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# Distributions of time-averaged wall shear stress around the cylinder; the clockwise direction is positive.

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Large-eddy simulations were used to investigate the supercritical aerodynamics of a square cylinder with rounded corners in comparison with those in the subcritical regime. First, the numerical methods, especially the dynamic mixed model, were validated on the basis of their prediction of supercritical flows past a circular cylinder. Then, the supe...

## Context in source publication

**Context 1**

... order to describe the flow features near the wall, Fig. 8 shows close-ups of the time-averaged velocity in the vicinity of the side face. Moreover, the quantitative distributions of time-averaged wall shear stress are plotted in Fig. 9. At sub- critical Re, a large-scale recirculation region (also called the secondary vortex) exists immediately behind the frontal corner and beneath the separated shear layer. However, its velocity is actually very low, as evidenced by the small positive wall shear stress when θ ≈ [60,90]. At supercritical Re, the free stream separates ...

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## Citations

... Widely studied configurations derived from the square cylinder are various modifications of its corners, for example, rounding (Cao and Tamura 2017), chamfering (Tamura et al. 1998;Tamura and Miyagi 1999), and corner recesses (He et al. 2014). Other variations such as fins, strakes, and shrouds have also been explored (see, e.g., Naudascher et al. 1981). ...

The flow past a cactus-shaped cylinder with four ribs is investigated numerically using large eddy simulations (LES) at Reynolds number of 20,000 and experimentally using particle image velocimetry (PIV) at Reynolds number of 50,000. In both approaches, the full range of angle of attack is covered. LES results show a good qualitative and quantitative match of the aerodynamic properties to previous experimental data, although the value of the critical angle of attack is slightly lower. The results confirm that there is no Reynolds number dependency within the investigated range allowing a comparison of the flow fields from the present LES and PIV. Significant variations of the flow patterns with the angle of attack are found and quantified using the recirculation length and wake width. Overall, the observed angle of attack dependence resembles the behaviour of the square cylinder. However, the studied cylinder has a narrower wake at all angular orientations. Proper orthogonal decomposition is used to identify large coherent structures in the flow. At all angles of attack the first two modes remain dominant making it possible to reconstruct the periodic vortex shedding process using a low-order model.

... The main methodologies of passive control are changing the roughness of the bluff body surface and modifying the geometry. Typical passive control methods include implementation of dimpled surfaces 42 or bumps, 29 rounded corners, 8 slits or slots, 23,24 perforated pipes, 9 and affiliated secondary components. 20,26,37 Despite the fact that passive flow control methods can indeed attenuate the mean drag and fluctuating lift forces acting on the bluff body, there is a drawback that cannot be ignored: the inefficiencies inherent in passive control. ...

The flow passing a circular cylinder can trigger flow-induced vibrations such as the vortex-induced vibration. In this paper, the authors investigated an active method to control the cylinder wake flow. The control scheme was achieved by active blowing through a structured porous surface that was manufactured by 3D printing precisely. The blowing momentum was changed by various mass flow rates so that it defined different values of a non-dimensional momentum coefficient Cμ. The experimental investigation was conducted in a wind tunnel. A 2D particle image velocimetry system was used to measure global flow fields. The Reynolds number based on D was 10 000 in the subcritical region, where D is the cylinder diameter. The proper orthogonal decomposition (POD) was utilized as a reduced-order model. Experimental results showed that transformations could be found in POD modal characteristics and vortex shedding frequencies. Fluctuations in the global wake were suppressed. Moreover, intensities of turbulence kinetic energy and elements of the Reynolds stress tensor T were decreased in the near wake region. It can be concluded that active blowing jets through the structured porous surface of the circular cylinder can be used to control the surrounding flow with effective Cμ values.

... The wall-mounted hemisphere can be regarded as either rough elements [1][2][3][4][5][6][7] or obstacles. [8][9][10][11][12][13][14][15] The studies on rough elements focused on their influence on the turbulent boundary layer and the associated heat transfer [16][17][18] and drag reduction. When obstacles are used, very complex flow patterns are introduced, such as an upstream horseshoe vortex system and a recirculation zone with trailing vortices in the wake area. ...

