OTC Copyright 2003, Offshore Technology Conference

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1 OTC 54 Model Test Experience on Vortex Induced Vibrations of Truss Spars Radboud van Dijk, Maritime Research Institute Netherlands, Allan Magee, Technip Offshore, Inc., Steve Perryman, BP Americas, Inc., Joe Gebara, Technip Offshore, Inc. Copyright 3, Offshore Technology Conference This paper was prepared for presentation at the 3 Offshore Technology Conference held in Houston, Texas, U.S.A., 5 8 May 3. This paper was selected for presentation by an OTC Program Committee following review of information contained in an abstract submitted by the author(s). Contents of the paper, as presented, have not been reviewed by the Offshore Technology Conference and are subject to correction by the author(s). The material, as presented, does not necessarily reflect any position of the Offshore Technology Conference or its officers. Electronic reproduction, distribution, or storage of any part of this paper for commercial purposes without the written consent of the Offshore Technology Conference is prohibited. Permission to reproduce in print is restricted to an abstract of not more than 3 words; illustrations may not be copied. The abstract must contain conspicuous acknowledgment of where and by whom the paper was presented. Abstract In order to evaluate the Vortex Induced Vibration (VIV) response of truss Spars and to optimize their strake configuration several model test programs have been carried out at MARIN. The results show that it is possible to optimize the strake design of Spars to obtain minimum VIV-response. The results of the model tests also suggest that modeling details, such as appendages, can have an influence on the Vortex Induced Vibrations. In order to reliably predict the fullscale VIV-behavior of the prototype Spar these details must therefore be accurately represented on the model. Furthermore, damping of attached structures such as the truss on a truss Spar can significantly contribute to the reduction of VIV. Loads on such structures have been measured in the model tests. An important aspect that needs consideration in VIV model testing is effect of model scale on the Reynolds number. Roughness can be added to the hard tank of the Spar to minimize scale effects. The paper discusses possible scale effects and the effect of hull roughness on model test results. The repeatability of VIV model tests and reliability of these tests in representing the full-scale situation is discussed. The effect of Spar heading with respect to the current direction as well as current speed will be discussed. Introduction Since 996 Spars have been used as production platforms in the Gulf of Mexico. Vortex Induced Vibrations (VIV) of the Spar are an important consideration in mooring system design. The Vortex Induced Vibrations of Spars are typically reduced by adding helical strakes to the Spar hull. The effectiveness of the strakes must be verified in the design stage of the Spar. At present numerical tools are not capable of accurately predicting VIV-behavior of Spars. Model tests are therefore currently the most practical method to verify and optimize the strake design. A new development in Spar design is the so-called truss-spar (Refs & ). In order to evaluate the VIV-behavior of this type of Spars dedicated model tests have been conducted on several truss Spars. Vortex Induced Vibrations A blunt structure placed in a flow (either air or water) will experience an oscillating force due to the shedding of vortices. This phenomenon is studied and discussed extensively (e.g. Ref. 3). If this structure is able to move in the flow Vortex Induced Vibrations (VIV) can occur. The predominant direction of these motions is transverse to the direction of the flow. Large steady state type oscillations occur when the vortex shedding frequency coincides with a natural frequency of the structure. This is known as lock-in. For offshore structures these vortex induced vibrations could add to the fatigue damage of mooring and risers, shortening the total fatigue life and also increase the overall drag on the structure. Experience has shown that in offshore structures cylindrical objects such as risers, calm buoys and Spars are most susceptible to VIV, but also other shapes can exhibit VIV-behavior. The vortex induced vibrations for moored Spars are characterized by a number of dimensionless numbers. These are defined as: ) Reynolds number : Re = U C D/υ ) Strouhal number : St = f VIV D/U C 3) Reduced velocity : U R = U C T SWAY /D 4) Dimensionless amplitude: A/D = (A max -A min )/( D) Where: U C is the free stream current velocity D is the diameter of the Spar υ is the kinematic viscosity f VIV is the vortex shedding frequency T SWAY is the natural period for sway of the Spar A is the single sway amplitude As the natural period for sway may vary with offset in the mooring system, the actual measured sway period of the Spar during each test is used. The Strouhal number St is more or less constant and typically in the range of.8 to. for cylinders, see Ref. 3. The reduced velocity is referred to as true reduced velocity, based on mean current velocity in line with the tow direction. The A/D-value is based on sway excursions perpendicular to the direction of incident current.

