Peak Vorticity Research Articles

Adjustment of Subgrid-Scale Parametrizations to Strong Streamline Curvature

A subgrid-scale model correction for large eddy simulations that address flowfields with embedded areas of poorly resolved strong streamline curvature effects is proposed. The devised modification is termed NaCoo and provides an isotropic correction of the subgrid-scale viscosity based on local centrifugal stability. The degree of stability is identified via a rotational Richardson number that is determined based on non-Galilean-invariant streamline curvature at every grid point. NaCoo allows for a more realistic representation of inadequately resolved coherent turbulent vortices. Its main benefits are 1) conservation of the peak vorticity in the vortex cores, 2) reduction of vortex core radius growth rates, 3) an approach to properties of tangential velocity profiles found in experiments 4) allowance for appropriate turbulence levels in the vicinity of the vortices, and 5) non suppression of vortex core meandering. The derivation of NaCoo, its properties, and sensitivity to numerical and vortex parameters are described in detail

A flow field study of an elliptic jet in cross flow using DPIV technique

The digital particle image velocimetry (DPIV) technique has been used to investigate the flow fields of an elliptic jet in cross flow (EJICF). Two different jet orientations are considered; one with the major axis of the ellipse aligned with the cross flow (henceforth referred to as a low aspect ratio (AR) jet), and the other with the major axis normal to the cross flow (henceforth referred to as a high aspect ratio jet). Results show that the vortex-pairing phenomenon is prevalent in the low aspect ratio jet when the velocity ratio (VR)≥3, and is absent in the high aspect ratio jet regardless of the velocity ratio. The presence of vortex pairing leads to a substantial increase in the leading-edge peak vorticity compared to the lee-side vorticity, which suggests that vortex pairing may play an important role in the entrainment of ambient fluid into the jet body, at least in the near-field region. In the absence of vortex pairing, both the leading-edge and the lee-side peak vorticity increase monotonically with velocity ratio regardless of the aspect ratio. Moreover, time-averaged velocity fields for both AR=0.5 and AR=2 jets reveal the existence of an “unstable focus” (UF) downstream of the jet, at least for VR≥2. The strength and the location of this focus is a function of both the velocity ratio and aspect ratio. In addition, time-averaged vorticity fields show a consistently higher peak-averaged vorticity in the low aspect ratio jet than in the high aspect ratio jet. This behavior could be due to a higher curvature of the vortex filament facing the cross flow in the low aspect ratio jet, which through mutual interaction may lead to higher vortex stretching, and therefore higher peak-averaged vorticity.

Effects of Pulsing on a Vortex Generator Jet

The evolution of a pulsed vortex generator jet embedded in a turbulent boundary layer was examined experimentally. The jet, which was pitched 45 deg and skewed 90 deg, had a velocity three times greater than the freestream. The velocity e eld in planes normal to the freestream was measured by the particle-image-velocimetry method at four stations downstream of the jet exit. The pulsed jet created a starting vortex ring followed by a pair of counter-rotating streamwise vortices, one of them being markedly stronger. Phase-averaged data indicate that the maximum circulation and peak vorticity of the stronger vortex are approximately 30% greater than the average values for a steady jet with the same velocity. However, circulation averaged over the entire pulse was less than that fora steady jet at the samelocation. Thecoreof theprimary streamwisevortex penetratesapproximately 50% farther into the boundary layer than a steady jet with the same velocity. The larger penetration takes place during the initial portion of the pulse and is caused by the jet starting vortex ring.

Development of a Steady Vortex Generator Jet in a Turbulent Boundary Layer

The development of a vortex generator jet within a turbulent boundary layer was studied by the particle image velocimetry method. Jet velocities ranging from one to three times greater than the freestream velocity were examined. The jet was pitched 45 deg and skewed 90 deg with respect to the surface and flow direction, respectively. The velocity field in planes normal to the freestream was measured at four stations downstream of the jet exit. The jet created a pair of streamwise vortices, one of which was stronger and dominated the flow field. The circulation, peak vorticity, and wall-normal position of the primary vortex increased linearly with the jet velocity. The circulation and peak vorticity decreased exponentially with the distance from the jet source for the jet-to-freestream velocity ratios of 2 and 3. The wandering of the streamwise vortex can be as much as ±30% of the local boundary layer thickness at the farthest measurement station.

