INVESTIGATION OF VORTEX SHEDDING INDUCED HYDRODYNAMIC VIBRATION IN VORTEX STREET FLOWMETER

Vortex street flowmeter has been used in steady flow measurement for about three decades The benefits of this type of flowmeter include high accuracy,good linearty,wide measuring range,and excellent reliability However,in unsteady flow measurement,the pressure disturbance as well as the noise from the system or surrounding can reduce the signal to noise ratio of the flowmeter seriously Aimed to use vortex street flowmeters in unsteady flow measurement,the characteristics of the vortex shedding induced hydrodynamic vibration around the prism bluff body in a vortex street flowmeter are investigated numerically and by expriments The results show that the hydrodynamic vibrations with 180° phase shift occur at the axisymmetric points of the channel around the bluff body The most intense vibration occurs at the points on the lateral faces close to the base of the prism The results provide therefore a useful reference for developing an anti interference vortex flowmeter using the different ial sensing technique.

INVESTIGATION OF DOMINANT FREQUENCIES IN TRANSITION REYNOLDS NUMBER RANGE OF FLOW AROUND A CIRCULAR CYLINDER PARTⅡ: THEORETICAL DETERMINATION OF THE RELATIONSHIP BETWEEN VORTEX SHEDDING AND TRANSITION FREQUENCIES AT DIFFERENT REYNOLDS NUMBERS

An attempt has been made to explore whether the power relation can be obtained from theoretical considerations. The classical laminar and turbulent boundary layer concepts have been employed to determine appropriate values of the scaling lengths associated with vortex shedding and shear layer frequencies to predict the power law relationship with Reynolds number. The predicted results are in good agreement with experimental results. The findings will provide a greater insight into the overall phenomenon involved.

Control of Vortex Shedding and Drag Reduction through Dual Splitter Plates Attached to a Square Cylinder

In this paper we have made a numerical study on the control of vortex shedding and drag reduction of a cylinder by attaching thin splitter plates. The wake structure of the cylinder of square cross-section with attached splitter plates is analyzed for a range of Reynolds number, based on the incident stream and height of the cylinder, in the laminar range. The Navier-Stokes equations governing the flow are solved by the control volume method over a staggered grid arrangement. We have used the semi-implicit method for pressure-linked equation （SIMPLE） algorithm for computation. Our results show that the presence of a splitter plate upstream of the cylinder reduces the drag, but it has a small impact on the vortex shedding frequency when the plate length is beyond 1.5 time the height of the cylinder. The presence of a downstream splitter plate dampens the vortex shedding frequency. The entrainment of fluid into the inner side of the separated shear layers is obstructed by the downstream splitter plate. Our results suggest that by attaching in-line splitter plates both upstream and downstream of the cylinder, the vortex shedding can be suppressed, as well as a reduction in drag be obtained. We made a parametric study to determine the optimal length of these splitter plates so as to achieve low drag and low vortex shedding frequency.

INVESTIGATION OF DOMINANT FREQUENCIES IN TRANSITION REYNOLDS NUMBER RANGE OF FLOW AROUND A CIRCULAR CYLINDER PART I:EXPERIMENTAL STUDY OF THE RELATION BETWEEN VORTEX SHEDDING AND TRANSITION FREQUENCIES

A comprehensive hot wire investigation of the flow around a circular cylinder is carried out in an 18＂ × 18＂ wind tunnel to look into the dominant frequencies at the stagnation, separation and separated shear layers in the transition Reynolds number range. The majority of the experiments are carried out at Reynolds number of 4.5×104, with additional transition frequency tests at Reynolds numbers of 2.9×104, 3.3×104 and 9.7×104 respectively. The results are analysed in terms of power spectral density. While the frequency associated with stagnation is found to be essentially due to vortex shedding, frequency doubling of vortex shedding is also evident in the separated shear layers. Two peaks associated with transition frequencies are detected and their possible implications are presented.

Effect of Bed Vicinity on Vortex Shedding and Force Coefficients of Fluid Flow on an Offshore Pipeline

The effect of rigid bed proximity on flow parameters and hydrodynamic loads in offshore pipelines exposed to turbulent flow is investigated numerically. The Galerkin finite volume method is employed to solve the unsteady incompressible 2D Navier–Stokes equations. The large eddy simulation turbulence model is solved using the artificial compressibility method and dual time-stepping approach. The proposed algorithm is developed for a wide range of turbulent flows with Reynolds numbers of 9500 to 1.5×10^4.Evaluation of the developed numerical model shows that the proposed technique is capable of properly predicting hydrodynamic forces and simulating the flow pattern. The obtained results show that the lift and drag coefficients are strongly affected by the gap ratio. The mean drag coefficient slightly increases as the gap ratio increases, although the mean lift coefficient rapidly decreases. The vortex shedding suppression happen at the gap ratio of less than 0.2.

