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.

Dynamics and Wake Interference Mechanism of Long Flexible Circular Cylinders in Side-by-Side Arrangements

“…In recent years, vortex-induced vibrations (VIV) of multiple circular cylinders have been extensively explored due to their importance in ocean engineering applications such as marine energy harvesting, marine drilling, production risers, heat exchanger tubes bundles, and offshore platforms [1,2]. The configuration of two side-by-side cylinders is considered fundamental among multiple cylinder setups and has gained increasing attention for its vibration responses and flow characteristics [3,4].…”

“…Supradeepan and Roy [9] numerically investigated the flow patterns around two side-by-side cylinders at Reynolds number Re = 100 and identified five different flow patterns with the s/D ranging from 1.1 to 8.0, i.e., the single bluff body periodic pattern, aperiodic pattern, anti-phase, in-phase, and the transformation pattern, respectively. Ren et al [2] numerically analyzed the wake patterns around two side-by-side cylinders at s/D < 3.5 and Re < 400 and found a flip-flopping flow pattern (FF, intermittently and randomly changing the direction of the gap flow) at s/D = 1.6~2. 8.…”

“…Experimental studies by Kim and Alam [10] focused on the vibration characteristics of two elastically supported cylinders in side-by-side arrangements with cross-flow (CF) motion. They identified four vibration patterns: (1) both cylinders reaching maximum vibration amplitudes at the same reduced velocity; (2) no vibration responses for either cylinder; (3) each cylinder reaching its maximum vibration amplitude at different reduced velocities; (4) vibration responses of each cylinder resembling that of a single isolated cylinder. In a numerical study by Chen et al [11], various wake patterns were observed for two side-by-side cylinders with CF vibration, including the irregular pattern, in-phase FF pattern, out-of-phase FF pattern, IP synchronized pattern, AP synchronized pattern, and the biased AP synchronized pattern.…”