A new family of uniform vortices related to vortex configurations before merging

Stimulated by experimental observations of vortex merging, we compute a new family of uniform-vorticity steady solutions of the Euler equations in two dimensions. In experiments with two co-rotating vortices, one finds that, prior to the convective merging phase, and the formation of vortex filaments, the initial pair diffuses into a single structure (with two vorticity peaks) in the form of a symmetric ‘dumb-bell’. In the present computations, our exploration of the existence of vortex solutions has been guided by the streamline patterns of the co-rotating reference frame, and by the simple concept that the vortex boundary must be one of these streamlines. By varying the parameters which define the vortex patches, we find a family of vorticity structures which pass from the limiting case of point vortices, through the case of two equal co-rotating uniform vortices (as previously computed by Saffman & Szeto 1980; Overman & Zabusky 1982; Dritschel 1985), to the regime where the vortices touch in the form of a dumb-bell. Further exploration of this family of solutions leads to an elliptic vortex, which joins precisely to the local transcritical bifurcation from elliptic vortices with ) found by Wu, Overman & Zabusky (1984).

Convection Velocity of Vortex Structures in the Near Wake of a Circular Cylinder

The convection velocity of vortex structures in the near wake of a circular cylinder was experimentally investigated over the region 1.6-2.5⩽x/D⩽12.0 for R=160-12,000. Dye injection technique of flow visualization and two completely noninvasive laser Doppler velocimeters were employed for R⩽320 and ⩾400, respectively. The convection velocity, Uc, is defined as the mean traveling velocity of vortex cores passing a streamwise separation during a mean elapsed time. For R⩽320,Uc was determined directly from the motion of dye-marked vortex cores filmed by a video camera. In the cases of R⩾400, the positions of peak vorticity and half of the half-velocity-defect width at each downstream section were first used to identify the mean path of vortex cores (i.e., the most probable trajectory of the vortex structures), along which spatial correlation measurements were then performed to determine the mean elapsed time corresponding to the maximum cross correlation. The present results show that, in laminar and transitional wakes, the ratio Uc/Uo increases from 0.53 to 0.84 over a region of 1.6⩽x/D⩽6.0 and then tends to be a constant of 0.84 for x/D⩾6.0. In a turbulent wake, Uc/Uo also increases from a certain value at a point downstream from the position of vortex formation to a mean value of about 0.86 at x/D⩾5.0-6.0, and then changes little with the increase of x/D. In addition, it is found that the dependence of Uc/Uo on R almost disappears for x/D⩾5.0.

Spacetime development of the onset of a shallow-water vortex

An impulsively started jet in shallow water gives rise to vortices having a characteristic diameter larger than the water depth. A technique of high-image-density particle image velocimetry allows characterization of the space–time development of the instantaneous flow patterns along planes representing the quasi-two-dimensional and three-dimensional vortex structure. The quasi-two-dimensional patterns exhibit different categories of vortex development and interaction, depending upon the depth of the shallow water layer. Despite these distinctions, the variations of normalized vortex position, diameter, and circulation, as well as peak vorticity within the vortex, are very similar for sufficiently small water depth.These quasi-two-dimensional patterns are, in turn, related to specific forms of three-dimensional flow structure, which is highly ordered. A prevalent feature is a vortex orthogonal to, and just ahead of, the primary, quasi-two-dimensional vortex. Its streamline topology, on a plane parallel to the axis of the quasi-two-dimensional vortex, exhibits a separation bubble with a well-defined separatix at the bottom (bed) surface. Moreover, its vorticity can exceed that of the quasi-two-dimensional pattern by a factor of two. This feature is consistent for all values of water depth. When the depth becomes sufficiently large, however, the three-dimensional vortex pattern involves an array of vorticity concentrations, which extends across the entire depth of the water.On a plane very close to the bottom surface (bed), global instantaneous distributions of velocity and vorticity exhibit large gradients; they are associated with small-scale vorticity concentrations characteristic of rapid transition. The corresponding streamline topology of the averaged flow close to the bed, however, exhibits a stable focus and is a direct indicator of the topology well above the bed.

Interaction of two equal vortices on a β plane

The interaction of two equal vortices under the influence of a gradient of background vorticity (β) is studied numerically and experimentally. If the initial shape and vorticity distribution of the vortices is fixed, two parameters determine the evolution: the normalized intercentroid distance d*=d/R, where R is the radius of the vortex; and the normalized gradient of background vorticity β*=βR/ω, where ω is the peak vorticity of the vortex. Alternate ways of identifying regimes of behavior in the parameter plane (d*,β*) are presented. These are applied to numerical simulations of interaction of vortices with steplike, steep and smooth vorticity profiles. It is found that the critical distance for merger decreases with increasing β* for all vortex types, and that vortices with smooth vorticity profile are the most merger-prone vortices. Laboratory experiments were done in a rotating water tank with a flat sloping bottom providing the β effect. The vortices produced have a smooth vorticity profile and show the same behavior observed in the simulations, except that, as a result of viscous effects, the critical merger distance is shifted towards larger values of d*.

