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joints, and refrigerant hoses, or it can be caused by system failure, recharging,
and intentional venting during repair and salvage operations.
2. The indirect GWP results from the creation of CO2 during the combustion of
fossil fuels to produce work to drive mechanical systems or to convert the fossil
fuel energy to thermal energy to drive heat driven systems.
This research project takes into consideration both the direct and indirect GWP of
a refrigeration system.
Project Objective
The objective of this project was to identify, analyze, and assess technologies
which could serve as alternatives to vapor compression for the purpose of accom-
plishing refrigeration.
Project Description
The project was conducted in three phases:
1. Identification and classification of refrigeration technologies.
2. Thermodynamic analysis of some of the more promising cycles.
3. Technical assessment of the alternative technologies.
U.S. patents and the technical literature were used as sources for identifying
the different means for accomplishing refrigeration. Once a representative group of
refrigeration method concepts had been identified, a method of classifying them for
thermodynamic analysis was developed.
6
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Some of the alternative refrigeration cycles were analyzed in detail. A thermo-
dynamic model was developed for each of these cycles and computer subroutines were
written for each model. In some cases, thermodynamic property subroutines were
also developed to approximate the properties of the working material used in the
cycle. An interactive main program was written to allow users to choose which cycles
they wished to consider and to vary specific parameters on a case-by-case basis. The
program was used to provide an estimate of the both the coefficient of performance
(COP) and the Second Law efficiency for the cycles (Chapter 4).
The final segment of this project was a technology assessment of refrigeration
concepts. Criteria which were common to all refrigeration systems were identified.
These criteria were rated on a scale of 1 (low) to 5 (high) for each technology and
application category. A computer program was written to rank the refrigeration
technologies from best to worst for each of the application areas.
7
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CHAPTER 2. IDENTIFICATION OF REFRIGERATION
TECHNOLOGIES
Introduction
The first phase of this project involved the identification of refrigeration tech-
nologies for the purposes of further analysis and technical assessment. A survey of
U.S. Patents and the literature was conducted to discover what refrigeration methods
were known to the technical community.
For this study, the term refrigeration technology is used to refer to a group
of refrigerating methods which operate with similar thermodynamic cycles, similar
methods of powering the system, and use similar working materials. For example,
absorption refrigeration can be accomplished using either a liquid or a solid absorbent.
Therefore, liquid absorption and solid absorption would be considered to be two
different refrigeration technologies in this study, although they are the same at a
higher level (the molecules of the refrigerant are absorbed by the sorbent during
the sorption process and thermal energy is transferred into the system from a high-
temperature source to desorb the refrigerant from the absorbent during the generation
process).
The starting date for the U.S. Patent survey was 1918 and continued through
1992. The 1918 date was chosen to predate the commercial introduction of household
8
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refrigerators using the vapor compression cycle, CFC refrigerants (~ 1930), and air
conditioning.
A literature survey was conducted in parallel with the patent survey. The pur-
poses of this survey were to:
• Identify additional refrigeration methods which may not have been found during
the survey of U.S. patents.
• Provide additional information regarding the theory underlying a particular
refrigeration method found during the patent survey.
• Provide additional information regarding hardware used to accomplish a refri-
geration method found during the patent survey.
. • Determine the environmental consequences related to the use of working mate-
rials commonly found in each refrigeration method found.
• Discover what alternative working materials were known for the refrigeration
methods.
• Identify the potential applications for which the refrigeration method was in-
tended.
• Identify the potential temperature lift for a single stage of a system using a
particular refrigeration method.
• Determine the actual COP range which had been observed by experiment for
a particular technology.
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• Identify the source of major performance losses for a particular refrigeration
method and the manner in which these losses could be reduced.
Sources for the literature survey included technical journals, thermodynamic
texts, refrigeration trade publications, and information supplied by the Environmen-
tal Protection Agency's Air and Energy Engineering Research Laboratory (AEERL).
U.S. Patent Survey
Patents are assigned a number in the chronological order in which they are
granted. An initial challenge in locating patents for this project was to determine
which patents (by number) should be candidates for review.
Patents are grouped into different technological categories through a system of
classes and subclasses. These classes and subclasses can be found in the Index to the
U.S. Patent Classification System [6]. This index is an alphabetical list of technology
subject headings, by indecia number, to the classification system.
The Manual of Classification [7] lists the numbers and brief descriptive titles
(more than 100,000 in all) of the classes and subclasses. If a more definitive descrip-
tion of a class or subclass is required, it can be found in the Classification Definitions.
There are continual changes in the classification system. New classes are estab-
lished as a result of advancements in science and technology. Conversely, old classes
and subclasses are abolished when rendered obsolete by technological advancement
[6],
10
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Search Method for Patents Granted Prior to 1950
The initial search for refrigeration patents was done manually at the Iowa State
University Library. An orderly search procedure similar to one recommended by
Ardis [8] was developed. The procedure for manually locating refrigeration patents
was as follows:
1. Determine the function or effect of the art or instrument to be investigated; in
this case, refrigerators, coolers, and air conditioning.
2. Scan the Index to the U.S. Patent Classification System or the Manual of Classi-
fication to determine the classes which appear to describe the invention sought.
3. After determining the applicable classes, review the subclasses in the Index or
Manual of Classification to determine which ones are applicable.
4. Locate the U.S Patent Index for the year being surveyed. Patents are listed by
number within the class and subclasses. Therefore, a list can be constructed
for all classes and subclasses of interest for a particular year.
5. Locate the volume of the Official Gazette of the United States Patent Office [9]
which contains the abstract of the patent being sought.
6. Review the patent abstract to determine the nature of the patent.
7. Accept or reject the patent for assessment based upon the information in the
abstract. If the abstract was accepted, a copy of the patent was ordered from
the Commissioner of Patents and Trademarks. If the abstract was rejected, no
further action was taken.
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Search Method for Patents Issued from 1950 to Present
Computerized databases are available which contain a complete listing of all U.S.
patent titles and abstracts granted from 1950 to present. The patents relating to a
particular technology are located in the database by supplying the computer with a
list of the appropriate class and subclass numbers.
Class and subclass numbers which had been identified during the manual patent
survey (for the time period from 1918 to 1950) were used as a starting point. Since
classes and subclasses within the system change with time, the 1991 Index to the U.S.
Patent Classification System, was used as a reference to determine if any additional
classes or subclasses which might be applicable had been added to the system. Table
2.1 contains a listing of the refrigeration and air conditioning classes and subclasses
used for the database search.
The procedure for the database survey was:
1. The database was queried using the list of patent classes and subclasses.
2. A list of patent titles (but not patent numbers) was returned along with a
number which was proprietary to Dialog Information Services [10].
3. These patent titles were reviewed to determine the probable nature of the
patent. If the patent title implied that the patent dealt exclusively with a
hardware item or other feature which was not applicable to this project, it was
discarded.
4. Abstracts were purchased from Dialog Information Services for patent titles
which appeared to have merit with respect to the project.
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Table 2.1: U.S. patent classes and subclasses surveyed.
Class Name
Subclass Name
Class No.
Subclass No.
Automobile
Cooler
62
243
Cooler
Air
62
404
Cooler
Air Conditioning
Equipment
D23
351
Cooler
Cooling and
Heating Apparatus
165
58
Cooler
Liquid
62
389
Refrigerators
Cabinet structure,
Combined
312
236
Refrigerators
Car
62
239
Refrigerators
Compositions to produce,
Chemical
62
532
Refrigerators
Compositions to produce,
Processes combined
62
114
Refrigerators
Compositions to produce,
Processes combined,
Sorption type
62
114
Refrigerators
Compositions to produce,
Refrigerants, Brines
252
71
Refrigerators
Compositions to produce,
Refrigerants, Evaporative
252
67
Refrigerators
Design of machine
D15
81
Refrigerators
Occupant type, Vehicle
62
244
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5. The abstracts were reviewed to determine the nature of the patent, as done in
the "manual" search.
6. Acceptance or rejection of the patent for further assessment was based upon
information in the abstract. If the abstract was accepted, a copy of the patent
was ordered from the Commissioner of Patents and Trademarks. If the abstract
was rejected, no further action was taken.
Survey Results
In all, approximately 2140 patent titles and abstracts were surveyed. Roughly
800 of these were from the 1918 to 1950 time period, and the remainder were taken
from the post-1950 group.
Many patents were rejected because they dealt with a minor hardware item,
such as the door latch on a refrigerator. Some were rejected since they were granted
for technologies which were no longer usable, ice boxes, for example. Several patents
were rejected because they dealt specifically with an unacceptable refrigerant such as
methyl chloride.
Many of the refrigeration technologies set forth in the remaining patents were
similar in nature. Therefore, patents were selected from the remaining group which
were representative of the types of technologies which were found during the sur-
vey. Seventy-one patents were selected as being representative of the refrigeration
technologies found during the patent survey. Three additional refrigeration technolo-
gies which had not been discovered during the patent survey were found during the
literature survey.
Once samples representative of refrigeration technologies were found, a method of
14
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classifying them into similar thermodynamic cycles was developed. This classification
procedure is presented in Chapter 3.
Appendix A contains a list of the refrigeration concepts found during the patent
and literature survey.
15
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CHAPTER 3. CLASSIFICATION OF REFRIGERATION
TECHNOLOGIES AND REFRIGERATION APPLICATIONS
Introduction
Two classification systems were developed for this project: one to classify refri-
geration technologies which had been identified during the U.S. Patent and literature
survey and the second to define the types of applications in which the refrigeration
technologies would be used.
Refrigeration Technology Classification System
During the review of the U.S. patents found during the patent survey, it was
determined that the technologies tended to fall into specific groups. Within these
groups, the technologies had many common features. These common features were
used to categorize the refrigeration technologies for the thermodynamic analysis and
technical assessment phases of the project.
Figure 3.1 is a diagram illustrating the classification method developed to cate-
gorize the refrigeration technologies found during the patent and literature surveys.
The number in parentheses indicates the number of representative technologies which
were placed in a particular category.
The first tier in Figure 3.1 represents the energy source used to power the re-
16
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Figure 3.1: Refrigeration technology classification diagram.
frigeration system. Heat, mechanical work, the direct conversion of electricity into
refrigeration, and the indirect conversion of electricity into refrigeration (through
electromagnetic fields) are the four sources of energy used to power the systems.
A change in phase of the working fluid occurred in the thermodynamic cycles for
all of the heat-driven systems. Most of the technologies powered by mechanical work
involved a change in phase during the processes transferring heat into and out of the
system. Heat transfer with a change in phase of the working fluid is desirable because
the thermal capacity of the working fluid is large during the phase change process.
17
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Therefore, the mass flow rate in the refrigeration system will be small as compared to
systems of equivalent refrigerating capacity which do not have a change in phase of
the working fluid during heat transfer. Low mass flow rates result in smaller piping,
smaller charge quantities of the working fluid, and lower pressure drops in the system.
The second desirable characteristic of phase change heat transfer processes is a lower
thermal resistance in the heat exchangers (as compared to single phase heat transfer
in which the working fluid is in a vapor state) due to higher convective heat transfer
coefficients for both the liquid and two-phase (liquid and vapor) mixture in the heat
exchangers.
The mechanically powered refrigeration technologies which did not have a phase
change heat transfer processes used either a gas or liquid as the working material.
Helium and air were the working gases most commonly used. Liquid working fluids
were CO2 and propylene.
The working materials used in all of the direct electric conversion and magnetic
systems were solids which did not undergo a phase transformation during the refri-
geration cycle. Tellurium-based semiconductors are used for direct electric conversion
refrigeration, and gadolinium or gadolinium salts are used in magnetic refrigeration.
The thermodynamic cycle used to accomplish refrigeration was determined dur-
ing the review and selection of representative patents. Table 3.1 summarizes the
thermodynamic cycles used to accomplish refrigeration in each technology category.
Classification of Refrigeration Applications
During the refrigeration technology identification and classification phases, no
consideration was given as to the application of the refrigeration system. The next
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Table 3.1: Thermodynamic cycles used to accomplish refrigeration identified during
the survey of technologies.
Ref. Technology Category
Thermodynamic Cycle
or Process
Heat-driven
Absorption
Adsorption
Ejector
Mechanical Work, Phase Change
Vapor-Compression
Evaporative
Mechanical Work, No Phase Change
Reversed Brayton
Reversed Stirling
Pulse Tube & Thermoacoustic
Reversed Malone
Direct Electric
Thermoelectric
Magnetic
Magnetic
step was to define general application areas. These application areas were selected:
1. Domestic air conditioning.
2. Commercial air conditioning.
3. Mobile air conditioning.
4. Domestic refrigeration.
5. Commercial refrigeration.
The temperatures of the thermodynamic source (from which heat is accepted)
and sink (to which heat is rejected) were established for each of the applications.
A survey of standards and other technical literature was conducted to determine a
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practical set of source and sink temperatures for each application area. Standardized
procedures to determine the performance of domestic air conditioners and refriger-
ators have been promulgated by the Association of Home Appliance Manufacturers
(AHAM). These performance standards have been adopted by the American National
Standards Institute (ANSI) to help bring about uniformity in the domestic refriger-
ation industry. Guidelines for testing the performance of commercial air conditioners
and refrigerators are established by the Air-Conditioning and Refrigeration Institute
(ARI) and the American Society of Heating, Refrigerating, and Air-Conditioning
Engineers (ASHRAE). ASHRAE has also established a standard for the environmen-
tal conditions in buildings. As with the AHAM standards, ANSI has adopted the
ASHRAE standards to bring about uniformity in the refrigeration industry.
Standards for establishing the performance of domestic and commercial air con-
ditioners [11, 12, 13] all specified the temperature to which heat is rejected (sink
temperature) during performance tests to be 35 C (95 F). All three standards spec-
ified a room air temperature (source temperature) of 26.7 C (80 F) for performance
testing. This temperature appeared to be too high for actual domestic and com-
mercial air conditioning applications. Therefore, the ANSI/ASHRAE Standard for
Thermal Environmental Conditions for Human Occupancy [14] was consulted. The
optimum temperature for people during light, primarily sedentary activity at 50%
relative humidity and mean air speed < 0.15 ™ was given as 24.5 C (76 F) with an
acceptable temperature range of ± 1.5 C.
Multerer and Burton [15] established an interior temperature for automobiles as
24 C for a study of alternative automotive air conditioning systems.
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For domestic refrigerators, AHAM lists three ambient (sink) temperatures for
testing refrigerators, freezers, and refrigerator-freezers [16]:
• 21.1 C (70 F)
• 32.2 C (90 F)
• and 43.3 C (110 F)
AHAM also recommended an average freezer compartment temperature of -17.8 C
(0 F).
ARI Standard 420 [17] specifies an ambient temperature of 35 C for the perfor-
mance testing of commercial refrigerators. Four groups were established by the ARI
for the performance testing of commercial refrigerators. Each group corresponds to a
cooling space temperature for different commercial refrigeration applications such as
the storage of produce, dairy products, meat, and frozen food. These temperatures
are given in Table 3.2.
Based upon this survey, a set of source and sink temperatures has been estab-
lished for each of the five application categories. Table 3.2 is a summary of the five
refrigeration application categories and the source and sink temperatures to be used
for comparing refrigeration technologies in each category.
In this chapter, the refrigeration methods were classified into technology groups
based upon the form in which energy source used to power the refrigeration system is
supplied and the phase of the working material. If the working material was a fluid,
heat transfer involving a change in phase was also used as a characteristic used to
classify the refrigeration technology. A set of refrigeration and air conditioning appli-
cation categories was identified. These application categories are ones in which the
21
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Table 3.2: Thermal source and sink temperatures for the five refrigeration applica-
tion categories.
Ref. Application Category
Source Temp. (C)
Sink Temp. (C)
Domestic Air Conditioning
25.0
35.0
Commercial Air Conditioning
25.0
35.0
Mobile Air Conditioning
25.0
35.0
Domestic Refrigeration
-18.0
35.0
Commercial Refrigeration
ARI Group I
2.8
35.0
ARI Group II
1.7
35.0
ARI Group III
-2.2
35.0
ARI Group IV
-23.3
35.0
refrigeration technologies could be used. A set of source and sink temperatures were
established for each application category using refrigeration industry performance
testing standards. The method used to compare the performance of one refrigeration
technology to another will be discussed in Chapter 4.
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CHAPTER 4. COMPARING THE PERFORMANCE OF
REFRIGERATION SYSTEMS
Introduction
In this chapter, methods of comparing the performance of refrigeration systems
will be discussed.
The refrigeration technologies found during the survey use mechanical work, heat
transfer, and electricity to power them. The cycle efficiency was used to compare the
relative performance of the different technologies at the source and sink temperatures
for the five application areas which were identified in Chapter 3.
The Clausius statement of the second law of thermodynamics is: " It is impos-
sible to construct a device that operates in a cycle and produces no effect other than
the transfer of heat from a colder to a hotter body." [18]. For refrigeration systems,
the Clausius statement implies that a system that accomplishes the transfer of heat
from a cooler source to a hotter sink requires the input of additional work or energy
to cause the temperature lift. The performance of refrigeration systems can be deter-
mined and compared using the coefficient of performance (COP) which is discussed
in the next section.
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Coefficient of Performance
The performance of refrigeration and air conditioning systems is characterized
in terms of the ratio of the amount of heat accepted from the cooling space to the
amount of heat or work required to drive the refrigeration system. This ratio is known
as the coefficient of performance (COP) [18].
Figure 4.1 illustrates a mechanical work-driven refrigeration system communi-
cating with two thermal reservoirs: the source at temperature Tj^ and the sink at
temperature Tjj. The COP is defined as:
COPw = (4.1)
vyin
where,
COPw — the coefficient of performance for a work-driven system
Q£ = the amount of heat accepted from the source reservoir
W^n = the net amount of work from an external system.
Heat-driven refrigeration systems can be considered as two combined thermal
systems: a refrigeration system and a heat engine to power the refrigeration system.
Figure 4.2 is a schematic of the two combined systems. Three thermal reservoirs at
three different temperatures are required.
The heat engine accepts heat from a high-temperature reservoir at temperature
TGen and rejects heat to the sink reservoir at temperature Tjj producing work. The
refrigeration system accepts heat from the source reservoir at temperature T£ and
rejects heat to the sink reservoir. The net work from the heat engine is used to drive
the refrigeration system.
24
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WDRK
HEAT
SDURCE
Figure 4.1: Schematic of a refrigeration system
driven by mechanical work.
The COP for the refrigeration system is given by Equation 4.1.
The thermal efficiency of the heat engine can be defined as,
W
"th ' QGeJ
where,
W = the net work output of the heat engine
QGen = heat transferred to the heat engine.
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Figure 4.2: Schematic of a refrigeration system driven by heat transfer.
26
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The COP for heat-driven systems is then,
(4.3)
Ql
(4.4)
(4.5)
QGen.
Vth'COPw
Equation 4.5 illustrates that the COP for heat-driven refrigeration systems,
COPfo, will be lower than the COP for systems powered by mechanical work, COPw
The ratio of the heat-driven COP to the mechanical work-driven COP is the thermal
efficiency, 77^, of the heat engine. If the system boundary of a mechanical work-
driven system is chosen to include the heat engine which delivers the mechanical
power to it, then it too becomes a heat-driven system. For example, consider the
original source of the energy which is converted to the mechanical work used to op-
erate work-driven refrigeration systems. Most work-driven systems are powered by
an electric motor which receives electrical energy generated by a power plant. The
typical thermal efficiency for the cycle converting fossil fuel-stored energy into elec-
trical energy is approximately 33% [19]. A general estimate of the transmission losses
in transmitting the electricity from the power plant to the user is approximately 5%
[20]. Therefore, the overall thermal efficiency of the heat engine providing the power
to the refrigeration system is 31.4%. The performance of heat-driven refrigeration
systems compares favorably with that of mechanical work-driven systems when the
original energy source is used as in the comparison.
Refrigeration systems of a given capacity with high COPs are desirable because
they are less expensive to operate energywise, and they have a lower indirect GWP
since less fuel must be burned to operate them.
27
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Ideal COP
An ideal refrigeration system would transfer heat reversibly between the source
and sink. The COP for a reversible refrigeration system would be the highest the-
oretically possible. Using the definition of the Kelvin temperature scale, it can be
shown that the ideal COP for a work-driven refrigeration cycle can be expressed in
terms of the absolute temperatures of the source and sink reservoirs [18]. The ideal
COP (COPiw) for a work-driven system is [21],
For heat driven systems, the ideal COP (COPwould be that of a reversible
heat engine driving a reversible refrigerator. It can be expressed in terms of the
absolute temperatures of the high-temperature reservoir, sink, and source. Using
Equation 4.2 and the definition of the thermal efficiency for an ideal heat engine, an
expression involving absolute temperatures can be written for the ideal heat driven
refrigeration system:
While reversible operation (and thus an ideal COP) is not possible for actual
refrigeration systems, it can be shown as a corollary to the second law of thermo-
dynamics that any two reversible refrigeration cycles accepting and rejecting heat
between two particular thermodynamic (absolute) temperature levels must have the
same COP. Therefore, the ideal COP can be used as a standard of comparison for
the performance of modeled and actual refrigeration systems.
(4.6)
(4.7)
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Modeled COP
The COP of refrigeration systems can be estimated through modeling of the ther-
modynamic cycle with which the system operates. The models attempt to account
for some of the irreversibilities which occur in actual systems.
There are different levels of sophistication in thermodynamic models, ranging
from simply multiplying the ideal COP by an efficiency through multi-dimensional
transient models in which the energy, momentum, and continuity equations are si-
multaneously solved for elemental control volumes or mass elements throughout the
system. As the level of sophistication of the model increases, so does the amount of
information which must be known or assumed about the system.
For this project, models were constructed in which the thermodynamic state
was determined at the end of each process comprising the cycle. Where possible,
component efficiencies were accounted for. The properties corresponding to the ther-
modynamic state were determined as needed using property routines.
Actual COP
The actual COP is that of an actual refrigeration system as is determined through
experiments conducted using laboratory refrigeration systems or production systems.
For work-driven systems, the COP is calculated using Equation 4.1, while for heat-
driven systems, it is calculated using Equation 4.4.
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Cycle Efficiency
The cycle efficiency, T}QyCie, will be used to examine the efficiency of a refriger-
ation technology operating at different source temperatures and operating conditions.
It will also be used to compare the relative efficiencies of different technologies at the
same source temperature. The cycle efficiency is defined as
_ COP
ICycle C0PCarrwt ( ' '
The COP in the numerator of Equation 4.8 can be either a modeled or actual
value. However, consistency in choice should be maintained when comparing one
technology to another.
Closure
The cycle efficiency, VCyclei be used to compare the performance of the dif-
ferent refrigeration technologies in the five different application areas. The following
chapters will discuss some of the alternative refrigeration technologies in detail.
30
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CHAPTER 5. REVERSED BRAYTON CYCLE REFRIGERATION
Introduction
Refrigeration can be accomplished by employing a gas cycle rather than a vapor
cycle in which the working fluid undergoes changes from the liquid phase to the
vapor phase and vice versa. Gas refrigeration cycles include the reversed Brayton,
reversed Stirling, and pulse-type cycles including the pulse tube developed by Gifford
and Longsworth [22] and thermoacoustic devices which have been studied by Garrett
and Hoffler [23]. In this chapter the reversed Brayton cycle, with and without a
regenerator, will be examined.
The refrigeration effect per unit mass of fluid circulated in a vapor compression
cycle is equivalent to a large fraction of the enthalpy of vaporization. In contrast,
the refrigeration effect in a gas cycle is directly related to the temperature rise of the
working gas passing through the low-temperature heat exchanger and the constant-
pressure specific heat (cp) of the gas. Therefore, when compared to the vapor com-
pression cycle, a larger mass flow rate is required in the gas cycle to produce the same
refrigerating effect.
Gas-cycle refrigeration can be designed and operated either as an open or closed
system. In open systems the gas, commonly air, is expanded into the space to be
cooled which is at atmospheric pressure. Open systems often require dehumidification
31
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of the air prior to expansion to prevent ice formation at the low-temperature points of
the system. Open-cycle air systems have become a common method of cooling used
in the heating ventilating and air conditioning (HVAC) systems on board commercial
aircraft. The principal advantages of the open-cycle air system in aircraft applications
are:
1. Pressurization of the cabin is required during flight at altitudes above 3810 m
(12500 ft) MSL. The compressor for the open refrigeration system can be used
to change to cabin pressure.
2. Ventilation air is required in the aircraft cabin. The configuration of the open
refrigeration system lends itself to ventilation, with and without cooling.
3. Compressed air is available and is a small fraction of the air compressed in the
• aircraft engine compressor section.
4. Cool ambient air is available for cooling the compressed air.
In closed-cycle gas refrigeration systems, the refrigerant gas is contained in the
piping and component parts of the system at all times. Historically, the term "dense-
air system" was derived from the higher pressures maintained in the closed system
as compared to the open system [24].
A description of the reversed Brayton cycle without regeneration and a schematic
(Figure 5.1) are presented in the section entitled, "Non-Regenerative Reversed Bray-
ton Cycle."
History
Open- and closed-cycle gas refrigeration systems using air as the refrigerant were
some of the earliest mechanical refrigeration means dating back to 1834 [25]. The
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first commercial air cycle machine was an open-cycle machine introduced by Franz
Windhausen in 1889 [26]. The primary application for the Windhausen system was
cold-storage and space conditioning aboard ships. Air-cycle refrigeration machinery
was favored by the shipping industry because ammonia or carbonic acid used in
other refrigeration cycles of that era were unavailable in many ports of call. Air-
cycle refrigeration was also used in other commercial applications as land-based cold-
storage and theater cooling. Another advantage of the air system was a completely
safe and inexpensive refrigerant [24].
The principal objections to the Windhausen open-cycle design were directly re-
lated to moisture in the air which created the need for increased maintenance of the
machinery, and frost contamination of the cold-storage cargo. The Allen dense-air
system, incorporating a closed-air system operating at a low pressure of 60 to 70 psig
and a pressure ratio of 3 or 4, was adopted to solve the moisture-related problems
[24].
When the air-cycle refrigeration machine's advantages of safety and low refrig-
erant cost were lost due to the development of CFC refrigerants, vapor compression
systems gained favor due to their higher efficiencies, capacities, and compactness. The
vapor compression system was thus more adaptable to different cooling applications.
U.S. Patent Survey
A U.S. patent survey was conducted to discover different gas-cycle technologies
for refrigeration applications. In our survey, one patent was discovered for an air
reversed-Bray ton cycle machine.
U. S. Patent number 1,295,724 was issued February 25, 1919 to Julius Franken-
33
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berg for an "Air-Refrigerating Machine" [27]. This machine was a unitized compres-
sor, expander, and high-temperature system. It incorporated rotary compressor and
expander sections connected by a common shaft. A water-cooled heat exchanger was
mounted above the compressor/expander unit to cool the air between the compressor
and expander stages. No claim for a low-temperature heat exchanger or regenerator
was made in the patent.
Literature Review
The technical literature was reviewed to determine what present research has
been conducted to develop reversed Brayton or modified reversed Brayton refriger-
ation cycles.
Kauffeld et al. [28] investigated the reversed Brayton cycle as a replacement
for vapor compression in refrigeration and air conditioning applications. Analyses of
15 variations of the reversed Brayton cycle were conducted. The major variations
included:
• open cycle,
• regeneration,
• and two-stage compression with intercooling.
Kauffeld reported calculated coefficients of performance ranging from 0.6 to 1.16
for the different system configurations. The calculations assumed an ambient tem-
perature of 30 C, a coldroom entry temperature of 5 C, and isentropic efficiencies of
80% for the expansion and compression devices .
34
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Kauffeld also discussed experiments with an open-cycle reversed Brayton test
apparatus using both single- and two-stage compression. Measured COPs of up to
0.45 were reported [28]. Problems with moisture removal, oil odor, and noise were
also reported.
Henatsch and Zeller [25] thermodynamically modeled the Joule (reversed Bray-
ton) process and a modified Joule-Ericsson process including the effects of regenera-
tion. The model included adiabatic two-stage compression with intercooling.
Henatsch and Zeller [25] also conducted an investigation of commercially avail-
able turbines, radial-flow compressors, and dry-type screw compressors. The isen-
tropic efficiencies and volumetric flow rates of these off-the-shelf components were
compared. Efficiencies of approximately 88% for large displacement turbines and
radial flow compressors and 80% for large radial flow compressors were noted. For
a non-regenerative open cycle, coefficients of performance ranging from 0.61 to 0.77
were noted for mass flow rates of 0.10 and 0.35 respectively, an ambient temper-
ature of 42 C, and an absolute temperature ratio of 1.1.
Thermodynamic Model
Introduction
Thermodynamic models for the non-regenerative and regenerative reversed Bray-
ton cycles were constructed and programmed in FORTRAN for analysis on an IBM-
compatible personal computer. A subroutine to calculate the thermodynamic prop-
erties of the air was also developed.
35
-------
Non-Regenerative Reversed Brayton Cycle
The thermodynamic model of the reversed Brayton cycle includes two isentropic
and two isobaric processes [29]. Since the actual compression and expansion processes
are irreversible, provisions were made in the model to allow for and vary the degree
of irreversibility using isentropic compressor and expander efficiencies.
Figures 5.1 and 5.2 are the schematic and temperature versus entropy diagrams
for a non-regenerative reversed Brayton cycle.
High Temp.
Heat Exch.
1 _
Low
Temp.
1
4
Heat
Exch.
Ql
Figure 5.1: Schematic of a non-regenerative re-
versed Brayton cycle.
The gas exiting the low-temperature heat exchanger undergoes a compression
process from state 1 to state 2. The reversible process is illustrated in Figure 5.2
36
-------
CD
L
d
L
CD
CI
£
CD
Specific Entropy, s
Figure 5.2: Temperature vs. entropy diagram for a reversed Bray-
ton cycle.
as a solid line from state 1 to state 2s and in Figure 5.2, the irreversible process is
illustrated as a dashed line from state 1 to state 2 since the specific path during the
irreversible compression process is unknown. Heat is rejected at constant pressure to
the surroundings from the compressed gas through a high-pressure heat exchanger
(state 2 to state 3). The gas is then expanded through an expander (commonly
a turbine) from state 3 to state 4. The unknown path of the irreversible expansion
process is again illustrated as a dashed line in Figure 5.2. Heat is removed at constant
pressure from the space to be cooled through the low-pressure heat exchanger (state
4 to state 1), completing the cycle.
37
-------
The following assumptions were made to simplify the model:
1. Steady state operation.
2. Adiabatic compression.
3. Adiabatic expansion.
4. Negligible changes in potential and kinetic energy of the fluid.
5. Negligible pressure drop through the heat exchangers and related piping (no
fluid friction).
6. Ideal gas with variable specific heats.
7. The heat exchangers were of types and sizes to permit the exiting gas to ap-
proach the source and sink temperatures by a fixed temperature difference.
Therefore, the temperatures of the air at states 1 and 3 can be written as,
where ST is a small incremental temperature.
The isentropic compressor and expander efficiencies ((r/c) and (j/e), respectively)
were defined as [30],
rl = Tlow - ST
(5.1)
T3 = Th,gh + ST
(5.2)
(5.3)
m
Ve ~
m
(5.4)
where, Wc is the compressor work rate, We is the expander work rate, m is the mass
flow rate, and the subscript s denotes the isentropic process.
38
-------
Applying an energy balance to each of the four system components in the cycle,
expressions can be obtained for the coefficient of performance (COP):
Qjn
COP = -r&— (5.5)
WNet
m
Qi
in
(5.6)
(5.7)
(Wc - We)
ih - H)
[(h2 - hi) - (/i3 - fc4)]
where
Qjn = the heat into the low temperature heat exchanger
Wjyet = the net mechanical power supplied to the system = Wc — We
Wc = the mechanical power supplied to the compressor
We — the mechanical power produced by the expander
h} = the specific enthalpies at state i (1 through 4 in Figure 5.2)
Regenerative Reversed Brayton Cycle
The regenerative reversed Brayton cycle includes another heat exchanger to cool
the gas entering the expander below the ambient temperature [30]. Figures 5.3 and
5.4 are the schematic and temperature versus entropy diagrams for a regenerative
reversed Brayton cycle, respectively. Gas exiting the low-pressure heat exchanger
(state B) enters the regenerator and cools the gas exiting the high-pressure heat
exchanger (state A). The remainder of the cycle is similar in operation to the non-
regenerative cycle.
The following assumptions were made to simplify the model:
39
-------
Qh
Oj
"Z5
c
d
a
x
LlJ ^
A
1
High Tenp.
Heat Exch.
1
-2
wwvw
Regenerator
1 _
Low
Tenp.
1
4
Heat
Exch.
a
c
o
u
V c
Ql
Figure 5.3: Schematic of the regenerative reversed
Brayton cycle.
1. Steady state operation
2. Adiabatic compression
3. Adiabatic expansion
4. Negligible changes in potential and kinetic energy of the fluid
5. Negligible pressure drop through the heat exchangers and related piping (no
fluid friction)
6. The working fluid is an ideal gas with variable specific heats.
7. The regenerator operates adiabatically.
8. The heat exchangers were of types and sizes to permit the exiting gas to ap-
proach the source and sink temperatures by a fixed temperature difference.
40
-------
Qj
L
3
d
L
Qj
a
E
Qj
I—
Specific Entropy; s
Figure 5.4: Temperature vs. entropy diagram for the regen-
erative reversed Brayton cycle.
The temperatures at which heat is transferred to and from the working fluid in
the system can be expressed as,
TB = Tlow - 6T (5-8)
TA = Thigh + ST- (8-9)
The regenerator effectiveness (rjr) is defined as the ratio of the amount of heat
transferred from the high-pressure gas in the regenerator to the amount of heat which
would be transferred if reversible regeneration occurred. The regenerator effectiveness
41
-------
(r)r) can be expressed as,
ir = (5-10)
["¦A ~ hB)
Applying an energy balance to each of the system components in the cycle, an
expression can be derived for the COP for the regenerative reversed Brayton cycle,
Qj.n
COP = ¦ m (5.11)
^Total
m
Qi
m (5.12)
(5.13)
(Wc - We)
(hB - A4)
p2 - hi) -(/i3 - /i4)]'
Thermodynamic Properties
A FORTRAN subroutine was written to determine the specific properties of the
working gas. Given two properties to fix the thermodynamic state (pure substance),
the subroutine finds the remaining properties for that state and inputs them into the
cycle model.
It was assumed that the gas behaved ideally in the temperature and pressure
range over which the cycles operated. The constant pressure specific heat (cp(T))
was variable over the temperature range of —73 C to 827 C.
A functional relationship was found for cp(T) data published by Reynolds [31].
The specific enthalpy is found by integrating the constant pressure specific heat func-
tion directly,
h(T) - h0 = J*cp(T)dT. (5.14)
42
-------
The specific internal energy is found from the definition of enthalpy and the ideal gas
equation of state,
u{T) = h(T) - RT. (5.15)
The specific entropy can also be found from the specific heat function and the pressure
ratio,
(5'16)
The reference state for determining the properties was established as —273.15 C and
101.325 kPa. The thermodynamic property code is given in Appendix B.
Results
The coefficients of performance and cycle efficiencies were calculated for three
cases:
1. The ideal case in which the heat was transferred reversibly (no heat exchanger
temperature difference, 6T). The compression and expansion processes were
isentropic. For regenerative cycles, the regenerator effectiveness was 1.0
2. The actual case which used estimated compressor and expander isentropic effi-
ciencies and regenerator effectiveness. A minimum approach temperature of 5
C was interposed between the sink and high-temperature heat exchanger and
the source and low-temperature heat exchanger to account for irreversibilities
due to heat transfer.
3. The "best possible" case in which higher compressor and expander isentropic
efficiencies and a larger regenerator effectiveness were chosen. These values
43
-------
were estimates of the upper limit for component efficiencies in the future, given
further technological development in the turbomachinery and heat exchanger
industries.
Table 5.1 summarizes the parameters for the actual, best possible and ideal cases.
Each case was modeled at several different pressure ratios to establish trends for the
COP and cycle efficiency.
Table 5.1: Parameter values for the actual, best possible and ideal reversed Brayton
and regenerative reversed Brayton model case study.
Case
vc
VE
VR
Heat Exchanger Temp.
Difference, AT (C)
Ideal
1.0
1.0
1.0
0
Best Possible
0.95
0.95
0.95
5
Actual
0.85
0.85
0.85
5
Figure 5.6 is a graph of the COP versus source temperature for an ideal reversed
Brayton refrigeration system using air as the working gas. The model parameters are
given in Table 5.1 for three cases. The COP was highest for a pressure ratio of 2.5;
increasing the pressure ratio resulted in lower COPs at the same source temperature.
The COP remained constant over the entire range of source temperatures from —24
C to 28 C. Figure 5.6 is a graph of the cycle efficiency versus source temperature
for the ideal reversed Brayton system. For each pressure ratio, the highest cycle
efficiencies occurred at low source temperatures and decreased almost linearly with
increasing source temperature.
The COP versus source temperature graphs for the "best possible" reversed
Brayton cycle case are presented in Figure 5.7. At source temperatures above 20 C,
44
-------
5
Pressure Ratio * 25
Pressure Ratio « 3.0
Pressure Ratio = 4.0
Pressure Ratio > S.O
Pressure Ratio = 6.0
Legend
Sink Temperature « 35 C
Isentroplc Compression
Isentroplc Expansion
Heat Exch. Minimum Approach Temperature = 0 C
4
3
Q.
O
o
2
1
0 1 1 1 1 1 1 1 1 1 1 1 1 1 ¦ 1 1 1 1 ¦ 1 1 1 1
-30 -20 -10 0 10 20 30
Source Temperature (C)
Figure 5.5: COP vs. source temperature for an ideal reversed Brayton
refrigeration system.
the highest COPs were produced by cycles operating at pressure ratios below 3.0.
The lowest source temperature achieved by the cycle operating at a pressure ratio
of 1.5 was 14 C. A pressure ratio of 3.0 was required to accomplish the temperature
lift over the entire range of source temperatures (—24 C to 30 C) studied here. As
the pressure ratio was increased, the slope of the lines decreased until a relatively
constant COP of approximately 1.0 was noted over the entire source temperature
range at a pressure ratio of 6.0. The cycle efficiencies for this case are shown in
Figure 5.8. For pressure ratios of 3.0 and below, the cycle efficiency versus source
temperature line was parabolic. A maximum cycle efficiency occurred at a specific
45
-------
£
c
S
'o
s
a>
£
O
- Sink Temperature ¦ 35 C
. Isentioplc Compression
Isentroplc Expansion
Heat Exchanger Minimum Approach Temperature - o
-30
Legend
Pressure Ratio » 2.5
— — — Pressure Ratio => 3.0
Pressure Ratio - 4.0
— Pressure Ratio » 5.0
— — Pressure Ratio = 6.0
-20 -10 0 10
Source Temperature (C)
20
30
Figure 5.6: Cycle efficiency vs. source temperature for an ideal
reversed Brayton refrigeration system.
source temperature for the three lowest pressure ratio cases. This indicates that
different optimum pressure ratios exist for reversed Brayton systems operating at a
fixed sink temperature, but different source temperatures. For a given pressure ratio,
the range of source temperatures at which the system will operate at near-maximum
cycle efficiency is narrow.
Figure 5.9 is a graph of COP versus source temperature for the actual reversed
Brayton cycle model case. For low pressure ratios, the COP decreased rapidly with
decreasing source temperature. As the pressure ratio was increased, the slope of the
COP versus source temperature line decreased. At source temperatures below 0 C,
46
-------
4
3
a.
82
1
0
-30 -20 -10 0 10 20 30
Source Temperature (C)
Figure 5.7: COP vs. source temperature for the "best possible" re-
versed Brayton refrigeration system.
the COP increased with the pressure ratio for a given source temperature. At higher
source temperatures, the COP increased with decreasing pressure ratio.
The trend of parabolic cycle efficiency versus source temperature lines was more
evident at higher pressure ratios than for the previous (best possible) case. Decreas-
ing the isentropic compressor and isentropic expander efficiencies from 0.95 to 0.85
resulted in a lower maximum cycle efficiency for a given pressure ratio. Also, the
maximum efficiency occurred at a higher source temperature than for the ideal or
best possible cases.
Sink Temperature » 35 C
Compressor Isentropic Efficiency = 0.95
Expander Isentropic Efficiency = 0.95
Heat Exchanger Minimum Approach Temperature »5C
Legend
—— Pressure Ratio = 1.5
Pressure Ratio - 2.0
— Pressure Ratio » 3.0
—— Pressure Ratio = 4.0
- » Pressure Ratio * 5.0
— Pressure Ratio » 6.0
- V
X
/
/
1 1 11 1 1 1 1 1 1 1 1
1 1 '
47
-------
0.4
0.3
£
c
®
| 0.2
JS
£
o
0.1
0.0
-30 -20 -10 0 10 20 30
Source Temperature (C)
Figure 5.8: Cycle efficiency vs. source temperature for a reversed
Brayton refrigeration system operating with parame-
ters given in the "best possible" case.
Figures 5.11 and 5.12 are graphs of the COP and cycle efficiency versus source
temperature, respectively, for an ideal regenerative reversed Brayton cycle.
The COP is higher at the upper end of the source temperature range than it was
for the ideal non-regenerative cycle. At —24 C, the cycle efficiency was approximately
the same as it was for the ideal reversed Brayton cycle without regeneration (Figure
5.6). At higher source temperatures, the cycle efficiencies were higher. Also, the high-
est efficiencies occurred at lower pressure ratios than for the ideal non-regenerative
cycle.
Sink Temperature - 35 C
Compressor Isentropic Efficiency * 0.95
Expander Isentropic Efficiency > 0.95
Heat Exchanger Minimum Approach Temperature =¦ 5 C
Legend
— Pressure Ratio = 1.5
— Pressure Ratio = 2.0
Pressure Ratio = 3.0
— Pressure Ratio ¦ 4.0
— Pressure Ratio = 5.0
— Pressure Ratio = 6.0
1 '
' 1
1 1
I I I
11111
48
-------
1.5
1.0
a.
O
O
0.5
0.0
-30 -20 -10 0 10 20 30
Source Temperature (C)
Figure 5.9: COP vs. source temperature for a reversed Brayton
refrigeration system operating with parameters given
in the actual case.
The COP and cycle efficiency versus source temperature for the "best possible"
regenerative reversed Brayton cycle are shown in Figures 5.13 and 5.14, respectively.
In contrast to the non-regenerative "best possible" case, the temperature lift could
be accomplished over the entire source temperature range. The COP increases with
increasing source temperature, while the cycle efficiency increases with decreasing
source temperature. For all pressure ratios, the maximum cycle efficiency occurred
at a source temperature below — 24 C.
The COP and cycle efficiency versus source temperature for the regenerative
reversed Brayton cycle "actual case" are presented in Figures 5.15 and 5.16, respec-
49
Legend
Sink Temperature a 35 C
Pressure Ratio » 2.5
Compressor Isentropic Efficiency ^ 0.85
Expander Isentropic Efficiency * 0.85
Regenerator Effectiveness = 0.85
— - — Pressure Ratio =¦ 3.0
Heat Exchanger Minimum Approach Temperature = 5 C
" Pressure Ratio = 4.0
— Pressure Ratio - 5.0
- — Pressure Ratio 3 6.0
-
^ ^ - —
- ' , —
\
\
\
y ' /
' ~
\
\
\
\
1 1 1 1 1 1
-------
Source Temperature (C)
Figure 5.10: Cycle efficiency vs. source temperature for a reversed
Brayton refrigeration system operating with param-
eters given in the actual case.
tively. The COP increases with increasing source temperature at a faster rate when
operated at low pressure ratios rather than high pressure ratios (Figure 5.15). The
temperature lift can be accomplished over the entire source temperature range at all
pressure ratios. The cycle efficiency increased with decreasing source temperature.
For a pressure ratio of 1.5, the maximum efficiency occurred at approximately —10
C. The maximum cycle efficiency occurred below —24 C for pressure ratios of 2.0 and
above.
50
-------
Legend
— — — Pressure Ratio »1.5
— — Pressure Ratio = 2.0
* — Pressure Ratio * 3.0
Sink Temperature =¦ 35 C
Isentroplc Compression
Regenerator Effectiveness = 1.0
Isentropic Expansion
Heat Exchanger Minimum Approach Temperature > 0 C y
— — Pressure Ratio => 4.0
-
^ --
—
-30 -20 -10 0 10 20 30
Source Temperature (C)
Figure 5.11: COP vs. source temperature for an ideal regenerative
reversed Brayton refrigeration system.
51
-------
Sin k Temperature = 35 C
Isentroplc Compression
Regenerator Effectiveness => 1.0
Isentroplc Expansion
Heat Exchanger Minimum Approach Temperature » 0 C
Legend
Pressure Ratio * 12.
Pressure Ratio = 1.5
Pressure Ratio >2.0
Pressure Ratio =3.0
Pressure Ratk> = 4.0
I I
111111
I I I
I I I
1 1 1
-30
-20
-10 0 10
Source Temperature (C)
20
30
Figure 5.12: Cycle efficiency vs. source temperature for an ideal
regenerative reversed Brayton refrigeration system.
52
-------
0 1 1 ¦ 1 1 1 1 1 ¦ 1 ¦ 1 1 ¦ 1 1 11 1 1 11 1
-30 -20 -10 0 10 20 30
Source Temperature (C)
Figure 5.13: COP vs. source temperature for a regenerative reversed
Brayton refrigeration system operating with parameters
given in the "best possible" case.
53
-------
>%
o
c
CD
'.a
*=
LU
©
&
o
0.5
0.4
0.3
0.2
0.1
0.0
SnkTemperature = 35 C
Compressor Isentropfc Efficiency = 0.9
- Expander Isentroplc Efficiency = 0.95
Regenerator Effectiveness ¦ 0.95
Heat Exchanger Minimum Approach Tempera
Legend
Pressure Ratio »1.5
Pressure Ratio = 2.0
Pressure Ratio ^ 2.5
Pressure Ratio = 3.0
Pressure Ratio ¦ 4.0
Pressure Ratio = 5.0
_L
-30
-10 10
Source Temperature (C)
30
Figure 5.14: Cycle efficiency vs. source temperature for a regener-
ative reversed Brayton refrigeration system operating
with parameters given in the "best possible" case.
54
-------
SlnkTamp. =¦ 35 C
Comp. laentropic Eft. =¦ 0.B5
Exp. laentropic Eft. = 0.85
Regen. Effectiveness =¦ 0.8S
. Heat Exch. Min. Approach Temp. ¦ 5 C
- -
- - -—
— _ -
— — ...
- — -
Legend
Prase. Ratio « 2.0
-
— Prasa. Ratio = 2.5
— Press. Ratio « 3.0
— — Press. Ratio * 4.0
Press. Ratio = 5.0
; Press. Ratio = 6.0
-30 -20 -10 0 10 20 30
Source Temperature (C)
Figure 5.15: COP vs. source temperature for a regenerative re-
versed Brayton refrigeration system operating with
parameters given in the actual case.
55
-------
0.20
0.15
>»
o
c
©
S.2
£
©
O
0.10
0.05
0.00
Sink Temp- = 35 C
Camp. Isentroplc Elf. 3 0.85
Exp. Isentroplc Elf. =¦ 0.S5
Rogen. Effectiveness => 0.S5
Heat Exctv Uln. Approach Temp. =
5C
Legend
Press. Ratios 1.5
Press. Ratio - 20
Press. Ratio * 2.5
Press. Ratio =» 3.0
Press. Ratio - 4.0
Press. Ratio = 5.0
Press. Ratio » 6.0
' 1
1 1 1 1 1
-30 -10 10
Source Temperature (C)
Figure 5.16: Cycle efficiency vs. source temperature for a regen-
erative reversed Brayton refrigeration system oper-
ating with parameters given in the actual case.
