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Motore Stirling Motore Stirling Document Transcript

  • Team Solaris Final Design (Fall 2003) Group 12 Chris Newton Asegun Henry Hunter Ashmore Dustin Harrelson Sponsor: Dr. A. Krothapalli 1
  • Abstract_______________________________________________________________ 1 1.0 Introduction ________________________________________________________ 2 1.1 Background _____________________________________________________ 2 2.0 Project Planning ____________________________________________________ 5 2.2 WBS _______________________________________________________ 5 2.1 Schedule ____________________________________________________ 5 2.2 Project Procedures ____________________________________________ 6 3.0 Design Specifications______________________________________________ 7 3.1 Customer Needs and Specifications _______________________________ 7 3.2 Conceptual Designs ___________________________________________ 8 Design Concept 1_____________________________________________________ 8 Design Concept 2_____________________________________________________ 9 Design Concept 3____________________________________________________ 10 4.0 Concept Selection________________________________________________ 12 4.1 Selection Process ____________________________________________ 12 6.0 Solar Concentrator__________________________________________________ 22 7.0 Heat Containment System ____________________________________________ 26 8.0 Stirling Engine _____________________________________________________ 33 Two Basic Engine Designs ___________________________________________ 35 ALPHA Type _____________________________________________________ 39 BETA Type_______________________________________________________ 40 GAMMA Type ____________________________________________________ 41 Stirling Engine Design Selection _________________________________________ 42 Figure 8.9 The alpha type model Stirling engine rated up to 3000rpm. _______ 44 9.0 Tracking Control System _____________________________________________ 49 10.0 Frame ___________________________________________________________ 53 Appendix A ___________________________________________________________ 55 Appendix B ___________________________________________________________ 56 Appendix C ___________________________________________________________ 57 Appendix D___________________________________________________________ 58 Appendix D cont’d _____________________________________________________ 59 Appendix E ___________________________________________________________ 60 Appendix E cont’d _____________________________________________________ 61 Appendix F ___________________________________________________________ 62 Stirling Engine References ___________________________________________ 62 2
  • Abstract As fossil fuel technologies become obsolete, mostly due to the depletion of fuel sources, the demand for alternative energy technologies, such as solar power, fuel cells, and wind power, grows. The reason as to why these alternative energy sources have not been more widely utilized is that fossil fuels are relatively low cost compared to the initial setup price for these alternative sources, and the lack of efficient devices that are readily available for obtaining alternative energy. Of the available alternative energy sources, the sun is quite possibly the easiest to obtain, and is a great source of pollution free energy. The goal of our project, Solaris, is to harness the suns energy and in turn, generate electricity. This is to be done by use of a stirling engine/generator system which will be placed at the focal point of the parabolic reflector. 1
  • 1.0 Introduction 1.1 Background A potentially great source of radiant energy is the sun. The sun emits electromagnetic radiation with a solar irradiance of 1367 W/m2 on the earth’s surface. Of this solar radiation reaching the earth, it is comprised mostly of radiant energy ranging in wavelengths between 0.3 and 2 µm. This radiant energy is then comprised of two types of radiation, beam and diffuse radiation. If a flat surface collector is utilized, both beam and diffuse radiation is collected, but if an optical (i.e. parabolic/focusing) collector is used, then only beam radiation is collected. The purpose of a focusing solar collector is to increase the intensity of the solar radiation falling on the collector. The factor by which the solar irradiance is increased is known as the concentration ratio, CR, which is defined in Equation 1.1, Dm 2 CR = 1.156 E (4)( ) (1.1) F where Dm is the dimension of the collector and F is the focal length. Figure 1.1 shows the principle of light concentration for a parabolic reflector. 2
  • Figure 1.1 A parabolic reflector (Dm) concentrates the solar irradiance on the smaller collector (Di) at the focal point. By focusing the solar irradiance to a particular point, the system is capable of producing sufficiently high temperatures to use in a heat engine cycle to generate electrical power efficiently. This idea of using the suns heat as a source of power is not a new one. This concept is dated as far back as 1000AD with the development of focusing mirrors by Abu Ali al-Hasan al-Haitham. It is also noted that during the 1640s, in Rome, Father Athanasius Kircher had shown that sunlight could be concentrated to a point to ignite fires. Figure 1.2 shows an image of a German burning mirror of the 1700s. As shown in the picture, the mirror is being used to set fire to a pile of wood from a distance. Figure 1.2 Picture of ‘German burning mirror’ (Parabolic Reflector) of the 1700s. 3
  • By utilizing the high temperatures created at the focal point of parabolic reflectors, along with a heat engine, such as a stirling engine, it is possible to efficiently generate electrical power. A stirling engine is a closed-cycle, regenerative heat engine which uses and ‘external combustion’ process, which in this case is solar heat. The stirling engine works by converting heat energy to mechanical work, such as spinning a flywheel. This mechanical work can then be converted to electrical energy by use of a generator attached to the flywheel of the stirling engine. 4
  • 2.0 Project Planning 2.2 WBS The Work Breakdown Structure (WBS) Chart displays the structure of a project showing how a project is organized into a summary (phase) and detail levels. The WBS is a great way to organize a project into a schedule of duties and events that must take place throughout the project scope. Using a WBS chart is an intuitive approach to planning and displaying a project. As a planning tool, the WBS Chart can be used to quickly create a project by ‘drawing a picture’. Team Solaris’ WBS can be found in Appendix A. Our WBS shows the relationship between each of the activities the team is undertaking, and helps to give a clear view of the task that will be performed in this project. 2.1 Schedule The schedule for Team Solaris can be found in Appendix B. The schedule shows the breakdown of all the project activities. The chart shows all the dates by which activities will be started and/or completed by. All deliverables have been included in the schedule, allowing for preparation time before they are due. The dates on the schedule are tentative, and may be changed in order to complete the project in a timely fashion or to account for any unforeseen problems that may arise. 5
