Optimization of Stirling Engine Power Output Through Variation of Choke Point Diameter and Expansion Space Volume

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1 Optimization of Stirling Engine Power Output Through Variation of Choke Point Diameter and Expansion Space Volume Anna Brill Massachusetts Academy of Math and Science Abstract Fixed choke points of different diameters have been tested in a Stirling engine. The resultant power output was measured and the diameter which produces the most power was determined. Additionally, for each choke point diameter the optimum volume of the expansion space was determined. Adapting a quarter turn ball valve to adjust the choke point while the engine was running was deemed improbable because changing the size of the passageway also changes the direction of the air flow, preventing the engine from running. It was determined that the optimal choke point diameter was cm and the optimal expansion space volume was ml. Introduction A Stirling engine is an external combustion engine based on the Stirling Cycle. Developed first in 1816 by Robert Stirling, this engine produces power from differences in temperature. The working fluid inside the engine, typically air, hydrogen or helium, is heated on one end and cooled on the other, consequently causing the gas to expand and compress, respectively. In addition, the expansion and compression of the working fluid moves two pistons within the engine cylinder which in turn are, depending on the configuration, coupled in some manner with a drive mechanism to produce a net power output ( Energy Conversion 2010). For nearly two hundred years Stirling engines have been constantly improved upon with regards to efficiency. Gas combustion engines far outrun Stirling engines because they are inexpensive, but lately, with rising fossil fuel prices, Stirling engines have come back into the picture as a green, inexpensive alternative to the gas combustion engine. Stirling engines can achieve efficiencies of 65% to 75% that of the Carnot efficiency ( Stirling Engines, 2010). However, efficiency can be easily lost. Good heat transfer devices are crucial to achieving any kind of useful power output. Without the proper material, heat transfers can be ineffective and as a result not create a large enough temperature difference for the engine to have a net power output. Too much focus in research has been on regenerators and pistons while the heat transfers have been neglected. Stirling engines lack a throttling method inherently built into the engine. One method of changing power output is to change the diameter of the choke point of the engine, which is the point at which the hot air flows from the heat transfer to the engine cylinder. Choke points are often specifically designed to work optimally at one setting. A choke point that can be varied is advantageous because power output can be altered on the fly. The goal of this project is to develop a simple variable choke point for use in a small Stirling engine. 1

2 Definitions and Terminology A great amount of literature on the subject of Stirling engines exists, but no standard terminology does. Most of the literature was published sporadically over the past 200 years and there exists no standardization or clarification of terminology. Originally, types of Stirling engines were classified into three groups according to the Kirkley-Walker classification system: Alpha, Beta, and Gamma. Now these terms only describe the cylinder couplings of a Stirling engine. Cylinder coupling identifies the way in which the displacer piston and the power piston are connected, with respect to the connection of the variable volume working spaces. These are the spaces inside the engine cylinder where the working fluid is heated and cooled, respectively (Sandfort, 1962). An Alpha arrangement uses two separate cylinders that each has a sealed piston, either the displacer or the power piston. Power output is produced by the separate motion of the individual pistons. The term Beta covers the group of Stirling engines that use a single cylinder arrangement where the displacer and power piston are in tandem and power is produced by the action of the pistons together. In simple engines the piston and the displacer can often be just one piston. A Gamma arrangement is more or less a hybrid of the Alpha and Beta arrangements. Gamma engines have two separate cylinders like the Alpha, but power output is produced in the same manner as in Beta engines (Urieli, 2010). Figure 1. Three types of Stirling engines are: Alpha Twin Piston, Beta Piston-Displacer, and Gamma Piston-Displacer (Hooper & Reader, 1983). Lately this type of classification has become insufficient because the categorization does not identify the mode of operation, the form of crank-drive, or the power take-off mechanism of a Stirling engine. In order to classify Stirling engines correctly, the mode of operation, the form of cylinder coupling and the form of piston coupling should be identified. The mode of operation of an engine denotes how the components of a Stirling engine work together. There are six terms used to describe the mode of operation: double-acting, singleacting, single phase, multiphase, resonant, and non-resonant. A double-acting or differential Stirling engine has multiple cylinders that contain two pistons, the power piston and the displacer, whereas a single-acting Stirling engine has cylinders that separately house the power piston and the displacer. In a single-acting Stirling engine the multiple cylinders have to work 2

