Moran M.J., Shapiro H.N. Fundamentals of Engineering Thermodynamics

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466 Chapter 10 Refrigeration and Heat Pump Systems

better thermoelectric

materials by alter-

nately depositing 1- to

4-nanometer films of

different materials on

the same base. These

nanoengineered ma-

terials hold promise

for cooling electronic

circuits, and perhaps

even for improved

thermoelectric coolers.

New materials are

closing the perform-

ance gap, but much re-

mains to be done be-

fore thermoelectric refrigerators are commonplace. Still, a vast

market would be served if researchers succeed.

New Materials May Revive

Thermoelectric Cooling

Thermodynamics in the News...

You can buy a thermoelectric cooler powered from the ciga-

rette lighter outlet of your car. The same technology is used in

space applications. These simple coolers have no moving parts

and use no ozone-depleting refrigerants. Despite such advan-

tages, thermoelectric cooling has found only specialized ap-

plication because of low coefficients of performance that don’t

allow them to compete with commonplace vapor-compression

systems. However, new materials and novel production meth-

ods involving engineering at a nanometer level may make

thermoelectrics more competitive, material scientists say.

The basis of thermoelectric cooling is two dissimilar semi-

conductors coming together in specially designed electric

circuits. Effective materials for thermoelectric cooling must

have low thermal conductivity and high electrical conductiv-

ity, a rare combination in nature. One laboratory has produced

diagram. The principal states of the vapor-compression cycles of Fig. 10.5 are located on this

p–h diagram. It is left as an exercise to sketch the cycles of Examples 10.1, 10.2, and 10.3

on p–h diagrams. Property tables and p–h diagrams for many refrigerants are given in hand-

books dealing with refrigeration.

SELECTING REFRIGERANTS. The temperatures of the refrigerant in the evaporator and

condenser are governed by the temperatures of the cold and warm regions, respectively, with

which the system interacts thermally. This, in turn, determines the operating pressures in

the evaporator and condenser. Consequently, the selection of a refrigerant is based partly

on the suitability of its pressure–temperature relationship in the range of the particular ap-

plication. It is generally desirable to avoid excessively low pressures in the evaporator and

excessively high pressures in the condenser. Other considerations in refrigerant selection in-

clude chemical stability, toxicity, corrosiveness, and cost. The type of compressor also af-

fects the choice of refrigerant. Centrifugal compressors are best suited for low evaporator

pressures and refrigerants with large specific volumes at low pressure. Reciprocating com-

pressors perform better over large pressure ranges and are better able to handle low specific

volume refrigerants.

Condenser

pressure

Evaporator

pressure

Constant s

Constant T

 Figure 10.6 Principal features of the

pressure–enthalpy diagram for a typical

refrigerant, with vapor-compression cycles

superimposed.

10.4 Cascade and Multistage Vapor-Compression Systems 467

Variations of the basic vapor-compression refrigeration cycle are used to improve perform-

ance or for special applications. Two variations are presented in this section. The first is a

combined cycle arrangement in which refrigeration at relatively low temperature is achieved

through a series of vapor-compression systems, with each normally employing a different re-

frigerant. In the second variation, the work of compression is reduced through multistage

compression with intercooling between the stages. These variations are analogous to power

cycle modifications considered in Chaps. 8 and 9.

 10.4.1 Cascade Cycles

Combined cycle arrangements for refrigeration are called cascade cycles. In Fig. 10.7 a cas-

cade cycle is shown in which two vapor-compression refrigeration cycles, labeled A and B,

are arranged in series with a counterflow heat exchanger linking them. In the intermediate

heat exchanger, the energy rejected during condensation of the refrigerant in the lower-

temperature cycle A is used to evaporate the refrigerant in the higher-temperature cycle B.

The desired refrigeration effect occurs in the low-temperature evaporator, and heat rejection

from the overall cycle occurs in the high-temperature condenser. The coefficient of

performance is the ratio of the refrigeration effect to the total work input

b 

 W



10.4 Cascade and Multistage

Vapor-Compression Systems

Low-temperature

evaporator

High-temperature

condenser

Intermediate

heat exchanger

Expansion

valve

Expansion

valve

Compressor

out

Cycle A

Cycle B

 Figure 10.7 Example of a cascade

vapor-compression refrigeration cycle.

