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  1. 1. 1.0 IntroductionThe Mechanical Engineering department of Dalhousie University has contracted thedevelopment and construction of a solar powered Stirling engine. The design teamselected for this endeavor consists of Paula Cook, Dale DeMings, Susan Foster, JonathanFraser, and Charles Harrison. The design team is supervised by Dr. Murat Koksal.The Stirling engine is to be used in thermodynamics and energy conversion classroomdemonstrations. For this reason, the engine is designed to best demonstrate the principlesof these courses. Another design parameter was that the final product is be poweredsolely by solar energy.2.0 RequirementsThe final project was to consist of a constructed engine to be easily transported forclassroom demonstrations. The engine was to be simple and safe to use. The engine wasto be able to operate using only the energy supplied from the solar collector. Extrathermal input may be utilized for demonstration purposes in place of, or in addition to,solar energy. The operation of the engine was to be visible through transparentcomponents. Various sensors were to be included to enhance the effectiveness ofclassroom demonstration. The engine was designed to heat quickly for a fast startup time.3.0 TheoryStirling engines are very different from the common internal combustion engines foundin most present day vehicles. Stirling engines do not require the use of fossil fuels andtherefore can be used without producing harmful waste products. They can use solarenergy or waste energy from other sources to produce power. This capability makes theStirling engine a very environmentally friendly power source.
  2. 2. The Stirling engine creates work as a result of temperature and pressure differentials. Tounderstand the project, it is important to first understand the Stirling cycle.The Stirling cycle is a heat addition and heat dissipation process just like the well-knownCarnot cycle. Heat addition comes from the high temperature reservoir, TH, and thenlater in the cycle, heat is rejected to the low temperature reservoir, TL. In our Stirlingengine, the high temperature reservoir is provided by the sun’s solar energy. During theheat addition and rejection stages, the ideal Stirling cycle is a constant temperatureprocess. During the other two stages of the cycle, a regenerator causes an increase intemperature while volume remains constant within the system. Figure 1: P-v and T-s Diagram for the Ideal Stirling Cycle.Figure 1 shows the P-v and T-s diagrams of an ideal Stirling Cycle with regeneration.
  3. 3. The four steps are summarized as follows:1-2 T = constant → expansion (heat addition from external source)2-3 ν = constant → regeneration (internal heat transfer from the working fluid to the regenerator)3-4 T = constant → compression (heat rejection to external sink)4-1 ν = constant → regeneration (internal heat transfer from regenerator back to the working fluid)Because it is impossible to attain an ideal cycle, the P-v and T-s diagrams will most likelyhave more rounded edges and therefore the four stages will mesh into one another. Thatis, during the first stage (expansion), T will not exactly be constant, but it will remainincreasing through the first part of that stage.The cycle we predict for our Stirling engine is the four step process shown in Figure 2.For simplicity, the regeneration is left out of this diagram.
  4. 4. Figure 2: The Sirling Cycle Stages.
  5. 5. 4.0 Design SelectionThe following section describes the designs that were considered for our Stirling engineand solar collector. Pros and cons of these ideas are discussed and followed by aweighted chart that aided our final design selection. From this, our final design of thedisplacer regenerator engine using a parabolic solar collector was chosen.4.1 Displacer PistonA half-disk displacer is contained in a shallow cylinder filled with gas. As the gas isheated it expands and is forced into the piston. The movement of the piston pushes thedisplacer disk to the hot side, allowing the remaining air to cool and contract. Thiscontraction will pull the piston, and force the displacer from the hot side. Figure 3: Displacer Piston.
  6. 6. 4.2 Dynamic Heat SleeveA heated metal sleeve is mounted concentrically to the piston. This sleeve is raised up tosurround the cylinder to heat and expand gas inside. When the gas inside is expanded, thepiston raises and causes the heat sleeve to lower. This allows the hot gas inside thecylinder to cool, bringing the piston down and raising the sleeve. This design wouldlikely use two pistons. Figure 4: Dynamic Heat Sleeve.
  7. 7. 4.3 Rotary ChamberA shaft is eccentrically mounted in a cylinder with four perpendicular telescopic arms.Each arm creates a seal with the sides of the cylinder, isolating four distinct chambers. Aseach of the four chambers reaches smallest volume, it is exposed to an outside heatsource, which causes the gas to expand and forces the compartment to a larger volumeand into the next stage of the cycle. As each chamber expands, it causes the shaft torotate, and aids in the contraction of the other three chambers. As a chamber rotates awayfrom the heat source, it is cooled by the ambient air and contracts, aiding in the shaftrotation. Figure 5: Rotary Chamber Design.
  8. 8. 4.4 Large PistonRather than using a coupled displacer-piston device, a large piston is used to act as itsown displacer. The air and piston are heated at the bottom, causing the air to expand anddriving the piston to the cooled area. The piston is cooled, cooling the air below it andcausing contraction. This pulls the piston back to the heated area to begin the cycle again.A hollow piston could be used to increase the speed of temperature change. Figure 6: Large Piston.4.5 Regenerator in PistonA displacer piston and a power piston are connected by a drive shaft. The displacer pistonis insulated and loosely-fitted in its chamber. The displacer isolates the gas, causing it tobe alternately heated and cooled. A conduit connects the displacer and power pistons, andas hot gas is transferred to the power piston the movement is converted to power.
  9. 9. Figure 7: Regenerator in Piston.4.6 BellowsTwo flexible-walled chambers are connected by a conduit, and their movement isconstrained by a drive shaft and cams. Both chambers start at the top. As the air in onechamber is heated, expansion occurs and the bottom of the chamber is driven downwards,rotating the shaft. Because of the CAM, the second chamber remains at the top. Asrotation continues, the cam on the heated chamber reaches maximum height, the pistonsthen move the gas from the hot side to the cold side maintaining a constant volume ofgas. The air in this chamber is cooled and contracted, and as its cam reaches maximumheight, the air is transferred back to the first chamber, where it is heated again. Thisdesign could incorporate a regenerator in the transfer conduit to improve efficiency.
