On Undecidable Dynamical Properties of Reversible One-Dimensional Cellular Automata

Cellular automata are models for massively parallel computation. A cellular automaton consists of cells which are arranged in some kind of regular lattice and a local update rule which updates the state of each cell according to the states of the cell's neighbors on each step of the computation. This work focuses on reversible one-dimensional cellular automata in which the cells are arranged in a two-way in_nite line and the computation is reversible, that is, the previous states of the cells can be derived from the current ones. In this work it is shown that several properties of reversible one-dimensional cellular automata are algorithmically undecidable, that is, there exists no algorithm that would tell whether a given cellular automaton has the property or not. It is shown that the tiling problem of Wang tiles remains undecidable even in some very restricted special cases. It follows that it is undecidable whether some given states will always appear in computations by the given cellular automaton. It also follows that a weaker form of expansivity, which is a concept of dynamical systems, is an undecidable property for reversible one-dimensional cellular automata. It is shown that several properties of dynamical systems are undecidable for reversible one-dimensional cellular automata. It shown that sensitivity to initial conditions and topological mixing are undecidable properties. Furthermore, non-sensitive and mixing cellular automata are recursively inseparable. It follows that also chaotic behavior is an undecidable property for reversible one-dimensional cellular automata.

Two-dimensional drift-diffusion simulation of organic solar cells

The aim of this master's thesis is to develop a two-dimensional drift-di usion model, which describes charge transport in organic solar cells. The main bene t of a two-dimensional model compared to a one-dimensional one is the inclusion of the nanoscale morphology of the active layer of a bulk heterojunction solar cell. The developed model was used to study recombination dynamics at the donor-acceptor interface. In some cases, it was possible to determine e ective parameters, which reproduce the results of the two-dimensional model in the one-dimensional case. A summary of the theory of charge transport in semiconductors was presented and discussed in the context of organic materials. Additionally, the normalization and discretization procedures required to nd a numerical solution to the charge transport problem were outlined. The charge transport problem was solved by implementing an iterative scheme called successive over-relaxation. The obtained solution is given as position-dependent electric potential, free charge carrier concentrations and current densities in the active layer. An interfacial layer, separating the pure phases, was introduced in order to describe charge dynamics occurring at the interface between the donor and acceptor. For simplicity, an e ective generation of free charge carriers in the interfacial layer was implemented. The pure phases simply act as transport layers for the photogenerated charges. Langevin recombination was assumed in the two-dimensional model and an analysis of the apparent recombination rate in the one-dimensional case is presented. The recombination rate in a two-dimensional model is seen to e ectively look like reduced Langevin recombination at open circuit. Replicating the J-U curves obtained in the two-dimensional model is, however, not possible by introducing a constant reduction factor in the Langevin recombination rate. The impact of an acceptor domain in the pure donor phase was investigated. Two cases were considered, one where the acceptor domain is isolated and another where it is connected to the bulk of the acceptor. A comparison to the case where no isolated domains exist was done in order to quantify the observed reduction in the photocurrent. The results show that all charges generated at the isolated domain are lost to recombination, but the domain does not have a major impact on charge transport. Trap-assisted recombination at interfacial trap states was investigated, as well as the surface dipole caused by the trapped charges. A theoretical expression for the ideality factor n_id as a function of generation was derived and shown to agree with simulation data. When the theoretical expression was fitted to simulation data, no interface dipole was observed.

