Flow around a confined cylinder LES and PIV study

. We study the flow over a cylinder placed between two parallel rigid walls using Large-eddy simulations and Particle Image Velocimetry. The Reynolds number based on the inflow velocity and diameter of the cylinder is 3750 corresponding to the subcritical regime with laminar separation. Three-dimensional visualization shows the presence of the horseshoe vortex system prior to the cylinder. The comparison of time-averaged velocity fields and fluctuations shows good agreement between simulations and experiments. Spectral analysis suggests the presence of low-frequency modulations of the recirculating bubble.


Introduction
Flows over obstacles in a duct are common in many engineering applications such as cooling systems, bridge piers, heat exchangers, building sections, junctions in wing-body and turbine blade-rotor systems, among others. In such configurations a horseshoe vortex system appears prior to a bluff body increasing the local shear stress and heat transfer [1] while the flow is characterized by periodic shedding of large-scale vortices behind the body that form the Kármán vortex street. Low-frequency modulations of the recirculating zone are detected for various configurations such as a cylinder [2,3], disk and sphere [4], prism [5], bullet [6], among others. The period is typically 10 ÷ 100 times lower compared to the main vortex shedding frequency. In the present work we consider a flow over confined cylinder in a narrow rectangular duct to investigate the effect of walls on the dynamics of the recirculation bubble.

Computational and experimental details
We study a water flow over a circular cylinder which is fixed perpendicular to a pair of side walls at the Reynolds number Re = 3750 based on the bulk inflow velocity U b and cylinder diameter D. The inflow velocity distribution represents a steady laminar parabolic profile. The distance between narrow parallel walls is H = 0.4 D. The case is studied using numerical simulations and experiments described below. We perform Large-eddy simulations (LES) using the unstructured finite-volume computational code T-FlowS. The filtered Navier-Stokes and continuity equations for incompressible fluid are closed with the dynamic Smagorinsky subgrid-scale model. The spatial discretization is performed with the second-order central-difference scheme, whereas for the time-marching we use a fully-implicit three-level scheme. The velocity and pressure are coupled with the SIMPLE algorithm. The computational domain shown in Fig.  1 represents a box with a size x × y × z = 29D × 20D × H, where x, y, z stand for the streamwise, spanwise and wall-normal directions. The computations were performed on two meshes with 8.7 × 10 6 and 16.6 × 10 6 cells, respectively, with no significant differences in the results. Both meshes satisfy wall-resolved LES criteria. In particular, even the 'coarse' mesh corresponds to high resolution since the first cell near the cylinder did not exceed the following limits: Δr + < 1, (RΔφ) + < 8 and Δz + < 4, where '+' denotes the wall units and R = D/2. The total computational time was around 10 3 D/U b with a nondimensional timestep 2.5 × 10 -3 .
The experiments were performed in a slot channel with the length and width of 38D and 20D, respectively, where D = 10 mm. In order to provide steady velocity distribution close to parabolic at the inflow, the flow passed through a set of two honeycombs. Velocity fields were measured using Particle Image Velocimetry (PIV) technique. The system consists of a digital PCO camera (1024 × 1280 pix, 500 Hz max. frame rate) and dual cavity Nd:YAG laser (1000 Hz max. rate, 10 mJ max. pulse energy). The camera was located perpendicular to the main channel. The thickness of the laser sheet was equal to 0.7 mm. PIV measurements were performed in a 2D × 2D region behing the cylinder. The averaged characteristics were calculated using 1000 instantaneous velocity fields. The spatial resolution was estimated to be 0.3 mm.

Results
The flow regime corresponds to the subcritical one at this relatively low Reynolds number with the separation of the laminar boundary layer and subsequent turbulization of the shear layer. A highly three-dimensional flow appears in the near wake region within the recirculating bubble due to the bounding narrow walls. The hourseshoe vortices decay while interacting with the shear-layer turbulence (Fig. 1). Further downstream the wake becomes fully developed. Figures 2 and 3

Discussion
We performed LES and PIV of the flow over a confined cylinder in a narrow duct at Re = 3750. Spectral analysis suggests the presence of low-frequency modulations of the recirculating bubble. This will be the topic for the future study. Another issue is the effect of bounding walls on the developed wake. Our observations [7,8] in confined jets revealed the existence of streamwise meandering vortices in the flow influencing the heat transfer across the channel. It is expected that a similar phenomenon should be present in a confined wake flow.