  • 2.2 Project Procedures Documentation and e-mails: 1. All Documents will be dated as received; a copy of all documents will be available to every team member as a hard copy, e-mail, or team folder on blackboard. 2. All e-mails concerning the project will be sent to every team member regardless of relevance to individual tasks. 3. The official copy of all documents will be held by Chris Newton, and will be brought to every group meeting. Meetings: 1. Regular meetings with the customer will be held no less then every other week to update him on the progress of the project. 2. Regular team meetings will be held no less then once every week to update group members on project progress. 3. All team members required to attend meetings unless notification of absence is given 24 hours before time of meeting. Reports and deliverables: 1. All group members will approve all reports. 2. Deliverables will be started no less then four days before they are due. 3. All team members must be present to prepare deliverables. 4. If a team member cannot be present to help in the preparation of the deliverables, he must give notice to rest of team. 6
  • 3.0 Design Specifications 3.1 Customer Needs and Specifications According to Dr. A. Krothapalli, Team Solaris’ final design needs to be capable of producing an optimum amount of electricity. Dr. A. Krothapalli wishes for Team Solaris to generate 1 kW or electricity, but due to the budget, the final output is negotiable. The electricity is to be generated from a stirling engine which obtains its heat from a solar collector. The solar collector, as instructed by our sponsor, is to be made from a surplus satellite dish. Another constraint, which was also place on the project, is that the dish must track the sun throughout the course of the day. This whole design and construction of the project is to be done for less than $5000. Table 3.1 Wish/Demand List of Sponsor and Importance Wish/Demand Requirement Importance Demand Solar Collector made from large parabolic dish 10 Demand Device to be self sufficient 10 Device to have a minimum output of 1kW of Demand electricity after sustaining itself (batteries, servos, 10 computer) Demand Dish must track the sun 10 Demand Dish must reset itself in the evening 10 Demand Type of engine to be used: Stirling Engine 10 Wish AC generator 8 The generation of electricity for this project is to be done by harnessing the suns energy with the use of a large parabolic dish, which must track the position of the sun throughout the day. The dish will be coated in aluminized Mylar because of its reflectivity, workability, and relatively low cost. The dish must then reset itself at night under its own power and be ready to operate the following day. The Stirling engine will 7
  • use the heat at the focal point of the dish to change heat energy to mechanical energy. A DC motor/generator will be attached to the Stirling engine, either by belt, or directly on the shaft. The generator needs to produce enough electricity to supply enough power to sustain the system, plus generate an optimum useable amount of electricity. 3.2 Conceptual Designs Once the needs of the customers’ ‘problem’ were understood, Team Solaris was able to come up with several basic conceptual ideas. Design Concept 1 This particular design consists of a parabolic dish with a stirling engine and generator located at the focal point of the dish. Solar radiation is reflected to the focal point, onto the expansion (heat) cylinder of the stirling engine. The one downside to this design concept is that there is a large amount of weight that needs to be supported at the focal point. Figure 3.1 shows a drawing of Design Concept 1. 8
  • Figure 3.1 Design Concept 1 – Components of system located at focal point Design Concept 2 This design concept, as shown in Figure 3.2, utilizes a heat containment unit, filled with a working fluid such as molten salt, which will transfer the heat from the focal point of the dish to the expansion (heat) piston of the stirling engine. The stirling engine will be located on the ground/platform beneath the parabolic dish. This design simplifies the design of the dish from the first concept, in that the supports at the focal point do not have to undergo as much stress. 9
  • Figure 3.2 Design Concept 2 – Heat containment at focal point. Use of working fluid to transfer heat to stirling engine. Design Concept 3 In this design concept, the solar radiation is focused onto a concave mirror, which is then reflected and focused downward through the center of the parabolic dish. Directly below the dish is where the stirling engine will be located, along with a heat reservoir, if needed. This concept is the most feasible, in that weight will not be a factor at the focal point, which simplifies the design, as shown in Figure 3.3. 10
  • Figure 3.3 Design Concept 3 – All components of system are placed below the center of the dish, and the solar energy is redirected from the focal point. 11
  • 4.0 Concept Selection 4.1 Selection Process In order to choose the best concept for the design, the team looked at each option, taking into consideration which design would be the most feasible and the simplest to construct. With this in mind, the team chose Concept Design 3 as its preliminary design. Before Team Solaris would permanently choose this design, it needed to be tested to make sure the optics ideology behind it would work. The testing was performed with a 24-inch parabolic reflector and a 35-mm gold plated concave spherical mirror. An apparatus was constructed to allow for adjustments of the mirror at the focal point. It was found that the idea behind the optics idea for transferring the suns energy did work, in that it transferred the light, but failed in that it did not transfer enough heat. Thus the simplest, and most favored design idea failed. Not wanting to deal with a working fluid, and a means of a pump system that could withstand high temperatures, Team Solaris decided that Design Concept 1 was the design to go with. Since Design Concept 2 failed, and the team chose to go with Design Concept 1, the temperature at the focal point needed to be determined. This was done with an Omega k- type thermocouple, and an Omega DPi8A digital display. It was found that the 12
  • temperature at the focal point would reach 700°F with out any problem. This proved to be an adequate amount of heat for the stirling engines which had been located for use on the project; with the operating temperatures of the stirling engines ranging from 300 to 1200°F. 5.0 Solar Collector The purpose of the solar collector is to collect the radiation incident from the sun. The parabolic shape is used to collect light from a larger area and condense it down to a much smaller area. The reduction in area increases the radiation power density, as the same radiation that would have been spread over a few square meters, can be collected and spread over an area less than a square meter. This concentration of radiation is used as a form of heating for the Stirling engine. The goal of the collector design is to maximize its efficiency within the project budget of $5000. Using some initial guess efficiencies for each energy conversion process, it was estimated that to produce a kilowatt of power output from the generator, that a twenty-foot diameter dish was needed. This option was not feasible because of cost, thus a ten-foot diameter dish was used. The ten-foot diameter dish was obtained and required assembly. The circular collector mesh was separated into four partitions. Each partition was supported by curved metal supports and could be subdivided into four sub-partitions as in the following figure. 13
