Intrinsic relationship of vorticity between modes A and B in the wake of a bluff body

The intrinsic physical relationship of vorticity between modes A and B in the three-dimensional wake transition is investigated.Direct numerical simulations for the flow past a square-section cylinder are carried out at Reynolds numbers of 180 and 250,associated with modes A and B,respectively.Based on the analysis of spacial distributions of vorticity in the near wake,characteristics of the vertical vorticity in modes A and B are identified.Moreover,the relationship of three vorticity components with specific signs is summarized into two sign laws,as intrinsic physical relationships between two instability modes.By the theory of vortex-induced vortex,such two sign laws confirm that there are two and only two kinds of vortex-shedding patterns in the near wake,just corresponding to modes A and B.In brief,along the free stream direction,mode A can be described by the parallel shedding vertical vortices with the same sign,while mode B is described by the parallel shedding streamwise vortices with the same sign.Finally,it is found out that the|-type vortex is a basic kind of vortex structure in both modes A and B.     

Effect of perforation on flow past a conic cylinder at <Emphasis Type="Italic">Re</Emphasis> = 100: vortex-shedding pattern and force history

The flow past a circular-section cylinder with a conic shroud perforated with four holes at the peak was simulated numerically at \(Re=100\), considering two factors, viz. the angle of attack and the diameter of the holes. The effects of the perforated conic shroud on the vortex shedding pattern in the near wake was mainly investigated, as well as the time history of the drag and lift forces. In the investigated parameter space, three flow regimes were generally identified, corresponding to weak, moderate, and strong disturbance effects. In regime I, the wake can mainly be described by alternately shedding Kármán or Kármán-like vortices. In regime II, the spanwise vortices are obviously disturbed along the span due to the appearance of additional vorticity components and their interactions with the spanwise vortices, but still shed in synchronization along the spanwise direction. In regime III, the typical Kármán vortices partially or totally disappear, and some new vortex shedding patterns appear, such as \(\Omega \)-type, obliquely shedding, and crossed spanwise vortices with opposite sign. Corresponding to these complex vortex shedding patterns in the near wake, the fluid forces no longer oscillate regularly at a single vortex shedding frequency, but rather with a lower modulation frequency and multiple amplitudes. An overview of these flow regimes is presented.     

Spanwise effects on instabilities of compressible flow over a long rectangular cavity

The stability properties of two-dimensional (2D) and three-dimensional (3D) compressible flows over a rectangular cavity with length-to-depth ratio of \(L/D=6\) are analyzed at a free-stream Mach number of \(M_\infty =0.6\) and depth-based Reynolds number of \(Re_D=502\). In this study, we closely examine the influence of three-dimensionality on the wake mode that has been reported to exhibit high-amplitude fluctuations from the formation and ejection of large-scale spanwise vortices. Direct numerical simulation (DNS) and bi-global stability analysis are utilized to study the stability characteristics of the wake mode. Using the bi-global stability analysis with the time-averaged flow as the base state, we capture the global stability properties of the wake mode at a spanwise wavenumber of \(\beta =0\). To uncover spanwise effects on the 2D wake mode, 3D DNS are performed with cavity width-to-depth ratio of \(W/D=1\) and 2. We find that the 2D wake mode is not present in the 3D cavity flow with \(W/D=2\), in which spanwise structures are observed near the rear region of the cavity. These 3D instabilities are further investigated via bi-global stability analysis for spanwise wavelengths of \(\lambda /D=0.5{-}2.0\) to reveal the eigenspectra of the 3D eigenmodes. Based on the findings of 2D and 3D global stability analysis, we conclude that the absence of the wake mode in 3D rectangular cavity flows is due to the release of kinetic energy from the spanwise vortices to the streamwise vortical structures that develops from the spanwise instabilities.     

