Characteristics of endwall and sidewall boundary layers in a rotating cylinder with a differentially rotating endwall

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Abstract

The flow in, a rotating cylinder driven by the differential rotation of its top endwall is studied by numerically solving the time-dependent axisymmetric Navier-Stokes equations. When the differential rotation is small, the flow is well described in terms of similarity solutions of individual rotating disks of infinite radius. For larger differential rotations, whether the top is co-rotating or counter-rotating results in qualitatively distinct behaviour. For counter-rotation, the boundary layer on the top endwall separates, forming a free shear layer and this results in a global coupling between the boundary layer flows on the various walls and a global departure from the similarity flows. At large Reynolds numbers, this shear layer becomes unstable. For a co-rotating top, there is a qualitative change in the flow depending on whether the top rotates faster or slower than the rest of the cylinder. When the top rotates faster, so does the bulk of the interior fluid, and the sidewall boundary layer region where the fluid adjusts to the slower rotation rate of the cylinder is centrifugally unstable. The secondary induced meridional flow is also potentially unstable in this region. This is manifested by the inflectional radial profiles of the vertical velocity and azimuthal vorticity in this region. At large Reynolds numbers, the instability of the sidewall layer results in roll waves propagating downwards.

Original languageEnglish (US)
Pages (from-to)49-79
Number of pages31
JournalJournal of Fluid Mechanics
Volume359
StatePublished - Mar 25 1998
Externally publishedYes

Fingerprint

rotating cylinders
boundary layers
Boundary layers
Reynolds number
shear layers
Fluids
Boundary layer flow
Rotating disks
counter rotation
Vorticity
meridional flow
Navier Stokes equations
boundary layer flow
fluids
rotating disks
Navier-Stokes equation
vorticity
counters
radii
profiles

ASJC Scopus subject areas

  • Computational Mechanics
  • Mechanics of Materials
  • Physics and Astronomy(all)
  • Condensed Matter Physics

Cite this

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title = "Characteristics of endwall and sidewall boundary layers in a rotating cylinder with a differentially rotating endwall",
abstract = "The flow in, a rotating cylinder driven by the differential rotation of its top endwall is studied by numerically solving the time-dependent axisymmetric Navier-Stokes equations. When the differential rotation is small, the flow is well described in terms of similarity solutions of individual rotating disks of infinite radius. For larger differential rotations, whether the top is co-rotating or counter-rotating results in qualitatively distinct behaviour. For counter-rotation, the boundary layer on the top endwall separates, forming a free shear layer and this results in a global coupling between the boundary layer flows on the various walls and a global departure from the similarity flows. At large Reynolds numbers, this shear layer becomes unstable. For a co-rotating top, there is a qualitative change in the flow depending on whether the top rotates faster or slower than the rest of the cylinder. When the top rotates faster, so does the bulk of the interior fluid, and the sidewall boundary layer region where the fluid adjusts to the slower rotation rate of the cylinder is centrifugally unstable. The secondary induced meridional flow is also potentially unstable in this region. This is manifested by the inflectional radial profiles of the vertical velocity and azimuthal vorticity in this region. At large Reynolds numbers, the instability of the sidewall layer results in roll waves propagating downwards.",
author = "Juan Lopez",
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N2 - The flow in, a rotating cylinder driven by the differential rotation of its top endwall is studied by numerically solving the time-dependent axisymmetric Navier-Stokes equations. When the differential rotation is small, the flow is well described in terms of similarity solutions of individual rotating disks of infinite radius. For larger differential rotations, whether the top is co-rotating or counter-rotating results in qualitatively distinct behaviour. For counter-rotation, the boundary layer on the top endwall separates, forming a free shear layer and this results in a global coupling between the boundary layer flows on the various walls and a global departure from the similarity flows. At large Reynolds numbers, this shear layer becomes unstable. For a co-rotating top, there is a qualitative change in the flow depending on whether the top rotates faster or slower than the rest of the cylinder. When the top rotates faster, so does the bulk of the interior fluid, and the sidewall boundary layer region where the fluid adjusts to the slower rotation rate of the cylinder is centrifugally unstable. The secondary induced meridional flow is also potentially unstable in this region. This is manifested by the inflectional radial profiles of the vertical velocity and azimuthal vorticity in this region. At large Reynolds numbers, the instability of the sidewall layer results in roll waves propagating downwards.

AB - The flow in, a rotating cylinder driven by the differential rotation of its top endwall is studied by numerically solving the time-dependent axisymmetric Navier-Stokes equations. When the differential rotation is small, the flow is well described in terms of similarity solutions of individual rotating disks of infinite radius. For larger differential rotations, whether the top is co-rotating or counter-rotating results in qualitatively distinct behaviour. For counter-rotation, the boundary layer on the top endwall separates, forming a free shear layer and this results in a global coupling between the boundary layer flows on the various walls and a global departure from the similarity flows. At large Reynolds numbers, this shear layer becomes unstable. For a co-rotating top, there is a qualitative change in the flow depending on whether the top rotates faster or slower than the rest of the cylinder. When the top rotates faster, so does the bulk of the interior fluid, and the sidewall boundary layer region where the fluid adjusts to the slower rotation rate of the cylinder is centrifugally unstable. The secondary induced meridional flow is also potentially unstable in this region. This is manifested by the inflectional radial profiles of the vertical velocity and azimuthal vorticity in this region. At large Reynolds numbers, the instability of the sidewall layer results in roll waves propagating downwards.

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