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    Asymptotic stability and transient growth in pulsatile Poiseuille flow through a compliant channel

    253467.pdf (1.785Mb)
    Access Status
    Open access
    Authors
    Tsigklifis, Konstantinos
    Lucey, Anthony
    Date
    2017
    Type
    Journal Article
    
    Metadata
    Show full item record
    Citation
    Tsigklifis, K. and Lucey, A. 2017. Asymptotic stability and transient growth in pulsatile Poiseuille flow through a compliant channel. Journal of Fluid Mechanics. 820: pp. 370-399.
    Source Title
    Journal of Fluid Mechanics
    DOI
    10.1017/jfm.2017.163
    ISSN
    0022-1120
    School
    Department of Mechanical Engineering
    Remarks

    This article has been published in a revised form in the Journal of Fluid Mechanics http://doi.org/10.1017/jfm.2017.163 This version is free to view and download for private research and study only. Not for re-distribution, re-sale or use in derivative works

    URI
    http://hdl.handle.net/20.500.11937/54533
    Collection
    • Curtin Research Publications
    Abstract

    The time-asymptotic linear stability of pulsatile flow in a channel with compliant walls is studied together with the evaluation of modal transient growth within the pulsation period of the basic flow as well as non-modal transient growth. Both one (vertical-displacement) and two (vertical and axial) degrees-of-freedom compliant-wall models are implemented. Two approaches are developed to study the dynamics of the coupled fluid-structure system, the first being a Floquet analysis in which disturbances are decomposed into a product of exponential growth and a sum of harmonics, while the second is a time-stepping technique for the evolution of the fundamental solution (monodromy) matrix. A parametric study of stability in the non-dimensional parameter space, principally defined by Reynolds number , Womersley number and amplitude of the applied pressure modulation , is then conducted for compliant walls of fixed geometric and material properties. The flow through a rigid channel is shown to be destabilized by pulsation for low , stabilized due to Stokes-layer effects at intermediate , while the critical approaches the steady Poiseuille-flow result at high , and that these effects are made more pronounced by increasing . Wall flexibility is shown to be stabilizing throughout the range but, for the relatively stiff wall used, is more effective at high . Axial displacements are shown to have negligible effect on the results based upon only vertical deformation of the compliant wall. The effect of structural damping in the compliant-wall dynamics is destabilizing, thereby suggesting that the dominant inflectional (Rayleigh) instability is of the Class A (negative-energy) type. It is shown that very high levels of modal transient growth can occur at low , and this mechanism could therefore be more important than asymptotic amplification in causing transition to turbulent flow for two-dimensional disturbances. Wall flexibility is shown to ameliorate mildly this phenomenon. As is increased, modal transient growth becomes progressively less important and the non-modal mechanism can cause similar levels of transient growth. We also show that oblique waves having non-zero transverse wavenumbers are stable to higher values of critical than their two-dimensional counterparts. Finally, we identify an additional instability branch at high that corresponds to wall-based travelling-wave flutter. We show that this is stabilized by the inclusion of structural damping, thereby confirming that it is of the Class B (positive-energy) instability type.

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