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LIBRARY

Michigan State
University

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This is to certify that the
thesis entitled

DESIGN OF A 5 KW MICROTURBINE GENERATOR

presented by
Michael Thomas Kusner

has been accepted towards fulfillment
of the requirements for the

MS. degree in Mechanical Engineering

Major Professor’s Signature
00/56/06

Date

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DATE DUE DATE DUE DATE DUE

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

2/05 p:/ClRC/DateDue.indd-p.1

DESIGN OF A 5 KW MICROTURBINE GENERATOR
By

Michael Thomas Kusner

A THESIS
Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of
MASTER OF SCIENCE
MECHANICAL ENGINEERING

2006

ABSTRACT
DESIGN OF A 5 KW MICROTURBINE GENERATOR
By
MICHAEL THOMAS KUSNER

Recently many natural disasters and power grid failures have plagued
homeowners and businesses all around the country. Until now, many have sought
gasoline and diesel powered generators as the solution to maintaining power security.
However, piston engine generators are often loud, expensive and time consuming to
maintain. Furthermore, there is an ongoing movement that is seeking to distribute the
nation's power supply fiom a few large power plants to many smaller plants. The term
used for this movement is "distributed generation".

The objective of this thesis project was to develop the groundwork for an electric
generator that is competitive with current piston engine generators in power production,
yet less expensive, quieter, easier to maintain and adaptable to distributed generation. The
solution to this problem was the development of a design and prototype for a 5 kW gas
turbine generator.

This thesis will discuss the motivation and details of this very simple and
inexpensive design and highlight the benchmarks that have already been attained through

testing. Recommendations for subsequent phases of the project are also discussed.

TABLE OF CONTENTS

LIST OF TABLES ............................................................................................................... v
LIST OF FIGURES ........................................................................................................... vii
Introduction ......................................................................................................................... 1
Design ............................................................................................................................... 10
Determination of the Power Cycle ................................................................................ 10
Brayton Cycle ........................................................................................................... 12
Rankine Cycle ........................................................................................................... 19
Steam Injection Cycle ............................................................................................... 24
Cycle Constraints .......................................................................................................... 37
Combustion Chamber ....................................................................................................... 49
Recuperator ....................................................................................................................... 65
Double Tube Heat Exchanger ................................................................................... 71
Bank of Tubes Heat Exchanger ................................................................................ 74
Plate Heat Exchanger ................................................................................................ 79
Pressure Losses ............................................................................................................. 83
Generator Subsystems ....................................................................................................... 86
Testing ............................................................................................................................... 91
Conclusions ..................................................................................................................... 100
Recommendations ........................................................................................................... 101
Appendix A - Cycle Model Equations ............................................................................ 103
Rankine Cycle ............................................................................................................. 103
Steam Injection Cycle ................................................................................................. 107

iii

Gas Cycle .................................................................................................................... 110

Appendix B - Turbine and Compressor Maps ................................................................ 112
Appendix C - Calculation of Adiabatic Flame Temperature .......................................... 114
Appendix D - Heat Exchanger Design Formulas ........................................................... 115
Double Tube Heat Exchanger ..................................................................................... 115
Bank of Tubes/ Shell and Tube ................................................................................... 117
Plate Heat Exchanger .................................................................................................. 119
Heat Exchanger Quantities ......................................................................................... 120
Appendix E - Cost Analysns ........................................................... 121
References ....................................................................................................................... 122

iv

LIST OF TABLES

Table 1. Generator comparison chart .................................................................................. 2
Table 2. Validation of the Brayton cycle model ............................................................... 19
Table 3. Validation of the Rankine cycle model ............................................................... 23
Table 4. Thermodynamic properties of exhaust gas ......................................................... 27
Table 5. Natural convection heat transfer data ................................................................. 29
Table 6. Radiation heat transfer data ................................................................................ 29
Table 7. Thermal resistance values ................................................................................... 30
Table 8. Copper tube geometrical values .......................................................................... 32
Table 9. List of specific and total work values output from turbocharger ....................... 46
Table 10. Energy content comparison of common fuels ................................................ 50
Table 1 1. Thermodynamic data for propane ..................................................................... 51
Table 12. Air and fuel flow and mixture data ................................................................... 54
Table 13. Thermodynamic values of air at the operating point ........................................ 56
Table 14. Tabulated compressor map data points ............................................................. 59
Table 15. Thermodynamic properties of cool air .............................................................. 70
Table 16. Thermodynamic properties of hot air ............................................................... 70
Table 17. Heat transfer data for all recuperator models .................................................... 71
Table 18. Results of recuperator optimization .................................................................. 80
Table 19. Recuperator design parameters ......................................................................... 83
Table 20. Pressure loss data .............................................................................................. 85
Table 21. Recuperator fluid properties ............................................................................. 85
Table 22. Enthalpy values for flame temperature calculation ........................................ 114

Table 23. Cost data from project ..................................................................................... 121

vi

LIST OF FIGURES

Figure 1. T-s diagram of the Brayton cycle ...................................................................... 13
Figure 2. Thermal efficiency plot for the Brayton cycle model ....................................... 17
Figure 3. Thermal efficiency of the ideal Brayton cycle, shown with varying temperature
and pressure ratios (22) ..................................................................................................... 18
Figure 4. T-s diagram of the Rankine cycle ...................................................................... 19
Figure 5. Thermal efficiency plot of the Rankine cycle model ........................................ 24
Figure 6. Picture of steam injector/ recuperator ................................................................ 25
Figure 7. Thermal resistance circuit of conditions surrounding the exhaust pipe ............ 26
Figure 8. Copper pipe heat transfer model ........................................................................ 31
Figure 9. Thermal resistance model used to determine heat transfer rate to water from
exhaust pipe ...................................................................................................................... 33
Figure 10. T-S diagram of the steam injection cycle ........................................................ 35
Figure 11. T-S diagram of the steam injection spreadsheet model ................................... 37
Figure 13. Garrett GT1241 turbocharger used in the prototype 5 kW gas turbine ........... 44
Figure 14. Thermal efficiency of the Rankine cycle with design component efficiencies4 6
Figure 15. Thermal efficiency plot for the Brayton cycle at design efficiencies .............. 47
Figure 16. Illustration of combustion chamber ................................................................. 55
Figure 17. Picture of combustion chamber ....................................................................... 57
Figure 18. Plot of the mass flow rate of air versus speed ................................................. 58
Figure 19. Plot of pressure ratio versus speed .................................................................. 59
Figure 20. Propane mass flow rate versus speed .............................................................. 60
Figure 21. Diameter of combustion chamber versus speed .............................................. 61

vii

Figure 22. Diagram of ignition system ............................................................................. 62

Figure 23. Picture of combustion chamber ....................................................................... 63
Figure 24. Illustration of bank of tubes model .................................................................. 75
Figure 25. Illustration of flow through bank of tubes ....................................................... 77
Figure 26. Illustration of entrance region needed to plate heat exchanger ....................... 82
Figure 27. Picture of the end'of the recuperator ............................................................... 82
Figure 28. Illustration of regions of high pressure loss .................................................... 84
Figure 29. Picture of oil pump and filter (top left) ........................................................... 87
Figure 30. Picture of oil reservoir and tubing ................................................................... 88
Figure 31. Picture of valves and manual mass flow controller in the propane delivery

system. .............................................................................................................................. 95
Figure 32. Illustration of combustion at low speeds, approximately 20,000 RPM .......... 97
Figure 33. Illustration of combustion at high speeds, approximately 40,000 RPM ......... 98
Figure 34. T-s diagram of the Rankine cycle .................................................................. 103
Figure 35. T-S diagram of the Steam Injection cycle ..................................................... 107
Figure 36. T-s diagram of the Brayton cycle .................................................................. 110
Figure 37. Garrett GT1241 compressor map (Garrett Product Catalog 4 [Ref. 16]). ..... 112
Figure 38. Turbine map for Garrett GT1241 (Garrett Product Catalog 4 [Ref. 16]). ..... 113
Figure 39. Double tube recuperator illustration .............................................................. 115
Figure 40. Bank of tubes illustration. .............................................................................. 1 17
Figure 41. Plate heat exchanger illustration .................................................................... 1 19

viii

Introduction

The overwhelming number of energy crises in the world today are starting to
demand solutions. Gasoline prices are astronomically high and many homeowners suffer
under the additional demands of household heating costs. The apparent rise in natural
disaster occurrence is leaving many cities around the world without power for extended
periods of time. Furthermore "inexpensive" energy produced from fossil fiiel-burning
power plants is becoming expensive due to the environmental constraints placed on the
plants. In fiill view of all of these problems, it is evident that the world would benefit
from portable power generating units that can provide emergency power and meet the
cost and comfort requirements of homeowners, businesses, and governments alike.

Initially, it may seem obvious that gasoline or diesel powered electric generators
already fulfill the need for portable power generating units, but these generators are loud
and expensive to own and operate. According to the National Institute on Deafness and
Other Communication Disorders (NIDCD), lawnmowers and motorcycles are two
machines that operate at 90 dB, therefore it is forthright to assume that household
generators operate at the same noise level because the engines used in lawnmowers are
the same engines used in gasoline powered generators (NIDCD 2005). It goes on to write
that, “Prolonged exposure to any noise above 90 decibels can cause gradual hearing loss”
(NIDCD 2005). This is a serious issue with the current line of household power
generators, and even though the operators of such equipment are not typically within a
range where their hearing can be affected, such a loud noise is irritating to homeowners

and neighbors alike when the generator is operated for an extended period.

Not only are current generators loud, they are also expensive. Generators in the 5
kW range vary widely in price by application. Generators of this capacity have enough
power to operate the most important electrical equipment of a typical home. Some
generators are just meant for portability while others are meant for industrial use and
emergency power. The more important the task that the generator will be used for, the
more expensive it will be. A generator used for emergency power will be more expensive
than a construction-site generator used to power an air compressor and a radio. A large
range of generators are compared in Table 1, which lists the price, model, and power

output of some common generators in the 5 kW range (Amazon.com, Inc. 2006).

Table l. Generator comparison chart

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

I Make Model Power Price ‘
Portable

McCulloch FGS7OOAK 5130 Watt $639.99

Briggs and Stratton 30241 5550 Watt $649.94

Coleman PM0525300.17 5500 Watt $649.99

Porter-Cable BSI525-WH 5250 Watt $699.94

STD 9 HP 5250 Watt $759.95
AVG. $679.96

_T:ommerclall

Portable

Winco Consumer 4500 Watt $1,840.00

Porter-Cable H451CS-W 4500 Watt $1,299.99

lMakita MAKG43OOL 4300 Watt $1,350.39

DeWaIt 064300 4300 Watt $1,398.94

North Star 9 HP 5500 Watt $1,599.99
AVG. $1,497.86

RVI Emergency

Generac 6 kW 6000 Watt $2,199.99

Onan RV Generator 4000 Watt $2,899.99

Winco 8 kW 8000 Watt $4,090.00
AVG. $3,063.33

 

 

 

 

 

 

The table illustrates how the average price of 5 kW range generators increases
with the importance of the task for which it is needed. The major difference between the
categories of generators is how well they are built. The portable models have light

frames, a few outlets, and a decent engine. The RV and emergency generators have low

oil warning systems, speed control devices, and advanced electronic control systems for
fuel pumps, power regulation and ease of troubleshooting. Additionally, the quality of
generators of this type are enhanced by low maintenance designs.

The third downfall of using current household generators is the price of fuel.
According to the Energy Information Administration (EIA) of the United States of
America, during the first week of January 2006, the average price of a gallon of gasoline
was $2.23 while the price of liquefied propane was $2.00 per gallon. The most recent
price information about natural gas, obtained during the month of October 2005, was that
it was set at an average price of $16.49 per thousand cubic feet (EIA 2006). This
translates to a cost of $1.98 per gallon of liquefied natural gas. Gasoline is 12% -14%
more expensive per gallon than propane and natural gas. For this reason, it is logical to
design a system that uses a fuel that costs less and will ease the burdens of consumers and
business owners alike.

In addition to the need for a redesigned power generation system, many
companies including the United States Department of Energy are examining ways of
incorporating microturbine technologies into everyday life. Currently, the United States
Department of Energy is wrapping up a 6-year investigation into microturbine generators
that can be used to aid in military applications and ease the burden currently shouldered
by massive fossil-fuel-burning power plants. The program is called the Advanced
Microturbine Systems program and the goals are to create designs for microturbines that
can be manufactured for less that $500/kW, operate for 11,000 hours before major
maintenance is needed, and have a fuel to electricity efficiency of around 40% (DOB

2001). Currently Capstone, a leading manufacturer of microturbine generators in the 25

kW range and up, have produced microturbines that can attain overall cycle efficiencies
of 80% when the exhaust gases are used for heating and cooling (Capstone Microturbines
2005).

The use of microturbine generators encompasses a wide variety of applications
that can benefit national, commercial, and residential interests. Emergency power
generation is desperately needed for natural disasters or for when the unexpected power
failure occurs such as the August 2003 power failure in the northeastern part of the
United States. Emergency power is needed to keep the medical equipment of ill persons
operating effectively, protecting our nation’s food supply, and enabling communication
capability. Beyond emergency power generation, quiet, reliable and inexpensive power
generation would be extremely useful for small businesses, farms and construction sites
where it would be helpful to not rely on the power grid for energy needs, rather using the
generator for peak shaving. Infinitely many derivatives of microturbine generators can be
designed to suit almost any person, from turbine generators small enough to power a cell
phone to household power generation to supplying power to the local fast food restaurant.

Microturbines can also operate on methane produced by landfills; reducing
pollution and creating power while the heat from the exhaust gases can be used to operate
small scale chillers for refrigeration and heat exchangers for heating homes and
businesses. The Environmental Protection Agency states that, “Microturbines are an
emerging landfill gas (LFG) energy recovery technology option, especially at smaller
landfills where larger electric generation plants are not generally feasible due to
economic factors and lower amounts of LFG" (EPA 2002). A growing trend in the United

States and around the world is going to be the use and implementation of small scale

power systems that cut down on the reliance on the power grid while improving
portability and decreasing the emissions of pollutants.

Microturbines bring many new options to the energy sector that improve upon
stationary power stations. The DOE defines a microturbine as "small combustion
turbines, approximately the size of a refrigerator, with outputs of 25-500 kW" (DOE
2005). These small turbine-generators have many more advantages than the surface-level
advantages discussed earlier. Microturbines comprise a sector of the energy market
typically labeled as "distributed generation". They reduce the dependence on the power
grid and have the ability to lessen the chance of a regional or state-wide power failure.
They can also be made extremely small, the size of a small household appliance such as a
stove or dishwasher and they have the ability to be produced with only one moving part —
a single shaft that provides power to the compressor and generator and which receives
power input from the turbine. Few moving parts means less maintenance and more
importantly, a lesser chance of having a part fail on the generator, increasing the quality
and reliability. The California Distributed Energy Resource Guide (CDERG) states that
current microturbine generators have maintenance intervals of 5-8 thousand hours
(CDERG 2002). This interval allows for companies and homeowners to avoid worrying
about mechanical failures that so often plague internal combustion (IC) generators that
rely on engines that must constantly be monitored for oil levels, debris buildup in
carburetors and wear on engine parts.

However, with the numerous strengths of current microturbine generators, there
are also plenty of disadvantages that are making potential owners reconsider purchasing

the latest and greatest microturbine. The efficiency of microturbines are sensitive to the

ambient temperature at which they operate (CDERG 2002). The higher the ambient
temperature, the more work must be consumed by the compressor to compress the air to
operating conditions. One peak-load test during summer time conditions concluded that a
30 kW microturbine produced only 24 kW and a 75 kW unit produced only 60 kW due to
the increase in the turbine inlet temperature (Davis et al 1559). Many regions that need
distributed generation are located in areas where the environment is hot most of the year
such as California, which is experiencing many energy problems and in desert regions,
where the United States Military is currently involved in wartime operations overseas.

Finally, the current costs to own and operate a microturbine are making
microturbines a costly investment for small companies and businesses. The price to own
a new microturbine can be estimated as being between $700 and $1100 dollars per
kilowatt (CDERG 2002). Therefore, for the local small business, a 30 kW microturbine
can cost over $30,000. Upkeep and maintenance is estimated at $0.005-$0.016 per kWh,
which can be expensive for larger microturbines (CDERG 2002). However, the United
States Government has also passed the Energy Policy Act of 2005 that gives tax credit
incentives to microturbine users and widens the existing power production tax credits
(Blankenship 148). Even though the price for distributed generation is quite high at this
time, many see the need for such systems and are enthusiastic about promoting these new
power options.

There are a handful of companies around the world currently working on
microturbines in the 25-250 kW range. To understand the state of the industry, a brief
overview of some of the companies and their products are discussed. The name

"Capstone" often arises in conversations dealing with microturbine generators. One of

their smaller generators is a 30 kW load-following device that is set up for combined heat
and power (CHP). The device is 26% electrically efficient and boasts one moving part,
namely the compressor-turbine-generator shafl. From the heating and cooling end, the
unit emits 85 kW of thermal energy that can be used to power an absorption chiller or
heat exchanger. One major advantage of this device is that it is a relatively quiet machine,
operating at 65 dB when measured 10 m away (Capstone 2003). Capstone has also
developed a larger 65 kW device that is 29% electrically efficient and outputs 78 kW of
thermal energy for CHP applications. It has a total firel efficiency of 64% (Capstone
2005)

Bowman Power has an 80 kW device that outputs a modulated thermal output of
between 136 and 216 kW of thermal energy. It is rated at 70 dB at 1 meter away
(Bowman 2002). This unit includes a boiler for utilizing the waste heat to produce steam
for CHP applications. It also has the flexibility to operate with a multitude of fuels such
as natural gas, propane, and butane (Bowman 2002). One of the more important parts of
this generator is the power electronics and computer controls that regulate the engine and
condition the signal from the generator for maintaining waveform quality (Bowman
2002). To complete the overview of companies, Ingersoll-Rand has also developed a 70-
kW device that is 29 % electrically efficient and is rated at 78 dB at 1 m and 58 dB at 10
m (Ingersoll-Rand 2006).

Some universities are studying microturbine applications and testing the
reliability of current microturbines. The University of Maryland has developed the
Integrated Energy Systems (IES) test center. Researchers at the University of Maryland

are looking at ways to implement microturbine generators and other integrated energy

systems into small buildings (DOE 2001). This is interesting because microturbine
generators are going to be shifting to smaller and smaller units such as small office
buildings and stores; and it is important to know how these devices operate under the
range of load and environmental conditions that will affect the unit while it is installed.
This will certainly help both manufacturers of the devices and homeowners alike. It will
help the manufacturers because the information given to them will help them to design
more user fiiendly devices while business owners will benefit from the ease of
installation, saving time and money, and eliminating the problems associated with a
particular machine before it is installed and relied upon to produce consistent power.

