structure the magnitude of the response depends critically on the damping level and viscous effects may make a significant contribution to this damping. Estimates of damping coefficients are required to predict both surge and heave motions. Here we will present some direct measurements of the viscous damping of components of TLP hulls obtained by displacing them and recording their decay in still water. By appropriately combining these it should be possible to approximate the damping of a complete hull. It is intended to check the accuracy of this procedure by also measuring the damping of a model of a TLP hull.
In reality, of course, the fluid is always viscous and the damping is just that part of the total loading that happens to be in phase with the structure velocity. When a structure is excited into oscillation by wave forces is it permissible to predict the response using damping levels obtained in still water? Sarpkaya (1) has expressed a similar concern about this approach and states “damping is used to lump into one parameter our inability to solve the fluid-structure interaction problem”. However, until we are able to solve satisfactorily this interaction problem designers will need estimates of damping. Hence damping values, expressed in terms of drag coefficients, will be presented in this paper.
When considering the damping of TLP hulls in real seas the relative motion between the water and the structure is considerably more complex than the harmonic motion considered in simple decay tests. The relative flow has three components which in the general case are not collinear. These motions are due to waves, currents and the response of the structure. The wave motion may excite response of the structure in three distinct frequency ranges appropriate to slow drift response, wave response and springing response. There is evidence available to suggest that damping due to a current and waves, together with response in surge, can be dealt with by the relative motion form of Morison's equation, provided there is no resonance with vortex shedding. The heave response in the springing mode is characterised by relatively high frequencies and very small motions and it may not be appropriate to lump this motion together with the others into Morison's equation. One possibility is that it may act independently within a much slower varying velocity field. It is clear that there are many outstanding questions surrounding the concept of hydrodynamic damping. However, the study of viscous effects for small amplitude oscillatory motion is in itself an interesting subject and some new results, and perhaps some fresh understanding, may result from our experiments.
Assuming that the fluid loading on an oscillating body can be described by Morison's equation then the hydrodynamic damping is related to the drag term in this equation. It can be shown, see for example Bearman and Mackwood (2), that the logarithmic decrement of damping, δ, is related to the drag coefficient of a body, CD, through the relationship:
In this expression ρ is water density, D a length scale used in CD (in the case of a circular cylinder it would normally be the diameter), KC is Keulegan Carpenter number and m is the effective mass per unit length of the body. KC is defined as UT/D, where U is the maximum velocity of the body relative to the water during a cycle and T is the period of oscillation. For harmonic motion KC can be defined as 2πA/D, where A is the amplitude of oscillation.
The viscous drag coefficient is composed of a skin friction component and a component related to the pressure force on the body. For circular cylinders, at KC values of order unity or less the contributions from pressure and skin friction are of a similar magnitude. However, at higher KC numbers separation occurs and the drag coefficient, and hence damping, is then dominated by the pressure component. Mooring lines, tethers and risers experience large motions relative to their diameters and hence their KC numbers are also large and in a range where there is considerable data available on drag coefficients. Apart from large amplitude slow drift oscillations, the flow around hulls is characterised by small KC numbers and is in a regime where there is sparse information on CD values that can be applied with confidence to full scale structures.
In the case of TLP hulls viscous damping arises from flow about the vertical columns and from the pontoon. The columns are usually circular whereas the pontoon may be constructed from square or rectangular section with various degrees of corner rounding. The damping level is dependent on characteristics of the boundary layer flow and on whether separation occurs from the circular members