Vortex induced vibration excitation competition between bare and buoyant segments of flexible cylinders
Introduction
It is hypothesized that the presence of buoyancy modules on a flexible cylinder may decrease the fatigue damage rate due to the decrease in vortex shedding frequency associated with a larger diameter. At the same flow speed, a bare cylinder will vibrate at a higher frequency than a cylinder fully covered by buoyancy modules of a much larger diameter. When a flexible cylinder with both bare and buoyant regions is excited by the uniform flow, two different frequencies are excited and a competition exists between lift forces at these two frequencies. The point of this study was to answer the question, “Under what fractional coverage of buoyancy, would the VIV excitation on buoyant regions dominate the response?”
There exists some previous research on the excitation competition between bare and buoyant segments of a pipe. Lie et al. (1998) used the RMS amplitude ratio associated with the buoyant segments divided by the total RMS to determine whether the excitation on buoyant regions dominates the VIV response, while Vandiver and Peoples (2003), Li et al. (2011) and Jhingran et al. (2012) used the frequencies of the peak spectral components to determine which excitation will dominate VIV response. Their preliminary data analysis showed that the coverage of buoyancy modules and the ratio of the two diameters play a major role in the excitation competition between bare and buoyant segments.
Lie et al. (1998) stated that the ratio between the lift force on the bare segments and that on the buoyant segments was proportional to the ratio of . Where Lbare and Lbuoyancy are the length of bare and buoyant segments, respectively; Dbare and Dbuoyancy are the outer diameter of bare and buoyancy segments, respectively. Vandiver (2000) also came up with a similar formula, where the amplitude ratio between the modal responses due to the excitation on bare segments and buoyant segments was proportional to the ratio of . Both expressions show that when a pipe has two different diameters, the larger diameter region is favored to dominate the response.
This paper explores the excitation competition between bare and buoyant regions of a 38 m long model riser. The power dissipated by the damping at each excitation frequency is the metric used to determine the winner. The distinguishing identifiable feature of the excitation on either region is the excitation frequency. Two excitation frequencies are well known to exist in the spectrum of a pipe with staggered buoyancy modules. The higher frequency is associated with bare regions and the lower one is associated with buoyant regions according to the Strouhal relationship f=StU/D. In addition to these two excitation frequencies, a new phenomenon was observed. A third frequency was found to be an unexpected combination of these two excitation frequencies. This is the first known report of such behavior.
The main objectives of this paper are to:
- (1)
Offer potential explanations on the presence of the third frequency.
- (2)
Investigate the effect of the excitation at the third frequency on the VIV response.
- (3)
Determine the winner of the excitation competition between bare and buoyant regions.
- (4)
Propose an expression to predict the winner of the excitation competition for a pipe with staggered buoyancy modules in uniform flow.
- (5)
Investigate the effect of buoyancy distribution on fatigue damage rate.
- (6)
Provide a general guidance for staggered buoyancy design.
Section snippets
Riser and buoyancy configurations
The total pipe length was 38 m. Three kinds of pipes with different diameters were studied in this paper. Pipe, pipe30, had a diameter of 30 mm and was made from a continuous length of fiberglass tubing. Pipe, pipe80, used pipe30 as the inner core. Ninety-three pairs of clamshell modules, 80 mm in diameter, were clamped onto the outside of the 30 mm inner pipe. Each module was 0.4086 m in length and was made from two flexible urethane half shells which snapped together around the pipe30 and secured
Nonlinear interaction between two excitation frequencies
If the system is linear, the frequency components in response will be the same as those in excitation forces. If the system is nonlinear, excitation frequency components will include those in the excitation forces plus additional frequencies. These additional frequencies are due to the nonlinear interaction of the response of the cylinder at the excitation frequency components. Hereafter, the additional frequency component is called the nonlinear interaction frequency.
For a flexible cylinder
Frequency components in uniform bare pipe
Fig. 2 shows the curvature spectrum of the pipe30 (red line) and the pipe80 (blue dash). The data was the averaged spectrum of 30 different sensors at 1.0 m/s uniform flow, corresponding to Test 3007 and Test 4004, respectively.
Excitation frequency is usually determined from the dominant peaks in the curvature power spectrum. Dating back to the 1980s, Vandiver and Chung (1988) reported that vibrations associated with the normally expected VIV excitation frequency were often accompanied by
Conclusions
The primary contribution of this work was to explore the excitation competition between bare and buoyant segments in uniform flow, to study factors affecting the fatigue damage rate for a pipe with staggered buoyancy and provide a general guidance for buoyancy configuration design.
A summary of observations and preliminary conclusions from the VIV analysis of the pipe with staggered buoyancy modules in uniform flow includes:
- (1)
The use of staggered buoyancy leads to a previously unknown response
Recommendations
The SHELL Tests have shown that staggered buoyancy arrangement can reduce fatigue damage rate and the experiments presented in this paper yielded some insight as to the role of , and in fatigue damage rate. But more work needs to be done to achieve minimize fatigue damage rate by tuning parameters mentioned above. It will be useful if future experiments are conducted for a pipe with:
- −
Lbuoyancy/Dbuoyancy smaller than 5, and especially
Acknowledgement
The authors gratefully acknowledge Deepstar and the SHEAR7 JIP members (BP, Chevron, ExxonMobil, Petrobras, Shell, Statoil & Technip) for supporting this research, and especially SHELL Exploration and Production for providing the data. We also thank Dr. Themistocles L. Resvanis of MIT for valuable discussions and revisions.
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