Incorporating the Higher Harmonics in Viv Fatigue Predictions

Vortex-Induced Vibrations (VIV) are an important source of fatigue damage for risers in the Oil and Gas industry. Results from recent VIV experiments by Vandiver et al. [1] indicate significant dynamic strain energy at not only the Strouhal frequency, but also its harmonics. In certain regions of the pipe, these higher harmonics accounted for more that half of the measured RMS strain and increased fatigue damage by a factor exceeding twenty. However, the state-of-the-art in VIV prediction only accounts for the vibrations at the Strouhal frequency. Preliminary results from a second set of experiments, described in this paper, confirm the importance of the higher harmonics in fatigue life estimates of pipes. Further, the authors formulate an approach to incorporate the higher harmonics in VIV related fatigue design. Finally, the authors identify the estimation of the higher harmonics, in both location and magnitude, as an important area of ongoing research, the results of which will be required to implement this proposed method. INTRODUCTION Vortex-Induced Vibrations (VIV) response has been discussed in the offshore engineering literature for over twenty five years and the higher harmonics have also been noticed since the early experiments [2, 3]. It is common knowledge that the in-line frequency is twice the Strouhal frequency. The third and fifth harmonics were noticed in accelerometer measurements described in the late 1980s [3], but were not considered to be of significant concern when making fatigue life estimates. This was because the response at the frequency of the third and fifth harmonics was quite small in these early, low mode number experiments on flexible cylinders in uniform and sheared flows. Recent experiments [1], where higher modes were excited, have shown that the higher harmonics can be very important for VIV related fatigue damage. These higher harmonics were found to cause large amplifications, sometimes greater than twenty, in fatigue damage in certain regions of a pipe undergoing VIV. However, the state-of-the-art in VIV prediction does not account for the higher harmonics. In fact, a hydrodynamic explanation for the existence of the third harmonic was only recently presented by Williamson et al. [4]. New data, from the second Gulf Stream experiments, sometimes shows the occurrence of a strong fifth harmonic. These higher harmonics present an interesting challenge for an engineer designing risers. They have been shown to have important fatigue-related consequences in certain regions of the pipe. On the other hand, no method or guidance is available to include their effects in design. In fact, the procedures used to predict VIV related fatigue damage were not developed with the higher harmonics in mind. It is therefore important that we revisit these formulations and modify them in light of the findings from the Gulf Stream experiments. EXPERIMENT DESCRIPTION The second Gulf Stream experiment is the third of a series of field experiments, conducted by Deepstar and MIT, to study VIV response of flexible pipes at high mode numbers. The first experiment was carried out at a US Navy test facility on Lake Seneca in upstate New York in the summer of 2004. The Lake Seneca tests focused on the effect of VIV at high mode numbers for a pipe in uniform flow. The second experiment was conducted in the Gulf Stream near Miami. The first of the Gulf Stream tests, conducted in the fall of 2004, focused on a long pipe in sheared flow. The second Gulf Stream test, the focus of this paper, was conducted in the fall of 2006. All three tests were part of a larger testing program developed by DEEPSTAR, a joint industry technology development project, aimed at improving the ability to model and mitigate VIV. The goals of the overall test program were to understand the different aspects of the dynamics of a pipe undergoing VIV at high mode numbers. These aspects included VIV suppression with strakes, drag coefficients of bare and straked pipes, in-line and cross-flow VIV, and damping factors. The importance of the higher harmonics to fatigue, as reported by Vandiver et al. [1], was found in data collected in these experiments. This 1 Copyright © 2007 by ASME paper outlines a methodology to include these higher harmonic frequencies in the fatigue damage calculations for a flexible pipe. The Second Gulf Stream Experiment The Gulf Stream tests were conducted on the Research Vessel F. G. Walton Smith from the University of Miami using a flass fiber composite pipe 500.4 ft. long and 1.43 inches in diameter. The pipe was spooled on a drum that was mounted on the aft portion of the ship. The pipe was lowered directly from the drum into the water. A railroad wheel weighing 805 lbs (dry weight, 725 lbs in water), was attached to the bottom of the pipe to provide tension, as was done in the Lake Seneca experiment. The top end of the pipe was attached to the stern of the boat with a universal joint to provide a pinned boundary condition. The boat steered on various headings relative to the Gulf Stream so as to produce a large variety of sheared currents, varying from nearly uniform to highly sheared in speed and direction. Eight optical fibers were embedded in the outer layers of the composite pipe. Each fiber contained thirty five strain gauges, which use the principle of Bragg diffraction to measure strain with a resolution of approximately 1 micro-strain. Two