  10. 10. Figure 8: Bellows.4.7 Weighted Chart for Engine SelectionTable 1: Engine Selection. Demonstration Construction Workability Portability Durability Simplicity Efficiency Weight Ease of Ease of Total Cost Weighting 8 9 7 6 5 8 6 10 9 1 Rotary Displacer 6 4 5 7 8 8 9 6 7 442 2 Dynamic Heat 341 7 6 7 4 6 7 6 4 4 Sleeve 3 Rotary Chamber 3 5 6 5 8 8 9 5 6 353 4 Large Piston 10 8 7 4 7 8 7 2 8 438 5 Regenerator in 467 8 10 8 8 8 8 7 9 7 Piston 6 Bellows 7 8 3 5 7 6 8 5 8 382
  11. 11. 4.8 Selected DesignWe chose a displacer design which incorporates the use of a regenerator that will improvethe overall engine efficiency. This is a unique design as displacer engines do notnormally incorporate regenerators. The displacer design uses one cylinder to expose thecontained gas to either a hot or a cold source and a second cylinder to convert the hot gasexpansion to power. The cylinders are connected by a conduit to allow the gas to betransferred. Some of the components were to be constructed from transparent materialsto facilitate the demonstration of thermal principles acting on the mechanicalcomponents. Refer to Figure 9 for a conceptual view of our selected design. Figure 9: Selected DesignDominant factors that were considered when selecting the design were: - Simple – good demonstration tool - Uses a regenerator – better efficiency - Ease of construction - Closed system allows use of gases other than air, i.e. helium
  12. 12. - Durable - Parabolic solar collector – reaches high temperatures quickly, easily positioned and inexpensive to manufacture 5.0 Parts The main components of our engine are: a solar collector, two pistons, a regenerator, a flywheel and a drive shaft. These components will be discussed later on in this report. 5.1 Solar Collector A parabolic solar collector was purchased to concentrate the solar rays. The concentrated thermal energy could then be transferred to heat the air inside the displacer chamber. 5.1.1 Parabolic Collector Theory The parabolic shape of the collector reflects and concentrates the parallel solar rays to a focal point. The focus is given by p = x2 4y 10 8 6 yFigure 10:Focal Point of a 4 F o c a l P o in tParabola 2 y = 0 .1 x 2 0 -1 0 -8 -6 -4 -2 0 2 4 6 8 10 x
  13. 13. The parabola above (Figure 10) has the equation y = 0.1x2, and has a focal point at p =x2/0.4x2 = 2.75, as shown on the figure. On a solar collector, the focus represents thepoint to which all parallel solar rays will be reflected.The collector was purchased from Edmund Scientifics, and has the followingspecifications (Table 2).Table 2: Solar Collector SpecificationsMaterial AluminumThickness 0.04 inchAperture (top opening) 24 inch diameterDepth 6 inchCentre Hole 1.5 inch diameterThe geometry of the collector is further described by ρ= 2f (1 + cosθ)where ρ = distance from focal point to mirror surface f = focal length (= 6”) θ = angle between optical axis and ρ See Figure 11Figure 11: Solar Collector Geometry 7 6 5 ρ θ 4 In c h e s 3 2 1 0 -1 2 -8 -4 0 4 8 1 2 In c h e s
  14. 14. Taking the focal length as 6”, as specified by the manufacturer, the equation yields a ρ of12” at the rim of the collector (θ = 90º), as anticipated from the specified 24” diameter. 5.1.2 Theory of Solar CollectionThe aperture size of the collector determines the amount of solar energy that can becollected. Our collector will be tilted so that the top opening is always perpendicular tothe solar rays. This means that the solar incident area is given by the circular area of thetop of the collector, an area of 3.14 ft2, or 0.292 m2. At our latitude, the sun provides600 W/m2 of energy to the earth. We therefore estimate collecting energy at a rate of~175 W. 5.1.3 Transmission of Energy to the EngineTo transmit the energy collected by the solar collector to the engine a rod assembly wasconstructed (Figure 12). The insulation theory will be discussed later. The basic principleemployed in the rod design was the conduction of heat through a highly conductivemedium (copper). The collector focuses heat energy to a focal point near the top of thecopper rod. This rod is attached to the solar collector, passing through the hole in its base.The bottom of the rod is threaded into the copper top of the displacer chamber. Heat isconducted down the rod and into the copper top, which heats the enclosed air byradiation.
  15. 15. Copper Collecting Rod Bisque Ceramic Tile Steel Tube Bisque Ceramic Tile Copper Block Figure 12: Conducting Rod Assembly5.2 InsulationInsulation was needed to ensure effective transfer of heat from the focal point of thecollector to the displacer chamber. The insulation had to minimize heat loss at two majorlocations: to the air surrounding the collecting rod and to the ambient air above thedisplacer top.Initial testing of the solar collector and collector rod was carried out in January byattaching a thermocouple to the rod at the focal point. A temperature of 550ºC wasachieved in 40 seconds, at which point the thermocouple burnt off (Figure 13).
  16. 16. Figure 13: Solar Collector Testing - Thermocouple at Focal PointThis experimentation led us to use 500ºC as a probable rod temperature to design around.Most conventional insulation is not effective to this extreme a temperature, so insulationselection was difficult. A ceramic wrap insulation was located which was effective to2300ºF (~900ºC). This product was intended for use inside walls, and is dangerous towork with (inhalation hazard), so we decided not to use this to insulate the rod. 5.2.1 Air as an InsulatorOn further research, we determined that a thin film of air could be an effective means ofinsulating the rod. An enclosed air space of 1/8” has an insulation value of 0.0263 W/mK.By enclosing a thin air space around the rod, the losses to the ambient would be reduced. 5.2.2 Mechanism of Enclosing AirThe air was enclosed around the copper rod by using an insulated steel tube, separated bya ceramic spacer (Figure 12). The steel is less conductive than the copper rod, andAluminum-vinyl pipe insulation provides further insulation value. The insulating air
  17. 17. reduces the overall temperature of the steel tube so that the pipe wrap can be used; theAluminum-vinyl insulation is not effective on a 500ºC rod.The ceramic spacer is used to reduce direct heat conduction from the rod to the steel tube.A hole was drilled in a small ceramic tile, which was then slid onto the rod. The ceramichas an insulation value of 0.1 W/ºC, to reduce direct conduction from the hot copper tothe steel. 5.2.3 Reducing Heat Loss from the DisplacerA second larger tile was placed over the copper top of the displacer casing to prevent heatloss to the ambient air from the exposed top. The goal of the inclusion of all theinsulation materials was to direct as much of the collected heat into the displacer chamberas possible. 5.2.4 Testing of the Collector and RodThe first tests of the solar collector were carried out in January, as mentioned above.Tests were also completed on the rod assembly, and on the rod attached to the displacerchamber. Four series of tests were performed. A summary of the results appears below(Table 3). The testing locations are found in Figure 14.