30
56
-------
Closure
The regenerative cycle provided better performance than the non-regenerative
cycle in the source temperature range considered in this study. The primary perfor-
mance benefit of the regenerator occurred when the cooling application required large
temperature lifts. This was particularly evident when the source temperature was
below 0 C, as in the case of refrigeration applications. The maximum cycle efficiency
occurred below the lowest source temperature, —24 C, which was the lowest tem-
perature considered in this project. The reversed Brayton cycle, particularly with
regeneration, appears to be best suited for low-temperature applications requiring
operation at source temperatures below — 24 C.
A technology assessment of refrigeration systems using the reversed Brayton
cycle is presented in Chapter 10.
57
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CHAPTER 6. REVERSED STIRLING CYCLE REFRIGERATION
Introduction
The Stirling cycle was first used as an external combustion heat engine for the
conversion of thermal energy to mechanical work. The Stirling cycle is composed of
two isothermal processes, expansion and compression, and two isometric processes
during regenerative heat transfer. If the cycle is reversed, it can be used as a refri-
gerator.
Stirling refrigerators have been employed as cryocoolers in chemical and indus-
trial applications. As a cryocooler the heat source temperature for a Stirling refri-
gerator is typically between —193 C and —93 C.
Concern about the use of CFC refrigerants has brought about renewed interest
in Stirling refrigerators for applications near room temperature.
History
Robert Stirling, a Scottish minister, first developed an external combustion en-
gine using air as the working fluid in 1817 [32]. Although the Stirling cycle makes use
of regenerative heat transfer, the thermodynamic significance of regeneration was not
understood until 1854 when the concept of regeneration was explained by Rankine
(33].
58
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In the 1940s, N. V. Philips Company's research laboratory began a project to
design an air-process engine that made use of modern heat transfer methods, fluid
flow concepts, and materials [34]. In the 1950s, N. V. Philips made use of this
technology to develop a Stirling refrigeration machine. The design objective was to
produce refrigeration in a single stage between the temperatures of —180 C and room
temperature [35].
U.S. Patent Survey
A U.S. patent survey was conducted to discover Stirling-type refrigeration tech-
nologies.
Patent number 1,508,522 was granted to Ivar Lundgaard on September 16, 1924
for "an air refrigerating machine of the closed-cycle type." This patent was for a
modification of a concept previously patented by the same inventor (U.S. patent
number 1,240,862).
Lundgaard's machine was composed of expansion and compression cylinders,
a regenerator, and high- and low-temperature heat exchangers. The reciprocating
motion of the pistons was accomplished by a rotating camshaft which displaced roller
followers. The followers were connected to the expansion and compression pistons. A
spring return mechanism was attached to each follower to keep the follower in contact
with the cam [36].
Literature Review
Rinia and Du Pre [32] first modeled the Stirling cycle as an idealized cycle but
with harmonic piston motion. They also defined the regenerator "efficiency" for the
59
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Stirling cycle as being the percentage of heat contained in the air in-flow that is stored
in the regenerator and transferred back to the air as it returns to the regenerator.
The part of the heat not stored during regeneration is carried off by the cooler and
lost for the cycle.
Kohler and Jonkers [35] reviewed the idealized Stirling cycle for refrigerators in
detail. They also applied the harmonic piston motion analysis to a Stirling refriger-
ation cycle. In a second paper [37] Kohler and Jonkers discussed the deviations of
the actual cycle from the ideal cycle. These deviations include losses which result
in increased shaft power, reduced the refrigerating capacity, regeneration losses, and
heat exchanger losses.
Chen et al. [38] tested an off-the-shelf Stirling cryocooler and investigated the im-
plications of the experimental results to household refrigeration applications. It was
found that the optimum expansion temperature was between —173 C and —123 C.
The optimum operating temperature range was defined in terms of the expansion
head (low-temperature heat exchanger) temperature. At an expansion head temper-
ature of —23 C, the COP was 0.37 (VCycle = 0-07). ^ was concluded that the COP
would need to be tripled if the Stirling technology was to be a viable alternative to
vapor compression for household refrigeration applications.
Bauwens and Mitchell [39] published experimental and numerical data intended
to verify a one-dimensional transient thermodynamic model of a Stirling refrigerator.
It was assumed that the working fluid was a perfect gas, (i.e., with constant specific
heats). The solution to the equations used in the model is time dependent due to the
periodic piston motion. A comparison of the experimental and model performance
data indicated that the agreement between prototype and model was, at best, one or-
60
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der of magnitude. The model predicted higher performance than what was measured
in the prototype.
Carlsen et al. [40] constructed a computer model which accounted for cylinder
volume, phase angle, temperature ratio, and dead volume in the analysis of a Stirling
refrigeration cycle. They made the following assumptions to simplify their model:
1. Reversible regeneration.
2. Perfect mixing of gas in the cylinder volumes.
3. No frictional losses in the machinery.
4. No fluid friction losses.
5. Ideal gas.
The number of transfer units (NTU) was chosen as an independent variable which
accounted for heat exchange within the expansion and compression cylinder volumes.
The NTU number is defined as,
NTU = (6.1)
mcp
where
U = overall heat transfer coefficient
= heat exchanger area
m = mass flow rate
cp = constant pressure specific heat
61
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Two cases were chosen: case A, in which the expansion and compression cylinder
walls were at the same temperature as the low- and high-temperature heat exchang-
ers, respectively. And case B, in which the cylinder wall temperatures (particularly
the piston) differed from the heat exchanger temperatures. This condition resulted
in temporary heat transfer between the cylinder walls and the working gas in the
cylinders.
Carlsen et al. [40] found that the thermal performance of actual systems (which
more like case B) would be reduced (as compared to the ideal) due to losses that are
associated with heat transfer between the piston, cylinder and the gas. In terms of
heat transfer, they concluded that the cylinder of an actual system has an inherently
low NTU-number (below 5) which limits performance. For a temperature ratio of
1.18, which is the approximate value for applications near room temperature, the
cycle efficiency, fJCycle' was ^ess ^an 0-7- It was concluded that it would be very
difficult to design a Stirling refrigerator with a COP competitive with that of the va-
por compression cycle when the additional losses associated with non-ideal operating
conditions are considered for Stirling refrigeration operating at source temperatures
above —24 C..
Several other references discussing Stirling refrigeration performance were found.
Carrington and Sun [41] concluded that regenerator heat transfer losses increase
sharply at lower cold-end (expansion) temperatures. On the other hand, frictional
losses dominate at the compression end. Fabien [42] reported experimental results
for prototype free-piston Stirling coolers intended for domestic refrigeration. Fabien's
results are summarized in Table 6.1. Berchowitz and Unger [43] reported a cycle
efficiency of 0.3 for a free-piston Stirling cooler operating between —26 C and 41 C.
62
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The COP was calculated as the ratio of measured heat removal to the electrical power
input.
Table 6.1: Experimental results reported by Fabien [42] for prototype free-piston
Stirling coolers intended for domestic refrigerators.
Unit Number
Tsource (C)
1sink (^)
Cycle
1
-33
18
0.217
2
-57
16
0.240
3
-75
42
0.226
Stirling Cycle Models
Introduction
Models for the Stirling refrigeration cycle vary in complexity from the ideal
thermodynamic model to transient numerical models which take into account fluid
flow and heat transfer through the system.
Idealized Stirling Refrigeration Cycle Model
A schematic of an idealized model of a Stirling refrigeration cycle is illustrated
in Figure 6.1. The state points for the cycles are given on the P-V diagram and T-S
diagrams for the cycle (Figures 6.2 and 6.3, respectively).
The assumptions made for the ideal model are:
1. Ideal gas.
63
-------
Figure 6.1: Schematic of a Stirling refrigeration cycle.
2. The rate at which heat is accepted and rejected from the system is unchanging
with time.
3. Perfect heat transfer to the heat source and sink.
4. 100% regenerator effectiveness.
5. Discontinuous motion of the pistons.
6. Negligible changes in potential and kinetic energy of the fluid.
7. Negligible pressure drop in the heat exchangers and related piping.
8. No clearance volume in expansion or compression cylinders.
Since an ideal gas has been assumed, internal energy is a function of temper-
ature only in the closed system; u = u(T). During the Stirling refrigeration cycle
development, it will be assumed that heat transfer into the system and work done by
the system are positive.
The process from state 1 to state 2 is assumed to be isothermal expansion,
therefore, there is no change in internal energy. An energy balance on the expansion
cylinder yields,
Qin ~ WeXp = m{uout - uin) (6.2)
64
-------
Specific Volume, v
Figure 6.2: Pressure vs. specific volume diagram for a Stirling refri-
geration cycle.
where
Qin = heat transfer into the expansion cylinder
Wexp. = work due to the expansion of the cylinder volume
m = mass of the gas in the expansion cylinder
iij = specific internal energy of the working gas in the i th state
Since uout - uin = 0,
Qin = Wexp- (6.3)
65
-------
Specific Entropy, s
Figure 6.3: Temperature vs. entropy diagram for a Stirling refriger-
ation cycle.
The expansion work is given by,
Wexp
= J pdv (l
Substituting the ideal gas equation of state,
f2 / _ N dV
Wexp — (jnRTexpj ~y~ ('
= mRTexpln^j^j (I
= mRTi In >0 (I
66
-------
where = T2 = Texp and m, R, and Texp are constants.
Similarly, the work of compression from state 3 to state 4 is given by
Wcomp = —mRTcomp In ^
= mRTz In ^ (6.8)
where T3 = T4 and ^
During regenerative heat transfer from state 2 to state 3 and from state 4 to state
1, an energy balance yields
Qregeneration 2—>3 = \Q regeneration 4—>¦ 11- (6-9)
The COP for the idealized Stirling refrigeration cycle is then
C0Pideal Stirling = (6-10)
JlCv
= jAjr (6.11)
r4 ~T1
= COPcarnot (6-12)
Ideal Stirling Refrigeration Model with Harmonic Piston Motion
For practical application of the Stirling refrigeration cycle, the piston motion
would be continuous. An approximate continuous cycle can be realized by harmonic
movement of the compression and expansion pistons with a phase displacement be-
tween them. If it is assumed that the assumptions for the idealized model apply, a
thermodynamic analysis of the cycle can be conducted if the following parameters
are known:
67
-------
Vexp = expansion space volume, excluding clearance volume
Texp — absolute temperature of the expansion fluid
Vcomp = volume of the compression space
Tcomp = absolute temperature of the compression fluid
Vq = maximum volume of the expansion space
wVq = maximum volume of the compression space
w = ratio of the maximum values of Vcomp and Vexp
V$ = volume of all non-displaced spaces in the system
Ts = average absolute temperature of all non-displaced spaces
a = crankshaft angle
if = phase angle between Vexp and Vcomp
s = relative reduced dead space,
, , Tcomp
temperature ratio, m r
1 exn
TT)l
•(^) 1^11
I
exp
phase angle of the pressure with respect to
the expansion cylinder volume
dummy variable relating r, w, ip, and s
The volumes of the expansion and compression spaces can be written as functions
of the crank and phase angles,
Vexp = ~^(1 + cos a) (6.13)
/ - wVo
*cornp — 2
[1 + cos (a — ip)\. (6-14)
The pressure can be written as a function of the crank and phase angles using the
ideal gas law,
P = Pmax 1 , a (6.15)
l+o cos a — 6
where
, VT +w + 2™ cos (p .
0 = (b.lb)
r + w + 2s
. trsin^ ,n
tan 0= . (6.17)
r + w cos
-------
If the polar coordinate system is defined such that the minimum pressure, Pm{n,
occurs at a — 0 = 0 and the maximum pressure, Pmax> occurs at a — 9 = 7r, then
the pressure ratio can be defined as,
Pmax 1 + 8
Pmin 1 ^
(6.18)
An expression can be obtained for the mean pressure, P, by integrating the pressure
(as given in Equation 6.15) with respect to the crank angle, a
P - Pmaxy Y+~£* (6.19)
The quantity of heat transferred to the fluid during a cycle in which the pressure
and volume both vary sinusiodally is found from,
Q = j>PdV. (6.20)
For the expansion process, the solution is,
C
Qexp = vPV\q , sin# (6.21)
l + \Jl-62
and for the compression process,
£
Qcomp = ttPwVq . sin 0 - y> (6.22)
1 + VI " <*2
= w(Qexp) - V> (6.23)
= Qexp (w - Q^x^j (6.24)
= T-Qexp (6.25)
The COP for the idealized Stirling refrigeration cycle with harmonic piston move-
ment is then:
COPideal Stirling, harmonic = Wnef (6.26)
69
-------
Qexp
(6.27)
|Qcomp ~ Qexp\
(6.28)
Tcomp — Texp
1
(6.29)
(6.30)
T — 1
COPCarnot
where r is defined as,
\Qcomp\ _ Tcomp
Qexp Texp
(6.31)
The constraint of harmonic piston movement does not affect the reversibility
of the cycle, so the COP remains the same as for the basic ideal reversed Stirling
model. The resulting cycle is no longer composed of two isothermal and two isometric
processes, but rather, the pressure and volume vary continuously throughout the
cycle. Figure 6.4 illustrates the pressure versus volume relationship for the expansion
space, compression space, and regenerator for a Stirling refrigerator with harmonic
piston motion. By comparing Figure 6.4 to the P-V diagram for the ideal case
(Figure 6.2), it can be seen that the regeneration processes are no longer isometric.
Furthermore, the compression and expansion processes are no longer isothermal.
Discussion
It has been shown that the COP for an ideal Stirling refrigerator is the reversed
Carnot cycle COP regardless of piston motion. The continuity of piston motion does
not affect the reversibility of the system. Irreversibilities in the Stirling cycle result
from:
1. Mechanical losses (friction).
70
-------
Specific Volume, v
Figure 6.4: Pressure vs. specific volume diagram for a Stirling refrigerator
with harmonic piston motion.
2. Non-isothermal operation.
3. Heat losses through machine members.
4. Heat exchange via finite temperature differences between the system and the
environment.
5. Imperfect regeneration.
6. Fluid frictional losses in the cylinders, heat exchangers and regenerator.
7. Fluid leakage.
71
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Other Models
A demonstration version of the Mitchell/Stirling MS*2 computer program was
reviewed [39]. This is a one-dimensional transient model which simultaneously solves
the equations for the conservation of mass, momentum, and energy within the system
boundary. The model employs empirical correlations to calculate the heat transfer
coefficients at the wall. The geometry of the solution domain is determined by the
length, heat transfer area and net cross-section in the spaces, and the periodic motion
of the pistons.
The MS*2 program requires the specification of all of the physical dimensions
related to the geometry of a basic Stirling engine or refrigerator. These include:
1. Expansion cylinder bore and stroke
2. Compression cylinder bore and stroke
3. Clearance volumes for the expansion and compression cylinders
4. Initial pressure
5. Compression ratio
6. Phase angle
7. For the high and low temperature heat exchangers:
(a) Tube numbers
(b) Length
(c) Inner and outer diameters
(d) Material properties
8. For the regenerator:
72
-------
(a) Length
(b) Diameter
(c) Material properties
(d) Mesh size
(e) Fill factor
9. Working fluid.
10. Shaft speed (rpm).
The requirement to establish specific design parameters, including materials and
dimensions, makes the MS*2 program difficult to use as a tool for comparing the
generic Stirling refrigeration system with other different refrigeration technologies.
Kelly et al. [44] concluded that the actual thermodynamic cycle which occurs in
Stirling-type refrigeration systems more closely resembles a modified regenerative re-
versed Brayton cycle. The thermodynamic processes by which this modified reversed
Brayton cycle is accomplished are:
1. Compression to a temperature greater than that of the thermal sink.
2. Isobaric heat rejection to the thermal sink.
3. Isometric regeneration.
4. Expansion to a temperature below that of the thermal source.
5. Isobaric heat acceptance from the thermal sink.
6. Isometric regeneration, thus completing the thermodynamic cycle.
73
-------
Results
Figure 6.5 is a graph of the Stirling refrigeration cycle COP versus source tem-
perature. The only irreversibilities present in the system result from irreversible heat
transfer during the heat acceptance and rejection processes. A minimum approach
temperature of 10 C was used for each heat transfer process. The cycle efficiency ver-
sus source temperature for this system is shown in Figure 6.6. The cycle efficiency is
low at the upper end of the source temperature range and increases to approximately
0.7 at -24 C.
12
10
8
0.
O 6
O
4
2
0
-30 -10 10 30
Source Temperature (C)
Figure 6.5: COP vs. source temperature for a Stirling refrigerator
with irreversible heat exchange processes.
74
-------
1.0
Sink Temperature-35 C
Heat Exchanger Minimum Approach Temperature »10 C
0.8 -
0.2 -
0.0 1 1 1 1 1 ¦ ¦ 1 1 1 1 1 1 1 1 1 ¦ 1 ¦ 1 1 1 1
-30 -20 -10 0 10 20 30
Source Temperature (C)
Figure 6.6: Cycle efficiency vs. source temperature for a Stirling
refrigerator with irreversible heat exchange processes.
75
-------
Since other irreversibilities are known to exist in Stirling refrigerators, the Kelly
model [44] was used to calculate the COP and cycle efficiencies for a Stirling-type
refrigeration system.
The sink temperature was 35 C. The isentropic compression and expansion ef-
ficiencies were both 0.85, as was the regeneration effectiveness. A 10 C minimum
approach temperature was used to account for the high- and low-temperature heat
exchanger irreversibilities.
Figure 6.7 is a graph of the COP vs. source temperature calculated using the
model developed by Kelly et al. Figure 6.8 is a graph of the corresponding cycle
efficiencies for the same set of parameters. The cycle efficiency is 0.28 at Tsource —
—24 C and decreases to 0.13 at Tsource = 28 C.
Closure
A technical assessment of the reversed Stirling cycle for use in domestic and
commercial cooling and refrigeration applications is presented in Chapter 10. It will
be shown that although the COP for the ideal reversed Stirling cycle is identical to
the Carnot COP, the actual COP is much lower.
76
-------
2.5
2.0
1.5
1.0
0.5
0.0
Sink Temp. * 35 C
- Compression tatentroplc Eft. =» O SS
. Expansion tatentroplc EH.» 0.85
Regan. Effectiveness =¦ 0.85
Heat Exch. Mln. Approach Temp. = 10 C
" Pressure Ratio-1.5
-30
-10 10
Source Temperature (C)
30
Figure 6.7: COP vs. source temperature for a Stirling-type refri-
gerator calculated using the Kelly model.
77
-------
0.5
0.4
0.3
0.2
0.1
0.0
Sink Temperature « 35 C
Compression Isentroplc Efficiency - 0.85
Expansion Isentroplc Efficiency =• o.BS
Regenerator Effectiveness >0.85
Heat Exchanger Minimum Approach Temperature »10 C
Pressure Ratio * 1.5
I
-30
-10 10
Source Temperature (C)
30
Figure 6.8: Cycle efficiency vs. source temperature for a Stir-
ling-type refrigerator using the Kelly model.
78
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CHAPTER 7. PULSE TUBE AND THERMOACOUSTIC
REFRIGERATION
Introduction
Two refrigeration concepts utilizing a gas-filled column in which the pressure is
varied cyclically to produce cooling will be discussed in this chapter. The pulse-tube
system uses a compressor to pressurize the gas; the thermoacoustic system relies upon
a diaphragm displaced by an electromagnetic coil for the same task.
Pulse Tube Refrigeration
History
The pulse-tube concept was developed by GifFord and Longsworth in the mid-
1960s [22]. Mikulin et al. [45] and Radebaugh et al. [46] improved the COP of the
pulse tube by adding an orifice and expansion chamber to the high-temperature end
of the tube.
U.S. Patent Survey
No patents were found for pulse tube refrigeration methods during the survey of
U.S. patents.
79
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Theory of Operation
Operating Principle of an Ideal Pulse Tube An ideal pulse tube system
is composed of a compressor, regenerator, high-temperature heat exchanger, and
the tube. The system is filled with a working gas (generally helium) which has a
static pressure of several atmospheres. Figure 7.1 contains two schematics illustrating
alternative methods of periodically compressing the working gas in a pulse tube.
Periodic compression can be accomplished by a steady flow compressor and rotary
control valve, as shown on the left side of Figure 7.1 or by a reciprocating compressor,
as shown on the right.
Win
Win
| QH2
Th
UJ
03
•D
h-
id
(/i
_J
3
Q_
__ TC
Ql
Figure 7.1: Two pulse tube refrigerator concepts.
80
-------
The heat generated due to compression of the gas, Qjj\, is rejected by a high-
temperature heat exchanger. A regenerative heat exchanger is interposed between
the high-temperature heat exchanger and the cold end (at Tq) of the pulse tube.
The primary purpose of the regenerative heat exchanger is to isolate the cold end of
the pulse tube from the high-temperature heat exchanger.
The tube wall is constructed of a material with a low thermal conductivity, com-
monly stainless steel. The ends of the tube are capped with a highly conductive ma-
terial like copper. The heat is accepted by the low temperature {Tq) heat exchanger
located at the entrance end of the tube, and rejected by the high temperature {Tjj)
heat exchanger at the opposite end.
The principle of operation of the ideal cycle may be understood by considering
a thin cylindrical control mass segment, m, as shown in Figure 7.2. The control
volume in the tube contains a series of infinitely thin mass segments adjacent to one
another from the top to the bottom of the tube. The arbitrarily chosen mass segment
illustrated in Figure 7.2 is initially at height xj^ in the tube and has thickness h2-
The following assumptions are made regarding the system:
1. No frictional effects.
2. The changes in pressure from low to high and vice versa are both step functions
with respect to time as shown in Figure 7.3.
3. Perfect regeneration.
4. The heat is transferred to and from the mass segment through the tube wall.
The transfer of heat from one mass segment to another through the top and
bottom surfaces of the segments is neglected.
81
-------
v3,T3,pH
v2,T2,pL
Dl
Figure 7.2: Cycle executed by a control mass el-
ement in a pulse tube.
5. Ideal gas.
6. Isentropic compression.
7. The compressor, valve, and ducts connecting the system are adiabatic.
The working gas in the segment has an initial volume, V is found by dividing the volume, V2, by the mass of the gas
in the segment. The mass segment is also shown at position x^ in Figure 7.4. As
82
-------
PH
CD
L
l/l
l/l
CD
L
CL
PL
I-* : A "t At
T ime
Figure 7.3: Step function pressure change in an ideal pulse tube.
the pressure and temperature of the gas in the element are changed during the cycle,
the thickness of the mass segment (and thus the specific volume of the gas in the
segment) will also change.
Since the tube wall is rigid, the diameter of the circular element will not change,
however, the thickness of the element must change. The gas in the mass segment
is at a thermodynamic state having the properties Pj^ (low pressure) and T2, and
an initial height in the tube, x£. When the pressure in the tube is increased to
Pfj, the volume in the mass segment is compressed to V3, elevated to position Xfj,
83
-------
Figure 7.4: Positions and thermodynamic states of an arbi-
trary mass segment during the pulse tube cycle.
and its temperature is raised to T% (Figure 7.4). If all of the mass segments in the
tube are considered, a temperature gradient ranging from the source temperature,
to the sink temperature, Tjj, exists along the length of the tube. The local
temperature of the tube wall at position xjj is lower than the mean temperature of
the mass segment, T3. Therefore, heat will be transferred from the mass segment to
the pulse tube wall. As a result of cooling thermodynamic properties of the segment
will become T4, Pfj, and 174 (Figure 7.4). When the pressure in the tube is lowered to
Pthe working gas in mass segment, m, undergoes an isentropic expansion to state
84
-------
1. The thermodynamic properties at state 1 will be T^, U]_, and P^. The temperature
of the gas, Tj, is lower than the wall temperature of the tube at position xj^. Heat
will be transferred from the pulse tube to the mass segment. As the gas in the mass
segment is re-heated by the tube wall, the segment will be returned to the original
thermodynamic state (state 2) , thus completing the cycle.
Ideally, the control mass of gas in the tube would undergo an isentropic com-
pression process from state 2 to state 3, isobaric cooling process from state 3 to state
4, an isentropic expansion from state 4 to state 1, and isobaric heating from state
1 to state 2. The ideal cycle formed by the series of processes undergone by the
control mass is the reversed Brayton cycle (see Chapter 5). Furthermore, the cycle
for the entire mass of gas in the pulse tube is an interconnected series of reversed
Brayton cycles as shown in Figures 7.5 and 7.6. The tube wall acts as a continuous
regenerator [47].
The regenerator shown in Figure 7.1 serves, in part, to isolate the cold end of the
tube from the pressure source which is at a higher temperature. Swift [48] concluded
that the regenerator serves an additional function which produces a Stirling-type re-
frigeration effect. He reasoned that since both heat and mass are transferred through
the regenerator, a Stirling-type cycle must exist within the regenerator. This cycle
(within the regenerator) produces an additional refrigeration effect. Since the addi-
tional cycle in the regenerator involves two constant pressure (rather than constant
volume as in the reversed Stirling cycle) processes and two isentropic processes, it is
more nearly a second reversed Brayton cycle serving to remove additional heat from
the low-temperature heat exchanger.
The total refrigeration effect in the ideal pulse tube refrigerator is the sum of
85
-------
Ph
Specific Entropy, s
Figure 7.5: Temperature vs. specific entropy diagram for the
pulse tube refrigeration cycle.
these two heat removal mechanisms. Ideally, if the effectiveness of both the tube and
the regenerator were the same, the cycle for the entire system could be viewed as one
continuous reversed Brayton cycle (states a, b, c, and d) as depicted in Figures 7.5
and 7.6.
Losses Associated with the Actual Cycle The principal losses in the actual
cycle are attributable to:
1. Non-isentropic compression.
2. Compression which does not occur instantaneously.
86
-------
CL
Qj
L
if]
if)
CD
L
a_
s=c
s=c
Specific Volume, v
Figure 7.6: Pressure vs. specific volume diagram for the pulse tube
refrigeration cycle.
3. Frictional flow losses in the piping and valves.
4. Dissipation of the work of re-expansion due to wall friction and therefore not
recoverable.
5. Imperfect regeneration in the regenerator and tube.
6. The boundary layer at the wall serves as an impediment to heat transfer.
7. Axial conduction of heat in both the tube and gas column.
87
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Theoretical Model
A simple approximation of the maximum theoretical performance of "pulse"
refrigeration cycles can be made by considering the entire system to be operating as
a reversed regenerative Brayton cycle. Small control mass elements of the working
gas are oscillating within the tube (pulse tube) or along the stack (thermoacoustic)
and executing a reversed Brayton cycle as shown in Figures 7.5 and 7.6. This model
assumes that the end thermodynamic states of one control mass element are the same
as opposite end states for the adjacent elements on each side.
Thermoacoustic Refrigeration
History
The first documented experiments involving thermoacoustic heat engines were
conducted by Higgins in 1777. His research eventually lead to pulse combustion used
in the German V-l rocket during World War II and the Lennox pulse furnace in 1982
[49]. Other thermoacoustic engines include the Rijke tube, an acoustic laboratory
demonstration used in physics, and the Sondhauss tube which generated mechanical
work in the form of resonant vibration due to the expansion of the heated air [46].
The thermoacoustic refrigeration concept, in which the gas in a closed tube is
periodically compressed and expanded using an electromagnetic coil and diaphragm
to produce cooling, is less well known. Wheatley et al. [50] first published a paper
regarding the concept in 1983. He was granted U.S. patents in 1983 and 1984. Later,
Hofler conducted experimental research in which the performance of a thermoacoustic
refrigerator was measured [48, 23].
88
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U.S. Patent Survey
Two United States Patents were found which covered thermoacoustic refriger-
ation. Patent number 4,398,398 entitled "Acoustical Heat Pumping Engine," was
granted in August 1983 to John Wheatley [52]. A second patent, number 4,489,553,
entitled "Intrinsically Irreversible Heat Engine," was also granted to Wheatley in
December 1984 [51].
Theory of Operation
The thermoacoustic refrigerator uses a modified loudspeaker as an acoustic gen-
erator to compress the working gas. The loudspeaker generates a standing wave in
the gas-filled tube. Figure 7.7 illustrates the basic components in a thermoacoustic
refrigerator. The acoustic generator (speaker) diaphragm oscillates at frequency, f.
The tube length and resonator are chosen such that there will be a resonant fre-
quency in the tube. A stack of closely spaced plates are located between the high-
and low-temperature heat exchangers. According to Garrett and Hofier [23], the heat
transfer between the gas and the plates in the stack occurs primarily in a narrow re-
gion near the plate surfaces which is defined by the thermal penetration depth, 8^.
The spacing between the plates is chosen to be several thermal penetration depths
{Sfc). The thermal penetration depth represents the distance over which heat will be
transferred into and out of the working gas during one acoustic period (T = y) [50].
The equation for the thermal penetration depth, 8£, is:
(7.1)
89
-------
where
k = the thermal conductivity of the gas
/ = the frequency of the loudspeaker
p = the density of the gas
cp = the constant pressure specific heat of the gas.
The stack plate spacing is a critical parameter in thermoacoustic refrigerators.
Heat is alternately accepted and rejected as the gas translates back and forth due
to acoustic oscillation. As with the pulse tube, the gas is adiabatically compressed and
expanded. Therefore, the thermoacoustic and pulse tube processes are the same. The
cycle undergone by an arbitrary mass segment of working gas in the thermoacoustic
refrigerator stack can be represented in Figure 7.4. Heat is exchanged with the
tube wall in the pulse tube and with the stack in the thermoacoustic refrigerator.
A temperature gradient exists along the stack, and the acoustic work is used to
transport heat from the source to the sink. The thermoacoustic refrigerator and
pulse tube are thermodynamically the same. A complete description of the processes
in the cycle was given in the pulse tube subsection entitled, "Theory of Operation."
An experimental thermoacoustic refrigerator, the space thermoacoustic refriger-
ator (STAR) developed by the Naval Postgraduate School [23], uses helium as the
working gas. Figure 7.7 is a schematic of a thermoacoustic refrigerator. The working
gas is maintained at a mean pressure of 10 atmospheres in the stack and resonator.
The present stack configuration uses polyester film with monofilament fishing line as
a spacer. The copper-fin high- and low-temperature heat exchangers are located at
either end of the stack. The acoustic power used pressurize the gas comes from an
acoustic generator at one end of the tube.
90
-------
High-Temperature
Heat Exchanger
Driver
(Speaker)
Low-Temperature
Heat Exchanger
Stack
Figure 7.7: Schematic of a thermoacoustic refrigerator.
Results
A computational model was constructed using the regenerative reversed Brayton
cycle as an approximation of the pulse tube cycle (see description in Chapter 5).
A thermodynamic property routine for helium gas was written to determine the
properties of the working gas.
Isentropic compressor and expander efficiencies were assumed to be 0.80. The
regenerator effectiveness was assumed to be 0.80. The sink temperature was 35 C,
and the source temperature was varied from -24 C to 28 C. A 10 C minimum approach
temperature was assumed to exist between the heat exchangers and the source and
sink.
Figure 7.8 is a graph of the COP versus the source temperature for six different
pressure ratios. At pressure ratios of 3.5 and below, the pulse tube cycle was not
capable of producing the required temperature lift over the entire range of source
temperatures considered in this project (—28 C to 24 C). The COP remained rela-
91
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tively constant over the entire source temperature range for each pressure ratio. The
lowest pressure ratios provided the highest COPs.
Figure 7.9 is a graph of the cycle efficiency versus source temperature for the
same operating conditions and pressure ratios. The cycle efficiencies were highest at
the lowest source temperatures. Even so, 0.10 was the highest efficiency noted for
this parameter set.
0.8
0.6
8 °-4
0.2
0.0
-30 -20 -10 0 10 20 30
Source Temperature (C)
Figure 7.8: Coefficient of performance vs. source temperature for
the pulse tube cycle using helium gas.
Swift [48] measured a cycle efficiency of 0.12 for a thermoacoustic refrigerator
T
operating at a source/sink temperature ratio (ttA) of 0.82. The cooling load was 3
Sink Temperalure » 35 C
Compression Process Isentropic Efficiency « 0.80
Expansion Process Issntroplc Efficiency » 0.80
Regenerator Effectiveness > 0.80
- Heat Exchanger Minimum Approach Temperature. * 10
-
-
Legend
——— Pressure Ratio =» 1.5
— - — Pressure Ratio = 2.5
— — — Pressure Ratio =» 3.5
— — Pressure Ratio =» 4.5
— — Pressure Ratio = 5.5
— Pressure Ratio = 6.5
92
-------
>N
o
c
g>
o
£
©
>>
O
0.20
0.15
0.10
0.05
0.00
Sink Temperature - 35 C
. Compression Process laentroplc Efficiency - 0.80
Expansion Process Isentroplc Efficiency > 0.80
Regenerator Effectiveness • 0.80
Heat Exchanger Minimum Approach Temperature » 10
-30
Legend
——— Pressure Ratio =¦ 1.5
— Pressure Ratio-2.5
Pressure Ratio = 3.5
— — Pressure Ratio =¦ 4.5
— — Pressure Ratio « 5.5
Pressure Ratio =» 6.5
J I I L
J L
-10 10
Source Temperature (C)
30
Figure 7.9: Cycle efficiency vs. source temperature for the pulse
tube cycle using helium gas.
watts from an electrical resistance heater. The COP was defined as
COP = ¦ Qelec
^acoustic
(7.2)
where
Qelec = the electric power dissipated by the heater
Wacoustic ~ measured acoustic power delivered by the loudspeaker.
Garrett and Hofler [23] reported measured cycle efficiencies of up to 0.16. The
test conditions and temperatures were not reported. Garrett also reported experi-
mental data for the STAR project (Figure 7.10).
93
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0.20
0.15
8 °-10
0.05
0.00
0 1 2 3 4 5
Cooling Load, Q (Watts)
Figure 7.10: Measured coefficient of performance for the STAR
refrigerator [62].
Closure
Both the pulse tube and the thermoacoustic refrigerator have been demonstrated
by experiment to be workable refrigeration technologies. Neither system has been
developed for use in actual refrigeration applications.
The pulse tube and the thermoacoustic refrigerator both use a working gas (gen-
erally helium) which oscillates in the tube. The cycle undergone by the working gas
in the system is a reversed Brayton cycle.
The cycle efficiency, rjCycle, for either the pulse tube or the thermoacoustic
refrigerator will be similar to that of the reversed Brayton cycle. It will be much
94
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lower than the VCycle ^or vaPor compression refrigeration in the source temperature
range considered in this study (-28 C to 24 C). As discussed in Chapter 5, f]QyCie
increases as the source temperature decreases for refrigeration technologies using the
reversed Brayton cycle . These cycles are best suited for applications requiring a low
source temperature such as cryogenics and some industrial refrigeration processes.
The pulse tube and thermoacoustic refrigeration technologies for use in domestic
and commercial refrigeration and cooling applications will be assessed in Chapter 10.
95
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CHAPTER 8. THERMOELECTRIC REFRIGERATION
Introduction
Refrigeration can be accomplished by the direct conversion of electrical to ther-
mal energy. Thermoelectric refrigeration technology has been used commercially to
cool electronic equipment and for small portable refrigerators used for recreational
activities [47].
Thermoelectric devices use two dissimilar semi-conducting materials, one P-type
and one N-type. Since these materials are generally poor conductors of heat [53], they
are often joined by a conducting material such as copper to form the junction between
the two.
A thermodynamic analysis of the thermoelectric refrigeration system requires
the consideration of the following physical phenomena:
1. Joulean power loss.
2. Seebeck effect.
3. Peltier effect.
4. Thomson effect.
5. Conduction heat transfer.
96
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Literature Survey
A literature survey was conducted to find information regarding thermoelectric
energy conversion methods and the physical effects which determine the principle of
operation.
The Seebeck, Peltier, and Thomson effects are discussed in electrical engineering
and materials science texts; for example, Smith [53], and Van Vlack [54]. A rela-
tionship between these effects was first predicted by Thomson (later to become Lord
Kelvin). Thomson assumed the system to be internally reversible. Results of his
experiments were verified by Jaumont [55]. The inter-dependence of the Seebeck,
Peltier, and Thomson effects was later demonstrated to be the same in a system
which was assumed to be irreversible [56].
An analysis of the thermodynamics of direct conversion of thermal to electrical
energy was conducted by Ioffe [57] and Angrist [58]. Ioffe also studied the thermo-
dynamics of thermoelectric refrigeration [59].
Theory
Introduction
The thermal and thermoelectric effects which determine the operation of a ther-
moelectric refrigeration system will be discussed briefly, followed by a discussion of
the development of the idealized thermoelectric refrigeration model. Two expressions
for the coefficient of performance (COP) will be derived. The first is a general ex-
pression of the COP for the thermoelectric refrigerator; the second is an expression
for the maximum possible (or ideal) COP for a given pair of P- and N-type materials.
97
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Joulean Power Loss
When an electric current, /, flows through an electrical resistance, i?, an irre-
versible conversion of electrical to thermal energy occurs.
I = the current (amperes)
Rj = the electrical resistance of the conductor (ohms)
The electrical resistance, R, is determined by the resistivity, p, and the length
to area ratio of the conducting material.
Seebeck Effect
If the junctions of two dissimilar electrical conductors are at different temper-
atures, Tjj and T^, an electrical potential will be created at each junction. This
voltage is equal to the sum of the voltages at each junction.
The Seebeck coefficient, a, is defined as the constant of proportionality relating
the change in potential to the temperature change,
Qj — I2Rj (watts)
(8.1)
where
a = —-
dV
dT'
(8.2)
(8.3)
where i denotes the material.
98
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Figure 8.1 depicts a simple circuit consisting of two conductors, one P-type
and one N-type. One junction at which the two conductors are connected is at
temperature Tjj, the other junction is at temperature Tjj. The Seebeck voltage is
the sum of the voltages in the circuit. The Seebeck voltage for a P-type and an
N-type material in the same circuit can be written as,
VPN = faidT (8-4)
= EH «PdT + frLaNdT (8-5)
L J1H
T
= jT^ {aP~aN)dT- (8-6)
P-Conductor
Junction at
Temperature TL
Junction at
Temperature TH
N-Conductor
Figure 8.1: Simple electrical circuit consisting of two dissimilar
junctions at different temperatures.
Peltier Effect
The Peltier effect occurs at the junction of two dissimilar materials because
energy must be conserved. Figure 8.2 illustrates a junction between two dissimilar
conducting materials. When direct current flows through the junction, electrical
energy is brought to the junction by charge carriers in the first material at a rate
99
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Qp and carried from the junction through the second material at rate a Qjy. The
Peltier coefficient, irfor each material, i, is defined as,
Qi
= r
(8.7)
The unit for the Peltier coefficient is the volt.
Qi
P-conductor
Junction
Figure 8.2: Junction of two dissimilar electrical conducting
materials used to illustrate the Peltier effect.
The junction has a finite electrical resistance, Rj, which results in the irreversible
dissipation of Joulean power. The net heat transfer rate at the junction can be found
by applying an energy balance to the junction while operating at steady state,
Qp- Qn ~ Qj + = 0
Qj = Qp - Q]\[ + Rj
Qj = I (rp — + I^Rj (8.8)
= litp jy + I^Rj (8.9)
100
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The Peltier effect can provide a net heating or cooling effect, depending upon
the relative magnitudes of the Peltier coefficients of the two junction materials, or by
a reversal in the direction of current flow in the circuit. The cooling effect cannot be
as large as the heating effect since the Joulean power loss term is always positive.
Thomson Effect
When a temperature gradient exists in a homogeneous material through which
electric current is flowing, a voltage gradient also exists due to thermal agitation of
the charge carriers. This voltage gradient is additive to the customary voltage drop
resulting from the resistance of the material. The Thomson coefficient is defined as
AVr = the voltage change due to thermal agitation
AT = the temperature gradient.
Figure 8.3 illustrates a conductor in which a temperature gradient exists. The
temperature of the conductor at point 1 is higher than at point 2. The rate of energy
in which the temperature gradient exists. This heat loss is the sum of the Thomson
power loss and the Joulean power loss in the material
(8.10)
where
transfer by electrical current is the same at 1 and 2 (Q\ = Q2)- The heat loss in the
radial direction, QRa(foai, can be determined by an energy balance on the conductor
Q Heat, Radial'OW^ + pR
(8.11)
where
101
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QHeat Radial = transfer rate in the radial direction (W)
I = electrical current flow (amperes)
r = the Thomson coefficient (volts/K)
AT = temperature gradient (K)
R = electrical resistance of the conductor material (ohms).
(V+AVT) + IR
T+AT
V
T
Q
1
Q.
y Q RacJial
2
Figure 8.3: Heat transfer from an electrical conductor with a tem-
perature gradient.
The Seebeck, Peltier, and Thomson effects are interrelated phenomena. Lord
Kelvin predicted the form of the relationships between these effects using macroscopic
thermodynamics and assuming complete reversibility. A complete development of
these relationships (known as Kelvin's first relation and Kelvin's second relation) is
given in Direct Conversion of Heat to Electricity [55].
Kelvin's first relation is:
T dT^ ) = ^PN^T (8"12^
102
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Kelvin's second relation is:
T
(8.13)
where Vpjy is the voltage in the P-type and N-type materials. The subscript T
indicates that the Peltier coefficient, 7rpjy, and the Thomson coefficients, Tp — rjy,
are to be evaluated at temperature T.
Figure 8.4 illustrates a thermoelectric refrigerator in communication with a ther-
mal source and sink. Heat is accepted from the source at Tj^ and rejected to the sink
at Tjj. Direct current electric power (P) is supplied to the system from an external
source.
Figure 8.5 is a schematic of the thermoelectric refrigeration circuit. It is assumed
that conductors C\ and C2 are both at a uniform absolute temperature, Tjj, and
conductor C3 is at a uniform absolute temperature, Tj^. Furthermore, these conduc-
tors are assumed to have negligible thermal and electrical resistances as compared
to the P- and N-type semiconductors. Both semiconductors are assumed to have a
uniform rectangular cross-section; the electrical resistivity (p{), thermal conductivity
(fcj), and Seebeck coefficient (o^) for each material, i, are assumed to be constant.
Heat is conducted through both legs of the thermoelectric refrigerator in parallel
whereas the current flows in series. The combined coefficient of heat transfer,
(W/K), can be expressed as
Thermoelectric Refrigeration Model Development
(8.14)
103
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Sink
Th
Qh
T.E.
System
Ql
Tl
Source
Figure 8.4: Schematic of a ther-
moelectric refrigerator
and its surroundings.
where
k} = the thermal conductivity of the conductor material, i,
Am
— the area to length ratio of the conductor, i, cm.
Assuming the electrical resistances of the material junctions and other circuit
members are negligible in comparison to those of the two semiconductors, the total
104
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Figure 8.5: Schematic of a thermoelectric refri-
geration circuit.
electrical resistance in the system can be calculated
I
fyotal = PN ( + PP
where
Pi = the electrical resistivity of the material, i, ohms • cm
-^7 = the length to area ratio of material, i,
(8.15)
The rate at which heat can be accepted, Q£, and rejected, Qjj, by the device
105
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can be expressed in terms of the Peltier effect, heat conduction rate, and Joulean
power loss rate. The Peltier effect at the junctions can be expressed as:
Qp cold junction = IirPN = IaPNTL• (8-16)
QP hot junction = ~IirPN = ~IaPNTH• (8-17)
The relationship between the Peltier and Seebeck coefficients in the above equa-
tions can be derived using the definition of the Peltier coefficient (Equation 8.7) and
Kelvin's second relation (Equation 8.13)
= TapN = *pN- (8J8)
The sign change between Equations 8.16 and 8.17 is due to the change in direction
of current flow in the cold and hot junctions. The cooling rate can now be expressed
as
Ql = IaTL - KAT - ±I2Rt. (8.19)
Similarly, the rate of heat rejection can be written as
Qh = IccTh - KAT +\l2at- (8.20)
The Joulean power loss (rj/^ify) is distributed equally between the hot and cold ends
of the semiconductors (the last term in Equations 8.19 and 8.20).
The electrical power required, P, is then the difference in the heat rejection and
acceptance rates,
P = Qh-Ql = IaAT + I2Rt. (8.21)
An equation for the COP for an ideal thermoelectric refrigerator can be derived
from the definition of the COP, Equation 8.19, and Equation 8.21
COPideai = ^ (8.22)
106
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IaTL - KAT - \l2Rt
I a AT + I2Rt
(8.23)
Although the coefficient of performance of the ideal thermoelectric device has
been found, a more useful form for determining the maximum COP can be expressed
in terms of the Carnot COP and a figure of merit, Z [47].
To find the maximum COP, the numerator and denominator in Equation 8.23
R
are multiplied by —k to obtain,
aL
Using the combined heat transfer coefficient, Kf (Equation 8.14), total electrical
resistance, Rt (Equation 8.15), and the Seebeck coefficient, a, a figure of merit, Z
(1/K), can be defined as
The value of the Seebeck coefficient, a, is a material property and depends upon
which P- and N-type materials are used in the refrigeration system. The combined
heat transfer coefficient, K^, and the resistance, Rf, are functions of the material
types (P- or N-type) and the geometry of the conductors. For a particular pair of
materials, the maximum Z occurs when the denominator, RfKf, is minimized with
respect to the area-to-length ratios of the semiconducting materials.
To minimize the denominator (R^Kt) in Equation 8.25, Equations 8.14 and 8.15
are combined. Equations 8.14 and 8.15 are written in terms of the area-to-length
ratios of the two junction materials. Letting the variable /3 represent the area/length
ratio, multiplying Equation 8.15 by Equation 8.14, and taking the derivative with
COP
maximum
(8.24)
107
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respect to yields the following expression:
(RtK)min = ((PN)(kN))°5 + ((Pp)(kp))
10.512
(8.26)
Therefore, the maximum Z for a particular semiconductor pair is,
2
¦>max —
aNP
(RtK)min
(8.27)
The maximum COP for a thermoelectric refrigeration system with a particu-
lar pair of semiconducting materials can now be found by taking the derivative of
(I Ri\
Equation 8.24 with respect to the term I 1, setting the result equal to zero, and
(I Ri \
solving for (—^ I. Inserting this expression into Equation 8.24 yields an expression
for the maximum COP for an ideal thermoelectric refrigeration cycle,
,0.5
COPi
max
(l + Z\
max^avg
r-%
(l + ZmaxTavg) + 1
where
Tavg —
{Th+Tl)
(8.28)
(8.29)
The first term on the right side of Equation 8.28 is the Carnot COP, and the
bracketed term is a measure of the internal irreversibility of the thermoelectric re-
frigeration system. Equation 8.28 accounts for the major sources of irreversibility in
the system; however, it does not take into account Joulean heating in the conductors
and junctions, heat transfer due to radiation, or losses associated with heat exchange
with the source and sink.
108
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Results
A FORTRAN subroutine was written to calculate the COP of a thermoelectric
refrigeration system using the equations developed in the previous section. This
routine was used to calculate the COP and cycle efficiency for a thermoelectric system
rejecting heat to a thermal sink at 35 C for source temperatures ranging from —24 C
to 28C. Four values of Z were considered. A 5 C minimum approach temperature was
assumed to exist between the thermal source and sink and the hot and cold surfaces
of the thermoelectric refrigeration system.
Figure 8.6 is a graph of the COP versus the source temperature. The source
temperatures range from —24 C to 28 C. Four different values of Z were considered.
The COP increases with the source temperature at an increasing rate with increasing
temperature. The COP also increases with increasing values of Z.
Figure 8.7 is a graph of the cycle efficiency, t)q, for the same source temperature
range. The maximum cycle efficiency was approximately 0.075 at 14 C for Z = 0.003.
Increasing Z has two effects: increased cycle efficiency and a shift of the maximum
cycle efficiency to a lower source temperature. It should be noted that the highest
value of Z (in practice) for semiconductor pairs is presently 0.003 [60].