Development of a Testing Method for Convertibility of Paperboard

Työssä tutkittiin muovattujen kartonkivuokien sekä muovattujen kartonkinäytteiden rinnastettavuutta. Puristusvaiheen prosessiolosuhteiden miellettiin vaikuttavan eniten multidimensionaliseen muodonmuutokseen. Multidimensionaalista muodonmuutosta simuloitiin uudella muovaamiseen soveltuvalla muovauslaitteella. Kirjallisuusosassa keskeisiä teemoja ovat kartongin muovaus sekä kuitupohjaisen materiaalin reologinen käyttäytyminen. Kirjallisuusosassa esitellään lisäksi yksi tekninen sovellus, jonka avulla kyetään ennustamaan kuitumateriaalin muovautuvuutta sekä mittaamaan tapahtunutta muodonmuutosta. Prosessiparametrien teoreettista vaikutustakuituihin tarkastellaan myös kirjallisuusosassa. Kokeellisessa osassa toteutettiin kartonkivuokien valmistus puristamalla. Vastaavilla prosessiparametreilla muovattiin myös pienemmät testinäytteet. Perinteiset yksidimensionaliset deformaatiomittaukset toteutettiin lujuusominaisuuksien laboratoriomäärityksinä. Myös kitka, joka toimii tärkeänä muuttujana prässäysprosessissa, mitattiin laboratorio-olosuhteissa. Tämän työn tulokset osoittavat uuden kehitetyn muovausmenetelmän toimivuuden. Asema-voima kuvaajat ovat selkeitä sekä helposti luettavia. Tuloksissa havaittiin materiaalin muovauspotentiaalin sekä asema-voima kuvaajan välillä vallitseva yhteys. Erittäin merkittävä huomio oli myös, että muovipäällystetyllä kartongilla oli yhteys päällystämättömän kartongin asema-voima kuvaajaan. Tämä tulos osoittaa, että muovipäällystetyn kartongin muovautuvuutta voi olla mahdollista ennustaa pohjakartongin muovautuvuustulosten perusteella. Perinteiset yksidimensionaliset laboratoriomittaukset eivät kykene antamaan riittävää informaatiota muovautuvuuden ennustamiseen. Tästä näkökulmasta on tärkeää että kartongin multidimensionalista muotoutuvuutta voidaankin tutkia kehitetyllä muovausmenetelmällä.

Studies of Eu- and Yb-induced Reconstructions on the Si(100) Surface

This thesis presents experimental studies of rare earth (RE) metal induced structures on Si(100) surfaces. Two divalent RE metal adsorbates, Eu and Yb, are investigated on nominally flat Si(100) and on vicinal, stepped Si(100) substrates. Several experimental methods have been applied, including scanning tunneling microscopy/spectroscopy (STM/STS), low energy electron diffraction (LEED), synchrotron radiation photoelectron spectroscopy (SR-PES), Auger electron spectroscopy (AES), thermal desorption spectroscopy (TDS), and work function change measurements (Δφ). Two stages can be distinguished in the initial growth of the RE/Si interface: the formation of a two-dimensional (2D) adsorbed layer at submonolayer coverage and the growth of a three-dimensional (3D) silicide phase at higher coverage. The 2D phase is studied for both adsorbates in order to discover whether they produce common reconstructions or reconstructions common to the other RE metals. For studies of the 3D phase Yb is chosen due to its ability to crystallize in a hexagonal AlB2 type lattice, which is the structure of RE silicide nanowires, therefore allowing for the possibility of the growth of one-dimensional (1D) wires. It is found that despite their similar electronic configuration, Eu and Yb do not form similar 2D reconstructions on Si(100). Instead, a wealth of 2D structures is observed and atomic models are proposed for the 2×3-type reconstructions. In addition, adsorbate induced modifications on surface morphology and orientational symmetry are observed. The formation of the Yb silicide phase follows the Stranski-Krastanov growth mode. Nanowires with the hexagonal lattice are observed on the flat Si(100) substrate, and moreover, an unexpectedly large variety of growth directions are revealed. On the vicinal substrate the growth of the silicide phase as 3D islands and wires depends drastically on the growth conditions. The conditions under which wires with high aspect ratio and single orientation parallel to the step edges can be formed are demonstrated.

