The team designed and built a working Stirling engine suitable for classroom demonstration that could run on solar energy. The engine uses a two cylinder inline "alpha" configuration. Through iterative testing and design refinements, the team was able to get the engine running using a handheld heat source. With more time, they believe the engine could be powered solely by solar energy as originally intended. The report documents the full design process, including initial concept selection, component design and fabrication, testing and design improvements made to optimize performance.

1. TEAM 04
SOLAR AND WASTE HEAT POWERED STIRLING ENGINE
FINAL REPORT
“The Little Engine that Could… and Did!”
The goal of team 04 was to design and build a working Stirling engine suitable
for classroom demonstration. As an added challenge the group is planning to
have the engine run entirely from solar energy as well as other heat sources.
Andrew McMurray
B00406524
Alex Morash
B00410812
Bryan Neary
B00401625
Kristian Richards Submission Date: April 9th
B00411178 Submitted To: Dr. Militzer
Dr. Groulx

2. TABLE OF CONTENTS
LIST OF ILLUSTRATIONS ............................................................................................................................... iv
.
LIST OF TABLES .............................................................................................................................................. v
ABSTRACT ..................................................................................................................................................... vi
1. INTRODUCTION ..................................................................................................................................... 1
2. BACKGROUND ....................................................................................................................................... 2
2.1. Ideal Stirling Engine Cycle ............................................................................................................. 2
2.2. Real Stirling Engine Cycle .............................................................................................................. 3
3. DESIGN REQUIREMENTS ....................................................................................................................... 6
4. DESIGN SELECTION ............................................................................................................................... 7
.
4.1. Rotary Stirling Engine .................................................................................................................... 8
4.2. Gamma Stirling Engine .................................................................................................................. 8
4.3. Alpha Stirling Engine ‐ 90° Arrangement ...................................................................................... 9
5. COMPONENT DESIGN, FABRICATION AND BUILD PROCESS ............................................................... 10
5.1. Frame .......................................................................................................................................... 10
5.2. Cylinders and Cylinder Heads ..................................................................................................... 11
5.3. Pistons ......................................................................................................................................... 12
5.4. Cranks ......................................................................................................................................... 12
.
5.5. Flywheel and Collars ................................................................................................................... 13
5.6. Piston Rods and Brass Connection Fittings ................................................................................. 14
5.7. Fresnel Spot Lens ........................................................................................................................ 14
6. DESIGN ANALYSIS AND REVISED CALCULATIONS ............................................................................... 16
6.1. Schmidt Analysis of Ideal Isothermal Model .............................................................................. 16
.
6.2. Fin Heat Transfer ......................................................................................................................... 18
7. INITIAL TESTING .................................................................................................................................. 19
7.1. Testing Observations................................................................................................................... 19
7.2. Design Solutions .......................................................................................................................... 20
8. DESIGN REFINEMENTS & PERFORMANCE IMPROVEMENTS .............................................................. 21
8.1. Design Refinements .................................................................................................................... 21
8.1.1. Frame Heat Dissipation ....................................................................................................... 21
8.1.2. Compression Reduction ...................................................................................................... 22
8.1.3. Transfer Tube ...................................................................................................................... 23
8.2. PERFORMANCE IMPROVEMENTS ............................................................................................... 24
ii

3. 8.2.1. Internal Fins ........................................................................................................................ 24
8.2.2. Regenerator ........................................................................................................................ 25
9. Testing and Troubleshooting .............................................................................................................. 27
9.1. Fresnel Lens Testing .................................................................................................................... 27
9.1.1. Test #1 ‐ General Testing Results ‐ January 23rd (2 pm) ...................................................... 27
9.1.2. Test #2‐ Temperature Measurements ‐ April 1st (12:40 to 1:10 pm) ................................. 28
.
9.1.3. Test #3 ‐ Solar Energy Input to Gamma ‘Windmill’ Stirling Engine ‐ April 1st ..................... 30
9.2. Iterative Testing and Troubleshooting Procedure ...................................................................... 30
9.3. Temperature Data Acquisition .................................................................................................... 33
9.3.1. Thermocouples ................................................................................................................... 33
9.3.2. Benchtop Digital Display ..................................................................................................... 34
9.3.3. Thermocouple arrangement ............................................................................................... 35
9.4. Stirling Engine Optimization........................................................................................................ 35
9.4.1. Test #1 ‐ March 30th, 2009 .................................................................................................. 36
9.4.2. Test #2 ‐ April 1st, 2009 ....................................................................................................... 37
9.4.3. Test #3 ‐ Run A ‐ April 4th, 2009 .......................................................................................... 39
9.4.4. Test #3 ‐ Run B ‐ April 4th, 2009 ........................................................................................... 42
9.4.5. Test #3 ‐ Run C ‐ April 4th, 2009 ........................................................................................... 43
9.5. Repeatability and Comparison to Theory ................................................................................... 44
10. BUDGET ............................................................................................................................................... 45
11. CONCLUSION ....................................................................................................................................... 46
11.1. Design Requirements Fulfillment ............................................................................................ 46
11.2. Optimal System Operating Condition ..................................................................................... 47
12. REFERENCES ........................................................................................................................................ 48
APPENDIX A – Gantt Chart
APPENDIX B – Ideal Isothermal Analysis
APPENDIX C – Heat Transfer Calculations
APPENDIX D – Engineering Drawings
iii

4. LIST OF ILLUSTRATIONS
Figure 1 ‐ Solar Energy Project Proposal of Solar Array sited in California Mojave Desert using
SunCatcherTM Technologies from SES Stirling Energy Systems ..................................................................... 1
Figure 2 ‐ Ideal Stirling Cycle P‐v and T‐s Diagrams ...................................................................................... 2
Figure 3 ‐ Real Stirling Cycle P‐v Diagram Approximation ............................................................................ 4
Figure 4 ‐ Rotary Stirling Engine .................................................................................................................... 8
Figure 5 ‐ Gamma Stirling Engine .................................................................................................................. 9
Figure 6 ‐ Alpha Stirling Engine – 90° Arrangement ..................................................................................... 9
Figure 7 ‐ Final Concept to Build Comparison ............................................................................................. 10
Figure 8 ‐ Assembled Frame and New Bearing Seat ................................................................................... 11
Figure 9 ‐ Hot and Cold Cylinders and Cylinder Heads ............................................................................... 12
Figure 10 ‐ Piston Manufacturing and Final Product .................................................................................. 12
Figure 11 ‐ Crank Design Showing Force Couple and Stroke Length .......................................................... 13
Figure 12 ‐ Stirling Cycle Flywheel Dependance ......................................................................................... 14
Figure 13 ‐ Brass Fittings and Connecting Rods .......................................................................................... 14
Figure 14 ‐ Fresnel Lens and Frame ............................................................................................................ 15
Figure 15 ‐ Simplified Isothermal Alpha Stirling Engine .............................................................................. 16
Figure 16 ‐ Sinusoidal Volume Dependence on Crank Angle ...................................................................... 17
Figure 17 ‐ Heat Transfer and Fin Efficiency ............................................................................................... 18
Figure 18 ‐ Initial Testing Setup .................................................................................................................. 19
Figure 19 ‐ Heat Damage to Temporary Transfer Tube .............................................................................. 20
Figure 20 ‐ Hot Cylinder Insulation ............................................................................................................. 21
Figure 21 ‐ Thermal Image .......................................................................................................................... 22
Figure 22 ‐ Stroke Length Reduction .......................................................................................................... 23
.
Figure 23 ‐ Heat Damaged Transfer Tube ................................................................................................... 23
Figure 24 ‐ Steel Transfer Tube ................................................................................................................... 24
Figure 25 ‐ Internal Fins Fabrication Process .............................................................................................. 25
Figure 26 ‐ Internal Fin Placement .............................................................................................................. 25
Figure 27 ‐ Regenerator Components ........................................................................................................ 26
.
Figure 28 ‐ Installed Regenerator with Ice Water Bath .............................................................................. 26
Figure 29 ‐ Fresnel Lens and Infrared Thermometer Readings .................................................................. 27
Figure 30 ‐ Various Objects Held under the Fresnel Lens ........................................................................... 28
Figure 32 ‐ Temperature Increase of Steel Stock vs. Time ......................................................................... 29
.
Figure 31 ‐ Cylindrical Steel Object ............................................................................................................. 29
Figure 33 ‐ Gamma 'Windmill' Stirling Engine ............................................................................................ 30
Figure 34 ‐ Surface Thermocouple .............................................................................................................. 33
Figure 35 ‐ Probe Thermocouple Setup ...................................................................................................... 34
Figure 36 ‐ Omega MDSSi8 Digital Thermometer ....................................................................................... 34
Figure 37 ‐ Thermocouple Setup ................................................................................................................ 35
.
Figure 38 ‐ Optimization Test #1 Setup ...................................................................................................... 36
Figure 39 ‐ Optimization Test #2 Setup with Regenerator ......................................................................... 37
iv

5. Figure 40 ‐ Optimization Test #2 Hot Cylinder Temperatures .................................................................... 38
Figure 41 ‐ Optimization Test #2 Cold Cylinder Temperatures ................................................................... 38
Figure 42 ‐ Optimization Test #2 Clamp and Regenerator Temperatures .................................................. 39
Figure 43 ‐ Optimization Test #3 ‐ Run A ‐ Hot Cylinder Temperatures ..................................................... 40
Figure 44 ‐ Optimization Test #3 ‐ Run A ‐ Cold Cylinder Temperatures .................................................... 40
Figure 45 ‐ Optimization Test #3 ‐ Run A ‐ Clamp and Regen Temperatures ............................................. 41
Figure 46 ‐ Optimization Test #3 ‐ Run A ‐ RPM and Power ....................................................................... 42
Figure 47 ‐ Optimization Test #3 ‐ Run B ‐ RPM and Power ....................................................................... 43
Figure 48 ‐ Schmidt Analysis Results for December Design .......................................................................... 4
Figure 49 ‐ Schmidt Analysis Results for January Revised Design ................................................................. 5
Figure 50 ‐ Schmidt Analysis Results Using Actual Results from April Optimizations .................................. 5
LIST OF TABLES
Table 1 : Ideal Stirling Cycle Process Summary ............................................................................................. 3
Table 2 : Design Requirements ..................................................................................................................... 6
Table 3 : Design Selection Matrix ................................................................................................................. 7
.
Table 4 : Results of Schmidt Analysis of Ideal Isothermal Model ............................................................... 17
Table 5 : Troubleshooting Parameters ........................................................................................................ 31
Table 6 : Successive Iterative Testing Process ............................................................................................ 32
Table 7 : Optimization Test#1 Results ........................................................................................................ 36
.
Table 8 : Theory and Testing Results .......................................................................................................... 44
Table 9 : Team 04 Budget ........................................................................................................................... 45
Table 10 : Design Requirement Status ........................................................................................................ 46
Table 11 : Optimal Engine Conditions ......................................................................................................... 47
v