The mass flow rates in cycles A and B normally would be different. However, the mass flow

rates are related by mass and energy rate balances on the interconnecting counterflow heat ex-

changer serving as the condenser for cycle A and the evaporator for cycle B. Although only two

cycles are shown in Fig. 10.7, cascade cycles may employ three or more individual cycles.

A significant feature of the cascade system illustrated in Fig. 10.7 is that the refrigerants

in the two or more stages can be selected to have reasonable evaporator and condenser pres-

sures in the two or more temperature ranges. In a double cascade system, a refrigerant would

be selected for cycle A that has a saturation pressure–temperature relationship that allows re-

frigeration at a relatively low temperature without excessively low evaporator pressures. The

refrigerant for cycle B would have saturation characteristics that permit condensation at the

required temperature without excessively high condenser pressures.

 10.4.2 Multistage Compression with Intercooling

The advantages of multistage compression with intercooling between stages have been cited

in Sec. 9.8, dealing with gas power systems. Intercooling is achieved in gas power systems

by heat transfer to the lower-temperature surroundings. In refrigeration systems, the refrig-

erant temperature is below that of the surroundings for much of the cycle, so other means

must be employed to accomplish intercooling and achieve the attendant savings in the required

compressor work input. One arrangement for two-stage compression using the refrigerant

itself for intercooling is shown in Fig. 10.8. The principal states of the refrigerant for an ideal

cycle are shown on the accompanying T–s diagram.

468 Chapter 10 Refrigeration and Heat Pump Systems

Compressor

out

Condenser

Evaporator

Direct contact

heat exchanger

Flash

chamber

Expansion

valve

Expansion

valve

(1)

(x)

(1)

(1 – x)

 Figure 10.8

Refrigeration cycle with two stages of compression and flash

intercooling.

10.5 Absorption Refrigeration 469

Intercooling is accomplished in this cycle by means of a direct contact heat exchanger.

Relatively low-temperature saturated vapor enters the heat exchanger at state 9, where it

mixes with higher-temperature refrigerant leaving the first compression stage at state 2. A

single mixed stream exits the heat exchanger at an intermediate temperature at state 3 and is

compressed in the second compressor stage to the condenser pressure at state 4. Less work

is required per unit of mass flow for compression from 1 to 2 followed by compression from

3 to 4 than for a single stage of compression 1–2–a. Since the refrigerant temperature en-

tering the condenser at state 4 is lower than for a single stage of compression in which the

refrigerant would enter the condenser at state a, the external irreversibility associated with

heat transfer in the condenser is also reduced.

A central role is played in the cycle of Fig. 10.8 by a liquid–vapor separator, called a flash

chamber. Refrigerant exiting the condenser at state 5 expands through a valve and enters the

flash chamber at state 6 as a two-phase liquid–vapor mixture with quality x. In the flash

chamber, the liquid and vapor components separate into two streams. Saturated vapor exit-

ing the flash chamber enters the heat exchanger at state 9, where intercooling is achieved as

discussed above. Saturated liquid exiting the flash chamber at state 7 expands through a sec-

ond valve into the evaporator. On the basis of a unit of mass flowing through the condenser,

the fraction of the vapor formed in the flash chamber equals the quality x of the refrigerant

at state 6. The fraction of the liquid formed is then (1  x). The fractions of the total flow

at various locations are shown in parentheses on Fig. 10.8.



10.5 Absorption Refrigeration

Absorption refrigeration cycles are the subject of this section. These cycles have some fea-

tures in common with the vapor-compression cycles considered previously but differ in two

important respects:

 One is the nature of the compression process. Instead of compressing a vapor between

the evaporator and the condenser, the refrigerant of an absorption system is absorbed

by a secondary substance, called an absorbent, to form a liquid solution. The liquid

solution is then pumped to the higher pressure. Because the average specific volume of

the liquid solution is much less than that of the refrigerant vapor, significantly less work

is required (see the discussion of Eq. 6.53b in Sec. 6.9). Accordingly, absorption

refrigeration systems have the advantage of relatively small work input compared

to vapor-compression systems.

