Development of a Fluids Laboratory Experience in Dimensional Analysis and Similitude Applied to Vortex Shedding From a Cylinder in Cross-Flow

2013 ◽  
Author(s):  
Matthew Anderson ◽  
Dylan Shiltz ◽  
Christopher Damm
Keyword(s):  
Reynolds Number ◽  
Data Acquisition ◽  
Strouhal Number ◽  
Dimensional Analysis ◽  
Vortex Shedding ◽  
Free Stream ◽  
Cross Flow ◽  
Laboratory Experience ◽  
Analysis And Design ◽  
Wide Range

A fluids laboratory experience that introduces students to dimensional analysis and similitude was designed and performed in a junior-level first course in fluid mechanics. After students are given an introduction to dimensional analysis, the technique is applied to the phenomenon of vortex shedding from a cylinder in cross-flow. With help from the instructor, lab groups use dimensional analysis to ascertain the relevant dimensionless pi terms associated with the phenomenon. After successfully determining that the pi terms are the Strouhal number and the Reynolds number, experiments are performed to elucidate the general functional relationship between the dimensionless groups. To conduct the experiments, a wind-tunnel apparatus is used in conjunction with a Pitot tube for measurements of free stream velocity and a platinum-plated tungsten hot-wire anemometer for rapid (up to 400 kHz) measurements of velocity fluctuations downstream of the cylinder. Utilizing an oscilloscope in parallel with a high-speed data acquisition system, students are able to determine the vortex shedding frequency by performing a spectral analysis (via Fourier transform) of the downstream velocity measurements at multiple free stream velocities and for multiple cylinder diameters (thus a varying Reynolds number). The students’ experimental results were found to agree with relationships found in the technical literature, showing a constant Strouhal number of approximately 0.2 over a wide range of Reynolds numbers. This exercise not only gives students valuable experience in dimensional analysis and design of experiments, it also provides exposure to modern data acquisition and analysis methods.

Effect of Free-Stream Turbulence on Characteristics of Fluctuating Forces Acting on Two Square Prisms in Tandem Arrangement

1988 ◽  
Vol 110 (2) ◽  
pp. 140-146 ◽  
Author(s):  
H. Sakamoto ◽  
H. Haniu
Keyword(s):  
Reynolds Number ◽  
Strouhal Number ◽  
Turbulence Intensity ◽  
Vortex Shedding ◽  
Free Stream ◽  
Switching Frequency ◽  
Tandem Arrangement ◽  
Free Stream Turbulence ◽  
Fluid Forces ◽  
Bistable Flow

The effect of the addition of the turbulence intensity to the free stream on the characteristics of the bistable flow which takes place around two square prisms in tandem arrangement was studied experimentally at a Reynolds number of 3.32 × 104. A method of obtaining the fluid forces acting on two prisms in the bistable flow regimes where two flow patterns appear intermittently was introduced, and then the characteristics of the fluid forces, the Strouhal number, and the switching frequency of the switch phenomenon with the variation of the freestream turbulence intensity were investigated. Furthermore, the behavior of the fluid forces and the vortex shedding for other spacings between the two prisms were presented for the variation of the turbulence intensity.

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.

Two- and Three-Dimensional Simulations of the Flow Around a Cylinder Fitted With Strakes

2012 ◽  
Author(s):  
Bruno S. Carmo ◽  
Rafael S. Gioria ◽  
Ivan Korkischko ◽  
Cesar M. Freire ◽  
Julio R. Meneghini
Keyword(s):  
Reynolds Number ◽  
Vortex Shedding ◽  
Free Stream ◽  
Three Dimensional ◽  
The Body ◽  
Vortex Wake ◽  
Two Dimensional ◽  
Flow Around A Cylinder ◽  
Three Dimensional Simulations ◽  
Angle Of Rotation

Two- and three-dimensional simulations of the flow around straked cylinders are presented. For the two-dimensional simulations we used the Spectral/hp Element Method, and carried out simulations for five different angles of rotation of the cylinder with respect to the free stream. Fixed and elastically-mounted cylinders were tested, and the Reynolds number was kept constant and equal to 150. The results were compared to those obtained from the simulation of the flow around a bare cylinder under the same conditions. We observed that the two-dimensional strakes are not effective in suppressing the vibration of the cylinders, but also noticed that the responses were completely different even with a slight change in the angle of rotation of the body. The three-dimensional results showed that there are two mechanisms of suppression: the main one is the decrease in the vortex shedding correlation along the span, whilst a secondary one is the vortex wake formation farther downstream.

