京都大学 / 0048 / 新制・課程博士 / 博士(工学) / 甲第18271号 / 工博第3863号 / 新制||工||1592(附属図書館) / 31129 / 京都大学大学院工学研究科航空宇宙工学専攻 / (主査)教授 稲室 隆二, 教授 泉田 啓, 教授 青木 一生 / 学位規則第4条第1項該当 / Doctor of Philosophy (Engineering) / Kyoto University / DFAM

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O problema da condução de calor, envolvendo mudança de fase, foi resolvido para o caso de uma cavidade limitada por duas superfícies cilíndricas indefinidamente longas. As condições de contorno impostas consistem em manter a temperatura da superfície interna fixa e abaixo da temperatura de fusão do material que preenche a cavidade, enquanto que a temperatura da superfície externa é mantida fixa e acima da temperatura de fusão. Como condição inicial se fixou a temperatura de todo o material que preenche a cavidade no valor da temperatura da superfície externa. A solução obtida consiste em duas soluções da equação de condução de calor, uma escrita para o material solidificado e outra escrita para o material em estado líquido. As duas soluções são formalmente escritas em termos da posição da frente de mudança de fase, que é representada por uma superfície cilíndrica com raio em expansão dentro da cavidade. A posição dessa superfície é, a princípio, desconhecida e é calculada impondo o balanço de energia através da frente da mudança de fase. O balanço de energia é expresso por uma equação diferencial de primeira ordem, cuja solução numérica fornece a posição da frente como função do tempo. A substituição da posição da frente de mudança de fase em um instante particular, nas soluções da equação de condução de calor, fornece a temperatura nas duas fases naquele instante. A solução obtida é ilustrada através de exemplos numéricos. / The heat conduction problem, in the presence of a change of state, was solved for the case of an indefinitely long cylindrical layer cavity. As boundary conditions it is imposed that the internal surface of the cavity is maintained below the fusion temperature of the infilling substance and the external surface is kept above it. The solution, obtained in non-dimensional variables, consists in two closed form heat conduction equation solutions for the solidified and liquid regions, which formally depend of the, at first, unknown position of the phase change front. The energy balance through the phase change front furnishes the equation for time dependence of the front position, which is numerically solved. Substitution of the front position for a particular instant in the heat conduction equation solutions gives the temperature distribution inside the cavity at that moment. The solution is illustrated with numerical examples.

O problema da condução de calor, envolvendo mudança de fase, foi resolvido para o caso de uma cavidade limitada por duas superfícies cilíndricas indefinidamente longas. As condições de contorno impostas consistem em manter a temperatura da superfície interna fixa e abaixo da temperatura de fusão do material que preenche a cavidade, enquanto que a temperatura da superfície externa é mantida fixa e acima da temperatura de fusão. Como condição inicial se fixou a temperatura de todo o material que preenche a cavidade no valor da temperatura da superfície externa. A solução obtida consiste em duas soluções da equação de condução de calor, uma escrita para o material solidificado e outra escrita para o material em estado líquido. As duas soluções são formalmente escritas em termos da posição da frente de mudança de fase, que é representada por uma superfície cilíndrica com raio em expansão dentro da cavidade. A posição dessa superfície é, a princípio, desconhecida e é calculada impondo o balanço de energia através da frente da mudança de fase. O balanço de energia é expresso por uma equação diferencial de primeira ordem, cuja solução numérica fornece a posição da frente como função do tempo. A substituição da posição da frente de mudança de fase em um instante particular, nas soluções da equação de condução de calor, fornece a temperatura nas duas fases naquele instante. A solução obtida é ilustrada através de exemplos numéricos. / The heat conduction problem, in the presence of a change of state, was solved for the case of an indefinitely long cylindrical layer cavity. As boundary conditions it is imposed that the internal surface of the cavity is maintained below the fusion temperature of the infilling substance and the external surface is kept above it. The solution, obtained in non-dimensional variables, consists in two closed form heat conduction equation solutions for the solidified and liquid regions, which formally depend of the, at first, unknown position of the phase change front. The energy balance through the phase change front furnishes the equation for time dependence of the front position, which is numerically solved. Substitution of the front position for a particular instant in the heat conduction equation solutions gives the temperature distribution inside the cavity at that moment. The solution is illustrated with numerical examples.

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We propose a moving-boundary scenario to model the penetration of diffusants into rubbers. Immobilizing the moving boundary by using the well-known Landau transformation transforms the original governing equations into new equations posed in a fixed domain. We solve the transformed equations by the finite element method and investigate the parameter space by exploring the eventual effects of the choice of parameters on the overall diffusants penetration process. Numerical simulation results show that the computed penetration depths of the diffusant concentration are within the range of experimental measurements. We discuss numerical estimations of the expected large-time behavior of the penetration fronts. To have trust in the obtained simulation results, we perform the numerical analysis for our setting. Initially, we study semi-discrete finite element approximations of the corresponding weak solutions. We prove both a priori and a posteriori error estimates for the mass concentration of the diffusants, and respectively, for the a priori unknown position of the moving boundary. Finally, we present a fully discrete scheme for the numerical approximation of model equations. Our scheme is based on the Galerkin finite element method for the space discretization combined with the backward Euler method for time discretization. In addition to proving the existence and uniqueness of a solution to the fully discrete problem, we also derive a priori error estimates for the mass concentration of the diffusants, and respectively, for the position of the moving boundary that fit to our implementation in Python. Our numerical illustrations verify the obtained theoretical order of convergence in physical parameter regimes.

