Laboratory Tests for VIV Prediction of Deepwater Risers

Transcription

1 Laboratory Tests for VIV Prediction of Deepwater Risers Ir. Jaap J. de Wilde, MARIN (Maritime Research Institute Netherlands), Abstract One of the great challenges in the offshore industry is still the assessment of the motions of risers in waves and current in deep or ultra deep water (3,000 m deep). Here the fatigue life of riser systems is often dominated by the VIV phenomena. State-of-the-art VIV prediction codes, such as Shear7 or VIVARRAY, are based on the assumption that the forces exerted by the fluid flow on the structure can be locally described by empirical lift and drag coefficients of 2-D riser sections and that the excitation frequency is dictated by the Strouhal relation. The excitation of the vortex shedding is accounted for by so-called negative damping. The approach has been used for a few decades and in spite of a lot of criticism it has survived and is still the most commonly used approach for real offshore risers. MARIN is working on two experimental fronts to get a better handle on the VIV phenomenon. First, a new High Reynolds test facility has been developed for measuring the dynamic lift and drag loads of 2-D riser sections. The new apparatus is deployed for research as well as commercial projects. Secondly, an instrumented scale model riser of 12.6 m length and 16 mm diameter has been tested recently. Recent findings from both experiments are presented and discussed in the paper. Keywords VIV, vortex shedding, riser, Reynolds number, high mode, test facility 1. Introduction Economically interesting offshore oil and gas reservoirs are increasingly being found in deeper water in the oceans with water depth up to 1000 to 3000 m. This means that drilling as well as production and subsequent transportation to the markets is becoming exponentially expensive and only big reservoirs justify the enormous capital investments and operating costs. Produced oil and gas has to be transported from the reservoir via the seabed to the platform at the water surface for processing and compression and subsequently has to be transported to the seabed again for

2 eventual transportation by pipeline. This vertical transportation generally takes place by so-called steel catenary risers of 0.4 to 0.7 m diameter which are spanning between 1000 to 5000 metres. The fatigue life of these deepwater risers is frequently dominated by Vortex-Induced Vibrations (VIV). The fundamental cause of this phenomenon can be understood from the figure below, which shows an experimentally observed vortex street behind a stationary cylinder; [1], [3] and [4]. The vortices trail in two rolls, alternatively from the top and the bottom of the cylinder. This causes alternating lift forces, which trigger a cylinder motion (if permitted) across the flow. If the cross-flow motion develops, however, the moving cylinder can change the vortex street dramatically, forcing it to follow its own motion. Due to this complex interaction between fluid forces and cylinder motions, VIV can be designated as a non-linear hydro-elastic phenomenon. FLUID FORCES FLUID DYNAMICS VIV RESPONSE STRUCTURAL DYNAMICS FLUID/STRUCTURE MOTIONS 2. High Reynolds Test Apparatus A new test apparatus has been developed for measuring the dynamic VIV loads on an oscillating cylinder at full scale Reynolds numbers, [5], [6] and [8]. A 3.4 m section of the riser is towed and oscillated at the same time. The forces on the cylinder are measured and processed to obtain dimensionless coefficients for drag, lift and added mass. The measurements at full scale Reynolds numbers provide new insights in the scale effects when entering the critical regime. The development of the test facility started in 1999 as an in-house research activity and continued afterwards for the VIVARRAY JIP and various commercial projects.

3 Vertical struts. 2. Linear bearings 3. Test pipe. 4. End plates. 5. Drive shafts. 6. Oscillator kw electric motor. Figure 1 - High Reynolds VIV test apparatus The test pipe is horizontally suspended on two streamlined struts with linear bearings, from the carriage at mid tank depth. The oscillation is forced by the electric oscillator using a crank-shaft mechanism. The tow speed, oscillation frequency and oscillation amplitude can be accurately adjusted. The overhead carriage runs on rails over the 210 m long towing tank, which is 4 m wide and 4 m deep. The carriage can run in forward or backward direction, which means that the cylinder is either pushed or pulled through the tank. Both directions experience an uniform flow field with a low turbulence. The apparatus can deal with large drag loads up to 10 kn, tow speeds up to 4 m/s, oscillation frequencies up to 3 Hz and oscillation amplitudes up to 330 mm. 3. Results Bare Pipe at Reynolds 40,000 Figure 2 shows the results of measured loads for a roughened cylinder at Reynolds 40,000. Presented is the lift coefficient Clv as a function of the reduced velocity Ur and the oscillation amplitude A/D. A clear peak can be observed for a reduced velocity of Ur = 6 and an amplitude of 0.5 diameter. The peak occurs in the middle of the lock-in region. The highest maximum of the lift coefficient is approximately 1.0. The zero lift line in the graph denotes the boundary between positive and negative damping, where negative damping means excitation by the vortex shedding process. The highest amplitude with a crossing from positive to negative lift occurs at about one cylinder diameter, which is in agreement with the self-limiting nature of the VIV phenomenon. The results are qualitatively in good agreement with Gopalkrishnan data at Reynolds 10,000 [2].

