Vortex Dislocations Research Articles

Large eddy simulation of turbulent wake from dual-step cylinders

Numerical computations of the three-dimensional flow past dual-step cylinders using large eddy simulations are performed. The Reynolds number based on the diameter of the large cylinder, ReD, is fixed at 2000. The diameter ratio between the two cylinders is kept constant in all computations, i.e., D/d=2, where d is the diameter of the small cylinder. Investigations are carried out at different aspect ratios (ARs), defined as the ratio between the length of the large cylinder and its diameter L/D=0.2,0.5,1.0,1.5. Vortex dislocation phenomenon is observed in all the cases near the step discontinuity. The higher AR cases, L/D=1.0,1.5, exhibit similar trends with regard to wake dynamics, while they are quite different in the lower AR cases, L/D=0.2,0.5. Kelvin–Helmholtz instability is present in the wake of the dual-step cylinder with higher AR. Stable in-phase shedding and downwash characterize the wake of higher AR configurations, while oblique shedding (and flipping) is the key feature in the lower AR counterparts. Unique features are observed in the L/D=1.0 configuration that marks the transition between shedding modes.

Wake Three-Dimensionality of Profiled Blunt Trailing Edge Bodies with Varying Chord Length

This paper investigates experimentally the structure of turbulent blunt trailing edge body wakes with varying boundary-layer thicknesses controlled through the freestream velocity and the chord length. The intrinsic effect of transition to turbulence on the vortex-shedding frequency, strength, and its three-dimensional structure is explored. At large-scales, the vortex shedding is characterized by significant phase variations along the span, which vary stochastically and are punctuated by vortex dislocations when the phase differences grow large. These features of the vortex shedding are quantitatively examined in a streamwise–spanwise plane of the wake with particle image velocimetry. When the point of transition shifts upstream due to an increasing Reynolds number, greater phase variations in the vortex shedding along the span and more frequent dislocation events are produced. These changes are linked to the spanwise correlation of the streamwise velocity in the wake. In the turbulent boundary-layer regime, it is found that the phase drift does not change significantly. The decline in the spanwise correlation with increasing boundary-layer thickness in this regime is instead linked to the relative strength of the vortex shedding compared to the random turbulent fluctuations in the wake.

Dynamics and Wake Interference Mechanism of Long Flexible Circular Cylinders in Side-by-Side Arrangements

The vortex-induced vibrations of two side-by-side flexible cylinders in a uniform flow were studied using a three-dimensional direct numerical simulation at Reynolds number Re = 350 with an aspect ratio of 100, and a center-to-center spacing ratio of 2.5. A mixture of standing-traveling wave pattern was induced in the in-line (IL) vibration, while the cross-flow (CF) vibration displayed a standing-wave characteristic. The ninth vibration mode prominently occurred in both IL and CF directions, along with competition between multiple modes. Proximity effects from the neighboring cylinder caused the primary frequency to be consistent between IL and CF vibrations for each cylinder, deviating from the IL to CF ratio of 2:1 in isolated cylinder conditions. Repulsive mean lift coefficients were observed in both stationary and vibrating conditions for the two cylinders due to asymmetrical vortex shedding in this small gap. Comparatively, lift and drag coefficients were notably increased in the vibrating condition, albeit with a lower vortex shedding frequency. Positive energy transfer was predominantly excited along the span via vortex shedding from the cylinder itself and the neighboring one, leading to increasing lower-mode vibration amplitudes. The flip-flopping (FF) wake pattern was excited in the stationary and vibrating cylinders, causing spanwise vortex dislocations and wake transition over time, with the FF pattern being more regular in the stationary cylinder case.

