LOW FREQUENCY WAKE DYNAMICS OF CANTILEVERED CIRCULAR CYLINDERS AT AN ASPECT RATIO OF 4

Abstract

Near-wake characteristics of a low aspect ratio (h/d = 4) cantilevered circular cylinder protruding a thin laminar boundary layer have been investigated both experimentally (Re = 10,400) and numerically (Re = 300). Despite the substantial differences in the investigated Re, the unsteady wake topology exhibits similar instability mechanisms: (i) a Kármán-like vortex shedding instability, and (ii) a lowfrequency instability which manifests as a coupling between the flow over the free end and the base flow near the cylinder-wall junction. Attention is drawn to the lowfrequency instability, which comprises a significant portion of the kinetic energy content in the wake, and has not been reported in previous experimental or numerical investigations. It appears to be characteristic of intermediate aspect ratio cantilevered circular geometries. INTRODUCTION The flow across cantilevered bluff bodies is ubiquitous in the natural environment and in industrial applications, e.g.: wind loadings on trees, buildings, cross-flow heat exchangers and chimney stacks. Hence, it is not surprising that such geometries have been the subject of a multitude of experimental and numerical studies over the last century (e.g., Fox & Apelt (1993), Rodi (1997), Okamoto & Yagita (1973), Martinuzzi & Havel (2004), Rostamy et al. (2012)). Previous experimental studies on cantilevered bluff bodies have shown that the flow development and related structural loading characteristics strongly depend on the oncoming boundary layer characteristics, the body aspect ratio and the Reynolds number Re of the flow based on the characteristic length scale of the body (e.g., Okamoto & Yagita (1973) and others). It is widely accepted that above a critical aspect ratio, the oscillatory dynamics due to a vortex shedding instability dominate the wake development. For Reynolds numbers relevant to turbulent vortex shedding conditions, the dominant vortical structures exhibit significant temporal modulations in their strength (amplitude) which are linked to a low-frequency drift in the base flow (Bourgeois et al., 2013). The base flow modulation is resolvable with Proper Orthogonal Decomposition (POD) analysis and is consistent with mean-field theory (Stuart, 1958): an energetic exchange exists between the modes associated with vortex shedding and the low-frequency shift mode (Noack et al., 2003). At low Re, this energetic exchange occurs at the onset of the vortex shedding instability (Noack et al., 2003), until the system reaches a dynamically stable state with a constant shedding amplitude. For higher Re turbulent flows, Bourgeois et al. (2013) showed that the vortex shedding is continuously perturbed from its limitcycle oscillation and this process is modelled well with mean-field theory. Presently, it remains unclear if a lowfrequency shift mode persists for all turbulent bluff body wakes exhibiting quasi-periodic vortex shedding. The focus of the present study is to investigate laminar and turbulent vortex shedding from a cantilevered circular cylinder of aspect ratio 4. The goal is to identify the dominant energetic structures in the wake, and provide insight into low frequency phenomena occurring under both laminar and turbulent shedding conditions. METHODOLOGY The flow development over a low aspect ratio (h/d = 4) cantilevered circular cylinder is investigated for Re = 300 and 10,400. For the test case Re = 300, results are from numerical simulation, while experiments have been conducted for Re = 10,400 in a wind tunnel facility. For brevity, the test cases will be referred to by their Reynolds number. Numerical Methodology Simulations were carried out using the open-source code package of Field Operation and Manipulation (OpenFoam) on a parallel platform with 64 processors. The computational domain consists of a structured O-type mesh around the cylinder and an H-type in the remainder of the domain which has been refined following the procedure of McClure et al. (2015). A Dirichlet boundary condition us-