Shed Circulation Research Articles

Moving Surface Actuation, Effects of Frequency-based Shear Layer Excitation on the Response of a Bluff Body Wake

The effect of actuation frequency, using moving surface actuation, is investigated for a square cylinder bluff body wake. Pressure sensor data are used to optimize actuation characteristics through the implementation of an NSGA-II evolutionary algorithm. Velocity field data are obtained using Particle Image Velocimetry (PIV) for baseline and optimized actuation cases. A Proper Orthogonal Decomposition (POD) analysis shows that the vortex shedding frequency shifts between frequencies associated with the actuation, moving between regions of lock-on and quasi-periodicity. Additionally, the POD shows that the energy contained in the coherent shedding motion is reduced through actuation, while the total energy in the velocity field stays relatively constant. A reconstruction of the first 10 POD modes indicates that the coherent contribution to the Reynolds stresses significantly decreases compared to the non-actuated case. The mechanism for drag reduction is investigated using the shed circulation flux and Kochin’s drag formulation model. The drag obtained using PIV measurements and Kochin’s formulation is consistent with trends observed for the base pressure as a function of actuation frequency.

Experimental Investigation of Transverse and Vortex Gust Encounters at Low Reynolds Numbers

This paper aims to study the lift response of transverse and vortex gust encounters. A sine-squared transverse gust was created in a water towing tank using a water jet, whereas a vortex gust was created in a water channel by clockwise half-rotation of an upstream gust generator plate. Forces and flowfields were acquired for both gust types. The effects of the gust ratio and vertical positioning of the gust generator plate were investigated for the transverse gust and the vortex gust encounters, respectively. For a flat plate at a 0 deg angle of attack, changing the gust ratio for the transverse gust was found to have a major effect on the peak lift and a minor effect on the recovery phase; whereas changing the vertical positioning of the gust generator plate for the vortex gust was found to cause relatively minor effects at almost every point in the lift response. Both gust encounters resulted in large transients in the lift force, and the unsteady forcing was found to depend on the circulation shed from the leading edge of the wing. The lift force experienced and the circulation shed showed a steeper increase for the transverse gust encounters despite the same gust ratio of one. Average velocity variations in time were obtained from the flowfield measurements along an upstream line for both gust types, and variations in the gust-induced angle of attack were computed. The Helmbold equation was then used to predict the lift coefficients based on the calculated gust-induced angle of attack. The trends in the measured and predicted lift coefficients were found to compare well with each other, but the values were found to agree well only when the gust-induced angle of attack was low.

Effect of Transverse Gust Velocity Profiles

A large variety of gusts that develop in the atmospheric boundary layer affect aerial vehicles. This study, performed in water tow tanks, compares the response of a flat plate wing to transverse vertical gusts with a top-hat and a sine-squared velocity profile at Reynolds numbers of 20,000–30,000. Experiments are performed for a wide range of gust ratios (0.5–1.5) and angles of attack (0–20 deg). Force measurements for a sine-squared gust show a smoother increase in lift and a lower peak compared with a top-hat gust for the same gust ratio. Linear models are found to work reasonably well predicting the force response for the sine-squared gust, whereas the top-hat gust exhibits significant nonlinear effects at the largest gust ratios. This nonlinear behavior is linked to high levels of circulation shed from the wing edges and the development of nonplanar wakes. Nevertheless, the gust momentum inflow on the wing is directly linked to many characteristics of the lift response, independently of gust velocity profile. In addition, the lift response for the two gusts is found to increase with angle of attack until the wing inclination is large enough to produce a separated wake before gust entry.

On the Effects of Tip Clearance and Operating Condition on the Flow Structures Within an Axial Turbomachine Rotor Passage

Abstract Effects of tip clearance size and flowrate on the flow around the tip of an axial turbomachine rotor are studied experimentally. Visualizations and stereo-particle image velocimetry (PIV) measurements in a refractive index-matched facility compare the performance, leakage velocity, and the trajectory, growth rate, and strength of the tip leakage vortex (TLV) for gaps of 0.49% and 2.3% of the blade chord, and two flowrates. Enlarging the tip clearance delays the TLV breakup in the aft part of the rotor passage at high flowrates but causes earlier breakup under pre-stall conditions. It also reduces the entrainment of endwall boundary layer vorticity from the separation point where the leakage and passage flows meet. Reducing the flowrate or tip gap shifts the location of the TLV detachment from the blade suction side (SS) upstream to points where the leakage velocity is 70–80% of the tip speed. Once detached, the growth rates of the total shed circulation are similar for all cases, i.e., varying the gap or flowrate mostly shifts the detachment point. The TLV migration away from the SS decreases with an increasing gap but not with the flowrate. Two mechanisms dominate this migration: initially, the leakage jet pushes the TLV away from the blade at 50% of the leakage velocity. Further downstream, the TLV is driven by its image on the other side of the endwall. Differences in migration rate are caused by the smaller distance between the TLV and its image for the narrow gap, and the increase in initial TLV strength with decreasing flowrate and gap.

