deployment of an otec pipeline
279
where 4tt /T
cosh kn(z + d) 'y exp kn(z + d), d is the water
depth, g is the accélération due to gravity, and kn = u„/g.
The foregoing formulation of Morison’s équation was derived from laboratpry
tests of groupe of circulât cylinders in oscillatory flow. These tests showed that
whenever the ratio of cylinder diameter D to water wave length A exceeded 0.2,
the Kuelegan-Carpenter number is small, and the drag-related viscous term
becomes unimportant. In such cases, Morison’s équation (10.133) is no longer
correct since the flow field is modified by the presence of the cylinder. In such
cases, a diffraction analysis based on potential flow theory is used.
In the présent case of the OTEC pipe, this ratio D/X approaches 0.2 for
the shorter wavelengths in the wave excitation spectrum. Therefore, although
a diffraction analysis is not required, it is clear that the inertia term dominâtes
the excitation history. Separate calculations not included here indicate that the
drag-related term accounts for only about 10 percent of the maximum induced
loads. This observation was not particularly surprising since it is in agreement
with the results of other investigators, notably Hogben (1976) and Hogben and
Standing (1975). Therefore an attractive and obvious alternative, which is the
one employed here, is to neglect the drag term in équation (10.133) and at the
same time increase the remaining inertia term by 10 percent. The effect of this
approximation on pipe stability is negligible.
The excitations needed for solutions v(a:, t) of équation (10.123) are defined
by équations (10.127)-(10.134). The solutions lead to the bending moment responses given by
,U(z.t) = £/^
(10.135)
From these moments, the critical bending stresses are calculated using elementary theory.
For convenience, ail 25 System parameters for this OTEC pipeline System
are summarized in Table 10.2, together with typical numerical values used for
exploratory solutions. In a given océan location, the values of d, g and p remain
essentially constant. The remaining 22 parameters fall in the following four
categories:
Six wave height spectrum parameters: (A, B, N,ui,ijJn,i^p)
Five barge sway motion parameters: (Bq, c, ei>e2, wt>)
Nine pipe, restraint, and ballast parameters: (D, E, El. A, L, Mo,Mi- n, i )
Two wave-pipe interaction parameters: (Cju-Cp)
279
where 4tt /T
cosh kn(z + d) 'y exp kn(z + d), d is the water
depth, g is the accélération due to gravity, and kn = u„/g.
The foregoing formulation of Morison’s équation was derived from laboratpry
tests of groupe of circulât cylinders in oscillatory flow. These tests showed that
whenever the ratio of cylinder diameter D to water wave length A exceeded 0.2,
the Kuelegan-Carpenter number is small, and the drag-related viscous term
becomes unimportant. In such cases, Morison’s équation (10.133) is no longer
correct since the flow field is modified by the presence of the cylinder. In such
cases, a diffraction analysis based on potential flow theory is used.
In the présent case of the OTEC pipe, this ratio D/X approaches 0.2 for
the shorter wavelengths in the wave excitation spectrum. Therefore, although
a diffraction analysis is not required, it is clear that the inertia term dominâtes
the excitation history. Separate calculations not included here indicate that the
drag-related term accounts for only about 10 percent of the maximum induced
loads. This observation was not particularly surprising since it is in agreement
with the results of other investigators, notably Hogben (1976) and Hogben and
Standing (1975). Therefore an attractive and obvious alternative, which is the
one employed here, is to neglect the drag term in équation (10.133) and at the
same time increase the remaining inertia term by 10 percent. The effect of this
approximation on pipe stability is negligible.
The excitations needed for solutions v(a:, t) of équation (10.123) are defined
by équations (10.127)-(10.134). The solutions lead to the bending moment responses given by
,U(z.t) = £/^
(10.135)
From these moments, the critical bending stresses are calculated using elementary theory.
For convenience, ail 25 System parameters for this OTEC pipeline System
are summarized in Table 10.2, together with typical numerical values used for
exploratory solutions. In a given océan location, the values of d, g and p remain
essentially constant. The remaining 22 parameters fall in the following four
categories:
Six wave height spectrum parameters: (A, B, N,ui,ijJn,i^p)
Five barge sway motion parameters: (Bq, c, ei>e2, wt>)
Nine pipe, restraint, and ballast parameters: (D, E, El. A, L, Mo,Mi- n, i )
Two wave-pipe interaction parameters: (Cju-Cp)