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Hydrodynamic Aspects of Flexible Risers H.J.J. van den Boom and F. van Walree, MARIN
Copyright 1990, Offshore Technology Conference
This paper was presented at the 22nd Annual OTC in Houston. Texas, May 7-10. 1990.
This paper was selected for presentation by the OTC Program Committee following review of information contained in an abstract submitted by the author(s). Contents of the paper, as presented, have not been revlewed by the Offshore Technology Conference and are subject to correction by the author@). The material, as presented, does not necessarily reflect any position of the Offshore Technology Conference or its officers. Permission to copy is restricted to an abstract of not more than 300 words. Illustrations may not be copied. The abstract should contain conspicuous acknowledgment of where and by whom the paper is presented.
For the evaluation of extreme loads and the assessment of the fatigue life of flex risers, use is made of discrete element models. Most of the models describe the fluid forces by means of empirical formulations using coefficients from 2-D cylinder tests. Recent research has shown that the fluid force modelling should incorporate lift forces perpendicular to the incoming flow. More- over, model tests on typical flex riser sections have proven that the 2-D cylinder formulations are not applicable and may lead to significant errors.
In this paper a new fluid model formulation is presented. This formulation is derived from both model tests and theoretical vortex simulations. Results of systematic drag tests for riser sec- tions are discussed. Capabilities of vortex simu- lation~ are evaluated.
Flexible risers have proven to be a key item for cost effective floating production systems. Most problems involved with the application of rigid risers, such as restricted horizontal floater motions and heavy and costly heave compen- sators, can be eliminated with the application of flexibles. Many flow lines have already been used in mild environments and for limited exposure times .
In harsh environments such as the North Sea, the large diameter and relatively stiff flexible risers for permanent floating production (Fig. l ) , require extensive design and engineering analysis.
Riser systems have to be evaluated for extreme conditions as well as fatigue life. To this end analysis of the dynamic behaviour of the riser system is of prime importance. Typical items of investigation are:
- extreme motions; - interference with mooring or other risers; - minimum bending radii; - end-connector loading; - dynamic tension; - dynamic torsion; - flow induced vibrations.
The motions of the riser and the fortes are primarily excited by floater motions, direct wave forces on the riser and by current. These exciting forces are counteracted by the riser-end fortes, the internal forces (bending, stretch and torsion) and the fluid reactive forces due to the riser motions relative to the water.
During the last four years several tomputa- tional methods have been developed for the analy- sis of the dynamic behaviour of riser systems. Discrete element techniques such as the Finite Element Method (FEM) and the Lumped Mass Method (LMM) are nowadays available for the design, engineering and operation of flexibles (see amongst others refs. [l] and [ 2 ] ) . These tech- niques utilize a spacewise discretization of the riser (Fig. 2) describing the relevant fortes on each of the elements and nodes. Knowing the forces and mass properties of each section the accefera- tions can be solved and numerically integrated to velocities and excursions.
Although in reality the fluid force-riser motion mechanism is both complicated and impor- tant, the fluid load models used in the discrete
References and illustrations at end of paper.
2 hYDRODYNAMIC ASPECTS OF FLEXIBLE RISERS OTC 6438
element methods are normally rather simple and in- accurate. The models are generally based on the well-known Morison approach using relative fluid velocities. Constant drag and inertia coefficients are derived from 2-D cylinder tests.
Flexible risers, though slender in overall dimensions, comprise 3-D curvature, subsea buoys, tethers and buoyancy beads in various shapes. These features provide 3-D flow ensuing not only large in-line drag forces but also lift forces perpendicular to the incident flow. Correlation studies [ 3 ] have clearly demonstrated that use of conventional 2-D cylinder data may lead to e.g. significant under estimation of tensions.
For slender pipe sections it is also well known that vortex shedding from the boundary layer around the cylinder results in non-stationary forces and hydroelastic response.