Experimental and analytical investigation into lift prediction on large trailing edge flaps

The present work aims to demonstrate the relationship between circulation production and force production on rapidly maneuvering wings using experimental measurements and two forms of low order modeling: an empirical model based on Lamb’s point vortex impulse theory and an analytical model stemming from classical airfoil theory. Experiments were performed on a 50%-chord trailing-edge flap deflecting with a linear motion profile. Both flap-down (0° − δf) and flap-up (δf − 0°) motions were examined, where δf = 20° or 40°. All cases were run at a Reynolds number of Re ∼ O(104), corresponding to convective times on the order of the free stream or faster, with the fore element of the wing fixed at zero incidence. Time-resolved circulation measurements confirmed that bound circulation on the wing equated to circulation shed into the wake from the trailing edge for the duration of flap deflection. A two-vortex model matched well with the experimental results, regardless of whether the plate experienced fully attached or massively separated flow. An analytical model based only on flap kinematics showed an equivalence between its time-dependent quantities proportional to the motion rate (δ̇,δ̈) and those proportional to the circulation rate (Γ̇) in the empirical model. Agreement between force measurements and both low order models emphasizes the need for future investigation into the direct relationship between force and circulation production.

On the Interactions of a Rotor Blade Tip Flow With Axial Casing Grooves in an Axial Compressor Near the Best Efficiency Point

Experiments in a refractive index-matched axial turbomachine facility show that semicircular skewed axial casing grooves (ACGs) reduce the stall flowrate by 40% but cause a 2.4% decrease in the maximum efficiency. Aiming to elucidate mechanism that might cause the reduced efficiency, stereo-PIV measurements examine the impact of the ACGs on the flow structure and turbulence in the tip region near the best efficiency point (BEP), and compare them to those occurring without grooves and at low flowrates. Results show that the periodic inflow into the groove peaks when the rotor blade pressure side (PS) overlaps with the downstream end of the groove, but diminishes when this end faces the suction side (SS). Entrainment of the PS boundary layer and its vorticity generates a vortical loop at the entrance to the groove, and a “discontinuity” in the tip leakage vortex (TLV) trajectory. During exposure to the SS, the backward tip leakage flow separates at the entrance to the groove, generating a counter-rotating circumferential “corner vortex,” which the TLV entrains into the passage at high flowrates. Interactions among these structures enlarge the TLV and create a broad area with secondary flows and elevated turbulence near the groove's downstream corner. A growing shear layer with weaker turbulence also originates from the upstream corner. The groove also increases the flow angle upstream of the blade tip and varies it periodically. Accordingly, the circulation shed from the blade tip and strength of leakage flow increase near the blade leading edge (LE).

Computation of the Starting Vortex Flow Past a Flat Plate

This paper compares two numerical methods applied to compute the starting vortex flow past a flat plate. The plate is inclined relative to a constant background flow at angle α, with α = 90°, 60°, 30°. The numerical methods considered are (1) direct numerical simulation of the viscous flow (DNS), and (2) an inviscid vortex sheet model. The viscous DNS solves the Navier- Stokes equations by an operator splitting finite-difference method, for Reynolds numbers Re = 250, 500, 1000, 2000. The inviscid flow is computed by a regularized vortex sheet method, with the unsteady Kutta condition imposed at the edges of the plate, for regularization parameters δ = 0.2, 0.1, 0.05. We present viscous vorticity contours, and compare streaklines and shed circulation obtained with both methods. Good agreement is found in the large-scale features of the separated spiral streaklines and the shed circulation as Re increases and δ decreases. For small inclination angle α, secondary separation on the downwind side of the plate introduces small-scale features in the viscous flow that are absent in the inviscid model. The vortex sheet model is much less costly than the viscous DNS, but it is limited by the omission of the boundary layers present in the viscous flow.