  18. 18. Table 3: Testing Results Test 1 Test 2 Test 3 Test 4 Collector and Collector on Collector and Collector and Rod Engine Rod RodDay March 31, 2004 March 31, 2004 April 1, 2004 April 1, 2004Time 3:20 pm 4:30 pm 11:30 am 11:45 amWeather Intermittent Intermittent Sunny Sunny Clouds CloudsAmbient Air 10 8 12 12Temperature (ºC)Temperatures (ºC) (1) Focal Point 200 250 330 360 (2) Ceramic Spacer 76 - 150 170 (3) Top of Insulation 49 - 90 125(4) Middle of Insulation 44 - 55 80(5) Bottom of Insulation 40 - 44 68(6) Nut Below Collector 44 50 - - (7) Bottom of Rod 85 N/A 150 170 (8) Side of Displacer N/A 38 N/A N/A (top) (9) Side of Displacer N/A 18 N/A N/A (bottom)
  19. 19. The testing results demonstrate that theinsulation is doing its job, since the (1)temperature at the bottom of the rod is (2)consistently higher than the temperature (3) (4)along the insulation. The majority of theheat is being transferred into the displacer (5)chamber. (6) (7)The heat values on the outside of theinsulation are higher than desired, however. (8)For safety, the insulation should be coolenough to touch, and temperatures in excessof 100ºC reveal that heat energy is beinglost as it travels down the copper rod. Figure 14: Testing Locations (9)5.3 Piston SizingThe power piston casing was designed to be well sealed to prevent air losses and to allowmaximum work to be obtained from the volume change. The power piston should be assmall and light as possible, while still capable of transferring work. The size of the powerpiston was determined by the desired power output and the volume of the displacercasing. The shafts of both the displacer and power piston are lubricated for ease ofsliding.
  20. 20. 5.3.1 CalculationsThe following calculations were made to estimate the size of the power and displacercylinders needed as well as the work output of the engine. Calculations were based onthe ideal Stirling cycle, the ideal gas law, and the following assumptions corresponding tothe ideal Stirling cycle: P2 = P4 = 101.325kPa TL = 20°C = 293K TH = 200°C = 473K Qin = 400 J / s = 400W R = 287 J / kg ⋅ K (air ) N = 1rpmIdeal efficiency of the cycle can be calculated immediately from the reservoirtemperatures. ⎛ TL ⎞ ⎛ 293K ⎞ η = ⎜1 − ⎟ × 100% = ⎜1 − ⎟ × 100% = 38% ⎝ TH ⎠ ⎝ 473K ⎠Step 4 to 1 is a constant volume process so the following formula can be used to find P : 1 P4 × T1 P4 × TH (101.325kPa ) × (475K ) P1 = = = = 164kPa T4 TL 300 KThe same thing can be done to find P3 : P2 × T3 P2 × TL (101.325kPa ) × (300 K ) P3 = = = = 63kPa T2 TH 475K
  21. 21. The ideal gas law can also be used to find specific volumes, ν 1 and ν 3 . Based on theideal Stirling cycle, we can also assume that ν 1 = ν 4 and ν 3 = ν 2 . R × T1 (0.287kJ / kg ⋅ K ) × (475K ) ν1 =ν 4 = = = 0.83m 3 / kg P1 160kPa R × T3 (0.287kJ / kg ⋅ K ) × (300 K ) ν3 =ν 2 = = = 1.34m 3 / kg P3 64kPaThe qin required per kilogram of gas per cycle can be determined by the followingformula (note: T2=T1 so that term becomes zero): ⎛ ⎛T ⎞ ⎛P ⎞⎞ ⎛ ⎛ 101.325kPa ⎞ ⎞qin = T∆s = TH ⎜ C P ln⎜ 2 ⎜T ⎟ − R ln⎜ 2 ⎟ ⎜P ⎟ ⎟ = 473K ⎜ − (0.287 ) ln⎜ ⎟⎟ ⎜ ⎟ ⎟ = 65kJ / kg ⎟ ⎜ ⎝ 164kPa ⎠ ⎠ ⎝ ⎝ 1 ⎠ ⎝ 1 ⎠⎠ ⎝A similar calculation can also be made for qout: ⎛ ⎛T ⎞ ⎛P ⎞⎞ ⎛ 101.325kPa ⎞ ⎞q out = T∆s = TL ⎜ C P ln⎜ 4 ⎜T ⎟ − R ln⎜ 4 ⎟ ⎜P ⎟ ⎟ = 300 K ⎜ − (0.287 ) ln⎛ ⎟⎟ ⎜ ⎜ ⎟ ⎟ = 40kJ / kg ⎟ ⎜ ⎝ ⎝ 63kPa ⎠ ⎠ ⎝ ⎝ 3 ⎠ ⎝ 3 ⎠⎠Since the cycle happens once per second and the Qin only lasts for half of the cycle, it canbe said that only 200 of the 400 J are transferred to the system. The following calculationdetermines the mass of air capable of running in this ideal cycle. Qin 0.200kJ m= = = 0.0031kg qin 65kJ / kgWe can now calculate the actual volumes of air at every stage:
  22. 22. ( ) V1 = V4 = ν 1 × m = 0.83m 3 / kg (0.0031kg ) = 0.0025m 3 = 2.6 L V2 = V3 = ν 2 × m = (1.34m 3 / kg )(0.0031kg ) = 0.0041m 3 = 4.1LTotal work generated, Wout, by the cycle may be calculated now. Since 1rpm wasassumed, this value is also our output wattage. Wout = m(qin − qout ) = (0.0031kg )(65kJ / kg − 40kJ / kg ) = 0.076kJTo check to see if our calculations are correct, we can check our efficiency using heattransfer. η= qin × m × 100% = (65kJ / kg )(0.0031kg ) × 100% = 38% Wout 0.076kJThis efficiency agrees with the efficiency calculated via temperatures. Finally, now thatwe have the upper and lower volume limits, we can determine the size of the displacercylinder and the power cylinder. Since the power cylinder should not contain anyvolume at minimum, V1 and V4 is equal to the displacer cylinder volume, 2.6L. Thedifference between V2=V3 and V1=V4 is therefore the power cylinder volume, 1.5L.From these volumes we can determine ideal sizes of pistons. If we were to assume apower piston diameter of 10cm and displacer piston width of 10cm, the heights of thepower cylinder and displacer cylinder would then be 20cm and 26cm, respectively. SeeAppendix A for the Microsoft Excel spreadsheet of these calculations and the generatedP-v diagram.Subsequent to making these calculations, we received our working solar collector. Webegan testing of the collector to see realistically, how well it would perform as a sourceof heat for the hot side of our Stirling Engine. As is discussed already, the solar collectorperformed well and led us to change our preliminary assumptions and consequently thecalculated size of our engine. Firstly, we increased our high temperature reservoirtemperature to 300ºC instead of the 200ºC we originally had. However, we felt that our
