Dans le contexte énergétique actuel, nous assistons au développement de technologies de production d'énergie « propre ». Ainsi, de nouvelles perspectives comme la conversion thermodynamique de l'énergie solaire ou la valorisation des déchets sont offertes à la recherche sur les « énergies renouvelables ». Dans ce cadre, nous nous intéressons aux moteurs thermiques à apport de chaleur externe : les moteurs Stirling et Ericsson.<br />Cette thèse porte tout d'abord sur l'étude d'un petit moteur Stirling sur lequel nous avons mesuré la température instantanée et la pression instantanée en différents points. Les résultats tout à fait originaux obtenus ont été confrontés aux résultats issus de deux analyses différentes. Nous avons conclu à l'inadéquation de ces modèles.<br />Ensuite, nous avons étudié un système de micro-cogénération basé sur un moteur Ericsson couple à un système de combustion de gaz naturel. Un moteur Ericsson est une machine alternative fonctionnant selon un cycle thermodynamique de JOULE. L'objectif de ce système est de produire 11 kW de puissance électrique ainsi que de la chaleur utile. Dans le but de dimensionner ce système, nous avons réalisé des études énergétique, exergétique et exergo-économique de cet ensemble.

This work is concerned with the design, development and performance evaluation of an inertance Pulse Tube Cryocooler (PTC). The main components of a PTC are the compressor, regenerator, pulse tube and inertance tube coupled to a reservoir. The inertance tube is a key component that affects the pressure and mass flow and phase shift between them and hence the performance. In conjunction with the compressor, it also plays a strong role in determining the frequency of operation. The PTC is designed based on system level numerical models (SAGE and DeltaE), component level thermo-acoustic models (DeltaE) of inertance tube and regenerator and experimental data of earlier fabricated Stirling coolers. As a starting point, an inertance tube with a diameter of 3 mm and 3.1 m long was chosen through component level analysis that provides phase shift of around 50 degrees at a pressure ratio of 1.1 for an acoustic power of about 4 W (in order to achieve 1 W of net cooling at 80 K) at 25 bar mean pressure and 60 Hz. From this inertance tube geometry, an estimate of the mass flow rate at the cold heat exchanger is obtained. Based on this mass flow rate, the initial dimensions of the pulse tube and regenerator are arrived at. A parametric study using system level model is carried out to obtain the maximum COP by varying inertance tube length and regenerator diameter. A flexure bearing compressor consisting of moving coil linear motor coupled to a piston is designed for the above cold head. Based on the above design considerations, the PTC compressor and cold head are fabricated and assembled. The PTC is charged with helium at mean pressure of 25 bar and instrumented with pressure and position transducers, temperature sensors and a skin-bonded heater for simulating the heat load on the cold head. Experimental data for the PTC were obtained with two different inertance tube lengths for different frequencies of operation. The cold head temperature exhibited a minimum with respect to the frequency. This optimum frequency shifts towards lower frequency with increased length of the inertance tube. The experimental data clearly shows that with different inertance tube lengths the optimum frequency locates itself for obtaining zero phase shift at the middle of the regenerator. It is observed that the optimum frequency is closely linked to the natural frequency of the pressure wave in the inertance tube suggesting a standing wave within the inertance tube with the pressure node at the reservoir. Thus the inertance tube is found to be analogous to a quarter wave resonator in a thermo-acoustic device. It may thus be possible to pre-fix an operating frequency for a given PTC cold head by choosing an inertance tube length close to quarter wave resonator length. This study has given insights on the phase shift between pressure and mass flow rate governed by the inertance tube and the connection between the optimum and natural frequencies which can be used for better design of PTCs.

Made available in DSpace on 2014-06-11T19:24:51Z (GMT). No. of bitstreams: 0 Previous issue date: 2012-09-19Bitstream added on 2014-06-13T19:31:57Z : No. of bitstreams: 1 caire_e_me_rcla.pdf: 1389119 bytes, checksum: ea2e9b574c106bff7f9cf806fe23534b (MD5) / Esta investigação tem como objetivo a história da origem da curva normal identificando a contribuição de Abraham de Moivre na dedução da fórmula para a função densidade de distribuição normal. Serão analisados trechos de obras originais de Abraham de Moivre, Jacob Bernoulli, James Stirling / This research aims at the history of the origin of the normal curve identifying the contribution of Abraham de Moivre in deducing the formula for the density function of normal distribution. Parts of original works of Abraham de Moivre, Jacob Bernoulli, James Stirling will be analysed

