Numerical and experimental investigation of thermal louvers for space applications

Thermal louvers, using movable or rotating shutters over a radiating surface, have gained a wide acceptance as highly efficient devices for controlling the temperature of a spacecraft. This paper presents a detailed analysis of the performance of a rectangular thermal louver with movable blades. The radiative capacity of the louver, determined by its effective emittance, is calculated for different values of the blades opening angle. Experimental results obtained with a prototype of a spacecraft thermal louver show good agreement with the theoretical values.

Gas-solid two-phase flow in the riser of circulating fluidized beds: mathematical modelling and numerical simulation

A mathematical model is developed for gas-solids flows in circulating fluidized beds. An Eulerian formulation is followed based on the two-fluids model approach where both the fluid and the particulate phases are treated as a continuum. The physical modelling is discussed, including the formulation of boundary conditions and the description of the numerical methodology. Results of numerical simulation are presented and discussed. The model is validated through comparison to experiment, and simulation is performed to investigate the effects on the flow hydrodynamics of the solids viscosity.

Chaos and Unpredictability in the Vibration of an Elasto-Plastic Beam

This contribution discusses the nonlinear dynamics of a pin-ended elasto-plastic beam with both kinematic and isotropic hardening. An iterative numerical procedure based on the operator split technique is developed in order to deal with the nonlinearities in the equations of motion. Free and forced responses for harmonic sinusoidal and square wave excitations are investigated. Numerical simulations present many interesting behaviors such as jump phenomena, sensitivity to initial conditions, chaos and transient chaos. These results indicate that there are practical problems in predicting the response of the beam even when periodic steady state response is expected.

Numerical Simulation of the Cavitation in the Hydrodynamic Lubrication of Journal Bearings: a Parallel Algorithm

In this paper we present an algorithm for the numerical simulation of the cavitation in the hydrodynamic lubrication of journal bearings. Despite the fact that this physical process is usually modelled as a free boundary problem, we adopted the equivalent variational inequality formulation. We propose a two-level iterative algorithm, where the outer iteration is associated to the penalty method, used to transform the variational inequality into a variational equation, and the inner iteration is associated to the conjugate gradient method, used to solve the linear system generated by applying the finite element method to the variational equation. This inner part was implemented using the element by element strategy, which is easily parallelized. We analyse the behavior of two physical parameters and discuss some numerical results. Also, we analyse some results related to the performance of a parallel implementation of the algorithm.

Numerical study of wedge supported oblique shock wave-oblique detonation wave transitions

The results of a numerical study of premixed Hydrogen-air flows ignition by an oblique shock wave (OSW) stabilized by a wedge are presented, in situations when initial and boundary conditions are such that transition between the initial OSW and an oblique detonation wave (ODW) is observed. More precisely, the objectives of the paper are: (i) to identify the different possible structures of the transition region that exist between the initial OSW and the resulting ODW and (ii) to evidence the effect on the ODW of an abrupt decrease of the wedge angle in such a way that the final part of the wedge surface becomes parallel to the initial flow. For such a geometrical configuration and for the initial and boundary conditions considered, the overdriven detonation supported by the initial wedge angle is found to relax towards a Chapman-Jouguet detonation in the region where the wedge surface is parallel to the initial flow. Computations are performed using an adaptive, unstructured grid, finite volume computer code previously developed for the sake of the computations of high speed, compressible flows of reactive gas mixtures. Physico-chemical properties are functions of the local mixture composition, temperature and pressure, and they are computed using the CHEMKIN-II subroutines.

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.

Modal testing and numerical modeling of the dynamic properties of layered sheet-steel structure

