Environmental Engineering Reference
In-Depth Information
Fig. 2.42 Relative signi
cance of the various types of force [17]
Particularly interesting is the limit value of the inertia coefficient c
M
or c
M1
for k
a
!
0.
We can see from Figure 2.41 that for k
a
0.6, that is for D/
l
1/5, according
to potential theory, c
M
¼
c
M1
¼
2.0, that is c
a
¼
1.0, may be used in the calculations for
a good approximation! This result is identical with the assumption of a hydrodynamic
mass equal to the displaced mass of water, as is the case for an infinitely long cylinder in
an accelerated fluid unconfined in all directions.
Diffraction effects can therefore be ignored in the range D/
l
1/5. As on the other
hand in a real fluid the viscosity-related effects prevail in this range, c
M
depends on
factors that were dealt with in Section 2.6.2.
Diffraction effects have to be considered for D/
1/5, which for the cylinder consid-
ered here are covered analytically by the coefficients c
M1
,c
M
and b. As D/
l>
grows, so the
drag effects become less significant, which means that the potential theory calculation
results in a good approximation for large-volume, compact structures. The D/
l
l¼
1/5
limit is also the basis for the Morison formula evaluation shown in Figure 2.42.
For further information and examples please see [17].
2.6.6 Higher-order potential theory
Non-linearities in the behaviour of a marine structure or its components can, for
example, be caused by:
- viscosity-related unsteady drag forces,
- finite deformations,
