A Model Scale Experimental Investigation on Vortex

Proceedings of the ASME 2013 32nd International Conference on Ocean, Offshore and Arctic Engineering OMAE2013 June 9-14, 2013, Nantes, France

OMAE2013-10447 A MODEL SCALE EXPERIMENTAL INVESTIGATION ON VORTEX-SELF INDUCED VIBRATIONS (VSIV) OF CATENARY RISERS Felipe Rateiro

Rodolfo T. Gonçalves

Celso P. Pesce

Numerical Offshore Tank - TPN University of São Paulo São Paulo, SP, Brazil


Offshore Mechanics Laboratory University of São Paulo São Paulo, SP, Brazil

André L. C. Fujarra

Guilherme R. Franzini

Pedro Mendes


Offshore Mechanics Laboratory University of São Paulo São Paulo, SP, Brazil

CENPES Petrobras Rio de Janeiro, RJ, Brazil

ABSTRACT Vortex Self-Induced Vibrations (VSIV) of a reduced scale model of a catenary riser are experimentally investigated. The riser model dynamics was assessed with a submerged optical motion capture system and significant VSIV were revealed as result of oscillatory vertical motion imposed to the top. Such a behavior recovers similar ones reported in the technical literature by other authors and resembles previous fundamental studies, by Sumer and Fredsoe, with rigid cylinders forced to oscillate in a plane and elastically mounted in the transversal direction. The present experiments are preliminary and pertain to a much more comprehensive experimental set, within a research project aimed at studying the nonlinear dynamic behavior of risers, through experimentally validated analytical and numerical, nonlinear reduced-order models. KEYWORDS: Vortex self-induced vibrations (VSIV), catenary risers, model tests, imposed motions, oscillatory flow, image tracking. INTRODUCTION Dynamic of risers remains a relevant and current topic in offshore engineering, particularly in the oil production scenario, in which the feasibility of floating systems and their subsystems, in water depths down to 3000 meters, has been

extensively addressed. Several topics still deserve special attention; [1] . The present experiments are part of a comprehensive research project aimed at studying the nonlinear dynamic behavior of risers, through experimentally validated analytical and numerical nonlinear reduced-order models. Particularly, the research project intends to investigate some relevant nonlinear dynamic phenomena, at the touch-down zone, were impacting and dynamic compression may play an important role, as well as their nonlinear interactions with riser global dynamics, including regular VIV and, as in this particular case, vortex self-induced vibrations (VSIV). VSIV in catenary risers is indeed a very intriguing phenomenon, well reported in experimental studies by a number of authors; see, e.g., Le Cunff et al [2] , Fernandes et al, [3] and [4] . Full scale evidences of VSIV were reported by Fernandes et al, [5] , monitored in the Petrobras-P18-SCR. Essentially, VSIV1 is a non-linear dynamic vibration response of a catenary riser to forced motions imposed to its top end. It is a fluid-structure interaction phenomenon, in which the elastic structure – the catenary riser – is put in strongly correlated vibrations, coupling motions in two perpendicular directions, essentially in a plane that is normal to the axis of the line. The fluid-structure interaction takes place as a result of periodic vortex shedding caused by the forced oscillatory motion. In this case, as a periodic vertical motion is imposed to the top of the 1 Le Cunff et al [2] named such a phenomenon HILM – heave induced lateral motion.

