Unsteady RANS and detached-eddy simulations of flow around a circular cylinder in ground effect

Unsteady Reynolds-averaged Navier–Stokes (URANS) simulations and detached-eddy simulations (DES) were performed of flow around a circular cylinder placed near and parallel to a moving ground, on which substantially no boundary layer developed to interfere with the cylinder. The results were compared with experiments previously reported by the authors to examine how accurately the URANS and DES can predict the cessation of von Kármán-type vortex shedding and the attendant critical drag reduction of the cylinder in ground effect. The DES, which were performed in a three-dimensional domain with spanwise periodicity imposed, correctly captured the cessation of the vortex shedding, whereas both two- and three-dimensional URANS also predicted it but at a much smaller gap-to-diameter ratio compared with the experiments. The wake structures of the cylinder predicted by the DES were in good agreement with the experiments in both large- and small-gap regimes, and also in the intermediate-gap regime, where the DES captured the intermittence of the vortex shedding in the near-wake region. Based on the results obtained, further discussions are also given to the reason why the von Kármán-type vortices in the URANS solutions incorrectly ‘survived’ until the cylinder came much closer to the ground.     

FLOW PAST TWO CYLINDERS IN TANDEM: INSTANTANEOUS AND AVERAGED FLOW STRUCTURE

A technique of high-image-density particle image velocimetry is employed to characterize the instantaneous and averaged patterns of velocity, vorticity and Reynolds stress due to flow past two cylinders in tandem. These features of the flow patterns are characterized in the gap region as a function of the distance between the cylinders. In turn, they are related to the patterns in the near-wake of the two-cylinder system. Along the gap between the cylinders, small-scale concentrations of vorticity are formed in the separated shear layers. These concentrations buffet the surface boundary layer on the downstream cylinder, and thereby influence the eventual shedding of large-scale vortices. Within the gap, the instantaneous structure of the recirculation zones can exhibit both symmetrical and asymmetrical patterns. In the near-wake of the downstream cylinder, the form of the vortex shedding, as well as the averaged patterns of the flow structure, are substantially altered, relative to the case of a single cylinder. The width of the near-wake, as represented by averaged patterns of vorticity, is substantially narrower and the magnitudes of the peak Reynolds stress are significantly attenuated. On the other hand, if the gap region is sufficiently large such that Kármán-like vortices form between the cylinders, the near-wake of the downstream cylinder shows distinctive patterns, and both the wake width and the magnitude of the Reynolds stresses become larger, relative to those at smaller gap width.     

Simulation of the reduction of unsteadiness in a passively controlled transonic cavity flow

A 30 dB reduction of the peak pressure tone and a reduction by 6 dB of the background pressure found in an experiment of high-subsonic cavity flow controlled by a spanwise rod are retrieved numerically. The injection of deterministic upstream fluctuations in the large-eddy simulation (LES) domain is found to be of crucial importance, in contrast with the baseflow case. Reduction of the vortex impingement onto the aft edge of the cavity is confirmed, together with reduction of mass flow rate breathing through the grazing plane. Visual evidence of merging between the Kelvin–Helmholtz-type vortices shed downstream of the fore edge of the cavity and the von Kármán vortices shed behind the cylinder is provided. Shocklets downstream of the cylinder are also observed.     

Phenomenology of Kármán vortex streets in oscillatory flow

Vortex wakes of circular cylinders at low Reynolds numbers have been investigated. Sound waves are superimposed on the flow in mean flow direction. In this configuration the Kármán vortices are shed at the sound frequency or at subharmonics of the sound frequency. The Karman vortex street is treated as a nonlinear self-excited flow oscillator with forced oscillations. Using a flow visualization technique a variety of wake structures has been identified as a function of sound frequency and sound amplitude, but independent of the Reynolds number. The superimposed sound influences the distribution of circulation and accordingly the shedding mechanism. Primary vortex and secondary vortex are shed simultaneously from one side of the cylinder. The alternate vortex shedding is arranged spatially and temporally. Structures along the vortex axes are revealed.Parts of this paper have been presented at IUTAM Congress 1984, Lyngby, Denmark, and at ICNM Conference 1985, Shanghai, P. R. China     

Experimental investigation of a circular radially deforming cylinder near wake using an infrared technique

The present experimental study aims at developing a method to control the circular cylinder near wake by radial deformation and understand the underlying physics. Using an infra-red camera, we examine the temperature distribution of the near wake center line of a sinusoidal law radially deforming circular cylinder. From these measurements, the near wake is characterized by the length of the recirculation zone, the vortex formation zone length, the temperature fluctuation maximum intensity and the vortex street shedding frequency. For several deformations frequencies, we study the radial deformation influence on the near wake characteristics. It is noted that the wake structure is strongly affected by the deformation frequency. Among other things, we note the recirculation zone length reduction and the vortex formation zone length reduction when the radial vibrations are close to the “Lock-in” fundamental range. It is also noted that the variations of the vortex shedding frequency depend on the deformation frequency.     

