Showing papers on "Vortex shedding published in 1992"

Aspect ratio and end plate effects on vortex shedding from a circular cylinder

Abstract: Aspect ratio effects on the vortex shedding flow from a circular cylinder have been studied by using moveable end plates. Experiments were carried out to measure fluctuating forces, shedding frequency and spanwise correlation whilst varying end plate separation and Reynolds number. The aspect ratio (0.25-12) was found to have a most striking effect on the fluctuating lift. Within a certain range of Reynolds number an increase of the sectional fluctuating lift was obtained for reduced aspect ratio, and showed a maximum for an aspect ratio of 1, where the fluctuating lift could be almost twice the value for very large aspect ratios. This increase of the lift amplitude was found to be accompanied by enhanced spanwise correlation of the flow. The measurements were carried out over the Reynolds number range 8 > 103 < Re < 1.4 x 105. The strong increase in fluctuating lift with small aspect ratio did not occur at the lower and upper boundaries of this range. In the lower Reynolds number range (Re < 2 x 104) the trend could be reversed, i.e. the fluctuating lift decreased with decreasing aspect ratio. Also, with small aspect ratio, a shedding breakdown was found in the upper Reynolds number range (Re = 1.3 x 105). The main three dimensional feature observed was a spanwise variation in the phase of vortex shedding, accompanied by amplitude modulation in the lift signal. However, the level of three-dimensionality can be reduced by using a small aspect ratio. Three-dimensional vortex shedding features are discussed and comparison of the results with those from both two-dimensional numerical simulations and other experiments using large aspect ratios are presented.

The natural and forced formation of spot-like vortex dislocations in the transition of a wake

Abstract: The three-dimensional transition of the flow behind a bluff body is studied, with an emphasis placed on the evolution of large-scale structures in the wake. It has previously been found that there are two fundamental modes of three-dimensional vortex shedding in the wake of a circular cylinder (each mode being dependent on the range of Reynolds number), with a spanwise lengthscale of the same order as the primary streamwise wavelength of the vortex street. However. it is shown in the present study that the wake transition also involves the appearance of large-scale spot-like ‘vortex dislocations’, that grow downstream to a size of the order of 10–20 primary wavelengths. Vortex dislocations are generated between spanwise vortex-shedding cells of different frequency. The presence of these dislocations explains the large intermittent velocity irregularities that were originally found by Roshko (1954) and later by Bloor (1964) to characterize transition. The presence of these vortex dislocations in wake transition is largely responsible for the break-up to turbulence of the wake as it travels downstream.In order to study their evolution in detail, dislocations have been (passively) forced to occur at a local spanwise position with the use of a small ring disturbance. It is found that ‘two-sided’ dislocations are stable in a symmetric in-phase configuration, and that they induce quasi-periodic velocity spectra and (beat) dislocation-frequency oscillations in the near wake. Intrinsic to these dislocations is a mechanism by which they spread rapidly in the spanwise direction, involving helical twisting of the vortices and axial core flows. This is felt to be a fundamental mechanism by which vortices develop large-scale distortions in natural transition. As the wake travels downstream, the energy at the low dislocation frequency decays slowly (in contrast to the rapid decay of other frequencies), leaving the downstream wake dominated by the large dislocation structures. Distinct similarities are found between the periodic forced dislocations and the intermittent dislocations that occur in natural transition. Further similarities of dislocations in different types of flow suggest that vortex or phase dislocations could conceivably be a generic feature of transition in all shear flows.

An arbitrary Lagrangian-Eulerian finite rigid element method for interaction of fluid and a rigid body

Abstract: A computational procedure is developed to solve the problems of coupled motion of a rigid body and a viscous incompressible fluid; the former is mounted on elastic springs, and the latter is surrounding the rigid body. The arbitrary Lagrangian-Eulerian method is employed to incorporate the interface conditions between the body and the fluid. The streamline upwind/Petrov-Galerkin finite element method is used for the spatial discretization of the fluid domain, and the predictor-corrector method is used for the time integration. The method is applied to evaluate the added mass and the added damping of a circular cylinder as well as to simulate the vibration of a circular cylinder induced by vortex sheddings.

