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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Theoretical and computational fluid dynamics 7 (1995), S. 159-171 
    ISSN: 1432-2250
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Abstract Linear stability analysis of incompressible attachment-line flow is presented within the spatial framework. The system of perturbation equations is solved using spectral collocation. This system has been solved in the past using the temporal approach and the current results are shown to be in excellent agreement with neutral temporal calculations. Results amenable to direct comparison with experiments are then presented for the case of zero suction. The global solution method utilized for solving the eigenproblem yields, aside from the well-understood primary mode, the full spectrum of least-damped waves. Of those, a new mode, well separated from the continuous spectrum is singled out and discussed. Further, relaxation of the condition of decaying perturbations in the far-field results in the appearance of sinusoidal modes akin to those found in the classical Orr-Sommerfeld problem. Finally, the continuous spectrum is demonstrated to be amenable to asymptotic analysis. Expressions are derived for the location, in parameter space, of the continuous spectrum, as well as for the limiting cases of practical interest. In the large Reynolds number limit the continuous spectrum is demonstrated to be identical to that of the Orr-Sommerfeld equation.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Journal of engineering mathematics 34 (1998), S. 111-129 
    ISSN: 1573-2703
    Keywords: direct numerical simulation ; transition to turbulence ; Euler equations ; finite-time singularities.
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Technology
    Notes: Abstract Numerical methods for tackling the inviscid instability problem are discussed. Convergence is demonstrated to be a necessary, but not a sufficient condition for accuracy. Inviscid flow physics set requirements regarding grid-point distribution in order for physically accurate results to be obtained. These requirements are relevant to the viscous problem also and are shown to be related to the resolution of the critical layers. In this respect, high-resolution nonlinear calculations based on the inviscid initial-boundary-value problem are presented for a model shear-layer flow, aiming at identification of the regions that require attention in the course of high-Reynolds-number viscous calculations. The results bear a remarkable resemblance with those pertinent to viscous flow, with a cascade of high-shear regions being shed towards the vortex-core centre as time progresses. In parallel, numerical instability related to the finite-time singularity of the nonlinear equations solved globally contaminates and eventually destroys the simulations, irrespective of resolution.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 16 (1993), S. 153-170 
    ISSN: 0271-2091
    Keywords: Hydrodynamic stability ; Leading edge boundary layer ; 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 numerical study is performed in order to gain insight to the stability of the infinite swept attachment line boundary layer. The basic flow is taken to be of the Hiemenz class with an added cross-flow giving rise to a constant thickness boundary layer along the attachment line. The full Navier-Stokes equations are solved using an initial value problem approach after two-dimensional perturbations of varying amplitude are introduced into the basic flow.A second-order-accurate finite difference scheme is used in the normal-to-the-wall direction, while a pseudospectral approach is employed in the other directions; temporally, an implicit Crank-Nicolson scheme is used. Extensive use of the efficient fast Fourier transform (FFT) algorithm has been made, resulting in substantial savings in computing cost.Results for the two-dimensional linear regime of perturbations are in very good agreement with past numerical and theoretical investigations, without the need for specific assumptions used by the latter, thus establishing the generality of our method.
    Additional Material: 11 Ill.