Conservation Laws in Cellular Automata

Conservation laws in physics are numerical invariants of the dynamics of a system. In cellular automata (CA), a similar concept has already been defined and studied. To each local pattern of cell states a real value is associated, interpreted as the “energy” (or “mass”, or . . . ) of that pattern.The overall “energy” of a configuration is simply the sum of the energy of the local patterns appearing on different positions in the configuration. We have a conservation law for that energy, if the total energy of each configuration remains constant during the evolution of the CA. For a given conservation law, it is desirable to find microscopic explanations for the dynamics of the conserved energy in terms of flows of energy from one region toward another. Often, it happens that the energy values are from non-negative integers, and are interpreted as the number of “particles” distributed on a configuration. In such cases, it is conjectured that one can always provide a microscopic explanation for the conservation laws by prescribing rules for the local movement of the particles. The onedimensional case has already been solved by Fuk´s and Pivato. We extend this to two-dimensional cellular automata with radius-0,5 neighborhood on the square lattice. We then consider conservation laws in which the energy values are chosen from a commutative group or semigroup. In this case, the class of all conservation laws for a CA form a partially ordered hierarchy. We study the structure of this hierarchy and prove some basic facts about it. Although the local properties of this hierarchy (at least in the group-valued case) are tractable, its global properties turn out to be algorithmically inaccessible. In particular, we prove that it is undecidable whether this hierarchy is trivial (i.e., if the CA has any non-trivial conservation law at all) or unbounded. We point out some interconnections between the structure of this hierarchy and the dynamical properties of the CA. We show that positively expansive CA do not have non-trivial conservation laws. We also investigate a curious relationship between conservation laws and invariant Gibbs measures in reversible and surjective CA. Gibbs measures are known to coincide with the equilibrium states of a lattice system defined in terms of a Hamiltonian. For reversible cellular automata, each conserved quantity may play the role of a Hamiltonian, and provides a Gibbs measure (or a set of Gibbs measures, in case of phase multiplicity) that is invariant. Conversely, every invariant Gibbs measure provides a conservation law for the CA. For surjective CA, the former statement also follows (in a slightly different form) from the variational characterization of the Gibbs measures. For one-dimensional surjective CA, we show that each invariant Gibbs measure provides a conservation law. We also prove that surjective CA almost surely preserve the average information content per cell with respect to any probability measure.

An experimental and theoretical study of multiphase flow in a circulating fluidized bed

A systematic averaging procedure has been derived in order to obtain an integral form of conservation equations for dispersed multiphase flow, especially applicable to fluidized beds. A similar averaging method is applied further to formulate macroscopic integral equations, which can be used in one-dimensional and macroscopic multi dimensional models. Circulating fluid bed hydrodynamics has been studied experimentally and both macroscopic and microscopic flow profiles have been measured in a cold model. As an application of the theory, the one dimensional model has been used to study mass and momentum conservation of gas and solid in a circulating fluid bed. Axial solid mixing has also been modelled by the one dimensional model and mixing parameters have been evaluated.

A study of combustion phenomena in circulating fluidized beds by developing and applying experimental and modelling methods for laboratory-scale reactors

The results shown in this thesis are based on selected publications of the 2000s decade. The work was carried out in several national and EC funded public research projects and in close cooperation with industrial partners. The main objective of the thesis was to study and quantify the most important phenomena of circulating fluidized bed combustors by developing and applying proper experimental and modelling methods using laboratory scale equipments. An understanding of the phenomena plays an essential role in the development of combustion and emission performance, and the availability and controls of CFB boilers. Experimental procedures to study fuel combustion behaviour under CFB conditions are presented in the thesis. Steady state and dynamic measurements under well controlled conditions were carried out to produce the data needed for the development of high efficiency, utility scale CFB technology. The importance of combustion control and furnace dynamics is emphasized when CFB boilers are scaled up with a once through steam cycle. Qualitative information on fuel combustion characteristics was obtained directly by comparing flue gas oxygen responses during the impulse change experiments with fuel feed. A one-dimensional, time dependent model was developed to analyse the measurement data Emission formation was studied combined with fuel combustion behaviour. Correlations were developed for NO, N2O, CO and char loading, as a function of temperature and oxygen concentration in the bed area. An online method to characterize char loading under CFB conditions was developed and validated with the pilot scale CFB tests. Finally, a new method to control air and fuel feeds in CFB combustion was introduced. The method is based on models and an analysis of the fluctuation of the flue gas oxygen concentration. The effect of high oxygen concentrations on fuel combustion behaviour was also studied to evaluate the potential of CFB boilers to apply oxygenfiring technology to CCS. In future studies, it will be necessary to go through the whole scale up chain from laboratory phenomena devices through pilot scale test rigs to large scale, commercial boilers in order to validate the applicability and scalability of the, results. This thesis shows the chain between the laboratory scale phenomena test rig (bench scale) and the CFB process test rig (pilot). CFB technology has been scaled up successfully from an industrial scale to a utility scale during the last decade. The work shown in the thesis, for its part, has supported the development by producing new detailed information on combustion under CFB conditions.

