Hydrodynamic forces on small-diameter pipelines in combined wave-and-current flows

In this paper, the hydrodynamic forces on small-diameter pipelines laying on a plane seabed under combined wave-and-current flow conditions are investigated experimentally. Three sets of force coefficients, i.e., the peak coefficients, the Morison-type coefficients and the Fourier-type coefficients are obtained based on 56 physical tests, with the Keulegan-Carpenter (KC) number ranging from 20 to 2000 and the current-to-wave ratio M ranging from 0 to 1. Present testing results extend the upper KC limit of these coefficients from O(100) to O(1 000), which well covers the KC range related to small-diameter pipelines, e.g., cables and umbilicals. Results show that peak force coefficients keep decreasing with the increasing KC number at certain tested values of M, due to the velocity reduction in the wave boundary layer. Morison coefficients perform well in describing the peak forces in the forward duration, but poorly in the reversal duration under combined flow conditions. Fourier coefficients are demonstrated to reconstruct the time-history of hydrodynamic forces well. Empirical formulas for peak coefficients and Fourier coefficients are provided as functions of KC and M based on the present results. Moreover, a predicting method for the time-dependent forces is proposed based on the neural-network fit, which is applicable for engineering applications, e.g., dynamic on-bottom stability analysis of pipelines.