  • Figure 5.1 Satellite Dish Partition The used ten-foot dish was donated to the team and therefore did not hinder the budget, however, being undersized for the initial power requirements made many design modifications become necessary. In order to optimize the design of the collector a material was needed to coat the shape and serve as a light reflector. The goal was to choose a material that could adhere to the satellite dish surface. The surface of the dish, shown below was made of a conformable metal meshing. 14
  • Figure 5.2 Satellite Dish Metal Mesh This mesh was the surface in which the reflective material would have to adhere to and therefore its composition had to be factored into the material selection. To get the maximum radiation reflected off the dish surface up to the focal point, a material with a high reflectivity had to be chosen. The radiation incident to an object must be absorbed, reflected or transmitted. Different amounts of radiation are transmitted and reflected for different types of surfaces, however, the following energy conservation equation shows how the total amount of radiation energy must be accounted for through each of the modes. Gabs = G ⋅ α , Gtr = G ⋅ τ , Gref = G ⋅ ρ (5.1) Gabs + Gtr + Gref = G , α + τ + ρ = 1 (5.2) 15
  • G is the incident radiation, α is the absorptivity, τ is the transmissivity, and ρ is the reflectivity. Each mode of radiation takes a fraction of the incident energy such that the sum of the coefficients is one. These three dimensionless constants are properties of any material and for an opaque surface τ is zero and the remaining coefficients transfer all the energy. For this application the goal is to find a material that could adhere to the parabolic shape of the collector while also having a high reflectivity. In the search for this material, aluminized mylar was chosen because it has the texture of wall paper and has a reflectivity of 0.83. Figure 5.3 Aluminized Mylar Film This particular material was also readily available and cheap, which made it an easy choice for the design. In addition to having a high reflectivity, the mylar also has an emissivity of .76, which is good because a high emissivity denotes that it emits a large portion of the radiation it absorbs. This would add back into the energy that is lost due to absorption. 16
  • Measurements of the dish dimensions were taken to calculate the equation to describe its shape. This was needed to accurately calculate the shape and focal point of the dish. Focal Point Hypotenuse Depth Radius Figure 5.4 Dish Parabola Equation and Focal Length By measuring the labeled radius and hypotenuse of the dish the depth could be back calculated using Pythagorean theorem. Depth = Hypotenuse 2 − Radius 2 (5.3) From this calculation the constant needed to calculate the equation of the parabola could be determined, where the shape of a symmetric parabola is given by, f ( x) = a ⋅ x 2 + b (5.4) where f(x) is the function describing the shape of the parabola, and x is the horizontal distance from the center. The constants a and b describe the shape, where b can be made zero by placing the bottom center of the dish at the origin. From this constraint, the value of f(x) is equal to the depth when x is equal to the dish radius. Therefore the constant a can be calculated using the following equation. Depth a= (5.5) Radius 2 17
  • Once the constant is solved for, the focal point can be found. The focal length of a parabola is the distance from the bottom to the focal point. The focal point for a symmetric parabola lies along the axis of symmetry, and the distance above the intersection of the axis and curve is given by. 1 fl = (5.6) 4⋅a Where fl is the focal length, which establishes the position of the focal point. The measurements for the ten-foot dish can be applied to equations (5.3) through (5.6) and the actual focal length can be determined. The following table indicates the measurements for the ten-foot dish and shows the corresponding calculated values. Table 5.5 Dish Measurements and Calculations Value (S I) Value (Eng ) Radius 1.524 m 5 ft Hypotenus e 1.613 m 5.292 ft Depth .528 m 1.732 ft a 0.227 (1/m) 0.745 (1/ft) fl 1.1 m 3.609 ft The calculation of the focal length is useful, however due to the dynamics involving the sun and earth the focal point will not be an exact point as it will actually be a focal area. The area in which the radiation is condensed is what will determine the radiation intensity. The higher the radiation intensity is the higher the temperature of heat reservoir will be, which supplies heat to the Stirling engine. There is a limit on the size of the focal area as the ratio of the collector area to the focal area can be calculated as the concentration ratio. The limit to the concentration ratio arises from the combination of the size of the sun with its distance from the earth. There is a small variation in angle of the incident radiation from the sun when its center is aligned with that of the dish. 18
  • Figure 5.6 Sun Diameter and Distance Affect on Concentration Ratio Figure 5.6 shows that the angle θs , causes a small variation in the angle at which incident radiation impinges the collector surface. This variation causes the focal point to spread over the area created by the rays that are not aligned perpendicular with the collector surface. This small area creates a limit for how small the focal area can be and can be calculated by knowing the angle θs and the area of dish. The angle θs is determined from the diameter of the sun and distance to the earth given by the following equation. r sin(θs ) = (5.7) R Where r is the sun radius and R is the distance from the sun using this equation the angle θs can be calculated as 0.27 degrees. The maximum concentration ratio for a circular collector is given by the following equation. Ac R 2 1 C max = = 2 = (5.8) Afp r sin (θs ) 2 Where C is the concentration ratio, Ac is the collector area, and Afp is the area of the focal point. The maximum concentration ratio for a circular parabolic collector is 45,000. The purpose in calculating the actual concentration ratio is to relate it to the maximum obtainable temperature of the receiver placed at the focal region where the relationship is given the following figure. 19
  • Figure 5.7 Concentration Ratio vs. Temperature It is clear from this figure that in order for the receiver temperature to be maintained in the regime over 1,000 degrees C the concentration ratio must approach 1,000. This is a useful calculation as will be demonstrated in the following section. Using the area of the ten-foot dish, the necessary focal area can be determined to bring the receiver into the 1,000 degree C temperature range. The following graph shows how the concentration ratio varies, where the focal area is described by a circle of diameter dfp. The diameter is shown in meters and the corresponding concentration ratio is calculated. 20