6. ABSTRACT
Team 4 was responsible for designing and delivering a working solar powered Stirling engine to the
Dalhousie Mechanical Engineering Department in April 2009. A Stirling engine is the closest real engine
to approximate the theoretical Carnot cycle engine and consists of rapidly heating and cooling a gas
within a piston/cylinder device. The gas is fully contained meaning there is no exhaust or intake and
therefore the Stirling engine is considered an external combustion engine as the heat is applied
externally. Team 4 intended to utilize the power of the sun to provide the necessary energy to the
system instead of burning conventional fuels. The main purpose of the project served to promote the
use of Stirling engines in ‘green energy’ applications. Due to the high theoretical efficiencies of Stirling
engines they are a prime candidate for future solar energy generation research. Solar powered Stirling
engines are now commercially available up to 25 kW of generating capacity.
The final prototype consists of a two cylinder inline alpha arrangement. The project has been completed
with a multitude of testing and troubleshooting phases. The team was successful in getting the engine to
run with a hand held heat source and give more time, feels confident that the engine could run on solar
power. A detailed section of testing is provided in this report and summarizes the steps taken to
develop a working stirling engine.
The following report presents the design selection process, final design with inclusive engineering
drawings, the associated engineering design calculations, define requirements, testing analysis, a
finalized budget, and a conclusion summarizing the optimal operating conditions of our engine.
vi

7. 1. INTR
RODUCTI
ION
In the recent ‘green‐en
nergy’ movem ment the Stirling cycle has received renewed interesst in the area of
solar enerrgy generatio
on, and it is th of team 04 to help raise aw
he intention o wareness and promote
renewable energies by y demonstrating the poten ntial of the Sti
irling engine.
Stirling en
ngines are kno own for havinng a high therrmodynamic efficiency. Id deally, a Stirlin
ng cycle enginne
can be de esigned to app proximate thee theoretical Carnot cycle engine. For e example, Stirrling Energy
Systems, Inc (SES), a co ompany based in California, USA specia alizing in solar
r energy gene eration equipment
is currently recognized d for holding t
the world reccord for solar‐‐to‐grid conve ersion efficienncy of 31.25% %
TM
T 1
with theirr SunCatcher solar powe ered Stirling e
engine and mi irrored dish c collector. See Figure 1 forr a
TM
picture off a proposed a array of SunC
Catcher unit ts. SES has proposed to bu uild 70,000 of these units in
the Californian Mojave e Desert and IImperial Valle
ey that will yield a combined generating g capacity of
1,750 MW W of electricity. Team 04 a
accredits thesse SES project ts as well as oother projects s of similar
aspirationns for inspiring the team too design and build a working Stirling en ngine to fulfill the requirem ments
of Dalhou usie Design Prroject 2008/009.
Figure 1 ‐ S
Solar Energy Pro
oject Proposal o ted in California Mojave Desert using SunCatch TM Technolog
of Solar Array sit her gies
2
from SES SStirling Energy Systems
The reporrt will outline a background of the ideal Stirling cyclee, summarize the design seelection process,
present th
he final design and individual compone ents, discuss t
the calculations and technical engineering
decisions made to refin ne the final design, presen nements and testing proce
nt design refin edures. The t
team
budget will also be preesented as we ell as a detaile
ed conclusionn outlining the
e design requ
uirements
establishe
ed in first sem
mester. The fiinal engineering drawings are attached d in the Appen
ndix D.
1 th
Stirling Energy Systems, SES. (2008a). New Wo
orld Record for Sola
ar‐to‐Grid Convers
sion Efficiency. Ac
ccessed on Septem
mber 20 , 2008 fro
om
http://www.s
stirlingenergy.com
m/downloads/12‐F
February‐2008‐SES
S‐Stirling‐Energy‐and‐Sandia‐National‐Laboratories‐se
et‐New‐World‐Rec
cord.pdf
2
Stirling Ene
ergy Systems, SEES. (2008b). Sola d on November 15th, 2008 from
ar Two. Accessed
http://www w.stirlingenergy.c
com/projects/de efault.asp
1

8. 2. BACKGROUND
The following sections are intended to provide a brief overview of the ideal Stirling cycle
thermodynamics and assumptions made in the analysis of a real Stirling engine. It is very important to
note that the real Stirling cycle is very complex and relies on a combination of design approximations
and experimental tests to successfully design and build a working Stirling engine. Since the analyses
developed for designing Stirling engines are inaccurate and because experimentation is expensive the
accepted course for building a Stirling engine is to model off of existing engines using experimental
scaling parameters. Unfortunately, for the design of this project there is a lack of reference material
that could be used for scaling purposes. Hence, the team has relied heavily on scaling the design from a
known working gamma type Stirling engine, property of Dalhousie. By using these approximations with
ideal Stirling cycle theory and analyses the team is confident that the project will be successful given the
time allotted for testing and refinement in 2009. The project has been designed to allow for refinement
and adjustments which is critical given the lack of known theory.
2.1. Ideal Stirling Engine Cycle
The ideal Stirling cycle is represented in Figure 2 and consists of four processes which combine to form a
closed cycle: two isothermal and two isochoric processes. The processes are shown on both a pressure‐
volume (P‐v) diagram and a temperature‐entropy (T‐s) diagram as per Figure 2. The area under the
process path of the P‐v diagram is the work and the area under the process path of the T‐s diagram is
the heat. Depending on the direction of integration the work and heat will either be added to or
subtracted from the system. Work is produced by the cycle only during the isothermal processes. To
facilitate the exchange of work to and from the system a flywheel must be integrated into the design
which serves as an energy exchange hub or storage device. Heat must be transferred during all
processes. See Table 1 for a description of the 4 processes of the ideal Stirling cycle (Borgnakke et al.,
2003).
Figure 2 ‐ Ideal Stirling Cycle P‐v and T‐s Diagrams3
3
Power from the Sun. (2008a). Power Cycles for Electricity Generation. Accessed on October 12th, 2008 from
http://www.powerfromthesun.net/chapter12/Chapter12new.htm#12.3.1%20%20%20%20%20Stirling%20Engines
2

9. The net work produced by the closed ideal Stirling cycle is represented by the area 1‐2‐3‐4 on the P‐v
diagram. From the first law of thermodynamics the net work output must equal the net heat input
represented by the area 1‐2‐3‐4 on the T‐s diagram. The Stirling cycle can best approximate the Carnot
cycle out of all gas powered engine cycles by integrating a regenerator into the design. The regenerator
can be used to take heat from the working gas in process 4‐1 and return the heat in process 2‐3. Recall
that the Carnot cycle represents the maximum theoretical efficiency of a thermodynamic cycle. Cycle
efficiency is of prime importance for a solar powered engine for reasons that the size of the solar
collector can be reduced and thus the cost to power output ratio can be decreased.
Table 1 : Ideal Stirling Cycle Process Summary
Process 1‐2 : Isothermal compression
• Heat rejection to low temperature heat sink
• 1Q2 = area 1‐2‐b‐a on T‐s diagram
• Work is done on the working fluid (energy exchange from flywheel)
• 1W2 = area 1‐2‐b‐a on P‐v diagram
Process 2‐3 : Isochoric heat addition
• Heat addition (energy exchange from regenerator)
• 2Q3 = area 2‐3‐c‐b on T‐s diagram
• No work is done
• 2W3 = 0
Process 3‐4 : Isothermal expansion
• Heat addition from high temperature heat sink
• 3Q4 = area 3‐4‐d‐c on T‐s diagram
• Work is done by the working fluid (energy exchange to flywheel)
• 3W4 = area 3‐4‐a‐b on P‐v diagram
Process 4‐1 : Isochoric heat rejection
• Heat rejection (energy exchange to regenerator)
• 4Q1 = area 1‐4‐d‐a on T‐s diagram
• No work is done
• 4W1 = 0
2.2. Real Stirling Engine Cycle
The real Stirling engine cycle is represented in Figure 3 below. As can be seen there is work being done
during processes 2‐3 and 4‐1 unlike the prediction of zero work in the ideal cycle. One of the major
causes for inefficiency of the real Stirling cycle involves the regenerator. The addition of a regenerator
adds friction to the flow of the working gas. In order for the real cycle to approximate the Carnot cycle
the regenerator would have to reach the temperature of the high temperature thermal sink so that
TR=TH. A measure of the regenerator effectiveness is given by Equation 1, with the value of e=1 being
ideal.
3

10.
Figure 3 ‐ Real Stirling Cycle P‐v Diagram Approximation4
……………………………………………………………………………………… (1)
TH = Temperature of high thermal sink
TL = Temperature of low thermal sink
TR = Mass averaged gas temperature of regenerator leaving during heating
The Carnot efficiency is denoted by Equation 2 and the real cycle efficiency with regenerator is denoted
by Equation 3. Though regeneration is not required for a Stirling cycle, its inclusion can help improve
the efficiency if applied properly. Note how the regenerator efficiency does not tend to zero as the
regenerator effectiveness tends to zero.
1 ……………………………………….………….………….……………… (2)
⁄ ⁄ ⁄ ⁄
……………………………………… (3)
………………………………………………………………………... (4)
4
Power from the Sun. (2008b). Power Cycles for Electricity Generation. Accessed on October 12th, 2008 from
http://www.powerfromthesun.net/chapter12 /Chapter12new.htm#12.3.1%20%20%20%20%20Stirling%20Engines
4

11. Another major cause for inefficiencies of the real Stirling cycle engine is that not all of the working gas
participates in the cycle, i.e. dead volume. The dead volume involves the volume that does not
participate in the swept volume of the piston stroke. Martini (2004) states that the relationship
between the percentage of dead volume in the system to the decrease in work done per cycle is linear.
Therefore, if the engine has 20% dead volume then the power output would be 80% of the power that
would be produced with zero dead volume. In actuality, dead space will always be present because the
addition of internal heat exchangers, clearances, transfer tubes, and regenerators are required to
enhance the heat exchange of the real system.
Though the ideal Stirling cycle can be analyzed using known thermodynamic principles, the analysis
exists as an approximation of the real Stirling engine. Team 4 took this into consideration in the final
design of the Stirling engine so that certain design parameters such as the stroke length, temperature
differential, and flywheel mass could be altered during the testing phase to optimize the Stirling engine.
5

