Tesi sul tema "Finite-time thermodynamics"

In this thesis we have thermodynamically characterized finite time processes performed on a colloidal particle, kept in contact with thermal reservoir(s). Thermodynamic processes are implemented on the colloidal particle by systematically changing the confining potential in a time dependent way, according to an external driving protocol or by controlling the environmental conditions over a finite duration. First, we study two externally driven systems: one in which the driving is deterministic, and another where the driving is stochastic. These models have appeared in the literature as the building blocks of microscopic machines such as Brownian heat engines and are hence of interest to analyze. In particular, it is of interest to understand the distribution of work done by the colloidal particle as well as the distribution of heat dissipated. These distributions are known in all generality only in a very few cases. In the work we present here, we determine exactly the asymptotic forms of the work distributions (for a finite time duration of the process), which is shown to have non-Gaussian fluctuations. We also find a method to obtain the exact moment generating function of the work distribution, using which we can explicitly calculate aspects of a recently discovered relation for non-equilibrium systems, namely the thermodynamic uncertainty relation. To our knowledge, our model provides the only non-trivial example of a system where the uncertainty relation can be investigated exactly for all times. We have studied the system in various temporal regimes, and have found interesting features such as a time of minimum uncertainty, which may be relevant for the functioning of microscopic machines. Finally, we discuss, an experimentally realized colloidal heat engine model which consists of a single colloidal particle as the working substance. Exact finite time statistics can be obtained for this model using the methods we discuss in the thesis. We present our preliminary results illustrating this.

Since the need of energy conservation has become more and more urgent in the past decades, there has been an increased interest in the study and development of more efficient energy conversion systems. One of the fields that have arisen from that endeavor is a branch of physics called Finite Time Thermodynamics (FIT). It may be said that FIT was initiated through the famous paper by Curzon and Ahlborn (1975) that established new bounds on the efficiency of a finite time Carnot heat engine. Before, the traditional treatments gave a fundamental upper limit on the efficiency of any heat engine. However, this figure, the well-known Carnot efficiency, is far too optimistic in comparison to real heat engines. The reason lies in the fact that the traditional Carnot engine is operating infinitely slowly, thus having zero power output. Curzon and Ahlborn were able to improve upon this treatment and to set an upper limit on engines producing finite power.

Modifications to the quasistatic Carnot cycle are developed in order to formulate improved theoretical bounds on the thermal efficiency of certain refrigeration cycles that produce finite cooling power. The modified refrigeration cycle is based on the idealized endoreversible finite time cycle. Two of the four cycle branches are reversible adiabats, and the other two are the high and low temperature branches along which finite heat fluxes couple the refrigeration cycle with external heat reservoirs. This finite time model has been used to obtain the following results: First, the performance of a finite time Carnot refrigeration cycle (FTCRC) is examined. In the special case of equal heat transfer coefficients along heat transfer branches, it is found that by optimizing the FTCRC to maximize thermal efficiency and then evaluating the efficiency at peak cooling power, a new bound on the thermal efficiency of certain refrigeration cycles is given by $\epsilon\sb{m} = (\tilde\tau\sp2\sb{m}\ (T\sb{H}/T\sb{L}) - 1)\sp{-1},$ where $T\sb{H}$ and $T\sb{L}$ are the absolute high and low temperatures of the heat reservoirs, respectively, and $\tilde\tau\sb{m}=\sqrt{2}$ + 1 $\simeq$ 2.41 is the dimensionless cycle period at maximum cooling power. Second, a finite time refrigeration cycle (FTRC) is optimized to obtain four distinct optimal cycling modes that maximize efficiency and cooling power, and minimize power consumption and irreversible entropy production. It is found that to first order in cycling frequency and in the special symmetric case, the maximum efficiency and minimum irreversible entropy production modes are equally efficient. Additionally, simple analytic expressions are obtained for efficiencies at maximum cooling power within each optimal mode. Under certain limiting conditions the bounding efficiency at maximum cooling power shown above is obtained. Third, the problem of imperfect heat switches linking the working fluid of an FTRC to external heat reservoirs is studied. The maximum efficiency cycling mode is obtained by numerically optimizing the FTRC. Two distinct optimum cycling conditions exist: (1) operation at the global maximum in efficiency, and (2) operation at the frequency of maximum cooling power. The efficiency evaluated at maximum cooling power, and the global maximum efficiency may provide improved bench-mark bounds on thermal efficiencies of certain real irreversible refrigeration cycles.