Scaling behaviour in impulsively started viscous flow past a finite flat plate

AbstractViscous flow past a finite flat plate which is impulsively started in the direction normal to itself is studied numerically using a high-order mixed finite-difference and semi-Lagrangian scheme. The goal is to resolve the details of the vorticity generation, and to determine the dependence of the flow on time and Reynolds number. Vorticity contours, streaklines and streamlines are presented for a range of times$\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}t\in [0.0002,5]$and Reynolds numbers$\mathit{Re}\in [250,2000]$, non-dimensionalized with respect to the driving velocity and the plate length. At early times, the starting vortex is small relative to the plate length and is expected to grow as if an external length scale were absent. We identify three different types of scaling behaviours consistent with this premise. (i) At early times, solutions with different values of$\mathit{Re}$are identical up to rescaling. (ii) The solution for fixed$\mathit{Re}$satisfies a viscous similarity law in time, locally in space, as illustrated by the core vorticity maximum, the upstream boundary layer thickness, and the maximum speed, in three different regions of the flow. (iii) The vortex core trajectory and the shed circulation satisfy inviscid scaling laws for several decades in time, and are consequently essentially$\mathit{Re}$-independent at these times. In addition, the computed induced drag and tangential forces are found to follow approximate scaling laws that define their dependence on time and$\mathit{Re}$.

The interaction of helical tip and root vortices in a wind turbine wake

Analysis of the helical vortices measured behind a model wind turbine in a water channel are reported. Phase-locked measurements using planar particle image velocimetry are taken behind a Glauert rotor to investigate the evolution and breakdown of the helical vortex structures. Existing linear stability theory predicts helical vortex filaments to be susceptible to three unstable modes. The current work presents tip and root vortex evolution in the wake for varying tip speed ratio and shows a breaking of the helical symmetry and merging of the vortices due to mutual inductance between the vortical filaments. The merging of the vortices is shown to be steady with rotor phase, however, small-scale non-periodic meander of the vortex positions is also observed. The generation of the helical wake is demonstrated to be closely coupled with the blade aerodynamics, strongly influencing the vortex properties which are shown to agree with theoretical predictions of the circulation shed into the wake by the blades. The mutual inductance of the helices is shown to occur at the same non-dimensional wake distance.

Scaling the circulation shed by a pitching panel

AbstractA new scaling parameter is developed for the circulation shed by a rigid, rectangular panel pitching periodically about its leading edge. This parameter is the product of a kinematic and a geometric component. The kinematic component describes the relationship between the mean vorticity flux from the panel surface and the panel motion. The geometric component depends on the ratio of pitching amplitude to the span of the panel. The kinematic component is developed based on the connection between the surface pressure distribution and the resulting surface vorticity flux, which are supported in a stroke-averaged sense by pressure measurements on the surface of the panel. The parameter gives a robust scaling for the total spanwise circulation shed in a half-cycle by the panel. It provides a useful predictive tool, in that it can be either complementary to the formation number or provide an alternative scaling parameter when vortex saturation and pinch-off do not occur.

Development of a Tip-Leakage Flow Part 2: Comparison Between the Ducted and Un-ducted Rotor

The vortical flow in the tip region of a three-bladed rotor was examined using particle imaging velocimetry (PIV). The vortex forming at the tip of the un-ducted propeller was compared to the tip-leakage vortex of the ducted rotor. The planar flow fields were used to identify regions of concentrated vorticity and determine instantaneous vortex properties, revealing the presence of a primary tip-leakage vortex surrounded by a number of secondary vortices. Comparison between the ducted and un-ducted rotor indicated that the presence of the duct reduced the relative strength of the primary tip vortex, making its strength a smaller fraction of the overall shed circulation near the tip. The weaker tip-leakage vortex then became closer in strength to the other secondary vortices in the tip-flow region. However, for the rotor tip geometry considered here, the radius of the primary vortex core did not vary substantially between the ducted and un-ducted cases. The variability of the flow was larger for the ducted case, in terms of the primary vortex position, its identified circulation, core size, and inferred core pressure. This variability was also observed in the scaled velocity fluctuations near the core of the vortex.

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.

Unsteady forces on an accelerating plate and application to hovering insect flight

The aerodynamic forces on a flat plate accelerating from rest at fixed incidence in two-dimensional power-law flow are studied analytically and numerically. An inviscid approximation is made in which separation at the two plate edges is modelled by growing spiral vortex sheets, whose evolution is determined by the Birkhoff–Rott equation. A solution based on a similarity expansion is developed, valid when the scale of the separated vortex is much smaller than the plate dimension. The leading order is given by the well-known similarity growth of a vortex sheet from a semi-infinite flat plate, while equations at the second order describe the asymmetric sweeping effect of that component of the free-stream parallel to the plate. Owing to subtle cancellation, the unsteady vortex force exerted on the plate during the starting motion is independent of the sweeping effect and is determined by the similarity solution, to the order calculated. This gives a mechanism for dynamic stall based on a combination of unsteady vortex lift and pure added mass; the incidence angle for maximum vortex lift is independent of the acceleration profile. Circulation on the flat plate makes no direct contribution. Both lift and drag force predictions from the unsteady inviscid theory are compared with those obtained from numerical solutions of the two-dimensional unsteady Navier–Stokes equations for an ellipse of high aspect ratio, and with predictions of Wagner's classical theory. There is good agreement with numerical results at high incidence and moderate Reynolds number. The force per unit span predicted by the vortex theory is evaluated for parameters typical of insect wings and is found to be in reasonable agreement with numerical simulations. Estimates for the shed circulation and the size of the start-up vortices are also obtained. The significance of this flow as a mechanism for insect hovering flight is discussed.

