Oscillatory flow regimes around four cylinders in a diamond arrangement

Abstract

Oscillatory flow around a cluster of four circular cylinders in a diamond arrangement is investigated using two-dimensional direct numerical simulation over Keulegan–Carpenter numbers (KC) ranging from 4 to 12 and Reynolds numbers (Re) from 40 to 230 at four gap-to-diameter ratios (G) of 0.5, 1, 2 and 4. Three types of flows, namely synchronous, quasi-periodic and desynchronized flows (along with 14 flow regimes) are mapped out in the (G, KC, Re)-parameter space. The observed flow characteristics around four cylinders in a diamond arrangement show a few unique features that are absent in the flow around four cylinders in a square arrangement reported by Tong et al. (J. Fluid Mech., vol. 769, 2015, pp. 298–336). These include (i) the dominance of flow around the cluster-scale structure at $G=0.5$ and 1, (ii) a substantial reduction of regime D flows in the regime maps, (iii) new quasi-periodic (phase trapping) $\text{D}^{\prime }$ (at $G=0.5$ and 1) and period-doubling $\text{A}^{\prime }$ flows (at $G=1$) and most noteworthily (iv) abnormal behaviours at ($G\leqslant 2$) (referred to as holes hereafter) such as the appearance of spatio-temporal synchronized flows in an area surrounded by a single type of synchronized flow in the regime map ($G=0.5$). The mode competition between the cluster-scale and cylinder-scale flows is identified as the key flow mechanism responsible for those unique flow features, with the support of evidence derived from quantitative analysis. Phase dynamics is introduced for the first time in bluff-body flows, to the best knowledge of the authors, to quantitatively interpret the flow response (e.g. quasi-periodic flow features) around the cluster. It is instrumental in revealing the nature of regime $\text{D}^{\prime }$ flows where the cluster-scale flow features are largely synchronized with the forcing of incoming oscillatory flow (phase trapping) but are modulated by localized flow features.

The upper-bound limit of Stokes-Wang solution for oscillatory flow around a circular cylinder

“…The spanwise averaged cross-sectional flow fields (not shown here) are similar to their counterparts obtained from 2-D DNS. This observation is consistent with previous findings in literature of oscillatory flow past cylinder(s)[14,[16][17][18]. Since the primary objective of this study is on CD and CM and 3-D simulations at high β constitute a daunting task computationally, the following discussions are based on the results from 2-D DNS.…”

Wake transitions behind a cube at low and moderate Reynolds numbers

“…Previous studies (e.g. Ren et al 2019) have shown that the stroboscopic view of flow fields sampled at the higher frequency over the entire period of the low frequency constitutes an effective way of revealing the physical mechanism of quasi-periodic oscillation. The regular vortex shedding frequency St 1 ≈ 0.0982 is used as the sampling frequency over the secondary period in the following flow visualisations.…”

Bistabilities in two parallel Kármán wakes

“…This method has been applied in the community of fluid mechanics to elucidate the synchronisation behaviours of quasi-periodic phenomena in self-excited jets (Li & Juniper 2013), thermoacoustic systems (Kashinath, Li & Juniper 2018) and bluff-body flows (Ren et al. 2019; Konstantinidis et al. 2020; Aswathy & Sarkar 2021) and demonstrated to be effective in revealing the nature of flows that involves complex interactions.…”