Turbulent channel flows around a wall-mounted hemisphere numerically are investigated by large eddy simulation, and the Reynolds number based on the hemisphere’s diameter is 3 × 10 ⁴ . The statistical characteristics and turbulent structure evolution are revealed in the Eulerian frameworks and Lagrangian frameworks. The vortex identification and Dynamic Mode Decomposition (DMD) are used to study the evolution of turbulent structure in the Eulerian frameworks, and the finite-time Lyapunov exponents are applied to identify Lagrangian coherent structures (LCS) in the Lagrangian framework. It is found that the developing angle of the hairpin vortex is ∼7° at two frameworks. What is more, there are some hairpin vortices formed behind the hemisphere and some turbulent structures formed near the wall by DMD method. The correlation analysis is applied to investigate the angle variation and scale variation of turbulent structures, and it is observed that the angle of turbulent structures is negative at Y/ d ≥ 1.2 and the spanwise length scales of turbulent structures increase as it moves downstream. By studying the LCS behind a wall-mounted hemisphere, there is formation of “kink” caused by viscous interaction between some hairpin vortex legs, which is the characteristic of hairpin vortex deformation. The comparisons of statistical characteristics between Eulerian frameworks and Lagrangian frameworks are conducted by the correlation analysis, the spectrum analysis, and the structure functions.

... For rounded corners, despite the number of studies assessing the large-Reynolds number case (see for e.g. Lamballais, Silvestrini & Laizet 2008Cao & Tamura 2017), few works have considered the dependence of the onset of the instabilities on the corner curvature. Park & Yang (2016) determined, via linear stability analysis, how the primary two-dimensional and the three-dimensional instabilities are affected by rounding the four corners of a rectangular cylinder with AR = 1, exploring the shapes ranging between the square cylinder with sharp edges and the circular cylinder. ...

The primary instability of the flow past rectangular cylinders is studied to comprehensively describe the influence of the aspect ratio $AR$ and of rounding the leading- and/or trailing-edge corners. Aspect ratios ranging between $0.25$ and $30$ are considered. We show that the critical Reynolds number ( $\textit {Re}_c$ ) corresponding to the primary instability increases with the aspect ratio, starting from $\textit {Re}_c \approx 34.8$ for $AR=0.25$ to a value of $\textit {Re}_c \approx 140$ for $AR = 30$ . The unstable mode and its dependence on the aspect ratio are described. We find that positioning a small circular cylinder in the flow modifies the instability in a way strongly depending on the aspect ratio. The rounded corners affect the primary instability in a way that depends on both the aspect ratio and the curvature radius. For small $AR$ , rounding the leading-edge corners has always a stabilising effect, whereas rounding the trailing-edge corners is destabilising, although for large curvature radii only. For intermediate $AR$ , instead, rounding the leading-edge corners has a stabilising effect limited to small curvature radii only, while for $AR \geqslant 5$ it has always a destabilising effect. In contrast, for $AR \geqslant 2$ rounding the trailing-edge corners consistently increases $\textit {Re}_c$ . Interestingly, when all the corners are rounded, the flow becomes more stable, at all aspect ratios. An explanation for the stabilising and destabilising effect of the rounded corners is provided.

... They found that rounding greatly decreases drag and lift forces and at R/D = 0.2 (radius of the corner to the cylinder diameter) the minimum in the mean drag coefficient value is observed. In [8,10] 3D LES are conducted with Re = 4·10 4 and 6·10 5 respectively. Rocchio et al. [8] found that even with smallest corner rounding the agreement with experimental data is better since such rounded corners cause the recirculation bubble at the side faces of the cylinder to be larger, thereby, drag coefficient is decreased. ...

... The drag coefficient attained minima when the angle of incidence was between 5 and 10 degrees. Cao and Tamura [22] simulated subcritical and supercritical flows around square cylinder with a rounded corner ratio r/D = 0.167. Two Reynolds numbers, Re = 2.2 × 10 4 and Re = 1.0 × 10 6 were considered, denoting the subcritical and supercritical regimes, respectively. ...