Boundary identification in the domain of a parabolic partial differential equation

Bakgrunden och inspirationen till föreliggande studie är tidigare forskning i tillämpningar på randidentifiering i metallindustrin. Effektiv randidentifiering möjliggör mindre säkerhetsmarginaler och längre serviceintervall för apparaturen i industriella högtemperaturprocesser, utan ökad risk för materielhaverier. I idealfallet vore en metod för randidentifiering baserad på uppföljning av någon indirekt variabel som kan mätas rutinmässigt eller till en ringa kostnad. En dylik variabel för smältugnar är temperaturen i olika positioner i väggen. Denna kan utnyttjas som insignal till en randidentifieringsmetod för att övervaka ugnens väggtjocklek. Vi ger en bakgrund och motivering till valet av den geometriskt endimensionella dynamiska modellen för randidentifiering, som diskuteras i arbetets senare del, framom en flerdimensionell geometrisk beskrivning. I de aktuella industriella tillämpningarna är dynamiken samt fördelarna med en enkel modellstruktur viktigare än exakt geometrisk beskrivning. Lösningsmetoder för den s.k. sidledes värmeledningsekvationen har många saker gemensamt med randidentifiering. Därför studerar vi egenskaper hos lösningarna till denna ekvation, inverkan av mätfel och något som brukar kallas förorening av mätbrus, regularisering och allmännare följder av icke-välställdheten hos sidledes värmeledningsekvationen. Vi studerar en uppsättning av tre olika metoder för randidentifiering, av vilka de två första är utvecklade från en strikt matematisk och den tredje från en mera tillämpad utgångspunkt. Metoderna har olika egenskaper med specifika fördelar och nackdelar. De rent matematiskt baserade metoderna karakteriseras av god noggrannhet och låg numerisk kostnad, dock till priset av låg flexibilitet i formuleringen av den modellbeskrivande partiella differentialekvationen. Den tredje, mera tillämpade, metoden kännetecknas av en sämre noggrannhet förorsakad av en högre grad av icke-välställdhet hos den mera flexibla modellen. För denna gjordes även en ansats till feluppskattning, som senare kunde observeras överensstämma med praktiska beräkningar med metoden. Studien kan anses vara en god startpunkt och matematisk bas för utveckling av industriella tillämpningar av randidentifiering, speciellt mot hantering av olinjära och diskontinuerliga materialegenskaper och plötsliga förändringar orsakade av “nedfallande” väggmaterial. Med de behandlade metoderna förefaller det möjligt att uppnå en robust, snabb och tillräckligt noggrann metod av begränsad komplexitet för randidentifiering.

Modeling study of limestone reactions in fluidized bed conditions

Traditionally limestone has been used for the flue gas desulfurization in fluidized bed combustion. Recently, several studies have been carried out to examine the use of limestone in applications which enable the removal of carbon dioxide from the combustion gases, such as calcium looping technology and oxy-fuel combustion. In these processes interlinked limestone reactions occur but the reaction mechanisms and kinetics are not yet fully understood. To examine these phenomena, analytical and numerical models have been created. In this work, the limestone reactions were studied with aid of one-dimensional numerical particle model. The model describes a single limestone particle in the process as a function of time, the progress of the reactions and the mass and energy transfer in the particle. The model-based results were compared with experimental laboratory scale BFB results. It was observed that by increasing the temperature from 850 °C to 950 °C the calcination was enhanced but the sulfate conversion was no more improved. A higher sulfur dioxide concentration accelerated the sulfation reaction and based on the modeling, the sulfation is first order with respect to SO2. The reaction order of O2 seems to become zero at high oxygen concentrations.