Recently, due to the increasing total construction and transportation cost and difficulties associated with handling massive structural components or assemblies, there has been increasing financial pressure to reduce structural weight. Furthermore, advances in material technology coupled with continuing advances in design tools and techniques have encouraged engineers to vary and combine materials, offering new opportunities to reduce the weight of mechanical structures. These new lower mass systems, however, are more susceptible to inherent imbalances, a weakness that can result in higher shock and harmonic resonances which leads to poor structural dynamic performances. The objective of this thesis is the modeling of layered sheet steel elements, to accurately predict dynamic performance. During the development of the layered sheet steel model, the numerical modeling approach, the Finite Element Analysis and the Experimental Modal Analysis are applied in building a modal model of the layered sheet steel elements. Furthermore, in view of getting a better understanding of the dynamic behavior of layered sheet steel, several binding methods have been studied to understand and demonstrate how a binding method affects the dynamic behavior of layered sheet steel elements when compared to single homogeneous steel plate. Based on the developed layered sheet steel model, the dynamic behavior of a lightweight wheel structure to be used as the structure for the stator of an outer rotor Direct-Drive Permanent Magnet Synchronous Generator designed for high-power wind turbines is studied.

Application and development of numerical methods for the modelling of innovative gas cooled fission reactors

Innovative gas cooled reactors, such as the pebble bed reactor (PBR) and the gas cooled fast reactor (GFR) offer higher efficiency and new application areas for nuclear energy. Numerical methods were applied and developed to analyse the specific features of these reactor types with fully three dimensional calculation models. In the first part of this thesis, discrete element method (DEM) was used for a physically realistic modelling of the packing of fuel pebbles in PBR geometries and methods were developed for utilising the DEM results in subsequent reactor physics and thermal-hydraulics calculations. In the second part, the flow and heat transfer for a single gas cooled fuel rod of a GFR were investigated with computational fluid dynamics (CFD) methods. An in-house DEM implementation was validated and used for packing simulations, in which the effect of several parameters on the resulting average packing density was investigated. The restitution coefficient was found out to have the most significant effect. The results can be utilised in further work to obtain a pebble bed with a specific packing density. The packing structures of selected pebble beds were also analysed in detail and local variations in the packing density were observed, which should be taken into account especially in the reactor core thermal-hydraulic analyses. Two open source DEM codes were used to produce stochastic pebble bed configurations to add realism and improve the accuracy of criticality calculations performed with the Monte Carlo reactor physics code Serpent. Russian ASTRA criticality experiments were calculated. Pebble beds corresponding to the experimental specifications within measurement uncertainties were produced in DEM simulations and successfully exported into the subsequent reactor physics analysis. With the developed approach, two typical issues in Monte Carlo reactor physics calculations of pebble bed geometries were avoided. A novel method was developed and implemented as a MATLAB code to calculate porosities in the cells of a CFD calculation mesh constructed over a pebble bed obtained from DEM simulations. The code was further developed to distribute power and temperature data accurately between discrete based reactor physics and continuum based thermal-hydraulics models to enable coupled reactor core calculations. The developed method was also found useful for analysing sphere packings in general. CFD calculations were performed to investigate the pressure losses and heat transfer in three dimensional air cooled smooth and rib roughened rod geometries, housed inside a hexagonal flow channel representing a sub-channel of a single fuel rod of a GFR. The CFD geometry represented the test section of the L-STAR experimental facility at Karlsruhe Institute of Technology and the calculation results were compared to the corresponding experimental results. Knowledge was gained of the adequacy of various turbulence models and of the modelling requirements and issues related to the specific application. The obtained pressure loss results were in a relatively good agreement with the experimental data. Heat transfer in the smooth rod geometry was somewhat under predicted, which can partly be explained by unaccounted heat losses and uncertainties. In the rib roughened geometry heat transfer was severely under predicted by the used realisable k − epsilon turbulence model. An additional calculation with a v2 − f turbulence model showed significant improvement in the heat transfer results, which is most likely due to the better performance of the model in separated flow problems. Further investigations are suggested before using CFD to make conclusions of the heat transfer performance of rib roughened GFR fuel rod geometries. It is suggested that the viewpoints of numerical modelling are included in the planning of experiments to ease the challenging model construction and simulations and to avoid introducing additional sources of uncertainties. To facilitate the use of advanced calculation approaches, multi-physical aspects in experiments should also be considered and documented in a reasonable detail.

