Instabilities in multi-hole converging flow of viscoelastic fluids

Studies of the onset of instabilities were conducted on single hole and multi-hole contractions using laser speckle visualization. A well characterized elastic fluid was used with constant viscosity of 13.1 Pa · s and elasticity characterized by a longest relaxation time constant of 2.233 s. The onset of instabilities was characterized in terms of the Deborah number and the contraction ratio. Three types of instabilities were observed: pulsing vortices, azimuthally rotating vortices, and swirling vortices. For the single hole contractions the critical Deborah number for instability increased from 4.4 to 5.07 to 5.25 as the contraction ratio increased from 4: 1 to 8: 1 to 12: 1. The magnitude of the instabilities was much greater for the 4: 1 contraction than for the other two contraction ratios. For the multi-hole contraction a square array of nine holes was used and the ratio of the hole diameter to hole spacing was varied. The height of the vortices is very similar for the single hole and multi-hole contractions at low Deborah numbers. At high Deborah numbers the effect of adjacent holes is to reduce the height of the vortices by a factor of three. For the 4: 1 spacing no secondary vortex was observed below a Deborah number of De = 3.7. Secondary vortices occurred for the 8:1 and 10:1 spacing at all Deborah numbers. Unstable pulsing vortices appeared for all spacings at a critical Deborah number around 5.5. Adjacent holes decreased the strength of the unsteady vortex motions. The centerline velocities were measured for the multi-hole contraction at shear rates of 5, 30, and 300 s^–1. The elongational strain rates are similar at a low shear rate of 5 s^–1. As shear rate is increased the onset of stretching occurs closer to the plane of the contraction for the smaller contraction ratios.     

Flow-induced vibrations of low aspect ratio rectangular membrane wings

An experimental study of a low aspect ratio rectangular membrane wing in a wind tunnel was conducted for a Reynolds number range of 2.4×10⁴–4.8×10⁴. Time-accurate measurements of membrane deformation were combined with the flow field measurements. Analysis of the fluctuating deformation reveals chordwise and spanwise modes, which are due to the shedding of leading-edge vortices as well as tip vortices. At higher angles of attack, the second mode in the chordwise direction becomes dominant as the vortex shedding takes place. The dominant frequencies of the membrane vibrations are similar to those of two-dimensional membrane airfoils. Measured frequency of vortex shedding from the low aspect ratio rigid wing suggests that membrane vibrations occur at the natural frequencies close to the harmonics of the wake instabilities. Vortex shedding frequency from rigid wings shows remarkably small effect of aspect ratio even when it is as low as unity.     

An experimental investigation of flow past a dual step cylinder

Flow development in the wake of a dual step cylinder has been investigated experimentally using Laser Doppler Velocimetry and flow visualization. The dual step cylinder model is comprised of a large diameter cylinder (D) mounted at the mid-span of a small diameter cylinder (d). The experiments have been performed for a Reynolds number (Re _D ) of 1,050, a diameter ratio (D/d) of 2, and a range of large cylinder aspect ratios (L/D). The results show that the flow development is highly dependent on L/D. The following four distinct flow regimes can be identified based on vortex dynamics in the wake of the large cylinder: (1) for L/D ≥ 15, three vortex shedding cells form in the wake of the large cylinder, one central cell bounded by two cells of lower frequency, (2) for 8 < L/D ≤ 14, a single vortex shedding cell forms in the wake of the large cylinder, (3) for 2 < L/D ≤ 6, vortex shedding from the large cylinder is highly three-dimensional. When spanwise vortices are shed, they deform substantially and attain a hairpin shape in the near wake, (4) for 0.2 ≤ L/D ≤ 1, the large cylinder induces vortex dislocations between small cylinder vortices. The results show that for Regimes I to III, on the average, the frequency of vortex shedding in the large cylinder wake decreases with L/D, which is accompanied by a decrease in coherence of the shed vortices. In Regime IV, small cylinder vortices connect across the large cylinder wake, but these connections are interrupted by vortex dislocations. With decreasing L/D, the frequency of dislocations decreases and the dominant frequency in the large cylinder wake increases toward the small cylinder shedding frequency.     

