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Keywords: VIV, flow visualization, circular cylinder, pressure measurements

1. ABSTRACT

The interaction between a flow and an oscillating circular cylinder has been widely investigated in the past, but few of those experiments concerned set-up with high values of mass-ratio (m*). In the Politecnico di Milano wind tunnel have been performed studies concerning set-up characterized by high values of m* and low values of damping-ratio (ξs), with the aim to investigate the pressure fields on the surface of a circular cylinder (Zasso et al. 2006; Zasso et al. 2008). In this paper we provided, together with the measurements of the displacement and of the pressure distribution on the cylinder, the reconstruction of the flow field structure downstream the body. The flow field reconstruction was provided by using a time resolved PIV technique, SPIV (Stripe Particle Image Velocimetry); phase average method was applied on the velocity field to evidence the vortex shedding structures. The displacement of the cylinder was measured both with a couple of accelerometer and via image analysis detecting on each SPIV image the position of a marker placed on the cylinder. The proposed flow field reconstruction and analysis allowed us to better understand the vortex shedding phenomenon and compare flow structure and pressure distribution on the cylinder for the investigated case.

2. INTRODUCTION

Vortex induced vibrations are a key feature to consider in designing slender structures with circular section, because of fatigue damage that they could produce. This typology of structures has several

Contact person: S. Muggiasca, Politecnico di Milano, Via La Masa 1, +390223998072, FAX: +390223998081.

E-mail sara.muggiasca@polimi.it

Wake visualization and pressure field analysis on an oscillating cylinder

S. Malavasi1, R. Corretto1, M. Belloli2, S. Giappino2, S. Muggiasca2 1Dip. DIIAR, Politecnico di Milano – stefano.malavasi@polimi.it –roberto.corretto@mail.polimi.it

Piazza Leonardo da Vinci, 32 – 20133 Milano – 2Dip. Meccanica, Politecnico di Milano – marco.belloli@polimi.it - stefano.giappino@polimi.it – sara.muggiasca@polimi – Via La Masa 1 –

20156 Milano

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engineering applications as overhead transmission line, stays of cable-stayed bridges or hangers of suspension bridges: over the last decades many experimental activities have been performed to study the aerodynamic behavior of bluff bodies, with particular reference to circular section.

For this reason the aerodynamic of the circular cylinder has been studied by several authors in the past; the most part of the literature concerns experiments performed in water channel on cylinder, while only few studies have been carried on cylinder in air.

The different aspects of the problem have been studied implementing set-up with the aim to investigate the influence of the many parameters involved, for example Williamson and Roshko (1988) discovered that there is a particular shedding mode related to the different conditions of oscillation amplitude and incoming wind velocity, Brika & Laneville (1993), Khalak & Williamson (1999) and Govardhan & Williamson (2000) performed studies concerning the behavior of the circular cylinders freely oscillating in the flow matching the instant flow fields imagines captured, with the relative A*-U* parameters (where A* is the non-dimensional amplitude value defined as A/D and U* is the non-dimensional velocity value defined as U/(fs*D)), after a few years Jauvits & Williamson (2004) highlighted also another shedding mode related to the low mass-ratio cylinders. In parallel with this studies has been stated that the shedding modes are strictly related to the behavior of lift force.

Williamson and Roshko (1988) evidenced the different wake modes that occurred varying the dimensionless parameters A* and U*. To explore this field they used a set-up where they could impose the values of two variables A* and U* and they visualized the instant flow fields that occurred behind the cylinder, so they could define a plot where it is possible to predict which type of mode will occur for a particular A*-U* couple. The main shedding modes that they found were: 2S (two oppositely signed vortices per oscillatory cycle) and 2P ( two pairs of vortices per cycle with each pair comprised of two oppositely signed vortices convected laterally outwards from the wake centre-line).

Brika & Laneville (1993) used a free oscillating cylinder (with m*≥100) to perform their studies

and they observed that the experimental values are placed along two different branches named “initial” and “lower” in the A*-U* plane. In particular they took pictures of instant fields to visualize the modes of the wake that occur for every experiment. They pointed out how the points belonging to the initial branch are related with a 2S shedding mode; the points that belong instead to the lower branch are characterized by a 2P shedding mode. Superimposing their plot with the one obtained by Williamson and Roshko (1988) they pointed out that there is not a perfect relation between their result and the plot, in fact the final part of the initial branch extended also in the 2P area for some values of U*.