3-D measurements of separated flow over rigid plates with spanwise periodic cambering at low Reynolds number

Measurements of the flow field around a flat plate and rigid plates with spanwise periodic cambering were performed using volumetric three-component velocimetry (V3V) at a Reynolds numbers of 28,000 at α=12° where the flow is fully separated. The Reynolds normal and shear stresses, and the streamwise, spanwise and normal components of the vorticity vector are investigated for three-dimensionality. Flow features are discussed in context of the periodic cambering and corresponding aerodynamic force measurements. The periodic cambering results in spanwise variation in the reversed-flow region, Reynolds stresses and spanwise vorticity. These spanwise variations are induced by streamwise and normal vortices of opposite directions of rotation. Moreover, measurements were carried out for the cambered plates at α=8°, where a long separation bubble exists, to further understand the behavior of the streamwise and normal vortices. These vortices become more organized and increase in strength and size at the lower angle of attack. It is also speculated that these vortices contribute to the increase in lift at and beyond the onset of stall angle of attack.     

Three-dimensional wake structure measurement using a modified PIV technique

Three-dimensional vortical structures have been measured in a circular-cylinder wake using particle imaging velocimetry (PIV) for the Reynolds number range of 2×10³ to 1×10⁴. The PIV was modified, compared with the conventional one, in terms of its light sheet arrangement to capture reliably streamwise vortices. While in agreement with previous reports, the presently measured spanwise structures complement the data in the literature in the streamwise evolution of the near-wake spanwise vortex in size, strength, streamwise and lateral convection velocities, shedding new light upon vigorous interactions between oppositely signed spanwise structures. The longitudinal vortices display mushroom patterns in the (x, z)-plane in the immediate proximity to the cylinder. Their most likely inclination in the (x, y)-plane is inferred from the measurements in different (x, z)-planes. The longitudinal vortices in the (y, z)-plane show alternate change in sign, though not discernible at x/d > 15. They decay in the maximum vorticity and circulation rapidly from x/d = 5 to 10 and slowly for x/d > 10, and are further compared with the spanwise vortices in size, strength and rate of decay.     

The Tilting Mechanism of a Longitudinal Vortical Structure in a Homogeneous Shear Flow with and Without Spanwise Rotation

A longitudinal vortical structure is typically observed in near-wall turbulence. This vortical structure is elongated in the streamwise direction, though it is also tilted in the spanwise direction. The sense of this spanwise tilting is determined by the sign of the streamwise vorticity associated with the vortex, and longitudinal vortical structures with a different streamwise vorticity become asymmetric (mirror symmetric). The tilting must be due to the combined effects of the non-linear terms and mean spanwise vorticity associated with the mean shear. However, the detailed mechanism of the tilting is not well known. To study the tilting in detail, we performed direct numerical simulations of a homogeneous shear flow where the longitudinal vortical structures similar to those in the near-wall region are observed. In particular, the effects of spanwise system rotation as well as the Reynolds number on the vortical structure are studied. As a result, we found that spanwise system rotation has more marked effects on the vortical structure than the Reynolds number. When the system rotation is imposed in the same direction as the mean spanwise vorticity, the tilting is enhanced, while the system rotation of the opposite direction attenuates it. We also found that when the longitudinal vortical structure is tilted in the spanwise direction, it is sandwiched between the streamwise vorticity of the opposite sign. The cyclonic rotation enhances the streamwise vorticity of the opposite sign, though the longitudinal vortical structure at the center is attenuated. In the anticyclonic case, the streamwise vorticity of the opposite sign almost disappears and the longitudinal vortical structure is isolated from the surrounding flow.     

