Flow Between a Cylinder and a Rotating Coaxial Cylinder, Axisymmetric Shaft With Axially-Periodic Radius Variation, or Screw
Cotrell, David Lee
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https://hdl.handle.net/2142/83788
Description
Title
Flow Between a Cylinder and a Rotating Coaxial Cylinder, Axisymmetric Shaft With Axially-Periodic Radius Variation, or Screw
Author(s)
Cotrell, David Lee
Issue Date
2003
Doctoral Committee Chair(s)
Pearlstein, Arne J.
Department of Study
Mechanical Engineering
Discipline
Mechanical Engineering
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Engineering, Mechanical
Language
eng
Abstract
"Flow between a circular cylinder and an inner shaft driven by an axial pressure gradient or boundary rotation is considered computationally. In spiral Poiseuille flow (SPF), where the inner shaft is a circular cylinder, complete linear stability boundaries are determined for a wide range of parameters. The analysis accounts for arbitrary infinitesimal disturbances over the entire range of Reynolds numbers (Re) for which SPF is stable. For flows satisfying the zero-Re Rayleigh criterion, connection of centrifugal instability of circular Couette flow to Tollmien-Schlichting (TS) instability of nonrotating annular Poiseuille flow is elucidated. This transition is quite abrupt, with SPF being unstable at all Taylor numbers (Ta) beyond the Re at which annular Poiseuille flow becomes unstable. For the remaining co-rotating cases, it is shown that there is no instability for Re below a minimum value. For some ratios of the radii and angular velocities, disconnected neutral curves lead to a multi-valued stability boundary. It is also shown that the smallest radius ratio for which annular Poiseuille flow is linearly unstable is about 0.12, below which no TS instability occurs. Extensive comparison to experiment sheds light on subcritical instability and insufficient axial development length in previous experimental work. Computations are also reported for steady flows driven by a rotating shaft with axisymmetric axially-periodic radius variation. For this axisymmetric case and a fixed value of the ratio of the mean radius to the outer cylinder radius, the flow is computed as a function of Ta for several dimensionless amplitudes of the radius variation. For small amplitude and sufficiently small Ta, only a ""modified"" Couette flow is found. As the amplitude of the radius modulation increases, solution structure and bifurcation behavior are significantly affected. Beyond a critical modulation amplitude, only a single solution branch is found. For a coaxial screw, use of a reference frame rotating with the screw and a helical coordinate system renders helically fully-developed flows steady and allows computation on a two-dimensional domain. The computations show how the flow, torque, and radial transport depend on the geometry of the helical groove and Ta."
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