On the Spacing of Karman Vortices

1969 ◽  
Vol 36 (2) ◽  
pp. 370-372 ◽  
Author(s):  
D. W. Sallet
Keyword(s):  
Strouhal Number ◽  
Cross Section ◽  
Vortex Shedding ◽  
Bluff Body ◽  
Slenderness Ratio ◽  
The Body ◽  
Vortex Street ◽  
Circular Cylinders ◽  
Flat Plates ◽  
Uniform Cross Section

Equations for the absolute dimensions of the Karman vortex street are developed in terms of the coefficient of drag and the Strouhal number of the vortex shedding bluff body. The body is assumed to be of large slenderness ratio and of uniform cross section. The predicted vortex spacings are compared with the experimental results of other investigators for circular cylinders, flat plates, and a wedge.

Vortex Shedding From Two Circular Cylinders in a Staggered Arrangement

2003 ◽  
Author(s):  
D. Sumner ◽  
M. D. Richards
Keyword(s):  
Strouhal Number ◽  
Vortex Shedding ◽  
Bluff Body ◽  
Incidence Angle ◽  
Power Spectra ◽  
Circular Cylinders ◽  
Aerodynamic Forces ◽  
Staggered Arrangement ◽  
Pitch Ratio ◽  
Small Increments

Vortex shedding from two circular cylinders of equal diameter in a staggered configuration was studied experimentally in the subcritical Reynolds number regime, for Re = 3.2×104–7.4×104. The dimensionless centre-to-centre pitch ratio of the staggered cylinders was ranged from P/D = 1.125–4.0, and the incidence angle was varied in small increments from α = 0°–90°. The behaviour of the Strouhal number measurements was broadly classified according to whether the cylinders were closely, moderately, or widely spaced, corresponding to P/D < 1.5, 1.5 ≤ P/D ≤ 2.5, and P/D > 2.5, respectively. For closely spaced staggered configurations, the flow around the cylinders is similar to a single bluff body, and only a single Strouhal number is measured. For moderately spaced cylinders, two distinct Strouhal numbers are measured when α > 30°, but there is considerable scatter in the Strouhal data when α < 30°. For widely spaced cylinders, the Strouhal numbers remain close to that of a single circular cylinder, in contrast to the behaviour of the aerodynamic forces. Evidence of the outer lift peak is seen in the power spectra for the downstream cylinder.

scholarly journals The onset of unsteadiness of two-dimensional bodies falling or rising freely in a viscous fluid: a linear study

2011 ◽  
Vol 690 ◽  
pp. 173-202 ◽  
Author(s):  
Pauline Assemat ◽  
David Fabre ◽  
Jacques Magnaudet
Keyword(s):  
Reynolds Number ◽  
Viscous Fluid ◽  
Strouhal Number ◽  
Cross Section ◽  
Vortex Shedding ◽  
The Body ◽  
Mode Switching ◽  
Two Dimensional ◽  
Body Dynamics ◽  
Mass Ratios

AbstractWe consider the transition between the steady vertical path and the oscillatory path of two-dimensional bodies moving under the effect of buoyancy in a viscous fluid. Linearization of the Navier–Stokes equations governing the flow past the body and of Newton’s equations governing the body dynamics leads to an eigenvalue problem, which is solved numerically. Three different body geometries are then examined in detail, namely a quasi-infinitely thin plate, a plate of rectangular cross-section with an aspect ratio of 8, and a rod with a square cross-section. Two kinds of eigenmodes are observed in the limit of large body-to-fluid mass ratios, namely ‘fluid’ modes identical to those found in the wake of a fixed body, which are responsible for the onset of vortex shedding, and four additional ‘aerodynamic’ modes associated with much longer time scales, which are also predicted using a quasi-static model introduced in a companion paper. The stability thresholds are computed and the nature of the corresponding eigenmodes is investigated throughout the whole possible range of mass ratios. For thin bodies such as a flat plate, the Reynolds number characterizing the threshold of the first instability and the associated Strouhal number are observed to be comparable with those of the corresponding fixed body. Other modes are found to become unstable at larger Reynolds numbers, and complicated branch crossings leading to mode switching are observed. On the other hand, for bluff bodies such as a square rod, two unstable modes are detected in the range of Reynolds number corresponding to wake destabilization. For large enough mass ratios, the leading mode is similar to the vortex shedding mode past a fixed body, while for smaller mass ratios it is of a different nature, with a Strouhal number about half that of the vortex shedding mode and a stronger coupling with the body dynamics.

