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.

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.

Fluctuating Lift Forces of the Karman Vortex Streets on Single Circular Cylinders and in Tube Bundles: Part 1—The Vortex Street Geometry of the Single Circular Cylinder

1972 ◽  
Vol 94 (2) ◽  
pp. 603-610 ◽  
Author(s):  
Y. N. Chen
Keyword(s):  
Reynolds Number ◽  
Strouhal Number ◽  
Vortex Street ◽  
Circular Cylinders ◽  
Number Range ◽  
Pressure Drag ◽  
Minimum Drag ◽  
Vortex Streets ◽  
Karman Vortex ◽  
Better Than

The geometry of the vortex street for single circular cylinders will be calculated from the measured values given by numerous investigators about the steady pressure drag coefficient and the Strouhal number, whereby the Kronauer minimum drag criterion comes into use. The calculated results will be compared with the experimentally determined ones. A good agreement can be achieved between both. The Bearman-Strouhal number SB = fh/Us will also be computed as a function of the Reynolds number. Furthermore a new wake number C = fh2/Γ will be introduced. It will be shown that this new number is universally much better than the Bearman one. It remains constant at 0.165 for an ideal flow over the whole Reynolds number range up to the highest value of 107 ever measured hitherto.

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.

Global Stability Analysis of the Wake behind a Circular Cylinder Based on the POD-Chiba Method

2011 ◽  
Vol 137 ◽  
pp. 72-76
Author(s):  
Wei Zhang ◽  
Xian Wen ◽  
Yan Qun Jiang
Keyword(s):  
Stability Analysis ◽  
Circular Cylinder ◽  
Global Stability ◽  
Dimensional Model ◽  
Global Stability Analysis ◽  
The Stability ◽  
Low Dimensional ◽  
Proper Orthogonal ◽  
Calculated Amount ◽  
Good Agreement

A proper orthogonal decomposition (POD) method is applied to study the global stability analysis for flow past a stationary circular cylinder. The flow database at Re=100 is obtained by CFD software, i.e. FLUENT, with which POD bases are constructed by a snapshot method. Based on the POD bases, a low-dimensional model is established for solving the two-dimensional incompressible NS equations. The stability of the flow solution is evaluated by a POD-Chiba method in the way of the eigensystem analysis for the velocity disturbance. The linear stability analysis shows that the first Hopf bifurcation takes place at Re=46.9, which is in good agreement with available results by other high-order accurate stability analysis methods. However, the calculated amount of POD is little, which shows the availability and advantage of the POD method.

Strouhal Number for VIV Excitation of Long Slender Structures

2018 ◽  
Author(s):  
Andrew E. Potts ◽  
Douglas A. Potts ◽  
Hayden Marcollo ◽  
Kanishka Jayasinghe
Keyword(s):  
Reynolds Number ◽  
Strouhal Number ◽  
Degrees Of Freedom ◽  
Measurement Techniques ◽  
Cross Flow ◽  
Degree Of Freedom ◽  
Circular Cylinders ◽  
Two Degrees Of Freedom ◽  
Shedding Frequency ◽  
Eddy Shedding

The prediction of Vortex-Induced Vibration (VIV) of cylinders under fluid flow conditions depends upon the eddy shedding frequency, conventionally described by the Strouhal Number. The most commonly cited relationship between Strouhal Number and Reynolds Number for circular cylinders was developed by Lienhard [1], whereby the Strouhal Number exhibits a consistent narrow band of about 0.2 (conventional across the sub-critical Re range), with a pronounced hump peaking at about 0.5 within the critical flow regime. The source data underlying this relationship is re-examined, wherein it was found to be predominantly associated with eddy shedding frequency about fixed or stationary cylinders. The pronounced hump appears to be an artefact of the measurement techniques employed by various investigators to detect eddy-shedding frequency in the wake of the cylinder. A variety of contemporary test data for elastically mounted cylinders, with freedom to oscillate under one degree of freedom (i.e. cross flow) and two degrees of freedom (i.e. cross flow and in-line) were evaluated and compared against the conventional Strouhal Number relationship. It is well established for VIV that the eddy shedding frequency will synchronise with the near resonant motions of a dynamically oscillating cylinder, such that the resultant bandwidth of lock-in exhibits a wider range of effective Strouhal Numbers than that reflected in the narrow-banded relationship about a mean of 0.2. However, whilst cylinders oscillating under one degree of freedom exhibit a mean Strouhal Number of 0.2 consistent with fixed/stationary cylinders, cylinders with two degrees of freedom exhibit a much lower mean Strouhal Number of around 0.14–0.15. Data supports the relationship that Strouhal Number does slightly diminish with increasing Reynolds Number. For oscillating cylinders, the bandwidth about the mean Strouhal Number value appears to remain largely consistent. For many practical structures in the marine environment subject to VIV excitation, such as long span, slender risers, mooring lines, pipeline spans, towed array sonar strings, and alike, the long flexible cylinders will respond in two degrees of freedom, where the identified difference in Strouhal Number is a significant aspect to be accounted for in the modelling of its dynamic behaviour.

