It is well known that for small Reynolds numbers, flow around a cylinder is laminar and stable. For larger Reynolds numbers, although the flow regime remains laminar, the formation of complex periodic structures appear downstream. The cyclic nature of this periodic flow is well characterized by the vortex shedding frequency and Strouhal number. However, complexities of these periodic structures downstream continue to be a topic of research. Periodic laminar 2D incompressible viscous flow around a cylinder is simulated using OpenFoam, an open source computational fluid dynamics program. To better understand these complex structures downstream, a customized computer graphical tool, VerFlow-V.01, was created to analyze and study OpenFoam simulation results. This study includes an investigation of calculating the details of drag and lift coefficients for the cylinder using mathematical models that integrate properties in subdomains, an approach not previously explored to the knowledge of the author. Numerical integration is accomplished using a finite difference approach for solving surface and contour integrals in subdomains of interest. Special attention is given to pressure and to the second invariant of the velocity gradient, as they have a clear mathematical relationship, which is consistent with results previously published. A customized visual data analysis tool, called VerFlow-V.01, allowed investigators to compare simulation data variables in a variety of useful ways, revealing details not previously understood. Main subroutines and a user's manual are included as appendices to encourage reproducibility and future development of the numerical, analytical and graphical models developed here. Together these models resulted in a new understanding of periodic laminar flow around a cylinder. A unique approach was developed to qualitatively understand the origins of drag and lift coefficients associated with properties mapped as images in subdomains of interest downstream. These results explain the development of convergent, eddy, and stream zones embedded in flow fields downstream. / Master of Science

The objective of the thesis is to characterize the linear and nonlinear aspects of inertial and pressure effects in turbulent flows. In the first part of the study, computations of Navier-Stokes and 3D Burgers equations are performed in the rapid distortion (RD) limit to analyze the inviscid linear processes in homogeneous turbulence. By contrasting the results of Navier- Stokes RD equations and Burgers RD equations, the effect of pressure can be isolated. The evolution of turbulent kinetic energy and anisotropy components and invariants are examined. In the second part of the thesis, the velocity gradient dynamics in turbulent flows are studied with the help of inviscid 3D Burgers equations and restricted Euler equations. The analytical asymptotic solutions of velocity gradient tensor are obtained for both Burgers and restricted Euler equations. Numerical computations are also performed to identify the stable solutions. The results are compared and contrasted to identify the effect of pressure on nonlinear velocity gradient dynamics. Of particular interest are the sign of the intermediate principle strain-rate and tendency of vorticity to align with the intermediate principle strain-rate. These aspects of velocity gradients provide valuable insight into the role of pressure in the energy cascade process.

Durante a floculação, a agitação promove dois efeitos simultaneamente, a agregação e a ruptura. A ruptura ocorre devido à atuação de forças de cisalhamento sobre os flocos. O aumento da agitação com, conseqüentemente, aumento do gradiente de velocidade médio, em água com flocos formados, promove o aumento das forças de cisalhamento e a degradação parcial ou total dos mesmos, em poucos segundos. Retornando à condição anterior de agitação, pode ocorrer o recrescimento dos flocos. Através de ensaios em reatores estáticos (em equipamento de jarteste) foram estudados os efeitos da ruptura e da refloculação na sedimentação dos flocos, para velocidades de sedimentação entre 0,9 e 7,0 cm/min. A água de estudo foi preparada com caulinita, resultando turbidez de 100 uT, e coagulada com sulfato de alumínio. Foram realizadas as etapas de coagulação, mistura rápida, floculação, ruptura (G=75, 150 e 250 \'S POT.-1\') e refloculação (G=25, 20 e 15 \'S POT.-1\'). A ruptura, em poucos segundos, prejudicou a remoção dos flocos por sedimentação. Quanto maior o gradiente de velocidade na ruptura, maiores foram os valores da turbidez remanescente do sobrenadante, mesmo após a refloculação. A refloculação, mesmo nos primeiros minutos, diminuiu a turbidez remanescente do sobrenadante se comparada a logo após a ruptura. Quanto menor o gradiente de velocidade durante a refloculação, menores foram os valores da turbidez remanescente do sobrenadante. Apenas para velocidades de sedimentação, gradientes de velocidade de ruptura e gradientes de velocidade de refloculação menores ou iguais a 2,5 cm/min, 75 \'S POT.-1\' e 15 \'S POT.-1\', respectivamente, foi possível obter sobrenadante com valores de turbidez remanescente similares aos encontrados inicialmente, sem ruptura. / During the flocculation, the shear rate promotes two effects simultaneously, growth and breakage of flocs. The break up of flocs is caused as a result of disruptive forces. The increase of the shear rate in water with formed flocs increases the disruptive forces and it also can break the flocs partial or totally in a few seconds. Restoring the previous low shear conditions, flocs can grow back. By using the jar test equipment, the effects of breakage and reflocullation on the efficiency of floc sedimentation were studied, using settling velocities between 0.9 e 7.0 cm/min. Water of study was prepared with groundwater and kaolin, resulting a turbidity of approximately 100 NTU. Coagulation was performed by using aluminum sulfate. Coagulation, flocculation, breakage (G=75, 150 e 250 \'S POT.-1\') and reflocculation tests were carried out. In a few seconds the breakage of flocs hindered the settling removal of turbidity. The higher the average shear rate in the break-up, the higher result the residual turbidity even after the reflocculation. In the first minutes, the reflocculation decreased the residual turbidity after sedimentation if compared to the residual turbidity just after the break-up and sedimentation. The lower the average shear rate during the reflocculation, the lower result the supernatant values of residual turbidity. Supernatant could only be obtained with the value of residual turbidity similar to the values found initially (without breakage of flocs) for the settling velocity, the average velocity gradient of break-up and the average velocity gradient of reflocculation equal or less than 2.5 cm/min, 75 \'S POT.-1\' e 15 \'S POT.-1\', respectively.