  • 8000 8000 6000 Concentration Ratio ( ) C dish d fp 4000 2000 400 0.04 0.06 0.08 0.1 0.12 0.14 1.5in d fp 6in Focal Area Diameter (m) Figure 5.8 Concentration Ratio vs. Diameter of Focal Area From this plot it is evident that in order to get the receiver temperature in the 1,000 degree range the focal area would need to be reduced to a small circle less than four inches in diameter (0.1m). With this in mind, the necessity of coating the dish with the mylar effectively increased. A few different methods were explored involving attempts to put screws through the mylar and bolt it to the metal mesh of the dish. These methods were unsuccessful as they stressed the mylar and caused large wrinkle deformations in the shape. These deformations would cause the radiation to deviate from the prescribed path and would serve to increase the focal area. Different types of adhesives were researched and a spray adhesive that was weather resistant was found. This adhesive was then used to coat the dish with the mylar, over the screws. 21
  • Figure 5.9 Mylar Cut Around Screws The mylar was cut into strips the size of the sub-partitions and then cut into smaller sizes. Each piece was glued to the mesh and small slits were cut where the screws were attached to allow the mylar to lie more flat against the mesh. After the mylar was laid the focal area was measured, and was found to be about two feet in diameter. This large focal area is largely due to wrinkles and imperfections in the dish’s shape. To further condense the light a magnifying glass, or solar concentrator, were used to decrease the focal area and increase the temperature. 6.0 Solar Concentrator The purpose of the concentrator is to condense the light reflected off the satellite dish. The dish is moderately effective at collecting the light, however imperfections in the surface compounded with its loss of reflectivity from handling prevent it from creating the necessary heating to run the engine. The goal is to design a magnifier that can focus 22
  • the light into a smaller region to increase the power density. By decreasing the focal area the concentration ratio can be increased, and subsequently, the operating temperature of the heat reservoir can be increased. By increasing the temperature of the reservoir the heat to the engine can be amplified to result in an increase in efficiency. This is best understood in relation to the idealized carnot efficiency given by, TH − TC η= (6.1) TH where η in the ideal heat engine efficiency, TH is the hot temperature and TC is the cold temperature. This relationship is useful because it gives an upper limit to the feasible efficiency and also shows how the efficiency is increased, by increasing the difference between TH and TC. The Stirling engine portion of the energy conversion process is expected to be the least efficient, therefore persistent efforts must be made to boost the engines efficiency. Subsequently the goal of optimizing this component of the design is to capture most of the reflected radiation and significantly reduce the focal area. To do this an optical magnifier must be used to further condense the sun’s light into a small region of intense heating. To focus the radiation, a Fresnel lens will be used, which is a prism ridge approximation to a magnifying glass. A Fresnel lens uses a series of ridges as circular rings to bend light rays toward its focal point. Each ridge is an approximate prism with the corresponding shape to focus light towards the focal point. The lens will be used instead of a glass magnifying glass to save cost, as a magnifying glass of the size required for this application could easily exceed the budget. The Fresnel lens, as an approximate magnifying lens, can be made from a plastic sheet, which dramatically reduces its cost. The following figures illustrate the manner in which it manages incoming light rays and directs them to its focal point. 23
  • Figure 6.1 Fresnel Lens Ray Ddiagram Figure 6.2 Fresnel Lens Characteristics The Fresnel lens uses concentric ridges to focus the light and the density of the ridges determines the image quality. For this application image quality is not the objective, and therefore a low ridge density can be used for the purpose of light collection. The Fresnel lens will be mounted below the focal point of the dish, so that the focal points for the dish and lens coincide. For this design a Fresnel lens from Edmund Optics will be used, which 24
  • has a diameter of 18.25 inches and a focal length of two feet. The following figure illustrates the positioning of the solar concentrating lens with respect to the dish. Focal Point 2 feet Lens Figure 6.3 Positioning of Solar Concentrator The solar concentrator increases the operating temperature of the heat reservoir by directly increasing the concentration ratio. The factor of concentration ratio increase is denoted by the reduction in area given by the following equation. Ai = K ⋅ Ar (6.2) Where, Ai is the initial concentrated area, Ar is the reduced area and K is the concentration increase factor. With the initial radius approximately two feet in diameter and reduced area approximately four inches in diameter the concentration factor is approximately 36. This is well over ten, which would boost the temperature from the low temperature (approximately 400 degrees C) regime to the high temperature regime (approximately 1000 degrees C). Thus this component serves as the solar concentrator, which intensifies the solar radiation into a small focal region. With the heat collected the need for its containment arises. With such a high power density the energy could easily exceed that of which a Stirling engine is designed for. Therefore the need for a thermal buffer arises. The thermal buffer should store the intense heat and supply it to the Stirling engine component at a rate that is acceptable. 25
  • 7.0 Heat Containment System The heat containment system is needed to buffer between the solar radiation and the Stirling engine. The need for the buffer arises from the need to supply the engine with a consistent heat input. By building a thermal buffer that can absorb radiation, store thermal energy and deliver it to the engine, a thermal reservoir can be achieved. A few benefits arise from this component including absorption maximization, time constant extension and heat loss minimization. These three characteristics are the advantages of implementing such a system and they are the target factors in the system optimization. To accomplish the three target goals the heat containment system will include different materials, which are best suited for each factor in the design. These different materials will each serve an individual purpose and will be optimally designed to interface with each other. To maximize absorption the containment system will need to be made of a material with a high absorptivity. This material may not have all the characteristics that will be best for the design however a material with a high absorption and low emissivity and high thermal conductivity will be the best to interface with the incident radiation. To design a material for this application, a cheaper material such as aluminum, which will make up the bulk of the system, can simply be coated or plated with another material with the high absorption and low emissive properties needed. The two most likely coatings are black nickel oxide and black chrome. It is known that black surfaces approach the characteristics of the idealized black body, and therefore a black coating is necessary. The black nickel oxide would be the most effective candidate when comparing the ratio of its absorptivity and emissivity, however this plating can be 26
