Estudo numérico de escoamento turbulento em padrão anular gás-líquido em dutos verticais

Multiphase flows in ducts can adopt several morphologies depending on the mass fluxes and the fluids properties. Annular flow is one of the most frequently encountered flow patterns in industrial applications. For gas liquid systems, it consists of a liquid film flowing adjacent to the wall and a gas core flowing in the center of the duct. This work presents a numerical study of this flow pattern in gas liquid systems in vertical ducts. For this, a solution algorithm was developed and implemented in FORTRAN 90 to numerically solve the governing transport equations. The mass and momentum conservation equations are solved simultaneously from the wall to the center of the duct, using the Finite Volumes Technique. Momentum conservation in the gas liquid interface is enforced using an equivalent effective viscosity, which also allows for the solution of both velocity fields in a single system of equations. In this way, the velocity distributions across the gas core and the liquid film are obtained iteratively, together with the global pressure gradient and the liquid film thickness. Convergence criteria are based upon satisfaction of mass balance within the liquid film and the gas core. For system closure, two different approaches are presented for the calculation of the radial turbulent viscosity distribution within the liquid film and the gas core. The first one combines a k- Ɛ one-equation model and a low Reynolds k-Ɛ model. The second one uses a low Reynolds k- Ɛ model to compute the eddy viscosity profile from the center of the duct right to the wall. Appropriate interfacial values for k e Ɛ are proposed, based on concepts and ideas previously used, with success, in stratified gas liquid flow. The proposed approaches are compared with an algebraic model found in the literature, specifically devised for annular gas liquid flow, using available experimental results. This also serves as a validation of the solution algorithm

Lítio e parâmetros orbitais em sistemas binários com componentes evoluídas

One of the best established properties of the single late type evolved stars is that their rotational velocity and lithium content decrease with effective temperature and age. Nevertheless, the root cause of this property, as well as the link between rotation and lithium abundance and, in particular, the effects of binarity on rotation and lithium content in binary systems with evolved component, are not yet completely established. How does the gravitational tides, in binary systems, affects rotational evolution and lithium dilution? Trying to answer these questions, we have carried out an observational survey, in the lithium region centered at the lithium I line A6707.81A, for a large sample of about 100 binary systems with evolved component along the spectral range F, G and K, with the CES spectrometer mounted at the CAT 1.44 m Telescope of the ESO, La Silla, Chile. By combining the abundances of lithium issued from these observations with rotational velocity and orbital parameters, we have found a number of important results. First of all, we confirm that in this class of binary systems rotation is effectively affected by tidal effects. Binary systems with orbital period lower than about 100 days and circular or nearly circular orbits, present rotational velocity enhanced in relation to the single giant stars and to the binary systems with an orbital period larger than 100 days. This is clearly the result of the synchonization between the rotational and orbital motions due to tidal effects. In addition, we have found that lithium abundances in binary systems with giant components present the same gradual decreasing with effective temperature, observed in the single giants of same luminosity class and spectral types. We have found no lithium-rich binary systems, in contrast with single giants. A remarkable result from the present study is the one showing that synchronized binary systems with giant component retains more of their original lithium than the unsynchronized systems. In fact, we have found a possible "inhibited zone", in which synchronized binary systems with giant component having lithium abundance lower than a threshold level should be unusual. Finally, the present study also shows that the binary systems with giant component presenting the highest lithium contents are those with the highest rotation rates

Aglomerado estelar M67: processos de diluição e a evolução do Momentum Angular

Galactic stellar clusters have a great variety of physical properties that make valuable probes of stellar and galactic chemical evolution. Current studies show a discrepancy between the standard evolutionary models and observations, mainly considering the level of mixing and convective dilution of light elements, as well as to the evolution of the angular momentum. In order to better settle some of these properties, we present a detailed spectroscopic analysis of 28 evolved stars, from the turn-off to the RGB, belonging to the stellar open cluster M67. The observations were performed using UVES+FLAMES at VLT/UT2. We determined stellar parameters and metallicity from LTE analysis of Fe I and Fe II lines between 420 1100 nm. The Li abundance was obtained using the line at 6707.78 ˚A, for the whole sample of stars. The Li abundances of evolved stars of M67 present a gradual decreasing when decreasing the effective temperature. The Li dilution factor for giant stars of M67 with Teff ∼ 4350K is at least 2300 times greater than that predicted by standard theory for single field giant stars. The Li abundance as a function of rotation exhibits a good correlation for evolved stars of M67, with a much smaller dispersion than the field evolved stars. The mass and the age seem to be some of the parameters that influence this connection. We discovered a Li-rich subgiant star in M67 (S1242). It is member of a spectroscopic binary system with a high eccentricity. Its Li abundance is 2.7, the highest Li content ever measured for an evolved star in M67. Two possibilities could explain this anomalous Li content: (i) preservation of the Li at the post turn off stage due to tidal effects, or (ii) an efficient dredge-up of Li, hidden below the convective zone by atomic diffusion occurring in the post turn off stage. We also study the evolution of the angular momentum for the evolved stars in M67. The results are in agreement with previous studies dedicated to evolved stars of this cluster, where stars in the same region of the CM-diagram have quite similar rotations, but with values that indicate an extra breaking along the main sequence. Finally, we analize the distributions of the average rotational velocity and of the average Li abundance as a function of age. With relation to the average Li abundances, stars in clusters and field stars present the same type of exponencial decay law t−β. Such decay is observed for ages lesser than 2 Gyr. From this age, is observed that the average Li abundance remain constant, differently of the one observed in the rotation age connection, where the average rotational velocity decreases slowly with age

