We have performed direct numerical simulations of flow past a tapered circular cylinder during the early transition to three dimensions for two successive taper ratios (TR) of 20 and 12.5. Our results indicate the random occurrence of vortex splits and dislocations as the topology of the shedding signature. In particular, we observe oblique cellular shedding with multiple spanwise patterns and oppositely oriented oblique cells in the shed structure. Unlike flow imposed shear, the vortex formation length becomes sensitive to the taper ratio, which removes oblique frequency waves noticed for lower shear rate. The local Strouhal frequency (Stz) at the higher TR case exhibits a decreasing trend with remarkably smaller finite jumps at the cell boundaries and is found close to uniform cylinder flow. The wavelet analysis reveals the narrowing of the spectrum at a lower TR. A higher TR case shows a distinctly regular and evenly spaced spectrum which does not reach the maximum Stz, making it a rare event. The present results show that tapering causes the appearance of a secondary motion, which completely reverses at the downstream cylinder wake. Our numerical calculations show that pressure has an indirect role in the growth of the secondary instabilities, where isobars align along with the taper profile. The geometrically induced shear promotes greater mixing in the near wake, and we found that the maximum cross-stream velocity never exceeds 10% of the mean flow even with the steepest TR. The streamwise growth of the defect layer is slower for increasing TR and reaches an early saturation. Although the velocity deficit is higher at the steepest TR, it causes a delay in the momentum recovery along the streamwise direction. The shape factor for the lower TR case shows a delay in the laminar–turbulent transition. Finally, our global stability analysis results employing dynamic mode decomposition revealed a nonlinear dynamical system with spanwise dissipation of the dynamic modes.

Three-dimensional wake dynamics behind a tapered cylinder with large taper ratio

This work aims to find the origin and connection of the surface, near-wake, and far-wake structures in the flow encompassing a high-rise building for a high Reynolds number. The origin and interconnection of the stream-wise tip vortices, with the other components of the wake, is analysed in this study for the current scenario. The Unsteady Reynolds Averaged Navier-Stokes equations (URANS) together with the realizable k-ϵ turbulence model have been used in this investigation to study the turbulent wake flow following a ground-surface-attached square shape building. A moderately big obstacle aspect ratio of 4, a Reynolds number of 12,000, and a thin evolving boundary layer thickness have been used in the flow modeling. The designed flow addresses the reversed-flows at the outlet during computation to improve the accuracy of the realizable k-ϵ model. The Reynolds stress components are retrieved using the Boussinesq approach. The wake’s principal compositions, including span-wise-side eddies and area of high stream-wise vorticity in the uppermost portion of the wake, are illustrated by both three-dimensional (3D) representations and planner projections of the mean flow distributions. A braided vortex formation, composed of asymmetric hairpin vortexes, is witnessed in the far-wake area. The association of the near-wake vortex structures with the far-wake and near-wall flow, which is associated with the flow strengths, is also discussed. In this investigation, few areas of large stream-wise vorticity magnitude, like tip vortexes, are correlated to the 3D curving of the fluid motion, and tip vortices did not continuously reach to the free end part of the building. The 3D fluid motion interpretation, which combined several measurements of the flow distribution encompassing the cylinder, shows that the time-averaged near-wake structures are formed of two segments of distinct source and section of dominance. Furthermore, addressing reversed-flow during computation shows notable improvement in the results.

Unsteady RANS simulation of wind flow around a building shape obstacle

We experimentally investigate the characteristics of a dynamic wake and of flow separation for a square cylinder with steady suction at its leading-edge corners. The wind tunnel experiments were conducted at a Reynolds number of 5946, and suction slots were manufactured symmetrically at the leading corners of the square cylinder. Steady suction was characterized with a suction momentum coefficient Cμ varying from 0.0227 to 0.3182. A time-resolved particle image velocimetry system was used to evaluate the control of leading-edge suction at different Cμ. Next, the measurements were analyzed by applying a proper orthogonal decomposition (POD) to study the control effectiveness. The POD results suggest that the first four modes of wake vortex shedding are transformed in controlled cases and that periodic Karman vortex shedding is suppressed. The results also show that, even with a very small momentum coefficient, the steady suction at the leading-edge corners stabilizes the cylinder wake. The wake region becomes longer and narrower in comparison with the baseline case. In addition, modifications of separation flow were visualized. At quite small Cμ, flow separation at the leading-edge corners is considerably suppressed. Upon increasing the suction momentum coefficient to 0.1364, flow separation at the leading edges is almost eliminated. Finally, we estimate the effect of drag reduction due to the leading-edge suction. 