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Copyright © 2013 by ASME

catenary, structural vibrations are prone to occur predominantly in the vertical plane – in the tangential and normal directions all along the line. Alternate vortices are then shed, essentially in the plane normal to the line – the plane containing the normal and binormal directions - causing oscillatory pressure forces that mobilize the riser in that binormal direction. If the frequency of the forced vertical motion is close to one of the natural frequencies associated to a structural eigenmode in the plane of the catenary, resonance is expected in that mode. For a particular eigenmode, the antinodal regions are those of larger velocity amplitudes, at the corresponding eigenfrequency. In other words, a reduced velocity may be defined locally, in the normal direction, which is modulated in time and in space, along the line. Accordingly, a local Keukegan-Carpenter (KC) number may be also defined, linearly proportional to the modulated reduced velocity. Moreover, if such a frequency is low enough and the amplitude of motion is large enough, well defined modulated and alternating vortex ‘streets’ may take place all along the line, causing significant vortex induced vibrations in the binormal direction - which couple with the vibration in the normal direction. A lock-in-like phenomenon occurs, and spanwise correlations make antinodal regions the dominant ones, establishing dominant shedding frequencies. The number of vortices that are shed by fundamental cycle is then linearly proportional to the locally dominant shedding frequency and defines the number of loops that characterize the resulting trajectories of a given section of the riser. In other words, the response behavior is strongly dependent on the frequency and amplitude of the imposed motion at the top end of the line. As pointed out in [2] , [3] and [4] , the comprehension of such a complex dynamic behavior may be brought to light by recognizing a remarkable resemblance with the fundamental study by Sumer and Fredsoe, [6] , after [7] , [8] [9] . In that study, a rigid cylinder is forced to oscillate in a plane and elastically restrained to move in the perpendicular direction. A parametric study regarding KC and reduced velocity numbers shows an overall picture on how the resulting amplitude and frequency of oscillation in the perpendicular direction are governed. The present paper aims at discussing such a resemblance a little further. Small scale catenary riser model tests were carried out at the Numerical Offshore Tank wave basin at the University of São Paulo (TPN-USP). The small scale model was designed by preserving dynamic similarity with a full-scale riser. Such similarity considers axial stiffness, bending behavior, inertial parameters and other characteristics that govern the global dynamics; see Rateiro et al. [10] . Forced motions were imposed at the top end of the riser model to simulate those that are driven by FPU (floating production unit) responding to the action of surface waves. A set of regular (monochromatic) forced motion experiments, varying frequency and amplitude, was carried out as well as a set of forced irregular motions experiments, representing the Brazilian offshore environmental conditions.

EXPERIMENTAL SETUP Riser model and some similarity with full scale It is desirable that the experimental planning be made up by imposing dynamic and geometric similarity with full scale risers. The description of the methodology can be found in [10] . This practice intends to further allow checking theoretical models towards representative simulations of the dynamic behavior of risers in full scale. The applied methodology preserves, to some extent, similarity between the reduced (1:) scale model and a real riser. As usual, Froude scaling was adopted, to preserve similarity regarding the motions imposed by the floating unity. As a matter of fact a whole nondimensional group may be shown to govern the dynamic similarity of the riser. However, similarity may be shown to be partially preserved by a reduced number of dominant parameters. Similarities regarding geometry and immersed weight guarantee geometric stiffness similarity, which is dominant in global dynamics, [1] , [11] [12] . Besides those, the following ones are also considered: axial rigidity, bending stiffness, added inertia and mass parameter. Bending stiffness is of local influence and gauged by the flexural length parameter λf; [13] [14] . Added inertia is fundamental to guarantee eigenvalues similarity; [12] . The mass parameter, , is a fundamental parameter regarding VIV. Soil stiffness rigidity, [11] [13] , was not taken into account, as the riser model was laid on the ‘rigid’ ocean basin bottom. On the other hand, as well known, viscous forces similarity is governed by the Reynolds number. However, , if Froude similarity is followed. Usual ‘correcting’ methods, as roughening surfaces to induce turbulence, were discarded as would impair fixing the reflexive targets that are used in the image tracking technique. Using the same scale for diameter is however not practical, as, in this case the model diameter would be reduced to circa 2mm. Adopting a distorted scale in diameter is usual in these circumstances, what helps increasing model Reynolds number. In fact, if D is such a distorted scale, then (Re)R = (D1/2(Re)M. This, however, might impair similarity regarding KC number, a crucial parameter in VSIV. Anyhow, the experimental results at model scale may be used for comparing and validating numerical models. The riser model was then built by using a 22.2mm external diameter silicon pipe, (D=9.87), filled with stainless steel microspheres to set both the immersed weight and added inertia similarities; see [10] . The mass parameter resulted in Figure 1 shows typical eigenmodes, for the real riser taken as the basis and for its reduced scale model. Table 1 shows the data of the base real riser, as well as the designed and the as-built model data. The length scale is 1:100 and the diameter scale 1: 9.9. All parameters were measured with high precision equipment.

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Table 1: Data Summary Data Internal diameter (mm) External diameter (mm) Weight in water (N/m) Axial rigidity, EA (kN) Bending stiffness, EI (Nm²) Flexural length, λf (mm) Added mass, a=ma/m

Scaled (1:100) 1.826 2.191 0.726 2.362 1.20E-03 71.0 0.522

Designed model 15.800 22.200 7.308 1.910 8.86E-02 61.0 0.520

Table 2: Natural frequencies; numerical; experimental; n.a. refers to not assessed.

