Vortex Shedding Process Research Articles

Aspects of the equilibrium puff in transitional pipe flow

Flow-visualization studies in transitional pipe flow are used to reveal the mechanism responsible for the self-sustenance of a turbulent equilibrium puff. The upstream laminar fluid continuously enters the relatively-slower-moving turbulent puff around the pipe centre. The passage of this high-speed laminar plug flow past the slower fluid that resides near the wall at the upstream interface leads to the shedding of a train of three-dimensional wake-like vortices near the wall. A helical motion near the upstream interface is associated with the vortex-shedding process. The remainder of the puff is a cone of turbulence filled with these wake-like vortices that are decaying slowly; the prominent feature of the decay region is the longitudinal vortices that are apparently undergoing stretching. No toroidal vortex has been observed in the instantaneous flow field at the upstream interface of an individual puff. On the other hand, the wake-like vortices reported here have not been observed before because their three-dimensional and random nature does not allow detection by an ensemble-averaging that is not phase-referenced appropriately.

Local instability characteristics and frequency determination of self-excited wake flows

As suggested by the strong effect resonances and feedback mechanisms can exert upon vortices shed from blunt bodies, it is proposed that the discrete frequency, self-excited vortex shedding process itself is governed by a resonance-like mechanism. With the assumption that to a first approximation the shedding frequency is determined by the behaviour in the linear regime, the resonance hypothesis is found to lead to a bifurcation condition (direct resonance condition) of the local instability eigenvalue. In a corresponding initial value formulation the same condition separates a subcritical region of locally absolute instability from a supercritical region of locally convective instability. The critical basic wake profile corresponding to the bifurcation condition is found to be near the end of the potential core. The pertinent frequency is close to experimentally found values if, in the absence of numerically determined (physically unstable) solutions of the steady Navier-Stokes equations, the steady basic wake flow is modelled realistically. For asymmetrical steady wakes a limiting asymmetry seems to exist beyond which no time-harmonic resonance could be determined. This provides a link to mixing layers where apparently only convective instabilities are possible.

有限要素法による円柱まわりの非定常流れの解析

A newly developed algorithm, GSMAC, remove the main problems for analyzing unsteady flow fields by finite element method, CPU time consumption and maximum storage limitation. This algorithm uses the concept of orthogonal decomposition and cycle-to cycle self-adjustment method. Unsteady viscous flow fields around a circular cylinder are considered to prove the effectiveness. The solution obtained by GSMAC agrees very well with the experimental results by Perry et al., especially for Karman vortex shedding process. Shapes, length and other properties of a pair-vortex behind a cylinder are also compared and in good agreement with the experimental results by Bouard & Coutanceau.

Hydroelastic instabilities of square cylinders

Experiments were conducted to investigate the vortex resonance and galloping instabilities of a square cylinder, mounted elastically and with oscillations restricted to a plane normal to the incident water flow. The cylinders tested comprised sharp-edged sections and sections with corner radius ratios of 0·164 and 0·318. The still water added mass of a cylinder was found to be independent of the oscillation amplitudes, while the still fluid damping was observed to be viscous for amplitudes up to 30% of the cylinder width. In the dynamic tests of sharp-edged cylinders, the vibrations began at a reduced flow velocity slightly less than the vortex resonance speed. In the amplitude domain, depending on the magnitude of the response parameter K s = β (nU r 2) (β = reduced damping, n = mass parameter and U r = vortex resonance speed), three different patterns were identified. In the first pattern, associated with the tests with K s < 0·69, the vortex resonance was found to be indistinguishable from galloping, while in the second pattern, belonging to the tests with 0·73 < K s < 1·4, at reduced flow velocities close to the vortex resonance speed, a build up-drop off behaviour in oscillation amplitudes was observed. This behaviour appeared to have been replaced by a complete separation of vortex resonance from galloping in the third pattern, associated with the tests with K s > 1.64. The system response frequency in a streaming flow was always found to be less than the system natural frequency. Both the vortex resonance and galloping excitations were found to be sensitive to the value of the corner radius ratio. The well known quasi-steady theory was modified to take into account the forces induced by the vortex shedding process.