NEAR-WAKE FLOW STRUCTURE OF A CYLINDER WITH A HELICAL SURFACE PERTURBATION

The near-wake of a circular cylinder having a helical wire pattern about its surface is characterized using a technique of high-image-density velocimetry. Patterns of vorticity in three orthogonal planes show substantial influence of a wire having a diameter an order of magnitude smaller than the cylinder diameter. The distinctive patterns of vorticity in these three planes are associated with lack of formation of large-scale Kármán-like clusters of vorticity (ω_z) in the near-wake region of the cylinder. The instantaneous structure of the separating spanwise vorticity (ω_z) layers on either side of the cylinder involve small-scale concentrations of vorticity analogous to the well-known Kelvin–Helmholtz vortices from a smooth cylinder. Moreover, a dual vorticity layer, i.e., two adjacent layers of like vorticity (ω_z), can form from one side of the cylinder. Along the span of the cylinder, distributions of instantaneous velocity and transverse vorticity (ω_y) show a spatially periodic sequence of wake-like patterns, each of which has features in common with the very near-wake of a two-dimensional bluff body, including a large velocity defect bounded by vorticity layers with embedded small-scale vorticity concentrations. In the cross-flow plane of the wake, patterns of streamwise vorticity (ω_x) show small-scale, counter-rotating pairs of vorticity concentrations (ω_x) emanating from the inclined helical perturbation, rather than isolated concentrations of vorticity of like sign, which would indicate single streamwise vortices. All of the aforementioned patterns of small-scale vorticity concentrations are scaled according to the local wake width/local pitch of the helical wire pattern in the respective plane of observation.     

Topology of the vorticity field in three-dimensional shear layers and wakes

An experimental and numerical study of the three-dimensional transition of plane wakes and shear layers behind a flat plate is presented. Flow visualization techniques are used to monitor the response of laminar flows at moderate Reynolds numbers (≈100) to perturbations periodically distributed along the span. In this way, the formation and evolution of streamwise vortex tubes and their interaction with the spanwise vortices are analyzed. The flow was studied numerically by means of three-dimensional inviscid vortex dynamics. Assuming periodicity in the spanwise and the streamwise direction, we discretize the vorticity field into two layers of vortex filaments with finite core diameter. Comparison between experiment and visualization indicates that important features of the three-dimensional evolution can be reproduced by inviscid vortex dynamics. Vortex stretching in the strain field of the spanwise rollers appears to be the primary mechanism for the three-dimensional transition in this type of flows.     

Transition phenomena in the wake of an inclined square cylinder

The division of flow regimes in a square cylinder wake at various angles of attack (α) is studied. This study provides evidence of the existence of modes A and B instabilities in the wake of an inclined square cylinder. The critical Reynolds numbers for the inception of these instability modes were identified through the determination of discontinuities in the Strouhal number versus Reynolds number curves. The spectra and time traces of wake streamwise velocity were observed to display three distinct patterns in different flow regimes. Streamwise vortices with different wavelengths at various Reynolds numbers were visualized. A PIV technique was employed to quantitatively measure the parameters of wake vortices. The wavelengths of the streamwise vortices in the modes A and B regimes were measured by using the auto-correlation method. From the present investigation, the square cylinder wake at various angles of attack undergoes a similar transition path to that of a circular cylinder, although various quantitative parameters measured which include the critical Reynolds numbers, spanwise wavelength of secondary vortices, and the circulation and vorticity of wake vortices all show an α dependence.     

The wake flow downstream of a propeller-rudder system

We report wall-resolved, large-eddy simulations for the case of a propeller operating upstream of a hydrofoil, mimicking a rudder. Our primary objective is the identification of wake features that are unique to this coupled system, when compared to open-water cases, which are usually the focus of experiments and computations in the literature. We were able to achieve unprecedented levels of numerical resolution, which capture the dynamics of all energetic eddies in the flow by using a scalable, conservative, structured solver in cylindrical coordinates. The boundary conditions on the rotating propeller and hydrofoil were enforced via an immersed boundary formulation. The largest values of turbulent stresses in the wake of the hydrofoil are achieved outwards from the radial coordinate of the tip of the propeller blades. This is due to spanwise gradients across the hydrofoil (in the direction parallel to the span of the hydrofoil), producing a displacement of the pressure side legs of the tip vortices towards outer coordinates, where they experience shear with the wake of the hydrofoil. The evolution of turbulence is non-monotonic across the streamwise direction. This is a consequence of the growing shear resulting from the complex interactions involving the shear layers from the trailing edge, the tip vortices and the two branches of the hub vortex coming from the two sides of the hydrofoil. Such a shear is reinforced by the spanwise velocities developed by the two branches of the propeller wake across the hydrofoil. Compared to an isolated propeller, these phenomena enhance turbulence production. The present results highlight that a downstream hydrofoil, typical of surface ships, is able to significantly intensify the wake signature of a propeller.     