Manufacturers are working to produce devices that enable the distributed energy
market to push away from large megawatt plants to embrace smaller kilowatt-sized plants
that take advantage of distributed generation. These manufacturers and even the United
States government recognize that large power plants are only a hindrance to energy
consumers in the United States and around the world. There is also a trend to cater to the
needs of small businesses by creating units that are relatively quiet and extremely energy
efficient while operating on fuels that are often not utilized as much as they could be, like
natural gas and propane, and fuels that are typically flared, like methane fi'om landfills.
According to McDonald and Rodgers (835), "The technology to deploy a compact 5 kW
PT (personal turbine) exists today, and commercialization could be achieved within four
years, it really just being a matter of resolve".

It is the objective of this thesis to design a microturbine that will bring distributed
power generation to the average homeowner. It will be proven that current microturbine

technology in the 25 — 200 kW range can be scaled down to benefit an average

homeowner in the United States. There are a few important objectives of this project. It is
a goal to design a system that can compete with current backup generators in price,
keeping the cost around $1500 for 5 kW electrical outpu, that is about $300/ kW. On
average, 5 kW of electrical power would be a good amount of energy to operate the most
important appliances of a small to medium sized home in the event of a power failure. To
maintain that competition, the unit must be small, taking up the space of a small
refiigerator or less. Current piston-engine generators in the 5 kW range take up the space
of a dishwasher and can be as large as a refiigerator. The unit should also be designed to
run quieter than current IC engine generators and obtain a prototype efficiency that will
allow the unit to operate by itself (stand-alone) with no outside help (extra fans or
blowers to keep the compressor and turbine running). Finally, the design should be
extremely simple, allowing for quick prototype production and low manufacturing costs.
The design of a complicated turbo generator defeats the overall goal of bringing
affordable emergency and standby power to homeowners and small business owners.

To meet the objective, it was necessary to examine current gasoline and diesel
generator alternatives. The first step was the comparison of alternative power cycles.
Common alternative cycles to the Otto and Diesel IC cycles are the Brayton and Rankine
cycles for a gas turbine and steam turbine respectively. The Brayton and Rankine cycles
were analyzed to determine which cycle would be best suited for a small turbo generator.
Then the components of the cycle were designed and optimized. These included the
compressor and turbine, combustion chamber and recuperator. Finally, the prototype was

constructed and tested as a first phase of the project.

Design

A significant amount of engineering design work was completed during the
creation of the 5 kW gas turbine-generator prototype. This section will detail the steps
taken in the design process to create a theoretically sound engineering model and a
prototype that closely approximates the engineering model. There were two parts to the
engineering model. The first part commenced with the determination of the most efficient
and simple power cycle. The second part was the design and optimization of the
turbomachines and heat exchangers that contribute to the operation of the turbo
generator.

Determination of the Power Cycle

The determination of the correct power cycle relied on a complex engineering
spreadsheet designed to facilitate the optimization of key power cycles. Accepted
thermodynamic formulas for each cycle analyzed were input into the spreadsheet and
linked together. The outputs of these equations were plotted on temperature versus
entropy diagrams (T-s diagram) for each cycle that was analyzed. Values for the
turbomachine efficiencies, pressure ratio, temperature ratio, and source-fluid
thermodynamic data were input manually and used to compute the thermal efficiency and
work output for all cycles so that they could be compared simultaneously at any operating
point.

Input thermodynamic property data for the cycle models was obtained from
thermodynamic property software, while the thermodynamic properties of the working

fluids at other points on the T-s diagrams were calculated from thermodynamic

10

equations. The input thermodynamic data included the initial temperature, enthalpy,
entropy, specific heat and specific volume for each working fluid used.

It was not feasible to include every thermodynamic power cycle in the
comparison spreadsheet. The spreadsheet was created to obtain a basic idea of the type of
cycle that would produce the best thermal efficiency and work output given a specific
operating point. The power cycles included in the spreadsheet were the Brayton, Rankine
and steam injection cycles. The Brayton cycle is the ideal cycle for gas turbine power
plants and the Rankine cycle is the ideal cycle for steam power plants. The steam _
injection cycle is a cycle that was derived fi'om both the Brayton cycle and Rankine
cycle. The idea behind this power cycle is to inject steam into the combustion chamber,
in small quantities, and mix it with the combustion gases to increase the density of the
mixture and therefore increase power output. The current model of the steam injection
cycle was established during the analysis of the power cycles used in this thesis.

Only the simplest forms of each cycle were modeled because the objective of the
cycle model analysis was only to prove which cycle would work best at a specific
operating point. Therefore, cycle models including regeneration, reheating, and
recuperation were not included. The focus was on determining how the components of
the cycle would react to the operating point and determining the cycle that would produce
the best thermal efficiency. The components of the power cycles are defined as the
pumps, compressors, turbines, heat exchangers, and combustors that work together to add
and take away energy fiom the working fluid.

In addition, the Diesel and Otto cycles were not included in the analysis because

they already comprise the status quo. The piston engines that are based on the Diesel and

11

Otto cycles are expensive to operate due to high fuel costs, loud and costly to maintain
due to the constant changing of oil, oil filters, air filters and cleaning the carburetors or
firel injectors.

The combined cycle is another power cycle that was not analyzed in the cycle
spreadsheet because it was considered too complex for this analysis. According to Cengel
and Boles (544), in reference to the combined cycle, “In general, more than one gas
turbine is needed to supply sufficient heat to the steam”. While there is a definite shift in
the industry toward using combined cycles due to their thermal efficiencies in the range
of 54-56 percent, it would defeat the purpose of this project to design and build a system
that uses multiple turbines, compressors, pumps and heat exchangers (Khodak and
Romakhova 265). It would result in a costly and complicated design and would not fit the
simplistic needs of today's home and business owner.

It was important that simple designs were utilized in the cycle model analysis so
that the focus of the work was not directed toward enhancing cycle models, but
determining the simplest and most effective cycle model that could attain the goals this

thesis set out to achieve.

Brayton Cycle
The simplest cycle modeled on the spreadsheet was the Brayton cycle, the ideal

cycle for gas-turbine engines. A diagram of the Brayton cycle is shown in Figure l. The
Brayton cycle is characterized by isentropic compression of the working fluid (air),
constant-pressure heat addition (combustion of fuel/air mixture), isentropic expansion,
and finally constant-pressure heat rejection (release of exhaust gases to the atmosphere)

(Cengel and Boles 471 ). To adequately model the cycle, the thermodynamic properties of

12

temperature, pressure, enthalpy, entropy, and specific volume were needed at each point
in the cycle.

T (K)
Gas (Brayton) Cycle

 

 

s (kJ/kg'K)

Figure l. T-s diagram of the Brayton cycle
The thermodynamic model begins at point 1 of Figure 1. Thermodynamic

properties such as specific heat and specific heat ratio (isentropic coefficient) of the fluid
were obtained fiom Cengel and Boles page 826 based on the temperature of the ambient
air. These values were held constant throughout the cycle model. The initial values for
enthalpy and entropy were obtained from the property tables listed in standard
thermodynamics texts. The specific volume was determined fiom Equation (1), which is
a modification of the ideal gas law equation of state.

R . T
v=——"1’f (1)

The ideal gas law was used many times when determining the thermodynamic properties
of the Brayton cycle. The treatment of air as an ideal gas arises fi'om the air-standard
assumptions. The air-standard assumptions are that air is the working fluid and it acts like
an ideal gas because it is composed mostly of nitrogen, which remains unchanged
throughout the cycle. The second assumption is that all processes are internally

reversible. The third assumption is that the heat addition process models the combustion.

13

Finally, the fourth assumption is that the exhaust is modeled by heat rejection and the air
returns to its normal state after it exits the system. This is in fact the case because fiesh
air at unchanging temperature and pressure is constantly drawn in to the system and the
exhaust gases never mix with the fresh air. The air standard assumptions are discussed in
detail in Thermodynamics by Cengel and Boles, page 456. The initial temperature and
pressure in the cycle come from standard ISO conditions of 59° F and 1 atmosphere.

The thermodynamic properties at point 1 of Figure 1 have been established and
the next step in the thermodynamic process was to compress the air isentropically with
the compressor. This requires work input into the compressor. The equations that are
listed in the rest of the Brayton cycle analysis can be found in Chapters 6 and 8 of
Thermodynamics by Cengel and Boles. The enthalpy is determined first from the
isentropic relations for an ideal gas assuming constant specific heats. Equation (2) was
used to determine the enthalpy at the end of the compression process. Equation (2) is a
combination of the enthalpy change with the addition of the temperature change given an
isentropic process.

[a
h2 = htable +61), air T1 'PR k ”Ti / ”compressor (2)
At point 2 of Figure 1, the enthalpy is based on the initial enthalpy of the air and the
isentropic relationship between temperature and pressure. The efficiency of the
compressor is also an input to determining the enthalpy at point 2. The pressure ratio is
an input to the spreadsheet and indicates the pressure ratio of the air from ambient to its
compressed state. The pressure at point 2 is determined simply by multiplying the

ambient pressure by the pressure ratio of the compressor. The temperature is calculated

14

from the change in enthalpy, knowing that it is equal to the specific heat of the working
fluid multiplied by the change in temperature. The specific heat is known so it is
straightforward to obtain the temperature of the compressed air.

The entropy at point 2 is calculated from Equation (3) and is based on the
temperature ratio, pressure ratio, and gas constant.

T2 P2
32=s1+c . ln——Rln—— (3)

,alr
1’ T1 P1

The specific volume of the air at point 2 is calculated from the ideal gas law and is
dependent on the temperature and pressure at point 2. Finally, the compressor work must
be calculated because it is an input to the cycle thermal efficiency calculation. The
specific compressor work, the work per unit mass, is just the change in enthalpy fiom
point 1 to point 2.

Moving forward from point 2 to point 3 in Figure 1, this is where the air is heated
to the turbine inlet temperature. In the cycle model, all combustion effects are neglected,
according to the air-standard assumption imposed previously. The combustion process is
treated as reversible with constant pressure heat addition, neglecting the pressure losses
due to friction that occur during the process. This means that the pressure will not change
from point 2 to point 3 and the output temperature, turbine inlet temperature (TIT), is
specified. Enthalpy at point 3 is determined fiom the initial enthalpy at point 2 added to
the specific heat multiplied by the change in temperature, which is specified. Finally, the
entropy and specific volume were determined fiom Equations (1) and (3). Point 3 is the

end of the combustion process and the beginning of the expansion process of the air

through the turbine.

15

Once the air is heated to its design value, it is expanded isentropically through the
turbine to produce work. This is the process that takes place fiom point 3 to point 4 on
Figure l. The final pressure is simply the ambient air pressure because the air is
exhausted to ambient conditions. The enthalpy was determined according to Equation (4),
used in the analysis of the isentropic compression analysis. This time however, the
pressure ratio is the inverse of the pressure ratio used previously and the final enthalpy is
less than at point 3 because some of the thermal energy contained in the air is converted
to turbine work. Entropy and specific volume values are again calculated fi'om the
equations used to determine them for the compression process. The turbine work is
calculated from the true enthalpy, meaning the efficiency of the turbine is taken into
account in the enthalpy calculation just as in the compression process. However, instead
of dividing the second half of Equation (2) by the compressor efficiency, the turbine

efficiency multiplies the second term of the equation to obtain Equation (4).
_ -1)/k
h4 ‘ h3 +cp,air(T3 ’(PRfk " 3)'nturbine (4)

The cycle is closed with the Tds relations (point 4 to 1), however in reality the air
is rejected through the turbine exit and fresh air is brought in through the compressor
(Cengel and Boles 325). This means the cycle is never closed but operates as an open

cycle since the working fluid is constantly regenerated.

16

Simple Brayton Cycle l
Thermal Efficiency vs. Pressure Ratio, all Temperature Ratios }
Turbomachine Efficiencies of 100% 1

 

60 l
50 l
40 ~ *
30 l
20 . J

 

Thermal Efficiency

 

 

 

{ 2 3 4 5 6 7 8 9 10 1
Pressure Ratio ‘

Figure 2. Thermal efficiency plot for the Brayton cycle model
The purpose of the spreadsheet was to determine what kind of cycle efficiencies would be

possible by changing the pressure ratio and temperature ratio of the cycle. The inlet
conditions, meaning the ambient thermodynamic properties of the air, are generally held
constant along with the compressor and turbine efficiencies. Figure 2 is a plot of the
thermal efficiency of the Brayton cycle versus the pressure ratio. Note that this plot is for
all temperature ratios. When the turbine and compressor efficiencies are 100%, the
thermal efficiency is a function of pressure ratio only and not temperature ratio. It should
also be noted that the thermal efficiency increases with increasing pressure ratio. The
trend shown in Figure 2 makes sense, but really should be validated in other ways to
ensure accuracy.

The spreadsheet for the Brayton cycle calculation was verified two different ways.
First, the results are compared to Figure 3, which comes fiom a paper by Mueller and
Frechette titled "Performance Analysis of Brayton and Rankine Cycle Microsystems for
Portable Power Generation" (Mueller and F rechette 1). The figure has been enhanced to

improve clarity of the axis properties and readability.

l7

 

I .___. -___. _ - __ _ ___-_ .____. __- .____. __.. _ ._ .____.___ _._ _._ . __ _._.. _ - .____._ _—

 

 

 

 

 

 

0.6

1.0 . . °°
I Field of Practical
1'] I Application of Gas 1T
0 8 Turbines . 500
3 _ __ I :1
IT
A

 

 

 

0.4"

I ,

I K=1.4. -

o /l r 1 1
6 8

0 2 4W 10

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 3. Thermal efficiency of the ideal Brayton cycle, shown with varying temperature and
pressure ratios (22)

Although the data is displayed differently, assuming the component efficiencies
are 1, the thermal efficiency does not change with temperature ratio and is only
dependent on pressure ratio. Thermal efficiency increases with pressure ratio.

Next the cycle model spreadsheet was compared to a Brayton power cycle
example in Thermooflmamics by Cengel and Boles. The pressure ratio, temperature ratio
and ambient conditions that were outlined by the example were input into the Brayton
cycle model spreadsheet. The example is located on page 476 of Cengel and Boles. Table
2 shows the results of the book example and the spreadsheet example. Notice that the
thermal efficiency values are practically identical. With the validation of the paper by
Mueller and the example by Cengel and Boles, the results of the Brayton cycle

spreadsheet model can be trusted.

18

Table 2. Validation of the Brayton cycle model

 

 

 

 

 

 

I Cengel and Boles Spreadsheet
ISource Air Temperature (K) 300 300
IPressure Ratio 8 8
Frurbine Inlet Temperature (K) 1300 1300
IThermaI Efficiency 44.80% 44.78%
IPercent Error 0.04

 

 

 

 

Rankine Cycle

The Rankine cycle was the next model to be analyzed. Figure 4 is an illustration

of a T-s diagram of the Rankine cycle. As in the description of the last model, the

analysis of the Rankine cycle will be discussed on a point by point basis. A

thermodynamic property program titled "Excel Steam Tables Version 2.2" was used to

determine the thermodynamic properties of the water at different locations around the T-s

diagram. The program was written by Magnus Holrngren and can be obtained at www.x-

eng.com as fi'eeware.

Starting with Point 1 on Figure 4, the water is drawn into the system by a pump.

The source water conditions were held at 59°F and a pressure of 1 atmosphere.

 

 

 

 

 

T(K)
Vapor Cycle
5
2 3 .4
K / 6
. 1 7 * ~\
s(kJ/kg'K)

Figure 4. T-s diagram of the Rankine cycle
Once the thermodynamic properties of the inlet water have been specified, it is

possible to proceed from point to point on the T-s diagram and determine the

19

thermodynamic properties of the water and steam at all points along the Rankine cycle T-
s diagram. The next paragraphs will detail the setup of the Rankine spreadsheet model.
The analysis starts at point 1, where the temperature and pressure of the ambient
water has already been specified. The enthalpy, entropy, and specific volume for the
water at this point can all be calculated using the property software. The values at point 2
are calculated a little differently. The enthalpy is determined by adding the pump work to

the enthalpy at point 1. The equation for the pump work is shown in Equation (5).

Wpump = (vpump inlet * (P2 — P1))/‘Ipump (5)
This equation uses the specific volume of the water, the pressure difference across the
pump, and the efliciency of the pump to calculate the specific work. Note that the value
of the pump work will remain essentially the same over a wide range of temperatures due
to the specific volume of water not deviating much based on temperature. Now the
temperature of the water after being compressed by the pump is determined fi'om the
pressure and enthalpy values using the property software. Once temperature and pressure
are determined, the entropy and specific volume can also be calculated, also using the the
property software.

Sub-cooled water enters the boiler at point 2. Point 3 is represents the water
reaching its saturation temperature at the point of the vapor dome. To determine the
thermodynamic properties of the water at point 3, the temperature is the saturation
temperature at the given pressure and since pressure is given, enthalpy, entropy, and
specific volume can all be calculated at that point.

Water at point 3 now begins to undergo a phase change from liquid to gas. Its

path along the T-s diagram puts its location under the vapor dome, where there is a

20

mixture of water and water vapor. At point 4, all of the energy needed to change the
water into steam has been given by the boiler and the steam sits at its saturation
temperature given the pressure. The temperature and pressure of the steam are exactly the
same as the water at point 3.

The cycle model begins to get interesting again at point 4, where the steam can be
modeled to enter a superheater or enter the turbine directly. For most Rankine cycle
analyses, the temperature of the steam must be raised (superheated) so that more work
can be extracted fiom the turbine due to the increase in thermal energy of the steam. If
the steam goes through a superheater, then the superheater exit temperature is specified to
be the temperature at point 5 and the pressure remains the same because the steam
undergoes constant pressure heat addition. Once the temperature and pressure are known,
the enthalpy, entropy and specific volume can all be calculated from the property
software. The change in enthalpy from point 4 to point 5 indicated how much energy
needed to be input into the superheater to raise the steam to the turbine inlet temperature.
However, if no superheater is used, then the temperature and pressure of the steam are
already known fiom saturation conditions and the enthalpy, entropy and specific volume
can be determined using the property software. Note that most of the energy input
through the boiler goes to the latent heat of vaporization of the water.

Point 5 is the turbine inlet and the thermodynamic properties of the steam at this
point are calculated from knowing the pressure and temperature at point 5 and then using
the property software to determine the enthalpy, entropy and specific volume. The steam
now expands through the turbine to produce work for the turbo generator. As the steam

travels through the turbine fiom points 5-6, it undergoes isentropic expansion. The

21

process of calculating the thermodynamic properties of the vapor begins with
determining the entropy of point 6. Isentropic expansion is not expected because the
turbine is not 100% efficient and the process in real use is certainly not isentropic.
However, the isentropic entropy value is known from point 5. Given the temperature and
pressure, the enthalpy value after isentropic expansion can be determined and knong
the turbine efficiency, the actual enthalpy can be determined. All that is needed to
calculate the turbine outlet temperature is the pressure, which is known at point 6, and the
actual enthalpy, which is now known at point 6. The values of actual entropy and specific
volume are now able to be calculated.

If the turbine output is a saturated mixture, then the quality of the saturated
mixture must be determined. The temperature and pressure are known and by using the
value for quality, the properties for enthalpy, entropy and specific volume can all be
determined. The value of the quality is straightforward and is found through the entropy
values. If the entropy value is greater than the value of the entropy based on saturation
conditions, then there is no quality and the steam is a vapor. If the entropy value is less
than the entropy value at saturation conditions, then the quality is given by Equation (6)
where x is the quality of the mixture.

