VORTEX-INDUCED MOTION OF A MONOCOLUMN PLATFORM: NEW ANALYSIS AND COMPARATIVE STUDY. Escola Politécnica University of São Paulo São Paulo, SP, Brazil

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1 Proceedings of OMAE9 8 th International Conference on Ocean, Offshore and Arctic Engineering 3 May 5 June 9, Honolulu, Hawaii OMAE VORTEX-INDCED MOTION OF A MONOCOLMN PLATFORM: NEW ANALYSIS AND COMPARATIVE STDY Rodolfo T. Gonçalves (rodolfo_tg@tpn.usp.br) Guilherme F. Rosetti (guilherme.feitosa@tpn.usp.br) Marcos Cueva (mcueva@oceanicabr.com) André L. C. Fujarra (afujarra@usp.br) Kazuo Nishimoto (knishimo@usp.br) Elizabeth F. N. Siqueira 3 (frauches@petrobras.com.br) Department of Naval Architecture and Ocean Engineering Escola Politécnica niversity of São Paulo São Paulo, SP, Brazil Ocêanica Offshore São Paulo, SP, Brazil 3 Research and Development Center (CENPES) PETROBRAS Rio de Janeiro, RJ, Brazil ABSTRACT This paper presents a new analysis and a comparison of results obtained from Vortex-Induced Motion (VIM) model tests of the MonoGoM platform, a floating unit designed for the Gulf of Mexico. The choice of scale between the model and the platform in which the tests took place was a very important issue that took into account the basin dimensions and mooring design. The tests were performed in three different basins: the IPT Towing Tank in Brazil (September 5), the NMRI Model Ship Experimental Towing Tank in Japan (March 7) and the NMRI Experimental Tank in Japan (June 8. The objective of this work is to discuss the most relevant issues regarding the concept, execution and procedures to analyze comparatively the results obtained from model tests. The approach employed in the tests was designed to build a reliable data set for comparison with theoretical and numerical models for VIM prediction, especially that of Monocolumn platforms.. INTRODCTION The petroleum industry has recently been challenging its own records in ultra deep water offshore exploration. This scenario favors technological innovations in the search for new concepts for offshore units, such as the monocolumn platform. This type of unit has already been the target of technical viability studies at several locations, such as in the Gulf of Mexico, where environmental conditions are considered severe. This paper presents experimental studies regarding the VIM phenomenon of monocolumn offshore platforms, in particular, the MonoGoM - further information can be seen in Cueva, M. et al. (6). In general terms, the VIM phenomenon represents another type of fluid-structure interaction, which greatly resembles the VIV phenomenon. What distinguishes both phenomena is the large amplitude associated with long periods presented by VIM. These periods of oscillation are highly influenced by a group of restoration characteristic parameters as well as the system geometry. The Copyright 9 by ASME

2 responsible exciting force itself - marine current - also plays a role in this characteristic behavior. It is a self excited phenomenon, which can be observed on bluff bodies that are immersed and free to oscillate as well as in specific fluid flow conditions, exhibiting amplitudes values of the same magnitude order as that of the transverse section of the system. Thus, on SPAR platforms, or even on monocolumns, the VIM phenomenon ends up representing great drift on the surface, which reflects on the dimensioning of the mooring lines and the production ducts, regarding both extreme tensions and useful life. The study of the VIM phenomenon has been being carried out since the beginning of the decade, mainly on SPAR platforms, as seen in Huang, K. et al. (3), Finn, L.D. et al. (3) and van Dijk, R. et al. (3). Nevertheless, similar VIM studies on monocolumn platforms are more recent. The development of research in this field is being carried out by a group at the niversity of Sao Paulo Brazil, whose works are seen in Cueva, M. et al. (6) and Fujarra, A.L.C. et al. (7). The former work, which is an experimental study of the MonoGoM, is taken as basis for the present research. In general terms, regarding the VIM phenomenon, the relevant difference between SPARS and monocolumns is that the later present a smaller draft/breadth ratio, leading to a greater tridimensionality on the flow, thus, differentiating it from the VIV phenomenon of rigid structures with a higher draft/breadth ratio. The present paper complements the studies made by Cueva, M. et al. (6) by comparing its result with those obtained in two other basins. The main idea here was to create a comprehensive data base which can be used as an element of comparison for the development of analytical/numerical models. Section describes the experimental setup and experiments in detail. Section 3 covers the definition of parameters as well the analysis of the procedures. Section 4 presents the results and comments and conclusions about them. Finally, section 5 presents the final comments and conclusions regarding the full extent of the executed experimental work and also suggests further works to complement the present one.. EXPERIMENTAL SETP The execution of the VIM study of the MonoGoM platform took place in three different basins, namely: Towing Tank of the Instituto de Pesquisas Tecnológicas do Estado de São Paulo (IPT), Brazil, in September 5; Model Ship Experimental Towing Tank (Middle Towing Tank) at the National Maritime Research Institute, Japan, during March 7, and; 4 meter Experimental Tank of the National Maritime Research Institute, Japan, during June 8. A detailed insight of each of the three tests is presented further in this paper, whereas their main characteristics are shown on Table. Tank IPT - Brazil (5) NMRI - Japan (7) NMRI - Japan (8) Table - Main characteristics of the tests. Dimensions L x W x D [m] 8. x 6.6 x x 7.5 x x 8. x 8. Model Scale Number of Springs Reynolds Number It is worth mentioning that, in all of the three experiments, the same platform the MonoGoM - was used as a reference. Nevertheless, the model scale utilized for the tests in Brazil was of a scale of :, whereas in Japan it was of a scale of :9. When taking into account these differences between the scale models, the possibility of an interesting result comparison is also established. All tests were based upon one single draft condition. While Table presents the main characteristics of the MonoGoM, Figure shows the dimensions of the unit profile. Table - Main dimensions of the unit. Breadth at the bottom 8.85 m Main Breadth. m Depth 58. m Draft test 39.5 m Displacement 6, ton Figure - Sketch with main dimensions of the platform. Model Tests at IPT-Brazil (5): These tests were the first performed on a monocolumn platform. The results of these tests were firstly introduced in Cueva, M. et al. (6) and are presented here but with a different analysis procedure. Vrn Total of runs : 4 or x 4 x :9 3.5x 5 3.5x Low.5x 5 3.5x :9 3 High 5.5x 5 x Copyright 9 by ASME