Sobre a relação entre rotação, atividade crosmosférica e abundância de lítio em estrelas subgigantes

The connection between rotation, CaII emission flux and lithium abundance is analyzed for a sample of subgiant stars, with evolutionary status was determined from the Toulouse-Geneve code and HlPPARCOS trigonometric parallax measurements. We noted that the distribution of rotation and CaII emission flux, as a function of effective temperature, shows a discontinuity located around the same spectral type, F8IV. Stars located blueward of this spectral type, exhibit a large spread of values of rotation and CaII flux, whereas stars redward of F8lV show essentially low ratation anel low CaII flux. The strength of these declines nevertheless, depends on stellar mass. The distribution of lithium abundances also shows a discontinuity, however with behavior a little more complex for subgiants with mass lower than about 1.2 Solar Masses, this decrease is observed later than that in rotation and CaII flux, whereas for masses higher than 1.2 Solar Masses the decrease in lithium abundance is located around the spectral type F8IV. The discrepancy between the location of the discontinuities of rotation and CaII flux and log n(Li) for stars with masses lower than 102 Solar Masses, seems to reflect the sensitivity of these phenomena to the mass of the convective envelope. The drop in rotation, which results mostly from a magnetic braking, requires an increase in the mass of the convective envelope less than that required for the decrease in lithium abundance The location of the discontinuity in log n( Li) in the same region of the discontinuity ties in rotation and CaII flux, for stars with masses higher than 1.2 Solar Masses, may also be explained by the behavior of the deepening of the convective envelope. In contrast to the relationship between rotation and CaII flux the relationship between lithium abundance and rotation shows no dear tendency toward linear behavior. Similarly, the same tendency is observed in the relationship between lithium abundance and CaII flux in spite of these facts, subgiants with high lithium content also have high rotation and high CaII emission flux. We also observed that stars with high lithium content present, in its majority, an undeveloped convective envelope, whereas stars with low lithium content have a developed convective envelope. In the case of the rotation, stars with undeveloped convective envelope, show rotational velocities as much high as low, whereas stars with developed convective envelope only present low rotation

Lítio e rotação nas estrelas análogas solares: análise teórica das observações

The projected rotational velocity together with lithium abundance and the onset of the dilution by the deepening in mass of the convective envelope provide a key tool to investigate the so far poorly understood processes at work in stellar interiors of solar-analog stars. To investigate the link between abundances, convection and rotational velocities in solar-analog G dwarf stars, we study a bona fide sample of 118 selected solar-analog G dwarf stars presenting measured lithium abundances, rotational velocities, and fundamental parameters together with computed evolutionary tracks (Toulouse-Geneva code) for a range of stellar masses around 1 M and metallicity consistent with the solar-analog range. The aim of this work is to build up an evolution of lithium and rotation as a function of stellar age, mass, effective temperature, and convection. We analyze the evolutionary status of the sample of 118 solar-analog G dwarf in the HR diagram based on Hipparcos data and using a grid of stellar models in the effective temperature and mass range of the solar-analog stars. We discuss the deepening (in mass) of the convective envelope and the influence on the Li abundances and projected rotational velocities. We determined the stellar mass and the mass of the convective envelope for a bona fide sample of 118 selected solar-analog G dwarf and checked the evolutionary link between the rotational velocity, lithium abundance, and the deepening of the convective envelope. Fast rotators (vsini 6 km s��1) are also stars with high Li content. Slow rotators present a wide range of values of log n(Li). Our results shed new light on the lithium and rotational behavior in G dwarf stars. We confirmed the presence of a large Li abundance spread among the solar-analog stars and concluded that the solar twins probably share a similar mixing history with the Sun

Sobre a composição química em estrelas evoluídas do aglomerado aberto M67

The Galaxy open clusters have a wide variety of physical properties that make them valuable laboratories for studies of stellar and chemical evolution of the Galaxy. In order to better settle these properties we investigate the abundances of a large number of chemical elements in a sample of 27 evolved stars of the open cluster M67 with different evolutionary stages (turn-off, subgiant and giant stars). For such a study we used high-resolution spectra (R 47 000) and high S/N obtained with UVES+FLAMES at VLT/UT2, covering the wavelength interval 4200-10 600 Å. Our spectral analysis is based on the MARCS models of atmosphere and Turbospectrum spectroscopic tool. The oxygen abundances were determined from the [O I] line at 6300 Å. In addition, we have also computed abundances of Si I, Na I, Mg I, Al I, Ca I, Ti I, Co I, Ni I, Zr I, La II and Cr I. The abundances investigated in this work, combined with their stellar parameters, offers an opportunity to determine the level of mixing and convective dilution of evolved stars in M67. Based on the obtained parameters, the abundances of these seem to follow a similar trend to the curve of solar abundances. Additionally, following strategies of other studies have investigated the relative abundances as a function of effective temperature and metallicity, where it was possible to observe an abundance of Na, Al and Si to the stars in the field of giants. A large dispersion from star to star, is observed in the ratios [X / Fe] for the Co, Zr and La, and the absence of Zr and La, in the stars of the turn-off. Comparisons made between our results and other studies in the literature show that values of abundances are in agreement and close to the limits of the errors