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Mostrando recursos 1 - 16 de 16

  1. Non standard linear algebra with error analysis

    Justino, Júlia
    Systems of linear equations, called flexible systems, with coefficients having uncertainties of type o (.) or O (.) are studied from the point of view of non-standard analysis. Then uncertainties of the afore-mentioned kind will be given in the form of so-called neutrices, for instance the set of all infinitesimals. In some cases an exact solution of a flexible system may not exist. Still conditions are presented that guarantee the existence of an admissible solution, in terms of inclusion, and also conditions that guarantee the existence of a maximal solution. These conditions concern restrictions on the size of the uncertainties...

  2. Cramer’s Rule applied to flexible systems of linear equations

    Justino, Júlia; van den Berg, Imme
    We study systems of linear equations with coefficients and second member having uncertainties of type o (.) or O(.); in fact, we do not use this functional form of neglecting but an alternative formulation within non-standard analysis using sets of infinitesimals. We call this kind of systems flexible systems of linear equations. In some cases an exact solution may not exist but we present a general theorem that guarantees the existence of a maximal solution. This maximal solution is produced by Cramer’s Rule; depending on the size of the uncertainties appearing in the matrix of coefficients and the second member...

  3. Uma Aplicação do Teorema dos Resíduos

    Moreira, Miguel; Antunes, J.; Pina, H.
    O movimento rotativo de um rotor numa região confinada determina o escoamento do fluído envolvente e o desenvolvimento de forças de interacção fluído-estrutura, cujo conhecimento é essencial na previsão do comportamento dinâmico deste sistema. A determinação explícita das forças referidas a partir das equações de Navier-Stokes conduz à necessidade de resolução de integrais definidos do tipo [equação]. A aplicação de uma forma particular do teorema dos resíduos da análise complexa constitui a solução natural do problema anterior, concretizada recorrendo ao auxílio de um manipulador simbólico para fazer face à extensão das manipulações algébricas necessárias.

  4. An Improved Linear Model for Rotors Subject to Dissipative Annular Flows

    Moreira, Miguel; Antunes, J.; Pina, H.
    In a previous paper, Antunes, Axisa and co-workers developed a linearized model for the dynamic of rotors under moderate fluid confinement, based on classical perturbation analysis covering two different cases: (i) dissipative motions of a centered rotor; (ii) motions of an eccentric rotor for a frictionless flow. Following the same procedures and assumptions, we derive here an improved model to cover the more general case of a dissipative linearized motion of an eccentric rotor. Besides the natural position variables, a new flow variable, which can be physically interpreted as the fluctuating term of average tangential velocity, was introduced, yielding an...

  5. Analysis of the Nonlinear Orbital Motions of Immersed Rotors Using a Spectral/Galerkin Approach

    Moreira, Miguel; Antunes, J.; Pina, H.
    Recently, we developed a symbolic-numerical formulation for the nonlinear planar motion of rotors under fluid confinement, based on a spectral/Galerkin approach, for gap geometries of about [equação] where H is the average annular gap and R is the rotor radius. Results showed a quite good agreement between the class of approximate models generated, the corresponding analytical exact planar model and experiments. Note that this methodology can be almost entirely automated on a symbolic computing environment. In the present paper this symbolic-numerical spectral/Galerkin procedure is extended in order to deal with nonlinear orbital motions - X (t) and Y (t) taking...

  6. Nonlinear Vibrations of Vertical Asymmetrically-Supported Rotors Under Fluid Confinement: Theoretical Results

    Moreira, Miguel; Pina, H.; Antunes, J.
    This paper is concerned about vertical rotors immersed in fluid annulus of moderate confinement. Such rotors are subjected to the dynamical effects of the fluctuating co-rotating flows. For high enough spinning velocities, the fluid-elastic forces become significant, and often lead to unstable dynamical regimes. These depend on the fluid gap and density, on the rotor eccentricity and spinning velocity, as well as structural properties. We developed an improved linear model for rotors under moderate fluid confinement as well as an exact model for the corresponding nonlinear rotordynamics. Recently a symbolic-numerical formulation based on a spectral/Galerkin approach was also developed by...

  7. Destilador com Evaporação por Spray para Dessalinização de Água do Mar

    Joyce, A.; Loureiro, D.; Collares Pereira, M.; Moreira, Miguel
    O presente trabalho descreve um destilador para dessalinização de água do mar, em que a evaporação é efectuada através de um 'spray', com a finalidade de aumentar a produção diária de água. É apresentado o princípio de funcionamento do sistema, descrito o protótipo construído e apresentados e discutidos os resultados já obtidos durante os ensaios em laboratório. A produção aumenta com a temperatura, de uma forma quadrática, e com a diminuição quer do caudal de entrada quer do diâmetro das gotas produzidas pelos pulverizadores. A câmara pode ser associada a um sistema de Colectores Solares Planos ou Colectores CPC, sendo...

  8. Modelação Computacional de um Dessalinizador com Evaporação por Spray para Dessalinização de Água do Mar

    Moreira, Miguel; Joyce, A.; Pina, H.
    O desenvolvimento dum evaporador com evaporação por "Spray" motivou a elaboração dum seu modelo computacional. A comparação dos resultados da simulação com resultados experimentais revelou um idêntico comportamento qualitativo e erros relativos de 20%. Simulações computacionais posteriores evidenciam a possibilidade de atingir desempenhos energéticamente atractivos.

