College of Engineering
Mechanical Engineering Department
Advanced Exergy Analysis for Thermal Systems
A Senior Design Project (MENG 490) Report
Submitted in partial fulfillment of the
requirements for the degree of
B.Sc. in Mechanical Engineering
Ali Abdulla Ali AlAradi
Professor Teoman Ayhan
January 2nd, 2018
I would like
to express my thanks and appreciation my supervisor Prof. Teoman Ayhan for his
continuous support and advice.
Special thanks to my family and colleagues in the
University of Bahrain, as well as every member of the university’s staff. This
would have been impossible to do without them.
This abstract is a
very important and obligatory part of the report allowing the potential reader
to judge, if he is the target of this report. The abstract is a summary of the
entire report and not an introduction to the report. It should be written with
broadly understandable technical language and should be self-contained, i.e.
should not contain any references or citations. Also the usage of abbreviations
and acronyms should be avoided, since the same acronyms or abbreviations can
have different meanings on different research fields. The abstract should
typically contain about 400 words and in any cases not more than one page. The
definition of the research field and the most important outcome of the
presented research are the obligatory components of the abstract.
(Limited to Only one page)
1 Introduction. 1
Chapter 2 Background. 3
of Exergy. 3
Exergy Analysis History. 4
Exergy Analysis History. 5
Chapter 3 Design and Implementation. 6
Mathematical Representation & Definition. 6
Exergy Analysis. 6
Exergy Analysis. 8
Study 1: Vapor Compression Refrigeration System.. 11
Chapter 4 Results and Discussion. 12
Chapter 5 Conclusion and Future Work. 13
You can add Appendices here, if needed. Starting from Appendix A and so on. 15
Appendix A 16
Work schedule (Gantt Chart) 16
List of Figures
Figure (1.1): The UOB Logo. 1
Figure (2.6): The Logo. 5
Figure (3.10): The Logo. 8
List of Tables
Table (1.1) The
Table (2.4) Statistical Data ………
Bachelor of Science
List of Symbols
Number of channels for user j
The purpose of this report is to
explain exergy and advanced exergy analysis and how they can be used to improve
thermal systems. Explaining the difference between conventional exergy analysis
and advanced exergy analysis is also necessary to understand the advantages
that the advanced exergy analysis has over the conventional one, and if it is
worth the extra time and effort to do the analysis.
Exergy analysis is an important
tool to evaluate and understand the efficiency and performance of any system,
thermal or otherwise. Its currently the most wildly taught and used method to
measure how much of the system’s true potential is being utilized, and how far
it is possible to improve it before hitting the theoretical ceiling. The
controversial exergy analysis methods do provide the theoretical maximum
performance and how much exergy is lost in the system, but it fails to provide
much else. For practical application, we must understand where the losses
occur, in the components of the system rather than the system as a whole. We
must also understand how the physical and scientific limitations affect how
close we can get to that theoretical maximum performance. As such, to get a
clearer look into what can be improved, how much it can be improved, and what
would be the benefits of improving it, an alternative to the controversial
exergy analysis method must be used. This report discusses the alternative.
Advanced exergy analysis.
Advanced exergy analysis
specializes in analyzing the exergy losses in the processes, known as the
exergy destruction. It divides the exergy destruction into two separate parts
depending on two different criteria’s. The exergy destruction is either divided
into avoidable and unavoidable exergy destruction, or into endogenous and
exogenous exergy destruction.
The first criteria is
self-explanatory. The avoidable exergy destruction can be eliminated by either
improving the component or the system as a whole. The unavoidable exergy
destruction cannot be avoided due to technological limitations. This criterion
provides a simple method to understand just how much the component can be
improved, as well as the maximum possible performance after going through all
the possible improvements.
The second one is slightly less
straightforward. The endogenous exergy destruction is the exergy destruction in
a specific component while assuming the remaining components are all functioning
ideally. The exogenous exergy destruction is the remaining exergy destruction,
influenced by both the component’s own irreversibilities and flaws as well as
the other components’ flaws. Using the endogenous exergy destruction, we can
calculate how much we can improve the component by improving itself, without
having to touch the remaining components at all.