scholarly journals Flow-Induced Vibrations of Single and Multiple Heated Circular Cylinders: A Review

Energies ◽  
2021 ◽  
Vol 14 (24) ◽  
pp. 8496
Author(s):  
Ussama Ali ◽  
Md. Islam ◽  
Isam Janajreh ◽  
Yap Fatt ◽  
Md. Mahbub Alam
Keyword(s):  
Heat Transfer ◽  
Vortex Shedding ◽  
Heat Exchangers ◽  
Power Plants ◽  
Bluff Body ◽  
The Body ◽  
Circular Cylinders ◽  
Fluid Forces ◽  
Spacing Ratio ◽  
Flow Induced Vibrations

This study is an effort to encapsulate the fundamentals and major findings in the area of fluid-solid interaction, particularly the flow-induced vibrations (FIV). Periodic flow separation and vortex shedding stretching downstream induce dynamic fluid forces on the bluff body and results in oscillatory motion of the body. The motion is generally referred to as flow-induced vibrations. FIV is a dynamic phenomenon as the motion, or the vibration of the body is subjected to the continuously changing fluid forces. Sometimes FIV is modeled as forced vibrations to mimic the vibration response due to the fluid forces. FIV is a deep concern of engineers for the design of modern heat exchangers, particularly the shell-and-tube type, as it is the major cause for the tube failures. Effect of important parameters such as Reynolds number, spacing ratio, damping coefficient, mass ratio and reduced velocity on the vibration characteristics (such as Strouhal number, vortex shedding, vibration frequency and amplitude, etc.) is summarized. Flow over a bluff body with wakes developed has been studied widely in the past decades. Several review articles are available in the literature on the area of vortex shedding and FIV. None of them, however, discusses the cases of FIV with heat transfer. In particular systems, FIV is often coupled to heat transfer, e.g., in nuclear power plants, FIV causes wear and tear to heat exchangers, which can eventually lead to catastrophic failure. As the circular shape is the most common shape for tubes and pipes encountered in practice, this review will only focus on the FIV of circular cylinders. In this attempt, FIV of single and multiple cylinders in staggered arrangement, including tandem and side-by-side arrangement is summarized for heated and unheated cylinder(s) in the one- and two-degree of freedom. The review also synthesizes the effect of fouling on heat transfer and flow characteristics. Finally, research prospects for heated circular cylinders are also stated.

An Experimental Investigation of Staggered Circular Cylinders in a Uniform Planar Shear Flow

2002 ◽  
Author(s):  
O. O. Akosile ◽  
D. Sumner
Keyword(s):  
Shear Flow ◽  
Strouhal Number ◽  
Vortex Shedding ◽  
Bluff Body ◽  
Incidence Angle ◽  
Lift Coefficient ◽  
Circular Cylinders ◽  
Aerodynamic Forces ◽  
Planar Shear ◽  
Critical Incidence

Two circular cylinders of equal diameter, arranged in staggered configurations of P/D = 1.125 and 1.25, were immersed in a uniform planar shear flow, at Re = 5.0×104 and a dimensionless shear parameter of K = 0.05. The mean aerodynamic forces and the vortex shedding frequencies were measured for the upstream and downstream cylinders at each P/D. Under uniform, no-shear flow conditions, K = 0, the flow field of the cylinder group is similar to a single bluff body. As the incidence angle is varied from α = 0° to 90°, the forces on each cylinder undergo discontinuous changes, or attain local minimum or maximum values, at several critical incidence angles. At small α, the Strouhal number is greater than that of a single, isolated circular cylinder, whereas at high α the Strouhal number is lower than the single-cylinder value. The effects of shear, K = 0.05, on the aerodynamic forces were different depending on whether the downstream cylinder was situated at a higher or lower centreline velocity compared to the upstream cylinder. The planar shear flow had its greatest influence when the cylinders were in a nearly side-by-side arrangement. This indicated that the effect of shear was mostly on the flow through the gap between the cylinders. The lift coefficient data were mostly unchanged by the shear flow, the drag coefficient data were lowered, and there were shifts in the critical incidence angles. The influence of shear on vortex shedding was less pronounced, but there was a small reduction in Strouhal number compared to the no-shear case.