3 In taking into account the existing literature regarding VIM of SPAR units, tests were developed with the goal of verifying certain characteristics: Model Surface Roughness: Studies of the influence of the roughness are presented in Allen, D.W. and Henning, D.L. () and have significant importance due to the fact that it is not possible to maintain both Froude and Reynolds numbers simultaneously constant on a reduced scale. Heading: A great sensibility of the VIM phenomenon with relation to the flow direction was observed on SPAR units, as can be seen in Yung, T.W. et al. (3), Irani, M. and Finn, L. (4), Finnigan, T. and Roddier, D. (7); External Hull Appendices: The appendices can significantly change the flow around the hull, as can be seen in Huang, K.. et al. (3) and Yung, T.D. et al. (3); Motion Suppressors: In SPARs, the presence of motion suppressors, such as strakes, has been proved efficient, as can be seen in Finn, L.D. et al. (3), van Dijk, R. et al. (3) and also in Irani, M. and Finn, L. (5). Two mooring configurations were recreated in order to represent different current incidences. The denominated configuration SE was composed by two springs transversal to the flow, whereas the configuration denoted as NW was composed by four springs, two in the transversal direction and two in the parallel direction to the flow, as seen in Figure. The springs were allocated slightly out of the XY plane. Tables A and A present in detail the configuration of these tests. The coordinates of the initial mooring point of the spring i are (x i, y i, z i ), the coordinates of the platform mooring point of the spring i at the initial instant (t=) are (x i, y i, z i ) and Z= represents the water line level. High roughness (k/d=4.x -3 ) and high superficial density, Figure 3-3; High roughness (k/d=4.x -3 ) and low superficial density, Figure Figure 3 - Type of roughness: [] smooth [] low roughness [3] high roughness and high density [4] high roughness and low density. By analyzing the results, it is seen that the most adequate roughness was the high one (k/d=4.x -3 ) with low superficial density. In this case, the hull appendices (fairleads, chains and ladders) were included and the tests were executed on both NW and SE headings. The experiment was completed with the running of a test with the spoiler plates also positioned in the NW configuration. Spoiler plates Y 3 X SE incidence 3 Y X NW incidence fairleads and chains Mooring Line 4 Mooring Line 4 Figure 4 - Details of the external appendages. Figure - Configuration of the tests at IPT - Brazil. Four different roughness configurations were tested in the NW configuration in order to choose that which would better represent the flow on the post-critical region. Bare hull, Figure 3-; Low roughness (k/d=.6x -3 ), Figure 3-; Model Tests at NMRI-Japan (7): The tests executed in the MITAKA N.3 Model Ship Experimental Towing Tank (Middle Towing Tank) had as its goal the completion of the tests initiated at IPT. As verified in the IPT tests, the VIM phenomenon occurs on monocolumn platforms. The NMRI tests were run with a :9 scale model, therefore allowing the Reynolds number effect to be analyzed. 3 Copyright 9 by ASME

