simulation of sea current vortex shedding induced...

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BBAA VI International Colloquium on: Bluff Bodies Aerodynamics & Applications

Milano, Italy, July, 20-24 2008

SIMULATION OF SEA CURRENT VORTEX SHEDDING INDUCED VIBRATIONS IN THE NEMO TOWER

Fabio Fossati∗, Gabriele Fichera∗

∗ Dipartimento di Ingegneria Industriale e Meccanica Facoltà di Ingegneria, Università degli Studi di Catania, Viale A. Doria 6, 95125 Catania, Italy

e-mail: [email protected]

Keywords: Vortex Induced Vibrations (VIV), equivalent oscillator model, multibody systems.

Abstract. This paper presents the basic principles and the main features of the analysis per-formed to simulate the dynamic behavior of the underwater neutrino telescope NEMO with particular reference to marine current vortex induced vibrations. The NEMO telescope is a complex underwater structure made of several towers ballasted at the seabed level (> 3000 m depth). Each tower has a total length of 780 m and is made of 16 reticular substructures, called floors, connected by means of ropes whose tension is given by a buoy attached at the top of the tower. The use of an appropriate mathematical model to predict the effects of VIV on a single NEMO tower is fundamental both for the global performance of the telescope in tracking neutrinos both for the strength of ropes and floors to oscillating loads. By means of multibody system dynamics a complex model of a single tower was created. The model takes into account the structural behavior of the floors and the connecting ropes. The drag forces due to marine current have been introduced by using ESDU standards. The forces generated by vortex shedding have been modeled by means of equivalent non-linear oscillators applied both at ropes and floors. Several simulations have been performed with different values of current velocity and orientation.

F. Fossati, G. Fichera

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1 INTRODUCTION The NEutrino Mediterranean Observatory (NEMO) project is concerned with an underwa-

ter Cherenkov telescope looking for high energy neutrinos. Scientists are interested in neutri-nos because they can reveal the secrets of an Active Galactic Nucleus engine. Active galactic nuclei are extremely powerful sources of radiation and particles which travel the entire uni-verse. Since protons are deflected or adsorbed during their journey in space and electromag-netic radiation is strongly absorbed, only neutrinos may come from the deepest space to the earth. Sea depth is the one of the most suitable environment to place a neutrinos’ telescope because of very low biological and electrical activities. The aim of the NEMO project is to design the so called KM3Net, a neutrino telescope equipped with 4096 light detectors distrib-uted in a volume of at least one cubic kilometer at the bottom of the Mediterranean Sea. Sev-eral sites have been investigated in the Mediterranean Sea. The site of Capo Passero (35° 50’ N, 16° 10’ E) in the Jonian sea revealed very appealing due to the presence of a flat bathymet-ric profile (> 10 km2) at 3300 m depth and 80 km from the Sicily coast. Several measurements performed in this site highlighted very low biological activity, sedimentation rate and fouling rate. Numerous current meters were also placed in the site (August 1998 – running) in order to provide a statistical database. The expected maximum value of mean current velocity is about 10 cm/s with an average current intensity of 3.6 cm/s. The Nemo telescope consists of 64 un-derwater vertical floating structures – named towers – ballasted at the seabed level at more than 3000 m depth. Each tower is a slender structure (750 m high) composed by modular sub-structures connected by means of ropes having different tensions and lengths. Each tower is equipped with 64 optical modules for tracking neutrinos. The distance among towers is 200 m and the telescope may achieve more than 2 km2 trigger area.

When designing a slender marine structure for a deepwater application, marine current ef-fects on the structural behavior are a major concern with respect to both static and dynamic conditions. With particular reference to the design of the NEMO tower, characterized by a large flexibility, Vortex Induced Vibrations (VIV) must be carefully evaluated because of the possible occurrence of marine currents and the large uncertainties in the evaluation of envi-ronmental conditions. The combination of these factors can lead to vibrations that may sig-nificantly reduce the structure operative performance. As well known, VIV come from “lock-in” phenomena that cause the vortex shedding frequency (depending on the flow velocity and the geometrical shape of the structure) tuning on the natural frequencies of the structure itself. The skill to predict the occurrence of VIV under a large spectrum of operating conditions is hence a major factor for the success of the design process.

