Effects of variable force coefficients Cd and Cm on the dynamic response of a Tension-Leg Platform

Abstract

The Morison hydrodynamic force prediction equation is commonly used to compute the wave forces on offshore structures composed of "small members". The computations are carried out assuming that the force coefficients, C[d] and C[m], found in this equation are constant values. However, some recent work using the Morison equation with harmonic flows on single cylinders indicates that the coefficients are actually a function of time. Furthermore, data collected from an instrumented platform in the real ocean environment indicates that the coefficients vary spatially, as well. Thus, in this study, a methodology is developed for permitting temporal and spatial variation in the force coefficients used for computing the forces on a typical multi-membered offshore structure. The methodology is then incorporated into a coupled, nonlinear, time-domain dynamic analysis model of a Tension-Leg Platform so that a comparison may be made between the response due to constant Fourier-averaged coefficients and that due to the corresponding variable coefficients. The Fourier-averaged coefficients and the corresponding variable coefficients are both obtained from the same existing available experimental data on sinusoidal flows. To evaluate the effects of variable force coefficients on the dynamic response, a parametric study is undertaken in which the only environmental forces on the TLP are the wave forces due to regular Airy waves. The parameters considered in the study are wave period, wave height, water depth, leg stiffness, initial tension and wave direction. Using two data cases that have their Fourier-averaged coefficient values within the recommended API code ranges, a significant difference is found to exist between the response due to constant coefficients and that due to variable coefficients. In one case, the response due to constant coefficients is significantly larger than that due to variable coefficients while in the other case, the reverse is true.