4 The advantage of this basin in relation to the IPT one is its width, which allows larger transversal motions of the model and, therefore, the use of a :9 scale. The disadvantage of this basin in relation to the IPT basin is its shorter length, which implies a limited number of cycles in fully developed flow (or regime). The tests were performed with a bare hull. The inclusion of roughness was not taken into account since there was an increase of the Reynolds number due to the scale change. These tests had the objective of verifying the influence of the following aspects: Heading and, consequently, mooring configuration change. The concern about the mooring configuration was firstly expressed by Dijk, R. et al. (3) regarding SPAR units. Changes in the restoration values. The tests were performed with three springs as shown in Figure 5. In this case, the springs, were fixed on a vertical stem and the restoration on the horizontal plane was transmitted to the model through pulleys. Figure 6 shows a schematic configuration of the springs in these tests and Table A 3 presents in detail this configuration. Three restoration values were tested: 5, and 5 N/m (values without current) on both incident conditions. The novelty about these tests was the measurement of the forces on the mooring lines. The restoration forces were obtained directly both in the transversal and parallel directions to the flow. There was no need to rely on linear analytical models to estimate the forces as previously done in the tests at IPT. Model Tests at NMRI-Japan (8): The same series of tests that were ran at the NMRI in the previous year were once more ran at the same institute, though this time using a 4m in length towing tank, one of the largest in the world. See illustrative picture in Figure 7. The model also was without roughness. 8 degree incidence degree incidence 3 Y X Mooring Line Figure 5 - Configuration of the Tests at NMRI-Japan. CCD camera Spring Spring Spring Wire Figure 6 - Spring system configuration at NMRI-Japan. Figure 7 - Picture of the 4m Experiment Tank at the NMRI-Japan. The execution of the same tests in a new basin aimed at obtaining a temporal series with more cycles in fully developed condition as well as higher Reynolds number, obtained by the increase of the carriage speed. The tests were once again executed with two flow directions and with different restoration values. The restoration values used in the tests were: Low Reynolds Numbers: Transversal restoration with values of 5, and 5 N/m; High Reynolds Numbers: Transversal restoration with values of 3, 3, 38 and 45 N/m. The difficulties faced during the tests regarding the Reynolds numbers can be attributed to the increase of drag force, which causes both the necessity of more rigid springs and also the occurrence of a high trim due to the moment created by the current on the model. 4 Copyright 9 by ASME

5 In these tests, the mooring configuration was similar to the one used in the 7 tests. Nevertheless, the length of the mooring lines could be increased given the width of 8m of the basin. More information on the mooring configuration is in table A ANALYSIS PROCEDRE Due to the fact that the results of the three tests are being presented in the same way, it is desirable to present the analysis procedure adopted. The standard procedure intends to be robust and was structured based on the current literature regarding fluid structure interaction, in particular, the VIV and VIM phenomenon. Therefore, the most important formulations of the phenomenon together with the main references from which they were extracted permeate the following sections. Restoration Forces: The restoration forces are calculated through the decomposition of each of the mooring forces. The forces on each mooring line were obtained analytically or directly from measurements, depending on the test. Therefore, the restoration can be defined in each test in the inline direction, and also in the cross-flow direction by using the following equation and the least square method, as seen in Figure 8. where X t, Y t, Z t is the instant position of the center of gravity of the unit. where A Y is the value of the maximum positive amplitude and A Y is the value of the maximum negative amplitude of the motion. It is also suggested that, due to modulation of motion amplitudes, that the characteristic amplitude should be defined as a function of the RMS Root Mean Square of the signal, therefore, / This amplitude value is usually used to calculate the fatigue of the mooring and risers of the platform. The characteristic amplitude parameter defined above stops, nevertheless, characterizing the phenomenon when there is a high motion signal modulation, which frequently happens in situations of fluid structure interaction of low spanwise correlation or of a low precision of procedures and experimental techniques. Due to this fact, searching for a way of defining a characteristic amplitude which would neither over estimate the phenomenon A Y /D nor be excessively conservative, A Y /D, the value of A Y /D as being the average of the % highest peaks of the motion signal. Therefore, / 5 where Y is the value of i th peak amplitude, the peaks are ordered from highest to lowest with Y being the highest of all peaks and n represents the number of peaks of the motion signal. Figure 9 presents a comparison of the three definitions for the characteristic amplitude value. It is observed that the adopted A Y /D definition represents well the VIM motion range and prevents distortions caused by the use, for example, of extreme values, or even of values which need the harmonic character of the motion to be representatives, such as the RMS. Figure 8 - Calculation of cross-flow and inline restorations. Non-Dimensional Motion Amplitudes: In accordance with the literature, the value of the non-dimensional amplitude, A/D, which characterizes each VIM condition, can be defined in several ways. It is suggested in Irani, M. and Finn, L. (5) that, regarding the maximum strength for the design of the mooring lines, the adopted maximum amplitude value should be defined as / A Time [s] Figure 9 - Comparison between A/D definitions. Y max =.3 Y * =.9 Y /5 =. Hydrodynamic Forces: The linear rigid body motion equations for a platform with two uncoupled dof. are represented by Sarpkaya, T. (4) as shown below: 5 Copyright 9 by ASME