Heat transfer inside internal combustion engine: modelling and comparison with experimental data

The paper is devoted to study specific aspects of heat transfer in the combustion chamber of compression ignited reciprocating internal combustion engines and possibility to directly measure the heat flux by means of Gradient Heat Flux Sensors (GHFS). A one – dimensional single zone model proposed by Kyung Tae Yun et al. and implemented with the aid of Matlab, was used to obtain approximate picture of heat flux behavior in the combustion chamber with relation to the crank angle. The model’s numerical output was compared to the experimental results. The experiment was accomplished by A. Mityakov at four stroke diesel engine Indenor XL4D. Local heat fluxes on the surface of cylinder head were measured with fast – response, high – sensitive GHFS. The comparison of numerical data with experimental results has revealed a small deviation in obtained heat flux values throughout the cycle and different behavior of heat flux curve after Top Dead Center.

Heat flux measurement inside internal combustion engine with gradient heat flux sensor.

This master’s thesis is devoted to study different heat flux measurement techniques such as differential temperature sensors, semi-infinite surface temperature methods, calorimetric sensors and gradient heat flux sensors. The possibility to use Gradient Heat Flux Sensors (GHFS) to measure heat flux in the combustion chamber of compression ignited reciprocating internal combustion engines was considered in more detail. A. Mityakov conducted an experiment, where Gradient Heat Flux Sensor was placed in four stroke diesel engine Indenor XL4D to measure heat flux in the combustion chamber. The results which were obtained from the experiment were compared with model’s numerical output. This model (a one – dimensional single zone model) was implemented with help of MathCAD and the result of this implementation is graph of heat flux in combustion chamber in relation to the crank angle. The values of heat flux throughout the cycle obtained with aid of heat flux sensor and theoretically were sufficiently similar, but not identical. Such deviation is rather common for this type of experiment.

Model based analysis of the post-combustion calcium looping process for carbon dioxide capture

This thesis presents a one-dimensional, semi-empirical dynamic model for the simulation and analysis of a calcium looping process for post-combustion CO2 capture. Reduction of greenhouse emissions from fossil fuel power production requires rapid actions including the development of efficient carbon capture and sequestration technologies. The development of new carbon capture technologies can be expedited by using modelling tools. Techno-economical evaluation of new capture processes can be done quickly and cost-effectively with computational models before building expensive pilot plants. Post-combustion calcium looping is a developing carbon capture process which utilizes fluidized bed technology with lime as a sorbent. The main objective of this work was to analyse the technological feasibility of the calcium looping process at different scales with a computational model. A one-dimensional dynamic model was applied to the calcium looping process, simulating the behaviour of the interconnected circulating fluidized bed reactors. The model incorporates fundamental mass and energy balance solvers to semi-empirical models describing solid behaviour in a circulating fluidized bed and chemical reactions occurring in the calcium loop. In addition, fluidized bed combustion, heat transfer and core-wall layer effects were modelled. The calcium looping model framework was successfully applied to a 30 kWth laboratory scale and a pilot scale unit 1.7 MWth and used to design a conceptual 250 MWth industrial scale unit. Valuable information was gathered from the behaviour of a small scale laboratory device. In addition, the interconnected behaviour of pilot plant reactors and the effect of solid fluidization on the thermal and carbon dioxide balances of the system were analysed. The scale-up study provided practical information on the thermal design of an industrial sized unit, selection of particle size and operability in different load scenarios.

Omistuksen tavoitteellisuus perheyrityksissä - kartoitus omistamisen tavoitteista ja tavoitteiden määrittelystä

