Environmental Engineering Reference
In-Depth Information
A 30m depth of water is assumed. In order to calculate the wave loads, the structure is
modelled as a panel model (Figure 2.48b) in a diffraction program based on the
boundary element method. As a comparison, the structure is modelled in another
program based on the Morison formula (Figure 2.48c). The inertia coefficient c
M
¼
2.0
and drag coefficient c
D
¼
0.7 are used again here.
According to the definition, the empirical Morison formula may only be applied to
cylindrical, slender elements. That results in a problem when modelling the conical
bottom segment of the structure. The only way of modelling this section is to consider it
as a series of short cylindrical segments, each of which has a diameter slightly larger
than the previous one.
The individual elements of the Morison model only supply hydrodynamic components
normal to the bar axis. Consequently, in contrast to the diffraction panel model, this
model cannot be used to calculate vertical forces nor their contribution to the pitch
moment M
y
. Linear wave theory states that the maxima of the vertical wave force
exhibit a 90
phase shift with respect to the maxima of the horizontal force. This and the
fact that our typical structure offers very much more horizontal than vertical surface on
which forces can act means that the errors in the Morison calculation - due to the
fact that the vertical components are ignored when calculating the maximum moment
M
y
- can be expected to remain small.
The hydrodynamic forces on the structure are calculated using linear wave theory and
for various wave periods [32]. The results plotted in Figures 2.49 and 2.50 show the
total hydrodynamic forces - again in relation to the values according to the Morison
formula - over the wave period T.
The diagrams show that the results obtained using the Morison formula are always
larger than those obtained using diffraction theory. The difference is largest for small
wave periods. The difference remains more or less constant for the larger wave
periods.
Fig. 2.49 Ratios of horizontal forces over wave period
