An experimental investigation of the forces on cylinders in a steady current is reported. The damping of structures in calm water or currents is discussed in view of the experiments and it is concluded that the hydrodynamic damping based on Morisons formula may be strongly unconservative. Structures in waves are also discussed and the authors expect similar results for that case.
In the design of offshore structures dynamics is of paramount importance. This is true for floating structures, jackets and concrete gravity structures, and also for cables and risers and articulated platforms, tension leg platforms, guyed towers and so on.
To avoid excessive dynamic motions and stresses, jackets and concrete gravity structures are designed to have their fundamental period well below the period of the stronger wave action. Articulated platforms and tension leg platforms are designed to have their fundamental period well above the wave period. The dynamic equation for a linearized dynamic system in water may be written
Equation (1) (Available in full paper)
Here (mathematical symbols) are structural displacements, velocities and accelerations respectively, Mtot is structural mass plus added mass, Ctot is the damping matrix including hydrodynamic effects and Ktot is the structural stiffness matrix, including hydrodynamic; restoring coefficients. The external forces F do not contain any terms that depend on (mathematical symbols) since the left hand side of (1).
The critical term Ctot is usually calculated from an extension of the Morison formula in the form
Equation (2) (Available in full paper)
in which ftot is the force per unit cylinder length, u is water particle velocity, D the pile diameter and ? is the water density. Cd is assumed to be constant throughout the wave cycle and the structural cycle.
For very slow variations in u and on (mathematical symbols) the flow is quasi steady and (2) will make sense, though one may argue that Cd ought to be adjusted to the instantaneous Reynolds number. But the authors are not aware of any studies that justify formula (2) for more realistic cases in which u or on (mathematical symbols)varies relatively rapidly compared to the vortex shedding period. Neither do the published full scale measurements that the authors are aware of support it.
It may be beneficial to illustrate the importance of the damping estimates by means of an example. There are two reasons why a tension leg platform subjected to wind forces has been chosen for this example. One is that a fairly good estimate of its dynamic response may be obtained by quite simple means, and the other is that the resulting displacements are quite significant.
The following parameters have been assumed: The platform mass is m = 5?l0 7kg (= 50 000 t), the force in the tethers totals TO = 15 000 kN (= 15 000 t) and the exposed wind area is A = 2 500 m2.