Simulation of vortex shedding behind a bluff body flame stabilizer using a hybrid U-RANS/PDF method

The present study aims at the investigation of the effects of turbulence-chemistry interaction on combus- tion instabilities using a probability density function （PDF） method. The instantaneous quantities in the flow field were decomposed into the Favre-averaged variables and the stochastic fluctuations, which were calculated by unsteady Reynolds averaged Navier-Stokes （U-RANS） equations and the PDF model, respectively. A joint fluctuating velocity- frequency-composition PDF was used. The governing equa- tions are solved by a consistent hybrid finite volume/Monte- Carlo algorithm on triangular unstructured meshes. A non- reacting flow behind a triangular-shaped bluff body flame stabilizer in a rectilinear combustor was simulated by the present method. The results demonstrate the capability of the present method to capture the large-scale coherent struc- tures. The triple decomposition was performed, by divid- ing the coherent Favre-averaged velocity into time-averaged value and periodical coherent part, to analyze the coherent and incoherent contributions to Reynolds stresses. A sim- ple modification to the coefficients in the turbulent frequency model will help to improve the simulation results. Unsteady flow fields were depicted by streamlines and vorticity con- tours. Moreover, the association between turbulence produc- tion and vorticity saddle points is illustrated.

Control of Vortex Shedding at Moderate Reynolds Numbers

The suppression method of vortex shedding from a circular cylinder has been studied experimentally in the Reynolds number range from 300 to 1600. The test is performed in a water channel. The model cylinder is 1 cm in diameter and 38 cm in length. A row of small rods of 0.18 cm in diameter and 1.5 cm in length are perpendicularly connected to the surface of the model cylinder and distributed along the meridian, The distance between the neighboring rods and the angle of attack of the rods can be changed so that the suppression effect on vortex shedding can be adjusted. The results show that vortex shedding can be suppressed effectively if the distance between the neighboring rods is smaller than 3 times and the cylinder diameter and the angle of attack is in the range of 30degreesless than or equal tobeta<90&DEG;.

Vortex Shedding Lock-in on Tapered Poles with Polygonal Cross-Section

A study to investigate the effects of taper on vortex shedding coherence on High Mast Lighting Towers (HMLT) with models of eight-, twelve-, and sixteen-sided polygonal cross-section was performed in Purdue’s Boeing Low-Speed Wind Tunnel. Partial tower models were mounted on springs to recreate a flutter phenomenon seen on high mast lighting towers and data was taken using a stationary configuration within the wind tunnel. The model was later oscillated at specified frequencies and amplitudes and the resulting wake and surface pressures were recorded and compared to the stationary cases. The researchers aim to study the characteristics of a “lock-in” phenomenon, that is, a region of pole height where there is a vortex cell with a single shedding frequency, instead of different shedding frequencies for different diameters as Strouhal theory dictates. Results show the existence of vortex cell shedding for clamped models. Using a motor and a forcing cam to recreate the elastic movement of the HMLT in ambient conditions has yielded a specific range of diameters to determine the size of the locked in vortex cells. According to standard Department of Transportation manufacturing standards for tapered HMLT, the lock in distance for small excitations (0.254 cm) would be approximately 305 cm in tower height.

PROPULSIVE PERFORMANCE AND VORTEX SHEDDING OF A FOIL IN FLAPPING MOTION

The propulsive performance and vortex shedding of oscillating foil, whichmimics biological locomotion, were numerically investigated. The objectives of this study were todeal with unsteady force, in particular thrust force, exerted on the foil in pitching and plungingmotions, and to explore the relation of the propulsive performance with vortex structures near thefoil and vortex shedding in the near wake. The two-dimensional incompressible Navier-Stokesequations in the vorticity and stream-function formulation were solved by fourth-order essentiallycompact finite difference schemes for the space derivatives and a fourth-order Runge-Kutta schemefor the time advancement. To reveal the mechanism of the propulsive performance, the unsteady forceand the shedding of the trailing- and leading-edge vortices of the foil were analyzed. The effectsof some typical factors, such as the frequency and amplitude of the oscillation, the phasedifference between the pitching and plunging motions, and the thickness ratio of the foil, on thevortex shedding and unsteady force were discussed.