12. 3. DESIGN REQUIREMENTS
The following design requirements of Table 2 summarize the scope of the project, the final goals, and
objectives team 04 intended to achieve.
Table 2 : Design Requirements
Design & Operational Elements
• Must be able to operate using a solar heat source.
• Must be able to operate using a compact heat source that is safe for indoor use.
• Must be able to operate unassisted after starting for a minimum of 5 minutes (except for a
controlling heat source).
• Must be built to a standard which delivers a minimum service life expectancy of 5 years, if
properly maintained.
Size, Weight and Complexity
• Total engine size and weight to be such that safe and easy transportation is possible by 1
person.
• Must be mounted on a compact support structure for stability and safety.
• Will be designed for ease of maintenance and assembly.
Aesthetics & Safety
• High temperature regions must be clearly indicated.
• Engine cylinder must be equipped with a removable fitting for piston inspection and pressure
release.
Documentation
• Supporting documentation and user instructions to be provided for later usage within the
Mechanical Engineering department of Dalhousie University.
Cost & Materials
• Pending the usage of machining time and salvaged components, the prototype is estimated to
cost less than $3500.
• Construction materials for the support frame and engine will consist mainly of steel or
aluminum, depending on cost, availability, and component purpose.
• Precision components such as pistons, piston rings, and bearings may be purchased off the shelf
or salvaged.
6

13. 4. DESIGN SELECTION
In order to ensure the best design was chosen the design selection process was evaluated with respect
to 8 design criteria. Options were brainstormed and researched within each category to weight each
design selection based on a scale of importance. Weighted design selection charts were assembled with
all important considerations to determine the best choice. The categories are: Power output, friction
losses, simplicity, thermal isolation, available literature, temperature differential, efficiency, and visual
aesthetics. These categories are weighted from most important (x5) to least important (x1) which acts
as a multiplier. Table 3 shows the design selection matrix.
Table 3 : Design Selection Matrix
Each design concept is rated from best (x5) to worst (x1) with respect to the design criteria. Team 04
prioritized these criterions with power generation and visual aesthetics for classroom demonstration as
the most important. The other criterions were chosen based on clear differences between the design
concepts and necessary design components. The major issues to overcome when building a Stirling
engine are friction losses, maintaining a high temperature differential and thermal isolation. Each
criterion was weighted based on how easy the issue is to overcome. The available literature for each
concept was rated least important because it has little to do with design. Any available literature may
however, aid in thermodynamic calculations for the chosen concept. From Table 3 the team concluded
that the Inline Alpha Stirling Engine was the best design concept for this project.
7

14. 4.1. Rotary Stirling Engine
Figure 4 displays the Rotary Stirling Engine in its four main positions. It is clear that the rotary design has
few moving parts and therefore has the least amount of losses due to friction. As shown in the design
selection matrix, the Rotary Stirling Engine performs poorly in the categories of: power output, thermal
isolation, available literature, temperature differential and efficiency. This poor performance ultimately
caused the rotary concept to fail the team’s selection process.
Figure 4 ‐ Rotary Stirling Engine5
a) The air is in the cold lower portion, contracting, and drawing the piston upwards.
b) The inertia of the flywheel continues rotation in this neutral phase.
c) The air is in the hot upper portion, expanding, and pushing the piston downwards.
d) The inertia of the flywheel continues rotation in this neutral phase.
4.2. Gamma Stirling Engine
The Gamma Stirling Engine appears to be a popular design for working models. The main difference in
this model is the use of two cylindrical pistons as per Figure 5. The motion of the displacer piston in the
gamma concept is reciprocating as opposed to rotational in the rotary design. As outlined in the design
selection matrix, the gamma concept shows an increase in friction losses when compared to the rotary
design. This would be a result of an increase in moving parts and an increase in complexity of design.
Thermal isolation and maintaining a temperature differential become easier with the gamma model as
this design uses two isolated pistons.
5
Lewis, Jim. (2001). New Simplified Heat Engine. Modified from http://www.emachineshop.com
/engine/animation.htm
8

15. Figure 5 ‐ G
Gamma Stirling E
Engine
4.3. Alp
pha Stirling
g Engine ‐ 90° Arrang
gement
The 90° arrangement o of the Alpha SStirling Engine
e shown in Figure 6 featur
res two sealed d pistons with
h a
transfer tube and optio onal regeneraator between n the two cylin
nders. Whenn compared to o the rotary a
and
gamma co oncepts in thee selection m
matrix, the alpha arrangement is the mo ost efficient and produces the
most powwer. However r, due to the 9
90° orientatioon this concept has the po
otential to cre
eate more fricction.
Alignment of the shaft ts would be crrucial and anyy error would
d add to the s
system friction: ultimately
deciding wwhether or no ot the design succeeds.
Figure 6 ‐ Alpha Stir
rling Engine – 90
0° Arrangement
a) Expanssion ‐ Most of f the gas is in the hot cylinder and begin ns to expand driving both pistons inward.
Work i is output duriing the onset t of this proceess.
b) Transfeer ‐ Cold pisto
on is forced ddownward allo owing the heated gas to b be transfer to the cold cylin
nder.
c) Contraction ‐ Expan nded gas is in the cold cylin nder and cont tracts drawing both pistonns outward.
d) Transfeer ‐ The contrracted gas is s still located in
n the cold cylinder. Work is input into t
the system byy the
inertia
al energy of thhe flywheel w which carries t the crank throough 90°, transferring the gas back to tthe
hot cylinder, and co ompleting the e cycle.
9

16. 5. COMPONENT DESIGN, FABRICATION AND BUILD PROCESS
Following the design selection process the Inline Alpha Stirling Engine Arrangement shown in Figure 7
was chosen for the final design. This design excelled in the categories of power output, thermal
isolation, temperature differential and visual aesthetics.
Figure 7 ‐ Final Concept to Build Comparison
The design of our engine was based on ease of assembly and disassembly. Because of this, all
components are fastened together using either nuts and bolts or cap head machine screws. This was
beneficial for our team as it allowed for quick engine component modifications, such as size of stroke
length and piston rod length. The entire fabrication process took approximately one month. This was
due to the large number of parts and high level of precision required. The following sub‐sections will
outline the design methods of various components as well as discuss any modifications made to the
initial designs.
5.1. Frame
As depicted in Figure 8, the frame will be used to support the piston cylinders and flywheel rotating
assembly. The frame was constructed of ½” 6061 Aluminum Plate because it is light weight, durable and
easy to machine. The majority of the frame manufacturing was completed using a milling machine, with
the exception of parts that require a precision circular hole (i.e. flywheel supports and cylinder clamps).
The bearing seats in the supports for the flywheel were slightly changed during the fabrication process.
For a cleaner look, instead of having the bearing flush with the outside edge of the frame, the bearing
was pushed further into the stand and an internal retaining ring was used to hold it in place (Figure 8).
10

17.
Figure 8 ‐ Assembled Frame and New Bearing Seat
5.2. Cylinders and Cylinder Heads
To maximize the heat transfer between the cold cylinder and the surrounding water bath the team
designed a simple array of annular fins to increase the external surface area of the cylinder. Heat
transfer calculations for steel and brass, available in Appendix C, show an approximate 320‐400%
increase in heat transfer with the addition of a fin 15mm in length. Based on these calculations the
team selected brass as the cold cylinder material as it enabled a larger heat transfer when compared to
steel. Other benefits of choosing brass over steel are that it will not rust in the ice bath and it has
improved dry frictional characteristics with steel (i.e. brass is a self lubricating metal).
The team chose a large number of fins with a spacing 2.5 times the thickness to ensure maximum
surface area. Because the system involves free convection it was important to choose large fin spacing.
By increasing the water volume between the fins the result is effectively an increase in the engine
efficiency. A larger volume of water between fins will take longer to heat up, thus maintaining a higher
temperature differential for an extended period of time.
The original cylinder design was a one piece cylinder and cylinder head. After some brainstorming and
discussions with our technician, our team decided it was best to construct the cylinder and cylinder head
in two pieces. This would allow for a more precise finish on the inside bore of the cylinders as well as
allow for easy assembly and troubleshooting if required. The manufacturing process was carried out
using a lathe. The finalized cylinders can be seen in Figure 9.
11

18.
Figure 9 ‐ Hot and Cold Cylinders and Cylinder Heads
5.3. Pistons
To help reduce friction and increase durability, grooved pistons are used in our system. The grooves
around the piston serve as a pressure seal when the piston and cylinder are machined to low tolerances.
The piston was originally going to be constructed of cold rolled steel to ensure consistency in thermal
expansion for the hot cylinder assembly. However, our technician supplied us with a similar material
that was easier to machine and finish. This was considered to be important due to the high tolerances
between the piston and cylinder walls. The better the surface finish the lower the friction generated.
The brass‐on‐steel interaction between the cold cylinder and piston will not pose an issue for thermal
expansion due to the low temperature gradient across the cold cylinder assembly as designed. The
interaction of brass and steel has low sliding frictional properties. Figure 10 displays the manufacturing
process of one of the pistons on the lathe as well as the finished product.
Figure 10 ‐ Piston Manufacturing and Final Product
5.4. Cranks
The design of the cranks had to incorporate two things, stroke length and the generation of a force
couple. The stroke length of our system is twice the distance from the center of rotation of the crank to
12

19. the location where the piston rod is connected. The stroke length could be easily lengthened or
shortened by changing the location of the hole accordingly.
In addition to stroke length, the other governing factor on the design of the crank was the need to
create a force couple that would cancel the linear translational force exerted on the system due to the
mass of the piston accelerating over its stroke length. As the piston reaches top and bottom dead
center in its stroke, the acceleration of the piston mass changing directions generates a sinusoidal force
on the system which has the potential to produce undesired and damaging vibrations. In order to cancel
this sinusoidal force caused by the piston mass, the crank is typically designed as an eccentric mass that
creates a balancing force. Figure 11 shows the initial design of the crank with the force couple indicated.
Here FC defines the balancing force of the eccentric crank and FP is the force due to the sinusoidal
motion of the piston.
½ Stroke Length
Fp Fc
Figure 11 ‐ Crank Design Showing Force Couple and Stroke Length
5.5. Flywheel and Collars
One of the major components of our design is the flywheel; a mechanical device designed to have a
significant rotational moment of inertia. Flywheels are used as rotational energy storage devices to
resist changes in rotational speed, thus aiding in maintaining smooth shaft rotation. In addition to this,
flywheels assist in driving the system over the duration of a cycle in which no net power is being
produced. During these periods the flywheel uses its stored energy to power the system through the
portion of the cycle where no power is produced. This feature is very important in the design of a
Stirling Engine because 25% of the cycle is flywheel dependant (both pistons are compressing the
working fluid); hence work is required by the system. Another 50% of the cycle does not involve any
work input or output; here the flywheel is required to provide the power necessary to smoothly
overcome any frictional forces in the system. This concept is presented in Figure 12. The states of the
cycle can be referenced as per Figure 2, Figure 3 and Figure 16. It was manufactured from steel using a
lathe.
13