Planar velocity measurements of a two-dimensional compressible wake

The present study describes the application of particle image velocimetry (PIV) to investigate the compressible flow in the wake of a two-dimensional blunt base at a freestream Mach number M∞=2. The first part of the study addresses specific issues related to the application of PIV to supersonic wind tunnel flows, such as the seeding particle flow-tracing fidelity and the measurement spatial resolution. The seeding particle response is assessed through a planar oblique shock wave experiment. The measurement spatial resolution is enhanced by means of an advanced image-interrogation algorithm. In the second part, the experimental results are presented. The PIV measurements yield the spatial distribution of mean velocity and turbulence. The mean velocity distribution clearly reveals the main flow features such as expansion fans, separated shear layers, flow recirculation, reattachment, recompression and wake development. The turbulence distribution shows the growth of turbulent fluctuations in the separated shear layers up to the reattachment location. Increased velocity fluctuations are also present downstream of reattachment outside of the wake due to unsteady flow reattachment and recompression. The instantaneous velocity field is analyzed seeking coherent flow structures in the redeveloping wake. The instantaneous planar velocity and vorticity measurements return evidence of large-scale turbulent structures detected as spatially coherent vorticity fluctuations. The velocity pattern consistently shows large masses of fluid in vortical motion. The overall instantaneous wake flow is organized as a double row of counter-rotating structures. The single structures show vorticity contours of roughly elliptical shape in agreement with previous studies based on spatial correlation of planar light scattering. Peak vorticity is found to be five times higher than the mean vorticity value, suggesting that wake turbulence is dominated by the activity of large-scale structures. The unsteady behavior of the reattachment phenomenon is studied. Based on the instantaneous flow topology, the reattachment is observed to fluctuate mostly in the streamwise direction suggesting that the unsteady separation is dominated by a pumping-like motion.

Contraction of westward-travelling nonlocal modons due to the vorticity filament emission

Abstract. Long-term evolution of westward-travelling non-local modons on the β-plane, i.e. dipolar vortices imbedded in slowly damping Rossby wave fields, is studied numerically. In the framework of the nondivergent (barotropic) model, two stages of the evolution are observed. At the first stage (for about 30 synoptic periods), the parameters and the form of the vortex practically remain constant, whereas at the second stage, vorticity filaments are emitted. Due to the filamentation, the vortex core contracts, the potential vorticity peaks of the vortex pair get closer, and the modon speeds up. In the divergent (equivalent-barotropic) model, nonlocal modons and the Lamb modon (that has no wave field outside the dipolar core) evolve much more slowly, essentially preserving the initial shape and propagation speed until about 100 synoptic periods.

Transient vortex events in the initial value problem for turbulence.

A vorticity surge event that could be a paradigm for a wide class of bursting events in turbulence is studied. The coherent mechanism is characterized by locally transverse vortex configurations that are intrinsically helical in both physical and Fourier space when there is a peak of the maximum vorticity parallel omega parallel(infinity)(t). At no time are nonhelical, antiparallel vorticity elements observed. This event precedes the appearance of the traditional signatures of an energy cascade such as strong growth of the dissipation, spectra approaching -5/3, and strongly Beltramized vortex tubes. Comparing how different large-eddy simulations reproduce these properties demonstrates the importance of properly modeling nonlinear transport of both energy and helicity.

Numerical study of fluid flow through double bell‐shaped constrictions in a tube

The effects of steady fluid flow through double bell‐shaped constrictions in tubes were investigated numerically for the Reynolds number range of 5 to 400. The double constrictions studied were for similar first and second constrictions of 1/3, 1/2 and 2/3. A dimensionless constriction spacing of 1.0 was considered. Study showed that the major part of the mean dimensionless pressure drop in the constricted tube occurs predominantly across the first constriction when flow moves towards the valley region formed by the two constrictions. Minimum pressures along the constricted tubes occurs downstream of each constrictions. When the constriction magnitudes increased, the pressure drop across the same length of the tube increases exponentially. The effect of increasing the Reynolds number for all the constriction values considered here is to increase the spreading of the recirculation region between the valley region of the constrictions. The recirculation region formed between the two constrictions has a deminishing effect on the generation of wall vorticity near the second constriction. The effects are more pronounce when the recirculatory flow from the first constriction has spread over the second constriction. In general, a peak wall vorticity is found slightly upstream of each of the constrictions. When the Reynolds number is increased, the peak wall vorticity increases and its location moved upstream. It is noted for the cases considered here that the peak wall vorticity generated by the first constriction is always greater than the peak wall vorticity generated by the second constriction.