Entropy value - Entropy watersat

_ Entropy vaporsat — Entropy watersat

 

(6)

Finally, the work output of the turbine is determined from the change in enthalpy
from point 5 to point 6. The remainder of the cycle is heat rejection by incorporating
either an open or closed cycle. If the cycle is closed, then the water vapor would be
condensed by rejecting heat to the surroundings and the pump would start the cycle all

over again. An open cycle would consist of rejecting the steam to the environment and

22

drawing in flash water firm a reservoir. The thermal efficiency of the model is
determined fiom the turbine work output divided by the amount of heat input into the
system through the boiler. The pump work, although taken into account in the work
calculation, can effectively be neglected because it is much smaller than the turbine work.

The accuracy of the Rankine cycle model was also verified similar to the Brayton
cycle. A Rankine cycle model example on page 520 of Thermoajmamics by Cengel and
Boles was input into the cycle model and the results fi'om the model were compared to
the results in the example. Table 3 shows the results of the validation. There is a 5%
difference between the results of the spreadsheet and the results of the book example,
with the spreadsheet overestirnating the cycle efficiency by about 2%. The overall error is
acceptable and shows that the spreadsheet can produce accurate Rankine cycle model
efficiency approximations. Figure 5 is a plot of the thermal efficiency of the Rankine
cycle versus pressure ratio. The analysis is completed for a small range of temperature

ratios to show the trends.

Table 3. Validation of the Rankine model

Air T
Pressure Ratio 1766
urbine Inlet T

36% 38%

Error

 

The plot shows that the thermal efficiency of the Rankine cycle increases with
increasing temperature ratio and pressure ratio for turbine and compressor efficiencies of
1. This result is expected and is consistent with the general understanding of the Rankine

cycle model.

23

Rafi, AW? 7 #r . ’_ _.___ _._—_.— ,7, 7A A”

Thermal Efficiency vs. Pressure Ratio. Varying TR - Ranvk—ine Cycle L
rTurbine-and Pump Efficiencies of 1

 

 

 

5.00 Ti.— ——‘ ’“T—_ ~""—YT_“— —_T --'T_T—— -_' T—' ' ‘n‘i!’ ' ——'”“_T———

. 2 4 5 6 7 8 9 10
L 3 Pressure Ratio

 

 

 

Figure 5. Thermal efficiency plot of the Rankine cycle model

Steam Injection Cycle
The last power cycle to be examined is the steam injection cycle, named

according to the way in which the cycle operates. The motivation for analyzing this cycle
is to increase the power density of the working fluid by adding steam to the system
through recuperation of the exhaust gas energy and an additional water mass stream. The
base cycle is a Brayton cycle where the exhaust gas is used to heat a small amount of
water into steam. The steam is then fed back into the system via the combustion chamber
thus adding mass into the system before the turbine. The inlet water is heated to steam by
a copper coil recuperator wrapped around the exhaust pipe (turbine outlet). In theory,
there are no gains that appear without some sort of loss in the system. When the steam is
added to the hot combustion gases, the mixture will cool below the specified turbine inlet
temperature. Therefore the hot air coming fi'om the Brayton cycle must be heated to an
even higher temperature so that when the steam is added, the mixture will cool to the
turbine inlet temperature. Figure 6 shows the copper coil heat exchanger attached to the

turbine outlet.

24

l
6

’a

x mm ‘ H” ,1... .
\\-r‘.\‘ in “\nm \V 1‘11“
\ ‘ / ”

 

Figure 6. Picture of steam injector/ recuperator
The most important aspect of the steam injection cycle is finding the balance of

steam to air such that an optimum efficiency arises. If too much steam is added to the hot
gases, the amount of additional energy needed to raise the temperature of the hot air will
be too high because there is a limit to the combustion temperature of fuel in air. Also, if
the steam is not superheated, its thermodynamic state may be too close to a saturated
mixture and if any condensation occurs, these water droplets may enter the turbine
directly and cause major problems with erosion of turbine blades since the gas—steam
mixture does go through the turbine. The analysis to follow will detail the steps involved
in approximating the steam temperature out of the copper-coil heat exchanger.
Determining the steam temperature and how long it takes for the water to be
heated into steam is a complicated process that involves many simplifying assumptions.
The first objective was to calculate the outside surface temperature of the steel exhaust
pipe to determine the heat transfer rate possible to the water. A simple thermal resistive
circuit was created to approximate the steady-state conditions that would be present
around the exhaust pipe without the recuperator on it. The model involved the
combustion gases flowing through the exhaust pipe and natural convection and radiation

on the outside of the exhaust pipe with low thermal resistance steel, the steel exhaust

25

pipe, inserted between the two gases. The simple thermal resistance circuit is shown in

Figure 7.

Rc1=1lhc1

Rs=tslk

   
   

300 K 1023 K

Rcz=1lh02
R,=1/hr

Figure 7. Thermal resistance circuit of conditions surrounding the exhaust pipe
RC1 and Rr represent the thermal resistances due to natural convection and radiation

respectively. Rs and R32 represent the thermal resistance of the steel pipe and forced
convection of the hot exhaust gases moving through the exhaust pipe respectively. The
end temperatures are approximate temperatures of the ambient air and exhaust gases,
calculated from the Brayton cycle spreadsheet. Table 4 shows the values used to
determine the forced convection heat transfer coefficient inside the exhaust pipe. These
values come fi'om design values of the turbo generator to be discussed in detail in later
sections, but their use here is important for understanding the design process of the steam
injection model. The geometry of the exhaust pipe is needed because the diameter of the
pipe is used for the Reynolds number calculation and so is the velocity, which can be

determined from the mass flow rate, density and area of the pipe.

26

Table 4. of exhaust

     

Exhaust T CSA
m
Outside Diameter m
Inside Diameter m
m
Area

Diameter

of Air 3 0.328
Kinematic of Air m"2/s 0.000174
Hot Gas T 1023

Hot Gas T 1023

Hot Gas 1 14.3

Re 33360

Friction Factor 0.024

Nu Gas 44.60
Notice that the flow can be considered turbulent because the Reynolds number is larger
than 104. Once the Reynolds number was calculated, Equations (7) and (8) were used to
determine the convective heat transfer coefficient for the flow through the exhaust pipe.

The equations were taken from page 441 of Heat Transfer by Yunus Cengel.

 

fh =(o.791nReh -1.64)‘2 (7)
hh = (fh/8)RehPrhkh ( W J (8)
[1+12.7(fh/8)0'5(Prh2/3 —1)]Dh,h m2 -K

Equation (7) is used to determine the fiiction factor in the pipe and Equation (8) is the
Nusselt number equation for the turbulent pipe flow multiplied by the thermal
conductivity of the air and divided by the diameter of the pipe to obtain the convective
heat transfer coefficient. Both equations are valid for Reynolds numbers greater than 10".
The thermal resistance of the fluid flow is defined as the inverse of the convective heat

transfer coefficient.

27

The next step was to calculate the thermal resistance of the steel exhaust pipe. The
pipe consists of relatively thin steel with large conductivity value, so there is only a very
small temperature gradient expected between the exhaust gas temperature and the
temperature of the outside of the pipe. The thermal resistance of the pipe is defined as
L/k, where L is the thickness of the steel and k is the thermal conductivity of steel. Both
values are known from the design.

Third, the natural convection and radiation resistances are calculated. Radiation is
important and can not be neglected due to the expected high temperature of the exhaust
pipe compared to the temperature of the surroundings. Natural convection is present due
to the high temperature of the exhaust pipe heating the air around it. It is assumed that
tests on any prototype built will be conducted in a facility where there will not be air
blown over the exhaust pipe and therefore forced convection will be neglected in this
analysis. Equation (9) is used to determine the radiation resistance value and it is simply
the inverse of the radiation heat transfer coefficient.

Rr " 1 (9)

‘ 3 3
was“ 48,,” )

 

The emissivity of the exhaust pipe was taken to be .81 for oxidized carbon steel (Cengel
878)

The analysis was more difficult for the determination of the natural convection
heat transfer coefficient. All of the equations used in the analysis in this section can be
found in Chapter 9 of Heat Transfer by Yunus Cengel. The natural convection model for
a vertical plate was used to determine the convection coefficient. This model is

acceptable because D, the diameter of the exhaust pipe, conforms to D 2 3%; and this
Gr

28

condition has to be satisfied to use the vertical plate approximation. The Nusselt number

correlation for a vertical plate is

Nu = .59RaL“4 (10)

To determine the Nusselt number equation, the Rayleigh number and consequently the
Grashof numbers needed to be calculated. These correlations appear in Equations (11)
and (12) below.

Ra=GrL~Pr (11)

(T-T)L3
GrL=g S 3°flc (12)
v

 

The equation for the Grashof number is dependent on the acceleration of gravity,
temperature difference between the surface and ambient, the height of the pipe and the
kinematic viscosity of the air. Beta is the inverse of the ambient air temperature and is
called the coefficient of volume expansion. Table 5 and Table 6 show the values needed

to calculate the convection and radiation thermal resistances.

Table 5. Natural convection heat transfer data

Number 2.

Number 1.
1 0.001
m"2/s A 6.42E
Number

 

Table 6. Radiation heat transfer data

of oxidized steel 0.81

of 300

of Steel 985
5.67E-08

from surface 42861
of 0.50

 

29

Now that all the thermal resistive values are known, the temperature of the outside
surface of the exhaust pipe can be determined. Solving the thermal resistance model is
analogous to solving a simple voltage-resistance circuit with the voltage represented by
the temperature difference, the current represented by the heat flux and the resistance
represented by the thermal resistances. Table 7 lists all of the thermal resistances
illustrated in Figure 7. Knowing the heat lost to the surroundings, it is possible to
determine how much of this energy can be used to heat water into steam for the steam
injection cycle. Approximately 2 kW of energy can be used to convert the water in the
copper coil to steam.

Table 7. Thermal resistance values

,,,(K*m2NV) 0.02
Rm..(K*m2/w) 0.0001
Rm..e(K*m NV) 0.27

(K‘mzNV) 004

from 2174
to 185

 

Water enters the system from a reservoir and a water flow controller is used to
control the mass flow rate and pressure. The heat exchanger material of choice is copper
tubing because it has excellent thermal conductivity properties and is inexpensive. The
design was such that the tubing would be wrapped around the outside of the exhaust pipe
and carries the water, pressurized and mass flow regulated, from the reservoir. The heat
transfer fiem the exhaust pipe to the copper tubing would come primarily from radiation
because of contact resistance affecting the conduction heat transfer. The copper tube,

designed to wrap tightly around the exhaust pipe, will never be in perfect contact. While

30

there will be some heat transfer by conduction, the majority of the heat transfer should

come from radiation.

 

 

 

 

 

 

 

 

H20
Cu Cu
Cu
L. L. L.
e Ire—p

Figure 8. Copper pipe heat transfer model
Now that the temperature of the outside of the exhaust pipe has calculated, along

with the heat transfer fi'om the pipe, it is necessary to model the heat transfer from the
outside of the exhaust pipe to the water coming into the system. The heat transfer model
for energy transfer through the copper tube to the water is shown in Figure 8. The wall
thickness of the copper pipe is illustrated by L1 and the inside diameter of the pipe is
illustrated by L2. The model is designed so that the maximum heat flux to the water will
be calculated. The maximum heat flux occurs when the water just enters the copper pipe
and the temperature difference between the water and the copper pipe is largest at this
point, which means the heat flux at this point is at its largest value. Realistically, the
water will heat up as it travels through the copper coil and the exhaust gases will cool,
lowering the rate of heat transfer. Therefore, the model works by calculating the
maximum rate of heat transfer and then determining how long the water will be in the

tubes and how much energy will be needed to heat the water into steam. If, at the

31

maximum rate, the water is heated into steam with ample amount of time left before it
exits the pipe, calculated from mass flow rate calculations, then it is acceptable to use the
model to determine if the water will be turned into steam by the mass recuperator. Table
8 lists the numeric values used in Figure 8. The thermal resistance network model is

shown in Figure 9.

Table 8. tube values

    

The temperature on the right hand side is the approximation to the outside
temperature of the exhaust pipe, calculated earlier, while the temperature on the left is
taken to be the ambient air temperature. The temperature of 300 K at the top of the figure
represents the constant temperature heat sink provided by the water entering the heat
exchanger, the initial condition. As discussed previously, the temperature of the water
will rise as more thermal energy is transferred to the water as it travels through the copper
coil surrounding the exhaust pipe. Rr is the thermal resistance due to radiation fi'om the
outside of the copper due to the surroundings, Rc is the resistance due to natural
convection and the Rcu's are the thermal resistances within the copper pipe itself. Finally,

Rw is the thermal resistance of the water.

32

300 K

300 K 985 K

 

Rc=1lhc Rcu=L2lk

Figure 9. Thermal resistance model used to determine heat transfer rate to water from exhaust pipe
Because L1 is very small, about two millimeters, the temperature at the intersection of Rw

and Rcu can be assumed to be the same temperature as the outside of the pipe. Knowing
the thermal resistance of the water, due to forced convection, it is possible to calculate the
amount of energy that the water obtains up fiem the combustion gases. The convection
coefficient is calculated fi'om laminar flow through tubes based on the velocity of the
water through the copper tubing, which is very small due to the low water mass flow rate.
The Nusselt number correlation is:

Nu =4.36=P§— (13)

The value for the convection coefficient can simply be calculated fi'orn here. The value
for the Reynolds number for this case was 2245, which is contained in the laminar-flow
region for fluid flow through pipes.

The maximum heat flux to the water and the time that it takes the water to turn
into steam at this rate can both be calculated. The amount of mass flow can be controlled
by making sure that the amount of water input does not exceed the amount of water the
recuperator can turn into steam. The amount of time that it takes the water to be

converted into steam is about 1.6 seconds. Based on the mass flow rate of the water

33

through the copper coil, if water was flowing through the coil with no heat transfer to it,
it would take about 90 seconds to flow through the coil because of the length and cross
sectional area of the coil. Therefore, since there is heat transfer, and the water will be
converted to steam in 1.6 seconds, more water could theoretically be added to the system.
However, more water would increase the amount of mass that needed to be heated up to
1200 K, the turbine inlet temperature. The optimum rate of water is about 1 gram per
second, so that a gain in thermal efficiency is observed in the model..

The temperature of the steam entering the combustion chamber is the saturation
temperature of the water and the enthalpy value is its corresponding enthalpy value fiem
the steam tables based on the pressure inside the combustion chamber. The temperature
of the steam is the saturation temperature because once the water is converted into steam
in the copper coil, it expands rapidly and only stays in the copper coil for a tenth of a
second. The steam does obtain more thermal energy as it expands through the coil, but it
is not enough to significantly raise its temperature from the saturation temperature. The
value of the temperature and enthalpy of the steam, along with the mass flow rate of
water are inputs into the Brayton cycle. The following analysis will explain how the
model considers the steam mixing with hot air.

The basic idea behind the steam injection cycle is that some of the thermal energy
exhausted fi'om the turbine is recuperated by heating up a copper coil containing water.
The water is heated into steam and enters the heat exchanger at the saturation temperature
and pressure according to the temperature and pressure conditions in the Brayton cycle.
The combustion gas must be heated slightly higher than the anticipated turbine inlet

temperature so that the steam-gas mixture will cool to the turbine inlet temperature

34

(raising the temperature of the steam and lowering the temperature of the hot exhaust
gases). Figure 10 is the T-S diagram of the steam injection cycle. Air is drawn into the
system at source temperature, pressure and enthalpy. The entropy value of the cycle is
measured in total entropy because when the two gases mix, the entropy increases, as

expected.

T (K) 33 3b

 

 

s (kJ/K)

Figure 10. T-S diagram of the steam injection cycle
However, the specific entropy actually decreases because the mass fraction of air is

much higher than the mass fraction of water in the system. Since water has a much higher
specific entropy than air, this creates a distorted diagram and is very hard to read if
temperature versus specific entropy is plotted. Using total entropy gives the reader insight
into what is actually happening in the cycle. The value of entropy at point 1 is set to zero,
using the value of zero as the reference entropy. Point 2 specifies the thermodynamic
property conditions for the air after the compressor outlet. The temperature, enthalpy,
entropy and specific volume are all calculated according to the thermodynamic equations
used in the Brayton cycle calculations.

The interesting modeling begins to take place between points 2 and 3a. The
constant-pressure combustion process occurs between these two points; but because of

the steam being added at point 3a, the temperature of the combustion products must be

35

higher than the anticipated turbine inlet temperature. The temperature of the combustion
products is determined according to Equation (14) (Cengel and Boles 643).

T _ (T1 'TRkhsteam Cp,steam + tilair Cp,air }' Ii‘stcam Cp,steam TI,steam
3a,air _ -
mair Cp,air

(14)

 

The equation describes the energy balance of the two gases. If two gases at different
temperatures were suddenly mixed, this equation describes the end state of the
temperature of the gas mixture. The temperature that the air must be heated to is
calculated so that the energy input to the combustion chamber can be determined. The
energy input corresponds to putting more fuel into the system. One of the great
simplifications behind this analysis is that steam, at the input temperature and pressure,
can be treated as an ideal gas (Cengel and Boles 90). The temperature and pressure at the
operating point of the system are low enough that water vapor can be treated as an ideal
gas. The operating point will be discussed in the next section. After mixing, the pressure
of the two gases will remain the same and the enthalpy and entropy of the mixture are
obtained by adding the mass fiaction of those respective properties of each gas together
before they were mixed together. The specific volume is determined fiom the ideal gas
law equation with the gas constant being the gas constant of the mixture. The mixture gas
constant is calculated by the universal gas constant divided by the molar mass of the
mixture (Cengel and Boles 634).

To finish the cycle, the mixture is expanded through the turbine to produce work.
All of the thermodynamic properties fi'orn point 3b to point 4 are calculated according to
the ideal gas equations that were used in the Brayton cycle analysis, but this time with the

mixture.

36

 

l T-S Dhgram for Steam Injection Cycle

1

l

1400 l
1200 a l
l

l

l

l

 

a 1000 -
5 800 -
8. 600 »
g- 400 4
,3 200 ~

 

 

 

 

O I 7* T I I

l
l
: 0.000 0.020 0.040 0.060 0.080 0.100 0.120 1
1 Total Entropy (kl/K) l
l l

 

Figure 11. T-S diagram of the steam injection spreadsheet model
For a simple validation of the steam injection cycle, when the water mass flow

rate was set to 0, using the same temperature and pressure ratios as in the Brayton cycle
analysis resulted in the exact same cycle efficiency produced by the Brayton cycle
analysis. Figure 11 shows the cycle model diagram of the steam injection cycle with

component efficiencies of 100%.