A ratchet is an asymmetric, non-equilibrated system that can produce a directed current of particles without the need for macroscopic potential gradients. In rocked quantum electron ratchets, tunnelling and wave-reflection can induce reversals in the direction of the net current as a function of system parameters. An asymmetric quantum point contact in a GaAs/GaAlAs heterostructure has been studied experimentally as a realisation of a quantum electron ratchet. A Landauer model predicts reversals in the direction of the net current as a function of temperature, amplitude of the rocking voltage, and Fermi energy. Artifacts such as circuit-induced asymmetry, also known as self-gating, were carefully removed from the experimental data, which showed net current and net differential conductance reversals, as predicted by the model. The model also predicts the existence of a heat current where the net electron current changes sign, as equal numbers of high and low energy electrons are pumped in opposite directions. An idealised quantum electron ratchet is studied analytically as an energy selective electron heat engine and refrigerator. The hypothetical device considered consists of two electron reservoirs with different temperatures and Fermi energies. The reservoirs are linked via a resonant state in a quantum dot, which functions as an idealised energy filter for electrons. The efficiency of the device approaches the Carnot value when the energy transmitted by the filter is tuned to that where the Fermi distributions in the reservoirs are equal. The maximum power regime, where the filter transmits all electrons that contribute positively to the power, is also examined. Analytic expressions are obtained for the power and efficiency of the idealised device as both a heat engine and as a refrigerator in this regime of operation. The expressions depend on the ratio of the voltage to the difference in temperature of the reservoirs, and on the ratio of the reservoir temperatures. The energy selective electron heat engine is shown to be non-endoreversible, and to operate in an analogous manner to the three-level amplifier, a laser based quantum heat engine. Implications for improving the efficiency of thermionic refrigerators and power generators are discussed.

Les phénomènes thermoélectriques sont un moyen de convertir directement l’énergie thermique en énergie électrique ; ils sont à ce titre au cœur de nombreuses recherches dans le domaine de l’énergétique. Au-delà de l’optimisation des matériaux constituants les générateurs thermoélectriques, il est également nécessaire de mener une réflexion sur la manière dont ces générateurs sont utilisés. La contribution des contacts thermiques entre le générateur et les réservoirs thermiques est un facteur qui va modifier les conditions de fonctionnement optimales du générateur. En utilisant la notion de courant thermique convectif, développée par Thomson il y a plus de 150 ans, nous généralisons les expressions classiques du fonctionnement à puissance maximum pour le générateur pour ce cas de figure. Nous constatons toutefois que ces conditions se réduisent à une adaptation d’impédance, à la fois thermique et électrique Outre son intérêt pratique, le générateur thermoélectrique est également un système modèle de choix pour étudier la théorie du transport couplé et des phénomènes irréversibles. En utilisant la description donnée par Ioffe de ce système, nous montrons que l’efficacité à maximum de puissance, un coefficient de performance au cœur de la thermodynamique à temps fini, s’exprime comme une fonction relativement simple des paramètres du système. La nouveauté de ce travail repose sur une prise en compte appropriée des dissipations internes associées au processus de conversion d’énergie. Les résultats sont généralisés enfin aux cas d’autres machines thermiques telle que la roue à rochet de Feynman<br>Thermoelectric phenomena are a way to directly convert thermal energy into electrical energy; they thus are at the heart of several researches in the field of energy conversion. The optimization of the thermoelectric generators includes materials improvement but a reflection on their working conditions is also mandatory. The contribution of the thermal contacts between the generator and the heat reservoirs is a factor that will change the optimum operating conditions of the generator. Using the concept of convective heat flow, developed by Thomson more than 150 years ago, we generalize the classical expression of maximum power conditions. Moreover, we note that these conditions may be reduced to impedance matching conditions, both thermal and electrical. In addition to its practical interest, the thermoelectric generator is also an ideal model system to study the theory of coupled transport and of irreversible phenomena. Using the description of this system given by Ioffe, we show that the maximum power efficiency, a coefficient of performance at the heart of finite time thermodynamics, expressed as a simple function of the system parameters. The novelty of this work is based on a proper consideration of internal dissipation associated with the energy conversion process. The results are then generalized to other thermal engines such as the Feynman ratchet

