An excellent review can also be found in the doctoral thesis by (Halse 97), which is oriented to numerical simulations of VIV on circular cylinders. Although it is not the intention of this paper to produce another review on the subject, remembering some main aspects is deemed useful in the present context.
A particular condition possible to occur is the so-called lock-in vibration. Under a constant current a circular cylinder generates vortex at a frequency proportional to the fluid velocity. In the case of a flexible cylinder, when the vortex shedding frequency and the natural vibration frequency are close, the vibration frequency controls the shedding. This occurs for a range of incident velocity, as confirmed by laboratory experiments. The first paper reporting the observation of the lock-in phenomena has been presented by (Bishop and Hassan 64). In 1968, (Feng 68) has simulated the lock-in phenomena in a laboratory for a circular cylinder fixed to the earth by an elastic base in a transverse flow. Since then, a lot of papers have been written trying to bring more light to the matter. In his review paper (Pantazopoulos 94) shows that, for experiments similar to the Feng's test, in the frequency range where lock-in occurs, the added mass suffers an expressive change. (Khalak and Williamson 97) showed that in the lock-in range the vortex-shedding frequency is not exactly constant and tuned to the natural frequency of the cylinder. It depends on the mass ratio, which indirectly reflects the influence of the added mass on the natural frequency. These are just some aspects of the complexity involving the simulation of the fluid loads on the cylinder.
For the case of a cylinder exposed to a periodic flow in a non-lock-in condition (Berman, Obasaju and Graham 84) developed an empirical expression to represent the fluid forces based on experimental results. To consider the simultaneous influence of current, waves and the motions of the top connection point of the riser, (Ferrari 98) in his doctoral thesis heuristically has extended the expression obtained by Obasaju et al. in a quasi-three-dimensional form. (Sertã 99) has made use of a three-dimensional extension of the Ferrari-Berman's model. Although this seems to be a natural way to advance in the fluid load representation, it is still restricted to the case of non lock-in situations. Another approach for the structural analysis was adopted by Vandiver in the development of the computer program SHEAR 7 (Vandiver and Li 94), which seems to be the industry most popular analysis tool for VIV. Another available software is (LIC 94). They are both based on modal superposition models. The most complicated part of the analysis, the simulation of the forces induced by the fluid, is based on a series of empirical data. Experimental results and experience in the field are used to define added mass, damping and lift coefficients. It does not mean that the simulated behavior correspond exactly to what is physically happening, but in the average the damage caused by the vortex induced vibration is supposed to be taken into account. A limitation of SHEAR 7 is that the only source of excitation considered is current, but it is developed to analyze both the lock-in and the non-lock-in conditions. In the authors point of view the good use of those procedures are very dependent on the experience and good comprehension of the phenomena. Hence, the final results depend on the user's judgment.
When the analysis concerns to fatigue damage, a basic question arises: for how long lock-in occurs during the structure service life? (Vandiver 91) reports the observation of the lock-in phenomena in a 274 meters long cable exposed to pure current in a river. In a full three-dimensional situation of a riser in deep water (1000 meters or more) exposed to current varying in intensity and incidence with depth, to waves and the motions of the top connection, the probability of lock-in occurrence becomes very low.
FATIGUE ANALYSIS STRATEGIES
The API RP 2RD (API 98) establishes that all loads and load combinations that can contribute significantly to fatigue should be accounted to evaluate the riser final fatigue life. Additionally, this code states that fatigue damage caused by VIV should also be evaluated and combined. However, the ways to combine this fatigue damage with the damage coming from other sources are not clear. Actually, for combining the fatigue damage caused by VIV with the fatigue damage due to riser imposed motions and direct action of waves two strategies could be considered in the design process:
(i) Calculate the damage corresponding to each of these two parcels separately, and add up them to estimate the total damage.
(ii) Compute all cyclic loads to determine the resultant stresses caused by these parcels acting simultaneously, and then calculate the total damage.
When using the first strategy, one assumes that VIV and other cyclic loads are totally uncoupled, which is probably a non-realistic assumption. On the other hand, there is no available reliable-calibrated model (at least to the authors knowledge) that includes VIV and other dynamic excitations that can be used in a second strategy type methodology.
Figure 1 - Usual Riser Design Sequence for Fatigue Analysis (extracted from (Sertã et all 96))
Due to such difficulties, it has been usual to see fatigue methodologies similar to the one shown in the figure 1. In this case, one can see that the "VIV Analysis" is actually not part of the "Fatigue Analysis", but a different step of the design process. In the first one, only currents are considered as an excitation source for VIV. The fatigue caused by this loading is assessed and, if deemed significant, suppressors are considered to minimize it below a level for which it can be neglected. Then, the traditional "Fatigue Analysis" is performed, when the imposed motions (1st and 2nd order) and direct action of waves are taken as inputs. By doing like that, designer does not need to combine fatigue damage coming from VIV with the fatigue damage coming from other sources of loads, and neither strategy type (i) nor (ii) is used. However, in some cases this simplified design methodology may lead to VIV suppressors recommendation, while a design done using more accurate methodology would confirm they are not necessary.
In order to overcome these difficulties, a second type strategy methodology is proposed here. This is based on what could be called Ferrari & Bearman Model (Sertã 99) to take account of the hydrodynamic forces on the in-line and transverse directions of the flow simultaneously, as exposed next.
PROPOSED METHODOLOGY
The main highlights of the proposed fatigue design methodology are presented below.
