Full and Model-Reduced Structure-Preserving Simulation of Incompressible Fluids

This thesis outlines the construction of several types of structured integrators for incompressible fluids. We first present a vorticity integrator, which is the Hamiltonian counterpart of the existing Lagrangian-based fluid integrator. We next present a model-reduced variational Eulerian integrator for incompressible fluids, which combines the efficiency gains of dimension reduction, the qualitative robustness to coarse spatial and temporal resolutions of geometric integrators, and the simplicity of homogenized boundary conditions on regular grids to deal with arbitrarily-shaped domains with sub-grid accuracy.

Both these numerical methods involve approximating the Lie group of volume-preserving diffeomorphisms by a finite-dimensional Lie-group and then restricting the resulting variational principle by means of a non-holonomic constraint. Advantages and limitations of this discretization method will be outlined. It will be seen that these derivation techniques are unable to yield symplectic integrators, but that energy conservation is easily obtained, as is a discretized version of Kelvin's circulation theorem.

Finally, we outline the basis of a spectral discrete exterior calculus, which may be a useful element in producing structured numerical methods for fluids in the future.

The separation of atomic and molecular gases from helium by cataphoresis

The cataphoretic purification of helium was investigated for binary mixtures of He with Ar, Ne, N₂, O₂, CO, and CO₂ in DC glow discharge. An experimental technique was developed to continuously measure the composition in the anode end-bulb without sample withdrawal. Discharge currents ranged from 10 ma to 100 ma. Total gas pressure ranged from 2 torr to 9 torr. Initial compositions of the minority component in He ranged from 1.2 mole percent to 7.5 mole percent.

The cataphoretic separation of Ar and Ne from He was found to be in agreement with previous investigators. The cataphoretic separation of N₂, O₂, and CO from He was found to be similar to noble gas systems in that the steady-state separation improved with (1) increasing discharge current, (2) increasing gas pressure, and (3) decreasing initial composition of the minority component. In the He-CO₂ mixture, the CO₂ dissociated to CO plus O₂. The fraction of CO₂ dissociated was directly proportional to the current and pressure and independent of initial composition.

The experimental results for the separation of Ar, Ne, N₂, O₂, and CO from He were interpreted in the framework of a recently proposed theoretical model involving an electrostatic Peclet number. In the model the electric field was assumed to be constant. This assumption was checked experimentally and the maximum variation in electric field was 35% in time and 30% in position. Consequently, the assumption of constant electric field introduced no more than 55% variation in the electrostatic Peclet number during a separation.

To aid in the design of new cataphoretic systems, the following design criteria were developed and tested in detail: (1) electric field independent of discharge current, (2) electric field directly proportional to total pressure, (3) ion fraction of impurity directly proportional to discharge current, and (4) ion fraction of impurity independent of total pressure. Although these assumptions are approximate, they enabled the steady-state concentration profile to be predicted to within 25% for 75% of the data. The theoretical model was also tested with respect to the characteristic time associated with transient cataphoresis. Over 80% of the data was within a factor of two of the calculated characteristic times.

The electrostatic Peclet number ranged in value from 0.13 to 4.33. Back-calculated ion fractions of the impurity component ranged in value from 4.8x10^-6 to 178x10^-6.

Desenvolvimento de membranas de poli(éter imida) sultonada para a permeacão de gases