4 Contor Plot of Lift Coefficient with Vr and A/D, Single Pipe Tests Amplitude, A/D (-) Reduced Velocity, Vr Figure 2 - Lift coefficient in phase with velocity versus Ur and A/D Single rough pipe, Reynolds 40,000, MARIN new test apparatus, Reynolds Scale Effect Offshore riser systems operate at Reynolds numbers well above 10,000, where the following Reynolds regimes can be distinguished, see Figure 3: Sub-critical regime: 2,000 < Re < 200,000 The turbulent vortex street has an almost constant vortex shedding frequency (St 0.20). The boundary layer is laminar up to the separation point at about 80 from the upstream stagnation point. The drag coefficient of a smooth circular cylinder in the sub-critical Reynolds regime is very constant with a value close to 1.2. Critical regime: 200,000 < Re < 500,000 The boundary layer becomes unstable, but separates before becoming turbulent. The width of the wake decreases and the drag coefficient drops to a value near 0.3. The vortex shedding frequency is very variable. Supercritical regime: 500,000 < Re < 3,500,000 There is first a laminar separation at about 100 from the stagnation point. The flow becomes turbulent and then re-attaches, forming a separation bubble before finally separating from the body near 140. The regime is recognised with a drag coefficient increasing from 0.5 to 0.7. The wake is disorganised and the shedding frequency is very variable.

5 Sub-critical Critical Super-critical St Cd Re Figure 3 - Drag coefficient and Strouhal number of circular cylinder, Re 10 4 to 10 6 The drop of the drag coefficient for Reynolds numbers between 200,000 and 500,000 is known as the drag crisis or drag bucket. For a very smooth cylinder the drag coefficient can be as low as An example of the measured Reynolds sensitivity for an oscillating smooth pipe with the MARIN test apparatus is presented in Figure 4. Similarly as for the non-oscillating cylinder, the drag coefficient drops when entering the critical Reynolds regime. The sensitivity for the oscillation amplitude and the reduced velocity can be clearly observed from the graph. The measured drag coefficient of the oscillating smooth cylinder in the tests ranged between 0.5 and 2.0, depending on tow speed, amplitude and frequency. Another example of Reynolds scale effects is presented in Figure 5. The measured lift coefficients Clv for a smooth and a rough cylinder at Re 40,000 and Ur 6.0 are plotted on top of Triantafyllou data at Reynolds 10,000. Significantly higher lift loads were found in our Re 40,000 tests for amplitudes above 0.6. The zero-crossing amplitude of 1.1 is about 50% higher than the Triantafyllou zero-crossing amplitude of 0.75, for the same reduced velocity. This result is surprising for a circular cylinder in the sub-critical regime. Possibly the effective Reynolds number of an oscillating cylinder is higher, taking into account the cross flow speed which is in the same order of magnitude as the tow speed.

6 Smooth Pipe, Drag Coefficient with Reynolds Number Drag Coefficient, Cd (-) Reynolds Number, Re (x10 3 ) A/D 0.5, Vr 6.0 A/D 0.5, Vr 7.0 A/D 0.5, Vr 8.0 A/D 0.5, Vr 10.0 Figure 4 - Reynolds sensitivity for smooth pipe Rough and smooth pipe lift forces, Ur 6.0, Re 40,000 Comparison with Triantafyllou data at Re 10, Lift Coefficient, CLV (-) Triantafyllou Vr 5.8 Positive Negative Amplitude, A/D (-) Smooth 1 Smooth 2 Smooth 3 Rough 1 Rough 2 Rough 3 Figure 5 - Lift coefficient Clv at Reynolds 40,000, smooth and a rough pipe were tested 5. Unexpected Results for Spring Blade Mounted Cylinder Earlier tests were carried out with the 200 mm cylinder mounted on 2.5 m long spring blades. These tests showed an unexpected large discrepancy, when comparing certain forward and backward towed tests. The differences were found for amplitude ratios of more than 0.5 diameter and reduced velocities close to lock-in. The cylinder on the spring blades does not perform a pure transverse oscillation but an oscillation that actually lies on an arc of a circle, as shown below. Therefore, the direction of the in-line motions changes with the towing direction. The motions are convex with the flow when the carriage moves forward (pushing)

7 and concave for backwards towing (pulling). The observed forward-backward differences were also found for effectively 7.5 m long spring blades with in-line motions as small as 1% of the cross flow oscillation. Flow Tow speed L Figure 6 - Circular motion of spring blade mounted cylinder Figure 7 shows an example of the observed differences for a series of forced oscillation experiments. The forced oscillation tests are particularly interesting, because the motions are completely under control, thereby removing uncertainties related to mechanical friction and/or (viscous) flow forces on the spring blades. The positive lift coefficients for amplitudes above 0.85 give incentives for thought. Extrapolation of the lift coefficients suggests a zero crossing at an amplitude ratio of 1.6, which is approximately three times the expected value for this reduced velocity. For a free VIV experiment with low structural damping this would mean much larger oscillation amplitudes than expected otherwise. 1.5 VIV Lift Force Excitation Unexpected Positive Lift Clv [-] 0.0 Damping old fwd old bwd new fwd new bwd Gopalk A/D [-] Figure 7 - Spring blade mounted cylinder, lift coefficient Clv forward and backward towing 6. Experiments with 12.6 m Long Riser Model A scale model riser of 16 mm diameter and 12.6 m long was towed horizontally in a towing tank at speeds between 0.5 and 3.0 m/s. Pretensions ranged between 0.5 and 2.5 kn. Measurements were made of the drag loads at the pipe ends. The pipe accelerations were measured at 2 locations of the pipe. Optical fibres were deployed for motion measurement at 10 other locations.