Influence of aspect ratio on the mean flow field of a surface-mounted finite-height square prism

The flow around surface-mounted, finite-height square prisms at a Reynolds number of Re = 4.2 × 10⁴ was investigated experimentally in a low-speed wind tunnel using particle image velocimetry. The thickness of the boundary layer on the ground plane relative to the width of the prism was δ/D = 1.5. Four prism aspect ratios were tested, AR = 9, 7, 5, and 3, to study how the aspect ratio influences the flow field close to the prism. Upstream of the prism, lowering the aspect ratio from AR = 9 to AR = 3 causes the stagnation point on the upstream face to move closer to the free end, but there is no influence on the location and strength of the horseshoe vortex. Lowering the aspect ratio from AR = 9 to AR = 3 causes the cross-stream vortices in the upper and lower halves of the wake to move downstream and upstream, respectively; the latter vortex is absent for AR = 3, suggesting this prism sits below the critical aspect ratio. Above the free end of the prism, within the region of separated flow, lowering the aspect ratio from AR = 9 to AR = 3 shifts the location of the cross-stream vortex farther downstream. For the prism of AR = 3, reverse flow above the free end is stronger yet more unsteady compared to the more slender prisms, while the streamwise edge vortices are smaller and weaker.     

Near-ground tornado-like vortex structure resolved by particle image velocimetry (PIV)

The near-ground flow structure of tornadoes is of utmost interest because it determines how and to what extent civil structures could get damaged in tornado events. We simulated tornado-like vortex flow at the swirl ratios of S = 0.03–0.3 (vane angle θ_v = 15°–60°), using a laboratory tornado simulator and investigated the near-ground-vortex structure by particle imaging velocimetry. Complicated near-ground flow was measured in two orthogonal views: horizontal planes at various elevations (z = 11, 26 and 53 mm above the ground) and the meridian plane. We observed two distinct vortex structures: a single-celled vortex at the lowest swirl ratio (S = 0.03, θ_v = 15°) and multiple suction vortices rotating around the primary vortex (two-celled vortex) at higher swirl ratios (S = 0.1–0.3, θ_v = 30°–60°). We quantified the effects of vortex wandering on the mean flow and found that vortex wandering was important and should be taken into account in the low swirl ratio case. The tangential velocity, as the dominant velocity component, has the peak value about three times that of the maximum radial velocity regardless of the swirl ratio. The maximum velocity variance is about twice at the high swirl ratio (θ_v = 45°) that at the low swirl ratio (θ_v = 15°), which is contributed significantly by the multiple small-scale secondary vortices. Here, the results show that not only the intensified mean flow but greatly enhanced turbulence occurs near the surface in the tornado-like vortex flow. The intensified mean flow and enhanced turbulence at the ground level, correlated with the ground-vortex interaction, may cause dramatic damage of the civil structures in tornadoes. This work provides detailed characterization of the tornado-like vortex structure, which has not been fully revealed in previous field studies and laboratory simulations. It would be helpful in improving the understanding of the interaction between the tornado-like vortex structure and the ground surface, ultimately leading to better predictions of tornado-induced wind loads on civil structures.     

Scanning PIV investigation of the laminar separation bubble on a SD7003 airfoil

A laminar separation bubble occurs on the suction side of the SD7003 airfoil at an angle of attack α =  4–8° and a low Reynolds number less than 100,000, which brings about a significant adverse aerodynamic effect. The spatial and temporal structure of the laminar separation bubble was studied using the scanning PIV method at α =  4° and Re = 60,000 and 20,000. Of particular interest are the dynamic vortex behavior in transition process and the subsequent vortex evolution in the turbulent boundary layer. The flow was continuously sampled in a stack of parallel illuminated planes from two orthogonal views with a frequency of hundreds Hz, and PIV cross-correlation was performed to obtain the 2D velocity field in each plane. Results of both the single-sliced and the volumetric presentations of the laminar separation bubble reveal vortex shedding in transition near the reattachment region at Re = 60,000. In a relatively long distance vortices characterized by paired wall-normal vorticity packets retain their identities in the reattached turbulent boundary layer, though vortices interact through tearing, stretching and tilting. Compared with the restricted LSB at Re = 60,000, the flow at Re = 20,000 presents an earlier separation and a significantly increased reversed flow region followed by “huge” vortical structures.     