A busca por membranas com propriedades adequadas a separação de gases em escala industrial tem levado a modificação e sIntese de polImeros de engenharia, com objetivo de obter membranas com propriedades adequadas. Uma das modificaçoes que tem se apresentado promissora é a inserção de grupos sulfônicos em polImeros comerciais. Espera-se que o polImero sulfonado apresente um aumento na permeação de gases polares, em relação a gases apolares, devido a sua estrutura mais polar e flexIvel. Neste contexto, o objetivo do presente trabalho é a sIntese e caracterização de membranas de poli(éter imida) sulfonada para a permeação de gases. Um planejamento experimental foi desenvolvido, em diferentes condiçoes reacionais de temperatura, tempo e excesso de um dos reagentes (ácido acético), para a sIntese de poli(éter imida) sulfonada (SPEI). Através deste planejamento, constatou-se que as variáveis que mais influenciam o grau de sulfonação são a temperatura e o tempo. O polImero com o maior grau de sulfonação, determinado por capacidade de troca iônica (IEC= 92 mEq H+/g), foi utilizado para o preparo da membrana de SPEI, obtida pela técnica de inversão de fase por evaporação do solvente, utilizando-se clorofórmio como solvente. Este filme foi caracterizado a partir das seguintes análises: espectroscopia de infravermelho (FTIR), calorimetria diferencial de varredura (DSC), análise termogravimétrica (TGA) e microscopia eletrônica de varredura (MEV), a fim de avaliar a influência da inserção do grupo sulfônico na matriz polimérica. O espectro de infravermelho de SPEI apresentou bandas relacionadas as vibraçoes assimétricas em 1240 cm-1 (ligação O=S=O), ligação simétrica em 1171 cm-1 (O=S=O) e ligação S-O entre 1010-1024 cm-1. Isto indica a presença de grupos sulfônicos. A análise de DSC foi realizada entre 150-250C. Nesta faixa, não foram observadas alteraçoes na temperatura de transição vItrea (Tg) do polImero modificado (217C). Acredita-se que a decomposição do grupo sulfona aconteça antes da temperatura atingir o Tg do polImero. Esta suposição é confirmada na análise de TGA. As imagens de MEV mostraram que foram obtidos filmes livres de poros e defeitos. A membrana da SPEI foi utilizada no ensaio de permeaçao dos gases 02, N2 e C02, a fim de determinar a permeabilidade e seletividade da membrana. As permeabilidades encontradas para o gas oxigênio foram de 0,76 barrer para a PEI e 0,46 barrer para a SPEI. A seletividade do dióxido de carbono em relaçao ao oxigênio aumentou de 3,5, na membrana de PEI, para 4,83, na membrana de SPEI. Em relaçao ao nitrogênio, as permeabilidades medidas foram 0,064 barrer e 0,043 barrer, para a PEI e para a SPEI, respectivamente, enquanto a seletividade em relaçao ao C02 aumentou de 41,1 para 55,5. Estes resultados indicam que o efeito de sorçao predominou devido ao aumento das interaçöes moleculares, reduzindo assim o volume livre, o que tornou a membrana sulfonada mais compacta, com permeabilidade menor e maior seletividade. Estes resultados corroboram com a premissa de que a sulfonaçao é um processo promissor para o desenvolvimento de membranas mais eficientes.

The reduced-alpha-width of the lowest 1¯ state of ^(16)O

Cross sections for the reaction ¹²C(α,γ)¹⁶O have been measured for a range of center-of-mass alpha particle energies extending from 1.72 MeV to 2.94 MeV. Two 8"x5" NaI (Tℓ) crystals were used to detect gamma rays; time-of-flight technique was employed to suppress cosmic ray background and background due to neutrons arising mainly from the ¹³C(α,n)¹⁶O reaction. Angular distributions were measured at center-of-mass alpha energies of 2.18, 2.42, 2.56 and 2.83 MeV. Upper limits were placed on the amount of radiation cascading through the 6.92 or 7.12-MeV states in ¹⁶O. By means of theoretical fits to the measured electric dipole component of the total cross section, in which interference between the 1¯ states in ¹⁶O at 7.12 MeV and at 9.60 MeV is taken into account, it is possible to extract the dimensionless, reduced-alpha-width of the 7.12-MeV state in ¹⁶O. A three-level R-matrix parameterization of the data yields the width Θ_α,F² = 0.14^+0.10_-0.08. A "hybrid" R-matrix-optical-model parameterization yields Θ_α,F² = 0.11^+0.11_-0.07. This quantity is of crucial importance in determining the abundances of ¹²C and ¹⁶O at the end of helium burning in stars.

Studies of noble gases in meteorites and in the earth

The isotopic and elemental abundances of noble gases in the solar system are investigated, using simple mixing models and mass-spectrometric measurements of the noble gases in meteorites and terrestrial rocks and minerals.

Primordial neon is modeled by two isotopically distinct components from the interstellar gas and dust. Neon from the gas dominates solar neon, which contains about ten times more ²⁰Ne than ²²Ne. Neon from the dust is represented in meteorites by neon-E, with ²⁰Ne/²²Ne less than 0.6. Isotopic variations in meteorites require neon from both dust and gas to be present. Mixing dust and gas without neon loss generates linear correlation lines on three-isotope and composition-concentration diagrams. A model for solar wind implantation predicts small deviations from linear mixing, due to preferential sputtering of the lighter neon isotopes.

Neon in meteorites consists of galactic cosmic ray spallation neon and at least two primordial components, neon-E and neon-S. Neon was measured in several meteorites to investigate these end- members. Cosmogenic neon produced from sodium is found to be strongly enriched in ²²Ne. Neon measurements on sodium-rich samples must be interpreted with care so not to confuse this source of ²²Ne with neon-E, which is also rich in ²²Ne.