Vortex Shedding From a Circular Cylinder of Finite Length Placed on a Ground Plane

Abstract: This paper describes a study of changes in the vortex formation and the turbulent wake from a circular cylinder with a finite aspect ratio, placed on a ground plane. The experiment was carried out in an N.P.L. blow down type wind-tunnel, with a working section of 500 mm × 500 mm × 2,000 mm, and between the Reynolds number 2.5 × 104 and 4.7 × 104 . The surface-pressure distributions on the circular cylinder were measured and the drag coefficient was determined from these measurements. Vortices of two kinds generated in the flow-field around the cylinder were observed. The power spectrum, auto-correlation, space-correlation, velocity defects, and turbulent intensities in the turbulent wake behind a circular cylinder were also measured. It was found that the flow pattern changed rapidly above aspect ratio H/D = 4, with vortex shedding changing from symmetric “arch” type to antisymmetric “Karman” type.

Viscous and inviscid instabilities of a trailing vortex

Abstract: The linear stability of the trailing line vortex model of Batchelor (1964) is studied using a spectral collocation and matrix eigenvalue method. The entire unstable region in the swirl/axial wavenumber parameter space is mapped out for various azimuthal wavenumbers for both the inviscid and viscous stability problem. The results of the study provide a direct numerical validation of the large-azimuthal-wavenumber asymptotic analysis of Leibovich and Stewartson (1983). It is shown that accurate results are obtained up to azimuthal wavenumbers of 10,000 and greater, and the agreement with the asymptotic theory is excellent.

Numerical prediction of vortex shedding behind a square cylinder

Abstract: It is common knowledge that flow around bluff bodies exhibits oscillatory behaviour. The aim of the present study is to compute the steady two-dimensional flow around a square cylinder at different Reynolds numbers and to determine the onset of unsteadiness through a linear stability analysis of the steady flow. Stability of the steady flow to small two-dimensional perturbations is analysed by computing the evolution of these perturbations. An analysis of various time-stepping techniques is carried out to select the most appropriate technique for predicting the growth of the perturbations and hence the stability of the flow. The critical Reynolds number is determined from the growth rate of the perturbations. Computations are then made for periodic unsteady flow at a Reynolds number above the critical value. The predicted Strouhal number agrees well with experimental data. Heat transfer from the cylinder is also studied for the unsteady laminar flow.

A finite element study of incompressible flows past oscillating cylinders and aerofoils

Abstract: We present our numerical results for certain unsteady flows past oscillating cylinders and aerofoils. The computations are based on the stabilized space-time finite element formulation. The implicit equation systems resulting from the space-time finite element discretizations are solved using iterative solution techniques. One of the problems studied is flow past a cylinder which is forced to oscillate in the horizontal direction. In this case we observe a change from an unsymmetric mode of vortex shedding to a symmetric one. An extensive study was carried out for the case in which a cylinder is mounted on lightly damped springs and allowed to oscillate in the vertical direction. In this case the motion of the cylinder needs to be determined as part of the solution, and under certain conditions this motion changes the vortex-shedding pattern of the flow field significantly. This nonlinear fluid-structure interaction exhibits certain interesting behavior such as 'lock-in' and 'hysteresis', which are in good agreement with the laboratory experiments carried out by other researchers in the past. Preliminary results for flow past a pitching aerofoil are also presented.

Stratified flow past a sphere

Abstract: The flow of a linearly stratified fluid past a sphere is considered experimentally in the Froude number Fi, Reynolds number Re, ranges 0.005 ≤ Fi ≤ 20 and 5 ≤ Re ≤ 10000. Flow visualization techniques and density measurements are used to describe the rich range of characteristic flow phenomena observed. These different flow patterns are mapped on a detailed Fi against Re flow regime diagram. In most instances the flow patterns were found to be very different from those observed in homogeneous fluids. Vortex shedding characteristics, for example, were found to be dramatically affected by the presence of stratification. Where possible, the results are compared with available analytical and numerical models.

Numerical investigation of confined wakes behind a square cylinder in a channel

Abstract: The structure of confined wakes behind a square cylinder in a channel is investigated via the numerical solution of the unsteady Navier–Stokes equations. Vortex shedding behind the cylinder induces periodicity in the flow field. Details of the phenomenon are simulated through numerical flow visualization. The unsteady periodic wake can be characterized by the Strouhal number, which varies with the Reynolds number and the blockage ratio of the channel. The periodicity of the flow is, however, damped in the downstream region of a long duct. This damping may be attributed to the influence of side walls on the flow structure.