Numerical simulation of flow in a circular duct fitted with air‐jet vortex generators

AbstractMost of the fundamental studies of the use of air‐jet vortex generators (AJVGs) have concentrated on their potential ability to inhibit boundary layer separation on aerofoils. However, AJVGs may be of use in controlling or enhancing certain features of internal duct flows. For example, they may be of use in controlling the boundary layer at the entrance to engine air intakes, or as a means of increasing mixing and heat transfer. The objective of this paper is to analyse the flow field in the proximity of an air‐jet vortex generator array in a duct by using two local numerical models, i.e. a simple flat plate model and a more geometrically faithful sector model. The sector model mirrors the circular nature of the duct's cross‐section and the centre line conditions on the upper boundary. The flow was assumed fully turbulent and was solved using the finite volume, Navier–Stokes Code CFX 4 (CFDS, AEA Technology, Harwell) on a non‐orthogonal, body‐fitted, grid using the k–ε turbulence model and standard wall functions. Streamwise, vertical and cross‐stream velocity profiles, circulation and peak vorticity decay, peak vorticity paths in cross‐stream and streamwise direction, cross‐stream vorticity profiles and cross‐stream wall shear stress distributions were predicted. Negligible difference in results was observed between the flat plate and the sector model, since the produced vortices were small relative to the duct diameter and close to the surface. The flow field was most enhanced, i.e. maximum thinning of the boundary layer, with a configuration of 30° pitch and 75° skew angle. No significant difference in results could be observed between co‐ and counter‐rotating vortex arrays. Copyright © 2002 John Wiley & Sons, Ltd.

Flow visualisation of the orthogonal blade-vortex interaction using particle image velocimetry

AbstractThe flow field produced by the orthogonal blade-vortex interaction (BVI) was examined through the application of a particle image velocimetry (PIV) technique, and acquisition of comparative unsteady surface pressure measurements. The velocity vector maps obtained revealed a significant radial flow from the vortex core after severing, in the form of an outward flow from the core when the flow is directed towards the surface (lower), and inward when directed away (upper). With progression of the vortex over the chord of the blade, the interaction led to a decrease in peak vorticity levels on the lower surface, but a steady level was maintained on the upper surface. Assessment of the effect of the interaction on the out-of-plane mass flux was performed through calculation of the divergence, revealing that there is no further variation in the axial flow on either side of the blade after the initial cut.

Phase averaged velocity field in the near wake of a square cylinder obtained by a PIV method

Phase averaged velocity fields in the near wake region behind a square cylinder have been successfully obtained using randomly sampled PIV data sets. The Reynolds number based on the flow velocity and the model height was 3,900. To identify the phase information, we examined the magnitude of circulation and the center of peak vorticity. The center of vorticity was estimated from lowpass filtered vorticity contours adopting a sub-pixel searching algorithm. Due to the sinusoidal nature of circulation which is closely related to the instantaneous vorticity, the location of peak vorticity fits well with a sine curve of the circulation magnitude. Conditionally averaged velocity fields represent the Karman Vortex shedding phenomenon quite successfully within ± 5° phase uncertainty. The oscillating nature of the separated shear layers and the separation bubble at the upper and lower surfaces are clearly observed. With the hot-wire measurement of Strouhal frequency, we found that the convection velocity changes its magnitude very rapidly from 25 to 75 percent of the free stream velocity along the streamwise direction when the flow passes the recirculation region.

Imaging 2D turbulence

Gravity-driven flow in a soap film tunnel is spatially almost two-dimensional. A modification of particle-image velocimetry technique produces a comprehensive quantitative description of the flow. The technique allows simultaneous acquisition of the velocity (two components) in the plane of the film and the film thickness. The latter behaves as a scalar advected by the flow. The visualization method developed for these data sets uses the thickness field, the vorticity field and the instantaneous velocity streamline pattern for surface elevation, color and bump maps respectively, resulting in color surface images that reveal important features of the flow. In decaying turbulence behind a row of cylinders (2D grid turbulence), the images demonstrate the coarsening of the flow structure with downstream distance, which is the feature specific to turbulence in two dimensions. Strong correlation between thickness fluctuations and vorticity peaks also becomes apparent.

