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).

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 (PhD)-- Stellenbosch University, 2013. / ENGLISH ABSTRACT: Control of beta-type free-piston Stirling engines has been the topic of research and development for many years. In this dissertation, an alternative approach to free-piston Stirling engine control, namely direct piston displacement control, is proposed. Direct piston displacement control entails the instantaneous and direct control of the piston displacement to control the engine according to preferred criteria, e.g. maximum power conversion or efficiency. To control free-piston engines in this manner, it is necessary to independently control both the displacement of the displacer and the power piston in real time. The primary arrangement by which to achieve this is through external control of the instantaneous forces exerted by the linear electrical machines fixed to the pistons. The challenge of displacement control is whether suitable linear machine technology exists or whether technology could be established that would adhere to the requirements of real time direct control. To answer the question whether direct piston displacement control is at all possible, a process was followed to set specifications that linear machines should adhere to and to set design guidelines for linear machines and free-piston Stirling engines. The first step was to establish the ability to simulate free-piston Stirling engine dynamics accurately. This was done by adapting a second order formulation and to verify and improve the accuracy thereof by comparing simulated results with experimental results of one of the best documented Stirling engines, namely the GPU-3 engine. It was found that this second order formulation could simulate the GPU-3 engine to a fair degree of accuracy. Key indicators were defined and later refined with the view of setting specifications. A case study of the influence of a range of variations, including operational, dimensional and other variations, on the dynamics of the GPU-3 was then undertaken. From the findings of this case study, specifications of the key indicators and design guidelines were established. A design optimisation approach was proposed to evaluate linear machine topologies. This approach makes specific provision for the specifications that linear machines need to adhere to, as well as for representative dynamic responses of the forces exerted on the linear machine by the displacer or the power piston. These representative responses and the associated piston displacement were determined for the displacer, the power piston and the combination of the two from the study conducted to set specifications. An air-core, longitudinal flux linear machine with surface mounted permanent magnets (LFPM) was then evaluated to determine its suitability for direct piston displacement control. This linear machine topology was optimised for the traditional approach to establish a benchmark with which to compare subsequent optimisations. The LFPM linear machine not only compared well with other topologies for the traditional application in resonant free-piston Stirling engines, but it was found also to be able to perform displacement control for both the displacer and the power piston. For both pistons, displacement should however be limited to sinusoidal displacement, and in the case of the displacer, an important qualification is that the linear machine should be assisted by spring forces to reach practical design optimisations. Direct piston displacement control is shown to be possible. Future work should concentrate on the practical implementation thereof in free-piston Stirling engines. / AFRIKAANSE OPSOMMING: Die beheer van beta-tipe vrysuier Stirling enjins is al vir baie jare die onderwerp van navorsing en ontwikkeling. In hierdie proefskrif word ’n alternatiewe benadering tot vrysuier Stirlingenjins voorgestel, naamlik direkte suierverplasingsbeheer. Direkte suierverplasingsbeheer behels die oombliklike en direkte beheer van die suierverplasing om die enjin volgens voorkeur kriteria, soos maksimum drywingsomsetting of benuttingsgraad, te beheer. Om vrysuier enjins op hierdie wyse te beheer, is dit noodsaaklik om intyds die verplasing van beide die verplaser en die werksuier onafhanklik te beheer. Die primêre wyse om dit te bereik is deur eksterne beheer van die oomblikskragte wat uitgevoer word deur die lineêre masjiene wat vas is aan die suiers. Die uitdaging van verplasingsbeheer is of toepaslike lineêre masjien tegnologie bestaan en of tegnologie gevestig kan word wat sal voldoen aan die vereistes van intydse direkte beheer. Om die vraag te beantwoord of direkte suierverplasingsbeheer hoegenaamd moontlik is, is ’n proses gevolg om spesifikasies daar te stel waaraan lineêre masjiene moet voldoen en om ontwerpsriglyne vir lineêre masjiene en vrysuier Stirling enjins te stel. Die eerste stap was om die vermoë daar te stel om vrysuier Stirling enjin dinamika akkuraat te simuleer. Dit is gedoen deur ’n tweede orde formulering aan te pas en om die akkuraatheid daarvan te kontroleer en te verbeter deur gesimuleerde resultate met eksperimentele resultate van een van die bes gedokumenteerde Stirling enjins, naamlik die GPU-3 enjin, te vergelyk. Daar is bevind dat die tweede orde formulering die GPU-3 tot ’n redelike mate akkuraat kon simuleer. Sleutel aanwysers is gedefinieer en later verfyn met die oog op die daarstelling van spesifikasies. ’n Gevallestudie van die invloed van ’n reeks variasies, insluitende operasionele, dimensionele en ander variasies, op die dinamika van die GPU-3 is onderneem. Gegrond op die bevindinge van hierdie gevallestudie kon spesifikasies en ontwerpsriglyne vasgestel word. ’n Ontwerpsoptimeringsbenadering is voorgestel om lineêre masjiene te evalueer. Hierdie benadering maak spesifiek voorsiening vir die spesifikasies waaraan lineêre masjiene moet voldoen, sowel as verteenwoordigende dinamiese response van die kragte wat op die lineêre masjien van die verplaser en die werksuier uitgeoefen word. Vanaf die bevindinge van die studie wat uitgevoer is om spesifikasies daar te stel, is verteenwoordigende response en gepaardgaande suierverplasing bepaal vir die verplaser, die werksuier en die kombinasie van die twee. ’n Lugkern, longitudinale vloed lineêre masjien met oppervlak-gemonteerde permanente magnete (LVPM) is toe geëvalueer om die geskiktheid daarvan te bepaal vir direkte suierverplasingsbeheer. Hierdie lineêre masjien topologie is geoptimeer vir die tradisionele benadering om ’n maatstaf te vestig waarteen daaropvolgende optimerings vergelyk kan word. Die LVPM lineêre masjien vergelyk nie net goed met ander topologieë vir die tradisionele toepassing in resonante vrysuier Stirling enjins nie, maar daar is ook bevind dat dit in staat is om verplasingsbeheer te doen vir beide die verplaser en die werksuier. Vir beide suiers moet die verplasing egter tot sinusvormige verplasing beperk word en in die geval van die verplaser, is ’n belangrike kwalifikasie dat die lineêre masjien ondersteun moet word deur veerkragte om praktiese ontwerpsoptimerings te bereik. Daar is aangetoon dat direkte suierverplasingsbeheer moontlik is. Toekomstige werk moet konsentreer op die praktiese implementering daarvan in vrysuier Stirling enjins.