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Two-dimensional (2-D) and three-dimensional (3-D) direct numerical simulations are conducted for flow past rectangular cylinders with various cross-sectional aspect ratios. The primary focuses are the interactions between the 2-D wake transitions in the spanwise vortex street (with distance downstream) and the 3-D wake transitions in the streamwise vortices, and the influence of both 2-D and 3-D wake transitions on the hydrodynamic forces on the cylinder. The 2-D wake transitions generally move upstream with increasing Reynolds number and decreasing aspect ratio. The corresponding reasons are explained. The 2-D wake transitions emerging close to the cylinder may directly alter the hydrodynamic forces on the cylinder, e.g. the Strouhal number, time-averaged drag coefficient and root-mean-square lift coefficient. By using specifically designed numerical cases to decompose the effects of the two 2-D transitions, it is found that the first 2-D transition from the primary to the two-layered vortex street results in reductions in the hydrodynamic forces, while the second 2-D transition to the secondary vortex street results in increases in the forces. The reduction/increase in the hydrodynamic forces becomes more significant when the transition location moves closer to the cylinder. The physical mechanisms for the influence on the hydrodynamic forces are elucidated. The upstream movement of the 2-D wake transitions also induces complex interactions between the 2-D and 3-D wake transitions (which also depends on the type of the 3-D mode). Correspondingly, the 3-D hydrodynamic forces may be governed by both 2-D and 3-D wake transitions (and their mutual influence). [ABSTRACT FROM AUTHOR]

This paper presents a new flow control approach to suppress the vortex shedding in the wake of a circular cylinder through high-frequency oscillation. The circular cylinder is forced to oscillate in the streamwise direction at high-frequency and low amplitude, corresponding to a high Stokes number (β = 100–1000) and low Keulegan–Carpenter number (KC = 0.001–4). Two-dimensional (2-D) and three-dimensional (3-D) direct numerical simulations of an oscillating circular cylinder in steady current have been carried out in the parameter space of KC, Rec, and β. Our numerical results show that when the flow remains in the two-dimensional vortex shedding regime, the cylinder wake sequentially experiences transitions from the vortex shedding regime to the suppression of the vortex shedding regime and finally to the symmetry breaking regime, with increasing KC. Corresponding wake characteristics and variations of hydrodynamic forces over the three wake regimes are explored. Three quantities that represent shear-layer characteristics, including the length of separating shear layers, the circulation of shear layers and wake recirculation length, reach maxima at the onset of suppression. The physical mechanisms for the suppression of vortex shedding and occurrence of symmetry breaking are also explained. Once the flow becomes 3-D, vortex shedding from the cylinder cannot be suppressed, primarily because the outer shear layers induced by the steady approaching flow are enhanced in 3-D flows. The cylinder oscillation over the frequency range investigated in the present study delays wake transition to 3-D. The cylinder oscillation alters the 3-D vortical structure and its spanwise wavelength significantly. [ABSTRACT FROM AUTHOR]

The turbulent kinetic energy and energy dissipation rate in the wake of a circular cylinder are examined at a Reynolds number of 1000. The turbulence characteristics are quantified using direct numerical simulation, which provides a comprehensive dataset that is almost impossible to acquire from physical experiments. The energy dissipation rate is decomposed into the components due to the mean flow, the coherent primary vortices and the remainder. It is found that the remainder component, which develops only in a three-dimensional turbulent wake and resides mainly in the regions of vortices, accounts for 95 % and 97 % of the total dissipation rate for 10 and 20 cylinder diameters downstream of the cylinder, respectively (while the remainder accounts for 62 % and 83 % of the total turbulent kinetic energy). Based on the remainder component, the validity of local isotropy, local axisymmetry, local homogeneity and homogeneity in the y–z plane for the turbulent dissipation in the wake is examined. The analysis reveals that the turbulent dissipation is largely locally homogeneous, but not locally isotropic or axisymmetric, even after the annihilation of the primary vortex street. In addition, the performances of the four corresponding surrogates to the true dissipation rate are evaluated. Owing to the general validity of local homogeneity, the surrogates of local homogeneity and homogeneity in the y–z plane perform well. Although local axisymmetry does not hold, the corresponding surrogate performs well, because errors from different terms largely cancel out. However, the surrogate of local isotropy generally underestimates the true dissipation rate. [ABSTRACT FROM AUTHOR]