Tall buildings are often subjected to steady and unsteady forces due to external wind flows. Measurement and mitigation of these forces becomes critical to structural design in engineering applications. Over the last few decades, many approaches such as modification of the external geometry of structures have been investigated to mitigate wind-induced load. One such proven geometric modification involved rounding of sharp corners. In this work, we systematically analyze the effects of rounded corner radii on the flow-induced loading for a square cylinder. We perform 3-Dimensional (3D) simulations at a high Reynolds number of $Re = 1\times 10^5$ which is more likely to be encountered in practical applications. An Improved Delayed Detached Eddy Simulation (IDDES) formulation is used with the $k-\omega$ Shear Stress Transport (SST) model for near-wall modelling. IDDES is capable of capturing flow accurately at high Reynolds numbers and prevents grid induced separation near the boundary layer. The effects of these corner modifications are analyzed in terms of the resulting mean and fluctuating components of the lift and drag forces compared to a sharp corner case. Plots of the angular distribution of the mean and fluctuating pressure coefficient along the square cylinder's surface illustrate the effects of corner modifications on the different parts of the cylinder. The windward corner's separation angle was observed to decrease with an increase in radius, resulting in a narrower and longer recirculation region. Furthermore, with an increase in radius, a reduction in the fluctuating lift, mean drag, and fluctuating drag coefficients has been observed.

... As shown in the previous numerical simulation performed by Tamura et al. (1998), a rounded corner applied to a square cylinder affected the wake separation and reduced the drag and lift coefficients. Subsequently, that the rounded corner of square cylinders can suppress the wake separation and influence the vortex shedding frequency has been repeatedly observed in experiments and simulations (e.g., Hu et al., 2006;Park and Yang, 2016;Zhang and Samtaney, 2016;Cao and Tamura, 2017). Moreover, an application rounding the roof's trailing edge to suppress the wake separation was employed for a hatchback Ahmed body by Thacker et al. (2012). ...

The wake bi-stability behind notchback Ahmed bodies is investigated by performing wind tunnel experiments and large eddy simulations (LESs). The focus of this study is on the suppression of bi-stable wakes achieved by rounding the roof's trailing edge of the body. The suppression effect is found to depend on the Reynolds number (Re). The wake behind a sharp edge remains bi-stable for all tested Re. However, for a rounded edge with small radius, wake bi-stability at Re=0.5×10^5 and wake symmetrization with 0.75×105≤Re≤1.5×10^5 are observed. Increasing Re with Re≥1.75×10^5, the wake returns to the bi-stable state. Particularly, with Re≥2×10^5, a stable asymmetric wake state with no switches is observed for long periods. Performing LES confirms the expected wake asymmetry at Re=0.5×10^5 and symmetry at Re=1×10^5 for the case of rounded edge with a small radius. Besides, another wake symmetry is observed for the rounded edge with a large radius at Re=0.5×10^5. For the two wake symmetries shown in the LES results, the symmetrization is attributed to wake suppression in the notchback region, forcing the flow separation from the rear roof to attach to the slant on both sides of the body.

... Perfectly sharp corners are obviously just an idealisation: a laboratory model will always have corners affected to some extent by manufacturing inaccuracies. The effect of rounding the corners has been mostly studied for a square cylinder (where the recirculation region on the side is missing) by for example [33] and [7] for low and high Reynolds numbers. For rectangular cylinders with larger A we recall the works [18,19] that investigate both three-dimensional and two-dimensional infinite D-shaped bodies changing the curvature radius R of the upstream corners. ...

The BARC flow is studied via Direct Numerical Simulation at a relatively low turbulent Reynolds number, with focus on the geometrical representation of the leading-edge (LE) corners. The study contributes to further our understanding of the discrepancies between existing numerical and experimental BARC data. In a first part, rounded LE corners with small curvature radii are considered. Results show that a small amount of rounding does not lead to abrupt changes of the mean fields, but that the effects increase with the curvature radius. The shear layer separates from the rounded LE at a lower angle, which reduces the size of the main recirculating region over the cylinder side. In contrast, the longitudinal size of the recirculating region behind the trailing edge (TE) increases, as the TE shear layer is accelerated. The effect of the curvature radii on the turbulent kinetic energy and on its production, dissipation and transport are addressed. The present results should be contrasted with the recent work of Rocchio et al, JWEIA 2020, who found via implicit Large-Eddy Simulations at larger Reynolds numbers than even a small curvature radius leads to significant changes of the mean flow. In a second part, the LE corners are fully sharp and the exact analytical solution of the Stokes problem in the neighborhood of the corner is used to locally restore the solution accuracy degraded by the singularity. Changes in the mean flow reveal that the analytical correction leads to streamlines that better follow the corners. The flow separates from the LE with a lower angle, resulting in a slightly smaller recirculating region. The corner-correction approach is valuable in general, and is expected to help developing high-quality numerical simulations at the high Reynolds numbers typical of the experiments with reasonable meshing requirements.