Thermodynamic processes in finite time are in general irreversible. But there are chances to avoid irreversibility. For instance, there are canonical ensembles of special quantum systems with a given probability distribution describing the likelihood to find the system at time t=0 in a particular state with energy E_i(0), which can be controlled in a specific way, such that the initial probability distribution is recovered at the end of the process (t=T), but the state energies did change, hence E_i(0) is not equal to E_i(T). This allows to change thermodynamic quantities (expectation values) adiabatically, reversibly and in finite time. Such special processes are called Shortcuts to Adiabaticity. The presented thesis analyzes the origin of these shortcuts utilizing special Hamiltonian systems with dynamical algebra. Their main feature is to provide canonical invariance, which means a canonical ensemble stays canonical under Hamiltonian dynamics. This invariance carried by the dynamical algebra will be discussed using Lie group theory. In addition, the persistence of the dynamical algebra with respect to calculating expectation values will be deduced. This allows to benefit from all intrinsic symmetries within the discussion of ensemble trajectories. In consequence, these trajectories will evolve under Hamiltonian dynamics on a specific manifold given by the so-called Casimir companion. In addition, the deformation of this manifold due to non-Hamiltonian (dissipative) dynamics will be discussed, which allows to present a framework for modeling irreversible processes based on Hamiltonian systems with dynamical algebra. An application of this framework based on the parametric harmonic oscillator will be presented by determining time-optimal controls for transitions between two equilibrium as well as between non-equilibrium and equilibrium states. The latter one will lead to time-optimal equilibration strategies for a statistical ensemble of parametric harmonic oscillators<br>Thermodynamische Prozesse in endlicher Zeit sind im Allgemeinen irreversibel. Es gibt jedoch Möglichkeiten, diese Irreversibilität zu umgehen. Ein kanonisches Ensemble eines speziellen quantenmechanischen Systems kann zum Beispiel auf eine ganz spezielle Art und Weise gesteuert werden, sodass nach endlicher Zeit T wieder eine kanonische Besetzungverteilung hergestellt ist, sich aber dennoch die Energie des Systems geändert hat (E(0) ungleich E(T)). Solche Prozesse erlauben das Ändern thermodynamischer Größen (Ensemblemittelwerte) der erwähnten speziellen Systeme in endlicher Zeit und auf eine adiabatische und reversible Art. Man nennt diese Art von speziellen Prozessen Shortcuts to Adiabaticity und die speziellen Systeme hamiltonsche Systeme mit dynamischer Algebra. Die vorliegende Dissertation hat zum Ziel den Ursprung dieser Shortcuts to Adiabaticity zu analysieren und eine Methodik zu entwickeln, die es erlaubt irreversible thermodynamische Prozesse adequat mittels dieser speziellen Systeme zu modellieren. Dazu wird deren besondere Eigenschaft ausgenutzt, die kanonische Invarianz, d.h. ein kanonisches Ensemble bleibt kanonisch bezüglich hamiltonscher Dynamik. Der Ursprung dieser Invarianz liegt in der dynamischen Algebra, die mit Hilfe der Theorie der Lie-Gruppen näher betrachtet wird. Dies erlaubt, eine weitere besondere Eigenschaft abzuleiten: Die Ensemblemittelwerte unterliegen ebenfalls den Symmetrien, die die dynamische Algebra widerspiegelt. Bei näherer Betrachtung befinden sich alle Trajektorien der Ensemblemittelwerte auf einer Mannigfaltigkeit, die durch den sogenannten Casimir Companion beschrieben wird. Darüber hinaus wird nicht-hamiltonsche/dissipative Dynamik betrachtet, welche zu einer Deformation der Mannigfaltigkeit führt. Abschließend wird eine Zusammenfassung der grundlegenden Methodik zur Modellierung irreversibler Prozesse mittels hamiltonscher Systeme mit dynamischer Algebra gegeben. Zum besseren Verständnis wird ein ausführliches Anwendungsbeispiel dieser Methodik präsentiert, in dem die zeitoptimale Steuerung eines Ensembles des harmonischen Oszillators zwischen zwei Gleichgewichtszuständen sowie zwischen Gleichgewichts- und Nichtgleichgewichtszuständen abgeleitet wird

