The objectives of the research study are to:
- Study the extreme response and collision behavior of a pair of flexible cylinders in close proximity, in both regular and random seaways;
- Characterize the wave-induced response and forces on the cylinders as a function of their orientation and spacing with respect to the incident waves;
- Compare the measure wave-induced forces and response of the cylinders to those predicted by finite element models of the cylinders;
- Address the use of distorted scale modeling techniques for the scale modeling and testing of flexible, deep water structures.
Task 1 focuses on the application of distorted scale modeling techniques to flexible deep water structures. The “inspectional analysis” approach (Le Méhauté 1964) is used to determine distorted scaling relationships from the differential equation of motion. This approach is illustrated by using a simple example of a uniform beam subjected to lateral loading and axial tension. The case of a flexible cylinder with uniformly varying tension, representative of a riser or tendon, is then considered. For this case the use of distorted modeling leads to inconsistencies between the scaled mass and weight of the structure. These inconsistencies are discussed and guidelines are presented to allow the selection of parameters for the model. The final section focuses on the more general application of this methodology to the design of a distorted physical model of a TLP.
Task 2 describes in detail the experimental design, set-up and test matrix for the experimental investigation. The physical models are designed based on the distorted scale relationships and guidelines derived in the previous section, using typical prototype properties of TLP risers and tendons in 1006 m (3300 ft) of water. The technique and instrumentation used to estimate the displacement field of the cylinders from the curvature measurements is presented. Extensive numerical simulations of the models were conducted with a finite element model of the cylinder to verify the technique, determine the number and location of the curvature transducers, and in the selection of force and tension instrumentation. The cylinders were instrumented to obtain the inline and transverse curvature field, the top and bottom inline and transverse reactions, and the tension at the ends of the cylinders. The experimental test matrix and procedures used are summarized at the end of the section.
The data obtained from the experiments are analyzed in Task 3. The single cylinder data are studied as a function of non-dimensional parameters like the Keulegan-Carpenter number and the reduced velocity to allow comparison with results obtained from previous experimental investigations (Belvins 1990). Comparisons between the experimental data and the numerical simulations are for the inline reaction and curvature. The paired cylinder data are presented as interference ratios, relative to the rot mean square (r.m.s.) response of a single cylinder, as a function of cylinder orientation and spacing. Some examples were also chosen to further illustrate the complex behavior observed.
Task 4 focuses on the probabilistic formulation of the collision process between the two cylinders arranged in tandem. The collision behavior of the cylinders is formulated as a random process with a collision being equivalent to crossing a barrier equal to the spacing between the cylinders. This allows the use of barrier crossing and first-passage time formulations from probabilistic mechanics to describe the extreme statistics of the collision process. Due to the non-Gaussian nature of the response, non-Gaussian extreme response formulations are obtained by applying the Hermite transformation technique using the first four moments of the response (Winterstein 1985). Comparisons are made between the Gaussian and non-Gaussian statistics, and non-parametric estimates from the experimental data. The comparisons show the appropriateness of the first-passage formulation to describe the collision behavior of the cylinders and the importance of accounting for the non-Gaussian nature of the response in determining the extreme statistics.
Task 5 summarizes the results obtained from the various aspects of this research study and concludes with a perspective on the future research.
Related Publications: Niedzwecki, J.M. and Duggal, A.S., “Collision Mechanisms and Behavior of Long Flexible Risers or Tendons in Close Proximity,” Offshore Mechanics and Arctic Engineering Conference, Glasgow, U.K., Vol.1, Offshore Technology, pp.291-298.
Niedzwecki, J.M. and Duggal A.S., “Wave Run-up and Forces on Cylinders in Regular and Random Waves, ” Journal of Waterway, Port, Coastal and Ocean Engineering, ASCE, Vol. 118, No. 6, 615-634, November 1992.
Duggal, A.S. and Niedzwecki J.M., “An Experimental Study of Tendon/Riser Pairs In Waves,” Offshore Technology Conference, Houston, TX, May 1993, Vol. 3, 323-333.
Duggal, A.S. and Niedzwecki J.M. “Regular and Random Wave Interaction with a Long, Flexible Cylinder,”Offshore Mechanics and Arctic Engineering Conference, Glasgow Scotland, June 20-24, 1993, Vol. I, 283-290.
Niedzwecki J.M. and Duggal A.S., “Collision Mechanisms and Behavior of a Pair of Long, Flexible Cylinders in Close Proximity,” Offshore Mechanics and Arctic Engineering Conference, Glasgow Scotland, June 20-24, 1993, Vol. I, 291-298. (Presentation)
Duggal, A.S. and Niedzwecki, J.M., “A Probabilistic Model for the Collision Between a Pair of Flexible Cylinders,” Applied Ocean Research, Vol.16, No.3, pp.165-176, 1994.