Flow above the free end of a surface-mounted finite-height circular cylinder: A review

The wake of a surface-mounted finite-height circular cylinder and the associated vortex patterns are strongly dependent on the cylinder aspect ratio and the thickness of the boundary layer on the ground plane relative to the dimensions of the cylinder. Above a critical aspect ratio, the mean wake is characterized by streamwise tip vortex structures and Kármán vortex shedding from the sides of the cylinder. Below a critical aspect ratio, a unique mean wake structure is observed. Recent experimental studies in the literature that used phase-averaged techniques, as well as recent numerical simulations, have led to an improved physical understanding of the near-wake vortex flow patterns. However, the flow above the free end of the finite circular cylinder, and its relationship to the near wake, has not been systematically studied. The effects of aspect ratio and boundary layer thickness on the free-end flow field are also not completely understood, nor has the influence of Reynolds number on the free-end flow field been fully explored. Common features associated with the free end include separation from the leading edge, a mean recirculation zone containing a prominent cross-stream arch (or mushroom) vortex, and reattachment onto the free-surface. Other flow features that remain to be clarified include a separation bubble near the leading edge, one or two cross-stream vortices within this separation bubble, the origins of the streamwise tip or trailing vortices, and various critical points in the near-surface flow topology. This paper reviews the current understanding of the flow above the free end of a surface-mounted finite-height circular cylinder, with a focus on models of the flow field, surface oil flow visualization studies, pressure and heat flux distributions on the free-end surface, measurements of the local velocity field, and numerical simulations, found in the literature.     

虚拟边界法研究正交双圆柱及串列双圆球绕流

把Goldstein等人提出的虚拟边界法推广到三维情况,研究了 Re=150时不同间距下正交双圆柱绕流,和Re=250时不同间距下串列双 圆球绕流流场. 对于正交双圆柱绕流,当间距比大于3,下游圆柱对上游圆柱尾流的影响只 限定在下游圆柱的尾流所扫过的范围之内;当间距比小于等于3,下游圆柱对上游圆柱尾流 的影响扩大,下游圆柱尾流扫过区上下出现两排三维流向二次涡结构. 对于串列圆球绕流, 研究发现,在小间距比(L/D≈ 1.5)的情况下,由于上下游圆球尾流区的相互抑 制消除了压力不稳定性,整个流场呈现稳 态轴对称特征;间距比为2.0时,周向压力梯度诱发出流体的周向输运,流场呈现稳态非对 称性,但流场中存在特定的对称面;间距比增大到2.5后,绕流场开始周期振荡,原有的对 称面依旧存在;在间距比3.5时下游圆球下表面的涡结构强度有所减弱,导致占优频率发生 交替;间距比增至7.0时,整个流场恢复稳态特征,两圆球尾部同时出现双线涡,这时流场 对称面的位置发生了变动.     

Stability analysis of the onset of vortex shedding for wakes behind flat plates

Above a critical Reynolds number, wake flows behind flat plates become globally unstable, the leading modal instability in this case is known as Kelvin–Helmholtz mechanism. In this article, both local and BiGlobal linear instability analyses are performed numerically to study the onset of the shedding process. Flat plates with different base shapes are considered to assess geometry effects, and the relation between the critical shedding Reynolds number, \(Re_\mathrm{cr}\), and the boundary layer thickness is studied. Three types of base shapes are used: square, triangular and elliptic. It is found that the base shape has a great impact on the growth rate of least stable disturbance mode, thus would influence \(Re_\mathrm{cr}\) greatly, but it has little effect on the vortex shedding frequency. The shedding frequency is determined mainly by boundary layer thickness and has little dependence on the Reynolds number and base shape. We find that for a fixed Reynolds number, increasing boundary layer thickness acted in two ways to modify the global stability characteristics: It increases the length of the absolute unstable region and it makes the flow less locally absolutely unstable in the near-wake region, and these two effects work against each other to destabilize or stabilize the flow.     