Experimental Analysis of Vortex Induced Vibration in the Bladeless Small Wind Turbine

2019 ◽  
Author(s):  
Micha Premkumar Thomai ◽  
Lasoodawanki Kharsati ◽  
Nakandhrakumar Rama Samy ◽  
Seralathan Sivamani ◽  
Hariram Venkatesan
Keyword(s):  
Energy Conversion ◽  
Wind Turbine ◽  
Natural Frequency ◽  
Cross Section ◽  
Vortex Shedding ◽  
Rectangular Cross Section ◽  
The Body ◽  
Test Facility ◽  
Vortex Induced Vibration ◽  
Small Wind Turbine

Abstract Vortex-induced vibration is one of the predominant fundamental concepts for forced oscillation which attracts considerable practical engineering application for energy conversion. In this work, an oscillation of a mast arising as a result of wind force is utilized for energy conversion. The paradigm for energy conversion from vortex-induced vibration in the mast is the bladeless wind turbine. It consists of a rigid mass known as a mast, fixed in the spring of stiffness (k) and allowed to oscillate along the direction of the flow. In this work, four different types of mast have been fabricated and tested. The first is uniform tapered hollow conical mast (MAST1), the cross-section of the second is uniform tapered plus symbol (MAST2), the third is uniform tapered inversed plus symbol (MAST3) and the fourth is uniform tapered simple rectangular cross-section (MAST4). All the masts were fabricated using fiber carbon. The experiments were conducted in a versatile small wind turbine testing facility of Hindustan Institute of Technology and Science, Chennai. This test facility contained an open jet wind tunnel with variable frequency drive and other measuring instruments. The vibration sensor was located in the mast where it experienced a large oscillation in a free stream. In this experiment, an increase in wind velocity led to a terrible change in the amplitude of vibration. A vigorous oscillation was experienced in this mast at this critical frequency, when the natural frequency of the mast was synchronized with the frequency of the vortex shedding and the frequency of the oscillation of the mast. The total force in this oscillation was a summation of the body force due to the mass of the mast and vorticity force that is mainly which was the result of the shedding of the vortices. In this work, extensive studies have been carried out for Reynolds number ranging from 2.5 × 105 to 5.0 × 105. The mast length to diameter ratio of 13 was exposed to various speeds of wind and response was measured. The occurrence of the maximum oscillation in a simple rectangular mast was seen where vortex shedding due to the bluff body was large for constant mass and spring stiffness. The frequency of the oscillation at maximum amplitude of the rectangular cross-section mast was equal to the natural frequency, due to vortices shedding at critical velocity. This demonstrated the appropriateness of the simple rectangular cross-section for harnessing the low rated wind energy and its suitability for renewable energy conversion in the small bladeless wind turbine.

Numerical analysis of bluff body wakes under periodic open-loop control

2013 ◽  
Vol 739 ◽  
pp. 94-123 ◽  
Author(s):  
Derwin J. Parkin ◽  
M. C. Thompson ◽  
J. Sheridan
Keyword(s):  
Strouhal Number ◽  
Cross Section ◽  
Vortex Shedding ◽  
Open Loop ◽  
Wake Flow ◽  
Dynamic Mode ◽  
Two Dimensional ◽  
Near Wake ◽  
Recirculation Bubble ◽  
Number Range