Dean instability and secondary flow structure in curved rectangular ducts

The pressure driven, fully developed turbulent flow of incompressible viscous fluid (water) in 120° curved ducts of rectangular cross-section is investigated experimentally and numerically. Three different types of curved duct (A-CL, B-SL and C-IL) with continuously varying curvature conform to blade profile as the inner and outer curvature walls to simplify and guide the impeller design of pumps. After validating the numerical method against Particle Image Velocimetry (PIV) measurements, the flow development in the ducts is analyzed in detail by Computational Fluid Dynamics (CFD) for a wide range of Reynolds numbers (Re = 2.4 × 10⁴–1.4 × 10⁵) and aspect ratios (Ar > 1.0, =1.0 and <1.0). The results clearly depict the existence of multiple Dean vortices along the duct: while the axial velocity profile is more related to an inner Dean vortex (called split base vortex), the wall pressure is more influenced by the Dean vortex attached to the inner curvature wall (called ICW Dean vortex). The induced multiple Dean vortices and the secondary flow patterns in the duct cannot be faithfully predicted by using traditional techniques. Therefore, a new criterion based on the vortex core velocities is proposed. With this approach, the effects of Re, Cr and Ar on the Dean instabilities in curved ducts are carefully studied. Decreasing Re promotes the generation of Dean vortices closer to the duct inlet, a trend that is as opposed to laminar flow. In addition, a new pair of vortices called entrainment Dean vortex occurs near the outlet of the curved duct with Ar = 1.0, which has not been previously reported in the literature.     

Laminar co-rotating Batchelor vortex merging

The dynamics of laminar co-rotating vortex pairs without axial flow have been recently thoroughly studied through theoretical, experimental and numerical studies, which revealed different instabilities contributing to the decay of the vortices. In this paper, the objective is to extend the analysis to the case of co-rotating vortices with axial flow at low Reynolds numbers. A high-order incompressible Navier–Stokes flow solver is used. The momentum equations are spatially discretized on a staggered mesh by finite differences and all derivatives are evaluated with 10th order compact finite difference schemes with RK-4 temporal discretization. The initial condition is a linear superposition of two co-rotating circular Batchelor vortices with q = 1. It is found that there is an initial evolution that resembles the evolution that single q = 1 vortices go through. Azimuthal disturbances grow and result in the appearance of large-scale helical sheets of vorticity. With the development of these instability waves, the axial velocity deficit is weakened. The redistribution of both angular and axial momentum between the core and the surroundings drives the vortex core to a more stable configuration, with a higher q value. After these processes, the evolution is somewhat similar to a pair of co-rotating Lamb–Oseen vortices. A three-dimensional instability develops, with a large band of unstable modes, with the most amplified mode corresponding scaling with the vortex initial separation distance. P. J. S. A. Ferreira de Sousa wishes to acknowledge the support of FCT—SFRH/BD/1129/2000 and SFRH/BPD/21778/2005.     

On the formation of Taylor–G?rtler vortices in RMF-driven spin-up flows

This paper is concerned with a liquid metal flow driven by a rotating magnetic field inside a stationary cylinder. We consider especially the secondary meridional flow during the time when the fluid spins up from rest. The developing flow is investigated experimentally and by direct numerical simulations. The vertical profiles of the axial velocity are measured by means of the ultrasound Doppler velocimetry. Evolving instabilities in the form of Taylor–G?rtler vortices have been observed just above the instability threshold (Ta ≥ 1.5· Ta ^cr). The rotational symmetry may survive over a distinct time even if a first Taylor–G?rtler vortex pair has been formed as closed rings along the cylinder perimeter. The transition to a three-dimensional flow in the side layers results from the advection or a precession and splitting of the Taylor–G?rtler vortex rings. The predictable behaviour of the Taylor–G?rtler vortices disappears with increasing magnetic field strength. The numerical simulations agree very well with the flow measurements.     

Three-dimensional numerical simulation of the wake flow of an afterbody at subsonic speeds

We numerically investigate the wake flow of an afterbody at low Reynolds number in the incompressible and compressible regimes. We found that, with increasing Reynolds number, the initially stable and axisymmetric base flow undergoes a first stationary bifurcation which breaks the axisymmetry and develops two parallel steady counter-rotating vortices. The critical Reynolds number (Re _cs) for the loss of the flow axisymmetry reported here is in excellent agreement with previous axisymmetric BiGlobal linear stability (BiGLS) results. As the Reynolds number increases above a second threshold, Re _co, we report a second instability defined as a three-dimensional peristaltic oscillation which modulates the vortices, similar to the sphere wake, sharing many points in common with long-wavelength symmetric Crow instability. Both the critical Reynolds number for the onset of oscillation, Re _co, and the Strouhal number of the time-periodic limit cycle, St_sat, are substantially shifted with respect to previous axisymmetric BiGLS predictions neglecting the first bifurcation. For slightly larger Reynolds numbers, the wake oscillations are stronger and vortices are shed close to the afterbody base. In the compressible regime, no fundamental changes are observed in the bifurcation process. It is shown that the steady state planar-symmetric solution is almost equal to the incompressible case and that the break of planar symmetry in the vortex shedding regime is retarded due to compressibility effects. Finally, we report the developments of a low frequency which depends on the afterbody aspect ratio, as well as on the Reynolds and on the Mach number, prior to the loss of the planar symmetry of the wake.     