Table 8.1 provides a comparison of the COPs for selected refrigeration and air-
conditioning applications at Z = 0.003, and a 5 degree C temperature difference
between the heat exchangers and the air.
109
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4
Q.
o
o
2
0
-30 -20 -10 0 10 20 30
Source Temperature (C)
Figure 8.6: COP vs. source temperature for an ideal thermoelectric
refrigerator.
Closure
The thermoelectric refrigeration system presently offers the advantages of sim-
ple and compact design, high reliability, and the utilization of non-ozone depleting
working materials. However, the COP of current thermoelectric systems is low when
compared to vapor-compression systems.
Equation 8.28 indicates that improvement of the COP hinges upon finding semi-
conducting material pairs which have a larger figure of merit, Z. Presently the highest
value of Z is approximately 3.25 x 10~^ if radiant heat transfer is neglected.
If the radiant load is considered, the maximum effective value of Z has been found
110
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>.
o
c
®
£
©
£
o
0.25
. Sink Temperature = 35 C
Heat Exchanger Minimum Approach Temperature = 5 C
0.20
0.15
0.10
0.05
Legend
Z ^ 0.003
— 2 = 0.004
— Z a 0.006
Z-0.009
X
\
\
\
\
0.00 1 ¦ ¦ 1 ¦ ' ' 1
-30 -20 -10
¦ 1 1 1 1 1 1 1 ¦ 1 1 ¦ 1 1
0 10 20 30
Source Temperature (C)
Figure 8.7: Cycle efficiency vs. source temperature for an ideal
thermoelectric refrigerator.
to be 2.74 x 10—^ (~K^) [60]- Research continues in the quest for semiconductor
pairs which will provide a higher value of Z [58]. Until these materials are devel-
oped, thermoelectric refrigeration is not a viable alternative to vapor-compression
for refrigeration and air conditioning applications.
A technical assessment of thermoelectric refrigeration for use in domestic and
commercial cooling and refrigeration applications is presented in Chapter 10.
Ill
-------
Table 8.1: Thermoelectric cycle coefficients of performance for different refrigeration
and air-conditioning applications.
Application
Tsource ( C)
Tsink (C)
COP
Domestic Refrigeration
-17.8
35.0
0.18
Commercial Refrigeration, ARI Grp. 1
2.8
35.0
0.58
Commercial Refrigeration, ARI Grp. 2
1.7
35.0
0.56
Commercial Refrigeration, ARI Grp. 3
-2.2
35.0
0.50
Commercial Refrigeration, ARI Grp. 4
-23.3
35.0
0.11
Domestic Air Conditioning
25.0
35.0
1.95
Commercial Air Conditioning
25.0
35.0
1.95
Mobile Air Conditioning
25.0
35.0
1.95
112
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CHAPTER 9. MAGNETIC REFRIGERATION
Introduction
The magnetic refrigerator transports heat from a cold reservoir to a hot reservoir
by means of a material with suitable magnetic properties in the presence of a mag-
netic field. The cooling process which results from the alternate magnetization and
de-magnetization of the material is known as the magnetocaloric effect. The mag-
netic heat pump has been proposed as an alternative to vapor-compression cycles for
refrigeration and air conditioning applications.
In this chapter the magnetic refrigerator will be discussed, beginning with its
history of development. The principle of operation will be discussed, followed by a
survey of patents and technical literature. The thermodynamic models of theoreti-
cal cycles utilizing thermomagnetic processes will be discussed. An idealized model
of one cycle is developed. The results of these analyses are presented and conclu-
sions regarding the feasibility of their utilization for present-day refrigeration and air
conditioning applications are drawn.
Literature Survey
Magnetocaloric cooling was first employed in 1933 when Giauque and MacDougal
[61] conducted adiabatic demagnetization experiments to produce cooling at source
113
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temperatures from —269.65 C to —272.65 C.
Magnetic cryogenic refrigerators were developed by Heer et al. in 1949 [62] and
by Rosenblum et al. in 1976 [63]. These were low-power systems for operation at
source temperatures below —272.15 C. Both devices operated intermittently in what
could be termed a semi-continuous refrigeration process.
In 1976, G. V. Brown [64] investigated the application of the magnetocaloric
effect to refrigeration applications near room temperature. Brown concluded that
a magnetic refrigerator operating at 1 C was theoretically feasible. He proposed a
system in which a gadolinium core would be translated back and forth in a tube filled
with a recuperative fluid. Electrical coils located at the ends of the tube would apply
the magnetic field.
The feasibility of magnetic refrigerators using a rotating core which passes through
regions of high and low magnetic field with regeneration accomplished using a recu-
perative fluid has been studied by Steyert [65], Kirol and Dacus [66], and Hull et al.
[67, 68].
Barclay [69, 70] made a comparison of the expected thermodynamic losses in
gas and magnetic refrigeration systems. He also provided an overview of the applica-
tions of magnetic refrigeration at source temperatures from —273.05 C to near room
temperature.
Chen et al. [71] conducted an assessment of several theoretical thermodynamic
refrigeration cycles for refrigeration applications requiring source temperatures above
the cryogenic temperature range.
114
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Theory
Ideal Magnetic Materials
Some materials exhibit a physical characteristic in which the entropy of the
material changes when the strength of a magnetic field surrounding the material is
varied. As the field strength is increased, the entropy of the material decreases. If
the temperature of the material is to remain constant as the entropy decreases, heat
must be rejected from the material specimen to the surroundings. Conversely, if the
magnetic field strength is decreased, heat must be accepted from the surroundings
with an increase in entropy of the material if the material specimen is to remain at
a constant temperature. This phenomenon is the magnetocaloric effect [72].
An ideal magnetic substance is one which behaves according to a magnetic equa-
tion of state known as the Curie law,
M = ^-, (9.1)
where
M = the magnetization
H = the external magnetic field
Cq = the Curie constant
T — the thermodynamic (absolute) temperature.
Modified Helmholtz and Gibbs functions, magnetic Tds equations, functional
thermodynamic relationships, and the Curie law can be used to derive the ther-
modynamic properties (internal energy, enthalpy, and entropy) for ideal magnetic
materials. Furthermore, constant magnetic field and constant magnetism specific
115
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heats can be derived. These ideal magnetic properties are analogous to those derived
for gases. Two differences between the thermodynamic properties of ideal magnetic
solids and ideal gases are important in the development of magnetic refrigeration
cycle theory:
1. Lines of constant pressure and constant volume remain parallel on the T-S
diagram for an ideal gas.
2. Lines of constant magnetism remain parallel on the T-S diagram for an ideal
magnetic material; however, lines of constant field strength do not.
Figure 9.1 is a temperature versus entropy diagram for an ideal magnetic sub-
stance which obeys the Curie law. Lines of constant field strength and lines
of constant magnetism are illustrated. These constant property lines are analogous
to lines of constant pressure and volume for an ideal gas, with one important ex-
ception: lines of constant field strength are not independent of temperature. The
horizontal distance between lines of constant field strength decreases with increasing
temperature; i.e., the lines tend to converge as temperature increases and diverge
as temperature decreases. Therefore, energy can not be conserved in a thermody-
namic cycle (operating under steady conditions) composed of two isothermal and two
constant field processes.
Thermodynamic Properties of Actual Magnetic Materials
Actual magnetic materials exhibit a characteristic temperature at which the
material changes from a ferromagnetic material to a paramagnetic material. This
temperature is known as the Curie temperature or Curie point. Most materials
116
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cy.:
=3
<
U
Q_
21
LxJ
Mhigh
Mldv
CONST. FIELD STRENGTH
CONST. MAGNETISM
Hhigh
ENTRDPY
Figure 9.1: Temperature versus entropy diagram for an ideal ferromagnetic
material.
which exhibit a suitable magnetocaloric effect for magnetic refrigeration have a Curie
temperature below 20 C.
One consequence of the transition from ferro- to paramagnetism is illustrated
in Figure 9.2. The rate of temperature change with respect to entropy at constant
field strength, ^ > increases dramatically above the Curie temperature. This
phenomenon is particularly pronounced for the zero field strength line where a sudden
change in the slope occurs at the Curie temperature.
If the magnetic working material is a solid and assumed to be incompressible,
the infinitesimal work, 8W, interaction in the presence of a magnetic field, H, is due
117
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solely to the opposition to changes in orientation of the magnetic dipole moment, M,
of the material. Thus,
SW = -HdM. (9.2)
The total entropy change in the material is brought about by three separate interac-
tions of particles. From the strongest to the weakest, these entropy changes are:
1. Ion spin, ASj^.
2. Lattice vibration, AS^.
3. Conduction electron flow, ASg.
The total entropy change, ASy, is the sum of the three individual changes.
118
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CD
L
3
-P
c5
CD
CL
£
Qj
I—
Entropy
Figure 9.2: Relationship between temperature and entropy for a fer-
romagnetic material at constant field strengths of 0, 1, 3,
5, and 7 tesla.
119
-------
Chen et al. [71] present a set of equations which can be used to calculate the
theoretical change in Aand A.Sg. The method was validated by demon-
strating agreement between calculated values and experimental data obtained by
Griffel et al. [73].
Several theoretical refrigeration cycles can be constructed by combining a series
of isofield, isomagnetic, and isothermal processes. These include the "magnetic"
reversed Stirling and reversed Ericsson cycles and a cycle composed of isothermal,
isofield, and isentropic processes.
Magnetic Reversed Stirling Cycle
Figure 9.3 illustrates the T-S diagram for a magnetic reversed Stirling cycle
for an ideal magnetic material. The material is heated isomagnetically from state
1 to state 2. Heat is rejected isothermally from state 2 to state 3. The material
is cooled during a second isomagnetic process from state 3 to state 4. Finally, the
cycle is completed by an isothermal heat acceptance process from state 4 to state 1.
The heating and cooling during the isomagnetic processes is accomplished through
regeneration. Since the two lines of constant magnetism are parallel, this cycle would
be capable of perfect regeneration.
It can be shown that the COP for this cycle is the COP(jarno^ as would be
expected for the reversed Stirling cycle. However, if the system boundaries are chosen
to include the hot and cold thermal reservoirs and since a temperature difference
will exist at each reservoir and heat exchanger interface, the COP for the magnetic
120
-------
Ld
(Y.
C
tX
U
Q.
Mhidh
I LOW
ENTRDPY
Figure 9.3: Temperature versus entropy diagram for a magnetic reversed Stir-
ling cycle.
reversed Stirling cycle would be
COP Magnetic Reversed Stirling
tl -
(9.3)
{TH + &TH) - (tl - &TLy
The net effect of temperature differences between the heat exchangers and the low
and high temperature thermal reservoirs (source and sink) is a reduction in the COP.
The larger the temperature difference between either thermal reservoir and the heat
exchanger, the greater the reduction in the COP from the Carnot COP.
121
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Magnetic Reversed Ericsson Cycle
A magnetic reversed Ericsson cycle is depicted in Figure 9.4. This cycle consists
of two isofield and two isothermal processes. Since the lines of constant field strength
do not remain parallel over the temperature range, additional heat is required from
an external source for energy to be conserved. Thus, both constant field processes (1-
2 and 3-4) in Figure 9.4 cannot be followed during steady operating conditions. This
situation is illustrated in Figure 9.4 as a larger regenerative cooling area bounded by
a-b-3-4-a in contrast to the regenerative heating area bounded by c-d-2-l-c.
The magnetic polytropic cycle, in which energy is conserved, is illustrated in Fig-
ure 9.5. To maintain ideal regeneration, the field strength during the cooling process
from state 3 to state 4 would be continuously lowered as a function of temperature
so as to maintain a constant entropy difference throughout the temperature range.
This would be analogous to a polytropic process in an ideal gas. The path of this
magnetic polytropic process would be parallel to the low constant field strength line.
The COP for this cycle would also be COP(jarno^ as it was for the magnetic reversed
Stirling cycle. Similarly, if the boundary of the system was chosen to include the hot
and cold thermal reservoirs and a temperature difference exists at each reservoir/heat
exchanger interface, the COP for the magnetic reversed Ericsson cycle would be
Equation 9.4 is identical to Equation 9.3. Therefore, the COP will be the same for
both cycles when both cycles are operating between thermal reservoirs (sources and
COP Magnetic Reversed Ericsson
TL -
(9.4)
sinks) having the same temperatures (T^ and Tfj) and the with same temperature
differences between the thermal reservoirs and the heat exchangers.
122
-------
ENTRDPY
Figure 9.4: Temperature versus entropy diagram for a magnetic reversed Er-
icsson cycle.
123
-------
ENTRDPY
Figure 9.5: Temperature versus entropy diagram for a cycle involving a mag-
netic polytropic process.
124
-------
As with the magnetic reversed Stirling cycle, the effect of increasing the tem-
perature difference between the thermal reservoirs and the heat exchangers will be a
reduction in the COP.
A second method of conserving energy during a cycle in which the magnetism
and demagnetism of the working core follows lines of constant magnetic field strength
is the combined magnetic cycle shown in Figure 9.6. This cycle is composed of an
isofield heating process from state 1 to state 2, isothermal heat rejection from state 2
to state 3, and isofield cooling from state 3 to state 4. After all of the heat has been
transferred during the regeneration process an isentropic process would proceed until
the low temperature is reached. In other words, when the area bounded by a-b-3-4-a
is equal to the area bounded by c-d-2-l-c, an isentropic process commences at state
4 and ends at state 5. Heat would then be accepted isothermally from 5 to 1.
During the combined cycle, all of the heat is transferred during the regenera-
tion process as evidenced by the equal areas bounded by a-b-3-4-5-a and c-d-2-l-c.
However, since the heat is now transferred through a finite temperature difference,
an inherent internal irreversibility exists and the COP will be less than the Carnot
coefficient of performance.
125
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Q REGEN.
Q REGEN.
Q 10
ENTRDPY
Figure 9.6: Temperature versus entropy diagram for a combined cycle.
126
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Computer Model
The coefficient of performance for the ideal magnetic reversed Stirling and re-
versed Ericsson cycles is identical to the COP for the ideal gas Stirling model. The
ideal Stirling model in the alternative refrigeration cycle modeling program (Ap-
pendix B) can be used to estimate the COP for these cycles. A more realistic mag-
netic refrigeration cycle is the combined or ideal regenerative cycle. A computer
subroutine developed for the combined magnetic cycle is discussed in the following
sections.
Thermodynamic Properties
A consideration in developing a magnetic heat pump model for refrigeration and
air conditioning applications is the behavior of real ferromagnetic materials in con-
trast to the ideal (Curie law) approximation. The best ferromagnetic materials, like
gadolinium, have a Curie point in the temperature range of interest. As noted earlier,
there is a sudden change in the temperature-entropy relationship at the Curie point.
If the change in entropy was calculated based upon the Curie law equation of state,
considerable error between calculated and actual values would exist, particularly at
temperatures near the Curie point. Therefore, it was necessary to develop a ther-
modynamic property routine which was based upon the behavior of actual magnetic
materials.
A thermodynamic property routine was written in FORTRAN using total en-
tropy change versus absolute temperature data from Chen et al. [71]. The tempera-
ture data were for magnetic field strengths of 0, 1, 3, 5, and 7 teslas for gadolinium.
These data were fitted with a second-degree polynomial in both temperature and
127
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field strength. This function can be used to determine the entropy change due to
changes in temperature and field strength. A FORTRAN subroutine, GD.FOR, was
written to calculate entropy change using the curve fitted polynomial. The subrou-
tine GD.For is included in Appendix B. This subroutine returns a entropy value in
for a given absolute temperature and a magnetic field strength in teslas.
Combined Magnetic Cycle
The combined magnetic cycle model calculates the COP for a magnetic refriger-
ator operating between two field strengths.
Figures 9.7 and 9.8 illustrate the graphical technique used to calculate the COP
for the combined cycle.
The following parameters are specified by the user:
1. Sink temperature {Tjj).
2. High temperature heat exchanger minimum approach temperature (ATjj).
3. Low temperature heat exchanger minimum approach temperature (AT^).
4. High magnetic field strength
5. Low magnetic field strength (^Low)•
A sixth parameter, source temperature (7^), is established in the program. During
execution of the computer model, the source temperature is incremented from —24 C
to 28 C.
The T-s diagram in Figure 9.8 is broken into four areas, numbered I to IV.
Between states 1 and 2, the area under the low field strength curve (Area I) is found
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by numerical integration. Area I is bounded by c-d-2-l-c, and represents the heat
transferred from the regenerator to the gadolinium core,
Area II is bounded by the high temperature isotherm, Tjj, at the top, abscissa
(T = OK) on the bottom, an isentropic line passing through state 3 on the left, and
an isentropic line through state 2 on the right. Thus, Area II includes Area I and
represents the total amount heat which must be transferred by regeneration (Area I)
or be rejected to the sink (Area II - Area I) during the cycle. The heat transferred
from the gadolinium core to the regenerator, Qftegen Left' *s rePresented by Area
III which is bounded by a-b-3-4-a. This area is determined by performing a second
numerical integration, beginning at state 3, and proceeding to the left along the line
of high constant magnetic field For operation under steady conditions,
Area III must equal Area I. The computer program compares the current value of
Area III with Area I. When the two areas are equal, state 4 is established. It is
assumed that an isentropic process occurs between state 4 and state 5. Therefore,
state 5 is known since it must lie on the low temperature isotherm and along the
isentropic line passing through state 4.
Area IV (bounded by a-b-c-l-5-a), the amount of heat accepted from the thermal
source during the cycle, Q{n, can now be determined,
The magnetic work, is represented by the area enclosed by the high and
low constant field lines, isentropic line segment 4-5, and the high and low temperature
(9.5)
Qin = TL(S1- S5).
(9-6)
129
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isotherms,
WM = AIII+AII-AI~AIV-
(9.7)
The COP is
Qi
p . ^in
utyrCombined Magnetic Cycle ~
M
(9.8)
Tu
U
ac
ZD
I—
<
QC
u
CL
s:
u
Tl
lo
ENTROPY
Figure 9.7: Temperature versus entropy diagram illus-
trating the determination of areas for the
combined cycle.
130
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Hhigh
/
Hldw
/
/
/
Ic
4
sj
a be d
ENTRDPY
Figure 9.8: Temperature versus entropy diagram illustrating the magnetic
work and heat acceptance areas for the combined cycle.
131
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Magnetic Refrigeration Cycle Results
From theory, the maximum COP for both the magnetic reversed Stirling and
magnetic reversed Ericsson cycles is C0Pqarnot. As with the gas reversed Stirling
model, it was assumed that the only external irreversibility for this system was caused
by the temperature difference between the heat exchangers and the thermal source
and sink. The equation of the COP for the magnetic reversed Stirling and magnetic
reversed Ericsson cycles is the same (Equations 9.3 and 9.4, respectively).
The COP for the combined model was calculated using the "graphical" model.
The coefficients of performance for the magnetic Stirling, reversed Ericsson, and
combined refrigeration cycles were calculated for a sink temperature of 35 C at dif-
ferent source temperatures from —24 C to 28 C. The low and high field strengths
were 0 and 7 teslas, respectively. A minimum approach temperature of 10 C was
assumed to exist between both heat exchangers and the thermal source and sink. A
10 C difference, rather than a 5 C value, was chosen because it was assumed that
fluid heat transfer loops would be interposed between the solid core and the source
and sink. Thus, two additional heat exchangers would be needed in the system with
each heat exchanger having a 5 C minimum approach temperature. The loops were
assumed to have adiabatic, inviscid flows. The pumping work was neglected.
Figure 9.9 illustrates the maximum theoretical COP for the combined magnetic
refrigeration cycle. In practice, the actual cycle efficiency for any of these cycles
would be a less than 0.10. The principal reasons for this poor cycle efficiency {iJCycle)
are:
• the need for almost perfect regeneration due to the small temperature lift of
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11
9
7
Q.
o
o
5
3
1
-30 -20 -10 0 10 20 30
Source Temperature (C)
Figure 9.9: COP versus source temperature for an ideal combined
magnetic refrigeration cycle.
the magnetic core material and
• cooling of present magnets is needed when operating
Figure 9.10 illustrates the cycle efficiency for an ideal
geration cycle over a range of source temperatures.
Closure
The cycle efficiencies for the theoretical magnetic refrigeration cycles presented
in this chapter are much higher than can presently be attained in practice. Since
Sink Temp. > 35 C
High Field Strength >71
Low Field Strength = 0 T
Heat Exch. Mln. Approach Temp. ¦ 5 C
1 1 ' 1 1 1 ' 1 ¦ 1 1 1 ¦ 1 1 1 ¦ 1 1 1 1 ' 1
at high field strengths,
combined magnetic refri-
133
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0.6
0.5
c 0.4
2
"g
it=
HI
®
£ 0.3
O
0.2
0.1
i i
-30
Sink Temp. »35 C.
High Field Strength = 7 T.
Low Field Strength = 0 T.
Heat Exch. Mln. Approach Temp. = 5 C.
i i t i
¦ 1 '
1 1 1 1 1 ' 1 1
-20 -10 0 10
Source Temperature (C)
20
30
Figure 9.10: Cycle efficiency versus source temperature for an ideal
combined magnetic refrigeration cycle.
the cycle efficiency increases with decreasing source temperature, the cycle would be
better suited to low-temperature cooling applications rather than air conditioning.
A technical assessment of magnetic refrigeration for use in domestic and com-
mercial cooling and refrigeration applications is presented in Chapter 10.
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CHAPTER 10. TECHNICAL ASSESSMENT OF ALTERNATIVE
REFRIGERATION TECHNOLOGIES
Introduction
The assessment of alternative refrigeration technologies involved the evaluation
of two fundamental criteria categories common to all refrigeration and air condition-
ing applications. These criteria are environmental acceptability and system cost.
Environmental Acceptability Considerations
Environmental acceptability considerations include:
1. Ozone depletion potential (ODP) of the working material. It was decided that
only alternative refrigeration technologies which were capable of using working
materials which are not ozone depleting would be considered in this study.
2. Global warming potential (GWP) of the refrigeration technology. There are
two GWP components which can be contributed by a refrigeration system:
direct GWP, and indirect GWP. Direct global warming results from the leak-
age or release of a working material which is known to have a GWP. Indirect
global warming results from the release of CO2 into the atmosphere. CO2 is a
combustion product released during the burning of fossil fuels during the gen-
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eration of electricity or for heating. All refrigeration systems which utilize heat
or electricity to drive the system which was derived from fossil fuel combustion
contribute to global warming. Refrigeration systems which have a high COP
require less heat to produce the same amount of cooling as refrigeration systems
with a low COP. The COP of a refrigeration system is inversely proportional
to its indirect GWP. Therefore, systems which have a high COP are desirable
from a global warming perspective since they have a lower indirect GWP. Over
the life of a refrigeration system, the indirect global warming contribution can
be many times larger than its direct global warming contribution. For the
technologies assessed in this project, the indirect global warming potential is
considered through the energy costs, i.e., COP of the system.
3. Flammability. It is recognized that some working materials which have been
or could be used in refrigeration systems are flammable. By the same token,
it is known that fuels are intentionally burned to provide heating in buildings.
If the liability issue is set aside for a moment, the comparative risk of fire
resulting from the release of a flammable working gas from a modern closed
refrigeration system is small as compared to the combustion of fuel gases for
heating. The risk could be further minimized through the use of devices which
provide an alarm, stop the heat or work input, and provide external venting
of the escaping flammable material. The incorporation of any or all of these
devices into a refrigeration system would translate directly into a higher cost
of the system.
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4. Noise. Noise emitted by a refrigeration system is an environmental factor
which can be dealt with by providing vibration isolation, acoustic insulation,
and other techniques to achieve acceptable sound pressure levels. The addition
of these devices to a refrigeration system would result in higher first costs.
In conclusion, alternative refrigeration technologies with environmental assess-
ment criteria which are unacceptable from an ODP or toxicity standpoint were not
considered in this project. Technologies which could have other environmental haz-
ards, such as noise, which could be minimized or eliminated by design were considered.
Cost-Related Technology Assessment Considerations
Cost-related technology assessment considerations include:
1.. State-of-the-Art. Some alternative refrigeration technologies are more ma-
ture than others. Research and development were considered in two broad areas:
basic technology development and system development. For this study, a basic
technology was defined as one which is not unique to refrigeration and would
have many potential applications in other areas. An example would be the de-
velopment of materials with high-temperature superconducting (HTSC) prop-
erties to reduce electrical resistance losses. HTSC would improve the perfor-
mance of the thermoelectric and magnetic refrigeration technologies. It would
also be important in electric power generation and transmission, electric motor
design, and other applications using electric energy. Generally, improving a
basic technology is extremely expensive and there are no guarantees of success.
For this project, system development costs were defined as the research and
development (R & D) costs which would be incurred in advancing the maturity
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of a refrigeration technology to the point at which marketable systems could
be sold. It would include costs for developing the system hardware beyond the
prototype stage to its final marketable form, and building the infrastructure
necessary to manufacture the system.
2. Size/weight. Size and weight considerations are important for many refri-
geration applications. Larger, heavier systems with the same cooling capacity
contain more material which generally increases the first cost of the system.
Increased size and weight create higher first costs for structures in which they
are used, or reduce the usable space within the structure. This is particularly
true in the transportation industry where it is desirable to maximize the useful
pay load of the vehicle.
3. System complexity. Assessment of system complexity includes considera-
tions regarding the number of subsystems, number of moving parts, and un-
common materials used in an alternative refrigeration system. The difficulty
in manufacturing the system, including likely manufacturing techniques and
precision requirements, were also considered. These issues relate directly to the
first cost of the refrigeration system.
4. Useful life. Useful life of the refrigeration system was defined as the length
of time during which the major components would remain functional while
operating with a nominal duty cycle and receiving normal maintenance. For
example, the useful life of a domestic central air conditioner would be the life
of the compressor unit.
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5. Maintenance. Maintenance cost considerations include the amount of repair
and preventive maintenance required, skill level of maintenance personnel, por-
tion of time an operator would need to attend to the system, likelihood of
component failure, and recurring costs (such as the periodic recharging of a
system with working material) for normal system operation.
6. Efficiency. Two factors are affected by the efficiency of the system: the cost
to operate the refrigeration system and the indirect component of the global
warming potential. It is assumed for this study that all heat or electricity
required to operate the refrigeration systems originates from the combustion
of fossil fuels. The efficiency criterion rating is based upon the cycle efficiency
(fraction of the Carnot COP) at which the refrigeration system could operate
for a particular application. This rating is based upon what is technically
feasible in the 1990s. As technology advances, the cycle efficiency of some the
less mature technologies may improve. Therefore, some of these technologies
may become more attractive in the future.
Rating Factors
In the following sections, the technical assessment criteria will be evaluated for
the refrigeration technologies. A table which summarizes the technical assessment
numerically is included at the end of each technology assessment section. The number
is a rating factor which is the investigators' best estimate on a scale of 1 (very low)
to 5 (very high) of the merit of a particular technology for a technical assessment
criterion. A rating of 5 for a criterion would indicate that that aspect is particularly
attractive for a technology. A rating of 1 would indicate that the technology was very
139
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unattractive with respect to the criterion being considered. Table 10.1 summarizes
the interpretations of the extreme ratings (1 and 5) for each criterion. The rating
numbers for the cycle efficiency criteria are listed in Table 10.2; efficiency is the only
criterion for which the rating numbers correspond to numerical values.
Table 10.1: Interpretation of the numerical ratings for technology assessment crite-
ria.
Criterion
Rating of 1
Rating of 5
State-of-the-art
Theory only
Fully matured
Complexity
Very complex
Very simple
Size/Weight
High
Low
Maintenance
High
Low
Useful Life
Short
Long
Efficiency
0 to 0.12
Above 0.50
Table 10.2: Numerical definition of the efficiency rating scale in terms of cycle effi-
ciency (fraction of the Carnot COP).
Efficiency Rating Number
Cycle Efficiency Range
1
0.00 to 0.12
2
0.13 to 0.24
3
0.25 to 0.36
4
0.37 to 0.49
5
Above 0.50
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Examples of extreme technical assessment criteria ratings would be:
• A system which required no maintenance would receive a rating of 5 since there
would be a major cost savings benefit and high reliability over the life of the
system.
• An air conditioning system that has a cycle efficiency of 0.01 would receive
an energy cost rating of 1 (very low) since it would be costly to operate and
have a negative impact on the environment through additional indirect global
warming since extra fuel would have to be burned to achieve the same amount
of cooling as a more efficient system.
The following sections discuss in detail the rating numbers assigned to the tech-
nologies evaluated during this study.
Reversed Brayton Cycle Refrigeration
The reversed Brayton refrigeration cycle was presented in Chapter 5.
Environmental Acceptability of Reversed Brayton Cycle Systems
The open-cycle reversed Brayton system uses air as the working fluid. Closed-
cycle reversed Brayton systems can use air or other gases. Properties such as specific
heat and viscosity over the operating temperature range are considerations in select-
ing a working gas. Helium is an ideal choice due to its high specific heat and low
viscosity. It is an inert gas with no ODP or direct GWP. Also, it will not react with
the materials used to construct the system.
141
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Noise generated by the compressor, expander, or high-velocity air is one consid-
eration which may limit the type of application in which open-cycle Brayton systems
can be used. Since escaping air is not a problem in closed-cycle reversed Brayton
systems, the noise level may be acceptable, or it can be brought to a reasonable level
using sound insulation or other acoustic engineering methods.
State-of-the-Art
The basic technology used in reversed Brayton systems is well developed. Com-
pressors and turbines are capable of reasonably long life, although not as long as that
of compressors used in vapor compression refrigeration systems.
Kauffeld et al. [28] performed a theoretical and experimental investigation of nine
different reversed Brayton cycle systems. The cycle configurations included open and
closed systems, multistage compression with intercooling, and regeneration. It was
found that the highest COPs for air conditioning applications would be achieved by
open cycle systems with multi-stage compression and intercooling. The COP of the
reversed Brayton cycle is very sensitive to the isentropic efficiencies of the compressor
and expander. Table 10.3 illustrates the effect of increasing the isentropic efficiency
of the expander and compressor for a reversed Brayton cycle operating on air. The
source temperature was 4 C and the sink temperature was 35 C.
Henatsch and Zeller [25] list the isentropic efficiencies of off-the-shelf compres-
sors and turbines as being between 63% and 88%. Small capacity units have lower
isentropic efficiencies. As the capacity increases, so does the isentropic efficiency.
The largest improvements of the reversed Brayton cycle COP would be realized
if the isentropic efficiency of the expander and compressor could be raised. Turbine
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Table 10.3: COP of the theoretical reversed Brayton cycle for three different isen-
tropic compressor and expander efficiencies. Tsource = 4 C, Tsink = 35
C, Pressure ratio = 2.5.
Isentropic Efficiency
(Compressor and Expander)
Theoretical COP
Cycle Efficiency
0.60
0.12
0.014
0.65
0.19
0.021
0.70
0.27
0.031
0.75
0.39
0.044
0.80
0.55
0.062
0.85
0.79
0.088
0.90
1.16
0.130
0.95
1.82
0.204
1.00
3.30
0.369
design is a mature technology. The state-of-the-art is advanced as a result of applica-
tion of turbomachinery in the gas turbine, jet engine, and electric power generation
industries. Any further improvements in the efficiency of either the compressor or
the expander will be small. Consequently, improvements in the COP of reversed
Brayton-type refrigeration systems will be small as well.
Based on the above factors, a rating of 3 (moderate) was assigned to the state-
of-the-art category for all air conditioning applications and domestic refrigeration
applications. A rating of 4 (high) was assigned to the commercial refrigeration state-
of-the-art category due to the low source temperature capability of the reversed
Brayton cycle.
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Complexity
The basic reversed Brayton system is composed of a compressor, expander, and
one or two heat exchangers (depending upon whether the system cycle is open or
closed). The COP of the basic system is low, as shown in Chapter 5.
Higher COPs can be achieved by incorporating regeneration, multistage compres-
sion, and intercooling between compression stages. Kauffeld et al. [28] determined
that the COP for an air conditioning application could theoretically be raised from
0.59 (for a basic closed reversed Brayton cycle) to about 1.1 by using an open cycle
with regeneration and two-stage compression with interstage cooling. In all cases, an
isentropic efficiency of 0.80 was assumed for the both the compressor and expander.
A 10 C minimum approach temperature was assumed for external heat exchangers.
Although adding components to the system will increase the COP, it will also result
in higher first cost and maintenance costs.
For air conditioning, the required volumetric flow rate of air would be approxi-
3
mately 2.3 m^nufe (81.7 cfm) per kW of refrigeration. Ducting to deliver cool air to
the conditioned space would represent an additional first cost of the system. Ducts
would need to be large enough to reduce the noise generated due the velocity of air
entering the room in open-cycle refrigeration systems.
Since the highest COPs are achieved at relatively low pressure ratios (and over
a narrow range of pressure ratios), the pressure drop in the duct system would be
an important consideration requiring custom design of each application. The added
engineering time would result in higher first costs.
A method of dehumidifying the air in open-cycle systems would be required
applications where high relative humidity was encountered or at source temperatures
144
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below freezing (TSource < 0 C). The COP decreases as the relative humidity in the
air increases.
Based on the above factors, a rating of 3 (moderate) was assigned to the com-
plexity category for all cooling applications and domestic applications. A complexity
rating of 4 was given to commercial refrigeration applications since these systems are
usually more complex (relatively speaking) than domestic refrigeration applications.
Size/Weight
Given the low pressure ratios and high volumetric flow rates encountered in
reversed Bray ton refrigeration systems, the hardware volume would be large as com-
pared to vapor compression machinery of similar capacity. This would be particularly
true of systems using multistaging with or without intercooling and regeneration. If
dehumidification were required to remove water from the air, additional space would
be required to house a desiccant or dehumidification system.
Based on the above factors, a rating of 3 (moderate) was assigned to the size/weight
category for commercial refrigeration applications. A rating of 2 (low) was given to
the size/weight category rating for all air conditioning and domestic refrigeration
applications.
Maintenance
The primary maintenance activities for open reversed Brayton cycle cooling
equipment would include changing air filters and inspecting and cleaning heat ex-
changer and regenerator surfaces. These procedures would be necessary to ensure
that the maximum heat transfer rate could be maintained.
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Open-cycle systems using a desiccant for moisture removal would require periodic
cleaning and replacement of the desiccant media. If heat were used to remove the
moisture from the media, the heat source may require additional attention.
In both open- and closed-cycle systems, field service of the compressors and
expanders would involve replacement of the failed unit. Reconditioning of these
replaced units would be done at a centralized location with specialized equipment and
personnel. Field maintenance personnel would not require a high level of expertise.
A rating of 3 (moderate) was assigned to the maintenance category for all air
conditioning and refrigeration applications.
Useful Life
The reversed Brayton cycle uses at least two rotating machines, the compressor
and the expander. If multistaged compression or expansion were used, each additional
stage could be considered another rotating machine. Although the life of high-speed
rotating turbomachinery used in compressors and expanders is reasonably long, it is
doubtful that the useful life of reversed Brayton turbomachinery would exceed that
of the compressor used in vapor compression systems of equivalent thermal capacity.
Even if the life of each rotating component used in a reversed Brayton system were
as long, there would be increased probability of system failure due to the additional
rotating machines in the system.
Based on the above factors, a rating of 3 (moderate) was assigned to the useful
life category for all air conditioning and refrigeration applications.
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Efficiency
The COP is low for reversed Brayton cycles operating in the temperature ranges
used in refrigeration and air conditioning applications. The primary reasons for the
low COP are the thermodynamic behavior of the working gas (specific heat, cp),
frictional losses due to viscous flow of the working gas and bearing lubrication in the
compressor and expander, irreversible heat transfer, and non-isentropic compression
and expansion processes. Thus, the efficiency category rating for all reversed Brayton
cycle air conditioning applications was 1 (very low), and the efficiency category rating
for reversed Brayton refrigeration applications was 2 (low).
Closure
The numerical technical assessment ratings for Brayton cycle refrigeration are
given in Table 10.4.
Table 10.4: Technology assessment for reversed Brayton refrigeration.
Criterion
Rating (1=
= lowest, 5
= highest)
Dom. AC.
Com. AC.
Mob. AC.
Dom. Ref.
Com. Ref.
State of art
3
3
3
3
4
Complexity
3
3
3
3
4
Size/Weight
2
2
2
2
3
Maintenance
3
3
3
3
3
Life
3
3
3
3
3
Energy Effic.
1
1
1
2
2
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Reversed Stirling Cycle Refrigeration
The theoretical reversed Stirling cycle was developed in Chapter 6. In prac-
tice, the theoretical reversed Stirling cycle is not a good approximation of the actual
cycle undergone by actual "Stirling" refrigeration machinery. The practical consider-
ations of using reversed Stirling-type machinery for air conditioning and refrigeration
applications will be discussed in this section.
Environmental Acceptability of Reversed Stirling Cycle Systems
Reversed Stirling-type refrigeration machinery typically uses helium as the work-
ing gas. Based on the assumption that helium or another inert gas would be used in
Stirling refrigerating machinery, there would be no ODP, GWP, or toxicity problems
related with the working material.
As with other cooling systems utilizing secondary heat transfer loops to transport
heat between the cooled space and the refrigeration unit, a fluid with a low freezing
point would be necessary. Usually, the fluid is a mix of water and glycol, which has
a low toxicity. Water/glycol mixtures are the heat transport fluid of choice in the
automotive industry. If leakage is minimized and used fluid is recycled, the additional
use as a heat transport fluid in refrigeration systems should not present an additional
environmental hazard.
State-of-the-Art
Reversed Stirling refrigeration has long been used in cryogenic cooling appli-
cations where low cooling temperatures and small cooling capacities are required.
The source temperature for these applications is generally in the —213 C to —173 C
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range. When traditional reversed Stirling machinery has been used at higher source
temperatures (—23 C, for example), cycle efficiencies were found to be on the order
of 0.10 to 0.20 [37, 38].
The ideal reversed Stirling thermodynamic cycle consists of two isothermal and
two isometric processes. In practice, isothermal compression and expansion are not
possible due to practical limitations of heat exchanger area and flow of the working
gas in the closed-cycle reciprocating machinery. Non-isothermal heat transfer is a
major reason actual systems cannot operate with the Carnot COP.
The COP of reversed Stirling cooling systems is further degraded by thermody-
namic losses associated with imperfect regeneration, friction, and unintentional heat
transfer throughout the system. The net effect of these losses is an actual COP which
is much lower than the ideal. Kelly et al. have proposed a modified reversed regen-
erative Brayton cycle as being a more realistic model of the actual thermodynamic
processes in Stirling-type refrigeration machinery [44].
As discussed in Chapter 6, the causes for the low COP in reversed Stirling
refrigeration equipment are work-related when operated at source temperatures com-
monly found in domestic and commercial refrigeration applications. Some of these
losses could be minimized by reducing the friction in the rotating and sliding elements
of the machinery. Current development of reversed Stirling systems has centered
around a free piston design using a linear motor and gas spring to eliminate the ro-
tating components traditionally found in reciprocating machinery, thus reducing the
frictional power requirement of the system. Both Sunpower and Stirling Technology
Company have tested prototype free-piston reversed Stirling systems at source tem-
peratures of —23 C [42, 43, 74]. The cycle efficiency for these systems was found (by
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experiment) to be between 0.25 and 0.32. Both companies determined the COP by
measuring the electrical power input and the heat accepted at the expansion (cold)
heat exchanger. Neither experiment took into account the temperature differences
or pumping power across the cold-side secondary heat transfer loop. If these factors
had been taken into account, the experimental COP would have been lower.
A second source of losses in reversed Stirling refrigerators is in-cylinder heating
of the working gas during the compression process and in-cylinder cooling during the
expansion process. The heating and cooling are due to heat exchange between the
gas and the piston and cylinder walls.
The current state-of-the-art for Stirling-type refrigeration technology is:
• The basic technology used in Stirling-type refrigeration has been demonstrated
to be workable. The technology has been developed to the extent that it has
been used commercially in cryogenic refrigeration applications.
• To create a refrigeration system which could be used as a replacement for vapor
compression systems, heat exchangers or heat transfer methods must still be
developed which will allow heat to be exchanged between the system and the
cooled space, as well as the system and the environment, at a reasonable rate.
This heat transfer would have to be accomplished without losses which would
degrade the coefficient of performance below current levels.
• Bearings must be developed which will reduce the frictional losses in the system
and improve the useful life of the system.
• Sealing systems must be developed not only to minimize the escape of the
working gas, but to reduce leakage past the piston (blow-by).
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• Regenerators must be developed which have high effectiveness, low pressure
drop, and minimum volume (dead space).
• A means of providing compression and expansion spaces which approach isother-
mal heat transfer conditions must be developed.
Based on the above factors, a rating of 3 (moderate) was assigned to the state-
of-the-art category for all refrigeration and air conditioning applications.
Complexity
Reciprocating and free-piston Stirling-type refrigerators can make use of stan-
dard materials, including ferrous and non-ferrous metals for most of the hardware.
Special materials may be necessary for seals and sliding surfaces if the useful life is
to be lengthened and friction is to be reduced. Insulating coatings (such as ceramics)
might be used to insulate the piston and cylinder. Neither modification is expected
to add appreciably to the cost of the hardware.
The Stirling-type refrigeration system will require at least one secondary heat
transfer loop (on the cold side). Realistically, a second loop would be required for
the hot side as well in order to reject heat from the system high-temperature heat
exchanger at a reasonable rate. Each secondary loop would require an air-to-fluid
heat exchanger, piping, a means of circulating the fluid, and a reservoir. These
additional requirements will increase the complexity of the total system.
Based on the above factors, a rating of 3 (moderate) was assigned to the com-
plexity category for all cooling applications and domestic applications. A complexity
rating of 4 was given to commercial refrigeration applications since these systems are
usually more complex (relatively speaking) than domestic refrigeration applications.
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Size/Weight
The basic Stirling-type cooling system without the secondary heat transfer loops
is reasonably compact and lightweight. The addition of the secondary heat transfer
systems will cause the system to be similar in size to a comparable vapor compression
system.
There has been some development of a duplex reversed Stirling heat pump [75].
This system uses heat rather than mechanical work to drive the system. In a conven-
tional reversed Stirling refrigerator, mechanical work is put into the system. Usually,
this work is done by an electric motor. In the duplex Stirling system, heat is used to
drive a Stirling engine which drives the reversed Stirling refrigerator. An additional
size/weight penalty would be encountered for the duplex system when the combustor
to convert fuel to heat is considered as being part of the refrigeration system package.
Based on the above factors, a rating of 4 (high) was assigned to the size/weight
category for all applications.
Maintenance
Present Stirling-type refrigeration machinery does not use lubricants. Given
the small clearances and small tolerances for the cylinder to piston fits, periodic
replacement of the reciprocating system is expected. Complete refrigeration units
would be interchanged in the field. Depending upon their size, the units would either
be rebuilt (systems with larger cooling capacity) or discarded. The latter case is
likely if the systems are hermetically sealed.
Hermetic sealing may be a likely means of construction for small Stirling-type
refrigeration units to prevent leakage of the working gas from shaft seals. This would
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eliminate the need for periodic recharging of the system with gas. Helium is even
more difficult to contain than R-12 or R-22. Units which are not completely enclosed
will require recharging of the working gas as needed.
If secondary heat transfer loops are used, some periodic maintenance will need
to be performed on these subsystems as well. As previously discussed for other
alternative technologies, these loops may require repair of the circulating devices,
flushing of the system and replacement of the coolant, cleaning of the air-side heat
exchanger surfaces, and repair of leaks.
In summary, a moderate amount of maintenance is expected to be required
for Stirling-type refrigeration systems used in all applications; in comparison, vapor
compression requires little or no maintenance. A rating of 3 (moderate) was assigned
to the maintenance category for all air conditioning and refrigeration applications.
Useful Life
Presently, the useful life of Stirling-type refrigerators is expected to be well below
that of vapor compression systems. The primary cause for the reduced life of the
system is lubrication. Reciprocating compressors used in vapor compression systems
use oil to reduce friction, assist in sealing the piston in the cylinder, and aid in
transferring heat from the compression space. The compression and expansion spaces
of current reversed Stirling machinery are operated without a lubricant. If life is to
be increased, low-friction, wear-resistant material combinations or an effective piston
ring (seal) combination which allows lubrication of the piston and wall, but which
precludes contamination of the compression and expansion spaces, must be developed.
A rating of 4 (high) was assigned to the useful life category for domestic and
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mobile air conditioning and domestic refrigeration applications. The useful life cat-
egory rating for commercial air conditioning and refrigeration applications was 3
(moderate).
Efficiency
Although the coefficient of performance for the ideal reversed Stirling cycle equals
COP(jarnot, experience has shown that actual systems have low COPs at source tem-
peratures of —23 C and above. Kohler and Jonkers [37] reported an cycle efficiency
of approximately 0.08 for an unmodified Philips cryocooler operating between the
temperatures of 27 C and —23 C. Chen [38] reported a cycle efficiency of 0.07 for
an off-the-shelf cryocooler operating at similar temperatures. Sunpower and Stirling
Technologies report cycle efficiencies ranging from 0.25 to 0.32 for free-piston Stirling
coolers [42, 43, 74].
In all cases, the COP was determined by measuring the cooling rate and the
electrical power input. The temperatures were those of the high- and low-temperature
heat exchangers. The effect of secondary heat transfer loops was not considered.
Assuming a minimum approach temperature of 5 C for each loop, no pumping losses,
and neglecting pumping power, the COPs would be about 80% of the reported values.
Note that this is an idealized estimate and that the actual value would be much lower.
Although the COP of the classic reversed Stirling cycle model is the Carnot COP
when operated between the same temperature limits , Tj^ and Tjj, the performance
of actual Stirling refrigeration systems is much lower, as shown by the experimental
results. The reasons are:
1. The classic ideal model does not accurately reflect the true thermodynamic
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processes in the actual cycle.
2. Inherent losses in the refrigeration system due to mechanical friction, fluid
friction, imperfect heat transfer, motor losses, and refrigerant leakage.
3. Additional losses due to heat transfer and work in the complete system which
is in communication with the cooled space and the environment.
The efficiency category rating for all reversed Stirling cycle air conditioning appli-
cations was 2 (low). The efficiency category rating for reversed Stirling refrigeration
applications was 3 (moderate).
Closure
Reversed Stirling-type machinery is not considered to be a viable alternative to
vapor compression refrigeration, particularly for air conditioning applications. Al-
though the state-of-the-art is such that hardware is commercially available for cryo-
genic applications, much development remains to be done to improve the useful life
of the hardware and the cycle efficiency at source temperatures above —24 C. The
system is best suited to applications requiring source temperatures between —193
C and —73 C [37], far below the temperatures needed for domestic and commercial
refrigeration. Many of the technical improvements which must still be developed are
applicable to vapor compression technology. These technology improvements could
be used to also improve the efficiency of vapor compression refrigeration technology.
For example, linear motors, dry lubrication, improved piston sealing, and minimiz-
ing in-cylinder heating are all directly applicable to vapor compression compressor
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design. All of these concepts could be used to improve the efficiency of the vapor
compression cycle.
The numerical technical assessment ratings for Stirling-type refrigeration are
given in Table 10.5.
Table 10.5: Technology assessment for reversed Stirling-type refrigeration.
Criterion
Rating (1=
= lowest, 5
= highest)
Dom. AC.
Com. AC.
Mob. AC.
Dom. Ref.
Com. Ref.
State of art
3
3
3
3
3
Complexity
3
3
3
3
4
Size/Weight
4
4
4
4
4
Maintenance
3
3
3
3
3
Life
4
3
4
4
3
Energy Effic.
2
2
2
3
3
Pulse Tube and Thermoacoustic Refrigeration
The operating principal and underlying theory for the pulse tube and thermoa-
coustic refrigerators was presented in Chapter 7. In this section, some of the practical
considerations in applying these alternative refrigeration technologies to refrigeration
and air conditioning applications will be discussed.