Submitted by ANA KARLA PEREIRA RODRIGUES (anakarla_@hotmail.com) on 2017-09-04T15:09:18Z No. of bitstreams: 1 arquivototal.pdf: 1305751 bytes, checksum: e328135f0399052c0b94303d6ed26e2d (MD5) / Approved for entry into archive by Viviane Lima da Cunha (viviane@biblioteca.ufpb.br) on 2017-09-04T15:54:43Z (GMT) No. of bitstreams: 1 arquivototal.pdf: 1305751 bytes, checksum: e328135f0399052c0b94303d6ed26e2d (MD5) / Made available in DSpace on 2017-09-04T15:54:43Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 1305751 bytes, checksum: e328135f0399052c0b94303d6ed26e2d (MD5) Previous issue date: 2017-01-19 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / The Euler's Number, denoted by e and corresponding to the base of the Natural Logarithms, despite being one of the most important constants in Mathematics, both by the variety of its mathematical implications and by the number of its practical applications, remains unknown to many people. It is common to nd Engineering or even Exact Sciences students who only became aware of the existence of e after taking a Calculus Course. It is also not di cult to nd students who, even after such contact, seem to never realize the importance of this number. The e is a versatile constant. Although, in general, it appears related to results involving Di erential and Integral Calculus, it is present in several problems of di erent Mathematics areas. We can nd it, besides Analysis and Function Theory, in Financial Mathematics, Combinatorial Analysis, Probability, Trigonometry, Geometry, Statistics, Number Theory. In this work, we make a brief historical analysis about the discovery of the Euler's Number, we present its de nition, as well as alternative ways of characterizing it through in nite sums and products. We also address two interesting problems in which it is present: the counting of the number of partitions of a nite non-empty set and obtaining an approximation for the factorial of a natural number, in which we nd the Stirling's Approximation. / O Número de Euler, denotado por e e correspondente à base dos Logaritmos Naturais, apesar de ser uma das constantes mais importantes da Matemática, tanto pela variedade de suas implicações matemáticas quanto pela quantidade de suas aplicações práticas, permanece desconhecido por muitos. É comum encontrarmos estudantes de Engenharia, ou até mesmo das Ciências Exatas, que só tomaram conhecimento da existência do e após um curso de Cálculo. Também não é difícil nos depararmos com alunos que, mesmo após tal contato, parecem nunca terem percebido a importância desse número. O e é uma constante versátil. Apesar de, em geral, aparecer relacionado a resultados envolvendo o Cálculo Diferencial e Integral, ele se faz presente em diversos problemas de diferentes áreas da Matemática. Podemos encontrá-lo, além da Análise e Teoria de Funções, na Matemática Financeira, na Análise Combinatória, na Probabilidade, na Trigonometria, na Geometria, na Estatística, na Teoria dos Números. Neste trabalho, realizamos uma breve análise histórica sobre o descobrimento do Número de Euler, exibimos sua de nição, além de formas alternativas de caracterizá-lo através de somas e produtos in nitos, e abordamos dois interessantes problemas nos quais ele se faz presente: o da contagem do número de partições de um conjunto não vazio nito e o da obtenção de uma aproximação para o fatorial de um número natural, no qual nos deparamos com a Fórmula de Stirling.

This thesis deals with the construction proposal of the combustion chamber of Stirling engine. The introduction briefly describes the history and practical application of Stirlinova engine today. The following section explains the differences between theoretical and real cycle and the principle of beta Stirling engine modifications. The next section is devoted to the calculation of fuel and air consumption and fuel compared to each other. The proposed design is based not only on the calculation of fuel and air, but also heat transfer between flue gas and preheated air. The last part is devoted to calculating the flow of LPG and flow model of the combustion chamber.

My doctoral thesis deals with study and analyse of Stirling thermodynamical cycle. Cycle that is composed of two isochoras and two isotherms. I describe functional principle of Stirling engine and all its parts, constructional variations of pistons system and possible engine working modes. Next chapter contains analyse of engine constructional parameters. Measuring of torque and load characteristics, p - V schemes and output work for various engine inputs is part of this analyse. There is composed mathematical engine characterization by means of Schmidt theory in chapter five. Mathematical characterization is consequently applied to engine model. Theoretical analysis and practical measurement were base for concepts, realization and verification of constructional correction. One part of my thesis is attended to design of new lamella for regenerative exchanger. For optimal lamella constructional proportions were used computational algorithm and simulations. There is concept of cogeneration unit with Stirling engine and its benefits check in last chapter. General theoretical and practical analyse of workable Stirling engine is result of my thesis. Analyse in this extent was not nowhere publishing yet. Design of regenerative exchanger lamella is then practical input of my thesis.