AbstractLarge eddy simulations at$Re= 23\hspace{0.167em} 000$are used to investigate the drag on a two-dimensional elongated cylinder caused by rear-edge periodic actuation, with particular focus on an optimum open-loop configuration. The 3.64 (length/thickness) aspect-ratio cylinder has a rectangular cross-section with rounded leading corners, representing the two-dimensional cross-section of the now genericAhmed-body geometry. The simulations show that the optimum drag reduction occurs in the forcing Strouhal number range of$0. 09\leq S{t}_{act} \leq 0. 135$, which is approximately half of the Strouhal number corresponding to shedding of von Kármán vortices into the wake for the natural case. This result agrees well with recent experiments of Henninget al. (Active Flow Control, vol. 95, 2007, pp. 369–390). A thorough transient wake analysis employing dynamic mode decomposition is conducted for all cases, with special attention paid to the Koopman modes of the wake flow and vortex progression downstream. Two modes are found to coexist in all cases, the superimposition of which recovers the majority of features observed in the flow. Symmetric vortex shedding in the near wake, which effectively extends the mean recirculation bubble, is shown to be the major mechanism in lowering the drag. This is associated with opposite-signed vortices reducing the influence of natural vortex shedding, resulting in an increase in the pressure in the near wake, while the characteristic wake antisymmetry returns further downstream. Lower-frequency actuation is shown to create larger near-wake symmetric vortices, which improves the effectiveness of this process.

A Free-Streamline Model for Bluff Bodies in Confined Flow

1977 ◽  
Vol 99 (3) ◽  
pp. 585-592 ◽  
Author(s):  
V. J. Modi ◽  
S. E. El-Sherbiny
Keyword(s):  
Potential Flow ◽  
Bluff Body ◽  
Flow Model ◽  
Circular Cylinders ◽  
Bluff Bodies ◽  
Two Dimensional ◽  
Flat Plates ◽  
Surface Loading ◽  
Confined Flow ◽  
Potential Flow Model

A potential flow model is presented for two-dimensional symmetrical bluff bodies under wall confinement. It provides a procedure for predicting surface loading on a bluff body over a range of blockage ratios. Experimental results with normal flat plates and circular cylinders for blockage ratios up to 35.5 percent substantiate the validity of the approach.

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.

scholarly journals The characteristics of a Karman vortex street in a channel of finite breadth

1928 ◽  
Vol 120 (784) ◽  
pp. 34-46 ◽  
Keyword(s):  
Perfect Fluid ◽  
Bluff Body ◽  
Two Dimensions ◽  
The Body ◽  
Vortex Street ◽  
Stable Configuration ◽  
Cylindrical Shape ◽  
Double Row ◽  
Finite Breadth ◽  
The Individual

It is well known that the classical potential flow of a perfect fluid past a bluff body is not a satisfactory representation of the actual flow, and that, in particular, it fails to give any indication of the resistance or drag which is experienced by the body. If the body is of a long cylindrical shape with axis normal to the axis, and may be conceived as proceeding in two dimensions only. In this case it is found experimentally that thin sheets of vorticity spring from the two sides of the body and enclose a dead-water region behind it, but owing to their essential instability these vortex sheets rapidly disintegrate and give rise to a succession of independent vortices which pass down stream in the form of a double vortex row. The characteristics of such a vortex street in its ultimate form far behind the body have been examined by Karman, who derives an expression for the drag of the body in terms of the strength of the individual vortices and of the breadth of the vortex street. More recently the results of a comprehensive series of experiments on the flow past a flat plate have been published by Fage and Johansen, and these results have been compared with Karman's theory. In view, however, of the fact that the experimental results are of necessity obtained from experiments in a channel of finite breadth, the present investigation has been undertaken to determine the constraint of the channel walls on the characteristics of the vortex street. 2. Karman's Theory of the Vortex Street . Karman considers the behaviour in a perfect fluid of a double row of point vortices in the configuration shown in fig. 1, deducing the relationships which are necessary for the stability of the system, and the corresponding drag force on the body to which the vortex street is due. It appears that the only stable configuration is that in which each vortex of one row is opposite the point mid-way between two successive vortices of the other row.

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