Experimental investigation into the vortex formation in the wake of

Paper No. 2006-JSC-434 de Wilde Page 1 of 10

Experimental investigation into the vortex formation in the wake of an oscillating cylinder using Particle Image Velocimetry

Ir. J.J. de Wilde, Dr. R.H.M. Huijsmans and Dr. J. Tukker

Maritime Research Institute Netherlands (MARIN) Wageningen, The Netherlands

ABSTRACT In this paper a novel experimental investigation into the vortex formation in the wake of a fixed and an oscillating circular cylinder is presented. The aim of the study is to acquire a better understanding of the complex three-dimensional vortex flow around the cylinder at high Reynolds numbers, as well as to set up a method for the validation of CFD for riser VIV applications. The Reynolds number in the experiments ranged from 40,000 to 200,000. A 200 mm rigid cylinder of 3.4 m length was towed at constant speed in a 210 m long towing basin. The fluid loads on the cylinder were measured and state-of-the-art 3 component Particle Image Velocimetry (PIV) measurements were carried out in a 2-D plane of 400 x 700 mm in the downstream wake of the cylinder. A fixed cylinder and a oscillating cylinder were tested. The range of amplitudes and frequencies was tested for the oscillating cylinder in the lock-in region. The tests give new insight in the vortex synchronisation and will provide a valuable set of data for future CFD-code validation. KEY WORDS Particle Image Velocimetry, PIV, Vortex Induced Vibrations, VIV, riser, Reynolds number, CFD INTRODUCTION One of the grand challenges in the offshore industry is still the assessment of the motions of a circular cylinder in waves and current for application to risers or riser bundles up to 10,000 feet water depth. Here the fatigue life is dominated by the VIV phenomena and also the possibility of riser collision is governed by VIV effects. The nature of the vortex induced vibration (VIV) problem relates to a hydro-elastic problem in which the vibrations are triggered by force fluctuations due to the generation of vortices. The force fluctuations in return are strongly influenced by the subsequent motions of the riser in a truly coupled fashion.

As is already known, the vortex shedding is a three-dimensional phenomena, where the three-dimensionality of the flow around the cylinder mainly stem from the fact that the cylinder is excited in a few normal modes. The actual fluid loading can, as a first approximation, be regarded as two-dimensional. THREE-DIMENSIONAL PARTICLE IMAGE VELOCIMETRY Fluid force measurements, as well as Particle Image Velocimetry measurements (PIV) were carried out on a fixed and an oscillating cylinder in a uniform and stationary flow. The aim of the study is to acquire a better understanding of the complex three-dimensional vortex flow around the cylinder at high Reynolds numbers, as well as to set up a method for the validation of CFD for riser VIV applications. The flow is assumed to be basically two-dimensional. The Reynolds number in the experiments ranged from 40,000 to 200,000. The 3-component – 2-dimensional (3C-2D) PIV technique uses a powerful laser sheet for illuminating the measuring area and two high-sensitivity digital cameras for recording the displacement of the tracer particles in the flow. The PIV principle is illustrated in Figure 1. The x, y and z components of the velocity vector in the planar measurement area are measured.

Figure 1 – PIV principle The tracer particles are illuminated twice with the laser, with a short time lapse. The two synchronised digital cameras record the displacement of the particles between the two illumination times from two subsequent images. The velocities can then be derived


from displacements using the known time lapse. A cross-correlation technique is used for deriving the particle displacement in a pair of images. The out of plane component of the velocity vector is obtained by the stereoscopic images from the two cameras, as shown in Figure 2.

Figure 2 – 3D-PIV principle for third velocity component measurement

Details of the PIV measurements are presented in Appendix 1. 3C-2D PIV CONFIGURATION IN HIGH REYNOLDS VIV TEST SET-UP After the calibration, the 3C-2D PIV system was mounted under the towing carriage of the High Reynolds VIV test set-up in the high speed basin. The 114 mm camera house was mounted perpendicular to the basin axis and the supporting mast was tilted 49.6 degrees with respect to the horizon. With the camera house at about 0.64 m immersion, the downstream wake of the test cylinder at 1.7 m immersion was captured in the field of view of the cameras.

