Reynolds number effects on the bistable flows over a wavy circular cylinder

TL;DR

This study investigates how varying Reynolds numbers influence the bistable wake states of a wavy cylinder, revealing complex flow physics, transition behaviors, and the effects of unsteady inflow conditions on wake stability and turbulence.

Contribution

It provides new insights into the Reynolds number effects on bistable wake states and the transition mechanisms under unsteady inflow conditions for wavy cylinders.

Findings

Steady vortical structures sway with increasing Reynolds number, causing low-frequency drag fluctuations.

Emergence of a secondary spectral peak in lift at higher Reynolds numbers.

Wakes transition to turbulence with small-scale vortices at high Reynolds numbers.

Abstract

The wake of wavy cylinder has been shown to exhibit bistability. Depending on the initial condition, the final state of the wake can either develop into a steady flow (state I), or periodic shedding (state II). In this paper, we perform direct numerical simulations to reveal the Reynolds number effects on these two wake states. With increasing Reynolds number, the steady vortical structures in state I wake sways back and forth in the spanwise direction, resulting in low-frequency fluctuations in drag forces, but not in lift. For state II, the increase in Reynolds number is associated with the emergence of another spectral peak in the lift coefficient. The secondary frequency is associated with highly three-dimensional vortical structures in the wake. For both states, the wakes transition to turblent flows at higher Reynolds numbers, with the development of small-scale vortices. We further study the streamwise gust flows over the wavy cylinder. The time-varying inflow velocity results in a wide range of instantaneous Reynolds number spanning from the absolutely unstable flow regime to the bistable regime. Depending on the period of the inflow velocity variation, the wake perturbations grown at the absolutely unstable flow regime can be damped out in state I wake, or grow large enough to trigger the transition state II, resulting in loss of flow control efficacy. The above analyses reveal novel flow physics of the bistable states at unexplored Reynolds numbers, and showcase the complex transition behavior between the two states in unsteady flows. The insights gained from this study improve the understanding of the wake dynamics of the wavy cylinder.