FLUID-INDUCED STRUCTURAL FORCES
21
Nonetheless, the rigid body assumption may be warranted if oniy an estimate of
the overall dynamic stability of the platform-soil foundation System is needed.
Thus the choice of the mathematical model is strongly tempered by the particular goals of the analysis.
2.2 FLUID-INDUCED STRUCTURAL FORCES
There is a wealth of literature on the theory and measurement of forces on solid
bodies moving or at rest in dynamic fluid fields. An excellent critique of this
literature that extends back to the early nineteenth century and up to 1981 is
given by Sarpkaya and Isaacson (1981). The essential physical ideas and governing nondimensional loading parameters presently perceived as characterizing
these dynamic forces are now highlighted. Most of the following discussion is
limited to an isolated, fully submerged, right circular cylindrical solid for which
the incident fluid velocity is perpendicular to its longitudinal axis. In the plane
flow cases considered, shown in Figures 2.3 through 2.6, the fluid or cylinder
motion is in line with its net force per unit length, q. The fluid is assumed
to be incompressible, and for the présent, effects of nearby objects and solid
boundaries are not included. As restrictive as these assumptions may seem, the
results none the less demonstrate the basic ideas of fluid loading for a major
portion of offshore structures and their components, including pipelines, cables,
tubular structural members, and many types of submerged tanks and caissons.
Classical Inviscid Fluid Flow
One classical loading parameter is the inertie. coefficient, Cm, alternatively
denoted as C/ or G, a parameter that originated with hydrodynamics or the
theory of idéal, inviscid flow, formulated during the nineteenth and early twentieth centuries (Batchelor, 2000; Lamb, 1945). This coefficient relates the force
per unit length qr that is required to hold a rigid cylinder stationary in a fluid
of uniform, constant free stream accélération of magnitude û. That is,
D2
Qi 7 CM pir—û
(2.7)
where p is the fluid density and D is the cylinder diameter. Shown in Figure
2.3 is this case of unseparated, unsteady, idéal flow, together with values of Cm
for several ratios of cylinder length to diameter, t/D. These results, reported
by Wendel (1956), are based on theoretical values of another nondimensional
parameter, the added mass coefficient CA, defined by
CA =Cm-1
(2.8)
It is observed from the theoretical data in Figure 2.3 that as the cylinder length
becomes much larger than its diameter, the value of Cm approaches the limit
of 2, for which CA approaches unity by équation (2.8).
21
Nonetheless, the rigid body assumption may be warranted if oniy an estimate of
the overall dynamic stability of the platform-soil foundation System is needed.
Thus the choice of the mathematical model is strongly tempered by the particular goals of the analysis.
2.2 FLUID-INDUCED STRUCTURAL FORCES
There is a wealth of literature on the theory and measurement of forces on solid
bodies moving or at rest in dynamic fluid fields. An excellent critique of this
literature that extends back to the early nineteenth century and up to 1981 is
given by Sarpkaya and Isaacson (1981). The essential physical ideas and governing nondimensional loading parameters presently perceived as characterizing
these dynamic forces are now highlighted. Most of the following discussion is
limited to an isolated, fully submerged, right circular cylindrical solid for which
the incident fluid velocity is perpendicular to its longitudinal axis. In the plane
flow cases considered, shown in Figures 2.3 through 2.6, the fluid or cylinder
motion is in line with its net force per unit length, q. The fluid is assumed
to be incompressible, and for the présent, effects of nearby objects and solid
boundaries are not included. As restrictive as these assumptions may seem, the
results none the less demonstrate the basic ideas of fluid loading for a major
portion of offshore structures and their components, including pipelines, cables,
tubular structural members, and many types of submerged tanks and caissons.
Classical Inviscid Fluid Flow
One classical loading parameter is the inertie. coefficient, Cm, alternatively
denoted as C/ or G, a parameter that originated with hydrodynamics or the
theory of idéal, inviscid flow, formulated during the nineteenth and early twentieth centuries (Batchelor, 2000; Lamb, 1945). This coefficient relates the force
per unit length qr that is required to hold a rigid cylinder stationary in a fluid
of uniform, constant free stream accélération of magnitude û. That is,
D2
Qi 7 CM pir—û
(2.7)
where p is the fluid density and D is the cylinder diameter. Shown in Figure
2.3 is this case of unseparated, unsteady, idéal flow, together with values of Cm
for several ratios of cylinder length to diameter, t/D. These results, reported
by Wendel (1956), are based on theoretical values of another nondimensional
parameter, the added mass coefficient CA, defined by
CA =Cm-1
(2.8)
It is observed from the theoretical data in Figure 2.3 that as the cylinder length
becomes much larger than its diameter, the value of Cm approaches the limit
of 2, for which CA approaches unity by équation (2.8).