Figure 3 - PIV probe in High Reynolds VIV test set up The PIV probe could be shifted horizontally to adjust the downstream position of the measuring area relative to the test pipe. A forward and backward position were used during the test campaign, as shown in Figure 4. The first position was directly

downstream of the test cylinder and the second one shifted 0.46 m downstream, while the vertical position and 49.6 degrees inclination angle of the camera were kept the same.

Flow

Position 1 Position 2

FlowFlow

Position 1 Position 2

Figure 4 – Position 1 and 2 of the measurement area The sample rate of the PIV recordings was set to 10 Hz, whereas the motions and loads of the cylinder were measured simultaneously at 100 Hz sample rate. The test runs were carried out for the maximum possible length in the 210 m long basin. The PIV images were recorded for a duration of 100 s, resulting in a total of 1000 images in each run. About 20 pipe oscillations were recorded at the minimum pipe oscillation frequency of 0.2 Hz. The PIV measurements were synchronised with the data acquisition of the motions and loads, using an external trigger signal. 3C-2D PIV MEASUREMENTS ON A SMOOTH CIRCULAR CYLINDER In the next section we will address the vortical flow behaviour for low Re cases as observed by Williamson and Roshko [10]. 2S and 2P behaviour, as observed by Williamson and Roshko In the late eighties of the previous century it was discovered that several regions exists for the vortex synchronisation in the reduced velocity - amplitude plane [10]. The well known lock-in region occurs when the trajectory wave length is comparable with the distance that a non-oscillating cylinder travels through the fluid in one full cycle of the shedding. This occurs for reduced velocities around 5. In this fundamental lock-in region, the acceleration phase of the cylinder motion at the start of each half cycle has the effect of rolling-up both of the separating shear layers into a fresh pair of vortices. The continuously accelerating and decelerating cylinder thereby sheds four regions of vorticity in each cycle, rather than simply two Karman-type vortices, as observed for a non-oscillating cylinder. Below a critical trajectory wavelength, each half cycle sees the coalescence of two vortices of the same sign, so that two regions of opposite vorticity are fed into the wake per cycle. This mode of vortex formation creates a Karman-type wake, known as “2S”. If, however, the wave length exceeds a critical value, each of the two like-signed vortices pairs up with an opposite-signed vortex in the wake. The resulting vortex street comprises a system of vortex pairs convecting away from the centreline, known as “2P”. Two pairs of vortices can be observed in each cycle, as schematically presented in Figure 5


2S

2P

2S

2P

Figure 5 – “2S” and “2P” mode for oscillating cylinder in a flow [10]

Types of tests for High Re VIV investigation A description of the High Reynolds VIV test set-up can be found in Appendix 2. Basically three types of tests can be carried out with the test apparatus: Test type 1: Vertical oscillation in still water (KC and Sarpkaya

beta test) Test type 2: Non-oscillating tow test (Drag test) Test type 3: Vertical oscillation while towing (VIV test)

Test type 1: Forced oscillation in still water

The forced oscillation tests in still water provide the added mass coefficient Cm and drag coefficient CD in the Morison equation.

2m D

1F(t) C D u(t) C Du(t) u(t)4 2π

= ρ + ρ&

The added mass and drag coefficient depend on the Keulegan-Carpenter number and the Sarpkaya beta:

au T AKC 2D D

= = π

and:

2D ReT KC

β = =ν

Test type 2: Non-oscillating tow tests

The drag load on a cylinder in current can be calculated as follows:

2D D

1F C Du2

= ρ

The drag coefficient CD depends on the Reynolds number:

UDRe =ν

The kinematic viscosity, ν, of fresh water at 16 degrees Celcius is 1.11E-6 m2/s. Test type 3: Forced oscillation in current

The lift force of an oscillating cylinder in current may have a phase difference with the motions of the cylinder. For harmonic signals this can be written as follows: z(t) = A sin(2πf0t