A rotating elliptic airfoil in fluid at rest and in a parallel freestream

This paper reports results of DPIV measurements on a two-dimensional elliptic airfoil rotating about its own axis of symmetry in a fluid at rest and in a parallel freestream. In the former case, we examined three rotating speeds (Re _c,Ω = 400, 1,000 and 2,000), and in the later case, four rotating speeds (Ro _c,Ω = 2.4, 1.2, 0.6 and 0.4), together with two freestream velocities (Re _c,u  = 200 and 1,000) and two starting configurations of the airfoil (i.e., chord parallel to (α ₀ = 0°) or normal (α ₀ = 90°) to the freestream). Results show that a rotating airfoil in a stationary fluid produces two distinct types of vortex structures depending on the Reynolds number. The first type occurs at the lowest Reynolds number (Re _c,Ω = 400), where vortices shed from the two edges or tips of the airfoil dissipated quickly, resulting in the airfoil rotating in a layer of diffused vorticity. The second type occurs at higher Reynolds numbers (i.e., Re _c,Ω = 1,000 and 2,000), where the corresponding vortices rotated together with the airfoil. Due to the vortex suction effect, the torque characteristics are likely to be heavily damped for the first type because of the rapidly subsiding vortex shedding, and more oscillatory for the second type due to persistent presence of tip vortices. In a parallel freestream, increasing the tip-speed ratio (V/U) of the airfoil (i.e., decreasing the Rossby number, Ro _c,Ω) transformed the flow topology from periodic vortex shedding at Ro _c,Ω = 2.4 to the generation of a “hovering vortex” at Ro _c,Ω = 0.6 and 0.4. The presence of the hovering vortex, which has not been reported in literature before, is likely to enhance the lift characteristics of the airfoil. Freestream Reynolds number is found to have minimal effect on the vortex formation and shedding process, although it enhances shear layer instability and produces more small-scale flow structures that affect the dynamics of the hovering vortex. Likewise, initial starting configuration of the airfoil, while affecting the flow transient during the initial phase of rotation, has insignificant effect on the overall flow topology. Unfortunately, technical constraint of our apparatus prevented us from carrying out complimentary force measurements; nevertheless, the results presented herein, which are more extensive than those computed by Lugt and Ohring (1977), will provide useful benchmark data, from which more advanced numerical calculations can be carried out to ascertain the corresponding force characteristics, particularly for those conditions with the presence of hovering vortex.     

Aspect-ratio dependence of transient Taylor vortices close to threshold

We perform a detailed numerical study of transient Taylor vortices arising from the instability of cylindrical Couette flow with the exterior cylinder at rest for radius ratio η = 0.5 and variable aspect ratio Γ. The result of Abshagen et al. (J Fluid Mech 476:335–343, 2003) that onset transients apparently evolve on a much smaller time–scale than decay transients is recovered. It is shown to be an artefact of time scale estimations based on the Stuart–Landau amplitude equation which assumes frozen space dependence while full space–time dependence embedded in the Ginzburg–Landau formalism needs to be taken into account to understand transients already at moderate aspect ratio. Sub-critical pattern induction is shown to explain the apparently anomalous behaviour of the system at onset while decay follows the Stuart–Landau prediction more closely. The dependence of time scales on boundary effects is studied for a wide range of aspect ratios, including non-integer ones, showing general agreement with the Ginzburg–Landau picture able to account for solutions modulated by Ekman pumping at the disks bounding the cylinders.      

