Traversing field of view and AR-PIV for mid-field wake vortex investigation in a towing tank

Wake vortex flow experiments are performed in a water tank where a 1:48 scaled model of a large transport aircraft A340-300 is towed at the speed of 3 and 5 ms^-1 with values of the angle of attack !={2°, 4°, 8°}. Particle image velocimetry (PIV) measurements are performed in a plane perpendicular to the towing direction describing the streamwise component of the wake vorticity. The instantaneous field of view (I-FOV) is traversed vertically with an underwater moving-camera device tracking the vortex core during the downward motion. An adaptive resolution (AR) image-processing technique is introduced that enhances the PIV interrogation in terms of spatial resolution and accuracy. The main objectives of the investigation are to demonstrate the applicability of PIV diagnostics in wake vortex research with towing-tank facilities. The specific implementation of the traversing field-of-view (T-FOV) technique and the AR image processing are driven by the need to characterize the vortex wake global properties as well as the vortex decay phenomenon in the mid- and far-field. Relevant aerodynamic information is obtained in the mid-field where the time evolution of the vortex structure (core radius and tangential velocity) and of the overall vortex wake (vortex trajectory, descent velocity, circulation) are discussed.     

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.     

The effect of a splitter plate on the flow around a finite prism

The effect of a wake-mounted splitter plate on the flow around a surface-mounted finite-height square prism was investigated experimentally in a low-speed wind tunnel. Measurements of the mean drag force and vortex shedding frequency were made at Re=7.4×10⁴ for square prisms of aspect ratios AR=9, 7, 5 and 3. Measurements of the mean wake velocity field were made with a seven-hole pressure probe at Re=3.7×10⁴ for square prisms of AR=9 and 5. The relative thickness of the boundary layer on the ground plane was δ/D=1.5–1.6 (where D is the side length of the prism). The splitter plates were mounted vertically from the ground plane on the wake centreline, with a negligible gap between the leading edge of the plate and rear of the prism. The splitter plate heights were always the same as the heights of prisms, while the splitter plate lengths ranged from L/D=1 to 7. Compared to previously published results for an “infinite” square prism, a splitter plate is less effective at drag reduction, but more effective at vortex shedding suppression, when used with a finite-height square prism. Significant reduction in drag was realized only for short prisms (of AR≤5) when long splitter plates (of L/D≥5) were used. In contrast, a splitter plate of length L/D=3 was sufficient to suppress vortex shedding for all aspect ratios tested. Compared to previous results for finite-height circular cylinders, finite-height square prisms typically need longer splitter plates for vortex shedding suppression. The effect of the splitter plate on the mean wake was to narrow the wake width close to the ground plane, stretch and weaken the streamwise vortex structures, and increase the lateral entrainment of ambient fluid towards the wake centreline. The splitter plate has little effect on the mean downwash. Long splitter plates resulted in the formation of additional streamwise vortex structures in the upper part of the wake.     

On vortex shedding from low aspect ratio dual step cylinders

A dual-step cylinder is comprised of two cylinders of different diameters. A large diameter cylinder (D) with low aspect ratio (L/D) is attached to the mid-span of a small diameter cylinder (d). The present study investigates the effect of Reynolds number (Re_D) and L/D on dual step cylinder wake development for D/d=2, 0.2≤L/D≤3, and two Reynolds numbers, Re_D=1050 and 2100. Experiments have been performed in a water flume facility utilizing flow visualization, Laser Doppler Velocimetry (LDV), and Particle Image Velocimetry (PIV). The results show that vortex shedding occurs from both the large and small diameter cylinders for 1≤L/D≤3 at Re_D=2100 and 2≤L/D≤3 at Re_D=1050. At these conditions, large cylinder vortices predominantly form vortex loops in the wake and small cylinder vortices form half-loop vortex connections. At lower aspect ratios, vortex shedding from the large cylinder ceases, with the dominant frequency in the large cylinder wake attributed to the passage of vortex filaments connecting small cylinder vortices. At these lower aspect ratios, the presence of the large cylinder induces periodic vortex dislocations. Increasing L/D increases the frequency of occurrence of vortex dislocations and decreases the dominant frequency in the large cylinder wake. The identified changes in wake topology are related to substantial variations in the location of boundary layer separation on the large cylinder, and, consequently, changes in the size of the vortex formation region. The results also show that the Reynolds number has a substantial effect on wake vortex shedding frequency, which is more profound than that expected for a uniform cylinder.     