Environmental Acceptability of Pulse/Thermoacoustic Systems
The working fluid in prototype thermoacoustic refrigerators in the space ther-
moacoustic refrigerator (STAR) program is a gas mixture of 97.1% helium and 2.9%
xenon. Xenon is added to reduce fluid frictional losses by lowering the viscosity of
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the gas mixture. Helium and xenon are inert gases. They will not react with ozone
in the upper atmosphere nor do they present a global warming hazard.
Thermoacoustic refrigerators operate at frequencies in the audible range (~
400Hz)] however, experimental results indicate that the noise level is low outside
the tube. The ambient sound level of an operating thermoacoustic refrigerator has
been likened to that of an electric fan [49].
State-of-the-Art
Much of the basic research for pulse tube and thermoacoustic refrigeration has
been done. Both the pulse tube and thermoacoustic refrigerator concepts have been
brought to the prototype stage and demonstrated to be workable by experiment. The
remaining system development would involve optimizing system performance and to
creating marketable hardware. While the costs associated with this development are
not expected to be as high as for less proven concepts like the magnetic refrigerator,
they would be higher than the cost of converting vapor compression refrigeration
technology to use non-CFC refrigerants. Thus, a rating of 2 (low) was assigned to
the state-of-the-art category for all refrigeration and air conditioning applications.
Complexity
The materials used in pulse tube and thermoacoustic refrigerators are common
engineering materials. The tube is generally stainless steel. The heat exchangers are
a metal with high thermal conductivity like copper. The pulse tube refrigerator would
require a compressor. The thermoacoustic refrigerator would require an acoustic wave
generator (speaker) to pressurize the working gas.
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Since the high- and low-temperature heat exchangers in pulse tube and thermoa-
coustic refrigerators are small, secondary heat transfer systems would be necessary
to exchange heat at a reasonable rate with the air on both the hot and cold sides.
These systems would utilize forced convection or a circulating liquid. In either case,
cost and size would be added to the system.
Manufacturing costs are expected to be approximately the same as for current
vapor compression systems. Although the thermoacoustic refrigerator does not use
a compressor, the generating spherical end of the resonator section would require
manufacturing methods which could add to the cost of creating the system hardware.
On experimental systems, the resonator is constructed of fiberglass to facilitate its
manufacture, and to reduce conduction heat transfer through the tube wall.
The pulse tube would require a compressor and prime mover (electric motor).
Since the pressure ratio between the high and low pressure could be approximately
2 or 3. The compressor may need to be capable of operating at pressures higher
than those for vapor compression systems. This conclusion is drawn from the fact
that the static (low) pressure for the experimental thermoacoustic refrigerators is
10 atmospheres [23]. The compressors for direct-acting compression systems would
need to be capable of higher speeds than vapor compression compressors to create
a high pulse frequency. Systems using a continuous flow compressor would require
a rotary valve. Therefore, the cost of manufacturing a compression system for pulse
tube refrigerators would be significantly higher than the cost for vapor compression
compressors.
The materials (stainless steel and copper) will be slightly more expensive (per
unit volume) than those used in vapor compression system compressors since pulse
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tube refrigerators may need to be capable of higher operating pressures and speeds
than those used in vapor compression systems.
Based on the above factors, a rating of 2 (low) was assigned to the complexity
category for all cooling and refrigeration applications.
Size/Weight
Pulse refrigeration systems are not as compact as vapor compression systems.
This added volume is due, in part, to secondary heat transfer systems and the added
equipment size necessary to house the working gas which has a high specific volume.
Thus, a rating of 3 (moderate) was given to the size/weight category for domestic and
commercial air conditioning applications and domestic and commercial refrigeration
applications. A rating of 2 (low) was given to the size/weight category for mobile air
conditioning applications.
Maintenance
Operation and maintenance levels and expertise do not appear to be markedly
different than for vapor compression systems.
Preventive maintenance would be mainly the periodic recharging. Given the low
molecular weight of helium and the high pressure, sealing of the system to preclude
the escape of the working fluid would pose a problem. Periodic (possibly frequent)
recharging of the system is anticipated.
When failures did occur, it is expected that components would be replaced rather
than repaired on site. Components for both pulse tubes and thermoacoustic refri-
gerators would probably be disposable rather than remanufactured. If cracks did
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occur in a tube, resonator, or acoustic diaphragm, it would be indicative that ad-
ditional fatigue related cracks are likely in the future, indicating the need for tube
replacement.
Since system repair would be a diagnosis and component interchange process,
technicians repairing pulse refrigerators would require skills similar to those needed
to repair vapor compression systems.
Based on the above factors, a rating of 2 (low) was assigned to the maintenance
category for all air conditioning and refrigeration applications.
Useful Life
The life of both pulse tube and thermoacoustic refrigerators is expected to be less
than that of vapor compression systems. Both high-pressure compressors and acoustic
generator diaphragms have finite life expectancies. The high operating pressures and
lack of lubricating oil in the gas would cause compressors to fail sooner than vapor
compression compressors. Although the remaining components of these systems are
largely static, given the pressure ratios and resonant operating frequency, the cyclic
stresses in the tube may result in fatigue cracking. Consequently, the tube could have
a limited fatigue life.
Based on the above factors, a rating of 3 (moderate) was assigned to the useful
life category for all air conditioning and refrigeration applications.
Efficiency
Experimental results for thermoacoustic refrigerators indicate that the cycle ef-
ficiency for temperature lifts commonly experienced in refrigeration applications is
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about 0.16 of the Carnot COP [23]. It should be noted that this measurement was
the ratio of the rate heat was accepted from a heater placed at the low-temperature
heat exchanger to the acoustic power required to accomplish the heat lift. The system
did not include heat exchangers communicating with the air (as would be expected in
practical applications). Therefore, it is expected that the COP of a practical system
in communication with the source and sink would be much lower.
From a theoretical standpoint, a reversed regenerative Brayton cycle operat-
ing with helium, isothermal regeneration, and isentropic compression and expansion
would have a cycle efficiency of approximately 0.30 for the same temperature lift
as the experimental unit. This would suggest that the potential level of cooling
performance for pulse refrigerators is far below that of vapor compression systems.
Thus, a rating of 1 (very low) was assigned for all cooling and refrigeration
applications due to the low cycle efficiency of present systems.
Closure
Although the pulse tube and thermoacoustic refrigeration have been demon-
strated to be workable methods of accomplishing heat lift experimentally, a technical
assessment indicates that neither system is a viable replacement for vapor compres-
sion in refrigeration and air conditioning applications, even though both can use
environmentally safe working materials. The principal reason these systems are not
good alternatives to vapor compression is their low COP when they are operated in
the temperature range used for refrigeration and air conditioning. When secondary
heat transfer loops are added to facilitate the transfer of heat between the system
and air, the COP of the system would be lowered even further.
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The numerical technical assessment ratings for pulse tube and thermoacoustic
refrigeration are given in Table 10.6.
Table 10.6: Technology assessment for pulse and thermoacoustic refrigeration.
Criterion
Rating (l=lowest, 5= highest)
Dom. AC.
Com. AC.
Mob. AC.
Dom. Ref.
Com. Ref.
State of art
2
2
2
2
2
Complexity
3
2
3
3
3
Size/Weight
3
3
2
3
3
Maintenance
3
3
3
3
3
Life
3
3
3
3
3
Energy Effic.
1
1
1
1
1
Thermoelectric Refrigeration
The theory underlying the direct conversion of electrical power to refrigeration
capacity was presented in Chapter 8. In this section, thermoelectric refrigeration for
commercial and domestic refrigeration and air conditioning will be assessed from a
practical standpoint.
Environmental Acceptability of the Systems
The solid, semiconductor working materials used in thermoelectric refrigerators
do not pose an ozone-depletion or direct global warming hazard.
Thermoelectric refrigerators operate silently; they have been considered for use
as an air conditioning system on submarines [76].
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State-of-the-Art
Thermoelectric refrigeration is currently marketed as a cooling/heating device
for transporting food and beverages. These small units are operated on 12-volt DC
electrical sources. Generally, the electrical power source is the electrical system of
the motor vehicle. When the polarity is connected in one direction, heat is accepted
from the interior of the insulated container and rejected to the environment, provid-
ing refrigeration for the contents. When the polarity is reversed, heat is accepted
from the environment and rejected within the container, heating the contents. Cole-
man Industries [77] and Igloo [78] market thermoelectric coolers with an advertised
maximum temperature difference of 22.2 C (40 F). In the 1950s, the Johnson Wax
building in Milwaukee, WI used a thermoelectric system for heating and cooling [76].
The system was incorporated into the wall panels of the building. On a smaller scale,
thermoelectric cooling has been used to cool electronic circuitry [47].
The present state-of-the-art for thermoelectric cooling systems is:
• The technology has been developed to the point that marketable systems can
be built, but with a low COP.
• The COP of thermoelectric systems is low even when the best working materials
are used (those containing tellurium). Tellurium is in short supply, limiting the
number of units which could be produced.
• To improve the cooling performance of thermoelectric systems, new, more ef-
fective, working material pairs must be developed.
Both the cooling performance and temperature lift could be increased by im-
proving the figure of merit, Z (as discussed in Chapter 8). Developing semiconductor
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material pairs with a higher value of Z would require developing mixtures which have
a low thermal conductivity, but high electrical conductivity. The most promising so-
lution to finding efficient working materials for thermoelectric refrigeration lies in
high temperature superconductors. This area of basic research would be expensive
with no assurance of success.
Based on the above factors, a rating of 3 (moderate) was assigned to the state-of-
the-art category for all air conditioning applications. A rating of 2 (low) was assigned
to domestic and commercial refrigeration applications due to the limited single-stage
temperature lift capability of existing semiconducting materials.
Complexity
Bismuth and tellurium are the primary elements commonly used in thermoelec-
tric refrigerator semiconductors [47]. Tellurium is a trace element which is extracted
from the waste generated when refining of copper and, to a lesser extent, gold. The
total annual production of tellurium is approximately 3.65 x 10^ kg. About 10% of
the production is consumed by the semiconductor industry, largely for the production
of thermoelectric modules. Since this material must be refined to a higher purity, the
net yield is even less from an already scarce source. The remaining 90% is consumed
by the steel and chemical industries for material processing.
Mathiprakasam et al. [79] estimated that approximately 400 standard thermo-
electric modules would be required to provide cooling for one automobile. Therefore,
if the total tellurium available for thermoelectric module production were dedicated
solely to the production of automotive air conditioners, only 20,000 automobile air
conditioners could be constructed per year. If the demand for thermoelectric refri-
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geration increased, the price would increase as well.
Thermoelectric refrigerators utilize a direct current (DC) power supply. An
added first cost would be incurred in providing a rectifier or generator system to con-
vert alternating current (AC) to DC for applications which do not have DC electrical
supplies readily available.
Manufacturing costs are expected to be approximately the same as for current
vapor compression systems. The technology to produce thermoelectric modules is
already in place, but increased production (assuming working material availability)
would require facility expansion.
Present thermoelectric devices rely upon natural convection and/or conduction
to exchange heat between the system and the source and sink. Hardware has been
proposed for transportation applications which would employ a circulating liquid
(water and glycol, for example) to transport heat from the source to the system.
Additional development costs would be expected if active thermoelectric systems
were to be marketed.
Based on the above factors, a rating of 1 (very low) was assigned to the com-
plexity category for domestic and commercial refrigeration applications and 2 (low)
for all cooling applications.
Size/Weight
Thermoelectric refrigeration modules are thin rectangles which can be incorpo-
rated into the walls of the building or cabinet to be cooled. The interior walls of
buildings are often composed of structural members, electrical wiring, plumbing, and
an outer wall covering. If portions of the inner wall covering were replaced with
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thermoelectric refrigeration modules, cooling could be provided without intruding
into the interior volume of the building. While this may be an advantage from a
functional perspective, it may well be a disadvantage from an aesthetic standpoint
since wall decoration would be limited.
The exterior walls of refrigeration cabinets are filled with insulation. If the
insulation thickness is not reduced, a portion of the interior cabinet volume would
have to be occupied by thermoelectric modules. A second option would be to provide
the refrigeration unit outside the cabinet and transport cooled air (or another fluid)
to and from the cabinet. In either case, the space-saving advantage of incorporating
the thermoelectric modules into the structure would be lost.
If thermoelectric cooling was used for mobile air conditioning, a substantial
weight and size penalty would be realized due to the electrical generation system
necessary to power the thermoelectric modules. For example, if the peak capacity of
the mobile air conditioning system was 10.55 kW (3 tons) and the peak temperature
lift was 23 C (41.4 F), the COP for an ideal system using semiconductor material with
a Z value of 0.003 would be 0.92. The electrical system would have to be capable of
supplying 11.47 kW power. In comparison, a 70-ampere alternator on an automobile
can supply slightly under 1 kW of DC electrical power.
Based on the above factors, a rating of 5 (very high) was assigned to the
size/weight category for domestic and commercial refrigeration and air condition-
ing applications. A rating of 2 (low) was given to the size/weight category rating for
mobile air conditioning applications due to the need for a large electrical generator
on board the motor vehicle.
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Maintenance
Operation and maintenance levels and expertise would appear to be less than
for vapor compression. Little preventive maintenance would be required. Failed
components would be replaced rather than repaired on-site and would be recycled to
recover the tellurium.
Since system repair would be a diagnosis and component interchange process,
technicians repairing thermoelectric refrigerators would require skills similar to those
needed to repair vapor compression systems.
Based on the above factors, a rating of 3 (moderate) was assigned to the mainte-
nance category for mobile air conditioning applications and 5 (very high) for domestic
and commercial air conditioning and refrigeration applications.
Useful Life
The life of thermoelectric refrigerators is expected to be long assuming a con-
stant, continuous DC power supply. If pumps are used to circulate heat transfer fluid,
pump life would have to be considered. It is expected that the life of thermoelectric
modules will exceed that of vapor compression systems.
The life of an electric generator for mobile applications would probably be shorter
than the life of reciprocating or rotary compressors currently used on automobiles.
This would be due to the life of the commutator brushes and sealed bearings normally
used in automotive electrical systems which is approximately 3 to 4 years (100,000
to 160,000 km traveled distance).
Thus, a rating of 5 (very high) was assigned to the useful life category for do-
mestic and commercial air conditioning and refrigeration applications. The useful
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life category rating for mobile air conditioning applications was 4 (high).
Efficiency
The energy cost for thermoelectric refrigerators will be high. The New York City
Transit Authority commissioned a study of the space conditioning requirements in
subway cars [80, 81].
Braking of subway trains is accomplished by reversing the DC electric drive
motors used to propel the cars, causing the motors to become electric generators. The
electric power generated during braking is dissipated through large electric resistors,
causing the train to decelerate. Heat generated in the resistors is rejected to the
environment.
It was proposed that the power generated during braking be used to operate a
thermoelectric system to provide cooling in the cars. The system was to be an active
system, in which the thermoelectric unit would be used to chill water which in turn
would be circulated to heat exchangers in the subway cars.
It was calculated that 66.8 kW (19 tons) of refrigeration were necessary to provide
cooling during peak demand and that 46 kW of electrical power would be available
from dynamic braking of the train. The COP would then have to be 1.45 if the
thermoelectric system were to supply the entire cooling load. The thermoelectric
system investigated was capable of providing 20.7 kW (5.9 tons) of cooling, i.e., the
COP was 0.45.
A combined vapor compression thermoelectric system was considered for the
same application. This system, while theoretically lower in operating cost than a
standard vapor compression air conditioning system, was estimated to be two times
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higher in first cost. It was not considered cost effective over a 20-year-life cycle.
Mathiprakasam et al. [79] conducted a study of thermoelectric technology for
air conditioning in automobiles. He concluded that the COP would be 0.42 for a 1.14
ton (4.0 kW) system. Furthermore, the power required to operate the system would
represent approximately 10% of the total power capability of the vehicle engine.
Thermoelectric refrigeration has a relatively low actual COP, particularly for
large temperature lifts, and therefore, the energy cost will be high. Therefore, the
efficiency criterion rating for all thermoelectric refrigeration and air conditioning
applications was 1 (very low).
Closure
Although thermoelectric refrigeration has been developed to a marketable stage
for recreational applications, its performance is currently too low to be used as a
general replacement for vapor compression refrigeration. The limited availability of
the element tellurium limits the extent to which thermoelectric refrigeration could
be applied even if first costs and energy costs were not a consideration.
The temperature lift of present thermoelectric refrigerators is limited. Current
recreational models advertise a temperature lift of about 22 C, although the theoret-
ical lift is higher. A lift of 75 C (from = —40 C to Tjj = 35 C) is theoretically
possible for a material pair with a figure of merit (Z) of 0.003; however, the cycle
efficiency would only be 0.01.
If materials can be developed which provide improved figures of merit, better
performance and temperature lifts will be possible. Thermoelectric refrigeration has
the benefits of:
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1. Silent operation
2. Low preventive maintenance
3. Space saving due to the ability to be incorporated into the members of the
structure
4. Simple operation and repair
The numerical technical assessment ratings for thermoelectric refrigeration are
given in Table 10.7.
Table 10.7: Technology assessment for thermoelectric refrigeration.
Criterion
Rating (l=lowest, 5= highest)
Dom. AC.
Com. AC.
Mob. AC.
Dom. Ref.
Com. Ref.
State of art
3
3
3
2
2
Complexity
2
2
2
1
1
Size/Weight
5
5
3
5
5
Maintenance
5
5
3
5
5
Life
5
5
4
5
5
Energy Effic.
1
1
1
1
1
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Magnetic Refrigeration
The theory underlying magnetic refrigeration is presented in Chapter 9. In this
section, the practical considerations of applying magnetic refrigeration to commercial
and domestic refrigeration and air conditioning will be assessed.
Environmental Acceptability of the Technology
Currently, the best working materials for use in magnetic refrigerators operating
at cooling temperatures above —43 C are gadolinium and gadolinium salts. Gadolin-
ium is rare-earth metal which reacts slowly with oxygen and water. It is non-toxic
and does not pose an ozone-depletion or direct global warming hazard.
Heat transfer systems would be necessary to exchange heat with the core during
the cycle. These systems would use a liquid with a low viscosity and high thermal
conductivity. This heat transfer technology is well developed. Non-toxic liquid-
materials which do not pose a threat to the environment are available.
Questions exist within the medical community regarding the health effects of
electromagnetic fields upon humans and animals [82, 83, 84]. Shielding to minimize
the risk of exposure to the electromagnetic fields generated by magnetic refrigeration
may be possible. Addition of shielding would increase the first cost and weight of
magnetic refrigeration systems.
The noise level for magnetic refrigerators is not expected to be higher than for
vapor compression systems. The source of noise would be liquid pumps for the heat
transfer loops in fixed core systems and the machinery to move the core in rotary
systems.
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State-of-the-Art
Although the existence of the magnetocaloric effect has been known since the
early 1930s, magnetic refrigeration at temperatures of —23 C and above is a relatively
new concept (1970s). Very little experimental work has been done at the higher
(—23 C and above) source temperatures. All prior experimental work was at source
temperatures in the low cryogenic range (approaching absolute zero).
Theoretically, ideal magnetic refrigeration cycles are capable of high cycle effi-
ciencies (0.60 to 1.00).
Experimentation has verified that small temperature lifts can be accomplished
at source temperatures above — 23 C. Technical problems in three basic areas must
be overcome in order to realize high COPs from magnetic refrigerators:
1. Regeneration (need to improve).
2. Magnets (need higher field strengths).
3. Materials (need higher temperature lift for a given magnetic field strength).
The practical magnetic field strength limit of current electromagnet technology
is approximately 7 teslas without cooling [71, 86]. Cooling of the magnets is re-
quired when they are operated at high field strengths to remove heat generated due
to electrical resistance in the coil windings and to lower the resistivity of the winding
material. Providing cooling for the magnets would create an additional cooling load
on the magnetic refrigeration system, thus reducing its cycle efficiency. If materials
were developed with high electrical conductivity at room temperature, the magnets
could operate at higher field strengths without cooling. The net effects would be
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to reduce the electrical work input to the magnetic refrigeration system and provide
magnets capable of operating at a higher field strength differential. Both improve-
ments would result in higher COPs.
Magnetic refrigeration systems will require a regenerator which is capable of
nearly ideal regeneration, due to the small temperature lift of the magnetocaloric
effect. Therefore, the regenerator must be capable of heat transfer at very low tem-
perature differences. At the same time, pumping losses due to fluid friction must be
kept to a minimum [64]. It is expected that regenerators for magnetic refrigeration
will be expensive to develop and manufacture for these reasons. Waynert et al. [87],
DeGregoria [88], and Brown [64, S5, 86] have investigated regenerator designs for
magnetic refrigeration. All three concluded that developing regenerators with high
effectiveness is the largest single technical challenge in designing a workable magnetic
refrigerator using gadolinium cores.
The COP of all magnetic refrigeration cycles could be improved if the slope
p\t-p
of the constant field lines, ^ (illustrated on the temperature-entropy diagram
in Figure 9.2), was greater for the working material used in the core. At present,
materials which exhibit this property relationship are unknown. The search for work-
ing materials with better inherent thermodynamic properties for high-temperature
magnetic refrigeration would be expensive, with no guarantee of success.
Manufacturing development costs are also expected to be high. Once basic
technology has been developed to raise the performance of the magnetic refrigerator
to an acceptable level, hardware must be developed to create a marketable system.
Manufacturing development costs would include design costs and tooling costs.
It is anticipated that the demand for high-efficiency electromagnets would exist in
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a variety of technological applications other than magnetic refrigeration. Therefore, a
portion of the hardware development costs could be shared by other industries; even
so, the manufacturing development costs are expected to be quite high compared to
vapor compression technology.
Based on the above factors, a rating of 1 (very low) was assigned to the state-
of-the-art category for all refrigeration and air conditioning applications.
Complexity
Magnetic refrigeration system costs due to hardware complexity are related to
the cost of the working material and system components. Waynert et al. [87] esti-
mated the cost of gadolinium at slightly over ^ . Approximately 1 kg of gadolinium
is required per kW of cooling. It was projected that the cost would decrease to
in large quantities. The greatest material cost would result from building electro-
magnets capable of delivering the high magnetic field strengths necessary to create a
significant magnetocaloric effect within the core.
Secondary heat transfer loops consisting of heat exchangers, pumps, piping, and
a fluid would be needed to transport heat to and from the magnetic core, and through
the regenerator. One heat exchanger would accept heat from the cooled space, and the
other would reject heat to the environment. Providing these secondary heat transfer
loops would involve an additional investment in heat exchangers, pumping equipment,
piping, and fluid. The net effect of the added heat-exchange interface between the
magnetic core and the thermal source and sink would be a reduction in the COP.
This is due to the additional irreversibilities introduced by the minimum approach
temperatures in the heat exchangers, pumping work, and heat losses throughout the
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piping and fluid storage system.
For mobile applications, an electrical source would have to be provided. If the
vehicle were not powered by an external electricity source (such as the third rail in a
mass transit rail system), an electric generation or storage system would have to be
carried on board. The capacity of this system would relate to the COP and cooling
capacity of the refrigeration system as well as the generating or storage capacity of
the electrical system. The need for an electrical system will be a major penalty for
mobile magnetic refrigeration applications in terms of system complexity, size and
weight, maintenance, and useful life.
Based on the above factors, a rating of 1 (very low) was assigned to the com-
plexity category for mobile air conditioning applications and 2 for domestic and
commercial air conditioning and refrigeration applications.
Size/Weight
No estimate of the size and weight of magnetic refrigerators relative to vapor
compression systems was found in the literature. However, it is clear that at least
one electromagnet capable of generating high magnetic fields would be necessary.
Electromagnets would be heavy due to the wire coils around the core. The secondary
heat transfer loops would also contribute to the size and weight of magnetic refriger-
ation systems. Finally, if shielding were required to make the system suitable for use
in the proximity of humans and animals, an additional cost penalty would exist.
Heat transfer loops containing a liquid, heat exchangers, and pumps would add
to both the size and weight of the system.
Thus, a rating of 1 (very low) was assigned to the size/weight category for mobile
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air conditioning applications and 2 for domestic and commercial air conditioning and
refrigeration applications.
Maintenance
It is expected that little maintenance would be required for the core, magnets,
and solid-state controls used in magnetic refrigeration systems. However, the sec-
ondary heat transfer loops and the regenerator may require some periodic mainte-
nance of the pumps, motors, heat exchangers, piping, and heat transfer fluid. This
maintenance could include periodic flushing of the system and replacement of the
fluid and rebuilding or replacing pumps and motors.
On-site repair of the actual magnetic system would most likely involve replace-
ment of subsystems such as controllers and magnets. These components would be
discarded or rebuilt at another location.
Once a magnetic refrigeration system was in service, operation and maintenance
levels and expertise would not appear to be markedly different from vapor compres-
sion systems. Little preventive maintenance is foreseen. When failure does occur, it
is expected that components would be replaced, rather than repaired on site. Re-
pair of electromagnets would probably be done on a regional or factory return basis.
Control devices, heat exchangers, and other minor components would be disposable.
Since system repair would be a diagnosis and component interchange process,
technicians repairing magnetic refrigerators would require skills similar to those needed
to repair vapor compression systems.
Based on the above factors, a rating of 2 (low) was assigned to the mainte-
nance for mobile air conditioning applications and 3 (moderate) for domestic and
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commercial air conditioning and refrigeration applications.
Useful Life
The life of magnetic refrigerators (both fixed core and displaced core systems)
is expected to be comparable to that of vapor compression systems. This conclusion
is supported by the observation that electromagnet applications generally have a
relatively long service life.
Magnetic refrigerators using the displaced core concept would require machinery
to either rotate or translate the core with respect to the magnets; this is common
technology which is also capable of long life. Pumps to circulate heat transfer fluid
could be off-the-shelf items of designs which have demonstrated high reliability. Given
the low reactivity of the core material and heat transfer fluid, corrosion related failures
are not expected to be a problem. Finally, heat transfer fluid can be circulated
at constant, low pressure. Therefore, failure of the piping, regenerator, and heat
exchanger walls due to fatigue will not occur since the pressure would be non-cyclic.
Secondly, burst-failures would not be a problem given the low operating pressure.
For mobile applications, the life of an electrical generation or storage system to
provide power for the air conditioning system must be considered. It is expected that
either a generating or storage system would have a shorter life than the refrigeration
system itself, particularly if the power-to-weight ratio of the electric power system
was maximized.
Based on the above factors, a rating of 2 (low) was assigned to the useful life
category for mobile air conditioning applications and 4 for domestic and commercial
air conditioning and refrigeration applications.
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Efficiency
Several studies have been performed to predict the performance of magnetic
refrigerators by using theoretical models. Chen et al. [71] projected a cycle efficiency
of 0.60 of the Carnot value for a magnetic refrigerator operating with a constant field
cycle between the source and sink temperatures of —13 C and 47 C. In Chapter 9, a
theoretical model of a combined cycle magnetic refrigerator was described. The cycle
efficiency was found to be 0.63 of the Carnot COP assuming a 5 C minimum approach
temperature between the source and sink and the system. Neither of these models
accounted for magnetic field, regeneration, or magnet cooling losses. In contrast, the
limited experimentation which has been done with magnetic refrigerators indicates
that the actual COP of present designs is very low. Brown [64] obtained a 47 C
temperature lift with no load (hence no COP) at room temperature. Steyert [65] •
measured a cycle efficiency of 0.26 for a rotary magnetic refrigerator operating with
a magnetic reversed Brayton cycle at room temperature; however, the temperature
lift was only 7 C. The efficiency criterion for magnetic refrigerators was rated 1 (very
low) for all cooling and refrigeration applications due to the low cycle efficiency of
present systems.
Closure
Clearly, considerable technical development at a relatively basic level remains
to be done before the magnetic refrigerator can be seriously investigated through
experimentation. Although the theoretical COP of the magnetic refrigeration system
is high, it is expected that the COP of an actual system would be much lower. The
reasons for the lower actual COP are:
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• The effectiveness of the regenerator is unlikely to exceed 95%.
• The actual system would include the secondary heat transfer loops which entail
heat losses and add pumping requirements.
Magnetic refrigeration is not well suited to mobile applications requiring an
on-board electrical system to provide electrical power due to the large additional
electrical generating capacity which would have to be added to the motor vehicle's
electrical system.
The numerical technical assessment ratings for magnetic refrigeration are given
in Table 10.8.
Table 10.8: Technology assessment for magnetic refrigeration.
Criterion
Rating (l=lowest, 5= highest)
Dom. AC.
Com. AC.
Mob. AC.
Dom. Ref.
Com. Ref.
State of art
1
1
1
1
1
Complexity
2
2
1
2
2
Size/Weight
2
2
1
2
2
Maintenance
3
3
2
3
3
Life
4
4
2
4
4
Cycle Effic.
1
1
1
1
1
Absorption Refrigeration
Absorption refrigeration uses heat transfer from a high-temperature source rather
than mechanical work as the energy input. The working material is the refrigerant
while the material with which it is in solution is the absorbent. The absorbent can be
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either in the liquid or solid phase. When separated from the absorbent, the refriger-
ant is generally in the liquid or vapor phase, depending upon which thermodynamic
process it is undergoing in the refrigeration cycle. In a simple single-stage absorp-
tion cycle, heat from an external source is supplied to the generator causing some
of the refrigerant to be vaporized from the binary mixture. The refrigerant vapor is
condensed to the liquid phase in a condenser by rejecting heat to the environment.
The liquid refrigerant is expanded by a throttling process through an expansion valve
or capillary tube before entering the evaporator. In the evaporator the refrigerant
accepts heat from the conditioned space. During the evaporation process, the re-
frigerant is vaporized. The refrigerant vapor is re-absorbed by the binary mixture
creating a strong solution in the absorber. Additional heat is rejected to the environ-
ment during the absorption process. A complete description of simple single-stage
absorption cycles can be found in the ASHRAE Handbook of Fundamentals [89] or
in thermodynamic textbooks such as Fundamentals of Engineering Thermodynamics
[30].
Environmental Acceptability of Absorption Refrigeration Systems
Traditional absorbent-refrigerant pairs are aqua-ammonia (H2O — NH%) and
lithium bromide-water (LiBr — H2O). Ammonia is mildly toxic but has no ODP
or direct GWP. Both lithium bromide and water are non-toxic and have no ODP or
direct GWP.
Other absorbent-refrigerant combinations have been studied. Iyoki and Uemura
[90] studied the theoretical efficiencies of absorption cycles using water as the refrig-
erant and multi-component absorbents which were mixtures of the inorganic salts
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lithium chloride, zinc chloride, calcium chloride, and calcium bromide as the ab-
sorbent. Iyoki and Uemura also considered adding ethylene glycol (C2HQO2) to the
lithium bromide-water pair. None of these materials have an ODP or a direct GWP.
Procedures for the proper disposal of used material would have to be established to
prevent groundwater contamination.
Organic absorbent-refrigerant pairs have also been studied. Huber [91] tested
a heat pump using HCFC-22 as the refrigerant and DEGDME [(diethylene glycol
dimethyl ether, (CH^OCH^C#2)2^)]- Although HCFC-22 is slated for phase-out
due to its high chlorine content and direct GWP, the task of finding an environmen-
tally acceptable replacement organic refrigerant for use in absorption refrigeration
remains.
State-of-the-Art
The aqua-ammonia refrigeration cycle predates vapor compression systems. Ba-
sic technologies used in liquid absorption refrigeration (such as boiling and conden-
sation heat transfer) are well developed.
The level of development of technology which is specific to liquid absorption refri-
geration differs with absorbent-refrigerant pair. Aqua-ammonia refrigeration systems
have not been commercially produced on a large scale for 20 years. Consequently, lit-
tle development work has been done. Development has continued on lithium bromide-
water absorption (LiBr — #2O) systems for chiller applications. Hitachi [92] man-
ufactures 100- to 1500-ton LiBr — H2O chillers which are available as direct-fired,
steam heated, or units heated with waste-heat. The waste heat driven system makes
use of exhaust gases from gas turbines, diesel engines, and other heat sources with
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an outlet temperature of 288 C or higher.
Sanyo [93] produces LiBr — fyO chillers ranging from 35 kW to 4050 kW capac-
ity. These systems use a double-effect generation cycle in which the vapor from the
diluted absorbent in the high temperature generator is used to heat the intermediate-
strength absorbent in the low temperature generator and boil off additional refriger-
ant from the intermediate-strength mixture.
More complex absorption systems using multiple stages or multiple effects have
been developed. Siddiqui and Riaz [94] have developed a two-stage absorption cycle
which can be operated using biogas (principally methane) as the fuel. The first
stage uses a lithium bromide-water refrigerant/absorbent pair. Heat from the second
stage absorber is accepted by the first stage evaporator. The second stage uses the
ammonia-water refrigerant/absorbent pair. If the temperature of the re-absorption
process is too low, the refrigerant can form solid crystals. This condition is generally
considered to be a problem; however, a system in which the solid refrigerant crystals
are allowed to form in a slurry and the latent heat of fusion is utilized in the cycle
has been patented [95].
Liquid absorption systems can take many configurations. They can have multiple
stages and multiple effects. Each stage could utilize a different refrigerant-absorbent
pair. With respect to the refrigerant-absorbent pairs themselves, much work remains
to be done to determine:
• Which pairs, both inorganic and organic, have the highest COP for a given
condensing and evaporation temperature.
• The ODP and direct GWP of the pair.
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• Toxicity of the pair.
Based on the above factors, a rating of 5 (very high) was assigned to the state-of-
the-art category for commercial air conditioning applications. A rating of 4 (high) was
given to the state-of-the-art category rating for domestic air conditioning, domestic
refrigeration, and commercial refrigeration applications. A rating of 2 (low) was given
to the state-of-the-art category for mobile air conditioning applications.
Complexity
Basic liquid single-stage absorption systems require a generator, condenser, ex-
pansion device, evaporator and absorber. Other necessary equipment includes liquid
pumps, piping, heat input system, and a temperature control system. Multiple stag-
ing and/or multiple effect systems could be used in absorption systems to:
1. Improve the COP of the systems.
2. Enable the systems to operate with the desired temperature lift.
Multiple staging and/or multiple effect cycles would require additional system com-
ponents, resulting in higher first costs.
In some systems, the potential for corrosion of components could be high due
to the reactive nature of the refrigerant or the absorbent used in the system. The
materials used in the system must be corrosion resistant for the particular refrigerant-
absorbent pair chosen. For example, copper and copper alloys such as brass or bronze
are susceptible to corrosion when exposed to ammonia. Intergranular corrosion is also
known to occur in cast iron after prolonged exposure to an ammonia atmosphere.
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Corrosion will lead to eventual failure of the component, rendering the system in-
operable. Therefore, none of the components selected for use in an aqua-ammonia
system should include copper-based or cast iron materials. This would include small
off-the-shelf items such as pipe fittings. Corrosion-related material problems could
be unique to a particular refrigerant-absorbent pair. The need for corrosion resistant
materials will add to the first costs of the system.
Lithium bromide-water absorption systems reject heat from the absorber and
condenser through a cooling tower. The cooling tower would add to the first cost and
maintenance costs of the system.
Operating pressure would be another consideration related to the first costs and
maintenance costs of the system. Generators operating at high pressures could fall
under the ASME direct-fired pressure vessel code. Certification of the generator to
assure that the design and construction was in compliance with the pressure vessel
code would add to the first cost of the system. Periodic hydrostatic testing as required
by the code would add to the maintenance costs.
Based on the above factors, a rating of 3 (moderate) was assigned to the complex-
ity category for domestic cooling applications and all refrigeration applications. A
complexity rating of 4 (high) was given to commercial cooling applications since these
systems are usually more complex (relatively speaking) than domestic refrigeration
applications. A rating of 2 (low) was given to mobile cooling applications.
Size/Weight
In general, absorption systems are characterized by a relatively large size and
high weight per ton of cooling. Single-stage systems operating with a large tempera-
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ture lift have a correspondingly high operating pressure, requiring heavier construc-
tion of the high pressure side of the system. If multistaging is used to accomplish
the same temperature lift, the number of components is increased by the number of
stages. Multistaging adds to both the size and weight of the refrigeration system.
Multiple effect systems have an additional generator and heat exchanger for each
"effect" added to the system to raise the COP. Generally, for a given temperature
lift, capacity, and refrigerant-absorbent pair, a system with a higher COP would also
have a correspondingly larger size and greater weight.
Liquid absorption systems using water as the refrigerant require a cooling tower.
Although these systems would be used in large commercial air conditioning systems
(and possibly shipboard), finding a location either on or adjacent to the structure
could be an important consideration in some applications.
Thus, a rating of 3 (moderate) was assigned to the size/weight category for
domestic and commercial refrigeration and air conditioning applications. A rating
of 2 (low) was given to the size/weight category rating for mobile air conditioning
applications.
Maintenance
Maintenance needed for liquid absorption refrigeration systems would include
periodic repair of pumps, repair of leaks, and service of the heating system. The
system would require periodic inspection for internal and external corrosion. High
pressure systems would require periodic inspection, testing, and recertification of the
generator. Cooling towers would require additional maintenance, including repair
of circulating pumps and fans, cleaning water filters, and treatment of coolant to
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control bacteria, fungi, and other biological growth in the tower. A rating of 4 (high)
was assigned to the maintenance category for commercial air conditioning. The
maintenance category rating for domestic air conditioning as well as domestic and
commercial refrigeration applications was 3 (moderate). The mobile air conditioning
maintenance category rating was 2 (low).
Useful Life
The useful life of liquid absorption refrigeration systems would be long assuming
that proper materials had been chosen and proper maintenance had been performed.
The primary driving component of a liquid absorption system is the high temperature
generator. These units do not fail as a result of wear stemming from the relative
motion of moving parts or mechanical stresses, as is the case with reciprocating or
rotary compressors. The principal causes of failures in the system would be:
1. Corrosion.
2. Erosion.
3. Cracks.
Corrosion can be minimized by the selection of materials and the refrigerant-absorbent
pair during the design of the system and by maintenance to stop corrosion after the
system has been placed in service. Erosion can be minimized by keeping the working
fluid free of particulates and by assuring that a high enough pressure is maintained at
the liquid pump inlet to prevent cavitation. The occurrence of cracks due to thermal
and mechanical stresses could be minimized by proper design and construction.
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In summary, an absorption refrigeration system represents a high first cost per
kilowatt investment. If a major component of the system fails, replacement of the
component can be justified due to the high replacement cost of the entire system. The
primary components are not as subject to mechanical wear as mechanically driven
refrigeration systems. If proper maintenance is performed throughout the life of the
system, the useful life should be long.
Based upon the above factors, a rating of 4 (high) was assigned to the useful
life category for commercial air conditioning. A useful life category rating of 3 (mod-
erate) was given to domestic refrigeration applications and domestic and mobile air
conditioning applications. A rating of 2 (low) was assigned to the useful life category
for mobile air conditioning applications.
Efficiency
The ideal absorption refrigeration system would be a Carnot refrigerator driven
by a Carnot heat engine. Figure 10.1 illustrates an ideal absorption refrigeration
system. If it is assumed that the condenser and absorber reject heat to the sink at
Tjj, the COP for the ideal absorption cycle can be written as
(10.1)
where
T£ = the absolute temperature of the source
th = the absolute temperature of the sink
Tq = the absolute temperature of the generator.
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Figure 10.1: Schematic diagram of an ideal absorption refrigeration
system.
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The theoretical COP of absorption refrigeration systems has been studied. Iyoki
and Uemura [90] reported calculating theoretical COPs ranging from 0.8 to 0.88 for
single-stage absorption cycles operating at the following temperatures:
TL = 8C
Th = 30 C
Tq = 57 C
For double-effect absorption cycles, Iyoki and Uemura calculated COPs ranging from
1.3 to 1.7 for the following operating temperatures:
TL = 8C
Th = 30 C
Tg1 = 117 C to 127 C
TG2 = 80 C
Several refrigerant-absorbent pairs were assumed in their study, all of which used
water as the refrigerant. The absorbent mixtures were lithium-based with differing
mixtures of other substances added.
Siddiqui and Riaz [94] modeled a two-stage system using the water-lithium bro-
mide pair in the first stage and ammonia-lithium trioxide in the second stage. A
theoretical COP of 0.55 was calculated for Tjj= —10 C. For T^ = —25 C, a COP
of 0.48 was calculated. The other system temperatures were:
Ta = 25 C
Th = 35 C
TG1 = 90 C
tG2 = 100 C
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where T4 is the absorber temperature and Tq^ and Tq2 are the temperatures of
the first and second effect generators, respectively.
DeVault and Marsala [96] determined a theoretical cooling COP of 1.41 for a
triple-effect aqua-ammonia cycle operating at:
Tl = 2.2 C
TA1 = 75 C
tA2 = 110 C
Th = 28 C
Tg1 = 116 C
TG 2 = 219 C
where Tai and T42 are the first and second effect absorber temperatures, respec-
tively.
Actual COPs for liquid absorption refrigeration systems in service reported in
the literature include:
• Sanyo [93] advertises a COP of 0.96 for their double-effect absorption chillers
(No operating temperatures were reported).
• Hitachi [92] advertises a COP of 1.21 for their two-stage chiller heated by steam
(No operating temperatures were reported).
A rating of 5 (very high) was assigned to the efficiency category for all refriger-
ation and air conditioning applications.
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Closure
Liquid absorption refrigeration cycles using water as the refrigerant can not be
used for most refrigeration applications due to the high freezing temperature of water
(0 C).
As compared to absorption systems which operate at source temperatures above
0 C, absorption systems which are capable of operating at temperatures below 0 C
are generally characterized by:
1. Higher generator temperatures.
2. Lower COP.
3. Larger size and weight per kilowatt of cooling capacity due to the heavier con-
struction needed to enable the system to operate at high pressures or due to
multistaging.
4. Higher first cost.
The numerical technical assessment ratings for absorption refrigeration are given
in Table 10.9.
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Table 10.9: Technology assessment for absorption refrigeration.
Criterion
Rating (1= lowest, 5= highest)
Dom. AC.
Com. AC.
Mob. AC.
Dom. Ref.
Com. Ref.
State of art
4
5
2
4
4
Complexity
3
4
2
3
3
Size/Weight
3
3
2
3
3
Maintenance
3
4
2
3
3
Life
3
4
2
3
3
Energy Effic.
5
5
5
5
5
Solid Sorption Refrigeration
Solid absorption and adsorption are two alternative refrigeration technologies
which utilize similar hardware, but the manner in which the refrigerant bonds to the
sorbent differs. Both technologies use heat transfer from a high-temperature source,
rather than mechanical work, as the energy transfer into the system. Solid systems
using heat from direct-fired, steam, engine exhaust gas, and solar sources have been
proposed [97].
Solid absorption refrigeration utilizes refrigerant-absorbent pairs which are in
the solid phase after absorption. The refrigerant fluid is chemically bonded with the
absorbent to form a third compound. When the compound containing the absorbed
refrigerant is heated during generation, refrigerant vapor is released by breaking the
chemical bonds. Therefore, the composition of the solid compound changes due to
the removal of the refrigerant.
In solid adsorption, the refrigerant molecules bond physically, rather than chem-
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ically, to the surface of the adsorbent when it is cooled below a given temperature.
When the adsorbent is heated, the physical bonds between the adsorbent and refrig-
erant are broken causing the refrigerant vapor to be released.
Both solid sorption cycles use a batch process in which multiple canisters are
alternately heated and cooled. The canisters serve as both generators and sorbers in
the system, depending on their temperature.
Once the refrigerant has been liberated from the sorbent by heating the canister,
the most common sorption cycle (for both adsorption and absorption) is as follows:
1. The refrigerant vapor is cooled to the liquid state in a condenser.
2. The pressure of the refrigerant is then lowered by a throttling process, and the
refrigerant is expanded in an evaporator.
3. The refrigerant vapor is then re-combined with the solid sorbent compound in
another canister which has been cooled.
4. When the desorbing canister is exhausted and the absorbing canister is filled,
valves switch the system to another pair of canisters in the piping network
and the cycle is repeated. The canisters which were just taken off line begin a
cooling or heating process (depending upon whether they are now charged with
refrigerant or empty) to prepare them for another turn in the cycle [98, 99].
An alternative solid absorption cycle could be achieved with some refrigerant-
absorbent pairs without condensing the vapor. After liberating the refrigerant by
heating a canister, the temperature of the gaseous refrigerant would be lowered by
passing it through a heat exchanger at ambient temperature. The cooled refrigerant
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gas would then be re-absorbed in a discharged (empty) canister which had also been
allowed to cool. During this absorption process, heat would be accepted by the
canister from the surroundings due to the endothermic chemical reaction occurring
as the refrigerant and absorbent re-combine.
Douss and Meunier [100] developed a novel cascaded adsorption cycle using two
water-zeolite stages and a methanol-activated carbon third stage to enable the system
to operate at temperatures below 0 C. Jones [101] was granted a patent for a multiple
canister solid sorption refrigeration system.
Environmental Acceptability of Solid Sorption Refrigeration Systems
Solid absorption uses ammoniates or oxides of materials such as calcium. These
compounds have an affinity for water. When heated, the ammoniates release am-
monia vapor as the refrigerant. Calcium-based compounds release water as the re-
frigerant when heated. Neither solid refrigerant-absorbent pair contributes to ozone
depletion or direct global warming.
The three adsorbents most commonly used in adsorption systems are: zeolites,
silica gel and activated carbon. These materials do not have an ODP or direct GWP.
Adsorption refrigerants which have been proposed or tested are:
• Water
• Ammonia
• Methanol
• HFC-134a
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• Blends of HFC-134a, HFC-152a, and HCFC-124.
State-of-the-Art
The technology used in solid sorption refrigeration is well known but presently
is immature. Some experimentation has been done, but no working prototypes of
refrigeration systems for the marketplace have been built. The primary areas of
current solid sorption development are canister design, canister heating and cooling
system design and system development which could provide continuous, rather than
batch refrigeration.
For both absorption and adsorption, the rate at which canisters release and ac-
cept refrigerant is a function of the uniformity of the heat transfer within the canister.
Portions of the canister volume with low heat flux will have a correspondingly low
rate of sorption and desorption. Therefore, methods of enhancing the heat transfer
into and out of the canisters must be improved.
The maximum refrigerant capacity of a canister (as well as the rate of refrigerant
release and acceptance) is a function of the sorbent surface area to volume ratio.
Methods of increasing the ratio through sorbent particle shape and porosity are of
current interest [102].
Most of the proposed solid sorption refrigeration system concepts use a circulat-
ing fluid to heat and cool the canisters. Recovering heat to be used to heat another
canister which will be active in a future batch cycle will be important in improving
the COP of solid sorption cycles.
Further technology development for solid absorption refrigeration would include:
• Identifying additional refrigerant and absorbent pairs which are environmen-
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tally acceptable
• Improving the efficiency of the desorption and absorption processes
• Developing an improved method of connecting absorbing canisters with desorb-
ing canisters
t Improving the heat transfer within the canister volume during heating and
cooling.
Based on the above factors, a rating of 2 (low) was assigned to the state-of-the-art
category for all applications.
Complexity
Solid sorption systems will require multiple canister pairs if the systems are to
operate continuously. Canisters will require some method of providing uniform heat
flux within the interior volume. Fins, mesh, or some other heat transfer enhance-
ment method will be necessary. The sorbent material would need to be uniformly
distributed over the heat transfer surface within the canister. Like the catalytic con-
verter used in automobile exhaust systems, this technology may be expensive when
first introduced, but become cheaper over time.
Three piping and valve systems would be needed. One would direct the flow of
refrigerant to and from the canisters, the second would direct the heating fluid to
the generating canister and the third would direct the cooling fluid to the absorbing
canister. Controls would be necessary to direct the flow of each of the fluids to
different canisters as they reached the fully desorbed or absorbed charge condition.