2 OTC 54 The VIV-behavior between different configurations can be compared when the measured A/D-values are plotted as function of reduced velocity (U R ). Figure shows an example of typical VIV-behavior of a cylinder in current. In this example a Strouhal value of.8 is used. f VIV /f SWAY [ ].5.5 Stationary cylinder shedding frequency Figure : Typical VIV-behavior and A/D-values as function of Ur The top figure shows the ratio between the period of vortex shedding (f VIV ) and the natural frequency for sway (f SWAY ). The bottom figure shows the VIV-response expressed in dimensionless amplitude A/D. Below U R 5 almost no vortex induced vibrations are seen and the frequency of vortex shedding increases linearly with the free stream current velocity. Above values of U R 5 the vortex shedding frequency locks-in on the natural frequency for sway, i.e. the motions of the Spar cause the shedding frequency to lock-in on the natural frequency for sway. Due to this lock-in effect large steady state type motions occur and the A/D-values peak. Above U R -values of approximately 8 to 9 the lock-in can no longer be maintained. The vortex shedding frequency returns to its normal value and the A/D-values decrease. Test set-up Current was simulated by towing the truss Spar through a towing basin. As a result a uniform current profile was obtained. The main dimensions of the basin were 4x8x8 m (LxBxD). This resulted in sufficient clearance between the truss Spar model and the basin walls to neglect possible effects of the basin walls on the Spar motions. All tests were performed using a mooring system with a horizontal stiffness equivalent to the full-scale mooring system. Each full-scale mooring leg was represented by a single mooring line with one or more linear springs. The model spring characteristics were chosen such that the variation of sway period with surge offset resembled the fullscale situation. The mooring lines on the model were attached at the height of the fairleads. The mooring points on the carriage were just above the water line. This resulted in an upward angle of the mooring lines as shown in figure. The truss Spar model consisted of (bottom to top) a soft tank, a truss section, a hard tank (with or without strakes) and simplified topsides. Figure : Set-up of horizontal equivalent mooring 4-line mooring Measurements During the test programs the following quantities were measured and derived: ) Tow carriage velocity. By definition the tow carriage velocity is equal to the simulated free stream current velocity. ) Motions of the Spar. The six degrees of freedom motions of the Spar were measured using an infrared optical tracking device. From the measured motions at the top of the Spar the motions at CoG were derived. 3) Loads in the mooring lines. The mooring line loads were measured at the fair leads. Based on these measured loads, the offset of the Spar and the geometry of the mooring system the total drag load on the Spar was calculated. 4) Loads between hard tank and truss. By measuring the loads between hard tank and truss the total drag load on the truss was derived. Based on the measured load on the truss also the damping due to the truss could be derived. Comparing the overall drag load on the Spar and the drag load on the truss only, also the drag coefficient of the hard tank could be derived. Tested Spar Configurations The truss Spars have been tested for a range of tow speeds as well as headings ranging over 36. The reason to test for different Spar headings is that the strake configuration is not symmetrical, due to practical limitations in the full-scale Spar design. Although the main purpose of the model tests was to verify the Spar VIV-response for a given strake design, additional research type tests have been performed to increase the knowledge on Spar VIV-behavior. These tests included: Spar with and without strakes on the hard tank (i.e. bare hull tests). The tests without strakes were done to present a base case and to assess the effectiveness of the strakes (i.e. do the strakes really suppress the VIV). Spar hull with and without added roughness. As the Spar was tested near the critical Reynolds regime, roughness was added to the hull to decrease the possibility of sudden changes in drag coefficient. Variations in strake geometry and strake dimensions. Both the size of the strakes and the coverage of the hull were varied to investigate the effect on VIV-response. Drag Coefficient and Reynolds Number The drag coefficient (C D ) of an unstraked cylinder changes noticeably with Reynolds number. The actual change in C D -