Control of vortex shedding behind circular cylinder for flows at low Reynolds numbers

It has been observed by researchers in the past that vortex shedding behind circular cylinders can be altered, and in some cases suppressed, over a limited range of Reynolds numbers by proper placement of a second, much smaller, ‘control’ cylinder in the near wake of the main cylinder. Results are presented for numerical computations of some such situations. A stabilized finite element method is employed to solve the incompressible Navier–Stokes equations in the primitive variables formulation. At low Reynolds numbers, for certain relative positions of the main and control cylinder, the vortex shedding from the main cylinder is completely suppressed. Excellent agreement is observed between the present computations and experimental findings of other researchers. In an effort to explain the mechanism of control of vortex shedding, the streamwise variation of the pressure coefficient close to the shear layer of the main cylinder is compared for various cases, with and without the control cylinder. In the cases where the vortex shedding is suppressed, it is observed that the control cylinder provides a local favorable pressure gradient in the wake region, thereby stabilizing the shear layer locally. Copyright © 2001 John Wiley & Sons, Ltd.     

Flow past a sphere in density-stratified fluid

Stratified flow past a three-dimensional obstacle such as a sphere has been a long-lasting subject of geophysical, environmental and engineering fluid dynamics. In order to investigate the effect of the stratification on the near wake, in particular, the unsteady vortex formation behind a sphere, numerical simulations of stratified flows past a sphere are conducted. The time-dependent Navier–Stokes equations are solved using a three-dimensional finite element method and a modified explicit time integration scheme. Laminar flow regime is considered, and linear stratification of density is assumed under Boussinesq approximation. The effects of stratification is implemented by density transport without diffusion. The computed results include the characteristics of the near wake as well as the effects of stratification on the separation angle. Under increased stratification, the separation on the sphere is suppressed and the wake structure behind the sphere becomes planar, resembling that behind a vertical cylinder. With further increase in stratification, the wake becomes unsteady, and consists of planar vortex shedding similar to von Karman vortex streets.     

Experimental and high-order LES analysis of the flow in near-wall region of a square cylinder

A coupled experimental/numerical analysis of turbulent flow past a square cylinder is performed at the ERCOFTAC Reynolds number Re = U_∞D/ν = 21,400, where U_∞ is the inflow velocity and D the cylinder height. Complementary Laser Doppler Velocimetry (LDV) and high-order large-eddy simulations (LES) approaches, based on a spectral vanishing technique (SVV-LES), provide a comprehensive data base including both instantaneous data and post-processed statistics. Beyond these results, an achievement of the paper is to investigate the coherent structures developing on the sides and in the wake of the cylinder with a special focus on the flow features in the near-wall region. The flow is found to separate at the leading edge of the cylinder with the occurence of three-dimensional Kelvin-Helmholtz (KH) pairings localized in the separating shear layer. The interaction between these KH vortical structures and Von Kármán vortex shedding (VK) in the near wake is discussed based on both visualisations and frequency analysis. In particular, signatures of VK and KH vortical structures are found on velocity time samples.     

Nonlinear bending of rectangular orthotropic plate with two free edges and the other edges having nonuniform rotational flexibility

this paper presents a series solution to von Kármán nonlinear equations of a rectilinearly orthotropic rectangular plate under the combined action of lateral load and in-plane tension with the titled edge restraints. In the formulation the edge moments are replaced by an equivalent pressure near the edges. Using generalized double Fourier series for the deflection and stress function, governing equations are reduced to an infinite set of algebraic equations for coefficients in these series. Numerical results for deflections, bending moments and in-plane forces are graphically presented for various values of aspect ratio and material properties and for different edge conditions.     

Fluctuating fluid forces acting on a circular cylinder and interference with a plane wall

The flow around a circular cylinder placed close to a horizontal plane wall was investigated experimentally. Fluctuations of lift and drag of the cylinder and wall interference effects were studied in terms of the gap height between the cylinder and wall and the thickness of the turbulent wall boundary layer. The fluctuating fluid forces acting on the cylinder sharply increased, and the regular vortex shedding, i.e. Kárman vortex streets, started to form beyond a critical gap height. The formation of Kárman vortex streets was abruptly interrupted when the bottom of the cylinder came in contact with the outer layer of the boundary layer developed on the wall. This critical gap height correlated well with the thickness of the boundary layer.     