The aim of this paper is to present the research activities carried out by the authors in order to assess the dynamic behavior of the underwater telescope Nemo with particular reference to marine current vortex induced vibrations. In order to predict the effects of VIV on NEMO towers, a detailed multibody model of a single tower was created. The model takes into ac-count the flexibility of floors and connecting ropes. The drag forces due to marine current have been introduced by using ESDU standards. The forces generated by vortex shedding have been modeled by means of equivalent non-linear oscillators applied both at ropes and floors. Several simulations have been performed with different values of current velocity and orientation. Preliminary results are presented and future activities are outlined.

2 THE NEMO TOWER The NEMO tower (fig.1) is a slender structure composed by 16 reticular substructures

named floors. Two consecutive floors are disposed with main longitudinal x-axes rotated by 90 deg with respect to the vertical z-axis and are connected by means of 4 crossed ropes as


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shown in figure 1. The tower has a total length of 780m while the distance between the first and the last floor is 600m. Each floor has a main length of 15m. The distance between the seabed and the first floor is 150 m while the distance between two subsequent floors is 40m. A buoy is placed at the top of the tower to provide ropes tensioning.

Figure 1 – Sketch of the NEMO tower

2.1 The floors A floor is a reticular structure made of 5083 aluminum alloy tubes of different sizes. A 3D

CAD model of the floor is illustrated in figure 2. The main structural elements are 4 longitu-dinal tubes, connected with smaller tubes and X-braces, with two plates at the ends. The rope winding systems and the electric boxes (not represented in the figure) are attached to the plates. Two frames made of flat-faced members extend outside the plates. Within this frames the four optical modules for neutrinos’ tracking are located. Each module consists of a glass sphere for deep underwater application which contain the optical device. The four spheres give about 900 N net buoyant force applied to the floor. The CAD model was used to estimate inertia parameters and global buoyant force applied to the floor. The floor tends to sink hav-ing a negative net buoyant force of about 150 N.

Figure 2: 3D CAD model of the NEMO floor.

Net buoyant force = -150 N

4 main tubes end plate with ropes attachments

Mass = 320 kg Ixx≈37 kgm2 Iyy≈Izz≈18450 kgm2 with respect to the cg

∼780 m

∼15 m

∼40 m

single floor

Nemo Tower

16 floors 1 buoy at

top

4 ropes

r1

r3

r2

r4


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3 ANALYSIS PERFORMED ON A SINGLE NEMO FLOOR

3.1 Finite Element modeling and analysis The first step of the work was the creation of a Finite Element model (using MSC/Nastran)

of a single floor starting from the 3D CAD model shown above. The FE model was first used to calculate the normal modes of the structure in order to evaluate the possible effects due to lock in phenomena of VIV. Then the model was used to introduce the floor as a flexible body into the multibody model of the tower that will be discussed later.

According to the aim of this modeling phase, that do not need specific information about stresses and strains, the FE model is made of beam elements (CBEAM) connected through rigid elements (RBE2). Concentrated masses (CONM2) were added to include the masses due to the welding process of the tubes, the reinforcement plates and the plates supporting the rope wiring systems. The total mass and inertia moments of the FE model are illustrated in figure 2. A normal mode analysis in free-free condition was then performed and the main re-sults are summarized in table 1. After the normal modes were calculated, the model was con-densed using a component mode synthesis approach based on the Craig-Bampton method in order to include the floors as flexible bodies inside the multibody model. For the condensation procedure only two interface nodes were chosen. These are the centers of the plates where the rope wiring systems are attached.

Mode n. Mode shape Freq. [Hz] Main plane

1

4.1 x-y

2

6.5 x-y

3

10.1 x-z

4

11.5 y-z

5

19.3 x-y

6

26.7 x-y

7

27.4 x-z

Table 1: Free-free normal modes of a floor of the NEMO tower.


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3.2 Validation of the FE model using Experimental Modal Analysis In order to validate the FE model and estimate the amount of modal damping, an Experi-

mental Modal Analysis (EMA) was performed. As expected, a good accordance between FE and real model was obtained. The most interesting aspect was the estimation of very low val-ues of modal damping. The EMA was conducted using a roving technique with a piezoelectric hammer. Four piezoelectric accelerometers were mounted on the structure to calculate FRF. The floor was suspended by using flexible cables in order to reproduce a free-free condition (figures 3 and 4). The time history of acceleration outputs and force input were processed us-ing LMS Cada-X software to calculate FRF, summed FRF (fig. 5) and to estimate eigen-frequencies, eigen-modes and damping (table 2).