3 together in order to produce a net power output, and so a single-acting engine must have at least two cylinders. Single-phase and multiphase refer to the state of the working fluid inside a Stirling engine. The working fluid in a single-phase engine stays at a constant pressure while the working fluid in a multiphase engine varies. The terms resonant and non-resonant refer to the properties of the cylinders themselves and how they behave under the stress of a working Stirling engine. Piston coupling is very important in Stirling engines. There are three basic forms with many further subdivisions. A rigidly coupled Stirling engine uses a solid mechanical linkage that connects the reciprocating elements to each other and the power take-off mechanism. Typical types of rigid coupling include: slider-crank, rhombic drive, swashplate, Scotch Yoke, crankrocker, and Ross rocker. In gas coupled machines the pistons are coupled by gas dynamic effects rather than solid mechanical linkages. A few examples of this type of coupling are: free-piston, free-displacer, and free-cylinder. Liquid coupled Stirling engines use liquid to connect the pistons. There are at least three ways Stirling engines can be liquid coupled: jet-stream, rocking beam, and pressure feedback. The classification of liquid coupling can also be used to describe hybrid Stirling engines that have the power piston rigidly coupled with the output shaft but the displacer gas coupled to the power piston (Hooper & Reader, 1983). Stirling Engine Function and Design A Stirling Engine is a heat engine that operates on a closed regenerative cycle. Energy transfer occurs through the cylinder walls of the heat exchanger. The modern Stirling engine is based on the hot-air engine invented by Robert Stirling in These engines cool the working fluid and compress it, heat the fluid, and then expand it in the basic heat engine cycle. What makes a Stirling Engine different is that heat energy is transferred into and out of the engine through the cylinder walls or heat exchanger. Moreover, the gas stays permanently inside. In order for a Stirling engine to run, a necessary temperature difference must occur between the hot end and the cold end. To obtain this, the engine is divided into a cold and hot space between which the fluid can be moved by pistons. The volume variations that occur when the working fluid is moved by the pistons must be out of phase with each other if power is to be produced. Because the heating (expansion) process occurs at a greater working pressure than the cooling (compression) process, a net work output is produced. A displacer is a piston that just fits inside the working chamber with a small distance, the annulus, between it and the walls of the chamber that allows the working fluid to pass through. The displacer moves the working fluid between the hot space and the cold space, and so the fluid is alternatively heated and cooled, and work can be produced. Because the power piston and the displacer also move out of phase with each other, the Stirling engine requires an unconventional drive system. Stirling engines lose efficiency due to large differences in the temperature of the working fluid and the heating and cooling spaces. As the fluid passes around the displacer constant heat is being added, and the fluid reaches the cold space at a higher temperature than necessary. This occurs again in reverse when the fluid passes around the displacer on the way back, arriving at the hot space colder than necessary. A regenerator, or economizer as Robert Stirling called it, was developed to increase the efficiency of a Stirling engine. The design was originally a mass of steel wire located in the annulus that absorbed excess energy as the working fluid passed through it. A regenerator is essentially a pre-cooler, reducing the thermal load on the main 3

4 cooler, as well as a pre-heater, reducing the energy required by the main heater to heat the working fluid. Figure 2. A regenerator in the annulus of simple Beta configuration Stirling engine (Hooper & Reader, 1983). Philips developed a more efficient Stirling engine that eliminates the problem of rapid energy transfers. Instead of placing the regenerator directly in the annulus, Philips researchers made use of tubular heat exchangers seen in Figure 3 (Hargreaves, 1991). Figure 3. The complete cycle of a Beta Stirling engine with tubular regenerators (Hooper & Reader, 1983). Regenerators can improve the performance of a Stirling Engine by alternatively storing and returning heat energy so that the heat input can be kept to a minimum while still producing a useful power output. As the working fluid flows between the ends of the engine, it passes through a choke point, or a narrow hole. The choke point allows for regulation of the speed and amount of working fluid that passes through the engine cylinder. 4