3 OTC 54 3 value depends on surface roughness. For full scale Spars the Reynolds number will always be in the post critical regime (i.e. Re > 5 6 ), see figure 3. For the model tests Froude scaling is used. As a result the Reynolds numbers change, according to formula. Re Re λ Full Scale MODEL = 3/... () The model tests were performed at Reynolds numbers in the range of 3 4 < Re < 4 5. Figure 3 shows typical values of the drag coefficient for -dimensional flow around a bare cylinder as function of Reynolds number. In this figure the relevant Reynolds number ranges for both model scale and full-scale are shown as well as the different regimes for a smooth hull (i.e. sub critical, critical, super critical and post critical). Schlichting (smooth) Sarpkaya (smooth) Achenbach k/d =. Achenbach k/d =.45 Achenbach k/d =.9 CoG during lock-in can be described by a figure-of-eight, as can be seen in figure 4. Full test VIM tests with bare hull Single oscillation Figure 4: Figure-of-eight trajectory for Spar without strakes In this figure the surge and sway motions are made dimensionless using the Spar diameter. Plotting the A/Dvalues of all tests on the truss Spar without strakes as function of reduced velocity results in figure 5. Lock-in starts at Ur 5. The maximum A/D-value measured is.68 for Ur = 8. Truss Spar, bare hull.9 model test Re full scale Re.8 Drag coefficient [ ] sub critical critical super critical post critical Reynolds number [ ] Figure 3: Drag coefficient as function of Reynolds number From figure 3 it follows that to avoid large variations in drag coefficient and to minimize possible scale effects a certain hull roughness is required. The data presented above is valid for a -D unstraked cylinder. It is assumed that it will also be valid for 3-D flow on the Spar hard tank with strakes. Refs 3 and 6 mention that the VIV-response for smooth, moderately damped cylinders can be reduced by a factor of 4 in the critical Reynolds regime. This reduction is not observed for rough cylinders. In order to obtain reliable model test results and to minimize the variation in drag coefficient in the critical Reynolds regime all VIV model tests were performed with a surface roughness (k/d) of the hard tank hull of approximately 4-3. Discussion of results First a comparison was made between VIV-response of the truss Spar with and without strakes. Both were tested with roughness on the hard tank hull. The VIV model tests on a truss Spar without strakes were performed for two tow directions and a range of reduced velocities (3 Ur 8). All these tests were performed with surface roughness on the hard tank of the truss Spar. In these tests VIV-behavior as described in literature was observed (Ref. 3). The trajectory of the Spar Figure 5: A/D as function of Ur for Spar without strakes From this figure it is clear that the VIV-behavior of the Spar without strakes would be very large. When strakes are added to the Spar the VIV-response reduces significantly. Typically strakes are used with a height of % of the Spar diameter. Comparing A/D-values between the Spar with and without strakes results in figure 6. This figure shows A/D-values for the Spar with and without strakes for the same tow direction Truss Spar, straked hull, tow direction = Bare hull Straked hull Figure 6: A/D as function of Ur for Spar with and without strakes

4 4 OTC 54 In this case the Vortex Induced Vibrations of the Spar are almost completely suppressed. For other tow directions the VIV-response of the Spar reduced significantly, but was still present due to variations in strake geometry and hull coverage. Besides a clear reduction in VIV-response also the trajectory of the Spar is different when strakes are fitted to the hard tank. Figure 7 shows a typical trajectory plot of a straked Spar during a VIV model test, plotted at the same scale as figure 4. Instead of a clear figure-of-eight motion the straked Spar exhibits a more or less semi-circular trajectory. Full test VIM tests with straked Spar Figure 7: VIV-trajectory of Spar with strakes Single oscillation Figure 4 and 7 are both for the same tow direction and tow speed (and Ur). The only difference between these tests is the presence of strakes. The difference in trajectories is quite noticeable. Due to practical limitations in the strake design the strakes do not always cover the hard tank in the best possible way (Ref. 7). Some strakes have cutouts for the mooring chains and often one side of the Spar has a reduced strake height to allow dry transport of the Spar. As a result, the strake design may be less effective and for certain current directions the VIVresponse will be higher than with an optimum strake, although still much lower than for the hull without strakes. Figure 8 below shows measured A/D-values of the straked Spar as function of both reduced velocity and current direction. From this figure it is clear that the VIV-response for the straked Spar is concentrated on a small number of current directions. Reduced velocity [ ] A/D = F(Ur,dir) tow direction [deg] Figure 8: A/D as function of Ur and current direction Using this information the Spar can be installed in an orientation where the most sensitive direction will encounter the lowest design current velocity. At present it is not possible to predict for which current directions VIV can be expected. Therefore model tests are currently the most practical method to optimize strake design. The above test results also show that VIV-response can change very rapidly with only a small change