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As built Mode

15.800 22.200 7.308 1.0 - 1.6 5.60E-02 49.0 0.520

1 2 3 4 5 6 7 8 9 10

[Hz] 0.336 0.560 0.666 0.883 1.001 1.215 1.340 1.348 1.684 1.686

[Hz] n.a. 0.58 0.67 0.93 n.a. 1.17 1.33 n.a. n.a. n.a.

Vibration Mode Out of plane In plane Out of plane In plane Out of plane In plane In plane Out of plane In plane Out of plane

Figure 1: Example of natural mode of vibration (left SCR 8 ", right: reduced scale model) Model test setup A sketch of the general configuration of the test and the respective coordinate axis are shown in Figure 2.

Figure 3: Driving mechanism and load cell

Model test matrix

a. b. Figure 2: Model test configuration and coordinate system Figure 3 shows a picture of the driving mechanism, used to impose motion to the top of the riser model, with the load cell, used to gauge the resulting tension. Table 2 shows a comparison between natural frequencies in water: the numerically determined ones - used as imposed frequencies - and corresponding experimentally assessed natural frequencies. These last ones were obtained from FFT analyses of the measured trajectories in decay tests, observing the dominant motions in or out of the catenary plane. The comparison is fair, even though not all frequencies could be experimentally assessed.

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d.

Five experimental sets were carried out, grouped as: Sets 1 and 2: (2x18 cases) regular motions with upwards initial speed condition; Set 3: (1x10 cases) regular motions with downwards initial speed condition; Set 4: (2x3 cases) irregular motions, simulating the dynamics of a floating unit, subject to a typical Brazilian sea condition modeled through JONSWAP spectra; Set 5: (6 cases) decaying tests excited by impulsive motions at top, to obtain the natural frequencies of vibrations.

The discussion hereinafter will be restricted to regular imposed motions only (sets 1, 2 and 3). Characteristics of the tests sets 1, 2 and 3 are shown in Table 3, where: and are the frequency and the amplitude of the motion imposed by the driving mechanism; is the model diameter.

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Table 3: Model test matrix: regular (sinusoidal) motions Battery 1/2/3 1/2/3 1/2/3 1/2/3 1/2/3 1/2/3 1/2/3 1/2/3 1/2/3 1/2/3 1/2 1/2 1/2 1/2 1/2 1/2 1/2 1/2

Test ID 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 21 22 23

[Hz] 0.336 0.560 0.666 0.883 1.001 1.215 1.340 1.348 1.684 1.686 0.336 0.560 0.666 0.883 1.001 0.336 0.560 0.666

Vibration mode plane Out In Out In Out In In Out In Out Out In Out In Out Out In Out

[mm] 20 20 20 20 20 20 20 20 20 20 50 50 50 50 50 100 100 100

2.9 4.8 5.7 7.5 8.5 10.4 11.4 11.5 14.4 14.4 7.2 11.9 14.2 18.8 21.3 14.3 23.9 28.4

5.7 5.7 5.7 5.7 5.7 5.7 5.7 5.7 5.7 5.7 14.3 14.3 14.3 14.3 14.3 28.6 28.6 28.6

immersed part of the riser model opens new perspectives for experimental observations, including some aspects of nonlinear dynamic behavior not yet explored in the context of fluid structure interactions. Not only VSIV, as well as deeper investigations on TDZ (touchdown zone) riser dynamics or even nonlinear interactions of regular VIV and VSIV may benefit with from the use of underwater image tracking systems. These other phenomena will be covered in further papers. Figure 4 presents the manufactured riser model, together with the motion acquisition system (yellow arrows) that was used in the test. In this case, two image tracking systems were concomitantly used: (i) immersed, tracking the riser model at TDZ and (ii) emerged, tracking the reflexive targets installed above the waterline.