Spanwise phase transition between pure modes A and B in a circular cylinder’s wake. Part II: spatiotemporal evolution of vorticity

Through direct numerical simulation, the transition from pure mode A to mode B in the near wake of a circular cylinder is studied without consideration of vortex dislocations. The Reynolds number is calculated from 100 to 330 with a computational spanwise length of 4 diameters. In the present section, the spatiotemporal evolution of the vorticity and its sign are analyzed. The results show that mode B, as a kind of weak disturbed vorticity with opposite signs, actually appears partially on the rear surface of the cylinder and in the shear layers once Re exceeds 193. With increasing , the vortex-shedding patterns in the near wake undergo the initial generation stage of mode B coupling with the fully developed pure mode A (), the mode swapping or coexistence stage between modes A and B (), the self-adjustment stage of the nondimensional spanwise wavelength from 0.8 to 1 in dominant mode B (), and the full development stage of mode B (). In particular, the spanwise phase transition initially occurs at a certain spanwise position in the initial generation stage where a part of mode A and a part of mode B with specific vorticity signs appear, e.g. the vortex in mode A and the vortex in mode B, in which and vortices are vortices with three vorticity components satisfying the vorticity sign law and shed from the upper and lower shear layers, respectively.

How vortex dynamics affects the structural load in step cylinder flow

The vortex dynamics and the structural load in a step cylinder (consisting of a small, d, and a large, D, cylinder) flow are investigated numerically at Reynolds number ( $Re_D$ ) 150 for diameter ratios $D/d=2.0, 2.4$ and 2.8. First, the formation mechanism of a non-uniform oblique vortex shedding (the vortex shedding frequency remains unchanged as the oblique shedding angle varies) behind the small cylinder is explained: an increase in the production rate of the vortex strength and a farther downstream movement of the vortex formation position occur simultaneously as the vicinity of the step is approached along the small cylinder. Second, the structural load (the drag and lift) along the step cylinder is investigated, where four local extremes (two local minima and two local maxima) are observed. An in-depth investigation of the vortex dislocation effects on the structural load is provided, showing that the decreased circulation in the near wake and the weakened staggered Kármán vortex shedding pattern cause a major reduction (90 %) of the sectional lift amplitude and a relatively modest reduction (5.7 %) of the sectional drag amplitude, compared with the corresponding sectional force when no vortex dislocation occurs. This new knowledge combined with the three-dimensional effect of the step cylinder wake (caused by the blending of the small and larger cylinder wakes around the step) explain the formation of the four local extremes and the distribution of the structural load between them. Finally, it is found that the increasing $D/d$ amplifies the structural load variation along the step cylinder.

Coexistence of natural and forced vortex dislocations in step cylinder flow

The wake behind a step cylinder [consisting of a small diameter cylinder (d) and a large diameter cylinder (D)] with diameter ratio D/d=2 at Reynolds number ReD = 200 (the mode A* regime) is simulated by direct numerical simulations. New detailed information of the interaction between natural vortex dislocations and forced vortex dislocations is described. In the large cylinder wake, the forced and natural vortex dislocations coexist. The regular formation of forced vortex dislocation is found to be delayed under the effect of natural vortex dislocations. The occurrence of natural vortex dislocations is suppressed in the large cylinder wake close to the small cylinder. Moreover, the effect of vortex dislocations on structural loads is described. The results of this paper provide a more thorough understanding of the formation and interaction between the natural and forced vortex dislocations.

Phase transition between pure modes A and B in a circular cylinder’s wake. Part I: analysis of fluid forces

Through direct numerical simulations, the transition from pure mode A to mode B in the near wake of a circular cylinder is studied with no effect of vortex dislocations. The Reynolds number is computed from 100 to 330 with the computational spanwise length of 4 diameters. In the present part, fluid forces are analyzed. The results show that mode swapping still exists in the range of Reynolds numbers from 230 to 240. In this range, fluid forces with low and high levels occur intermittently. Moreover, when the critical Reynolds number of 193 (0.5) is exceeded, with the increase of the Reynolds number, the vortex-shedding frequency gradually shifts from a single low frequency, high and low frequency coexistence to a single high frequency.