FORCE CHARACTERISTICS AND VORTEX SHEDDING OF A PITCHING FOIL IN SHEAR FLOWS

The objective of this study is to deal with unsteady force acting on a pitching foil in shear flow and to study the relation of the force characteristics with vortex shedding near the foil. The two dimensional incompressible Navier Stokes equations in the vorticity and stream function formulation were solved with the fourth order essentially compact finite difference schemes for the space derivatives and a fourth order Runge Kutta scheme for the time advancement. The force characteristics and vortex shedding of the pitching foil in shear flows were investigated. The effects of some typical factors, including the incoming flow shear, the oscillating frequency and amplitude, on the vortex shedding and force behavior were analyzed and discussed.

Effect of perforation on flow past a conic cylinder at Re=100:vortex-shedding pattern and force history

The flow past a circular-section cylinder with a conic shroud perforated with four holes at the peak was simulated numerically at Re = 100, considering two factors, viz.the angle of attack and the diameter of the holes. The effects of the perforated conic shroud on the vortex shedding pattern in the near wake was mainly investigated, as well as the time history of the drag and lift forces. In the investigated parameter space, three flow regimes were generally identified, corresponding to weak, moderate, and strong disturbance effects.In regime I, the wake can mainly be described by alternately shedding Kármán or Kármán-like vortices. In regime II, the spanwise vortices are obviously disturbed along the span due to the appearance of additional vorticity components and their interactions with the spanwise vortices, but still shed in synchronization along the spanwise direction. In regime III,the typical Kármán vortices partially or totally disappear,and some new vortex shedding patterns appear, such as-type, obliquely shedding, and crossed spanwise vortices with opposite sign. Corresponding to these complex vortex shedding patterns in the near wake, the fluid forces no longer oscillate regularly at a single vortex shedding frequency, but rather with a lower modulation frequency and multiple amplitudes. An overview of these flow regimes is presented.

NUMERICAL STUDY OF VORTEX SHEDDING FROM A SQUARE CYLINDER AND ITS EFFECTS ON HEAT TRANSFER OF MIXED CONVECTION

The influence of buoyancy on vortex shedding from a heated square cylinderand its effects on the heat transfer of mixed convection were simulated. The flow equations, basedon the velocity and the pressure, were solved along with the energy equation by a modified SIMPLERalgorithm - the Quick Scheme and small Control Volume (QSCV) algorithm developed by the authors ofthe present paper. A set of optimized computational domain and artificial lateral boundaryconditions were used along with the QSCV algorithm. Several cases were simulated for the Grashofnumbers up to 1. 8 X 10~5, the Reynolds numbers up to 500, and a range of angles between free streamvelocity and gravity from 0 to 1.5π. In opposing flow, the results distinguish two different flowpatterns: periodic flow for Gr < Gr_c and steady flow with attached twin vortices for Gr > Gr_c, anda precise correlation between Gr_c and Re expressed as Gr_c = 0. 00166(Re)^(2.97795) for Re up to500 was firstly obtained. In cross flow, it could be seen that the Ri = Gr/Re^2 plays a great rolein the wake vortex patterns and the temperature fields. In aiding flow, it is found that the mainflow currents cause a large expansion of the streamlines and isotherms in the direction normal tothe free stream velocity. These changes in the wake vortex patterns and the temperature fieldsgreatly modify the heat flux along the surface of the square cylinder and consequently, the heattransfer rate is strongly dependent upon the Reynolds numbers, the Grashof numbers, and the gravitydirection.

Vortex shedding in the flow around two side-by-side circular cylinders of different diameters

In this paper,the 3-D turbulent flow around two side-by-side circular cylinders of different diameters,at sub-critical Reynolds number（Re=3 900）,is numerically simulated by the large eddy simulation（LES）.The spacing ratios（T/D）between the two cylinders are considered in four cases（T/D=1.2,1.5,1.8 and 2.7）to study the vortex shedding and turbulent properties in the flow field.The main results are focused on the drag and lift coefficients,the vortex shedding frequency,the coherent structure,and the scale properties.It is shown that when T/D is equal to 1.2,the vortex shedding of the main cylinder is strongly suppressed by the small cylinder,the drag and lift coefficients of the main cylinder are smaller than those in other three cases.While T/D is equal to 1.5,the vortex shedding of the main cylinder can be improved,the drag and lift coefficients of the main cylinder are larger than those in other three cases.The empirical mode decomposition（EMD）method is applied to decompose the velocity signals traced by the LES.It is shown that there is a linear relationship between the mean period and the mode in the semi-log coordinates.The vortex shedding period of the main cylinder is consistent with the period of the restructured coherent structures quantitatively.