The Maritime Research Institute Netherlands (MARIN) at Wageningen is involved in the develop- ment of riser analysis tools such as DYNFLX [ 4 ] . As part of this R&D-work much attention has been paid to the mechanism and numerical modelling of the dominant fluid loads on flexible risers. In this paper a general review of the hydromechanic aspects of flexible risers is given. Furthermore an accurate description of drag forces on buoyancy bead sections as well as a practical model of non- stationary vortex induced forces are presented.
HYDROMECHANICS OF FLEXIBLE RISERS
Flexible risers are subjected to a complicated flow field generated by directionally spread ir- regular seas and current. The top-motions of the riser system can normally be considered as forced motions due to the large displacement of the floater (e.g. Floating Production and/or Storage Vessel). The riser is normally free to deploy large amplitude 3-D motions.
Such motions typically feature the following components: - Low frequency (period > 30 S) due to horizontal floater motions, changes in current etc.
- Wave frequency (2 < period < 30 S) due to wave induced floater motions at the top and the direct wave forces on the riser components.
- High frequency (period < wave period) due to vortex shedding, instabilities, production oper- ations etc.
The riser always operates in the vicinity of a floater such as an FPS. The floater disturbs the flow field due to the current flow around the vessel as well as wave diffraction by the vessel. Detailed diffraction analyses, however, have indicated that these disturbances are normally not relevant for the riser response.
The generally accepted description of the local flow along the riser is based on linear wave theory. Using direct summation, FFT or impulse response techniques  the orbital fluid veloci- ties and acceleration can be derived from the given wave elevation. Current velocity may be summed to the local orbital velocity components taking into account current profile and direction.
Relative fluid velocities are then derived by subtracting the local riser ('nodet) velocities from the absolute fluid velocities at that loca- tion.
The most widely used method to compute fluid forces on risers are based on the well-known Morison approach. This approach distinguishes an force component which is proportional to the fluid acceleration ('inertiat) and a component propor- tional to the relative velocity squared ('drag').
For stationary (e.g. current only) and for quasi-static (e.g. low frequency motions) the con- tribution of inertia components is negligible. The dynamic behaviour in these frequency ranges is often approximated by using damping terms only.
When looking to responses in the wave frequen- cy region, the inertia contribution in the fluid forces is often of minor importance. In survival conditions the wave energy is concentrated in the lower frequency region (periods > 10 S). Floater motion response normally also peaks in this region. Furthermore it should be noticed that the fluid inertia is often smaller than the inertia of the riser itself. Drag forces are therefore con- sidered to be dominant for the response of riser systems to extreme wave conditions.
Flexible risers are slender when compared to the water depth and the wave lengths of interest. When using a discrete element model for the analy- sis of such risers it can also be assumed that element length/wave length and element length/ water depth ratio's are small. This implicates that the dynamic drag forces may be approximated by stationary methods.
This evaluation clearly indicates that for the analysis of flexible risers in extreme wave condi- tions, a major obstacle of the Morison approach viz. a proper choice of the drag and inertia coefficient, can be by passed. Costly large scale forced oscillation tests with riser sections can be replaced by straightforward drag tests. In the following section this approach will be presented in detail.
For the dynamic response in the high frequency regions the above method is invalid, Though small in amplitude this type of response is of im- portance for fatigue analysis, flutterfstrumming
OTC 6438 VAN DEN BOOM AND VAN WALREE 3
vibrations and it may also be responsible for a significant increase of low frequency in-line drag.
Since the basic assumptions made for the description of the low frequency fluid forces are not valid, a more detailed evaluation is required here.
Time varying forces are caused by the periodic shedding of vortices from the boundary layer of cylindrical blunt bodies. Hydroelastic body oscil- lations can result from these non-stationary forces provided the internal structural damping is sufficiently low. The vortex shedding frequency then locks on to the natural frequency of the system. Motion amplitudes may increase to values of once to twice the characteristic body length. An important issue is the increa