The concept of the Wake II model for the determination of the hydrodynamic forces on marine pipelines is extended to include the wave plus current case. There are two main differences between the Wake II and the traditional model that uses Morison’s equation. In the Wake II model the velocity is modified to include the pipe’s encounter with the wake flow when the velocity reverses. The model also uses time dependent drag and lift coefficients. For the wave plus current case, the flow field is assumed to be the linear superposition of pure wave and pure current and is treated as wave only but in two different phases. The model requires eight empirical parameters that are obtained from comparisons with field data for various Keulegan-Carpenter numbers and current to wave ratios. The effective velocity and the force predictions are compared with field data from Exxon Production Research Company and with the conventional model.
The model gives satisfactory results when applied to wave plus current cases and it predicts lift forces that in shape, magnitude and phase relative to the velocity are in very close agreement with the measured forces for all the cases. A substantial improvement is obtained over the predictions with the conventional model. This work is applicable to the design of submarine pipelines laying on the sea bottom in water depths where waves or waves and currents contribute to the hydrodynamic forces. An alternative formula for the wake velocity is presented that requires only four empirical parameters. The results with the alternative model are similar to the results with the Wake II model.
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