Figure 3: the single NEMO floor suspended during EMA. Figure 4: accelerometer mounted on one of the main tubes during EMA.

Mode n. FE

Freq.[Hz]

EMA Freq. [Hz]

% error EMA % damp-

ing 1 4.1 3.96 -3.5 0.12 2 6.5 5.77 -8.9 0.82 3 10.1 9.56 -5.7 0.20 4 11.5 11.06 -3.9 0.56 5 19.3 17.97 -7.4 0.75 6 26.7 24.5 -8.9 0.27 7 27.4 26.29 -4.2 0.42

Figure 5: summed FRF. Table 2: results from EMA.


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4 THE MULTIBODY MODEL OF THE NEMO TOWER The VIV effects on the NEMO tower were simulated by creating a specific multibody

model (using MSC/ADAMS). The model takes into account the flexibility of floors and con-necting ropes, the drag forces due to marine current and the forces generated by vortex shed-ding, modeled by means of equivalent non-linear oscillators applied both at ropes and floors. A detailed description of the model is presented in the following paragraphs.

4.1 General description of the model The model is made of 16 flexible bodies which represent the floors. The flexible bodies

were modeled using a component mode synthesis approach based on Craig-Bampton method according to ADAMS/Flex module. Two interface nodes are located at the centers of the two plates were the rope wiring systems are mounted. Each floor has two rigid bodies attached to the interface nodes by means of rigid joints. The rigid bodies represent the rope wiring sys-tems and they bring the markers the rope forces are applied to (fig.6).

Figure 6: particular of the multibody model.

The rope are modeled by using point mass parts. A point mass is a part with no inertia rota-tional properties and only 3 d.o.f. in the space. The point masses are connected each other and to the floors through single component action-reaction translational forces. The direction of a force is along the line segment connecting the i- and the j- markers belonging to two consecu-tive point masses along the rope. Thus, if the force is positive, the markers experience a repel-ling force along this line, and if the force is negative, the markers experience an attracting force. The magnitude of the translational force applied to the parts containing the two markers is linearly dependent upon the relative displacement and velocity of the two markers. The fol-lowing linear constitutive equation describes the force applied at the i- marker:

( ) ii

i

iiiii

i

iiropei S

dtdL

LAELL

LAEF −−−−=−

00

0

ζ , (1)

where: • Li is the calculated distance between the markers; • L0i is the initial distance between the markers; • EiAi is the EA product for the i-th rope, • ζi is a coefficient proportional to stiffness used to introduce an equivalent axial vis-

cous damping; • Si is the tension in the i-th rope when the whole tower is in the default static posi-

tion.

Interface node at plate center Rope attachment markers


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The four ropes connecting the first floor to the seabed have a length of 150 m in the static design position. They have been divided into 9 point masses and 10 force elements having L0=15 m. This choice give the possibility to well represent the local mode shapes of the ropes up to the third mode. The rope connecting two consecutive floors have a total length of 40 m. They have been divided into 4 point masses (fig.7) and 5 force elements (L0=8m), having the possibility to represent the first two mode shapes. In order to introduce damping for transver-sal vibration of the ropes specific forces are added to the point masses. In table 3 the main da-ta of the ropes are reported. A rigid part representing the buoy is attached to the last floor of the tower. A 9800 N net buoyant force is applied to the buoy and transferred to the tower through 4 ropes (fig.7). The model of the tower is completely parametric so that it is possible to change quickly all the main geometric features (distance between floors, length of the ropes and location of attachment points of the ropes to the floor and the buoy), the rope tensions, the product EiAi, the mass of ropes per unit length for automatic point mass estimation, the rope diameters and the coefficients for damping calculation.

Material Dynema d [mm] 5 A [m2] 19.63 EA [N] 1654480

m [kg/m] 0.0181 Strength [N] 26950.0 Lseabed [m] 150 n. point mass 10 Li seabed [m] 15

Lfloors [m] 40 n. point mass 5 Li floors [m] 8

ζ [s] 2e-4 Table 3: ropes specs. Figure 7: buoy connected to the last floor of the tower.