NUMERICAL STUDY OF THE FLOW PAST A CYLINDER EXCITED TRANSVERSELY TO THE INCIDENT STREAM. PART 2: TIMING OF VORTEX SHEDDING, APERIODIC PHENOMENA AND WAKE PARAMETERS

In Part 1 of the present study, it was found that the phase angle between the transverse force and the motion of a cylinder subjected to oscillations in the cross-flow direction, is strongly dependent on the parameters of the cylinder excitation. Since the phase angle is associated with the timing of vortex shedding, i.e., the phase of vortex formation with respect to the cylinder motion, the alteration of the phase angle at different conditions of forced excitation suggests a change in timing. For the investigation of timing at different excitation conditions, a detailed numerical visualization in the near-wake was conducted, by superimposing the vorticity contours on the streamlines when the cylinder displacement had reached the uppermost position. Flow visualization during a half-cycle for characteristic cases of the cylinder excitation was also performed, in an attempt to explain the alterations induced in the vortex spacing by the cylinder motion, which were also observed in Part 1. The numerical solution revealed a switch in timing when the excitation frequency is increased over the natural shedding frequency, which is accompanied by an instability in the near-wake which renders the wake aperiodic. Various examples of aperiodic flows are illustrated, and an explanation for the initiation of aperiodicity is provided. Finally, a balance between the circulation shed into the wake per oscillation cycle and that surviving in the vortices is conducted, while the distribution ofu ′rmsalong the wake centreline and the base pressure on the cylinder for various excitation conditions are also presented.

On the formation of vortex rings and pairs

The axisymmetric vortex sheet model developed by Nitsche & Krasny (1994) has been extended to study the formation of vortex rings (pairs) at the edge of circular (2D) tube and opening. Computations based on this model are in good agreement with the experiments (Didden (1979) for circular tube and Auerbach (1987) for 2D tube and opening). Using this new model, evidences are provided to show that the main failure of the similarity theory (the false prediction of axial trajectory of vortex ring) is due to its ignorance of the self-induced ring velocity (mutual induction for vortex pair). We further reason why the similarity theory succeeds in its prediction of radial movement of vortex ring. The effects of various parameters such as turning angle α and piston speedU p (t) on the formation of vortex ring are investigated. Numerical result shows that turning angle α has no effect on circulation shed τ. We also discuss Glezer (1988)'s summary on the influence ofU p upon the shedding circulation, and finally give the variation of core distribution of vortex ring with α andU p (t).

Fish foot prints: morphology and energetics of the wake behind a continuously swimming mullet (Chelon labrosus Risso).

The structure of the wake behind a continuously swimming mullet was analysed qualitatively and quantitatively by applying two-dimensional particle image velocimetry. A detailed analysis of the flow pattern and of the swimming movements of the fish allowed us to derive a kinematic explanation of the flow pattern as well as an estimate of the relative contributions of the body and the tail to thrust production. During active propulsion, the undulatory swimming fish shed a wake consisting in the medio-frontal plane of a rearward, zigzagging jet flow between alternating vortices. The fish shed one vortex per half tailbeat when the tail reached its most lateral position. Part of the circulation shed in the vortices had been generated previously on the body by the transverse body wave travelling down the body. This undulatory pump mechanism accounted for less than half of the energy shed in the wake. The remainder was generated by the tail. The vortex spacing matched the tailbeat amplitude and the stride length.

