79 / 2019-09-30 11:06:59

Physical mechanisms of Flip-flop flows of two interacting Kármán vortex streets

Low-Reynolds-number flow, Bluff-body flow, Kármán vortex streets

The modeling of vortex-induced vibration of a cylinder cluster using low dimensional models (LDMs) has attracted researchers’ attention, especially for the simplest scenario of two side-by-side cylinders. The understanding of interaction mechanisms of two Kármán vortex streets formed behind cylinders is vitally important for the development of LDMs to represent the complex systems correctly. The flip-flop flow (FF), where primary vortex shedding from the cylinders are modulated by a gap flow alternatively switching from one wake to the other over a longer period than the period of primary vortex shedding, is one of the main features of the flow at Reynolds number (Re) near the Hopf bifurcation point of an isolated cylinder. Although the characteristics of the flow have been studied previously, insufficient focus has been placed on the physical mechanisms responsible for the formation of FF flows. Carini et al. [1] attributed the instability of the in-phase (IP) shedding to the formation of FF flows, through a linear stability analysis and direct numerical simulation (DNS) over a narrow range of the gap width to diameter ratio (g*).
The objective of the present study is to further explore the physical mechanisms that are responsible for the formation of FF flows in steady flow around two identical side-by-side cylinders. To this end, a number of DNSs and specifically-designed numerical tests are conducted over a parameter space 47 < Re < 80 and 0.5 <g* < 3.0 by using an open-access spectral-element code Nektar++ [2]. In addition to the conventional analysis methods, phase dynamics is introduced to quantify the physical mechanisms of FF flows. The significant findings derived from the present study include (1) a new type of FF flows is discovered outside the regions identified through linear stability analysis with an IP base flow [1], as illustrated in Figure 1, (2) the mode competition between IP and anti-phase (AP) vortex shedding from cylinders is identified as the dominant mechanism for FF flows, (3) the IP and AP modes dominant at strong and weak coupling strengths (corresponding to small and large g* values) respectively, and (4) FF flows are classified as high-order synchronized flows where frequencies of vortex shedding are locked but the phases of vortex shedding are free.