Page 120 - Pipelines and Risers

Hydrodynamics around Pipes 93

L = Characteristic length (Diameter for pipelines)
v = Cinematic viscosity

The Keulegan-Carpenter number give information on how the flow separation around
cylinders will be for ambient oscillatory planar flow (U=UM sin((2n /T)t +E ))and is given as:

KC= - (6.33)
UMT
D
where:
UM = Flow velocity amplitude
T =Period
D =Diameter
E =Phaseangle
t =Time

The current flow ratio may be applied to classify the flow regimes:
(6.34)

where:
U, typical current velocity normal to pipe
U,c significant wave velocity normal to pipe given for each sea state (Hs, Tp, Ow)

Note that a = 0 corresponds to pure oscillatory flow due to waves and a = 1 corresponds to
pure (steady) current flow.
The presence of a fixed boundary near the pipe (proximity effect) has a pronounced effect on
the mass coefficient. The added mass will increase as the pipe approaches a solid boundary,
(see equation below).
(6.35)

where:
e / D is the gap ratio

The natural period of the pipe oscillation will increase as the added mass increases.

The roughness number (k/D) have a large influence on the flow separation and therefore also
on the drag and mass coefficient. (k = Characteristic cross-sectional dimension of the
roughness on the body surface).