The cooling capacity of the system would vary with the charge state of the desorbing
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and absorbing canisters. The initial desorption and absorption processes would occur
at a faster rate initially and then slow as the fully charged condition is approached.
Therefore, a sophisticated logic system would be required to deliver a nearly constant
cooling capacity.
Condensers, evaporators, and expansion valves currently used for vapor com-
pression systems could be used with some refrigerants. This would be true if organic
refrigerants which are also used in vapor compression systems were chosen.
In summary, the complex piping and control system for a continuous cooling
solid absorption refrigeration system could be expensive, particularly for small capac-
ity units since the cost of valves and controls do not vary appreciably with size. Solid
sorption systems which provide intermittent (batch) cooling would not require mul-
tiple canisters, complicated valve networks, or sophisticated controls. Consequently,
they can be produced at a much lower cost.
Based on the above factors, a rating of 3 (moderate) was assigned to the com-
plexity category for all cooling and refrigeration applications.
Size/Weight
System size would depend upon the cooling capacity and refrigerant flow rate
of the canisters. It would also depend upon the sorbent material density in the
canister. Since adsorption is a process in which the refrigerant molecules are attached
to the surface of the adsorbing material, the surface area must be large to achieve a
reasonable refrigerant capacity and flow rate per canister. For efficient heat transfer
within the canister during heating and cooling, a minimum temperature difference
between the heat transfer fluid and the canister surface would be necessary; thus,
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sorption canisters are likely to be large.
Thus, a rating of 3 (moderate) was assigned to the size/weight category for
domestic and commercial refrigeration and air conditioning applications. A rating
of 2 (low) was given to the size/weight category rating for mobile air conditioning
applications.
Maintenance
Valve failure may be a potential maintenance problem in continuously operating
solid sorption refrigeration systems. Given the complexity of the three piping and
valve systems, troubleshooting the system to determine the location of a malfunc-
tioning valve could be a time consuming process. Refrigerant leakage from the pipe
fittings, valves, and canisters would necessitate periodic recharging of the system
with refrigerant. Jones [103] reported that long-term corrosion is a common failure
mode for solid absorption canisters.
Alternate heating and cooling of the heat exchanger in the canister could result
in two thermal stress-related failure modes:
• The bond between the sorbent material and the heat exchanger surface may
fail, reducing contact (and thereby increasing thermal resistance between the
two materials) or causing the sorbent material to fracture and flake way.
• Heat exchanger tube cracking resulting in leaks which would be very difficult
to repair.
Solid sorbent canisters may fail due to mechanical vibration from the surround-
ings (in mobile applications, for example). Vibration could cause cracks which cause
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leaks. Vibration could also cause the sorbent material to detach from the heat ex-
changer surface in the canister.
Sorbent materials may have a finite life linked to the number of cycles they have
undergone and may require periodic replacement. Maintenance costs for solid sorbent
refrigeration are likely to be high.
A rating of 3 (moderate) was assigned to the maintenance category for all air
conditioning and refrigeration applications.
Useful Life
If the canisters represent a large portion of the first cost of the solid sorption
refrigeration system, then the life of the system is expected to be short. On the other
hand, if the canisters could be made inexpensively and periodic replacement of the
canisters was an accepted maintenance procedure, then the life of the refrigeration
system would be based upon the life of other system components. Considering the
system life to be that of the valves, control system, piping, pumps, evaporator, con-
denser and the heating unit, the useful life would be somewhat shorter than that of
a vapor compression refrigeration system.
A rating of 3 (moderate) was assigned to the useful life category for all air
conditioning and refrigeration applications.
Efficiency
The ideal COP for solid absorption and solid adsorption systems would be that
of a Carnot refrigerator driven by a Carnot heat engine. If it is assumed that the
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condenser and absorber reject heat to the sink at Tfj, the COP for ideal solid sorption
cycles would be given by Equation 10.1.
Some theoretical COPs have been reported for solid sorption refrigeration sys-
tems. Douss and Meunier [100] reported a theoretical COP of 1.06 for their cascading
cycle solid adsorption refrigeration system. The temperatures were:
TL = 2C
Th = 30 C
Tq = 250 C
Critoph [102] predicted a COP of 0.57 for a single-stage solid absorption cycle
operating with a methanol-activated carbon/refrigerant adsorbent pair. The cycle
was assumed to operate without heat recovery.. The operating temperatures were
assumed'to be:
Tl = -10 C
Th = 25 C
Tq = 100 C
Jones [103] reported a predicted COP of 1.0 for an adsorption system studied by
Tchernev in 1988. The theoretical system used water as the refrigerant and operated
at the following temperatures:
Tl = 4.4 C
Th = 37.8 C
Tq was not given.
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Jones [104] predicted a cooling COP of at least 0.92 for a heat pump operating
with a 12-canister regenerative solid adsorption system using the HFC-134a and zeo-
lite refrigerant-adsorbent pair. A cooling COP of 1.47 was predicted for a six-canister
regenerative system using the water-zeolite pair. The operating temperatures were
assumed to be:
Tl = 4.4 C
Th = 37.8 C
Tq = 204.4 C
The efficiency category rating for all solid sorption air conditioning applications
was 3 (moderate). The efficiency category rating for solid sorption refrigeration
applications was 4 (high).
Closure
The numerical technical assessment ratings for solid sorption refrigeration are
presented in Table 10.10.
Table 10.10: Technology assessment for solid sorption refrigeration.
Criterion
Rating (1= lowest, 5= highest)
Dom. AC.
Com. AC.
Mob. AC.
Dom. Ref.
Com. Ref.
State of art
2
2
2
2
2
Complexity
3
3
3
3
3
Size/Weight
3
3
2
3
3
Maintenance
3
3
3
3
3
Life
3
3
3
3
3
Energy Effic.
3
3
3
4
4
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Vapor Compression Refrigeration
A technical assessment of vapor compression refrigeration systems is presented
to provide a measure of comparison for the alternative refrigeration cycles which have
been studied during this project.
The vapor compression refrigeration cycle uses mechanical work to drive the
cycle. The source of the work input for domestic and commercial refrigeration and
air conditioning is usually an electric motor. Power to operate a mobile air conditioner
is taken from the motor vehicle's engine. The vapor compression cycle is currently
used for all of the refrigeration and air conditioning applications considered in this
study.
A detailed description of the basic vapor compression cycle can be found in
references such as:
• The Fundamentals of Engineering Thermodynamics [30].
• ASHRAE Handbook of Fundamentals [89].
• Modern Refrigerating Machines [29].
Environmental Acceptability of Vapor Compression Systems
The most common working fluids for vapor compression refrigeration have been
CFC-11, CFC-12, HCFC-22, CFC-114, CFC-502, and CFC-13 (It is acknowledged
that other refrigerants have been used in some applications). CFC-12 has been used
almost universally in domestic refrigerators and mobile air conditioning applications.
HCFC-22 is the principal refrigerant for domestic air conditioners. CFC-12, HCFC-
22, CFC-502 and CFC-13 are used in commercial vapor compression refrigeration.
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CFC-11 and CFC-114 are used in vapor compression chillers. Alternative refrigerants
which can be used in vapor compression systems and which have no (or very low)
ODP and low (to moderately low) direct GWP have been synthesized. The ther-
modynamic properties of many of these new refrigerants are similar to those of the
refrigerants which they replace. Consequently, little or no modification of existing
vapor compression system designs is necessary to utilize these refrigerants.
State-of-the-Art
Vapor compression technology for domestic, commercial, and mobile refriger-
ation and air conditioning applications is mature. Even so, some opportunities exist
to further improve performance:
• New compressor designs. Oil-free, variable displacement, and linear compres-
sors could offer higher compressor efficiencies.
• Heat transfer enhancement in the evaporator and condenser.
• New refrigerants.
• Variable speed motors.
• Check valves to prevent refrigerant migration between cycles.
• In the case of domestic refrigeration, two evaporator systems.
The use of nonazeotropic refrigerant mixtures (NARMs) is being investigated.
Pure refrigerants and azeotropic mixtures condense and evaporate at a constant tem-
perature. Large temperature differences exist between the air and refrigerant sides of
203
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the heat exchanger, resulting in the introduction of irreversibilities. NARMs, on the
other hand, condense and evaporate with a temperature glide. The temperature of
the refrigerant exiting the heat exchanger is different from that of the entering fluid.
If the refrigerant and the air (or other fluid) are passed through the heat exchangers
in counterflow, the temperature difference between the two fluids is reduced, thereby
reducing the irreversibilities during heat transfer.
Based on the above factors, a rating of 5 (very high) was assigned to the state-
of-the-art category for all applications.
Complexity
With the possible exception of cabinetry or air handling units, the compression
system is the most complex and expensive component in a vapor compression refri-
geration or air conditioning system. The expansion device, evaporator, and condenser
are relatively simple and inexpensive devices to manufacture.
There is a high degree of interchangeable technology (transfer) between the man-
ufacturing of vapor compression refrigeration systems and the manufacturing of many
other items used in modern society. Liquid-to-air heat exchangers, similar to those
used as vapor compression system evaporators and condensers, are used in the trans-
portation, chemical process, and heat power industries. Reciprocating machinery is
used not only on refrigeration compressors, but in internal combustion engines, liquid
pumps, etc. Reciprocating, screw, and centrifugal machines are used for compressing
air and other gases in a wide variety of commercial and industrial applications.
The first cost-per-kilowatt of refrigeration for a vapor compression system is low
when compared to other refrigeration technologies. The primary reason is industry's
204
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present level of expertise in building the components used in vapor compression refri-
geration. A second reason is that the systems are built of commonly used materials
like cast iron, steel, and aluminum.
Based on the above factors, a rating of 4 (high) was assigned to the complexity
category for all cooling and refrigeration applications.
Size/Weight
On a size and weight-per-unit of refrigeration basis, vapor compression refriger-
ation and air conditioning systems are relatively small and compact. The reasons
are:
• Vapor compression systems require relatively few components. Unlike the mag-
netic refrigeration and reversed Stirling cycles, secondary heat transfer systems
are not needed to transport heat between the refrigeration system, the cooled
space, and the environment.
• The primary heat has already been converted to mechanical work by a power
plant (either electrical generating or an internal combustion engine). Therefore,
the generator used in sorption or ejector cycles is not required.
• Although the refrigerants themselves have a high molecular weight, the refrig-
erant charge-per-unit of refrigeration is small. A secondary material such as a
solid or liquid sorbent is not required.
• The organic refrigerants used for vapor compression systems are non-reactive.
205
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• The condensing and evaporating pressures of the system are low enough to
allow the use of lightweight materials (like aluminum) and thin walls in the
heat exchangers and piping.
• The organic refrigerants are dielectric; electric motors can be entirely enclosed
with the compressor.
A rating of 4 (high) was given to the size/weight category for all applications.
Maintenance
Domestic refrigerator vapor compression systems are hermetically sealed, i.e., the
compressor and its drive motor are sealed within one enclosure. The recommended
preventive maintenance is to periodically clean the air-side surface of the condenser
coils to remove dust. Domestic window air conditioners also use sealed refrigeration
systems. Periodic maintenance for vapor compression refrigeration systems would
include cleaning the air-side surfaces of the condensers and evaporators.
Central air conditioning systems have a condensing unit (condenser) and com-
pressor mounted outside the building. The piping system connecting the condensing
unit to the evaporator (located in the air handling unit) often contains fittings which
can leak. Leak repair and recharging the system with refrigerant may be necessary
over the life of these systems. As with window units, periodic cleaning of the evapo-
rator and condenser surfaces is a preventive maintenance function.
Small commercial refrigeration and air conditioning systems are often configured
like their domestic counterparts. Consequently, the causes of refrigerant release from
these systems are the same as for the domestic systems (leakage from the condenser,
evaporator and piping).
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Large commercial systems often use compressors which are shaft-driven. Re-
frigerant leakage can occur from the seal/shaft interface, releasing refrigerant to the
environment. Large commercial systems use piping with joints which are also poten-
tial causes of refrigerant leaks.
Mobile air conditioners also use shaft-driven compressors and pipe joints. The
shaft seals and pipe joints are potential refrigerant leakage points. Mobile systems are
also subjected to engine and road vibration. Hoses are used to connect the compressor
to the condenser and evaporator, and these hoses are often a leak source. Leaks can
develop in evaporators and condensers due to vibration-induced cracks. Leaks can
also develop in condensers due to contact with foreign objects. Finally, the entire
system is subject to leaks as a result of a collision or other damage.
The primary failure mode for vapor compression refrigeration systems used in
all applications is leakage of refrigerant to the surroundings. The leakage path can
be through the heat exchangers (evaporator and condenser) and the piping used to
connect the system components. For systems using non-hermetically sealed compres-
sors, the seals around the input shaft are another leakage path. The frequency of
refrigerant leaks developing in evaporators, condensers and piping is small and the
rate of refrigerant leakage from the shaft seals of non-hermetically sealed compressors
is usually very small. In general, vapor compression refrigeration systems are charac-
terized by low maintenance. A rating of 5 was assigned to the maintenance category
for domestic and commercial air conditioning and refrigeration applications. A rat-
ing of 4 was given to the maintenance category for mobile air conditioning, domestic
refrigeration,and commercial refrigeration applications.
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Useful Life
Studies have been conducted regarding the median life of hermetically sealed
compressors used in commercial and residential vapor compression heat pump appli-
cations. Ross [105] analyzed service work orders for 2820 sealed compressors used
in cabinet-type perimeter heat pumps used in office buildings. Based upon these
data, he found that 94% of the compressors remained in service after 9.3 years. Ross
projected a median service life (50% failure rate) of 47 years. Ross also examined the
service work orders for 518 larger hermetically sealed compressors used in what he
termed 'core' heat pumps. He projected a median compressor service life of between
11.8 and 18 years.
Bucher et al. [106] analyzed the service records for 2184 residential vapor com-
pression heat pumps. The median service life was 14.5 years. These data also indi-
cated that only 4.6% of the heat pumps had multiple compressor replacements.
Based upon the above factors, a rating of 5 (very high) was assigned to the useful
life category for all air conditioning and refrigeration applications.
Efficiency
The COP for an ideal vapor compression cycle with an isentropic expansion
process would be the Carnot COP. Even though nearly isothermal heat acceptance
and rejection can be achieved, some practical characteristics of the hardware prevent
approaching the ideal cycle condition:
1. Compressing two-phase mixtures of vapor and liquid can damage mechanical
compressors. Therefore, a certain amount of superheating is required to assure
that only refrigerant vapor enters the compressor.
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2. Isentropic compression cannot be achieved due to heat transfer, fluid friction,
and mechanical friction in the compressor.
3. The expansion process is not isentropic.
4. Fluid friction causes additional pressure losses in the piping and heat exchang-
ers.
Literature regarding the theoretical COP for vapor compression systems was
studied. Bare et al. [107] studied the theoretical performance of 15 NARMs in a
two-evaporator domestic refrigerator/freezer using a modified version of the single-
evaporator refrigerator cycle (SERCLE) model. The COPs for these mixtures were
compared with a baseline case using a single evaporator and CFC-12. They de-
termined that the most promising NARMs exhibited a COP 30% higher than the
baseline case. Increasing the evaporator area by 20% resulted in an additional COP
improvement of 2.4% to 2.7%. A compressor efficiency of 55% was assumed for all
cases. The temperatures were:
TLl = 3.35 C
TL2 = -20 C
Th = 32.2 C
where Tli and TL2 were the temperatures of the freezer evaporator and refriger-
ator evaporator, respectively. Radermacher and Jung [108] modeled a residential
air-conditioner using binary and ternary refrigerant substitutes for HCFC-22. Their
model assumptions were:
1. The compressor efficiency was 70%.
2. Pressure drops were neglected.
209
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3. No evaporator subcooling.
4. No condenser superheating.
5. Tl = 11.1 C.
6. Th = 35 C.
For the ternary blend consisting of 20% R-32, 20% R-152a, and 60% R-124, a theo-
retical COP of 3.8 was calculated. This was a 13.7% improvement over the baseline
case using R-22.
Braun et al. [109] modeled the performance of a 19.3 MW (5500 ton) variable-
speed chiller at the Dallas/Fort Worth airport. The model involved the simultaneous
solution of a system of mass, momentum, and energy balance equations written for the
components of the system. Assuming a mechanical efficiency of 91% and a polytropic
compressor efficiency of 82%, they determined a COP of 5.0 for a 28 C temperature
lift at full chiller load using the refrigerant R-500.
Bare [110] modeled the theoretical performance of chillers using alternatives to
CFC-11 and CFC-114. The model assumed constant pressure evaporation and con-
densation, isentropic compression, and adiabatic expansion. The COPs were between
6.2 and 6.9 when no subcooling or superheating was assumed for an evaporating tem-
perature of 4.4 C and a condensing temperature of 40 C.
Sand et al. [Ill] reported experimental performance results for 12 refrigerants.
The vapor compression system was a small laboratory unit with a water-cooled con-
denser and water-heated evaporator. The cooling COP was 2.6 for HFC-152a and
2.45 for HFC-134a. In comparison, the cooling COP for CFC-12 was 2.4 and 2.1 for
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HCFC-22. The condensing temperature was 35 C and the evaporator water outlet
temperature was 15 C.
Energy Efficient Alternatives to Chlorofluorocarbons [112] reports the actual
COP for commercial frozen food freezers is between 1.0 and 1.2, approximately 1.9
for dairy display cases, and 2.5 for produce display cases. Multerer and Burton [15]
report a COP of 2.35 for automotive vapor compression systems using CFC-12.
A rating of 5 (very high) was assigned to the efficiency category for all refriger-
ation and air conditioning applications.
Closure
The numerical technical assessment ratings for vapor compression refrigeration
are presented in Table 10.11.
Table 10.11: Technology assessment for vapor compression refrigeration.
Criterion
Rating (1= lowest, 5=highest)
Dom. AC.
Com. AC.
Mob. AC.
Dom. Ref.
Com. Ref.
State of art
5
5
5
5
5
Complexity
4
4
4
4
4
Size/Weight
4
4
4
4
4
Maintenance
5
5
4
4
4
Life
5
5
5
5
5
Energy Effic.
5
5
5
5
5
Ejector Refrigeration
Ejector cycles using organic refrigerants were analyzed during this study. They
were found to be environmentally unacceptable when using the best currently known
211
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working fluids. The most promising ejector systems use CFC-11 or CFC-114 as the
refrigerant. Both of these materials have an ODP of 1.0 [3]. The 100-year integrated
time horizon GWP (Chapter 1) of CFC-11 is 3500 and for CFC-114 it is 6900 [113].
If an environmentally suitable alternative refrigerant could be found (one possible
alternative refrigerant could be HFC-236ea), the ejector refrigeration system would
offer a relatively simple system which could be operated using waste heat.
Ejector refrigeration cycles use heat transfer from a high temperature source
rather than mechanical work to drive the cycle. The basic operating principle of
ejector refrigeration can be understood by thinking of the cycle as a vapor compression
cycle in which the compressor has been replaced by a pump generator (boiler), and
ejector. Figure 10.2 is a schematic diagram for a simple ejector refrigeration cycle.
High pressure' refrigerant vapor is produced in the generator by the addition of
heat from an external high temperature source. The heat source could be from:
• a primary source such as a direct-fired burner
• waste heat
• the sun.
The ejector consists of two sections, a nozzle and a mixing and diffuser section.
The vapor from the generator is expanded through the converging-diverging nozzle.
The resulting low pressure at the nozzle throat causes flow of the second stream for
refrigerant from the evaporator. The two streams are mixed and the pressure of
the mixed stream is increased in the mixing and diffuser (diverging) section. The
mixed stream of vapor is condensed in the condenser where heat is rejected to the
environment. The condensed liquid is divided into two streams: one stream flows
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Figure 10.2: Schematic diagram of a simple ejector refrigeration
system.
to the expansion device where it under goes a throttling process, while the second
stream flows to a pump which increases its pressure to the generator's pressure. The
low pressure flow from the expansion valve is expanded in the evaporator, accepting
heat from the cooling space during the process.
Sokolov and Hershgal [114,115,116] considered two modified ejector refrigeration
cycles for use with a low grade external heat source:
• A hybrid ejector/compression cycle in which a low pressure compressor was
interposed between the evaporator and ejector to raise the pressure of the vapor
at the ejector mixing chamber inlet
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• A multiple ejector cycle in which two or more ejectors are connected in parallel.
The ideal COP for ejector refrigeration systems would be that of a Carnot refri-
gerator driven by a Carnot heat engine. If it is assumed that the condenser rejects
heat to the environment at the COP for an ideal ejector refrigeration cycle would
be given by Equation 10.1.
The theoretical COP for a simple ejector refrigeration system has been reported
to be approximately 0.25. The theoretical COP for the hybrid system was 0.84 [114].
The system temperatures for both calculations were:
TL = - 8 C
Th = 30 C
Tq = 86 C
Sokolov and Hershgal [116] measured a COP of 0.42 for an experimental hybrid
ejector refrigeration system using R-114. The system temperatures were:
Tl = 8.2 C
Th = 53.5 C
Tq = 93 C
Closure
The numerical technical assessment data from the previous sections of this chap-
ter were incorporated in a technical assessment computer program. The program and
the results are discussed in Chapter 11.
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CHAPTER 11. RESULTS OF TECHNOLOGY ASSESSMENT AND
SUMMARY OF CONCLUSIONS
Introduction
The alternative refrigeration technologies considered during this project were
rated using a computer program. This program uses an algebraic equation and the
numerical technology assessment rating data presented in Tables 10.8 through 10.11
in Chapter 10 to rate the air conditioning and refrigeration technologies in the five
cooling application areas:
1. Domestic air conditioning.
2. Commercial air conditioning.
3. Mobile air conditioning.
4. Domestic refrigeration.
5. Commercial refrigeration.
These technology assessment rating data in the computer program are a numer-
ical summary of the patent search, computer modeling, and technology assessment
done during this project.
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Technical Assessment Ratings for the Refrigeration Technologies
To rate suitability of the refrigeration technologies considered during this study
for use in domestic, commercial, and mobile air conditioning and domestic and com-
mercial refrigeration applications, an algebraic expression was developed which is the
sum of the products of the individual technical assessment criterion ratings for each
technology multiplied by a weighting factor which reflects the relative emphasis of
each criterion for a particular application:
T = (wf^xA^ + (wfgxB^ + (wffjxC) + (wfpxD) +
(wfgxE} + (wfpxF} (ll-1)
F
= /C wfa 'i (1L2)
i—A
where
T = overall technology rating
wfi = technical assessment weighting factor for each criterion
i — criterion rating for each technology.
The technology assessment criteria rating data were presented in Tables 10.8
through 10.11 in Chapter 10.
The individual weighting factors, tu/j, used in Equation 11.1 are chosen so that
the sum equals 1; i.e.,
F
£ <"/; = 1.0 (11.3)
i=A
A set of weighting factors was developed for each application to measure the relative
importance of each of the six criteria for each application. These weighting factors are
216
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given in Table 11.1. The higher the value of T, the more preferable the refrigeration
technology for a given application.
A computer program using Equation 11.1 was developed to calculate the overall
rating,T, and rank the refrigeration technologies from high to low based upon the
value of T for each technology.
A description of the computer program usage and code are presented in Appendix
D.
Technology Assessment Criteria Weighting Factors
A set of technology assessment criteria weighting factors were developed for
each of the five applications areas. These weighting factors were selected to reflect
the relative importance of the six criteria (state-of-the-art, complexity, size/weight,
maintenance, useful life, and energy efficiency) for each application. Table 11.1 con-
tains the weighting factor numerical values we chose for this study. These values
were selected to reflect our opinion as to the relative importance of the six techni-
cal assessment criteria (with respect to one another) for each application category.
Other weighting factor sets can be chosen to change the relative importance of the
six technology assessment criteria.
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Table 11.1: Technology assessment criteria weighting factors by application cate-
gory.
Assessment
Dom.
Com.
Mobile
Dom.
Com.
Criterion
AC
AC
AC
Ref.
Ref.
State-of-the-Art
0.20
0.20
0.15
0.20
0.20 '
Complexity
0.15
0.10
0.20
0.20
0.10
Size/Weight
0.05
0.05
0.30
0.10
0.05
Maintenance
0.15
0.15
0.20
0.10
0.15
Useful Life
0.15
0.20
0.05
0.15
0.20
Efficiency
0.30
0.30
0.10
0.25
0.30
218
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Results
Domestic Refrigeration Assessment
Table 11.2 contains the technology ratings for domestic refrigeration. The tech-
nology ratings were distributed into four groups:
1. High (Rating of 4.60) Vapor compression was the most suitable technology
for domestic refrigeration applications.
2. Medium (Rating of 3.70 to 3.25) Absorption received a medium rating.
Absorption systems are characterized by a high cycle efficiency, however, the
absorption refrigeration technology was penalized for use in domestic refriger-
ation applications because of additional complexity, increased size, increased
maintenance, and shorter useful life than vapor compression systems.
The hardware to accomplish the reversed Stirling refrigeration cycle is compact.
However, additional heat transfer loops are required so that the small heat
exchangers used in the reversed Stirling system can be in communication with
the thermal source (interior of the refrigerator) and the thermal sink to which
heat is rejected (usually the ambient air for domestic refrigeration applications)
and transfer heat to and from the reversed Stirling system at a reasonable rate.
These additional heat transfer loops will add to the complexity (and capital
cost) of the refrigerator and reduce the cycle efficiency which is already low when
compared to the cycle efficiency of vapor compression domestic refrigeration
systems.
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3. Low (Rating of 3.05 to 2.60) The solid sorption, reversed Brayton, and pulse
tube/thermoacoustic technologies received low ratings. Presently, solid sorption
refrigeration and the pulse tube/thermoacoustic technologies are immature.
Therefore, the cost to develop these refrigeration technologies into marketable
domestic refrigeration systems will be high.
4. Very Low (Rating of 2.20 to 1.95) Two technologies (thermoelectric re-
frigeration and magnetic refrigeration) received the lowest rating for domestic
refrigeration applications. Both of these technologies have very low cycle effi-
ciencies. For thermoelectric refrigeration, another limiting feature is the small
amount of tellurium-based material which is available for producing the semi-
conductors used in thermoelectric cooling modules. Therefore, the capital cost
of thermoelectric systems will be high. No other materials are known which can
be used to produce thermoelectric modules with a cycle efficiency as high (or
higher) than that of the tellurium-based modules. Furthermore, the maximum
temperature lift for a single stage of thermoelectric refrigeration is approxi-
mately 22 C which is insufficient for refrigeration applications (Table 3.2). It
would be necessary to cascade thermoelectric systems in order to achieve low
enough source temperatures for refrigeration applications. Cascading systems
would further reduce the already low cycle efficiency.
Magnetic refrigeration technology is immature. Experimental systems have
been investigated on a very limited basis. The results of these investigations
have merely demonstrated that heat can be transferred from a cold region to
a hotter region by a magnetic core and field. In theory, magnetic refriger-
ation could be capable of high cycle efficiencies; however, in practice, the cycle
220
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efficiencies have been very low. The principal technical area which must be
developed to achieve higher cycle efficiencies is regenerative heat transfer with
a very high effectiveness.
Table 11.2: Ranking of domestic refrigeration technologies from most favored to
least favored.
Ranking
Refrigeration Technology
Rating
1
Vapor Compression
4.60
2
Absorption
3.70
3
Reversed Stirling
3.25
4
Solid Sorption
3.05
5
Reversed Brayton
2.65
6
Pulse Tube/Thermoacoustic
2.60
7
Thermoelectric
2.20
8
Magnetic Refrigeration
1.95
221
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Domestic Air-Conditioning Assessment
Table 11.3 contains the refrigeration technology ratings for domestic air condi-
tioning. Four rating groups were observed for domestic air conditioning applications:
1. High (Rating of 4.80) Vapor compression received the highest suitability
rating for use in domestic air conditioning applications.
2. Medium (Rating of 3.80) Absorption received a medium rating. Absorption
systems used in air conditioning applications are characterized by high cycle ef-
ficiencies and long useful lifetimes in air conditioning applications. However, the
absorption refrigeration technology rating was lower for domestic air condition-
ing applications because of additional complexity, increased size, and increased
maintenance when compared to vapor compression systems. Although absorp-
tion refrigeration is capable of high cycle efficiencies, it is not as attractive as
vapor compression for domestic air conditioning applications from the perspec-
tive of increased complexity, larger size and weight, and higher maintenance
(and thus higher cost) per ton of refrigeration than vapor compression systems.
3. Low (Rating of 2.95 to 2.80) The pulse tube/thermoacoustic, reversed Stir-
ling, and solid sorption technologies had a low rating for domestic air condi-
tioning applications. The pulse tube/thermoacoustic technology is immature
and has low cycle efficiencies at source temperatures of 20 C and above.
The most promising technology in this group for domestic air conditioning
applications is solid sorption. The cycle efficiency of solid sorption systems
should be high in the temperature lift range used for air conditioning. In
contrast, the cycle efficiencies of the other technologies in this group (reversed
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Stirling, reversed Brayton, and pulse tube/thermoacoustic) all decrease with
increasing source temperature (Chapter 10).
4. Very Low (Rating of 2.35 to 1.95) The reversed Brayton, thermoelectric re-
frigeration, and magnetic refrigeration were rated as having very low suitability
for domestic air conditioning applications.
The principal reasons for the very low rating of the reversed Brayton technology
are: a large physical size per ton of cooling effect of the hardware ( compressor,
expander, and ducts), high complexity (and therefore high capital cost) of the
turbine and expander, and a low cycle efficiency. In humid environments, de-
humidification of the incoming air would be necessary to prevent ice formation
during the expansion process (due to the temperatures at the expander exit)
which would be below freezing. The addition of a dehumidification process
to the reversed Brayton system would result in an even higher capital cost of
the equipment and higher operating and maintenance costs per ton of cooling
effect.
The COP for thermoelectric refrigeration is low as compared to other technolo-
gies, even at source temperatures used in domestic air conditioning (18 C and
above), as shown in Figure 8.1. As discussed in Chapter 10, there is a limited
availability of the element tellurium which is used to make the thermoelectric
modules. Also, no alternative material which can produce comparable COPs
has been developed. Therefore, the cost per ton of cooling would be high for
these systems.
223
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The magnetic refrigeration rating was low due to immaturity of the technology,
high complexity, and the low cycle efficiency of present systems.
Table 11.3: Ranking of domestic air-conditioning technologies from most favored to
least favored.
Ranking
Refrigeration Technology
Rating
1
Vapor Compression
4.80
2
Absorption
3.80
3
Pulse Tube/Thermoacoustic
2.95
4
Reversed Stirling
2.90
5
Solid Sorption
2.80
6
Reversed Brayton
2.35
7
Thermoelectric
2.05
8
Magnetic Refrigeration
1.95
Mobile Air-Conditioning Assessment
Table 11.4 contains the refrigeration technology ratings for mobile air condition-
ing applications. The size/weight criterion received a high relative importance and
the efficiency criterion weighting was reduced for mobile air conditioning applications
(Table 11.1). The useful life of mobile air conditioning systems is shorter than for
the other four application areas (A 10-year average life was used as an estimated life
of mobile air conditioners for this study).
The ratings of the refrigeration technologies in Table 11.4 were considered to be
in four groups of suitability for mobile air conditioning applications:
1. High (Rating of 4.30) Vapor compression was rated highest. The primary
reasons for rating were a relatively low weight and small hardware size per ton of
224
-------
cooling effect in mobile applications. Mobile vapor compression cooling systems
also require little maintenance and are relatively inexpensive to produce.
2. Medium (Rating of 3.25) The reversed Stirling technology was rated as
medium for mobile cooling applications. The important attributes of reversed
Stirling technology for mobile applications are compactness and low mainte-
nance of the refrigeration system. Additional heat transfer loops would be
required so that the small heat exchangers used in the reversed Stirling system
could be in communication with the thermal source (interior of the vehicle)
and the thermal sink to which heat is rejected (usually the ambient air for mo-
bile air conditioning applications) and transfer heat to and from the reversed
Stirling system at a reasonable rate. These additional heat transfer loops will
add to the complexity (and capital cost) of the air conditioner and reduce the
cycle efficiency which is already low when compared to the cycle efficiency of
vapor compression mobile air conditioning systems. The low cycle efficiency,
particularly at higher source temperatures, was the principal reason that re-
versed Stirling did not receive a high rating for mobile cooling applications.
The useful life should be that of the vehicle.
3. Low (Rating of 2.65 to 2.30) The pulse tube/thermoacoustic, solid sorption,
reversed Brayton, and absorption technologies received low ratings for mobile
air conditioning applications. The principal reason for the low rating was the
large size and high weight per ton of cooling capacity of air conditioning systems
using these technologies compared to vapor compression systems. A second
reason for the low rating was the higher capital cost of systems using these
225
-------
technologies due to the higher complexity and relative immaturity of these
technologies compared to vapor compression air conditioning systems.
4. Very Low (Rating 2.15 to 1.25) Thermoelectric cooling and magnetic re-
frigeration were rated lowest for mobile air conditioning. The reasons for the
very low rating were a low cycle efficiency and the need for a large electrical
generation system aboard the vehicle for both technologies.
Table 11.4: Ranking of mobile air-conditioning technologies from most favored to
least favored.
Ranking
Refrigeration Technology
Rating
1
Vapor Compression
4.30
2
Reversed Stirling
3.25
3
Pulse Tube/Thermoacoustic
2.65
4
Solid Sorption
2.55
5
Reversed Brayton
2.50
6
Absorption
2.30
7
Thermoelectric
2.15
8
Magnetic Refrigeration
1.25
226
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Commercial Air-Conditioning Assessment
Table 11.5 contains the refrigeration technology ratings for commercial air con-
ditioning applications. The suitability ratings were distributed into three groups:
1. High (Rating of 4.85 to 4.45) Vapor compression was the most suitable
technology for commercial air conditioning applications. Absorption was also
rated highly. Since commercial air conditioning systems generally have a larger
cooling capacity and longer life expectancy than domestic systems, they were
not penalized as heavily for additional complexity and increased maintenance.
Emphasis was placed on the efficiency of commercial air conditioning systems.
2. Medium (Rating of 3.10 to 2.75) The pulse tube/thermoacoustic, solid
sorption, reversed Stirling, and reversed Brayton technologies were in the medium
suitability rating group. These gas cycle refrigeration technologies have low cy-
cle efficiencies at the higher source temperatures used in air conditioning appli-
cations (see Figures 5.10, 6.8, and 7.9). Solid sorption refrigeration technology
has the highest cycle efficiency in the medium group.
3. Low (Rating of 2.35 to 1.95) Thermoelectric and magnetic refrigeration
have very low cycle efficiencies. Presently, the amount of tellurium-based ma-
terial for semiconductors is limited. Therefore, the first cost of thermoelectric
systems will be high. Magnetic refrigeration technology is immature. Highly
effective regenerative heat transfer is the principal technical area which must
be developed to improve the cycle efficiency of magnetic air conditioning.
227
-------
Table 11.5: Ranking of commercial air-conditioning technologies from most favored
to least favored.
Ranking
Refrigeration Technology
Rating
1
Vapor Compression
4.85
2
Absorption
4.45
3
Pulse Tube/Thermoacoustic
3.10
4
Solid Sorption
2.80
5
Reversed Stirling
2.75
6
Reversed Brayton
2.35
7
Magnetic Refrigeration
2.05
8
Thermoelectric
1.95
Commercial Refrigeration Assessment
Table 11.6 contains the technology ratings for commercial refrigeration applica-
tions. The suitability ratings were distributed into four groups:
1. High (Rating of 4.70) Vapor compression received the highest rating for
commercial refrigeration applications.
2. Medium (Rating of 3.80) Absorption refrigeration was rated next highest.
Although absorption refrigeration is capable of high cycle efficiencies, it is not
as attractive as vapor compression from the perspective of complexity, size and
weight, and maintenance (particularly for supermarket applications).
3. Low (Rating of 3.10 to 2.80) The gas cycle refrigeration technologies (re-
versed Stirling, reversed Brayton, and pulse tube/thermoacoustic refrigeration)
were in the low suitability rating group. The cycle efficiencies of refrigeration
systems using these technologies increases with decreasing source temperature.
228
-------
All of these technologies are best suited for cryogenic and low-temperature in-
dustrial refrigeration applications.
4. Very Low (Rating of 2.05) Thermoelectric and magnetic refrigeration were
in the lowest suitability rating group for commercial refrigeration applications.
Both of these technologies have very low cycle efficiencies. For thermoelectric
refrigeration, another limiting feature is the small amount of tellurium-based
material which is available for producing the semiconductors used in thermo-
electric cooling modules. Therefore, the first cost of thermoelectric systems
will be high. No other materials are known which can be used to produce
thermoelectric modules with a cycle efficiency as high (or higher) than that of
the tellurium-based modules. Furthermore, the maximum temperature lift for
a single stage of thermoelectric refrigeration is approximately 22 C which is
insufficient for refrigeration applications (see Table 3.2). It would be necessary
to cascade thermoelectric systems in order to achieve source temperatures low
enough for refrigeration applications. This would reduce the already low cycle
efficiency even further.
Magnetic refrigeration technology is immature. Limited investigation of exper-
imental systems has been conducted. The results of these investigations have
merely demonstrated that heat can be transferred from a cold region to a hotter
region by a magnetic core and field. In theory, magnetic refrigeration could be
capable of high cycle efficiencies; however, in practice, the cycle efficiencies have
been very very low. The principal technical area which must be developed to
achieve higher cycle efficiencies is regenerative heat transfer with a very high
effectiveness.
229
-------
Table 11.6: Ranking of commercial refrigeration technologies.
Ranking
Refrigeration Technology
Rating
1
Vapor Compression
4.70
2
Absorption
3.80
3
Reversed Stirling
3.15
4
Solid Sorption
3.10
5
Reversed Brayton
3.00
6
Pulse Tube/Thermoacoustic
2.80
7
Magnetic Refrigeration
2.05
8
Thermoelectric
2.05
Table 11.7 is a comparison of the ratings for all refrigeration technologies and
application areas (Tables 11.2 through 11.6 combined).
Table 11.7: Refrigeration technology suitability ratings for the five application areas.
Refrigeration Technology
Rating
Dom.
Dom.
Mobile
Com.
Com.
Refrig.
AC
AC
AC
Refrig.
Vapor Compression
4.60
4.80
4.30
4.85
4.70
Absorption
3.70
3.80
2.30
4.45
3.80
Reversed Stirling
3.25
2.90
3.25
2.75
3.15
Solid Sorption
3.05
2.80
2.55
2.80
3.10
Reversed Brayton
2.65
2.35
2.50
2.35
3.00
Pulse Tube/Thermoacoustic
2.60
2.95
2.65
3.10
2.80
Thermoelectric
2.20
2.05
2.15
1.95
2.05
Magnetic Refrigeration
1.95
1.95
1.25
2.05
2.05
230
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Conclusions
Vapor compression refrigeration using non-CFC refrigerants is the most desir-
able technology for the five application areas considered in this study.
Absorption refrigeration is attractive for commercial refrigeration and air con-
ditioning. If the complexity and maintenance levels can be reduced, it could
also be attractive for domestic applications.
Solid sorption refrigeration technology is immature. This technology may have
some advantages over absorption systems using liquid absorbents, particularly
for domestic refrigeration and air conditioning applications. Canister sorption
and heat transfer efficiencies must be improved above present levels. Complete
systems must be developed to demonstrate reasonable useful lives and accept-
able maintenance levels. Solid sorption is the most promising new refrigeration
technology in terms of technical feasibility, particularly for air conditioning and
refrigeration applications where batch processes can be used.
The highest cycle efficiencies for the gas-cycle refrigeration technologies (re-
versed Stirling, reversed Brayton, and pulse tube/thermoacoustic) occur at
source temperatures below the lowest temperature considered in this study
(—24 C). These technologies are best suited to cryogenic and low-temperature
commercial and industrial refrigeration applications.
The thermoelectric and magnetic refrigeration technologies are impractical for
refrigeration and air conditioning applications at this time because of their low
cycle efficiency.
231
-------
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1001 Douss, N., F. Meunier. "Experimental Study of Cascading Adsorption Cycles."
Chemical Engineering Science. Vol. 44, No. 2, 1989: 225-235.
1011 Jones, J. "Regenerative Adsorbent Heat Pump." U.S. Patent, No. 5 046 319.
Washington, DC: Commissioner of Patents and Trademarks, 1991.
1021 Critoph, R.E. "Activated Carbon Adsorption Cycles for Refrigeration and Heat
Pumping." Carbon. Vol. 27, No. 1, 1989: 63-70.
1031 Jones, J. "Sorption Refrigeration Research at JPL/NASA." In Proceedings
of the International Institute for Refrigeration, Solid Sorption Refrigeration
Conference held in Paris, France, November 18-20, 1992.
1041 Jones, J., V. Christophilos. "High Efficiency Adsorbent Heat Pump." In Pro-
ceedings of the ASHRAE Winter Annual Meeting held in Chicago, IL, January
1993.
1051 Ross, D.P. "Service Life of Water-loop Heat Pump Compressors in Commercial
Buildings." ASHRAE Transactions, 1990, Part 1. Transaction No. AT-90-29-2.
1061 Bucher, M.E., et al. "Heat Pump Life and Compressor Longevity in Diverse
Climates." ASHRAE Transactions. 1990, Part 1. Transaction No. AT-90-29-3.
1071 Bare, J.C., et al. "Simulation of Nonazeotropic Refrigerant Mixtures for Use
in a Dual-circuit Refrigerator/Freezer with Countercurrent Heat Exchangers."
ASHRAE Transactions. 1991, Part 2. Transaction No. 3540.
1081 Radermacher, R., D. Jung. "Theoretical Analysis of Replacement Refrigerants
for R-22 for Residential Uses." ASHRAE Transactions. 1993, Part 1. Transac-
tion No. 3654.
1091 Braun, J.E., et al. "Models for Variable-speed Centrifugal Chillers." ASHRAE
Transactions. 1987, Part 1. Transaction No. NY-22-2.
1101 Bare, J.C. "Simulation of Performance of Chlorine-free Fluorinated Ethers
and Fluorinated Hydrocarbons to Replace CFC-11 and CFC-114 in Chillers."
ASHRAE Transactions. 1993, Part 1. Transaction No. 3661.
240
-------
[111] Sand, J.R., et al. "Experimental Performance of Ozone-safe Alternative Refrig-
erants." ASHRAE Transactions. 1990, Part 1. Transaction No. 3399.
[112] Energy Efficient Alternatives to Chlorofluorocarbons, Revised final report. Cam-
bridge, MA: Arthur D. Little, Inc. April 1992. U.S. Department of Energy
Report No. 66384.
[113] Fisher, D.A., et al. "Relative Effect on Global Warming of Halogenated
Methanes and Ethanes of Social and Industrial Interest." Scientific Assessment
of the Stratospheric Ozone: 1989, Vol.11, Appendix: AFEAS Report, World
Meteorological Organization, Global Ozone Research and Monitoring Project -
Report No. 20.
[114] Sokolov, M., D. Hershgal. "Enhanced Ejector Refrigeration Cycles Powered by
Low Grade Heat. Part 1. Systems characterization." International Journal of
Refrigeration. Vol. 13, No. 6, 1990: 351-356.
[115] Sokolov, M., D. Hershgal. "Enhanced Ejector Refrigeration Cycles Powered by
Low Grade Heat. Part 2. Design procedures." International Journal of Refri-
geration. Vol. 13, No. 6, 1990: 357-363.
[116] Sokolov, M., D. Hershgal. "Enhanced Ejector Refrigeration Cycles Powered
by Low Grade Heat. Part 3. Experimental results." International Journal of
Refrigeration. Vol. 14, No. 1, 1991: 24-31.
241
-------
APPENDIX A. TECHNOLOGIES IDENTIFIED DURING PATENT
AND LITERATURE SURVEYS
242
-------
Category Cycle Type
Heat, Primary Absorption
Heat, Primary Absorption
Heat, Primary Absorption
Heat, Primary Absorption
Heat, Primary Absorption
Heat, Primary Absorption
Item or Title
Refrigerating Apparatus
Refrigerator
Apparatus for Refrigeration
Source
Comments
U.S. Patent 1369365 Uses vacuum to flash sub-cool liquid
U.S. Patent 1369366 NH^
U.S. Patent 1477127 Potassium carbonate and water used as
refrigerant/absorbent mixture
U.S. Patent 1524297 Utilizes multiple generator tanks
Absorption Refrigerating Apparatus U.S. Patent 654395 Steam-heated generator and steam-
driven pumps
Automatic Absorber Refrigerator U.S. Patent 1273364 Intermittent regeneration at night to take
advantage of favorable utility rates
Liquid Phase Separation in Absorption U.S. Patent 4283918 Immiscibility property of refrigerant
Refrigeration allows separation of refrigerant and
absorbent in liquid phase.
References:
1. Norland, J. "$2.4 Million Financing for Compressorless A/C." Air Conditioning, Heating & Refrigeration News, November 11,1992.
2. Swift, G. W. "Malone Refrigeration," ASHRAE Journal, American Society of Heating, Refrigerating, and Air-Conditioning Engineers,
November 1990.
3. Swift, G. W. "A Stirling Engine with a Liquid Working Substance," Journal of Applied Physics, American Institute of Physics.
Volume 65, Number 11, June 1989
4. Wood, B. D. Applications of Thermodynamics, 2nd Edition, Addison-Wesley, Reading, MA, p. 406-407.
5. Chen, F. C., et al. "Loss Analysis of the Thermodynamic Cycle of Magnetic Heat Pumps." Oak Ridge National Laboratory,
Oak Ridge, TN, Report Number ORNL/TM— 11608, February 1991.
6. Miller-Picking Corporation. "Report on the Preliminary Design for a Desiccant Based A/C Unit," Ref.: T-14940, Miller-Picking Corp.,
Johnstown, PA, 1990.
-------
to
rf*-
Category Cycle Type
Heat, Primary Absorption
Heat, Primary Absorption
Heat, Primary Absorption
Heat, Primary Absorption
Heat, Primary Absorption
Heat, Primary Vapor
Compression
Heat, Primary Vapor
Compression
Heat, Primary Adsorption
Heat, Primary Adsorption
Heat, Waste Absorption
Item or Title
Source
Hyperabsorption Space Conditioning U.S. Patent 4413480
Process and Apparatus U.S. Patent 4487027
Absorption Refrigeration Process U.S. Patent 4475352
U.S. Patent 4475353
Liquid Phase Separation in Absorption U.S. Patent 4283918
Refrigeration
Absorption Type Heat Pump System U.S. Patent 4448040
Compressorless Air Conditioner
Refrigeration System
[Reference 1]
U.S. Patent 4378681
Method of Cold Production and U.S. Patent 4070871
Devices for the Practical Application
of Said Method
Refrigeration Cycle Apparatus Having U.S. Patent 4972676
Refrigerant Separating System With
Pressure Swing Adsorption
Regenerative Adsorbent Heat Pump U.S. Patent 5046319
Process and Apparatus for
Refrigeration
U.S. Patent 1265037
Comments
Generator employs liquid to solid
crystallization of saturated salt solution
to vaporize liquid refrigerant.
Process utilizes alternative organic and
inorganic binary mixtures as refrigerant
-absorbent pairs.
Refrigerant is methyl diethylamine
Absorbent is water
Utilizes two LiBr/water absorption
cycles
Evaporative cooling/ lithium bromide
dehumidification of incoming air stream
Uses an ejector as the compression
device
Employs a constant pressure expansion
in a variable volume chamber
Refrigerant is a binary mixture of R-22
and R-l 14. The adsorbing tower is
charged with activated alumina.