  23. 23. actual power input from the collector may have been optimistic at 400W so we reducedthis value to 300W based on an assumed 600W/m2 solar output on a sunny day. Bycompleting the same calculations as above with the new assumptions, we found anoptimal size of 1.13L for the displacer casing, 1.08L for the power cylinder and an actualwork output of 73kJ as compared to our 76kJ found previously. These calculations arealso completed in a Microsoft Excel spreadsheet and attached in Appendix A. 5.3.2 Displacer CasingWith these volumes in mind, we had to decide on actual dimensions of the squaredisplacer casing as well as the power cylinder. Because we were concerned withconduction down the metal sides of the displacer casing, we decided that it would be agood idea to make the sides fairly long compared to the cross section of the casing. Thiswould mean that the cold end would not be influenced by the extremely hot end asquickly and therefore maintain a temperature differential and run the engine longer. Inaddition to these long sides, we chose 1/8” stainless steel as our material for the threemetal sides for its relatively low conduction rate compared to other metals. The top andbottom ends of the displacer casing were to be made of highly conductive metal to ensurethat the heat and cold reached the air appropriately. Copper is the ideal metal for theseends, however a reasonably thick piece was needed to act as a thermal capacitor and sucha piece of copper was found to be scarce. We located enough copper for one end, wechose that to be the hot end, and used 3/4” thick plate to hold our heat with. On the coldend, we used the same size piece of aluminum as it was the next best conducting metalthat was readily available. Ultimately, our displacer casing had internal dimensions of3.25” by 3.25” square and 7.5” high. This came very close to meeting our calculated sizeof 1.13L. The constructed displacer casing is seen in figure 15.
  24. 24. Figure 15 - Displacer Casing 5.3.3 Power Piston CasingThe power cylinder was going to be approximately the same size as discussed above;however, it was to have a cylindrical shape. We were not particularly concerned withconduction in the power cylinder so we chose steel as our working metal because it wasfairly inexpensive. To allow for the air duct to plug into the top of the power cylinder,we wanted its height to be not as large as that of the displacer casing. Therefore weconstrained it vertically and found the appropriate diameter. We decided on a pistonthrow of 5” and a diameter of 4”. This gave us our desired volume change ofapproximately 1.08L and still gave us room to place the cylinder on the engine stand andconnect via a duct to the displacer casing side (near the hot side). The piston itself wasalso machined from steel to allow for smooth operation in the steel cylinder, and also tohave a comparable thermal expansion coefficient in the event that this side of the enginebecame hot. The sides of the piston were built long to reduce binding, but the inside wasmachined out to reduce as much weight as possible and effectively reducing efficiencyloss. Figure 16 shows a picture of our initial power piston and cylinder.
  25. 25. Figure 16 - Power Piston and Cylinder 5.3.4 Testing and ModificationTesting on the current design began at this time and instead of using the solar collector,we felt it would be more efficient use of time to use a propane torch for ease ofexperimentation. It was found that after disconnecting the drive shaft and allowing thedisplacer piston to be maneuvered manually, the power piston yielded very littlemovement as a result of displacer actuation. After this unsuccessful experimentation, weconcluded that changes needed to be made to our design. Specifically, two main issuesconcerning the thermal workings of the engine were found. The first was constrainedflow within the air duct, and second and more importantly, it seemed that the enginerequired too large of a volume change in the power piston. Initially, we shortened thethrow of the power piston from 5” to 2” by modifying drive shaft linkages, in effectreducing the expansion volume by 60%. After doing this, we began testing and yet againwere unsuccessful. We then decided that our next step would be to increase the air ductsize to allow easier flow. At that time, we also felt that the power piston was too large,heavy and caused excessive friction so we decided to replace this with a smaller versionof the same concept.
  26. 26. In determining the new power piston size, we decided that a drastic size drop wasnecessary so we reduced its size from a 4” to a 1” diameter as this was most likely ourlast chance given the time constraints. Furthermore, we increased our duct size from 1/2”inner diameter to 7/8” inner diameter in an attempt to eliminate the majority of theefficiency losses. We introduced labyrinth seals on the power piston to maintainlubrication within the cylinder and to reduce pressure blowback past the piston as airleakage seemed to be a problem as well. The new power cylinder is seen in Figure 17. Figure 17 - Power CylinderDuring this modification process, the stainless steel displacer casing sides were replacedwith aluminum sides and the duct connection location was moved from the hot side of thedisplacer casing to the middle. This choice of location is understood within the StirlingEngine community as an ideal location for maximum efficiency.Future recommendations to the power piston would be to ensure an excellent seal toprevent any air leakage around the piston through to the bottom of the cylinder. Thisleakage issue plagues the displacer casing as well and in the future, a square casing wouldnot be advisable. Ideally, a cylindrical casing would be the most effective, and to allowfor viewing of the displacer, an entirely Pyrex cylinder could be used. This would alsoreduce internal conduction from the hot to the cold end of the cylinder.
