Primary oscillatory instability in low-aspect-ratio rotating disk - cylinder system (rotor - stator cavity)

TL;DR

This study numerically investigates the three-dimensional oscillatory instability in low-aspect-ratio rotating disk-cylinder systems, revealing how the critical azimuthal wavenumber increases as the aspect ratio decreases, with results aligning well with experiments.

Contribution

It provides a comprehensive stability diagram for the transition to oscillatory flow in low-aspect-ratio systems, highlighting the growth of azimuthal wavenumber and discussing destabilization mechanisms.

Findings

Critical azimuthal wavenumber increases as aspect ratio decreases.

Good agreement between numerical results and experimental data.

Instability cannot be solely attributed to B"odewadt flow or boundary layer effects.

Abstract

Three-dimensional instability of axisymmetric flow in a rotating disk - cylinder configuration is studied numerically for the case of low cylinders with the height/radius aspect ratio varying between 1 and 0.1. A complete stability diagram for the transition from steady axisymmetric to oscillatory three-dimensional flow regime is reported. A good agreement with experimental results is obtained. It is shown that critical azimuthal wavenumber grows with the decrease of the aspect ratio, reaching the value of 19 at the aspect ratio 0.1. It is argued that the observed instability cannot be described as resulting from a B\"odewadt flow or from a boundary layer only. Other reasons that can destabilize the flow are discussed.