Im Bereich der industriellen Metallurgie und Kristallzüchtung treten bei zahlreichen Anwendungen, wo magnetische Wechselfelder zur induktiven Beeinflussung von leitfähigen Werkstoffen eingesetzt werden, auch Strömungen mit freier Oberfläche auf. Das Anwendungsspektrum reicht dabei vom einfachen Aufschmelzen eines Metalls in einem offenen Tiegel bis hin zur vollständigen Levitation. Auch der sogenannte RGS-Prozess, ein substratbasiertes Kristallisationsverfahren zur Herstellung siliziumbasierter Dünnschichtmaterialien, ist dafür ein Beispiel. Um bei solchen Prozessen die Interaktion von Magnetfeld und Strömung zu untersuchen, ist die numerische Simulationen ein wertvolles Hilfsmittel. Für beliebige dreidimensionale Probleme werden entsprechende Berechnungen bisher durch eine externe Kopplung kommerzieller Programme realisiert, die für Magnetfeld und Strömung jeweils unterschiedliche numerische Techniken nutzen. Diese Vorgehensweise ist jedoch im Allgemeinen mit unnötigem Rechenaufwand verbunden. In dieser Arbeit wird ein neu entwickelter Methodenapparat auf Basis der FVM vorgestellt, mit welchem sich diese Art von Berechnungen effizient durchführen lassen. Mit der Implementierung dieser Methoden in foam-extend, einer erweiterten Version der quelloffenen Software OpenFOAM, ist daraus ein leistungsfähiges Werkzeug in Form einer freien Simulationsplattform entstanden, welches sich durch einen modularen Aufbau leicht erweitern lässt. Mit dieser Plattform wurden in foam-extend auch erstmalig dreidimensionale Induktionsprozesse im Frequenzraum gelöst.

博士<br>國立成功大學<br>機械工程研究所<br>84<br>In this study, a steady-flow approach in finite-time thermo- dynamics has been used to study on the performance optimizations of heat engines and heat pumps from the viewpoints of various ob- jective functions. The topics studied include: (1) ecological- criterion-function optimizations of endoreversible Brayton heat engines with isothermal heat sources, (2) power optimiztions of endoreversible regenerative Brayton heat engines with isothermal heat sources, (3) power optimizations of endoreversible inter- cooled Brayton heat engines with isothermal heat sources, (4) performance-of- coefficient optimizations of irreversible Carnot heat pumps with isothermal heat sources, (5) power optimizations of irreversible Brayton heat engines with isothermal heat sour- ces,(6) efficiency optimizations of irreversible Brayton heat en- gines with isothermal heat sources, (7) ecological- criterion- function optimizations of irreversible Carnot heat engines with variable-temperature heat sources. The results obtained are: (1) The better design point of a heat engine is positioned between the maximum-power point and the maximum- efficiency point, and with ecological criterion functions as objective functions, a heat engine has a balance between its power output, thermal efficiency and entropy gene- ration rate. (2) The irreversible models consider three types of irreversibilities: finite thermal conductance between the working fluid and reservoirs, heat leaks between the resevoirs and irreversibilities in the processes of expansion and com- pression, and the power-efficiency relationship obtained by this model is a closed loop-like curve, similar to the charac- terisitic curves of real heat engines.

