### 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 language | English (US) |
---|---|

Pages (from-to) | 49-79 |

Number of pages | 31 |

Journal | Journal of Fluid Mechanics |

Volume | 359 |

State | Published - Mar 25 1998 |

Externally published | Yes |

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### ASJC Scopus subject areas

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

### Cite this

**Characteristics of endwall and sidewall boundary layers in a rotating cylinder with a differentially rotating endwall.** / Lopez, Juan.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - Characteristics of endwall and sidewall boundary layers in a rotating cylinder with a differentially rotating endwall

AU - Lopez, Juan

PY - 1998/3/25

Y1 - 1998/3/25

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.

UR - http://www.scopus.com/inward/record.url?scp=0032024829&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0032024829&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0032024829

VL - 359

SP - 49

EP - 79

JO - Journal of Fluid Mechanics

JF - Journal of Fluid Mechanics

SN - 0022-1120

ER -