ADVANCED NUMERICAL METHODS FOR SIMULATING MICROBUBBLE IN AN AERATED MIXING TANK

Fluid mixing in mechanically agitated tanks is one of the major unit operations in many industries. Bubbly flows have been of interest among researchers in physics, medicine, chemistry and technology over the centuries. The aim of this thesis is to use advanced numerical methods for simulating microbubble in an aerated mixing tank. Main components of the mixing tank are a cylindrical vessel, a rotating Rushton turbine and the air nozzle. The objective of Computational Fluid Dynamics (CFD) is to predict fluid flow, heat transfer, mass transfer and chemical reactions. The CFD simulations of a turbulent bubbly flow are carried out in a cylindrical mixing tank using large eddy simulation (LES) and volume of fluid (VOF) method. The Rushton turbine induced flow is modeled by using a sliding mesh method. Numerical results are used to describe the bubbly flows in highly complex liquid flow. Some of the experimental works related to turbulent bubbly flow in a mixing tank are briefly reported. Numerical simulations are needed to complete and interpret the results of the experimental work. Information given by numerical simulations has a major role in designing and scaling-up mixing tanks. The results of this work have been reported in the following scientific articles: ·Honkanen M., Koohestany A., Hatunen T., Saarenrinne P., Zamankhan P., Large eddy simulations and PIV experiments of a two-phase air-water mixer, in Proceedings of ASME Fluids Engineering Summer Conference (2005). ·Honkanen M., Koohestany A., Hatunen T., Saarenrinne P., Zamankhan P., Dynamical States of Bubbling in an Aerated Stirring Tank, submitted to J. Computational Physics.

Assessment of meshing techniques for fatigue analysis of load carrying welded joints using the effective notch approach

The effective notch stress approach for the fatigue strength assessment of welded structures as included in the Fatigue Design Recommendation of the IIW requires the numerical analysis of the elastic notch stress in the weld toe and weld root which is fictitiously rounded with a radius of 1mm. The goal of this thesis work was to consider alternate meshing strategies when using the effective notch stress approach to assess the fatigue strength of load carrying partial penetration fillet-welded cruciform joints. In order to establish guidelines for modeling the joint and evaluating the results, various two-dimensional (2D) finite element analyses were carried out by systematically varying the thickness of the plates, the weld throat thickness, the degree of bending, and the shape and location of the modeled effective notch. To extend the scope of this work, studies were also carried out on the influence of

Ecological and Epidemiological Analyses of Multiple Sclerosis Relapse Rate

The underlying cause of many human autoimmune diseases is unknown, but several environmental factors are implicated in triggering the self-destructive immune reactions. Multiple Sclerosis (MS) is a chronic autoimmune disease of the central nervous system, potentially leading to persistent neurological deterioration. The cause of MS is not known, and apart from immunomodulatory treatments there is no cure. In the early phase of the disease, relapsing-remitting MS (RR-MS) is characterized by unpredictable exacerbations of the neurological symptoms called relapses, which can occur at different intervals ranging from 4 weeks to several years. Microbial infections are known to be able to trigger MS relapses, and the patients are instructed to avoid all factors that might increase the risk of infections and to properly use antibiotics as well as to take care of dental hygiene. Among those environmental factors which are known to increase susceptibility to infections, high ambient air inhalable particulate matter levels affect all people within a geographical region. During the period of interest in this thesis, the occurrence of MS relapses could be effectively reduced by injections of interferon, which has immunomodulatory and antiviral properties. In this thesis, ecological and epidemiological analyses were used to study the possible connection between MS relapse occurrence, population level viral infections and air quality factors, as well as the effects of interferon medication. Hospital archive data were collected retrospectively from 1986-2001, a period in time ranging from when interferon medication first became available until just before other disease-modifying MS therapies arrived on the market. The grouped data were studied with logistic regression and intervention analysis, and individual patient data with survival analysis. Interferons proved to be effective in the treatment of MS in this observational study, as the amount of MS exacerbations was lower during interferon use as compared to the time before interferon treatment. A statistically significant temporal relationship between MS relapses and inhalable particular matter (PM₁₀) concentrations was found in this study, which implies that MS patients are affected by the exposure to PM₁₀. Interferon probably protected against the effect of PM₁₀, because a significant increase in the risk of exacerbations was only observed in MS patients without interferon medication following environmental exposure to population level specific viral infections and PM₁₀. Apart from being antiviral, interferon could thus also attenuate the enhancement of immune reactions caused by ambient air PM₁₀. The retrospective approach utilizing carefully constructed hospital records proved to be an economical and reliable source of MS disease information for statistical analyses.