)tf2sin()cos(F)tf2cos()sin(F)tf2sin(F)t(F 00L00L00LL πφ+πφ=φ+π= The lift coefficients in-phase with the velocity, CLv, and in-phase with the acceleration ,CLa, are defined as follows:

221

0LLv

UDL

)sin(FC

ρ

φ=

and 2

21

0LLa

UDL

)cos(FC

ρ

φ−=

Using the same sign conventions as Gopalkrishnan [3] a positive CLv coefficient denotes power transfer from the fluid to the cylinder oscillation and a positive CLa coefficient denotes a negative added mass. The lift coefficients depend on the amplitude ratio A/D, the Reynolds number Re and the reduced velocity Ur:

=r0

UUf D

Test scope The following forced oscillation and non-oscillating tests were carried out in the PIV test campaign: − tests with Field of View of PIV system near cylinder − tests with Field of View of PIV system at 2.3 diameters

downstream of the cylinder The range of test parameters was: − Tow speed: 0.2, 0.5 and 1.0 m/s − Reduced velocity: 2, 6, 7 and 12 − Amplitude ratio: 0.4. 0.9 and 1.6 3C-2D PIV measurement on an oscillating cylinder An example of a raw image of the PIV camera is presented in Figure 6.

Test set 1 Vertical oscillation

Test set 2 Horizontal tow

Test set 3 Vertical oscillation, Horizontal tow


Figure 6 - Raw PIV image The illuminated cloud of seeding particles can be observed in the downstream wake of the cylinder. The whole measuring area was in focus and the individual 60 micron Rilsan particles can be distinguished when zooming in. Since the cross correlation technique uses the patterns in the cloud rather than the individual particles, the technique is somewhat forgiving in case the images should not be fully in focus. An example of a derived velocity contour map is shown in Figure 7. The in-plane velocity vector in each interrogation unit is presented with an arrow, and the out of plane velocity component is presented with the colours in the background. The total map consists of 58 x 71 velocity vectors in the 400 x 700 mm measuring area. The grey area near the edges is the “masked” area due to the overlapping field of view of the two cameras, the opening angle of the laser sheet and light reflections in the vicinity of the test pipe. In the upper right hand corner the undisturbed current velocity of 0.2 m/s can be observed in the velocity map, taking into account that the probe was tilted by 49.6 degrees. A large clock-wise rotating vortex can be observed in the centre of the figure. The maximum local velocity in the vortex is about twice the undisturbed velocity in the corner. The maximum local out of plane velocity is about 0.4 m/s going both inward and outward (yellow and blue areas), suggesting important three-dimensionality of the flow in the centre of the vortex.

-400 -380 -360 -340 -320 -300 -280 -260 -240 -220 -200 -180 -160 -140 -120 -100 -80 -60 -40 -20 0 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 320 340 36mm-300

-250

-200

-150

-100

-50

0

50

100

150

200

mm

-0.600 -0.514 -0.429 -0.343 -0.257 -0.171 -0.086 -0.000 0.086 0.171 0.257 0.343 0.429 0.514 0.600

Vector map: 3D vectors, 58×71 vectors (4118)Burst#; rec#: 1; 229 (325), Date: 23/11/2005, Time: 16:45:27:344

Figure 7 - Velocity map A series of 12 successive images of the measured velocity field in the wake of the oscillating cylinder is presented in Appendix 3. The 12 images cover one full cycle of the cylinder oscillation of 5.93 s with a 0.49 s time step. At 10 Hz sample rate, the total number of PIV images in this cycle was 59. The results in Appendix 3 are obtained from an forced oscillating test with a tow velocity of 0.2 m/s (Re 36,000), an oscillation frequency 0.167 Hz (Ur 6) and an amplitude of 180 mm (A/D 0.9). The actual measured force on the cylinder is drawn in the images with a black arrow and the relative velocity vector of the cylinder in the flow with a blue arrow. A schematic interpretation of the observed vortex flow has been added by the authors to image 224 (t = 3.46 s). Based on the map of vortex synchronisation regions of Williamson and Roshko [10], a “2P” type vortex shedding can be expected for the oscillating cylinder at A/D 0.9 and Ur 6. Our preliminary observations form the PIV flow maps are: − The force vector is in phase with the cross flow velocity,

suggesting a positive power transfer from the fluid flow to the cylinder motion. This is confirmed by the harmonic analysis of the measured lift forces in section 3.6 of this paper. The PIV

images show that the lift vector points in opposite direction than the downstream wake. The downward suction force in image 224 can be explained by the large flow velocity on the downward side of the cylinder.