  • expensive and may prove to hinder the budget. The black nickel oxide absorptivity is 0.92, while its emissivity is 0.08. As with these characteristics, it will effectively capture the reflected radiation and will have minimal surface radiation. The ratio of these properties is 11.5, however for the black chrome, the absorptivity is 0.87 and its emissivity is 0.09, yielding a ratio of 9.7. Although this ratio is smaller this coating will be more cost effective and easily obtained, therefore it will be used as the coating in this design. The heat containment system will be used as a thermal buffer and in essence it will serve as a large thermal capacitor, because it will store the sun’s energy and provide it at a desirable rate. The thermal reservoir will need a material with a large specific heat. The systems time constant must be determined, so that the correct amount of mass can be used to store enough energy in the thermal capacitor so that the system does not fluctuate throughout the day’s operation. To determine the systems time constant, the following energy balance must be evaluated to determine the transient temperature profile of the reservoir. dT Qin − Qout = m ⋅ Cp ⋅ (7.1) dt Where Qin is the heat supplied by the collector and concentrator, Qout represents the convective and linear approximated radiation losses, m is the mass of the reservoir, Cp is dT the specific heat of aluminum and is the time rate of change of the temperature. The dt convective losses will be for all exposed surfaces. The radiation losses will be treated as the linearized approximation ε ⋅ σ ⋅ A ⋅ T 3 to reduce model complexity, where T is an overestimated 1200 degrees C for the purpose of worst-case analysis. The emissivity ε 27
  • will be that of the chrome plating and the heat input will be calculated based on the reflectivity of the mylar and absorptivity of the chrome plating. For this analysis the heat supplied to the engine will be estimated at three kilowatts. The lost heat will be calculated using one inch thick ceramic tile insulation with a thermal conductivity of 0.09 W/mK at 1000 degrees C. Using these assumptions and reductions this differential equation can be solved, where the result has the following form.  −t  T (t ) = T∞ + Qin ⋅ Rth ⋅ 1 − e m⋅Cp⋅ Rth  (7.2)     T(t) is the transient temperature function and Rth is the thermal resistance given by the following equation which takes into account the natural convection from all surfaces, the radiation from all surfaces, and the conduction through the insulation. −1    1  Rth = h ⋅ A + ε ⋅σ ⋅ A ⋅T 3 +  (7.3)  ∆x 1   +   k ⋅ A hA  h is the natural convective heat transfer coefficient, A is the surface area, ε is the emissivity of the chrome plating, σ is Boltzman’s constant, T is the overestimated temperature, ∆x is the insulation thickness, and k is the insulation thermal conductivity. The thermal resistance was derived by relating the resistances from the following thermal loss modeling circuit, which models all separate heat transfer modes in parallel. 28
  • Reservoir Temp Convection Ambient Temp Radiation Conduction/Insulation Convection Figure 7.1 Thermal Reservoir Heat Loss Resistance Circuit To further optimize the heat reservoir, the thermal losses to the surroundings must be minimized so that it can remain at the highest possible temperature. To do this only, one face of the reservoir must absorb the radiation as the other surfaces can be insulated from the outside air. Solarguard insulation will be used to reflect the radiation emitted by the reservoir back onto itself. Solarguard insulation is a foil-like wrapping that can be included in the design in between the reservoir and insulating ceramic tiles. By insulating the reservoir the Qout term in Equation (7.1) can be minimized, which can result in a higher operating temperature. Considering these components, optimization will lead to greater and more efficient performance. The geometry of the reservoir should be one that minimizes the surface area and maximizes the mass. To do this the triangular shaped interface was selected because it has the smallest amount of faces, and minimizes surface area. Therefore all other shapes with the same cross sectional area will have greater surface area. In addition to optimal geometry highly conductive thermal grease will be interfaced between the engine and 29
  • reservoir to minimize contact resistance. Subsequently the triangular shape was used as the basis for the design and is shown in three dimensions in the following figures. Figure 7.2 Heat Containment System 30
  • Figure 7.3 Heat Containment Front View Using the thermal model, a transient simulation of the thermal reservoir performance was run as it displays the time response of the system using the above design, in which the dimensions are shown in inches. 31
  • 1000 974.214 800 Temp ( t ) 600 400 298 200 4 4 4 0 5000 1 .10 1.5 .10 2 .10 0 t 4 2×10 Figure 7.4 Heat Capacitor Transient Temperature Profile The solution to Equation (7.2) yields Figure 7.4, which is the transient response of the temperature reservoir. The denominator in the exponential of equation (7.2) gives the system time constant which is 1.4 hours such that the time to steady state is approximately 7.1 hours. Assuming the sun rises around seven o’clock, the reservoir should reach steady state as the sun reaches its maximum flux around two o’clock in the afternoon. This large time constant will serve to minimize fluctuations in the heat input to the Stirling engine as it should also run for 7 hours after the heat input is diminished at sunset. According to the simulation the reservoir should supply the heat to the engine above 980K (700 degrees C), as this is useful information to selecting the proper Stirling engine. 32
  • 8.0 Stirling Engine A Stirling engine is a closed-cycle, regenerative heat engine which uses an external combustion process, heat exchangers, pistons, a 'regenerator' and a gaseous working fluid contained within the engine to convert heat to mechanical work (motion). The regenerator is an important feature of the Stirling engine because is used to store energy from the gas as it passes through on the way to the cooler (low temperature heat exchanger) and gives energy to the gas as the gas flows back through the regenerator going to the heater (high temperature heat exchanger). It is the regenerator that makes the Stirling Engine. The operation of the Stirling engine is not complicated. There are no carburetors, ignition systems, valves, or other complicated mechanisms. Stirling engines run off of the expansion of air as it is heated, and the contraction of the same air as it is cooled. The source of heat can be wood, fuel oil, sunlight, or geothermal sources. Because the Stirling engine uses external combustion, it is extremely environmentally friendly. The actual combustion process can be controlled to deliver maximum heat with extremely low emissions. The engine’s suitability for renewable energy sources such as geothermal, biomass and solar energy make it a true "green" machine. It is a quiet engine, addressing noise pollution concerns. 33
  • The Stirling Cycle The cycle consists of four internally reversible processes; isothermal compression at the cold temperature source (Fig 8.1, curve 1), constant volume heating (curve 2), isothermal expansion at the hot temperature source (curve 3), and constant volume cooling (curve 4). These processes are performed on a sealed volume of working gas which is most often air. Figure 8.1 P-V Diagram of the Stirling cycle. 34