Numerical simulation of rotor-stator interaction and tip clearance flow in centrifugal compressors

The effect of the tip clearance and vaneless diffuser width on the stage performance and flow fields of a centrifugal compressor were studied numerically and results were compared to the experimental measurements. The diffuser width was changed by moving the shroud side of the diffuser axially and six tip clearances size from 0.5 to 3 mm were studied. Moreover, the effects of rotor-stator interaction on the diffuser and impeller flow fields and performance were studied. Also transient simulations were carried out in order to investigate the influence of the interaction on the impeller and diffuser performance parameters. It was seen that pinch could improve the performance and it help to get more uniform flow at exit and less back flow from diffuser to the impeller.

Numerical Studies of Dark Energy Models and Observations

The cosmological standard view is based on the assumptions of homogeneity, isotropy and general relativistic gravitational interaction. These alone are not sufficient for describing the current cosmological observations of accelerated expansion of space. Although general relativity is extremely accurately tested to describe the local gravitational phenomena, there is a strong demand for modifying either the energy content of the universe or the gravitational interaction itself to account for the accelerated expansion. By adding a non-luminous matter component and a constant energy component with negative pressure, the observations can be explained with general relativity. Gravitation, cosmological models and their observational phenomenology are discussed in this thesis. Several classes of dark energy models that are motivated by theories outside the standard formulation of physics were studied with emphasis on the observational interpretation. All the cosmological models that seek to explain the cosmological observations, must also conform to the local phenomena. This poses stringent conditions for the physically viable cosmological models. Predictions from a supergravity quintessence model was compared to Supernova 1a data and several metric gravity models were studied with local experimental results. Polytropic stellar configurations of solar, white dwarf and neutron stars were numerically studied with modified gravity models. The main interest was to study the spacetime around the stars. The results shed light on the viability of the studied cosmological models.

Numerical simulation of two-chamber plasma sources using finite element method

Numerical simulation of plasma sources is very important. Such models allows to vary different plasma parameters with high degree of accuracy. Moreover, they allow to conduct measurements not disturbing system balance.Recently, the scientific and practical interest increased in so-called two-chamber plasma sources. In one of them (small or discharge chamber) an external power source is embedded. In that chamber plasma forms. In another (large or diffusion chamber) plasma exists due to the transport of particles and energy through the boundary between chambers.In this particular work two-chamber plasma sources with argon and oxygen as active mediums were onstructed. This models give interesting results in electric field profiles and, as a consequence, in density profiles of charged particles.

Partikkelikokojakaumamenetelmän testaus INCA Feature

Tässä työssä testattiin partikkelikokojakaumien analysoinnissa käytettävää kuvankäsittelyohjelmaa INCA Feature. Partikkelikokojakaumat määritettiin elektronimikroskooppikuvista INCA Feature ohjelmaa käyttäen partikkeleiden projektiokuvista päällystyspigmenttinä käytettävälle talkille ja kahdelle eri karbonaattilaadulle. Lisäksi määritettiin partikkelikokojakaumat suodatuksessa ja puhdistuksessa apuaineina käytettäville piidioksidi- ja alumiinioksidihiukkasille. Kuvankäsittelyohjelmalla määritettyjä partikkelikokojakaumia verrattiin partikkelin laskeutumisnopeuteen eli sedimentaatioon perustuvalla SediGraph 5100 analysaattorilla ja laserdiffraktioon perustuvalla Coulter LS 230 menetelmällä analysoituihin partikkelikokojakaumiin. SediGraph 5100 ja kuva-analyysiohjelma antoivat talkkipartikkelien kokojakaumalle hyvin samankaltaisen keskiarvon. Sen sijaan Coulter LS 230 laitteen antama kokojakauman keskiarvo poikkesi edellisistä. Kaikki vertailussa olleet partikkelikokojakaumamenetelmät asettivat eri näytteiden partikkelit samaan kokojärjestykseen. Kuitenkaan menetelmien tuloksia ei voida numeerisesti verrata toisiinsa, sillä kaikissa käytetyissä analyysimenetelmissä partikkelikoon mittaus perustuu partikkelin eri ominaisuuteen. Työn perusteella kaikki testatut analyysimenetelmät soveltuvat paperipigmenttien partikkelikokojakaumien määrittämiseen. Tässä työssä selvitettiin myös kuva-analyysiin tarvittava partikkelien lukumäärä, jolla analyysitulos on luotettava. Työssä todettiin, että analysoitavien partikkelien lukumäärän tulee olla vähintään 300 partikkelia. Liian suuri näytemäärä lisää kokojakauman hajontaa ja pidentää analyysiin käytettyä aikaa useaan tuntiin. Näytteenkäsittely vaatii vielä lisää tutkimuksia, sillä se on tärkein ja kriittisin vaihe SEM ja kuva-analyysiohjelmalla tehtävää partikkelikokoanalyysiä. Automaattisten mikroskooppien yleistyminen helpottaa ja nopeuttaa analyysien tekoa, jolloin menetelmän suosio tulee kasvamaan myös paperipigmenttien tutkimuksessa. Laitteiden korkea hinta ja käyttäjältä vaadittava eritysosaaminen tulevat rajaamaan käytön ainakin toistaiseksi tutkimuslaitoksiin.