 The other main difference between absorption and vapor-compression systems is that

some means must be introduced in absorption systems to retrieve the refrigerant vapor

from the liquid solution before the refrigerant enters the condenser. This involves heat

transfer from a relatively high-temperature source. Steam or waste heat that otherwise

would be discharged to the surroundings without use is particularly economical for this

purpose. Natural gas or some other fuel can be burned to provide the heat source, and

there have been practical applications of absorption refrigeration using alternative

energy sources such as solar and geothermal energy.

The principal components of an absorption refrigeration system are shown schematically

in Fig. 10.9. In this case, ammonia is the refrigerant and water is the absorbent. Ammonia

circulates through the condenser, expansion valve, and evaporator as in a vapor-compression

system. However, the compressor is replaced by the absorber, pump, generator, and valve

shown on the right side of the diagram.

 In the absorber, ammonia vapor coming from the evaporator at state 1 is absorbed by

liquid water. The formation of this liquid solution is exothermic. Since the amount of

flash chamber

absorption refrigeration

absorber

ammonia that can be dissolved in water increases as the solution temperature decreases,

cooling water is circulated around the absorber to remove the energy released as ammo-

nia goes into solution and maintain the temperature in the absorber as low as possible.

The strong ammonia–water solution leaves the absorber at point a and enters the pump,

where its pressure is increased to that of the generator.

 In the generator, heat transfer from a high-temperature source drives ammonia vapor

out of the solution (an endothermic process), leaving a weak ammonia–water solution in

the generator. The vapor liberated passes to the condenser at state 2, and the remaining

weak solution at c flows back to the absorber through a valve. The only work input is

the power required to operate the pump, and this is small in comparison to the work

that would be required to compress refrigerant vapor between the same pressure levels.

However, costs associated with the heat source and extra equipment not required by

vapor-compressor systems can cancel the advantage of a smaller work input.

Ammonia–water systems normally employ several modifications of the simple absorption

cycle considered above. Two common modifications are illustrated in Fig. 10.10. In this cy-

cle, a heat exchanger is included between the generator and the absorber that allows the

strong water–ammonia solution entering the generator to be preheated by the weak solution

returning from the generator to the absorber, thereby reducing the heat transfer to the gen-

erator, The other modification shown on the figure is the rectifier placed between the

generator and the condenser. The function of the rectifier is to remove any traces of water

from the refrigerant before it enters the condenser. This eliminates the possibility of ice

formation in the expansion valve and the evaporator.

Another type of absorption system uses lithium bromide as the absorbent and water as the

refrigerant. The basic principle of operation is the same as for ammonia–water systems. To

achieve refrigeration at lower temperatures than are possible with water as the refrigerant, a

lithium bromide–water absorption system may be combined with another cycle using a re-

frigerant with good low-temperature characteristics, such as ammonia, to form a cascade

refrigeration system.

470 Chapter 10 Refrigeration and Heat Pump Systems

Expansion

valve

Evaporator

Condenser

High-

temperature

source

Generator

Weak solution

Strong solution

Absorber

Valve

Pump

Refrigerated

region

Cooling

water

out

 Figure 10.9 Simple

ammonia–water absorption

refrigeration system.

generator

rectifier

10.6 Heat Pump Systems 471

The objective of a heat pump is to maintain the temperature within a dwelling or other building

above the temperature of the surroundings or to provide a heat transfer for certain industrial

processes that occur at elevated temperatures. Heat pump systems have many features in

common with the refrigeration systems considered thus far and may be of the vapor-

compression or absorption type. Vapor-compression heat pumps are well suited for space

heating applications and are commonly used for this purpose. Absorption heat pumps

have been developed for industrial applications and are also increasingly being used for space

heating. To introduce some aspects of heat pump operation, let us begin by considering

the Carnot heat pump cycle.