Suomi tarvitsee menestyviä yrittäjiä, uusia yrityksiä, kasvuyrityksiä ja kansainvälistymistä. Yrittä-jyydelle asetetaankin suuria odotuksia. Suurin huomio yrittäjyyden tarkastelussa on kuitenkin keskittynyt liiketoimintojen kehittämiseen – sen sijaan omistajuuden ja yrittäjyyden yhteyttä ei ole juurikaan huomioitu. Tämän seurauksena myös omistajuuden vaikutusta yrityksen kehittymi-seen ja menestykseen on analysoitu vähän. Edistääkseen yrityksen kehittymistä, tulee omistuksen olla tavoitteellista. Omistamisen tavoittei-den tarkastelu on kuitenkin harvinaista ja parhaimmillaankin yksiulotteista: omistamisen tavoit-teiden nähdään liittyvän lähes yksinomaan taloudellisiin tavoitteisiin, ja tavoitteiden moninaisuus unohdetaan. Tässä tutkimuksessa tarkastellaan suomalaisten perheyrittäjien omistamisen tavoit-teellisuutta, tavoitteiden määrittelyä sekä omistajaohjauksen keinoja, lähinnä hallituksen roolia, omistukseen liittyvien ratkaisujen tekijänä. Tutkimushankkeen aineisto kerättiin EK:n ja Perheyritysten liiton jäsenyrityksistä. Aineisto kerät-tiin joulukuussa 2013 ja tammikuussa 2014 web-pohjaisella kyselyllä ja siihen vastasi määräajan kuluessa 332 vastaajaa. Vastaajista perheyrityksiä oli 241 kpl. Tarkemman analyysin kohteeksi jäi 233 perheyritystä. Tutkimuksen tulokset osoittavat, että suomalaisten yrittäjien omistajuuteen liittyvät tavoitteet ovat monipuolisempia kuin yleisesti oletetaan. Puhtaasti taloudellisiin motiiveihin perustuvan yri-tysten omistamisen ohella liiketoimintaan kohdistuva mielenkiinto ja halu toimia yrittäjänä ovat merkittäviä omistamisen vaikuttimia. Suuri joukko yritysten omistajista ei kuitenkaan tietoisesti pohdi omistamisen tavoitteita vaan omistuksen tavoitteet määrittyvät liiketoiminnan tavoitteiden tai totuttujen tapojen ja perinteiden kautta. Osalla yritysten omistajista omistus muuttuu tavoit-teellisemmaksi yrityksen kehittyessä ja omistajajoukon kasvaessa. Ensimmäisen sukupolven yrittäjät näyttävät toimivan ennen kaikkea yrittäjäideologian mukaisesti pyrkien kasvattamaan yritystä ja painottaen liiketaloudellisia arvoja päätöksenteossa. Yritystoi-minnan kehittyessä ja sukupolvien lisääntyessä yrityksen omistamiseen liittyvät tavoitteet moni-puolistuvat ja monimutkaistuvat, eivätkä enää perustu pelkästään liiketoiminnallisiin menes-tysodotuksiin. Hallitustoiminnan aktivointi aktivoi myös omistuksen tavoitteellisuuden kehittymistä. Omistus-pohjan hajaantuminen lisää tarvetta erilaisten omistajaohjauksen mekanismien hyödyntämiselle. Hallituksella näyttää olevan rooli omistusratkaisuiden arvioinnissa sekä yrityksen operatiiviseen toimintaan liittyvissä omistusratkaisuissa, mutta myös läheisemmin omistamiseen ja omistajapoh-jaan liittyvissä omistusratkaisuissa. Perheomistukseen liittyvien tavoitteiden huomioiminen on tärkeää perheyrityksen hallituksen toiminnassa myös yrityksen toiminnan vakiintuessa. Sen sijaan, että perheeseen liittyvät omista-misen tavoitteet katoaisivat yrityksestä, muuttuu niiden määrittely tietoisemmaksi ja osaksi yri-tyksen hallintoa. Määräysvallan merkitys tavoitteena pienenee, kun omistajan etäisyys operatiivi-sesta toiminnasta, tai sen johtamisesta kasvaa. Tutkimuksen tulokset kertovat omistamisen tavoitteista ja tavoitteiden määrittelystä. Selvityksen lopussa luotiin määritelmä päämäärätietoiselle omistajalle: Päämäärätietoinen omistaja on omista-ja, joka tietoisesti pohtii tavoitteita omistamiselleen sekä käyttää aktiivisesti omistajavaltaansa valitsemiensa päämäärien saavuttamiseksi.