Cycle Constraints
The goals of this project must be reiterated before making a decision concerning

the cycle model that is the best fit for the project. It was the objective of this thesis to
design a turbine generator that can compete with gasoline and diesel generators in price,
noise and maintenance intervals. For this reason, manufacturing costs must be kept low,
designs that enhance maintenance procedures must be implemented, and fuels that
produce low emissions must be considered. In addition, a design power output of 5 kW is
desired. To keep the costs down, simple turbomachines must be utilized. The cost of
turbomachinery certainly increases with larger pressure and temperature ratios, which

require larger mass flow rates and larger turbomachinery, however, cycle efficiency

37

increases as well. Therefore, a balance must be determined between cycle efficiency and
cost.

It would be advantageous to utilize turbomachinery designs that operate under
low pressure ratios. The effects toward this project are two-fold. Low pressure ratios
increase the simplicity of design, leading to lower costs and increase the safety of the
design. The lower the pressure ratio, the lower the stress the machine will be under; an
important idea to think about if the machine might someday operate in someone's home.

As research for this project was being conducted, the idea arose to investigate the
use of an automotive turbocharger as a compressor-turbine pair. The idea is not original
as many experts and amateurs alike have implemented such a design for larger gas
turbines. The use of a turbocharger eliminates manufacturing of small and complex
turbomachinery, high-speed bearings are already included in the setup, and it is a proven
technology used at low pressure ratios and high temperature ratios in automotive
applications. Another reason for using turbochargers is that they come in many sizes and
can be matched to the particular power application.

Many temperature constraints are eliminated with the use of a turbocharger. It is
well known that the exhaust gas temperature of an automotive engine approaches 1800° F
under extreme conditions. This is the approximate upper limit of the exhaust gas
temperature from an automotive engine operating under harsh conditions (Motion Trends
2006). In fact, Garrett, a turbocharger manufacturer, claims that they test their
turbochargers by heating them up until they are red-hot and cycling between cool and hot
environmental conditions every 10 minutes over the period of 200 hours (Garrett GT

Catalog 37 [Ref 15]). The major temperature constraint in the project will therefore be in

38

the use of the materials in any heat exchanger or recuperator. Copper and aluminum are
obvious choices for these tasks because of their high thermal conductivity values, but
their melting temperatures are much lower than that of steel.

Based on the temperature and pressure constraints and the possibility of using a
simple automotive turbocharger, which cycle is the best to use for this application? This
question can ultimately be addressed by answering the following questions. What cycle
will be the easiest to manufacture? Which cycle will be the safest? Which cycle leads to
the least design work and finally which cycle will lead to the least expensive design?

Most of the design work in a project like this goes into the design of the
components and resolving manufacturing issues. It is obvious that the best design is the
simplest design that works. From these issues alone it can be concluded that the use of
an automotive turbocharger as the compressor/ turbine pair would be the best choice
when considering the time and energy that can go into designing a compressor/ turbine
pair fi'om scratch. Automotive turbochargers have been proven in industry and can
operate at temperatures and pressures that allow work to be produced. The compression
range of most turbochargers is in the 1.5 to 4 pressure ratio range. This means that a
typical turbocharger will pressurize the ambient air entering an engine by a factor of 1.5
to 4. Even though the pressure ratio is fairly small compared to modern gas turbine
engines, any kind of boost fiom the compressor will lead to a feasible cycle, however the
efficiency of the cycle will be lower with lower pressure ratios.

The price range of turbochargers makes this design even more attractive, because
a turbine/ compressor pair can be purchased for under $1000 if they are purchased

separate fiom a kit. There is only one moving part in a turbocharger; the shaft on which

39

the compressor and turbine are mounted. The only design work involved is in matching
the combustion chamber and recuperator to the amount of air flow expected through the
system.

Last, there is no substitute for safety and it is justifiable to trust the quality of a
commercially-available turbocharger. These devices operate under harsh conditions and
are designed to do so for many hours. Designing the system to operate within the design
operating conditions of the turbocharger enhances the confidence in the safety and quality
of the design.

The determination of using a turbocharger for the compressor/ turbine pair seems
to eliminate the Rankine cycle as a possible cycle alternative since the turbocharger
operates on a Brayton cycle. This is where the cycle model spreadsheet is most useful,
however. It needs to be proven that the Brayton cycle will outperform or at least match
the cycle efficiency of Rankine cycle at lower temperatures and pressures. If the Rankine
cycle model proves that it would be much more efficient than the Brayton cycle at lower
pressures and temperatures, then the decision to use an automotive turbocharger could be

called into question.

40

To set up the model, the constraints on the cycles were first chosen. The
approximate maximum turbine pressure ratio for an automotive turbocharger is 4. To stay
within our design constraints, the cycle models must be examined at pressure ratios less
than 4. To examine the trends, the cycles were modeled with pressure ratios up to 10. The
temperature constraint is a maximum turbine inlet temperature of 1800° F (1255 K). In
addition to this being the upper limit of the turbochargers, it is also well past the melting
point of copper and aluminum and approaching the melting point of steel, 2445° F.

The maximum temperature ratio for the Brayton cycle is 4.5, which is the largest
temperature ratio that can be used based on our temperature constraints. A temperature
ratio of 4.5 leads to a turbine inlet temperature of 1296 K.

Now that the pressure and temperature constraints have been established, and the
desired power output of 5 kW is known, the next step is to choose a turbocharger that will
match these conditions.

It is beneficial to understand exactly what a turbocharger does. A turbocharger
compresses the air entering the engine so that its density increases. More air in the engine
during a typical engine cycle results in more power output. The exhaust from the engine
spins the turbocharger turbine to produce enough work to keep the compressor supplying
air to the engine.

The first step in the turbocharger matching process was to determine the air flow
rate through the system that would produce a work output close to 5 kW. The air flow
rate needed came from the cycle model spreadsheet. The procedure was to look through
the Garrett turbocharger catalog and input the turbocharger data into the cycle model

spreadsheet and determine the air mass flow rate needed. The Excel tool Goal Seek was

41

used to determine the air flow rate that would produce 5 kW of power output. The Garrett
turbocharger catalog was used because they manufacture a wide range of turbochargers
and provides many numerical charts and graphs to help people determine the
turbocharger that will work best for their automotive application. The data that was input
into the spreadsheet was the compressor and turbine efficiency data, and the pressure
ratio corresponding to the maximum efficiency of the turbocharger compressor and
turbine. The turbine inlet temperature was held constant at 1200 K, matching the
maximum temperature that the turbocharger can handle safely. Most of the turbocharger
compressor efficiencies were in the 70%-80% range while the turbine efficiencies were in
the 60% to 70% range (Garrett Product Catalog 4 [Ref.16]). This means that since the
efficiencies stay relatively constant, the only parameter that needed to be varied was the
maximum pressure ratio. It was determined from the cycle model that the approximate
amount of air needed to produce 5 kW of power at the design turbocharger efficiencies
was about 9.5 lbs of air per minute (.071 kg/s).

After examining the catalog, the turbocharger that best fit the constraints of this
project was the Garrett GT1241 turbocharger. It has maximum compressor efficiency at a
pressure ratio of about 2.5 and the air mass flow rate at this point is approximately 9.5
lbs/min, exactly the mass flow rate that is needed under the design compressor and
turbine efficiencies. Most turbochargers come in a kit and can range fi'om $500 to well
over $2000 dollars. It was important to find turbochargers that could be sold separately
from the kit to cut down on the price since it is an objective of this thesis to keep the cost
of the entire prototype under $1500. The Garrett GT 1241 turbocharger used in this

project was obtained for $350, separate from the kit. The turbocharger included a

42

compressor, turbine, oil and water cooling connections and bolts used to connect to the
engine block.

Thousands of dollars were saved by obtaining a standard mass-produced
turbocharger rather than designing and trying to build a turbine and compressor pair in
the turbomachinery laboratory. The compressor and turbine maps from the Garrett
Turbocharger catalog are placed in Appendix B due to their low resolution (Garrett
Product Catalog 4 [Ref. 16]). Notice on the compressor map that at this operating point,
the speed of the turbocharger shaft is about 215,000 RPM. However, the size of the
compressor is only 41 mm in diameter, so considering the size of the turbomachines,
those kinds of speeds are more realistic. The only major problem with this speed is the
fact that it will be impossible to connect a standard generator to the shaft. Electric motors
operate at about 3600 RPM for a reason: the fiequency of the output electrical signal is
standard to most electrical appliances. Operating such a motor at such high speeds will
require advanced electronic signal modification. The turbine map has only one line and
represents the operation of the turbine at maximum efficiency. Figure 12 shows a picture

ofthe Garrett GT1241.

43

 

Figure 12. Garrett GT1241 turbocharger used in the prototype 5 kW gas turbine
One of the most important issues concerning using a turbocharger to power a

generator is that a turbocharger is designed so that the work extracted fi'orn the turbine
matches the work input by the compressor. In this way no excess power is produced by
the turbine. Matching of the turbine and compressor occurs because the pressure ratio
across the turbine is actually less than the compressor pressure ratio because the turbine
would extract more energy than is needed if the pressure ratios matched. In this
application, however, that extra work is desired for producing electrical energy to the
generator. Therefore, while some of the exhaust gas is waste-gated in normal automotive
applications, all of the mass flow will expand through the turbine in this project so that
the turbine can extract more work for the generator.

Since the turbocharger is matched, the issue of extracting more work must be
addressed. A temperature ratio of 4.2 and pressure ratio of 2.5 will be the thermodynamic
constraints set on the project so that the turbocharger will operate in its design range. The

temperature ratio was lowered to 4.2 instead of 4.5 because it was believed that operating

the turbocharger at the maximum temperature ratio would have adverse effects in the
long run. The efficiency of the compressor is 78% and the efficiency of the turbine is
65% (Garrett Product Catalog 4 [Ref 16]). Oil and water lubrication will be provided to
the turbocharger just as in a regular automotive engine. The oil and water cooling will
form a heat barrier between the compressor and turbine since the heat must travel by
conduction from the turbine to the compressor.

The specific work needed to operate the compressor and which is extracted fiom
the turbine must be calculated. Equations (15) and (16) are used in calculating the

compressor specific work and turbine specific work, respectively.

~ —1 /k

ecompressor =°pTc1(7‘(k ) “1)hlc (15)
~ —l /k

ewe... “paler“ ’ -1>*nc 06>

The specific work is calculated based on the specific heats, which are kept constant
throughout the analysis, pressure ratio, initial temperature of the gas, isentropic
coefficient and efficiency of the turbomachine. The values of the specific work calculated
from Equations (15) and (16) above are shown in Table 9. The total work values are also
computed and listed in Table 9. The total work values are calculated by determining the
product of the mass flow rate and the specific work values. Finally, subtracting the
compressor work fiom the turbine work determines the amount of work that can be used
to power the generator. This value is 5.2 kW and is exactly what is needed to power this 5

kW turbine generator.

45

Table 9. List of and total work values from turbocharger

    

 

180:6 Turbine Work
8.3 Work

13.5 urbine Work
Out

The turbocharger is matched for a normal operating gas temperature of around
1088 K (1088° F), compressor pressure ratio of 2.5, and turbine pressure ratio of 1.81 at
the listed turbine and compressor efficiencies. To produce 5 kW, the normal operating
temperature through the turbine was increased to 1200 K (1700° F) with the compressor
and turbine pressure ratios both equaling 2.5. The isentropic coefficients were held
constant at 1.4 during the analysis.

Now that the pressure ratio, temperature ratio, air mass flow ratio and design
efficiencies are known, it is possible to further analyze the Brayton, Rankine and Steam
Injection cycles to verify that the Brayton cycle still outperforms the other two cycles.
Figure 13 and Figure 14 show a comparison of the thermal efficiency of the Brayton

cycle and Rankine cycle versus pressure ratio at design efficiencies.

 

E Thennal Efficiency vs. Pressure Ratio, Varying TR - Rankine Cycle
*Design Efficiencies for Turbine and Pump

 

+TR=3.5|
,—I—TR=4
i+TR=4.5J

[Le—$3 _‘l

 

 

 

 

Thermal Efficiency

 

 

 

Pressure Ratio

 

 

Figure 13. Thermal efficiency of the Rankine cycle with design component efficiencies

46

 

Thermal Efficiency vs. Pressure Rafio, Varying TR - Brayton Cycle

 

 

 

 

 

 

1

*Design Efficiencies for Turbine and Compressor l

l

>. 14 7 l

2% ‘2 r355”) l
-— 10 "

ris’ 8 TR = 3.5 l

E 6 TR = 4 l l

m = j

g 4 TR 4:51 l l

E 2 1

0 l

1 Pressure Ratio

L__ __ _ .r. __ __ ._, i __ a _-_ ___. ____.. _._,fi..- __ __ __ ________ , __k (E

 

Figure 14. Thermal efficiency plot for the Brayton cycle at design efficiencies
The Brayton cycle only outperforms the Rankine cycle for pressure ratios less than 6

when design efficiencies are taken into account. This occurs because the pump work in
the Rankine cycle is negligible, allowing the thermal efficiency to increase with
increasing temperature and pressure ratios. In the Brayton cycle, the compressor work
increases dramatically with the increase in pressure ratio. What is physically happening is
that the compressor requires more work than the turbine can produce at certain pressure
and temperature ratios and the thermal efficiency becomes zero. The point at which this
occurs increases with increasing temperature ratios, so that for higher pressure ratios to
be realized, the temperature ratio must also be higher. This case is also heavily dependent
on the efficiencies of the turbomachines, which are quite low. Therefore, since the
Brayton cycle has higher thermal efficiencies at the operating point of a temperature ratio
of 4.2 and pressure ratio of 2.5, it can be concluded that the Brayton cycle should be used
as the simplest, most efficient solution to a cycle model for the 5 kW gas turbine
generator project. The thermal efficiency of the Brayton cycle at the operating point is
8.63%, determined from the cycle model spreadsheet with all of the input data entered

into the system. The small value of the thermal efficiency sources directly to the low

47

compressor and turbine efficiencies which degrade any possible chance of obtaining a
decent efficiency out of the system. There is only one way to improve this problem, while
holding the compressor and turbine efficiencies constant, and that is through the use of a
recuperator to enhance the thermal efficiency to a value more consistent with small gas
turbines manufactured today.

Even though the steam injection cycle is difficult to compare directly to the
Brayton and Rankine cycles, its thermal efficiency must be evaluated at the operating
point to determine if it would be a feasible option. The spreadsheet analysis concluded
that the steam injection cycle shows an increase of efficiency by only a few tenths of a
percent. This is due to the small amount of water that is allowed to be injected to the
system, on the order of 1 gram per second. Any larger amount of water might not be
converted into steam and would cause problems with water droplets forming and
impinging on the turbine blades. Due to the small increase in efficiency and major
increase in complexity of the steam injection cycle, there is no reason to choose it as the
cycle of choice for this project. The next step in the 5 kW gas turbine design is to design
a combustion chamber that can increase the air temperature coming fi'om the compressor,

to the turbine inlet temperature of 1200 K.

48

Combustion Chamber

The next challenge comes in the form of designing a combustion chamber that
will provide the thermal energy necessary to raise the air temperature to .1200 K, the
turbine inlet temperature. The temperature and pressure ratios have been established for
the cycle in addition to the air mass flow rate that is required to produce a power output
of 5 kW. The first step is the combustion chamber design process was to choose the fuel
that would be used. There were only two realistic firel possibilities; propane and natural
gas.

Natural gas is not a fuel that is normally stored in portable containers like
propane. The goal of creating a portable generator therefore eliminates natural gas as a
fuel option. In addition, its energy content is similar to that of propane, but slightly less,
as shown in Table 10 (www.propanecarbs.com). This fact solidifies the decision to use
propane as the fuel gas in this project. The text on Table 10 has been modified for

readability.

49

Table 10. Energy content comparison of common fuels (25)

 

 

 

 

 

 

 

.r” * “'110‘"
120 100 m l
100‘; ——“

‘ 74 1
80.r——-88—88— — — 7
%60-’?—49 — —~
401725 — J!
20+ —- -l

l

0 .- I _ I l — I I o I _ l

3 8 9 8 2 .g 8
o 2 _.l g —| O .9
° 8 m 3 0
8 2 (9

©

(9

Z

O

Propane is basically equivalent to gasoline in price per unit of energy. The ratio of
the energy equivalence of propane to gasoline is 1.36, meaning it takes 1.36 liters of
liquid propane to yield the same power output of one liter of gasoline (Cengel and Boles
864). However, since propane is 11% cheaper than gasoline, the price for energy remains
about the same (EIA 2006). The energy content of propane is higher than other fuel
options as shown in Table 10. Propane ranks third in energy content per unit volume
behind gasoline and diesel fuel; fuels that are not desirable in this project.

The second step in the design of the combustion chamber was to determine the
thermodynamic values of propane so that the combustion chamber could be designed to
mix the fuel effectively. Propane has a relatively high auto ignition temperature of 540 C,
but still remains close to that of other fuels (www.propanecarbs.com). The flammability
limit of propane in air is 2.05% to 11.38% by volume and the stoichiometric air/fuel ratio

by volume is 4.02% (Kuo 511). The flame speed of propane is also an important

50

parameter that must be accounted for in the design of the combustion chamber because it
is desirable that the velocity of air through the combustion chamber would be equal to the
flame speed. If this happens, the flame will be held in place, not oscillating in the
combustion chamber. Ifthe air velocity is too great it will push the flame into the turbine.
In an ideal situation, the fuel would mix with air, ignite, mix with the secondary air and
cool to the turbine inlet temperature before entering the region of the system containing
the turbine. The flame speed of propane is dependent on temperature and pressure and

this correlation is shown in Equation (17) (Kuo 500).

sL =SL0( T Tub)“ (17)

E

8;, is the flame speed and Sm is the flame speed based on standard conditions. The
temperature and pressure at operating conditions scale the flame speed according to the
exponents m and n which vary based on the equivalence ratio of the fuel. The flame
speed for the combustion of propane is about 32 cm/s at standard conditions and an
equivalence ratio of 1 (Kuo 500). Table 11 is a summary of the combustion properties of

propane where the stoichiometric A/F ratio is the mass ratio.

Table 11. Thermod namic data for propane
Stoichiometric F/A Auto Ignition Flammability Limits Energy Content, Standard Flame
Ratio (vol. %) Temperature °C (vol. %) LHV, (kJIkg) Speed (cm/s)
[ 4.02% 540 2.05-11.38 48,340’ | 32

 

 

 

 

 

 

 

The next step in the analysis was to calculate the mass flow rate of the
combustion gases and bypass air that will mix to attain the correct turbine inlet
temperature. The temperature of the air leaving the compressor was determined to be 398
K. Enough thermal energy was needed to raise the air temperature fi'om 398 K to the

turbine inlet temperature of 1200 K. Using a specific heat of air of 1.005 kJ/kg-K and the

51

difference in temperature, the desired heat input was calculated to be 806 kJ/kg. The
product of this specific thermal energy value and the mass flow rate of 9.5 lbs/min (.071
kg/s) lead to an input thermal energy value of 61 kW. Since the energy content of the fuel
was known, the mass flow rate of propane could be determined and was calculated to be
.00135 kg/s.