Three-dimensional numerical simulation of flow past a rotating step cylinder

Flow past a rotating step cylinder is investigated through three-dimensional numerical simulations for a diameter ratio of 0.5 and a Reynolds number of 150. The step cylinder comprises two cylinders with different diameters arranged coaxially with a step between them. The rotation rate α is defined as the ratio of the rotation speed of the larger cylinder surface to the free-stream velocity. Vortex shedding happens for both cylinders at α = 0, 0.5 and 1, and is suppressed only for the larger cylinder at α = 2 and 3 and fully suppressed for both cylinders at α = 4. The vortex shedding suppression for the larger cylinder or for both cylinders has significant effects on the wake. The S-, N- and L-cells at α = 0 are in good agreement with those reported in previous studies and still exist at α = 1. The N-cell disappears at α = 0.5, and as a result, the L- and S-cells interact with each other directly at the step position. An additional cellular zone is found at α = 0.5 and 1 and this zone has multiple cells with vortex dislocation between them. At α = 2 and 3, there is a strong hub vortex in the streamwise direction behind the step and the vortices in the wake of the smaller cylinder form helical vortices after they roll around this hub vortex. The hub vortex is generated by the difference between the Magnus effect between the smaller and larger cylinders. At α = 4, the hub vortex still exists but the helical vortices disappear because vortex shedding is suppressed for both cylinders. At this rotation rate, the pressure on the cylinder surface oscillates with a frequency much higher than the vortex shedding frequency. The oscillation of the pressure is caused by the combination of periodic generation of ring vortices and their motion along the span of the larger cylinder.

Three-dimensional study of flow past blunt headed cylinder at low Reynolds numbers

In this paper, a numerical model is proposed to study the transition to three-dimensionality and the evolution of vortices in the wake of a blunt-headed cylinder considering air as the working fluid in the Reynolds number (Re) range 130–2000. An experimental setup is developed to validate the numerical model on the basis of heat transfer characteristics. Based on symmetry and time dependence characteristics of flow, it is categorized as dynamically steady symmetric flow (50 ≤ Re ≤ 200), dynamically steady unsymmetric flow (220 ≤ Re ≤ 270) and unsteady flow (Re ≥ 280). The vortex dislocation phenomenon showing intermittent low frequency pulsations during the transition to three-dimensionality is studied. Aerodynamic characteristics are studied by computing force coefficients and Strouhal number (St). Brief overview of heat transfer characteristics is given. Dynamic mode decomposition (DMD) analysis is carried out to determine quantitatively the critical Re at which secondary instability occurs and hence clear demarcation of the Re regime is obtained for the validity of two-dimensional analysis of blunt headed cylinder.

End boundary effects on wakes dynamics of inclined circular cylinders

We perform direct numerical simulations to characterize the three-dimensional wake dynamics of long inclined circular cylinders with inhomogeneous end boundary conditions. Three Reynolds numbers, Re=100, 200 and 300, corresponding to the regimes of laminar flow, mode A* wake, and mode B wake, respectively, are considered to reveal the roles of the intrinsic secondary instabilities and the extrinsic end boundary effects in shaping the three-dimensional flows. At Re=100, the end boundary effects are felt over the entire cylinder span by inducing oblique vortex shedding, which is associated with stronger spanwise flow in the wake than a parallel shedding. The Strouhal number of the oblique shedding is related to that of the parallel shedding of straight cylinder by the cosine law, considering the combined inclination angle and oblique angle. At Re=200, the intrinsic secondary instability results in large-scale vortex dislocation, precluding the propagation of the end boundary effects towards further span. Nevertheless, for the inclined cases, oblique shedding is still observed within limited span from the upstream end boundary. The oblique vortices feature intact and straight vortex cores, and are related to the two-dimensional flow at Re=200 (that are void of vortex dislocations) from the viewpoint of cosine law. Further along the span, the oblique vortices destabilizes with the formation of small-scale vortices, and the flow transitions to the typical mode A* wake. At Re=300, the highly three-dimensional flow near the end boundary creates disturbances that travel along the cylinder span, creating vortex dislocations for cases with low inclination angles. For high inclination angle, oblique vortex shedding is again observed over the cylinder span, and is not disrupted by vortex dislocations of either intrinsic or extrinsic causes. The present study offers renewed insights into the three-dimensional wake dynamics of inclined cylinders, and lays the foundation for the designs of long flexible engineering structures and related flow control techniques.