On drag, Strouhal number and vortex-street structure

2002 ◽  
Vol 30 (6) ◽  
pp. 379-399 ◽  
Author(s):  
Boye Ahlborn ◽  
Mae L Seto ◽  
Bernd R Noack
Keyword(s):  
Strouhal Number ◽  
Vortex Street

scholarly journals Stability and Sensitivity Analysis of Hydrodynamic Instabilities in Industrial Swirled Injection Systems

2017 ◽  
Author(s):  
Thomas L. Kaiser ◽  
Thierry Poinsot ◽  
Kilian Oberleithner
Keyword(s):  
Stability Analysis ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Vortex Core ◽  
Large Eddy Simulations ◽  
Mode Shapes ◽  
Mean Flow ◽  
Precessing Vortex Core ◽  
Large Eddy ◽  
Good Agreement

The hydrodynamic instability in an industrial, two-staged, counter-rotative, swirled injector of highly complex geometry is under investigation. Large eddy simulations show that the complicated and strongly nonparallel flow field in the injector is superimposed by a strong precessing vortex core. Mean flow fields of large eddy simulations, validated by experimental particle image velocimetry measurements are used as input for both local and global linear stability analysis. It is shown that the origin of the instability is located at the exit plane of the primary injector. Mode shapes of both global and local linear stability analysis are compared to a dynamic mode decomposition based on large eddy simulation snapshots, showing good agreement. The estimated frequencies for the instability are in good agreement with both the experiment and the simulation. Furthermore, the adjoint mode shapes retrieved by the global approach are used to find the best location for periodic forcing in order to control the precessing vortex core.

scholarly journals Unsteady Boundary Layers on a Flat Plate Disturbed by Periodic Wakes: Part I — Measurement of Wake-Affected Heat Transfer and Wake-Induced Transition Model

1994 ◽  
Author(s):  
K. Funazaki
Keyword(s):  
Heat Transfer ◽  
Flat Plate ◽  
Rotating Disk ◽  
Circular Cylinders ◽  
Transition Model ◽  
Time Diagram ◽  
Test Conditions ◽  
Intermittency Factor ◽  
Unsteady Boundary Layers ◽  
Good Agreement

Measurements of wake-affected heat transfer distributions on a flat plate are made by use of a wake generator that consists of a rotating disk and several types of circular cylinders. The main purpose of this study is to construct a wake-induced transition model in terms of an intermittency factor, considering the evolution of the wake-induced turbulent region, a so-called turbulent patch in a distance-time diagram. A comparison between the proposed transition model and the measured heat transfer data reveals that the transition model yields good agreement with the measured data of all test conditions in this study.

scholarly journals A full wave description for thin wire structures with TLST and perturbation theory

2018 ◽  
Vol 16 ◽  
pp. 123-133
Author(s):  
Fabian Ossevorth ◽  
Ralf T. Jacobs ◽  
Hans Georg Krauthäuser
Keyword(s):  
Perturbation Theory ◽  
Closed Form ◽  
Current Distribution ◽  
Perturbation Approach ◽  
Mixed Potential ◽  
Thin Wire ◽  
Method Of Moment ◽  
Initial Current ◽  
Full Wave ◽  
Good Agreement

Abstract. A full wave description of a thin wire structure, that includes mutual interactions and radiation, can be obtained in closed form with the so-called Transmission Line Super Theory or a refined variant of this method that utilises perturbation theory. In either procedure, a set of mixed potential integral equations is solved for the currents that propagate along a wire. With the perturbation approach, no iteration is required to approximate the initial current distribution on the wire. This procedure will be applied to solve multi-wire problems. The theory will be derived and computed results will be shown to be in good agreement with method of moment computations.

scholarly journals Kestabilan Model Matematika Infeksi Primer Penyakit Varicella Dan Infeksi Rekuren Penyakit Herpes Zoster Oleh Virus Varicella Zoster

2020 ◽  
Vol 17 (1) ◽  
pp. 82-91
Author(s):  
Hardiyanti ◽  
R Ratianingsih ◽  
Hajar
Keyword(s):  
Herpes Zoster ◽  
Stability Analysis ◽  
Varicella Zoster Virus ◽  
Critical Point ◽  
Postherpetic Neuralgia ◽  
Primary Infection ◽  
Skin Diseases ◽  
Varicella Zoster ◽  
Stable Conditions ◽  
Disease Free

Varicella and herpes zoster are two infectious skin diseases of human that caused by varicella zoster virus, where varicella disease is a primary infection that often infected younger people while herpes zoster disease is a recurrent disease that often infected older people because of reactivation of latent varicella-zoster virus. If the pain caused by herpes zoster after recurrent phase is a appeared then the condition is known as postherpetic neuralgia. This study builds a mathematical model of primary infection (varicella disease) and recurrent infection (herpes zoster disease) developed from the SIR model (Susceptible, Infected, Recovered). The human population is divided into seven subpopulations, namely susceptible, infection, recovered of varicella, herpes zoster and postherpetic neuralgia subpopulation. Stability analysis at the critical point by linearization method gives a critical point 𝑇1 that guaranted to exist and unstable if 𝛼 𝜇(𝛽1+𝜇) 𝐴 , while the critical point 𝑇1 does not have any reqruitment. Stability analysis at the endemic disease-free critical point is represented 𝑇1 that will be unstable if 𝑇2 exist and stable 𝑇1 if 𝑇2 exist. Numerical simulations by simulated to describe such temporary disease-free conditions and an endemic stable conditions.

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