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Stirling engines are promising candidates for applications where air breathing engines cannot be used. Self contained engines capable of operating independently of the environment are required to convert thermal energy into electric power, or to perform other necessary functions. These are ideally suited for power generation onboard spacecrafts with radioisotope heat source. These engines can power interplanetary missions to Mars and beyond. The problem of parametric analysis, sensitivity and numerical optimization of Stirling cycle engine is discussed and applied to a specific example of a 2kWe free piston Stirling engine. Stirling cycle simulation programs are generated with emphasis and adaptations peculiar to free piston design for space use. Design algorithms are generated in MatLab and optimization toolbox is used for the parametric analysis adopted in this thesis. A free piston beta Stirling engine with a linear alternator configuration has been studied for the interdependency and performance effects of various important operational parameters. The analysis has been carried out in order to optimize the primary parameters, weight vis a vis envelope (length and diameter) and stroke of the engine, to make it suitable for space use. The major cycle parameters considered are operating pressure, linear speed, dead space ratio and swept volume ratio, classified as secondary parameters. The whole analysis has been carried out at a cycle temperature ratio of 0.4 for a heat source temperature of 873 K, typical of a radioisotope heat source. The optimization is carried out for the defined design requirements viz. envelope of 50 × 50 cm , stroke of less than 10 cm, and heat source temperature of 873 K. The process of parametric optimization of the primary parameters viz engine envelope and stroke are carried out with respect to the secondary parameters. Iterations are carried out on the design programs in MatLab. The results indicate that the three primary parameters have a different set each, of the secondary parameter values when optimized to the design requirement. The fmincon solver of MatLab in the optimization tool box is selected in order to validate the optimization results. The solver is used to find a minimum of a constrained nonlinear multivariable function defining the primary parameters. The results obtained concur with the optimization results generated by the design algorithm. Further, the interdependency amongst the primary and secondary parameters is studied by generating MatLab plots for all possible combinations among the various parameters. The effect of variations in the pressure and linear speed on the system envelope and stroke are more pronounced at lower range values of the pressure and speed and the variations of the primary parameter values are constant at higher ranges. The effect of dead space ratio and swept volume ratio (>1.0) is not pronounced. The requirements in the environment of space place a number of constraints upon a Stirling engine/alternator design that are not present in terrestrial applications. High specific power is achieved by designing the engine for higher pressure and frequency operation than a terrestrial Stirling engine, and by using light weight materials where appropriate. Cylinder is the heart of the engine and it forms a major proportion of the total system mass. Mass and heat loss estimates and analysis have been carried out on the cylinder for various materials of construction. Based on the analysis feasibility exists for a Cu-Ni combination. The system would have a mass of 7kg with a specific power estimate of 0.28kW/kg and a conduction heat loss to mass ratio of 159W/kg. The system obtained by numerical analysis is modeled in system simulation software SIMULATIONX. The simulation of the system is studied and a sensitivity analysis performed in order to assess the parametric interdependency of the whole free piston Stirling engine system. The system sensitivity to piston and displacer mass is studied using the simulation model. Sensitivity results indicate that there is a range of mass values within which the system is operational, mass values outside the range makes the system non-functional. Also the range is a function of various parameters and detailed analysis is required in this direction in order to further optimize all the functional parameters. Engineering approximation is carried out using the curve fitting toolbox in MatLab to generate design equations in order to provide preliminary design data for the designer, further a scaling study is carried out at various power levels in order to assess the sensitivity of system geometry at various power levels.

Thesis. 1975. M.S.--Massachusetts Institute of Technology. Dept. of Aeronautics and Astronautics. / Includes bibliographical references. / by David L. Akin. / M.S.

Thesis (M.S.)--West Virginia University, 1998. / Title from document title page. Document formatted into pages; contains x, 82 p. : ill. (some col.). Vita. Includes abstract. Includes bibliographical references (p. 69-70).