20.
Figure 12 ‐ Stirling Cycle Flywheel Dependance
5.6. Piston Rods and Brass Connection Fittings
The fittings used to connect the piston rods to the pistons and cranks were made of brass due to its low
sliding frictional properties. During the manufacturing process a slight modification was made to one of
the brass fittings. The length of the piece closest to the piston was increased from 0.875” to 1.125” to
allow for more threads for the machine screw holding the piston in place. As a result the original piston
rod length was shortened by 0.250”. Team 04 made sure to make brass fitting design simple to inter‐
change piston rod length as it might be necessary during the testing phase of the project. The piston rod
and brass fitting setup can be seen in Figure 13.
Figure 13 ‐ Brass Fittings and Connecting Rods
5.7. Fresnel Spot Lens
For the solar aspect of our design project our team selected a Fresnel Spot Lens. A spot lens was chosen
for its concentrated beam shape and adjustability in focusing the incident solar radiation onto the hot
cylinder head. The Lens was purchased online and measures 27” x 36”. Our team constructed a frame
for the lens that allows for vertical adjustments as well as 360° rotation about the horizontal axis. This
14

21. was crucial as it allowed for tracking of the sun which is required to maintain spot temperature intensity.
Figure 14displays the Fresnel lens and frame.
Figure 14 ‐ Fresnel Lens and Frame
15

22. 6. DESIGN ANALYSIS AND REVISED CALCULATIONS
The following sections summarize the results of intensive engineering calculations concerned primarily
with the external heat transfer and thermodynamics of the working fluid. The raw data and calculations
can be found in the Appendices. The calculations have been re‐done to reflect the changes made to the
design in January and the final optimized configuration as of April 2009.
6.1. Schmidt Analysis of Ideal Isothermal Model
To determine the theoretical energy output an ideal isothermal analysis was performed on a simplified
model of the final engine design. The ideal isothermal analysis is incapable of predicting results for the
real cycle but can be used as a guide for design refinement purposes and to gauge the maximum
theoretical capabilities of the engine. The assumptions of an ideal isothermal model are defined below:
• Temperature of compression space/cold cylinder is at the lower limit of the cold sink
• Temperature of expansion space/hot cylinder is at the upper limit of the hot sink
• Heat exchangers are 100% effective
• Regenerator is 100% effective
• Volume of the working spaces vary sinusoidally with crank angle
Refer to Figure 15 for a representation of the isothermal alpha Stirling engine. The issue with the
isothermal analysis is that the heat transfer from the internal heat exchangers is zero because there is
no temperature differential to facilitate the flow of heat. The net heat exchange between the
compression and expansion spaces with the surroundings is equal to the net work. A more accurate
model would involve an adiabatic analysis; however, the solution is much more complicated and
requires an iterative solver. The solution to the adiabatic analysis is still an approximation and it could
not be justified for this design.
Figure 15 ‐ Simplified Isothermal Alpha Stirling Engine6
6
Urieli, Israel. (2002a). Isothermal Analysis of Alpha Stirling Engine. Accessed on November 1st, 2008 from
http://www.sesusa.org/DrIz/isothermal/isothermal.html
16

23. The ideal isothermal approximation of the Stirling cycle was used to generate a list of equations
describing the thermodynamic process. The Schmidt analysis was then used to solve these equations
for pressure, temperature and energy transfer by assuming that volume varies sinusoidally with the
crank angle as per Figure 16. The states of the cycle from 1‐4 are labeled as per Figure 2 and Figure 3 as
per Section 2. Please refer to Appendix B for the derivation and solution of the isothermal Schmidt
analysis.
1 2 3 4
Figure 16 ‐ Sinusoidal Volume Dependence on Crank Angle7
The analysis was performed using the original design specified in December, the refined design specified
by the final build report in January, and by using the test results and configuration of the optimized
design specified at the beginning of April. The results are presented in Table 4. The optimized design is
discussed in more detail in Section 9. In Section 9 the results from April will be used in a comparison of
theory to experimental results to determine the overall performance of the engine and the accuracy of
the Schmidt analysis.
Table 4 : Results of Schmidt Analysis of Ideal Isothermal Model
Results December January April
PMEAN (kPa) 299 306 177
PMAX (kPa) 715 747 201
PMIN (kPa) 125 125 156
QOUTPUT(J) ‐25.94 ‐17.07 ‐0.6338
QINPUT (J) 54.45 35.82 1.424
WNET (J) 28.51 18.75 0.7906
RPM assume 200 assume 200 measured 384
Power (W) 95 94 5
Efficiency (%) 52 52 56
7
Urieli, Israel. (2002b). Schmidt Analysis. Accessed on November 1st, 2008 from http://www.sesusa. org/DrIz/isothermal/Schmidt.html
17

24. 6.2. Fin Heat Transfer
To prove the effectiveness of adding external fins to the cold cylinder a heat transfer analysis was
carried out. Calculations were carried out for both steel and brass. The results are shown in Figure 17.
As a result of this analysis the initial fin length of 10mm was increased to 15mm as results show a
considerable increase in heat transfer. The fin length, in theory, should have been increased to 30mm
for maximum heat transfer in steel. When using brass for the cylinder material the heat transfer
continues to increase with fin length; this is due to its high thermal conductivity. However; due to frame
clearance issues and ease of machining a fin length of 15mm was chosen. With this fin length there is an
approximate 320% increase in heat transfer for steel and 400% for brass when compared to using no
fins. The calculation results for 10mm and 15mm are depicted in Appendix C.
Heat Transfer and Fin Efficiency with Varying Fin Length
120 1
0.9
100
0.8
0.7
80
Fin Efficiency
Heat Transfer (W)
Heat Transfer Without Fins
0.6
Steel Fins
60 Brass Fins 0.5
Steel Fin Efficiency
0.4
Brass Fin Efficiency
40
0.3
0.2
20
0.1
0 0
0 0.01 0.02 0.03 0.04 0.05
Fin Length (m)
Figure 17 ‐ Heat Transfer and Fin Efficiency
18

25. 7. INITIAL TESTING
Following the completion of engine component fabrication and assembly a preliminary test was
performed to evaluate engine performance. The test was performed with the engine configuration as
seen in Figure 18. The test consisted of applying a propylene heat source to the hot cylinder head with
no ice water cooling applied to the cold cylinder. The test was performed with all engine components
being unmodified except for the use of a rubber transfer tube as procurement of additional materials
was required.
Figure 18 ‐ Initial Testing Setup
7.1. Testing Observations
After applying the heat source and achieving temperatures of approximately 350˚C on the hot cylinder
head, operation of the engine was unsuccessful. In addition to unsatisfactory performance many
undesired conditions were witnessed. Following the initial testing failure, it became immediately
apparent that a number of issues would have to be addressed: 1) the flexible transfer tube with low
melting point would have to be replaced for a more permanent and robust connection, 2) as expected,
the metal to metal contact of the frame with the hot cylinder acted as a thermal short that would need
to be isolated/insulated to prevent large heat transfer losses to the frame and for safety reasons, and 3)
high bending stresses and deflections from the large compression ratios were significant and would have
to be reduced. Maximum system pressure was found to be 10 psi with single cylinder pressures capable
of reaching 20 psi. Figure 19 illustrates the damage to the rubber transfer tube as a result of heat
transfer to the brass push‐on connections.
19

26. Heat Damage
Figure 19 ‐ Heat Damage to Temporary Transfer Tube
7.2. Design Solutions
Initial testing provided useful information regarding engine performance and highlighted undesirable
conditions. Solutions to these issues were addressed during the design refinement process and include
reducing stroke length to decrease compression, insulating hot cylinder from the frame, replacing the
rubber transfer tube with a metal pipe, and promoting heat transfer to the working gas.
20

27. 8. DESIGN REFINEMENTS & PERFORMANCE IMPROVEMENTS
To address the problems identified during our initial testing, a rigorous design refinement was
undertaken. Because the art of designing a Stirling engine is not a hardened science, the design
refinement process is not as simple as selecting a new electric motor from a catalogue, or picking up a
new piece of hardware from a supplier. This meant that often several iterations were required in order
to see an improvement in performance. Many performance solutions were designed and tested in
sequence with increasing success. The following sub‐sections will discuss in detail the major design
refinements and performance improvements undertaken. It is in Section 9 that the iterative testing and
troubleshooting procedure is demonstrated along with the testing results.
8.1. Design Refinements
8.1.1. Frame Heat Dissipation
Following our initial application of heat to the engine, it was apparent that there was a significant
amount of heat being dissipated from the hot cylinder through the aluminum frame. This caused the
entire engine assembly to become hot to the touch and transferred significant amounts of heat to the
cylinder being cooled. This however was expected and a solution to the problem was readily available.
To prevent heat from transferring to the frame from the hot cylinder, an insulating layer of material was
required at their point of contact. In order to accommodate a layer of insulation between the cylinder
and the frame, modifications were required on the hot side of the cylinder clamps. 1/8“ was removed
from the cylinder clamps so that the hot cylinder floated freely. Two layers of Teflon wrap in addition to
Fiberglass paper insulation was then tightly wrapped around the hot cylinder to fill the 1/8” gap
between the cylinder and frame clamps, see Figure 20. After the insulation was secured and the clamps
adjusted, heat was again applied to the cylinder. A significant improvement was achieved with minimal
heat being transferred to the frame. With the cylinder head being upwards of 550°C, the region of the
frame in contact with the insulation would reach a maximum temperature of 65°C, safe enough to
touch. Figure 21 is a thermal image taken of the engine after being heated and illustrates the
temperature difference achieved between the cylinder head and the frame.
Figure 20 ‐ Hot Cylinder Insulation
21

28.
Figure 21 ‐ Thermal Image
8.1.2. Compression Reduction
It was evident from the initial test that the cylinder compression was too high for the scale of our
application. The pressures achieved in the cylinders were enough to cause significant vibration and
bending of the frame itself. High compression, however, is the main characteristic of the Alpha type
Stirling engine due to there being two sealed pistons and cylinders. Suitable compression ratios for
these types of engines are not well documented therefore an iterative design refinement was required
when trying to achieve a compression ratio that provided a significant performance increase.
To reduce the compression, two options were available. One was to decrease the stroke length which
would reduce the volume of air being compressed; the second was to reduce the connecting rod length
which would increase the minimum volume of the system there by decreasing the amount of
compression.
The stroke length was first reduced by ¾” by drilling new holes in the cranks. This significantly reduced
the compression and provided the first noteworthy performance gains. After testing this stroke length
with various sizes of connecting rods, the stroke was again reduced by 5/8”, see Figure 22. After
machining several new sizes of connecting rods, it was possible to significantly decrease the
compression of the system. The motor exhibited “signs of life” and would attempt to maintain itself in
operation.
22