Wake dynamics of external flow past a curved circular cylinder with the free-stream aligned to the plane of curvature

The fundamental mechanism of vortex shedding past a curved cylinder has been investigated at a Reynolds number of 100 using three-dimensional spectral/hp computations. Two different configurations are presented herein: in both cases the main component of the geometry is a circular cylinder whose centreline is a quarter of a ring and the inflow direction is parallel to the plane of curvature. In the first set of simulations the cylinder is forced to transversely oscillate at a fixed amplitude, while the oscillation frequency has been varied around the Strouhal value. Both geometries exhibit in-phase vortex shedding, with the vortex cores bent according to the body's curvature, although the wake topology is markedly different. In particular, the configuration that was found to suppress the vortex shedding in absence of forced motion exhibits now a primary instability in the near wake. A second set of simulations has been performed imposing an oscillatory roll to the curved cylinder, which is forced to rotate transversely around the axis of its bottom section. This case shows entirely different wake features from the previous one: the vortex shedding appears to be out-of-phase along the body's span, with straight cores that tend to twist after being shed and manifest a secondary spanwise instability. Further, the damping effect stemming from the transverse planar motion of the part of the cylinder parallel to the flow is no longer present, leading to a positive energy transfer from the fluid to the structure.     

Role of the shear layer instability in the near wake behavior of two side-by-side circular cylinders

Wakes, and their interaction behind two parallel cylinders lying in a plane perpendicular to the flow, have been investigated experimentally in the sub-critical Reynolds number regime. The experiments were performed in a water channel using laser Doppler velocimetry. The gap between the two cylinders was less than the cylinder diameter, a geometry referred to as strong interaction configuration. In this case the blockage is strong and a gap-jet appears between the cylinders. Two flow regimes of the near wake region have been identified: one below a critical Reynolds number Re _c ]1000;1700[, where the gap jet is stably deflected to one side and the double near-wake becomes asymmetric; the other, above Re _c, where the gap-jet deflection is unstable and a random flopping phenomenon takes place. When Re<Re _c, two different Strouhal numbers are identified, related to the Kármán vortex shedding behind each cylinder. When Re>Re _c, a third frequency appears in the near wake, related to the development of Kelvin-Helmholtz vortices in the separated shear layer of the cylinders [Prasad A, Williamson CHK (1997) J Fluid Mech 333:375]. The observed flopping behavior is attributed to the birth of these Kelvin-Helmholtz instabilities and their intermittent nature. Further downstream, beyond about five cylinder diameters, the random flopping flow phenomena disappear while a slightly asymmetric single wake persists. It is characterized by a Strouhal number St=0.13, a value that one would normally measure behind a single cylinder of twice its diameter.     

Stability of flow past a cylinder: Energy budget of eigenmodes

Global linear stability analysis of the flow past a circular cylinder at the onset of primary wake instability is carried out. The real and imaginary parts of the most unstable eigenmode, responsible for vortex shedding, are very similar but associated with a spatial shift in the vortex structures. This shift results in the convection of vortices that are observed in the unsteady flow, which is actually a consequence of global absolute instability. The kinetic energy density, associated with the most unstable eigenmode, is studied. At the onset of the instability the energy density of the disturbance field is found to be stronger in the far wake compared with the near wake. With increase in Re the region where the disturbance is strong moves upstream closer to the cylinder. However, the maximum value of the kinetic energy density of the disturbance lies outside the recirculation zone even for Re upto 100. A linearized mechanical energy equation for the time evolution of the kinetic energy density of the disturbance is utilized to examine the energy budget of the most unstable eigenmode at various Re. It is found that the most significant contribution to the growth rate of the disturbance arises from the transfer of the energy due to the strain rate of the base flow to the perturbation. The stabilizing effect of the viscous dissipation increases with increase in Re, but saturates for Re beyond ～70. Copyright © 2009 John Wiley & Sons, Ltd.     

Control of mean and fluctuating forces on a circular cylinder at high Reynolds numbers

A narrow strip is used to control mean and fluctuating forces on a circular cylinder at Reynolds numbers from 2.0 × 10⁴ to 1.0 × 10⁵. The axes of the strip and cylinder are parallel. The control parameters are strip width ratio and strip position characterized by angle of attack and distance from the cylinder. Wind tunnel tests show that the vortex shedding from both sides of the cylinder can be suppressed, and mean drag and fluctuating lift on the cylinder can be reduced if the strip is installed in an effective zone downstream of the cylinder. A phenomenon of mono-side vortex shedding is found. The strip-induced local changes of velocity profiles in the near wake of the cylinder are measured, and the relation between base suction and peak value in the power spectrum of fluctuating lift is studied. The control mechanism is then discussed from different points of view. The project supported by the National Natural Science Foundation of China (10172087 and 10472124). The English text was polished by Yunming Chen.     