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Thesis (MEng) -- Stellenbosch University, 2014. / ENGLISH ABSTRACT: The aim of this study was to design and manufacture an experimentally testable free-piston Stirling engine (FPSE), including a linear electric generator; to develop and validate a theoretical simulation model; to identify problem areas pertaining to its manufacture; and finally to assess the work undertaken, to lay out the groundwork for the future development of a 3 kWe FPSE suitable for incorporation in a solar Stirling dish power generator. A redesigned version of the Beale B- 10B demonstrator engine was manufactured to overcome design diffculties and to simplify testing. The design made use of an electric generator designed at the Department of Electrical and Electronic Engineering at Stellenbosch University. Experimental measurements included piston and displacer motions, hot side and cold side temperatures, working space pressure, electric generator output, as well as heat rejection via a water jacket. Experimental measurements were taken prior to and subsequent to the addition of the electric generator. Indicated power was calculated as 0,659 W at a frequency of 10,99 Hz prior to the addition of the electric generator. The addition of the electric generator was unsuccessful since it was not well matched with the engine. The indicated power calculated was between 0,138 W and 0,144 W for different loads on the electric generator, while the electrical output power ranged from 1,23 mWe to 1,79 mWe. The addition of the electric generator produced non-continuous motion caused by magnetic forces instead of engine pressure variations. The major manufacturing diffculty was the attachment of magnets for the electric generator, but this was overcome with the manufacture of a special assembly jig. The theoretical simulation model was a combination of a third-order and dynamic analysis. Working space values were solved by the application of the conservation of mass, momentum and energy equations for a one-dimensional discretised model of the engine, while the motion of the piston and displacer was determined by applying the equations of motion. The majority of experimental measurements were predicted more accurately when higher heat transfer coeficients were used between the working space and wall temperatures. The theoretical simulation model was used to gain insight into the effect of input parameters on engine operation. The displacer rod diameter was shown to have implications on output power and stability, while it was shown that there is a natural tendency to deliver constant output power at a near-constant frequency over a range of piston loads for an FPSE. It was also shown that the design of an FPSE is complex and that the design of all components should be done in parallel. The control of an FPSE was seen to be both a necessity and can be used to exploit the advantages of the uncoupled nature of an FPSE. / AFRIKKANSE OPSOMMING: Die doel van hierdie studie was om 'n eksperimentele toetsbare vrye-werksuier Stirling enjin te vervaardiging, wat 'n lineêre elektriese kragopwekker insluit; om 'n teoretiese simulasie model te ontwikkel en te yk; om vervaardiging probleme te identi seer; en om die ondernemende werk te assesseer om 'n fondasie te lê vir die toekomstige ontwikkeling van 'n 3 kWe vrye-werksuier Stirling enjin wat by 'n Stirling sonskottel ingelyf kan word. 'n Herontwerpte weergawe van die Beale B-10B demonstrasie enjin was vervaardig om ontwerp probleme te bowe te kom en om die toets daarvan te vereenvoudig. Die ontwerp het gebruik gemaak van 'n elektriese kragopwekker wat by die Departement Elektriese en Elektroniese Ingenieurswese aan die Universiteit van Stellenbosch ontwerp is. Eksperimentele metings het die werksuier en verplaser bewegings ingesluit, sowel as die warm kant en koue kant temperature, die werkruimte druk, die elektriese uitset van die kragopwekker, sowel as die hitteuitruiling wat met 'n water verkoelingskringloop gepaard gaan. Eksperimentele metings was geneem voor en na die byvoeging van die elektriese kragopwekker. Kraglewering was bereken op 0,659 W teen 'n frekwensie van 10,99 Hz voordat die elektriese kragopwekker bygevoeg is. Die byvoeging van die elektriese kragopwekker was onsuksesvol omdat die nie gepas was vir die enjin nie. Die kraglewering is bereken op vlakke wat gewissel het tussen 0,138 W en 0,144 W vir die verskillende belastings op die elektriese kragopwekker, terwyl die elektriese uitset gewissel het tussen 1,23 mWe en 1,79 mWe. Die byvoeging van die elektriese kragopwekker het 'n nie-aaneenlopende beweging veroorsaak weens die magnetiese kragte wat dit beinvloed het in plaas van enjindruk variasies. Die belangrikste ontwerpuitdagings was die ontwerp van 'n werksuier en verplaser wat 'n klein toleransie passing kon handhaaf om sodoende 'n seël te verseker terwyl dit aan temperatuur variasies blootgestel was. Die grootste vervaardigingsprobleem was die aanheg van magnete vir die elektriese kragopwekker, maar dit is te bowe gekom deur 'n spesiale voeg te vervaardig. Die teoretiese simulasie model was 'n kombinasie van 'n derde-orde en 'n dinamiese analise. Werkruimte waardes was opgelos deur die toepassing van die behoud van massa, momentum en energie vergelykings vir 'n een-dimensionele gediskretiseerde model van die enjin, terwyl die beweging van die werksuier en verplaser bepaal was deur die toepassing van die bewegingvergelykings. Die meerderheid van die eksperimentele metings was meer akkuraat voorspel wanneer hoër warmteoordrag koë siënte tussen die werkruimte en muurtemperature gebruik was. Die teoretiese simulasie model was gebruik om insig in terme van die e ek van invoer veranderlikes op die enjin gedrag te toon. Daar was getoon dat die verplaserstaaf diameter implikasies het op kragoplewering en stabiliteit, terwyl die natuurlike tendens van 'n vrye-werksuier Stirling enjin gewys was om 'n konstante kraguitvoer te lewer op 'n naby-konstante frekwensie oor 'n reeks werksuier laste. Daar was ook gewys dat die ontwerp van 'n vryewerksuier Stirling enjin kompleks is en dat die ontwerp van alle komponente in parallel gedoen moet word. Die beheer van 'n vrye-werksuier Stirling enjin was gewys om beide noodsaaklik te wees, sowel as gebruik kan word om die unieke voordele van 'n vrye-werksuier Stirling enjin se ongekoppelde natuur te ontgin.