Thesis (MScEng)--Stellenbosch University, 2012. / ENGLISH ABSTRACT: The focus of this project was on the potential application of waste heat recovery and utilisation (WHR&U) systems in pebble bed modular reactor (PBMR) technology. The background theory provided in the literature survey showed that WHR&U systems have attracted the attention of many researchers over the past two decades, as using waste heat improves the system overall efficiency, notwithstanding the cost of extra plant. PBMR waste heat streams were identified and investigated based on the amount of heat rejected to the environment. WHR&U systems require specially designed heat recovery equipment, and as such the used and/or spent PBMR fuel tanks were considered by the way of example. An appropriately scaled system was designed, built and tested, to demonstrate the functioning of such a cooling system. Two separate and independent cooling lines, using natural circulation flow in a particular form of heat pipes called thermosyphon loops were used to ensure that the fuel tank is cooled when the power conversion unit has to be switched off for maintenance, or if it fails. A theoretical model that simulates the heat transfer process in the as-designed WHR&U system was developed. It is a one-dimensional flow model assuming quasi-static and incompressible liquid and vapour flow. An experimental investigation of the WHR&U system was performed in order to validate the theoretical model results. The experimental results were then used to modify the theoretical heat transfer coefficients so that they simulate the experiments more accurately. Three energy conversion devices, the dual-function absorption cycle (DFAC), the organic Rankine cycle (ORC) and the Stirling engine (SE), were identified as suitable for transforming the recovered heat into a useful form, depending on the source temperatures from 60 ºC to 800 ºC. This project focuses on a free-piston SE with emphasis on the thermo-dynamic performance of a SE heat exchanger. It was found that a heat exchanger with a copper woven wire mesh configuration has a relatively large gas-to-metal and metal-to-liquid heat transfer area. Tube-in-shell heat exchanger configurations were tested, with the working fluid flowing in ten copper inner pipes, while a coolant flows through the shell tube. A lumped parameter model was used to describe the thermo-fluid dynamic behaviour of the SE heat exchanger. In order to validate the theoretical results, a uni-directional flow experimental investigation was performed. The theoretical model was adjusted so that it simulated the SE heat exchanger. It was found that after this correction the theoretical model accurately predicts the experiment. Finally, a dynamic analysis of the SE heat exchanger experimental set-up was undertaken to show that, although vibrating, the heat exchanger setup assembly was indeed acceptable from a vibrational and fatigue point of view. / AFRIKAANSE OPSOMMING: Die hoofoogmerk met hierdie projek was die moontlike aanwending van afvalhitteherwinningen- benutting-(WHR&U-) stelsels in modulêre-gruisbedreaktor-(PBMR-) tegnologie. Agtergrondteorie in die literatuurondersoek toon dat WHR&U-stelsels al menige navorser se belangstelling geprikkel het, hetsy vanweë die moontlike ekonomiese voordele wat dit inhou óf vir besoedelingsvoorkoming, bo-en-behalwe die koste van bykomende toerusting. Die PBMRafvalhittestrome is ondersoek en bepaal op grond van die hoeveelheid hitte wat dit na die omgewing vrystel. Om in die prosesbehoeftes van WHR&U-stelsels te voorsien, moet goed ontwerpte, doelgemaakte hitteherwinningstoerusting in ʼn verkoelings- en/of verhittingsproses gebruik word, dus is die PBMR as voorbeeld gebruik vir die konsep. ʼn Toepaslik geskaleerde WHR&U-stelsel is dus ontwerp, gebou en getoets om die geldigheid van die stelselontwerp te toon. Twee onafhanklike verkoelingslyne, wat van natuurlike konveksie gebruik maak, in die vorm van hitte-pype of termoheuwel lusse, was gebruik om te verseker dat verkoeling verskaf word wanneer die hoof lus breek of instandhouding nodig hê. ʼn Teoretiese model is ontwikkel wat die hitteoordragproses in die ontwerpte WHR&U-stelsel simuleer. Dié model was ʼn eendimensionele vloeimodel wat kwasistatiese en onsamedrukbare vloeistof- en dampvloei in die WHR&U-stelsel-lusse veronderstel. ʼn Eksperimentele ondersoek is op die WHR&U-stelsel uitgevoer ten einde die teoretiese model se resultate te bevestig. Die eksperimentele resultate was dus geneem om die teoretiese hitteoordragkoëffisiënte aan te pas sodat dit die eksperimente kon simuleer. Drie energieomsettingstoestelle, naamlik die dubbel funksie absorpsie siklus (DFAC), die organiese Rankine siklus (ORC) en die Stirling enjin (SE), is as geskikte toestelle uitgewys om die herwonne hitte op grond van brontemperature tussen 60 ºC en 800 ºC in ʼn bruikbare vorm om te sit. Hierdie tesis het op vryesuier-SE’s gekonsentreer, met klem op die hitteruiler. Meer bepaald is die termodinamiese werkverrigting van ʼn SE-hitteruiler ondersoek. Daar is bevind dat ʼn hitteruiler met ʼn geweefde koperdraadmaas-samestelling oor ʼn betreklik groot gas-totmetaal- en metaal-tot-vloeistof-oordragoppervlakte beskik. Die verhitter en verkoeler is in ʼn buis-in-mantel-vorm ontwerp, met die werksvloeistof wat deur tien koperbinnepype vloei en ʼn koelmiddel deur die mantelbuis. ʼn Saamgevoegde-parameter-model is gebruik om die termodinamiese gedrag van die SEhitteruiler te beskryf. Ten einde die teoretiese resultate te bevestig, is ʼn eenrigtingvloeiproefondersoek uitgevoer. Die teoretiese model is aangepas sodat dit die SE-hitteruiler kon simuleer. Ná die nodige verstellings is daar bevind dat die teoretiese model die proefneming akkuraat voorspel. Laastens was ʼn dinamiese ontleding van die SE-hitteruiler ook onderneem om te toon dat, hoewel dit vibreer, die hitteruiler proef samestel inderdaad veilig is.

