Bahrain University

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

Student name:

Ali Abdulla Ali AlAradi

20132414

Supervisor:

Professor Teoman Ayhan

Program :

Mechanical Engineering

Starting Date:

October19th, 2017

Submission Date:

January 2nd, 2018

Acknowledgment

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.

Abstract

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)

Contents

Chapter

1 Introduction. 1

Chapter 2 Background. 3

2.1 History

of Exergy. 3

2.2 Conventional

Exergy Analysis History. 4

2.3 Advanced

Exergy Analysis History. 5

Chapter 3 Design and Implementation. 6

3.1 General

Mathematical Representation & Definition. 6

3.1.1 Conventional

Exergy Analysis. 6

3.1.2 Advanced

Exergy Analysis. 8

3.2 Case

Study 1: Vapor Compression Refrigeration System.. 11

Chapter 4 Results and Discussion. 12

Chapter 5 Conclusion and Future Work. 13

References 14

Appendices 15

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

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0

0

Figure (2.6): The Logo. 5

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0

0

Figure (3.10): The Logo. 8

List of Tables

Table (1.1) The

Data of……………

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Table (2.4) Statistical Data ………

Acronyms

B. Sc.

Bachelor of Science

List of Symbols

Nj

Number of channels for user j

Chapter 1

Introduction

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.

Chapter 2

Background

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.

2.1

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

exergy.

2.2

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

analysis.

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

extensive research.

2.3

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

splitting 6.

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

foreseeable future.

Chapter 3

Design and Implementation

3.1

General Mathematical Representation &

Definition

3.1.1

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

anergy.

Using the Carnot efficiency to calculate the theoretical

exergy and anergy in the system:

Where

is the Carnot

efficiency

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:

Where

X2 – X1 is the change in exergy.

is the change in internal energy.

p0 is the pressure.

is the change

in volume

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

entropies:

Where

is the

velocity.

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

exergy:

Which would reduce the equation to:

The second equation is:

Where:

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:

Where

is the

entropy generation.

The exergy balance equation is the following:

Where Xin is the exergy entering the component,

and Xout is the exergy leaving the component.

3.1.2

Advanced Exergy Analysis

3.1.2.1 Theoretical

Systems

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

by:

Where:

n is the number of the component.

Xin is the exergy entering the component.

Xout is the exergy leaving the component.

is the

exergetic efficiency.

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

each component:

And

And

.

.

.

And

And

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:

3.1.2.2 Real

Systems

3.1.2.2.1 Endogenous

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:

If

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.

3.1.2.2.2 Avoidable

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:

Where

is

the actual exergy leaving the component/process.

3.1.2.2.3 Combining

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:

3.2

Case Study 1: Vapor Compression Refrigeration

System

The

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

Reading

Units

Value

Refrigerant Data

R-12 Mass flow rate

kg/s

6.5×10-3

Evaporator Pressure

(state 4)

KPa

362

Condenser pressure

(state 2)

KPa

700

Compressor inlet

temperature (state 1)

oC

5

Condenser inlet

temperature (state 2)

oC

68

Expansion valve

inlet temperature (state 3)

oC

28*

Evaporator inlet

temperature (state 4)

oC

5

Water Data

Water Flow Rate

kg/s

50×10-3

Condenser

inlet temperature (state 5)

oC

21

Condenser

outlet temperature (state 6)

oC

23

Air Data

Air

Flow Rate

kg/s

0.1

Evaporator inlet

temperature (state 7)

oC

20

Evaporator outlet

temperature (state 8)

oC

12

Surroundings Data

Surrounding

Temperature (T0)

oC

21

Surrounding

Pressure (P0)

KPa

100

3.2.1

Conventional exergy analysis for each component

The majority of the calculations were done by EES. The EES

code is available in the appendix.

The

following steps were performed:

1) Using

EES’ database, the specific enthalpy, specific entropy, and specific exergy

were obtained for each state.

2) Using

the following equation, the work done by the compressor was calculated:

3) The

exergy destruction in each component was calculated using the following

equations

4) The

input exergy is found using the following equations:

5) The

exergy output is found using the following equations

3.2.2

Advanced Exergy Analysis

3.2.2.1 Endogenous

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.

1) Heat

Exchangers (Evaporator and Condenser):

2) Condenser:

3) Evaporator:

4) Compressor:

Entropic efficiency = 100%. Exergy destruction = 0.

5) Expansion

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.

The follow

Chapter 4

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 .

Chapter 5

Conclusion

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.

References

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:

382–404.

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

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Appendices

You can add

Appendices here, if needed. Starting

from Appendix A and so on.