  • Two Basic Engine Designs Displacement Type There are two basic categories of Stirling engines. The first is the simpler of the two and is a basic displacement engine (Fig 8.2). Figure 8.2 Displacement type Stirling engine cycles. In the displacement engine there are two pistons. The smaller piston shown in Figure 1 is the power piston. All of the power for this model is provided by the power piston. The second larger piston is the displacer piston. Its function is to move the air between the hot and the cold sides of the air compartment. It provides no power at all. 35
  • The power piston for this model should be 90 degrees out of phase from the displacer piston. This model has four simple steps. Beginning at the top of the Figure 1, the first step is heating. The heating is caused by the movement of the displacer piston so that most of the gas is on the hot side. The temperature of the gas subsequently increases, causing an increase in pressure. Because of this increase in pressure there is an expansion of the gas causing the power piston to rise. Then, due to the 90 degree phase shift between the two pistons, the displacer piston is moved, resulting in the cooling of the gas. But when the gas is cooled, the pressure decreases, causing a contraction in the gas, thereby pulling the power piston back down. Then once again, due to the 90 degree phase shift, the displacer piston follows causing the gas to shift to the hot side of the chamber. The temperature of the gas then increases, which completes the cycle. This is the most basic model of the Stirling engine. The second model works on the same principles as the displacement type but it is a little more intricate and is known as a two-cylinder engine (Fig 8.3). 36
  • Figure 8.3 Two-cylinder Stirling engine cycle. 37
  • The two piston model is slightly more complex than the displacement model. There are still two pistons, and they are still 90 degrees out of phase from one another. However, in this model power is supplied by both pistons, and the displacement of the gas is caused by both as well. Yet same basic process occurs as with the displacement model. Once again, starting from the top of the illustration, the first step is the heating of the gas in the chamber. The flywheel is turning, and thus the cold piston moves up, and the hot piston moves down causing the gas to flow to the hot side. This then causes an increase in the temperature of the gas. The gas therefore expands, pushing both pistons downward. At this point the inertia of the flywheel causes it to continue rotating which in turn raises the hot piston and pulls the cold piston downward. The gas is then pulled to the cold side of the chamber, and the temperature of the gas is decreased. This decrease in temperature causes the gas to contract, and therefore pulls both pistons upwards. Then, once again, the inertia of the flywheel pulls the hot piston down and pushes the cold piston up. Thus the gas flows to the hot side of the chamber and is heated, ending the cycle where it began. There are hundreds of variations of types of these two designs. They are divided into Alpha (two-cylinder type), Beta (displacement type) and Gamma (displacement type). Then there are the double acting engines which are alpha engines in series. These can drive either a crankshaft drive, a swashplate drive or a cousin, the wobble drive. 38
  • ALPHA Type The Alpha engine (Fig 8.4) is a two-cylinder type having two pistons in separate cylinders which are connected in series by a heater, regenerator and cooler. The Alpha engine is conceptually the simplest Stirling engine configuration, however, it suffers from the disadvantage of both pistons requiring seals in order to contain the working gas. Figure 8.4 Alpha type Stirling engine. The Alpha engine can also be compounded into a compact multiple cylinder configuration (Fig 8.5), enabling an extremely high specific power output. The four cylinders are interconnected, so that the expansion space of one cylinder is connected to the compression space of the adjacent cylinder via a series connected heater, regenerator and cooler. The pistons are typically driven by a swashplate, resulting in a pure sinusoidal reciprocating motion having a 90 degree phase difference between the adjacent pistons. 39
  • Figure 8.5 Compounded Alpha type Stirling engine. BETA Type The Beta engine (Fig 8.6) has a single power piston and a displacer, whose purpose is to "displace" the working gas at constant volume, and shuttle it between the expansion and the compression spaces through the series arrangement cooler, regenerator, and heater. The Beta configuration is the classic Stirling engine configuration and has enjoyed popularity from its inception until today. 40 Figure 8.6 Beta type Stirling engine.
  • GAMMA Type Gamma type engines (Fig 8.7), like Beta, are also displacement type have a displacer and power piston, similar to Beta engines, but in different cylinders. This allows a convenient complete separation between the heat exchangers associated with the displacer cylinder and the compression and expansion work space associated with the piston. Thus they tend to have somewhat larger dead (or unswept) volumes than either the Alpha or Beta engines. Figure 8.7 Gamma type Stirling engine. In the gamma-type engine cycle, the isothermal compression occurs as the power piston reduces the volume of the working gas and the displacer chamber is in the cold source state. The displacer then insulates the cold source, moving the gas in the chamber to the hot source, resulting in constant volume heating. Isothermal expansion occurs as the power piston moves, allowing the working gas to expand. Finally, the displacer insulates the hot source, moving the working gas to the cold source, cooling the constant volume of gas. Note: During the expansion process some of the expansion must take place in the 41
  • compression space leading to a reduction of specific power. Gamma engines are therefore used when the advantages of having separate cylinders outweigh the specific power disadvantage. This is the type of engine that will be used for our design. Stirling Engine Design Selection In selecting a Stirling engine to generate our 1kW goal we quickly ran into a problem. There are tons of available plans for model Stirling engines, but very few are even rated over 100 W mechanical work output. It turns out that an affordable 1kW generating system is the goal of quite a few companies right now. Affordable is the key word here. The first problem is, almost all of them are in the prototype stage. The few that aren’t in prototype stage are designed for use with a fuel burner and would be near impossible to modify to mount at the focal point of a concentrating dish. Even if we could talk them into reprogramming the control computers and succeed in mounting it in the correct orientation at the focal point, we still have the problem of cost. The lowest priced complete 1kW unit that is for sale is somewhere around 3 times the budget of our entire project. There are several companies working on units in the 1kW range, but they do not like revealing too much about them. These people base their entire livelihood on these engines, so of course they are not going to let their plans out to anyone. Stirling Technology Company (STC) is one company with a commercially available 1kW system. 42