6 where represents the platforms mass; C the structural damping coefficient of the system; F H and F H are the total hydrodynamic forces acting on the system in the x and y directions. In the experiments, the hydrodynamic forces in each given direction are measured indirectly using these motion equations. The total hydrodynamic force is the sum of the inertial, dissipative, and restoring forces of the system. Preliminarily, the structural dissipative force (structural damping) can be disregarded, considering it has a smaller magnitude value than the other forces involved in the system dynamics. Therefore, the hydrodynamic force is obtained by the sum of the restoration and inertial forces. In this way, the force in the transverse direction to the flow (y, cross-flow) is commonly represented in the form of the nondimensional lift coefficient, C L, as in where ρ is the fluid density, S is the submerged projected area of the platform in relation to the transverse direction to the flow and is the flow speed. The force in the parallel direction to the flow (x, inline) can be divided in two parts, one related to the average drag force (of static origin) and a second one related to the dynamic drag force (of oscillatory origin). Thus, the average part of the drag can be described as where F H is the average total hydrodynamic force in the x direction and C D is the average drag coefficient. The oscillatory part can be described as where C D is the dynamic drag coefficient. Therefore, assuming an approximately harmonic VIM response, the total hydrodynamic force in the transversal direction can be described, as presented by Vikestad, K. et al. () and also by Sarpkaya, T. (4), as sin cos sin sin cos where F is the total hydrodynamic force amplitude in the transversal direction; is the angular frequency of the motion and is the phase of the motion. This fluid-originated force can be divided into two components, one in phase with the acceleration and the other in phase with the platform velocity. In this way, the nondimensional can be stated that sin cos where C is the added mass coefficient and C D is the damping term in y that originates from motion in this direction. In a less susceptible manner to the monochromatic harmonic character, Fujarra, A.L.C. and Pesce, C.P. (), proposes a classical analysis on the frequency domain for estimating the added mass coefficient. According to that analysis, the following relation can be stated where is the Fourier transformation of the signal, m is the added mass and c is the viscous damping coefficient. Therefore, where is the real part of the imaginary number resulted from the analysis through the Fourier transformation. In this case, the added mass coefficient is calculated for each motion frequency, allowing the identification only of the contribution of the force on the frequency of interest (dominant on the registry). Reduced Velocity: The reduced velocity is usually defined as where T is the natural period in calm waters. Nevertheless, during the occurrence of VIM, the added mass varies considerably, having influence on the period of oscillation. In the same way, the restoration in the y direction can also present slight changes due to the mean drift of the platform, mainly for high flow speeds, which can also have influence on the motion natural period in relation to a natural period in calm waters Therefore, a reduced velocity is defined for each drift level, taking into account the eventual alteration on the added mass and restoration, thus 6 Copyright 9 by ASME

7 The presented motions are non-dimensional. Figure demonstrates that the motion decreases when the roughness increases. where T is the natural period of the motion on the new drift condition and flow speed, calculated as A Y.5.5 smooth low roughness high roughness high density high roughness low density This new definition of Vr presents itself more coherent with the parameters that dictate the system in a given fluidstructure interaction, and therefore, it is more representative in relation to the VIM phenomenon, as also noted in Irani, M. and Finn, L. (5). A X RESLTS The main results of the VIM phenomenon analysis are presented in this section. In order to present the results, dimensionless quantities have been used, which is a common practice in fluid-structure interaction phenomenon studies. Therefore: For the results of response amplitude in the direction of the flow, the dimensionless quantity adopted was A D, where A refers to the dimensional motion amplitude in the indicated direction and D refers to the characteristic breadth of the floating unit during the tests; Similarly, for the results of response amplitude in the flow s transversal direction, the dimensionless quantity A D was adopted, where A refers to the motion amplitude in the transversal direction of the incident current; Regarding periodicity, the dimensionless quantities adopted were those given by the relation of the oscillating periods in each direction, inline and crossflow, divided by the natural period in the transverse motion, which is T T and T T. With regards to forces, the usual hydrodynamic dimensionless quantities were adopted, thus, C D for the medium drag; C D for the dynamic drag superposed to the medium drag; C L for the lift and C for the added mass. Results of combined motions on the XY plane will also be presented, which are plotted in polar diagrams and represent the real events that occur with a platform submitted to VIM. Model Tests at IPT-Brazil (5): Firstly, a demonstration of the results in the SE heading condition will be given for a comparison of the roughness effect on VIM = T n Figure - Variation of non-dimensional amplitudes as a function of reduced velocities for different roughness. The non-dimensional of the periodicity motion matches the result from the literature in which the body, when moving due to VIM, oscillates in the natural period of the transversal motion, thus in all cases, as can be seen in Figure. T Y T X smooth low roughness high roughness high density high roughness low density = T n Figure - Variation of non-dimensional periods as a function of reduced velocities for different types of roughness. For the motion due to VIM starts to present a double frequency in the inline motion, possibly due to the high transversal motion with simultaneous high inline motion. This fact occurs when the correlation of the vortex shedding formation is good. It was also observed on cylinders with DOF and a low mass ratio according to Jauvtis, N. & 7 Copyright 9 by ASME

