Predicting Lock-in on Drilling Risers in Sheared Flows

The kurtosis statistic is introduced as a sensitive tool for efficient preliminary analysis of flowinduced vibration response data. The kurtosis of sequential blocks of time series data allows one to distinguish single mode lock-in events. The problem of predicting lock-in is then discussed. Instructional examples are introduced to illustrate the relative importance of flow-speed, power-in length and diameter, when attempting to predict single frequency dominance. When VIV from two different flow speed regions compete, it is shown that the ratio of the flow speeds cubed is an important indicator, as is the ratio of the square of the length of the power-in regions. Two example cases from measured response on a drilling riser in the North Sea are presented. SHEAR7 predictions are compared to measured results. have kurtosis values of approximately 3. The occasional occurrence of a single frequency, lock-in event is characterized by steady sinusoidal behavior. When ( ) sin( ) x t t ω = , the kurtosis takes on the value of 1.5. By plotting the kurtosis of a typical response measurement over time it is possible to quickly identify transitions from multi-frequency behavior to single-frequency, constant amplitude lock-in events. Figure 1 is an example of VIV response data, taken every 48 minutes on the Scheihallion drilling riser in the North Sea. Time, spanning several days, is plotted horizontally in Figure 1. The maximum tidal current over all water depth is plotted with the kurtosis of the transverse acceleration response measured on the drilling riser at a position z/L = 1/8. z is the axial coordinate on the riser as measured up from the bottom, and L is the total riser length. This particular riser was in a water depth of 368 meters, and depending on the strength of the current responded with VIV in the 1 to 4 modes. The first four modes all have substantial modal amplitude at L/8. Twice per day tides dominated the current and for several days in a row as shown in Figure 1, current conditions permitted one mode to dominate the vibration. At these times the response in the mode favored by the current profile built up to the point that significant VIV at different frequencies from less favorable regions of the riser was suppressed. Wake synchronization was established in the power-in region and lock-in occurred. As a result, the response grew in amplitude, was dominated by a single frequency, and the kurtosis approached 1.5, the ideal sinusoidal value. This is seen several times in Figure 1. Further discussion of the Scheihallion data is to be found in Cornut & Vandiver(2000). This particular data covers a span of eleven days. The lowest line in the figure is the maximum current, which occurred in the entire water column, as measured by an acoustic Doppler profiler (ADCP). There is not a simple correlation between maximum current speed and lock-in events. The prediction of a lock-in event requires examination of each current profile to determine the power-in region of each possible contending mode. One must then have a means of comparing the relative strengths of each mode. When one mode has a dominant position, then lock-in occurs and other modes are squeezed out. The next section presents a model for the prediction of single mode dominance, based on structural dynamic properties and the flow profile. 3 PREDICTING MODAL DOMINANCE