  27. 27. 5.4 RegeneratorThe main purpose of the regenerator is to improve the efficiency of the engine. Apossible regenerator design involves using a series of wire mesh layers, using enclosedair spaces as insulators to trap the heat energy. This type of regenerator is illustrated inFigure 18. Figure 18: Wire Mesh Regenerator.A regenerator works by removing heat from the working fluid during the cooling process(steps 2-3 as seen on the P-v diagram) and storing it. This stored heat is then transferredback to the working fluid during the heating process (steps 4-1 as seen on P-v diagram).Through this method, energy that would normally be lost to the environment is used toreheat the gas, thus improving efficiency by requiring less outside energy to heat the gas. 5.4.1 CalculationsThere are some important considerations involved when designing a regenerator. Thefirst consideration is that the regenerator should not directly conduct heat from the hot
  28. 28. side to the cold side of the regenerator. The second consideration is that in order toincrease the effectiveness of the regenerator a certain amount of surface area must bepresent based on the speed of the working fluid. And finally, in our case we must alsoconsider the weight of the material.To ensure minimal heat conduction in the direction of heat flow, consider the equation ofconduction: qcond = -kA dT/dx where: qcond = heat rate (W) k = thermal conductivity (W/mK) dT/dx = the change of temperature over a distance x (K/m)Since the overall temperature change is fixed, changes in the thermal conductivity,determined by the choice of material, must be considered. Plain carbon steel is a poorchoice because its thermal conductivity is 60.5 W/m°K. Stainless steel is a better choice,since its conductivity is about 15 W/m°K. Preferred choices are Pyrex, with aconductivity of only 1.5 W/m°K, or ceramics, which can achieve even lower conductivitybased on their composition. One of the best insulators available is air having aconductivity of only 0.0263 W/mK. The problem with air is that its fluid compositionmakes it prone to convection losses, which eliminate the benefits of its low conduction.To stop this problem the air can be held in small volumes, which restrict its movement.The second consideration is the amount of surface area present. The more surface areaavailable, the more convection can occur. Since convection is the main method fortransferring heat from our system to the regenerator and back to the system, the systemshould incorporate the maximum possible surface area for the available volume.
  29. 29. The rate of heat flow from convection is defined by the equation: qconv = hA(Ts –Tinf) where: q = heat flow h = convection coefficient (typically between 25-250W/m2K)This depends on both air speed and temperature of the surface and air. A = Surface area (m2)From this formula it is seen that the surface area is the only value that can be easilymanipulated. The downside of having a high surface area is that it restricts the flow of thegas, resulting in more force needed to pass the gas through the regenerator.To calculate the size of the spacing required the following equation is used: δ = (2k/ωCpρ)-1/2 where: δ = optimal spacing (m) k = conduction coefficient Cp = specific heat at constant pressure (J/kgK) ρ = density (kg/m3)ω = 2πf where f is the frequency of the gas moving through the regenerator in cycles/secThis equation will give us the optimum spacing required, and hence surface area.Based on the background information and manufacturing availability. It was chosen touse a modular regenerator in the Stirling engine. This allows for testing of different
  30. 30. regenerator designs, and provides a method of demonstrating the benefits of the differentregenerators by showing the efficiency change of the engine. 5.4.2 Chosen Regenerator Design Figure 19 – RegeneratorThe current regenerator is composed of 10 aluminum sheets with an offset pattern ofholes. These are equally spaced to produce the regenerator (Figure 19). One benefit ofthis design is that spacing the aluminum sheets allows air to be used as an insulator. Thisair will insure the proper working of the regenerator by greatly limiting the amount ofconductive heat transfer from the hot to the cold side during the engines operation. Thesecond benefit is the pattern of holes in the sheets. These holes are 1/4” in diameter andare offset so that there is no straight path from one side of the regenerator to the other. Ifthese holes were not present the air would simply flow around the sides and very littlearea would be contacted, reducing the efficiency of the regenerator. Also, if the holeswere all in line with each other the air would flow straight through the regenerator andnot be forced to circulate within each of the air spaces in the sheets.
  31. 31. 5.4.3 ImprovementsPossible improvements to the selected regenerator design are to replace the aluminumsheets with stainless steel and to change the size of the holes in the sheets. Replacing thealuminum sheets with stainless steel would be done since aluminum has a highconductivity (237 W/m°K compared to stainless steel at 15 W/m°K), since conductivityis not desired, the stainless steel is a better choice. The stainless steel plates were the firstmaterial proposed for sheet construction, but stainless steel is more difficult to machinethan aluminum. Since time is a consideration in this project, and recognizing that thesheets are spaced apart to minimize the actual effects of conduction within theregenerator, it was decided that it would be sufficient to construct the sheets ofaluminum.Using smaller holes in the sheets has both advantages and disadvantages. The obviousadvantage is that by reducing the holes size, the amount of surface area in the displacer isincreased. The disadvantage is that by reducing the holes size, the flow rate of air that canflow through the displacer is reduced. For this reason a balance must be found betweenthe amount of surface area and the flow rate of air. The optimal hole size is based on thespeed of the engine during operation; the faster the engine runs, the larger the holes in thesheets need to be, and conversely the slower it runs, the smaller the holes.Besides the chosen regenerator design other regenerator possibilities include using a wiremesh between two plates; this has the advantage of a very large surface area, thedisadvantage is greater conduction. Ceramic is also a possibility; its advantage is a verylow thermal conductivity, but it has the problem of being brittle and difficult to machine.5.5 Connecting RodsThe connecting rods are used to connect the displacer and power pistons to the driveshaft. The original connecting rods were made of two 1/4” diameter steel shafts
  32. 32. connected with a pin joint to 1/8” thick flat bars. The pin joint allows the top and thebottom of the rods to move independently of one another and is required so that theengine can rotate. The top halves (steel shafts) of the rods move vertically up and downwith the pistons while the lower halves (steel bars) move in a circular pattern with thedrive shaft. The 1/4” diameter shafts and 1/8” bars were used to keep the overall weightof the engine down. The two rods are different lengths to accommodate the differentthrows of the pistons. The displacer piston connecting rod also has to travel through thebottom of the displacer casing while the power piston connecting rod is suspended in theair. 5.5.1 ModificationsAfter preliminary testing it was found that that the connecting rods needed to bemodified. The displacer piston connecting rod was too flexible due to its length and wasbinding against the bottom of the displacer casing. The power piston connecting rodneeded to be modified to account for the changes in throw that were decided upon fromthe testing results. To fix these issues the displacer connecting rod was changed to a 1/2”diameter steel shaft and an oilite bushing was added under the displacer casing to allowthe shaft to run without binding. The throw of this piston stayed the same and thereforeno changes were made to either the lengths of the top or bottom link. To adjust thepower piston connecting rod the top link was reduced by two-thirds its original lengthand the bottom link was doubled in length. These changes to the power pistonconnecting rod reduced the throw of the piston and therefore reduced the volume changerequired to rotate the drive shaft.After testing the engine thermally, it was realized that further modifications wererequired to get the engine to work properly. These modifications required changes to theconnecting rods. The top and bottom links and the pin joint needed to be remade to ahigher tolerance. The final connecting rods have the same overall dimensions as theprevious ones, but are made to a higher tolerance. The rods are more rigid and have fewermechanical losses then the previous rods. The final connecting rods are as light as the
  33. 33. previous rods and allow the engine to run mechanically sound when manually cranked.The bushing under the displacer casing was lengthened to provide more support to theconnecting rod and to further reduce the chance of it binding.The final connecting rods are well built and suitable for further use with this engine.Although the rods are well built, it will be difficult to make any future changes to thethrow. If modifications to the engine are needed that require a throw change in eitherpiston a new connecting rod will need to be fabricated.5.6 Drive ShaftThe drive shaft is an integral part of the Stirling engine. It ties the engine componentstogether and transfers the generated power from the engine to the output device. There is o oa 90 bend in the shaft to force the displacer and power pistons to be 90 out of phase.The phase difference means that if one piston is at the top dead center position(completely up) the other piston is in the half way up position and vise versa. This phasedifference is used to control the amount of air exposed to the heat source at a given timeand also to prevent the engine from reaching equilibrium. The phase difference preventsequilibrium from occurring because when the displacer piston is covering the heat source(top dead center), the air starts to cool and will approach its minimum volume. When theair does reach its minimum volume the displacer piston will have already moved to thehalf down position allowing the air to start to reheat. Due to this motion, the powerpiston (being 90o out of phase with the displacer piston) will always be chasing theequilibrium position, and therefore will keep the engine rotating.The preliminary drive shaft was constructed using 1/4” diameter steel threaded shaftsbolted to 1/8” thick steel bars. This design was chosen to keep the weight of the driveshaft to a minimum and also to keep the fabrication simple. Refer to Figure 20 for aphotograph of the preliminary drive shaft.
