Showing papers on "Strouhal number published in 1989"

Oblique and Parallel Modes of Vortex Shedding in the Wake of a Circular Cylinder at Low Reynolds Numbers

Abstract: Two fundamental characteristics of the low-Reynolds-number cylinder wake, which have involved considerable debate, are first the existence of discontinuities in the Strouhal-Reynolds number relationship, and secondly the phenomenon of oblique vortex shedding. The present paper shows that both of these characteristics of the wake are directly related to each other, and that both are influenced by the boundary conditions at the ends of the cylinder, even for spans of hundreds of diameters in length. It is found that a Strouhal discontinuity exists, which is not due to any of the previously proposed mechanisms, but instead is caused by a transition from one oblique shedding mode to another oblique mode. This transition is explained by a change from one mode where the central flow over the span matches the end boundary conditions to one where the central flow is unable to match the end conditions. In the latter case, quasi-periodic spectra of the velocity fluctuations appear; these are due to the presence of spanwise cells of different frequency. During periods when vortices in neighbouring cells move out of phase with each other, ‘vortex dislocations’ are observed, and are associated with rather complex vortex linking between the cells. However, by manipulating the end boundary conditions, parallel shedding can be induced, which then results in a completely continuous Strouhal curve. It is also universal in the sense that the oblique-shedding Strouhal data (S_θ) can be collapsed onto the parallel-shedding Strouhal curve (S_0) by the transformation, S_0 = S_θ/cosθ, where θ is the angle of oblique shedding. Close agreement between measurements in two distinctly different facilities confirms the continuous and universal nature of this Strouhal curve. It is believed that the case of parallel shedding represents truly two-dimensional shedding, and a comparison of Strouhal frequency data is made with several two-dimensional numerical simulations, yielding a large disparity which is not clearly understood. The oblique and parallel modes of vortex shedding are both intrinsic to the flow over a cylinder, and are simply solutions to different problems, because the boundary conditions are different in each case.

Airfoil self-noise and prediction

Abstract: A prediction method is developed for the self-generated noise of an airfoil blade encountering smooth flow. The prediction methods for the individual self-noise mechanisms are semiempirical and are based on previous theoretical studies and data obtained from tests of two- and three-dimensional airfoil blade sections. The self-noise mechanisms are due to specific boundary-layer phenomena, that is, the boundary-layer turbulence passing the trailing edge, separated-boundary-layer and stalled flow over an airfoil, vortex shedding due to laminar boundary layer instabilities, vortex shedding from blunt trailing edges, and the turbulent vortex flow existing near the tip of lifting blades. The predictions are compared successfully with published data from three self-noise studies of different airfoil shapes. An application of the prediction method is reported for a large scale-model helicopter rotor, and the predictions compared well with experimental broadband noise measurements. A computer code of the method is given.

Frequency selection and asymptotic states in laminar wakes

Abstract: A better understanding of the transition process in open flows can be obtained through identification of the possible asymptotic response states in the flow. In the present work, the asymptotic states in laminar wakes behind circular cylinders at low supercritical Reynolds numbers are investigated. Direct numerical simulation of the flow is performed, using spectral-element techniques. Naturally produced wakes, and periodically forced wakes are considered separately.It is shown that, in the absence of external forcing, a periodic state is obtained, the frequency of which is selected by the absolute instability of the time-average flow. The non-dimensional frequency of the vortex street (Strouhal number) is a continuous function of the Reynolds number. In periodically forced wakes, however, non-periodic states are also possible, resulting from the bifurcation of the natural periodic state. The response of forced wakes can be characterized as: (i) lock-in, if the dominant frequency in the wake equals the excitation frequency, or (ii) non-lock-in, when the dominant frequency in the wake equals the Strouhal frequency. Both types of response can be periodic or quasi-periodic, depending on the combination of the amplitude and frequency of the forcing. At the boundary separating the two types of response transitional states develop, which are found to exhibit a low-order chaotic behaviour. Finally, all states resulting from the bifurcation of the natural state can be represented in a two-parameter space inside ‘resonant horn’ type of regions.

