Flow instability in weakly eccentric annuli

H. V. Moradi

doi:10.1063/1.5088992

2019-04-10

PRE

H. V. Moradi

Stavros Tavoularis *

DOI：10.1063/1.5088992

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摘要

En 中文

A temporal linear stability analysis of laminar flow in weakly eccentric annular channels has been performed. It has been shown that, even for eccentricities epsilon and Reynolds numbers that were much smaller than those considered in previous studies, flow instability occurred in the form of travelling waves having characteristics that are very different from those of Tollmien-Schlichting waves and which were triggered at mid-gap by an inviscid mechanism that is associated with the presence of inflection points in azimuthal profiles of the base velocity. The critical stability conditions have been determined for 0 <= epsilon <= 0.1 and for diameter ratios 0 < gamma < 1. The critical Reynolds number Re-c decreased with increasing gamma for 0 < gamma less than or similar to 0.13, reached a minimum at gamma approximate to 0.13, and increased with further increase in gamma. The lowest observed Re-c was 529 and occurred for epsilon = 0.1 and gamma approximate to 0.13. As epsilon -> 0, Re-c proportional to epsilon(-2). The critical wave number and the critical frequency of the disturbances decreased with increasing gamma and approached zero as gamma -> 1, whilst their ratio was nearly constant in the range of parameters considered in this study. The most unstable regions were found to be at roughly mid gap on the two flanks of the annulus, and the phase speed of the disturbances was close to the base flow velocity at these regions. Published under license by AIP Publishing.

Keyword:

STABILITY

MECHANICS

ALGORITHM