Neon data for the carbonaceous chondrite Mokoia show that the end member composition of neon-Si in meteorites is ²⁰Ne/²²Ne = 13.7, the same as the present solar wind. The solar wind composition evidently has remained constant since before the compaction of Mokoia.

Ca, Al-rich inclusions from the Allende meteorite were examined for correlation between neon-E and oxygen or magnesium isotopic anomalies. ²²Ne and ³⁶Ar enrichments found in some inclusions are attributed to cosmic- ray-induced reactions on Na and Cl, not to a primordial component. Neon-E is not detectably enriched in Allende.

Measurements were made to determine the noble gas contents of various terrestrial rocks and minerals, and to investigate the cycling of noble gases between different terrestrial reservoirs. Beryl crystals contain a characteristic suite of magmatic gases including nucleogenic ²¹Ne and ²²Ne from (α,n) reactions, radiogenic ⁴⁰Ar, and fissiogenic ^131-136Xe from the decay of K and U in the continental crust. Significant concentrations of atmospheric noble gases are also present in beryl.

Both juvenile and atmospheric noble gases are found in rocks from the Skaergaard intrusion. The ratio ⁴⁰Ar/³⁶Ar (corrected for in situ decay of ⁴⁰K) correlates with δ¹⁸O in plagioclase. Atmospheric argon has been introduced into samples that have experienced oxygen-isotope exchange with circulating meteoric hydrothermal fluids. Unexchanged samples contain juvenile argon with ⁴⁰Ar/³⁶Ar greater than 6000 that was trapped from the Skaergaard magma.

Juvenile and atmospheric gases have been measured in the glassy rims of mid-ocean ridge (MOR) pillow basalts. Evidence is presented that three samples contain excess radiogenic ¹²⁹Xe and fission xenon, in addition to the excess radiogenic ⁴⁰Ar found in all samples. These juvenile gases are being outgassed from the upper-mantle source region of the MOR magma. No isotopic evidence has been found here for juvenile primordial noble gases accompanying the juvenile radiogenic gases in the MOR glasses. Large argon isotopic variations in a single specimen provide a clear indication of the late-stage addition of atmospheric argon, probably from seawater.

The Skaergaard data demonstrate that atmospheric noble gases dissolved in ground water can be transferred into crustal rocks. Subduction of oceanic crust altered by seawater can transport atmospheric noble gases into the upper mantle. A substantial portion of the noble gases in mantle derived rocks may represent subducted gases, not a primordial component as is often assumed.

Avaliação de gases efeito estufa na cidade do Rio de Janeiro

O presente trabalho teve como objetivo a validação de uma metodologia de amostragem para GEE Gases do Efeito Estufa, com a utilização de seringas e análise por cromatografia de fase gasosa com múltiplos detectores. O trabalho se dividiu em duas etapas. A primeira etapa consistiu em um teste de estabilidade avaliando o meio de amostragem proposto, a seringa, e comparando-o a dois meios de amostragem convencionais canister e bolsa de teflon -, utilizando uma amostra padrão de GEE. A segunda etapa foi a aplicação desta nova metodologia de amostragem na cidade do Rio de Janeiro, buscando a avaliação da concentração dos GEE em diferentes bairros da cidade e a correlação destas com dados meteorológicos e características da localização dos pontos amostrados. Nestas amostragens realizadas na cidade do Rio de Janeiro obteve-se uma média de 536 ppmv, 2,04 ppmv e 274 ppbv, para o CO2, CH4 e N2O, respectivamente, que foram os GEE analisados. Foi possível neste trabalho verificar o grau de correlação dos GEE estudados com variáveis meteorológicas, bem como com outros poluentes já legislados e participantes de monitoramento contínuo. As conclusões alcançadas foram que a nova metodologia proposta para amostragem de GEE é viável devido ao seu bom desempenho no teste de estabilidade, ao baixo custo do material empregado e à praticidade do mesmo, e que as concentrações dos GEE avaliados na cidade do Rio de Janeiro encontram-se superiores às concentrações indicadas como médias globais para os mesmos. Apontando desta forma, a necessidade de um monitoramento contínuo destes de forma a contribuir para a tomada de ações de mitigação dos GEE

Optimization of the pyrolysis process for the production of a biomass derived reducing agent and hydrogen-rich gases

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