A natural low-frequency oscillation of the flow over an airfoil near stalling conditions

Abstract: An experimental and computational study of the low-frequency oscillation observed in the flow over an airfoil at the onset of static stall is presented. Wind-tunnel results obtained with two-dimensional airfoil models show that this phenomena takes place only with a transitional state of the separating boundary layer. It is noted that the flowfield does not involve a Karman vortex street. The experimental results agree well with the results of a two-dimensional Navier-Stokes code. The present study demonstrates that the low-frequency oscillations produce intense flow fluctuations which impart much larger unsteady forces to the airfoil than experienced by bluff-body shedding and which may represent the primary aerodynamics of stall flutter of blades and wings.

Absolute and convective instability of a cylinder wake

Abstract: The stability behavior of a circular cross-section cylinder's wake at Reynolds number values of up to 45 is presently investigated by means of local linear stability theory. The steady-wake profiles computed are Navier-Stokes solutions of a uniform, incompressible viscous flow around a cylinder obtained by a spectral method. An absolutely unstable region is found to begin to form at a Reynolds number of about 20, and grows with incresing Reynolds number. The onset of global instability response must be characterized by a critical length of an absolutely unstable region; a critical Reynolds number criterion and preferred frequency are proposed based on linear stability analysis.

A numerical study of the interaction between unsteady free-stream disturbances and localized variations in surface geometry

Abstract: A numerical study of the generation of Tollmien-Schlichting (T-S) waves due to the interaction between a small free-stream disturbance and a small localized variation of the surface geometry has been carried out using both finite-difference and spectral methods. The nonlinear steady flow is of the viscous-inviscid interactive type while the unsteady disturbed flow is assumed to be governed by the Navier-Stokes equations linearized about this flow. Numerical solutions illustrate the growth or decay of the T-S waves generated by the interaction between the free-stream disturbance and the surface distortion, depending on the value of the scaled Strouhal number. An important result of this receptivity problem is the numerical determination of the amplitude of the T-S waves.

The Low Frequency Oscillation in the Flow Over a NACA0012 Airfoil with an “Iced” Leading Edge

Abstract: The unusually low frequency oscillation in the wake of an airfoil, studied in [1], is explored experimentally as well as computationally for a NACA0012 airfoil with a “glaze ice accretion” at the leading edge. Experimentally, flow oscillations are observed at low frequencies that correspond to a Strouhal number of about 0.02. This occurs in the angle of attack range of 8° to 9°, near the onset of static stall for this airfoil. With a Navier-Stokes computation, “limit-cycle” oscillations in the flow and in the aerodynamic forces are also observed at low Strouhal numbers. However, the occurrence of the oscillation is found to depend on the turbulence model in use as well as the Reynolds number.

Two-Component Phase-Averaged Turbulence Statistics Downstream of a Rotating Spoked-Wheel Wake Generator

Abstract: Flow-field measurements of unsteady turbulent flow downstream of a rotating spoked-wheel wake generator were performed in a short-duration light-piston tunnel, and the instantaneous-velocity data were phase averaged based on a signal synchronized with the bar-passing frequency. Mean axial velocities were found to agree well with those obtained from measurements behind a stationary cylinder and to be independent of both Reynolds and bar-passing Strouhal numbers. Reynolds stresses were found to be consistent with related cylinder-wake measurements, but were significantly higher than corresponding measurements obtained in large-scale research turbomachines. Phase-averaged triple velocity correlations were calculated from the digital velocity records, revealing the sign and the magnitude of skewness in the velocity probability density distributions for the two components.