− The clock-wise rotating vortices D1 and B2 can be clearly observed in image 224. The presence of the counter clockwise vortex C1 is not so convincing, but it seems plausible that the shear layer from the downward side rolls up in counter clockwise direction. The local velocities in the C1 region are quite small and the area may also be recognized as a “deadwater” region.

− A “2P” type vortex synchronisation will be established if the vortices C1 and B2 pair. Since the images in Appendix 3 are not fully conclusive on the type of vortex synchronisation, further analysis of the PIV data is required, especially considering the images at the second more downstream position of the camera.

− The vortices seem to convect away from the centreline, suggesting “2P” type vortex synchronisation.

Accuracy analysis The accuracy of the PIV measurements was checked by measuring the undisturbed uniform flow field in the field of view, without the presence of the upstream test cylinder. From the measurements it was found that the individual valid velocity vectors at each interrogation position at each time step were accurate within 5%. The accuracy of the time averaged velocity vectors was better than 2%. The initial adjustment and calibration of the cameras is a fundamental factor for the accuracy of the PIV measurements, but accuracy can also be lost in the post-processing. For instance when the concentration of detectable particles or clusters in the interrogation units is becoming too small or the out-of-plane velocities are too high, the cross correlation technique can become unreliable. For this reason abnormal velocity vectors are removed in an iterative fashion and if needed replaced by interpolated vectors, using neighbouring valid vectors. Hydrodynamic load measurements The total measured in-line drag load (FX TOT) and the cross flow lift loads (FL) are presented in Figure 8, together with the harmonic motion (Z MOT) of the pipe. The total load is the sum of the individually measured loads on both ends of the pipe. The presented cross flow lift load FL has the own inertia forces removed. A positive lift means a net upward force by the fluid on the pipe.

Figure 8 – Measured motions and loads from the test The phase angle of the lift load with respect to the motion is very important for the VIV phenomena. A positive phase angle means a


net power transfer from the fluid to the pipe motion, as can be observed in the VIV lock-in region. In the presented test, the lift load signal leads by about 20 degrees and the computed net power transfer over a full cycle is about 0.36 Joule per unit pipe length. For a freely vibrating cylinder, an equilibrium will be reached when the same amount of energy is dissipated by mechanical friction. Steel risers generally have a very small internal damping, being much less than 1% of critical. The following hydrodynamic coefficients were derived for the test: - in-line drag coefficient CD = 3.19 - oscillating lift load in phase with velocity of CLv = 0.86 - added mass coefficient of Cm = 1.41 Previously measured lift coefficients for other A/D and Ur values for the same cylinder were presented by de Wilde et al in 2004 [9]. CONCLUSIONS AND RECOMMENDATIONS Based on the results presented in this paper, the following conclusions and recommendations seem justified: - For the first time, high quality Particle Image Velocimetry

(PIV) measurements were carried out on a fixed and an oscillating cylinder at Reynolds numbers between 40,000 and 200,000.

- The PIV technique provides detailed information of the velocity field in the downstream wake of the cylinder. About 4,000 velocity vectors were measured in the approximately 400 x 700 mm planar measuring area at a sample rate of 10 Hz. All three velocity components (x, y and z) were measured using a stereoscopic technique with two cameras.

- The PIV technique requires careful calibration for accurate determination of the relationships between the image coordinates (x, y) of the two cameras and the object coordinates (X, Y, Z) in the physical frame.