4.2 Modeling of current drag forces One of the aim of the multibody model was the calculation of the static equilibrium of the

whole tower subjected to marine current drag forces and buoyancy. In order to overcome the lack of experimental data, ESDU standard 81027 for lattice structures has been used [5]. The main geometrical input parameters for the calculation are reported in the following table.

Enclosed Area, Ae [m2] 7.960 Chord member diameter, Dc [m] 0.073Shadow Area of flat-faced members, Asf [m2] 1.826 Roughness, ε 1.00E-03Solidity ratio flat, Ff=Asf/Ae 0.229 Surface roughness parameter, ε /Dc 1.37E-02Shadow Area of circ. section members, Asc [m2] 1.832 Diameter ratio, Db/Dc 0.62Solidity ratio circular, Fc=Asc/Ae 0.230 Frame spacing ratios , sj /B 0.860Shadow Area Total, As [m2] 3.658 Aspect Ratio, L/B 25.3Solidity Ratio Total, F=As/Ae 0.460

Table 3: ESDU 81027 input parameters

4 point masses of a 40 m rope


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Drag forces calculation was performed both in normal and inclined flow conditions. In normal flow condition the drag force of the floor structure is calculated according to the fol-lowing equation:

( ) 22100 2

1 VAffCF sssXdrag ρ+= , (2)

where: • CX0 is the normal force coefficient equal to 1.36, calculated using the data of table 3; • fs1 = 0.92 is the correction factor for effect of shielding on the first frame of the

double array; • fs2 = 0.23 is the correction factor for effect of shielding on the second frame; • ρ is the water density (1038 kg/m3); • As is the total shadow area reported in table 3; • V is the fluid velocity normal to the structure.

In case of inclined flow only the local yaw angle βi around the vertical axis of the tower was considered (fig.8). In this condition a correction factor fβ multiplies the CX0 coefficient (fig. 9).

Figure 8: inclined flow with a local yaw angle βi. Figure 9: correction factor fβ from ESDU.

The drag forces of the spheres and other cylindrical boxes that bring electronic devices were calculated using usual equations and added to eq. (2). Considering that the maximum marine current velocity registered in the NEMO site is 10 cm/s, the maximum drag force ap-plied to the whole floor resulted equal to about 32 N.

The drag forces were then introduced into the multibody model using the above equation and correction factor. The marine current velocity profile and the global yaw angle between the flow direction and the x-axis of the global reference of frame are input parameters settled by the user. The drag forces are reoriented automatically along the direction imposed by the global yaw angle. The local yaw angle between the current flow and the local transversal y-axis of a floor is automatically calculated according to the actual floor trim.

4.3 Modeling of equivalent oscillators for VIV dynamic analysis The forces generated by vortex shedding in the NEMO tower are reproduced by means of

equivalent oscillators technique. The equivalent oscillator is a non-linear 1 d.o.f. system (fig.10) which transmits to the structure the same forces produced by the vortex shedding phenomena, Fvor. As far as equivalent oscillator parameters values are concerned, a large amount of work has been carried out by the authors in previous researches with particular ref-erence to structures with cylindrical shapes like submarine cables [1], overhead lines [2] or offshore drilling and production marine risers [3].

90° βi


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A distribution of forces generated by equivalent oscillators is applied to specific markers of the multibody model of the structure in order to reproduce the dynamic effects of vortex shedding forces both on ropes and floors (fig. 11).

Figure 10: scheme of a single equivalent oscillators applied to a cylinder.

Figure 11: equivalent oscillators applied to a short rope and a floor of the NEMO tower.

The differential equation that define the motion of the aerodynamic mass of the j-th oscilla-tor introduced in the model is the following:

),,,,(),,,,( ________ jjajjajjaerjjajjajjvorjajaer VyyyyFVyyyyFyM −= . (3)

The forces Fvor_j and Faer_j are expressed by the subsequent equations:

3____

3_______

3____

3_______

),,,,(

)()(

)()(),,,,(

jajNLaerjajLaerjajNLaerjajLaerjjajjajjaer

jajjNLaccjajjLacc

jajjNLaccjajjLaccjjajjajjvor

yRyRyKyKVyyyyF

yyRyyR

yyKyyKVyyyyF

+−−=

−−−+

+−−−=

(4)

where • yj is the displacement of a j-th marker belonging to the structure along the cross-

flow direction with respect to its initial static position; • ya_j is the displacement of the j-th aerodynamic mass along the cross-flow direction; • Vj is the component of the current velocity orthogonal to the j-th cylinder axis.

