A universal Strouhal number for the ‘locking-on’ of vortex shedding to the vibrations of bluff cylinders

1978 ◽  
Vol 85 (3) ◽  
pp. 591-606 ◽  
Author(s):  
Owen M. Griffin
Keyword(s):  
Strouhal Number ◽  
Reynolds Numbers ◽  
Base Pressure ◽  
Circular Cylinders ◽  
Bluff Bodies ◽  
Pressure Drag ◽  
Wide Range ◽  
Pressure Parameter ◽  
The Individual ◽  
Good Agreement

It is well known that the vortices shed from a circular cylinder lock on in frequency to the vibrations when the cylinder is forced to vibrate or is naturally excited to sufficient amplitudes by flow-induced forces. This paper presents a model for a universal wake Strouhal number, valid in the subcritical range of Reynolds numbers, for both forced and vortex-excited oscillations in the locking-on regime. The Strouhal numbers thus obtained are constant atSt*= 0·178 over the range of wake Reynolds numbersRe*= 700-5 × 104. This value is in good agreement with the results obtained by Roshko (1954a) and Bearman (1967) for stationary circular cylinders and other bluff bodies in the same range of Reynolds numbers. A correspondence between the amplification of the cylinder base pressure, drag and vortex circulation is demonstrated over a wide range of frequencies and for vibration amplitudes up to a full cylinder diameter (peak to peak). The fraction ε of the shed vorticity in the individual vortices is found to be dependent upon the base-pressure parameter K = (1 −Cpb)½. Consequently, ε is also a function of the amplitude and frequency of the vibrations in the locking-on regime.

Supercritical Reynolds number simulation for two-dimensional flow over circular cylinders

1975 ◽  
Vol 70 (3) ◽  
pp. 529-542 ◽  
Author(s):  
Edmond Szechenyi
Keyword(s):  
Surface Roughness ◽  
Reynolds Number ◽  
Reynolds Numbers ◽  
Practical Significance ◽  
Circular Cylinders ◽  
Wind Tunnels ◽  
Bluff Bodies ◽  
Wide Range ◽  
Two Dimensional Flow ◽  
Different Diameters

In wind-tunnel tests on bluff bodies the Reynolds number is often limited to values that are very much smaller than those of the flows being simulated. In such cases the experiments may have no practical significance whatsoever since both the fluctuating and the steady aerodynamic phenomena can vary considerably with Reynolds number.This difficulty was encountered in an investigation of supercritical incompressible flow over cylinders, and an attempt at artificially increasing the Reynolds number by means of surface roughness was made. In order to evaluate this simulation technique, the influence of various grades of surface roughness on the aerodynamic forces acting on cylinders of different diameters was studied over a wide range of Reynolds numbers in two very different wind tunnels. The results allow very positive conclusions to be drawn.

Predictions of the Effect of Roughness on Heat Transfer From Turbine Airfoils

1998 ◽  
Author(s):  
Anil K. Tolpadi ◽  
Michael E. Crawford
Keyword(s):  
Heat Transfer ◽  
Side Surface ◽  
Suction Side ◽  
Reynolds Numbers ◽  
Surface Finishing ◽  
Transfer Coefficients ◽  
Average Roughness ◽  
Wide Range ◽  
Turbine Airfoils ◽  
Good Agreement

The heat transfer and aerodynamic performance of turbine airfoils are greatly influenced by the gas side surface finish. In order to operate at higher efficiencies and to have reduced cooling requirements, airfoil designs require better surface finishing processes to create smoother surfaces. In this paper, three different cast airfoils were analyzed: the first airfoil was grit blasted and codep coated, the second airfoil was tumbled and aluminide coated, and the third airfoil was polished further. Each of these airfoils had different levels of roughness. The TEXSTAN boundary layer code was used to make predictions of the heat transfer along both the pressure and suction sides of all three airfoils. These predictions have been compared to corresponding heat transfer data reported earlier by Abuaf et al. (1997). The data were obtained over a wide range of Reynolds numbers simulating typical aircraft engine conditions. A three-parameter full-cone based roughness model was implemented in TEXSTAN and used for the predictions. The three parameters were the centerline average roughness, the cone height and the cone-to-cone pitch. The heat transfer coefficient predictions indicated good agreement with the data over most Reynolds numbers and for all airfoils-both pressure and suction sides. The transition location on the pressure side was well predicted for all airfoils; on the suction side, transition was well predicted at the higher Reynolds numbers but was computed to be somewhat early at the lower Reynolds numbers. Also, at lower Reynolds numbers, the heat transfer coefficients were not in very good agreement with the data on the suction side.