CARNOT HEAT PUMP CYCLE

By simply changing our viewpoint, we can regard the cycle shown in Fig. 10.1 as a heat

pump. The objective of the cycle now, however, is to deliver the heat transfer to the warm

region, which is the space to be heated. At steady state, the rate at which energy is supplied

to the warm region by heat transfer is the sum of the energy supplied to the working fluid

from the cold region, and the net rate of work input to the cycle, That is

(10.8)

out

 Q

 W

net

out

Condenser

Expansion

valve

Evaporator Absorber

Valve

Pump

Heat

exchanger

Generator

Rectifier

out

 Figure 10.10 Modified ammonia–water

absorption system.



10.6 Heat Pump Systems

The coefficient of performance of any heat pump cycle is defined as the ratio of the heat-

ing effect to the net work required to achieve that effect. For the Carnot heat pump cycle of

Fig. 10.1

(10.9)

This equation, which corresponds to Eq. 5.10, represents the maximum theoretical coefficient

of performance for any heat pump cycle operation between two regions at temperatures T

and T

. Actual heat pump systems have coefficients of performance that are lower than would

be calculated from Eq. 10.9.

A study of Eq. 10.9 shows that as the temperature T

of the cold region decreases, the co-

efficient of performance of the Carnot heat pump decreases. This trait is also exhibited by ac-

tual heat pump systems and suggests why heat pumps in which the role of the cold region is

played by the local atmosphere (air-source heat pumps) normally require backup systems to

provide heating on days when the ambient temperature becomes very low. If sources such as

well water or the ground itself are used, relatively high coefficients of performance can be

achieve despite low ambient air temperatures, and backup systems may not be required.

VAPOR-COMPRESSION HEAT PUMPS

Actual heat pump systems depart significantly from the Carnot cycle model. Most systems

in common use today are of the vapor-compression type. The method of analysis of vapor-

compression heat pumps is the same as that of vapor-compression refrigeration cycles con-

sidered previously. Also, the previous discussions concerning the departure of actual systems

from ideality apply for vapor-compression heat pump systems as for vapor-compression

refrigeration cycles.

As illustrated by Fig. 10.11, a typical vapor-compression heat pump for space heating

has the same basic components as the vapor-compression refrigeration system: compressor,



 s

 T

21s

 s



 T



area 2–a–b–3–2

area 1–2–3–4–1

max



out



 W



472 Chapter 10 Refrigeration and Heat Pump Systems

Inside

air

Outside

air

Condenser

Compressor

Evaporator

out

Expansion

valve

 Figure 10.11 Air-source vapor-compression heat pump system.

vapor-compression

heat pump

10.7 Gas Refrigeration Systems 473

condenser, expansion valve, and evaporator. The objective of the system is different, how-

ever. In a heat pump system, comes from the surroundings, and is directed to the

dwelling as the desired effect. A net work input is required to accomplish this effect.

The coefficient of performance of a simple vapor-compression heat pump with states as

designated on Fig. 10.11 is

(10.10)

The value of  can never be less than unity.

Many possible sources are available for heat transfer to the refrigerant passing through

the evaporator. These include the outside air, the ground, and lake, river, or well water. Liq-

uid circulated through a solar collector and stored in an insulated tank also can be used as a

source for a heat pump. Industrial heat pumps employ waste heat or warm liquid or gas

streams as the low-temperature source and are capable of achieving relatively high condenser

temperatures.

In the most common type of vapor-compression heat pump for space heating, the evapo-

rator communicates thermally with the outside air. Such air-source heat pumps also can be

used to provide cooling in the summer with the use of a reversing valve, as illustrated in

Fig. 10.12. The solid lines show the flow path of the refrigerant in the heating mode, as de-

scribed previously. To use the same components as an air conditioner, the valve is actuated,

and the refrigerant follows the path indicated by the dashed line. In the cooling mode, the

outside heat exchanger becomes the condenser, and the inside heat exchanger becomes the

evaporator. Although heat pumps can be more costly to install and operate than other direct

heating systems, they can be competitive when the potential for dual use is considered.

g 

out





 h

out

Expansion

valve

Outside

heat exchanger

Inside

heat exchanger

Reversing

valve

Compressor

Heating mode

Cooling mode

 Figure 10.12 Example of an air-to-air

reversing heat pump.