Uses multiple zeolite canisters as
compressors
Requires no absorber or pump for the
water side
-------
Category
Heat, Waste
Heat, Waste
Cycle Type
Vapor
Compression
Vapor
Compression
Item or Title
Refrigeration Apparatus and Method
Twin Reservoir Heat Transfer Circuit
Heat, Waste Vapor
Compression
Heat, Other (Solar) Adsorption
Device to Create Cooling Through
Use of Waste Heat
Modular Solar Powered Heat Pump
Heat, Other (Solar) Absorption
Heat, Other (Solar) Absorption
Solar Powered Air Conditioning
System Employing Hydroxide Water
Solution
Cooling Method and System
Therefor
Work, Phase
Vapor
Refrigerating or Ice Making
Change
Compression
Apparatus
Work, Phase
Vapor
Process of Refrigeration
Change
Compression
Work, Phase
Vapor
Process of Refrigeration
Change
Compression
Work, Phase
Vapor
Process and Apparatus for
Change
Compression
Refrigeration
Source
U.S. Patent 4345440
U.S. Patent 4612782
U.S. Patent 4192148
U.S. Patent 4199952
U.S. Patent 4151721
U.S. Patent 4488408
U.S. Patent 1253895
U.S. Patent 1264807
U.S. Patent 1379102
U.S. Patent 1264845
U.S. Patent 1337175
Comments
Mobile application using waste heat
from engine exhaust gases
Vapor is produced in a tank heated by a
coil. The vapor passes through an
ejector and is then condensed. After
evaporation the refrigerant is collected
in an unheated tank.
Uses ejector to compress the working
fluid
Uses a silica gel adsorber
Insolation generates heat to drive
desorption process
Uses ammonium hydroxide-water as the
absorbent-refrigerant pair
Refrigerant/ absorbent pair is
lithium/bromide and water
Uses NH-} as the refrigerant, multiple
stage compression
Series compressors with intercooling
between stages
Multistage compression with
intercooling
Uses sulfur dioxide as the refrigerant
-------
Category
Work, Phase
Change
Work, Phase
Change
Cycle Type
Vapor
Compression
Vapor
Compression
Item or Title
Refrigerating System
Artificial Refrigeration System.
Work, Phase
Change
Work, Phase
Change
Work, Phase
Change
Vapor
Compression
Vapor
Compression
Vapor
Compression
Process and Apparatus for Multiple
Stage Compression for Refrigeration
Refrigerating Process and Apparatus
Refrigeration and Power System
Work, Phase
Change
Work, Phase
Change
Work, Phase
Change
Vapor
Compression
Vapor
Compression
Vapor
Compression
Refrigerant
Method of Improving Refrigerating
Capacity and Coefficient of
Performance in a Refrigerating
System, and a Refrigerating System
for Carrying Out Said Method
Refrigeration Apparatus and Method
Work, Phase
Change
Vapor
Compression
Direct Contact Heat Transfer System
Using Magnetic Fluids
Source
Comments
U.S. Patent 1455580 Series evaporators with liquid vapor
separator between stages
U.S. Patent 1520936 Refrigerant is sulfur dioxide or methyl
chloride
U.S. Patent 1471732 Intercooling between compression
stages using water
U.S. Patent 1512133 Water-driven compressor, water-cooled
condenser
U.S. Patent 1519353 Cascaded system using three separate
systems, each using a different
refrigerant; ammonia, sulfur dioxide,
and carbon dioxide
U.S. Patent 1547202 The refrigerant is methyl bromide.
U.S. Patent 4014182 The refrigerant is flashed to vapor in an
initially evacuated vessel.
U.S. Patent 4019337 The system utilizes two capillary tubes
and a flow control which senses
evaporator outlet temperature.
U.S. Patent 4078392 A ferrofluid is separated from a suitable
refrigerant by magnetic means and
circulated to the cooling load.
-------
Category
Cycle Type
Item or Title
Source
Work, Phase Vapor Dual Flash and Thermal Economized U.S. Patent 4141708
Change Compression Refrigeration System
Work, Phase Vapor Hydraulic Refrigeration System
Change Compression
U.S. Patent 4157015
U.S. Patent 4251998
U.S. Patent 4424681
to
-4
Work, Phase
Change
Work, Phase
Change
Work, Phase
Change
Work, Phase
Change
Reversed Rankine Vapor Compression Refrigeration and U.S. Patent 4235079
Cycle
Vapor
Compression
Vapor
Compression
Vapor
Compression
Heat Pump Apparatus
Refrigeration and Space Cooling Unit U.S. Patent 4235080
Vapor Compression Refrigeration
System and a Method of Operation
Therefor
Refrigerant Sub-Cooling
U.S. Patent 4258553
U.S. Patent 4285205
Work, Phase Vapor Heat Exchange Method Using Natural U.S. Patent 4295342
Change Compression Flow of Heat Exchange Medium
Comments
Uses a low temperature flash
economizer and a high temperature
flash economizer in conjunction with
two compressors.
Vapor from evaporator is entrained in a
vertically downward moving column of
fluid (water). The vapor is compressed
and condensed simultaneously.
The expansion valve is replaced with an
expansion turbine.
Converts a portion of the latent heat
into mechanical energy through a
turbine operating between the vapor
pressure and a vacuum.
Series compressors with intercooling
Commercial application with multiple
compressors in parallel. A heat
exchanger increases the suction gas
temperature and subcools the liquid
prior to expansion.
Uses natural convection to circulate
refrigerant in a circuit to transfer heat
from a warm to cold body. The system
requires a difference in heat exchanger
elevation and a bypass valve and circuit
around the compressor.
-------
Category
Work, Phase
Change
Work, Phase
Change
Work, Phase
Change
Cycle Type
Vapor
Compression
Vapor
Compression
Vapor
Compression
Item or Title
Gas Compression System
Method for Utilizing Gas-Solid
Dispersions in Thermodynamic
Cycles for Power Generation and
Refrigeration
Hybrid Heat Pump
Work, Phase Vapor Refrigerator Cooling and Freezing
Change Compression System
Work, Phase
Change
Work, Phase
Change
Vapor
Compression
Vapor
Compression
Refrigeration System with Refrigerant
Pre-Cooler
Refrigeration Process and Apparatus
Work, Phase
Change
Vapor
Compression
Apparatus for Maximizing
Refrigeration Capacity
Source
U.S. Patent 4311025
U.S. Patent 4321799
U.S. Patent 4481783
U.S. Patent 4513581
U.S. Patent 4577468
U.S. Patent 4586344
U.S. Patent 4599873
Comments
The refrigeration circuit utilizes a
rotating disc compressor.
Utilizes a circulating dispersion of solid
particles in a gaseous refrigerant
Uses both compression and absorption
processes in the cycle. The system uses
both a compressor and a generator.
Single compressor, multiple series
evaporators in freezer and food storage
compartments
Single circuit vapor compression system
with a condenser outlet subcooler
Two immiscible or partly miscible
refrigerants are mixed and evaporated in
an evaporator. The absorption system
absorbs a portion of the refrigerant; the
compression system condenses the non-
absorbed refrigerant vapor.
A pump is located at the condenser
outlet to raise the pressure and prevent
flashing. The condenser temperature
and pressure are allowed to fluctuate
with ambient conditions.
-------
Category
Work, Phase
Change
Cycle Type
Vapor
Compression
Item or Title
Refrigeration System
Work, Phase Vapor Refrigeration System with Hot Gas
Change Compression Pre-Cooler
Work, Phase Vapor Chemically Assisted Mechanical
Change Compression Refrigeration System
Work, Phase
Change
Vapor
Compression
Indirect Evaporative Cooling System
Work, Phase Vapor Refrigerating System Incorporating a
Change Compression Heat Accumulator and Method of
Operating the Same
Work, Phase Vapor Refrigerating System Having a
Change Compression Compressor With An Internally and
Externally Controlled Variable
Displacement Mechanism
Source
U.S. Patent 4640100
U.S. Patent 4702086
U.S. Patent 4707996
U.S. Patent 4827733
U.S. Patent 4833893
U.S. Patent 4882909
Comments
A pump is used to vary the condensing
pressure as the ambient temperature
fluctuates. The system has multiple
compressors in parallel for commercial
applications
A portion of the liquid refrigerant is
evaporated to pre-cool the vapor
between the compressor and condenser.
A refrigerant/solvent pair is separated
into vapor and liquid phases
respectively. Solvent is then used as a
coolant to be circulated through a jacket
around compressor. After heat exchange
in the condenser and a pre-mixer, the
fluids are again combined.
Water is evaporated to cool the
incoming air and to condense a portion
of the refrigerant vapor. A second heat
exchanger (evaporator) cools the room
air.
A heat accumulator stores heat from
vapor at compressor outlet for
defrosting and lowering starting torque.
Axial piston, variable displacement
compressor
-------
Category
Cycle Type
Item or Title
Work, Phase Vapor Refrigerating Cycle Utilizing Cold
Change Compression Accumulation Material
Work, Phase Vapor Binary Solution Compressive Heat
Change Compression Pump with Solution Circuit
Work, Phase Vapor Air Conditioning and Heat Pump
Change Compression System
Work, Phase
Change
Work, Phase
Change
Vapor
Compression
Vapor
Compression
Heat Pump Apparatus
Process to Expand the Temperature
Glide of a Non-Azeotropic Working
Fluid Mixture in a Vapor Compression
Cycle
Work, No Phase
Change
Work, No Phase
Change
Work, No Phase
Change
Work, No Phase
Change
Reversed Stirling Refrigerating Machine
Reversed Stirling Refrigerating Apparatus Based Upon
the Use of Air
Reversed Stirling Method and Apparatus for Inducing
Heat Changes
Reversed Brayton Air Refrigerating Machine
Source
U.S. Patent 4918936
U.S. Patent 4918945
U.S. Patent 4981323
U.S. Patent 4679403
U.S. Patent 4987751
U.S. Patent 1508522
U.S. Patent 1545587
U.S. Patent 1275507
U.S. Patent 1295724
Comments
A portion of the liquid refrigerant is
evaporated to cool a thermal sink during
part load conditions. The thermal sink
then provides temporary additional
thermal capacity during full load
conditions.
Hybrid vapor compression/
absorption cycle
Compressor housing and compressor
outlet flow are cooled by a variable
portion of the evaporator return flow.
Cycle utilizes a variable speed
compressor and a refrigerant blend
Refrigerant not specified in this patent
Reversed Stirling cycle, working fluid is
air
Reversed Stirling cycle
Reversed Stirling cycle, working fluid
is air
Reversed Brayton cycle
-------
Category
Cycle Type
Item or Title
Work, No Phase Reversed Stirling Heat Pump/ Refrigerator Using Liquid
Change Working Fluid
Direct Electric Thermoelectric Thermoelectric Refrigeration
Direct Electric Electrolytic Electrolytic System of Refrigeration
Magnetic Magnetic Magnetic Refrigeration
(Collapsing Field)
Magnetic Magnetic Magnetic Refrigeration
(Displaced Core)
Other
Evaporative Refrigerating Machine
Other
Evaporative Desiccant Air Conditioning Unit
Source
U.S. Patent 4353218
Reference [2]
Reference [3]
Reference [4]
U.S. Patent 1114006
U.S. Patent 4509334
U.S. Patent 4589953
Reference [5]
Reference [5]
U.S. Patent 1483990
Reference [6]
Comments
Multi-engine Stirling cycle with
regeneration. Working fluid can be
carbon dioxide or propylene in the
liquid state.
Direct conversion of electrical to
thermal energy
Refrigerant vapor is produced by
applying an electric potential across an
electrolyte in an electric cell. Uses an
evaporator and condenser for heat
transfer
Helium gas is used as the heat transfer
medium
Gadolinium core is displaced in and out
of a non-collapsing magnetic field
Multi-stage system utilizing steam
ejectors and a vacuum
Uses desiccant dehumidification and
air-to-air heat exchange
-------
APPENDIX B. ALTERNATIVE REFRIGERATION TECHNOLOGY
MODELING PROGRAM
Introduction
The objective of this program is to determine the modeled refrigeration COP
for different thermodynamic cycles and the ideal (reversed Carnot) COP at a fixed
sink temperature and over the range of source temperatures from -24 C to 28 C. All
models assume steady state operation of a system in communication with two infinite
thermal reservoirs, the source and sink. Both reservoirs are assumed to be at fixed
temperatures which are unchanging over time and with the amount of heat removed
from or added to them.
The computer program was developed to estimate the coefficient of performance
of the following refrigeration cycles:
• Reversed Stirling
• Reversed Brayton
• Regenerative reversed Brayton
• Thermoelectric
• Pulse tube and thermoacoustic
252
-------
• Magnetic Reversed Stirling
• Magnetic constant field/poly tropic
• Magnetic combined constant field/isentropic
This program was written in the FORTRAN language. The source code can be
compiled and used on any system having a FORTRAN compiler. The executable
version furnished here can be installed and run on IBM or IBM compatible personal
computers.
The program is structured in an easy to use, interactive, menu driven format.
The user is asked to supply information in a step by step process. Some of the input
data are supplied as default values which reflect reasonable estimates, consistent with
the present state of the art for each alternative technology. The user can substitute
other data in place of the default values, if desired.
Validation of the Program
All thermodynamic models used in this program were validated by comparing
the results of the numerical model with the results of hand calculations. The thermo-
dynamic property subroutines were validated by comparing the results with tabulated
values in Reynolds [31].
Program Structure
The program source code is contained in three files:
253
-------
1. l.FOR is the main program which contains the introductory screen formatted
output statements, decision logic for the menus to select a particular refriger-
ation technology, and the default values for input data.
2. CYCLES.FOR contains the thermodynamic modeling subroutines used to cal-
culate the theoretical COPs for the refrigeration cycles.
3. PROPS.FOR contains the thermodynamic property subroutines for air, helium,
and gadolinium.
The main program (l.FOR) calls the appropriate cycle subroutine from CYCLES.FOR,
which in turn calls a property subroutine from PROPS.FOR. The source code is well
documented with comment statements indicating the purpose of each block of code.
System Requirements
This program was written in FORTRAN code which is compatible with MI-
CROSOFT FORTRAN version 5.0. The executable version of the program has no
special requirement as to micro-processor type; it can be run on computers using the
8086 through 80486 processors.
One feature of MICROSOFT FORTRAN which must be kept in mind when
using this program is the choice of linking library options which are used to form the
executable file during the compiling and linking process. MICROSOFT has developed
separate libraries which are selected during the installation of its FORTRAN software.
For computers equipped with the 8087, 80287, or 80387 math coprocessor, the library
LLIBFOR007 is used. Since the math coprocessor is incorporated in all 80486 chips,
this library is utilized for these machines as well. For computers using the 8086, 80286,
254
-------
and 80386 microprocessor without the 8087, 80287, or 80387 math coprocessor, the
emulator library LLIBFORE is used. Therefore, if the program is linked using the
LLIBFOR007 library to form the executable file, it will not run on a computer that
does not have a math coprocessor.
Program Installation
The program includes some screen clearing commands during execution. A line
must be included in the computer's CONFIG.SYS file which reads exactly as follows:
DEVICE=C:\DOS\ANSI.SYS
If this line is not included, the code "2J]" will appear in the upper left corner of
the monitor screen; however, the program can still be run and will provide correct
results.
To install the program:
1. Choose or create a suitable directory on the hard disk.
2. Insert the diskette in the A drive and choose the directory entitled IFOR.
3. Type the command:
COPY l.EXE C:\(directory name)\l.EXE
Running the Program
To start the program, type "1" and press return. Each screen is self explanatory
and prompts the user for the required input action (such as pressing return to refresh
255
-------
a screen), numerical input value, or choice (yes or no). The user is also prompted to
furnish an output file name for the file to which the output data will be written.
At the end of a program sequence, the user can choose to either start a new
sequence or to exit the program by answering "Y" or "N" to the question appearing
on the screen.
The data from each run will be found in the data file named during the run
sequence. Each new case must have a unique file name. If the same file name is
given, the data from the previous run will be overwritten. It is suggested that the
file name be appended with a letter or number to indicate the order of the run. For
example, the file names TE1.DAT, TE2.DAT, and TE3.DAT could be used for the
data files for the first, second, and third runs used to consider different cases for a
thermoelectric cooling system. A sample data file is included as Appendix C.
256
-------
c ************************************************************************
c
C REFRIGERATIOH PERFORMANCE COMPARISON ROUTINE
C
C
C
C PREPARED BY:
C
C DON 6AUGER
C
C MECHANICAL ENGINEERING DEPARTMENT
C
C IOWA STATE UNIVERSITY
C
C AMES, IOWA
C
C MAY 1993
C
C ************************************************************************
c
c THIS ROUTINE COMPARES THE PERFORMANCE OF VARIOUS ALTERNATIVE
C REFRIGERATION CYCLES USING THERMODYNAMIC MODELS. THE PROGRAM
C IS IN THREE PARTS:
C
C 1) A MAIN PROGRAM (l.FOR) IN WHICH THE TEMPERATURES AND
C SPECIFIC PARAMETERS FOR THE MODELS ARE ENTERED, AND THE
C DESIRED MODEL IS SELECTED.
C
C 2) A SECOND FILE (CYCLES.FOR) CONTAINS A COLLECTION OF
C THERMODYNAMIC MODELS IN SUBROUTINE FORM.
C
C 3) THE THIRD FILE (PROPS.FOR) CONTAINS A COLLECTION OF
C THERMODYNAMIC PROPERTY SUBROUTINES WHICH ARE CALLED
C BY THE APPROPRIATE MODEL IN CYCLES.FOR.
C
C THE PROGRAM IS STRUCTURED IN AN INTERACTIVE MANNER IN WHICH THE USER
C IS PROMPTED TO ANSWER A SERIES OF QUESTIONS REGARDING THE CHOICE OF A
C SINK TEMPERATURE, HEAT EXCHANGER APPROACH TEMPERATURES, OUTPUT DATA
C FILE NAME, REFRIGERATION CYCLE MODEL CHOICE, AND MODEL-SPECIFIC
C PARAMETERS.
C
C WHERE POSSIBLE, REASONABLE DEFAULT VALUES OF PARAMETERS HAVE BEEN
C INCLUDED AS A STARTING POINT. THE USER CAN CHANGE THESE VALUES, IF
C DESIRED.
C
C WE HAVE TRIED TO MAKE THE PROGRAM AS "CRASHPROOF" AS POSSIBLE;
C HOWEVER, IN SOME INSTANCES THE PROGRAM EXECUTION WILL STOP IF
C CERTAIN MODEL-SPECIFIC CONSTRAINTS ARE EXCEEDED. THE PROGRAM MUST
257
-------
C BE RESTARTED AND NEW VARIABLE VALUES SHOULD BE CHOSEN.
C
C SYSTEM REQUIREMENTS:
C
C THE PROGRAM IS WRITTEN IN FORTRAN AND CAN BE COMPILED ON AN
C IBM OR IBM COMPATIBLE PERSONAL COMPUTER. MICROSOFT
C FORTRAN VERSION 5.0 WAS USED TO CREATE THE EXECUTABLE FILE.
C
C A LINE SHOULD BE INSERTED INTO THE CONFIG.SYS FILE WHICH
C LISTS THE ANSI.SYS FILE AS A DEVICE. THE LINE SHOULD READ:
C
C DEVICE= ANSI.SYS
C
C THE COMPUTER SHOULD THEN BE RE-BOOTED. IF THIS LINE IS NOT
C PRESENT IN THE CONFIG.SYS FILE, THE PROGRAM WILL STILL FUNCTION.
C HOWEVER, A CHARACTER STRING "2J]" WILL APPEAR IN THE UPPER LEFT-
C HAND CORNER OF THE SCREEN, AND THE SCREEN CLEARING FEATURE BET-
C WEEN PARAMETER CHOICES MAY NOT FUNCTION CORRECTLY.
C
C
C ********* ALL TEMPERATURE INPUTS MUST BE IN DEGREES CELSIUS! ***********
C
C ************************************************************************
c
C VARIABLE DECLARATION:
C
IMPLICIT REAL*8(A-H,0-Z)
INTEGER NCYCLE,II,JJ,KTT2
CHARACTER*50 OUTPUTFILE,WARN
CHARACTER*1 CH0ICE1,CH0ICE2,CH0ICE3,CH0ICE4,CHOICES,CH0ICE6,
* CH0ICE7,CH0ICE8
C
C ************************************************************************
c
C CLEAR THE SCREEN:
C
JJ = 27
WRITE(6,500) JJ
500 F0RMAT(1X,A1,'[2J')
C
C ************************************************************************
c
C INTRODUCTORY SCREEN:
C
WRITE(6,«0 ' '
WRITE(6,») ' '
WRITE(6,501) 'REFRIGERATION TECHNOLOGY COMPARISON ROUTINE'
258
-------
501 FORMAT (16X.A43,//)
C
WRITE(6,502) 'DEPARTMENT OF MECHANICAL ENGINEERING'
502 FORMAT(19X,A36,/)
C
WRITE(6,21) 'IOWA STATE UNIVERSITY'
21 F0RMAT(27X,A21)
C
WRITE(6,504) 'AMES, IOWA 50011'
504 F0RMAT(29X,A16,///////////)
C
C ************************************************************************
c
c CLEAR THE SCREEN:
C
II = CHAR(13)
WRITE(6,505)'PRESS RETURN'
505 F0RMAT(32X,A12)
C
READ(6,506) II
506 FORMAT(Al)
C
WRITE(6,500) J J
C
C ************************************************************************
c
WRITE(6,45) 'THIS PROGRAM CAN BE USED TO COMPARE DIFFERENT'
45 F0RMAT(15X,A45)
C
WRITE(6,48) 'REFRIGERATION TECHNOLOGIES AT A FIXED SINK TEMP.'
48 F0RMAT(15X,A48)
WRITE(6,509) 'OVER A RANGE OF SOURCE TEMPERATURES'
509 FORMAT(15X,A35,//////////)
WRITE(6,505)'PRESS RETURN'
C
C ************************************************************************
c
C OPTION TO CHANGE THE SINK TEMPERATURE:
C
READ(6,506) II
WRITE(6,500) JJ
C
C
C USER OPPORTUNITY TO CHANGE TO A DIFFERENT SINK TEMPERATURE:
C
4444 WRITE(6,37) 'THE DEFAULT SINK TEMPERATURE FOR THIS'
37 FORMAT(15X,A37)
259
-------
WRITE(6,539) 'APPLICATION IS 35.0 DEGREES C.'
539 FORMAT(15X,A30,/////)
WRITE(6,540) 'DO YOU WISH TO ACCEPT THIS TEMPERATURE? Y OR I'
540 FORMAT(15X.A47,//////)
WRITE(6,31)'MAKE SELECTION AND PRESS RETURN'
31 F0RMAT(15X,A31)
C
4001 READ(6,519) CH0ICE1
519 FORMAT(Al)
C
WRITE(6,500) JJ
IF ((CH0ICE1 .Eq. 'Y').OR.(CH0ICE1 .Eq. 'y')) THEN
TIC = 35.0
CONTINUE
ELSEIF ((CH0ICE1 .Eq. 'N').OR.(CH0ICE1 .Eq. 'n')) THEN
WRITE(6,42) 'ENTER THE NEW SINK TEMPERATURE IN DE6. C.'
42 FORMAT(15X.A42)
READ(6,*) T1CN
WRITE(6,500) JJ
WRITE(6,38) 'YOU HAVE CHOSEN A NEW SINK TEMPERATURE'
38 F0RMAT(15X,A38)
WRITE(6,543) 'OF: '.T1CN,' DEGREES C.'
543 FORMAT(15X,A4,F6.3,All,//////)
TIC = T1CN
ELSE
WRITE(6,752)'TYPE Y OR N AND PRESS RETURN'
752 FORMAT(15X,A29)
GO TO 4001
ENDIF
C
C ************************************************************************
C
WRITE(6,43)'THE RANGE OF SOURCE TEMPERATURES OVER WHICH'
WRITE(6,43)'THE COP WILL BE CALCULATED IS -24 C TO 28 C.'
43 F0RMAT(15X,A44)
C
C ************************************************************************
c
C CLEAR THE SCREEN:
C
WRITE(6,») ' '
WRITE(6,») ' '
WRITEC6,*) ' '
WRITE(6,») ' '
WRITE(6,*) ' '
WRITE(6,*) ' '
WRITE(6,505)'PRESS RETURN'
C
260
-------
READ(6,506) II
WRITE(6,500) JJ
C
C ************************************************************************
c
C MINIMUM APPROACH TEMPERATURE SELECTION:
C
DELTL = 5.0
DELTH = 5.0
C
WRITE(6,48)'THIS PROGRAM USES A MINIMUM APPROACH TEMPERATURE'
WRITE(6,43)'T0 ACCOUNT FOR HEAT EXCHANGER EFFECTIVENESS.'
WRITE(6,47)'THE DEFAULT VALUE IS 5 DEGREES CELSIUS FOR BOTH'
47 FORMAT(15X,A47)
WRITE(6,436)'THE SOURCE AND SINK HEAT EXCHANGERS.'
436 FORMAT(15X,A36,////)
WRITE(6,649)'DO YOU WISH TO ACCEPT THESE TEMPERATURES? Y OR N'
WRITE(6,31)'MAKE SELECTION AND PRESS RETURN'
C
1001 READ(6,519) CH0ICE2
C
WRITE(6,500) JJ
IF ((CH0ICE2 .Eq. 'Y').0R.(CH0ICE2 .Eq. 'y')) THEN
CONTINUE
ELSEIF ((CH0ICE2 .Eq. 'N').OR.(CH0ICE2 .Eq. 'n')) THEN
C
WRITE(6,50)'ENTER THE SOURCE MINIMUM APPROACH TEMP. IN DEG. C.'
50 F0RMAT(15X,A50)
READ(6,*) DELTL
WRITE(6,48) 'YOU HAVE CHOSEN A NEW SOURCE MIN. APPROACH TEMP.'
C
WRITE(6,543) 'OF: ',DELTL,' DEGREES C.'
C
WRITE(6,51) 'ENTER THE SINK MINIMUM APPROACH TEMPERATURE DEG. C.'
51 F0RMAT(15X,A51)
C
READ(6,*) DELTH
WRITE(6,39) 'YOU HAVE CHOSEN A NEW SINK MIN. APPROACH TEMP.'
39 F0RMAT(15X,A46)
C
WRITE(6,543) 'OF: '.DELTH,' DEGREES C.'
C
WRITE(6,*) ' '
WRITE(6,*) ' '
WRITE(6,*) ' '
WRITE(6,505)'PRESS RETURN'
READ(6,506) II
261
-------
WRITE(6,500) JJ
ELSE
WRITE(6,752)'TYPE Y OR I AND PRESS RETURN'
GO TO 1001
ENDIF
C
C ************************************************************************
C
C INPUT THE NUMBER OF THE REFRIGERATION TECHNOLOGY TO BE CONSIDERED:
C
WRITE(6,545)'ENTER THE NUMBER OF THE CYCLE FROM THE MENU'
545 FORMAT(15X,A43,///)
WRITE(6,546) 'STIRLING 1'
WRITE(6,546) 'REVERSED BRAYTON 2'
WRITE(6,546) 'REVERSED BRAYTON WITH REGENERATION 3'
WRITE(6,546) 'THERMOELECTRIC 4'
WRITE(6,546) 'PULSE TUBE 5'
WRITE(6,546) 'MAGNETIC HEAT PUMP 6'
546 FORMAT(15X.A43,/)
C
READ(6,*) NCYCLE
WRITE(6,500) JJ
C
C
WRITE(6,48)'YOU WILL BE GIVEN THE OPPORTUNITY TO CHANGE SOME'
WRITE(6,49)'OF THE DEFAULT VALUES OF PARAMETERS FOR THE CYCLE'
49 F0RMAT(15X,A49)
WRITE(6,115)'YOU HAVE CHOSEN'
115 F0RMAT(15X,A15,////)
1700 WRITE(6,45) 'FIRST, ENTER THE NAME OF THE DATA OUTPUT FILE'
READ(6,548) OUTPUTFILE
WRITE(6,500) JJ
548 FORMAT(A50)
C
OPEN(11,FILE=OUTPUTFILE,STATUS='UNKNOWN')
WRITE(11,517)'SINK TEMPERATURE =',T1C,'CELSIUS'
517 FORMAT(15X,A18,F3.0,2X,A7,/)
WRITE(11,518)'HIGH TEMP HX DELTA T =',DELTH,'CELSIUS'
518 FORMAT(15X,A22,F3.0,2X,A7,/)
WRITE(11,522)'LOW TEMP HX DELTA T =',DELTL,'CELSIUS'
522 FORMAT(15X,A21,F3.0,2X,A7,////)
C
C ************************************************************************
c
C CHOOSE REFRIGERATION CYCLES AND SPECIFIC PARAMETERS:
C
IF(NCYCLE .Eq. 1) THEN
C
262
-------
WRITE(6,46)'YOU HAVE CHOSEN THE STIRLING CYCLE. THE IDEAL'
WRITE(6,46)'THEORETICAL STIRLIIG CYCLE PROVIDES THE CARNOT'
46 FORMAT(15X.A46)
WRITE(6,47)'COP. HOWEVER, THE COP CALCULATED BY THIS MODEL'
WRITE(6,51)'WILL BE LOWER DUE TO THE IRREVERSIBILTIY INTRODUCED'
WRITE(6,24)'IN THE HEAT EXCHAKGERS.'
24 FORMAT(15X.A24)
WRITE(6,») ' '
WRITE(6,*) ' '
WRITE(6,*) ' '
WRITE(6,45)'AS A COMPARISON-THE BEST COPs CURRENTLY BEING'
WRITE(6,48)'OBTAINED EXPERIMENTALLY IN FREE PISTON STIRLING'
WRITE(6,SO)'REFRIGERATORS IS ABOUT 30'/. OF CARHOT WHEN OPERATED'
WRITE(6,125)'IN THIS TEMPERATURE RANGE'
125 FORMAT(15X,A25,///)
C
WRITE(6,505)'PRESS RETURN'
READ(6,506) II
WRITE(6,500) JJ
WRITEC11,515)'STIRLING CYCLE RESULTS'
515 FORMAT(15X.A22,//)
WRITE(11,899)'SOURCE TEMP.','CARNOT COP','COP','COP/COPC',
* 'COMMENTS'
899 FORMAT(7X,A12,2X,A10,6X,A3,4X.A8,10X.A8,/)
C
GO TO 3333
C ************************************************************************
c
C REVERSED BRAYTON CYCLE:
C
ELSE IF(NCYCLE .Eq. 2) THEN
C
WRITE(6,43)'YOU HAVE CHOSEN THE REVERSED BRAYTON CYCLE.'
C
C **********************************************************************
c
C ASSIGN VALUES TO THE PRESSURE RATIO, COMPRESSOR EFFICIENCY, AND
C EXPANDER EFFICIENCY:
C
WRITE(6,47)'THIS PROGRAM USES A PRESSURE RATIO WHICH CAN BE'
WRITE(6,47)'CHANGED BY THE USER. THE DEFAULT VALUE IS 3.0.'
WRITE(6,51)'IT IS RECOMMENDED THAT THE PRESS. RATIO NOT EXCEED'
WRITE(6,49)'4.0 IN THIS PROGRAM DO TO LOW TEMP. THERMODYNAMIC'
WRITE(6,321) 'PROPERTY LIMITATIONS.'
321 FORMAT(15X,A21,///)
WRITE(6,649)'D0 YOU WISH TO ACCEPT THE PRESSURE RATIO, Y OR N?'
263
-------
649 FORMAT(15X.A49,//////)
WRITE(6,31)'MAKE SELECTION AND PRESS RETURN'
C
C
C ************************************************************************
c
1002 READ(6,519) CH0ICE3
WRITE(6,500) JJ
IF ((CH0ICE3 .EQ. 'Y').OR.(CH0ICE3 .Eq. 'y')) THEN
C
PRATIO =3.0
CONTINUE
C
ELSEIF ((CH0ICE3 .Eq. 'N').OR.(CH0ICE3 .Eq. 'n')) THEN
C
WRITE(6,28) 'ENTER THE HEW PRESSURE RATIO'
28 FORMAT (15X.A28)
READ(6,*) PRATION
WRITE(6,E00) JJ
WRITE(6,36) 'YOU HAVE CHOSEN A NEW PRESSURE RATIO'
36 FORMAT(15X,A36)
WRITE(6,543) 'OF: '.PRATION,' '
PRATIO = PRATION
C
ELSE
C
WRITE(6,752)'TYPE Y OR N AND PRESS RETURN'
GO TO 1002
C
ENDIF
C
C **********************************************************************
c
WRITE(6,46)'ISENTROPIC EFFICIENCIES FOR THE COMPRESSOR AND'
WRITE(6,46)'EXPANDER ARE USED TO ACCOUNT FOR THE IRREVERS-'
WRITE(6,49)'IBILITIES PRESENT IN THESE COMPONENTS. PRESENTLY'
WRITE(6,51)'THE DEFAULT VALUES ARE 0.85 FOR BOTH THE COMPRESSOR'
WRITE(6,313)'AND EXPANDER.'
313 FORMAT(15X.A13,///)
C
WRITE(6,343)'DO YOU WISH TO ACCEPT THESE VALUES, Y OR N?'
343 FORMAT(15X.A43,///)
C
WRITE(6,31)'MAKE SELECTION AND PRESS RETURN'
C
C CLEAR THE SCREEN:
C
1003 READ(6,519) CH0ICE4
264
-------
WRITE(6,500) JJ
IF ((CH0ICE4 .EQ. 'Y').OR.(CH0ICE4 .EQ. 'y')) THEN
C
ETAE =0.85
ETAC =0.85
C
ELSEIF ((CH0ICE4 .Eq. 'I').OR.(CH0ICE4 .EQ. 'n')) THEN
C
WRITE(6,42) 'ENTER THE COMPRESSOR ISEHTROPIC EFFICIENCY'
READ(6,*) ETACN
WRITE(6,43) 'YOU HAVE CHOSEN A NEW COMPRESSOR EFFICIENCY'
WRITE(6,543) 'OF: ',ETACN,' '
C
WRITE(6,43) 'ENTER THE EXPANDER ISENTROPIC EFFICIENCY'
READ(6,*) ETAEN
WRITE(6,41)'YOU HAVE CHOSEN A NEW EXPANDER EFFICIENCY'
41 F0RMAT(15X,A41)
WRITE(6,543) 'OF: '.ETAEN,' '
ETAC = ETACN
ETAE = ETAEN
CONTINUE
C
ELSE
WRITE(6,752)'TYPE Y OR N AND PRESS RETURN'
GO TO 1003
ENDIF
C
C ************************************************************************
C
C WRITE THE REVERSED BRAYTON CYCLE RESULTS:
C
WRITEC11,520)'REVERSED BRAYTON CYCLE RESULTS'
520 FORMAT(15X,A32,/)
WRITE(11,590)'PRESSURE RATIO =',PRATIO
WRITE(11,590)'COMP. EFF.=',ETAC
WRITE(11,590)'EXPANDER EFF. =',ETAE
590 F0RMAT(12X,A16,F10.3,//)
WRITE(11,899)'SOURCE TEMP.','CARNOT COP','COP','COP/COPC',
ft 'COMMENTS'
C
WRITE(6,820)'EXECUTING REVERSED BRAYTON CYCLE MODEL'
820 FORMAT(15X,A38,/)
WRITE(6,590)'PRESSURE RATIO =',PRATIO
WRITE(6,590)'COMP. EFF.=',ETAC
WRITE(6,590)'EXPANDER EFF. =',ETAE
890 F0RMAT(15X,A16,F10.3)
C
265
-------
GO TO 3333
C ************************************************************************
c
C REVERSED BRAYTON CYCLE WITH REGENERATION:
C
ELSE IF(HCYCLE .Eq. 3) THEI
C
WRITE(6,48)'YOU HAVE CHOSEN THE REVERSED BRAYTOH CYCLE WITH'
WRITE(6,113)'REGENERATION.'
113 FORMAT(15X,A13,/)
C
C **********************************************************************
C
C ASSIGN VALUES TO THE PRESSURE RATIO, COMPRESSOR EFFICIENCY, AND
C EXPANDER EFFICIENCY:
C
WRITE(6,47)'THIS PROGRAM USES A PRESSURE RATIO WHICH CAN BE'
WRITE(6,47)'CHANGED BY THE USER. THE DEFAULT VALUE IS 1.5.'
WRITE(6,51)'IT IS RECOMMENDED THAT THE PRESS. RATIO NOT EXCEED'
WRITE(6,49)'4.0 IN THIS PROGRAM DO TO LOW TEMP. THERMODYNAMIC'
WRITE(6,321)'PROPERTY LIMITATIONS.'
WRITE(6,649)'DO YOU WISH TO ACCEPT THE PRESSURE RATIO, Y OR N?'
WRITE(6,31)'MAKE SELECTION AND PRESS RETURN'
C
C ************************************************************************
C
1004 READ(6,519) CH0ICE3
WRITE(6,500) JJ
IF ((CH0ICE3 .Eq. 'Y').OR.(CH0ICE3 .Eq. 'y')) THEN
C
PRATIO =1.5
CONTINUE
C
ELSEIF ((CH0ICE3 .Eq. 'N').OR.(CH0ICE3 .Eq. 'n')) THEN
WRITE(6,28) 'ENTER THE NEW PRESSURE RATIO'
READ(6,*) PRATION
WRITE(6,500) JJ
WRITE(6,36) 'YOU HAVE CHOSEN A NEW PRESSURE RATIO'
WRITE(6,543) 'OF: ',PRATION,' '
PRATIO = PRATION
C
ELSE
C
WRITE(6,752)'TYPE Y OR N AND PRESS RETURN'
GO TO 1004
C
ENDIF
C
266
-------
c **********************************************************************
c
WRITE(6,46)'ISOTROPIC EFFICIENCIES FOR THE COMPRESSOR AID'
WRITE(6,46)'EXPANDER ARE USED TO ACCOUNT FOR THE IRREVERS-'
WRITE(6,49)'IBILITIES PRESENT IN THESE COMPONENTS. PRESENTLY'
WRITE(6,51)'THE DEFAULT VALUES ARE 0.85 FOR BOTH THE COMPRESSOR'
WRITE(6,313)'AND EXPANDER.'
WRITE(6,343)'DO YOU WISH TO ACCEPT THESE VALUES, Y OR N?'
WRITE(6,31)'MAKE SELECTION AND PRESS RETURN'
C
C
1005 READ(6,519) CH0ICE4
WRITE(6,500) JJ
IF ((CH0ICE4 .Eq. 'Y').OR.(CH0ICE4 .Eq. 'y')) THEN
C
ETAE =0.85
ETAC = 0.85
C
ELSEIF ((CH0ICE4 .Eq. 'N').OR.(CH0ICE4 .Eq. 'n')) THEN
C
WRITE(6,42) 'ENTER THE COMPRESSOR ISENTROPIC EFFICIENCY'
READ(6,*) ETACN
WRITE(6,43) 'YOU HAVE CHOSEN A NEW COMPRESSOR EFFICIENCY'
WRITE(6,543) 'OF: ',ETACN,' '
C
WRITE(6,43) 'ENTER THE EXPANDER ISENTROPIC EFFICIENCY'
READ(6,*) ETAEN
WRITE(6,41)'YOU HAVE CHOSEN A NEW EXPANDER EFFICIENCY'
WRITE(6,543) 'OF: '.ETAEN,' '
ETAC = ETACN
ETAE = ETAEN
CONTINUE
C
ELSE
WRITE(6,752)'TYPE Y OR N AND PRESS RETURN'
GO TO 1005
ENDIF
C
C ************************************************************************
c
WRITE(6,45)'THIS PROGRAM USES A REGENERATOR EFFECTIVENESS'
WRITE(6,52)'T0 ACCOUNT FOR IRREVERSIBILITIES IN THE REGENERATOR.'
52 FORMAT(15X,A52)
WRITE(6,138)'THIS VALUE CAN BE CHANGED BY THE USER.'
138 FORMAT(15X.A38,/)
WRITE(6,226)'THE DEFAULT VALUE IS 0.88.'
226 FORMAT(15X.A26,//)
WRITE(6,641)'DO YOU WISH TO ACCEPT THIS VALUE, Y OR N?'
267
-------
641 F0RMAT(15X,A41,//////)
WRITE(6,31)'MAKE SELECTION AND PRESS RETURN'
C
C CLEAR THE SCREEN:
C
C ************************************************************************
c
1006 READ(6,519) CHOICES
WRITE(6,500) JJ
c
IF ((CHOICES .EQ. 'Y').OR.(CHOICES .EQ. 'y')) THEN
C
ETAR =0.88
CONTINUE
C
ELSEIF ((CHOICES .Eq. 'N').OR.(CHOICES .Eq. 'n')) THEN
WRITE(6,35)'ENTER THE REGENERATOR EFFECTIVENESS'
35 FORMAT (15X.A35)
READ(6,*) ETARN
WRITE(6,48) 'YOU HAVE CHOSEN A NEW REGENERATOR EFFECTIVENESS'
WRITE(6,543) 'OF: '.ETARN,' '
ETAR = ETARN
C
ELSE
WRITE(6,752)'TYPE Y OR N AND PRESS RETURN'
GO TO 1006
ENDIF
C
C **********************************************************************
c
C WRITE THE REVERSED BRAYTON CYCLE WITH REGENERATION RESULTS:
C
WRITE(11,620)'REVERSED BRAYTON CYCLE WITH REGENERATION RESULTS'
620 FORMAT(16X,A49,/)
WRITE(11,690)'PRESSURE RATIO = '.PRATIO
WRITE(l1,690)'COMP. EFF.= ',ETAC
WRITE(11,690)'EXPANDER EFF. = ',ETAE
WRITE(11,690)'REGEN. EFF. = ',ETAR
690 F0RMAT(12X,A17,F6.3,/)
WRITE(11,899)'SOURCE TEMP.','CARNOT COP','COP','COP/COPC',
& 'COMMENTS'
C
WRITE(6,821)'EXECUTING REVERSED BRAYTON CYCLE WITH REGEN. MODEL'
821 FORMAT(15X,A50,/)
WRITE(6,590)'PRESSURE RATIO =',PRATIO
WRITE(6,590)'COMP. EFF.=',ETAC
WRITE(6,590)'EXPANDER EFF. =',ETAE
WRITE(6,690)'REGEN. EFF. = ',ETAR
268
-------
c
GO TO 3333
C
C ************************************************************************
c
ELSE IF(NCYCLE .EQ. 4) THEN
C
WRITE(6,46)'YOU HAVE CHOSEH THE THERMOELECTRIC CYCLE. THE'
WRITE(6,46)'MODEL CONTAINS A FIGURE OF MERIT PARAMETER (Z)'
WRITE(6,48)'WHICH CAN BE VARIED BY THE USER. THIS PARAMETER'
WRITE(6,49)'IS A FUNCTION OF THE SEMI-CONDUCTOR MATERIAL PAIR'
WRITE(6,46)'USED II THE SYSTEM. THE DEFAULT VALUE IS 0.003'
WRITE(6,45)'WHICH IS CURRENTLY THE HIGHEST VALUE ACHIEVED'
WRITEC6.115)'EXPERIMENTALLY.'
WRITE(6,341)'HIGHER VALUES OF Z WILL IICREASE THE COP.'
341 F0RMAT(15X,A41,///)
C
C ************************************************************************
C
C FIGURE OF MERIT, Z:
C
WRITE(6,646)'DO YOU WISH TO ACCEPT THE VALUE OF Z, Y OR N?'
646 FORMAT(15X,A46,//////)
WRITE(6,31)'MAKE SELECTION AND PRESS RETURN'
C
C CLEAR THE SCREEN:
C
C ************************************************************************
c
1007 READ(6,519) CH0ICE6
WRITE(6,500) JJ
IF ((CHOICES .Eq. 'Y').OR.(CH0ICE6 .EQ. 'y')) THEN
C
Z = 0.003
CONTINUE
C
ELSEIF ((CH0ICE6 .Eq. 'N').OR.(CHOICES .Eq. 'n')) THEN
C
WRITE(6,224) 'ENTER THE NEW VALUE OF Z'
224 FORMAT (15X.A24,//)
READ(6,*) ZN
WRITE(6,32)'YOU HAVE CHOSEN A NEW Z VALUE OF'
32 FORMAT(15X,A32)
WRITE(6,543)'OF: ',ZN,' '
Z = ZN
C
ELSE
269
-------
WRITE(6,752)'TYPE Y OR H AID PRESS RETURN'
GO TO 1007
ENDIF
C
C **********************************************************************
c
WRITE(11,619)'THERMOELECTRIC CYCLE RESULTS'
619 FORMAT(15X,A28,//)
C
WRITE(11,596)'FIGURE OF MERIT (Z) = \Z
596 FORMAT(12X,A22,F5.4,/)
WRITE(11,899)'SOURCE TEMP.','CARNOT COP','COP','COP/COPC',
* 'COMMENTS'
C
VRITE(6,822)'EXECUTING THERMOELECTRIC CYCLE MODEL'
822 FORMAT(15X,A36,/)
WRITE(6,690) ' Z = \Z
GO TO 3333
C
C ************************************************************************
c
c PULSE TUBE CYCLE:
C
ELSE IF(ICYCLE .EQ. 5) THEN
C
WRITE(6,39)'YOU HAVE SELECTED THE PULSE TUBE CYCLE.'
WRITE(6,44)'THE MODEL IS AN IDEALIZED STEADY STATE MODEL'
44 FORMAT(15X,A44)
WRITE(6,46)'OPERATING WITH HELIUM AS THE WORKING MATERIAL.'
C
WRITE(6,47)'THIS PROGRAM USES A PRESSURE RATIO WHICH CAN BE'
WRITE(6,47)'CHANGED BY THE USER. THE DEFAULT VALUE IS 2.5.'
WRITE(6,*) ' '
WRITE(6,48)'CHANGING THE PRESSURE RATIO SIMULATES INCREASING'
WRITE(6,47)'THE PRESSURE RATIO IN A PULSE TUBE REFRIGERATOR'
WRITE(6,47)'OR INCREASING THE AMPLITUDE OF THE DIAPHRAGM IN'
WRITE(6,230)'A THERMOACOUSTIC REFRIGERATOR.'
230 F0RMAT(15X,A30,//)
WRITE(6,649)'DO YOU WISH TO ACCEPT THE PRESSURE RATIO, Y OR N?'
WRITE(6,31)'MAKE SELECTION AND PRESS RETURN'
C
C CLEAR THE SCREEN:
C
C ************************************************************************
c
1008 READ(6,519) CH0ICE3
WRITE(6,500) JJ
IF ((CH0ICE3 .Eq. 'Y').OR.(CH0ICE3 .Eq. 'y')) THEN
270
-------
c
PRATIO =2.5
CONTINUE
C
ELSEIF ((CH0ICE3 .Eq. 'N').OR.(CH0ICE3 .Eq. 'n')) THEN
C
WRITE(6,28) 'ENTER THE HEW PRESSURE RATIO'
READ(6,*) PRATION
WRITE(6,500) JJ
WRITE(6,36) 'YOU HAVE CHOSEN A NEW PRESSURE RATIO'
WRITE(6,543) 'OF: PRATION,' '
PRATIO = PRATION
C
ELSE
C
WRITE(6,752)'TYPE Y OR N AND PRESS RETURN'
60 TO 1008
C
END IF
C
C **********************************************************************
c
WRITE(6,48)'THE ISENTROPIC EFFICIENCY OF THE COMPRESSION AND'
WRITE(6,50)'EXPANSION PROCESSES CAN BE SPECIFIED IN THE MODEL.'
WRITE(6,42)'THIS EFFICIENCY IS USED TO ACCOUNT FOR THE'
WRITE(6,51)'IRREVERSIBILITIES RESULTING DURING THESE PROCESSES.'