8 Williamson, C.H.K. (3) and Sanchis, A., Sælevik, G. & Grue, J. (8). When comparing the motion on the XY plane of the smooth hull and the high roughness/high superficial density hull, reduced motions are observed in the later in the same Vr. As seen in Figure, none of the trajectories presented the eight shape trajectory Regarding the lift coefficient, it can be stated that it increases until Vr 9 and decreases from this value for both cases, which matches the values from the literature. The values of the added mass coefficient increase and stabilize around a value of C.6. In the smooth case, the values start to decrease for Vr 8. The decay of the added mass frequently occurs when the transversal motion is pronounced and coexists with the motion in the inline direction C L smooth low roughness high roughness high density high roughness low density Figure - Motions on the XY plane (cross-flow and inline) for different: (a) smooth and (b) high roughness and high density. The drag coefficient, C D in the smooth case and with low roughness decrease linearly and subsequently presents sudden growth. The cases with high roughness remained constant around C D.7 and only in the case with high roughness with low superficial density presented a sudden jump. This value of C D does not correspond to a post-critical region for smooth cylinders, perhaps, it should correspond to a 3D effect on the flow. The jump, which occurs in Vr is due to the coexistence of the inline motion, representing the dynamic drag amplification region, as can be seen in Figure C a = T n Figure 4 - Variation of the lift coefficient (C L ) above, and the added (C a ) below, as a function of the reduced velocity for different types of roughness. Based on the results for different levels of roughness and on the results presented by Allen, D.W. and Henning, D.L. (), a high roughness (k/d=4.x-3) and a low superficial density were chosen to proceed with this study. The development of the later would be made considering the flow on the drag post-critical region and, therefore, the low Reynolds numbers of the test would not have influence on the flow around the body. C D SE heading NW heading.4. smooth low roughness high roughness high density high roughness low density A Y.5.4 C Dd = T n Figure 3 - Variation of drag coefficients as a function of reduced velocities for different types of roughness. A X = T n Figure 5 - Variation of non-dimensional amplitudes as a function of reduced velocities for different headings. 8 Copyright 9 by ASME

9 The following results (Figure 5) are presented for two different configurations of headings (SE and NW, as seen on Figure ) It should be pointed out that in these cases the hull presents the external appendices (fairlead, chain and ladders) besides the above defined roughness. It is observed that, for the NW heading, values of Vr 4 are reached in comparison to the maximum values of Vr as observed on the SE heading. This difference occurs due to the different levels of transversal restoration, which define the value of Vr. The results for the different headings are similar until Vr for all the non-dimensionals. The non-dimensional motions increase in a greater speed from Vr, mainly on the NW heading, as can be seen in Figure 5. By analyzing the motion results together with the results of the non-dimensional periods and the drag coefficient a few conclusions can be stated. In the Vr region, the in-line motion in the double frequency of the motion coexists with the transversal motion, as seen in Figure 6. In the same region, there is a high level of dynamic amplification on both headings (higher for the NW heading), where the motions are higher (Figure 7). The polar motion graphics on the XY plane have clearly shown the presence of the coexistence of the inline and crossflow motions in both cases. On the NW heading, the formation of the typical eight shape trajectory is clear, whereas on the SE heading a double frequency is seen in the inline motion except that this is in a banana shape T Y.5 SE heading NW heading T X = T n Figure 6 - Variation of non-dimensional periods as a function of reduced velocities for different headings Figure 8 - Motions on the XY plane (cross-flow and inline) for different headings: (a) SE and (b) NW. It is interesting to observe in Figure 9 the decay of the added mass for the values of Vr, which could characterize a good correlation of vortex shedding formation..8.6 SE heading NW heading C L.4..8 C D.6.4. SE heading NW heading C a.5 C Dd = T n Figure 7 - Variation of drag coefficients as a function of reduced velocities for different headings = T n Figure 9 - Variation of the lift coefficient (C L ) above, and the added (C a ) below, as a function of the reduced velocity for different headings. 9 Copyright 9 by ASME

10 .5 without spoiler plates with spoiler plates without spoiler plates with spoiler plates.8 A Y C D A X. C Dd = T n Figure - Variation in non-dimensional amplitudes as a function of the reduced velocity due to the presence of spoiler plates. The results of the hull with spoiler plates are presented as follows. The motions due to VIM are mitigated in the region of 7 r, as can be seen in Figure. In region of Vr nothing could be concluded. Regarding motion periods, no double frequency motion in any of the tests was observed (Figure ). The values of drag coefficient were also not altered in relation to the case without spoiler plates (Figure ). Considerable changes are observed where the spoiler plate showed itself to be efficient, regarding the added mass and lift coefficients (Figure 3). Regarding added mass a great decrease can be observed in this region, due to the change in the pressure field which resulted from the change caused by the spoiler plates on the flow. T Y.5 without spoiler plates with spoiler plates Figure - Variation in drag coefficients as a function of the reduced velocity due to the presence of spoiler plates. C L C a = T n without spoiler plates with spoiler plates = T n Figure 3 - Variation of the lift coefficient (C L ) above, and the added (C a ) below, as a function of the reduced velocity due to the presence of spoiler plates T X = T n Figure - Variation in non-dimensional periods as a function of the reduced velocity due to the presence of spoiler plates. 4 7 Figure 4 - Motions on the XY plane (cross-flow and inline) for different headings: (a) SE and (b) NW Copyright 9 by ASME