Numerical modelling of small supersonic axial flow turbines

Supersonic axial turbine stages typically exhibit lower efficiencies than subsonic axial turbine stages. One reason for the lower efficiency is the occurrence of shock waves. With higher pressure ratios the flow inside the turbine becomes relatively easily supersonic if there is only one turbine stage. Supersonic axial turbines can be designed in smaller physical size compared to subsonic axial turbines of same power. This makes them good candidates for turbochargers in large diesel engines, where space can be a limiting factor. Also the production costs are lower for a supersonic axial turbine stage than for two subsonic stages. Since supersonic axial turbines are typically low reaction turbines, they also create lower axial forces to be compensated with bearings compared to high reaction turbines. The effect of changing the stator-rotor axial gap in a small high (rotational) speed supersonic axial flow turbine is studied in design and off-design conditions. Also the effect of using pulsatile mass flow at the supersonic stator inlet is studied. Five axial gaps (axial space between stator and rotor) are modeled using threedimensional computational fluid dynamics at the design and three axial gaps at the off-design conditions. Numerical reliability is studied in three independent studies. An additional measurement is made with the design turbine geometry at intermediate off-design conditions and is used to increase the reliability of the modelling. All numerical modelling is made with the Navier-Stokes solver Finflo employing Chien’s k ¡ ² turbulence model. The modelling of the turbine at the design and off-design conditions shows that the total-to-static efficiency of the turbine decreases when the axial gap is increased in both design and off-design conditions. The efficiency drops almost linearily at the off-design conditions, whereas the efficiency drop accelerates with increasing axial gap at the design conditions. The modelling of the turbine stator with pulsatile inlet flow reveals that the mass flow pulsation amplitude is decreased at the stator throat. The stator efficiency and pressure ratio have sinusoidal shapes as a function of time. A hysteresis-like behaviour is detected for stator efficiency and pressure ratio as a function of inlet mass flow, over one pulse period. This behaviour arises from the pulsatile inlet flow. It is important to have the smallest possible axial gap in the studied turbine type in order to maximize the efficiency. The results for the whole turbine can also be applied to some extent in similar turbines operating for example in space rocket engines. The use of a supersonic stator in a pulsatile inlet flow is shown to be possible.

Numerical Investigation of Flow Past a Circular Cylinder and in a Staggered Tube Bundle Using Various Turbulence Models

Transitional flow past a three-dimensional circular cylinder is a widely studied phenomenon since this problem is of interest with respect to many technical applications. In the present work, the numerical simulation of flow past a circular cylinder, performed by using a commercial CFD code (ANSYS Fluent 12.1) with large eddy simulation (LES) and RANS (κ - ε and Shear-Stress Transport (SST) κ - ω! model) approaches. The turbulent flow for ReD = 1000 & 3900 is simulated to investigate the force coefficient, Strouhal number, flow separation angle, pressure distribution on cylinder and the complex three dimensional vortex shedding of the cylinder wake region. The numerical results extracted from these simulations have good agreement with the experimental data (Zdravkovich, 1997). Moreover, grid refinement and time-step influence have been examined. Numerical calculations of turbulent cross-flow in a staggered tube bundle continues to attract interest due to its importance in the engineering application as well as the fact that this complex flow represents a challenging problem for CFD. In the present work a time dependent simulation using κ – ε, κ - ω! and SST models are performed in two dimensional for a subcritical flow through a staggered tube bundle. The predicted turbulence statistics (mean and r.m.s velocities) have good agreement with the experimental data (S. Balabani, 1996). Turbulent quantities such as turbulent kinetic energy and dissipation rate are predicted using RANS models and compared with each other. The sensitivity of grid and time-step size have been analyzed. Model constants sensitivity study have been carried out by adopting κ – ε model. It has been observed that model constants are very sensitive to turbulence statistics and turbulent quantities.

