Page 121 - Pipelines and Risers

94 Chapter 6

There is a connection between the VIV (Vortex-Induced Vibrations) and the drag force. A
crude approximation can be given as:
CdCw = 1 + 2(AZ/D) (6.36)
where:
CD = Drag coefficient with VIV
CW = Drag coefficient with no VIV
AZ = Cross-flow vibration amplitude

This formula can be interpreted as saying that there is an apparent projected area D+2Az due
to the oscillating cylinder.

6.5.2 Hydrodynamic Lift Forces
Lift force using constant lift coefficients
The lift force per unit length of a pipeline can be calculated according to:
1 2
p
Vertical lift force, FL = - D C v, (6.37)
2
where:
CL = Lift coefficient for pipe on a surface.
v,, = Transverse water particle velocity ( perpendicular to the direction of the lift force).
p = Density of seawater.
D = Total external diameter of pipe.

Lift force using variable lift coefficients
As can be imagined, the hydrodynamic lift coefficient (CL) will vary as a function of the gap
that might exist between the pipeline and the seabed. It can be seen from Figure 6.7 that a
significant drop in the lift coefficient is present even for very small ratios of em. This is true
both for the shear and the shear-free flow.

The lift coefficients according to Fredsae and Sumer (1997) are given in Figure 6.8.