11 A Y N/m N/m 5 N/m T Y N/m N/m 5 N/m..5 A X.4. T X = T n Figure 5 - Variation of non-dimensional amplitudes as a function of reduced velocities for different transversal restoration levels Incidence 8º - NMRI(7) = T n Figure 7 - Variation of non-dimensional periods as a function of reduced velocities for different transversal restoration levels Incidence 8º - NMRI(7). A Y N/m N/m 5 N/m T Y N/m N/m 5 N/m..5 A X.4. T X = T n Figure 6 - Variation of non-dimensional amplitudes as a function of reduced velocities for different transversal restoration levels Incidence º - NMRI(7). The result of the motion on the XY plane (Figure 4), shows that there is no presence of any usual observed shape. Reduced transversal motions can be verified as well as an asymmetry of the later, which is the consequence of the non symmetrical configuration of the spoiler plates in relation to the flow incident axis. The tests executed in Japan, complementing the results and conclusions obtained so far are presented in the following = T n Figure 8 - Variation of non-dimensional periods as a function of reduced velocities for different transversal restoration levels Incidence º - NMRI(7). Model Tests at NMRI-Japan (7): The results for the nondimensional amplitudes at the 8 degree incidence have shown maximum values of A D of about.5 as shown in Figure 5. This fact is due to the small range of values of Vr with which the tests were executed (6 r ). On the other hand, the non-dimensional amplitude for the degree incidence condition has shown maximum values for A D of about.9 (Figure 6); these values are closer to those verified in the IPT tests (Figure and Figure 5). This can be explained because in these tests the values of Vr overcome Vr. Copyright 9 by ASME

12 C D N/m N/m 5 N/m C L N/m N/m 5 N/m. C Dd.. C a = T n Figure 9 - Variation of drag coefficients as a function of reduced velocities for different transversal restoration levels Incidence 8º - NMRI(7). C D C Dd N/m N/m 5 N/m = T n Figure 3 - Variation of drag coefficients as a function of reduced velocities for different transversal restoration levels Incidence º - NMRI(7). A great dispersion can be observed in the results presented in Figure 6. This can be explained by the reduced acquisition time. Due to the length of the tank, L = 5m, a short running time was possible, hence few cycles were verified on the motion registry, which can misrepresent the motion in regime. The relation of the blockage ratio (model breadth/tank width.5) is also higher than the usual for VIV on cylinders. Some wall effect may have influence on the shedding vortex frequency and on the drag coefficient value. This relation in the other tests, IPT(5) and NMRI(8), is smaller than., which in the literature corresponds to a non significant blockage effect for cylinders with low aspect ratio = T n Figure 3 - Variation of the lift coefficient (C L ) above, and the added (C a ) below, as a function of the reduced velocity for transversal restoration levels Incidence 8º - NMRI(7). C L C a N/m N/m 5 N/m = T n Figure 3 - Variation of the lift coefficient (C L ) above, and the added (C a ) below, as a function of the reduced velocity for transversal restoration levels Incidence º - NMRI(7). and low oscillatory frequency, see for example Okajima, A. et al. (997). The graphics of Figure 7 and Figure 8 show that few tests presented the double frequency of the inline motion, only in cases with Vr. The results of the drag coefficient have shown increased values for the 8 degrees incidence as seen in Figure 9, which can misrepresent the post-critical drag region in which the drag is constant. The results for the degree incidence, see Copyright 9 by ASME

13 Figure 3, show values of about C D.65 and some peaks, due to the dynamic amplification in cases of Vr. The drag and added mass coefficients seen in Figure 3 and Figure 3 follow the same tendency presented as in the IPT-Brazil tests. The differences derive from the dispersion of the results of the NMRI-Japan (7), due to the reduced number of cycles. In analyzing the motions on the XY plane presented in Figure 33, greater amplitudes for the degree case incidence are seen, where there is highvr for high Reynolds numbers covered a much smaller Vr range (3.5 r 9.5) in which the transversal motions are reduced to A D.5. In the tests with high Reynolds numbers, where the current speed is high, the drag force is very high, and also the platform presents significant trim, which generates difficulties on the decomposition of the forces. A Y N/m N/m 5 N/m Figure 33 - Motions on the XY plane (cross-flow and inline) for different headings (a) 8º and (b) º - Transversal restoration 5 N/m - NMRI(7). Model Tests at NMRI-Japan (8): The non-dimensional amplitude for 8 degree incidence in Figure 35 shows a similar pattern as those obtained in the previous tests demonstrated in Figure 5. The only difference, as already expected, was related to the greater Vr value. A Y A X N/m N/m 5 N/m 3 N/m 3 N/m 38 N/m 45 N/m = T n Figure 34 - Variation of non-dimensional amplitudes as a function of reduced velocities for different transversal restoration levels Incidence º - NMRI(8) A X T Y T X = T n Figure 35 - Variation of non-dimensional amplitudes as a function of reduced velocities for different transversal restoration levels Incidence 8º - NMRI(8) N/m N/m 5 N/m = T n Figure 36 - Variation of non-dimensional periods as a function of reduced velocities for different transversal restoration levels Incidence 8º - NMRI(8). The results with high Reynolds numbers presented in Figure 34 have shown coherence when compared to the low Reynolds numbers, but it needs to be brought up that the tests 3 Copyright 9 by ASME