Heterogeneous mass transfer in fluidized beds by computational fluid dynamics

The main objective of this research is to estimate and characterize heterogeneous mass transfer coefficients in bench- and pilot-scale fluidized bed processes by the means of computational fluid dynamics (CFD). A further objective is to benchmark the heterogeneous mass transfer coefficients predicted by fine-grid Eulerian CFD simulations against empirical data presented in the scientific literature. First, a fine-grid two-dimensional Eulerian CFD model with a solid and gas phase has been designed. The model is applied for transient two-dimensional simulations of char combustion in small-scale bubbling and turbulent fluidized beds. The same approach is used to simulate a novel fluidized bed energy conversion process developed for the carbon capture, chemical looping combustion operated with a gaseous fuel. In order to analyze the results of the CFD simulations, two one-dimensional fluidized bed models have been formulated. The single-phase and bubble-emulsion models were applied to derive the average gas-bed and interphase mass transfer coefficients, respectively. In the analysis, the effects of various fluidized bed operation parameters, such as fluidization, velocity, particle and bubble diameter, reactor size, and chemical kinetics, on the heterogeneous mass transfer coefficients in the lower fluidized bed are evaluated extensively. The analysis shows that the fine-grid Eulerian CFD model can predict the heterogeneous mass transfer coefficients quantitatively with acceptable accuracy. Qualitatively, the CFD-based research of fluidized bed process revealed several new scientific results, such as parametrical relationships. The huge variance of seven orders of magnitude within the bed Sherwood numbers presented in the literature could be explained by the change of controlling mechanisms in the overall heterogeneous mass transfer process with the varied process conditions. The research opens new process-specific insights into the reactive fluidized bed processes, such as a strong mass transfer control over heterogeneous reaction rate, a dominance of interphase mass transfer in the fine-particle fluidized beds and a strong chemical kinetic dependence of the average gas-bed mass transfer. The obtained mass transfer coefficients can be applied in fluidized bed models used for various engineering design, reactor scale-up and process research tasks, and they consequently provide an enhanced prediction accuracy of the performance of fluidized bed processes.

Hygro-elasto-plastic behavior of planar orthotropic material

The mechanical and hygroscopic properties of paper and board are factors affecting the whole lifecycle of a product, including paper/board quality, production, converting, and material and energy savings. The progress of shrinkage profiles, loose edges of web, baggy web causing wrinkling and misregistration in printing are examples of factors affecting runnability and end product quality in the drying section and converting processes, where paper or board is treated as a moving web. The structural properties and internal stresses or plastic strain differences built up during production also cause the end-product defects related to distortion of the shape of the product such as sheet or box. The objective of this work was to construct a model capable of capturing the characteristic behavior of hygroscopic orthotropic material under moisture change, during different external in-plane stretch or stress conditions. Two independent experimental models were constructed: the elasto-plastic material model and the hygroexpansivity-shrinkage model. Both describe the structural properties of the sheet with a fiber orientation probability distribution, and both are functions of the dry solids content and fiber orientation anisotropy index. The anisotropy index, introduced in this work, simplifies the procedure of determining the constitutive parameters of the material model and the hygroexpansion coefficients in different in-plane directions of the orthotropic sheet. The mathematically consistent elasto-plastic material model and the dry solids content dependent hygroexpansivity have been constructed over the entire range from wet to dry. The presented elastoplastic and hygroexpansivity-shrinkage models can be used in an analytical approach to estimate the plastic strain and shrinkage in simple one-dimensional cases. For studies of the combined and more complicated effects of hygro-elasto-plastic behavior, both models were implemented in a finite element program for a numerical solution. The finite element approach also offered possibilities for studying different structural variations of orthotropic planar material, as well as local buckling behavior and internal stress situations of the sheet or web generated by local strain differences. A comparison of the simulation examples presented in this work to results published earlier confirms that the hygro-elasto-plastic model provides at least qualitatively reasonable estimates. The application potential of the hygro-elasto-plastic model is versatile, including several phenomena and defects appearing in the drying, converting and end-use conditions of the paper or board webs and products, or in other corresponding complex planar materials.