- The seeding of the flow with tracer particles is a difficult and crucial element for the PIV measurements. We used calibrated 60 µm Rilsan particles injected by an upstream seeding pipe in a continuous process during the tests.

- The preliminary analysis of the tests data reveal already very interesting results for the fundamental insight into the vortex shedding process at higher Reynolds numbers. An important three-dimensionality of the flow has been observed in the centre of the vortex.

- The results presented in Appendix 3 are not yet fully conclusive on the type of vortex synchronisation. Based on the map of vortex synchronisation regions of Williamson and Roshko, a “2P” type vortex shedding was expected for the oscillating cylinder at A/D 0.9 and Ur 6. Although the paring up of two counter-clockwise vortices has not yet been clearly observed, the fact that the vortices seem to convect away from the centreline suggests that the synchronisation is indeed of “2P” type.

- The 3C-2D PIV technique in combination with other more global measurements, such as body motions and forces, seem very promising for future CFD code validation.

NOMENCLATURE β : Sarpkaya beta φ0 : phase angle ν : kinematic viscosity ρ : fluid density A : amplitude of oscillation CD : drag coefficient

CLv : lift coefficient in phase with velocity CLa : lift coefficient in phase with acceleration Cm : added mass coefficient D : cylinder diameter (nominal pipe diameter in this report is 273 mm) F : fluid load FD : drag force FL : lift force FLa : lift force in phase with accelerations FLv : lift force in phase with velocity fo : oscillation frequency fs : vortex-shedding frequency KC : Keulegan-Carpenter number Re : Reynolds number St : Strouhal number t : time u, U : flow velocity Ur : reduced velocity z : heave motion (vertical) REFERENCES [1] Berchiche, N. and Janson, C., Flow simulation of a

propeller in open condition and experimental validation, 8-th Numerical Towing Tank Symposium, Bulgaria, 2005.

[2] Dautel, J. et al, Développement et application d’un nouveau système de PIV tri composantes (PIV-3C) adapte aux essais en basin de traction, submitted to 10 days of hydrodynamics, Nantes, 2005.

[3] Gopalkrishnan, R., Vortex-Induced Forces on Oscillating Bluff Cylinders, D.Sc. thesis, Department of Ocean Engineering, MIT, Cambridge, USA, 1993.

[4] Huijsmans, R.H.M., de Wilde, J.J. and Buist, J., “Experimental and numerical investigations into the effect of vortex-induced vibrations on the motions and loads of circular cylinders in tandem”, Parallel CFD 2000 conference, Trondheim, 2000.

[5] Huijsmans, R.H.M. and Borleteau, J.P., The flow around FPSO’s in steep regular waves, ISOPE 2003-PF-06, Toulon, 2003.

[6] Tukker, J., Blok, J.J., Kuiper, G. & Huijsmans, R.H.M. Wake Flow Measurements in Towing Tanks with PIV. Proceedings of the Ninth International Symposium on Flow Visualization, 2000.

[7] Wilde, J.J. de and Huijsmans, R.H.M., Experiments for High Reynolds Numbers VIV on Risers, ISOPE, Paper 2001-JSC-285, Stavanger, 2001.

[8] Wilde, J.J. de and Huijsmans, R.H.M. & Triantafyllou, M.S., Experimental Investigation of the Sensitivity to In-line Motions and Magnus-like Lift Production on Vortex-Induced Vibrations, ISOPE, Paper 2003-JSC-270, Hawaii, 2003.

[9] Wilde, J.J. de, Sworn, A, Cook, H, Willis, N. and Bridge, C., Cross Section VIV Model Test for Novel Riser Geometries, Deep Offshore Technology Conference, New Orleans, 2004.

[10] Williamson, C.H. and Roshko, A. Vortex formation in the


wake of an oscillating cylinder, Journal of fluids and structures, 1988.