  34. 34. Figure 20: Preliminary Drive ShaftAfter preliminary testing, the shaft proved to be too flexible and the shaft would not runproperly when manually cranked. 5.6.1 ModificationsAt this point a second drive shaft needed to be designed to solve the issues which arosefrom testing of the preliminary shaft. The new shaft would need to be rigid and yetremain lightweight. To accomplish this, the thickness of the steel bars was increased to1/2” and the shaft diameter was increased to 1/2”. To keep the weight of the shaft downaluminum was used for the bar sections. The shaft sections were also to be made ofaluminum to keep the weight to a minimum; but due to time constraints and poor contactresistance of aluminum on aluminum, threaded steel rod was used. The threaded steelrod increased the mechanical loses in the system but it was the best option available.Once the shaft was together it resolved the issues with the preliminary drive shaft.Although it was slightly heavier it was much more rigid and ran mechanically soundwhen manually cranked. Refer to Figure 21 for a photograph of the second drive shaft.
  35. 35. Figure 21: Second Drive ShaftAfter testing the engine thermally it was realized that further modifications were requiredto get the engine to work properly. These modifications required changes to the seconddrive shaft. The threaded rod needed to be replaced and the entire engine had to be madeto a higher tolerance.The final drive shaft has the same overall dimensions as the second drive shaft, but ismade to a higher tolerance. The threaded steel rod was replaced with a steel rod andbushings were incorporated at each end to reduce friction losses and play in the shaft. Inthe previous two designs the shaft simply rotated in the mounts attached to the stand.The shaft was also pinned and brazed together, instead of being bolted together. This Figure 22: Final Drive Shaftprocess made the drive shaft more rigid then the others. Refer to Figure 22 for aphotograph of the final drive shaft.
  36. 36. The final drive shaft is the most rigid and has fewer mechanical losses than the twoprevious shafts. It is also lighter then the second drive shaft and runs mechanically soundwhen manually cranked.The final drive shaft is well built and suitable for further use with this engine. However,future modifications probably will be required to get the engine to work. Although wellbuilt, it will be difficult to make any changes to the throw or the phase angle of the driveshaft. If the modifications to the engine require that either one of these parameters bechanged, a new drive shaft will need to be fabricated.5.7 FlywheelExperimentation with the constructed Stirling engine demonstrated that a flywheel isnecessary to maintain the rotation through all stages of the piston motion. A flywheel actsas a reservoir to absorb energy during the points of rotation where the turning moment isgreater than the resisting moment, and restores energy when the turning moment is lessthan the resisting moment. The absorbing of energy must be accompanied by an increasein speed, while restoring energy necessitates a decrease in speed. These speedfluctuations are small, but the flywheel must be properly proportioned so that thesechanges of speed do not exceed permissible limits. The kinetic energy of the flywheel isgiven by IKsω2 = ½ Efwhere I = mass moment of inertia of the flywheel = mass*(radius of gyration)2 = mk2 Ks = speed coefficient ω = mean angular speed Ef = energy fluctuation = area under torque vs. rotation angle diagram
  37. 37. For optimal flywheel performance, the effective weight must be as far from the centre ofthe shaft as possible (maximal radius of gyration). Figure 23: Flywheel #1The first flywheel constructed was a 7” round disk that was 1/8” thick (figure 23). Thisdesign was constructed of steel and had material removed from the inner portion tomaximize the performance of the flywheel with respect to weight. This flywheel was notintended to be the final design. The final design would only be determined after theengine was constructed and running; this is due to the fact that the size and weight of theflywheel is dependant on both the running speed of the engine and the amount of frictionthat exists in the drive train while running at the operating speed.After the engine was constructed, a large amount of friction was observed within thesystem, so a larger flywheel was constructed. This second flywheel had dimensions of 6”diameter and 3/4” thickness and was made of steel. Once the second flywheel wasinstalled on the second drive shaft, testing was done to ensure it was the proper size. Thiswas done by manually moving the power piston at approximately 60 RPM, which is theprojected running speed of the engine. It was then observed that at the top and bottom ofthe power pistons cycle that the flywheel proved sufficient to provide the required forceto maintain rotation in the drive shaft. This is important because the power piston isunable to provide power in these locations.