29.
Figure 22 ‐ Stroke Length Reduction
8.1.3. Transfer Tube
The original transfer tube, which was only selected for initial testing, had a maximum temperature
rating that was much less than the application required. Heat quickly conducted through the brass
fitting on the cylinder head, elevating the temperature of the hose beyond its melting point. Sufficient
testing was unable to be performed until a suitable replacement transfer connection was found.
Several attempts were made to build a transfer tube using ½”copper pipe; however, soldering the joints
was not an option as most solder has a melting temperature of around 190°C which is below the
operating temperature of the hot cylinder. The brass fitting on the cylinder head had the potential to
melt the solder. An alternative to soldering the joints was the use of JB weld. This provided initial
success however sufficient temperatures caused the JB weld to crack, reducing the integrity of the
transfer tube, see Figure 23. Finally the use of threaded steel fittings provided an adequate solution that
withstood repeated tests without diminished results, see Figure 24.
Figure 23 ‐ Heat Damaged Transfer Tube
23

30.
Figure 24 ‐ Steel Transfer Tube
8.2. PERFORMANCE IMPROVEMENTS
Following several iterations of design refinements, many of the initial complications were overcome. In
an effort to improve the performance and efficiency of the engine, several engineering improvements
were made. Due to the extensive amount of time dedicated to design and the high quality of machining,
the engine had a high mechanical efficiency. Frictional losses were not a major factor limiting
performance; however, it was evident that improvements were required to increase the thermal
efficiency of the system.
8.2.1. Internal Fins
Early in the design process initial brainstorming began on an internal fin array that would increase heat
transfer to and from the working gas. This concept was not finalized before fabrication of the engine had
commenced and the idea was put on hold. After the initial testing provided insight into the thermal
efficiency of the engine, it was decided that internal fins might provide increased engine performance.
The internal fin array was to be seated against the cylinder head (both hot and cold) and in the direct
path of the gas flow to maximize heat transfer. The fins of an aluminum vehicle radiator provided an
ideal solution with relatively minimal fabrication required. A used radiator was salvaged from an auto
shop and a portion of the fin structure was removed. A circular pattern equal to the internal diameter of
the cylinders was then applied to the section of radiator where it was then cut with a band saw and
sanded smooth, see Figure 25. Aluminum sleeves were machined to encase the circular fins and to
protect the cylinder walls from scratching. In addition to providing protection, the aluminum sleeves
ensure an intimate contact with the cylinder walls for the efficient heat transfer. Figure 26 shows the
completed fins situated in the cylinder. The internal fins proved effective at assisting heat transfer and
provided a notable performance increase.
24

31.
Figure 25 ‐ Internal Fins Fabrication Process
Figure 26 ‐ Internal Fin Placement
8.2.2. Regenerator
In an effort to further increase the thermal efficiency of the engine the use of a regenerator was
selected. The initial engine design called for the use of a regenerator, however, our limited
understanding of regenerator design and the difficulties we had already incurred due to troublesome
transfer tubes, made us reluctant to begin further modifications.
The effect of including a regenerator in the transfer tube had already been examined during the design
selection process and operates much like an economizer situated in the gas flow between the hot and
cold cylinders. The regenerator design consisted of a section of ¾”steel pipe with flanges welded on
each end, see Figure 27. The flanged pipe was fitted between the cylinders and replaced the existing
transfer tube, see Figure 28. Steel wool was inserted in the pipe to provide a dense thermal mass to
exchange heat with the gas flow between cylinders. The large surface area of the steel wool provided
25

32. efficient heat transfer to strip heat from the gas as it flowed into the cold cylinder and return that heat
to the cooled gas as it traveled back into the hot cylinder. The addition of the regenerator provided a
significant performance increase and allowed for sustained operation of the engine.
Figure 27 ‐ Regenerator Components
Figure 28 ‐ Installed Regenerator with Ice Water Bath
26

33. 9. Testing and Troubleshooting
The following sections will describe the various tests performed on the solar collector and Stirling engine
from January to April 2009. Of critical importance is the iterative testing procedure developed by the
team to progressively and successfully optimize engine performance. This procedure was necessary as
there are many parameters that must be considered when designing a Stirling engine which are not
easily determined and often require fine tuning and modification of the constructed engine. This proved
to be a gamble as the team would only get one shot to build an engine, so the team designed an engine
that could be easily modified to meet a wide range of operating conditions and assembly configurations.
It is for these reasons that team 4 planned in advance an extended testing period.
9.1. Fresnel Lens Testing
The solar collector used in the following tests is referred to as a Fresnel lens. The lens is a light weight
acrylic film fixed in a rectangular wooden frame of dimensions 36”x 27” for a total area of 0.627 m2.
Using a daily average solar insolation of ~ 500 W/m2 for the month of March as cited by Environment
Canada, the maximum solar input using the lens would be ~314 W. This number is a conservative
estimate and realistic heat rates were determined indirectly through experimental measurements in
Test #2 below. Proper safety precautions were strictly practiced when using the lens: 1) weld goggles
were used by the individual when required for recording temperatures, 2) the lens was tilted away from
the sun when transporting and left unattended, 3) the focal point was tracked and located using a long
piece of wood, and 4) fire extinguishers and/or water was close at hand in case of fire.
9.1.1. Test #1 ‐ General Testing Results ‐ January 23rd (2 pm)
Following the construction of the wooden frame depicted in Figure 29 required to support the Fresnel
lens, team 4 conducted numerous qualitative and quantitative tests which involved simply holding a
variety of objects under the focal point of the lens. These tests helped serve as a basis for
understanding the effects of surface conditions and types of materials on heat generation rates and
temperature distributions.
Figure 29 ‐ Fresnel Lens and Infrared Thermometer Readings
27

34. Figure 30 depicts some of the various objects used to demonstrate the concentrating power of the
Fresnel lens. The first object is of an aluminum can that was held under the focal point for
approximately 10 seconds. Aluminum has a melting temperature of 660°C. Even though aluminum
has a high thermal conductivity and reflective surface the lens was still able to concentrate enough
energy fast enough to melt the aluminum. The amount of heating could be increased by insulating
the object from the environment and by painting the surface a dull black to minimize reflectivity.
The lens was also capable of creating molten asphalt. It was also demonstrated that the lens could
set fire to wood instantaneously.
Figure 30 ‐ Various Objects Held under the Fresnel Lens
9.1.2. Test #2‐ Temperature Measurements ‐ April 1st (12:40 to 1:10 pm)
The intent of this test was to determine the rate of heat absorption of a cylindrical steel object of
dimensions 3”D x 2‐1/8”L. The surface of the object was painted black and the sides and base were
insulated. A digital picture of the cylindrical steel object is shown in Figure 31. The ambient
temperature was 5°C on a clear, sunny day. The temperature was read at a depth of three quarters the
length using an infrared thermometer and recorded every 30 seconds for a total of 30 minutes. The
results are displayed in Figure 32 below. The temperature increases over time in an exponential
relationship as expected from theory (as the surface temperature increases the losses due to convection
and radiation increase so a leveling off occurs). Temperatures just above 310°C were achieved at the 30
minute mark.
The test was repeated with the propylene torch which is the heat source used during testing. The idea
here is to compare the relative heat transfer rates of the torch and lens. Figure 32 shows that it took
the torch half the time to reach temperatures above 310°C, so a very crude approximation suggests that
the torch has double the heating potential in comparison to the lens. Note that the performance of the
lens depends on the time of year, weather, time, and ambient air conditions, as well as other numerous
factors so it is possible to improve on this. It is very important to consider the testing results from
Section 9.4.5 which required the team to apply the torch only 40 to 50% of the operating time to sustain
peak RPM above 300. From these results, it is not difficult to say that it is very possible for the engine to
operate with the Fresnel lens alone under the right conditions.
28

35.
Figure 31 ‐ Cylindrical Steel Object
Test #4 ‐ Fresnel Lens Testing
350
300
250
Temperature (°C)
200
150
100
50
0
0 5 10 15 20 25 30
Time (min)
Fresnel Lens Heat Source Propylene Torch Heat Source
Figure 32 ‐ Temperature Increase of Steel Stock vs. Time
By using the temperature data of heating the steel specimen over the 30 minutes a rough
estimate of the average net solar heating was calculated as 147 W. Considering an ideal solar
input of 314 W, the overall solar collection efficiency is about 47% depending on ambient
conditions. Since the heating rates of the torch are about double that of the Fresnel lens, a
conservative estimate for the amount of net heat input from the torch would be about 300 W.
These power rates are not absolute, but resemble the difference between input and losses and
would equal to zero once the temperature reaches steady state.
29

36. 9.1.3. Test #3 ‐ Solar Energy Input to Gamma ‘Windmill’ Stirling Engine ‐ April 1st
April 1st would prove to be the last available day to test the solar collector before the project deadline
on April 9th due to lack of permitting weather conditions. Thus, the team was not able to demonstrate
that the engine could be powered solely by solar radiation. Though the test was never performed on
the optimized and very much capable engine, the results from the lens testing show that it is very
possible to get the engine running from solar radiation alone using the existing solar collector (if not it
would be a simple matter of buying a slightly bigger lens!).
In spite of the lack of solar testing results, the team was able to get the model gamma displacer type
Stirling engine to run from solar radiation alone as depicted in Figure 33. This test itself demonstrates
that it is possible to power a Stirling engine using the existing solar collector. It is important to note that
the team’s engine was capable of operating much faster, longer and more efficiently than the gamma
engine when using the same propylene torch as a heat source. The scalability of the team’s alpha
engine to the gamma engine are similar geometrically (swept volume, piston diameter, etc.) which also
helps to validate the potential for the engine to be solar powered.
Figure 33 ‐ Gamma 'Windmill' Stirling Engine
9.2. Iterative Testing and Troubleshooting Procedure
Testing of the Stirling engine began on February 25th and was unsuccessful. The initial assembly is
depicted in Figure 18 and reveals the incomplete frame. Since the initial failure, multiple engine
configurations have been tested by manipulating the various design parameters. In the beginning it was
extremely difficult to diagnose why the engine refused to run because there were many parameters to
consider, many of which were multi‐dependent on each other (i.e. depending on the configuration, a
change in one parameter might improve the engine performance in some respect but negatively
influence other parameters so as to unexpectedly render the engine in a worse condition or result in no
effect at all).
Through trial and error team 4 began to develop a greater understanding of these relationships which are summarized in
are summarized in Table 5 below. Following a complicated but intelligent iterative testing and troubleshooting process team
30