Appendix 1: PIV Set-Up PIV probe The two cameras are mounted inside an underwater camera house composed of two watertight camera modules and two mirrors as shown in Figure 1.1, [1] and [2]. The optical axes of the cameras are aligned with the camera probe axis and the shooting angles are adjusted by the mirrors. Aperture and focusing adjustments are remotely controlled from the system central unit. The Scheimpflug angle adjustment, which consists in tilting the camera optical axis with respect to the lenses, is accessible for each camera from outside the probe by means of an adjustment knob. The Scheimpflug adjustment is needed when the measurement plane is not perpendicular to the camera optical axis, which is the case in most stereoscopic configurations, and allows for focusing over the whole field of view of the camera. The Dantec FlowSense 2M CCD cameras have 1600x1200 pixels and a 10 bits resolution. Interferential filters were used for reducing the influence of ambient light. The maximum image rate of the cameras is 15 Hz, but 10 Hz was used in the present test campaign. The camera probe is linked to the basin carriage by means of a mast. The electrical cables go from the underwater camera house to above water central unit through watertight hoses. The mast and hoses can be fitted with streamlined fairings to reduce the fluid forces and vibrations at high speed, but these fairings were not used in our test campaign.

⇒Flow

Figure 1.1 – 3D-PIV system scheme (side view) Laser sheet The stroboscopic laser sheet is generated by a pulsed laser and specific optical components for generating the sheet. The laser source is a Nd:YAG double cavity BigSky laser, allowing to generate 120 mJ 532 nm pulses with a repetition rate up to 15 Hz. Designed for military applications and water-cooled in close loop, it

is very robust and can be used in harsh environments and in any position. The light sheet is generated at the upper end of an optical arm. Focusing optics and an adjustable tilted mirror mounted on the upper platform allow the focusing of the laser beam on the sheet generating optics at the lower end of the arm. In our set-up, the optical arm was mounted inside the mast of the camera probe. A symmetrical camera set-up was used with the laser sheet in the middle and perpendicular to the probe, as shown in Figure 1.2.

Figure 1.2 – Symmetrical PIV set-up with two cameras Seeding The seeding of the flow with tracer particles is a crucial element for the PIV measurements. The following constraints must be respected: The tracer particles should be of small size and should have a density close to one to accurately follow the flow. The particle should not be too small for good visual detection by the cameras. The particle concentration should be chosen carefully. The particle distribution in the measurement area should be homogeneous to obtain velocity vectors in each interrogation area. Too much seeding may lead to loss of contrast in the images. The upstream seeding injector should not affect the flow. For our measurements we used calibrated 60 µm Rilsan particles. The particles were first mixed with 90% alcohol and this mixture was then mixed with the basin water in a 80 litre container with a mechanical mixer. The final mixture was pumped from the container to a streamlined seeding pipe rigidly mounted on a small sub carriage, about 5 m upstream of the test cylinder. After careful adjustment of the seeding concentration, pump rate and position of the seeding pipe, a homogeneous distribution of the particles in the light sheet plane was obtained. Continuous seeding was used during the runs. Image acquisition and processing The digital images were real time recorded by a hub device, containing a 32 GB LIFO buffer which allows up to 5 minutes of continuous acquisition. This device also ensured synchronisation between the two camera acquisitions and the laser pulses. At the end of the acquisition process, the raw images were transferred by Ethernet at a rate of 1 Gigabit/s from the hub to the central unit, containing a dual processor 2.8 GHz PC.