  • Figure 8.8 Stirling Technology Company’s RG-1000 1kW generator When first searching for the designs for a Stirling engine, we quickly found plans everywhere for working models. We found a few very good designs for model Stirling engines that had been built and tested. We thought of maybe scaling up one of these designs. A Japanese inventor by the name of Koichi Hirata developed the design we were thinking of scaling up. The plans for the model are all online and it is said to run at up to 3,000 rpm. Scaling this design up to our needs sounded like a good idea. The completed model can be seen in Figure 8.9. 43
  • Figure 8.9 The alpha type model Stirling engine rated up to 3000rpm. Another design by the same inventor is a rotary displacer prototype. We decided against this one since this is a very new prototype. There is no data available about it and there is not anything that even says it will work. Figure 8.10 The prototype rotary engine 44
  • It turns out the Stirling engine process is fairly simple in principle; however getting one to work properly is almost an art. There are so many factors that make a different in the performance of the engine. Even something as seemingly miniscule as a small temperature gradient in the piston wall is enough to throw the efficiency of the entire engine out of whack. After talking to numerous people that center their lives on Stirling engine design, it became clear that relying on a design that had never been tested before was out of the question. The only logical choice was to settle for a lower power output from an engine that is a proven working design. After countless hours of searching, a man by the name of Mr. Dieter Viebach in Germany was located that produces plans for a gamma type Stirling engine with a mechanical work output of 500 W an electrical output of 450 W. These plans are sold at the moderate cost of 65 euros, or about $79 USD. The castings are apparently available for about $905 USD. This is of course without shipping. 45
  • Figure 8.11 Viebach Synchrongenerator ST 05 G-G 450 Watt This engine stands a height of 600 mm, or about 23.6 inches. The surface area of the heating side is 350 x 300 mm, which is about 13.8 x 11.8 inches. The total weight when mostly made of aluminum casting is around 20 kg, or 44.1 lbs. The flywheel has a mass of 7.5 kg (16.5 lbs) and a diameter of 280 mm (11 inches). The working piston diameter is 85 mm (3.35 inches), the restrictor piston diameter is 96 mm (3.78 inches), and the stroke is 75 mm (2.95 inches). The engine was designed with air or nitrogen as 46
  • working fluid at an operating pressure of up to 10bar (145psi). The method of heating it arbitrary since it is a Stirling engine, but the prototype was heated with propane gas. With a fuel flow rate of 225 gram/hour the engine produces 300 W mechanical work. The gross calorific value for propane is 13.87 kWh/kg. The given mass flow rate equates to 3.121 kW of heat input which is less than our estimated heat input from the concentrating dish. There must be a source of constant water circulation to cool the engine. If no water is delivered to a Sterling engine the temperature begins to equalize after a matter of minutes, which soon stops the engine from running. The engine is estimated to have an efficiency of 22%. The engine starts running at 200°C (392°F) and produces 500W power output when near the max temperature of 650°C (1202°F). The idling speed is approximately 800 rpm and the torque output is 8 Nm. The cast set includes a majority of the parts necessary to build the engine. The parts are sand-cast and therefore need further machining before they can be used in the engine. The set includes the crankcase, quill, frame cover, cooler with guidance restrictor, actuator, cylinder head, working piston and piston rods, restrictor, one connecting tube elbow with flange, and one cooling water pick up flange. These parts are all for use up to the 10 bar rated pressure. Some parts must be made in addition to the cast parts. Standard parts like caps, seals, screws, pipe, and other miscellaneous items must also be bought. The following drawings are the only ones we have access to until we order the complete drawing set. Included with the drawings is a detailed list of the additional materials needed along with supply sources. The drawings include eleven sides text with seven illustrations, four parts list in DIN A4 format, four detailed materials lists, one design in 47
  • DIN A2, five designs in DIN A3, 55 designs in DIN A4, four sides manufacturing and testing instruction sheets, and one report. Figure 8.12 Two drawings of the ST 05 G (without generator) A group of hobbyists called the German Study Group are working on Stirling engines. The most powerful engines they are making are based of Mr. Viebach’s gamma type engine design. They have created multiple variations of Viebach’s design, running off of heat sources ranging from biomass to solar heat. Below is a 1kW unit that is based on Mr. Viebach’s design and is currently being developed by Epas Products in Germany. 48
  • Figure 8.13 EPAS Stirling BM 1000 uses biomass as a heat source 9.0 Tracking Control System In order to achieve the greatest potential ‘harvest’ of the suns energy at all times, we need a system capable of tracking the sun’s movement across the sky. This tracking system needs to be capable of continually adjusting the altitude and azimuth angles of our parabolic reflector so as to keep the reflector under maximum solar irradiance. Also, this system should be able to ignore transient shadows and lights from fast moving sources such as clouds, shrubbery, and birds, and also ignore oscillations of the parabolic reflector caused by wind. They system must also be capable of returning the parabolic reflector to its original ‘home’ position in anticipation of the next sunrise. The sun’s position is related in terms of several different angles, but for simplicity, its position can mainly be based on its altitude and azimuth angle. All the sun-angle relationships, however, are based on solar time. Solar time is the apparent 49
  • angular motion of the sun across the sky, with solar noon being the time when the sun crosses the meridian of the observer. Solar time is calculated by applying two different correction factors to the local standard time. The first correction factor is a constant which is a correction for the difference in longitude between the observers meridian and the meridian on which the local standard time, Lst, is based. For the continental United States time zones, the standard meridians are: Eastern - 75°W; Central - 90°W; Mountain - 105°W; and Pacific - 120°W. The second correction factor takes in account the perturbations in the earth’s rate of rotation. This second correction factor is found from the equation of time, E = 229.2(0.000075 + 0.001868 cos( B) − 0.032077 sin( B) K (9.1) K − 0.014615 cos(2 B) − 0.04089 sin( 2 B)) where 360 B = (n − 1) (9.2) 365 and n is equal to the day of the year, thus 1[n[365. The difference in minutes between solar time and standard time is thus Solar time – standard time = 4(Lst-Lloc) + E (9.3) 50