  38. 38. Figure 24: Flywheel #3The third and final flywheel (Figure 24) was constructed to accompany the third driveshaft. It is composed of an aluminum disk measuring 1.5cm by 12.5cm diameter. Thealuminum was chosen because its reduced density reduces the overall weight withoutaffecting the flywheel’s efficiency. The weight was reduced in order to minimize thebending in the drive shaft, which could cause misalignment and adversely affect therunning of the engine. After testing the flywheel, it was found to be slightly undersizedfor the amount of friction in the system. This conclusion was reached from moving thepower piston by hand; the flywheel will sometimes propel the drive shaft through thetrouble areas but not consistently. In order to fix this problem it is recommended to returnto the second flywheel design.A future improvement of the flywheel would be to optimize its size based on theequations above, once the engine’s running speed is known. For demonstrationalpurposes of the engine the second flywheel design should easily meet this requirement.5.8 Transparent SideOne of the design requirements was that the displacer piston be visible while inoperation. To accomplish this, a transparent material suitable to withstand approximately o500 C was required. The first materials researched were Plexiglas and Pyrex products.These products were the first choice due the machineability of the materials and also their
  39. 39. otransparent properties. The melting point of Plexiglas is approximately 70 C and thePyrex was more then our budget would allow.The second option available was to use a glass product. Although glass can withstandhigh temperatures, it is very difficult to machine and is very brittle. A glass supplier wascontacted who was able to supply and machine a piece of glass to fit our engine. Thisproduct is commonly used in wood stoves. The glass, Neoceram, has a melting otemperature of 2500 C, which more than exceeds our requirements. A rubber gasket wasmade and the glass was bolted to the displacer piston to allow for engine thermal testing.After the testing, the displacer was disassembled and the Neoceram cracked due to anunnoticed alignment issue. A slight leak was also detected during the initial testingbetween the glass and the displacer. Refer to Figure 25 for a photograph of the CrackedNeoceram Glass. Figure 25: Broken Neoceram GlassA redesign of the glass mounting system is required. The redesign will need to botheliminate the original alignment issue that caused the crack and also eliminate the sealingproblem. To accomplish this, a piece of the Neoceram glass should be pressed and sealedbetween two sheets of stainless steel. The steel could then be bolted to the existing
  40. 40. displacer casing and sealed. Unfortunately this modification will need to be completed inthe future. Refer to Figure 26 for a sketch of the proposed mounting system. Figure 26: Proposed Redesigned Glass Mounting5.9 Rotating Engine StandThe main purpose of the stand is to support the engine. The displacer and power pistonssit on top of a horizontal surface. This surface is pivoted to permit swiveling from thefull vertical position to a full horizontal position. This swivel is necessary to keep thesolar collector focused at the sun. Two mounting brackets are attached to the undersideof the flat surface to hold the drive shaft in position. The table is supported on either endby a set of legs.The stand proved fairly stable through the preliminary testing and it functioned well.However, there were several issues with the stand that needed to be resolved. The flattop itself was bowed in the middle causing the two piston casings to be on a slight angleaway from each other. This potentially could cause more mechanical loss than necessaryin the drive shaft. The mounting brackets that supported the drive shaft were flexible andthe drive shaft was set in holes cut in either bracket. This also proved to increase themechanical loses in the drive shaft. The stands legs moved independently of one anothermaking it awkward to carry.
  41. 41. No changes were made to the stand until the power piston, drive shaft and connectingrods were redesigned for the final time. When the stand was modified the flat table wasreplaced with a flatter piece of steel. The swivel and mounting brackets were bolted oninstead of welded on. This measure provided a more accurate mounting system for thedrive shaft. The mounting brackets were replaced with more rigid ones to eliminate theflexing issue. Instead of the drive shaft running in holes in the mounting brackets,bushings were added to the end of each bracket for the shaft to travel through. Thebushings reduced the mechanical losses encountered in the original stand. Finally thefeet of the stand were tied together with two lateral bars to make the stand more stablewhen being transported. The final stand can be seen in Figure 27. Figure 27: Tilted Stand With Engine
  42. 42. 6.0 Testing6.1 Temperature MeasurementTo measure the temperature drops across the engine we purchased a digital thermometerfrom Omega (Figure 28). This handheld thermometer was chosen with the intention ofmounting it directly to the engine. The two thermocouple inputs are useful to read thedifference in temperature between two points instantaneously. Figure 28: Omega Digital Two-Input ThermometerUsing the solar collector, we achieved the following values: Thermocouple Position Temperature Reading (˚C) Focal Point of Collector 360 Top of Displacer Casing 230 Bottom of Displacer Casing 26∆T = 204˚C for the displacer.The large temperature difference between the focal point and the top of the displacercasing does not correlate with our finite element analysis for the heat loss of the copperrod (Figure 29). The rod lost much more heat than anticipated for the insulation
  43. 43. surrounding it. It is possible that the gaps at the insulation seams may have been acontributing factor to these losses. There were also sections of the copper rod that couldnot be easily insulated because other parts of the engine were mounted to it; where thecollector was positioned and where the rod threaded into the copper plate on the top ofthe displacer were difficult areas to incorporate insulation. We also believe there wassome contact resistance between the threaded copper rod and the threads in the copperplate. This could also account for some of this temperature disparity. Due to the scarcityof available insulators able to withstand the anticipated rod temperatures, and due tospace and safety constraints, the results are in an acceptable range. The temperature at thetop of the displacer casing is still sufficiently hot to nullify the impact of these losses. Figure 29: ANSYS Prediction of Rod Heat ConductionA large temperature drop in the displacer casing is desired to optimize the performance ofour engine. However, we don’t want the heat to be lost before adequately heating the airin the hot side of the displacer. The material initially chosen for the displacer casing wasstainless steel, however, because of availability and time, we used aluminum. Aluminumis more conductive than ideally desired for the displacer casing walls; we would preferconduction from the outside to the inside but not in the vertical direction of the walls.
  44. 44. 6.1.1 RecommendationsStainless steel is a better suited material for the displacer due to its lower conductionvalue. We would suggest that the final displacer casing be constructed from stainlesssteel.Since conduction is not desired in the displacer piston casing, we further recommend thatthe casing around the middle of the displacer be constructed of a material with very lowconduction, such as ceramic. This would minimize the conduction of heat from the hotside to the cold side and vice versa.A very useful addition to the displacer design would be attaching fins to the inside wallsof the displacer casing. Fins on the inner walls of the hot side would increase start-uptime by transferring the heat from the copper to the air in the hot side of the piston morequickly than the current assembly. Fins would be useful on the inner and outer walls ofthe cold side allowing it to more rapidly transfer the heat from the chamber. We wouldhave liked to add fins, but they were not included on the current design primarily due totime constraints.6.2 Force MeasurementsUsing a force meter and pushing on the drive shaft, we measured a maximum requiredforce of 4lb. This was the maximum force because it was the force required to beginrotating the drive shaft or push the power piston upwards. This converted to a requiredtorque of 0.5 ft-lb by using the 1.5 inch link attaching the power piston connecting rod tothe shaft. These forces are reasonable for the size of the engine and its components. 6.2.1 RecommendationsFurther reduction of the frictional losses is desired. Reducing the throw would alsoincrease the rigidity of our links and could improve the performance of the drive shaft.