Pressure fluctuations on a square building model in boundary-layer flows

Spatio-temporal measurements of a fluctuating pressure field acting on the side faces of a square prism of finite height in boundary-layer flows are presented for 0° angle of attack. Two typical neutral atmospheric flow conditions were simulated in the wind tunnel to represent open country and urban flow environments. The fluctuating pressure field data allowed computations of the mean and r.m.s. (root mean square) pressure coefficients, power spectral density, autocorrelations, co-spectra, cross-correlations, orthogonal eigenfunction expansions and statistical dependence. Increased levels of turbulence in the incident flow have a marked influence on the fluctuating pressure field, through modifications which take place in the structure of the separated shear layers. The periodic vortex-shedding process is vitiated in the presence of high levels of turbulence intensity in the incident flow, resulting in redistribution of the energy associated with pressure fluctuations over a wider frequency range.

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.

An Investigation of the Effects of Incidence on the Flow Around a Square Section Cylinder

SummaryA study has been made of the changes that take place in the flow around a square section cylinder as the angle of incidence is increased from 0° to 45°. Measurements of the Strouhal number, S, and the vortex longitudinal spacing, a/d, are presented and used to estimate the vortex strength,, and vortex street spacing ratio, b/a.is found to vary between about 1.2 and 1.7 depending on incidence, and is given approximately by 0.52(1 - Cpb)/2πS, where Cpbis the mean base pressure coefficient. As the incidence is increased from 0°, S at first decreases slightly and then rises sharply to a maximum at 13.5° incidence, which is the incidence where reattachment of the shear layer, in some mean sense, is expected to commence. The spectra of pressure and velocity fluctuations were measured and subharmonic peaks were found in both spectra at 5° and 10° incidence. It is suggested that they may have been caused by an interaction between a vortex and a trailing edge corner. The degree of organisation of the vortex shedding process was estimated by calculating the sharpness factor, Q, of the spectral peaks at the vortex shedding frequency. In general Q fluctuated with changes in incidence. High values of Q occurred at angles of incidence where the rate of change of the mean base pressure coefficient with incidence is very small whereas low values occurred where the flow is changing to a different state.

The vortex-shedding process behind two-dimensional bluff bodies

Using a variety of flow-visualization techniques, the flow behind a circular cylinder has been studied. The results obtained have provided a new insight into the vortex-shedding process. Using time-exposure photography of the motion of aluminium particles, a sequence of instantaneous streamline patterns of the flow behind a cylinder has been obtained. These streamline patterns show that during the starting flow the cavity behind the cylinder is closed. However, once the vortex-shedding process begins, this so-called ‘closed’ cavity becomes open, and instantaneous ‘alleyways’ of fluid are formed which penetrate the cavity. In addition, dye experiments also show how layers of dye and hence vorticity are convected into the cavity behind the cylinder, and how they are eventually squeezed out.

Fluid dynamics of a flow excited resonance, part I: Experiment

This is the first of two companion papers concerned with the physics and detailed fluid dynamics of a flow excited resonance. The phenomenon has been examined by using a rather different approach from others to date, in which usually stability theory has been applied to small wave-like disturbances in an unstable shear layer with an equivalent source to describe the radiation of sound providing the feedback. The physics of the flow acoustic interaction is explained in terms of the detailed momentum and energy exchanges occurring in the fluid itself. Gross properties of the flow and resonance are described in terms of the parameters necessary to determine the behaviour of the self-oscillatory system. In this first paper a full experimental investigation of a flow excited Helmholtz resonator is described, in which the detailed fluid dynamical and acoustic data necessary to develop a mathematical model for the flow was obtained, and a new theory of the interaction process is presented in the companion paper (Part II). The investigation described involved the use of a two-component Laser-Doppler Velocimeter (L.D.V.) and probe microphones to specify completely the velocity and pressure fields and a flow visualization to give qualitative information of the vortex shedding process. The overall aim of the work described in the two papers was to increase fundamental understanding of flow/acoustic interactions.

Sound diffraction at a trailing edge

The diffraction of externally generated sound in a uniformly moving flow at the trailing edge of a semi-infinite flat plate is studied. In particular, the coupling of the sound field to the hydrodynamic field by way of vortex shedding from the edge is considered in detail, both in inviscid and in viscous flow.In the inviscid model the (two-dimensional) diffracted fields of a cylindrical pulse wave, a plane harmonic wave and a plane pulse wave are calculated. The viscous proess of vortex shedding is represented by an appropriate trailing-edge condition. Two specific cases are compared, in one of which the full Kutta condition is applied, and in the other no vortex shedding is permitted. The results show good agreement with Heavens’ (1978) observations from his schlieren photographs, and confirm his conclusions. It is further demonstrated, by an explicit expression, that the sound power absorbed by the wake may be positive or negative, depending on Mach number and source position. So the process of vortex shedding does not necessarily imply an attenuation of the sound.In the viscous model a high-Reynolds-number approximation is constructed, based on a triple-deck boundary-layer structure, matching the harmonic plane wave outer solution to a known incompressible inner solution near the edge, to obtain the viscous correction to the Kutta condition.