Three-dimensional wake transition for CO2 flow at supercritical pressure over single heated cylinder

The three-dimensional wake transition for supercritical CO2 (SCO2) with Reynolds number (Re) ranging from 100 to 300 is systematically investigated by large eddy simulation. Numerical results of the constant-property fluid are validated with the classical conclusions. The secondary instabilities, i.e., mode A (spanwise scale of ∼4.5 times cylinder diameter) and mode B (approximately equal to cylinder diameter), are well captured in the wake. The results at Re = 120 show that the evolution of vortex dislocations is mainly manifested in the alternating occurrence of three stages, i.e., the two-dimensional vortex shedding stage, pure mode A stage, and dislocation stage. The stable state of pure mode A is found at Re = 140. As Re continues to increase, the wake shows a gradual transition from mode A to mode B, rather than the transition from mode A* (mode A + dislocation) to mode B. The frequency spectrum in this process is the gradual shift of a single peak from the low frequency to the high frequency. The wake cycle sequence changes from the alternation of four structures at Re = 155 to the alternation of pure and “contaminated” mode B structures at Re = 170. The critical condition of wake “resonance” is determined at Re = 175, where the final state of the wake is relatively ordered mode B structure, representing the weakest three-dimensionality in the transition regime. After that, the three-dimensionality of the wake enhances with Re, and the probability of the occurrence of disordered structures increases accordingly. The vortex shedding frequency of the pure mode follows the order: 2D > B > A > A*. The width of the frequency spectrum is mainly related to whether the wake flow state is a continuous single mode or the alternation of multiple modes. Based on the Strouhal–Reynolds number relationship, flow pattern in the wake transition process is finally discussed.

Vortex Dislocation In The Near Wake Of A Cylinder With Span-Wise Variations In Diameter

We examined the evolution of three-dimensional vortex shedding patterns induced by spanwise variations of the cylinder diameter. Two distinct types of shedding patterns have identified through flow visualization: continuous (in-phase) oblique shedding where vortices shed with lower frequency stay attached to the vortices with higher frequency without any discontinuity or splitting and discontinuous (out-of-phase) shedding where the lower frequency vortices have no attachment to higher frequency vortices and vortex dislocation occurs. The dislocation seen in the flow is strongly influenced by the span wise irregularities. We observed a clear and strong in-phase spanwise vortex shedding for the three smooth cylinder configurations tested in the study. The tapered, bumps and steps configurations showed sections of strong coherent spanwise vortex shedding, and we identified hardly any coherent structures for the rib, sinusoidal, and helical configurations. Depending on the geometry and number of span wise irregularities, incoherent structures make difficult to determine the occurrence and location of vortex dislocations in the cylinder wake without a method that enables a reduction in the complexity. Here, we introduce a numerical approach that obtains the dominant structures of vortex shedding patterns by reducing the complexity in noisy data. The method maps the variations in the oblique shedding angle over time and provide quantitative conclusions on the intermittent occurrence and location of vortex dislocations in the 15000 snapshots taken for each of the different cylinder geometries regardless of turbulence.

Laminar forced convection heat transfer around wavy elliptic cylinders with different aspect ratios

The present study investigates the forced convection heat transfer around the wavy elliptic cylinders by considering wide range of wavelength (λ) for different aspect ratios (AR). The wake thermal structures were classified into four modes of the quasi-2D unsteady, quasi-2D steady, complex 3D unsteady and 3D steady structures, which is mapped in AR-λ plane. The short wavelengths formed the quasi-2D thermal structure for both steady and unsteady forced convections. The quasi-2D unsteady structure is characterized by the spanwise nearly invariant isothermal structures and the periodical time evolution of the Nusselt number. The long wavelengths formed the 3D thermal structure in the present range of AR. The complex 3D unsteady thermal structure is featured by the hole and spanwise separated formation of the temperature iso-surface owing to the vortex dislocation and hairpin vortex formation. The 3D steady thermal structure also appeared in the steady regime and the spanwise dependence of the thermal structure became considerable with decreasing AR. The surface distribution of the mean Nusselt number depended on the regime of the thermal structures. In the long wavelength region, the additional appearance of two types of the streamwise vorticities locally attenuated the heat transfer by weakening the reverse flow in the near wake. As the cylinder becomes more elliptic, the two types of the streamwise vorticities becomes weak and finally disappears, resulting in weakening the effect of the local attenuation of the heat transfer. Therefore, it can be concluded that the streamlined shape is predominant to the stabilization of the forced convection with decreasing AR, regardless of the wavelength .