Extra Drag Force on a Circular Cylinder Due to the Presence of Solid Particles in Subsonic Compressible Flow

1991 ◽  
Author(s):  
Stanley B. Mellsen
Keyword(s):  
Compressible Flow ◽  
Incompressible Flow ◽  
Aerodynamic Drag ◽  
Collection Efficiency ◽  
Reynolds Numbers ◽  
Solid Particles ◽  
Circular Cylinders ◽  
Critical Mach Number ◽  
Wide Range ◽  
Inertia Parameters

Abstract The effect of particles, such as dust in air on aerodynamic drag of circular cylinders was calculated for compressible flow at critical Mach number and for incompressible flow. The effect of compressibility was found negligible for particles larger than about 10 μm, for which the air can be considered a continuum. Drag coefficient and collection efficiency are provided for a wide range of inertia parameters and Reynolds numbers for both compressible and incompressible flow.

Fluctuating Lift Forces of the Karman Vortex Streets on Single Circular Cylinders and in Tube Bundles: Part 3—Lift Forces in Tube Bundles

1972 ◽  
Vol 94 (2) ◽  
pp. 623-628 ◽  
Author(s):  
Y. N. Chen
Keyword(s):  
Second Harmonic ◽  
Tube Bundle ◽  
Lift Coefficient ◽  
Reynolds Numbers ◽  
Circular Cylinders ◽  
Critical Flow Velocity ◽  
Pressure Drag ◽  
Tube Bundles ◽  
Karman Vortex ◽  
Lift Forces

The trend of the fluctuating lift coefficient CL and the dimensionless shedding frequency S (Strouhal number) of the vortex in tube bundles at higher Reynolds numbers R will be predicted by the course of the steady pressure drag coefficient CD at the corresponding R ranges. Furthermore, some measurements of the vortex lift forces in tube bundles will be given. It reveals that the lift force for certain small transverse tube spacings possesses a strong second harmonic. The tubes and, therefore, the transverse gas column in the tube bundle channel can be excited to vibrate in resonance either at the critical flow velocity or at its half value. Finally, the coupled vibration between the vortex shedding and the transverse gas column will be covered with some experiments.

Transverse Oscillations of a Jet in a Jet-Splitter System

1972 ◽  
Vol 94 (3) ◽  
pp. 675-681 ◽  
Author(s):  
D. O. Rockwell
Keyword(s):  
Reynolds Number ◽  
Strouhal Number ◽  
Nozzle Exit ◽  
Reynolds Numbers ◽  
Dimensionless Frequency ◽  
Two Dimensional ◽  
Vena Contracta ◽  
Wide Range ◽  
Jet Behavior ◽  
Transverse Oscillations

The fundamental transverse oscillations of a liquid jet which impinged upon a flow splitter were examined for a wide range of dimensionless splitter distance, nozzle exit Reynolds number, and dimensionless frequency. The results are presented in the form of a design map. The data, taken at low nozzle aspect ratio, reveal that fundamental (stage 1) oscillations can exist for Reynolds numbers up to at least 7000. Up to Reynolds numbers of about 3000, the jet behavior is Reynolds number dependent for all values of splitter distance. Beyond Reynolds number of 3000 the jet behavior is independent of Reynolds number. In general, the Strouhal number, based on nozzle exit-splitter distance, decreases with increasing values of splitter distance. Jets issuing from nozzles with no parallel development sections were considered. Jet nozzle shape influences the dimensionless frequency of oscillation in that the effect of a vena contracta formation outside the nozzle exit is to yield a higher value of dimensionless frequency relative to nozzles which produce parallel flow with small boundary layer thickness at the exit. Similar decreases have been found for two-dimensional jets. Of the above findings, the only comparable results for two-dimensional jets are variations in Strouhal number with nozzle exit-splitter distance.

Vortex shedding from bluff bodies in oscillatory flow: A report on Euromech 119

1980 ◽  
Vol 99 (2) ◽  
pp. 225-245 ◽  
Author(s):  
P. W. Bearman ◽  
J. M. R. Graham
Keyword(s):  
Vortex Shedding ◽  
Oscillatory Flow ◽  
Bluff Body ◽  
Circular Cylinders ◽  
Bluff Bodies ◽  
Unidirectional Flow ◽  
Low Reynolds Number Flows ◽  
Wide Range ◽  
Bluff Body Flow ◽  
Reynolds Number Flows

European Mechanics Colloquium number 119 was held at Imperial College on 16–18 July 1979, when the subject of vortex shedding from bodies in unidirectional flow and oscillatory flow, was discussed. A wide range of experimental work was presented including low-Reynolds-number flows around circular cylinders, the influence of disturbances on bluff body flow, the measurement of fluctuating forces and the influence of oscillations of the stream. About a third of the 33 papers presented concentrated on theoretical aspects and the majority of these were concerned with the ‘method of discrete vortices’.

