Low-Reynolds-number wakes of elliptical cylinders: from the circular cylinder to the normal flat plate

Abstract

While the wake of a circular cylinder and, to a lesser extent, the normal flat plate have been studied in considerable detail, the wakes of elliptic cylinders have not received similar attention. However, the wakes from the first two bodies have considerably different characteristics, in terms of three-dimensional transition modes, and near-and far-wake structure. This paper focuses on elliptic cylinders, which span these two disparate cases. The Strouhal number and drag coefficient variations with Reynolds number are documented for the two-dimensional shedding regime. There are considerable differences from the standard circular cylinder curve. The different three-dimensional transition modes are also examined using Floquet stability analysis based on computed two-dimensional periodic base flows. As the cylinder aspect ratio (major to minor axis) is decreased, mode A is no longer unstable for aspect ratios below 0.25, as the wake deviates further from the standard Bénard-von Kármán state. For still smaller aspect ratios, another three-dimensional quasi-periodic mode becomes unstable, leading to a different transition scenario. Interestingly, for the 0.25 aspect ratio case, mode A restabilises above a Reynolds number of approximately 125, allowing the wake to return to a two-dimensional state, at least in the near wake. For the flat plate, three-dimensional simulations show that the shift in the Strouhal number from the two-dimensional value is gradual with Reynolds number, unlike the situation for the circular cylinder wake once mode A shedding develops. Dynamic mode decomposition is used to characterise the spatially evolving character of the wake as it undergoes transition from the primary Bénard-von Kármán-like near wake into a two-layered wake, through to a secondary Bénard-von Kármán-like wake further downstream, which in turn develops an even longer wavelength unsteadiness. It is also used to examine the differences in the two-and three-dimensional near-wake state, showing the increasing distortion of the two-dimensional rollers as the Reynolds number is increased.

A universal three-dimensional instability of the wakes of two-dimensional bluff bodies

“…The unsteady solver is used to investigate the parameter range covering both the steady and unsteady regimes of flow. More details of the time-stepping scheme can be found in Thompson et al (2006), and the code has previously been used to accurately compute bluff-body flows in free stream (Sheard, Thompson & Hourigan 2004b;Ryan, Thompson & Hourigan 2005;Leontini, Thompson & Hourigan 2007;Rao et al 2013a; Thompson et al 2014) and for bodies near walls (Stewart et al 2006(Stewart et al , 2010Rao et al 2011Rao et al , 2012Rao et al , 2013c. It is also necessary to generate steady base flows for the stability analysis.…”

Flow past a rotating cylinder translating at different gap heights along a wall

“…This type of instability mode exists for a circular cylinder (Blackburn and Lopez, 2003;Blackburn et al, 2005) and a square cylinder in freestream (Robichaux et al, 1999). Another type of mode, which has a periodicity of 2T (i.e., it is subharmonic), has been found in wakes behind tori (Sheard et al, 2005a;Thompson et al, 2006b), inclined square cylinders (Sheard, 2011;Sheard et al, 2009), and in rotating cylinders (Rao et al, 2013a(Rao et al, , 2014. The description here is brief and more details can be found in, e.g., Ryan et al (2005), Leontini et al (2007Leontini et al ( , 2013, and Rao et al (2015a).…”

“…The unsteady solver was used to investigate the parameter range covering both the steady and unsteady regimes of flow. More details of the time-stepping scheme can be found in Thompson et al (2006a), and the code has previously been used to accurately compute bluff body flows in freestream (Sheard et al, 2004b;Ryan et al, 2005;Leontini et al, 2007;Rao et al, 2013a;Thompson et al, 2014), and for bodies near walls (Stewart et al, 2006(Stewart et al, , 2010Rao et al, 2011Rao et al, , 2013dRao et al, , 2012.…”

Stability analysis of the elliptic cylinder wake

“…The two-dimensional simulations resulted in a peak lift almost twice as large as the three-dimensional simulations, indicating the flow is truly three-dimensional for these conditions. More recently Thompson et al (2014) examined the three-dimensional transitions for elliptical cylinders with aspect ratios less than one, finding transitions similar to those that occur for a normal flat plate at low aspect ratios, and convergence towards the circular cylinder transition sequence as the aspect ratio became close to unity.…”