Effect of natural ventilation on the boundary layer separation and near-wake vortex shedding characteristics of a sphere

Experiments were conducted in water and wind tunnels on spheres in the Reynolds number range 6 × 10³ to 6.5 × 10⁵ to study the effect of natural ventilation on the boundary layer separation and near-wake vortex shedding characteristics. In the subcritical range of Re (<2 × 10⁵), ventilation caused a marginal downstream shift in the location of laminar boundary layer separation; there was only a small change in the vortex shedding frequency. In the supercritical range (Re > 4 × 10⁵), ventilation caused a downstream shift in the mean locations of boundary layer separation and reattachment; these lines showed significant axisymmetry in the presence of venting. No distinct vortex shedding frequency was found. Instead, a dramatic reduction occurred in the wake unsteadiness at all frequencies. The reduction of wake unsteadiness is consistent with the reduction in total drag already reported. Based on the present results and those reported earlier, the effects of natural ventilation on the flow past a sphere can be categorized in two broad regimes, viz., weak and strong interaction regimes. In the weak interaction regime (subcritical Re), the broad features of the basic sphere are largely unaltered despite the large addition of mass in the near wake. Strong interaction is promoted by the closer proximity of the inner and outer shear layers at supercritical Re. This results in a modified and steady near-wake flow, characterized by reduced unsteadiness and small drag. Received: 8 September 1998 / Accepted: 1 January 2000     

Investigations of wake flows of a flat plate in steady,oscillatory and combined flows

Numerical study on near wake flows of a flat plate in three kinds of oncoming flows is made by using the discrete vortex model and improved vorticity creation method. For steady oncoming flow, both gross and detailed features of the wake flow are calculated and discussed. Then, in harmonic oscillatory oncoming flow two different wake flow patterns withK _c=2,4 and 10 are obtained respectively. Our results present a new wake flow pattern for lowKc numbers (Kc<5) describing vortex shedding, pairing and moving in a period of the oscillatory flow starting from rest. The calculated drag and inertia force coefficients are closer to experimental data from the U-tube than the previous results of vortex simulation. For in-line combined oncoming flow the vortex lock-in and dynamic characteristics are simulated. The results are shown to be in good agreement with experiments. The project supported by National Natural Science Fundation of China and LNM of Institute of Mechanics. CAS     

Vortex shedding and structural loading characteristics of finned cylinders

The flow development and structural loading characteristics of cylinders with equispaced circular fins were studied experimentally for a range of fin pitches with constant fin thickness and diameter. The experiments were performed for a range of Reynolds numbers, corresponding to the shear layer transition turbulent shedding regime. Time-resolved planar Particle Image Velocimetry and direct mean drag and fluctuating lift measurements are employed to relate spatio-temporal flow development to structural loading. The results show that wake development is dominated by vortex shedding for all the cases examined. However, the fin pitch ratio has a significant effect on vortex shedding characteristics. The addition of fins increases the characteristic spatial and temporal scales of the main spanwise vortices forming in the near wake. As the fin pitch is decreased to a critical value, the coalescence of boundary layers between the adjacent fins leads to a significant enlargement of the vortex formation region. A modified vortex shedding frequency scaling is proposed, based on the effective diameter, that incorporates a Reynolds number dependence associated with the lateral boundary layers developing on the fin surfaces. A detailed analysis is conducted to characterize the strength of the vortical structures forming in the near wake. The addition of the fins is shown to produce a stabilizing effect on the roll-up process, associated with a reduction in the generation of smaller scale, three-dimensional structures. The results demonstrate that the addition of fins leads to an increase in the mean drag, which is driven primarily by the associated increase in skin friction. The significant effect of the fin pitch ratio on the characteristics of the shed vortices as well as the size of the vortex formation region is shown to lead to substantial variations in the fluctuating loads.     