WRITE(6,226)'THE DEFAULT VALUE IS 0.80.'
WRITE(6,343)'DO YOU WISH TO ACCEPT THESE VALUES, Y OR N?'
WRITE(6,31)'MAKE SELECTION AND PRESS RETURN'
C
C
1011 READ(6,519) CH0ICE4
WRITE(6,500) JJ
IF ((CH0ICE4 .Eq. 'Y').OR.(CH0ICE4 .Eq. 'y')) THEN
C
ETAE = 0.80
ETAC =0.80
C
ELSEIF ((CH0ICE4 .Eq. 'N').OR.(CH0ICE4 .Eq. 'n')) THEN
C
WRITE(6,31) 'ENTER THE ISENTROPIC EFFICIENCY'
READ(6,*) ETACN
WRITE(6,29) 'YOU HAVE CHOSEN AN EFFICIENCY'
29 FORMAT(15X.A29)
WRITE(6,543) 'OF: ETACN,' '
C
ETAC = ETACN
ETAE = ETACN
271
-------
CONTINUE
C
ELSE
VRITE(6,752)'TYPE Y OR N AND PRESS RETURN'
60 TO 1011
ENDIF
C
C ************************************************************************
c
WRITE(6,45)'THIS PROGRAM USES A REGENERATOR EFFECTIVENESS'
VRITE(6,S2)'T0 ACCOUNT FOR IRREVERSIBILITIES IN THE REGENERATION'
WRITE(6,51)'PROCESS OCCURRING AT THE TUBE WALL. THIS VALUE CAN'
VRITE(6,251)'BE CHANGED BY THE USER. THE DEFAULT VALUE IS 0.80.'
251 F0RMAT(15X,A51,//)
VRITE(6,641)'DO YOU WISH TO ACCEPT THIS VALUE, Y OR N?'
VRITE(6,31)'MAKE SELECTION AND PRESS RETURN'
C
C CLEAR THE SCREEN:
C
C ************************************************************************
c
1012 READ(6,519) CHOICES
WRITE(6,500) JJ
c
IF ((CHOICES .Eq. 'Y').OR.(CH0ICE5 .EQ. 'y')) THEN
C
ETAR = 0.80
CONTINUE
C
ELSEIF ((CHOICES .Eq. 'N').OR.(CHOICES .Eq. 'n')) THEN
WRITE(8,36)'ENTER THE REGENERATION EFFECTIVENESS'
READ(6,*) ETARN
WRITE(6,48) 'YOU HAVE CHOSEN A NEW REGENERATION EFFECTIVENESS'
WRITE(6,S43) 'OF: '.ETARN,' '
ETAR = ETARN
C
ELSE
WRITE(6,752)'TYPE Y OR N AND PRESS RETURN'
GO TO 1012
ENDIF
C
C **********************************************************************
c
WRITE(11,677)'PULSE TUBE CYCLE RESULTS'
677 FORMAT(15X,A24,/)
VRITE(11,690)'PRESSURE RATIO = '.PRATIO
WRITE(11,690)'COMP./EXP. EFF.= ',ETAC
272
-------
WRITE(11,690)'REGEN. EFF. = \ETAR
WRITE(11,899)'SOURCE TEMP.','CARHOT COP','COP','COP/COPC',
* 'COMMENTS'
WRITE(6,823)'EXECUTING PULSE TUBE CYCLE MODEL'
823 FORMAT(15X,A32,/)
WRITE(6,590)'PRESSURE RATIO =',PRATIO
GO TO 3333
C
C ************************************************************************
C
C MAGNETIC HEAT PUMP:
C
ELSE IF(NCYCLE .Eq. 6) THEN
C
WRITE(6,147)'YOU HAVE SELECTED THE MAGNETIC REFRIGERATION CYCLE.'
15 F0RMAT(15X,A51,/)
WRITE(6,44)'THE MODEL IS AN IDEALIZED STEADY STATE MODEL'
WRITE(6,46)'OPERATING BETWEEN TWO MAGNETIC FIELD STRENGTHS'
WRITE(6,140)'USING GADOLINIUM AS THE WORKING MATERIAL.'
140 FORMAT(15X,A40,/)
WRITE(6,45)'THE DEFAULT FIELD STRENGTHS ARE CURRENTLY SET'
WRITE(6,45)'AT THE MAXIMUM LIMITS - 0 AND 7 TESLAS. SEVEN'
WRITE(6,43)'TESLAS IS PRESENTLY THE PRACTICAL LIMIT FOR'
WRITE(6,42)'FIELD STRENGTH WITH TODAYS TECHNOLOGY. NO'
WRITE(6,147)'PROPERTY DATA IS AVAILABLE FOR FIELDS ABOVE 7T.'
147 F0RMAT(1SX,A47,/)
WRITE(6,45)'THE USER CAN CHANGE THE FIELD STRENGTH LIMITS'
WRITE(6,316)'BETWEEN 0 AND 7.'
316 FORMAT(15X,A16,///)
WRITE(6,643)'DO YOU WISH TO ACCEPT THESE LIMITS, Y OR N?'
643 F0RMAT(15X,A43,//////)
WRITE(6,31)'MAKE SELECTION AND PRESS RETURN'
C
C CLEAR THE SCREEN:
C
C ************************************************************************
c
1009 READ(6,519) CH0ICE7
WRITE(6,500) JJ
C
IF ((CH0ICE7 .Eq. 'Y').OR.(CH0ICE7 .Eq. 'y')) THEN
C
HL = 0.0
HH = 7.0
CONTINUE
C
ELSEIF ((CH0ICE7 .Eq. 'N').OR.(CH0ICE7 .Eq. 'n')) THEN
273
-------
c
WRITE(6,44) 'EHTER THE FIELD STRENGTH VALUES, HL AND HH.'
READ( 6, * )HLN,HHN
WRITE(6,41)'YOU HAVE CHOSEN NEW FIELD STRENGTH LIMITS'
WRITE(6,943)'0F: ',HLN,' AND ',HHN,' TESLAS'
943 FORMAT(15X,A4,F6.2,A5,F6.2,A7)
HL = HLN
HH = HHN
CONTINUE
C
ELSE
C
WRITE(6,752)'TYPE Y OR N AND PRESS RETURN'
GO TO 1009
C
ENDIF
C
C ************************************************************************
c
WRITE(11,617)'MAGNETIC REFRIGERATION CYCLE RESULTS'
617 FORMAT(15X,A36,/)
WRITE(11,454)'HIGH FIELD =',HH,'TESLAS'
454 F0RMAT(12X,A12,1X,F4.2,1X,A6,/)
WRITE(11,454)'LOW FIELD =',HL,'TESLAS'
WRITE(11,899)'SOURCE TEMP.','CARNOT COP','COP','COP/COPC',
* 'COMMENTS'
C
WRITE(6,824)'EXECUTING MAGNETIC REFRIGERATION CYCLE MODEL'
824 FORMAT(15X.A44,/)
WRITE(6,590)'HIGH FIELD =',HH
WRITE(6,590)'LOW FIELD =',HL
C
GO TO 3333
C
ENDIF
C
C ************************************************************************
c
C DO LOOP TO INCREMENT SOURCE TEMPERATURES:
C
3333 TOC = -24.0 ! CELSIUS
DO 9999 I = 1,27
C
C ************************************************************************
c
C CONVERT TO ABSOLUTE TEMPERATURES:
C
274
-------
TO = TOC + 273.15
T1 = TIC + 273.15
C
C ************************************************************************
c
C CALCULATE THE CARNOT COP:
C
CC = TO/(T1 - TO)
TLL = TO - DELTL
THH = T1 + DELTH
C
IF(NCYCLE .Eq. 1) THEN
WRITE(6,980)'ITERATION IUMBER',I,'OF 27'
980 F0RMAT(38X,A16,1X,I2,IX,A5)
60 TO 1000
ELSE IF(HCYCLE .Eq. 2) THE!
WRITE(6,980)'ITERATION NUMBER',I,'OF 27'
GO TO 1100
ELSE IF(NCYCLE .Eq. 3) THEN
WRITE(6,980)'ITERATION NUMBER',I,'OF 27'
GO TO 1200
ELSE IF(NCYCLE .Eq. 4) THEN
WRITE(6,980)'ITERATION NUMBER',I,'OF 27'
GO TO 1300
ELSE IF(NCYCLE .Eq. 5) THEN
WRITE(6,980)'ITERATION NUMBER',I,'OF 27'
GO TO 1400
ELSE IF(NCYCLE .Eq. 6) THEN
WRITE(6,980)'ITERATION NUMBER',I,'OF 27'
GO TO 1410
END IF
C
1000 CALL STIRLING(TO,DELTL,Tl,DELTH,COP)
GO TO 1500
C
1100 KTT2 = 1
CALL SBRAY(TLL,THH,ETAC,ETAE,PRATIO,COP,KTT2)
C
IF(KTT2 .Eq. 0) THEN
C0P=0
GO TO 1500
ELSE
GO TO 1500
ENDIF
C
1200 KTT2 = 1
CALL SBRAYR(TLL,THH,ETAC,ETAE,ETAR,PRATIO,COP,KTT2)
C
275
-------
IF(KTT2 .EQ. 0) THEN
C0P=0
GO TO 1500
ELSE
60 TO 1500
ENDIF
C
1300 CALL STE (TLL,THH,Z,COP)
GO TO 1500
1400 KTT2 = 1
CALL SPTSUB (TLL,THH,ETAC,ETAE,ETAR,PRATIO,COP,KTT2)
C
IF(KTT2 .Eq. 0) THEN
C0P=0
GO TO 1500
ELSE
GO TO 1500
ENDIF
C
1410 CALL SMHP (TLL,THH,HL,HH,COP)
GO TO 1500
C
C ************************************************************************
c
1500 IF (COP .LT. 0.0) THEH
WARN = 'TEMPERATURES OUT OF RANGE'
ELSE IF ((COP .GT. CC).AND.(NCYCLE .Eq. 2)) THEN
WARN = 'PRESSURE RATIO IS TOO LOW
ELSE IF ((KTT2 .Eq. 0).AND.(NCYCLE .Eq. 2)) THEN
WARN = 'COMP. OUTLET TEMP LESS THAN TH'
ELSE IF ((COP .GT. CC).AND.(NCYCLE .Eq. 3)) THEN
WARN = 'PRESSURE RATIO IS TOO LOW'
ELSE IF ((KTT2 .Eq. 0).AND.(NCYCLE .Eq. 3)) THEN
WARN = 'COMP. OUTLET TEMP LESS THAN TH'
ELSE IF ((COP .GT. CC).AND.(NCYCLE .Eq. 5)) THEN
WARN = 'PRESSURE RATIO IS TOO LOW'
ELSE IF ((KTT2 .Eq. 0).AND.(NCYCLE .Eq. 5)) THEN
WARN = 'COMP. OUTLET TEMP LESS THAN TH'
ELSE
WARN = ' '
ENDIF
C
RATIO = COP/CC
WRITE(11,552) TOC,CC,COP,RATIO,WARN
552 F0RMAT(5X,F10.3,2X,F10.3,2X,F10.3,2X,F10.3,3X,A30)
C
TOC = TOC +2.0
9999 CONTINUE
276
-------
WRITE(6,216)'MODEL COMPLETED'
215 F0RMAT(15X,A15,//)
WRITE(6,750)'OUTPUT IS IN'.OUTPUTFILE
750 F0RMAT(15X,A12,2X,AS0,///)
C
c
C CHOICE TO CONTINUE PROGRAM, OR HOT:
C
WRITE(6,632)'DO YOU WISH TO CONTINUE WITH ANOTHER CASE, Y OR N?'
632 FORMAT(15X.A50,///)
WRITE(6,31)'MAKE SELECTION AND PRESS RETURN'
C
C CLEAR THE SCREEN:
C
C ************************************************************************
c
1010 READ(6,519) CH0ICE8
WRITE(6,500) JJ
C
IF ((CH0ICE8 .Eq. 'Y').OR.(CH0ICE8 .Eq. 'y')) THEN
C
GO TO 4444
C
ELSE
C
CONTINUE
C
ENDIF
C
END
277
-------
SUBROUTINE STIRLING (TL,DELTL,TH,DELTH,COP)
C
IMPLICIT REAL+8(A-H,0-Z)
C
C THIS SUBROUTINE ESTIMATES THE COEFFICIENT OF PERFORMANCE OF AN IDEAL
C STIRLING REFRIGERATION CYCLE GIVEN THE ABSOLUTE TEMPERATURES OF THE
C SOURCE AND SINK AND THE MINIMUM APPROACH TEMPERATURE.
C
C ************************************************************************
C
TERM1 = (TH + DELTH)/(TL - DELTL)
TERM2 = TERM1 - 1.0
COP = 1/TERM2
C
RETURN
END
SUBROUTINE SBRAY (TL,TH,ETAC,ETAE,PRATIO,COP,JTT2)
C
IMPLICIT REAL*8(A-H,0-Z)
INTEGER NOP,JTT2
C
C ************************************************************************
C
c
C THIS SUBROUTINE IS USED TO CALCULATE THE COEFFICIENT OF
C PERFORMANCE OF THE REVERSED BRAYTON CYCLE WITHOUT
C REGENERATION.
C
C AIR IS THE WORKING FLUID AND ASSUMED TO BE AN IDEAL GAS.
C
C THE COMPRESSOR EFFICIENCY AND EXPANDER EFFICIENCY ARE SPECIFIED
C BY THE USER IN THE MAIN PROGRAM.
C
C THE LOW PRESSURE IS FIXED 1 ATMOSPHERE.
C
C ALL PRESSURES ARE IN KILOPASCALS.
C
C ALL TEMPERATURES ARE IN DEGREES KELVIN.
C
C **********************************************************************
C
C SET THE LOW PRESSURE:
C
PI = 101.32S !KPa
C
278
-------
c ************************************************************************
C ACCOUNT FOR THE MIHIMUM RECOVERY TEMPERATURES IH THE
C HIGH AND LOW TEMPERATURE HEAT EXCHANGERS:
C
T1 = TL
T3 = TH
C
C
C **********************************************************************
c
C STATE ONE - COMPRESSOR INLET/LOW TEMP. HEAT EXCHANGER OUTLET:
C
HOP = 1 ! T1 AND PI KNOUN
C
CALL APROP (T1,P1,V1,U1,H1,S1,H0P)
C
C **********************************************************************
C
C STATE TWO - COMPRESSOR OUTLET/HIGH TEMP. HEAT EXCH. INLET (ISENTROPIC):
C
C
C
C
P2 = PI * PRATIO
S2S = SI
HOP = 4 ! P2 AND S2S (= SI) KNOWN
CALL APROP (T2S,P2,V2S,U2S,H2S,S2S,NOP)
C
C **********************************************************************
C
C STATE TWO (ACTUAL):
C
C
C
C
H2 = (((H2S - HI) / ETAC) + HI)
NOP = 2 ! P2 AND H2 KNOWN
CALL APROP (T2,P2,V2,U2,H2,S2,NOP)
IF(T2 .LT. T3) THEN
JTT2 = 0
C0P=0.0
GO TO 8989
ELSE
JTT2 = 1
CONTINUE
ENDIF
279
-------
c **********************************************************************
c
C STATE THREE - HIGH TEMP. HEAT EXCH. OUTLET/ EXPANDER INLET:
C
C T3 WAS ESTABLISHED AS TH ON LINE 60.
C
P3 = P2
C
NOP = 1 ! T3 (FROM TH) AND P3=P2 KNOWN
C
CALL APROP (T3,P3,V3,U3,H3,S3,NOP)
C
C **********************************************************************
c
C STATE FOUR - EXPANDER OUTLET/ LOW TEMP. HEAT EXCH. INLET (ISENTROPIC):
C
C
C
C
S4S = S3
P4 = PI
NOP = 4 ! PI AND S4S (= S3) KNOWN
CALL APROP (T4S,P4,V4S,U4S,H4S,S4S,NOP)
C
C **********************************************************************
c
c STATE FOUR (ACTUAL):
C
C
C
H4 = (((H4S - H3) * ETAE) + H3)
NOP = 2 ! P4 AND H4 KNOWN
CALL APROP (T4,P4,V4,U4,H4,S4,NOP)
C
C **********************************************************************
c
C COEFFICIENT OF PERFORMANCE:
C
COP = ((HI - H4) / ((H2 - HI) - (H3 - H4)))
C
C **********************************************************************
c
8989 RETURN
END
280
-------
SUBROUTIHE SBRAYR (TL,TH,ETAC,ETAE,ETAR,PRATIO,COP,JTT2)
C
IMPLICIT REAL*8(A - H,0 - Z)
IITEGER JTT2
C
C
C **********************************************************************
c
C THIS SUBROUTINE IS USED TO CALCULATE THE COEFFICIENT OF
C PERFORMANCE OF THE CLOSED REVERSED BRAYTON CYCLE WITH RE-
C GENERATION.
C
C AIR IS THE WORKING FLUID AND ASSUMED TO BE AN IDEAL GAS.
C
C THE COMPRESSOR EFFICIENCY, EXPANDER EFFICIENCY, AND REGENERATOR
C EFFECTIVENESS ARE SPECIFIED BY THE USER.
C
C THE LOW PRESSURE IS FIXED AT 1 ATMOSPHERE.
C
C THE PRESSURE RATIO MUST BE SPECIFIED.
C
C ALL PRESSURES ARE IN KILOPASCALS.
C
C ALL TEMPERATURES ARE IN DEGREES KELVIN.
C
C ************************************************************************
c
C SET THE LOW PRESSURE:
C
PL = 101.32S !KPa
C
CGAS = 1
C ************************************************************************
C
TB = TL
TA = TH
C
C ************************************************************************
C
C STATE A - HIGH TEMP. HEAT EXCHANGER OUTLET/ REGEN. INLET:
C
C TA AND PA = PL * PRATIO ARE KNOWN
C
PA = PL * PRATIO
C
NOP = 1
C
CALL APROP (TA,PA,VA,UA,HA,SA,NOP)
281
-------
c
c ************************************************************************
c
C STATE B - LOW TEMP. HEAT EXCHANGER OUTLET/ REGEN. INLET:
C
C TB AID PB = PL ARE KNOWN
C
C
C
PB = PL
NOP = 1
CALL APROP (TB,PB,VB,UB,HB,SB,NOP)
C
C ************************************************************************
c
C STATE THREE - REGENERATOR OUTLET/ EXPANDER INLET:
C
C THE REGENERATOR EFFECTIVENESS IS DEFINED AS:
C
C (H3 - HA)/(HA - HB) = ETAR
C
C
C THE KNOWN PRESSURE IS P3 = PA.
C
P3 = PA
C
H3 = HA - ETAR * (HA - HB)
C
NOP = 2
C
CALL APROP (T3,P3,V3,U3,H3,S3,N0P)
C
C ************************************************************************
C
C STATE FOUR - EXPANDER OUTLET/ LOW TEMP. HEAT EXCH. INLET (ISENTROPIC):
C
S4S = S3
C
P4 = PB
C
HOP = 4
C
CALL APROP (T4S,P4,V4S,U4S,H4S,S4S,NOP)
C
C ************************************************************************
c
C STATE FOUR (ACTUAL):
C
282
-------
c
c
c
P4 = PB
H4 = ((H4S - H3) * ETAE) + H3
NOP = 2
CALL APROP (T4,P4,V4,U4,H4,S4,HOP)
C
C ************************************************************************
c
C STATE ONE - REGENERATOR EXIT/ COMPRESSOR INLET:
C
C
C
C
PI = PB
HI = (HA - H3) + HB
NOP = 2
CALL APROP (T1,P1,V1,U1,H1,S1,N0P)
C
C ************************************************************************
C
C STATE TWO - COMPRESSOR EXIT/ HIGH TEMP. HEAT EXCH. INLET (ISENTROPIC):
C
C
C
C
P2 = PA
S2S = SI
HOP = 4
CALL APROP (T2S,P2,V2S,U2S,H2S,S2S,NOP)
C
C ************************************************************************
C
C STATE TWO (ACTUAL):
C
C
C
C
C
P2 = PA
H2 = ((H2S - HI) / ETAC) + HI
NOP = 2
CALL APROP (T2,P2,V2,U2,H2,S2,NOP)
IF(T2 .LT. TA) THEN
JTT2 = 0
C0P=0.0
GO TO 8990
283
-------
ELSE
JTT2 = 1
CONTINUE
ENDIF
C
c ************************************************************************
c
C COEFFICIENT OF PERFORMANCE:
C
COP = ((HB - H4) / ((H2 - HI) - (H3 - H4)))
C
8990 RETURN
END
C
SUBROUTINE SPTSUB (TLL,THH,ETAC,ETAE,ETAR,PRATIO,COP,JTT2)
C
IMPLICIT REAL*8 (A - H,0 - Z)
INTEGER JTT2
C
C THIS SUBROUTINE IS USED TO CALCULATE THE COEFFICIENT OF
C PERFORMANCE, OF THE IDEAL PULSE TUBE REFRIGERATION CYCLE.
C
C HELIUM IS THE WORKING FLUID.
C
C THE COMPRESSOR EFFICIENCY, AND REGENERATOR
C EFFECTIVENESS ARE SPECIFIED.
C
C THE LOW PRESSURE IS 1 ATMOSPHERE.
C
C THE PRESSURE RATIO MUST BE SPECIFIED.
C
C ALL PRESSURES ARE IN KILOPASCALS.
C
C ALL TEMPERATURES ARE IN DEGREES KELVIN.
C
C **********************************************************************
c
c SET THE LOW PRESSURE:
C
PL = 101.325 !KPa
C
C ************************************************************************
c
TB = TLL
TA = THH
284
-------
c
c **********************************************************************
c
C STATE A - HIGH TEMP. HEAT EXCHANGER OUTLET/ REGEN. ISLET:
C
C TA AND PA = PL * PRATIO ARE KNOWN
C
PA = PL * PRATIO
NOP = 1
CALL HPROP (TA,PA,VA,UA,HA,SA,NOP)
C
C **********************************************************************
c
C STATE B - LOW TEMP. HEAT EXCHANGER / REGEN. INLET:
C
C TB AND PB = PL ARE KNOWN
C
PB = PL
C
NOP = 1
C
CALL HPROP (TB,PB,VB,UB,HB,SB,NOP)
C
C **********************************************************************
c
C STATE THREE - REGENERATOR OUTLET/ EXPANDER INLET:
C
C THE REGENERATOR EFFECTIVENESS IS DEFINED AS:
C
C (H3 - HA)/(HA - HB) = ETAR
C
C
C THE KNOWN PRESSURE IS P3 = PA.
C
P3 = PA
H3 = HA - ETAR * (HA - HB)
NOP = 2
CALL HPROP (T3,P3,V3,U3,H3,S3,NOP)
C
C **********************************************************************
c
c STATE FOUR - EXPANDER OUTLET/ LOW TEMP. HEAT EXCH. INLET (ISENTROPIC):
C
S4S = S3
C
P4 = PB
C
NOP = 3
285
-------
CALL HPROP (T4S,P4,V4S,U4S,H4S,S4S,HOP)
C
C **********************************************************************
c
C STATE FOUR (ACTUAL):
C
H4 = ((H4S - H3) * ETAE) + H3
C
NOP = 2
C
C CALL HPROP (T4,P4,V4,U4,H4,S4,NOP)
C
C **********************************************************************
c
C STATE ONE - REGENERATOR EXIT/ COMPRESSOR INLET:
C
C
C
C
PI = PB
HI = (H3 - HA) + HB
NOP = 2
CALL HPROP (T1,P1,V1,U1,H1,S1,N0P)
C
C **********************************************************************
C
C STATE TWO - COMPRESSOR EXIT/ HIGH TEMP. HEAT EXCH. INLET (ISENTROPIC):
C
C
C
C
P2 = PA
S2S = SI
NOP = 3
CALL HPROP (T2S,P2,V2S,U2S,H2S,S2S,NOP)
C
C **********************************************************************
C
C STATE TWO (ACTUAL):
C
C
C
C
P2 = PA
H2 = ((H2S - HI) / ETAC) + HI
NOP = 2
CALL HPROP(T2,P2,V2,U2,H2,S2,NOP)
286
-------
c
IF(T2 .LE. TA) THEN
JTT2 = 0
C0P=0.0
GO TO 8991
ELSE
JTT2 = 1
COITIIUE
ENDIF
C
C **********************=************************************************
c
C COEFFICIENT OF PERFORMANCE:
C
COP = (HB - H4) / (H2 - HI)
C
C **********************************************************************
c
8991 RETURN
END
SUBROUTINE STE(TL,TH,Z,COPTE)
IMPLICIT REAL*8(A-H,O-Z)
C
C ************************************************************************
c
C THERMOELECTRIC REFRIGERATION COEFFICIENT OF PERFORMANCE SUBROUTINE
C
C
C THIS SUBROUTINE IS USED TO CALCULATE THE MAXIMUM COEFFICIENT OF
C PERFORMANCE FOR A THERMOELECTRIC REFRIGERATION SYSTEM.
C
C ************************************************************************
c
C CALCULATE THE AVERAGE TEMPERATURE, TBAR:
C
TBAR = (TH+TL)/2.0
C
C ************************************************************************
c
C CALCULATE THE CARNOT COP:
C
COPC = TL/(TH - TL)
C
C ************************************************************************
c
C CALCULATE THE MAXIMUM IDEAL COP FOR THE THERMOELECTRIC REFRIGERATOR:
287
-------
c
XX = (1.0 + (Z*TBAR))**0.5
C
TERMA = (XX - (TH/TL))
TERMB = (XX + 1.0)
TERMC = TERMA/TERMB
C
COPTE = COPC+TERMC
C
RETURN
END
SUBROUTIIE SMHP(TL,TH,HL,HH,COP)
IMPLICIT REAL*8(A-H,0-Z)
C
C ************************************************************************
c
C MAGHETIC REFRIGERATION CYCLE
C
C THIS SUBROUTINE IS INTENDED TO CALCULATE THE COP OF AN IDEALIZED
C MAGNETIC REFRIGERATION CYCLE OPERATING AT STEADY STATE IN A CONSTANT
C FIELD CYCLE (TWO ISOFIELD AND TWO ISOTHERMAL PROCESSES). THE
C MAGNETIC SOLID IS GADOLINIUM. THE CONSTANT FIELD STRENGTHS ARE
C BETWEEN OAND 7 TESLAS. THE SOURCE AND SINK TEMPERATURES ARE
C BETWEEN 260 AND 320 K.
C
C ************************************************************************
C
C READ THE FIELD STRENGTHS:
C
HL = 0.
HH = 7.
C
C ************************************************************************
C
C
C CALCULATE AREA THREE:
C
CALL GD(HL,TH,S2)
CALL GD(HH,TH,S3)
A3 = (S2-S3)*TH ! THIRD AREA ON TS DIAGRAM
C
C ************************************************************************
c
c CALCULATE DELTA T:
C
288
-------
I = 50
DELT = (TH-TL)/I
C
C ************************************************************************
c
C CALCULATE THE FOURTH AREA:
C
A = 0.0
AT = 0.0
SL = 0.0
SR = 0.0
TC = TL
HC = HL
CALL GD(HC,TC,SL)
C
DO 1000 I = 1,1
TC = TC + DELT
CALL GD(HC,TC,SR)
TMP = TC - DELT/2.0
A = (SR - SL)*TMP
AT = AT + A
SL = SR
1000 CONTIHUE
C
A4 = AT
C
C ************************************************************************
c
C CALCULATE THE EHTROPY AT STATE OHE:
C
C THE FIRST AREA MUST EqUAL THE FOURTH AREA
C
A1 = 0.0
A = 0.0
SL = 0.0
SR = S3
TC = TH
HC = HH
DELTS = 1.0E-01
C
999 DIFF = (A4 - Al)
C
IF (DIFF .GT. 1.0E-04) THEN
TC = TC - DELTS
CALL GD(HC,TC,SL)
TMP = TC + DELTS/2.0
A = (SR - SL)*TMP
Al = Al + A
289
-------
SR = SL
GO TO 999
ELSE
CONTINUE
END IF
C
S4 = SL
C
C ******>******************************************************************
C
C CALCULATE THE HEAT ACCEPTED FROM THE SIIK:
C
C
CALL GD(HL,TL,S1)
QC = (S1-S4)*TL ! J/KG.
A2 = qC ! AREA TWO OH TS DIAGRAM
C
C ************************************************************************
C CALCULATE THE WORK:
C
C
WORK = A1 + A3 - (A2 + A4)
C
C ************************************************************************
c
c CALCULATE THE COEFFICIENT OF PERFORMANCE:
C
COP = qC/WORK
RETURN
END
290
-------
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
SUBROUTINE APROP(TS,PS,VS,US,HS,SS,HOP)
IMPLICIT REAL*8(A-H,O-Z)
INTEGER NOP.KTR
**********************************************************************
THIS SUBROUTIHE CALCULATES THE THERMODYHAHIC PROPERTIES
OF GASES USING THE IDEAL GAS EQUATION OF STATE. THE CONSTANT
PRESSURE SPECIFIC HEAT FUNCTION WAS DERIVED FROM DATA FROM:
REYNOLDS, W.,C., THERMODYNAMIC PROPERTIES IN SI, DEPARTMENT
OF MECHANICAL ENGINEERING STANFORD UNIVERSITY, STANFORD, CA.
**********************************************************************
THE REFERENCE STATE IS ONE ATMOSPHERE AND ZERO DEGREES KELVIN
THE UNITS ARE AS FOLLOWS:
TEMPERATURE DEGREES KELVIN
PRESSURE KPa
SPECIFIC VOLUME M~3/KIL0GRAM
INTERNAL ENERGY KILOJOULES/KILOGRAM
ENTHALPY KILOJOULES/KILOGRAM
ENTROPY KILOJOULES/KILOGRAM*K.
SELECT OPTIONS:
IF (NOP .Eq. 1) THEN
GO TO 30
ELSE IF (NOP .Eq. 2) THEN
GO TO 20
ELSE IF (NOP .Eq. 3) THEN
GO TO 10
ELSE IF (NOP .Eq. 4) THEN
CONTINUE
ENDIF
! P AND T KNOWN
! H AND P KNOWN
! U AND P KNOWN
! S AND P KNOWN
**********************************************************************
ROUTINE TO ITERATE AND FIND T, V, U, AND H KNOWING S AND P:
PT = PS
KTR = 0
TTL = 150.0
DELT =20.0
291
-------
CALL AIR (TTL,PT,VT,UT,HT,ST)
C
11 DELS = SS - ST
KTR = KTR + 1
C
IF (ABS(DELS) .LT. 1.5E-04) THEN
TS = TTL
60 TO 30
ELSE IF (DELS .GT. 0.0) THEN
TTL = TTL + DELT
CALL AIR (TTL,PT,VT,UT,HT,ST)
GO TO 11
ELSE IF (DELS .LT. 0.0) THEN
DELT = DELT/2.0
TTL = TTL - DELT
CALL AIR (TTL,PT,VT,UT,HT,ST)
GO TO 11
CONTINUE
END IF
C
C **********************************************************************
C
C ROUTINE TO ITERATE AND FIND T, V, U, AND's KNOWING H AND P:
C
20 PT = PS
KTR = 0
TTL = 150.0
C
DELT = 20.0
C
CALL AIR (TTL.PT,VT,UT,HT,ST)
C
15 DELH = HS - HT
KTR = KTR + 1
C
IF (ABS(DELH) .LT. 1.5E-03) THEN
TS = TTL
GO TO 30
ELSE IF (DELH .GT. 0.0) THEN
TTL = TTL + DELT
CALL AIR (TTL,PT,VT,UT,HT,ST)
GO TO 15
ELSE IF (DELH .LT. 0.0) THEN
DELT = DELT/2.0
TTL = TTL - DELT
CALL AIR (TTL,PT,VT,UT,HT,ST)
GO TO 15
292
-------
CONTINUE
END IF
C
C **********************************************************************
c
C ROUTINE TO ITERATE AND FIND T, V, H, AND S KNOWING U AND P:
C
10 PT = PS
KTR = 0
TTL = 150.0
C
DELT =20.0
C
CALL AIR (TTL,PT,VT,UT,HT,ST)
C
25 DELU = US - UT
KTR = KTR + 1
C
IF (ABS(DELU) .LT. 1.5E-03) THEN
TS = TTL
GO TO 30
ELSE IF (DELU .GT. 0.0) THEN
TTL = TTL + DELT
CALL AIR (TTL,PT,VT,UT,HT,ST)
GO TO 25
ELSE IF (DELU .LT. 0.0) THEN
DELT = DELT/2.0
TTL = TTL - DELT
CALL AIR (TTL,PT,VT,UT,HT,ST)
GO TO 25
CONTINUE
END IF
C
C **********************************************************************
c
C ROUTINE TO FIND V, U, H, AND S KNOWING T AND P:
C
30 CALL AIR (TS.PS,VS.US,HS,SS)
C
RETURN
END
SUBROUTINE AIR (XT,XP,XV,XU,XH,XS)
C
IMPLICIT REAL*8(A-H,0-Z)
C
C THIS SUBROUTINE CALCULATES THE THERMODYNAMIC PROPERTIES
293
-------
C OF AIR USING THE IDEAL GAS EQUATION OF STATE.
C
C THE REFERENCE STATE IS ONE ATMOSPHERE AND ZERO DEGREES KELVIN.
C
C THE UNITS ARE AS FOLLOWS:
C
C TEMPERATURE
C PRESSURE
C SPECIFIC VOLUME
C INTERNAL ENERGY
C ENTHALPY
C ENTROPY
C
C
PO = 101.325
C
C **********************************************************************
c
C UNIVERSAL GAS CONSTANT:
C
RU = 8.314 ! KJ/KMOL*K.
C
C **********************************************************************
c
C CONSTANTS FOR AIR:
C
HTM = 28.97 ! KG/KMOL
ALPHA = 0.101630E01
BETA = -0.137524E-03
GAMMA = 0.277805E-06
DELTA = -0.203442E-09
EPSILON = -0.221745E-12
C
C **********************************************************************
c
R = RU/WTM ! KJ/KG*K.
C
C CALCULATE THE SPECIFIC VOLUME:
C
XV = (R*XT)/XP
C
C **********************************************************************
C
C EVALUATE THE ENTHALPY:
C
IF (XT .LT. 150.) THEN
C
HRITEC6,*) 'T4 MUST BE GREATER THAN 150 K., TRY A LOWER PRATIO'.XT
DEGREES KELVIN
KILOPASCALS
M*3/KIL0GRAM
KILOJOULES/KILOGRAM
KILOJOULES/KILOGRAM
KILOJOULES/KILOGRAM*K.
! KPa
294
-------
STOP
ELSE
CONTIHUE
EIDIF
C
XH = ((ALPHA+XT) + (BETA/2.)*(XTt<*2) + (GAMMA/3.)
* *(XT**3) +(DELTA/4.)*(XT**4) +(EPSIL0N/5.)
* *(XT**5))
C
C ****************:|<*****************************************************
c
C EVALUATE THE EHTROPY:
C
XS = (ALPHA*LOG(XT) + BETA*XT + GAMMA/2.*(XT**2) +
* (DELTA/3.)*(XT**3) + (EPSIL0N/4)*(XT**4)
* - R*LOG(XP/PO))
C
C **********************************************************************
c
C EVALUATE THE INTERNAL ENERGY:
C
XU = XH - R*XT
C
RETURN
END
SUBROUTINE HPROP (TS,PS,VS,US,HS,SS,NOP)
C
IMPLICIT REAL*8 (A-H.O-Z)
C
C **********************************************************************
c
C THIS SUBROUTINE CALCULATES THE THERMODYNAMIC PROPERTIES
C OF GASES USING THE IDEAL GAS EQUATION OF STATE. THE CONSTANT
C PRESSURE SPECIFIC HEAT CONSTANT IS FROM:
C REYNOLDS, W.,C., THERMODYNAMIC PROPERTIES IN SI, DEPARTMENT
C OF MECHANICAL ENGINEERING STANFORD UNIVERSITY, STANFORD, CA.
C
C **********************************************************************
c
c
C THE REFERENCE STATE IS ONE ATMOSPHERE AND ZERO DEGREES KELVIN
C
C THE UNITS ARE AS FOLLOWS:
C
C TEMPERATURE DEGREES KELVIN
C PRESSURE KPa
295
-------
C SPECIFIC VOLUME M~3/KIL0GRAM
C INTERNAL ENERGY KILOJOULES/KILOGRAM
C ENTHALPY KILOJOULES/KILOGRAM
C ENTROPY KILOJOULES/KILOGRAM*K.
C
C **********************************************************************
c
C SELECT OPTIONS:
C
IF (HOP .Eq. 1) THEN ! P AND T KNOWN
GO TO 30
ELSE IF (NOP .Eq. 2) THEN ! H AND P KNOWN
GO TO 20
ELSE IF (NOP .Eq. 3) THEN ! S AND P KNOWN
CONTINUE
ENDIF
C
C **********************************************************************
c
C ROUTINE TO ITERATE AND FIND T, V, U, AND H KNOWING S AND P:
C
PT = PS
KTR = 0
TTL = 1.0
DELT =20.0
CALL HELIUM(TTL,PT,VT,UT,HT,ST)
C
10 DELS = SS - ST
KTR = KTR + 1
C
IF (ABS(DELS) .LT. 1.5E-04) THEN
TS = TTL
GO TO 30
ELSE IF (DELS .GT. 0.0) THEN
TTL = TTL + DELT
CALL HELIUM(TTL,PT,VT,UT,HT,ST)
GO TO 10
ELSE IF (DELS .LT. 0.0) THEN
DELT = DELT/2.0
TTL = TTL - DELT
CALL HELIUM(TTL,PT,VT,UT,HT,ST)
GO TO 10
CONTINUE
END IF
C
C **********************************************************************
C
c
296
-------
c
C ROUTINE TO ITERATE AND FIND T, V, U, AND S KNOWING H AND P:
C
20 PT = PS
KTR = 0
TTL = 1.0
C
DELT = 20.0
C
CALL HELIUM(TTL,PT,VT,UT,HT,ST)
C
15 DELS = HS - HT
C
KTR = KTR + 1
C
IF (ABS(DELH) .LT. 1.5E-04) THEN
TS = TTL
GO TO 30
ELSE IF (DELH .GT. 0.0) THEN
TTL = TTL + DELT
CALL HELIUM(TTL,PT,VT,UT,HT,ST)
GO TO 15
ELSE IF (DELH .LE. 0.0) THEN
DELT = DELT/2.0
TTL = TTL - DELT
CALL HELIUM(TTL,PT,VT,UT,HT,ST)
GO TO 15
CONTINUE
END IF
C
C **********************************************************************
c
C ROUTINE TO FIND V, U, H, AND S KNOWING T AND P:
C
30 CALL HELIUM(TS,PS,VS,US,HS,SS)
C
END
SUBROUTINE HELIUM (THE,PHE,VHE,UHE,HHE,SHE)
C
IMPLICIT REAL*8 (A-H.O-Z)
C
C
C THIS SUBROUTINE CALCULATES THE THERMODYNAMIC PROPERTIES
C OF HELIUM USING THE IDEAL GAS EQUATION OF STATE.
C
297
-------
C
c
THE REFERENCE STATE IS ONE ATMOSPHERE AND ZERO DEGREES KELVIN.
c
THE UNITS ARE AS
FOLLOWS:
c
TEMPERATURE
DEGREES KELVIN
c
PRESSURE
KILOPASCALS
c
SPECIFIC VOLUME
M-3/KIL0GRAM
c
INTERNAL ENERGY
KILOJOULES/KILOGRAM
c
ENTHALPY
KILOJOULES/KILOGRAM
c
c
EHTROPY
KILOJOULES/KILOGRAM*K.
V
c
**********************************************************************
K,
c
c
UNIVERSAL GAS CONSTANT:
RU = 8.314
! KJ/KMOL+K.
r*
PO = 101.325
! KPa
c
**********************************************************************
I
c
CONSTANTS FOR HELIUM:
c
WTM = 4.0026 ! KG/KMOL
ALPHA = 5.2328746 ! KJ/(KG-HOL)(K.)
C
C **********************************************************************
C
R = RU/WTM ! KJ/KG*K.
C
C CALCULATE THE SPECIFIC VOLUME:
C
VHE = (R*THE)/PHE
C
C **********************************************************************
C
C EVALUATE THE ENTHALPY:
C
C
HHE = (ALPHA*THE)
C
C **********************************************************************
C
C EVALUATE THE EHTROPY:
C
RSI = (ALPHA*LOG(THE))
RS2 = PHE/PO
C
IF (RS2 .LE. 1E-06) THEN
298
-------
RS2 = 1.0
ELSE
CONTINUE
ENDIF
C
RS3 = (R*L0G(RS2))
C
SHE = RSI - RS3
C
C **********************************************************************
c
C EVALUATE THE INTERNAL ENERGY:
C
UHE = HHE - R*THE
C
RETURN
END
SUBROUTINE GD(YH,TT,SS)
IMPLICIT REAL*8(A-H,0-Z)
DIMENSION TERM(9)
C
C ************************************************************************
c
C GADOLINIUM ENTROPY ROUTINE FOR USE WITH MAGNETIC HEAT PUMP MODEL
C
C ************************************************************************
c
c THIS SUBROUTINE IS USED TO CALCULATE THE ENTROPY OF GADOLINIUM AS A
C FUNCTION OF ABSOLUTE TEMPERATURE AND MAGNETIC FIELD STRENGTH. THE
C DATA USED FOR THE CURVE FIT WERE TAKEN FROM: CHEN,F.C.,ET AL.,"LOSS
C ANALYSIS OF THE THERMODYNAMIC CYCLE OF MAGNETIC HEAT PUMPS", U.S. DEPT.
C OF ENERGY REPORT 0RNL/TM--11608, FEBRUARY 1991, FIGURE 2.2, PAGE 39.
C
C ss = J/KG-K.
C TT = K.
C YH = TESLAS
C
C ************************************************************************
C
C SCALE VARIABLES USING SCALING FACTORS FROM CURVE FIT:
YO = -0.77777779E+00
RY = .77777778E+01
TO = .2S333333E+03
RT = .66666667E+02
299
-------
c
YYH = ((YH-YO)/RY)
TTT = ((TT-TO)/RT)
C
C ************************************************************************
c
C ASSEMBLE TERMS:
C
TERM(l) = 3.862186E-04
TERM(2) = (8.144588E-05)*TTT
TERM(3) = (-2.630953E-05)*(TTT**2)
TERM(4) = (-1.408800E-05)*YYH
TERM(5) = (-6.804424E-06)*(YYH*TTT)
TERM(6) = (2.192644E-05)*(TTT**2)*YYH
TERM(7) = (4.165092E-06)*(YYH**2)
TERM(8) = (-2.592406E-06)*(TTT*(YYH**2))
TERM(9) = (-9.646258E-06)*(YYH**2)*(TTT**2)
C
C *************<***********************************************************
c
C CALCULATE SS:
C
SS= 0.0
C
DO 40 1=1,9
SS = SS + TERM(I)
40 CONTINUE
C
RETURN
END
300
-------
APPENDIX C. SAMPLE DATA FROM ALTERNATIVE
REFRIGERATION TECHNOLOGY CYCLE PROGRAM
301
-------
SIIK TEMPERATURE =35. CELSIUS
HIGH TEMP HX DELTA T = 5. CELSIUS
LOW TEMP HX DELTA T = 5. CELSIUS
REVERSED BRAYTON CYCLE RESULTS
PRESSURE RATIO = 2.500
COMP. EFF.= .850
EXPANDER EFF. = .850
SOURCE TEMP.
CARNOT COP
COP
COP/COPC
COMMENTS
-24.000
4.223
-.284
-.067
TEMPERATURES OUT
OF
RANGE
-22.000
4.406
-.199
-.045
TEMPERATURES OUT
OF
RANGE.
-20.000
4.603
-.118
-.026
TEMPERATURES OUT
OF
RANGE
-18.000
4.814
-.042
-.009
TEMPERATURES OUT
OF
RANGE
-16.000
5.042
.031
.006
-14.000
5.289
.100
.019
-12.000
5.556
.165
.030
-10.000
5.848
.228
.039
-8.000
6.166
.287
.047
-6.000
6.516
.345
.053
-4.000
6.901
.398
.058
-2.000
7.328
.451
.062
.000
7.804
.500
.064
2.000
8.338
.549
.066
4.000
8.940
.594
.066
6.000
9.626
.638
.066
8.000
10.413
.680
.065
10.000
11.326
.721
.064
12.000
12.398
.760
.061
14.000
13.674
.798
.058
16.000
15.218
.833
.055
18.000
17.126
.868
.051
20.000
19.543
.902
.046
22.000
22.704
.936
.041
24.000
27.014
.966
.036
26.000
33.239
.996
.030
28.000
43.021
1.026
.024
302
-------
APPENDIX D. ALTERNATIVE REFRIGERATION CYCLE
TECHNICAL ASSESSMENT PROGRAM
Introduction
The objective of this program is to compare refrigeration and air conditioning
technologies on the basis of the technical assessment criteria established for this
project. The program uses a three dimensional array which contains all of the ratings
for the alternative refrigeration technologies discussed in Chapter 10.
The program was developed to estimate the coefficient of performance of the
following refrigeration cycles:
1. Reversed Stirling
2. Reversed Brayton
3. Thermoelectric
4. Pulse tube and thermoacoustic
5. Magnetic
6. Liquid absorption
7. Solid adsorption
303
-------
8. Vapor compression
This program was written in FORTRAN. The source code can be compiled and
used with any system having a FORTRAN compiler. The executable version fur-
nished here can be installed and run on IBM or IBM compatible personal computers.
The program is structured in an easy to use, interactive, menu driven format.
The user is asked to supply information in a step by step process. The user first
asked to select the refrigeration application he wishes to consider. On subsequent
screens, the user selects which of the technical assessment criteria he wishes to use
to assess the technologies. The user is then asked to weight the criteria in terms of
relative importance. A default weighting of equal importance can be selected. Based
on the criteria which have been selected, the weighting, and the ratings established
during the technical assessment, the program ranks the technologies from high to low
in descending order of the calculated (numerical) rating value.
Validation of the Program
The operability of the program was validated by comparing the results with hand
calculations.
Program Structure
The program source code is contained in a single file, TEKA.FOR.
304
-------
System Requirements
This program was written in FORTRAN code which is compatible with MI-
CROSOFT FORTRAN version 5.0. The executable version of the program has no
special requirement as to the microprocessor type; it can be run on computers using
the 8086 through 80486 processors.
One feature of MICROSOFT FORTRAN which must be kept in mind when
using this program is the choice of linking library options which are used to form the
executable file during the compiling and linking process. MICROSOFT has developed
separate libraries which are selected during the installation of its FORTRAN software.
For computers equipped with the 8087, 80287, or 80387 math co-processor, the library
LLIBFOR007 is used. Since the math co-processor is incorporated on all 80486 chips,
this library is utilized for these machines as well. For computers using the 8086, 80286,
and 80386 microprocessor without the 8087, 80287, or 80387 math co-processor, the
emulator library LLIBFORE is used. Therefore, if the program is linked using the
LLIBFOR007 library to form the executable file, it will not run on a computer that
does not have a math co-processor.
Program Installation
The program includes some screen clearing commands during execution. A line
must be included in the computer's CONFIG.SYS file which reads exactly as follows:
DEVICE=C:\DOS\ANSI.SYS
305
-------
If this line is not included, the code "2J]" will appear in the upper left corner of
the monitor screen; however, the program can still be run and will provide correct
results.
To install the program:
1. Choose or create a suitable directory on the hard disk.
2. Insert the diskette in the A drive and choose the directory entitled TECH.
3. Type the command:
COPY l.EXE C:\(directory name)\TEKA.EXE.
