Actions on wind turbines - Concrete Structures for Wind Turbines - page 56

gravity structures, pipelines, risers, cables, etc.). However, the evaluation of a large number
of measurements has revealed that the Morison formula in the above form can only be used
when its c M and c D coefficients are neither constants nor variables that are independent of
each other. It can be shown that the coefficients depend not only on the roughness of the
surface of the body but also on two dimensionless parameters. The latter are defined as
follows for a cylinder of diameter D acted upon by a primary wave:
- Reynolds number: Re ðÞ¼ u ðÞ D
n
- Keulegan-Carpenter number: N KC ðÞ¼ u ðÞ T
D

where
u ðÞ amplitude of orbital velocity at height z
T period

kinematic viscosity (1.3 10 6 m 2 /s at þ 10 C [27]) n

Applying the Morison formula in practice requires special care when it comes to
specifying the c M and c D coefficients. For further details of this topic please refer to [17].
Tables 2.12 and 2.13 can be used for practical applications. The critical parameters are
the Keulegan-Carpenter number at the still water level (z ¼ 0) and the description of the
properties of the surface of the structural member instead of the Reynolds number.

Table 2.12 Inertia coef cients c M for the Morison formula (after [24])

c M Surface finish of structural member

N KC (z ¼ 0) smooth rough

2 N Kc 6 2.0 2.0

6 < N KC < 30 linear interpolation

N KC 30 1.65 1.2

Table 2.13 Drag coef cients c D for the Morison formula (after [24])

c D Surface finish of structural member

N KC (z ¼ 0) a)

smooth rough

2 N Kc 6 0.65 1.05

<

N KC <

6 13 linear interpolation

N KC ¼ 13 0.85 1.50

13 < N KC < 30 linear interpolation

N KC 30 0.65 1.05

a) The drag term may be neglected when N KC <

2.