14 T Y.5 5 N/m N/m 5 N/m N/m N/m 5 N/m.5 C D.4..5 T X.5 C Dd = T n Figure 37 - Variation of non-dimensional periods as a function of reduced velocities for different transversal restoration levels Incidence º - NMRI(8). In comparing the results presented in Figure 34 and the results presented in Figure 6 it was verified that the result of the later is less dispersive than the former, due to the longer running time and, therefore, cycles in regime. In these tests, few dots were observed where the inline motion presented a double motion frequency as seen in Figure 36 and Figure 37. C D C Dd N/m N/m 5 N/m = T n Figure 38 - Variation of drag coefficients as a function of reduced velocities for different transversal restoration levels Incidence 8º - NMRI(8) = T n Figure 39 - Variation of drag coefficients as a function of reduced velocities for different transversal restoration levels Incidence º - NMRI(8). The results regarding the drag coefficient were practically constant for the 8 degrees incidence, C D.7 as seen in Figure 38. In the degree incidence case in Figure 39, results were similar to the previous case, where the dynamic amplification phenomenon for values Vr was verified. The lift coefficient results show the same tendency until a maximum value of about C L.6 as seen in Figure 4 and Figure 4. The added mass coefficient also followed the same tendency as the previous with an average value of C.5. C L C a N/m N/m 5 N/m = T n Figure 4 - Variation of the lift coefficient (C L ) above, and the added (C a ) below, as a function of the reduced velocity for transversal restoration levels Incidence 8º - NMRI(8). 4 Copyright 9 by ASME

15 C L C a Figure 4 - Variation of the lift coefficient (C L ) above, and the added (C a ) below, as a function of the reduced velocity for transversal restoration levels Incidence º - NMRI(8). In comparing the results for different levels of transversal restoration on both of the NMRI-Japan tests, it was noticed that this restoration change did not interfere with the nondimensional results presented. The motion on the XY plane presented in Figure 4 shows the existence of higher motions due to higher Vr values = T n 4 5 N/m N/m 5 N/m Figure 4 - Motions on the XY plane (cross-flow and inline) for different headings (a) 8º and (b) º - Transversal restoration 5 N/m - NMRI(8). 5. CONCLSIONS The present paper has presented an extensive database on the effects of VIM of monocolumn platforms which can be used advantageously for the initial design of such platforms. The results coming from different basins can be considered similar, exempting their own peculiarities. The main conclusions are: The inclusion of roughness on the model is capable of representing the post-critical drag region and also increases the repeatability of the tests If the roughness is not included it is necessary to carry out the tests at high Reynolds numbers by increasing the speed of the current. Nevertheless, this condition is usually not available in most of the basins. When dimensioning VIM experiments, it is necessary to choose the model scale in such a way as to allow for the greatest acquisition time to improve statistics. Tests for Vr are necessary to allow not only the identification of the lock-in region, but also better behaved motions with clear observations of double frequency and eventual motion drop. The paper presented by Fujarra, A.L.C. et al. (9) aims to complement the previous work in the literature and mainly to provide continuity to this present work, in the way VIM tests are made for a new configuration of a monocolumn platform. More information regarding these aspects and other mitigating effects can be found on the same work. The present paper and the paper presented by Fujarra, A.L.C. et al. (9) together can be used in the future as a basis for VIM numerical prediction software. NOMENCLATRE Fluid density A D Non-dimensional longitudinal amplitude (% highest peaks) / Non-dimensional transversal amplitude (% largest peaks) / Non-dimensional transversal amplitude (rms) / Non-dimensional transversal amplitude (maximum values) C Structural damping Added mass coefficient C D Static drag coefficient C D Dynamic drag coefficient (oscillatory) C L Lift coefficient c Viscous damping coefficient D Characteristic diameter of the platform Restoration coefficient in the x axis Restoration coefficient in the y axis k/d Non-dimensional roughness F H Total hydrodynamic force in the y F H Total hydrodynamic force in the x Restoration force in x axis Restoration force in y axis Mass of the platform m Added mass S Projected immersed area of the platform T Natural period of transversal motion in calm waters T Y Natural period of transversal motion in the new offset position T Longitudinal or inline motion period T Transversal or cross motion period Flow velocity 5 Copyright 9 by ASME

