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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
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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
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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
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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
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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
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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.
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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
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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.
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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
5
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.
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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.
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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.
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.
Table 3 : Design Selection Matrix
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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
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10
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).
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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.
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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
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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.
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.
FcFp
½ Stroke Length
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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
15
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
16
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
17
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.
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
7 Urieli, Israel. (2002b). Schmidt Analysis. Accessed on November 1st, 2008 from http://www.sesusa. org/DrIz/isothermal/Schmidt.html
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
1 2 3 4
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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.
Figure 17 ‐ Heat Transfer and Fin Efficiency
0
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ransfer (W)
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Heat Transfer and Fin Efficiency with Varying Fin Length
Heat Transfer Without Fins
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Steel Fin Efficiency
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Fin Efficiency
19
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.
20
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.
Heat Damage
21
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
22
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.
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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
24
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.
25
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
26
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
27
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
28
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.
29
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.
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Test #4 ‐ Fresnel Lens Testing
Fresnel Lens Heat Source Propylene Torch Heat Source
Figure 31 ‐ Cylindrical Steel Object
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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
31
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
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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
1 Reduce stroke length
• Compression ratio is decreased • Reduced potential for friction and binding (slower piston travel and less severe crank angle) • Reduced swept volume (reduced theoretical power output for engine size‐scale)
√
√
X
2 Increase dead space
• Compression ratio is decreased (greatest effect) • Reduces heat transfer and efficiency
√
X
3 Internal Heat Exchangers
• Improve heat transfer between cylinder walls and working gas (air) by increasing surface area • Increases dead space (see 2 – will be considered negative as dead space added is not an option) • Increases system flow friction
√
X
X
4 No lubrication (dry‐running)
• Reduced friction compared to liquid lube (for hot cylinder oil is cooked, and cold cylinder oil thickens) • The lack of lubrication reduces the pressure sealing ability of pistons
√
X
5 Solid graphite lubrication
• Excellent friction reduction (can resist high hot cylinder temperatures of maximum 550°C) • Suitable alternative to oil lubrication but still lacks high pressure sealing abilities
√
X
6 Increase flywheel size
• Increases stored energy of the system (allows more consistent operation at high compression ratios) • Longer rev‐up time (actual energy output is low, therefore slower acceleration)
√
X
7 Metal transfer tube vs. Flexible rubber
• Threaded NPT connections provide tighter pressure seals • Metal can withstand the higher operational temperatures • Undesirable heat transfer to cold cylinder is increased significantly
√
√
X
8 Add or increase size of regenerator
• Improve efficiency • Reduce the heat transfer requirements from the thermal reservoirs to the working gas • Increases system flow friction • Increases dead space (see 2 – will be considered negative as dead space added is not an option)
√
√
X
X
9 Helium injection
• Helium has a higher heat capacity (5x more than air) and thermal conductivity (6x more than air) • Helium has a lower density (7x less than air), for the same pressure this is negative
√
X
10 Use higher heating value fuel
• Increases heat transfer rates into the system • Can cause extreme localized temperatures (warping, hot spots, added friction etc.)
√
X
11 Improve heat distribution
• Will help in heat transfer lag • Could cause hot spots or heat unwanted areas as access to hot cylinder is limited at end and side
√
X
12 Insulation of hot cylinder
• Improves the performance by limiting heat transfer losses • Potential alignment issues due to non‐rigid clamping surfaces
√
X
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Table 6 : Successive Iterative Testing Process Test Date/Configuration Results Action
#1
February 25th – Failure to run
• Large stroke length (2.5”) • Minimum cylinder dead space • Flexible rubber transfer tube • Propane torch heat source
Extreme compression ratios (possible solutions: 1, 2, 6)
• 20 psi single cylinder, 10 psi system pressure • Significant frame bending of base ½” aluminum plate Transfer tube melting (possible solutions: 7)
• Tube used was only for testing purposes until a more permanent fixture could be fabricated upon final results (tube length, diameter)
Transfer of heat through clamps and frame (possible solutions: 12)
• Significant impact on performance and efficiency • Safety hazard (must be addressed immediately)
12
#2
March 9th – Failure to run
• Addressed insulation of hot cylinder by adding layer of insulation between clamps
Transfer of heat through clamps and frame (resolved)