The effects of yaw angle on wake characteristics of a stationary square cylinder were investigated in terms of the hydrodynamic forces, the vortex shedding frequency, and the vortical structures using direct numerical simulations (DNS) at a Reynolds number of 1000. In total, four yaw angles, namely, α = 0°, 15°, 30°, and 45°, were considered. The three-dimensional (3D) Navier–Stokes equations were solved directly using the finite volume method in OpenFOAM. It was found that the first-order statistics of the drag coefficient and the Strouhal number satisfied the independence principle (IP) closely. However, the second-order statistics of the drag and lift coefficients deviated apparently from the IP for α ≥ 25°. The iso-surfaces of the spanwise vorticity gradually disorganized and the magnitudes of the spanwise vorticity contour decreased as the yaw angle α was increased from 0° to 45°. By contrast, the streamwise vorticity iso-surfaces were found to become more organized and the magnitudes of the spanwise velocity contour became larger as a result of the increase in yaw angle, indicating the impairment of the quasi-two-dimensionality and the enhancement of the three-dimensionality of the wake flow. Extensive comparisons were also made with previous DNS results for a yawed circular cylinder, and both similarities and differences between these two kinds of cylinder wakes are discussed. [ABSTRACT FROM AUTHOR]

Three-dimensional (3-D) wake transition for flow past a diamond cylinder is investigated numerically. Detailed 3-D direct numerical simulations (DNS) show that the wake is represented by mode A with global vortex dislocations for Reynolds numbers Re = 121–150, followed by a mode swapping between modes A and B for Re = 160–210 and increasingly disordered mode B for Re ≥ 220. In the mode swapping regime, different characteristics of the dislocation and non-dislocation periods are revealed by decomposing flow properties (e.g. the root-mean-square lift coefficient) into the values corresponding to the dislocation and non-dislocation periods. Such decomposition helps to explain some major differences observed for the cases of a diamond and a circular cylinder. In addition to DNS, Floquet stability analyses are conducted to identify the 3-D wake instability modes of a diamond cylinder up to Re = 300. Phase-averaged base flow is used to eliminate the quantitative uncertainties induced by the aperiodic secondary vortex street of the base flow. Interestingly, a subharmonic instability mode is identified at Re ≥ 285, whereas mode B is absent. The origin of the subharmonic mode is explained. The disagreement between the DNS and the Floquet analysis regarding the existence of mode B and the subharmonic mode is also explained. It is found that the natural 3-D flow involves complex interactions between the streamwise and spanwise vortices, as well as between the 3-D wake transition and the two-dimensional base-flow transition, which excite mode B and suppress the subharmonic mode. [ABSTRACT FROM AUTHOR]

The benchmarking case of flow past a circular cylinder at the Reynolds number (Re) of 3900 is computed with two open-source codes, OpenFOAM and Nektar++, which are based on the conventional finite volume method (FVM) and the high-order spectral/hp element method, respectively. By using the Nektar++ model, mesh convergence for the case Re = 3900 is demonstrated (perhaps for the first time) through a systematic mesh dependence study, which includes separate examinations of the spanwise domain length (Lz/D), spanwise resolution, and the resolution in the plane perpendicular to the spanwise direction. The computational efficiencies for the Nektar++ and OpenFOAM approaches are then compared. This benchmarking study adds value to the broad Nektar++ and OpenFOAM communities and to the numerical modeling of bluff-body flows in general. Based on the Nektar++ approach, the computations are then generalized to a range of Re = 400–3900. It is found that Lz/D = 3 is adequate for Re = 2500–3900, while an increased Lz/D = 6 is recommended for Re = 400–2000. Based on the present high-fidelity numerical data, the physical mechanisms for the variations in the wake recirculation length and the hydrodynamic forces and pressure on the cylinder with Re are explored. In particular, the physics behind the inverse correlation between the root mean square lift coefficient (CL′) and the wake recirculation length, which includes a significant decrease in CL′ over Re = 270–1500, is highlighted. [ABSTRACT FROM AUTHOR]

Flow (of a Newtonian and incompressible fluid) separation around a square cylinder for Reynolds numbers (Re) in the range of 10–400 is investigated through direct numerical simulations. In contrast to the general belief that for a square cylinder, the flow would always separate at the leading and/or trailing edges of the cylinder, this study shows that the flow (both time-averaged and instantaneous) may not separate at the sharp corners for a certain range of moderate Re values. Instead, separation emerges at approximately a quarter of the cylinder length downstream of the leading edge at critical Re values of 100.36 and 96 for the time-averaged and instantaneous flows, respectively. With the increase in Re, the time-averaged separation location gradually moves toward the leading edge, while its instantaneous variation range reduces. The evolution of the separation pattern with Re is categorized with a fine Re resolution of 1. A critical point is identified at Re = 156 (for the time-averaged flow), where a saddle point emerges away from the upper/lower surface of the cylinder to give rise to wake flow entrainment to the upper/lower side of the cylinder. The rate of the entrained flow is governed by the location of the saddle point. The flow three-dimensionality occurring at Re > 165.7 affects the location of the saddle point but has almost no influence on the location of the separation point. The corresponding physical mechanism is explained. [ABSTRACT FROM AUTHOR]