Effects of the corner radius on the near wake of a square prism

The near wake of square cylinders with different corner radii was experimentally studied based on particle imaging velocimetry (PIV), laser doppler anemometry (LDA) and hotwire measurements. Four bluff bodies, i.e., r/d=0 (square cylinder), 0.157, 0.236, 0.5 (circular cylinder), where r is corner radius and d is the characteristic dimension of the bluff bodies, were examined. A conditional sampling technique was developed to obtain the phase-averaged PIV data in order to characterize quantitatively the effect of corner radii on the near-wake flow structure. The results show that, as r/d increases from 0 to 0.5, the maximum strength of shed vortices attenuates, the circulation associated with the vortices decreases progressively by 50%, the Strouhal number, St, increases by about 60%, the convection velocity of the vortices increases along with the widening of the wake width by about 25%, the vortex formation length and the wake closure length almost double in size. Meanwhile, both the vortex wavelength, λ _x , and the lateral spacing, λ _y , decrease as r/d increases, but the ratio of λ _y to λ _x is approximately 0.29, irrespective of r/d, which is close to the theoretical value of 0.281 for a stable Karman vortex street. The decrease in wavelength is probably responsible for the change in the flow structure from the approximately circular-shaped vortex at r/d=0 to the laterally stretched vortex at r/d=0.5. The leading edge corner radius is more important than the trailing one in influencing the near wake structure since it determines to a great extent the behavior of the streamlines, the separation angle and the base pressure. It is further found that the ratio of the mean drag coefficient to the total shed circulation, C _d/Γ₀, approaches a constant, about 0.25 for different bluff bodies in the subcritical flow regime. The streamwise evolution of vortices and the streamwise fluctuating velocity along the centerline for rounded cylinders are also discussed.     

Investigation of the vortex induced unsteadiness of a separation bubble via time-resolved and scanning PIV measurements

A transitional separation bubble on the suction side of an SD7003 airfoil is considered. The transition process that forces the separated shear layer to reattach seems to be governed by Kelvin–Helmholtz instabilities. Large scale vortices are formed due to this mechanism at the downstream end of the bubble. These vortices possess a three-dimensional structure and detach from the recirculation region, while other vortices are formed within the bubble. This separation of the vortex is a highly unsteady process, which leads to a bubble flapping. The structure of these vortices and the flapping of the separation bubble due to these vortices are temporally and spatially analyzed at angles of attack from 4° to 8° and chord-length based Reynolds numbers Re _c = 20,000–60,000 using time-resolved PIV measurements in a 2D and a 3D set-up, i.e., stereo-scanning PIV measurements are done in the latter case. These measurements complete former studies at a Reynolds number of Re _c = 20,000. The results of the time-resolved PIV measurements in a single light-sheet show the influence of the angle of attack and the Reynolds number. The characteristic parameters of the separation bubble are analyzed focusing on the unsteadiness of the separation bubble, e.g., the varying size of the main recirculation region, which characterizes the bubble flapping, and the corresponding Strouhal number are investigated. Furthermore, the impact of the freestream turbulence is investigated by juxtaposing the current and former results. The stereo-scanning PIV measurements at Reynolds numbers up to 60,000 elucidate the three-dimensional character of the vortical structures, which evolve at the downstream end of the separation bubble. It is shown that the same typical structures are formed, e.g., the c-shape vortex and the screwdriver vortex at each Reynolds number and angle of attack investigated and the occurrence of these patterns in relation to Λ-structures is discussed. To evidence the impact of the freestream turbulence, these results are compared with findings of former measurements.     

Application of an acoustic analogy to PIV data from rectangular cavity flows

The present paper describes a method to derive information about the acoustic emission of a flow using particle image velocimetry (PIV) data. The advantage of the method is that it allows studying sound sources, the related flow phenomena and their acoustic radiation into the far field, simultaneously. In a first step the time history of two-dimensional instantaneous pressure fields is derived from planar PIV data. In a successive step the Curle’s acoustic analogy is applied to the pressure data to obtain the acoustic radiation of the flow. The test cases studied here are two rectangular cavity flows at very low Mach number with different aspect ratios L/H. The main sound source is located at the cavity trailing edge and it is due to the impingement of vortices shed in the shear layer. It is shown that the flow emits sound with a main directivity in the upstream direction for the smaller aspect ratio and the directivity is more uniform for the larger aspect ratio. In the latter case the acoustic pressure spectra has a broader character due to the impact of the downstream recirculation zone onto the shear layer instabilities, destroying their regular pattern and alternating the main sound source.     