A model for the formation of oblique shedding and ‘‘chevron’’ patterns in cylinder wakes

Abstract: It is demonstrated that many features of flow visualizations involving oblique vortex shedding from two‐dimensional bluff bodies, cylinders in particular, are qualitatively well described by a one‐dimensional model, which represents diffusively coupled oscillators arranged along a line parallel to the cylinder. In mathematical terms, the idealized model consists of a transverse Ginzburg–Landau equation, in which the coefficients are determined experimentally. In physical terms, the model describes the formation of a pattern of tracer particles (e.g., smoke) over a very short streamwise interval which is subsequently only convected downstream. It is shown that, as in impulsively started experiments, ‘‘vortex shedding’’ in the model starts parallel to the cylinder. Regions of oblique shedding then develop from the cylinder ends and lead to steady‐state chevrons for symmetric end conditions. Selection rules for the shedding angle as a function of Reynolds number are derived from the model and compared to experiments.

An exploration of the wake three dimensionalities caused by a local discontinuity in cylinder diameter

Abstract: The wake three‐dimensionality caused by a local discontinuity in cylinder diameter (a stepped cylinder) was studied. Changes in vortex shedding frequency caused by the discontinuity took place in either a direct or an indirect mode, depending on the diameter ratio and the Reynolds number. The roles of oblique shedding and frequency modulation of vortex shedding were studied. The physical change in vortex shedding frequency occurred differently for each mode. A wavelet analysis is used to explore frequency modulations in the wake. The relationship between vortex linkages, frequency changes, secondary instability, and these two modes is discussed.

The response and symmetry properties of a cylinder wake subjected to localized surface excitation

Abstract: Symmetric and antisymmetric periodic disturbances introduced directly into the boundary layer on a circular cylinder at low Reynolds number are shown by experiment to be capable of modifying the vortex formation process and changing the vortex shedding frequency. Spectral measurements have shown that the antisymmetric vortex shedding mode is strongly coupled to the symmetric first harmonic mode. When symmetric excitation is applied, three different shapes of the mean velocity profiles can be identified as the forcing amplitude is increased. At low forcing amplitudes nonlinear interaction between the forcing field and the natural wake oscillator produces sum and difference modes. Symmetric forcing with intermediate-amplitude disturbances suppresses the natural shedding frequency, and the dominant vortex shedding energy appears as a sinuous mode at half the excitation frequency. At high symmetric forcing amplitudes a threshold is reached, above which the large-scale vortices do not form. The symmetries of the combination modes follow two simple rules based on the symmetries of the interacting modes. The symmetry rules provide an explanation for the fundamental difference in wake structure that occurs between symmetric forcing and antisymmetric forcing.

A numerical study of vortex shedding from flat plates with square leading and trailing edges

Abstract: This paper describes a numerical study of the flow around flat plates with square leading and trailing edges on the basis of a finite-difference analysis of the two-dimensional Navier-Stokes equations. The chord-to-thickness ratio of a plate, d/h, ranges from 3 to 9 and the value of the Reynolds number based on the plate's thickness is constant and equal to 103. The numerical computation confirms the finding obtained in our previous experiments that vortex shedding from flat plates with square leading and trailing edges is caused by the impinging-shear-layer instability. In particular, the Strouhal number based on the plate's chord increases stepwise with increasing d/h in agreement with the experiment. Numerical analyses also provide some crucial information of the complicated vortical flow occurring near the trailing edge in conjunction with the vortex shedding mechanism. Finally, the mechanism of the impinging-shear-layer instability is discussed in the light of the experimental and numerical findings.

Sources of High Alpha Vortex Asymmetry at Zero Sideslip

Abstract: A review of existing experimental results for slender bodies and delta wings, tested at high angles of attack, reveals that no physical evidence exists that vortex asymmetry on slender pointed bodies or delta wings has ever occurred through the so-called hydrodynamic instability process. It will be shown that in the numerous tests performed, asymmetric flow separation and/or asymmetric flow reattachment, were the flow mechanisms triggering the vortex asymmetry. Slender wing rock is found to result from a basic lack of roll damping, existing for attached leading-edge vortices, and the vortex-asymmetry is generated at nonzero roll angle, i.e., for asymmetric flow conditions. Nomenclature b = wingspan c = reference length, d CQ = delta wing center chord d = maximum diameter of body of revolution € = rolling moment, coefficient C€ = €/(p00U£/2) Re = Reynolds number based on d and freestream conditions S — reference area, ird2/4 or projected wing area U = horizontal velocity Y = side force, coefficient CY = Y/(pJJl/2) a = angle of attack OA = aPex half-angle Oc = cone half-angle A = leading-edge sweep p = air density = body roll angle Subscripts A = apex c = cone oo = freestream conditions