Dependence of the wake on inclination of a stationary cylinder

Three-dimensional vorticity in the wake of an inclined stationary circular cylinder was measured simultaneously using a multi-hot wire vorticity probe over a streamwise range of x/d = 10–40. The study aimed to examine the dependence of the wake characteristics on cylinder inclination angle α (=0°–45°). The validity of the independence principle (IP) for vortex shedding was also examined. It was found that the spanwise mean velocity which represents the three-dimensionality of the wake flow, increases monotonically with α. The root-mean-square (rms) values of the streamwise (u) and spanwise (w) velocities and the three vorticity components decrease significantly with the increase of α, whereas the transverse velocity (v) does not follow the same trend. The vortex shedding frequency decreases with the increase of α. The Strouhal number (St _N), obtained by using the velocity component normal to the cylinder axis, remains approximately a constant within the experimental uncertainty (±8%) when α is smaller than about 40°. The autocorrelation coefficients ρ _u and ρ _v of the u and v velocity signals show apparent periodicity for all inclination angles. With increasing α, ρ _u and ρ _v decrease and approach zero quickly. In contrast, the autocorrelation coefficient ρ _w of w increases with α in the near wake, implying an enhanced three-dimensionality of the wake.     

Separated flow structures around a cylindrical obstacle in a narrow channel

A detailed experimental study is performed on the separated flow structures around a low aspect-ratio circular cylinder (pin-fin) in a practical configuration of liquid cooling channel. Distinctive features of the present arrangement are the confinement of the cylinder at both ends, water flow at low Reynolds numbers (Re = 800, 1800, 2800), very high core flow turbulence and undeveloped boundary layers at the position of the obstacle. The horseshoe vortex system at the junctions between the cylinder and the confining walls and the near wake region behind the obstacle are deeply investigated by means of Particle Image Velocimetry (PIV). Upstream of the cylinder, the horseshoe vortex system turns out to be perturbed by vorticity bursts from the incoming boundary layers, leading to aperiodical vortex oscillations at Re = 800 or to break-away and secondary vorticity eruptions at the higher Reynolds numbers. The flow structures in the near wake show a complex three-dimensional behaviour associated with a peculiar mechanism of spanwise mass transport. High levels of free-stream turbulence trigger an early instabilization of the shear layers and strong Bloor–Gerrard vortices are observed even at Re = 800. Coalescence of these vortices and intense spanwise flow inhibit the alternate primary vortex shedding for time periods whose length and frequency increase as the Reynolds number is reduced. The inhibition of alternate vortex shedding for long time periods is finally related to the very large wake characteristic lengths and to the low velocity fluctuations observed especially at the lowest Reynolds number.     

On vortex shedding behind a circular disk

Abtract  Experiments were performed for individual realizations of the vortex shedding process behind a circular disk at Reynolds numbers of 10³–10⁵, at which periodic vortex shedding prevails in the wake. The phase differences regarding the individual vortex shedding structures detected at multiple circumferential locations in the wake were obtained by analyzing the hot-wire signals with a conditional-sampling scheme. The phase differences of vortex shedding detected at circumferential positions 90° apart show a wide scatter, but the anti-phase character is largely preserved in the individual vortex shedding process as detected at circumferential locations 180° apart. The randomness of phase differences involved in the vortex shedding process is noted to be essential in order to satisfy the axisymmetric property of the global flow. Received: 4 April 19969/Accepted: 29 January 1997     