Some defects in two-dimensional spin-1/2 Heisenberg antiferromagnets: a numerical study of magnetic effects

En del av de intressantaste fenomenen inom dagens materialfysik uppstår ur ett intrikat samspel mellan myriader av elektroner. Högtemperatursupraledare är det mest berömda exemplet. Varken klassiska teorier eller modeller där elektronerna är oberoende av varandra kan förklara de häpnadsväckande effekterna i de starkt korrelerade elektronsystemen. I vissa kopparoxider, till exempel La2CuO4, är det känt att valenselektronerna till följd av en stark ömsesidig växelverkan lokaliseras en och en till kopparatomerna i föreningens CuO2 plan. Laddningarnas inneboende magnetiska moment—spinnet—får då en avgörande roll för materialets elektriska och magnetiska egenskaper, vilka i exemplets fall kan beskrivas med Heisenbergmodellen som är den grundläggande teoretiska modellen för mikroskopisk magnetism. Men exakt varför föreningarna kan bli supraledande då de dopas med överskottsladdningar är än så länge en obesvarad fråga. Min avhandling undersöker orenheters inverkan på Heisenbergmodellens magnetiska egenskaper—ett problem av både experimentell och teoretisk relevans. En etablerad numerisk metod har använts—en kvantmekanisk Monte Carlo teknik—för att utföra omfattande datorsimuleringar av den matematiska modellen på två dedikerade Linux datorkluster. Arbetet hör till området beräkningsfysik. De teoretiska modellerna för starkt korrelerade elektronsystem, däribland Heisenbergmodellen, är ytterst invecklade matematiskt sett och de kan inte lösas exakt. Analytiska utredningar bygger för det mesta på antaganden och förenklingar vars inverkningar på slutresultatet är ofta oklara. I det avseende kan numeriska studier vara exakta, det vill säga de kan behandla modellerna som de är. Oftast behövs bägge tillvägagångssätten. Den röda tråden i arbetet har varit att numeriskt testa vissa högaktuella analytiska förutsägelser rörande effekterna av orenheter i Heisenbergmodellen. En del av dem har vi på basen av mycket noggranna data kunnat bekräfta. Men våra resultat har också påvisat felaktigheter i de analytiska prognoserna som sedermera delvis reviderats. En del av avhandlingens numeriska upptäckter har i sin tur stimulerat till helt nya teoretiska studier.

Charge transport in disordered materials : simulations, theory, and numerical modeling of hopping transport and electron-hole recombination