The idea behind advanced exergy
analysis is not to use a single one of the aforementioned exergy destruction
separations on its own, but rather to combine them both together in order to
find the endogenous available, endogenous unavailable, exogenous available, and
exogenous unavailable parts of the exergy destruction in each component.
This report starts with background
and historical information on the concepts and applications of exergy,
conventional exergy analysis, and advanced exergy analysis, followed by
explaining the methodology of performing the analysis, and finally concluded by
two case studies showcasing the analysis in action.
In order to begin understanding
either exergy analysis methods one must understand what exergy itself is. To
put it in the simplest terms energy is divided into two parts, exergy and
anergy. Exergy is the usable energy that can be utilized. Anergy, on the other
hand, is the energy that cannot be used or utilized. While energy is preserved
in the universe and cannot be destroyed or created, the same cannot be said
about exergy. Exergy can be destroyed. In fact, with the exception of
theoretical, ideal, reversible processes the second law of thermodynamics
dictates that exergy must be destroyed. This brings forth the importance of
exergy analysis. It would be unrealistic to expect any system to be an ideal
reversible system, and as such, all systems would have a certain amount of
exergy destruction. Performing exergy analysis would allow us to diagnose the
system and find out which process has the most exergy destruction. Seeing that
the loss of exergy is a flaw in all systems, we would naturally want to lower
the exergy destruction of system, and conventional exergy analysis allows us to
priorities the processes and parts that have higher exergy destruction in order
to improve them individually and lower the exergy destruction of the system.
While our current mathematical
understanding of exergy dates back to at least the early 1870s and the first
American engineering doctorate holder Dr. Josiah Willard Gibbs1, the term
‘exergy’ itself would not come to use until Zoran Rant derives it from Greek
terminology in the middle 20th century 2.
History of Exergy
The earliest and most basic
concepts of exergy and second law of thermodynamics are traced back to the
1820s instead of the 1870s, and to a man by the name of Sadi Carnot 3. His
work was almost exclusively theoretical, and involved no mathematics. This,
alongside the fact that it was thought out in the time where caloric theory was
more widely accepted than the kinetic theory in the study of thermodynamics,
meant that despite Carnot’s brilliant concept, some of which like the Carnot
Engine are still in use to this very day, his work would be ignored and unused
for nearly half a century.
Over four decades later, Dr. Gibbs
would utilize Carnot’s concepts, alongside his own understanding of
thermochemistry and research, to derive the mathematics of what is now known as
Conventional Exergy Analysis History
While the basic definition and
mathematical derivation of exergy was done in the 1870s, it would still take
close to a century before worldwide acceptance and agreeance of Zoran Rants’
terminology 4. Even the most
innovative of applications of the conventional exergy analysis did not occur
until the late 1950s and early 1960s, by works of Keller on steam power cycles
in 1959, and Fratzscher, Gašperši?, and Rant in 1961. Because the theoretical
work was not completed and accepted until the end of the 1960s, only a few
people were confident enough in this new methodology that was basically in its
infancy enough to test it on practical applications, let alone use it on major
systems and power plants.
This all would come to change in
the 1970s. Exergy and the second law of thermodynamics were widely accepted by
the scientific and engineering community to the point where it was in textbooks
and paved the way for engineering thermodynamics to become its own field.
Coupled with the sudden need to maximize every oil fueled system’s efficiency
that immerged due to the oil crisis of 1973, and the world had both motive and
opportunity to embark into an age of scientific advancement in terms exergy
The practical applications did
start with the aforementioned works on steam power cycles, but they soon spread
to cover over thermal systems such as gas turbine cycles starting with
Chambadal’s work in 1965, the renewable energy cycles in the early 1980s by
Edgerton and Bejan, heat exchangers by Elsner in 1960, Cryogenics by
Martinowsky in 1950, and distillation by Freshwater in 1951. Works on exergy on
topics other than thermal systems also pioneered the exergy study itself, most
notably Rant’s work in 1947 and Denbigh’s in 1956 on chemical processes and
systems rather than thermal ones.