Modes of vortex shedding from a rotary oscillating plate

The wake of a two-dimensional rotary oscillating plate of chord to thickness ratio B/H=3.0 was investigated by smoke wire visualization and hot-wire measurement in a wind tunnel at Re=1500 and oscillation amplitudes and reduced frequencies in the ranges ofα=2.5°-50°and f_(e)H/V_(∞)=0.02-0.25,respectively,where fe is oscillation frequency,V_(∞) is on-coming wind speed.There are six modes of synchronized vortex shedding observed,including three new modes,i.e.,3P—three vortex pairs shed in one period,2S_(2)—two pairs of vortex twins shed in one period,and T—three vortices shed in one period of plate oscillation.The zone of every mode was found out and drawn on the amplitude-reduced frequency plane.Numerical simulation was carried out,and the simulated vorticity field,velocity profiles,and wake width were verified by experiment at typical oscillation conditions.At higher oscillation frequencies,the linear local unsteady term of inertial force dominates,and the simulated moment is an accurate linear function of rotary displacement and angular velocity.At lower frequencies,where 2T,3P,and 2S_(2) modes of vortex shedding occur,however,the nonlinear convective term of inertial force dominates,and the simulated fluctuating moment deviates from Scanlan’s expression.Statistical results of numerical data show that the root-mean-square(r.m.s)value of fluctuating moment is an exponential function of single parameter η=αf_(e)H/V_(∞).

VORTEX SHEDDING FREQUENCY DETERMINED BY SURFACE PRESSURE FLUCTUATIONS OF THREE EQUISPACED CYLINDERS

In his paper, the frequency of vortex shedding from three cylinders of the same diameter in equilateral triangular arrangement is determined experimentally by the spectrum analysis of surface pressure fluctuations at a Reynolds number of 3.0×10 4. For α=0°, there exists ‘bistable’ flow at the spacing 2.0. For α=30°, the vortex shedding of the front cylinder is found at small spacing less than 2.0. It is quite different from the case of two cylinders in tandem arrangement only. The side cylinder has great effects on the flow between the other two cylinders in close arrangement. For α=60°, there exists a critical spacing of about 2.5 that the frequency of each cylinders is nearly half of f s below this spacing and equal to f s above it respectively. The interference among three cylinders was negligible in the spacing range above 3.0 at α=0 and 60 deg., and each cylinder behaves as a single cylinder with the same vortex shedding frequency f s. In these small spacing (spacing<3.0), interference occurs seriously and has great effects in a complex fashion on the flow state around three cylinders.

Vortex-Induced Vibrations of Two Cylinders in Tandem Arrangement at Low Reynolds Number

The objective of this study is to apply numerical methods to investigate the effects of the spacing on the vortex shedding of two elastically mounted cylinders in tandem arrangement. 2-D computational simulations are carried out at low Reynolds number of 100. The study utilized a commercial software ANSYS FLUENT to carry out the computational simulations. First, a number of test cases, including flows past one and two cylinders with predetermined motions, are simulated to evaluate the solver’s accuracy. The vortex shedding and hydrodynamic forces from the current findings and those from literature show good agreement, which supports the accuracy of the current solver. Multiple simulations were the performed for flow around two elastically mounted cylinders in tandem arrangement. The subsequent relative flow fields demonstrated that for a certain range of spacing, vortex shedding was completely eliminated while it remained completely unaffected or partially reduced for other ranges of spacing. This suggests that the spacing between the two cylinders can be utilized as a passive method of suppressing vortex shedding.

Shedding vortex simulation method based on viscous compensation technology research

Owing to the influence of the viscosity of the flow field,the strength of the shedding vortex decreases gradually in the process of backward propagation.Large-scale vortexes constantly break up,forming smaller vortexes.In engineering,when numerical simulation of vortex evolution process is carried out,a large grid is needed to be arranged in the area of outflow field far from the boundary layer in order to ensure the calculation efficiency.As a result,small scale vortexes at the far end of the flow field cannot be captured by the sparse grid in this region,resulting in the dissipation or even disappearance of vortexes.In this paper,the effect of grid scale is quantified and compared with the viscous effect through theoretical derivation.The theoretical relationship between the mesh viscosity and the original viscosity of the flow field is established,and the viscosity term in the turbulence model is modified.This method proves to be able to effectively improve the intensity of small-scale shedding vortexes at the far end of the flow field under the condition of sparse grid.The error between the simulation results and the results obtained by using fine mesh is greatly reduced,the calculation time is shortened,and the high-precision and efficient simulation of the flow field is realized.

