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  • 1
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 17 (1993), S. 731-754 
    ISSN: 0271-2091
    Keywords: Instability ; Non-parallel flow ; Fourier-rational Chebyshev mode ; Vortex street ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The local instability of a full non-parallel flow is investigated. The basic flow is a horizontal uniform flow about a vertical array of periodic bound eddies. This flow was found by Kovasznay as an exact solution to the Navier-Stokes equations. The problem is formulated as an initial value problem with two sets of complete orthogonal functions. A new approach to the problem with semi-infinite domain is given computationally with a new modified rational Chebyshev function. The linear stability analysis of the Kovasznay flow is performed with respect to the odd-rational Chebyshev mode and the even-rational Chebyshev mode for the evolution of disturbances. While symmetrical vortex sheets appeared through the process of big eddies breaking into small eddies in the odd-rational Chebyshev mode, the von Kármán vortex street phenomena is found in the even-rational Chebyshev mode. The mode corresponding to antisymmetric velocity perturbation is found to be far more unstable than symmetric disturbance. An organized structure is developed after the onset of instability. Several general characteristics of non-parallel flow stability are discussed.
    Additional Material: 18 Ill.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 23 (1996), S. 379-396 
    ISSN: 0271-2091
    Keywords: rotating flow ; three-dimensional rectangular channel ; pseudospectral matrix method ; eigenvalue decomposition ; two- and four-cell flow pattern ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A Fourier-Chebyshev pseudospectral method is used for the numerical simulation of incompressible flows in a three-dimensio nal channel of square cross-section with rotation. Realistic, non-periodic boundary conditions that impose no-slip conditions in two directions (spanwis e and vertical directions) are used. The Navier-Stokes equations are integrated in time using a fractional step method. The Poisson equations for pressure and the Helmholtz equation for velocity are solved using a matrix diagonalization (eigenfunction decomposition) method, through which we are able to reduce a three-dimensional matrix problem to a simple algebraic vector equation. This results in signficant savings in computer storage requirement, particularly for large-scale computations. Verification of the numerical algorithm and code is carried out by comparing with a limiting case of an exact steady state solution for a one-dimensional channel flow and also with a two-dimensional rotating channel case. Two-cell and four-cell two-dimensional flow patterns are observed in the numerical experiment. It is found that the four-cell flow pattern is stable to symmetri cal disturbances but unstable to asymmetrical disturbances.
    Additional Material: 17 Ill.
    Type of Medium: Electronic Resource
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