Onset of vortex shedding around a short cylinder

TL;DR

This study investigates how aspect ratio and Reynolds number influence the onset of vortex shedding around short cylinders using DNS and linear stability analysis, revealing new steady wake patterns and vortex shedding behaviors.

Contribution

It provides the first detailed analysis of steady wake patterns for aspect ratios less than or equal to 1.75 and links vortex shedding frequencies to global modes in the flow.

Findings

Steady wake pattern identified for AR ≤ 1.75.

Two distinct vortex shedding patterns observed at different Re.

Vortex shedding frequencies match eigenfrequencies of global modes.

Abstract

This paper presents results of three-dimensional direct numerical simulations (DNS) and global linear stability analyses (LSA) of a viscous incompressible flow past a finite-length cylinder with two free flat ends. The cylindrical axis is normal to the streamwise direction. The work focuses on the effects of aspect ratios (in the range of $0.5\leq \rm{\small AR} \leq2$, cylinder length over diameter) and Reynolds numbers ($Re\leq1000$ based on cylinder diameter and uniform incoming velocity) on the onset of vortex shedding in this flow. All important flow patterns have been identified and studied, especially as $\rm{\small AR}$ changes. The appearance of a steady wake pattern when $\rm{\small AR}\leq1.75$ has not been discussed earlier in the literature for this flow. LSA based on the time-mean flow has been applied to understand the Hopf bifurcation past which vortex shedding happens. The nonlinear DNS results indicate that there are two vortex shedding patterns at different $Re$, one is transient and the other is nonlinearly saturated. The vortex-shedding frequencies of these two flow patterns correspond to the eigenfrequencies of the two global modes in the stability analysis of the time-mean flow. Wherever possible, we compare the results of our analyses to those of the flows past other short-$\rm{\small AR}$ bluff bodies in order that our discussions bear more general meanings.