Numerical Simulations of the Flow Field around a Cylindrical Lightning Rod

As an important lightning protection device in substations,lightning rods are susceptible to vibration and potential structural damage under wind loads.In order to understand their vibration mechanism,it is necessary to conduct flow analysis.In this study,numerical simulations of the flow field around a 330 kV cylindrical lightning rod with different diameters were performed using the SST k-ωmodel.The flow patterns in different segments of the lightning rod at the same reference wind speed(wind speed at a height of 10 m)and the flow patterns in the same segment at different reference wind speeds were investigated.The variations of lift coefficient,drag coefficient,and vorticity distribution were obtained.The results showed that vortex shedding phenomena occurred in all segments of the lightning rod,and the strength of vortex shedding increased with decreasing diameter.The vorticity magnitude and the root mean square magnitudes of the lift coefficient and drag coefficient also increased accordingly.The time history curves of the lift coefficient and drag coefficient on the surface of the lightning rod exhibited sinusoidal patterns with a single dominant frequency.For the same segment,as the wind speed increased in a certain range,the root mean square values of the lift coefficient and drag coefficient decreased,while their dominant frequencies increased.Moreover,there was a proportional relationship between the dominant frequencies of the lift coefficient and drag coefficient.The findings of this study can provide valuable insights for the refined design of lightning rods with similar structures.

Experimental study of vortex-induced vibrations of a cylinder near a rigid plane boundary in steady flow

In this study, the vortex-induced vibrations of a cylinder near a rigid plane boundary in a steady flow are studied experimentally. The phenomenon of vortex-induced vibrations of the cylinder near the rigid plane boundary is reproduced in the flume. The vortex shedding frequency and mode are also measured by the methods of hot film velocimeter and hydrogen bubbles. A parametric study is carded out to investigate the influences of reduced velocity, gap-to-diameter ratio, stability parameter and mass ratio on the amplitude and frequency responses of the cylinder. Experimental results indicate： （1） the Strouhal number （St） is around 0.2 for the stationary cylinder near a plane boundary in the sub-criti- cal flow regime; （2） with increasing gap-to-diameter ratio （eo/D）, the amplitude ratio （A/D） gets larger but frequency ratio （f/fn） has a slight variation for the case of larger values of eo/D（eo/D 〉 0.66 in this study）; （3） there is a clear difference of amplitude and frequency responses of the cylin- derbetween the larger gap-to-diameter ratios （e0/D 〉 0.66） and the smaller ones （e0/D 〈 0.3）; （4） the vibration of the cylinder is easier to occur and the range of vibration in terms of Vr number becomes more extensive with decrease of the stability parameter, but the frequency response is affected slightly by the stability parameter; （5） with decreasing mass ratio, the width of the lock-in ranges in terms of Vr and the frequency ratio （f/fn） become larger.

Liquid vortexes and flows induced by femtosecond laser ablation in liquid governing formation of circular and crisscross LIPSS

Orientations of laser induced periodic surface structures(LIPSS)are usually considered to be governed by the laser polarization state.In this work,we unveil that fluid dynamics induced by femtosecond(fs)laser ablation in liquid(fs-LAL)can easily break this polarization restriction to produce irregular circular-LIPSS(CLIPPS)and crisscross-LIPSS(CCLIPSS).Fs laser ablation of silicon in water shows formation of diverse LIPSS depending on ablation conditions.At a high power of 700 mW(repetition rate of 100 kHz,pulse duration of 457 fs and wavelength of 1045 nm),single/twin CLIPSS are produced at the bottom of macropores of several microns in diameter due to the formation of strong liquid vortexes and occurrence of the vortex shedding effect.Theoretical simulations validate our speculation about the formation of liquid vortex with an ultrahigh static pressure,which can induce the microstructure trenches and cracks at the sidewalls for fs-LAL of Si and tungsten(W)in water,respectively.At a low power of 50 mW,weak liquid vortexes are produced,which only give birth to curved LIPSS in the valleys of grooves.Consequently,it is deduced that liquid vortex plays a crucial role in the formation of macropores.Mountain-like microstructures induce complex fluid dynamics which can cause the formation of CCLIPSS on them.It is believed that liquid vortexes and fluid dynamics presented in this work open up new possibilities to diversify the morphologies of LIPSS formed by fs-LAL.