Vortex Shedding from Slender Cones at Low Reynolds Numbers

Abstract: The phenomenon of vortex shedding arising from bluff bodies in a fluid flow has been investigated for over a hundred years. Most previous research has concentrated on circular cylinders normal to the flow, and has shown that the frequency associated with shedding depends on Reynolds number. The present investigation has been concerned with vortex shedding from cones, that is bodies of circular cross-section possessing a slight spanwise taper. The resulting presence of a continuously varying Reynolds number along the span of the cone induces a continuously varying ‘natural’ shedding frequency. Earlier experiments have shown that, at low Reynolds numbers, spanwise ‘cells’ are formed along the cone, in each of which the frequency is constant [1].

Dynamics of singular vortices on a beta-plane

Abstract: A new singular-vortex theory is presented for geostrophic, beta-plane dynamics The stream function of each vortex is proportional to the modified Bessel function Ko(pr), where p can be an arbitrary positive constant If p−1 is equal to the Rossby deformation scale Rd, then the vortex is a point vortex; for p−1 ≠ Rd the relative vorticity of the vortex contains an additional logarithmic singularity Owing to the β-effect, the redistribution of the background potential vorticity produced by the vortices generates a regular field in addition to the velocity field induced by the vortices themselves Equations governing the joint evolution of singular vortices and the regular field are derived A new invariant of the motion is found for this system If the vortex amplitudes and coordinates are set in a particular way then the regular field is zero, and the vortices form a system moving along latitude circles at a constant speed lying outside the range of the phase velocity of linear Rossby waves Each of the systems is a discrete two-dimensional Rossby soliton and, vice versa, any distributed Rossby soliton is a superposition of the singular vortices concentrated in the interior region of the soliton An individual singular vortex is studied for times when Rossby wave radiation can be neglected Such a vortex produces a complicated spiral-form regular flow which consists of two dipoles with mutually perpendicular axes The dipoles push the vortex westward and along the meridian (cyclones move northward, and anticyclones move southward) The vortex velocity and trajectory are calculated and applications to oceanic and atmospheric eddies are given

Experimental investigation of uniform-shear flow past a circular cylinder

Abstract: Extensive laboratory experiments were carried out to investigate the uniform-shear flow approaching a circular cylinder. The aim was to present the Strouhal number (St)- Reynolds number (Re) diagrams over a broad range of the shear paramenter K (0≤K≤0.25) and at higher values of Re (600≤Re≤1600). An image processing technique, in conjuction with flow visualization studies, was used to secure more quantitative depictions of vortex shedding from the cylinder. The Strouhal number increases with increasing shear parameter

Numerical simulation of vortex shedding phenomenon in 2D test case solid rocket motors