The linear and non linear terms multiplying displacements and velocities are defined by the following expressions:

Ma

Mc

Kaer Raer

Kacc Racc

Kst Rst

η

xa

FAer

FVor

FVor

FVor V

ya

y

Maer


10

;1

;1

;1

;1

_1_

_1_

_1_

_1_

jjjaerjjLaer

jjaerjjLaer

jjjaccjjLacc

jjaccjjLacc

DrAAR

DkAAK

DrAAR

DkAAK

⋅⋅⋅=

⋅⋅=

⋅⋅⋅=

⋅⋅=

ω

ω

(5)

;1

;1

;1

;1

33_2_

3_2_

33_2_

3_2_

jjjaerjjNLaer

jjaerjjNLaer

jjjaccjjNLacc

jjaccjjNLacc

DrAAR

DkAAK

DrAAR

DkAAK

⋅⋅⋅=

⋅⋅=

⋅⋅⋅=

⋅⋅=

ω

ω

(6)

where • AAj is the product 0.5 ρ Dj Lj Vj

2; • Dj is the diameter of the j-th cylinder or the reference dimension of the j-th struc-

ture; • Lj is the reference length; • ki_j and ri_j are experimentally determined coefficients; • wj is the term depending on the Strouhal frequency and the Strouhal number of the

j-th structure, STj, according to the following equation:

j

jjjSTj D

VSTf ππω 22 _ == .

(7)

The aerodynamic mass present in eq. (3) is given by:

2

2_1_1

_ 2)(5.0

j

jjjaerjaccjaer ST

DLkkM

πρ+

= (8)

Equivalent oscillator parameters ki_j and ri_j of eq. (5) and (6) have been identified in pre-vious researches ([1][2]) by means of water tank tests on cylindrical sectional models: these parameters have been used for oscillator distribution concerning ropes.

As far as the floor structures are concerned, it should be noted that the equivalent oscillator parameters should be tuned considering the Strouhal number associated to the typical section topology involved and in order to reproduce the energy input due to VIV mechanism consid-ering this particular geometrical feature. In order to perform a preliminary analysis and con-sidering that the floor structure shape can be basically considered as a 4 cylinders cluster with the pitch/diameter ratio of about 6, the same parameters have been used also for the oscillators applied to the floor. According to [6], considering the pitch/diameter ratio value, a Strouhal number equal to 0.2 has been assumed.

The differential equations and the forces Fvor_j are implemented into the multibody model by means of specific user written macros each time an oscillator has to be introduced. A pa-rametric procedure was defined to apply the oscillator forces and calculate the rope cross-flow displacements depending on the marine current local direction (fig.12). Reference markers (those highlighted in figure 12) are applied to the ground at the same location of the centre of gravity of the point masses or specific points of the floors. For the ropes, the zj axis of the ref-erence marker is parametrically oriented along the axis of the rope. The yj axis is automati-cally oriented 90 deg with respect to the flow direction xj. For the floors, the y axis of the reference marker is always oriented along the global vertical axis. The yj ropes and floors dis-placements are calculated through specific internal functions of the multibody software with respect to the position achieved after the static equilibrium under the current drag forces was found.


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Figure 12: direction of yj displacements and Fvor_j forces applied to the structure for a given yaw angle β.

5 RESULTS FROM MULTIBODY SIMULATIONS

5.1 Static equilibrium analysis

The complete multibody model of the NEMO tower was initially used to evaluate the static equilibrium position under buoyant and marine current drag forces. Different flow conditions were simulated varying both mean velocity and yaw angle. In tables 4 and 5 the rope tensions corresponding to V=0 (buoyancy only) and to marine current V=0.1 m/s incoming flow with zero yaw angle are summarized. As expected the tensions of the ropes decrease moderately while moving to the seabed level. The tensions of the rope of the same level have small changes when passing from only buoyancy condition to maximum current velocity.