While conventional exergy analysis
has found its place as an important tool for both economic and environmental
evaluation and analysis of thermal and chemical systems, it is still a work in
progress in other departments, and that is what conventional exergy analysis
students and researchers focus on, as well as improving its accessibility for
existing systems. Even today, four decades after the scientific community
accepted the concepts exergy, it is still a field in need, and demand, of
Advanced Exergy Analysis History
Advanced Exergy Analysis is quite new and is unheard of even
among fresh graduates of Mechanical Engineering. The term ‘advanced exergy
analysis’ does not appear to have been used prior to 2009, and the earliest I
have been able to track some of its methodology is to 2002 for the avoidable
and unavoidable splitting 5 and 2006 for the endogenous and exogenous
The avoidable and unavoidable exergy destruction splitting
originates, in concept, from the economical avoidable and unavoidable cost
analysis, but it does not function on the same principles. In accounting and
economics, the avoidable costs refer to costs that can be avoided by making
specific choices, like spending less on advertising for a service or quality
control on a product. In exergy analysis, it is done by comparing the minimum
scientific theoretical cost and the minimum technological applicable cost. To
put it simply, it compares between the lowest possible operation cost in the
Design and Implementation
General Mathematical Representation &
Conventional Exergy Analysis
The energy in heat transfer can be divided into two parts:
Where Q is the heat transfer, X is the exergy, and A is the
Using the Carnot efficiency to calculate the theoretical
exergy and anergy in the system:
is the Carnot
T0 is the ambient temperature
T is the component temperature.
The theoretical exergy and anergy are:
Exergy can be mathematically represented by two equations,
the first of which is:
X2 – X1 is the change in exergy.
is the change in internal energy.
p0 is the pressure.
is the change
T0 is the ambient temperature.
is the change in entropy.
is the change in kinetic energy.
is the change in potential energy.
Using the following equations:
The same equation can be represented as the following when
using specific internal energy, volume, kinetic and potential energies, and
g is the gravitational acceleration.
z is the height.
The following equation can be used to further simplify the
exergy balance equation:
To the following form:
Where h is the specific enthalpy.
The following equation can be used to define the specific
Which would reduce the equation to:
The second equation is:
Tc is the temperature of component that receives
that heat transfer.
Q is heat transfer into the system.
W is the useful work out of the system.
Xdes is the exergy destruction.
By subtracting the two equations, we get the following equation:
Both equations can be rearranged to be in term of the Exergy
destruction, which is the variable we want to calculate from the exergy balance
to be as such
Alternatively, an entropy balance can be performed and after
finding the entropy generation, the exergy destruction can be calculated using
the following equation:
The exergy balance equation is the following:
Where Xin is the exergy entering the component,
and Xout is the exergy leaving the component.
Advanced Exergy Analysis
Assuming we have a theoretical system where all the
components are in series, and either the exergy output or input of the whole
system is constant.
Let the exergetic efficiency of each component be defined
n is the number of the component.
Xin is the exergy entering the component.
Xout is the exergy leaving the component.
Regardless of the case (Xin constant or Xout
constant), the following equation would define the total unavoidable exergy destruction
of the system:
The exergy destruction and endogenous exergy destruction for
The unavoidable exergy destruction for the system:
Combining the unavoidable and endogenous
exergy destruction rules to find the unavoidable endogenous exergy destruction:
Under either assumption, the results should be the same provided
that the exergy input and output satisfy the following equation:
and exogenous exergy destruction splitting
In order to split the exergy to endogenous and exogenous
exergy, we must establish theoretical cycles and hybrid. The concept of said
theoretical cycles is simple: minimize the exergy destruction. It would change
depending on the component, but the general rules are:
If it is a component that can have the theoretical
isentropic efficiency of 1 such as pumps and turbines:
the component is a heat exchanger or something similar:
Which occurs when the difference in temperature is zero.
After establishing the perfect, ideal, theoretical cycle, we
calculate the endogenous exergy destruction of each component by putting
the actual data of that specific component in the theoretical cycle, thus
creating the hybrid cycle.
and unavoidable exergy destruction splitting
To find the unavoidable exergy destruction we must use a
simulation to find how the processes in the component would function under
near-ideal conditions that cannot be achieved in the foreseeable future.