  9. O Problema da Escassez da Água Potável e a Questão da Dessalinização

    Moreira, Miguel; Joyce, A.; Pina, H.
    No presente texto introduz-se o problema da escassez de água potável apontando-se algumas das soluções indicadas por diferentes autores. Os mais importantes métodos de dessalinização são resumidamente descritos e o seu desempenho é caracterizado e assinalado. O desenvolvimento de diferentes técnicas de dessalinização, impulsionado pela escassez deste recurso constitui igualmente a motivação para estudo, construção e desenvolvimento dum destilador com evaporação por " spray ", no departamento de Energias Renováveis do INETI cuja necessidade de otimização levou à elaboração do modelo computacional aqui descrito. A comparação dos resultados da simulação computacional com resultados de testes experimentais revelou um idêntico comportamento...

  10. Uma Aplicação do Teorema dos Resíduos

    Moreira, Miguel; Antunes, J.; Pina, H.
    O movimento rotativo de um rotor numa região confinada determina o escoamento do fluído envolvente e o desenvolvimento de forças de interacção fluído-estrutura, cujo conhecimento é essencial na previsão do comportamento dinâmico deste sistema. A determinação explícita das forças referidas a partir das equações de Navier-Stokes conduz à necessidade de resolução de integrais definidos do tipo [equação]. A aplicação de uma forma particular do teorema dos resíduos da análise complexa constitui a solução natural do problema anterior, concretizada recorrendo ao auxílio de um manipulador simbólico para fazer face à extensão das manipulações algébricas necessárias.

  11. Experimental Validation of Theoretical Models for the Nonlinear Vibrations of Immersed Rotors

    Moreira, Miguel; Tissot, A.; Antunes, J.
    Vibration of rotating shafts has been studied for different gap geometries, ranging from bearing configurations to pump systems. This paper deals with the rotor-flow dynamics of immersed shafts unde.r moderate confinement—clearance gap about [equação] (where H is the average gap and R is the rotor radius). Following simplified assumptions, analytical models for the linearized forces, for both centered and eccentric immersed rotors have been developed as well as a theoretical nonlinear model which fully describes the nonlinear flow terms. These models were supported by encouraging results from preliminary experiments. In the present paper, we discuss some recent and representative results...

  12. Finite length bearings and squeeze-film dampers: a two-dimensional dynamical solution

    Antunes, J.; Moreira, Miguel; Piteau, P.
    In this paper we develop a non-linear dynamical solution for finite length bearings and squeeze-film dampers based on a Spectral-Galerkin method. En this approach the gap-averaged pressure is approximated, in the lubrication Reynolds equation, by a truncated double Fourier series. The Galerkin method, applied over the residuals so obtained, generate a set of simultaneous algebraic equations for the time-dependent coefficients of the double Fourier series for the pressure. In order to asse:t the validity of our 2D—Spectral-Galerkin solution we present some preliminary comparative numerical simulations, which display satisfactory results up to eccentricities of about 0.9 of the reduced fluid gap...

  13. A nonlinear model for the fluid-coupled vibrations of spent nuclear racks

    Moreira, Miguel; Antunes, J.
    In the near-past we introduced a simplified linearized model for the fluid-coupled vibratory responses of nuclear fuel racks, neglecting three-dimensional flow effects and assuming small gaps between the fuel assemblies. In this paper, using the same basic approach, we generalize the above-mentioned model to account for nonlinear squeeze-film and dissipative flow effects. The proposed methodology can be automatically implemented on a symbolic computer environment. Numerical simulations highlight the significance of nonlinear flow effects at high vibration amplitudes, yielding more realistic predictions.

  14. Nonlinear flow effects on immersed spent nuclear racks

    Moreira, Miguel; Antunes, J.
    Fluid-coupling effects lead to a complex dynamical behavior of immersed spent fuel assembly storage racks. Predicting their responses under strong earthquakes is of prime importance for the safety of nuclear plant facilities. In the near-past we introduced a simplified linearized model for the vibrations of such systems, in which gap-averaged velocity and pressure fields were described analytically in terms of a single space-coordinate for each fluid inter-rack channel. Using such approach it was possible to generate and assemble a complete set of differentialalgebraic equations describing the multi-rack fluid coupled system dynamics. Because of the linearization assumptions, we achieved computation of...

  15. Optimization of baffle configurations to prevent aeroacoustic instabilities in heat exchangers - preliminary experiments

    Moreira, Miguel; Antunes, J.; Debut, V.; Pina, H.
    It is well known that gas heat exchangers are prone to aeroacoustic instabilities, which often lead to severe noise levels, structural vibrations and fatigue. These are unacceptable, as they threaten the component integrity and expose the plant workers to excessive noise levels. Such phenomenon is due to a cooperative interplay between the Karman vortices generated by the cross-flow and the heat exchanger acoustical modes (mainly those transverse to the tube banks). Energy exchanges are then such that, for certain operating velocities, self-excitation of one or more acoustical modes arises. Actually, this problem is solved by placing rigid baffles inside the...

  16. Flow-acoustic interaction in corrugated pipes: Time-domain simulation of experimental phenomena

    Debut, V.; Antunes, J.; Moreira, Miguel
    A phenomenological model based on the coupling between a set of “pressure vortex oscillators” and an acoustic field is considered to simulate the dynamical behaviour of a corrugated pipe. The effect of a random Gaussian dispersion of the Strouhal number is investigated by means of nonlinear numerical time-domain simulations and also in terms of the modeshapes of the linearized aeroacoustical model. The results demonstrate that such perturbations may qualitatively change the dynamics of the model and might cause localization phenomenon.

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