Connection r1-4 S [N] Buoy - f16 2481 f16 - f15 2470 f15 - f14 2431 f14 - f13 2393 f13 - f12 2354 f12 - f11 2316 f11 - f10 2278 f10 - f9 2239 f9 - f8 2200 f8 - f7 2162 f7 - f6 2124 f6 - f5 2085 f5 - f4 2047 f4 - f3 2008 f3 - f2 1970 f2 - f1 1931 f1 - f0 1854

Connection r1-3 S[N] r2-4 [N] Buoy - f16 2482 2482 f16 - f15 2446 2494 f15 - f14 2407 2455 f14 - f13 2368 2418 f13 - f12 2330 2379 f12 - f11 2291 2341 f11 - f10 2252 2302 f10 - f9 2213 2265 f9 - f8 2175 2227 f8 - f7 2136 2189 f7 - f6 2098 2151 f6 - f5 2059 2113 f5 - f4 2020 2074 f4 - f3 1981 2037 f3 - f2 1943 1999 f2 - f1 1898 1970 f1 - f0 1820 1890

∆x max at top = 13.5 m

Table 4: rope tensions at V=0 Table 5: rope tensions and buoy displacement at V=0.1 m/s

Fvoryj

Vj

Vj

yj

Fvor

Reference marker for rope cross-flow dis-placement zj

xj

V=0.1 m/s β=0


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5.2 Natural frequencies and normal modes analysis

The normal modes analysis is fundamental to understand if lock-in phenomena between vortex shedding frequencies and structural natural frequencies can occur. The NEMO tower is a complex structure with different kinds of mode shapes (i.e global, local and coupled).

The mode shapes and the natural frequencies of the structure were calculated after static equilibrium analysis under current drag forces. The calculation was performed in different current flow conditions, varying both mean velocity and yaw angle. Since the ropes’ tensions remain quite constant at different current velocities (as shown in table 4 and 5) the global modes of the whole tower and the local modes of the ropes do not vary significantly. In the following figures the most interesting modes referred to a condition of 0.036 m/s velocity at 45deg yaw angle are shown.

n.1 lateral x-z f = 0.0081 Hz

n.3 torsion x-y f = 0.0183 Hz



n.23 vertical along z f = 0.228 Hz

Figure 13: a choice of global modes of the NEMO tower.

n.50 1st mode of

seabed ropes f = 1.03 Hz

n.74 2nd mode of seabed ropes f = 2.16 Hz

n.98 3rd mode of seabed ropes f = 3.18 Hz

n.107 1st mode of ropes cou-pled with 1st mode of floor

f = 4.01 Hz

Figure 14: a choice of local and coupled modes of ropes and floors of the NEMO tower.


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In the following table the Strouhal frequencies of ropes and floors are calculated for differ-ent current velocities. For the floor it was assumed a diameter of 0.073 m equal to the diame-ter of the main structural elements forming the squared array. The Strouhal number is 0.2.

fST = ST V / D [Hz] ropes FloorsV = 0.036 1.44 0.098 V = 0.1 4.00 0.273

Table 6: Strouhal frequencies for ropes and floors.

From the comparison of Strouhal frequencies of table 6 with natural frequencies, it can be argued that vortex shedding phenomena could lock-in some global vertical mode of the struc-ture in the range 0.090-0.23 Hz and local or coupled modes from 1 to 5 Hz.

5.3 Dynamic analysis for VIV In this section some results of VIV analysis are presented. Different kinds of current flow

condition were simulated. A choice of results is shown in the following figures. The effects of VIV on floors are first discussed. Figures 15 and 16 show the vertical displacement of the centre of gravity of the 9th and 15th floor at two different current velocities. The displacements are normalized with respect to the diameter of the main tubes (73 mm). The lock-in phenom-ena occur only when velocity is near the value of 0.1 m/s and it is normal to pare (β =0) or spare floors (β=90°). As expected, the lock-in frequency (fig.16) is near 0.228 Hz related to the mode n.23 of figure13. The ratio z/D increases with the distance from the seabed.

Figure 15: normalized vertical displacement of floors 9 and 15 at 0.036 and 0.1 m/s velocities (β=90°).