16 X x x Y y Z z z Reduced velocity in calm waters Reduced velocity (corrected) X position of the center of gravity of the platform x position of the initial mooring point of the spring i x position of the mooring point of the spring i at initial instant Y position of the center of gravity of the platform y position of the initial mooring point of the spring i y position of the mooring point of the spring i at initial instant Z position of the center of gravity of the platform z position of the initial mooring point of the spring i z position of the mooring point of the spring i at initial instant ACKNOWLEDGMENTS The authors of the present paper are thankful to PETROBRAS for the concretization of the tests hereby presented, as well as to the partnership PETROBRAS/JOGMEC for the execution of the Japan based tests and specifically to Dr. K. Maeda and Dr. M. Saito for the close monitoring of the later. A special acknowledgment goes to CAPES for the financial help that has made this work possible. REFERENCES. Allen, D., & Henning, D. (). Surface Roughness Effects on Vortex-Induced Vibration of Cylindrical Structures at Critical and Supercritical Reynolds Numbers. Proceedings of the Offshore Technology Conference. OTC-33.. Cueva, M., Fujarra, A. L., Nishimoto, K., Quadrante, L., & Costa, A. (6). Vortex Induced Motion: Model Testing of a Monocoulmn Floater. Proceedings of the 5th International Conference on Offshore Mechanics and Artic Engineering. OMAE Finn, L. D., Maher, J. V., & Gupta, H. (3). The Cell Spar and Vortex Induced Vibrations. Proceedings of the Offshore Technology Conference. OTC Finnigan, T., & Roddier, D. (7). Spar VIM Model Tests at Supercritical Reynolds Numbers. Proceedings of the 6th International Conference on Offshore Mechanics and Artic Engineering. OMAE Fujarra, A. L., & Pesce, C. P. (). Added Mass of an Elastically Mounted Rigid Cylinder in Water Subjected to Vortex-Induced Vibrations. Proceedings of the st International Conference on Offshore Mechanics and Artic Engineering. Oslo, Norway: OMAE Fujarra, A., Pesce, C., Nishimoto, K., Cueva, M., & Faria, F. (7). Non-stationary VIM of Two Mono- Column Oil Production Platforms. Fifth Conference on Bluff Body Wakes and Vortex-Induced Vibrations - BBVIV, (pp. -5). Costa do Sauipe, Bahia, Brazil. 7. Fujarra, A.L.C., Gonçalves, R.T., Faria, F., Cueva, M., Nishimoto, & Siqueira, E.F.N. (9). Mitigation of Vortex-Induced Motion of a Monocolumn Platform. Proceedings of the 8th International Conference on Ocean, Offshore and Artic Engineering. OMAE Huang, K., Chen, X., & Kwan, C. T. (3). The Impact of Vortex-Induced Motions on Mooring System Design for Spar-based Installations. Proceedings of the Offshore Technology Conference. OTC Irani, M., & Finn, L. (4). Model Testing for Vortex Induced Motions of Spar Platforms. Proceedings of the 3rd International Conference on Offshore Mechanics and Artic Engineering. OMAE Irani, M., & Finn, L. (5). Improved Strake Design for Vortex Induced Motions of Spar Platforms. Proceedings of the 4th International Conference on Offshore Mechanics and Artic Engineering. OMAE Jauvtis, N. & Williamson, C.H.K. (3). Vortex- Induced Vibration of a Cylinder with Two Degrees of Freedom. Journal of Fluids and Structures, pp Okajima, A., Ya, D., Kimura, S., & Kiwata, T. (997). The Blockage Effects for aa Oscillating Retangular Cylinder at Moderate Reynolds Number. Journal of Wind Engineering and Industrial Aerodynamics, pp Sanchis, A., Sælevik, G. & Grue, J. (8). Two- Degree-of-Freedom Vortex-Induced Vibrations of a Spring-Mounted Rigid Cylinder with Low Mass Ratio. Journal of Fluids and Structures, pp Sarpkaya, T. (4). A Critical Review of Intrisic Nature of Vortex-Induced Vibrations. Journal of Fluids and Structures, pp van Dijk, R. R., Magee, A., Perryman, S., & Gebara, J. (3). Model Test Experience on Vortex Induced Vibrations of Truss Spars. Proceedings of the Offshore Technology Conferece. OTC van Dijk, R. R., Voogt, A., Fourchy, P., & Mirza, S. (3). The Effect of Mooring System and Shared Currents on Vortex Induced motions of Truss Spars. Proceedings of the nd International Conference on Offshore Mechanics and Artic Engineering. OMAE Vikestad, K., Vandiver, J. K., & Larsen, C. M. (). Added Mass and Oscillation Frequency for a Circular Cylinder Subjected to Vortex-induced Vibrations and 6 Copyright 9 by ASME

17 External Disturbance. Journal of Fluids and Structures, pp Yung, T. W., Sandström, R. E., Slocum, S. T., & Ding, J. Z. (3). Advances in Prediction of VIV on Spar Hulls. Deep Offshore Technology Conference, (pp. - ). Marseilles, France. 7 Copyright 9 by ASME

18 ANNEX A Table A Configuration of the springs for NW incidence from IPT tests-brazil (5). Mooring Line ID x i [mm] y i [mm] z i [mm] x i [mm] y i [mm] z i [mm] Kx [N/m] Ky [N/m] Table A - Configuration of the springs for SE incidence from IPT tests-brazil (5). Mooring Line ID x i [mm] y i [mm] z i [mm] x i [mm] y i [mm] z i [mm] Kx [N/m] Ky [N/m] Table A 3 - Configuration of the springs in NMRI tests-japan (7). Mooring Line ID x i [mm] y i [mm] z i [mm] x i [mm] y i [mm] z i [mm] a 6 5 a a 6-5 a 3-79 a -564 a Table A 4 - Configuration of the springs in NMRI tests-japan (8). Mooring Line ID x i [mm] y i [mm] z i [mm] x i [mm] y i [mm] z i [mm] a 6 5 a a 6-5 a a -564 a 8 Copyright 9 by ASME