The frequencies were imposed at the natural frequencies of the model, determined numerically. A ‘reduced velocity’ parameter was then calculated as . In words, by normalizing the maximum imposed velocity at the top, , by , being , the third natural frequency of the riser model, that corresponds to the second out-of-plane mode. Notice that the nondimensional amplitude parameter, , just gives an indication on the order of magnitude of the KC number; similarly for the ‘reduced velocity’ parameter. In fact and already pointed out, as the steady-state response amplitude to the motion imposed at the top varies along the line, being modulated in space, a local KeukeganCarpenter (KC) number should be defined, which would be linearly proportional to a corresponding local reduced velocity. This point is discussed in the experimental results section. In this sense, at each antinodal region of a particular excited (in-plane) eigenmode, an average (in space) KC number could be thought of to represent the oscillatory flow conditions. This was not done so far and will be pursued in further analyses.

Figure 4: As built model and motion acquisition system Discussion on expected dynamic behavior In most of the regular motion tests, displacements out of the plane of the catenary were observed, as seen in the example given in Figure 5.

Instrumentation In this kind of tests, the use of strain gages and accelerometers is quite common, see e.g., [15] [16] [17] , which, after post processing, provide indirect measures of the actual geometric configuration of the line at each instant of time. Obviously, a direct measurement of Cartesian coordinates would be largely preferable. With the recent technological improvement of data acquisition systems, new measuring techniques are available. In the present experiments, a submerged image tracking acquisition system – Qualisys - was used to accurately measure the trajectories of reflexive targets installed along the line. Such kind of system has been in regular usage for floating systems model tests. In the riser scenario, former use of similar equipment has been reported by Le Cunff et al [2] . Tracking the geometrical configuration of the

Figure 5: Example of tracked trajectories . ( ).

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This typical VSIV behavior could be expected from former studies, [2] , [3] [4] . However, the numerical modal analysis indeed revealed out-of-catenary-plane vibration modes, confirmed experimentally for mode 3; see Table 2.

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Z [mm]

300

32 31 100 28 25 26 27

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Naturally, questions on the possible dominance of some nonlinear structural dynamic phenomena (parametric internal resonances) could be raised. Additional tests with the same riser model were then carried out in air (Figure 6). In those tests, the imposed frequencies were chosen to match the experimentally assessed natural frequencies. As a matter of fact, assessing the natural frequencies in air was a much easier task and confirmed the numerical predictions. As result, the tests in air showed, in general, transversal motions of very low amplitudes2. This fact strengthens vortex shedding as the cause for the immersed dynamics.

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Figure 7: Riser model: monitored targets (TDZ) EXPERIMENTAL RESULTS This section presents some experimental results. What is indeed surprising is that, despite using as a representative ‘reduced velocity’ parameter instead of an effective value, measured locally or even as a local average, the results showed fair qualitative agreement with former basic studies. As a matter of fact, Table 4 shows the values of the local reduced velocity and the KC number at target number 29, experimentally determined from the measured trajectories. Table 4: and at target 29, experimentally obtained, compared with and , respectively Test ID 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 21 22 23

Figure 6: Additional model test setup in air

Notice that the riser model kinematics was primarily tracked along the TDZ, so very close to the ocean basin bottom. In that portion, the riser model configuration is almost horizontal (Figure 7). So, since driven by the vertical motion imposed at the top, points along that part of the model move nearly vertical. This situation could be fundamentally modeled as a cylinder in an oscillatory flow, vibrating in the direction perpendicular to the imposed motion, due to vortex shedding.

2 Actually, in the in-air experiments, in some peculiar conditions, under very large imposed motions, parametric resonances appeared, coupling large inplane and out-of plane motions. This will be explored in another paper.

2.9 4.8 5.7 7.5 8.5 10.4 11.4 11.5 14.4 14.4 7.2 11.9 14.2 18.8 21.3 14.3 23.9 28.4

at target 29 1.2 4.2 6.6 11.7 13.9 16.2 17.8 18.1 19.4 19.5 3.9 10.4 15.7 21.7 25.1 8.7 19.8 25.0

5.7 5.7 5.7 5.7 5.7 5.6 5.6 5.6 5.6 5.66 14.1 14.2 14.1 14.2 14.1 27.3 27.9 27.9

at target 29 2.4 5.0 6.6 8.9 9.3 8.9 8.9 8.9 7.7 7.7 7.6 12.4 15.7 16.5 16.8 17.2 23.6 24.9

In fact, there is a spreading in the local KC number, as shown in Figure 8. However, data can be organized according to the local KC number, as shown in Figure 9. Notice that there are two sets of points corresponding to , related to KC