Khalak & Williamson (1999) conducted studies about a cylinder immersed in a water flow and they used a set-up characterized by low m*. They noticed that there is another branch besides the two already seen in the previous papers, this is related to the highest amplitudes and it is named as “upper branch”, the relative shedding mode is the 2P. Plotting the results on the usual A*-U* plane they saw that there is an abrupt jump passing by the initial branch to the upper branch and also going by the upper branch to the lower branch. This last jump has been demonstrated that is related to the change in the phase angle between the lift coefficient (CL) and the movement of the body (Govardhan & Williamson (2000)).

Finally it is important to pay attention about the in-line movement, in fact it has no effects in the vortex shedding only if its entity is negligible, and by the other way it is possible to see a figure-eight-type motion that involves in a sickle when the cross-flow amplitude reaches the maximum level. In this situation Jauvits & Williamson (2004) found a shedding mode named 2T which is characterized by the shedding of a triplet of eddies of same rotation per cycle.

An extensive study to investigate the VIV on a high mass-ratio cylinder were performed at Politecnico di Milano wind tunnel. The model response, in subcritical Reynolds range, has been studied both in terms of dynamic parameters and in terms of instantaneous surface pressure distribution (Zasso et al. (2006); Zasso et al. (2008)).

In the present paper we extended this campaign using a similar set-up where the results have been improved performing visualizations and analysis of the flow field structure behind the cylinder. To do

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this, we used a time resolved PIV technique named Stripe-PIV developed in water channel (Malavasi et al. 2004; Malavasi and Blois 2009). Changing the seeding apparatus of the hydraulic set-up with a soap bubble generator, we were able to study the flow field structure behind a cylinder mounted in air characterized by a relative high mass-ratio and a very low damping ratio. In particular we applied this technique simultaneously to the acquisition of the pressure data, with the aim of performing a complete fluid dynamic analysis of the phenomenon matching the pressure fields with the relative wake behavior.

3. EXPERIMENTAL SETUP

The subject of the present study is a rigid cylinder (diameter D=0.2; length L=2 m) oscillating in cross flow direction in the lock-in region. The experimental set-up is shown in Fig. 1. The very large test section (14x4m) allows for negligible blockage effects with smooth flow conditions (IT ≅ 2%) and wind speed in the range 3.2 < U < 5.3 m/s. No blockage effects together with 2 end plates placed on the extremities of the model permit to realize 2D flow conditions. The rigid cylinder has been suspended by means of tensioned cables allowing separation between horizontal, torsional and vertical modes, so that it was possible to study the vortex induced oscillations of the cylinder vibrating in cross wind direction at a frequency fs=3.2 Hz.

High frequency pressure scanners have been installed inside the model to map the instantaneous pressure field on 64 pressure taps, while the oscillation was acquired by two accelerometers.

The pressure taps have been placed along two separated sections (Ring A and Ring B) and aerodynamic forces acting on the sections have been defined integrating pressure data.

Tests have been carried out at low level of structural damping (4·10-4<ξs<13·10-4, where ξs is the damping-ratio), resulting in a low Scruton number range Sc < 1. It is worth remember that, being the tests performed in air, the mass ratio parameter m* shows very high values (m*=145) resulting in negligible flow added mass effects.

We noted that the cylinder reached maximum non-dimensional amplitude of about 1.2, this fact agrees with what we expected by the literature; in fact we used a set-up with a relative low value of structural damping that allows to reach higher amplitudes respect that related to the study of Brika & Laneville (1993) and Feng (1968).

The characterization of the vortex shedding was provided using a time resolved PIV technique SPIV (Stripe Particle Image Velocimetry) which differs by conventional PIV applications for both the acquisition system and the velocity detections methodology. As better explained in the following chapter, 2D velocity fields were obtained measuring the bi-dimensional trajectories of seeding particles in a defined time interval. This is possible by filming the seeding flow on the measurement plane and by using a delayed exposure time.

The length of each trajectory is due to the corresponding instantaneous local flow velocity and to the shutter time of the video-camera. A blob analysis algorithm identifies each particle trajectory signed on each single image and measures its geometric characteristics.

The image acquisition rig was composed by two optical fibre line-converters with a 150W light source, a seeding apparatus and a progressive scan camera driven by a personal computer.

