Non-Linear Time Domain Analysis of Vortex Induced Vibrations for Free Spanning Pipelines

Pipelines from offshore petroleum fields must frequently pass over areas with uneven seafloor. In such cases the pipeline may have free spans when crossing depressions. Hence, if dynamic loads can occur, the free span may oscillate and time varying stresses may give unacceptable fatigue damage. A major source for dynamic stresses in deep water free span pipelines is vortex induced vibrations (VIV) caused by current. Two alternative strategies for calculation of VIV are seen today. Practical engineering is still based on empirical models, while use of computational fluid dynamics (CFD) is considered immature mainly because of the needed computing resources. Most empirical models are based on frequency domain dynamic solutions and linear structural models, cf. Larsen (2000). The reason for this is simply that hydrodynamic coefficients as needed in a VIV analysis are available as functions of frequency, and therefore not directly applicable in a transient time domain simulation. A free span pipeline has, however, important nonlinearities that should be taken into consideration. Both tension variation and pipe-seafloor interaction at the span shoulders will contribute to nonlinear behaviour, which means that most empirical models will have significant limitations when dealing with the free span case. The need for non-linear time domain methods is therefore obvious. This paper describes a new approach for VIV analysis of free span pipelines where both linear frequency and non-linear time domain analyses are employed. The first step is to carry out a conventional VIV analysis that will determine response frequency and hydrodynamic coefficients by use of a linear response model. This result is then used in a time domain model that can handle non-linear boundary conditions at the span shoulders. This approach is valid as long as the response amplitudes at the main part of the span are the same for both analysis methods. The significance of the new method is that displacements, and hence also stresses, in the pipe at the shoulders will be far better described by the non-linear method than what is possible from linear theory. Since fatigue damage in most cases is larger at the shoulder than within the mid section of the span, the new approach represents an important step forward for free span pipeline analysis.