10.7 Gas Refrigeration Systems

All refrigeration systems considered thus far involve changes in phase. Let us now turn to

gas refrigeration systems in which the working fluid remains a gas throughout. Gas refrig-

eration systems have a number of important applications. They are used to achieve very low

temperatures for the liquefaction of air and other gases and for other specialized applications

air-source heat pump

gas refrigeration systems

474 Chapter 10 Refrigeration and Heat Pump Systems

such as aircraft cabin cooling. The Brayton refrigeration cycle illustrates an important type

of gas refrigeration system.

BRAYTON REFRIGERATION CYCLE

The Brayton refrigeration cycle is the reverse of the closed Brayton power cycle introduced

in Sec. 9.6. A schematic of the reversed Brayton cycle is provided in Fig. 10.13a. The re-

frigerant gas, which may be air, enters the compressor at state 1, where the temperature is

somewhat below the temperature of the cold region, T

, and is compressed to state 2. The

gas is then cooled to state 3, where the gas temperature approaches the temperature of the

warm region, T

. Next, the gas is expanded to state 4, where the temperature, T

, is well be-

low that of the cold region. Refrigeration is achieved through heat transfer from the cold re-

gion to the gas as it passes from state 4 to state 1, completing the cycle. The T–s diagram in

Fig. 10.13b shows an ideal Brayton refrigeration cycle, denoted by 1–2s–3–4s–1, in which

all processes are assumed to be internally reversible and the processes in the turbine and

compressor are adiabatic. Also shown is the cycle 1–2–3–4–1, which suggests the effects of

irreversibilities during adiabatic compression and expansion. Frictional pressure drops have

been ignored.

CYCLE ANALYSIS. The method of analysis of the Brayton refrigeration cycle is similar to

that of the Brayton power cycle. Thus, at steady state the work of the compressor and the

turbine per unit of mass flow are, respectively

In obtaining these expressions, heat transfer with the surroundings and changes in kinetic and

potential energy have been ignored. In contrast to the vapor-compression cycle of Fig. 10.2,

 h

 h

and

 h

 h

Heat exchanger

Turbine Compressor

out

cycle

– W

··

Warm region

at T

Cold region

at T

(a)

Constant pressure

(b)

 Figure 10.13

Brayton refrigeration cycle.

Brayton refrigeration

cycle

10.7 Gas Refrigeration Systems 475

the work developed by the turbine of a Brayton refrigeration cycle is significant relative to

the compressor work input.

The heat transfer from the cold region to the refrigerant gas circulating through the low-

pressure heat exchanger, the refrigeration effect, is

The coefficient of performance is the ratio of the refrigeration effect to the net work input:

(10.11)

In the next example, we illustrate the analysis of an ideal Brayton refrigeration cycle.

b 



 W





 h

2 1h

 h

 h

 h

EXAMPLE 10.4 Ideal Brayton Refrigeration Cycle

Air enters the compressor of an ideal Brayton refrigeration cycle at 1 bar, 270K, with a volumetric flow rate of 1.4 m

/s. If

the compressor pressure ratio is 3 and the turbine inlet temperature is 300K, determine (a) the net power input, in kW,

(b) the refrigeration capacity, in kW, (c) the coefficient of performance.

SOLUTION

Known: An ideal Brayton refrigeration cycle operates with air. Compressor inlet conditions, the turbine inlet temperature,

and the compressor pressure ratio are given.

Find: Determine the net power input, in kW, the refrigeration capacity, in kW, and the coefficient of performance.

Schematic and Given Data:

300K

270K

p = 3 bars

p = 1 bar

4s 1

Heat exchanger

Turbine Compressor

out

cycle

300K

(AV)

1.4 m

270K

1 bar

 Figure E10.4

Assumptions:

1. Each component of the cycle is analyzed as a control volume at steady state. The control volumes are indicated by dashed

lines on the accompanying sketch.

2. The turbine and compressor processes are isentropic.