The processing of pairs of images was performed on the central unit following several successive processing stages, whose script is to be defined in the Dantec FlowManager software. Distributed computing over 3 computers can be performed in order to reduce the processing time. In a first step, the background noise and possible light reflections from the test objects in the field of view are removed by subtracting an average image calculated over all the images in the run. Then the cross-correlation calculation is performed on each pair of images. Various validation functions can be used at this stage in order to remove abnormal vectors, and, if needed, to replace these vectors by interpolated vectors using neighbouring valid vectors. Masks, to be manually defined by the operator, can be applied to reject vectors obtained in certain zones (e.g. reflection zones). At this stage a two-component velocity map is obtained for the two images in a pair. The reconstruction of the out of plane velocity component is finally carried out by combining the 3D maps with the calibration results. Further exploitation of 3D post processing is possible, such as: subtraction of a uniform velocity field (e.g. relative velocity due to carriage speed), extraction of space and time velocity profiles and calculation of vorticity, turbulence intensity and power density spectrum maps. Calibration Calibration is needed for determining the relationships between the image coordinates (x, y) of the two cameras and the object coordinates (X, Y, Z) in the physical frame. The calibration was carried out prior to the test campaign. A rigid calibration plate was used, containing a grid of regularly spaced dots. This plate was placed parallel to the laser sheet, in the field of view common to both cameras. The plate could be transversely shifted to several positions within the thickness of the laser sheet. Due to perspective effects, the raw images are optically distorted, but after the calibration process, the software provides rectilinear and perpendicular data. Appendix 2: High Reynolds VIV test apparatus The 200 mm circular test cylinder was mounted in the High Reynolds VIV test set-up in the high speed basin as depicted in Figure 2.1.

6 7

5

4

3

2

1

1. Vertical struts.2. Linear bearings3. Test pipe.4. End plates.5. Drive shafts.6. Oscillator7. 30 kW electric motor.

6 7

5

4

3

2

1

6 7

5

4

3

2

1

1. Vertical struts.2. Linear bearings3. Test pipe.4. End plates.5. Drive shafts.6. Oscillator7. 30 kW electric motor.

Figure 2.1 - High Reynolds VIV test apparatus

The 3.4 m long rigid test cylinder is horizontally suspended on two streamlined struts from the carriage at approximately 1.7 m water depth. The high speed basin is 4 m deep, 4 m wide and 210 m long. The cylinder can be fixed in the flow or can be oscillated in cross flow direction on linear bearings at both ends of the pipe. A powerful electric oscillator is used for the forced oscillation in a harmonic fashion, consisting of a 30 kWatt motor, a 1:10 reduction and a crank-shaft mechanism. The frequency and amplitude of the oscillation can be accurately adjusted in each test. The set up has been designed for loads up to 10 kN, tow speeds up to 4 m/s, oscillation frequencies up to 3 Hz and oscillation amplitudes up to 330 mm. In previous test campaigns, a 200 mm smooth, rough and straked cylinder have been tested [7], [8] and [9]. Appendix 3: Test Results for Ur 6, A/D 0.9, Re 36,000

Test 102024image 189t = 0.00 s

61 N

Test 102024image 189t = 0.00 s

61 N

Image189, t = 0.00 s

Test 102024image 194t = 0.49 s

65 N

Test 102024image 194t = 0.49 s

65 N

Image194, t = 0.49 s


Test 102024image 199t = 0.99 s

57 N

Test 102024image 199t = 0.99 s

57 N

Image199, t = 0.99 s

Test 102024image 204t = 1.48 s

56 N

Test 102024image 204t = 1.48 s

56 N

Image 204, t = 1.48 s

Test 102024image 209t = 1.98 s

39N

Test 102024image 209t = 1.98 s

39N

Image 209, t = 1.98 s

Test 102024image 214t = 2.47 s

44 N

Test 102024image 214t = 2.47 s

44 N

Image 214, t = 2.47 s


Test 102024image 219t = 2.97 s

56 NTest 102024image 219t = 2.97 s

56 N

Image 219, t = 2.97 s

Test 102024image 224t = 3.46s

60 N

D1

B2

C1

Test 102024image 224t = 3.46s

60 N

D1

B2

C1

Image 224, t = 3.46 s

Test 102024image 229t = 3.96s

55 N

Test 102024image 229t = 3.96s

55 N

Image 229, t = 3.96 s

Test 102024image 233t = 4.45 s

47 N

Test 102024image 233t = 4.45 s

47 N

Image 233, t = 4.45 s


Test 102024image 238t = 4.94 s40 N

Test 102024image 238t = 4.94 s40 N

Image 238, t = 4.94 s

Test 102024image 243t = 5.44 s

47 NTest 102024image 243t = 5.44 s

47 N

Image 243, t = 5.44 s

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Experimental investigation into the vortex formation in the wake of