Min avhandling behandlar hur oordnade material leder elektrisk ström. Bland materialen som studeras finns ledande polymerer, d.v.s. plaster som leder ström, och mer allmänt organiska halvledare. Av de här materialen har man kunnat bygga elektroniska komponenter, och man hoppas på att kunna trycka hela kretsar av organiska material. För de här tillämpningarna är det viktigt att förstå hur materialen själva leder elektrisk ström. Termen oordnade material syftar på material som saknar kristallstruktur. Oordningen gör att elektronernas tillstånd blir lokaliserade i rummet, så att en elektron i ett visst tillstånd är begränsad t.ex. till en molekyl eller ett segment av en polymer. Det här kan jämföras med kristallina material, där ett elektrontillstånd är utspritt över hela kristallen (men i stället har en väldefinierad rörelsemängd). Elektronerna (eller hålen) i det oordnade materialet kan röra sig genom att tunnelera mellan de lokaliserade tillstånden. Utgående från egenskaperna för den här tunneleringsprocessen, kan man bestämma transportegenskaperna för hela materialet. Det här är utgångspunkten för den så kallade hopptransportmodellen, som jag har använt mig av. Hopptransportmodellen innehåller flera drastiska förenklingar. Till exempel betraktas elektrontillstånden som punktformiga, så att tunneleringssannolikheten mellan två tillstånd endast beror på avståndet mellan dem, och inte på deras relativa orientation. En annan förenkling är att behandla det kvantmekaniska tunneleringsproblemet som en klassisk process, en slumpvandring. Trots de här grova approximationerna visar hopptransportmodellen ändå många av de fenomen som uppträder i de verkliga materialen som man vill modellera. Man kan kanske säga att hopptransportmodellen är den enklaste modell för oordnade material som fortfarande är intressant att studera. Man har inte hittat exakta analytiska lösningar för hopptransportmodellen, därför använder man approximationer och numeriska metoder, ofta i form av datorberäkningar. Vi har använt både analytiska metoder och numeriska beräkningar för att studera olika aspekter av hopptransportmodellen. En viktig del av artiklarna som min avhandling baserar sig på är att jämföra analytiska och numeriska resultat. Min andel av arbetet har främst varit att utveckla de numeriska metoderna och applicera dem på hopptransportmodellen. Därför fokuserar jag på den här delen av arbetet i avhandlingens introduktionsdel. Ett sätt att studera hopptransportmodellen numeriskt är att direkt utföra en slumpvandringsprocess med ett datorprogram. Genom att föra statisik över slumpvandringen kan man beräkna olika transportegenskaper i modellen. Det här är en så kallad Monte Carlo-metod, eftersom själva beräkningen är en slumpmässig process. I stället för att följa rörelsebanan för enskilda elektroner, kan man beräkna sannolikheten vid jämvikt för att hitta en elektron i olika tillstånd. Man ställer upp ett system av ekvationer, som relaterar sannolikheterna för att hitta elektronen i olika tillstånd i systemet med flödet, strömmen, mellan de olika tillstånden. Genom att lösa ekvationssystemet fås sannolikhetsfördelningen för elektronerna. Från sannolikhetsfördelningen kan sedan strömmen och materialets transportegenskaper beräknas. En aspekt av hopptransportmodellen som vi studerat är elektronernas diffusion, d.v.s. deras slumpmässiga rörelse. Om man betraktar en samling elektroner, så sprider den med tiden ut sig över ett större område. Det är känt att diffusionshastigheten beror av elfältet, så att elektronerna sprider sig fortare om de påverkas av ett elektriskt fält. Vi har undersökt den här processen, och visat att beteendet är väldigt olika i endimensionella system, jämfört med två- och tredimensionella. I två och tre dimensioner beror diffusionskoefficienten kvadratiskt av elfältet, medan beroendet i en dimension är linjärt. En annan aspekt vi studerat är negativ differentiell konduktivitet, d.v.s. att strömmen i ett material minskar då man ökar spänningen över det. Eftersom det här fenomenet har uppmätts i organiska minnesceller, ville vi undersöka om fenomenet också kan uppstå i hopptransportmodellen. Det visade sig att det i modellen finns två olika mekanismer som kan ge upphov till negativ differentiell konduktivitet. Dels kan elektronerna fastna i fällor, återvändsgränder i systemet, som är sådana att det är svårare att ta sig ur dem då elfältet är stort. Då kan elektronernas medelhastighet och därmed strömmen i materialet minska med ökande elfält. Elektrisk växelverkan mellan elektronerna kan också leda till samma beteende, genom en så kallad coulombblockad. En coulombblockad kan uppstå om antalet ledningselektroner i materialet ökar med ökande spänning. Elektronerna repellerar varandra och ett större antal elektroner kan leda till att transporten blir långsammare, d.v.s. att strömmen minskar.

Characterization of novel genes predominantly expressed in the epididymis – from genome analyses to genetically modified mice

In mammals, post-testicular sperm maturation taking place in the epididymis is required for the spermatozoa to acquire the abilities required to fertilize the egg in vivo. The epididymal epithelial cells secrete proteins and other small molecules into the lumen, where they interact with the spermatozoa and enable necessary maturational changes. In this study different in silico, in vitro and in vivo approaches were utilized in order to find novel genes responsible for the function of the epididymis and post-testicular sperm maturation in the mouse. Available online genomic databases were analyzed to identify genes potentially expressed in the epididymis, gene expression profiling was performed by studying their expression in different mouse tissues, and significance of certain genes to fertility was assessed by generating genetically modified mouse models. A recently discovered Pate (prostate and testis expression) gene family was found to be predominantly expressed in the epididymis. It represents one of the largest known gene families expressed in the epididymis, and the members code for proteins potentially involved in defense against microorganisms. Through genetically modified mouse models CRISP4 (cysteine-rich secretory protein 4) was identified to regulate sperm acrosome reaction, and BMYC to inhibit the expression of the Myc proto-oncogene in the developing testis. A mouse line expressing iCre recombinase specifically in the epididymis was also generated. This model can be used to generate conditional, epididymis-specific knock-out models, and will be a valuable tool in fertility studies.