Computational study of viscous effects on lobed mixer flow features and performance

This article describes a computational study of viscous effects on lobed mixer flowfields. The computations, which were carried out using a compressible, three-dimensional, unstructured- mesh NavierStokes solver, were aimed at assessing the impacts on mixer performance of inlet boundary-layer thickness and boundary-layer separation within the lobe. The geometries analyzed represent a class of lobed mixer configurations used in turbofan engines. Parameters investigated included lobe penetration angles from 22 to 45 deg, stream-to-stream velocity ratios from 0.5 to 1.0, and two inlet boundary-layer displacement thicknesses. The results show quantitatively the increasing influence of viscous effects as lobe penetration angle is increased. It is shown that the simple estimate of shed circulation given by Skebe et al. (Experimental Investigation of Three-Dimensi onal Forced Mixer Lobe Flow Field, AIAA Paper 88-3785, July, 1988) can be extended even to situations in which the flow is separated, provided an effective mixer exit angle and height are defined. An examination of different loss sources is also carried out to illustrate the relative contributions of mixing loss and of boundary-layer viscous effects in cases of practical interest.

An experimental study of entrainment and transport in the turbulent near wake of a circular cylinder

This paper describes an experimental investigation of transport processes in the near wake of a circular cylinder at a Reynolds number of 140000. The flow in the first eight diameters of the wake was measured using X-array hot-wire probes mounted on a pair of whirling arms. This flying-hot-wire technique increases the relative velocity component along the probe axis and thus decreases the relative flow angle to usable values in regions where fluctuations in flow velocity and direction are large. One valuable fringe benefit of the technique is that rotation of the arms in a uniform flow applies a wide range of relative flow angles to the X-arrays, making them inherently self-calibrating in pitch. An analog circuit was used to generate an intermittency signal, and a fast surface-pressure sensor was used to generate a phase signal synchronized with the vortex-shedding process. The phase signal allowed sorting of the velocity data into 16 populations, each having essentially constant phase. An ensemble average for each population yielded a sequence of pictures of the instantaneous mean flow field, with the vortices frozen as they would be in a photograph. In addition to globally averaged data for velocity and stress, the measurements yield non-steady mean data (in the sense of an average a t constant phase) for velocity, intermittency, vorticity, stress and turbulent-energy production as a function of phase for the first eight diameters of the near wake. The stresses were resolved into a contribution from the periodic motion and a contribution from the random motion at constant phase. The two contributions are found to have comparable amplitudes but quite different geometries, and the time average of their sum (the conventional global Reynolds stress) therefore has a quite-complex structure. The non-steady mean-vorticity field is obtained with good resolution as the curl of the non-steady mean-velocity field. Less than half of the shed circulation appears in the vortices, and there is a slow decay of this circulation for each shed vortex as it moves downstream. In the discussion, considerable emphasis is put on the topology of the non-steady mean flow, which emerges as a pattern of centres and saddles in a frame of reference moving with the eddies. The kinematics of the vortex-formation process are described in terms of the formation and evolution of saddle points between vortices in the first few diameters of the near wake. One important conclusion is that a substantial part of the turbulence production is concentrated near the saddles and that the mechanism of turbulence production is probably vortex stretching at intermediate scales. Entrainment is also found to be closely associated with saddles and to be concentrated near the upstream-facing interface of each vortex.

Nonaxisymmetric Flow through Annular Actuator Disks: Inlet Distortion Problem

The passage of distorted flow through an annular axial compressor rotor or stator is analyzed in the actuator disk limit. In such a description the flow is steady in absolute coordinates. The resulting analysis yields an overall description of the blade row performance in the presence of inlet flow defects. The present (actuator-disk) analysis is compared successfully with Dunham’s earlier three-dimensional analysis as well as with recent experimental data. In addition, comparison with a recent theory by Greitzer, employing an alternative approach, is made. The analysis shows that at least two important distinct types of vorticity arise, the one being directly analogous to the trailing vorticity (shed circulation) of classical wing theory, and the second being analogous to the vorticity occurring in “secondary flow” theory. The latter arises directly as a result of inlet distortion. The resulting varying flow angles produce spanwise variation in blade loading, and consequent trailing vorticity (Beltrami Flow). The two types of vorticity are therefore interrelated. The static pressure field is also affected by this coupling in agreement with experiment. This problem provided a striking example for which three-dimensional and two-dimensional analyses disagree qualitatively. The vorticity as viewed in coordinates fixed in the rotor is discussed in the Addendum.

A hydrodynamical analysis of fish turning manoeuvres

Slender body theory, adapted here to the study of unsteady, curvilinear large amplitude movements in an inviscid fluid, is applied to the study of the turning mechanism in fishes. The vortex wake is represented by the circulation shed from the fins in the present theory. Examination of filmed sequences of turning fish show that the turning process includes three stages, distinguished by different movements of the centre of mass. In the first and third stages the centre of mass moves in straight lines in the initial and final directions of swimming while in the middle period it moves along an approximately circular connecting arc. The forces and moments acting on the fish, calculated by the present method are found to be in good agreement with these experimental observations.