5 Engine Efficiency The efficiency of a Stirling engine is dependent on several different parameters. They can achieve efficiencies of 65%-70% of the Carnot efficiency. However, the engine efficiency is reduced up to 0.5% for each degree rise in coolant temperature. Dead space in a Stirling engine, which is required to accommodate the necessary heat exchangers, accounts for up to 50% of the total internal gas volume of the engine. Depending on the location of the dead space it can have differing effects on the efficiency of the engine. Altering the location can also provide a means to control the power output. The diameter of the choke point, which regulates airflow from the expansion space to the main engine cylinder, also controls the power output. Torbjorn Bergstrom, a professor at Worcester Polytechnic Institute, noted that in professional applications, the choke point is often altered as a means of throttling the engine (personal communication). Efficiency is also dependent on the speed at which the engine is running. As the speed is increased, aerodynamic drag becomes a predominant factor because it is proportional to the square of the speed. To reduce these losses, light working fluids, such as helium and hydrogen, are used. However, these gasses are difficult to contain, especially hydrogen due to its ability to diffuse through solid material. Therefore, Stirling engines that use hydrogen or helium for their working fluid are often expensive and bulky. Stirling engines can be very quiet depending on their construction. Because they have no exhaust valves, they are significantly quieter than internal combustion engines. However, free piston Stirling engines can potentially be very noisy, depending on their operational mode. And these engines can get noisy due to the timing gears and combustion blower, but they are still relatively quiet compared to internal combustion engines. In addition, Stirling engines can utilize energy sources that do not pollute the atmosphere. Even when fossil fuels are used to power Stirling engines, the inherent steady flow combustion process reduces the amount of pollutants released (Walker, 1980). The fraction of cyclic energy rejected by the cooler in a Stirling engine is between 60% and 250% more than a conventional reciprocating engine. As a result, large radiators are needed to handle this large thermal loading. The theory behind a Stirling engine requires the heat transfer process to occur reversibly. For this to occur, several conditions must be met: 1. Reversible processes can only occur when the process is at all times in thermodynamic equilibrium. This means that the regenerator system needs to be quasi-static (passing through a series of equilibrium states) during the flow periods. However, this cannot happen in practice because the process needs to occur at an infinitely slow pace. Stirling engines often have high shaft speeds and thus have extremely high flow rates. Because this requirement can never be satisfied, the remaining requirements must be satisfied as well as possible. 2. Because the amount of excess energy given up by the working fluid as well as the rate of rejection are both extremely high, the bulk heat transfer must be infinite in order to balance the system. Yet again, this is not practically obtainable in the real world. Therefore, Stirling engine must obtain the highest bulk heat transfer possible within design constraints. 3. The heat transfer area (surface area) must be infinite in order to enable the ideal conditions under which Stirling engines operate optimally. Clearly this is not physically possible, and so certain steps must be taken to make the heat transfer area as large as possible within design 5