Turbulent wake and vortex shedding for a stack partially immersed in a turbulent boundary layer

The effect of the jet-to-cross-flow velocity ratio, R, on the turbulent wake and Kármán vortex shedding for a cylindrical stack of aspect ratio AR=9 was investigated in a low-speed wind tunnel using thermal anemometry. The cross-flow Reynolds number was Re_D=2.3×10⁴, the jet Reynolds number ranged from Re_d=7.6×10³ to 4.7×10⁴, and R was varied from 0 to 3. The stack was partially immersed in a flat-plate turbulent boundary layer, with a boundary layer thickness-to-stack-height ratio of δ/H=0.5 at the location of the stack. From the behaviour of the turbulent wake and the vortex shedding, the flow around the stack could be classified into three regimes depending on the value of R, which were the downwash (R<0.7), cross-wind-dominated (0.7R<1.5), and jet-dominated (R1.5) flow regimes. Each flow regime had a distinct structure to the mean velocity (streamwise and wall-normal directions), turbulence intensity (streamwise and wall-normal directions), and Reynolds shear stress fields, as well as the variation of the Strouhal number and the power spectrum along the stack height.     

Numerical investigations into effects of three-dimensional wake patterns on unsteady aerodynamic characteristics of a circular cylinder at Re=1.3×105

In contrast with a wide range of applications concerning flows around a circular cylinder at upper subcritical Reynolds numbers (Re), there is no systematic understanding about the fundamentals of so-called random flow patterns, and their effects on intermittent modulations in the time history of pressure or force, and the decrease in their spanwise correlations. This paper employed the large-eddy simulation (LES) technique to predict flows past a circular cylinder at Re=1.3×10⁵ and to provide images based on flow visualization that can clarify the physical mechanism responsible for these outcomes. A reasonably sufficient spanwise length was adopted for the numerical model by taking into consideration the effect of aspect ratios (the spanwise length to the diameter). We found that even at such high Res, a three-dimensional pattern of vortical field is present in the wake resulting in total force modulation and weak spanwise correlation, e.g., obvious oblique shedding. The whole development process of the three-dimensional wake is exhibited as a universal. The results revealed that local phase variations in primary vortex shedding are the starting points of three-dimensional wake patterns, which are induced by the “irregular” streamwise vortex. The three-dimensional near wake following local phase variations is associated with a successive evolution composed of certain stages in order. Quantitative analyses based on the time series of sectional lift coefficients show that intermittent increase in primary shedding periods and sectional lift streak divisions are closely related to local phase variations and vortex division in the development process of the three-dimensional pattern. In addition to the phase difference along the span, the three-dimensional pattern also weakens vortex shedding in cross sections perpendicular to the axis of the cylinder, resulting in modulation of the sectional lift coefficient.     

The effect of a wake-mounted splitter plate on the flow around a surface-mounted finite-height circular cylinder

The influence of a wake-mounted splitter plate on the flow around a surface-mounted circular cylinder of finite height was investigated experimentally using a low-speed wind tunnel. The experiments were conducted at a Reynolds number of Re=7.4×10⁴ for cylinder aspect ratios of AR=9, 7, 5 and 3. The thickness of the boundary layer on the ground plane relative to the cylinder diameter was δ/D=1.5. The splitter plates were mounted on the wake centreline with negligible gap between the base of the cylinder and the leading edge of the plate. The lengths of the splitter plates, relative to the cylinder diameter, ranged from L/D=1 to 7, and the plate height was always equal to the cylinder height. Measurements of the mean drag force coefficient were obtained with a force balance, and measurements of the vortex shedding frequency were obtained with a single-component hot-wire probe situated in the wake of the cylinder–plate combination. Compared to the well-studied case involving an infinite circular cylinder, the splitter plate was found to be a less effective drag-reduction device for finite circular cylinders. Significant reduction in the mean drag coefficient was realized only for the finite circular cylinder of AR=9 with intermediate-length splitter plates of L/D=1–3. The mean drag coefficients of the other cylinders were almost unchanged. In terms of its effect on vortex shedding, a splitter plate of sufficient length was able to suppress Kármán vortex shedding for all of the finite circular cylinders tested. For AR=9, vortex shedding suppression occurred for L/D≥5, which is similar to the case of the infinite circular cylinder. For the smaller-aspect-ratio cylinders, however, the splitter plate was more effective than what occurs for the infinite circular cylinder: for AR=3, vortex shedding suppression occurred for all of the splitter plates tested (L/D≥1); for AR=5 and 7, vortex shedding suppression occurred for L/D≥1.5.