    Type of Medium: Electronic Resource
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  • 4
    Publication Date: 2003-05-01
    Print ISSN: 0376-0421
    Electronic ISSN: 1873-1724
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Published by Elsevier
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  • 5
    Publication Date: 2020-05-15
    Print ISSN: 0022-1120
    Electronic ISSN: 1469-7645
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
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  • 6
    Publication Date: 1995-05-01
    Print ISSN: 0935-4964
    Electronic ISSN: 1432-2250
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Published by Springer
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  • 7
    Publication Date: 2020-10-21
    Print ISSN: 0022-1120
    Electronic ISSN: 1469-7645
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
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  • 8
    Publication Date: 2011-01-21
    Print ISSN: 0066-4189
    Electronic ISSN: 1545-4479
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Published by Annual Reviews
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  • 9
    Publication Date: 1998-01-25
    Description: The stability of an incompressible swept attachment-line boundary layer flow is studied numerically, within the Görtler-Hämmerlin framework, in both the linear and nonlinear two-dimensional regimes in a self-consistent manner. The initial-boundary-value problem resulting from substitution of small-amplitude excitation into the incompressible Navier-Stokes equations and linearization about the generalized Hiemenz profile is solved. A comprehensive comparison of all linear approaches utilized to date is presented and it is demonstrated that the linear initial-boundary-value problem formulation delivers results in excellent agreement with those obtained by solution of either the temporal or the spatial linear stability theory eigenvalue problem for both zero suction and a layer in which blowing is applied. In the latter boundary layer recent experiments have documented the growth of instability waves with frequencies in a range encompassed by that of the unstable Görtler-Hämmerlin linear modes found in our simulations. In order to enable further comparisons with experiment and, thus, assess the validity of the Görtler-Hämmerlin theoretical model, we make available the spatial structure of the eigenfunctions at maximum growth conditions. The condition on smallness of the imposed excitation is subsequently relaxed and the resulting nonlinear initial-boundary-value problem is solved. Extensive numerical experimentation has been performed which has verified theoretical predictions on the way in which the solution is expected to bifurcate from the linear neutral loop. However, it is demonstrated that the two-dimensional model equations considered do not deliver subcritical instability of this flow; this strengthens the conjecture that three-dimensionality is, at least partly, responsible for the observed discrepancy between the linear theory critical Reynolds number and the subcritical turbulence observed either experimentally or in three-dimensional numerical simulations. Further, the present nonlinear computations demonstrate that the unstable flow has its line of maximum amplification in the neighbourhood of the experimentally observed instability waves, in a manner analogous to the Blasius boundary layer. In line with previous eigenvalue problem and direct simulation work, suction is observed to be a powerful stabilization mechanism for naturally occurring instabilities of small amplitude.
    Print ISSN: 0022-1120
    Electronic ISSN: 1469-7645
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
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  • 10
    Publication Date: 2003-06-25
    Description: A simple extension of the classic Görtler-Hämmerlin (1955) (GH) model, essential for three-dimensional linear instability analysis, is presented. The extended Görtler-Hämmerlin model classifies all three-dimensional disturbances in this flow by means of symmetric and antisymmetric polynomials of the chordwise coordinate. It results in one-dimensional linear eigenvalue problems, a temporal or spatial solution of which, presented herein, is demonstrated to recover results otherwise only accessible to the temporal or spatial partial-derivative eigenvalue problem (the former also solved here) or to spatial direct numerical simulation (DNS). From a numerical point of view, the significance of the extended GH model is that it delivers the three-dimensional linear instability characteristics of this flow, discovered by solution of the partial-derivative eigenvalue problem by Lin and Malik (1996a), at a negligible fraction of the computing effort required by either of the aforementioned alternative numerical methodologies. More significant, however, is the physical insight which the model offers into the stability of this technologically interesting flow. On the one hand, the dependence of three-dimensional linear disturbances on the chordwise spatial direction is unravelled analytically. On the other hand, numerical results obtained demonstrate that all linear three-dimensional instability modes possess the same (scaled) dependence on the wall-normal coordinate, that of the well-known GH mode. The latter result may explain why the tree-dimensional linear modes have not been detected in past experiments; criteria for experimental identification of three-dimensional disturbances are discussed. Asymptotic analysis based on a multiple-scales method confirms the results of the extended GH model and provides an alternative algorithm for the recovery of three-dimensional linear instability characteristics, also based on solution of one-dimensional eigenvalue problems. Finally, the polynomial structure of individual three-dimensional extended GH eigenmodes is demonstrated using three-dimesional DNS, performed here under linear conditions.
    Print ISSN: 0022-1120
    Electronic ISSN: 1469-7645
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
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