6 constraints. Typical practical solutions include the use of wires or small particles to maximize the surface area of a regenerator. 4. The heat capacity of the regenerator must be zero or infinite. To ensure this, the ratio of the heat capacities of the working fluid to that of the regenerator material must be kept to a minimum. Additionally there should be no axial heat conduction and there should be maximum conduction perpendicular to the flow. As evident from the above requirements, a practical Stirling engine is very different from an idealized one. The working fluid properties of density, velocity, viscosity, and pressure will change within the engine, the heat transfer areas will not be infinite, there will be axial conduction, and the conduction perpendicular to the flow will be imperfect, and so on. Practical Stirling engine designers must therefore strive to fulfill the above requirements to the best of their ability. Variations in Stirling Engines Drive mechanisms pose a difficult problem for Stirling engines because discontinuous motion is required to achieve the volumetric changes that result in a net power output. There are four main drive mechanisms for Stirling engines: crank-rocker, rhombic drive, swashplate, and slider-crank. Crank-rocker was the original drive mechanism in which a rocker connects to a piston and displacer through two arms and the piston is driven off the crankshaft (Figure 4). Figure 4. A crank-rocker drive mechanism in a Stirling engine (Hooper & Reader, 1983). This set up is useful only in small engines because the crankcase has to be pressurized, and there is no way to dynamically balance a single cylinder engine. Because larger Stirling engines were needed, Phillips developed the rhombic drive in the 1950s (Hargreaves, 1991). This drive mechanism is dynamically balanced and the crankcase does not need to be pressurized. However, it has the disadvantage of being mechanically complicated. The swashplate configuration is mainly used where space is tight. This drive mechanism is dynamically balanced at a fixed swashplate angle, and the cylinders are easily sealed off so the entire crankcase does not need to be pressurized. The swashplate also adds the function of varying power output by changing the angle of the swashplate, but the engine is only dynamically balanced at one angle. 6

7 The slider-crank drive mechanism is very reliable and has been used widely in other internal combustion engines; however, it is almost impossible to balance dynamically. This is the mechanism generally used in twin-cylinder Stirling engines (Hooper & Reader, 1983). Figure 5. This slider-crank Stirling engine has tubular regenerators (Hooper & Reader, 1983). A free-piston Stirling engine is an engine where the pistons are not coupled mechanically. William Beale first developed this concept in a practical device, and so the term Beale freepiston engine is frequently used to describe free-piston Stirling engines (FPSE) (Walker, 1980). Figure 6. The diagram shows a Free-Piston Stirling engine in an alpha configuration (Hooper & Reader, 1983). This configuration is the same as the most basic alpha configuration, but there is no mechanical crank mechanism and the cylinder is fully sealed at both ends. As heat is applied to the fluid inside the engine it expands, causing the pressure to increase and the power piston as well as the displacer to move down the cylinder. To make sure the power piston and the displacer are out of phase with each other, the displacer is made lighter so even though the pressure change is approximately equal, the displacer has a smaller mass and therefore accelerates faster than the piston. The working fluid is then forced through a connecting passage (which could contain a regenerator) into the hot space where it is heated even more, causing an increase in pressure. Eventually, the displacer comes in contact with the power piston, and no more fluid flows into 7

8 the hot space. At this point the pressure begins to decrease, but the inertia of the pistons in tandem continues the expansion process. Then, because the displacer is lighter, it halts rapidly and becomes separated from the power piston. Once the displacer has stopped, the working fluid flows from the expansion space to the compression space, and the difference in pressure causes the displacer to move up rapidly in the cylinder, forcing all the fluid into the compression space. The power piston continues moving downward and then upward again, compressing the fluid. As a consequence, the working fluid pressure increases and now there is a downward force on the displacer. The displacer again comes in contact with the power piston, and the working cycle repeats. In all types of FPSEs the working cycle is the same but the machine dynamics are different. Applications and Recent Developments in Stirling Engine Technology Applications for Stirling engines are typically very specialized because of cheaper alternatives. Stirling engines also have the disadvantage of needing time to warm-up. Most often they are used in submarines and other marine applications because of their reduced engine noise and vibration. The speeds required of a marine-based Stirling engine are also much less than land-based ones and so helium, air, or nitrogen can be used as the working fluid instead of hydrogen without compromising any engine performance. In addition, with marine-based applications sea water can be efficiently used as a cooling method. Stirling engines for use in automobiles have been the most extensively tested. During the 1970s and 1980s, Ford tried outfitting some of its standard models with Stirling engines, and MTI built a car around a Stirling engine. Ultimately all of these ventures folded, either because of a lack of popular appeal or failure to create a safe, reliable, and efficient engine in an automobile (Hooper & Reader, 1983). The most popular mechanical (non-propulsive) application of Stirling engines is in pumping systems. If crank-type Stirling engines are used, however, the idiosyncrasies of the separate pumping system would still be intrinsic. Free-piston Stirling engines are therefore used in pumping systems because the pump then becomes an integral part of the engine. While Stirling engines have no specific application yet, their potential for a better alternative to current popular engines is great. For the past several years there has been renewed interest in Stirling engines and increasing their performance. These modifications have been mostly in regards to larger Stirling engines. Kroliczek, Nikitkin, and Wolf developed a different type of heat transfer where Loop Heat Pipes and Capillary Pumped Loops are used to transfer heat more efficiently (2010). Another modification of a Stirling engine increased power output by using a coaxial power mechanism (Lin, 2010). Much research has also been done involving regenerators in Stirling engines such as Abdulrahman s work in designing and testing low cost, efficient materials for engines (2011). Pistons, displacers, and types of working fluid have also been the object of several studies and patents in the past ten years. However, not as much investigation has been made into increasing the efficiency of small, tabletop Stirling engines. While they are not the most useful for applications that need large power outputs, the technology used in them can be scaled up to larger applications. 8