Sting-free measurements on a magnetically supported right circular cylinder aligned with the free stream

2008 ◽  
Vol 596 ◽  
pp. 49-72 ◽  
Author(s):  
HIROSHI HIGUCHI ◽  
HIDEO SAWADA ◽  
HIROYUKI KATO
Keyword(s):  
Circular Cylinder ◽  
Shear Layer ◽  
Free Stream ◽  
Aerodynamic Force ◽  
Cross Flow ◽  
Leading Edge ◽  
Magnetic Suspension ◽  
Recirculation Region ◽  
Mean Velocity ◽  
Wide Range

The flow over cylinders of varying fineness ratio (length to diameter) aligned with the free stream was examined using a magnetic suspension and balance system in order to avoid model support interference. The drag coefficient variation of a right circular cylinder was obtained for a wide range of fineness ratios. Particle image velocimetry (PIV) was used to examine the flow field, particularly the behaviour of the leading-edge separation shear layer and its effect on the wake. Reynolds numbers based on the cylinder diameter ranged from 5×104 to 1.1×105, while the major portion of the experiment was conducted at ReD=1.0×105. For moderately large fineness ratio, the shear layer reattaches with subsequent growth of the boundary layer, whereas over shorter cylinders, the shear layer remains detached. Differences in the wake recirculation region and the immediate wake patterns are clarified in terms of both the mean velocity and turbulent flow fields, including longitudinal vortical structures in the cross-flow plane of the wake. The minimum drag corresponded to the fineness ratio for which the separated shear layer reattached at the trailing edge of the cylinder. The base pressure was obtained with a telemetry technique. Pressure fields and aerodynamic force fluctuations are also discussed.

Numerical Simulation of Vortex Shedding Past a Circular Cylinder in a Cross-Flow at Low Reynolds Number With Finite Volume-Technique: Part 1 — Forced Oscillations

2007 ◽  
Author(s):  
Antoine Placzek ◽  
Jean-Franc¸ois Sigrist ◽  
Aziz Hamdouni
Keyword(s):  
Numerical Simulation ◽  
Reynolds Number ◽  
Circular Cylinder ◽  
Finite Volume ◽  
Vortex Shedding ◽  
Stokes Equations ◽  
Cross Flow ◽  
Forced Oscillations ◽  
Lift And Drag ◽  
Wake Characteristics

The numerical simulation of the flow past a circular cylinder forced to oscillate transversely to the incident stream is presented here for a fixed Reynolds number equal to 100. The 2D Navier-Stokes equations are solved with a classical Finite Volume Method with an industrial CFD code which has been coupled with a user subroutine to obtain an explicit staggered procedure providing the cylinder displacement. A preliminary work is conducted in order to check the computation of the wake characteristics for Reynolds numbers smaller than 150. The Strouhal frequency fS, the lift and drag coefficients CL and CD are thus controlled among other parameters. The simulations are then performed with forced oscillations f0 for different frequency rations F = f0/fS in [0.50–1.50] and an amplitude A varying between 0.25 and 1.25. The wake characteristics are analysed using the time series of the fluctuating aerodynamic coefficients and their FFT. The frequency content is then linked to the shape of the phase portrait and to the vortex shedding mode. By choosing interesting couples (A,F), different vortex shedding modes have been observed, which are similar to those of the Williamson-Roshko map.

Strouhal numbers of rectangular cylinders

1982 ◽  
Vol 123 ◽  
pp. 379-398 ◽  
Author(s):  
Atsushi Okajima
Keyword(s):  
Reynolds Number ◽  
Wind Tunnel ◽  
Velocity Distribution ◽  
Flow Pattern ◽  
Strouhal Number ◽  
Vortex Shedding ◽  
Water Tank ◽  
Height Ratio ◽  
Rectangular Cylinders ◽  
Good Agreement

Experiments on the vortex-shedding frequencies of various rectangular cylinders were conducted in a wind tunnel and in a water tank. The results show how Strouhal number varies with a width-to-height ratio of the cylinders in the range of Reynolds number between 70 and 2 × l04. There is found to exist a certain range of Reynolds number for the cylinders with the width-to-height ratios of 2 and 3 where flow pattern abruptly changes with a sudden discontinuity in Strouhal number. The changes in flow pattern corresponding to the discontinuity of Strouhal number have been confirmed by means of measurements of velocity distribution and flow visualization. These data are compared with those of other investigators. The experimental results have been found to show a good agreement with those of numerical calculations.

On vortex shedding from a circular cylinder in the critical Reynolds number régime

1969 ◽  
Vol 37 (3) ◽  
pp. 577-585 ◽  
Author(s):  
P. W. Bearman
Keyword(s):  
Reynolds Number ◽  
Circular Cylinder ◽  
Strouhal Number ◽  
Vortex Shedding ◽  
Critical Reynolds Number ◽  
Narrow Band ◽  
Critical Regime ◽  
Number Range ◽  
Velocity Fluctuations ◽  
Reynolds Number Range

The flow around a circular cylinder has been examined over the Reynolds number range 105 to 7·5 × 105, Reynolds number being based on cylinder diameter. Narrow-band vortex shedding has been observed up to a Reynolds number of 5·5 × 105, i.e. well into the critical régime. At this Reynolds number the Strouhal number reached the unusually high value of 0·46. Spectra of the velocity fluctuations measured in the wake are presented for several values of Reynolds number.

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.

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