A helium bubble generator allowed us extending the range of investigable phenomenon by the original SPIV system developed for water channel applications (Malavasi et al. 2004; Malavasi and Negri 2008; Malavasi and Blois 2009). It permits to use a material characterized by a specific weight that is of the same order respect that of the fluid you are using; in air are usually used helium bubbles that are able to float well in the air, moreover the bubbles are capable of tracing air motions without bursting or impacting on objects. The SAITM Helium Bubble Generator Modified Model 5 has been used. It is a tool able to generate helium-filled, naturally buoyant bubbles of uniform size adjustable by the operator from 1/32” to 3/16” in diameter. Two outputs positioned upstream respect to the cylinder has been used to generate bubble simultaneously.

In order to address both the flow velocity and the position of the oscillating cylinder, we use a

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reference marker on the cylinder to provide, within the same frame, the measurement of the flow velocity and the position of the model (Mirauda et al.2007). This method allows high resolution of the displacement as prove the comparison between the measurement via image analysis and accelerometer. The vortex shedding reconstruction was provided by a phase-averaged reconstruction of the flow velocity maps, using the cylinder motion as reference signal.

Figure 1: The instrumented rigid cylinder oscillating in cross flow direction in Politecnico di Milano Wind Tunnel

4. EXPERIMENTAL RESULTS

4.1 Analysis method

To perform the visualizations a method implemented by Malavasi et al. (2004) in Politecnico di Milano has been used. It consists in an acquisition of a sequence of images using a progressive CCD video-camera while the flow is inseminated with particles characterized by a specific weight of the same order of that of the fluid. Every frame is converted into a binary image imposing a threshold brightness as reference to decide if a pixel must be considered white or black. This methodology gives images containing a series of tracks related to every particle in movement in the flow, this tracks are named “blobs”. Analysing a single image it is possible to identify the position in the space, the orientation, and the length of each blob. Using two other threshold values related to the minimum and the maximum dimension (in pixel) of the blobs, it is possible to erase the reflection on the image due to the presence of the cylinder and other occasional reflections due to the complex set-up.

An example of this result is reported in Fig. 2, where a non-filtered and a filtered frame are compared. Fig. 3 shows the blobs identified on the same frame.

The consecutive frames are paired and compared to assign the direction of movement for every single blob, the field is then divided into a grid and every vector is addressed to a node of it.

Because of the few number of particles in each single frame, the flow field reconstruction has provided using the phase average analysis of the velocity field. To do this we used as reference signal, the movement of the cylinder. The latter was provided by the detection of the movement of a marker placed on the cylinder. We detected the position of the cylinder and the velocity of the flow on the same image. In this way the reconstruction of the flow field and the movement of the cylinder are strictly correlated (in Fig. 2 left is clearly visible the brightening marker).

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Figure 2: Comparison between a non-filtered frame (left) and a filtered one (right).

Figure 3: Effect of threshold imposed on the blob area.

The marker track is like an almost perfect sinusoid, this fact highlights that it is reasonable to use the phase average method by the way that we can find clearly a unique frequency inside the power spectrum of the displacement.

By the literature is possible to see how, usually, the mean phase of the periodic component of the velocity is divided into about twenty slots, doing this is possible to represent the flow field with an adequate time step and it is possible to have, in each slot, a series of fields that are referred to not so different instantaneous fields. As just pointed out we have not so much data available for every frame, this fact do not let us to use a so large number of slot, so it has been chosen to use only twelve slots to be able to obtain clear visualizations and, simultaneously, to use an enough time step.

The external trigger is represented by a brightening marker mounted on the cylinder, we will follow its track in the images to derive the frequency of movement related to the body. The method of the marker was already used and validated by Mirauda et al. (2007) to follow the movement of a sphere, in their study they compared the results derived by the analysis of images acquired by CCD camera with that relative to an analogue laser displacement sensor. They noted that there was good agreement between the two sets of data; in particular they calculated the r.m.s. for both the acquisitions and they saw that there was negligible difference between them.

4.2 Results

The cylinder behavior has been studied evaluating its steady state response in the lock in region: steady state conditions have been acquired at constant wind speed and each of these points was

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reached from the previous one changing by small steps the wind velocity. In Fig. 4, reproduced from Williamson & Roshko (1988), is given a plot of the state of the art knowledge related to the different states observed in the vortex street wake structure; showing superimposed the steady oscillations response curve obtained from present tests.