fibers were located in each of the four quadrants of the pipe, as seen in Figure 1. Figure 1 Cross-Section of the Pipe from the Gulf Stream Test Each fiber had a strain gauge spacing of 14 ft.. Each quadrant pair of fibers was positioned so that the strain gauges in one fiber were offset from the gauges in the other fiber by 7 ft., as shown in Figure 3. The fiber optic strain gauge system was provided by Insensys, Ltd. in the UK. The fibers were embedded in the pipe during manufacture by Fiberspar at their fabrication facility in Houston. Figure 2 Side View of the Pipe from the Gulf Stream Test The pipe was made of fiberglass with an HDPE liner. The pipe properties are found in Table 1. Table 1 –Gulf Stream Pipe Properties Inner Diameter 0.98 in (0.02489 m) Outer Diameter 1.43 in (0.03632 m) Optical Fiber Diameter 1.37 in (0.035 m) EI 2.14e5 lb.in (613 Nm) EA 1.33e6 lb/ in (9.21e9 N/m) Weight in Seawater 0.133 lb/ft (flooded in seawater) (1.942 N/m) Weight in air, wo/trapped water 0.511 lb/ft (7.46 N/m) Weight in air, w/trapped water 0.846 lb/ft (12.35 N/m) Effective Tension (at bottom end) 725 lbs submg. Bottom weight (3225) Material Fiberglass Length 500.4 ft (152.4) U-Joint to U-Joint An Acoustic Doppler Current profiler (ADCP) recorded the current velocity and direction along the length of the pipe. On the R/V F. G. Walton Smith, there are two ADCPs. Each ADCP uses a different frequency to obtain different currents at different depths. The broadband (600 kHz) ADCP records the current at greater resolution and accuracy to a depth of about 60 ft., whereas the narrowband (75 kHz) ADCP records the current up to about 1500 ft. During the Gulf Stream testing both ADCPs were used to gather data. Additional instrumentation included a tilt meter to measure the inclination at the top of the pipe, a load cell to measure the tension in the pipe, two mechanical current meters to measure current at the top and the bottom of the pipe and a pressure gauge to measure the lift of the pipe bottom during tow. Wave induced vessel motion during the Gulf Stream test added low frequency components to the strain time series. An elliptical filter with a 1.5 Hz cut-off was used to remove this vessel motion from the data without interfering with the VIV frequencies. The filtering was done such that no phase shift was applied to the data. 2 Copyright © 2007 by ASME ANALYSIS OF RESPONSE DATA Experiments done in the field, like the Gulf Stream and Lake Seneca tests, cannot achieve laboratory like control over environment conditions. Vessel motions and variability in boat speed, for example, can cause the incident velocity on the pipe to vary during an experiment. Further, manufacturing expenses and time schedules can prohibit the achievement of the desired level of perfection in the experimental equipment. In the Gulf Stream experiments, for example, the optical fibers were twisted during manufacturing of the pipe such that the circumferential location of a particular fiber changed along the length of the pipe. This resulted in no fiber being perfectly aligned with either cross-flow or in-line directions for the entire length of the pipe. Fortunately, these issues could be addressed using data post-processing techniques. In particular, steady state regions were identified to avoid frequent shifts in the fundamental VIV frequency caused due to changes in the incident current velocity on the pipe. Moreover, strain signals from two orthogonal sensors were combined to recover the total cross-flow and inline strain components. Establishing steady state regions Figure 3 (a) presents data from a bare pipe test (Test – 20061023203818) performed during the second Gulf Stream experiment. It shows time-frequency plots, called scalograms, at three locations on the pipe. The frequency range in these plots is chosen to show the Strouhal frequency, called the fundamental VIV frequency or 1x frequency in this paper. Figure 3 (b) shows the mean normal incident current 1 on the pipe during the test. The scalograms were calculated at sensor locations 232.5 ft (sensor 33), 302.5 ft (sensor 43) and 372.5 ft (sensor 53) measured axially from the top of the pipe. Their positions on the pipe are shown by dots in Figure 3 (b). The scalograms indicate that the fundamental frequency of VIV was not constant for the duration of the test. They suggest that the frequency reached a steady state value only in the last sixty seconds of the test. Since the motion of the pipe is mainly governed by the fundamental VIV frequency, we can make the assumption that steady state conditions are achieved when this frequency is steady with time. Experimental data from these steady-state regions can be used to make comparisons with results from predictive programs, like Shear7, which assume steady state conditions in their analysis. In this steady state region, the fundamental frequency of vibration and all its harmonics are narrow banded, almost single frequency responses. Figure 4 shows the strain Power Spectral Density (PSD) for the steady state duration of the test. These PSDs, shown for orthogonal quadrants Q4 and Q1, correspond to the same sensor locations as the scalograms. The PSD peaks are labeled as 1x, 2x, etc. where the “x” should be interpreted as “times the fundamental VIV frequency of vibration.” This terminology will be used for the rest of the paper. 1 The current profile had to be corrected for incidence angle of the pipe. F re q u e n c y ( H z ) (a) 2.5