  • where Lloc is the longitude of the location in question measured in degrees west. It is also a known fact that it takes the sun four minutes to transverse 1 degrees of longitude. Tallahassee is located in the Eastern time zone, therefore the standard meridian, Lst, for Tallahassee is 75°W, and its longitude is 84.28°W. For calculation purposes, considering the 365th day of the year, the correction to standard time is –2.64minutes, thus making 12-noon Eastern Standard Time equal to approximately 11:47:36 AM solar time. This means that the sun will cross directly overhead of Tallahassee at 12:02:64 PM Eastern Standard Time on the 365th day of the year. Appendix C shows how this calculation was performed and Figure C-1 of Appendix C shows the equation of time as a function of time of year for Tallahassee. By knowing the solar time, you can find when the sun will be directly overhead for that particular day, which will aid in locating the altitude and azimuth angle of the sun. The solar altitude angle, αs, is the angular distance above the horizon, with a maximum of 90 degrees. The azimuth angle, γs, of the sun, is the angular distance measured along the horizon in a clockwise direction. Figure 1.1 shows the relations of the different angles used in determining the suns position in the sky. 51
  • Figure 9.1 Angles related to position of sun and view showing azimuth angle. The tracking system for the collector will have two axis of motion. The system will have 90° of altitude travel and 240° of azimuth travel. The altitude drive will range from 0° to 90°, as measured from the horizontal, and the azimuth drive will travel from 60° to 300°. This will allow for the collector to remain in the direct sunlight throughout the day. A single Quadrant Photodiode (4-element array) Amplification Module will be used to control both axes. The module planned for used is Phresh Phontonics’ SiQu50-M module. The SiQu50-M combines a Silicon Quadrant Photodiode with amplifiers and position sensing circuitry, which provides output voltages of both the sum of the axes and of each axis independently. The Silicon Photodiodes produce a current that is proportional to the light falling on it. The detector is made of one monolithic piece of Silicon, thus the response from each element will be identical. By a comparison of the produced currents, the location of the light can then be determined. When each of the four elements produces an equal current, the source of light is centered. The outputs for the azimuth (X) and altitude (Y) angels can be compared as follows: 52
  • X=[(i1+i2)-(i3+i4)] 104/(i1+i2+i3+i4) (9.4) Y=[(i1+i4)-(i2+i3)] 104/(i1+i2+i3+i4) (9.5) This current is then converted and amplified to a useable voltage. The voltage input needed to control the module ranges from 5 to 18 volts. The sensing area of the module is 50 square millimeters, and has a spectral response of 400 to 100 nanometers with an output voltage of –Vcc-3/-Vcc+3. Appendix D shows an electrical diagram of the SiQu50- M module and a drawing of its outer casing. An issue that may need to be considered in the future with this product is the intensity of the light beam falling on the module, which could, if needed, be taken care of my creating a ‘mask’ for the module. All adjustments for the tracking system should be made on a clear day so as to have few clouds to interfere with setting procedures. 10.0 Frame For the chosen design, all of the components of the system are located at the focal point of the dish. A frame is to be constructed which is capable of withstanding the forces and moments that will be experienced at the focal point of the dish. The frame will have to securely house the heat containment unit, the stirling engine, and the generator. It is approximated that the maximum weight to be loaded at the focal point of the dish is 500 pounds. Because of this, it was decided that the frame should be constructed out of carbon steel square tubing and flat bar. It may seem a bit over-kill, but it leaves little chance for failure. 53
  • Aside from the structural design of the frame, it must also be capable of maneuvering the dish to track the sun. The frame must move the dish in both the altitude and azimuth directions; 90 degrees from the horizon in the altitude direction, and 240 degrees in the azimuth direction. This is to be accomplished by use of two separate linear actuators, which work in conjunction with the Silicon Quadrant Photodiode module. Preliminary drawings of the frame for the system are located in Appendix E. 54
  • Appendix A Activity Responsible Input Output 1.0 Meet with Sponsor Team 1.1 Customer Needs " 1.1.1 Needs Statement " 1.1.2 Product Specifications " 2.0 Research and Conceptualization Team 2.1 Design Concepts " 2.2 Calculations Books and Model Asegun Working Estimates Information 2.2 Initial Testing Temperature and Smaller dish and Chris and Dustin Heat Transfer stirling engine Estimate 2.3 Concept to Prototype Team 3.0 Design Team 3.1 Materials Selection " 3.2 Materials Location " 3.3 Components " 3.3.1 Parabolic Dish Forms, Vendor Begin Assembly, Chris Location, Trip Plan, Perform Tests and Setup Location Calculations 3.3.2 Aluminized Mylar Run actual test to Team Mylar and Adhesive calculate temperature and heat transfer 3.3.3 Frame Current components Optimized, robust Dustin and design functioning design optimization scheme 3.3.4 Tracking System Current design, motors, dish Optimized radiation Chris and Hunter infastructure and input supports 3.3.5 Operating System Team 3.3.5.a Windows 2000 " 3.3.5.b Labview " 3.3.5.c C++ " 3.3.6 Parabolic Mirror Locate Vendor and Begin Assembly, Hunter determine optimal Perform Tests and design Calculations 3.3.7 Heat Storage Calculations of heat Fluid Selection and Asegun storage and final Vendor Location optimization of design 3.3.8 Stirling Engine Locate Vendor and Begin system tests for Dustin and Hunter obtain required specs efficiency, cycling, and output and fatigue 3.3.9 Generator Locate Vendor, RPM Meet 1kW Requirement requirement; begin Asegun and Chris correlated with engine work on robustness output and consistency 4.0 Product Development Team 4.1 Drawings " 4.2 Ordering/Obtaining Parts " 4.3 Machining " 5.0 Construction of System Team 5.1 Assembly " 5.2 Testing " 6.0 Delivery of Product Team 55
  • Appendix B 56
  • Appendix C Solar time for Tallahassee Lst := 75deg Lloc := 84.28deg standardtime := 12 n := 365 360 B := ( n − 1) ⋅ 365 E := 229.2( 0.000075+ 0.001868cos ( B) − 0.032077sin ( B) − 0.014615cos ( 2B) − 0.04089sin ( 2B) ) E = −13.99 ( ) solartime := 4 Lst − Lloc + E + standardtime solartime = −2.638 Lst := 75deg Lloc := 84.28deg standardtime := 12 n := 1 , 31.. 365 360 B( n ) := ( n − 1) ⋅ 365 E( n ) := 229.2( 0.000075+ 0.001868cos ( B( n ) ) − 0.032077sin ( B( n ) ) − 0.014615cos ( 2 B( n ) ) − 0.04089sin ( 2 B( n ) ) ) E( n ) = -2.904 ( solartime( n ) := 4 Lst − Lloc + E( n ) + standardtime ) 5.348 solartime( n ) = 2.307 8.448 -14.224 E as a function of time of year 16.7 20 16.384 13.66 Equation of Time (Minutes) -6.23 -2.872 -3.362 10 27.736 3.05 5.122 E( n) 0.626 0 7.991 3.753 14.402 -13.589 10 11.978 15.456 15.105 -4.505 -2.237 20 0 100 200 300 400 26.808 n 6.847 Time of year (Days) 57
  • Appendix D Figure D-1 Electrical Schematic of SiQu50-M module Figure D-2 Drawing of SiQu50-M module 58
  • Appendix D cont’d 59
  • Appendix E 60
  • Appendix E cont’d 61
  • Appendix F Stirling Engine References http://www.stirlinghotairengine.com/about.htm www.precision-d.com/stirling/proposal.html http://www.ent.ohiou.edu/~urieli/stirling/engines/ http://www.ent.ohiou.edu/~urieli/stirling/engines Solo http://www.stirling-engine.de/engl/solare_energiesysteme.html Sandia Labs http://www.energylan.sandia.gov/sunlab/contacts.htm STM Power http://www.stmpower.com/Contact.asp Tamin Enterprises http://www.tamin.com/company.htm Sunpower http://www.sunpower.com/contact/contact.html STC http://stirlingtech.com/about/contact.shtml WhisperGen http://whispertech.co.nz/contact.html Japanese Inventor http://www.bekkoame.ne.jp/~khirata/ Sunmachines http://www.sunmachine.de/english/main.html 62