A computational model for a resonantly coupled alpha free-piston Stirling cooler is presented. The cooler consists of two isothermal working spaces for compression and expansion connected by a regenerator consisting of a stack of narrow parallel channels. The regenerator is assumed to have a linear temperature distribution along its axial direction and the working fluid is taken as an ideal gas. Control volume analysis is adapted in this model, in which each of the components of the cooler is considered a separate control volume. The compression piston is given a predetermined motion to provide the work needed by the cooler. The expansion piston and the gas trapped between the piston and the walls of the expansion cylinder are modeled as a mass, spring, and damper system. The motion of the compression piston generates a pressure difference across the cooler, and forces the working fluid to pass through the regenerator. The expansion piston responds to the pressure in its space according to Newton's second law of motion. The motion of the expansion piston is governed by the forces originating from the pressure and the cold side gas spring and dash-pot. In this way the dynamics of the moving pistons are coupled to the thermodynamics of the cooler system. A definition for the coefficient of performance (COP) that considers the heat transfer by conduction through the material making up the regenerator is introduced. This definition of the COP reflects the dependence of the cooler's performance on the length of the regenerator. From a systematic variation of this regenerator length, an optimal value can be found for a given set of operating parameters. Conservation laws of mass, momentum and energy along with ideal gas relations are used to form a set of equations fully describing the motion of the pistons and the thermal state of the cooler. A marching-in-time technique with a Runge-Kutta scheme of the fourth order is adapted to integrate the equation of motion. The plots of the motion of the pistons, the pressure-volume diagrams of the workspaces and the COP plots are provided to describe the cooler behavior. / Graduation date: 1999

Thesis (M.S.)--West Virginia University, 2000. / Title from document title page. Document formatted into pages; contains ix, 64 p. : ill. (some col.) Includes abstract. Includes bibliographical references (p. 42-43).

