DNS of Taylor-Couette flow between counter-rotating cylinders at small radius ratio

TL;DR

This study uses direct numerical simulations to explore how flow structures in Taylor-Couette flow between counter-rotating cylinders depend on the radius ratio, revealing a critical threshold where flow patterns change significantly.

Contribution

It provides new insights into the flow structure dependence on radius ratio and identifies a critical value affecting vortex and modal flow patterns.

Findings

Flow structure varies with radius ratio, with a critical point between 0.2 and 0.3.

At low radius ratio, outer side exhibits Tollmien-Schlichting-like waves.

Flow fluctuations are significant even when shear stress is near zero.

Abstract

A counter-rotating Taylor-Couette flow with relatively small radius ratios of $\eta$ = 0.2--0.5 was investigated over a wide range of the Reynolds number, from laminar to turbulent regime, by means of three-dimensional direct numerical simulations. We investigated the $\eta$ dependence of the flow structure and determined a critical value between $\eta$ = 0.2 and 0.3, below which, the stable outer cylinder side exhibited a modal structure that was different from the Taylor-vortex flow on the inner side. At $\eta \geq$ 0.3, the Taylor-vortex on the unstable inner side dominated the entire flow field between the cylinders, whose footprints were observed in the vicinity of the outer cylinder wall. However, for $\eta$ = 0.2, the influence from the inner side was limited up to the centre of the cylinder gap. Moreover, on the stable outer cylinder side, there appeared a modal structure that was axially homogeneous, azimuthally periodic, and similar to the Tollmien-Schlichting (TS) instability wave. As the Reynolds number increased with a fixed $\eta$ = 0.2, the modal structure changed its azimuthal wavenumber and thickened radially in the wall unit. Although the Reynolds shear stress on the outer side remained approximately zero, the intensity of the velocity fluctuations was comparable to the Taylor-vortex flows in the central part.