• Max hot cylinder temperature of 260°C • Clamps are warm but safe to the touch • Should install ice water bath on cold cylinder Transfer tube melting (possible solutions: 7) Extreme compression ratios (possible solutions: 1, 2, 6)
2
#3 March16th – Failure to run
• Reduced rod length 1/4” • Ice water bath installed
Reduction of compression ratio (possible solutions: 1, 2, 6)
• Improvement: flywheel carries the engine through more cycles • Reduction in frame flexure Transfer tube melting (possible solutions: 7) Potential heat transfer issue (possible solutions: 3, 8, 9, 10, 11)
1, 10
#4 March 17th – Failure to run
• Reduced stroke length (1.75”) • Acetylene torch heat source
Reduction of compression ratio (possible solutions: 1, 2, 6)
• Improvement: flywheel carries the engine through more cycles • Reduction in frame flexure Transfer tube melting (possible solutions: 7) Potential heat transfer issue (possible solutions: 3, 8, 9, 10, 11)
• External heat good, suspect internal transfer to the gas is insufficient Lubrication (possible solutions: 4, 5)
• Oil breaking down in hot cylinder
3, 4, 7
#5
March 20th– Failure to run
• Internal heat exchangers • Metal transfer tube • No lubrication in hot cylinder • Back to propane heat source
Compression ratio still too high (possible solutions: 1, 2, 6) Transfer tube melting (resolved) Potential heat transfer issue (possible solutions:, 8, 9, 10, 11)
• Installed aluminum internal heat exchanger inserts made from radiator • Noticeable improvement hints at heat transfer issues from prior
1,10
#6 March 23th – Failure to run
• Reduced stroke length (1.125”) • Propane to Propylene fuel source
Reduction of compression ratio (possible solutions: 2)
• Need to attempt maximum dead space configuration • At minimum stroke flywheel is sufficient for smooth cycle operation • Minimum stroke, noticeable improvement in smoothness of rotations Lubrication (possible solutions: 4, 5)
• Cold cylinder lubrication is cold and adds viscous friction
2, 4
#7
March 25th – Failure to run
• Reduced rod length to shortest • Maximum cylinder dead space • No lubrication in both cylinders
Reduction of compression ratio (resolved)
• Maximum dead space and stroke length Friction and binding of connections (possible solutions: 5)
• Not significant, but power output is minimal Lack of energy transfer (possible solutions: 8, 9, 11)
8,11
#8
March 26th – Failure to run
• Same configuration as before • Combined solar and torch heat
source
Lack of energy transfer (possible solutions: 8, 9)
• External heat input and internal heat exchangers not sufficient • Must change thermodynamic properties by lowering heat requirement
(regenerator) or changing gas (helium) Friction and binding of connections (possible solutions: 5)
5, 8, 9
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.
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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.
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
Adhesive Backing
Surface thermocouple wires
35
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.
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
Brass Compression Fitting
Exposed Junction
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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.
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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
38
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.
39
Figure 40 ‐ Optimization Test #2 Hot Cylinder Temperatures
Figure 41 ‐ Optimization Test #2 Cold Cylinder Temperatures
0
100
200
300
400
500
600
0 5 10 15 20 25 30 35
Tempe
rature (°C)
Time (min)
Test #2 ‐ Hot Cylinder Temperatures
Hot Air Hot Cylinder Side
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10
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25
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rature (°C)
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Test #2 ‐ Cold Cylinder Temperatures
Cold Air Cold Head Surface
40
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.
0
20
40
60
80
100
120
140
0 5 10 15 20 25 30 35
Tempe
rature (°C)
Time (min)
Test #2 ‐ Clamp and Regenerator Temperatures
Clamp (Hot) Regenerator
41
Figure 43 ‐ Optimization Test #3 ‐ Run A ‐ Hot Cylinder Temperatures
Figure 44 ‐ Optimization Test #3 ‐ Run A ‐ Cold Cylinder Temperatures
0
100
200
300
400
500
600
0 5 10 15 20 25 30
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rature (°C)
Time (min)
Test #3 ‐ Run A ‐ Hot Cylinder Temperatures
Hot Air Hot Cylinder Side
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6
8
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12
14
16
18
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rature (°C)
Time (min)
Test #3 ‐ Run A ‐ Cold Cylinder Temperatures
Cold Head Surface
42
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.
0
20
40
60
80
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120
140
0 5 10 15 20 25 30
Tempe
rature (°C)
Time (min)
Test #3 ‐ Run A ‐ Clamp and Regenerator Temperatures
Renenerator Clamp (Hot)
43
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.
020406080
100120140160180200
0 10 20 30 40 50
Pow
er (m
W) a
nd R
PM
t (sec)
Test #3 - Run A - RPM and Power
RPM Power Output
44
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.
0
50
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0 20 40 60 80
Pow
er (m
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nd R
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Test #3 - Run B - RPM and Power
RPM Power Output
45
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
46
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
47
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 solar heat source.
Pending Weather uncooperative. Unable to test with completed engine during sunny day.
Must be able to operate using a compact heat source for indoor use.
Propane, Butane, Propylene
Must be able to operate unassisted after starting for a minimum of 5 minutes.
Engine capable of 15 min + demonstrations.
Must be built to a standard which delivers a minimum service life expectancy of 5 years, if properly maintained.
Excellent design and fabrication quality. Routine maintenance required.
Safely transportable by 1 person. Engine weighs 35lb
Must be mounted on a compact support structure for stability and safety.
Compact aluminum frame provides stability and safety.
48
Will be designed for ease of maintenance and assembly.
Engine can be disassembled and reassembled with ease.
High temperature regions must be clearly indicated. Hot cylinder head labeled and
painted. Engine cylinder must be equipped with a removable fitting.
Fittings located in both cylinder heads and used for pressure sensors and thermocouples.
Supporting documentation and user instructions to be provided. Maintenance and operation
manual provided. Total cost to be less than $3500. Final cost of materials and
sensors: $1095 Frame material consists of steel and aluminum for low cost build. Frame constructed from
aluminum. Precision materials including bearings may be purchased. Bearings 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)
49
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
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APPENDIX A – Gantt Chart
51
1
APPENDIX B – Ideal Isothermal Analysis
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)
3
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 …
4
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
5
Figure 49 ‐ Schmidt Analysis Results for January Revised Design
Figure 50 ‐ Schmidt Analysis Results Using Actual Results from April Optimizations
6
APPENDIX C – Heat Transfer Calculations
APPENDIX D – Engineering Drawings
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