Page 147 - Pipelines and Risers

120 Chapter 9

9.2.2 Hydrodynamic Description
Reduced Velocity
For determination of velocity ranges where VIV may occur, the reduced velocity parameter,
VR, is used, defined as:

where:
U, current velocity normal to pipe
U, wave velocity normal to pipe
fo natural frequency of the span for a given vibration mode
D total outside diameter of the pipe including any coating or marine growth

Stability Parameter
The other main parameter controlling the motions is the stability parameter, K,, which is
given as:

where:
p is the sea water density
c T is the total modal damping ratio at a given vibration.

Damping
The total damping, c~, normally considered to comprise hydrodynamic damping, soil
is
damping and structural damping.

Hydrodynamic Damping
The hydrodynamic damping ratio accounts for the damping effect of the surrounding water.
Hydrodynamic damping is proportional to the water velocity, i.e. reduces to zero as the water
velocity tends towards zero. For VIV, the contribution to hydrodynamic damping within the
lock-in region is set to zero since damping is already included in the response model.

Soil Damping
Soil damping ratio is the contribution of the soil to the overall damping ratio of the pipe-soil
system. The soil damping is an end effect of the span therefore increasing the span length
reduces the overall effect to the total damping. The soil damping is larger for the inline
direction compared to the cross flow direction.