9 Research Plan Engineering problem being addressed: Problems with Stirling engine design, specifically the volume of the expansion space and choke point, result in decreased efficiency and power output. Hypothesis/Engineering Goal: The goal of this project is to develop a variable choke point for use in a small Stirling engine. Description in detail of methods or procedures: A Beta configuration Stirling engine similar to the one below in Figure 8 will be built. Figure 8. This diagram shows a Beta Stirling engine similar to the one used in this project ("Solar-13 stirling engine," 2010). To test the choke point the engine will first be run with the typical diameter choke and then the power output will be determined based on the speed and friction of the engine. To power the engine, a standard alcohol burner will be used. This allows the amount of heat applied to the engine to stay constant throughout all tests. Once the power output of the engine with the standard choke has been determined, the same process will be used to test with eight other different diameters (nine diameters will be tested in all). Testing of the expansion space volume will commence in a similar manner. The temperature applied to the engine will stay constant for all tests, and the standard volume will first be tested. Then, as the engine is running, the volume will be reduced by ml. Two magnets will be used to move a ball bearing (radius of cm) inside the test tube to reduce the volume. The temperature of the engine will never exceed 200 degrees Celsius. The testing will occur in a controlled environment when conditions will be kept the same throughout the different experiments. Methodology The Stirling engine was built from a kit (a modified version of the one manufactured by PM Research, Solar-13 model) used in the ME 1800 course at Worcester Polytechnic Institute in Massachusetts. The engine was powered by a standard alcohol burner with denatured alcohol used as the fuel. The heat transfer used was steel wool (4 g) and a ball bearing very close in diameter to the test tube (1.905 cm) was placed in the end of the tube. After the engine was heated for three minutes, it was kick-started. Using a tachometer (Monarch Instrument, Pocket 9

10 Laser Tach 200) the speed of the crankshaft was measured and recorded. The following procedure was used to determine the optimal expansion space volume for multiple choke point diameters. Once the initial speed was recorded, the ball bearing was moved 1 cm by placing a magnet on the glass where the ball bearing was and sliding it over. The volume of the test tube was changed in this manner. The speed was recorded, and again the ball bearing was moved over again. This process was repeated 5 times. The engine was then allowed to cool down. The choke point of cm in diameter was then taken out and replaced by one of cm in diameter. The process for measuring the speed of the crankshaft was then repeated for each movement of the ball bearing. Then seven more choke points of diameters , , 0.635, , , , and cm were tested in the same manner. These choke points were chosen based on drill bits which were in English units and then converted to metric. To calculate power, standard physics equations were used (see appendix). Results Table 1. Average power output for each choke point diameter and expansion space volume. 10

11 Choke Diameter Volume speed 1 speed 2 speed 3 speed 4 v avg St. Dev. a avg F avg P avg (cm) (ml) (rps) (rps) (rps) (rps) (m/s) (m/s 2 ) (N) (W) choke choke choke choke choke choke choke choke choke

