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  • 1
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    The effect of mainflow transverse velocities in linear stability theory (1971)
    Cambridge University Press
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    Publication Date: 1971-12-29
    Description: In studying the stability of the boundary layer with surface mass injection, a generalized version of the Orr–Sommerfeld equation was derived which takes account of the transverse velocity component in the mainflow. The new terms in the generalized Orr–Sommerfeld equation are inversely proportional to the Reynolds number. The resulting eigenvalue problem was solved numerically for a wide range of values of the mass injection intensity. It was found that the critical Reynolds number (based on the distance from the leading edge) decreases with increasing mass injection. The deviations between the critical Reynolds numbers from the generalized and conventional Orr–Sommerfeld equations have a different sign at low injection intensities from that at high injection intensities. © 1971, 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
    Published by Cambridge University Press
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  • 2
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    Stability of the developing laminar flow in a parallel-plate channel (1967)
    Cambridge University Press
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    Publication Date: 1967-11-09
    Description: The hydrodynamic stability of the developing laminar flow in the entrance region of a parallel-plate channel is investigated using the theory of small disturbances. The stability of the fully developed flow is also re-examined. A wide range of analytical (i.e. asymptotic) and numerical methods are employed in the stability investigation. Among the asymptotic methods, each of three viscous solutions (singular, regular and composite) is used along with the inviscid solution to provide critical Reynolds numbers and complete neutral stability curves. Two numerical methods, finite differences and stepwise integration, are applied to calculate critical Reynolds numbers. The basic flow in the development region is treated from two stand-points: as a channel velocity profile and as a boundary-layer velocity profile. Extensive comparisons among the various methods and flow models disclose their various strengths and ranges of applicability. As a general result, it is found that the critical Reynolds number decreases monotonically with increasing distance from the channel entrance, approaching the fully developed value as a limit.
    Print ISSN: 0022-1120
    Electronic ISSN: 1469-7645
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Published by Cambridge University Press
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  • 3
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    Stability of developing pipe flow subjected to non-axisymmetric disturbances (1974)
    Cambridge University Press
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    Publication Date: 1974-03-01
    Description: The linear stability of the developing flow of an incompressible fluid in the entrance region of a circular tube is investigated. The case of non-axisymmetric small disturbances is considered in the analysis. The main-flow velocity distribution used in the stability calculations is that from the solution of the linearized momentum equation. The eigenvalue problem consisting of the disturbance equations and the boundary conditions is solved by a direct numerical integration scheme along with an iteration procedure. An orthonormalization method is employed to remove the ‘parasitic errors’ inherent in the numerical integration of the coupled disturbance equations. The flow is found to be unstable to non-axisymmetric disturbances with an azimuthal wavenumber of one. Neutral-stability curves and critical Reynolds numbers at various axial locations are presented. A comparison of these results is made with those for axisymmetric disturbances reported by Huang & Chen. It is found that the first instability of the flow is due to non-axisymmetric disturbances and occurs in the entrance region of the pipe with a minimum critical Reynolds number of 19780. © 1974, 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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  • 4
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    Subcritical bifurcation of plane Poiseuille flow (1973)
    Cambridge University Press
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    Publication Date: 1973-04-01
    Description: We apply the perturbation theory which was recently developed and justified by Joseph & Sattinger (1972) to determine the form of the time-periodic solutions which bifurcate from plane Poiseuille flow. The results a t lowest significant order seem to be in good agreement with those following from the formal perturbation method of Stuart (1960) as extended by Reynolds & Potter (1967). Given the numerical results of the present calculation, the rigorous theory guarantees that the only time-periodic solution which bifurcates from laminar Poiseuille flow is a two-dimensional wave. The wave which bifurcates at the lowest Reynolds number exists, but it is unstable when its amplitude is small. Solutions which escape the small domain of attraction of laminar Poiseuille flow snap through this unstable time-periodic solution with a small amplitude to solutions of larger amplitudes. © 1973, 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
    Published by Cambridge University Press
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  • 5
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    Friction factors in the theory of bifurcating Poiseuille flow through annular ducts (1974)
    Cambridge University Press
    Details
    Publication Date: 1974-10-21
    Description: The objective of this paper is to show how to formulate a bifurcation theory for pipe flows in terms of the friction factor. We compute the slope of the friction factor vs. Reynolds number curve and the frequency change for the time-periodic solution which bifurcates from Poiseuille flow through annular ducts. © 1974, 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
    Published by Cambridge University Press
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