Once the amount of propane was determined, the amount of air could be
determined, leading to a combustion chamber designed to proportion the flow correctly to
obtain the correct fuel/air mixture at the operating point. The first step was to determine
the volume flow of the mass of propane at the operating point. The specific volume of
propane was determined fiom knowing the temperature and pressure in the combustion
chamber and the gas constant for propane, .185 kJ/kg-K. For Operating point values of
temperature equal to 398 K and pressure equal to 250 kPa, the specific volume of
propane was calculated to be .3 m3/kg. The volume flow rate of propane was determined
from multiplying the mass flow rate by the specific volume.

From the specific volume of air and the flammability limits based on the volume
percent, the mass flow rate of air was determined to fall between .0077 kg/s to .038 kg/s,

based on the amount of air used in combustion. This calculation is shown below.

m V
—Q£x100=#=2.1—11.4 (18)
a mava

Qp is the volume flow rate of propane and Qa is the volume flow rate of air. The mass

flow rate of propane was known, and so were the specific volumes for propane and air,
which are based on the temperature and pressure of the gases at the operating point.

Therefore, the mass flow rate for air could be determined because the flammability limits

52

of propane were also known. Notice that the mass flow rate of air through the system
(.071 kg/s) is out of the range of the air needed for combustion. For this reason, some of
the air was diverted and used to mix with the propane for combustion while the rest
flowed around the combustion chamber and mixed with the combustion gases at the end
of the combustion chamber to regulate the temperature of the mixture back down to the
turbine inlet temperature.

The next step was to determine the flame temperature that would be needed such
that mixing the combustion gases with the bypass air would result in the turbine inlet
temperature. First, the adiabatic flame temperature was determined for the combustion of
propane in air. Appendix C details the calculation of the adiabatic flame temperature. It
is known that the adiabatic flame temperature, the maximum flame temperature of the
combustion process of propane and air, will be much higher than the turbine inlet
temperature, approximately 2400 K. Using an energy balance, the mass flow rate of
bypass air that was needed to bring the temperature of the hot gases down to the turbine
inlet temperature was determined. The mass flow rate of bypass air subtracts from the
total mass flow rate such that the result lies within the range of the mass flow of air
needed for combustion, calculated previously (0.0077 kg/s to 0.038 kg/s). Equation (19)
shows the energy balance used to determine the mass flow rate of cool air needed to

regulate the turbine inlet temperature to the design value.

111 = . 1’ ( l ) (19)
c C T T
P,C( c1 c2)

 

The temperature of the combustion gases is variable, based on the amount of air used for

combustion. If the combustion process is lean, the temperature will be hotter while the

53

opposite is true for a rich mixture. An iterative method, using the method for determining
the adiabatic flame temperature, was used to determine the correct flame temperature
such that the air used in the combustion process subtracted from the total air mass flow
rate to give the bypass air mass flow rate. The number of moles of the products and
reactants must balance so that the flame temperature can be determined, as shown by the
example in Appendix C. The flame temperature that resulted in a turbine inlet
temperature of 1200 K under the design point conditions was calculated to be 2000 K.
Table 12 shows the final thermodynamic values for the mass flow rate needed for
combustion. Note that the volume percent of the fuel/air ratio is within the flammability
limits. The flame temperature and the required mass flow rate of air needed to bring

about complete combustion are now known.

Table 12. Air and fuel flow and mixture data

 

 

 

Mass Flow of Mass Flow of Mass Flow of
Propane (kg/s) Useable Air (kg/s) T” (K) V°"‘"‘e % Fm" Bypass Air (lg/s)
000135 | 0.030 1200 2.99 0.041 |

 

 

 

 

The parameters needed to design the geometry of the combustion chamber are
now in place. The goal was to design a simple combustor that allowed for the correct
mixture of air that has been calculated and take into account the flame speed and mixing
needed for combustion. The simplest combustion chamber is a can-type system. The
design strategy for the combustion chamber was to design a very simple, but effective
system that would allow the correct proportions of fuel and air to mix at the operating
point and during startup.

The combustion chamber was made up of an outer shell and an inner chamber,
where fuel-air mixing takes place. Cool air enters the combustion chamber and is

redirected around the inner chamber. The inner chamber has holes in it to entrain the

54

correct amount of air that mixes with the fuel for combustion. The pipe diameter for the
combustion chamber was designed to remain consistent with the diameter of the rest of
the system; therefore the diameter of the outside of the combustor (outer shell) was 2-
inch diameter steel pipe and a 1-inch diameter steel pipe was used on the inside as the
can-portion of the combustion chamber. The pattern of holes surrounding the chamber

can will be discussed shortly. Figure 15 is a diagram of the combustion chamber design.

Flow Direction

Ill

 

 

 

 

 

 

 

Mixing Holes
Outer Shell
Fuel Input - ....
Spark Plugs Inner Chamber
\ ..

 

ff

 

Figure 15. Illustration of combustion chamber
One of the more important aspects of the design was making sure the mixing of

the combustion gases and bypass air was complete before the combustion gases entered
the turbine. If combustion and mixing had not been completed, then a region of extremely
hot gas may have continuously touched the turbine and this would have caused thermal
stress on the very small turbine in addition to the system not being able to be cooled with
the secondary air. It was desired that the cool and hot air streams mix to the correct
turbine inlet temperature before entering the region containing the turbine. The design

was started by determining the maximum air speed through both concentric tubes of the

55

combustion chamber at the operating point. Table 13 shows the thermodynamic values of
the air at the operating point.

Table 13. Thermodynamic values of air at the operating point

Air Temperature (K) Air Pressure (kPa) I Air Density (kg/m3) Mass Flow Rate (kgs)
398 253 | 2.21 0.075

Knowing the area of the entrance to the combustion chamber, the air density and total

 

 

 

 

 

 

 

mass flow rate of air, it was possible to determine the air velocity through the inner
chamber. The velocity of the air through the inner chamber was calculated to be 17 m/s
through the following procedure. Since the volume flow rate at the entrance to the
combustion chamber was known (total mass flow rate), the volume flow rate could be
divided between air moving through the inner chamber and the bypass air moving around
the outside of the inner chamber as shown in Equation (20).

QTotal = QInner Chamber + QBypass (20)

Assuming the velocity of the air stays constant through each section of the combustor,
only the areas of each section are needed to determine the volume flow rate through each
section. The volume flow rate of air needed to mix with the fuel for the required gas
temperature has already been calculated, so the area of the inner chamber was adjusted
according to the known through-velocity of 17 m/s.

Using Equation (17), the flame speed was calculated to be .52 m/s, based on the
temperature and pressure of the mixture at the operating point. This means that the flame
tip will be traveling at about a half-meter per second while the air will be moving at 17
m/s. The major point of this conclusion is that the flame should not move back into the
combustion chamber during combustion. If the flame speed were faster than the speed of
the air coming out of the inner chamber, then the flame could flashback into the inner

chamber. That is not a desired situation because the spark plugs and fuel inlet are

56

contained within the inner chamber. However, the problem is that the flame speed is
much slower than the air flow through the inner chamber. This will cause the flame to be
extinguished by the bypass air unless a constant ignition source is used to continuously
ignite the mixture.

Finally, the combustion chamber design needed to enhance mixing of the fuel/air
mixture before ignition. The chamber was designed to mix based solely on geometry. The
length of the inner chamber was 15 inches. This was determined to be a suflicient length
for the propane and air to mix given geometry that induces mixing. Inlet air holes were
drilled around the circumference of the inner chamber as shown in Figure 16. The holes
were placed perpendicular to the movement of the cool air flow so the air would be
forced in at a 90 degree angle to the fuel flow. Larger holes, 1/2 inch in diameter, were
placed above the firel inlet so that a majority of the air would thoroughly mix with the

propane.

 

Figure 16. Picture of combustion chamber
The number and size of holes were determined fiorn the volume flow calculation

determined previously. The total amount of area in terms of holes in the inner chamber
needed to be equal to the area given by a 1-inch diameter circle. This area would
theoretically meter the correct amount of air into the inner chamber, the air needed for

combustion. This was accomplished by placing four 1/2-inch holes around the inner

57

chamber instead of one large 1" hole. It was also important to design the combustion
chamber to be effective for other operating points, such as at startup. These operating
conditions are significantly different than those at the full power operating point. To be
sure that the geometry of the inner chamber allowed the correct mixing at other operating
points, the volume flow rate of total air desired was calculated over the entire range of
operating points.

To obtain a curve for the flow data, the operating data from the turbocharger
compressor map was used to create a chart that gives a characteristic for the air flow
produced by the compressor as a fimction of speed. Figure 17 and Figure 18 show the

data plotted on charts with trend lines to extrapolate the data to all operating points.

 

 

 

 

 

 

 

Mass Flow Rate Air vs Speed I
in 0.08 !
0.06 ~
g I
3 0.04 ~
.9.
L: 0.02 -
g 0 I I I i .
0 50000 100000 150000 200000 250000

 

 

Figure 17. Plot of the mass flow rate of air versus speed

58

PR vs Speed I

 

 

 

3 I
, a: .
D-r : I
1 f— I

I 0 l -" ”T I’_‘ ' __ ' —"I— —" ——T— I ’ "T'—l I
~ 0 50000 100000 150000 200000 250000 I
I Speed (RPM) 1

 

Figure 18. Plot of pressure ratio versus speed

Notice that the airflow as a function of speed follows a linear trend while the PR

of the air versus speed happens to be fit by a third-order polynomial. Knowing that the

amount of air present in the system varies linearly with speed, it was also be assumed that

the amount of propane needed as a function of speed varied linearly. There are two points

that can specify the propane flow equation.

Table 14. Tabulated compressor map data points

 

 

 

 

 

 

 

Speed Corrected mallow

(RPM) PR (lbs/min) Airflow (kg/s)
0 1 0 0

120000 1.35 5 0.0378

140000 1.5 6 0.04536

200000 2.25 9 0.06804

220000 2.625 10 0.0756

 

 

 

 

 

The first point is where there is no propane flow and no speed fiom the

turbocharger. The second point is a propane flow of .00121 kg/s and a speed of 215,000

RPM, the operating point. These two points were used to create a linear trend line for the

propane flow, shown in Figure 19.

59

 

Mass Flow Rate Propane vs Speed

 

0.001500

0.001000 -

 

0.000500

 

Mass Flow Rate (kg/s)

 

 

 

0.000000 1 r r r I
0 50000 100000 150000 200000 250000 I

Speed (RPM)

I
I

L 2 -- n

I

Figure 19. Propane mass flow rate versus speed
Finally, knowing the propane mass flow rate needed, and the mass flow of air

needed to produce the correct exhaust temperature, the volume flow rate of air was
determined as a function of speed. From the volume flow, the velocity could be
determined at every operating point; knowing the mass flow rate, density and area of the
entrance region to the combustion chamber. Assuming, as before, that the air flow
velocity stays the same through both the inner chamber and bypass air passage, the
velocity of the air at every speed was determined. Knowing the velocity and the volume
flow rate needed for the combustion process, the area that was needed for the air to pass
through the combustion chamber at each point was determined. Figure 20 shows a plot of
the effective intake hole diameter needed in the inner chamber to meter the correct

amount of air at every operating point.

60

I

 

 

 

 

 

 

 

I Diameter of Combustion Chamber vs. Speed
I 2.00
i g 1.50 .

«go 100_,vvvvvvvvvvvn""'"°°¢°¢¢¢¢ceeecg4

5

5 0.50 .
I 0.00 i r .
I 50000 100000 150000 200000 250000
I

 

Speed (RPM)

 

 

Figure 20. Diameter of combustion chamber versus speed
Notice that over the entire operating range of operation of the turbocharger, the inlet area

to the combustion chamber inner chamber needed to remain almost unchanged over all
operating points. It can be concluded that the geometry of the combustion chamber will
not need to be changed as a function of the speed of the compressor.

Two spark plugs were placed at the end of the inner chamber to start the
combustion process. The spark plugs were placed at 90 degree angles to each other to
facilitate even more mixing as the propane and air pass by the ignition sparks. Since the
spark plugs protruded almost half way into the inner chamber, as the air/fuel mixture
approached them the flow would have to swirl around the spark plug tips, enhancing
turbulence just before ignition.

The ignition system was designed so that the mixture would be ignited after it had
adequate time to mix. Spark plugs were used because they are readily available and are
able to withstand the high temperatures of the ignition process. Other options were

available, perhaps using a BBQ style piezoelectric igniter or a match, but the spark plugs

61

give nice consistent sparks and the idea was to keep the sparks operating even after
ignition just incase the flame blew out, to keep the fuel mixture igniting.

The ignition system consists of a battery with a rotary switch hooked up to an
ignition coil used in small cars. Figure 21 shows a diagram of the ignition system.
Every time the breaker switch is closed, current moves through the coil, when the switch
is released, the transformer steps up the voltage to between 10 and 20 kV and the current

is forced to jump the spark plug gap.

Spark Plug
Breaker Switch [II]

/eI

 

 

 

 

 

 

 

 

 

 

 

 

 

Ignition Coil

 

Battery

Figure 21. Diagram of ignition system
Multiple spark plugs were used because the voltage at each spark plug remains

the same, but the current across each plug is reduced with each successive plug. The
sparks will not be as intense as if there was only one plug, but more little sparks with the
same temperature and doubling the frequency will occur, leading to a better chance of
ignition.

The last challenge to overcome was sealing the spark plug wires through the
combustion chamber walls so that there would be no leaks through the combustion
chamber. The solution was to seal the fuel line and spark plug wires through the

combustion chamber shell with rubber stoppers. Since all of the combustion took place

62

below the chamber, after the spark plugs, the rubber stoppers were not subjected to the
intense heat present with the combustion process. To further reduce the chances of heat
failure of the rubber stoppers, three 1.5-inch x 3 inch metal nipples were welded where
the fuel lines and spark plug wires fit in. Metal caps were screwed on to provide a seal
and easy access to the spark plugs, extensions further act to slow the heat transfer to the
rubber and protect the spark plug wire. Figure 22 shows the outside of the combustion
chamber. The fuel line is l/4 inch copper tubing that fits through the rubber stopper and
is inserted in to the middle of the inner chamber. The end is flattened and small holes are
drilled in a way that the propane is spread out in three directions, further enabling mixing

to take place in the swirling gas.

 

Figure 22. Picture of combustion chamber
Finally, two 40-psi spring-activated pressure relief valves were added to the

outside of the combustion chamber to prevent an explosion in the case of too much fuel
entering the chamber and some sort of catastrophic explosion taking place. These are also
shown as the two smaller protrusions fi'om the combustion chamber in Figure 22. The

expected pressure in the chamber was 35 psi (absolute) at the operating point, so 40 psi is

63

above the upper limit expected by the design. This was a good pressure relief point
because the turbine was not designed to run with boost pressures much higher than 40
psi. Ifthe turbine runs any faster, the safety valves will disengage and release some of the

air to regulate the pressure back to the design point.

Recuperator

The problem of trying to work with relatively low temperatures and pressures is
that the thermal efficiency of the cycle is not very high. To improve the efficiency, a
recuperator was designed for the system. A goal in the design of the recuperator was to
extract 10-15 kW of energy back fi'om being lost to the environment. The downfall is that
recovering 10 kW of heat only raises the thermal efficiency of the system by about 2%.
However, proving that there is a simple, cost effective design to increase the efficiency of
the system by 2% is all that is needed to satisfy the goals of this part of the thesis work.

There were a few constraints placed on the design of the recuperator. First, the
design is constrained to a total pressure loss of 10 kPa. This is even high since the entire
system is only pressurized to 253 kPa, but it is reasonable to expect such pressure losses
through the entire system. Pressure losses will come with or without a recuperator, as will
be discussed later so the actual pressure losses through the recuperator should be less.

Second, the recuperator must withstand the high exhaust gas temperatures and be
able to operate under the design pressure at those high temperatures. The exhaust gas
temperature entering the recuperator will be around 900 K so any material used should be
able to handle the design temperature and pressure.

Another major constraint is cost. The use of high thermal conductivity materials
and the large amount of surface area needed may lead to a high cost. The goal is to design
the recuperator to be less than 10% of the project cost. Of course this limits the
complexity of the design, and the materials that could be used, but cost is more important

than the small increase in thermal efficiency that is obtained. One of the major problems

65

with recuperators is their size relative to the system that they are being used in. For large
gains in energy recovery the recuperator is typically very large when comparing its size
to the turbomachinery (Fraas 10). To keep the design simple, it is expected that the
recuperator will need to be large compared to the system size.

Finally, the recuperator should not be permanently affixed to the system. It should
be able to be removed and replaced with a straight section of tubing so that the effect of
the recuperator can be determined. With the recuperator in place, the temperature of the
air entering the combustion chamber will be higher but there will also be more pressure
losses that lead to a lower pressure ratio across the turbine meaning less work produced.
Being able to calculate the increase in temperature and pressure loss across the
recuperator is essential for further design and learning where the system can be
optimized. In the future, different recuperators could be designed and would have the
capacity to be switched in and out to verify and experiment with the designs of other
recuperators.

To design the recuperator the heat transfer rates and outlet temperatures of the hot
and cold air must be determined. There are two methods commonly employed in the
analysis of heat exchangers. The first method is the Log-Mean Temperature Difference
method. This is useful when the inlet and outlet temperatures are already known (Cengel
690). It is used for determining the size and type of heat exchanger that would work best
for a particular application. The second method used is the Effectiveness-NTU (number
of transfer units) method. Using this method, the inlet temperatures, mass flow rates, size
and type of heat exchanger are already known. The method is used to determine the heat

transfer rates and outlet temperatures of the two airstreams (Cengel 693). The size and

66

type of recuperator are inputs to the spreadsheet model and the inlet temperatures and
mass flow rates of the hot and cool air streams are known. Therefore, since the
parameters needed for the Effectiveness-NTU method are known, this is the method that
will be used to design the recuperator. The equations and parameters about to be defined
are important for the analysis of heat exchangers by the Effectiveness-NTU method.
They will be defined ahead of the individual system analysis because they hold true for
each recuperator model that was analyzed. All of the equations and parameter definitions
can be found in Chapter 12 of Heat Transfer by Yunus Cengel.

The heat capacity rate is defined as the product of the specific heat of the fluid

and the mass flow rate of the air stream.

C=cp.rtt (21)

A heat capacity rate can be calculated for both cool and hot air streams and is dependent
only on the specific heat of the hot and cold air because the mass flow rates of the hot and
cold air remain the same throughout the analysis. The ratio of the heat capacities is
represented by a lowercase "c". It is the ratio of the minimum heat capacity rate to the
maximum heat capacity rate. Maximum heat transfer is defined according to Equation
(22):

Qmax = Cminahjn — Tc,in) (22)
The maximum heat transfer rate possible in a recuperator is the lowest specific heat of the
fluid multiplied by the temperature difference of the two fluid streams before entering the
recuperator. In other words, where the hot air stream is the hottest and the cool air stream

is the coolest. The overall heat transfer coefficient is specified by an upper case "U" and

is defined in Equation (23).

67

U = ___— (23)

Here the convective heat transfer coefficients of the hot and cold fluid streams are
combined to form one heat transfer coefficient for the entire analysis. The Number of
Transfer Units (N TU) is a measure of the heat transfer surface area and larger NTU

values mean larger heat transfer surfaces in the recuperator because are needed because U

and Cmin are typically known after the analysis.

