Line theory: Interaction with the sea surface

OrcaFlex lines are subdivided into segments, and the various forces are attributed to nodes at the ends of each segment. For a partially submerged segment, the hydrostatic and hydrodynamic forces are apportioned according to how much of the segment is submerged – the proportion wet, $\PW$. Proportion wet is available as a line result. We also define proportion dry as $1{-}\PW$.

For a segment whose axis is close to normal to the surface, the proportion wet could be calculated from the intersection of the segment centreline axis with the free surface. This simple approach breaks down, however, when the segment becomes tangential to the surface.

Instead, OrcaFlex uses a simple but effective modification of this concept. Rather than the centreline axis, we use the diagonal line joining the highest point on the segment circumference, at the 'dry' end, with the lowest point at the 'wet' end: the diagonal line in the figure below. As the segment passes through the tangent position, the diagonal line switches corners but the proportion wet varies continuously. The intersection of the diagonal line with the surface continues to give the appropriate proportion wet result, and the hydrostatic and dynamic forces are attributed correctly to the appropriate node.

This surface-piercing model enables OrcaFlex to model systems such as floating hoses, containment booms and wave suppression systems. You should be aware, however, that under this model a hose floats in still water as a wall-sided body; OrcaFlex does not take account of the variation in water plane area with draft that arises from the circular cross section. For practical dynamic systems, this simplification is of minor importance, but it does mean that if you check the immersion depth of a hose in still water you may find the answer slightly wrong if the hose is very buoyant, or just awash.

When modelling floating hoses, it is important to have enough segments to model the local curvature. If your hose is flexible, and the waves are short, then you will need at least ten and preferably twenty segments per wave to model the curvature properly. However a stiff hose tends to bridge the wave troughs, and fewer segments are required.

OrcaFlex requires constant drag coefficients for the floating hose, and you should select appropriate values based on the average immersion depth. Unfortunately the literature is of limited help – if you know of any good data source, we would be very pleased to hear of it.