碩士<br>崑山科技大學<br>機械工程研究所<br>91<br>First, the flow and heat transfer characteristics of an impinging laminar slot-jet, twin impinging laminar slot-jets, and heat sinks with sloped plate fins as well as with an inclined confinement surface are investigated by using the Star-CD software. Parameters examined for a single jet include the width of the jet, Reynolds number, the separation distance between the slot-jet exit plane and the impingement surface, free-jet impingement or semiconfined-jet impingement, uniform inlet flow or fully-developed inlet flow. An additional parameter, the separation distance between the twin jets is examined for the analysis on the dual jets. In addition, the effects of the titling of the crests of the plate fins relative to the approaching flow and the inclined confinement surface are found to be indeed the two important heat transfer augmentation features. Secondly, a steady-flow approach in finite-time thermodynamics is employed to investigate the ecological-criterion function optimizations of the endoreversible Diesel, Otto, and Atkinson heat engines with isothermal heat sources. The results show that adopting the ecological-criterion function as the objective function, a heat engine may achieve the balance among the power output, thermal efficiency and entropy generation rate.

碩士<br>國立成功大學<br>機械工程學系碩博士班<br>98<br>This study present finite time thermodynamic analysis of Stirling heat engine and obtained the maximum power output by using Genetic Algorithm (GA). The thermodynamic models include an endoreversible Stirling engine and an irreversible Stirling engine with imperfect regeneration and heat loss. Each one of those models has two cases which respectively are heat source by convection transfer and by radiation transfer. The relationship between maximum power output and thermal efficiency, moreover, the optimum working temperature of working fluid can be obtained. The case of heat source by convection transfer shows the accuracy of this method by comparing with analytic solution. The second case is about heat source by radiation transfer. We simulated solar driven Stirling engines in the second case and analyzed the effects of various parameters on maximum power output (i.e., times of regeneration process, compression ratio, temperature of heat source…) In the last case, we have build a model of solar thermal power system, including heat transfer model of collector and endoreversible Stirling engine. The effects of various solar intensity on maximum power output have been discussed.

博士<br>國立成功大學<br>機械工程學系碩博士班<br>93<br>Abstract 　Exergetic efficiency optimization that combines finite-time thermodynamics theory and exergy concept has been applied to an irreversible Carnot refrigeration system, an irreversible Brayton refrigeration system, an irreversible inter-cooled refrigeration system and a two-stage irreversible combined refrigeration system. Multi- irreversiblities considered in these systems include finite rate heat transfer, internal dissipation of the working fluid and heat leak between heat reservoirs. Exergetic efficiency defined as the ratio of rate of exergy output to rate of exergy input of the system is proposed as the objective function to be optimized. The goal of exergetic efficiency optimization is to maximize the objective function. These maximum values of the exergetic efficiency can be determined analytically. The corresponding optimum values of parameters of these systems are obtained simultaneously. These parameters of the system can be effective and important design criteria while evaluating the performance of these refrigeration systems. The influences of design parameters of the system on the maximum exergetic efficiency are discussed. The appropriation of using exergetic efficiency as objective function is discussed. Moreover, in the research of irreversible Carnot and Brayton refrigeration systems, the allocation of a fixed total thermal conductance between the two heat exchangers is discussed using numerical calculation. The results of optimum allocation are also obtained.