18F-Labeled Presynaptic Dopaminergic Tracers. Synthesis, Radiochemical Analyses, and Preclinical Evaluation of [18F]FDOPA and [18F]CFT

Dysfunction of the dopaminergic system in brain is involved in several pathological conditions such as Parkinson’s disease and depression. 2β-Carbomethoxy-3β-(4-[18F] fluorophenyl)tropane ([18F]CFT) and 6-[18F]fluoro-L-dopa ([18F]FDOPA) are tracers for imaging the dopaminergic function with positron emission tomography (PET). Peripheral uptake of [18F]FDOPA is also used in the localization and diagnosis of neuroendocrine tumors. [18F]FDOPA and [18F]CFT can be synthesized by electrophilic fluorodestannylation. However, the specific radioactivity (SA) in the electrophilic fluorination is low with traditional synthetic methods. In this study, [18F]FDOPA and [18F]CFT were synthesized using post-target-produced [18F]F2 as an electrophilic fluorination agent. With this method, tracers are produced with sufficient SA for neuroreceptor studies. Specific aims in this study were to replace Freon-11 in the production of [18F]FDOPA due to the ozone depleting properties of this solvent, to determine pharmacological specificity and selectivity of [18F]CFT with respect to monoamine transporters, and to compare the ability of these tracers to reflect the degree of nigral neuronal loss in rats in which the dopaminergic system in the brain had been unilaterally destroyed by 6- OHDA. Post-target-produced [18F]F2 was successfully used in the production of [18F]FDOPA and [18F]CFT. The SA achieved was substantially higher than in previous synthetic methods. Deuterated compounds, CD2Cl2, CDCl3 and C3D6O, were found to be suitable solvents for replacing Freon-11. Both [18F]FDOPA and [18F]CFT demonstrated nigrostriatal dopaminergic hypofunction and correlated with the number of nigral dopaminergic neurons in the 6-OHDA lesioned rat. However, the dopamine transporter (DAT) tracer [18F]CFT was more sensitive than the dopamine synthesis tracer [18F]FDOPA in detecting these defects because of the higher non-specific uptake of [18F]FDOPA. [18F]CFT can also be used for imaging the norepinephrine transporter (NET) because of the specific uptake into the locus coeruleus. The observation that [18F]CFT exhibits specific uptake in the pancreas warrants further studies in humans with respect to potential utility in pancreatic imaging

Testate amoebae (thecamoebians) as indicators of aquatic mine impact

The environmental impacts of a single mine often remain local, but acidic and metal-rich acid mine drainage (AMD) from the waste materials may pose a serious threat to adjacent surface waters and their ecosystems. Testate amoebae (thecamoebian) analysis was used together with lake sediment geochemistry to study and evaluate the ecological effects of sulphidic metal mines on aquatic environments. Three different mines were included in the study: Luikonlahti Cu-mine in Kaavi, eastern Finland, Haveri Cu-Au mine in Ylöjärvi, southern Finland and Pyhäsalmi Zn-Cu-S mine in Pyhäjärvi, central Finland. Luikonlahti and Haveri are closed mines, but Pyhäsalmi is still operating. The sampling strategy was case specific, and planned to provide a representative sediment sample series to define natural background conditions, to detect spatial and temporal variations in mine impacts, to evaluate the possible recovery after the peak contamination, and to distinguish the effects of other environmental factors from the mining impacts. In the Haveri case, diatom analyses were performed alongside thecamoebian analysis to evaluate the similarities and differences between the two proxies. The results of the analyses were investigated with multivariate methods (direct and indirect ordinations, diversity and distance measure indices). Finally, the results of each case study were harmonized, pooled, and jointly analyzed to summarize the results for this dissertation. Geochemical results showed broadly similar temporal patterns in each case. Concentrations of ions in the pre-disturbance samples defined the natural baseline against which other results were compared. The beginning of the mining activities had only minor impacts on sediment geochemistry, mainly appearing as an increased clastic input into the lakes at Haveri and Pyhäsalmi. The active mining phase was followed by the metallic contamination and, subsequently, by the most recent change towards decreased but still elevated metal concentrations in the sediments. Because of the delay in the oxidation of waste material and formation of AMD, the most intense, but transient metal contamination phase occurred in the post-mining period at Luikonlahti and Haveri. At Pyhäsalmi, the highest metal contamination preceded effluent mitigation actions. Spatial gradients were observed besides the temporal evolution in both the pre-disturbance and mine-impacted samples from Luikonlahti and Pyhäsalmi. The geochemical gradients varied with distance from the main source of contaminants (dispersion and dilution) and with water depth (redox and pH). The spatial extent of the highest metal contamination associated with these mines remained rather limited. At Haveri, the metallic impact was widespread, with the upstream site in another lake basin found to be contaminated. Changes in thecamoebian assemblages corresponded well with the geochemical results. Despite some differences, the general features and ecological responses of the faunal assemblages were rather similar in each lake. Constantly abundant strains of Difflugia oblonga, Difflugia protaeiformis and centropyxids formed the core of these assemblages. Increasing proportions of Cucurbitella tricuspis towards the surface samples were found in all of the cases. The results affirmed the indicator value of some already known indicator forms, but such as C. tricuspis and higher nutrient levels, but also elicited possible new ones such as D. oblonga ‘spinosa’ and clayey substrate, high conductivity and/or alkalinity, D. protaeiformis ‘multicornis’ and pH, water hardness and the amount of clastic material and Centropyxis constricta ‘aerophila’ and high metal and S concentrations. In each case, eutrophication appeared to be the most important environmental factor, masking the effects of other variables. Faunal responses to high metal inputs in sediments remained minor, but were nevertheless detectable. Besides the trophic state of the lake, numerical methods suggested overall geochemical conditions (pH, redox) to be the most important factor at Luikonlahti, whereas the Haveri results showed the clearest connection between metals and amoebae. At Pyhäsalmi, the strongest relationships were found between Ca- and S-rich present loading, redox conditions and substrate composition. Sediment geochemistry and testate amoeba analysis proved to be a suitable combination of methods to detect and describe the aquatic mine impacts in each specific case, to evaluate recovery and to differentiate between the effects of different anthropogenic and natural environmental factors. It was also suggested that aquatic mine impacts can be significantly mitigated by careful design and after-care of the waste facilities, especially by reducing and preventing AMD. The case-specific approach is nevertheless necessary because of the unique characteristics of each mine and variations in the environmental background conditions.