Streaming flows generated by high‐frequency small‐amplitude oscillations of arbitrarily shaped cylinders

Abstract: Small‐amplitude harmonic oscillations of arbitrarily shaped cylinders are considered both experimentally and theoretically. For the theoretical model, the flow regime is separated into inner and outer regions. In the inner region, the flow is governed by the classical Stokes boundary layer equation. In the outer region, the full Navier–Stokes equation for the steady streaming flow is solved numerically by using a finite difference method coupled with conformal mapping techniques. Numerical results of streaming, a nonlinear response to harmonic motion, show complicated flow schemes. Experimental results confirm the existence of such flows. Streaming flow around a sharp corner of a square cylinder is investigated through numerical calculation and experimental flow visualization. The absence of any vortex shedding on the time scale of the streaming flow is noted. These results suggest that in the limit of a small amplitude of oscillation, or equivalently large Strouhal numbers, sharp‐edged bodies experience attached flow in the mean sense.

Flow similitude and vortex lock-on in bluff body near wakes

Abstract: Some years ago a universal Strouhal number for bluff body wakes was introduced, which was based upon the Strouhal frequency fs0 of the vortex shedding, the measured wake width d’ at the end of the vortex formation region, and the mean velocity Ub at the edge of the separated boundary layer on the body. This universal parameter was shown to collapse these characteristic scales of bluff body flows onto a single curve for wake Reynolds numbers between 200 and 107. The results of more recent experiments show the concept of universal wake similitude to be even more general than was previously supposed. In this paper these similarity relationships are applied to the case of vortex lock‐on in oscillatory flow. A full understanding of the macroscopic averaged properties in the wake in this traditional manner is an important precursor to studying, in detail, the microscale wake properties using the most modern experimental measurements and diagnostic techniques and theoretical concepts such as the absolute‐convect...

The Influence of Boundary Layer State on Vortex Shedding from Flat Plates and Turbine Cascades

Abstract: The paper aims at a better understanding of the reasons for the wide range of Strouhal numbers observed on turbine blades. The investigation is restricted to the subsonic domain. Firstly, flat plate model tests are carried out to investigate the effect of both the boundary layer state and trailing edge geometry on the vortex shedding frequency. A particular objective of the tests is to obtain data for the very common case of a mixed laminar-turbulent separation from turbine blades. These basic tests are followed by three cascade tests with blades of very different suction side velocity distributions. Based on the experience gained from the flat plate test program, an attempt is made to interprete the Strouhal number variation with Mach number and Reynolds number, and to relate the vortex frequency change to the boundary layer state on the blade surfaces.Copyright © 1989 by ASME

Large amplitude acoustic excitation of swirling turbulent jets

Abstract: A swirling jet with a swirl number of S = 0.12 is exited by plane acoustic waves at various Strouhal numbers (St = fD/U sub alpha). The maximum forcing amplitude of excitation was at 6.88 percent of the time-mean axial velocity at a Strouhal number of St = 0.39. The maximum time-mean tangential and axial velocities at the nozzle exit were 18 and 84 m/sec respectively. It was observed that the swirling jet was excitable by plane acoustic waves and the preferred Strouhal number based on the nozzle diameter and exit axial velocity of the jet was about 0.39. As a result of excitation at this frequency, the time-mean axial velocity decayed faster along the jet centerline, reaching about 89 percent of its unexcited value at x/D = 9. Also the half velocity radius and momentum thichness, at 7 nozzle diameters downstream, increased by 13.2 and 5.8 percent respectively, indicating more jet spread and enhanced mixing. To our knowledge, this is the first reported experimental data indicating any mixing enhancement of swirling jets by acoustic excitation.

The effect of aspect ratio on the flow over a rearward-facing step

Abstract: In this study, we investigate the effect of the spanwise width on the mixing layer behind a rearward-facing step Results for aspect ratios (tunnel width/step height) of 10 and 4 and Reynolds numbers of 11,000 and 5,000 are presented A frequency shifted, single component LDV system was used to obtain mean streamwise velocity profiles, turbulence intensity profiles, and normal velocity spectra at four streamwise and three spanwise positions for each test case The mean velocity and turbulence intensity profiles are constant across the width of the test section for either of the Reynolds numbers considered, but there are significant differences among the cases studied At a distance greater than three step heights down-stream of the step, the peak turbulence intensity is greater for higher aspect ratio and is relatively insensitive to Reynolds number The peak frequency is lower and the spectrum is narrower for a higher aspect ratio in the region near the step

Flow around a circular cylinder in the high Reynolds number range. Effect of surface roughness.