The effect of calculators on the numerical problem-solving skills and attitudes of primary students towards mathematics /

The purpose of this study was to determine the effect that calculators have on the attitudes and numerical problem-solving skills of primary students. The sample used for this research was one of convenience. The sample consisted of two grade 3 classes within the York Region District School Board. The students in the experimental group used calculators for this problem-solving unit. The students in the control group completed the same numerical problem-solving unit without the use of calculators. The pretest-posttest control group design was used for this study. All students involved in this study completed a computational pretest and an attitude pretest. At the end of the study, the students completed a computational posttest. Five students from the experimental group and five students from the control group received their posttests in the form of a taped interview. At the end of the unit, all students completed the attitude scale that they had received before the numerical problem-solving unit once again. Data for qualitative analysis included anecdotal observations, journal entries, and transcribed interviews. The constant comparative method was used to analyze the qualitative data. A t test was also performed on the data to determine whether there were changes in test and attitude scores between the control and experimental group. Overall, the findings of this study support the hypothesis that calculators improve the attitudes of primary students toward mathematics. Also, there is some evidence to suggest that calculators improve the computational skills of grade 3 students.

Quantum Monte Carlo : some theoretical and numerical studies

In Part I, theoretical derivations for Variational Monte Carlo calculations are compared with results from a numerical calculation of He; both indicate that minimization of the ratio estimate of Evar , denoted EMC ' provides different optimal variational parameters than does minimization of the variance of E MC • Similar derivations for Diffusion Monte Carlo calculations provide a theoretical justification for empirical observations made by other workers. In Part II, Importance sampling in prolate spheroidal coordinates allows Monte Carlo calculations to be made of E for the vdW molecule var He2' using a simplifying partitioning of the Hamiltonian and both an HF-SCF and an explicitly correlated wavefunction. Improvements are suggested which would permit the extension of the computational precision to the point where an estimate of the interaction energy could be made~

Developing a numerical inverse-theory-based extraction of orientation-dependent relaxation rates from partially- relaxed spectra

Second-rank tensor interactions, such as quadrupolar interactions between the spin- 1 deuterium nuclei and the electric field gradients created by chemical bonds, are affected by rapid random molecular motions that modulate the orientation of the molecule with respect to the external magnetic field. In biological and model membrane systems, where a distribution of dynamically averaged anisotropies (quadrupolar splittings, chemical shift anisotropies, etc.) is present and where, in addition, various parts of the sample may undergo a partial magnetic alignment, the numerical analysis of the resulting Nuclear Magnetic Resonance (NMR) spectra is a mathematically ill-posed problem. However, numerical methods (de-Pakeing, Tikhonov regularization) exist that allow for a simultaneous determination of both the anisotropy and orientational distributions. An additional complication arises when relaxation is taken into account. This work presents a method of obtaining the orientation dependence of the relaxation rates that can be used for the analysis of the molecular motions on a broad range of time scales. An arbitrary set of exponential decay rates is described by a three-term truncated Legendre polynomial expansion in the orientation dependence, as appropriate for a second-rank tensor interaction, and a linear approximation to the individual decay rates is made. Thus a severe numerical instability caused by the presence of noise in the experimental data is avoided. At the same time, enough flexibility in the inversion algorithm is retained to achieve a meaningful mapping from raw experimental data to a set of intermediate, model-free