Fatigue study of the fillet weld waving on weld toe and the penetration in the weld root based on the effective notch stress approach

The fatigue failure of structures under fluctuating loads in fillet weld joints raises a demand to determine the parameters related to this type of loading. In this study, the stress distribution in the susceptible area of weld toe and weld root in fillet welded models analyzed by finite element method applying FEMAP software. To avoid the geometrical singularity on the path of analytical stress analysis in the toe and root area of a weld model the effective notch stress approach applied by which a proper fictitious rounding that mostly depend on the material of structure is applied. The models with different weld toe waving width and radius are analyzed while the flank angle of weld varied in 45 and 30 degrees. The processed results shows that the waving compare to the straight weld toe makes differences in the value of stress and consequently the stress concentration factor between the tip and depth of the waves in the weld toe which helps to protect the crack of propagation and gives enough time and tools to be informed of the crack initiation in the structure during the periodical observation of structure. In the weld root study the analyses among the models with the welding penetration percentage from non-penetration to the full-penetration shows a slightly increase in the root area stress value which comparing with the stiffening effect of penetration conclude that the half-penetration can make an optimization between the stress increase and stiffening effect of deep penetration.

Analysis and validation of space averaged drag model for numerical simulations of gas-solid flows in fluidized beds

This thesis presents an approach for formulating and validating a space averaged drag model for coarse mesh simulations of gas-solid flows in fluidized beds using the two-fluid model. Proper modeling for fluid dynamics is central in understanding any industrial multiphase flow. The gas-solid flows in fluidized beds are heterogeneous and usually simulated with the Eulerian description of phases. Such a description requires the usage of fine meshes and small time steps for the proper prediction of its hydrodynamics. Such constraint on the mesh and time step size results in a large number of control volumes and long computational times which are unaffordable for simulations of large scale fluidized beds. If proper closure models are not included, coarse mesh simulations for fluidized beds do not give reasonable results. The coarse mesh simulation fails to resolve the mesoscale structures and results in uniform solids concentration profiles. For a circulating fluidized bed riser, such predicted profiles result in a higher drag force between the gas and solid phase and also overestimated solids mass flux at the outlet. Thus, there is a need to formulate the closure correlations which can accurately predict the hydrodynamics using coarse meshes. This thesis uses the space averaging modeling approach in the formulation of closure models for coarse mesh simulations of the gas-solid flow in fluidized beds using Geldart group B particles. In the analysis of formulating the closure correlation for space averaged drag model, the main parameters for the modeling were found to be the averaging size, solid volume fraction, and distance from the wall. The closure model for the gas-solid drag force was formulated and validated for coarse mesh simulations of the riser, which showed the verification of this modeling approach. Coarse mesh simulations using the corrected drag model resulted in lowered values of solids mass flux. Such an approach is a promising tool in the formulation of appropriate closure models which can be used in coarse mesh simulations of large scale fluidized beds.