  45. 45. We also recommend replacing the current bushings in the drive shaft with ball bearings toremove some of the friction from the shaft.By completely sealing our displacer piston, the forces calculated above would be easilyachievable with air pressure changes. This will be expanded in the next section.6.3 Pressure MeasurementsTo measure the pressure our engine was capable of holding, we used a vacuum pump todrop the pressure in the piston casing. We read the pressure at which our seal gave waywith a pressure gage. We saw that our pressure was only 0.725 psi below atmosphericpressure when the seal failed. We approximated this pressure drop as the equivalentpressure increase our engine could withstand during operation. Using the force calculatedabove, and the cross-sectional area of our power piston, we were able to estimate arequired pressure drop/increase as 5 psi. The displacer piston needs alterations towithstand this pressure change. We initially underestimated the difficulty of sealing oursquare piston. 6.3.1 RecommendationsThe team decided on a displacer piston casing made from fewer pieces. One solution toconsider is to make the sides of the displacer casing from square tubing. Then we couldseal the holes to the connections and secure two end-caps. A cylindrical casing would beideal for better sealing. A better solution might be to use steel rod and machine the casingout of one piece of stock.
  46. 46. 7.0 Final BudgetBased on a current design, the following costs have been accrued: Solar collector mirror: $178.92 Digital Thermometer: $132.25 Metal: $260.00 Neoceram Glass: $46.00 Ceramic: $30.00 Miscellaneous: $62.21 Total: $709.388.0 Future RecommendationsSealing is the major problem with our Stirling Engine design. In order for the engine towork properly no air should be able to escape from the engine once it is sealed. Thereforeour first recommendation is to replace the current displacer piston casing with a square orcylindrical stainless steel tube. This would prevent the air from leaking out at the seamsas it does in our current design.To further improve sealing a cap could be manufactured to go over the hot end of thedisplacer. This would allow the cap to be sealed to the rest of the displacer casing at acooler location further from the top. This would keep the temperature of the sealed regionwithin the allowable limits of more readily available sealants.Fins should be incorporated in the displacer piston on the inside of the hot side and onboth the outside and the inside of the cold side. These fins would increase the rate atwhich the air in the system is heated and cooled.
  47. 47. We also propose that the displacer walls be separated in the center by an insulatingmaterial such as ceramic. This would help prevent heat propagation from the hot side tothe cold side of the displacer piston. A possible problem that may develop from thismodification is additional leaks in the displacer casing.Since the engine is to be used as a demonstrational tool the glass face of the displacercasing should be reintegrated. To accomplish this, a redesign of the glass mountingsystem is required. The redesign will need to both eliminate the original alignment issuethat caused the glass to crack and also eliminate the sealing problem. To accomplish this,a piece of the Neoceram glass could be pressed and sealed between two sheets ofstainless steel. Then the steel plates could be attached to the displacer casing and sealed.If a round displacer casing is incorporated it could be made entirely from Pyrex. Thiswould allow the displacer to be visible and provide minimal seams where air leakagecould occur.To make the drive shaft run true, counterweights could be added to balance the shaft.With the addition of counterweights, less force would be required to make the shaftcomplete a full rotation. The flywheel could also be made lighter with the addition ofcounterweights because it would have to overcome less force to keep the shaft rotating.Another recommendation would be to further reduce the mechanical losses of the system.Two main ways are proposed to accomplish this: (1) replacing the bushings with ballbearings to reduce the friction on the drive shaft, and (2) reduce the piston connecting rodlengths to make them more rigid and lighter. This could be done to allow the engine torun with a smaller pressure/temperature differential.It may be beneficial to try to incorporate an overhead drive shaft design with the solarcollector. With an overhead design, gravity would pull the pistons down and thegenerated pressure would push the pistons back up. Currently gravity pulls the pistonsdown and the generated pressure has to try to pull the pistons back up.
  48. 48. The regenerator could not be adequately tested without a fully operational engine.Therefore various regenerator combinations should be tested to determine the bestarrangement for this application. Variables in the regenerator design could include thematerial used, the volume, the hole pattern, size of holes/mesh, and others.9.0 ConclusionThe selected Stirling engine design has not yet met the specifications of our client. With asealed displacer piston, adequate pressure will be developed in the displacer chamber todrive the action. By incorporating the recommendations outlined above, we believe thatthe engine will meet the required design criteria described in the design requirementsmemo. Although the engine, in its anticipated future configuration, will not be able toproduce the 50 Watts of power initially envisioned, it will produce a visible poweroutput, be an asset to classroom demonstrations, be portable and run from a solar heatsource.
  49. 49. 10.0 ReferencesBevel, T. (1971). The Theory of Machines (3rd ed.). Great Britain: William Clowes andSons.Çengel, Y.A. & Boles, M.A. (1998). Thermodynamics. An Engineering Approach (3rded). New Jersey: McGraw-Hill.Daniels, F. (1964). Direct Use of the Sun’s Energy. New Haven and London: YaleUniversity Press.Diel Ltd. (2001). The Stirling Hot Air Engine. Retrieved September 9, 2003, fromhttp://www.stirlinghotairengine.comIncropera, F.P. & DeWitt, D.P. (2002). Introduction to Heat Transfer (4th ed.). NewYork: John Wiley & Sons, Inc.Lewitt, E.H. (1965). Thermodynamics Applied to Heat Engines (6th ed.). London: SirIsaac Pitman & Sons.Montgomery, R.H. (1978). The Solar Decision Book. New York: John Wiley.Mueller Solartechnik. (1998). Solar Collectors. Retrieved September 24, 2003, from, K. (n.d.). How Stirling Engines Work. In How Stuff Works Inc. RetrievedSeptember 9, 2003, from, A. (1977). Stirling Cycle Engines. Phoenix: Solar Engines.Schmidt, F.W. and A.J. Willmott. (1981). Thermal Energy Storage and Regeneration.New York: McGraw-Hill.The Solar Server. (n.d.). Solar Collectors: Different Types and Fields of Application.Retrieved September 16, 2003, from, A.M. (1963). Introduction to the Utilization of Solar Energy. New York:McGraw-Hill.