Meta-stability of equilibrium statistical structures for prototype geophysical flows with damping and driving

The most-probable states of an equilibrium statistical theory, which consist of monopole vortices, dipole vortex streets, and zonal shear flows for various parameter regimes, are shown to be meta-stable with respect to damped and driven quasigeostrophic dynamics in a periodic β-plane channel. Through a series of numerical experiments that include (1) pure decay, (2) both damping and driving, and (3) both direct and inverse cascades of energy, we demonstrate that statistically most-probable states evolve into other most-probable states with high accuracy, even as the energy changes substantially and the flow undergoes topological transitions from vortex to shear flow, or vice versa. The predictions of the equilibrium statistical theory are calculated by an algorithm, which we call an “approximate dynamics”, that constructs the most-probable states from the instantaneous values of a few quantities in the evolving flow. Qualitatively, the approximate dynamics predicts the correct topological structure — whether vortex flow or zonal shear — in the evolving flow. Quantitatively, the predictions are evaluated by measuring the relative errors between the velocity fields and vorticity fields of the evolving flow and the most-probable states. For evolving monopole vortices we find that errors in the velocity field are generally near 5% and errors in the potential vorticity field are generally near 15%. For evolving dipole vortex streets, the magnitude of the relative errors depends on the amplitude of the localized forcing. For pure decay, the errors in the velocity field are generally near 5% and errors in the vorticity field are generally near 12%; for runs in which the flow is strongly forced by small-scale vortices whose amplitude is nearly 3 10 the peak vorticity in the initial flow, the errors in the velocity field can rise to 20% and the errors in the vorticity field rise to 40%.

A numerical study of the application of vane and air-jet vortex generators

AbstractThe objective of the work described in this paper was to identify differences in the flow fields immediately downstream of air-jet and vane vortex generators. The flows were assumed to be incompressible and fully turbulent and were solved using the finite volume, Navier-Stokes code CFX 4 (CFDS, AEA Technology, Harwell) on a non-orthogonal, body-fitted grid using the k-ε turbulence model and standard wall functions. The behaviour of the longitudinal vortices produced by the vanes and air jets is presented in terms of stream-wise and cross-stream velocity profiles, circulation and peak vorticity decay, peak vorticity paths in the cross-stream and streamwise direction, cross-stream vorticity profiles, and cross-stream distribution of shear stress. The predicted results show that the vanes and air jets considered produce vortices with significantly different circulation strengths, but that the enhancement of skin friction was of similar magnitude in both cases.

Planar velocity measurements in compressible mixing layers

In the present study, we use particle image velocimetry (PIV) to obtain planar, two-component velocity fields in two-dimensional, turbulent mixing layers at convective Mach numbers Mc of 0.25, 0.63, and 0.76. The experiments are performed in a large-scale blowdown wind tunnel, with high-speed free-stream Mach numbers up to 2.25 and shear-layer Reynolds numbers up to 106. Specific issues relating to the application of PIV to supersonic flows are addressed. The instantaneous data are analysed to produce maps of derived quantities such as vorticity, and ensemble averaged to provide turbulence statistics. The results show that compressibility introduces marked changes in the disposition of instantaneous velocity gradients within the layer, and hence in the vorticity field. In particular, peak transverse vorticity values are seen to be confined to thin streamwise sheets under compressible conditions, with little transverse communication. The location of these sheets near the lab-frame sonic velocity suggests a sensitivity of the compressible layer to stationary disturbances. Turbulence statistics derived from the planar velocity measurements confirm previous observations of strong suppression of transverse velocity fluctuations and primary Reynolds stress as Mc increases between 0.25 and 0.76.

A Study on the Near Wake of a Square Cylinder Using Particle Image Velocimetry (III) - Phase Average -

Phase averaged velocity fields in the near wake region behind a square cylinder have been (successfully) obtained using randomly sampled PIV data sets. The Reynolds number based on the flow velocity and the vertex height was 3,900. To identify the phase information, we examined the magnitude of circulation and the center of peak vorticity. The center of vorticity was estimated from lowpass filtered vorticity contours (LES decomposition) adopting a sub-pixel searching algirithm. Due to the sinusoidal nature of firculation which is closely related to the instantaneous vorticity, the location of peak voticity fits well with a sine curve of the circulation magnitude. Conditionally-averaged velocity fields represent the barman vortex shedding phenomenon very well within 5 degrees phase uncertainty. The oscillating nature of the separated shear layer and the separation bubble at the top surface are clearly observed. With the hot-wire measurements of Strouhal frequency, we found thats the convection velocity changes its magnitude very rapidly from 25 to 75 percent of the free stream velocity along the streamwise direction when the flow passes by the recirculation region.