There are some clear differences between the practical (actual) cycle and the theoretical cycle (stan-

dard ideal cycle) primarily because of the pressure and temperature drops associated with refrigerant

ﬂow and heat transfer to or from the surroundings. Figure 4.5 shows an actual vapor-compression

Evaporator

Condenser

Compressor

Expansion

valve

2′

(

)(

)

Figure 4.5 An actual vapor-compression refrigeration system and its T –s diagram.

Refrigeration Cycles and Systems 167

refrigeration cycle. The refrigerant vapor entering the compressor is normally superheated. During

the compression process, because of the irreversibilities and heat transfer either to or from the

surroundings, depending on the temperatures of the refrigerant and the surroundings, entropy may

increase (for the irreversibility and heat transferred to the refrigerant) or decrease (for the irre-

versibility and heat transferred from the refrigerant), as shown by the two dashed lines 1–2 and

1–2’. The pressure of the liquid leaving the condenser becomes less than the pressure of the vapor

entering, and the temperature of the refrigerant in the condenser is somewhat higher than that of

the surroundings to which heat is being transferred. As always, the temperature of the liquid leav-

ing the condenser is lower than the saturation temperature. It may drop even more in the piping

between the condenser and expansion valve. This represents a gain, however, because as a result of

this heat transfer the refrigerant enters the evaporator with a lower enthalpy, which permits more

heat to be transferred to the refrigerant in the evaporator. There is also some pressure drop as the

refrigerant ﬂows through the evaporator. It may be slightly superheated as it leaves the evaporator,

and through heat transferred from the surroundings its temperature increases in the piping between

the evaporator and the compressor. This heat transfer represents a loss, because it increases the

work of the compressor, since the ﬂuid entering it has an increased speciﬁc volume.

A practical commercial mechanical vapor-compression refrigeration system is shown in

Figure 4.6. In the system shown, it is possible to use properly the temperature, pressure, and

High (pressure) side

Liquid

line valve

Suction

compressor

Discharge

Condenser

fan

Evaporator

fan

Evaporator

Thermostat

or cold

control

High pressure

liquid

High pressure

gas

Low pressure

gas

Low pressure

liquid

Low (pressure) side

Condenser

Receiver

tank

Heat exchanger

Accumulator

Strainer/drier

Expansion valve or

capillary tube

Crankcase

heater

Pressure

cutout

T-X Valve

sensor

bulb

Hermetic

Figure 4.6 A typical commercial refrigerating unit. 1. Evaporator inlet. 2. Evaporator outlet. 3. Accumulator.

4. Compressor. 5. Condenser inlet. 6. Condenser outlet. 7. Receiver outlet. 8. Heat exchanger. 9. Liquid

line strainer/drier. 10. Expansion valve. 11. Thermostat. 12. Compressor crankcase heater. 13. High- and

low-pressure cutout (Courtesy of Tecumseh Products Co.).

168 Refrigeration Systems and Applications

latent heat of vaporization. This system utilizes a water-cooled condenser, and water removes heat

from the hot refrigerant vapor to condense it. Therefore, the water carries away the heat that is

picked up by the evaporator as the refrigerant boils. The refrigerant is then recirculated through

the system again to carry out its function to absorb heat in the evaporator.

4.5.1 Superheating and Subcooling

Superheating (referring to superheating of the refrigerant vapor leaving evaporator) and subcooling

(referring to subcooling of refrigerant liquid leaving the condenser) are apparently two signiﬁcant

processes in practical vapor-compression refrigeration systems and are applied to provide better

efﬁciency (COP) and to avoid some technical problems, as will be explained below.

4.5.1.1 Superheating

During the evaporation process, the refrigerant is completely vaporized partway through the evap-

orator. As the cool refrigerant vapor continues through the evaporator, additional heat is absorbed

to superheat the vapor. Under some conditions such pressure losses caused by friction increase the

amount of superheat. If the superheating takes place in the evaporator, the enthalpy of the refrigerant

is raised, extracting additional heat and increasing the refrigeration effect of the evaporator. If it is

provided in the compressor suction piping, no useful cooling occurs. In some refrigeration systems,

liquid–vapor heat exchangers can be employed to superheat the saturated refrigerant vapor from the

evaporator with the refrigerant liquid coming from the condenser (Figure 4.7). As can be seen from

Figure 4.7, the heat exchanger can provide high system COP. Refrigerant superheating can also

be obtained in the compressor. In this case, the saturated refrigerant vapor enters the compressor

and is superheated by increasing the pressure, leading to the temperature increase. Superheating

obtained from the compression process does not improve the cycle efﬁciency, but results in larger

condensing equipment and large compressor discharge piping. The increase in the refrigeration

effect obtained by superheating in the evaporator is usually offset by a decrease in the refrigeration

effect in the compressor. Because the volumetric ﬂow rate of a compressor is constant, the mass

ﬂow rate and the refrigeration effect are reduced by decreases in the refrigerant density caused by

the superheating. In practice, it is well known that there is a loss in the refrigerating capacity of

1% for every 2.5

◦

C of superheating in the suction line. Insulation of the suction lines is a solution

to minimize undesirable heat gain. The desuperheating is a process to remove excess heat from

Evaporator

Condenser

Compressor

Heat exchanger

Expansion

valve

1′

3′

(

)

Enthalpy (kJ/kg)

Pressure (kPa)

Superheatin

Subcooling

Evaporator

Condenser

Compression

Expansion

(

)

Low pressure

1′

3′

Entropy (kJ/kg·K)

Temperature (K)

High pressure

Superheating

Subcooling

(

)

Figure 4.7 (a) A vapor-compression refrigeration system with a heat exchanger for superheating and sub-

cooling, (b) its T –s diagram, and (c) its log P –h diagram.