The evolution of Mode C wake characteristics with the Reynolds number (Re) for Re up to 400 is investigated numerically. The Mode C wake instability is generated by placing a small wire in the near wake of a main circular cylinder. This setup ensures that the wake is unstable to Mode C only (without potential mode interactions), as demonstrated by Floquet stability analysis. Based on three-dimensional direct numerical simulations, three evolution regimes are identified for the fully developed Mode C flow. In the uniform periodic regime (Re = 166.4–210), the Mode C structure is uniformly distributed along the spanwise direction. The flow structure is 2T-periodic (T being the vortex shedding period) but retains a spatiotemporal symmetry every 1T. In the nonuniform periodic regime (Re = 220–230), the slightly nonuniform Mode C structure remains 2T-periodic at Re = 220 but undergoes a period quadrupling to 4T-periodic at Re = 230 before transitioning to chaos. In the chaotic regime (Re ≥ 240), the flow loses periodicity and becomes increasingly chaotic with increasing Re. The progressive wake transition to chaos is found to originate from the instability in the braid shear layer region through the uneven growth in strength and the consequent nonuniformity of the Mode C streamwise vortices. The wake transitions to chaos through the routes of Mode C and Mode B (for an isolated circular/square cylinder) are compared. [ABSTRACT FROM AUTHOR]

Instabilities and flow characteristics in the far wake of a circular cylinder are examined through direct numerical simulations. The transitions to the two-layered and secondary vortex streets are quantified by a new method based on the time-averaged transverse velocity field. Two processes for the transition to the secondary vortex street are observed: (i) the merging of two same-sign vortices over a range of low Reynolds numbers (Re) between 200 and 300, and (ii) the pairing of two opposite-sign vortices, followed by the merging of the paired vortices into subsequent vortices, over a range of Re between 400 and 1000. Single vortices may be generated between the merging cycles due to mismatch of the vortices. The irregular merging process results in flow irregularity and an additional frequency signal ƒ2 (in addition to the primary vortex shedding frequency ƒ1) in the two-layered and secondary vortex streets. In particular, a gradual energy transfer from ƒ1 to ƒ2 with distance downstream is observed in the two-layered vortex street prior to the merging. The frequency spectra of ƒ2 are broad-band for Re = 200 –300 but become increasingly sharp-peaked with increasing Re because the vortex merging process becomes increasingly regular. The ratio of the sharp-peaked frequencies ƒ2 and ƒ1 is equal to the ratio of the numbers of vortices observed after and before the merging. The general conclusions drawn from a circular cylinder are expected to be applicable to other bluff bodies. [ABSTRACT FROM AUTHOR]

• Both hydrodynamic instability and vortex merging are possible formation mechanisms for the secondary vortices. • The formation mechanisms are mapped out over a parameter space of Reynolds number (Re) and aspect ratio (AR). • By increasing Re and decreasing AR , the formation mechanism changes from hydrodynamic instability to vortex merging. • By increasing free-stream perturbation amplitude, the formation mechanism may change at a decreased Re. The transition from the primary (Kármán) and two-layered vortex streets to a secondary vortex street in the relatively far wake of a rectangular cylinder is examined through direct numerical simulations. The parameter space spans a range of the cross-sectional aspect ratios (AR ; the ratio between the streamwise and transverse lengths) of the cylinder between 0.01 and 0.5, and a range of the Reynolds numbers (Re) between 50 and 200. Unlike some previous studies which attributed the formation of the secondary vortices to either hydrodynamic instability of the mean flow or vortex merging, the present study shows that both mechanisms exist. Over the (AR , Re) parameter space, the two formation mechanisms are mapped out. For relatively small Re and relatively large AR , the secondary vortices emerge at the streamwise locations downstream of the annihilation of the two-layered vortices, such that the secondary vortices cannot be formed from the merging of the two-layered vortices and are thus formed from the hydrodynamic instability of the two bare shear layers. In contrast, for relatively large Re and relatively small AR , the secondary vortices emerge at the streamwise locations where the two-layered vortices still exist, such that the secondary vortices are formed from the merging of the two-layered vortices. In addition, the influence of free-stream perturbation on the formation mechanism is examined. An increase in the perturbation amplitude may result in a decreased critical Re for the change in the formation mechanism. The general conclusions are expected to be applicable to other bluff-body flows. [ABSTRACT FROM AUTHOR]