Our society is becoming more and more electrified every day. However, a significant portion of the world’s electricity generation relies on the combustion of fossil fuels to produce heat, which is subsequently harnessed to generate electricity. One way of generating electricity from heat is by utilizing a Rankine cycle. The basis of a Rankine cycle is to heat a liquid to its boiling point, which causes an increase in pressure that is used to spin a turbine and a generator. Many industries, such as transportation and manufacturing, produce large amounts of waste heat that needs to be removed from the main process. A Rankine cycle variant called an organic Rankine cycle can be used in a heat power system to generate electricity from lower-temperature waste heat, which increases efficiency since less heat is wasted. This thesis focuses on constructing a dynamic model of Climeon’s heat power system called HP300. The HP300 utilizes an organic Rankine cycle to generate electricity. Dynamic modeling is valuable because it provides a deeper understanding of the system, which is beneficial for its development and improvement. Moreover, a system model has the potential to enhance the system’s performance by using advanced control methods. The HP300 consists of four main components: a pump, a turbine, an evaporator, and a condenser. Each component will be modeled individually, and the complete model will be constructed by combining the component models. Additionally, an in-depth investigation of an advanced modeling method for heat exchangers is to be conducted. The constructed model in this thesis has an average error of 4%. The pump and turbine were modeled as steady-state models, and the evaporator and condenser were modeled with data-driven state-space models. The most important output of the model is the power generated by the turbine. The power was modeled with an average error of 6%. The turbine model performs best for pressure ratios of 1.75 and above. The model for the condenser had larger errors than the evaporator since it had fewer input variables. Improving the model of the condenser would decrease the overall errors of the model. / Vårt samhälle blir mer och mer elektrifierat för varje dag som går. En betydande del av världens elproduktion är dock beroende av förbränning av fossila bränslen för att producera värme, som sedan utnyttjas för att generera el. Ett sätt att generera el från värme är att använda en Rankine-cykel. Grundprincipen för en Rankine-cykel är att värma upp en vätska till dess kokpunkt, vilket orsakar en tryckökning som används för att snurra en turbin, kopplad till en generator. Många industrier, som exempelvis transport och tillverkning, producerar stora mängder restvärme som måste avlägsnas från huvudprocessen. En variant av Rankine-cykeln som kallas organisk Rankinecykel kan användas i ett värmekraftsystem för att generera elektricitet från restvärme med lägre temperatur, vilket ökar effektiviteten eftersom mindre värme går förlorad. Detta examensarbete fokuserar på att konstruera en dynamisk modell av Climeons värmekraftsystem vid namn HP300. HP300 använder en organisk Rankine-cykel för att generera elektricitet. Dynamisk modellering är värdefull eftersom den ger en djupare förståelse av systemet, vilket är fördelaktigt för dess utveckling och förbättring. Dessutom har en systemmodell potentialen att förbättra systemets prestanda genom att använda avancerade reglermetoder. HP300 består av fyra huvudkomponenter: en pump, en turbin, en förångare och en kondensor. Varje komponent modelleras individuellt och hela modellen konstrueras genom att komponentmodellerna kombineras. Dessutom utförs en fördjupad undersökning av en avancerad modelleringsmetod av värmeväxlare. Den konstruerade modelled i detta arbete har ett genomsnittligt fel på 4%. Pumpen och turbinen modellerades som stationära modeller, medan förångaren och kondensorn modellerades med datadrivna state-space-modeller. Modellens viktigaste variabel är den effekt som genereras av turbinen. Den modellerade effekten hade ett genomsnittligt fel på 6%. Turbinmodellen presterar bäst för tryck-kvoter på 1, 75 och högre. Kondensor modellen hade större fel än förångaren eftersom den hade färre ingångsvariabler. En förbättring av kondensorns modell skulle förbättra modellens övergripande noggrannhet.