Time resolved PIV analysis of flow over a NACA 0015 airfoil with Gurney flap

A NACA 0015 airfoil with and without a Gurney flap was studied in a wind tunnel with Re _c = 2.0 × 10⁵ in order to examine the evolving flow structure of the wake through time-resolved PIV and to correlate this structure with time-averaged measurements of the lift coefficient. The Gurney flap, a tab of small length (1–4% of the airfoil chord) that protrudes perpendicular to the chord at the trailing edge, yields a significant and relatively constant lift increment through the linear range of the C _L versus α curve. Two distinct vortex shedding modes were found to exist and interact in the wake downstream of flapped airfoils. The dominant mode resembles a Kàrmàn vortex street shedding behind an asymmetric bluff body. The second mode, which was caused by the intermittent shedding of fluid recirculating in the cavity upstream of the flap, becomes more coherent with increasing angle of attack. For a 4% Gurney flap at α = 8°, the first and second modes corresponded with Strouhal numbers based on flap height of 0.18 and 0.13. Comparison of flow around ‘filled’ and ‘open’ flap configurations suggested that the second shedding mode was responsible for a significant portion of the overall lift increment.     

L1 Continuous Dependence Property¶for Systems of Conservation Laws

This paper is concerned with the uniqueness and L¹ continuous dependence of entropy solutions for nonlinear hyperbolic systems of conservation laws. We study first a class of linear hyperbolic systems with discontinuous coefficients: Each propagating shock wave may be a Lax shock, or a slow or fast undercompressive shock, or else a rarefaction shock. We establish a result of L¹ continuous dependence upon initial data in the case where the system does not contain rarefaction shocks. In the general case our estimate takes into account the total strength of rarefaction shocks. In the proof, a new time-decreasing, weighted L¹ functional is obtained via a step-by-step algorithm. To treat nonlinear systems, we introduce the concept of admissible averaging matrices which are shown to exist for solutions with small amplitude of genuinely nonlinear systems. Interestingly, for many systems of continuum mechanics, they also exist for solutions with arbitrary large amplitude. The key point is that an admissible averaging matrix does not exhibit rarefaction shocks. As a consequence, the L¹ continuous dependence estimate for linear systems can be extended to nonlinear hyperbolic systems using a wave-front tracking technique.     

An Existence Theorem¶for the Navier-Stokes Flow¶in the Exterior of a Rotating Obstacle

We consider the three-dimensional Navier-Stokes initial value problem in the exterior of a rotating obstacle. It is proved that a unique solution exists locally in time if the initial velocity possesses the regularity L^1/2. This regularity assumption is the same as that in the famous paper of Fujita &; Kato. An essential step for the proof is the deduction of a certain smoothing property together with estimates near t˸ of the semigroup, which is not an analytic one, generated by the operator \Cal Lu = -P[\De u+(\om×x)·\na u-\om×u]\Cal Lu= -P\left[\De u+(\om\times x)\cdot\na u-\om\times u\right] in the space L², where y stands for the angular velocity of the rotating obstacle and P denotes the projection associated with the Helmholtz decomposition.     

Vortex shedding modeling using diffusive van der Pol oscillatorsModélisation du détachement tourbillonnaire avec des oscillateurs de van der Pol interagissant par diffusion

A simple model for the near wake dynamics of slender bluff bodies in cross-flow is analyzed. It is based on a continuous distribution of van der Pol oscillators arranged along the spanwise extent of the structure and interacting by diffusion. Diffusive interaction is shown to be able to model cellular vortex shedding in shear flow, the cell size being estimated analytically with respect to the model parameters. Moreover, diffusive interaction succeeds in describing qualitatively the global suppression of vortex shedding from a sinuous structure in uniform flow. To cite this article: M.L. Facchinetti et al., C. R. Mecanique 330 (2002) 451–456.     