Characterization of Turbulent Structures in a Transonic Backward-Facing Step Flow

A transonic backward-facing step flow, at a free stream Mach number of 0.8 and a Reynolds number of 1.86 × 10⁵ with respect to the step height, was investigated experimentally by means of planar and stereo Particle Image Velocimetry (PIV) measurements for multiple fields of view. The primary aim of this analysis is to examine whether the large temporal variations of the reattachment location is associated with the presence of large scale coherent flow structures. The mean flow reattaches ≈6.1±0.2 times the step height downstream of the step. This value fluctuates temporally as much as ±3 step heights. Measurements of the wake flow in horizontal planes show that the strong variations of the reattachment length are associated with spanwise variations of the streamwise velocity. Two-point correlations revealed large–scale coherent regions with a length of up to 7 step heights and a dominant spanwise wave-length of 1.5…2.5 step heights. Furthermore, close to the step large structures are found, which span more than 5 step heights in spanwise direction. The Reynolds stress distribution of the separated region strongly suggests that the initial streamwise momentum is transferred to the vertical component as well as to the spanwise component in comparable portions by the deformation of the initial Kelvin-Helmholtz vortices and the generation of secondary ones. As a result, the separated shear layer is characterized by eddies of various sizes and orientations. The mean flow field only shows the primary separation bubble and a secondary recirculation region. No stationary streamwise vortices could be found for the tested Reynolds number.     

Turbulence in a skewed three‐dimensional wall‐bounded shear flow: effect of mean vorticity on structure modification

Mean‐flow three‐dimensionalities affect both the turbulence level and the coherent flow structures in wall‐bounded shear flows. A tailor‐made flow configuration was designed to enable a thorough investigation of moderately and severely skewed channel flows. A unidirectional shear‐driven plane Couette flow was skewed by means of an imposed spanwise pressure gradient. Three different cases with 8°, 34°and 52°skewing were simulated numerically and the results compared with data from a purely two‐dimensional plane Couette flow. The resulting three‐dimensional flow field became statistically stationary and homogeneous in the streamwise and spanwise directions while the mean velocity vector V and the mean vorticity vector Ω remained parallel with the walls. Mean flow profiles were presented together with all components of the Reynolds stress tensor. The mean shear rate in the core region gradually increased with increasing skewing whereas the velocity fluctuations were enhanced in the spanwise direction and reduced in the streamwise direction. The Reynolds shear stress is known to be closely related to the coherent flow structures in the near‐wall region. The instantaneous and ensemble‐averaged flow structures were turned by the skewed mean flow. We demonstrated for the medium‐skewed case that the coherent structures should be examined in a coordinate system aligned with V to enable a sound interpretation of 3D effects. The conventional symmetry between Case 1 and Case 2 vortices was broken and Case 1 vortices turned out to be stronger than Case 2. This observation is in conflict with the common understanding on the basis of the spanwise (secondary) mean shear rate. A refined model was proposed to interpret the structure modifications in three‐dimensional wall‐flows. What matters is the orientation of the mean vorticity vector Ω relative to the vortex vorticity vector ω _v, that is, the sign of Ω · ω _v. In the present situation, Ω · ω _v > 0 for the Case 1 vortices causing a strengthening relative to the Case 2 vortices. Copyright © 2011 John Wiley & Sons, Ltd.     