In this thesis, least-squares based finite element models (LSFEM) for the Poisson equation and Navier-Stokes equation are presented. The least-squares method is simple, general and reliable. Least-squares formulations offer several computational and theoretical advantages. The resulting coefficient matrix is symmetric and positive-definite. Using these formulations, the choice of approximating space is not subject to any compatibility condition. The Poisson equation is cast as a set of first order equations involving gradient of the primary variable as auxiliary variables for the mixed least-square finite element model. Equal order C0 continuous approximation functions is used for primary and auxiliary variables. Least-squares principle was directly applied to develop another model which requires C1continous approximation functions for the primary variable. Each developed model is compared with the conventional model to verify its performance. Penalty based least-squares formulation was implemented to develop a finite element for the Navier Stokes equations. The continuity equation is treated as a constraint on the velocity field and the constraint is enforced using the penalty method. Velocity gradients are introduced as auxiliary variables to get the first order equivalent system. Both the primary and auxiliary variables are interpolated using equal order C0 continuous, p-version approximation functions. Numerical examples are presented to demonstrate the convergence characteristics and accuracy of the method.

Durante a floculação, a agitação promove dois efeitos simultaneamente, a agregação e a ruptura. A ruptura ocorre devido à atuação de forças de cisalhamento sobre os flocos. O aumento da agitação com, conseqüentemente, aumento do gradiente de velocidade médio, em água com flocos formados, promove o aumento das forças de cisalhamento e a degradação parcial ou total dos mesmos, em poucos segundos. Retornando à condição anterior de agitação, pode ocorrer o recrescimento dos flocos. Através de ensaios em reatores estáticos (em equipamento de jarteste) foram estudados os efeitos da ruptura e da refloculação na sedimentação dos flocos, para velocidades de sedimentação entre 0,9 e 7,0 cm/min. A água de estudo foi preparada com caulinita, resultando turbidez de 100 uT, e coagulada com sulfato de alumínio. Foram realizadas as etapas de coagulação, mistura rápida, floculação, ruptura (G=75, 150 e 250 \'S POT.-1\') e refloculação (G=25, 20 e 15 \'S POT.-1\'). A ruptura, em poucos segundos, prejudicou a remoção dos flocos por sedimentação. Quanto maior o gradiente de velocidade na ruptura, maiores foram os valores da turbidez remanescente do sobrenadante, mesmo após a refloculação. A refloculação, mesmo nos primeiros minutos, diminuiu a turbidez remanescente do sobrenadante se comparada a logo após a ruptura. Quanto menor o gradiente de velocidade durante a refloculação, menores foram os valores da turbidez remanescente do sobrenadante. Apenas para velocidades de sedimentação, gradientes de velocidade de ruptura e gradientes de velocidade de refloculação menores ou iguais a 2,5 cm/min, 75 \'S POT.-1\' e 15 \'S POT.-1\', respectivamente, foi possível obter sobrenadante com valores de turbidez remanescente similares aos encontrados inicialmente, sem ruptura. / During the flocculation, the shear rate promotes two effects simultaneously, growth and breakage of flocs. The break up of flocs is caused as a result of disruptive forces. The increase of the shear rate in water with formed flocs increases the disruptive forces and it also can break the flocs partial or totally in a few seconds. Restoring the previous low shear conditions, flocs can grow back. By using the jar test equipment, the effects of breakage and reflocullation on the efficiency of floc sedimentation were studied, using settling velocities between 0.9 e 7.0 cm/min. Water of study was prepared with groundwater and kaolin, resulting a turbidity of approximately 100 NTU. Coagulation was performed by using aluminum sulfate. Coagulation, flocculation, breakage (G=75, 150 e 250 \'S POT.-1\') and reflocculation tests were carried out. In a few seconds the breakage of flocs hindered the settling removal of turbidity. The higher the average shear rate in the break-up, the higher result the residual turbidity even after the reflocculation. In the first minutes, the reflocculation decreased the residual turbidity after sedimentation if compared to the residual turbidity just after the break-up and sedimentation. The lower the average shear rate during the reflocculation, the lower result the supernatant values of residual turbidity. Supernatant could only be obtained with the value of residual turbidity similar to the values found initially (without breakage of flocs) for the settling velocity, the average velocity gradient of break-up and the average velocity gradient of reflocculation equal or less than 2.5 cm/min, 75 \'S POT.-1\' e 15 \'S POT.-1\', respectively.

