Wake transition in the flow around two circular cylinders in staggered arrangements

Abstract

The wake transition of the flow around two circular cylinders placed in staggered arrangements with fixed streamwise separation of 5D and cross stream separation varying from 0D to 3D has been studied. The wake transition is compared to that of a single isolated cylinder. Linear stability analysis utilising Floquet theory and direct numerical simulations, using the spectral/hp element method were carried out. It is found that besides modes A and B, mode C can also appear in the wake transition, depending on the relative positioning of the cylinders. The structure of mode C is analysed and the non-linear character of the bifurcation for this mode is investigated. IntroductionThe flow around circular cylinders has been extensively studied due to its practical importance in engineering and scientific relevance in fluid mechanics. On the engineering side, there are a number of applications in mechanical, civil and naval engineering that employ circular-cylindrical structures, such as heat exchangers, chimneys and off- shore platforms. In scientific terms, the flow around circular cylinders presents various important physical phenomena, such as separation, vortex shedding and transition.In the next two subsections, some of the relevant research that has been carried out on two different aspects of this flow is reviewed. These aspects are the wake transition in bluff body flows and the flow around circular cylinders in staggered arrangements, illustrated in figure 1. Wake transitionIn the last two decades, much effort has focused on the study of the three-dimensional transition that takes place in the von Kármán wake that appears in the flow downstream of a single cylinder. This line of research in its contemporary form was instigated by the seminal work of Williamson (1988), in which two distinct stages were identified in the wake transition, spanning 160 Re 300. The limits of these stages were identified by discontinuities in the curve obtained when the Strouhal number (St) was plotted against the Reynolds number (Re) and these discontinuities correspond to the manifestation of different three-dimensional structures in the wake. The first to appear is called mode A, and it has a spanwise wavelength of approximately 4 diameters. The second is called mode B, and its spanwise wavelength is close to 1 diameter. A number of papers on additional experiments and direct numerical simulations (DNS) for this Re range have Wake transition in staggered arrangements 3 been published since then with the aim of reproducing these findings, see for example Wu et al. (1994), Zhang et al. (1995) and Thompson et al. (1996). A great leap forward occurred with the work of Barkley & Henderson (1996), who performed high accuracy Floquet stability analyses of two-dimensional time periodic base flows, precisely identifying the critical Reynolds numbers and also characterising each of the modes that take part in the wake transition. Williamson (1996) presented an extensive study on the wake transition, setting the most significant results pre...

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