Different topologies of natural vortex dislocations in Mode A wake

The mode A wake behind a circular cylinder at Reynolds number 200 was simulated by directly solving the three-dimensional Navier–Stokes equations. A more detailed investigation of different topologies of natural vortex dislocations in the mode A wake was systematically described. In addition to the two-side natural vortex dislocation defined by Williamson [J. Fluid Mech. 243, 393–441 (1992)], three new topologies of vortex dislocations were identified. Additionally, the formation process and the mechanism of these newly identified dislocation topologies were addressed. The results in this Letter provide a more thorough understanding of the natural vortex dislocations in the mode A wake.

On wake modulation and interaction features of a pair of dual-step circular cylinders in side-by-side arrangements

The proximity interference and the vortex dislocation are fundamental fluid dynamic features that determine a wake pattern of dual-step circular cylinders in a side-by-side arrangement. Each dual-step cylinder consists of two coaxial cylinders with different diameters. A complex wake modulation is expected due to an intrinsic interaction between the vortex shedding of the larger-diameter cylinder (LC) and the smaller-diameter cylinder (SC), and to the cross-wake interaction of side-by-side cylinders in a uniform flow. To understand the physics of fluid wake modulations, three-dimensional direct numerical simulations of the flow around a pair of dual-step circular cylinders in side-by-side arrangements are performed and investigated. Six simulation cases are presented with different combinations of diameter ratio (1.33–2.00), gap ratio (1.00–3.17), and the Reynolds number (60–200) in a laminar flow regime, providing key insights into the two distinct LC-dominated and SC-governing wake modulation characteristics. For the LC-dominated wake modulation, the wake pattern of side-by-side cylinders is determined by the predominant vortex dynamics in the LC wake. For the SC-governing wake modulation, the LC wake pattern becomes modulated and controlled by the SC wake through the connections of vortex tubes shed downstream of the two nonuniform cylinders. Owing to the proximity interference and vortex dislocation, these new evolutionary wake modulations result in distinct wake patterns, vortex structures, and associated hydrodynamic force features for the pair of side-by-side dual-step circular cylinders.

Three-dimensional numerical investigation on flow past two side-by-side curved cylinders

Three-dimensional numerical simulations of flow past two side-by-side convex curved cylinders are performed for various spacing ratios (1.25 ≤ L/D ≤ 5) and Reynolds numbers (100 ≤ Re ≤ 500). A comprehensive investigation of the effects of spacing ratio and Reynolds number on the wake flow features, pressure coefficients and axial flow velocity is conducted. Four flow patterns: a single bluff body pattern, biased flow pattern, coupling vortex shedding pattern and co-shedding pattern are identified for the vertical straight sections. The flows along the curved sections of two cylinders are classified into five flow regimes: normal shedding, vortex dislocation, oblique shedding, non-shedding and instability of shear layer regimes. It is revealed that at L/D = 1.5, the switchover of the gap flow deflection along the curved spans leads to the oblique vortex shedding pattern for Re = 100 and 300. The Reynolds stress intensity, vortex strength, and the mean pressure coefficient are found to be reduced significantly from the vertical to the horizontal sections of the cylinders. With the increase of the spacing ratio, the axial flow velocity increases along the curved span of two cylinder, whereas the absolute value of base coefficient decreases.