Experimental investigation of the interaction between a plane wall jet and a parallel offset jet

The dual-jet flow generated by a plane wall jet and a parallel offset jet at an offset ratio of d/w = 1.0 has been investigated using Particle Image Velocimetry (PIV). The particle images are captured, processed, and subsequently used to characterize the flow in terms of the 2D velocity and vorticity distributions. Statistical characteristics of the flow are obtained through ensemble averaging of 360 instantaneous velocity fields. Also presented is a time series of instantaneous flow fields to illustrate the dynamic interaction between the two jets. Results reveal that the near field of the flow is characterized by a periodic large-scale Karman-like vortex shedding similar to what would be expected in the wake of a bluff body. The existence of the Karman-like vortices results in periodic interactions between the two jets; in addition, these vortices produce noticeable impact on the jet outer layers, i.e., the free shear layer of the offset jet and the wall boundary layer of the wall jet. A schematic of vortex/shear layer interaction is proposed to illustrate the flow pattern.     

Turbulence measurements around a body in a re-circulating water channel by a hot film probe

Measurements were made in the stern boundary layers and near wakes of an elliptic cylinder and a slender ship model. Turbulence intensities, Reynolds stresses, kinematic eddy viscosities and mixing lengths are presented. For the elliptic cylinder, furthermore, auto-correlation and power spectrum are obtained. It is shown that the separation from the cylinder increases the turbulence intensities, and the Kármán vortices enhance the turbulence power at the vortex frequency. All distributions of Reynolds stresses in the thick boundary layer and wake of the ship model show a secondary low peak at about half the thickness.     

Asymmetric vortex shedding flow past an inclined flat plate at high incidence

This paper reports an experimental investigation of the vortex shedding wake behind a long flat plate inclined at a small angle of attack to a main flow stream. Detailed velocity fields are obtained with particle-image velocimetry (PIV) at successive phases in a vortex shedding cycle at three angles of attack, α=20°, 25° and 30°, at a Reynolds number Re≈5,300. Coherent patterns and dynamics of the vortices in the wake are revealed by the phase-averaged PIV vectors and derived turbulent properties. A vortex street pattern comprising a train of leading edge vortices alternating with a train of trailing edge vortices is found in the wake. The trailing edge vortex is shed directly from the sharp trailing edge while there are evidences that the formation and shedding of the leading edge vortex involve a more complicated mechanism. The leading edge vortex seems to be shed into the wake from an axial location near the trailing edge. After shedding, the vortices are convected downstream in the wake with a convection speed roughly equal to 0.8 the free-stream velocity. On reaching the same axial location, the trailing edge vortex, as compared to the leading edge vortex, is found to possess a higher peak vorticity level at its centre and induce more intense fluid circulation and Reynolds stresses production around it. It is found that the results at the three angles of attack can be collapsed into similar trends by using the projected plate width as the characteristic length of the flow.     

Vortex shedding flow behind a slowly rotating circular cylinder

This paper investigates flow past a rotating circular cylinder at 3600?Re?5000 and α?2.5. The flow parameter α is the circumferential speed at the cylinder surface normalized by the free-stream velocity of the uniform cross-flow. With particle image velocimetry (PIV), vortex shedding from the cylinder is clearly observed at α<1.9. The vortex pattern is very similar to the vortex street behind a stationary circular cylinder; but with increasing cylinder rotation speed, the wake is observed to become increasing narrower and deflected sideways. Properties of large-scale vortices developed from the shear layers and shed into the wake are investigated with the vorticity field derived from the PIV data. The vortex formation length is found to decrease with increasing α. This leads to a slow increase in vortex shedding frequency with α. At α=0.65, vortex shedding is found to synchronize with cylinder rotation, with one vortex being shed every rotation cycle of the cylinder. Vortex dynamics are studied at this value of α with the phase-locked eduction technique. It is found that although the shear layers at two different sides of the cylinder possess unequal vorticity levels, alternating vortices subsequently shed from the cylinder to join the two trains of vortices in the vortex street pattern exhibit very little difference in vortex strength.