Flow Velocity Dependence of Damping in Tube Arrays Subjected to Liquid Cross-Flow

Experiments are conducted to determine the damping for a tube in tube arrays subjected to liquid cross-flow; damping factors in the lift and drag directions are measured for in-line and staggered arrays. It is found that: 1) fluid damping is not a constant, but a function of flow velocity; 2) damping factors in the lift and drag directions are different; 3) fluid damping depends on the tube location in an array; 4) flow velocity-dependent damping is coupled with vortex shedding process and fluid-elastic instability; and 5) flow velocity-dependent damping may be negative. This study demonstrates that flow velocity-dependent damping is important. These characteristics should be properly taken into account in the mathematical modeling of tube arrays subjected to cross-flow.

Interaction of induced sound with flow past a square leading edged plate in a duct

The interaction of resonant sounds with the flow past a thick, blunt, flat plate in a rigid walled square duct has been examined. Sound pressure levels of up to 146 dB ( re 20 μPa) have been recorded. It has been established that the resonant sound can initially be excited at a harmonic of the normal vortex shedding frequency. In some cases, the sound “feeds back” on the vortex shedding process causing a step change in the shedding frequency, increasing the Strouhal number for the plate by up to twice the normal value. This excited vortex shedding and associated resonances can be suppressed by locating the plate at incidence to the air flow direction. Complex duct modes can be generated by the vortex shedding resulting in different regions of the plate shedding at different Strouhal numbers.

Experiments on an aerofoil at high angle of incidence in longitudinal oscillations

Details of flow visualization, aerodynamic forces and pitching moment, static pressure and skin friction measurements have been carried out on a symmetrical aerofoil at fixed angle of incidence in longitudinal oscillations parallel to the uniform airstream of a wind-tunnel.This investigation shows weak unsteady effects at incidences below that of static stall. For higher incidences, strong unsteady effects appear and depend on the frequency and amplitude of the oscillations. The measurements indicate an overshoot of the instantaneous lift and drag which is explained by a strong vortex shedding process occurring during the dynamic stall encountered by the aerofoil in decelerated motion, as observed for profiles oscillating in pitch through stall. When the aerofoil is going forward in accelerated motion dynamic reattachment may be observed at very high incidence over a short part of the period of oscillation.Dynamic stall and dynamic reattachment contribute to a favourable effect of unsteadiness on the mean lift coefficient, which increases as compared to the steady state one, and which is expressed through an empirical formula involving incidence, frequency and amplitude of oscillations. At given incidence, optimization of this feature is achieved by matching the frequency and the amplitude of oscillation, respectively with the frequency linked with the highest peak of energy in the wake, and with the distance between two consecutive vortices in the mean wake when modelled as a von Kármán's vortex street.

Discrete tones of isolated airfoils

Recent experimental measurements reveal that discrete tones are emitted by isolated airfoils under certain operating conditions. Arguments are presented that these tones are unrelated to vortex shedding processes as has been suggested. It is proposed that the tones are generated by a self-excited feedback loop of aerodynamic origin. The loop consists of large-scale unstable disturbances in the boundary layer and wake flow and the feedback acoustic waves. Quantitative deductions based on the feedback loop model compare favorably with experimental measurements. It is also found that the proposed model is consistent with the observed characteristic features associated with the discrete tone phenomenon.

Aerodynamics of oscillating disks and a right-circular cylinder

Detailed studies are reported of the free and forced oscillation of disks and a right-circular cylinder constrained to rotate about a fixed diametrical axis passing through the centre of the body and normal to the free-stream direction. When a disk is free to rotate, it oscillates at a definite frequency with slowly varying amplitude and phase. A right-circular cylinder also oscillates at a definite frequency but with rapidly increasing amplitude. When the amplitude becomes large, after a few cycles of oscillation, the cylinder rotates steadily in one direction.Analogue computer elements, position sensors and a dynamic moment balance were used to study the static restoring moment, dynamic restoring moment, average damping moment, statistical properties of the disk motion and power spectrum of the turbulent moment. The behaviour of the disk and cylinder are explained using the measurements and the theory for random excitation of a linear system. The turbulent exciting moment is caused by the unsteady flow in the wake and can be changed by placing disks and splitter plates in the wake. A model is proposed for the unsteady flow field in the wake behind the disk. The model relates the turbulent moment to the vortex shedding process in the wake.