04
C

min

NTU=

 

(24)

The number of transfer units change for each model due to the change in surface area.
Most other parameters except for the effectiveness remain constant throughout the
analysis of each model. The effectiveness value in a recuperator calculation is the ratio of
the actual heat transfer rate to the maximum heat transfer rate. Therefore, its value will
remain between zero and one. Its value depends on the model of heat exchanger used and
is a function of the heat capacity ratio and the number of transfer units. An equation

showing the effectiveness is shown below.
Q=Qmare an
Finally, the equations for determining the cool air outlet temperatures and the hot air

outlet temperatures are shown in Equations (26) and (27) respectively.

129

Tc,out = c ’11] + E: (26)
_ Q
Th,out _ Th,in — E; (27)

68

Note that the cool air should get warmer after the recuperator because it is gaining
thermal energy while the hot air becomes cooler because it is losing thermal energy to the
cool air.

Three models were chosen to explore the simplest option for a recuperator. The
engineering analysis and all of the equations that were used to determine the best model
can be found in Appendix C.

The air inlet properties fi‘om both the exhaust and compressor remain constant for
each recuperator model. Table 15 shows the cool air inlet conditions. This is all data
consistent with the operating point conditions used earlier to determine the combustion
chamber parameters. Table 16 shows the hot gas data and Table 17 shows the heat
capacity and maximum heat transfer values based on the inlet conditions. The procedure
for determining the heat transfer rate for each model will now be discussed.

The first step was to determine the through-flow cross sectional area of the cool
air flow passage. This value is needed for finding the velocity of the cool air based on the
known values of mass flow rate, density and area. Next, using the velocity information,
the Reynolds number was calculated. The Reynolds number is dependent on the velocity,
diameter of the through-flow region and the kinematic viscosity. The characteristic of
laminar or turbulent flow is based on the Reynolds number. Once the flow was
determined to be laminar or turbulent, the Nusselt number correlation was obtained so

that the convective heat transfer coefficient could be calculated.

69

Table 15. Thermodynamic proErties of cool air
Compressed Air (Cool)

MFR Cool Air (kg/s) 0.075
Inlet Temp, cool air, K 398
Density, Cool Air, kgim3 2.21
cp, cool air (kJ/(kg*K)) 1.069
Thermal Conductivity Cool Air, W/(m2‘K) 0.05
Dynamic Viscosity, Cool Air, kgl(m*s) 3.26E-05
Kinematic Viscosity, Cool Air, m2/s 6.225-05
Prandtl Number, Cool Air 0.6948

 

 

 

 

 

 

 

 

 

 

 

 

The heat transfer surface area was an input that was varied with the changing geometric
properties associated with the spreadsheet. As the heat transfer surface area changes, so
does the rate of heat transfer. The rate of heat transfer is not the only important parameter
that must be optimized. The pressure loss of the air through the recuperator is also a
critical value that needed to be determined.

Table 16. Thermodynamic properties of hot air

 

 

 

 

 

 

 

 

 

 

 

Turbine Exhaust Gases
IMFR Hot Air (kg/s) 0.075
Exhaust Gas Temperature (K) 1023
Density, Hot Air, kg/m3 0.7331591
cp, hot air (kJ/(Q'M) ' 1.153
Thermal Conductivity Hot Air, W/(m2*K) 0.07
Dynamic Viscosity, Hot Air, kg(m*s) 4.362E-05
Kinematic Viscosity,Hot Air, m2/s 0.0001326
Prandtl Number, Hot Air 0.7149]

 

 

The pressure loss is a function of the roughness of the tubes, the density of the fluid,
length to diameter ratio of the recuperator and it is dependent on the velocity of the fluid
squared. The length of the recuperator and also the diameter are parameters that can be
varied and are needed to determine the heat transfer area

The same procedure is carried out for the hot air flow. At this point, the heat
transfer coefficient for each fluid should be determined so that the surface area can be

varied to determine the heat transfer rate. Once these have been determined, the number

70

of transfer units can be calculated which leads to solving for the effectiveness of a few

different models.

Table 17. Heat transfer data for all recuperator models

 

 

 

 

 

 

Heat Capacity and Maximum Heat Transfer Data
Ch 0.086475
Cc 0.080175
c 1.0785781
Qmax, kW 50.069513

 

 

 

Finally, when the effectiveness is known, the rate of heat transfer can be determined and
using Equations (26) and (27), the outlet temperatures of the hot and cool air can be
calculated. All of these calculations were completed quickly with the setup of a

recuperator spreadsheet.

Double Tube Heat Exchanger
The first model discussed is the double tube heat exchanger. In this model the

cool air flows through one pipe or multiple pipes and hot air flows in the same direction
(parallel flow) or opposite direction (counter flow) around the outside of the cool air
pipes. In this way, some of the thermal energy fi'om the hot air is lost to the cool air. The
heat transfer obtained in a parallel flow recuperator is less than in a counter flow
recuperator, but it is a simpler model to build, so that is the model that will be analyzed
here. The first step was determining the heat transfer coefficient and the pressure loss for
cool air. The through-flow area is the area of the pipes multiplied by the number of pipes
used in the recuperator and the hydraulic diameter was taken to be the diameter of the
smallest pipe used. For consistency, if a multiple-pipe model was used, each pipe had the
same diameter. The velocity of the cool air comes from the mass flow rate, cross
sectional area and density as discussed earlier. If a multiple-pipe model was used, then

the mass flow rate used in the determination of the velocity was the total mass flow rate

71

of the system divided by the number of tubes, assuming the cool air would be distributed
evenly between each pipe.
Equation (28) shows the correlation for the Reynolds number for the cool air

flow.

vein

Rec : h,c

(23)
V0

The Reynolds number is also needed in the determination of the fiiction factor, which is
used both in the pressure loss equation and in the convective heat transfer coefficient
equation. The fiiction factor equation is shown below (Cengel 441). It should be noted
here that this equation is valid for Reynolds numbers in the turbulent region (Re >

10000)
fc = (0.791nRec -1.64)’2 (29)
Turbulent flow occurred a majority of the time through the cool air pipes of the
recuperator. The convective heat transfer equation for turbulent flow through tubes is
shown in Equation (30) and is valid for Reynolds numbers greater than 3000 (Cengel
441). This is the Nusselt number correlation under turbulent flow conditions, multiplied

by the thermal conductivity of the cool air and dividing it by the hydraulic diameter of the

cool air pipes to obtain the convective heat transfer coefficient.

 

h _ (fc/8)RecPrckc I w I (30)

c _
[1 +12.7(fc/8)0'5(Prc2/3 ‘1’]th on2 -K

The convective heat transfer equation is dependent on the friction factor (heavy Reynolds

number dependence), Prandtl number, thermal conductivity, and hydraulic diameter.

72

The next task is to discuss the pressure loss through the pipes. Equation (31) is the

pressure loss equation.

2
L Pc*Vc
AP =r — —— (kP 31
° “[06] 2000 a) ( )

There is a balance that needs to be made between the desired heat transfer rate and the
pressure loss. Faster velocities of the air through the tubes will lead to greater heat
transfer, as shown by the Reynolds number dependency in Equation (30), but will also
lead to large pressure losses as shown above in the pressure loss equation. These
parameters were optimized using the Excel tool "Solver" to yield the maximum heat
transfer rate possible by specifying the maximum pressure loss through the tubes.

The next step was to determine the convective heat transfer coefficient and the
pressure loss for the hot air. The same procedure for the cool air was followed to obtain
the convection coefficient and pressure loss for the hot air, the major difference being the
calculation of the hydraulic diameter, which is dependent on the outer diameter of the
pipe minus the effective diameter of the combined area of the pipes. Equation (32)

demonstrates the determination of the hydraulic diameter.

 

Dh h = JIDzhsmoud —1r*.25"'D2pipe*#of Pipes) (32)

The hydraulic diameter was calculated by determining the area of the outer pipe through
which the hot air flows, and the inner pipes, which are contained also by the outer pipes.
The model seeks to determine the effective diameter of a number of small pipes by
combining the total cross sectional area of the pipes and determining the effective
diameter that would arise from that total area. This diameter was used as the effective

diameter of the inner pipe and was subtracted fiom the outer pipe diameter to determine

73

the hydraulic diameter. The hot air flow around the pipes stayed turbulent throughout the
model, so the same procedure for finding the pressure loss and convection coeflicient was
used.

Once both convection coefficients were determined, the overall heat transfer
coefficient was determined and therefore the number of transfer units was also able to be
calculated. The effectiveness of the double tube heat exchanger model was then
determined from Equation (33).

e _ l—exp[——NTU(l—c)]
—1—cexp[-NTU(l—c)]

 

(33)

Finally, since the model is set up, what parameters can actually be changed? The
thermodynamic properties of the air remain unchanged through the analysis so the only
parameters that make a difference are those of geometry. The area of the tubes and the
lengths of the tubes can be changed to optimize the heat transfer. Additionally, the mass
flow rate of hot air through the recuperator can also be changed, where the model can
take into effect the diverting of some of the hot air to the atmosphere and only sending a

fiaction through the recuperator to cut down on the pressure losses.

Bank of Tubes Heat Exchanger
The next model in the recuperator spreadsheet is the bank of tubes recuperator. It

has the advantage of being a cross flow device. Figure 23 shows an illustration of what it
would look like. This view is a side view of the recuperator. The hot air would be forced
over and around the outside of the tubes that are shown as little circles. The cool air,
flowing in and out of the page through the tubes, would be flowing in a crossing pattern
to the direction of the hot gas flow. The geometry of such a model is tricky, however, and

the parameters need to be tracked carefully so that the correct quantities are measured.

74

SL

30

 

Figure 23. Illustration of bank of tubes model
Pressure losses can be minimized by forcing the cool air through multiple tubes, but then

the long length of the tube, which is vital for good heat transfer, is not effective. When
the cross flow is effectively used in heat transfer, the tube carrying the cool air is long
and contributes to significant pressure losses. Imagine a coil of tubing winding itself
transversely to the flow. That situation is shown in the diagram above.

The first step in the model, as in all of the recuperator models, is to determine the
convection coefficient and the pressure loss of the cool air. The model consists of a large
shroud with a long piece of pipe wound in a rectangular coil in the vertical directoin. The
determination of the cross sectional area of the pipe that carries the cool air is straight
forward and is just the cross sectional area of the pipe, since there is only one cool air
pipe used in this model. The determination of the convection coefficient is the same as

for the double tube model and the discussion will be excluded.

75

The changes in the model come when trying to determine the convection
coefficient of the hot air moving over the rectangular coil inside the hot air shroud. The
arrangement of the cool air tube has a significant effect on the maximum velocity of the
air and consequently the heat transfer coefficient of the hot air. The cool air coil can be
wound within the shroud many different ways. The rectangular coil could be wound with
many horizontal passes and a few rows vertically, or fewer horizontal passes with more
vertical rows. The vertical rows could also be staggered so that the hot air would
constantly be twisting and turning around the tubes. There exists an optimum
configuration that produces a design that falls within the heat transfer and pressure loss
contstraints of this project.

The parameters S1,, ST and SD govern the winding of the coil. Sr, is the distance
between each vertical row of the coil while S1- is the distance between the tube passes
horizontally, a measure of how tight the coil is wound in the horizontal direction. Finally
SD is the diagonal distance between the coils. These parameters are used to determined
the maximum velocity of the hot air through the recuperator. The parameters are labeled
on Figure 25. The initial velocity of the hot air through the shroud is determined by
Equation (34).

= Iilh,corrected
Ph * A

V11

 

(34)
cs,h

However, the maximum velocity comes fiom Equations (35) and (36), depending on how

the tubes are arranged in the bank of tubes model (Cengel 390).

76

ST
V. . = V (35)
inline ST _ D

 

S

T
V = V 36
staggered 2(SD —D) ( )

The inline velocity equation, Equation (35), is used to find the maximum velocity when
the layers of the cool air coil are aligned on top of each other and Equation (36) is used
when the layers are staggered and the air is forced to move diagonally through the hot air
shroud. Figure 24 is another diagram illustrating the flow of the hot air through a bank of

tubes (Cengel 390).

77

 

Hills;

 

lst row 2nd row 3rd row
(a) In—Iine
. S I
“V, Ti i‘—L .-.- SD
_. ¢_ _______ , ......... g;
. 11’
—> ST | _ e IED I
\ """"" C9 ‘
—" A1 A, — — I
—~ 1411.}. _________ 63 _
I
—. l _ _ '
A, = STL '
AT = (ST —D)L (b) Staggered
A D = (SD -D)L

Figure 24. Illustration of flow through bank of tubes
The procedure remains essentially the same as the last model for determining the

convection coefficient and pressure loss of the hot air. The Reynolds number is calculated
using the maximum velocity and the convection coefficient can be calculated by using
the Nusselt number correlations and the fact that the Nusselt number is equal to Equation

(37).

Nu:

hD
“—k— (37)

78

The convection coefficient equations are shown in Equations (3 8) and (39) for the inline

coefficient and the staggered coefficient, respectively.

k
= 0.27Reo.63pr0.36 (Pr/PIS )0.25 __h__ N

h a a
1n11ne

1. (38)

k
= 0.35(sT/sL)°-2Re0-3Pr0-36(Pr/Prs)°~25 —D h NL (39)
th

hstaggered

These equations can be found on page 391 of Heat Transfer by Cengel. The parameter N,

is the tube correction factor used when the number of tube rows is less than 16 (Cengel
391).

Unfortunately, this model can not be totally optimized by a computer alone

because the pressure loss equation for this model is dependent on tabulated data. Two

values are needed to solve Equation (40), the fiiction factor, f, and the correction factor, x

(Cengel 393).

2

-N f phwh (kPa) (40)
L hx 2000

AP11

Now that the convection coefficients and pressure losses for each of the fluid
streams have been calculated, the NTU can be determined and therefore the effectiveness
of the heat exchanger. The equation for the effectiveness of a bank of tubes recuperator is

shown in Equation (41).

(41)

—1
— 2
8 21 c I1 c21+exp[ NTUV1+c ]I

1— exp[-NTU\/1 + c2]

The rate of heat transfer and the outlet temperatures can be calculated with the value of

the effectiveness.

79

Plate Heat Exchanger
The third model in the spreadsheet was a plate heat exchanger. This model is

advantageous because there is a large amount of surface area associated with a relatively
small space. The determination of the convection coefficients for the cool air is as
follows. The cross sectional area of the cool air duct is simply the product of the length
and width. The hydraulic diameter of geometries different fiom a circle is determined
from Equation (42) (Munson et al 360).

4Ac
P

D =

h,c (42)

The velocity of the air was calculated by dividing the mass flow rate by the number of
plate sections and then determining the flow characteristics through each plate section.
The Reynolds number for the cool air was calculated with the hydraulic diameter shown
previously in Equation (42). The only difference from this model to the double tube
model is how the geometry was modeled. The calculation of the heat transfer coefficient
and pressure losses for both the cold and hot fluid streams follows the procedure of the
previous models. Once the convection coefficients were calculated, they could be used to
determine the number of transfer units. The effectiveness of the plate recuperator is
modeled according to a double tube model, with the inner and outer tubes being
rectangles instead of cylinders.

8 _ l—exp[— NTU(1 -c)]
— 1 — cexpl— NTU(1 — c)]

 

(43)

Using a spreadsheet to store all the model information and equations for
determining the effectiveness, optimization becomes easy. This is done by holding some

parameters constant and varying others and by imposing constraints on the parameters

80

that vary to obtain the desired heat transfer rates and still keep the pressure losses to a
minimum. The parameters that were varied in the model were the area and number of
tubes, the pipe lengths and the number of tube rows for the bank of tubes model. The
desired heat transfer rate was set to 10 kW and the value of the total pressure losses of the
cool air and hot air were limited to 10 kPa.

The optimization process was carried out by Microsoft Excel's optimization tool
Solver, that enables the optimization parameters to be imposed on the model. Table 18
shows the constraints placed on the models and how each model responded to those

constraints.

Table 18. Results of recuperator

 

Double Tub. Plato Shell + Tuba Double Tub. Plate Shell + Tub.

Air
80.5
Air
Diameter NIA NIA 0.067 . NIA
values

NIA 0.3 NIA NIA . NIA

Width 4 4
ube

of Tube Rows NIA NIA 15 NIA NIA 10

The plate recuperator model and the double tube models fulfilled all of the criteria
satisfactorily. However, the bank of tubes model could not be optimized to keep the
pressure losses inline with the constraints of this project. It requires a pressure loss of
80.5 kPa due to the long tube needed to transfer the thermal energy. Therefore, the bank
of tubes recuperator can not be used in this project. Now that does not mean that every
bank of tubes model could not be used. It is obvious that there are an infinite number of
designs that might possibly work and hold to the constraints of this project. The point is

that the design of a recuperator for this project does not involve designing the best

81

recuperator, it is about designing a recuperator that is simple to manufacture and
inexpensive, to prove that it is possible for the prototype.

The obvious choice for a recuperator from Table 18 is the double tube model. The
plate recuperator has plates that are over 20 cm wide primarily to keep the pressure losses
down. This is simply too large when the maximum diameter of the outer pipe in the
double tube model is only a little over 2 inches. More so, the double tube is simple to
build, utilizing standard pipe sizes and practically no manufacturing. The use of the plate
heat exchanger would involve manufacturing the wide and thin duct work that would be
both expensive in terms of materials and expensive in the amount of time that it would
take to build.

Although the two models have similar pressure losses, the entrance region
pressure losses are neglected all together. A major challenge associated with the plate
heat exchanger would be the pressure losses that stem fiem spreading the flow from a 1"
diameter outlet to a 20 cm wide, .5 cm thick plate. The entrance region to such a system
would be enormous. A descriptive figure of this scenario is shown in Figure 25. To
distribute the air evenly to all plates, either a large entrance region would be necessary
incorporating the use of a diffuser or a complicated array of fins to direct the air coming
in from a relatively small diameter to a large diameter in a short distance, both of which

would create large pressure losses.

82

<— a

' IIIII

Flow

 

 

Figure 25. Illustration of entrance region needed to plate heat exchanger
The parameters of the double tube heat exchanger can be modified slightly to

conform to standard pipe sizes and even the correct size pipe used in the combustion
chamber so that every component matches equally. Table 19 shows the final heat
exchanger design parameters below as optimized fiom the recuperator design

spreadsheet. Figure 26 shows a picture of the final construction of the recuperator.

 

Figure 26. Picture of the end of the recuperator

83

Table 19.

    

m
Diameter

of Tubes
Diameter of Copper Tubes (in) 0. 0
m

Pressure Losses
This is a good point to discuss the total pressure losses in the system. There are 5

regions within the system where pressure losses should be calculated. As discussed in the
recuperator design section, the total pressure loss within the system is limited to a 10 kPa
loss based on the design. Pressure losses of less than 5 kPa were calculated for the
recuperator and more losses should come from regions of long pipe flow, curves and
bends, and through the turbine. Figure 27 below illustrates the regions where significant
pressure losses may occur. Point 1 is where the air is initially compressed by the
compressor to 253 kPa, the operating point pressure. From there the air travels either
through the recuperator or just through a straight section to point 2. Significant bending
of the pipe occurs between points 2 and 3, so the pressure loss analysis is important there
as well. There is another long stretch between points 3 and 4 and the air is heated up to
the operating point temperature between points 4 and 5. During the heating process, the
air will expand rapidly and fiictional losses will occur. Finally, the air exiting from the
turbocharger may still go through some tubes where pressure losses may occur.