8 Carriage Riser Tensioner Transducer 1.15 m 15.8 m Figure 8 - Experiment with 12.6 m horizontal pipe A length of 6 m of the test pipe was instrumented with 40 optical strain gauges. Four optical fibres were mounted inside the pipe surface, respectively located at the top, bottom, fore and aft. Each fibre contained 10 FBG (Fibre Bragg Grating) strain gauges, as indicated in the next sketch. 6.6 m 6 m Fx, Fy, Fz load cell Accelerometer Accelerometer FBG strain gauges Fx, Fy, Fz load cell Figure 9 - Instrumentation of test pipe with 40 FBG strain gauges An example of the measured motions is presented in Figure 10. The x-z motions were derived from the accelerometers at the pipe mid. The tow speed was 1.0 m/s (test ). The plots reveal a lying banana, where normally a figures of eight or a standing banana is expected. The measured amplitudes are roughly 0.5 pipe diameter. The response with 5 or 6 half waves had frequencies which were close to the theoretically expected frequencies, assuming an added mass coefficient of 1.0. Other results (test with 0.5 m/s speed) are presented in Figure 11.

9 +z +x Flow Figure 10 - Motions x-z at mid pipe, test , 1.0 m/s Test displacements at location 4 Test displacements at location 9 2.4E-02 2.E E-02 2.E E-03 8.E-03 y [m] 0.0E E E E E E E E-02 y [m] 0.E+00-2.E-02-2.E-02-8.E-03 0.E+00 8.E-03 2.E-02 2.E E-03-8.E E-02-2.E E-02 x [m] -2.E-02 x [m] Figure 11 - Measured motions at location 4 and 9, test , 0.5 m/s 7. Conclusions and Recommendations Based on the results presented in this paper and recent experience with VIV experiments, the following conclusions and recommendations seem justified: a. A new test apparatus has been developed for measuring the hydrodynamic drag, lift and added mass coefficients of an oscillating riser section at full scale Reynolds number. The apparatus can be used for calibration of VIV prediction programs for novel riser geometries, such as riser bundles, piggy-back and straked risers. b. Important Reynolds scale effects were found for the smooth and the rough cylinder when entering the critical regime.

10 c. Interesting scale effects were also found for the oscillating cylinder in the sub-critical regime at Reynolds 40,000. d. A large sensitivity was found for the VIV loads of a spring blade mounted cylinder. Even for very small in-line motions of 1% the measurements differed significantly from pure cross flow experiments. e. A very complex response was found for the 12.6 m long model riser of 16 mm diameter, where normally a figures of eight or a standing banana is expected. The measured amplitudes were roughly 0.5 pipe diameter. Further analysis and investigations are required to understand this. Symbols Cd : drag coefficient C Lv : lift coefficient in phase with velocity C La : lift coefficient in phase with acceleration Cm : added mass coefficient Re : Reynolds number St : Strouhal number U r : reduced velocity References [1] Blevins, R.D., Flow Induced Vibrations, Krieger Publishing Company, Malabar, Florida, second edition, [2] Gopalkrishnan, R., Vortex-Induced Forces on Oscillating Bluff Cylinders, D.Sc. thesis, Department of Ocean Engineering, MIT, Cambridge, USA, [3] Triantafyllou, M.S. et al., Pragmatic Riser VIV Analysis, Offshore Technology Conference, Paper OTC 10931, Houston, USA, [4] Vandiver, J.K., Dimensionless Parameters Important to the Prediction of Vortex-Induced Vibration of Long Flexible Cylinders in Ocean Currents, Journal of Fluids and Structures, Vol. 7, pp , [5] De Wilde, J.J. and Huijsmans, R.H.M., Experiments for High Reynolds Numbers VIV on Risers, ISOPE, Paper 2001-JSC-285, [6] De Wilde, J.J., Huijsmans, R.H.M. and Triantafyllou, M.S., Experimental Investigation of the Sensitivity to In-line Motions and Magnus-like Lift Production on Vortex-Induced Vibrations, ISOPE, Paper 2003-JSC-270, [7] De Wilde, J.J. and Huijsmans, R.H.M., Laboratory Investigation of Long Riser VIV Response, ISOPE, Paper 2004-EF-005, [8] De Wilde, J.J. et al., Cross Section VIV Model Test for Novel Riser Geometries, Deep Offshore Technology Conference, 2004.