碩士<br>國立成功大學<br>機械工程學系碩博士班<br>97<br>In this study, the finite-time thermodynamics method has been utilized on the performance optimization of cogeneration cycles. By using the total useful energy rate method to study the power and the useful heat output in a steady-state-flow system had been investigated. The research includes endoreversible Otto cogeneration cycle, endoreversible Atkinson cogeneration cycle, and internal irreversible Joule-Brayton cogeneration cycle. If the total useful energy-rate is an objective function on optimization, the total useful energy rate of the cycle is maximized and the efficiency at maximum total useful energy rate is also analyzed. Moreover, the effects of various cycle parameters (i.e., pressure-ratio parameter and user’s temperature ratio) on the maximum dimensionless total useful energy rate and the efficiency at maximum total useful energy rate have been assessed. Variations of dimensionless total useful energy rate on the heat efficiency have also been analyzed. In the internal irreversible Joule-Brayton cogeneration cycle, the effects of various irreversible situations on total useful energy rate of the cycle are discussed. Hence, the application of the total useful energy rate method for researching cogeneration cycles can not only save the consumption of energy, but reduce the industrial cost by the relation of system parameters.

碩士<br>國立高雄海洋科技大學<br>輪機工程研究所<br>98<br>In this paper, the viewpoint of finite-time thermodynamics theory and classical thermodynamics has been applied to analyze the irreversible alternative recuperative cycle (ARC), which is taken to compare with the conventional recuperative cycle (CRC).By considering the cycle to interact with the hot side and cold side of heat exchangers and the regenerator in different distributions of heat conductance and different rates of thermal capacity, the results of optimization of the maximum power out and cycle efficiency of the gas turbine regeneration cycle are thus employed to decide rates of distribution of heat transfer area of the hot side and the cold side of heat exchangers and the regenerator. The results, which are analyzed by using the intelligent computer design software, CyclePad, show that the alternative recuperative cycle can achieve the highest efficiency among the simple cycle and conventional recuperative cycle, but needs much lower specific work. When using the method which is called optimum distribution of pressure ratio between turbines, the efficiency and specific work of alternative recuperative cycle can be enhanced. Furthermore, the purpose of using the viewpoint of finite-time thermodynamics theory to optimize the abovementioned cycles is to obtain some corresponding parameters which affect the area of heat transfer. The result about reducing the area of heat transfer leads to design a smaller size of heat exchanger and is taken to reduce the manufacturing cost.

Im Bereich der industriellen Metallurgie und Kristallzüchtung treten bei zahlreichen Anwendungen, wo magnetische Wechselfelder zur induktiven Beeinflussung von leitfähigen Werkstoffen eingesetzt werden, auch Strömungen mit freier Oberfläche auf. Das Anwendungsspektrum reicht dabei vom einfachen Aufschmelzen eines Metalls in einem offenen Tiegel bis hin zur vollständigen Levitation. Auch der sogenannte RGS-Prozess, ein substratbasiertes Kristallisationsverfahren zur Herstellung siliziumbasierter Dünnschichtmaterialien, ist dafür ein Beispiel. Um bei solchen Prozessen die Interaktion von Magnetfeld und Strömung zu untersuchen, ist die numerische Simulationen ein wertvolles Hilfsmittel. Für beliebige dreidimensionale Probleme werden entsprechende Berechnungen bisher durch eine externe Kopplung kommerzieller Programme realisiert, die für Magnetfeld und Strömung jeweils unterschiedliche numerische Techniken nutzen. Diese Vorgehensweise ist jedoch im Allgemeinen mit unnötigem Rechenaufwand verbunden. In dieser Arbeit wird ein neu entwickelter Methodenapparat auf Basis der FVM vorgestellt, mit welchem sich diese Art von Berechnungen effizient durchführen lassen. Mit der Implementierung dieser Methoden in foam-extend, einer erweiterten Version der quelloffenen Software OpenFOAM, ist daraus ein leistungsfähiges Werkzeug in Form einer freien Simulationsplattform entstanden, welches sich durch einen modularen Aufbau leicht erweitern lässt. Mit dieser Plattform wurden in foam-extend auch erstmalig dreidimensionale Induktionsprozesse im Frequenzraum gelöst.