Said simulation will give us the value of
We then use that value to calculate the unavoidable exergy
destruction using the following equation:
the actual exergy leaving the component/process.
the two splittings
The method to do this one is rather straightforward, once we
actually do the previous two splitting methods. Using the same data we obtained
from the previous splitting methods, we use the following equation to get the
unavoidable endogenous exergy destruction:
Once the unavoidable endogenous exergy destruction is
calculated, the remaining information, namely the avoidable endogenous,
unavoidable exogenous, and avoidable exogenous exergy destruction can be
calculated using the following equations:
Case Study 1: Vapor Compression Refrigeration
following data were measured from a Vapor Compression Refrigeration System that
uses refrigerant R12 and a water supply to cool air.
Figure 1 Simple Vapor Compression Refrigeration System
Table 1 Vapor Compressor Readings
R-12 Mass flow rate
temperature (state 1)
temperature (state 2)
inlet temperature (state 3)
temperature (state 4)
Water Flow Rate
inlet temperature (state 5)
outlet temperature (state 6)
temperature (state 7)
temperature (state 8)
Conventional exergy analysis for each component
The majority of the calculations were done by EES. The EES
code is available in the appendix.
following steps were performed:
EES’ database, the specific enthalpy, specific entropy, and specific exergy
were obtained for each state.
the following equation, the work done by the compressor was calculated:
exergy destruction in each component was calculated using the following
input exergy is found using the following equations:
exergy output is found using the following equations
Advanced Exergy Analysis
and exogenous exergy destruction Splitting
To perform this splitting, a theoretical cycle is created.
In the theoretical cycle, the following conditions are given to minimize or
eliminate exergy destruction in each component, as well as the cycle.
Exchangers (Evaporator and Condenser):
Entropic efficiency = 100%. Exergy destruction = 0.
valve is replaced with an ideal expansion process, which does not occur
naturally. As such, Exergy destruction in the expansion valve is taken to be
equal to zero.
Results and Discussion
After the presenting
your design and work, the results obtained are shown and discussed in this
chapter. How do you kneo that your design workded and that the problem you
started out to solve has actually been solved. If not solved, then you need to
discuss the reasons and propose solutions .
and Future Work
Write your conclusions here. Typically 1-2
paragraphs where you tell what the problem was and how it was solve. Then the
main results in 1-2 paragraphs or possibly as a list. In addition, you can
describe topics for future research in the last paragraph.
1 J.W. Gibbs
(1873). “A method of geometrical representation of thermodynamic
properties of substances by means of surfaces: reprinted in Gibbs, Collected
Works, ed. W. R. Longley and R. G. Van Name (New York: Longmans, Green,
1931)”. Transactions of the Connecticut Academy of Arts and Sciences. 2:
David Sanborn Scott (2008). Smelling Land: The Hydrogen Defense Against Climate
Catastrophe. Queen’s Printer Publishing. p. 206. ISBN 978-0-9809674-0-1.
3 S. Carnot (1824). Réflexions sur la puissance motrice
du feu sur les machines propres a developper cette puissance. (Reflections on
the Motive Power of Fire and on Machines Fitted to Develop That Power.
Translated and edited by R.H. Thurston 1890). Paris: Bachelier.
4 Enrico Sciubba (2007), A brief
Commented History of Exergy From the Beginnings to 2004. Int. J. of
Thermodynamics ISSN 1301-9724 Vol. 10 (No. 1), pp. 1-26, March 2007.
5 George Tsatsaronis & Moung-Ho Parka (2002), On
avoidable and unavoidable exergy destructions and investment costs in thermal
systems, Energy Conversion and Management, Volume 43, Issues 9–12, June–August
2002, Pages 1259-1270
6 George Tsatsaronis, Solange O. Kelly and Tatiana V.
Morosuk (2006) ASME 2006 International Mechanical Engineering Congress and
Exposition, Advanced Energy Systems. Chicago, Illinois, USA, November 5 – 10,
2006, Conference Sponsors: Advanced Energy Systems Division, ISBN:
0-7918-4764-0 | eISBN: 0-7918-3790-4
You can add
Appendices here, if needed. Starting
from Appendix A and so on.