37. 4 was able to successfully optimize engine performance. The rest of this section will describe the various tests performed
and demonstrate the successive iteration process summarized in
31

38. Table 6.
As per Table 5, a list of potential actions is provided as a guide for making adjustments and for
troubleshooting suspected poor performance areas. A positive effect will be defined as an effect that
has the result of improving the overall efficiency or improving the conditions of operation from the
context of necessity, i.e. efficiency is reduced but the change is necessary for the engine to run as
intended. A negative effect will be defined as anything other than a positive effect. As indicated by the
results, each action has both negative and positive effects on engine performance which necessitates
the need for a structured iterative testing process.
Table 5 : Troubleshooting Parameters
ID Action Effects of Changing Parameter Result
• Compression ratio is decreased √
1 Reduce stroke
• Reduced potential for friction and binding (slower piston travel and less severe crank angle) √
length
• Reduced swept volume (reduced theoretical power output for engine size‐scale) X
2 Increase dead • Compression ratio is decreased (greatest effect) √
space • Reduces heat transfer and efficiency X
• Improve heat transfer between cylinder walls and working gas (air) by increasing surface area √
3 Internal Heat
• Increases dead space (see 2 – will be considered negative as dead space added is not an option) X
Exchangers
• Increases system flow friction X
4 No lubrication • Reduced friction compared to liquid lube (for hot cylinder oil is cooked, and cold cylinder oil thickens) √
(dry‐running) • The lack of lubrication reduces the pressure sealing ability of pistons X
5 Solid graphite • Excellent friction reduction (can resist high hot cylinder temperatures of maximum 550°C) √
lubrication • Suitable alternative to oil lubrication but still lacks high pressure sealing abilities X
6 Increase flywheel • Increases stored energy of the system (allows more consistent operation at high compression ratios) √
size • Longer rev‐up time (actual energy output is low, therefore slower acceleration) X
Metal transfer • Threaded NPT connections provide tighter pressure seals √
7
tube vs. Flexible • Metal can withstand the higher operational temperatures √
rubber • Undesirable heat transfer to cold cylinder is increased significantly X
• Improve efficiency √
Add or increase
8 • Reduce the heat transfer requirements from the thermal reservoirs to the working gas √
size of
• Increases system flow friction X
regenerator
• Increases dead space (see 2 – will be considered negative as dead space added is not an option) X
9 • Helium has a higher heat capacity (5x more than air) and thermal conductivity (6x more than air) √
Helium injection
• Helium has a lower density (7x less than air), for the same pressure this is negative X
10 Use higher • Increases heat transfer rates into the system √
heating value fuel • Can cause extreme localized temperatures (warping, hot spots, added friction etc.) X
11 Improve heat • Will help in heat transfer lag √
distribution • Could cause hot spots or heat unwanted areas as access to hot cylinder is limited at end and side X
12 Insulation of hot • Improves the performance by limiting heat transfer losses √
cylinder • Potential alignment issues due to non‐rigid clamping surfaces X
32

39. Table 6 : Successive Iterative Testing Process
Test Date/Configuration Results Action
Extreme compression ratios (possible solutions: 1, 2, 6)
• 20 psi single cylinder, 10 psi system pressure
February 25th – Failure to run • Significant frame bending of base ½” aluminum plate
• Large stroke length (2.5”) Transfer tube melting (possible solutions: 7)
#1 • Minimum cylinder dead space • Tube used was only for testing purposes until a more permanent fixture 12
• Flexible rubber transfer tube could be fabricated upon final results (tube length, diameter)
• Propane torch heat source Transfer of heat through clamps and frame (possible solutions: 12)
• Significant impact on performance and efficiency
• Safety hazard (must be addressed immediately)
Transfer of heat through clamps and frame (resolved)
March 9th – Failure to run • Max hot cylinder temperature of 260°C
• Addressed insulation of hot • Clamps are warm but safe to the touch
#2 2
cylinder by adding layer of • Should install ice water bath on cold cylinder
insulation between clamps Transfer tube melting (possible solutions: 7)
Extreme compression ratios (possible solutions: 1, 2, 6)
Reduction of compression ratio (possible solutions: 1, 2, 6)
March16th – Failure to run • Improvement: flywheel carries the engine through more cycles
#3 • Reduced rod length 1/4” • Reduction in frame flexure 1, 10
• Ice water bath installed Transfer tube melting (possible solutions: 7)
Potential heat transfer issue (possible solutions: 3, 8, 9, 10, 11)
Reduction of compression ratio (possible solutions: 1, 2, 6)
• Improvement: flywheel carries the engine through more cycles
• Reduction in frame flexure
March 17th – Failure to run
Transfer tube melting (possible solutions: 7)
#4 • Reduced stroke length (1.75”) 3, 4, 7
Potential heat transfer issue (possible solutions: 3, 8, 9, 10, 11)
• Acetylene torch heat source
• External heat good, suspect internal transfer to the gas is insufficient
Lubrication (possible solutions: 4, 5)
• Oil breaking down in hot cylinder
th
March 20 – Failure to run Compression ratio still too high (possible solutions: 1, 2, 6)
• Internal heat exchangers Transfer tube melting (resolved)
#5 • Metal transfer tube Potential heat transfer issue (possible solutions:, 8, 9, 10, 11) 1,10
• No lubrication in hot cylinder • Installed aluminum internal heat exchanger inserts made from radiator
• Back to propane heat source • Noticeable improvement hints at heat transfer issues from prior
Reduction of compression ratio (possible solutions: 2)
• Need to attempt maximum dead space configuration
March 23th – Failure to run
• At minimum stroke flywheel is sufficient for smooth cycle operation
#6 • Reduced stroke length (1.125”) 2, 4
• Minimum stroke, noticeable improvement in smoothness of rotations
• Propane to Propylene fuel source
Lubrication (possible solutions: 4, 5)
• Cold cylinder lubrication is cold and adds viscous friction
th Reduction of compression ratio (resolved)
March 25 – Failure to run
• Maximum dead space and stroke length
#7 • Reduced rod length to shortest Friction and binding of connections (possible solutions: 5) 8,11
• Maximum cylinder dead space
• Not significant, but power output is minimal
• No lubrication in both cylinders
Lack of energy transfer (possible solutions: 8, 9, 11)
th Lack of energy transfer (possible solutions: 8, 9)
March 26 – Failure to run
• External heat input and internal heat exchangers not sufficient
• Same configuration as before
#8 • Must change thermodynamic properties by lowering heat requirement 5, 8, 9
• Combined solar and torch heat
(regenerator) or changing gas (helium)
source
Friction and binding of connections (possible solutions: 5)
Throughout the iterative design process the team was able to manipulate the design parameters and
make gradual improvements and progress to the point that the engine needed only to be optimized to
operate continuously. In order to go through with optimization, it was necessary to gather more
detailed temperature readings of the entire system using a data acquisition system described below.
33

40. 9.3. Temperature Data Acquisition
Actual temperature measurement can be achieved with thermocouples. Depending on the application
different types of thermocouples can be used. Choosing the correct thermocouple requires looking at a
number of factors. The most important factors include thermocouple type and junction type.
Thermocouple type is important because it incorporates temperature ranges, accuracy, and cost.
Junction type is important when looking at probe thermocouples because this depends on the
atmosphere of the intended application, intended life span of the thermocouple, the process being
measured, and response time.
9.3.1. Thermocouples
Type K (CHROMEGA®‐ALOMEGA®) thermocouples were chosen based on a number of positive
attributes. The first was their high temperature differential capability of ‐270 to 1372°C. This was
positive because of the extreme temperatures of the alpha Stirling cycle. Also type K thermocouples are
reasonable priced, mechanically strong, and is resistant to chemical attack. Surface and working fluid
temperature measurements were desired for the system therefore surface and probe thermocouple
arrangements were used.
To measure the surface temperatures a type K surface thermocouple with self‐adhesive backing was
chosen. Figure 34is a picture of a new SA1‐K thermocouple. This is not a probe type thermocouple so
the junction type is always exposed directly to the applied surface. The wire is Teflon coated to protect
against heat damage.
Adhesive Backing
Surface
thermocouple wires
Figure 34 ‐ Surface Thermocouple
To measure the working fluid temperature a more complicated pressure tight thermocouple setup was
needed. A type K probe thermocouple with exposed junctions was chosen for this application. A probe
thermocouple was needed for this measurement because it would be located inside a closed system. To
34

41. keep system pressure a compression fitting was matched to the probe diameter and threaded into each
cylinder head. In an exposed junction the wires are welded together and the insulation is sealed against
penetration by liquid or gas. This type of thermocouple offers the least protection however was desired
for accurate ambient working fluid temperature and fast response time. Figure 35 shows a new
KMTSS-010E-6 Omega thermocouple and compression fitting setup.
Brass Compression Fitting
Exposed Junction
Figure 35 ‐ Probe Thermocouple Setup
9.3.2. Benchtop Digital Display
The department of Mechanical Engineering supplied a new digital display thermometer unit, Omega
MDSSi8, for testing. This Portable and Rugged Metal Benchtop Enclosure was perfect for testing. This
instrument allowed for easy thermocouple setup and the capability to monitor ten individual
thermocouples via a dial as seen in Figure 36. All exposed wires slide into screw down connections at
the back for the unit. Each wire terminal corresponds to the value on the dial at the front. The team
used junctions 5 through 10 for testing measurements.
Figure 36 ‐ Omega MDSSi8 Digital Thermometer
35

42. 9.3.3. Thermocouple arrangement
To accurately measure temperature distribution throughout the system, six thermocouples were
strategically positioned on the Stirling engine, according to Figure 37. Infrared images were also used to
see temperature distribution and are discussed in previous section. Thermocouples were placed on
multiple locations of interest: (1) Hot Cylinder Wall, (2) Hot Side Cylinder Clamp, (3) Hot Cylinder Head
Fluid, (4) Regenerator, (5) Cold Cylinder Head Fluid, and (6) Cold Cylinder Head. System fluid
temperatures were also needed for engineering calculations: (5) Cold Cylinder Head Fluid. The extreme
hot head surface had to be measured using an infrared thermometer with a maximum 500°C output.
The hot head was painted black with a flat matte finish to improve the infrared thermometer accuracy
which assumes an irradiance emissivity of 1.0 (blackbody radiation).
Figure 37 ‐ Thermocouple Setup
9.4. Stirling Engine Optimization
After attaining moderate success in preliminary testing and troubleshooting an effort was made to
record and monitor the conditions of operation to a greater detail so that further optimization could be
achieved. The following tests were conducted under controlled conditions to determine the
temperatures throughout the engine during static priming and dynamic operation.
Pressure gages of range 0 to 60 psig were used but did not generate usable results as the testable
engine configuration was of low compression ratio. Maximum pressures were not expected to exceed 1
psig, though pressures in excess of 20 psig have already been realized in high compression ratio testing
configurations, so leakage was not considered to be an issue.
36

