Computational Study of the Stability of Annular Couette-Poiseuille Flow to Axisymmetric Travelling Wave Perturbations
Author(s)
Wong, Andrew Wen Hao
Type
Thesis
Abstract
This thesis considers the axisymmetric stability of a flow, subject to an axial pressure gradient,
between concentric sliding cylinders, or annular Couette-Poiseuille flow (ACPF). The
flow geometry and governing equations are set out and we analyse the linear and nonlinear
stability of ACPF for a range of inner cylinder velocity, radius ratio and disturbance
amplitude. We establish that the flow is inviscidly stable and introduce an axisymmetric
travelling wave disturbance to the flow. We find that ACPF is linearly unstable and comparisons
are made with published work such as those of Walton (2004) and Webber (2008).
Using a continuation method, the linearly unstable solutions provide a starting point to
compute finite-amplitude, nonlinear axisymmetric travelling wave solutions. These nonlinear
solutions also exist in the wavenumber-Reynolds number, or neutral curve, space
where linear stability predicts no solutions. The nonlinear travelling wave solutions result
in lower critical Reynolds number and higher critical inner cylinder velocity compared to
that of linear stability predictions. The nonlinear wave disturbance influence is strongest
near the inner and outer cylinder walls and the mean flow distortion has the general effect of
slowing the basic flow velocity. We also present the existence of multiple neutral curves in
nonlinear space and these multiple neutral curves appear to unite as the disturbance amplitude
increases. In an effort to link our results to Hagen-Poiseuille flow (HPF), we analyse
the special case of ACPF where the maximum velocity of the flow is always achieved on
the inner cylinder and find that this flow is linearly stable.
between concentric sliding cylinders, or annular Couette-Poiseuille flow (ACPF). The
flow geometry and governing equations are set out and we analyse the linear and nonlinear
stability of ACPF for a range of inner cylinder velocity, radius ratio and disturbance
amplitude. We establish that the flow is inviscidly stable and introduce an axisymmetric
travelling wave disturbance to the flow. We find that ACPF is linearly unstable and comparisons
are made with published work such as those of Walton (2004) and Webber (2008).
Using a continuation method, the linearly unstable solutions provide a starting point to
compute finite-amplitude, nonlinear axisymmetric travelling wave solutions. These nonlinear
solutions also exist in the wavenumber-Reynolds number, or neutral curve, space
where linear stability predicts no solutions. The nonlinear travelling wave solutions result
in lower critical Reynolds number and higher critical inner cylinder velocity compared to
that of linear stability predictions. The nonlinear wave disturbance influence is strongest
near the inner and outer cylinder walls and the mean flow distortion has the general effect of
slowing the basic flow velocity. We also present the existence of multiple neutral curves in
nonlinear space and these multiple neutral curves appear to unite as the disturbance amplitude
increases. In an effort to link our results to Hagen-Poiseuille flow (HPF), we analyse
the special case of ACPF where the maximum velocity of the flow is always achieved on
the inner cylinder and find that this flow is linearly stable.
Date Issued
2013-02
Date Awarded
2013-04
Copyright Statement
Attribution NoDerivatives 4.0 International Licence (CC BY-ND)
Advisor
Walton, Andrew
Publisher Department
Mathematics
Publisher Institution
Imperial College London
Qualification Level
Doctoral
Qualification Name
Doctor of Philosophy (PhD)