Figure 16: FFT of normalized vertical displacement of floor n.15 at 0.1 m/s velocities (β=90°).

Figures 17 and 18 show the effects of VIV on the ropes. The normalized displacements (D=5mm) along cross-flow direction are plotted versus time. As shown in fig. 17, at low flow velocity only the 1st mode (≈ 1.1 Hz) of seabed ropes is locked-in. The short ropes of other floors moves together with floors with low frequency oscillations due to global modes.

When velocity increases the 2nd (≈ 2.1 Hz) and 3rd mode (≈ 3.3 Hz) of the seabed ropes are progressively locked-in. At 0.1 m/s flow velocity the worst condition is reached. Figure 18 shows that the 3rd mode of seabed ropes and the 1st mode of short ropes coupled with floor flexibility are locked-in. For both floor and ropes the maximum normalized displacement at the end of the transient resulted in the range 0.4-0.5.

0.24 Hz


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Figure 17: VIV on different ropes at V=0.036 m/s (β=90°).

Figure 18: VIV on different ropes at V=0.1 m/s (β=0°).

The forces that ropes transmit to the floor structure while vibrating do not produce such ef-

fects of floor vibration. The contribute of floor flexibility is negligible, as shown in figure 18 where the displacement of the center of mass of the 1st floor along the direction of ropes VIV is plotted. It is possible to notice that higher frequency components due to rope and floor cou-pled modes are summed to low frequency oscillation due to tower global modes. The calcu-lated displacements of the floor are not significant (less than 1 mm).

V (β=0°)

Rope 1 floor 1 central node

Rope 1 seabed lev 3rd node

1.13 Hz

3.3 Hz 3rd local mode of seabed rope 4 Hz

1st local mode of 1st floor ropes

V (β=90°)

Rope 1 floor 1 central node

Rope 1 seabed lev central node


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Figure 19: displacement of the 1st floor along the direction of ropes VIV, V=0.1 m/s, β=0°.

6 CONCLUSIONS The effects of VIV on underwater NEMO telescope tower due to marine current have been

investigated by means of a numerical model developed by the authors. From the preliminary results considering different marine current flow velocities and incoming directions it is pos-sible to notice that:

• even if the current velocity is low in the installation site, the VIV phenomena can affect the operating conditions of the structure;

• the ropes are subjected to VIV at almost all expected current velocity values and the problem of rope fatigue strength must be carefully analyzed;

• the VIV can affect the floors of the whole tower only at maximum value of flow velocity;

• the effect of floor flexibility and their local mode shapes are negligible.

In order to improve mathematical model reliability, some wind tunnel tests are scheduled in the next future. A carbon fiber manufactured sectional scaled model of the Nemo tower floor will be used to evaluate the Strouhal frequency and the vortex shedding behavior of this unconventional geometry and to tune the equivalent oscillator parameters. Moreover, experi-mental tests aiming to identify dynema ropes axial and flexural damping characteristics are scheduled in the next future.

REFERENCES [1] M. Falco, F. Fossati, F. Resta: On the vortex induced vibration on submarine cables:

design optimisation of wrapped cables for controlling vibrations, Third International Symposium on Cable Dynamics, Trondheim [1999].

[2] G. Diana, F. Fossati et al.: Vortex Shedding and Wake Induced Vibrations in Single and Bundle Cables, Journal of Wind Engineering and Industrial Aerodynamics n.74&76 [1998].

[3] F. Fossati, F. Resta: A numerical model to reproduce the dynamic behaviour of steel catenary riser, Fifth International Symposium on Cable Dynamics, S Margherita [2003].

3.3 Hz 3rd local mode of seabed rope

4 Hz 1st local mode of 1st floor ropes + floor flexibility

low frequency global modes


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[4] F. Fossati, G. Fichera, “Sea current vortex shedding induced vibrations of nemo tower”. Nuclear instruments & methods in physics research, Section A, accelerators, spectrome-ters, detectors and associated equipment. Vol. 567, pp. 502-504 [2006].

[5] ESDU Standard 81027

[6] M.M. Zdravkovich, Flow Around circular cylinders, Oxford University Press, 1997

simulation of sea current vortex shedding induced...

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