Running the Program
To start the program, type "TEKA" and press return. Each screen is self ex-
planatory and prompts the user for the required input action (such as pressing return
to refresh a screen), numerical input value, or choice (yes or no). The user is also
prompted to furnish an output file name for the file to which the output data will be
written.
At the end of a program sequence the user can choose to either start a new
sequence or to exit the program by answering "Y" or "N" to the question appearing
on the screen.
The data from each run will be found in the data file named during the run
sequence. Each new case must have a unique file name. If the same file name is
given, the data from the previous run will be overwritten. It is suggested that the
file name be appended with a letter or number to indicate the order of the run. For
306
-------
example, the file names TEKA1.DAT, TEKA2.DAT, and TEKA3.DAT could be used
for the data files for the first, second, and third runs used to consider different cases.
Changing the Technical Assessment Ratings
THE program currently used the ratings for each technical assessment criteria
and application which were given in the tables at the beginning of each technical
assessment section in Chapter 10 . If the user wishes to change the these ratings, it
must be done by altering the FORTRAN code. The technical assessment ratings are
located in a three dimensional array A(I,J,K)). Each element has been individually
assigned a value (rather than using DATA statements). The method of entering the
data as individual array elements was chosen to simplify the process of changing the
ratings. Comment statements at the beginning of the code clearly identify how the
array element values are arranged and assigned.
The code can then be re-compiled to create a new executable version with the
new ratings.
307
-------
c ************************************************************************
c
C ALTERNATIVE REFRIGERATION CYCLE TECHNICAL ASSESSMENT ROUTINE
C
C
C DON C. 6AUGER
C
C MECHANICAL ENGINEERING DEPARTMENT
C
C IOWA STATE UNIVERSITY
C
C 1993
C
C ************************************************************************
C
C THIS ROUTINE COMPARES SIX KEY TECHNICAL ASSESSMENT CRITERIA FOR
C ALTERNATIVE REFRIGERATION CYCLES USING A WEIGHTING SYSTEM.
C
C THE FORMAT IS MENU DRIVEN.
C
C THE USER IS ASKED TO MAKE CHOICES REGARDING THE TYPE OF REFRIGERATION
C APPLICATION TO BE CONSIDERED, WHICH TECHNICAL ASSESSMENT CRITERIA ARE
C TO BE CONSIDERED, AND THE WEIGHTING EACH CRITERION IS TO BE GIVEN.
C
C THE PROGRAM WILL RANK THE ALTERNATIVE TECHNOLOGIES FROM BEST TO WORST
C BASED UPON THIS INFORMATION.
C
C ************************************************************************
c
c VARIABLE DECLARATION:
C
REAL WC(6),TOTAL,DIFF,A(6,S,10),RATE(10),RMAX.DWF
INTEGER I,J,K,L,N
CHARACTER*50 OUTPUTFILE
CHARACTER*1 CH0ICE1,CH0ICE2,CH0ICE4,CH0ICE5,CH0ICE6,CH0ICE7,
* CH0ICE8,CH0ICE9,CH0ICE10,CH0ICE11
CHARACTERS CH0ICE3
CHARACTER*10 C2,C3,CS
CHARACTER*11 C6,C7,C8
CHARACTER*16 C1,C4,C9
C
C ************************************************************************
C
C INTEGER INDICATING THE NUMBER OF TECHNOLOGIES:
C
N = 8 ! IF TECHNOLOGIES ARE ADDED, INCREASE THIS
C NUMBER ACCORDINGLY.
C
308
-------
c ************************************************************************
c
C INPUT THE DATA FOR THE TECHNICAL ASSESSMENT ARRAYS:
C
C ARRAY FORMAT:
C
C THE TECHNOLOGY ASSESSMENT ARRAYS ARE THREE DIMENSIONAL, 6 BY 5 BY "N"
C IN SIZE.
C THE ROWS CONTAIN THE CRITERIA NUMBER, THE COLUMNS CONTAIN THE APPLICATION
C NUMBER, AND THE RANKS CONTAIN THE REFRIGERATION TECHNOLOGY CHOICES.
C
C DEFINITION OF ARRAY ELEMENTS:
C
C ROWS (ARRAY "I" TERM): TECHNOLOGY RATING SCALE:
C
C ROW 1 = STATE OF THE ART.
C ROW 2 = COMPLEXITY.
C ROW 3 = SIZE/WEIGHT.
C ROW 4 = MAINTENANCE.
C ROW 5 = USEFUL LIFE.
C ROW 6 = CYCLE EFFICIENCY.
C
C
C . COLUMNS (ARRAY "J" TERM):
C
C COLUMN 1 = DOMESTIC AIR CONDITIONING.
C COLUMN 2 = COMMERCIAL AIR CONDITIONING.
C COLUMN 3 = MOBILE AIR CONDITIONING.
C COLUMN 4 = DOMESTIC REFRIGERATION.
C COLUMN 5 = COMMERCIAL REFRIGERATION.
C
C
C RANK
C
C RANK
C RANK
C RANK
C RANK
C RANK
C RANK
C RANK
C RANK
C
C ************************************************************************
c
C TECHNICAL ASSESSMENT DATA ENTRIES FOR THE DIFFERENT REFRIGERATION
C TECHNOLOGIES ARE ENTERED HERE:
C
1 = LOWEST RATING.
5 = HIGHEST RATING.
(ARRAY "K" TERM):
1 = MAGNETIC REFRIGERATION.
2 = THERMOELECTRIC REFRIGERATION.
3 = PULSE/THERMOACOUSTIC REFRIGERATION.
4 = REVERSED STIRLING REFRIGERATION.
6 = REVERSED BRAYTON REFRIGERATION.
6 = ABSORPTION REFRIGERATION.
7 = SOLID SORPTION REFRIGERATION.
8 = VAPOR COMPRESSION REFRIGERATION.
309
-------
************************************************************************
TECH ASSESSMENT ARRAY FOR MAGNETIC REFRIGERATION:
a(i,i,i)
A(1,2,1)
= 1
A(1,3,1)
= 1
! STATE OF ART
A(1,4,1)
= 1
A(1,5,1)
= i
A(2,l,l)
= 2
A(2,2,1)
= 2
A(2,3,1)
= 1
! COMPLEXITY
A(2,4,1)
= 2
A(2,5,1)
= 2
A(3,l,1)
= 2
A(3,2,1)
= 2
A(3,3,1)
= 1
! SIZE/WEIGHT
A(3,4,1)
= 2
A(3,5,1)
= 2
A(4,l,l)
= 3
A(4,2,1)
= 3
A(4,3,1)
= 2
! MAINTENANCE
A(4,4,1)
= 3
A(4,5,1)
= 3
A(5,l,l)
= 4
A(5,2,1)
= 4
A(5,3,1)
= 2
! USEFUL LIFE
A(5,4,1)
= 4
A(5,5,1)
= 4
A(6,l,l)
= i
A(6,2,1)
= 1
A(6,3,l)
= i
! CYCLE EFFICIENCY
A(6,4,1)
A(6,5,1)
= 1
C
C ************************************************************************
c
C TECH ASSESSMENT ARRAY FOR THERMOELECTRIC REFRIGERATION:
C
A(l,l,2) = 3
A(1,2,2) = 3
A(l,3,2) = 3 ! STATE OF ART
A(1,4,2) = 2
310
-------
A(l,5,2) = 2
A(2,l,2)
= 2
A(2,2,2)
= 2
A(2,3,2)
= 2
! COMPLEXITY
A(2,4,2)
= 1
A(2,5,2)
= 1
A(3,l,2)
= 5
A(3,2,2)
= 5
A(3,3,2)
= 3
! SIZE/WEIGHT
A(3,4,2)
= 5
A(3,5,2)
= 5
A(4,1,2)
= 5
A(4,2,2)
= 5
A(4,3,2)
= 3
! MAINTENANCE
A(4,4,2)
= 5
A(4,5,2)
= 5
A(5,1,2)
= 5
A(5,2,2)
= 5
A(5,3,2)
= 4
! USEFUL LIFE
A(5,4,2)
= 5
A(5,5,2)
= 5
A(6,1,2)
= i
A(6,2,2)
= i
A(6,3,2)
= 1
! CYCLE EFFICIENCY
A(6,4,2)
= 1
A(6,5,2)
= 1
TECH ASSESSMENT ARRAY FOR PULSE/THERMOACOUSTIC REFRIGERATION:
A(l,l,3) = 2
A(l,2,3) = 2
A(l,3,3) = 2 ! STATE OF ART
A(1,4,3) = 2
A(l,5,3) = 2
A(2,l,3) = 3
A(2,2,3) = 2
A(2,3,3) = 3
A(2,4,3) = 3
A(2,5,3) = 3
! COMPLEXITY
311
-------
c
c
c
c
c
A(3,1,3)
=
3
A(3,2,3)
=
3
A(3,3,3)
=
2
! SIZE/WEIGHT
A(3,4,3)
=
3
A(3,5,3)
3
A(4,1,3)
=
2
A(4,2,3)
=
2
A(4,3,3)
=
2
! MAINTENANCE
A(4,4,3)
=
2
A(4,5,3)
=
2
A(5,1,3)
=
3
A(5,2,3)
=
3
A(5,3,3)
=
3
! USEFUL LIFE
A(5,4,3)
=
3
A(5,5,3)
=
3
A(6,1,3)
=
1
A(6,2,3)
=
1
A(6,3,3)
=
1
! CYCLE EFFICIENCY
A(6,4,3)
=
A(6,5,3)
=
1
TECH ASSESSMENT ARRAY FOR REVERSED
STIRLING REFRIGERATION:
A(1,1,4)
=
3
A(l,2,4)
=
3
A(l,3,4)
=
3
! STATE OF ART
A(1,4,4)
=
3
A(1,S,4)
=
3
A(2,1,4)
=
3
A(2,2,4)
=
3
A(2,3,4)
=
3
! COMPLEXITY
A(2,4,4)
=
3
A(2,5,4)
=
4
A(3,1,4)
=
4
A(3,2,4)
=
4
A(3,3,4)
=
4
! SIZE/WEIGHT
A(3,4,4)
=
4
A(3,S,4)
=
4
A(4,1,4)
sr
3
A(4,2,4)
=
3
312
-------
c
c
c
c
c
AC4.3.4)
=
3
! MAINTENANCE
A(4,4,4)
=
3
A(4,5,4)
=
3
A(5,1,4)
4
A(5,2,4)
=
3
A(5,3,4)
=
4
! USEFUL LIFE
A(5,4,4)
=
4
A(5,5,4)
=
3
A(6,1,4)
=
2
A(6,2,4)
=
2
A(6,3,4)
=
2
! CYCLE EFFICIENCY
A(6,4,4)
=
3
A(6,5,4)
=
3
************************************************************************
TECH ASSESSMENT ARRAY FOR REVERSED
BRAYTON REFRIGERATION:
1(1,1.5)
3
A(l,2,5)
=
3
A(1,3,5)
=
3
! STATE OF ART
A(1,4,5)
=
3
A(l,5,5)
4
A(2,1,5)
=
3
A(2,2,5)
=
3
A(2,3,5)
=
3
! COMPLEXITY
A(2,4,5)
=
3
A(2,5,5)
4
A(3,l,5)
=
2
A(3,2,5)
=
2
A(3,3,5)
=
2
! SIZE/WEIGHT
A(3,4,5)
=
2
A(3,5,5)
=:
3
A(4,1,5)
=
3
A(4,2,5)
=
3
A(4,3,5)
=
3
! MAINTENANCE
A(4,4,5)
=
3
A(4,5,5)
3
A(5,l,5)
=
3
A(5,2,5)
=
3
A(5,3,5)
=
3
! USEFUL LIFE
A(5,4,5)
=
3
313
-------
A(5,5,5) = 3
A(6,1,5)
A(6,2,5)
A(6,3,5)
A(6,4,5)
A(6,5,5)
! CYCLE EFFICIENCY
**it********************************************************************
TECH ASSESSMENT ARRAY FOR ABSORPTION REFRIGERATION:
ACl.1,6)
= 4
A(l,2,6)
= 5
A(l,3,6)
= 2
! STATE OF ART
A(l,4,6)
= 4
A(l,5,6)
= 4
A(2,1,6)
= 3
A(2,2,6)
= 4
A(2,3,6)
= 2
! COMPLEXITY
A(2,4,6)
= 3
A(2,5,6)
= 3
A(3,l,6)
= 3
A(3,2,6)
= 3
A(3,3,6)
= 2
! SIZE/WEIGHT
A(3,4,6)
= 3
A(3,5,6)
= 3
A(4,1,6)
= 3
A(4,2,6)
= 4
A(4,3,6)
= 2
! MAINTENANCE
A(4,4,6)
= 3
A(4,5,6)
= 3
A(5,1,6)
= 3
A(5,2,6)
= 4
A(S,3,6)
= 2
! USEFUL LIFE
A(5,4,6)
= 3
A(5,5,6)
= 3
A(6,1,6)
= 5
A(6,2,6)
= 5
A(6,3,6)
= S
! CYCLE EFFICIENCY
AC6.4.6)
= 5
A(6,5,6)
= 5
314
-------
************************************************************************
TECH ASSESSMENT ARRAY FOR SOLID ADSORPTION REFRIGERATION:
A(l,l,7)
= 2
A(l,2,7)
= 2
A(l,3,7)
= 2
! STATE OF ART
A(1,4,7)
= 2
A(1,5,7)
= 2
A(2,l,7)
= 3
A(2,2,7)
= 3
A(2,3,7)
= 3
! COMPLEXITY
A(2,4,7)
= 3
A(2,5,7)
= 3
A(3,l,7)
= 3
A(3,2,7)
= 3
A(3,3,7)
= 2
! SIZE/HEIGHT
A(3,4,7)
= 3
A(3,5,7)
= 3
AC4.1.7)
= 3
A(4,2,7)
= 3
A(4,3,7)
= 3
! MAINTENANCE
A(4,4,7)
= 3
A(4,5,7)
= 3
A(5,l,7)
= 3
A(5,2,7)
= 3
A(5,3,7)
= 3
! USEFUL LIFE
A(5,4,7)
= 3
A(5,5,7)
= 3
A(6,l,7)
= 3
A(6,2,7)
= 3
A(6,3,7)
= 3
CYCLE EFFICIENCY
A(6,4,7)
= 4
A(6,5,7)
= 4
C
C ************************************************************************
c
C TECH ASSESSMENT ARRAY FOR VAPOR COMPRESSION REFRIGERATION:
C
A(l,l,8) = 5
A(l,2,8) = 5
A(1,3,8) = 5 ! STATE OF ART
A(l,4,8) = 5
315
-------
A(1,5,8)
=
5
A(2,1,8)
=
4
A(2,2,8)
=
4
A(2,3,8)
=
4
! COMPLEXITY
A(2,4,8)
=
4
A(2,5,8)
4
A(3,1,8)
=
4
A(3,2,8)
=
4
A(3,3,8)
=
4
! SIZE/WEIGHT
A(3,4,8)
=
4
A(3,5,8)
=
4
A(4,1,8)
=
5
A(4,2,8)
=
5
A(4,3,8)
=
4
! MAINTENANCE
A(4,4,8)
=
4
A(4,5,8)
4
A(5,l,8)
=
5
A(5,2,8)
=
5
A(5,3,8)
=
5
! USEFUL LIFE
A(5,4,8)
=
5
A(S,5,8)
=
5
A(6,1,8)
=
5
A(6,2,8)
=
5
A(6,3,8)
=
5
! CYCLE EFFICIENCY
A(6,4,8)
=
5
A(6,5,8)
=
5
c ************************************************************************
c
C CLEAR THE SCREEN:
C
JJ = 27
WRITE(6,S00) JJ
500 F0RMAT(1X,A1,'[2J')
C
C ************************************************************************
c
C INTRODUCTORY SCREEN:
C
316
-------
WRITE(6,*) ' '
WRITE(6,*) ' '
WRITE(6,501)'REFRIGERATION TECHNOLOGY ASSESSMENT'
501 FORMAT (22X.A35)
WRITE(6,1501)'COMPARISON ROUTINE'
1501 F0RMAT(30X,A18,//)
C
WRITE(6,502) 'DEPARTMENT OF MECHANICAL ENGINEERING'
502 FORMAT(19X.A36,/)
C
WRITE(6,503) 'IOWA STATE UNIVERSITY'
503 FORMAT(27X.A21)
C
WRITE(6,504) 'AMES, IOWA 50011'
504 F0RMAT(29X,A16,///////////)
C
C ************************************************************************
c
C CLEAR THE SCREEN:
C
II = CHAR(13)
WRITE(6,505)'PRESS RETURN'
505 F0RMAT(32X,A12)
C
READ(6,506) II
506 FORMAT(Al)
C
WRITE(6,500) JJ
C
C ************************************************************************
c
4567 WRITE(6,507) 'THIS PROGRAM CAN BE USED TO COMPARE DIFFERENT'
507 FORMAT(15X.A45)
C
WRITE(6,508) ' REFRIGERATION TECHNOLOGIES IN SEVERAL APPLICATIONS'
508 F0RMAT(12X,A51,///)
C
WRITE(6,509) 'FIRST, THE APPLICATION MUST BE CHOSEN'
509 FORMAT(19X,A37,//)
C
WRITE(6,510) 'THE CHOICES ARE:'
510 FORMAT(29X,A16,/)
C
WRITE(6,511) 'DOMESTIC REFRIGERATION'
511 F0RMAT(25X,A22)
C
WRITE(6,512) 'COMMERCIAL REFRIGERATION'
512 FORMAT(25X,A24,/)
317
-------
c
WRITEC6.513) 'DOMESTIC AIR-CONDITIONING'
513 F0RMAT(25X,A25)
C
WRITE(6,514) 'COMMERCIAL AIR-CONDITIONING'
514 FORMAT(25X,A27)
C
WRITE(6,515) 'MOBILE AIR-COHDITIOHIHG'
515 F0RMAT(25X,A23,////)
C
C ************************************************************************
C
C CLEAR THE SCREEN:
C
WRITE(6,505) 'PRESS RETURN'
C
READ(6,506) II
C
WRITE(6,500) JJ
C
C ************************************************************************
C
C CHOOSE REFRIGERATION OR AIR-CONDITIONING:
C
911 WRITE(6,516) 'TO CONSIDER A REFRIGERATION APPLICATION, TYPE "R"'
516 FORMAT(15X,A49)
WRITE(6,517)'TO CONSIDER AN AIR-CONDITIONING APPLICATION,TYPE "A"'
517 FORMAT(15X,A51,//////////)
C
WRITE(6,518)'MAKE SELECTION AND PRESS RETURN'
518 F0RMAT(22X,A31)
C
READ(6,519) CH0ICE1
519 FORMAT(Al)
C
WRITE(6,500) JJ
C
IF (CH0ICE1 .Eq.
GO TO 600
ELSE IF (CH0ICE1
GO TO 600
ELSE IF (CH0ICE1
GO TO 603
ELSE IF (CH0ICE1
GO TO 603
ELSE
GO TO 911
END IF
'R') THEN
.EQ. 'r') THEN
.EQ. 'A') THEN
.Eq. 'a') THEN
318
-------
c
c ************************************************************************
c
C CHOOSE DOMESTIC OR COMMERCIAL REFRIGERATION:
C
600 Cl='REFRIGERATION '
C3=' '
WRITE(6,520) 'YOU HAVE SELECTED REFRIGERATION APPLICATIONS'
520 FORMAT(13X,A44,///)
C
2222 WRITE(6,521) 'TO SELECT DOMESTIC APPLICATIONS, TYPE MD"'
521 FORMAT(15X.A41)
C
WRITE(6,522) 'TO SELECT COMMERCIAL APPLICATIONS, TYPE "C"'
522 FORMAT(15X,A43,////////)
C
WRITE(6,518)'MAKE SELECTION AND PRESS RETURN'
C
READ(6,519) CH0ICE2
C
URITE(6,500) JJ
C
IF (CH0ICE2 .EQ. 'D') THEN
C2='DOMESTIC '
K = 4
GO TO 601
ELSE IF (CH0ICE2 .EQ. 'd')THEN
C2='DOMESTIC '
K = 4
GO TO 601
ELSE IF (CH0ICE2 .Eq. 'C') THEN
GO TO 222
ELSE IF (CH0ICE2 .Eq. 'c') THEN
GO TO 222
ELSE
GO TO 2222
END IF
C
222 C2='COMMERCIAL'
C3=' '
K = 5
GO TO 601
C
C ************************************************************************
C
C CHOOSE DOMESTIC, COMMERCIAL, OR MOBILE AIR-CONDITIONING:
C
603 Cl='AIR CONDITIONING'
319
-------
WRITE(6,527) 'YOU HAVE SELECTED AIR-CONDITIONING APPLICATIONS'
527 FORMAT(13X,A47,///)
C
707 WRITE(6,528) 'TO SELECT DOMESTIC APPLICATIONS, TYPE "DA"'
528 FORMAT(15X,A43)
WRITE(6,*) ' '
WRITE(6,S29) 'TO SELECT COMMERCIAL APPLICATIONS, TYPE "CA"'
529 F0RMAT(15X,A44,/)
WRITE(6,S30) 'TO SELECT MOBILE APPLICATIOHS, TYPE "MA"'
530 FORMAT(15X,A39,//////////)
C
WRITE(6,518)'MAKE SELECTION AND PRESS RETURN'
READ(6,531) CH0ICE3
531 FORMAT (A2)
C
WRITE(6,500) JJ
C
IF (CH0ICE3 .Eq. 'DA') THEN
C3='DOMESTIC '
K = 1
ELSE IF (CH0ICE3 .Eq. 'da') THEN
C3='DOMESTIC '
K = 1
GO TO 601'
ELSE IF (CH0ICE3 .EQ. 'dA') THEN
C3='DOMESTIC '
K = 1
GO TO 601
ELSE IF (CH0ICE3 .Eq. 'Da') THEN
C3='DOMESTIC '
K = 1
GO TO 601
ELSE IF (CH0ICE3 .Eq. 'CA') THEN
C3='COMMERCIAL'
K = 2
GO TO 601
ELSE IF (CH0ICE3 .EQ. 'ca') THEN
C3='COMMERCIAL'
K = 2
GO TO 801
ELSE IF (CH0ICE3 .Eq. 'Ca') THEN
C3='COMMERCIAL'
K = 2
GO TO 601
ELSE IF (CH0ICE3 .Eq. 'cA') THEN
C3='COMMERCIAL'
K = 2
320
-------
c
c
c
c
c
601
20
21
22
23
C
C
40
41
60 TO 601
ELSE IF (CH0ICE3 .Eq. 'MA') THEN
C3='MOBILE '
K = 3
GO TO 601
ELSE IF (CH0ICE3 .Eq. 'ma') THEN
C3='MOBILE '
K = 3
GO TO 601
ELSE IF (CH0ICE3 .Eq. 'mA') THEH
C3='MOBILE '
K = 3
GO TO 601
ELSE IF (CH0ICE3 .Eq. 'Ma') THEH
C3='MOBILE '
K = 3
GO TO 601
ELSE
GO TO 707
EHD IF
************************************************************************
TECHNICAL ASSESSMENT CRITERIA:
WRITE(6,20) 'THE TECHNICAL ASSESSMEHT CRITERIA ARE:'
FORMAT(15X,A39,//)
WRITE(6,21)'STATE OF THE ART.'
F0RMAT(20X,A17)
WRITE(6,22)'COMPLEXITY.'
FORMAT(20X,All)
WRITE(6,23)'SIZE/WEIGHT.'
F0RMAT(20X,A12)
WRITE(6,23)'MAINTENANCE.'
WRITE(6,23)'USEFUL LIFE.'
WRITE(6,21)'CYCLE EFFICIENCY.'
WRITE(6,*) ' '
WRITE(6,*) ' '
WRITE(6,*) ' '
WRITE(6,40)'THE OZOHE DEPLETION POTENTIAL (ODP) AND DIRECT GLOBAL'
F0RMAT(12X,AS3)
WRITE(6,40)'WARMING POTENTIAL (GWP) OF THE WORKING MATERIALS IS '
WRITE(6,40)'ZERO FOR ALL REFRIGERATION TECHNOLOGIES CONSIDERED IN'
WRITE(6,41)'THIS TECHNICAL ASSESSMENT.'
FORMAT(12X.A26)
WRITE(6,») ' '
321
-------
WRITE(6,*) ' '
WRITEC6,*) ' '
WRITE(6,505) 'PRESS RETURN'
READ(6,506) II
WRITE(6,500) J J
C
8787 URITE(6,24)'SELECT THE CRITERIA YOU WISH TO CONSIDER BY ANSWERING'
24 FORMAT(15X.A53,//)
WRITE(6,26)'YES (Y) OR NO (N) TO EACH OF THE FOLLOWING QUESTIONS'
26 FORMAT(15X,A53,///)
C
J= 0
C
101 WRITE(6,25)'STATE OF THE ART ? Y OR M'
25 FORMAT(20X.A33)
READ(6,S19) CH0ICE4
C WRITE(6,500) JJ
C
IF (CH0ICE4 .EQ. 'Y') THEN
J= J + 1
C4='STATE OF THE ART'
GO TO 102
ELSE IF (CH0ICE4 .EQ. 'y>) THEN
J= J + 1
C4='STATE OF THE ART'
GO TO 102
ELSE IF (CH0ICE4 .EQ. 'N') THEN
C4=' '
GO TO 102
ELSE IF (CH0ICE4 .Eq. 'n') THEN
C4=' '
GO TO 102
ELSE
GO TO 101
END IF
C
102 WRITE(6,25)'COMPLEXITY ? Y OR I'
READ(6,519) CHOICES
C WRITE(6,500) JJ
C
IF (CHOICES .EQ. 'Y') THEN
J = J + 1
C5='COMPLEXITY'
GO TO 103
ELSE IF (CHOICES .EQ. 'y') THEN
J = J + 1
CS='COMPLEXITY'
GO TO 103
322
-------
ELSE IF (CHOICES .Eq. 'N') THEN
C5=' '
GO TO 103
ELSE IF (CHOICES .EQ. 'n') THEH
C5=* '
GO TO 103
ELSE
GO TO 102
END IF
C
103 WEITE(6,2S)'SIZE/WEIGHT ? Y OR H'
READ(6,519) CHOICES
C WRITE(6,500) JJ
C
IF (CHOICES .Eq. 'Y') THEH
J = J + 1
C6='SIZE/WEIGHT'
GO TO 104
ELSE IF (CHOICES .Eq. 'y') THEH
J = J + 1
CS='SIZE/WEIGHT'
GO TO 104
ELSE IF (CHOICES .Eq. 'N') THEN
C6=' '
GO TO 104
ELSE IF (CHOICES .EQ. 'n') THEN
C6=' '
GO TO 104
ELSE
GO TO 103
END IF
C
104 WRITE(S,25)'MAINTENANCE ? Y OR N'
READ(6,519) CH0ICE7
C WRITE(S,500) JJ
C
IF (CH0ICE7 .Eq. 'Y') THEN
J = J + 1
C7='MAINTENANCE'
GO TO 10S
ELSE IF (CH0ICE7 .Eq. 'y') THEH
J = J + 1
C7='MAINTENANCE'
GO TO 105
ELSE IF (CH0ICE7 .Eq. 'N') THEH
C7=' '
GO TO 105
ELSE IF (CH0ICE7 .Eq. 'n') THEH
323
-------
C7=' '
GO TO 105
ELSE
GO TO 104
END IF
C
105 WRITE(6,25)'USEFUL LIFE ? Y OR I'
READ(6,519) CH0ICE8
C WRITE(6,500) JJ
C
IF (CH0ICE8 .EQ.
J = J + 1
C8='USEFUL LIFE'
GO TO 106
ELSE IF (CH0ICE8
J = J + 1
C8='USEFUL LIFE'
GO TO 106
ELSE IF (CH0ICE8
C8=' '
GO TO 106
ELSE IF (CH0ICE8
C8=' '
GO TO 106
ELSE
GO TO 105
END IF
C
106 WRITE(6,25)'CYCLE EFFICIENCY ? Y OR N'
READ(6,519) CH0ICE9
C WRITE(6,500) JJ
C
IF (CH0ICE9 .EQ. 'Y')
J = J + 1
C9='CYCLE EFFICIENCY'
GO TO 107
ELSE IF (CH0ICE9 .EQ.
J = J + 1
C9='CYCLE EFFICIENCY'
GO TO 107
ELSE IF (CH0ICE9 .Eq.
C9=' '
GO TO 107
ELSE IF (CH0ICE9 .Eq.
C9=' '
GO TO 107
ELSE
GO TO 106
'Y') THEN
.Eq. 'y') THEN
.Eq. 'N') THEN
.Eq. 'n') THEN
THEN
'y') THEN
'N') THEN
'n') THEN
324
-------
END IF
C
107 IF (J .EQ. 0) THEN
WRITE(6,109)'YOU MUST SELECT AT LEAST 1 CRITERIA!'
109 FORMAT(15X,A36,///)
GO TO 8787
ELSE
CONTINUE
END IF
C
WRITE(6,99)'NUMBER OF CRITERIA SELECTED =',J
99 F0RMAT(///,20X,A29.il,////)
WRITE(6,50)'YOU HAVE CHOSEN THE FOLLOWING APPLICATION:'
BO FORMATC12X,A42,/)
C
IF (CH0ICE1 .Eq.
GO TO 1600
ELSE IF (CH0ICE1
GO TO 1600
ELSE IF (CH0ICE1
GO TO 1603
ELSE IF (CH0ICE1
GO TO 1603
END IF
C
1600 WRITE(6,60) C2,' ',C1
60 F0RMAT(20X,A10,A1,A16,//)
GO TO 1602
1603 WRITE(6,61) C3,' ',C1
61 FORMAT(20X,A10,A1,A16,//)
1602 CONTINUE
C
C ************************************************************************
c
WRITE(6,505)'PRESS RETURN'
READ(6,506) II
WRITE(6,500) JJ
C
C
WRITE(6,80)'YOU HAVE CHOSEN TO CONSIDER \J
80 FORMAT(20X,A30,I1)
WRITE(6,81)'TECHNICAL ASSESSMENT CRITERIA:'
81 F0RMAT(20X,A30,///)
WRITE(6,82)C4
82 F0RMAT(25X,A16)
WRITE(6,83)C5
83 F0RMAT(25X,A10)
WRITE(6,84)C6
'R') THEN
.EQ. 'r') THEN
.EQ. 'A') THEN
.Eq. 'a') THEN
325
-------
84 FORMAT(25X,All)
WRITE(6,84)C7
WRITE(6,84)C8
WRITE(6,82)C9
C
DO 90, I = 1,6
VC(I) = 0.0
90 CONTIHUE
C
WRITE(6,500) JJ
WRITE(6,812)'THE NEXT STEP IS TO WEIGHT THE TA CRITERIA.'
812 F0RMAT(15X,A43,//)
WRITE(6,814)'YOU HAVE TWO OPTIONS:'
814 FORMAT(15X,A21,/)
WRITE(6,815)'ACCEPT THE DEFAULT VALUE OF EQUAL WEIGHTING.'
815 FORMAT(20X,A44)
WRITE(6,816)'WEIGHT THE TA CRITERIA YOURSELF.'
816 FORMAT(20X.A32)
WRITE(6,5638)'D0 YOU WISH TO ACCEPT THE DEFAULT, Y OR N ?'
5638 F0RMAT(///,15X,A43,//)
WRITE(6,518)'MAKE SELECTION AND PRESS RETURN'
C
READ(6,519) CH0ICE11
WRITE(6,500) JJ
C
IF ((CH0ICE11 .EQ. 'Y').OR.(CH0ICE11 .Eq. 'y')) THEN
C
DWF = (1.0/(J))
C
IF ((CH0ICE4 .EQ. 'Y').OR.(CH0ICE4 .EQ. 'y')) THEN
WC(1) = DWF
END IF
C
IF ((CHOICES .Eq. 'Y').OR.(CHOICES .Eq. 'y')) THEN
WC(2) = DWF
END IF
C
IF ((CH0ICE6 .EQ. 'Y').OR.(CH0ICE6 .Eq. 'y')) THEN
WC(3) = DWF
END IF
C
IF ((CH0ICE7 .Eq. 'Y').OR.(CH0ICE7 .Eq. 'y')) THEN
WC(4) = DWF
END IF
C
IF ((CH0ICE8 .Eq. 'Y').OR.(CH0ICE8 .Eq. 'y')) THEN
WC(5) = DWF
END IF
326
-------
c
IF ((CH0ICE9 .EQ. 'Y').0R.(CH0ICE9 .EQ. 'y')) THEN
WC(6) = DWF
END IF
GO TO 3030
C
END IF
C
WRITE(6,85) 'YOU MAY WEIGHT THESE CRITERIA AS YOU WISH. HOWEVER'
85 FORMAT(1SX.AS0)
3333 WRITE(6,86)'THE SUM OF THE WEIGHTING FACTORS FOR THE \J
86 F0RMAT(15X,A41.il)
WRITE(6,87)'CRITERIA MUST EQUAL 1.'
87 FORMAT(1SX,A22,///)
C
IF (CH0ICE4 .Eq. 'Y') THEN
WRITE(6,88)C4,' ?'
88 F0RMAT(20X,A16,A2)
READ(6,*) WC(1)
ELSE IF (CH0ICE4 .Eq. 'y') THEN
WRITE(6,88)C4,' ?'
READ(6,*) WC(1)
END IF
C
IF (CHOICES .Eq. 'Y') THEN
WRITE(6,89)CS,' ?'
89 F0RMAT(2OX,A10,A2)
READ(6,*) WC(2)
ELSE IF (CHOICES .Eq. 'y') THEN
WRITE(6,89)C6,' ?'
READ(6,*) WC(2)
END IF
C
IF (CH0ICE6 .Eq. 'Y') THEN
WRITE(6,9000)C6,' ?'
9000 FORMAT(20X,A11,A2)
READ(6,*) WC(3)
ELSE IF (CH0ICE6 .Eq. 'y') THEN
WRITE(6,9000)C6,' ?'
READ(6,*) WC(3)
END IF
C
IF (CH0ICE7 .Eq. 'Y') THEN
WRITE(6,9000)C7,' ?'
READ(6,*) WC(4)
ELSE IF (CH0ICE7 .Eq. 'y') THEN
WRITE(6,9000)C7,' ?'
READ(6,*) WC(4)
327
-------
END IF
C
IF (CH0ICE8 .EQ. 'Y') THEM
WRITE(6,9000)C8,' ?'
READ(6,*) WC(5)
ELSE IF (CH0ICE8 .Eq. 'y') THEN
WRITE(6,9000)C8,' ?'
READ(6,*) WC(5)
END IF
IF (CH0ICE9 .EQ. 'Y') THEN
WRITE(6,88)C9,' ?'
READ(6,*) WC(6)
ELSE IF (CH0ICE9 .Eq. 'y') THEN
VRITE(6,9000)09,' ?'
READ(6,*) WC(6)
END IF
C
C ************************************************************************
c
C CHECK:
C
T0TAL=0.0
DO 2000 1=1,6
TOTAL=TOTAL + WC(I)
2000 CONTINUE
C
DIFF=TOTAL - 1.0
C
IF (DIFF .GT. 0.05) THEN
WRITE(6,91)'SUM OF WEIGHTING FACTORS EXCEEDS 1..TRY AGAIN!'
91 FORMAT(12X,A46,//)
GO TO 3333
ELSE IF (DIFF .LT. -0.05) THEN
WRITE(6,92)'SUM OF WEIGHTING FACTORS LESS THAN 1..TRY AGAIN!'
92 FORMAT(12X.A48,//)
GO TO 3333
ELSE
CONTINUE
END IF
C
C
WRITE(6,500) JJ
C
3030
45
WRITE(6,45) 'ENTER THE NAME OF THE DATA OUTPUT FILE'
FORMAT(15X,A38,//)
READ(6,548) OUTPUTFILE
WRITE(6,500) JJ
FORMAT(A50)
548
328
-------
OPEN(11,FILE=OUTPUTFILE,STATUS='UNKNOWN')
C
C ************************************************************************
c
C TECH ASSESSMENT EQUATION:
C
DO 6666 L=1,N
RATE(L) =0.0
DO 7000 I = 1,6
RATE(L)= RATE(L) + (WC(I)) * (A(I,K,L))
7000 CONTINUE
C
6666 CONTINUE
C
C **************~********»**+********************************~***********+
c
C RANK THE TECHNOLOGIES FROM HIGH TO LOW AND DISPLAY OUTPUT:
C
WRITE(6,737)'RANKING OF ALTERNATIVE REFRIGERATION TECHNOLOGIES'
WRITE(11,737)'RANKING OF ALTERNATIVE REFRIGERATION TECHNOLOGIES'
737 FORMAT(15X.A49,/)
C
IF (CH0ICE1 .Eq. 'R') THEN
GO TO 2600
ELSE IF (CH0ICE1 .Eq. 'r') THEN
GO TO 2600
ELSE IF (CH0ICE1 .EQ. 'A') THEN
GO TO 2603
ELSE IF (CH0ICE1 .Eq. 'a') THEN
GO TO 2603
END IF
C
2600 WRITE(6,8601) 'FOR ',C2,' ',C1,' ',' APPLICATIONS'
WRITE(11,8601) 'FOR \C2,' '.CI,' ',' APPLICATIONS'
8601 FORMAT(20X,A4,A10,A1,A16,A1,A13,////)
GO TO 2602
2603 WRITE(6,611) 'FOR ',C3,' \C1,' APPLICATIONS'
WRITE(11,611) 'FOR \C3,' ',C1,' APPLICATIONS'
611 F0RMAT(20X,A4,A10,A1,A16,A13,////)
2602 CONTINUE
C
WRITE(6,80)'YOU HAVE CHOSEN TO CONSIDER \J
WRITE(11,80)'YOU HAVE CHOSEN TO CONSIDER ',J
C
WRITE(6,81)'TECHNICAL ASSESSMENT CRITERIA:'
WRITE(11,81)'TECHNICAL ASSESSMENT CRITERIA:'
C
WRITE(6,822)C4,WC(1)
329
-------
WRITE(11,822)C4,WC(l)
822 F0RMAT(25X,A16,4X,F4.2)
WRITE(6,833)C5,WC(2)
WRITE(11,833)C5,WC(2)
833 F0RMAT(25X,A10,10X,F4.2)
WRITE(6,844)C6,WC(3)
WRITE(11,844)C6,WC(3)
844 F0RMAT(25X,A11,9X,F4.2)
WRITE(6,844)C7,WC(4)
WRITE(11,844)C7,WC(4)
WRITE(6,844)C8,WC(5)
WRITE(11,844)C8,WC(5)
WRITE(6,822)C9,WC(6)
WRITE(11,822)C9,WC(6)
WRITE(6,*)' '
WRITE(6,*)' '
WRITE(6,*)' '
WRITE(11,*)' '
HRITE(11,*)' '
WRITEdl,*)' '
C
WRITE(6,505) 'PRESS RETURH'
READ(6,506) II
WRITE(6,500) JJ
C
WRITE(6,738)'RANKING','REFRIGERATION TECHNOLOGY','RATING'
WRITE(11,738)'RANKING','REFRIGERATION TECHNOLOGY','RATING'
738 FORMAT(14X,A7,2X,A24,6X,A6,//)
C
WRITE(6,971)'BEST/HIGHEST'
WRITE(11,971)'BEST/HIGHEST'
971 F0RHAT(65X,A12)
C
DO 4444 L = 1,N
RHAX = -1E2
C
DO 5555 K = 1,1
RHAX = MAX(RMAX,RATE(K))
5555 CONTINUE
C
IF (RMAX .EQ. RATE(l)) THEN
WRITE(6,739)L,'MAGNETIC REFRIGERATION',RATE(1)
WRITE(11,739)L,'MAGNETIC REFRIGERATION',RATE(1)
739 F0RMAT(17X,I1,5X,A22,10X,F4.2)
RATE(l) = 0.0
ELSE IF (RMAX .Eq. RATE(2)) THEN
WRITE(6,740)L,'PULSE/THERMOACOUSTIC',RATE(2)
WRITE(11,740)L,'PULSE TUBE/THERMOACOUSTIC',RATE(2)
330
-------
740 F0RMAT(17X,I1,5X,A25,7X,F4.2)
RATE(2) =0.0
ELSE IF (RMAX .Eq. RATE(3)) THEN
WRITE(6,741)L,'THERMOELECTRIC',RATE(3)
WRITE(11,741)L,'THERMOELECTRIC',RATE(3)
741 F0RMAT(17X,I1,5X,A14,18X,F4.2)
RATE(3) =0.0
ELSE IF (RMAX .Eq. RATE(4)) THEN
WRITE(6,742)L,'REVERSED STIRLING',RATE(4)
WRITE(11,742)L,'REVERSED STIRLING',RATE(4)
742 F0RMAT(17X,I1,5X,A17,15X.F4.2)
RATE(4) =0.0
ELSE IF (RMAX .EQ. RATE(5)) THEN
WRITE(6,743)L,'REVERSED BRAYTON',RATE(5)
WRITE(11,743)L,'REVERSED BRAYTON',RATE(5)
743 F0RMAT(17X,I1,5X,A16,16X,F4.2)
RATE(5) =0.0
ELSE IF (RMAX .Eq. RATE(6)) THEN
WRITE(6,744)L,'ABSORPTION',RATE(6)
WRITE(11,744)L,'ABSORPTION',RATE(6)
744 F0RMAT(17X,I1,5X,A10,22X,F4.2)
RATE(6) =0.0
ELSE IF (RMAX .Eq. RATE(7)) THEN
WRITE(6,743)L,'SOLID ADSORPTION',RATE(7)
WRITE(11,743)L,'SOLID ADSORPTION',RATE(7)
RATE(7) =0.0
ELSE IF (RMAX .Eq. RATE(8)) THEN
WRITE(6,742)L,'VAPOR COMPRESSION',RATE(8)
WRITE(11,742)L,'VAPOR COMPRESSION',RATE(8)
RATE(8) =0.0
END IF
4444 CONTINUE
C
WRITE(6,971)'WORST/LOWEST'
WRITE(11,971)'WORST/LOWEST'
C
CLOSE (11)
C
C ************************************************************************
c
C CHOICE TO CONTINUE PROGRAM, OR NOT:
C
WRITE(6,5632)'DO YOU WISH TO CONTINUE WITH ANOTHER CASE, Y OR N?'
5632 FORMAT(///,15X.A50,//)
WRITE(6,518)'MAKE SELECTION AND PRESS RETURN'
C
C ************************************************************************
c
331
-------
1010 READ(6,S19) CH0ICE10
WRITE(6,500) JJ
C
IF ((CH0ICE10 .Eq. 'Y')•OR.(CH0ICE10 .Eq. 'y')) THEN
C
GO TO 4B67
C
ELSE IF ((CH0ICE10 .Eq. 'N').OR.(CH0ICE10 .Eq. 'n')) THEN
C
CONTINUE
C
END IF
C
END
332
-------
APPENDIX E. SAMPLE DATA FROM THE TECHNOLOGY
ASSESSMENT PROGRAM
333
-------
RANKING OF ALTERNATIVE REFRIGERATION TECHNOLOGIES
FOR DOMESTIC AIR CONDITIONING APPLICATIONS
YOU HAVE CHOSEN TO CONSIDER 6
TECHNICAL ASSESSMENT CRITERIA:
STATE OF THE ART
.20
COMPLEXITY
.15
SIZE/WEIGHT
.05
MAINTENANCE
.15
USEFUL LIFE
.15
CYCLE EFFICIENCY
.30
RANKING REFRIGERATION TECHNOLOGY RATING
1 VAPOR COMPRESSION 4.80
2 ABSORPTION 3.80
3 PULSE TUBE/THERMOACOUSTIC 2.95
4 REVERSED STIRLING 2.90
5 SOLID ADSORPTION 2.80
6 REVERSED BRAYTON 2.35
7 THERMOELECTRIC 2.05
8 MAGNETIC REFRIGERATION 1.95
BEST/HIGHEST
WORST/LOWEST
334
-------
RANKING OF ALTERNATIVE REFRIGERATION TECHNOLOGIES
FOR COMMERCIAL AIR CONDITIONING APPLICATIONS
YOU HAVE CHOSEN TO CONSIDER 6
TECHNICAL ASSESSMENT CRITERIA:
STATE OF THE ART
.20
COMPLEXITY
.10
SIZE/WEIGHT
.05
MAINTENANCE
.15
USEFUL LIFE
.20
CYCLE EFFICIENCY
.30
RANKING REFRIGERATION TECHNOLOGY RATING
BEST/HIGHEST
1
VAPOR COMPRESSION
4.85
2
ABSORPTION
4.45
3
PULSE TUBE/THERMOACOUSTIC
3.10
4
SOLID ADSORPTION
2.80
5
REVERSED STIRLING
2.75
6
REVERSED BRAYTON
2.35
7
MAGNETIC REFRIGERATION
2.05
8
THERMOELECTRIC
1.95
WORST/LOWEST
335
-------
RANKING OF ALTERNATIVE REFRIGERATION TECHNOLOGIES
FOR MOBILE AIR CONDITIONING APPLICATIONS
YOU HAVE CHOSEN TO CONSIDER 6
TECHNICAL ASSESSMENT CRITERIA:
STATE OF THE ART
.15
COMPLEXITY
.20
SIZE/WEIGHT
.30
MAINTENANCE
.20
USEFUL LIFE
.05
CYCLE EFFICIENCY
.10
BEST/HIGHEST
WORST/LOWEST
336
RANKING REFRIGERATION TECHNOLOGY RATING
1 VAPOR COMPRESSION 4.30
2 REVERSED STIRLING 3.25
3 PULSE TUBE/THERMOACOUSTIC 2.65
4 SOLID ADSORPTION 2.55
5 REVERSED BRAYTON 2.50
6 ABSORPTION 2.30
7 THERMOELECTRIC 2.15
8 MAGNETIC REFRIGERATION 1.25
-------
RANKING OF ALTERNATIVE REFRIGERATION TECHNOLOGIES
FOR DOMESTIC REFRIGERATION APPLICATIONS
YOU HAVE CHOSEN TO CONSIDER 6
TECHNICAL ASSESSMENT CRITERIA:
STATE OF THE ART
.20
COMPLEXITY
.20
SIZE/WEIGHT
.10
MAINTENANCE
.10
USEFUL LIFE
.15
CYCLE EFFICIENCY
.25
BEST/HIGHEST
WORST/LOWEST
RANKING REFRIGERATION TECHNOLOGY RATING
1 VAPOR COMPRESSION 4.60
2 ABSORPTION 3.70
3 REVERSED STIRLING 3.25
4 SOLID ADSORPTION 3.05
5 REVERSED BRAYTON 2.65
6 PULSE TUBE/THERMOACOUSTIC 2.60
7 THERMOELECTRIC 2.20
8 MAGNETIC REFRIGERATION 1.95
337
-------
RA9KIIG OF ALTERIATIVE REFRIGERATIOS TECHIOLOGIES
FOR COMMERCIAL REFRIGERATIOI APPLICATION
YOU HAVE CHOSEI TO COHSIDER 6
TECHIICAL ASSESSMENT CRITERIA:
STATE OF THE ART
.20
COMPLEXITY
.10
SIZE/WEIGHT
.05
MAIITEIAICE
.15
USEFUL LIFE
.20
CYCLE EFFICIENCY
.30
RAIKING REFRIGERATIOI TECHHOLOGY RATIVG
BEST/HIGHEST
1
VAPOR COMPRESSIOM
4.70
2
ABSORPTIOI
3.80
3
REVERSED STIRLIVG
3.15
4
SOLID ADSORPTION
3.10
5
REVERSED BRAYTOI
3.00
6
PULSE TUBE/THERMOACOUSTIC
2.80
7
MAGHETIC REFRIGERATIOI
2.05
8
THERMOELECTRIC
2.05
WORST/LOWEST
338
-------