in current direction. This means that the increments in tow direction in the model test matrix should be chosen small enough to capture any unexpected VIV-response. The model test results show that maximum VIV-response is found for reduced velocities between 5 and 9. This is in agreement with theory. For model test programs that focus on VIV tow speeds should therefore be selected that cover at least the range 4 < Ur <, provided such conditions could occur at the platform location. Repeatability of Experiments In order to assess the repeatability of the experiments, a number of VIV-tests were repeated. One example is shown in figure 9. Here the original test and the repeat test were separated by a two-week period. The example concerns a test with Spar without strakes (bare hull). These tests show a high level of VIV, which makes it easier to compare the response. Bare hull tests, repeatability check 3 time [s] Figure 9: Repeat of same test after two weeks As can be seen from the figure the agreement between the two tests is very good. Overall the repeatability of the VIV tests was very high. Drag Loads Another significant difference between the tests with and without strakes is the measured surge offset. The straked hull has a surge offset that is 86% of that of the hull without strakes. Although the straked spar has a larger frontal area due to the strakes, the overall drag load is lower, resulting in a smaller surge offset. The drag load on the Spar is an important factor as it determines the sizing of the mooring lines. Based on the measured tow force and tow speed the drag coefficient of the Spar can be calculated. Figure shows a comparison of calculated drag coefficient of the Spar with and without strakes as function of reduced velocity. The drag coefficient is calculated using formula. C D = F /( ρ V A )... () TOW TOW For the Spar both with and without strakes the hard tank diameter (i.e. without strakes) is used to determine the frontal F

5 OTC 54 5 area A F. As a result the drag coefficient for the Spar with strakes would be expected to be slightly higher. Spar with strakes Spar without strakes Drag coefficient as function of Reduced velocity The drag coefficient of the Spar without strakes shows a small decrease for Reynolds numbers between 5 and 5. This corresponds to the reduction in drag coefficient in the critical Reynolds regime for a cylinder with a roughness of approximately k/d =.4. For the straked Spar there is no change in drag coefficient observed over the tested Reynolds number range. Drag coefficient Cd [ ] Tests were also performed with and without roughness on the hard tank hull. These tests were only done for a truss Spar with % strakes. In these tests no significant differences were found in drag coefficient as function of Reynolds number. However, the VIV-behavior of the Spar with added roughness was more consistent, resulting in more repeatable experiments Figure : Drag coefficient as function of reduced velocity Ur The drag coefficient for the Spar with strakes is more or less constant over the tested velocity range. For the Spar without strakes the drag coefficient is slightly lower for low reduced velocities, as a result of the smaller frontal area. A clear increase in drag coefficient is observed for reduced velocities from 6.5 and 8. This increase in drag coefficient is linked to the large sway motions observed for the bare hull Spar at these reduced velocities. For Ur = 7.5 the increase in C D reaches %. Because the straked Spar undergoes less VIV, there is less drag augmentation. Therefore, the C D for the straked Spar shows less variation over the same range of Ur. From these results it can be observed that although the spar with strakes has a larger frontal area to the current, the overall drag load is equal to or smaller than the drag load on a Spar without strakes due to the lower VIV-response. Truss Damping The loads between hard tank and truss were measured using a six-component force frame. This makes it possible to analyze the contribution of the truss to the damping of vortex induced vibrations in some detail. Only shear forces are considered here. The connection loads between hard tank and truss are dominated by: ) the drag load on the truss, ) the shear force due to the inclination (roll and/or pitch) of the truss Spar and the underwater weight of both truss and soft tank, 3) to a lesser extent the inertial forces of truss and soft tank due to the motions of the Spar. Figure shows the measured transverse force on the truss as function of sway excursion. This force is corrected for the shear force between hard tank and truss due to the Spar inclination. The force consists of damping and inertia loads. This example shows a test performed without strakes, so significant VIV is observed, which makes it easier to analyze the results. Besides plotting the drag coefficient as function of reduced velocity, the relation with Reynolds number can also be shown. Figure shows the calculated results for the Spar both with and without strakes. As no reliable drag coefficients were found for Re < 5 only results are plotted for Re > 5. Spar with strakes Spar without strakes Drag coefficient as function of Reduced velocity Transverse load on truss Drag coefficient Cd [ ].5.5 Figure : Drag load on truss versus A/D-value 5 6 Reynolds number [ ] Figure : Drag coefficient as function of Reynolds number Re From the above figure it can be seen that: The measured force on the truss and soft tank is very consistent over the full test length. Each sway cycle