43. 9.4.1. Test #1 ‐ March 30th, 2009
Testing using the thermocouple display began on March 30th and the initial setup is displayed in Figure
38. The configuration consisted of a stroke length of 1.125”, maximum dead space, no lubrication, and a
crude regenerator which was made by simply stuffing steel ribbon material into the existing transfer
tube. By using the thermal display the team was able to monitor the temperatures throughout the
system and safely run the engine at higher temperatures. In doing so the engine achieved a total
operating time of 30 seconds which was a huge improvement from before. The test results are
summarized in Table 7. The only noticeable differences between the static and operating conditions are
that the mean cold air temperature increases while the hot air temperature decreases but less
significantly. This is because the hot head where the temperature is being measured is being heated
directly while the major cooling in the cold cylinder occurs mostly deeper inside the cylinder where the
external fins project.
Figure 38 ‐ Optimization Test #1 Setup
Table 7 : Optimization Test#1 Results
Reading (°C) Static Priming Operating
Hot Air 453 450
Cold Air 14.5 51
Hot Head 446 480
Hot Cylinder 228 244.6
Cold Head 14.8 17.8
Transfer Tube 115 115.4
Clamp 53 56
37

44. 9.4.2. Test #2 ‐ April 1st, 2009
Following the moderate success of the previous test the team decided to design and install a ‘true’
regenerator with a larger capacity for steel ribbon to participate in heat exchange. The dead space was
also reduced to a minimum by swapping in longer rods. The installed regenerator can be seen in Figure
39. The testing was a success and the operating time was increased to approximately 60 seconds.
Figure 39 ‐ Optimization Test #2 Setup with Regenerator
The team took the following temperature readings using a sampling time of 60 seconds, where each of
the 6 temperature readings would be measured every 10 seconds. The total priming time (heating
under static conditions) was set for 30 minutes. In Figure 40 the hot air temperature is seen increasing
and decreasing. This was the result of the heat source being turned on and off to try and maintain the
hot air temperature around 400 to 450°C. The reason for doing this was because the cylinder head
heats up at a much higher rate than the side of the hot cylinder which was very pronounced. This
worried the team as this is an indication of heat transfer lag and could be detrimental to the design if
the heat required by the working gas to operate the Stirling cycle was greater than that being supplied.
The cold cylinder temperature readings are depicted in Figure 41 and are very closely related. The cold
air temperature only exceeds the cold head when the system is operating. The results from Figure 42
show that the clamps near the hot head only increase to a temperature of about 60 to 70°C which is safe
to the touch and indicate that the insulation is working. The temperature of the regenerator climbs to
about 120°C. The typical operating range recommended at this point would be when the hot air reaches
a temperature of about 500°C and the hot cylinder side at about 260°C. The next test attempts to
record the RPM and potential power output as well as prime the engine in a shorter period of time.
38

45. Test #2 ‐ Hot Cylinder Temperatures
600
500
Temperature (°C)
400
300
200
100
0
0 5 10 15 20 25 30 35
Time (min)
Hot Air Hot Cylinder Side
Figure 40 ‐ Optimization Test #2 Hot Cylinder Temperatures
Test #2 ‐ Cold Cylinder Temperatures
25
20
Temperature (°C)
15
10
5
0
0 5 10 15 20 25 30 35
Time (min)
Cold Air Cold Head Surface
Figure 41 ‐ Optimization Test #2 Cold Cylinder Temperatures
39

46. Test #2 ‐ Clamp and Regenerator Temperatures
140
120
100
Temperature (°C)
80
60
40
20
0
0 5 10 15 20 25 30 35
Time (min)
Clamp (Hot) Regenerator
Figure 42 ‐ Optimization Test #2 Clamp and Regenerator Temperatures
9.4.3. Test #3 ‐ Run A ‐ April 4th, 2009
For the third testing arrangement the team ran three separate Runs A, B, and C, and recorded the
results. Prior to testing, friction in the piston and cylinders was reduced by using graphite lubricant.
Also, the compression ratio was reduced further by increasing the dead space to a maximum. The
regenerator was also packed more densely with steel ribbon. Following the results from the prior test,
the engine was primed to about 260°C on the hot cylinder side before initializing the cycle around the 20
minute mark. The hot cylinder temperatures of Figure 43 appear smoother because the heat was
applied more consistently. The remaining results for the cold cylinder and regenerator and clamps of
Figure 44 and Figure 45 are consistent with the previous test.
The engine ran continuously for 11 minutes and 12 seconds , reaching a peak speed of 192 RPM. The
engine could have continued running but the team removed the heat source at 9 minutes and the
engine was able to run off stored energy for 2 minutes and 12 seconds.
The engine went through cycles of slowing down and then speeding back up. This could be explained by
the variability of friction as it does not require much friction loss to bring the engine to a halt, and subtle
changes in the alignment and bearing surfaces during operation can occur. It was observed that the
engine works best in a temperature range between 260°C to 300°C, which might imply that the hotter
temperatures affect the system negatively. It is unknown whether the high temperatures impose
constrictions on heat transfer or cause mechanical binding/friction.
40

47.
Test #3 ‐ Run A ‐ Hot Cylinder Temperatures
600
500
Temperature (°C)
400
300
200
100
0
0 5 10 15 20 25 30
Time (min)
Hot Air Hot Cylinder Side
Figure 43 ‐ Optimization Test #3 ‐ Run A ‐ Hot Cylinder Temperatures
Test #3 ‐ Run A ‐ Cold Cylinder Temperatures
20
18
16
Temperature (°C)
14
12
10
8
6
4
2
0
0 5 10 15 20 25 30
Time (min)
Cold Head Surface
Figure 44 ‐ Optimization Test #3 ‐ Run A ‐ Cold Cylinder Temperatures
41

48. Test #3 ‐ Run A ‐ Clamp and Regenerator
Temperatures
140
120
Temperature (°C)
100
80
60
40
20
0
0 5 10 15 20 25 30
Time (min)
Renenerator Clamp (Hot)
Figure 45 ‐ Optimization Test #3 ‐ Run A ‐ Clamp and Regen Temperatures
By replaying the video of the engine in slow motion following the initial energy input to the
flywheel a graph of RPM and Power vs. time was produced as per Figure 46. To determine the
RPM, the number of rotations in 5 seconds was taken starting from every 10 second interval
into the cycle to determine the 5 second forward difference average. From here a trend line
was fitted to the experimental results and the power was thus calculated. The flywheel and
cranks were treated as equivalent rotational disks of sizes 6.5”D x 1.25”T and 3”D x 0.5”T,
respectively. The translation of the pistons can be ignored because they do not gain energy as
they continuously decelerate and accelerate. The total mass moment of inertia was calculated
to be 0.01872 kgm2.
The average net power from start to peak RPM of 69 mW was calculated by finding the
difference in rotational kinetic energy and dividing by the time interval. The instantaneous net
power was found by taking the derivative of the kinetic energy equation and using the RPM
trend line. The maximum potential power output should a generator be connected would be
about 108 mW at about 130 RPM.
42

49. Test #3 - Run A - RPM and Power
200
180
160
Power (mW) and RPM
140
120
100
80
60
40
20
0
0 10 20 30 40 50
t (sec)
RPM Power Output
Figure 46 ‐ Optimization Test #3 ‐ Run A ‐ RPM and Power
9.4.4. Test #3 ‐ Run B ‐ April 4th, 2009
Following a similar process in Run ‘A’, the peak RPM of 312 was achieved at about 70 seconds
into the cycle. The average net power output was determined as 118 mW and the maximum
power potential was calculated as 162 mW at about 256 RPM. It is interesting to note the
difference in the power output and RPM between Runs ‘A’ and ‘B’, however, it was observed
that the engine experiences cyclic variations of both heat transfer and friction. The results are
displayed in Figure 47.
43

50. Test #3 - Run B - RPM and Power
350
300
Power (mW) and RPM
250
200
150
100
50
0
0 20 40 60 80
t (sec)
RPM Power Output
Figure 47 ‐ Optimization Test #3 ‐ Run B ‐ RPM and Power
9.4.5. Test #3 ‐ Run C ‐ April 4th, 2009
Video footage of the last run did not record the transient acceleration so a figure of the RPM and power
could not be reproduced. However, the fastest speeds were achieved in this run with a maximum RPM
of about 384. As suspected, towards the end of the video at about 4 minutes into the cycle, the sounds
of rubbing could be heard. This had been dealt with before and the team quickly identified the frictional
rubbing to be from the pin and piston rod connection in the hot cylinder. This connection was
lubricated with oil and once it was heated for prolonged periods the oil evaporated and an increase in
friction sufficient to slow the engine was realized. This was overcome by lubricating all bearing and
frictional surfaces with dry graphite lubrication.
44

51. 9.5. Repeatability and Comparison to Theory
The results of testing reveal that the operation and performance of the engine is repeatable. The
variations of friction and heat transfer make it difficult to get the engine to run consistently at
prescribed conditions, however, the engine can be primed and operated to run at the optimized
temperatures. The following Table 8 summarizes and compares the testing results to theoretical
predictions. The net power output predicted by theory does not consider the system friction losses.
The remaining values correlate better an expected to the gross approximations made by the isothermal
analysis. This is perhaps due to the fact that the actual heat requirement of the cycle is much lower
than the total stored energy. Also, the hot cylinder continued to heat up as the engine was operating
which indicates that there was sufficient heat transfer input to keep the engine running.
Table 8 : Theory and Testing Results
Parameter Theory ‐ April Test 3 ‐ A Test 3 ‐ B Test 3 ‐ C
Mean Pressure (psig) 5.17 < 1 < 1 < 1
RPM 384 192 312 384
Hot Temp (°C) 372 260‐500 280‐500 280‐500
Cold Temp (°C) 0 17 20 20
Net Power Output (mW) 5000 108 162 n/a
45