12 Average Power (W) Volume (ml) Stirling Engine Optimization Average Power (W) Average Power Choke size (cm) Figure 9. Power outputs for the Stirling engine with nine different choke point diameters and five different expansion space volumes. The maximum power output is Watts at a choke diameter of cm and a volume of ml. Table 2. Average power outputs arranged to create the three-dimensional graph in Figure 9. The maximum power output is inside the bolded cell. Choke sizes (cm) Volume P avg (ml) (W)

13 Data Analysis and Discussion The data reveal a specific point at which the power output of the engine is at its maximum. With a choke point diameter of cm and a volume of ml, the greatest power output is Watts. The goal of this engineering project was to find the optimal choke diameter and expansion space volume to produce the greatest power output. A trend in the data is that as the choke point diameter increases so does the power output, to a certain extent. If the choke becomes too large, the power output drastically drops off. A similar trend occurs with the expansion space volume. The percent increase from the weakest power output to the strongest power output was 7151%. From the standard choke point diameter (0.625 cm) and standard volume (50.5 ml) to the largest power output there was a percent increase of 1495%. The percent decrease from the largest power output to the largest choke point tested was 94%. There was a huge increase from the weakest to the strongest and there was also a large increase from the standard choke and volume used to the setting with the most power output. The drop off after the strongest power output was slight in comparison with the other numbers. For both the choke diameters and the expansion space volume, the optimal setting tends to be in the middle. Too large, and there is too much air, too small and there is not enough air to heat up. An anomaly occurred with choke point 2 ( cm) as the engine would not run with the smallest two volumes. A possible explanation for this is that at the small choke point size more hot air was needed to power the engine. However, this does not explain why the smallest choke point size ( cm) still ran at all volumes. Sources of error in this project include slight changes in the temperature of the engine over time, though this issue was minimized as much as possible by keeping the same level of alcohol in the burner, and allowing the engine to cool off before testing the next choke point. Additionally, at certain choke point diameters the speed was erratic, and significant standard deviations of to were achieved. This occurred in the two smallest chokepoints ( and cm). With the adapted quarter turn ball valve the engine did not run on any of the choke or volume settings. In preliminary analysis the quarter turn ball valve was determined to be the best choice for this project. Possible reasons why the ball valve was not successful in varying the choke diameter while the engine was running include the change in direction of the airflow due to the mechanics of the valve. Rather than channeling the air straight through, the valve changed the direction and eliminated the laminar flow necessary for the engine to run. Additionally, the copper material of the valve absorbed the heat from the working fluid and so the working fluid compressed before reaching the piston. Conclusions It was concluded that the optimal setting of the Stirling engine was a choke point of diameter cm and a volume of ml and the greatest power output was Watts. The engineering goal was to develop a variable choke point for a beta type Stirling engine. While testing a variable choke point was not accomplished, the results of this project indicate that continuing research might be valuable. Nine choke points have been tested and the 13