Thesis (MSc)--Stellenbosch University, 2015. / ENGLISH ABSTRACT: The design optimisation of a linear oscillatory electric generator for application in freepiston Stirling engines is described in this thesis. A basic overview of free-piston Stirling engine technology is given by firstly providing a brief description of the operation of the heat engine. The applications of free-piston Stirling engines in industry are given and the proposed future applications are described. Different types of electrical machine designs from industry and academia are evaluated in a literature study. A classification structure is also proposed based on the magnetic flux variation within the designs. Based on the literature study, a transverse flux, single-phase, moving magnet, tubular topology was chosen for investigation. Athree dimensional finite element simulation was chosen as the most appropriatemethod to model the linear electrical machine. A commercial simulation package was called from a simulation script and the outputs from the finite element simulation were again used to calculate the electrical machine performance parameters using the instantaneous voltageand current values. A sequential quadratic programming algorithm was used to perform optimisation of the machine topologies, with the optimisation variables being dimensional parameters that describe the machine geometry and the goal of the optimisation to minimise the active mass of the machine, while maintaining preset minima for the output power and the efficiency. The machine was optimised for a number of different translator configurations and the different configurations were analysed and compared. It was found that a quasi-Halbach arrangement of the permanent magnets yielded the lowest overall active mass. A comparative study is also presented, where this quasi-Halbach variant is compared to a commercial machine. It was found that the linear machine design with a quasi-Halbach arrangement compares well with the commercial machine. A prototype and test bed was designed and constructed. Due to manufacuring difficulties however, the machine could not be completed in time for testing. / AFRIKAANSE OPSOMMING: Die ontwerpsoptimering van ’n lineêre ossillerende elektriese generator vir toepassing in vrysuier Stirling enjins word beskryf in hierdie tesis. ’n Basiese oorsig van vrysuier Stirling enjin tegnologie word gegee deur eerstens ’n kort beskrywing te gee van die werking van die hitte-enjin. Die aanwending van vrysuier Stirling enjins in industrie word gegee en voorgestelde toekomstige toepassings word beskryf. Verskillende tipes elektriese masjien ontwerpe vanuit die industrie en die akademie word geëvalueer in ’n literatuurstudie. ’n Klassifiseringstruktuur, gebaseer op die magnetiese vloedverandering in die ontwerpe, word ook voorgestel. ’n Transverse vloed, enkelfase, bewegende magneet, tubulêre topologie is gekies vir die ondersoek, gebaseer op die onder andere die literatuurstudie. ’n Drie-dimensionele eindige element simulasie is gekies as die mees geskikte metode om die lineêre elektriese masjien te modelleer. ’n Kommersiële simulasie pakket is deur middel van ’n simulasie skrip geroep en die uitsette vanaf die eindige element simulasie is weer gebruik om die werksverrigtingsparameters van die elektriese masjien te bereken deur gebruik te maak van die oomblikswaardes van die spanning en stroom. ’n Sekwensiële kwadratiese programmering algoritme is gebruik om optimering van die masjien topologieë te doen, met die dimensionele parameters wat die masjien geometrie beskryf as die optimeringsveranderlikes en doel van die optimering om die aktiewe massa van die masjien te minimeer, terwyl die uitsetdrywing en die benuttingsgraad by voorafgestelde minima gehou word. Die masjien is geoptimeer vir verskeie translator konfigurasies en die verskillende konfigurasies is geanaliseer en vergelyk. Dit is bevind dat ’n kwasi-Halbach skikking van die permanente magnete die laagste totale aktiewe massa gelewer het. ’n Vergelykende studie is ook aangebied, waar die kwasi-Halbach variant vergelyk is met ’n kommersiële masjien. Dit is bevind dat die lineêre masjien met die kwasi-Halbach skikking baie goed vergelyk met die kommersiële masjien. ’n Prototiepe masjien en toetsopstelling is ontwerp en aan mekaar gesit. Maar as gevolg van vervaardigbaarheids tekortkominge kon toetse op die prototiepe nie betyds gedoen word nie.

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