In this thesis I present work done on the subject of star formation through the study of infrared dark clouds. We studied the velocity fields in several IRDCs using spectral line mapping. We also performed observations of a high density tracer and its deuterated counterpart. These observations allow me to assess the kinematics of these clouds and the evolutionary state of the observed targets. The sample observed is an important starting point for the search of early and quiescent high-mass regions. We mapped several IRDCs using the 22m ATNF Mopra Telescope in high-density molecular tracers at 3 mm, HNC (1-0) and N2H+ (1-0). We present integrated intensity emission and velocity field maps of these IRDCs. The molecular emission in the maps matches well with the extinction seen in the mid-IR. For an IRDC-complex we see connecting emission in the whole filament. We calculate kinematic distances and masses of the IRDCs. The IRDCs typically display an ordered velocity field within the clouds. The mean velocity gradient of the sample was 0.4 km/s/pc. We show how this velocity gradient can mean gas flows within the cloud into the central regions in order to feed the central cores. We observed 54 cores in IRDCs using N2H+ (1-0) and (3-2) to determine the kinematics of the densest material, where stars will form. We also observed N2D+ (3-2) towards 29 of the brightest peaks to analyze the level of deuteration which is an excellent probe of the quiescent of the early stages of star formation. There were 13 detections of N2D+ (3-2). This is one of the largest samples of IRDCs yet observed in these species. The deuteration ratio in the sources with detected N2D+ (3-2) has a mean of 0.024 and reaches a maximum value of 0.14. For most of the sources the material traced by N2D+ and N2H+ (3-2) still has significant turbulent motions, however three objects show subthermal N2D+ velocity dispersion. Surprisingly the presence or absence of an embedded 70 micron source shows no correlation with the detection of N2D+ (3-2), nor does it correlate with any change in velocity dispersion or excitation temperature. Comparison with recent models of deuteration suggest evolutionary timescales of these regions of several freefall times or less.

Tato práce se zabývá studiem vlivu kaolinitových ástic (reprezentujících látky tvo ící zákal vody) a peptidové/proteinové složky COM (Cellular Organic Matter) produkovaných sinicí Microcystis aeruginosa na velikost, strukturu a tvar tvo ených agregát v prom nných hydrodynamických podmínkách (gradientu rychlosti) p i úprav vody. Agregace probíhala v Taylor-Couettov reaktoru. Koagulace vybraných typ zne iš ujících p ím sí (kaolinitové ástice, COM peptidy/proteiny a jejich sm s) probíhala pomocí síranu hlinitého a síranu železitého. Vzniklé agregáty byly hodnoceny ve fázi homogenní velikosti (steady state) po 60 min míchání pomocí ukazatel : velikost (polom r) agregát , fraktální dimenze D2 a Dpf a velikostní distribuce. Bylo zjišt no, že velikost agregát je závislá na typu koagula ního inidla, typu koagulované p ím si a aplikovaném gradientu rychlosti. S rostoucím gradientem rychlosti se velikost agregát zmenšuje. Železité koagula ní inidlo produkuje v tší agregáty než hlinité koagula ní inidlo. Podle p ím si roste velikost agregát v po adí kaolinit < COM < kaolinit + COM. Struktura agregát se stává kompaktn jší s gradientem rychlosti. P i použití hlinitého koagula ního inidla vznikají ve srovnání s inidlem železitým kompaktn jší agregáty (mají vyšší hodnotu D2). Kompaktnost agregát klesá v po adí...