6 6 OTC 54 results in more or less the same force level on the truss - hard tank connection. The load on the truss and soft tank is more or less proportional to the sway offset, but there is a clear inphase & out-phase part of the force with the sway offset. The out-of-phase part can be attributed to the damping of the truss. An estimate of the damping due to the truss can be made. For each sway cycle the damping is calculated based on energy input and dissipation. The following formulas are used to derive the relative damping due to the truss: T = vy (t) dt T v... (3) T F LV = FY (t) vy (t) dt... (4) T v B FLV ω A =... (5) C ω Y CRIT = B... (6) B β =... (7) B CRIT For each sway cycle the relative damping can be calculated. Figure 3 shows the calculated relative damping values for each sway cycle in the present test. A/D relative damping β 4% 3% % cycle Figure 3: Calculated relative damping β for each sway cycle For the above example an average relative damping (β) of approximately 3% was found. In free decay tests for surge and sway in calm water an overall damping for both truss and hard tank of 5 to 8% was found. Modeling Details Part of the test programs focused on the effect of modeling details, such as mooring chains along the hard tank, cutouts in the strakes for the chains and caissons on the hard tank. The model test results show that small modifications of the model can have a significant impact on the VIV-response. Closing the cutouts in the strakes for the mooring chains decreases the VIV-response of the Spar. Adding or removing caissons on the hull also changes the VIV-response. The number of tests to investigate the effect of modeling details was limited. The results show that variations in the size of the strakes and coverage of the hull affected the VIV response. Further research is required. Conclusions Several truss Spars have been model tested to assess the effectiveness of the strake configuration in reducing VIVresponse. The model tests prove to be an effective tool in optimizing the strake configuration. To minimize scaling effects surface roughness is applied on the Spar hull. Also all details of the full-scale Spar are modeled. Adding strakes to a Spar greatly reduces the VIV-response. However, due to practical limitations the strake design is often not perfect for all current directions. Therefore, VIV may still occur for some directions. It is not accurately possible to predict at what headings VIV will occur. Therefore all headings should be tested for some tow speeds in the range 5 < Ur < 8, where VIV-response can be expected. Furthermore, as VIV response can be very sensitive to small heading variations, small heading increments must be used. For a truss Spar without strakes a large VIV-response is observed for reduced velocities between 5 and 8. For a truss Spar with strakes the VIV-response is much lower. Here too the VIV-response peaks at reduced velocities between 5 and 8. For reduced velocities above 8 the VIV-response becomes less regular and reduces. When lock-in occurs on a Spar without strakes, the trajectory describes a figure-of-eight pattern. This motion behavior is also found on other structures that are susceptible to VIV. The trajectory of a Spar with strakes is significantly different and describes more a semi-circular or banana-shaped trajectory. Acknowledgements The authors would like to acknowledge BP Americas, Inc. and Technip-Coflexip, for their permission to use this data and for their support during the testing of the Spars. Nomenclature A/D Dimensionless (sway) amplitude C D Drag coefficient CoG Center of Gravity Re Reynolds number St Strouhal number

7 OTC 54 7 Ur Reduced velocity VIV Vortex Induced Vibrations β Relative damping (beta) υ kinematic viscosity (.E-6 m/s ) References [] Magee, A.R. et al, Heave Plate Effectiveness In The Performance Of Truss Spars, OMAE-43, [] Bangs, A.S. et al., Design of the Truss Spars for the Nansen/Boomvang Field Development, OTC 49, [3] Blevins, R.D., Flow induced vibrations, Krieger publishing company, Malabar, Florida, second edition,. [4] Hoerner, Dr-Ing S.F., Fluid - Dynamic Drag, 965. [5] Achenbach, E., Heinecke, E. On Vortex Shedding from Smooth and Rough Circular Cylinders in the Range of Reynolds Numbers 6 3 to 5 6, Journal of Fluid Mechanics. 9, 39, 98. [6] Wootton, L.R., The Oscillations of Model Circular Stacks due to Vortex shedding at Reynolds Numbers from 5 to 3 6 National Physical Laboratory, Aerodynamics Division NPL Aero Report 67, 968 [7] Magee A.R., Sablok A., Mooring Design for Directional Spar Hull VIV, OTC 543, 3