Figure 4: Williamson & Roshko (1988) map of wake modes with superimposed steady state oscillating response (-•-).

The oscillation response curve of Fig. 4, obtained in terms of the non-dimensional oscillation amplitude reached by the cylinder during its free oscillating movement for each value of V/Vs, substantially agree with previous investigation an the same experimental set-up (Zasso et al. 2006 and Zasso et al. 2008). These results have been obtained considering a sampling frequency for the pressures and the displacement of 125 Hz. Besides displacement and pressure data, on the cylinder surface, have been taken for every point of the plot.

In the aim to correlate displacements, pressure distribution and flow field structure on our experimental set-up, we performed a series of SPIV acquisitions within the range defined by the oscillation response of our cylinder reported in Fig. 4. Here we report the case of V/Vs=1.191 at which correspond a maximum dimensionless amplitude z/D=0.6. The flow field image were acquired with a frame rate of 91 Hz and a shutter time of 0.011 sec. The total amount of frames per each acquisition was limited to 1000 by the RAM of the PC used.

Fig. 5 shows an example of the image analysis results in terms of the streamlines of the flow field in the first four slots of the phase analysis; the positions of the cylinder in the cycle of movement is highlighted in the scheme below each figures. The two cylinders which are drawn in the slots 1, 2 and 3 correspond to the position of the model at the initial edge of the slot (upper circle) and the final edge of the slot (lower circle). In the fourth slot the two cylinders are overlapped because of the cylinder is at the maximum of the oscillation and the minimum of the displacement within the slot.

The flow field description highlights a topology of the wake that seems more similar to a 2S mode respect to the expected 2P vortex shedding mode. However the observed oscillation amplitude and the velocity ratio should relative to the 2P region on the map of the vortex identified by Williamson & Roshko (1988), the amplitude of the wake and the detached vortex are more close to the ones observed for the 2S mode (Fig. 6). It is authors’ opinion that a transition in the cylinder aerodynamic

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behaviour is occurred as is possible to see in Fig. 4 where the steady state curve shows an abrupt jump in the oscillation amplitude at V/Vs=1.13. This jump results also in a changing in the displacement time history, the oscillation became more stable and sinusoidal-like shape for velocity ratio higher than 1.13. Nevertheless it is possible that this transition is not so evident in the main wake structure, because the performed test is placed in a boundary region between the two modes. As noticed also by Morse & Williamson (2009) it is possible to observe intermediate vortex shedding modes in the boundary region. Moreover the test conditions for the present experimental campaign are quite different to the ones of the set-up used to identify the map of vortices: as evidenced also by Brika & Laneville(1993) and Govardhan & Williamson (2000) high mass-ratio cylinder can experience different vortex shedding modes respect to low mass-ratio cylinder

Figure 5: The field visualization with streamlines and relative cylinder position scheme at V/Vs=1.191 response.

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Figure 6: 2S shedding mode scheme for Williamson & Roshko (1988)

On the other hand, the presence of a significant component of the velocity along the streamwise direction make the vortex shedding structure weakly visible, in order to improve the comprehension of the topological structure of the flow field we calculated the vorticity fields for every slot.

Fig. 7 shows the vorticity field correspondent to the four phases of the Fig. 5, below each vorticity field the population map, of the experimental data, is reported. The latter is useful to evaluate the reliability of the vorticity calculation which is obviously affected by the data distribution on the acquisition area. To make the visualization more understandable a threshold value of vorticity (ω’) of ±0.4 to erase the contours relative to the lowest levels of vorticity has been imposed, besides it has been chosen a step of ω’=0.4 between two contour lines to have a reasonable number of contours. The values are expressed in dimensionless terms ω’= ω*D/V where ω is the vorticity value calculated.

By comparing the number of data relative to every phase and comparing it with the plot of vorticity, we note that there’s a strong correspondence between the position of vortex and the area where we have the most of data acquired, this is probably due to the fact that the bubbles are captured by the vortex and subtracted from the other parts of the field (Fig. 7).

Fig. 8 reports the superimposing of the streamlines (Fig. 5) with the vorticity field (Fig. 7) for each of the four slots considered and the correspondent position of the cylinder in the phase, correlated with the pressure distribution. The two vectors within the cylinder represent the resultant of the pressure distribution and the relative velocity between upstream flow and cylinder.