Characteristics of forced flow past a square cylinder with steady suction at leading-edge corners

Abstract The unsteady wake dynamics of two finite wall-mounted cylinders of unequal height and arranged in tandem are investigated using time-resolved particle image velocimetry (TR-PIV). The cylinders were fully submerged in a turbulent boundary layer with a Reynolds number based on the cylinder diameter (d) of 5540 and boundary layer thickness of $\delta /d = 8.7$. The centre-to-centre spacing between the cylinders was fixed at 4d. The degree of sheltering was studied by varying the height of the upstream cylinder (UC) $(h/d \in [0.7\unicode{x2013} 7.0])$ while keeping the height of the downstream cylinder (DC) constant at $H/d\; = \; 7.0$. The resulting height ratios were $h/H = 0.10,0.25,0.50,0.75$ and $1.00$ denoted as HR10, HR25, HR50, HR75 and HR100, respectively. The wake dynamics of the DC were also compared to those of an isolated single cylinder (SC) with similar Reynolds number, aspect ratio and submergence ratio. TR-PIV measurements were performed in the symmetry plane for all test cases and five spanwise planes along the height of HR75. The results showed that as the height ratio increases, the downwash from the free end of the UC impinges directly on the frontal surface of the DC and induces a strong upwash on the opposite rear side of the DC. The induced upwash impedes the downwash from the free end of the DC much earlier than observed behind the SC, resulting in a reduced reverse flow area and high velocity deficit in the sheltered portion of the DC. Nonetheless, the reverse flow area behind the UC and DC undergoes a quasi-periodic pumping motion with frequencies that are synchronized for HR25 to HR100. Spectral analysis and proper orthogonal decomposition also reveal that the attachment of the shear layers of the UC on the DC also promotes a lock-in anti-symmetric vortex shedding behaviour.

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Effects of sheltering on the unsteady wake dynamics of tandem cylinders mounted in a turbulent boundary layer

A flow over a bluff-body is numerically investigated and validated using a Detached-Eddy Simulation (DES) technique at Re=21,400. An incompressible solver that is nominally second-order accurate employing an implicit constant backward time-stepping scheme with blended upwind-central differencing spatial discretization is used to study the massively separated wake that is generated. Measurements are taken up to 6 downstream characteristic lengths, evaluating the wake time-averaged first- and second-moment statistics alongside near-wall boundary layer quantities and surface-force integrals. Results advocate the use of DES methods, which are found to be significantly more accurate for capturing wake statistics, compared to two different Reynolds-Averaged (RANS) models calibrated with an identical grid. Although comparative accuracy can be obtained with the RANS techniques for the boundary layer and surface-forces, these techniques are unsuitable for modeling wake statistics as they are inherently dissipative, evident through early velocity recovery when evaluated against experimental data.

Numerical Capture and Validation of a Massively Separated Bluff-Body Wake

This paper presents the numerical solutions of flow around a surface-mounted square cylinder of aspect ratio h/d = 7 at Reynolds numbers of 652 and 13 041. The aim is to investigate the effect of the Reynolds number, between its medium-to-high range, on the flow and vortex structure around such a cylinder. The present simulations have successfully reproduced the primary flow, as well as the three-dimensional large-scale vortex structure in the wake of the finite wall-mounted body. The observation of base vortices, tip vortices, and a horseshoe vortex is consistent with previous experimental studies. A dipole wake is captured at the higher Reynolds number, while a quadrupole wake is captured for the lower, indicating that the Reynolds number strongly influences the wake structure. In the near-wake region, by plotting the isosurface of instantaneous second invariant of the velocity gradient, the full-loop structure is observed for the quadrupole wake, while the half-loop structure is observed for the dipole wake. In the far-wake region, a braided vortex structure formed by asymmetric hairpin vortices is observed at both Reynolds numbers and a new wake topology is proposed for flows with a similar geometry.This paper presents the numerical solutions of flow around a surface-mounted square cylinder of aspect ratio h/d = 7 at Reynolds numbers of 652 and 13 041. The aim is to investigate the effect of the Reynolds number, between its medium-to-high range, on the flow and vortex structure around such a cylinder. The present simulations have successfully reproduced the primary flow, as well as the three-dimensional large-scale vortex structure in the wake of the finite wall-mounted body. The observation of base vortices, tip vortices, and a horseshoe vortex is consistent with previous experimental studies. A dipole wake is captured at the higher Reynolds number, while a quadrupole wake is captured for the lower, indicating that the Reynolds number strongly influences the wake structure. In the near-wake region, by plotting the isosurface of instantaneous second invariant of the velocity gradient, the full-loop structure is observed for the quadrupole wake, while the half-loop structure is observed for the dipole...

You Qin Wang

Papers

Effects of Reynolds number on vortex structure behind a surface-mounted finite square cylinder with AR = 7