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.

Power generation from biomass based renewable energy technologies is a promising option in retrofitting our dependence in conventional power generation processes. The development of any society is not possible without sustainable energy and access to energy creates that environment that allows the world to thrive. Electricity access especially in developing regions of the world is of particular interest. This work provides results on electricity efficiency, the economic feasibility and environmental impact of biomass based power technologies in small scale setting using Aspen Plus software. The power generation processes analysed on standalone basis include - micro gas turbine, gas turbine, steam turbine, Stirling engine and internal combustion engine. Some of the processes are optimized in the design to suit the specific climate and available wood waste stream in Nigeria is considered in this work. Simulation results indicate that gas engines power technologies gave a better electric performance of more than 30% with its integration with biomass gasification technology in production of fuel gas. The stirling engine power technology shows a good prospect despite its yet to be commercial status. The modification of the engine (removal regenerator) gives a better electric efficiency. Also result shows that internal combustion engine process emits more of nitric oxides compared to other technologies which create doubts over its environmental compatibility. Economic studies show that for small scale power generation, internal combustion engines and stirling engines are economic feasible. Also, steam turbine and gas turbine illustrate why they are mostly applied in medium/large scale biomass power generation specially recommended to regions where more biomass resource are produced. The micro gas turbine power technology can also be applied in small scale despite its high total investment capital. Furthermore, the study shows that about from 1.8 million tonnes per year of saw dust (wood waste) produced from lumber industries in Nigeria, about 1.3 TWh of electricity can be generated from 1000 MW power plant. Power generation via the utilization of biomass prove to be a possible path to Nigeria’s economic, social and environmental sustainability but the extent to which this can achieved is strongly dependent institutional framework, investment, incentives and information policies. / Program: Masterutbildning i energi- och materialåtervinning

In its theoretical part, this thesis sums up the basic knowledge concerning permutations. Besides the representation of permutations and determination of their fundamental characteristics, the theoretical part is, first of all, aimed at results concerning the decomposition of permutations into disjoint cycles and at finding the number of permutations with a certain characteristic. We introduce the fundamental bijection that is useful for solving many problems concerning the permutations. Further on, we focus on the number of permutations without a fixed point, Eulerian numbers expressing the number of permutations with a given number of descents, and the number of permutations with a given number of excedances, Stirling numbers of the first kind expressing the number of permutations with a given number of cycles, and Catalan numbers representing the number of permutations avoiding a chosen pattern of length three. Attention is also paid to the Gilbreath permutations and their characteristics. The practical part consists of 14 solved problems. The solutions rely on the results presented in the theoretical part, and there are deduced some further interesting results concerning random permutations.