Direct simulation of breakdown to turbulence following oblique instability waves in a supersonic boundary layer

The late stages of transition to turbulence in a Mach two boundary layer are investigated by direct numerical simulation of the compressible Navier-Stokes equations. The primary instability at this Mach number consists of oblique waves, which are known to form a pattern of quasi-streamwise vortices. It is found that breakdown does not follow immediately from these vortices, which decay in intensity. The generation of new vortices is observed by following the evolution of the pressure and vorticity in the simulation, and analysed by consideration of vorticity stretching. It is found that the slight inclined and skewed nature of the quasi-streamwise vortices leads to a production of oppositely signed streamwise vorticity, which serves as a strong localised forcing of the shear layer alongside the original vortices, formed by convection and stretching of spanwise vorticity. The shear layer rolls up into many new vortices, and is followed by a sharp increase in the energy of higher frequencies and in the skin friction.     

Streamwise evolution of an inclined cylinder wake

The streamwise evolution of an inclined circular cylinder wake was investigated by measuring all three velocity and vorticity components using an eight-hotwire vorticity probe in a wind tunnel at a Reynolds number Re_d of 7,200 based on free stream velocity (U _∞) and cylinder diameter (d). The measurements were conducted at four different inclination angles (α), namely 0°, 15°, 30°, and 45° and at three downstream locations, i.e., x/d = 10, 20, and 40 from the cylinder. At x/d = 10, the effects of α on the three coherent vorticity components are negligibly small for α ≤ 15°. When α increases further to 45°, the maximum of coherent spanwise vorticity reduces by about 50%, while that of the streamwise vorticity increases by about 70%. Similar results are found at x/d = 20, indicating the impaired spanwise vortices and the enhancement of the three-dimensionality of the wake with increasing α. The streamwise decay rate of the coherent spanwise vorticity is smaller for a larger α. This is because the streamwise spacing between the spanwise vortices is bigger for a larger α, resulting in a weak interaction between the vortices and hence slower decaying rate in the streamwise direction. For all tested α, the coherent contribution to [`(v<sup>2</sup>)] \overline{{v^{2}}} is remarkable at x/d = 10 and 20 and significantly larger than that to [`(u²)] \overline{{u^{2}}} and [`(w<sup>2</sup>)]. \overline{{w^{2}}}. This contribution to all three Reynolds normal stresses becomes negligibly small at x/d = 40. The coherent contribution to [`(u²)] \overline{{u^{2}}} and [`(v²)] \overline{{v^{2}}} decays slower as moving downstream for a larger α, consistent with the slow decay of the coherent spanwise vorticity for a larger α.     

Three-dimensional vorticity in a turbulent cylinder wake

The three components of the vorticity vector in the intermediate region of a turbulent cylinder wake were measured simultaneously using a multi-hot-wire probe. This probe has an improved spatial resolution compared with those reported in the literature. The behavior of the instantaneous velocity and vorticity signals is examined. Both coherent and incoherent vorticity fields are investigated using a phase-averaged technique. The iso-contours of the phase-averaged longitudinal and lateral vorticity variances, and , wrap around the spanwise structures of opposite sign and run through the saddle point along the diverging separatrix. The observation conforms to the previous reports of the occurrence of the longitudinal structures based on flow visualizations and numerical simulations. The magnitude of these contours is about the same as that of the maximum coherent spanwise vorticity at the vortex center, indicating that the strength of the longitudinal structures is comparable to that of the spanwise vortices. Furthermore, and exhibit maximum concentration away from the vortex center, probably because of a combined effect of the large-scale spanwise vortices and the intermediate-scale longitudinal structures. Coherent structures contribute about 36% to the spanwise vorticity variance at x/d=10. The contribution decreases rapidly to about 5% at x/d=40. The present results suggest that vorticity largely reside in relatively small-scale structures.     