52. 10. BUDGET
Table 9 : Team 04 Budget
Part Name Description Vendor/Supplier Qty Subtotal To date
Piston/Cylinder $223.50 $199.00
Cold Cylinder Yellow Brass Round stock 4x7" Metals 'R' US 1 $182.00 $172.00
Hot Cylinder Steel Round stock 2.75x7" Metals 'R' US 1 $19.00 $13.90
Pistons Steel Round stock 2.25x2.5" Metals 'R' US 2 $15.00 $8.45
Connecting Rods Steel Round stock 0.25x7" Metals 'R' US 2 $4.00 $0.00
Rod Ends Brass Round stock 1x2" Metals 'R' US 2 $3.50 $4.65
Rotating Assembly $132.90 $41.57
Piston Counter weight Steel Plate 1x1x1/4" (ft.) Metals 'R' US 2 $18.90 $6.15
Shaft Steel Round stock 3/8x8" Metals 'R' US 1 $9.00 $0.00
Flywheel Steel Plate 1x1x3/4" (ft.) Metals 'R' US 2 $55.00 $29.90
Bearings Low Friction Ball Bearings Kinecor 2 $50.00 $5.52
Frame $467.80 $202.04
Frame Angle Aluminum Angle Stock 1x1x0.25"x2'L Metals 'R' US 1 $5.00 $2.70
Frame Base Aluminum Plate 6.5x12.25x0.5" Metals 'R' US 1 $43.80 $115.00
Frame Cylinder Aluminum Plate 6x6x0.5” Metals 'R' US 1 $30.00 ^included
Frame Shaft Aluminum Plate 7x13x0.5" Metals 'R' US 2 $135.00 ^included
Cylinder Clamps Aluminum Plate 12x10x0.5” Metals ’R’US 1 $80.00 ^included
Cylinder insulation Semi‐ridged high temp wool insulation McMaster Carr 1 $35.00 $47.74
Nuts and Bolts Various Various 1 $100.00 $36.60
Ice Water Bath Plexus Glass Sheet 1’x0.125”x4'L Home Depot 1 $39.00 $0.00
Measurement Tools $ 240.00 $284.50
Pressure Gauge Analog Gauge (1/4 MPT) Omega 1 $100.00 $50.00
Pressure Snubber PS‐4G Omega 2 $0.00 $32.00
Thermocouples SA1‐K (surface) Omega 5 $0.00 $75.00
Thermocouples KMTSS‐125E‐6 Omega 3 $140.00 $90.00
Compression Fittings BRLL‐18‐14, SSLK‐18‐14 Omega 3 $0.00 $37.50
Thermocouple DAQ Block Mechanical Engineering Lab Lab 1 $0.00 $0.00
Solar Power Collector $260.00 $117.73
Fresnel lens 47x35" Lens Ebay/Greenpower 1 $200.00 $102.16
Stand Wood 2x4"‐ 12ft. Home Depot 3 $60.00 $15.57
Miscellaneous $255.00 $124.18
Shipping Costs Various Various $100.00 $23.00
Stationary Cost Various $50.00 $38.19
Lubrication/ Consumables Various $75.00 $31.18
Transfer Tube Copper, Rubber Hose, Steel Tube Various $30.00 $31.81
Net Cost $1,579.20 $969.02
Tax 13% $205.90 $125.97
Total Cost $1,784.50 $1094.99
Supervisor Signature
_______________________________ $1,784.50 $1094.99
46

53. 11. CONCLUSION
11.1. Design Requirements Fulfillment
Following completion of testing all but one of the original design requirements were fulfilled. The engine
design allows for ease of assembly and provides the user with the ability to change operating
parameters including compression ratio and cylinder volume. The engine can sustain operation in excess
15 minutes which is ideal for demonstration purposes. Included with the engine are multiple
thermocouples to monitor internal and external temperatures across the system.
Lens testing prior to engine completion provided exceptional results with temperatures of a target steel
mass reaching 310°C. Sustained operation of the department owned gamma Stirling engine was
achieved with use of the Fresnel lens. However, final design refinements to our engine were not
completed at the time of solar testing. Following the completion of the design refinements and
performance improvements, weather conditions did not provided adequate solar exposure for testing.
Although weather conditions did not permit our group to operate our engine using the solar lens, we are
confident that we would achieve success given the extensive lens and engine testing that was
performed.
Table 10 provides a summary of the project design requirements and their fulfillment status.
Table 10 : Design Requirement Status
Design Requirement Status Comment
Must be able to operate on a Pending Weather uncooperative. Unable
solar heat source. to test with completed engine
during sunny day.
Must be able to operate using a Propane, Butane, Propylene
compact heat source for indoor
use.
Must be able to operate Engine capable of 15 min +
unassisted after starting for a demonstrations.
minimum of 5 minutes.
Must be built to a standard Excellent design and fabrication
which delivers a minimum quality. Routine maintenance
service life expectancy required.
of 5 years, if properly
maintained.
Safely transportable by 1 person. Engine weighs 35lb
Must be mounted on a compact Compact aluminum frame
support structure for stability provides stability and safety.
and safety.
47

54. Will be designed for ease of Engine can be disassembled and
maintenance and assembly. reassembled with ease.
High temperature regions must Hot cylinder head labeled and
be clearly indicated. painted.
Engine cylinder must be Fittings located in both cylinder
equipped with a removable heads and used for pressure
fitting. sensors and thermocouples.
Supporting documentation and Maintenance and operation
user instructions to be provided. manual provided.
Total cost to be less than $3500. Final cost of materials and
sensors: $1095
Frame material consists of steel Frame constructed from
and aluminum for low cost build. aluminum.
Precision materials including Bearings purchased.
bearings may be purchased.
11.2. Optimal System Operating Condition
Concluding the extensive testing period it was determined that optimal system conditions and engine
configurations existed. Maximum engine performance was experienced with an engine configuration
and temperature conditions summarized in Table 11.
Table 11 : Optimal Engine Conditions
Parameter Optimal Condition
Engine Configuration
Stroke Length 1.125” (minimum compression)
Connecting Rod Length Smallest (max volume)
Performance Improvements • Internal Fins
• Regenerator with durlon 8400 gaskets
Lubricant Graphite dry lubricant in both cylinders
Temperature Conditions
Hot Cylinder Head 500˚C
Hot Cylinder Body 260˚C
Temperature Priming Time ~20 Minutes
Cold Cylinder Head 17˚C
Cold Cylinder Body 0˚‐10˚C (Ice Water Bath)
48

55. 12. REFERENCES
Bergman, T. L., Dewitt, D. P., Incropera, F. P., & Lavine, A. S. (2007). Introduction to Heat Transfer. 5th ed.
John Wiley & Sons.
Borgnakke, C., Sonntag, R. E., & Wylen, G. V. (2003). Fundamentals of Thermodynamics. 6th ed. John
Wiley & Sons.
Hibbeler, R. C. (2005). Mechanics of Materials. 6th ed. Published by Pearson: Prentice Hall.
Martini, W. R. (2004). Stirling Engine Design Manual. Published by University PR of the Pacific.
Stirling Engine Society, SESUSA. (2006). Ideal Isothermal Analysis. Accessed on October 5th, 2008 from
http://www.sesusa.org/DrIz/isothermal/isothermal.html
49

56.
APPENDIX A – Gantt Chart
50

57.
51

58.
APPENDIX B – Ideal Isothermal Analysis
1

59. Ideal Isothermal Analysis – Schmidt Analysis
The foregoing analysis is referenced from SESUSA (2006).
Assumptions
• Temperature of compression space (cold cylinder) at lower limit of cold sink (TL=Tc=Tk = 0°C)
• Temperature of expansion space (hot cylinder) at upper limit of the hot sink (TH=Th=Te = 300°C)
• Heat exchangers are 100% effective
• Volume of working spaces varies sinusoidally
Equation Formulation
1. (Total Mass)
2. (Ideal Gas Law)
3. (Substitution 1 and 2)
4. (Effective Regenerator Temperature Assuming Linear Profile)
/
5. (Substituation 3 and 4)
/
Note: Equation 5 depicts pressure as a function of Vc and Ve (all other partial volumes are
constant)
6. (Cyclic Work Integral)
7. /
Note: From the ideal Stirling cycle we can determine intuitively the following heat transfer
results:
8. Qc = Wc=
9. Qe = We=
Qk = 0 (no temperature difference, no heat transfer)
Qh = 0 (no temperature difference, no heat transfer)
Qr = 0 (internal heat transfer does not result in a change in energy of the system)

60. The zero heat transfer in the heat exchanger sections is a paradox which results from the isothermal
assumption and is not realistic for real Stirling engine systems. A more appropriate analysis will employ
the ideal adiabatic assumption; however, the results from this analysis are still useful for qualitative
analysis and the solution is much simpler. This is a good starting point.
Solution
The following derivations use the equations formulated from basic isothermal theory above.
Volume
Note: for volume dependence on crank angle see the chart provided in reference section.
10. , , 1 θ /2
11. , , 1 cos α θ /2
12. , θ
13. , sin θ
Vcl =clearance volume
Vsw=swept (stroke) volume
=crank angle
=phase angle ( /2
Pressure
14.
, , / , ,
15.
16.
, ⁄
17. ⁄ ⁄
, ,
18. ⁄
, , , ,
19. 2
20. when 360° (n=0,1,2…)
21. when 180° 1,3,5 …
3

61. 22.
√
Energy
,
23. Qc = Wc =
,
24. Qe = We =
Integrated solution:
25. , √1 1 where
26. , sin √1 1 where
Numerical Results
Figure 48 ‐ Schmidt Analysis Results for December Design
4

62.
Figure 49 ‐ Schmidt Analysis Results for January Revised Design
Figure 50 ‐ Schmidt Analysis Results Using Actual Results from April Optimizations
5

63.
APPENDIX C – Heat Transfer Calculations
6

68.
APPENDIX D – Engineering Drawings

69.
No. Part Name Material Qty Build Group
1 Frame ‐ Base Aluminum 1 Angus MacPherson
2 Frame ‐ Cylinder Support Aluminum 1 Angus MacPherson
3 Frame ‐ Shaft Support Aluminum 2 Angus MacPherson
4 Angle ‐ Cylinder Support Aluminum 2 Angus MacPherson
5 Angle ‐ Shaft Support Aluminum 2 Angus MacPherson
6 Clamp ‐ Cylinder Aluminum 4 Angus MacPherson
7 Regenerator Steel 1 Angus MacPherson
8 Cylinder ‐ Hot Steel 1 Angus MacPherson
9 Cylinder ‐ Cold Brass 1 Angus MacPherson
10 Piston Steel 2 Angus MacPherson
11 Connector ‐ Piston Brass 2 Angus MacPherson
12 Connector ‐ Rod Steel 2 Angus MacPherson
13 Crank/Counter Weight Steel 2 Angus MacPherson
14 Shaft Steel 1 Angus MacPherson
15 Flywheel Steel 1 Angus MacPherson
16 Bearings Steel 2 Buyout
‐ Fresnel Lens Acrylic 1 Buyout
‐ Frame ‐ Fresnel Lens Pine N/A Team 04
‐ Ice Water Bath ‐ Cold Cylinder Plexus‐glass N/A Team 04
‐ Insulation ‐ Hot Cylinder Mineral Wool Fiber N/A Buyout
‐ Fasteners Steel N/A Buyout