14 differences in power output are large enough to encourage pursuing a choke point that can be varied while the engine is running. Despite the variable choke point being inoperative, several points can be taken from this experiment. It is of utmost importance to preserve the laminar flow of air through the engine in order to have it run. Rather than having a choke which diverts the flow of air when its diameter is changed, a choke which can expand and contract in a circle (like the iris of a camera) would be desired. However it was beyond the scope of this project to obtain or manufacture a choke similar to the iris of a camera. Moreover, the material the choke and cylinder are made of should not be a material with a high heat transfer to withstand the high heat of the engine. Limitations and Assumptions The current device is limited in the power it produces. The engine is on a small scale and does not generate a useful power output. By itself, the engine is not designed to produce much power, but is designed to only be a testing ground for the variable choke point. The focus of this project was not to use the power outputted. Instead, the focus was on developing a variable choke point for use in a Stirling engine. Another limit of this device is that it does not work for Stirling engines that use working fluids other than air. Most Stirling engines in commercial applications use hydrogen or helium as the working fluid. Using the current design would result in engine failure because the materials used would allow a leakage of the working fluid. The largest limitation of this device is that the variable choke point changes the direction of the air flow and so the engine cannot run. A solution to this problem would be to develop a valve like the iris of a camera that would not change the direction of the airflow, but only the diameter of the choke point. An assumption in this investigation is that the simplified Stirling engine used in the development of the variable choke point models the larger, more complex ones accurately. With this assumption the choke point can be easily scaled up in order to work with larger, more powerful engines where it would be of more use. The current engine is not one used in many applications and so using the device as it stands would not result in a useable amount of power. Additionally, this project assumes that the engine functions in the same way every time. Applications and Future Experiments The variable choke point can be enlarged for use in larger commercial engines. The current size of the engine seriously limits the power output and so a larger, more powerful engine would use the choke point more effectively. The Stirling engines used in marine applications, such as submarines, can utilize the variable choke point to adjust the power output of the engine on the fly. This can be very useful because it allows the engine to, based on its needs, adjust the power output and energy needed to run it. Consequently, when the engine does not need the full power output, the choke point can be changed and the amount of heat needed to power the engine can be lessened. Possible extensions of research include modifying the choke point to work with different types of working fluids. In most applications, Stirling engines use helium or hydrogen as a working fluid and to safely contain these light molecules the choke point would need to be made of different materials to prevent leakage of the working fluid. 14

15 Additional experiments can be performed to determine more precisely the best volume of the expansion space for each choke point diameter. The experiments performed in this project only found the power output for seven different choke point diameters and five different volumes for each diameter. Further research could determine the power output for more choke point diameters and expansion space volumes. In the current engine the differences between the choke point sizes of the three highest power outputs are so close that precise machinery would be needed to determine if there is a choke point diameter that produces more power than the current one. In a commercial sized engine however, the small differences between the settings would increase. More testing should be done when the choke points are scaled up to determine if there is another choke diameter which produces more power in between the choke diameters tested in this project. Another extension of this project would be to develop a variable choke point that does not alter the direction of the flow of the working fluid. This would allow changing the diameter to be done while the engine was running. Having the choke point mimic the iris of a camera might be one way to achieve this. Literature Cited Abdulrahman, A. S. (2011). Selection and experimental evaluation of low-cost porous materials for regenerator applications in thermoacoustic engines. Materials & Design, 32(1), doi: /j.matdes Energy Conversion. (2010.) In Encyclopedia Britannica. Retrieved September 22, 2010, From Encyclopedia Britannica Online: Hargreaves, C., M., (1991). The Philips Stirling engine. New York: Elsevier Science Publishers. Hooper, C., Reader, G. T., (1983). Stirling engines. Cambridge: University Press. Kroliczek, E. J., Nikitkin, M., Wolf, D. A. (2010) U.S. Patent No. 7,708,053. Washington D.C.: U.S. Patent and Trademark Office. Lin, P. (2010). U.S. Patent No. 7,712,310. Washington D.C.: U.S. Patent and Trademark Office. Sandfort, J. F. (1962) Heat engines. New York: Anchor Books Doubleday & Company, INC. Solar-13 Stirling engine model. (2010). Retrieved from product.php?productid=3101&cat=5&page=1 Stirling Engines. (2010). In Access Science. Retrieved September 22, 2010, Access Science online: Urieli, I. (2010, September). Stirling cycle machine analysis. Retrieved from 15

16 Walker, G. (1980) Stirling engines. Oxford, England: Clarendon Press Standard Physics Equations Used: Appendix Acknowledgements The author wishes to thank several mentors who assisted in various aspects of this project. Mr. Torbjorn Bergstrom kindly provided ongoing guidance and use of his lab and materials. He willingly gave materials and advice regarding construction of the engine. Mr. William Ellis additionally gave guidance and support in experiment design. The author also wishes to thank her parents for being supportive, no matter how many times she forgot her camera batteries. 16