Tendo em vista que os amidos (catiônicos ou não) não são nocivos a saúde do ser humano, uma vez que são utilizados na indústria de alimentos, e observando-se a potencialidade do seu uso como auxiliares de floculação, foi proposto o presente trabalho. Consiste na realização de ensaios de coagulação (com sulfato alumínio), floculação e sedimentação em equipamento de reatores estáticos, objetivando verificar a influência do gradiente de velocidade e do tempo de agitação na floculação com polímero sintético catiônico e amidos de milho e mandioca catiônicos. Concluiu-se que as condições de aplicação exercem influência na eficiência de remoção de turbidez e cor aparente, sendo que cada polímero estudado apresentou uma condição ótima específica. Em todos os ensaios realizados, o amido de mandioca catiônico foi o mais eficiente, indicando que os amidos catiônicos podem ser substitutos em potencial dos polímeros sintéticos no tratamento de águas de abastecimento, quando utilizados como auxiliares de floculação. / This present work was based on the fact that native and cationic starches are not harmful to man\'s health, since they have been largely used in food processing industries, and that they may be potentially used as flocculation aids in water treatment. Jar Test assays were performed, including coagulation with aluminum sulphate, flocculation and sedimentation, aiming to study the influence of the velocity gradient and mixing time on flocculation, using a cationic synthetic polymer and cationic com and manioc starches as aids. In the main, it was concluded that the conditions under which the polymers were applied, affect the efficiency of turbidity and color removals and that each polymer studied presented an specific optimum condition. It was also observed that manioc cationic starch resulted more effective than the others polymers studied, when used as flocculation aids.

Three different topics of turbulence research that cover modeling, theory and model computation categories are selected and studied in depth. In the first topic, "velocity gradient dynamics in turbulence" (modeling), the Lagrangian linear diffusion model that accounts for the viscous-effect is proposed to make the existing restricted-Euler velocity gradient dynamics model quantitatively useful. Results show good agreement with DNS data. In the second topic, "pressure-strain correlation in homogeneous anisotropic turbulence subject to rapid strain-dominated distortion" (theory), extensive rapid distortion calculation is performed for various anisotropic initial turbulence conditions in strain-dominated mean flows. The behavior of the rapid pressure-strain correlation is investigated and constraining criteria for the rapid pressure-strain correlation models are developed. In the last topic, "unsteady computation of turbulent flow past a square cylinder using partially-averaged Navier-Stokes method" (model computation), the basic philosophy of the PANS method is reviewed and a practical problem of flow past a square cylinder is computed for various levels of physical resolution. It is revealed that the PANS method can capture many important unsteady flow features at an affordable computational effort.

Three different topics of turbulence research that cover modeling, theory and model computation categories are selected and studied in depth. In the first topic, "velocity gradient dynamics in turbulence" (modeling), the Lagrangian linear diffusion model that accounts for the viscous-effect is proposed to make the existing restricted-Euler velocity gradient dynamics model quantitatively useful. Results show good agreement with DNS data. In the second topic, "pressure-strain correlation in homogeneous anisotropic turbulence subject to rapid strain-dominated distortion" (theory), extensive rapid distortion calculation is performed for various anisotropic initial turbulence conditions in strain-dominated mean flows. The behavior of the rapid pressure-strain correlation is investigated and constraining criteria for the rapid pressure-strain correlation models are developed. In the last topic, "unsteady computation of turbulent flow past a square cylinder using partially-averaged Navier-Stokes method" (model computation), the basic philosophy of the PANS method is reviewed and a practical problem of flow past a square cylinder is computed for various levels of physical resolution. It is revealed that the PANS method can capture many important unsteady flow features at an affordable computational effort.