Refrigeration Cycles and Systems 169

superheated refrigerant vapor, and if accomplished by using an external effect it will be more useful

to the COP. Desuperheating is often considered impractical, owing to the low temperatures (less

than 10

◦

C) and small amount of available energy.

4.5.1.2 Subcooling

This is a process of cooling the refrigerant liquid below its condensing temperature at a given

pressure (Figure 4.7). Subcooling provides 100% refrigerant liquid to enter the expansion device,

preventing vapor bubbles from impeding the ﬂow of refrigerant through the expansion valve. If the

subcooling is caused by a heat-transfer method external to the refrigeration cycle, the refrigerant

effect of the system is increased, because the subcooled liquid has less enthalpy than the saturated

liquid. Subcooling is accomplished by refrigerating the liquid line of the system, using a higher

temperature system. Simply we can state, subcooling cools the refrigerant more and provides the

following accordingly:

• increase in energy loading,

• decrease in electrical usage,

• reducing pulldown time,

• more uniform refrigerating temperatures, and

• reduction in the initial cost.

Note that the performance of a simple vapor-compression refrigeration system can be signiﬁcantly

improved by further cooling the liquid refrigerant leaving the condenser coil. This subcooling of the

liquid refrigerant can be accomplished by adding a mechanical-subcooling loop in a conventional

vapor-compression cycle. The subcooling system can be either a dedicated mechanical-subcooling

system or an integrated mechanical-subcooling system (Khan and Zubair, 2000). In a dedicated

mechanical-subcooling system, there are two condensers, one for each of the main cycle and

the subcooler cycle, whereas, for an integrated mechanical-subcooling system, there is only one

condenser serving both the main cycle and the subcooler cycle.

For example, subcooling of R-22 by 13

◦

C increases the refrigeration effect by about 11%. If

subcooling is obtained from outside the cycle, each degree increment in subcooling will improve the

system capacity (approximately by 1%). Subcooling from within the cycle may not be as effective

because of offsetting effects in other parts of the cycle. Mechanical subcooling can be added to

existing systems or designed into new ones. It is ideal for any refrigeration process in which more

capacity may be necessary or operating costs must be lowered. It has proved cost efﬁcient in a

variety of applications and is recommended for large supermarkets, warehouses, plants, and so on.

Figure 4.8 shows a typical subcooler for commercial refrigeration applications.

4.5.2 Defrosting

One of the most common applications of refrigeration systems is to produce and maintain space

temperatures by circulating air through a refrigerated coil. If the temperature of the refrigerant in

the coil is below 0

◦

C, water in the air freezes and accumulates on the coil. The ice blocks airﬂow

and acts as an insulator, penalizing coil performance. For efﬁcient performance, the coil must be

defrosted periodically. The defrost cycle is a necessary and important part of the design of the

refrigeration system.

Over the years, various defrost methods have been used. One of the ﬁrst methods was to arrange

the coil in such a manner that it could be isolated from the cold room. Warm air was circulated

over it until the ice melted. Another method is to run water over the coil. Careful design of the

water lines into and out of the cold room prevents freezing of the defrost water. Electric heater rods

170 Refrigeration Systems and Applications

Figure 4.8 A subcooler (Courtesy of Standard Refrigeration Company).

inserted into formed holes through aluminum ﬁns work effectively, and this type is common for

halocarbon systems. All of these have been used for ammonia coils, but the most common method is

hot gas from the compressor discharge. Hot gas defrost is simple and effective, removes ice rapidly,

and is relatively inexpensive to install. However, the control valves selection and the sequence of

operation must be correct for reliable and efﬁcient defrosts (for details, see Norton, 2000).

Defrost systems vary with the size and type of evaporator, with some choices possible for the

larger size coils. Electrical heating defrost via elements in the drip trays under the evaporator or

as elements through the coil ﬁns are the most common and economical for small evaporators. Hot

gas systems that pump hot refrigerant gas through the coils or defrosting by running ambient water

over the coils are more common on larger systems.

Auto cycle defrost is not as complicated as it sounds. In fact, cycle defrost systems are the least

complex in operation and most effective defrost systems available. Cycle defrost systems are feasible

only on all-refrigerator units because these units do not contain a freezer compartment. Cycle

defrost units contain a special thermostat which senses the evaporator plate temperature. At the

completion of each compressor run cycle, the thermostat disconnects the electrical power and turns

off the compressor. The thermostat will not connect the electrical power again to initiate the next

compressor run cycle until the evaporator plate reaches a preset temperature well above freezing.

During this evaporator warm-up period, the frost which has accumulated during the previous

compressor run cycle melts and becomes water droplets. These water droplets run down the vertical

surface of the evaporator and drop off into the drip tray located just underneath the evaporator, which

then empties into a drain tube. The drain tube discharges the water droplets into the condensation

pan located in the mechanical assembly under and outside the refrigerator compartment. There, the

compressor heat and the airﬂow from the condenser fan evaporate the moisture.

4.5.3 Purging Air in Refrigeration Systems

Air is known as the enemy of any refrigeration system. Purging, whether manual or automatic,

removes air and maximizes refrigeration system performance (Rockwell and Quake, 2001).