Abstract: Segmented Solid Rocket Motors tend to develop unpredicted thrust and uressure oscillations. linked to a criodic vortex shcdding phcnomenon. Aspart of Arianc $ PUO MPS solid motor stability assessmcnt. a research effort was initiated and aimed at il full numerical simulation of the unsteady, compressible internal flow. The objective of the present work is to demonstrate the feasibility of a direct numerical simulation of the vortex shedding henomenon on test case motors. The computer equations, by means of an expicit predictor/corrector Mc Cormack scheme with an improved (Jameson type) artificial viscosity algorithm. A r p e r test ,case motor was devised by means of a hydro ynamic stability analy+ of mean flow shear layer. Computations done wth optimized artificial viscosity terms gave rise to a marked self excited vortex shedding phenomenon of constant am litude close to the second axial mode frequency, in v excited phenomenon was observefwith both the Euler and Navler-Stokes codes. Moreover planar com utations artificial viscosity added, and gave rise to identical vortex shedding henomenon. First comparisons with Flandro’s codes, so P ve the 2D unstead , Euler or Navier-Stokes bot R axisymmetrie and planar confi urations. Similar self have been performed with the Euler code, w ~ t R out any linearize 2 approach are also presented. INTRODUCTION-OBJECTIVES This work is part of the overall combustion stability assessment of the Ariane 5 P230 MPS solid ro ellant motor and has been supported b CNES and E P J . Due to the segmented design of the P$ motor, it is believed that there exists a potentially severe risk for motor instabiMy, although the moFor is predicted stable by conventional linear acoustic balance computations. Indeed, a number of US works, related to segmented motors (Space Shuttle and Titan solid boosters) 11-51 have riported significant and un redicted chamber frequencies. Further studies [4,6] have shown that a periodic vortex sheddin phenomenon is likely to be at the source of these oscifations. First suggestion of acoustic mode excitation by vortex shedding in solid rocket motors was made by Flandro and ressure and thrust oscillations at t f e first axial mode 1) Jacobs [7l. The eriodic shedding of vortices is the result of a strong cou Ping between the instabilit of mean flow sense, vortex shedding can be viewed as a, by-product of grain segmentation which produces regons of highly sheared mean flow, due to port area discontinuities and protrusions of inhibitor rings. Several related cold flow e eriments [4, 6, 8-12 have these experiments assume that a pair of diaphragms, at least, are required to give rise to vortex sheddin vortices are enerated at the first diaphragm and provife However, this is not the ony,mechanism for vortex shedding acoustic driving: one diaphragm or one region of sheared flow can be sufficient, the feedback mechanism being provided by the exhaust nozzle. This was the case in the ex eriment of reference [7], and could be the case in the & motor (Fig.1). Among, possible nozzle feedback mechanisms are direct vortex impingement on the nozzle wall or modulation of !he exiting mass flow rate by inhomogeneous flow, associated with one vortex. Flandro [13], extending the work of reference [7] has pro osed a linearized approach to evaluate the vortex shesding risk and to incorporate a corresponding driving term in linear acoustic balance codes. A lication of Flandro’s linearized model to Ariane 5 P a m o t o r has been carried out 141 and concluded of a possible vortex Recognizing the possible failure of classical linear acoustic balance computations even improved by Flandro’s mqdel, to achieve reliable stability predictions in complex internal eometries, such as in the P230 numerical simulation of the unsteady, comprcssiblc, internal flow field. Such a simulation would naturally couple mean flow shear layer instabilities and acoustic motions, including nonlinear effects and nozzle res once to vortices. The present work is the first part, of that effort and is devoted to demonstrating the easibility of a direct numerical capture of the periodic vortex shcdding phenomenon in test case solid propellant motors. This work was made possible by recent rogresses at unsteady state flow fields [15,16]. shear layers an B acoustic motions in the clamber. In this documented the vortex shed 3 ing phenomenon. Mlost of the acoustic B eedback when im inging on the second onc. P shedding driving 1 or Ariane 5 P230. motor,, a research ef B ort was initiated, aiming at a full ONERA in numerical simulations of bot g steady and * Research scientist .. Research scientist, Member AIAA Copyright

Instability of fluid vortices and generation of sheared flow

Abstract: A fluid equilibrium consisting of a periodic array of counter‐rotating vortices is found to be unstable to the generation of one‐dimensional sheared flow along the direction of periodicity. This instability is inviscid (exists for zero viscosity μ) or viscous (with growth rate γ∼μ3/4) depending on the elongation of the vortices. Nonlinearly, the instability goes through a vortex reconnection or ‘‘peeling’’ phase in which one of the vortices per period is destroyed, leading to a state with a chain of islands. Without a source, the flow evolves to pure one‐dimensional shear flow, which decays because of viscosity on a much longer time scale. In the presence of a source driving the initial vortices, the flow evolves to an equilibrium having vortex flow plus shear flow and, for sufficiently high Reynolds number, having only one vortex per periodicity length rather than two, i.e., with islands.

Numerical simulation of laminar and turbulent flows around rectangular cylinders

Abstract: By a finite volume method, laminar flows around bluff bodies with a rectangular cross-section of various width-to-height ratios from 0.2 to 10 and with a cross-section of a round leading edge and a square trailing edge have been computed on body-fitted curvilinear co-ordinates at Reynolds numbers of (1, 4, 7)×10 3 . Turbulent flows have also been computed by a standard κ-e turbulence model. Computed results are compared with experimental data at a Reynolds number of 10 3 and clearly show the effects of the shape of the bluff body on the aerodynamic characteristics