Flow past a circular cylinder and a downstream sphere for Re < 300

Abstract

Insights into low Reynolds flow past finite curved cylinders

Spectral proper orthogonal decomposition (SPOD) is applied to experimental digital visualizations to scrutinize the properties of the wake flow behind curved cylinders. This technique has been applied to the image data of Shang et al. [“Flow past finite cylinders of constant curvature,” J. Fluid Mech. 837, 896–915 (2018)] to emphasize the main features of the flow and to extract the most energetically and dynamically relevant space-time coherent structures. The study considers different Reynolds numbers and angles of curvature for two cylinder aspect ratios. It is first shown that the SPOD structures reproduce the base flow topology of the digital visualizations, confirming the presence of a single oblique shedding regime for a low aspect ratio and both normal and oblique regimes for a high aspect ratio. The appearance of the instabilities typical of straight cylinders, usually referred to as type-A and -B in literature, is identified as well. As principal results obtained for curved cylinders, increasing the Reynolds number the analysis of SPOD spectra has revealed two reductions in the oscillation frequency of the leading coherent structures, attributed to the occurrence of type-A instability when the wake is still laminar, and to the development of a one-sided vortex dislocation in turbulent regime. The study has also highlighted the gradual transfer of energy between flow structures during the transition from type-A to type-B instabilities, accompanied by high-frequency scales excitement. Some peculiar aspects of SPOD field reconstruction are outlined here, which are suggested by the physical characteristics of the flow.

Second magnetization peak, rhombic-to-square Bragg vortex glass transition, and intersecting magnetic hysteresis curves in overdoped BaFe2(As1\u2212xPx)2 single crystals

The second magnetization peak (SMP) in the fourfold symmetric superconducting single crystals (such as iron pnictides and tetragonal cuprates) has been attributed to the rhombic-to-square transition (RST) of the quasi-ordered vortex solid (the Bragg vortex glass, BVG). This represents an alternative to the pinning-induced BVG disordering as the actual SMP mechanism. The analysis of the magnetic response of BaFe2(As1−xPx)2 specimens presented here shows that the SMP is not generated by the RST. However, the latter can affect the pinning-dependent SMP onset field if this is close to the (intrinsic) RST line, through the occurrence of a “shoulder” on the magnetic hysteresis curves m(H), and a maximum in the temperature variation of the DC critical current density. These features disappear in AC conditions, where the vortex system is dynamically ordered in the RST domain, emphasizing the essential role of vortex dislocations for an efficient accommodation of the vortex system to the pinning landscape and the SMP development. The m(H) shoulder is associated with a precipitous pinning-induced proliferation of dislocations at the RST, where the BVG elastic “squash” modulus softens. The DC magnetization relaxation indicates that the pinning-induced vortex system disordering continues above the RST domain, as the basic SMP mechanism.

Diameter ratio effects in the wake flow of single step cylinders

Vortex interactions behind step cylinders with diameter ratio 2 ≤ D/d ≤ 3 at Reynolds number (ReD) 150 were investigated by directly solving the three-dimensional Navier–Stokes equations. In accordance with the previous paper [C. Tian et al., “Vortex dislocation mechanisms in the near wake of a step cylinder,” J. Fluid Mech. 891, A24 (2020)], some interesting characteristics of vortex dislocations, e.g., two phase difference accumulation mechanisms, the trigger and threshold values of vortex dislocations, antisymmetric vortex interactions, and long N-cell cycles, were observed. By performing a detailed investigation of diameter ratio effects, more features of vortex dynamics were discovered. In addition to the known antisymmetric vortex interactions, a symmetric vortex interaction between neighboring N-cell cycles was observed. The long-time observations revealed an interruption of these two types of vortex interactions. By using a well-validated phase tracking method, we monitored the time trace of the phase difference accumulation process in different D/d cases from which decreasing (known) and increasing (new) phase difference tendencies were identified. Both caused the interruption of continuous symmetric or antisymmetric phenomena but through two distinct mechanisms. Meanwhile, the diameter ratio effects on the trigger and threshold values were discussed. Additionally, the likelihood of antisymmetric or symmetric vortex interactions and increasing or decreasing phase difference tendencies was analyzed. Moreover, diameter ratio effects on shedding frequencies and the extensions of three main vortex cells, i.e., S-, N-, and L-cell vortices, were described.