Plane jet excited by disturbances with spanwise phase variations

Evolution of the near-field structures of a plane jet excited by temporal periodic disturbances with spanwise phase variations was investigated with stereoscopic particle image velocimetry. The three-dimensional vorticity distributions were reconstructed by using Taylor’s frozen field hypothesis. When ?, the temporal phase difference of disturbances in the spanwise direction was π; chain-link-fence type structures were formed. The $\Uplambda$ vortices in the chain-link-fence structures were then distorted into an $\Upomega$ shape, and the head of the vortex was detached and reconnects to form a vortex ring, or reconnects to the adjacent V-shaped vortices to form an A-shaped vortex. After the reconnection stage, the flow field was occupied by uniformly distributed fine scale eddies. Here, the overall turbulent kinetic energy and shear stress were suppressed, and the jet width was narrower than that of the unexcited case and other forced cases. In the case of ? = π/2, spanwise rollers and rib structures were formed near the nozzle exit after the first vortex pairing. However, further vortex pairing did not occur downstream, and the rate at which the jet widened was reduced.     

PIV measurements of the near-wake behind a sinusoidal cylinder

The three-dimensional near-wake structures behind a sinusoidal cylinder have been investigated using a particle image velocimetry (PIV) measurement technique at Re=3,000. The mean velocity fields and spatial distributions of ensemble-averaged turbulence statistics for flows around the sinusoidal and corresponding smooth cylinders were compared. The near-wake behind the sinusoidal cylinder exhibited pronounced spanwise periodic variations in the flow structure. Well-organized streamwise vortices with alternating positive and negative vorticity were observed along the span of the sinusoidal cylinder. They suppress the formation of the large-scale spanwise vortices and decrease the overall turbulent kinetic energy in the near-wake of the sinusoidal cylinder. The sinusoidal surface geometry significantly modifies the near-wake structure and strongly controls the three-dimensional vortices formed in the near-wake.     

Approach towards self-preservation of turbulent cylinder and screen wakes

Two-dimensional wakes generated from a circular cylinder and a 50% solidity screen have significantly different initial conditions. Accordingly, the approach towards self-preservation is quite different for the two wakes. For the cylinder wake, the normalized Reynolds stresses and spanwise vorticity decrease with increasing distance from the wake generator; the inverse occurs in the screen wake. Distributions of mean velocity, Reynolds stresses, and rms spanwise vorticity indicate that self-preservation is reached at a much smaller streamwise distance for the screen than for the cylinder wake. This result is consistent with the previously reported topological differences between these two flows.     

Multisensor Hot Wire Vorticity Probe Measurements of the Formation Field of Two Corotating Vortices

Experimental evidence is reported, regarding the formation of a pair of co-rotating tip vortices by a split wing configuration, consisting of two half wings at equal and opposite angles of attack. Simultaneous measurements of the three-dimensional vector fields of velocity and vorticity were conducted on a cross plane at a downstream distance corresponding to 0.3 cord lengths (near wake), using an in-house constructed 12-sensor hot wire anemometry vorticity probe. The probe consists of three closely separated orthogonal 4-wire velocity sensor arrays, measuring simultaneously the three-dimensional velocity vector at three closely spaced locations on a cross plane of the flow filed. This configuration makes possible the estimation of spatial velocity derivatives by means of a forward difference scheme of first order accuracy. Velocity measurements obtained with an X-wire are also presented for comparison. In this near wake location, the flow field is dictated by the pressure distribution established by the flow around the wings, mobilizing large masses of air and leading to the roll up of fluid sheets. Fluid streams penetrating between the wings collide, creating on the cross plane flow a stagnation point and an “impermeable” line joining the two vortex centres. Along this line fluid is directed towards the two vortices, expanding their cores and increasing their separation distance. This feeding process generates a dipole of opposite sign streamwise mean vorticity within each vortex. The rotational flow within the vortices obligates an adverse streamwise pressure gradient leading to a significant streamwise velocity deficit characterizing the vortices. The turbulent flow field is the result of temporal changes in the intensity of the vortex formation and changes in the position of the cores (wandering).