Three-dimensional wake transitions of steady flow past two side-by-side cylinders

Abstract

Three-dimensional (3-D) wake transitions of a steady flow past two side-by-side circular cylinders are investigated through Floquet analysis and direct numerical simulations (DNS) over the gap-to-diameter ratio $g^*$ up to 3.5 and Reynolds number ${\textit {Re}}$ up to 400. When the flows behind two cylinders form in-phase and anti-phase wakes at large $g^*$ , the wake transition is similar to the isolated cylinder counterpart, with the critical ${\textit {Re}}$ for the onset of 3-D transition ( ${\textit {Re}}_{cr-1}$ ) happens at around 180. At small $g^*$ , 3-D transition becomes interestingly complex due to the distinct characteristics formed in base flows. The ${\textit {Re}}_{cr-1}$ suddenly drops to around 60–100 and forms distinct variation trends with $g^*$ . Precisely, the ${\textit {Re}}_{cr-1}$ of the single symmetric wake (SS, $g^*\lessapprox 0.25$ ) is more than half of the isolated cylinder counterpart due to the large length scale of the SS wake. Only mode A is detected in SS. In the asymmetric single wake (ASS, $g^* \approx 0.25\unicode{x2013}0.6$ ) and flip-flop wake (FF, $g^* \approx 0.6\unicode{x2013}1.8$ ), the 3-D transition develops at ${\textit {Re}} \approx 103\unicode{x2013}60$ and 75–60, respectively. The decrease in ${\textit {Re}}_{cr-1}$ with increasing $g^*$ is because of the increased level of wake asymmetry in ASS and irregular vortex shedding in FF. Floquet analysis predicts two new unstable modes, namely mode A $'$ and subharmonic mode C $'$ , of ASS. Both modes are transient features in 3-D DNS and the flow eventually saturates into a new 3-D mode, mode ASS. The gap flow of mode ASS is distinctly characterised by its time-independent spanwise waviness structure that is deflected towards different transverse directions with a long wavelength of about $14$ cylinder diameters. The 3-D mode of the FF is irregular both temporally and spatially. Variations of ${\textit {Re}}_{cr-1}$ with $g^*$ , the characteristics and the physical mechanisms of each 3-D mode are discussed in this study.