... The C f distribution for B/K = 0 and R/B = 1/7 is compared with a previous study on a round-corner square cylinder with R/B = 1/6 in Fig. 14. The present result fits well with the literature (Cao and Tamura, 2017). Since a zero-velocity condition is applied at the cylinder surface, the direction of the flow attached to the cylinder can be identified from the positive/negative C f . ...

Shape modification effectively reduces the wind loading and wind-induced vibrations of slender structures. Large-eddy simulation is used to investigate the flow around multiple square-like cylinders at a Reynolds number of 22,000. Based on a standard square cylinder, six square-like cylinders are simulated with sharp/rounded corners and straight/concave/convex sides. The combination of rounded corners and convex sides enables the best aerodynamic performance. Furthermore, a parametric study on the round-convex cylinder is conducted considering a fixed corner radius and various side curvatures B/K (B: nominal side length; K: side radius). The results show that both the aerodynamic characteristics of and the flow features around the cylinder change considerably with varying B/K and that three distinct flow regimes are observed. In Stage I (0 ≤ B/K ≤ 0.71), the flow separates at the front corners, and the aerodynamic forces decrease gradually. In Stage II (0.71 < B/K < 1.00), the shear layer separating at the front corner-side region reattaches to the lateral sides. The fluctuating coefficients rise at B/K = 0.74; thereafter, the aerodynamic forces drop and are minimized at B/K = 1.00. In Stage III (1.00 ≤ B/K ≤ 1.77), flow separates at the lateral sides, and the aerodynamic forces recover gradually.

... Sen and Mittal 23 numerically studied the FIV of a square cylinder at low Reynolds numbers (Re = 60-250) and found out that both VIV and galloping occur at the considered Re (where Re = UD/ν, where U is the velocity of the flow, D is the characteristic length, and ν is the kinetic viscosity of the fluid). Miran and Sohn, 24 Cao and Tamura, 25 and Zhao and Zhao 26 studied the FIV of square cylinders with rounded corners and discovered that galloping is fully suppressed when the radius of the rounded corners is over 0.1. Zhao 27 studied the effect of the side ratios (R, the ratio of height to width) of rectangular cylinders on the FIV responses at Re = 200 and concluded that the maximum amplitude of VIV and the critical reduced velocity of galloping decrease with an increase in R. Missai et al. 28 conducted similar experimental investigations on the FIV of rectangular cylinders with R ranging from 0.67 to 1.5. ...

A numerical study of the effect of the mass ratio (M*) on the flow-induced vibration of a trapezoidal cylinder at low Reynolds numbers (Re = 60–250) is presented. The response characteristics are divided into three classes with varying mass ratios (2, 5, 10, 20, 30, 50, and 100): (1) class I for low mass ratios (M* = 2), (2) class II for medium mass ratios (5 ≤ M* < 30), and (3) class III for high mass ratios (M* ≥ 30). In class I, for the vortex-induced vibration (VIV) regime, only one peak of maximum amplitude is observed at low Re (∼70). For the galloping regime, a double rise-up for amplitudes is observed, and the mean transverse displacements become positive at higher Re and increase rapidly. In class II, the double rise-up for amplitudes appears at both the VIV and galloping regimes, and the double lock-in is also found for oscillation frequency ratios. In class III, the double rise-up disappears in the VIV and galloping regimes at all considered Re. The onset Re of the galloping regime is much higher (Re > 200), and the peak amplitudes and ranges of lock-in in VIV become much smaller with an increase in M*. Among these three classes, similar distinctions are also observed in the hydrodynamic forces. In terms of X–Y trajectories, three types are found in class I, while there are only two and one in classes II and III, respectively. Wake structures are also investigated for these classes.