Table 20 shows the loss values for each section. The equation for calculating the pressure

losses comes fiom Munson et al, page 475.

84

 

 

 

 

 

G) (5,)

Turbo
Charger ——’I

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 27. Illustration of regions of high pressure loss

2
_ E. av
AP_f(D) 2 (44)

The term (L/D) stands for the ratio of the length of the pipe to the diameter of the pipe.
The (L/D) terms for sections that do not have long lengths are calculated experimentally.
These terms can be calculated experimentally for valves and tube bends. The values for
the 180 degree tube section comes from the book by Frass, page 447. The fiiction factor
in Equation (44) is for turbulent pipe flow through tubes, as discussed in the previous
section. Table 21 shows the heat exchanger fluid design values for the hot and cool air.
The temperature of the cool air rises to 512 K and the temperature of the exhuast gas

decreases to 917 K after leaving the recuperator.

85

Table 20. Pressure loss data

252.67 -0.328

252.18 -0.492

252.02 -O.164

251.56 -0.461
1.

 

Note that the pressure losses without the recuperator are quite small and can be neglected
theoretically. The pressure losses including the recuperator are still relatively small and

may be able to be neglected.

Table 21. Recuperator fluid properties

I- I Area (m2) Veloci_tLI’mls Dens k m3 Re [m
Cool Air] 0.00203 15.64 2.28 12772 0.0294

I Hot Air] 0.00203 48.52 I 0.735 18588 I 0.0266 I

 

 

 

 

 

 

86

Generator Subsystems

The first important subsystem is the oil lubrication system for the turbocharger.
The Garrett GT1241 is designed to run at operating conditions with oil pressure not to
exceed 35 psi. Pressure higher than this will force the oil out through the seals and cause
the oil to get caught up in the compressor and turbine wheels. The oil drains by gravity,
so the oil outlet drain must point toward the ground so that the oil can drain effectively.
Hoses used in the oil delivery system must be able to handle the oil at 35 psi and at a
temperature of above 180 F at steady state conditions. A filter must also be added to the
system to keep any metal or dirt particles fiom entering the turbocharger because any
small particle will get caught up in the oil ports of the turbocharger. In addition, the pump
should be inexpensive and not draw a lot of power.

The oil delivery system was designed with all of these parameters in mind. Many
oil pumps that would have delivered the correct pressure were driven by AC motors and
were very expensive, well over $100. This would have been about 10% of the cost of the
entire project. An inexpensive solution to this problem came in the form of obtaining an
inexpensive automotive oil pump fi'om a local auto parts store. The oil pump does not
have a motor attached because it is driven by the engine, but it was only $23. The only
problem was that the pump produced a lot of oil pressure and high volume at low RPM.
The oil pressure coming out of the pmnp at about 500 RPM was almost 80 psi. The
excessive volume flow was a problem. To solve this problem, most of the oil was
circulated back to the reservoir. This was a waste of energy, but the pump was very

inexpensive, easy to mount and simple so it was necessary to utilize it in some way. The

87

pump is driven by an electric drill motor geared down with the use of a 10:1 gearbox to a
suitable speed to control the oil pressure and volume flow. Since the maximum speed of

the drill is 3000 RPM as listed, the maximum possible oil pump speed is 300 rpm.

 

Figure 28. Picture of oil pump and filter (top left)
Heater hose was purchased for the system that was rated to 250 psi at 72 degrees

F. Although the temperature of the oil will be about 180 F, the pressure of the oil will
also be about 10 times less, so for this reason, failure of the heater hose is not anticipated.
An appropriate oil filter was also purchased along with the standard hose fittings and
hose clamps used to connect the oil filter to the pump and to the turbocharger. Finally, the
oil reservoir consistes of a PVC bucket that is resistant to just about any outside
contaminate. It was more than adequate to handle the hot oil. Figure 28 and Figure 29

show pictures of the oil delivery system.

88

 

Figure 29. Picture of oil reservoir and tubing

Another concern with the project is the stress that might be imparted to the steel based on
the increasing temperature of the steel due to the combustion process. It needs to be
proven that the steel will not fail if it is subjected to the temperatures and pressures of the
combustion process. As explained before, pressure relief valves have been added to the
combustion chamber just in case the pressure does exceed the design amount. Another
safety measure is that the system is not a closed system, meaning if an explosion were to
occur, the expanding air could leave through the turbine exit. The yield stress of a low
carbon steel at 900 C is about 35 N/mm2 (Ross 291). Using a simple hoop stress
measurement, the stress in the steel at 80 PSI is .5 N/m2 which is 4.72 times less than the
yield stress of the steel. That is almost twice the operating pressure of the system.
Therefore, it is assured that even at the operating point, the steel will still have plenty of
structural strength.

All of the flow modeling has been done under the assumption that the flow is not

compressible. Flow is not considered compressible unless it has a speed over Mach .3

89

(Munson et al 490). The air traveling in this system never reaches above 100 m/s, which
would be approximately Mach .3. The fastest velocity of the flow occurs just after
combustion and reaches a speed of about 55 m/s due to the expansion of the gas.

The final component that makes up the 5 kW gas turbine-generator is the
generator itself. The speed of the turbocharger shaft and the miniature design of the
system present complications for attaching a regular electric motor to the shaft of the
system. First, most gas turbines are designed to operate at 3600 RPM so that the correct
frequency of AC current (60 Hz) can be output from the generator. This is important for
all home appliances and most other electrical equipment that operate on AC current at 60
Hz. Attaching a regular generator to this project would not produce the correct AC
current fiequency for operating electrical equipment. One of the current solutions to this
problem is to use expensive power electronics with a high-speed electric generator to
output the correct AC current fiequency that electricity consumers need. The use of
power electronics will atleast double the cost of this prototype and may even extend the
price fiirther upwards.

The second problem comes with trying to attach the generator to the shaft of the
turbocharger. The attachment point needs to be designed so that if there is any dangerous
torque on the system, the shaft of the turbocharger will break away fiom the shaft of the
generator so that each will not be adversely affected. The attachment point is a safety
issue because even though a generator could be created on a relatively small scale, the
kinetic energy associated with a piece of metal rotating at 215,000 RPM is enormous.
The problem of obtaining a specialized generator proved too difficult to overcome in this

phase of the 5 kW gas turbine generator project.

90

Appendix E contains the cost data for most of the parts costing more than $2. The
approximate cost of the 5 kW gas turbine-generator prototype was $1040. This figure
excludes tax and the cost of the generator and power electronics, to be included in a
subsequent phase. It also neglects the fact that if this product were to be manufactured on
a mass scale, many of the prices on the list would easily be reduced. The major costs
came fi'om the turbocharger, steel pipe for the component to component piping and the
hose that is designed to carry propane. One of the goals of the project was to create a 5
kW generator that could compete in price with modern piston engine generators in price.
The cost of $1040 for this prototype is a good start, but it still does not have a generator
and the corresponding power electronics needed to produce electricity. About $500 is left
for these two components such that this project would be able to compete in price with
the piston engine generators.

This report has dealt with the design of a 5 kW gas turbine generator that is
competitive with current IC generators in cost and performance. What follows is an
evaluation of the testing of the prototype and some recommendations concerning the

parts of the gas turbine that can be improved in the next phase of this project.

91

Testing

Testing of the prototype began with making sure the ignition and oil systems
worked properly. Both systems were driven by a small electric drill. The shaft that
connected the drill gearbox to the oil pump also acted as a cam that opened and closed
the breaker switch used in the ignition system. Valuable information was gathered during
the tests of the oil delivery system and the ignition system. First, it was discovered that
the turbocharger requires only small amounts of oil at low speeds. The amount of oil
entering the system should increase with speed and a high volume of oil entering the
system at low speeds causes the turbine to slow down due to the high viscosity of the
cold oil. The resolution to this problem was simply to add a valve to the oil delivery hose.
This valve can be opened or closed during the test to supply oil when it is needed and to
regulate it to low flows when it is not.

A pressure gage was added to the oil line near the turbocharger to monitor the oil
pressure during operation. The gage measures from 5-100 psi and is a good range
because the oil pump is capable of producing pressurized oil up to 80 psi. The oil system
was actually turned off for many of the tests, after lubricating the turbocharger for a few
seconds before start up. This was done because the oil was too viscous and often hindered
the spooling up of the turbocharger. Once combustion had occurred, the oil was turned on
slightly. In other cases the oil was turned on at very low pressures, approximately 1 psi to
maintain constant lubrication. This proved to help the startup of the turbocharger, but the
oil pressure does need to be monitored because more pressure is needed as the turbine

increases in speed. It was easy to regulate the oil pressure simply by the use of the ball

92

valve being used as the control mechanism. Generally the oil pressure could be held
constant at any value below 80 psi, but most of the time the working pressure was onlly
5-10 psi.

One downfall of the ignition system was that sparks are produced at the breaker
switch during the operation of the ignition system. This could be dangerous because
propane is heavier than air and if some of the fuel remains unburned for any reason, it
could seep out of the system, drift close to the sparks and ignite. To eliminate this
situation, a breaker switch that is enclosed in a case should be used. However, for
preliminary tests, the cam shaft operated by the oil pump drill motor proved to work just
fine for opening and closing the breaker switch and it was reliable.

Another danger associated with the ignition system was the overloading of the
ignition coil used as the inductor. If the the drill motor was stopped at a time in the
testing such that the breaker switch remained closed on the ignition system, the ignition
coil would quickly heat up. On a few occasions the ignition coil heated up to dangerous
temperatures that could have caused a fire (with the wooded flame) or simply could have
burned out the coil. The solution for eliminating this problem was to make sure the
battery was removed fiem the setup after each test and checking the location of the cam
when the drill was shut off in the middle of a test.

The sparks produced by the spark plug were intense and the clicking fiom the arc
could be heard through the combustion chamber. When the fuel was proportioned
correctly, ignition was reliable. During testing, only one spark plug was used instead of
the two plugs installed because the sparks were less intense and not as consistent since

the current going to the spark plugs was cut in half. Once the second plug was removed,

93

excellent sparks were observed in the combustion chamber. It was desired that more
intense sparks were preferred over more sparks of less intensity, which was the scenario
when two spark plugs were used.

Once the oil delivery and ignition systems were tested, it was time to add fuel to
the system and test the combustion chamber. To start the system, an inexpensive leaf
blower was purchased. The blower was held against the compressor input while the oil
delivery and ignition systems were started. An optical tachometer used to measure the
speed of the shaft indicated approximately 8,000 RPM when the blower was operating
the system. The function of the blower was to get air flowing through the system and start
producing some boost so that when fuel was added, the system would be slightly
pressurized and could start right away.

The first test involving fuel was very successful. A 20 lb propane tank was used
as the fuel source. The flow was regulated by a common hose connection used to attach a
propane grill to a 20 lb propane tank. The pipe connection between the combustion
chamber and turbocharger was removed so the combustion could be examined separately
from the system. The blower, ignition system and oil delivery system were all turned on
and fuel was added to the system. One to two seconds later a low "thud" was heard and
combustion was underway. There was no flame shooting out of the combustion chamber,
which indicated that at low speeds, the combustion chamber was operating according to
our design. Recall that the issue of flame speed was discussed during the combustion
chamber design section. The combustion was smooth and consistent, as if a large burner

were operating in the middle of the chamber.

94

Since this first test was successful, the pipe between the combustion chamber and
turbocharger was replaced. The system was started up again and a slight increase in
turbocharger speed was indicated on the tachometer. The speed reading approached
10,000 RPM. It was hypothesized that there was not enough fuel coming from the tank to
obtain a significant increase in speed. The propane tank valves limited the firel flow and
therefore the power input to the system was also capped. In addition, it was thought that
too much oil was input to the turbocharger and that may have been putting an additional
load on the shaft.

To fix these problems, the oil delivery valve was closed so that the turbocharger
would spin fieely of the load induced by the oil. A 100 lb propane tank was purchased
and connected to the system. The resulting test was not successful. It was determined that
too much fuel was input to the system because whistling could be heard inside the
chamber as the tank valve was opened, some thing not heard during the first test. The
whistling that wash heard was propane rushing out of the small holes in the copper fuel
inlet pipe. The solution to this test involved obtaining a needle valve to control the flow
further.

The use of the needle valve proved successful. Additionally, for the third test a
thermocouple was installed to read turbine inlet temperature. During this test combustion
was obtained and the turbine sped up to 34,000 RPM. More oil was added to the
turbocharger, but this quickly lowered the speed and increased the temperature at the
turbine inlet due to the loss of airflow. Consequently, the test was shut down.
Combustion was still fairly hard to obtain. Unfortunately there was no way of

determining how much propane was flowing out of the valve. The propane versus speed

95

chart in the combustion chamber design details the amount of propane needed at every
operating point, but there was no measurement tool in place to determine how much
propane was entering the combustion chamber.

Mass flow controllers are very expensive, take a considerable amount of time to
set up and have not proved to operate in the range of fuel input needed in this project with
sufficient accuracy. One solution to the problem involved the use of an airflow meter in
series with a ball valve, needle valve and pressure regulator to manually control the flow

while still obtaining some sort of reading. Figure 30 illustrates the series of valves and the

mass flow controller that was used in the testing.

 

Figure 30. Picture of valves and manual mass flow controller in the propane delivery system.

The manual mass flow controller is illustrated in the left part of the diagram followed in
left to right by the pressure gage, needle valve and emergency shut off ball valve. The
needle valve was the first control valve and regulated the pressure out of the tank while

the mass flow controller regulated the mass flow of propane.

96

With the addition of the control valves, the combustion process could be regulated
very well. However, the leaf blower used in the startup of the turbocharger was not able
to get the turbocharger up to a speed at which it would be able to self-sustain. Early in the
testing phase it was determined that a minimum value of 100,000 RPM would be needed
by the compressor to produce enough boost such that with the combustion in place, the
turbocharger would be able to self-sustain.

This problem was difficult to overcome because many of the available
turbomachines in the turbo lab and in stores produce high volume-flows, but low static
pressure. A device was needed that could produce lower volume flows but higher
pressures. One solution was to use a large shop vacuum with a blower attachment. The
shop vacuum proved to double the startup speed compared to the leaf blower, but the
maximum speed at startup only reached about 25,000 RPM. The next solution was
adding a second vacuum in parallel with the the first vacuum. This produced quite a
punch of air, but the setup still did not have the static pressure behind it to increase the
speed to over 100,000 RPM.

Combustion at these startup speeds was consistent, but there was a lot of
sputtering heard in the chamber, much like the fuel was igniting, and then blowing out
over and over. The combustion was not as stable at high speeds as it was at low speeds.
Figures 32 and 33 show the turbine inlet temperature plot at low speeds of about 20,000
RPM to those at relatively high speeds, about 40,000 RPM. Note that at these speeds the
turbocharger was not self-sustained, but the increase in speed was due to the turbocharger
warming up and from the expansion of the fuel-air mixture, but since the compressor was

not producing boost, the turbine was not going to speed up with the addition of more fuel.

97

Figure 31 and Figure 32 illustrate the temperature of the combustion gases at the inlet to
the turbocharger turbine based on time. The combustion in Figure 31 was considered
stable because the temperature held constant over a specified time period and could be
easily controlled. Figure 32 illustrates unstable combustion because the temperature was

not able to be controlled and was constantly turning on and off, shown by the oscillations.

554.5°C
WMMWWW

 

Figure 31. Illustration of combustion at low speeds, approximately 20,000 RPM

98

Unstable: No consistent
temperature reading

 

 

 

 

 

 

Turbine Inlet Temperature

 

Figure 32. Illustration of combustion at high speeds, approximately 40,000 RPM
An interesting observation is that the peaks of the combustion in Figure 32 align very

well with the timing of the spark plugs. This means that most likely the correct air/fuel
mixture was present in the combustion chamber, but the air flow speed was faster than
the flame speed and the flame was blowing out and igniting again with each spark.

It was determined that the turbocharger had to be spooled up past 100,000 RPM
for startup. According to the compressor map, this is where a minimum amount of boost
would be produced and hopefully a point where, with stable combustion in place, the
turbine could be spooled up and self-sustain. After much fi'ustration with small vacuums
and a leaf blower, a one-inch compressed air line was discovered in the turbomachinery
laboratory. This produced more than enough static pressure and volume flow to push the
startup speed well over 100,000 RPM. Opening the air line fully during startup produced
an unexpected and harmfirl result. Dirt in the air line filled the turbocharger with a grimy

film. It is obvious that this is not good for the turbocharger; in addtion, the dirt and high

99

pressure air acted as a sandblaster to totally remove the reflective tape from the shaft of
the turbo. In the future, these issues will need to be taken into account if the compressed

air line is going to be used to start the turbogenerator.

100

Conclusions

The engineering design created and explained in this report was optimized to
create a prototype 5 kW gas turbine generator. All of the components of the gas turbine
generator are in place, except for the generator itself and the corresponding power
electronics. Tests of the prototype indicated that the oil delivery system and ignition
system fimction as designed. The startup mechanism of using compressed air was
successful in achieving turbocharger speeds well over 100,000 RPM needed for starting
the turbocharger and obtaining boost Item the system.

The prototype was created for under $1500 minus the generator and power
electronics. There is no estimate on the cost of the power electronics and generator at this
time, but the prototype as built could be mass-produced for less than the $1040 used to
build it.

The design of this prototype has proved that a 5 kW gas turbine can be built at a
low cost using simple and readily available parts. The information in this report can be
used to further develop subsequent prototypes and finally develop a working prototype 5

kW gas turbine generator.

101

Recommendations

The engineering design if the 5 kW turbogenerator has led to the creation of a
prototype that can be further refined during the upcoming phases of this project. There
are a few critical issues that must be addressed as safety concerns and design
modifications that can reduce the size of the current prototype and increase the ease of
startup.

The first critical issue is the use of the wooden fiame in supporting the
turbogenerator. While the wooden frame served its purposed during startup as a fast and
easily modifiable fiame, it is currently a fire hazard because it has dried out significantly
since being purchased and the temperatures of some of the materials in direct contact
with the wood are very high. Most significantly, the flame that holds the turbocharger is
in direct contact and gets very hot due to the combustion process. The frame should be
changed to metal and can be done with relative ease.

The second critical issue is the ignition coil and how it can heat up if the breaker
switch is left closed after use. The system needs to be redesigned so that there is an
emergency shut-off switch that operates when the temperature of the coil gets too high.
The coil is also a fire hazard when the breaker switch remains closed. It becomes too hot
to touch.