Αντικείμενο της παρούσας εργασίας είναι η πρόβλεψη τόσο της κίνησης, αλληλεπίδρασης και παραμόρφωσης δύο φυσαλίδων λόγω μεταβολής της πίεσης στο περιβάλλον ιξώδες υγρό, όσο και της ανοδικής κίνησης μιας φυσαλίδας λόγω άνωσης σε ένα Νευτωνικό ή ιξωδοπλαστικό ρευστό. Για τη μοντελοποίηση των αλληλεπιδρώντων φυσαλίδων, αναπτύχθηκε μιας νέα ελλειπτική μεθόδος κατασκευής του υπολογιστικού πλέγματος προκειμένου να αντιμετωπιστούν επιτυχώς τα ιδιάζοντα σημεία (πόλοι) των φυσαλίδων και οι μεγάλες παραμορφώσεις των διεπιφανειών τους. Με τη μέθοδο αυτή η πύκνωση του πλέγματος περιορίζεται μόνο στις περιοχές που είναι αναγκαίο, μειώνοντας έτσι το υπολογιστικό κόστος και αυξάνοντας την ακρίβεια των υπολογισμών. Για την επίλυση των παρακάτω προβλημάτων χρησιμοποιήθηκε η μέθοδος των μικτών πεπερασμένων στοιχείων κατά Galerkin. Στην περίπτωση των αλληλεπιδρώντων φυσαλίδων έχει εξετασθεί η επίδραση του σχετικού μεγέθους τους, της συχνότητας και του εύρους μεταβολής της επιβαλλόμενης πίεσης και πότε οδηγούν σε έλξη ή άπωση των φυσαλίδων. Στην περίπτωση ελκτικής δύναμης, ακολουθείται η κίνηση και η παραμόρφωσή τους μέχρι του σημείου που έρχονται σε επαφή, όπου αυτό είναι εφικτό. Για τη μελέτη του προβλήματος της φυσαλίδας που ανέρχεται λόγω άνωσης, υποθέτουμε αξονική συμμετρία και μόνιμη κατάσταση. Σύγκριση των προβλέψεών μας για το σχήμα των φυσαλίδων και το πεδίο ροής γύρω τους με προηγούμενα θεωρητικά και πειραματικά αποτελέσματα για Νευτωνικά ρευστά έδειξε άριστη συμφωνία. Στην περίπτωση του ιξωδοπλαστικού ρευστού εξετάστηκαν λεπτομερώς οι παραμορφώσεις των φυσαλίδων σαν συνάρτηση των αριθμών Bingham, Bond και Αρχιμήδη και υπολογίσθηκαν οι συνθήκες υπό τις οποίες είναι δυνατή η παγίδευση της φυσαλίδας μέσα σε αυτό. / The present study deals with the numerical simulation of the motion, interaction and deformation of two bubbles due to variation of the pressure of the ambient Newtonian fluid, and the buoyancy-driven rise of a bubble in a Newtonian or a viscoplastic fluid. A new elliptic mesh generation method is developed in order to deal with the singular points (poles) of the bubbles and the large deformations of their surface. This method permits us to increase the mesh resolution only in the regions that is necessary, decreasing thus the computational cost and increasing the precision of our calculations. The following problems are solved using the mixed finite element/Galerkin method. In the case of the interacting bubbles the effect of their relative size, the frequency and the width of the imposed pressure is examined as well as the conditions that lead in attraction or repulsion of the bubbles. In the case that attractive forces exist, the motion and the deformation of the bubbles followed up to the point that they come in contact, whenever this is possible. In order to study the problem of the bubble that rises due to buoyancy, axial symmetry and steady flow is assumed. Our results for the shape of the bubbles and the flow around them are in very good agreement with previous theoretical and experimental results for Newtonian fluids. The deformations of the bubbles rising in a viscoplastic material are also examined for various values of the Bingham, Bond and Archimedes numbers and the conditions under which entrapment of a bubble is possible are determined.

Support for this work from Praxair; the McMaster Advanced Control Consortium; and the Natural Sciences and Engineering Research Council of Canada (NSERC), Grant CRDPJ 445717, is gratefully acknowledged. / In the air separation industry, cryogenic distillation is the dominant technology for separating large quantities of air into individual high purity component products. Due to the complexity of the process, in addition to significant energy input, air separation units (ASUs) also have high degrees of material and thermal integration and low process agility. As markets become more competitive and dynamic, especially after electricity market deregulation, ASUs can no longer practice mostly stationary operations, and are in need for design and control strategies to achieve high adaptability. In this study, we address such issues through a dynamic optimization framework. The use of rigorous dynamic models is important for developing economically beneficial designs and operating practices. The first part of this study focuses on the modeling aspect. For the column section of the plant, a full-order stage-wise model and a collocation based reduced order model are proposed. Model size, simulation time and predication accuracy are compared. For the primary heat exchanger, a novel moving boundary model is derived to handle the phase change in such a multi-stream heat exchanger. Simulation results demonstrate the capability of the proposed model in tracking the boundary points of the phase change occurrence, as well as the potential pinch point, along the length of the heat exchanger. The second part of the study addresses the operation aspects of ASUs through conducting dynamic optimization studies with collocation based dynamic models. We first performed a comprehensive analysis for a storage-then-utilization strategy on a nitrogen plant, following a two-tier multi-period formulation. As the parameter varies with time, the plant collects liquid, either directly from liquid product or by liquefaction of overproduced gas product, and then redistributes it for meeting gas product demand or as additional reflux. Effects of electricity price and demand profiles, additional operation costs, as well as product specifications are explored. Then we investigated the economic incentive for employing preemptive actions on a super-staged argon system, which allows the plant to take actions before external changes arrive. In the evaluation, changes are in the gas oxygen product demand. During the preemptive period, the plant takes either a single set or multiple sets of control actions. In the demand increase case, operation degrees of freedom are introduced to or removed from the set of decision variables. The demand decrease scenarios are explored with an under-supplied or saturated liquid oxygen market. / Dissertation / Doctor of Philosophy (PhD)