Stability Analysis to Predict Vortex Street Characteristics and Forces on Circular Cylinders

1987 ◽  
Vol 109 (2) ◽  
pp. 148-154 ◽  
Author(s):  
G. Triantafyllou ◽  
M. Triantafyllou ◽  
C. Chryssostomidis
Keyword(s):  
Stability Analysis ◽  
Closed Form ◽  
Critical Point ◽  
Strouhal Number ◽  
Vortex Street ◽  
Circular Cylinders ◽  
Absolute Instability ◽  
Instability Analysis ◽  
Unsteady Forces ◽  
Good Agreement

The characteristics of the wake are predicted accurately by the critical point of the absolute instability supported by the wake profiles immediately behind the cylinder. Measured profiles at Rn = 56 provide Strouhal number St = 0.13 and at Rn = 140,000 St = 0.21 both in good agreement with experiment. It is also shown that at the undercritical Rn = 34 or for a symmetric array of vortices the instability is of the convective type, decaying behind the cylinder once the excitation is removed. Finally, it is shown that a model of the wake, based on the results of the instability analysis, is sufficient to obtain good estimates of the steady and unsteady forces on the cylinder. Closed-form expressions for the forces are obtained within this approximation.

On pressure invariance, wake width and drag prediction of a bluff body in confined flow

2009 ◽  
Vol 622 ◽  
pp. 321-344 ◽  
Author(s):  
W. W. H. YEUNG
Keyword(s):  
Experimental Data ◽  
Pressure Distribution ◽  
Bluff Body ◽  
Reynolds Numbers ◽  
Momentum Equation ◽  
Base Pressure ◽  
Vertex Angle ◽  
Bluff Bodies ◽  
Arbitrary Vertex ◽  
Confined Flow

In the present investigation, the form drag on a bluff body in confined flow is studied. From the observation of invariance in pressure distribution between a disk and a flat plate normal to free upstream in unconfined flow, a linear relation linking the drag to the base pressure is derived when the potential-flow model by Parkinson & Jandali (J. Fluid Mech., vol. 40, 1970, p. 577) is incorporated. A theoretical wake width deduced from well-documented experimental data for a disk is proposed such that the wake Strouhal number is independent of inclination. This width, when combined with the momentum equation and solved simultaneously with the aforementioned linear equation, leads to realistic predictions of the drag and the base pressure. The method is consistent when applied to a cone of arbitrary vertex angle, a circular cylinder at subcritical Reynolds numbers and a sphere at subcritical as well as supercritical Reynolds numbers. The case of the inclined disk is also discussed. As the pressure distribution is invariant under wall constraint, analytical expressions for the effect of confinement on the loading of bluff bodies are derived and found to provide the correct trend of experimental data.

The ‘zoo’ of secondary instabilities precursory to stratified shear flow transition. Part 2 The influence of stratification

2012 ◽  
Vol 708 ◽  
pp. 45-70 ◽  
Author(s):  
A. Mashayek ◽  
W. R. Peltier
Keyword(s):  
Three Dimensional ◽  
Reynolds Numbers ◽  
Shear Instability ◽  
Developed Turbulence ◽  
Wide Range ◽  
Stratified Shear Flow ◽  
High Reynolds ◽  
The Individual ◽  
Secondary Instabilities ◽  
Alternate Routes

AbstractThe linear stability analyses described in Mashayek & Peltier (J. Fluid Mech., vol. 708, 2012, 5–44, hereafter MP1) are extended herein in an investigation of the influence of stratification on the evolution of secondary instabilities to which an evolving Kelvin–Helmholtz (KH) wave is susceptible in an initially unstable parallel stratified shear layer. We show that over a wide range of background stratification levels, the braid shear instability has a higher probability of emerging at early stages of the flow evolution while the secondary convective instability (SCI), which occurs in the eyelids of the individual Kelvin ‘cats eyes’, will remain a relevant and dominant instability at high Reynolds numbers. The evolution of both modes is greatly influenced by the background stratification. Various other three-dimensional secondary instabilities are found to exist over a wide range of stratification levels. In particular, the stagnation point instability (SPI), which was discussed in detail in MP1, may be of great potential importance providing alternate routes for transition of an initially two-dimensional KH wave into fully developed turbulence. The energetics of the secondary instabilities revealed by our simulations are analysed in detail and the preturbulent mixing properties are studied.

Universal Similarity in the Wakes of Stationary and Vibrating Bluff Structures

1981 ◽  
Vol 103 (1) ◽  
pp. 52-58 ◽  
Author(s):  
Owen M. Griffin
Keyword(s):  
Vortex Formation ◽  
Reynolds Numbers ◽  
Bluff Bodies ◽  
Characteristic Parameters ◽  
Incident Flow ◽  
Mean Velocity ◽  
Pressure Drag ◽  
Vortex Shedding Frequency ◽  
The Mean ◽  
Shedding Frequency

A universal wake Strouhal number, St* =fsd′/Ub, has been proposed and is based upon the Strouhal frequency fs of the incident flow, 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. This universal parameter collapses these characteristic parameters for bluff bodies onto a single curve for wake Reynolds numbers between Re* = 100 and 107. The pressure drag, vortex shedding frequency and base pressure are related through an inverse dependence between St* and a wake drag coefficient CD* = CD/(d′/d) K2, where K = (1−Cpb)1/2. The product St* CD* is equal to a constant value of 0.073 ± 0.005 for Re* in this same range of Reynolds numbers.

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