The superimposing of the streamlines and vorticity fields highlights the hiding effect caused by the mean velocity concerning eddies during their downstream movement. Moreover it confirms the results previously presented relative to the vortex shedding topology. The pressure distribution evidences a good correlation with the flow structure, and the match of kinematic and dynamic measurement help the knowledge on the phenomenon. For example, according with results of Zasso et al. (2008), the position of the stagnation point in the slot 1 of Fig. 8 appears rotate towards the center of the cylinder; the position of the stagnation point is essential to complete the topology of the flow around the cylinder. Besides it is interesting to point out how the relative position of the stagnation point respecting on the center of cylinder follows the direction of the relative velocity vector. Moreover, in the fourth slot (maximum displacement), Fig. 8 shows the largest peak of pressure correlated to a large area of positive pressure.

5. CONCLUSIONS

This work proves that the SPIV technique is useful to obtain flow field reconstruction on relative large area in a wind tunnel; here we investigate an area of 1510 x 1150 mm. Using SPIV we obtained good reconstruction of the flow field downstream a oscillating cylinder where the movement of the obstacle is detected via image analysis of the same SPIV image using a reference marker on the cylinder. The result obtained allows to better understand the vortex shedding phenomenon downstream the cylinder. Moreover, matching the kinematic and dynamic measurement, it was possible to correlate the flow structure with the pressure distribution around the cylinder for all the position of the latter, obtained by the phase analysis. Further analysis have been planned in order to extended the observed area downstream and upstream the cylinder and in order to analyze some other points in the lock-in region.

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Figure 7: The vorticity fields with, superimposed, the verse of rotation of each eddy (upper figures) and the distribution of data inside the field (lower figures) at V/V s=1.191 response.

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Figure 8: Comparison between flow maps and pressure distribution for different cylinder positions at V/Vs=1.191 response.

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ACKNOWLEDGEMENT

The authors would like to thank Marco Negri for his support during the experimental tests and for his suggestion in the data analysis .

6. REFERENCES

Brika D., Laneville A. (1993), “Vortex-induced vibrations of a long flexible circular cylinder”, Journal of Fluid Mechanics, vol. 250, pp. 481-508.

Govardhan R., Williamson C. H. K. (2000), “Modes of vortex formation and frequency response of a freely vibrating cylinder”, Journal of Fluid Mechanics, vol. 420, pp. 85-130.

Jauvits N., Williamson C. H. K., (2004), “The effect of two degrees of freedom on vortex-induced vibration at low mass and damping, Journal of Fluid Mechanics, vol. 509, pp. 23-62.

Khalak A., Williamson C. H. K. (1999), “Motions, forces and mode transitions in vortex-inducd vibrations at low mass-damping, Journal of Fluids and Structures, vol. 13, pp. 813-851.

Malavasi S., Franzetti S., Blois G., (2004), “PIV investigation of flow around submerged river bridge“, In: Proceedings of the International Conference River Flow 2004, Napoli, Italy, pp. 601–608.

Malavasi S., Blois G. (2009), “Wall effects on the flow structure around a rectangular cylinder”, Meccanica, DOI 10.1007/s11012-009-9199-x.

Malavasi S., Negri M. (2008), “Analysis of non-stationary flow around a rectangular cylinder”, Sixth International Colloquium on: Bluff Body Aerodynamics & Applications. Milano 20-24 July.

Mirauda D., Malavasi S., Greco M., Volpe Plantamura A. (2007), “Effects of free surface flow on a tethered sphere” 9th Intl. Symp. Fluid Control, Measurement and Visualization, Flucome 2007, Paper 151, Tallahassee, FL.

Morse T.L., Williamson C.H.K., (2009), “Fluid forcing, wake modes, and transitions for a cylinder undergoing controlled oscillations’, J. Fluids Struct, article in press

Williamson C. H. K., Roshko A. (1988) “Vortex formation in the wake of an oscillating cylinder”, J. Fluids Struct. 2, 355-381.

Zasso A., Belloli M., Giappino S., Muggiasca S. (2008), “Pressure field analysis on oscillating circular cylinder”, Journal of Fluids and Structures 24 628–650

Zasso A., Belloli M., Giappino S., Muggiasca S. (2006), “On the Pressure and Force Field on a Circular Cylinder Oscillating in the Lock-In Region at Sub-Critical Reynolds Number” Proc. of PVP2006-ICPVT-11, ASME Pressure Vessels and Piping Division Conference, Vancouver, Canada (BC), July 23-27, 2006.