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  • 1995-1999  (6)
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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Theoretical and computational fluid dynamics 8 (1996), S. 415-433 
    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 Two industrially important free surface flows arising in polymer processing and thin film coating applications are modelled as lid-driven cavity problems to which a creeping flow analysis is applied. Each is formulated as a biharmonic boundary-value problem and solved both analytically and numerically. The analytical solutions take the form of a truncated biharmonic series of eigenfunctions for the streamfunction, while numerical results are obtained using a linear, finite-element formulation of the governing equations written in terms of both the streamfunction and vorticity. A key feature of the latter is that problems associated with singularities are alleviated by expanding the solution there in a series of separated eigenfunctions. Both sets of results are found to be in extremely good agreement and reveal distinctive flow transformations that occur as the operating parameters are varied. They also compare well with other published work and experimental observation.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Theoretical and computational fluid dynamics 8 (1996), S. 415-433 
    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. Two industrially important free surface flows arising in polymer processing and thin film coating applications are modelled as lid-driven cavity problems to which a creeping flow analysis is applied. Each is formulated as a biharmonic boundary-value problem and solved both analytically and numerically. The analytical solutions take the form of a truncated biharmonic series of eigenfunctions for the streamfunction, while numerical results are obtained using a linear, finite-element formulation of the governing equations written in terms of both the streamfunction and vorticity. A key feature of the latter is that problems associated with singularities are alleviated by expanding the solution there in a series of separated eigenfunctions. Both sets of results are found to be in extremely good agreement and reveal distinctive flow transformations that occur as the operating parameters are varied. They also compare well with other published work and experimental observation.
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  • 3
    Electronic Resource
    Electronic Resource
    Springer
    Nonlinear dynamics 7 (1995), S. 11-35 
    ISSN: 1573-269X
    Keywords: Periodic solutions ; stability ; local bifurcations ; Fourier series
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This paper explores the application of the method of variable-coefficient harmonic balance to nonautonomous nonlinear equations of the form XsF(X, t:λ), and in particular, a one-degree-of-freedom nonlinear oscillator equation describing escape from a cubic potential well. Each component of the solution, X(t), is expressed as a truncated Fourier series of superharmonics, subharmonics and ultrasubharmonics. Use is then made of symbolic manipulation in order to arrange the oscillator equation as a Fourier series and its coefficient are evaluated in the traditional way. The time-dependent coefficients permit the construction of a set of amplitude evolution equations with corresponding stability criteria. The technique enables detection of local bifurcations, such as saddle-node folds, period doubling flips, and parts of the Feigenbaum cascade. This representation of the periodic solution leads to local bifurcations being associated with a term in the Fourier series and, in particular, the onset of a period doubled solution can be detected by a series of superharmonics only. Its validity is such that control space bifurcation diagrams can be obtained with reasonable accuracy and large reductions in computational expense.
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  • 4
    Publication Date: 1996-11-01
    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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  • 5
    Publication Date: 1996-11-01
    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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  • 6
    Publication Date: 1995-09-10
    Description: Three mathematical models are developed for meniscus roll coating in which there is steady flow of a Newtonian fluid in the narrow gap, or nip, between two contrarotating rolls in the absence of body forces. The zero flux model predicts a constant pressure gradient within the central core and two eddies, each with an inner structure, in qualitative agreement with observation. The small flux model takes account of a small inlet flux and employs the lubrication approximation to represent fluid velocity as a combination of Couette and Poiseuille flows. Results show that the meniscus coating regime is characterized by small flow rates (λ ≪ 1) and a sub-ambient pressure field generated by capillary action at the upstream meniscus. Such flows are found to exist for small modified capillary number, Ca(R/H0)1/2 ≲ 0.15, where Ca and R/H0 represent capillary number and the radius to semi-gap ratio, respectively. A third model incorporates the full effects of curved menisci and nonlinear free surface boundary conditions. The presence of a dynamic contact line, adjacent to the web on the upper roll, requires the imposition of an apparent contact angle and slip length. Numerical solutions for the velocity and pressure fields over the entire domain are obtained using the finite element method. Results are in accord with experimental observations that the flow domain consists of two large eddies and fluid transfer jets or ‘snakes’. Furthermore, the numerical results show that the sub-structure of each large eddy consists of a separatrix with one saddle point, two sub-eddies with centres, and an outer recirculation. Finally finite element solutions in tandem with lubrication analysis establish the existence of three critical flow rates corresponding to a transformation of the pressure field, the emergence of a ‘secondary snake’ (another fluid transfer jet) and the disappearance of a primary snake. © 1995, Cambridge University Press. All rights reserved.
    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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