Theoretical Analysis and Numerical Simulation of Spectral Radiative Properties of Combustion Gases in Oxy/Air-Fired Combustion Systems

Energy efficiency is one of the major objectives which should be achieved in order to implement the limited energy resources of the world in a sustainable way. Since radiative heat transfer is the dominant heat transfer mechanism in most of fossil fuel combustion systems, more accurate insight and models may cause improvement in the energy efficiency of the new designed combustion systems. The radiative properties of combustion gases are highly wavelength dependent. Better models for calculating the radiative properties of combustion gases are highly required in the modeling of large scale industrial combustion systems. With detailed knowledge of spectral radiative properties of gases, the modeling of combustion processes in the different applications can be more accurate. In order to propose a new method for effective non gray modeling of radiative heat transfer in combustion systems, different models for the spectral properties of gases including SNBM, EWBM, and WSGGM have been studied in this research. Using this detailed analysis of different approaches, the thesis presents new methods for gray and non gray radiative heat transfer modeling in homogeneous and inhomogeneous H2O–CO2 mixtures at atmospheric pressure. The proposed method is able to support the modeling of a wide range of combustion systems including the oxy-fired combustion scenario. The new methods are based on implementing some pre-obtained correlations for the total emissivity and band absorption coefficient of H2O–CO2 mixtures in different temperatures, gas compositions, and optical path lengths. They can be easily used within any commercial CFD software for radiative heat transfer modeling resulting in more accurate, simple, and fast calculations. The new methods were successfully used in CFD modeling by applying them to industrial scale backpass channel under oxy-fired conditions. The developed approaches are more accurate compared with other methods; moreover, they can provide complete explanation and detailed analysis of the radiation heat transfer in different systems under different combustion conditions. The methods were verified by applying them to some benchmarks, and they showed a good level of accuracy and computational speed compared to other methods. Furthermore, the implementation of the suggested banded approach in CFD software is very easy and straightforward.

Multidata inverse problems and Bayesian solution methods in astronomy

Statistical analyses of measurements that can be described by statistical models are of essence in astronomy and in scientific inquiry in general. The sensitivity of such analyses, modelling approaches, and the consequent predictions, is sometimes highly dependent on the exact techniques applied, and improvements therein can result in significantly better understanding of the observed system of interest. Particularly, optimising the sensitivity of statistical techniques in detecting the faint signatures of low-mass planets orbiting the nearby stars is, together with improvements in instrumentation, essential in estimating the properties of the population of such planets, and in the race to detect Earth-analogs, i.e. planets that could support liquid water and, perhaps, life on their surfaces. We review the developments in Bayesian statistical techniques applicable to detections planets orbiting nearby stars and astronomical data analysis problems in general. We also discuss these techniques and demonstrate their usefulness by using various examples and detailed descriptions of the respective mathematics involved. We demonstrate the practical aspects of Bayesian statistical techniques by describing several algorithms and numerical techniques, as well as theoretical constructions, in the estimation of model parameters and in hypothesis testing. We also apply these algorithms to Doppler measurements of nearby stars to show how they can be used in practice to obtain as much information from the noisy data as possible. Bayesian statistical techniques are powerful tools in analysing and interpreting noisy data and should be preferred in practice whenever computational limitations are not too restrictive.

Numerical Simulation of Stochastic Di erential Equations

Stochastic differential equation (SDE) is a differential equation in which some of the terms and its solution are stochastic processes. SDEs play a central role in modeling physical systems like finance, Biology, Engineering, to mention some. In modeling process, the computation of the trajectories (sample paths) of solutions to SDEs is very important. However, the exact solution to a SDE is generally difficult to obtain due to non-differentiability character of realizations of the Brownian motion. There exist approximation methods of solutions of SDE. The solutions will be continuous stochastic processes that represent diffusive dynamics, a common modeling assumption for financial, Biology, physical, environmental systems. This Masters' thesis is an introduction and survey of numerical solution methods for stochastic differential equations. Standard numerical methods, local linearization methods and filtering methods are well described. We compute the root mean square errors for each method from which we propose a better numerical scheme. Stochastic differential equations can be formulated from a given ordinary differential equations. In this thesis, we describe two kind of formulations: parametric and non-parametric techniques. The formulation is based on epidemiological SEIR model. This methods have a tendency of increasing parameters in the constructed SDEs, hence, it requires more data. We compare the two techniques numerically.