Estudo numérico de modelos de arrasto e do coeficiente de restituição no escoamento gás-sólido em leito fluidizado

Pós-graduação em Engenharia Mecânica - FEG

Can Drag Force Suppress Fermi Acceleration in a Bouncer Model?

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Non-uniform drag force on the Fermi accelerator model

Some dynamical properties of a particle suffering the action of a generic drag force are obtained for a dissipative Fermi Acceleration model. The dissipation is introduced via a viscous drag force, like a gas, and is assumed to be proportional to a power of the velocity: F alpha -nu(gamma). The dynamics is described by a two-dimensional nonlinear area-contracting mapping obtained via the solution of Newton's second law of motion. We prove analytically that the decay of high energy is given by a continued fraction which recovers the following expressions: (i) linear for gamma = 1; (ii) exponential for gamma = 2; and (iii) second-degree polynomial type for gamma = 1.5. Our results are discussed for both the complete version and the simplified version. The procedure used in the present paper can be extended to many different kinds of system, including a class of billiards problems.

Effect of a frictional force on the Fermi-Ulam model

The dynamical properties of a classical particle bouncing between two rigid walls, in the presence of a drag force, are studied for the case where one wall is fixed and the other one moves periodically in time. The system is described in terms of a two-dimensional nonlinear map obtained by solution of the relevant differential equations. It is shown that the structure of the KAM curves and the chaotic sea is destroyed as the drag force is introduced. At high energy, the velocity of the particle decreases linearly with increasing iteration number, but with a small superimposed sinusoidal modulation. If the motion passes near enough to a fixed point, the particle approaches it exponentially as the iteration number evolves, with a speed of approach that depends on the strength of the drag force. For a simplified version of the model it is shown that, at low energies corresponding to the region of the chaotic sea in the non-dissipative model, the particle wanders in a chaotic transient that depends on the strength of the drag coefficient. However, the KAM islands survive in the presence of dissipation. It is confirmed that the fixed points and periodic orbits go over smoothly into the orbits of the well-known (non-dissipative) Fermi-Ulam model as the drag force goes to zero.

A note on the horseshoe confinement model: the Poynting-Robertson effect

In the present work we numerically simulated the motion of particles coorbital to a small satellite under the Poynting-Robertson light drag effect in order to verify the symmetry suggested by Dermott et al. (1979, 1980) on their ring confinement model. The results reveal a more complex scenario, especially for very small particles (micrometer sizes), which present chaotic motion. Despite the complexity of the trajectories the particles remain confined inside the coorbital region. However, the dissipative force caused by the solar radiation also includes the radiation pressure component which can change this configuration. Our results show that the inclusion of the radiation pressure, which is not present in the original confinement model, can destroy the configuration in a time much shorter than the survival time predicted for a dust particle in a horseshoe orbit with a satellite.

A software development process model for gesture-based interface

Gesture-based applications have particularities, since users interact in a natural way, much as they interact in the non-digital world. Hence, new requirements are needed on the software design process. This paper shows a software development process model for these applications, including requirement specification, design, implementation, and testing procedures. The steps and activities of the proposed model were tested through a game case study, which is a puzzle game. The puzzle is completed when all pieces of a painting are correctly positioned by the drag and drop action of users hand gesture. It also shows the results obtained of applying a heuristic evaluation on this game. © 2012 IEEE.

Development of a low-Reynolds-number k-ω model for FENE-P fluids

A low-Reynolds-number k-ω model for Newtonian fluids has been developed to predict drag reduction of viscoelastic fluids described by the FENE-P model. The model is an extension to viscoelastic fluids of the model for Newtonian fluids developed by Bredberg et al. (Int J Heat Fluid Flow 23:731-743, 2002). The performance of the model was assessed using results from direct numerical simulations for fully developed turbulent channel flow of FENE-P fluids. It should only be used for drag reductions of up to 50 % (low and intermediate drag reductions), because of the limiting assumption of turbulence isotropy leading to an under-prediction of k, but compares favourably with results from k-ε models in the literature based on turbulence isotropy. © 2012 Springer Science+Business Media Dordrecht.

Nebular gas drag and planetary accretion with eccentric high-mass planets

Aims.We investigate the dynamics of pebbles immersed in a gas disk interacting with a planet on an eccentric orbit. The model has a prescribed gap in the disk around the location of the planetary orbit, as is expected for a giant planet with a mass in the range of 0.1-1 Jupiter masses. The pebbles with sizes in the range of 1 cm to 3 m are placed in a ring outside of the giant planet orbit at distances between 10 and 30 planetary Hill radii. The process of the accumulation of pebbles closer to the gap edge, its possible implication for the planetary accretion, and the importance of the mass and the eccentricity of the planet in this process are the motivations behind the present contribution. Methods. We used the Bulirsch-Stoer numerical algorithm, which is computationally consistent for close approaches, to integrate the Newtonian equations of the planar (2D), elliptical restricted three-body problem. The angular velocity of the gas disk was determined by the appropriate balance between the gravity, centrifugal, and pressure forces, such that it is sub-Keplerian in regions with a negative radial pressure gradient and super-Keplerian where the radial pressure gradient is positive. Results. The results show that there are no trappings in the 1:1 resonance around the L 4 and L5 Lagrangian points for very low planetary eccentricities (e2 < 0.07). The trappings in exterior resonances, in the majority of cases, are because the angular velocity of the disk is super-Keplerian in the gap disk outside of the planetary orbit and because the inward drift is stopped. Furthermore, the semi-major axis location of such trappings depends on the gas pressure profile of the gap (depth) and is a = 1.2 for a planet of 1 MJ. A planet on an eccentric orbit interacts with the pebble layer formed by these resonances. Collisions occur and become important for planetary eccentricity near the present value of Jupiter (e 2 = 0.05). The maximum rate of the collisions onto a planet of 0.1 MJ occurs when the pebble size is 37.5 cm ≤ s < 75 cm; for a planet with the mass of Jupiter, it is15 cm ≤ s < 30 cm. The accretion stops when the pebble size is less than 2 cm and the gas drag dominates the motion. © 2013 ESO.

Studying Close Approaches for a Cloud of Particles Considering Atmospheric Drag

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

A Reynolds stress model for turbulent flows of viscoelastic fluids

A second-order closure is developed for predicting turbulent flows of viscoelastic fluids described by a modified generalised Newtonian fluid model incorporating a nonlinear viscosity that depends on a strain-hardening Trouton ratio as a means to handle some of the effects of viscoelasticity upon turbulent flows. Its performance is assessed by comparing its predictions for fully developed turbulent pipe flow with experimental data for four different dilute polymeric solutions and also with two sets of direct numerical simulation data for fluids theoretically described by the finitely extensible nonlinear elastic - Peterlin model. The model is based on a Newtonian Reynolds stress closure to predict Newtonian fluid flows, which incorporates low Reynolds number damping functions to properly deal with wall effects and to provide the capability to handle fluid viscoelasticity more effectively. This new turbulence model was able to capture well the drag reduction of various viscoelastic fluids over a wide range of Reynolds numbers and performed better than previously developed models for the same type of constitutive equation, even if the streamwise and wall-normal turbulence intensities were underpredicted.