On the frequency selection mechanism of the low-Re flow around rectangular cylinders

In the flow past elongated rectangular cylinders at moderate Reynolds numbers, vortices shedding from the leading- and trailing-edge corners are frequency locked by the impinging leading-edge vortex instability. The present work investigates how the chord-based Strouhal number varies with the aspect ratio of the cylinder at a Reynolds number (based on the cylinder thickness and the free-stream velocity) of $Re=400$ , i.e. when locking is strong. Several two-dimensional, nonlinear simulations are run for rectangular and D-shaped cylinders, with the aspect ratio ranging from $1$ to $11$ , and a global linear stability analysis of the flow is performed. The shedding frequency observed in the nonlinear simulations is predicted fairly well by the eigenfrequency of the leading eigenmode. The inspection of the structural sensitivity confirms the central role of the trailing-edge vortex shedding in the frequency locking, as already assumed by other authors. Surprisingly, however, the stepwise increase of the Strouhal number with the aspect ratio reported by several previous works is not fully reproduced. Indeed, with increasing aspect ratio, two distinct flow behaviours are observed, associated with two flow configurations where the interaction between the leading- and trailing-edge vortices is different. These two configurations are fully characterised, and the mechanism of selection of the flow configuration is discussed. Lastly, for aspect ratios close to the jump between two consecutive shedding modes, the Strouhal number is found to present hysteresis, implying the existence of multiple stable configurations. Continuing the lower shedding-mode branch by increasing the aspect ratio, we found that the periodic configuration loses stability via a Neimark–Sacker bifurcation leading to different Arnold tongues. This hysteresis can explain, at least partially, the significant scatter of existing experimental and numerical data.

Numerical Computations for Flow Patterns and Force Statistics of Three Rectangular Cylinders

In this work, numerical simulations are performed in order to study the effects of aspect ratio (AR) and Reynolds number (Re) on flow characteristics of three side-by-side rectangular cylinders for fixed spacing ratio ( g ), using the lattice Boltzmann method (LBM). The Reynolds number varies within the range 60 ≤ Re ≤ 180, aspect ratio is between 0.25 and 4, and spacing ratio is fixed at g = 1.5. The flow structure mechanism behind the cylinders is analyzed in terms of vorticity contour visualization, time-trace analysis of drag and lift coefficients, power spectrum analysis of lift coefficient and variations of mean drag coefficient, and Strouhal number. For different combinations of AR and Re, the flow is characterized into regular, irregular, and symmetric vortex shedding. In regular and symmetric vortex shedding the drag and lift coefficients vary smoothly while reverse trend occurs in irregular vortex shedding. At small AR, each cylinder experiences higher magnitude drag force as compared to intermediate and large aspect ratios. The vortex shedding frequency was found to be smaller at smaller AR and increased with increment in AR.

Linear stability of the steady flow past rectangular cylinders

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.

Interactions Between the Shear Layer Emanating From Rectangular Cylinders and the Near Wake Region

The interactions between the separated shear layer and the near wake region of rectangular cylinders of varying streamwise extents in a uniform flow are investigated using time resolved particle image velocimetry. The streamwise aspect ratios (AR) tested were 1 and 5, and the Reynolds number based on the oncoming flow velocity and cylinder height is 16200. The effects of varying AR on the mean flow, turbulent kinetic energy and Reynolds shear stresses are studied. Furthermore, the unsteady characteristics of the separation bubbles are examined in terms of frequency spectra analysis. The mean flow topology shows flow separation at the leading edge is not affected by the streamwise aspect ratios. However, the primary, secondary and wake vortexes show significant differences. Mean flow reattaches over the cylinder at 4.30 cylinder heights in the AR5 case while there is no mean reattachment in the AR1 case. The magnitudes of turbulent kinetic energy and Reynolds shear stress in the wake region are an order of magnitude higher in AR1 compared to AR5. Depending on the streamwise location, the vortex shedding motions in the near wake region reflect the dominant and second harmonic of the shear layer shedding frequency measured near the leading edge.