Abstract: Experimental investigations of the effect of the relative roughness on the transition of flow were examined in the Reynolds numbers range of 5×104≤Re≤107, using 8 cylinders with different relative surface roughnesses. Flow phenomena on the cylindrical surface are classified in four types irrespective of surface roughness. They are: subcritical, transitional, supercritical and transcritical regions. These regions are classified from the variations in the drag coefficient and Strouhal number with Reynolds number. The Reynolds number range at the interface of these flow regions, the variation procedure and the degree of variation, depend on the relative roughness. For example, the Reynolds number at the interface between the subcritical and transitional ranges can be properly determined as a transitional point of relation between the drag coefficient and the base pressure coefficient. With an increase in the surface roughness, the interface points shift into the lower Reynolds number range. The effect of the relative roughness on these flow phenomena is classified and discussions are also made.

Current-induced oscillations and instabilities of a multi-tube flexible riser: water tunnel experiments

Abstract: Experiments have been conducted on a five cylinder riser cluster in a steady water cross-flow; the geometry of the riser is similar to one previously investigated in air-flow. In the majority of the experiments the central cylinder and three of the four outer cylinders were sensibly rigid with the remaining peripheral cylinder being flexibly mounted. The flexible cylinder vibration was monitored in the radial and tangential directions. The complete riser bundle was mounted on a rotative arrangement, so that the flexible cylinder could be set at any desired azimuthal orientation to the flow vector. Other experiments were conducted with a fully rigid bundle where hot-film anemometers were used to measure periodicities in the flow within and downstream of the cluster. Three different sets of Strouhal numbers were detected for the cluster.

Mixing enhancement in flow past rectangular cavities as a result of periodically pulsed fluid motion

Abstract: Periodic elimination of the shear layer separating the mainstream and recirculatory regions in flow through a multicavity channel is possible by imposing a pulsatile flow component on an otherwise steady flow. Numerical and experimental results are correlated to show that pulsing the flow during half of a cycle leads to the destruction of the trapped vortex while simultaneously generating its replacement. During the other half of the cycle, when there is only steady flow, a new vortex grows to fill the cavity and protrudes into the mainstream, thus further enhancing mainstream and cavity mixing. The fluid motion is characterized by three nondimensional parameters: a Reynolds number based on the steady velocity component; a Reynolds number based on the unsteady velocity component; and a Strouhal number based on the frequency of oscillation and the unsteady velocity component. >

Effects of Excitation on Turbulence Levels in a Shear Layer

Abstract: Etude experimentale de la suppression de la turbulence comme resultat de grandes amplitudes d'excitation externe dans une couche de melange axisymetrique

Transverse forces on a circular cylinder oscillating in-line with a steady current

Abstract: Measurements are presented of transverse forces, together with spanwise correlation, on a circular cylinder oscillating in-line with a steady current at amplitudes corresponding to Keulegan Carpenter numbers of 10, 14, 18 and 34. Calculations made for cases with the current velocity greater than the maximum oscillatory velocity indicate that the transverse force can be described quite adequately by a quasi-steady model which assumes a constant Strouhal number.

Drag and vortex shedding from circular cylinder in the high reynolds numbers range. Effect of surface roughness.

Abstract: Discussions are made on the effect of surface roughness on the drag coefficient and Strouhal numbers 5×105≤Re≤107. There is the maximum value of surface roughness which does not effect the drag coefficient and Strouhal number in the subcritical and transitional range and at the critical point. This maximum value is determined as (Ks/d)crit=5×10-4. For a larger relative surface roughness value, there are some functional relations between the relative surface roughness (Ks/d) and the minimum drag coefficient and the Reynolds number which corresponds to CD min. In the transcritical Reynolds number range, the drag coefficient depends on the relative surface roughness. It increases with an increase in the relative surface roughness. There arise vortex streets in the wake of a cylinder which satisfy the Bearman's condition, i. e. St*=0.181 in the subcritical and transcritical Reynolds number ranges.