Influence of rounding corners on the wake of a finite-length cylinder: An experimental study

This study aims to investigate experimentally the influence of rounding corners (r) as well as aspect ratio (AR) on the flow structures of a surface-mounted finite cylinder. The cylinders with sharp (r* = r/D = 0) and rounded corners (r*=0.167, 0.25 and 0.5) and aspect ratio or height-to-width/diameter ratio (AR = H/D) between 2 and 7 are utilized. The experiments are based on the five-hole probe and hot-wire measurements as well as the oil flow visualization. Wake measurements are made in an open return wind tunnel at the Reynolds number, Re = 1.6 × 10⁴, where Re is defined based on the side width/diameter (D) of the cylinder cross-section and the freestream velocity. It is found that r* and AR have significant effects on the flow structure from the perspective of wake topology, strength of streamwise vortices, and vortex shedding frequency. For all r* considered, the wake is characterized by a quadrupole type (both the tip and base vortices are present) at AR = 7, while a dipole type occurs for AR = 2 and 4 (the base vortices are absent). The strength (circulation) of the streamwise vortex structures is affected by r*. For all AR examined in the present study, the strengths of tip and base vortex structures decrease with increasing r*. The oil flow visualization demonstrates that the features of the horseshoe vortex are sensitive to r* and AR. With increasing r*, the location of the separation line moves downstream and the distance between horseshoe vortex legs decreases. Velocity measurements reveal that the downwash flow enhances with increasing r*. It is also found that the Strouhal number increases progressively by 60% as r* increases from 0 to 0.5, regardless of AR.     

Tip gap height effects on the aerodynamic performance of a cavity squealer tip in a turbine cascade in comparison with plane tip results: part 2—aerodynamic losses

Tip gap height effects on aerodynamic losses downstream of a cavity squealer tip have been investigated in a linear turbine cascade for power generation, in comparison with plane tip results. Three-dimensional flow fields are measured with a five-hole probe for tip gap height-to-chord ratios of h/c = 0.5, 1.0, 1.5 and 2.0%. The cavity squealer tip has a full length squealer with its rim height-to-chord ratio of 5.51%. For a fixed value of h/c, the tip leakage vortex for the cavity squealer tip is always weaker than that for the plane tip, and the flow field in the passage vortex region for the cavity squealer tip is less influenced by the tip leakage flow than that for the plane tip. For the cavity squealer tip, there is no appreciable change in local aerodynamic loss with h/c in the passage vortex region, but local aerodynamic loss in the tip leakage vortex region increases with h/c. The roles of the cavity squealer tip in reducing aerodynamic loss in comparison with the plane tip case are twofold: (1) the cavity squealer tip decreases the leakage flow discharge in the region from the leading edge to the mid-chord, which leads to an aerodynamic loss reduction in the passage vortex region and (2) it also decreases the leakage flow discharge downstream of the mid-chord, which results in an aerodynamic loss reduction in the tip leakage vortex region.     

Dynamics of hairpin vortices generated by a mixing tab in a channel flow

To better understand mixing by hairpin vortices, time-series particle image velocimetry (PIV) was applied to the wake of a trapezoidal-shaped passive mixing tab mounted at the bottom of a square turbulent channel (Re _h =2,080 based on the tab height). Instantaneous velocity/vorticity fields were obtained in sequences of 10 Hz in the tab wake in the center plane (x–y) and in a plane (x–z) parallel to the wall. Periodically-shed hairpin vortices were clearly identified and seen to rise as they advected downstream. Experimental evidence shows that the vortex-induced ejection of the near-wall viscous fluid to the immediate upstream is important to the dynamics of hairpin vortices. It can increase the strength of the hairpin vortices in the near tab region and cause generation of secondary hairpin vortices further downstream when the hairpin heads are farther away from the wall. Measurements also reveal the existence of a type of new secondary vortice with the opposite-sign spanwise vorticity. The distribution of vortex loci in the x–y plane shows that the hairpin vortices and the reverse vortices are spatially segregated in distinct layers. Turbulence statistics, including mean velocity profiles, Reynolds stresses, and turbulent kinetic energy dissipation rate distributions, were obtained from the PIV data. These statistical quantities clearly reveal imprints of the identified vortex structures and provide insight into mixing effectiveness. Received: 24 February 2000/Accepted: 24 October 2000     

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 VR2. 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.Nomenclature A nozzle or jet cross-sectional area - AR aspect ratio, defined as the ratio of the nozzle cross-stream dimension to its streamwise dimension, =H/L - D characteristic jet diameter (for circular jet only) - D_h hydraulic diameter, =4A/P - D_major major axis of an elliptic nozzle - D_minor minor axis of an elliptic nozzle - H cross-stream dimension of the nozzle - L streamwise dimension of the nozzle - P perimeter of the nozzle - Re_j jet Reynolds number, =V_jD/ - VR velocity ratio, =V_j/V - V_j mean jet velocity - V mean cross-flow velocity - x downstream distance from jet center - X cross-plane vorticity - kinematic viscosity