The third critical issue is the combustion chamber. A significant amount of time
should be spent in testing the combustion chamber to make sure it operates well at all
operating points contained within the turbogenerator system. The current chamber would

be easy to test because it is modular, in effect, and has many mounting holes which can

102

 

be used to mount the chamber in many directions and standard parts can be purchased
that will mesh easily with the existing chamber. All that is needed is an accurate
measurement of the air flow and fuel being input to the combustion chamber. The fourth
critical issue is that the safety of the persons testing the 5 kW turbine generator needs to
be addressed. The current testing laboratory does not provide for the safety of the
researchers. Metal shields should be in place between the turbogenerator and the
researchers and the entire system should be able to be operated fi'om behind the shields.
A better exhuast system should also be included that can vent not only the exhaust gases,

but any other fumes that are released fiom the operation of the turbocharger.

103

Appendix A - Cycle Model Equations

The beginning of the design work accomplished during this thesis began with the
modeling of three thermodynamic power cycles. The modeling was performed using
Microsoft Excel. The inputs to the cycle model were the pressure ratio, temperature ratio,
turbomachine efficiencies and initial working fluid thermodynamic data. The following
pages will list the thermodynamic equations used to determine the thermodynamic
properties of the working fluid at each point on the T—s diagram. There is a separate list
for each cycle modeled.

The Excel spreadsheet program Excel Steam Tables Version 2.2 was used to
determine the thermodynamic properties at each point along the Rankine cycle T-s
diagram. The program was written by Magnus Holmgren and it can be obtained at

www.x-eng.com.

 

 

 

 

 

Rankine Cycle
T(K)
Vapor Cycle
5
2 ,3 '1 '4
.11 7 ~
s(kJ/kg*K)

Figure 33. T-s diagram of the Rankine cycle

1. Pump Inlet/ Condenser Outlet

104

Conrflrper Output
qout,condenser = [(116 - h 7 ) + I117 _ h1 II

Pump Inputs
0 Pressure Ratio
0

Pump Efficiency

Phase: Saturated Water

T1T1=T|

P: P I=P1

h: h1=Enthalpy water given (Tr, Pr)

s: sl=Entropy water given (Tr, Pl)

v: v1=Specific volume of water given (Tr, P1)

2. Pump Outlet / Recuperator Inlet

Pump Outputs

. Wpump = (Vpump inlet * (P2 — P1))/Tlpump
Phase: Sub-cooled Water
T: T2=T given P2, h2 from software program
P: P2=P1*PR
h: h2=hpump inlet + specific pump work
3: S2=Entropy water given (T2, P2)
v: V2=Specific volume of water given (T2, P2)

3. Recuperator Outlet! Boiler Input

Recumrator Outputs
. qin,recuperator =I 3 _h2)
Phase: Saturated Water
T:T3=T,at given P2 from software program
P: P 3=P2
h: h3=Enthalpy water given (T3, P2)
s: s3=Entropy water given (T3, P2)
v: V3=Specific volume of water given (T3, P2)

4. Boiler Outlet] Superheater Input

Boiler Output
. qin, boiler = (114 -113)
Phase: Saturated Vapor

T: T4=Tsat given P2 from the software program
P: P4=P2

105

h: h4=Enthalpy vapor given (T3, P2)
s: s4=Entropy vapor given (T3, P2)
v: v4=Specific volume of vapor given (T3, P2)

5. Superheater Output] Turbine Input

Superhegttir Outputs
qin,superheater = I115 _ h4)

Phase: Superheated Vapor

T: T5=T1*TR

P: P5=P2

h: h5=Enthalpy vapor given (T5, P2)

8: $5=Entropy vapor given (T5, P2)

v: v5=Specific volume of vapor given (T5, P2)

6. Turbine Output! Condenser Input

Turbine Outputs

v.Vturbine = I115 _h6is I'nturbine
Phase: Superheated Vapor
IsentropicQuality: determined given (ss,P6)
P: P6=P1

Isentropic h: h given (P6, s6)

Real 11: h6,real=(h5'h6,actual)*nturbine+h5

Isentropic s: 36.1sentropic=55
Real s: s given (T5, P6)
v: v given (T6, P6)

7. Saturation Point (Part of Condenser)
Phase: Saturated Vapor

T: T7=Tr

P: P7=P1

h: h7=Enthalpy vapor given (T1, P1)

s: s7=Entropy vapor given (T1, P1)

v: V7=Specific volume of vapor given (T1, Pl)

106

The next point in the data is the saturated water point at the corresponding T and P. The
cycle is closed by making the first point, the pump inlet, equal to the last point, condenser
outlet.

Curves Between 2-3, 4-5, 6-7

The temperature range is broken up into 10 increments and the entropy is calculated at
each incremental point using the software package given (T,P).

107

Steam Injection Cycle

T (K) 33 3.

 

 

s (kJ/K)

Figure 34. T-S diagram of the Steam Injection cycle
1. Compressor Input

Compressor Inputs
0 Pressure Ratio

0 Compressor Efficiency

T: T|=T1

P: P.=Pr

h: h.=Air Table value given T;

s: S.=MFRair*[(Air Table value given Tr)-
(Air Table Value Given Tr)]

Air Table Value Given T1=Soa; Used as Reference Entropy

2. Compressor Outlet/ Combustion Chamber Inlet

Compressor Outpfiut

Win,compressor = I112 _ hl)

r: T2 = T1 + (112 ‘h1)/Cp,air
P: P2=P|*PR

—I /I(
h: h2 = h] + Cp,air (T1 *(PR)(k ) "T1 )hlcompressor

' air T2 P2
S.SZ=SI+MFRa1r CP’airlnTl—_RIDP1_

108

3a. Steam and Gas Mixing
Burner Output
qin,burner = Ih3a — h2)

T T (TI * TR(msteamcpsteam + tilair-cp,air ) _ Iilstearncp,steamTI,s’tea,nn

 

3a,air maer p air
P: P3a=P2
h h

3a:h *T

+Cp,air ( 3a

2 ‘12)

T
s: s _ —s + MFRair * c —31
3a 2 p,air T
2
=R__a__rra T3
0 P2
3b. Combustion Chamber Outlet/ Turbine Inlet

v: V3

T: T3b=TI*TR

P: P3b=P[*PR

h: h3b= mfair (hz + Cp, air-(T3a _T 2)) + mfsteam * h(T3a ’ Rio)
mf is the mass fraction

T2

T
s: s3b = 82 + MFRair“ Cp’airlnI— 3a —I+ MFRwater * (80‘s. Ps)- s(T1,P1 ))
_Rmi___x____Tb

V
V: 3b_ P
2

4. Turbine Outlet

Turbine Outputs

' wturbine = Ih3b ‘h4I
T: T4 = T3b - Wturbine/Cp,mix
P: P4=P1

109

. _ ((kmix—1)/kmix) _
h. 114 _ h3b + (Cpmxa3b *(I/PR) ) T3

3‘ S4 = S3b + Cp,mix * “(U/13:3) ‘ Rmix * 1n(1’4”) 3b)
_ RmixT4
P1

**At this point the Air is expelled through the recuperator and the water is allowed
to condense

b)'nturbine

v: V4

110

Gas Cycle

T (K)
Gas (Brayton) Cycle

 

 

s (kJIkg‘K)
Figure 35. T-s diagram of the Brayton cycle

1. Compressor Inlet

Compressor Inputs
0 Compressor Efficiency

T: T1=T1
P: P1=Pl
h: h1=Table Value
5: s 1=Table Value

Rair II

P:

v: V1:

2. Compressor Outlet/ Burner Inlet

Compressor Outputs

0 compressor specific work Win, compressor = (hz — hl}

Burner Inputs
- Burner Efficiency

T: T2 =T1+(h2 -h1)/C
P: P2=P]*PR
—l /k
h: 1’12 = htable +Cp,air (T1 I“(PR)(k ) —T1 )hlcompressor
T P
s: 32=SI+C 1n——2——Rln—2—

,air
P T1 Pl

p,air

Rair T2

P2

v: V2:

111

3. Burner Outlet! Turbine Inlet

Turbine Inputs
0 Turbine Efficiency

Burner Output
. qin,bumer = (h3 _ ’12)

T: T3=Tl * TR
P: P3=P.*PR

h:h3=h2+C (T3'T2)

p,air

4. Turbine Outlet! Condenser Inlet (non-existent, open cycle, graph artificially
closed) .

Turbine Outputs
' wturbine =(h3 ’1‘4)’ “turbine

T‘ T4 = T3 ‘ “wand/Cm:
P: P4=P1
-1 /k
h: h4is = h3+(T3 *(PR)(k ) —T3)
h4=h3' wmbine
T P
3 3
V _ RairT4
V: 4 [)1

Curves from 2-3, 4—1 are created from the change in enthalpy relations for an ideal

T2 P2
gas 32 —s1 = Cp,avln———Rln——

T1 P1

112

Appendix B - Turbine and Compressor Maps

 

GT1241, 41 mm, 50 Trim, 0.33 AIR

 

 

 

2.5

 

N

 

Pressure Ratio

  
  

 

 

o
/ 20000

 

 

   

 

1.5

 

 

1 20000

 

QEEN

 

 

60%

1 80000

200000

 

 

 

 

 

1

L0

 

Figure 36. Garrett GT1241 compressor map (Garrett Product Catalog 4 [Retl 16])

*Note that the image has been modified to enhance the readability of the figure.

5 . 10 _
Corrected Arr Flow (lb/mm)

113

15

 

2y

 

' Corrected Gas Turbine Flow (lb/min)

0

\

 

GT1241, 72 Trim, 0.43 AIR

 

 

 

 

 

 

 

 

 

 

 

- c. 4. p —_ _ ____

 

 

 

 

 

 

 

 

 

 

 

1 .00

1.50

 

 

 

2 .00
Pressure Ratio

Maximum Efficiency 65%
J l 1
2.50 3.00

 

Figure 37. Turbine map for Garrett GT1241 (Garrett Product Catalog 4 [Ref. 16])

*Note that the image has been modified to enhance the readability of the figure.

114

 

Appendix C - Calculation of Adiabatic Flame Temperature

Fuel: Gaseous Propane

Assumptions:

1. Steady flow

2. Combustion chamber is adiabatic

3. No work interactions

4. Air and combustion gases are ideal gases

5. Changes in potential and kinetic energy are negligible

C3H8(g)+5(02 +3.76N2) —> 3c02 +4H20+19N2 (c1)

*Equation 1 is balanced for the reaction of propane and air
ZNp(hf°+h—h°)p =2Nr(fif°+E—H°), (02)

*Equation 2 governs the energy released in the reaction
* hf ° is the enthalpy of formation

* h is the enthalpy of the gas at the reaction temperature
* h° is the reference enthalpy of the reaction

(h

h

+E — ° )+5(E ° . +15 h°. )=
3 8 C3H8 C3H8,298K f ,all‘ air,298K _

3(H° +H —E° )+4(E°, +5 -H° )+19(E °, +3 ~h° )(c3)
f,c02 C02 C02,298K f H20 H20 H20,298K f N2 N2 N2,298K

f°,c H ,air ‘

*Equation 3 expands Equation 2 by replacing the sums with the appropriate terms
Table 22. Enthalpy values for flame temperature calculation

C3H8 Air H20 C02 N2
Enthalpy of Formation (kJ/krnol) -103850 - -241820 -393920

Reference Enthalplat 298 K (kJ/kmol) - 300 9904 9364 8669

 

 

 

 

 

 

 

 

 

 

 

*The enthalpy of the air coming into the combustion chamber (E air) is 300 kJ/kg
Replacing all the terms in Equation 3 with their values leads to

2349452kJ = 3hC02 + 4hH20 +19hNZ (C4)
Only the enthalpy values for each of the gases remain left to determine. The trick is to
guess and check the temperature of flame. In this case, a value of 2400 K was estimated.
The enthalpy for each gas at 2400 K was input into the equation. If the temperature is
correct, both sides of the equation should match in magnitude. The iteration continues
until the correct flame temperature is determined.

115

 

Appendix D - Heat Exchanger Design Formulas

Double Tube Heat Exchanger

 

Figure 38. Double tube recuperator illustration

Cool Air:

1.

2
Dh,c

 

Area of Pipe: Acs,c = 1:

m
. Velocity through one Pipe: Vc = _p,c__ (m/s); mp c = mc/# pipes
p 3

*
c Acs,c

. Hydraulic Diameter: Dh,c (Diameter of Pipe)

. Pipe Length: L= L0 /# of pipes
. Surface Area: As = 1r* Dh "' L ‘#ofpipes

,0

V9 *Dh,c . .
. Reynolds Number: Rec = j‘ ‘ )

 

vc

. Friction Factor (Turbulent): f = (0.79lnRec —1.64)"2 (dimensionless)
. Convection Heat Transfer Coefficient (Turbulent Flow through a Tube):

(fc/8)RecPrckc ( w J
[1+12.7(fc/8)0'5(Prc2/3 -1)]ph c m2 -K

 

h:

 

2
*
. Pressure Drop: APc =fc[—L—] Pc Vc (kPa)

DC 2000

116

Hot Air:

1. Cross Sectional Area of Shroud: Acs 2

h,h

til
Velocity through Shroud: Vh = * h,corrected
p h (Acs,h —# 0f pipes * Acs,c)

,h=D

5"

 

L

3. Hydraulic Diameter: Dh,h = \KDzhshroud - 1r*.25 * szipe*# of Pipes)
V * D
4. Reynold’s Number: Reh = h h’h
v
h
5. Friction Factor (turbulent): fh = (O.791n(Reh)—1.64)-2 or
fh = 64/Reh (laminar flow)
6. Convection Heat Transfer Coefficient:
h _ (fh/8)RehPrhk

h W
h" . 2/3 [ 2 )0‘
[1+12.7(fh/8)05(Prh —1)]ph,h m -K

k
hh = 4.36——b—(laminarflow)
D
h,h

 

2
L Ph * Vh
7. Pressure Drop: APh = fh (kPa)
Dh,h 2000

Heat Exchanger Model: Double Tube (_paraléel flow)

1 — expl— NTU( 1 - c)]

Effectiveness: e =
1 — cexp[— NTU(l — c)]

 

117

Bank ofTubes/Shell and Tube

SL

SD

 

Figure 39. Bank of tubes illustration

 

Cool Air:
2
Dh c
1. Area ofPipe: Acs,c = 1r 4
2. Velocity through Pipe: Vc = _Plc__ (m/s)
Pc Acs c

3. Hydraulic Diameter: Dh,c (Diameter of Pipe)

4. Pipe Length: L
5. Surface Area: As =n‘Dh,c*L

Vc "' Dh,c
6. Reynolds Number: Rec = (" ' ' )
Vc
7. Friction Factor (Turbulent): fc = (0.791n(Rcc)-1.64)‘2 (dimensionless)
8. Convection Heat Transfer Coefficient (Turbulent Flow through a Tube):
(fc/8)RecPrckc

w
{—J
[1+12.7(fc/8)0'5(Pr02/3 —1)]ph,c m2 -K

 

2
Pc * Vc
2000

9. Pressure Drop: APc = fCLL]
Dc

 

(kPa)

Bank of Tubes Parameters:
1. Vertical Spacing: SL
2. Horizontal Spacing: ST
3. Diagonal Spacing SD
Hot Air:
1. Cross Sectional Area of Shroud: A cs,h = Dh,h2

118

mh,corrected

2. Velocity through Shroud: V =
Ph * A

h

 

cs,h

ST

v, v = ___—v
staggered 2(sD — D)

. . . _ T
3. Maximum Velocity. Vinline — ————ST _ D

4. Hydraulic Diameter: Dh,h = Dh,shrou d — D *# of Pipe Columns

5. Reynold’s Number: Reh = _—
V
b

pipe

6. Friction Factor (turbulent): Tabular
7. Convection Heat Transfer Coefficient (Turbulent Flow through a Tube):
k
0.63 0.36 0.25
hinline =0.27Re Pr (Pr/Prs) B—LNL,
h,h
k
_ 0.2 0.8 0.36 0.25 h
rv 2
8 Pressure Drop: AP =N f th—JJ— (kPa)
' ' h L h 2000

l, N L, f are inputs fi'om Cengel p.393
Heat Exchanger Model: Shell and Tube

-—1
-NTU’ 2
8=21+C+V1+021+exmi l+c ]}

1- exp[—NTU\/l +c2]

119

 

Plate Heat Exchanger

 

Figure 40. Plate heat exchanger illustration
Cool Air:
1. Area ofPipe: Acs,c = wa

m
2. Velocity through Plates: Vc = ——*P-’c— (m/s); mp,c = I'hc/# plates
pc Acs,c
. . 4Ac

3. Hydraulic Diameter: Dh = —

9c p
4. Pipe Length: L = L0/# of plates
5. Surface Area: As = (2L + 2w) * L0

V0 I. Dh c . .

Vc ‘

7. Friction Factor (Turbulent): fc = (0.79ln(Rec)—1.64)_2 (dimensionless)
8. Convection Heat Transfer Coefficient (Turbulent Flow through a Tube):
(fc/8)RecPrckc

W J
[1+12.7(fc/8)0'5 (Prc2/3 —1)]ph,c [m2 .K

6. Reynolds Number: Rec = )

h:

 

2

*

9. Pressure Drop: APc = fc[D—L—] p303]; (kPa)
h,c

 

Hot Air:

. _ _ 2
1. Cross Sectional Area of Shroud. Acs,h — Dh,h

1hh(corrected)
ph * (A cs,h —# of plates * Acs,c)

 

2. Velocity through Shroud: V =

3. Hydraulic Diameter: Dh,h = Dh,shroud -#p1ates"I D
Vh * Dh,h

pipe
4. Reynold’s Number: Reh =
V
b
5. Friction Factor (turbulent): fh = (0.791n(Rch)—1.o4)‘2

120

6. Convection Heat Transfer Coefficient (Turbulent Flow through a Tube):
h _ (fh/8)RehPrhk

_ h W J
h [l+12.7(fh/8)0'5(Prh2/3-l)]Dh’h [mz-K

2
L p * V
hzootil (kPa)
h,h

 

 

7. Pressure Drop: AP =f

h hD

 

Heat Exchanger Model: Double Tube

1 -— exp[— NTU(] — c)]

Effectiveness: e =
1— ccxp[- NTU(] — c)]

 

Heat Exchanger Quantities
1. CC: cp,c "' mc - heat capacity rate
2. Ch: cp,h * mh - heat capacity rate

C .
3. c: @— - ratio of the heat capacities

Cmax

4. Overall Heat Transfer Coefficient: U = 1

1 1
__+__

5. Number of Transfer Units (NTU): NTU = 5A8

 

. min
6. Qmax: Qmax = Cmin(Th,in _chn)

7. Heat Transferred: O = Qmax *8

- . _ Q
8. Cool Air Temperature Out. Tc,out — Tc,in + C:
9 Hot Air Tem rature Out° T = T — —Q—
° pe ' h,out h,in Ch

121

Appendix E - Cost Analysis

Table 23. Cost data from project

1/4" T 50
1I2" T 50
2" Black
Wood for F
Oil
Heater Hose
Hex Bolts for 1
Nuts for Hex Bolts 16
3/8" Heater
1

Oil
2" to 1" Steel 3
2"Steel Tees
2" Steel
90° Steel Elbows 4

Gasket
Rubber 3
1 1/4" Extensions
2 1/4" 3

1" Black

Brass Hose

 

122

 

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125

   

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