Tc 67/sc 4 n date: 2005-03-9 iso/wd XXXXXX ISO tc 67/sc 4/wg 6 Secretariat: Design of dynamic risers for offshore production systems Élément introductif — Élément central — Élément complémentaire  Warning


Superposition of waves and currents



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Superposition of waves and currents


The design events of a riser may include the presence of waves and current. Under the extreme wave condition, the flow condition should be classified as oscillatory flow (i.e., umax/Un > 1). The effect of the associated current is represented by the mean drag and augmentation of viscous damping. The kinematics of the incident flow should be modeled based on superposition of velocities of waves, current and riser motions. In the event that the direction of the incoming waves is not co-planar with the current or a directional sea state is prescribed, the flow field as well as the global response of the riser are three dimensional.

In some areas such as the Gulf of Mexico, the east coast of continents or the outlet of major rivers (where strong currents may occur without the presence of an extreme storm) or in areas such as the Andaman and South China seas (where internal waves i.e. solitons have been observed during the operating condition) the design events may include a strong current profile superimposed with a moderate sea state. Under this condition, the current is the dominant factor for the riser response. The effect of waves and vessel motions should be regarded as a perturbation of the flow velocity.


        1. Hydrodynamic interaction of dual or multiple risers



          1. Dual risers

This subject is concerned with the behavior of a trailing riser in the wake of a leading riser. Measured data suggests that if the spacing of the risers is too close, adverse effects due to a suction force may be developed between the risers, thereby increasing the possibility of physical contact of the two risers. In common practice, the mean clearance between two risers is determined by the interference coefficients Cd1 , Cd2 , CL1 , CL2 , where the subscripts 1 and 2 denote the leading and trailing risers respectively. For two equal size cylinders arranged in tandem, these coefficients are given as a function of the longitudinal and transverse spacings.24,25 For unequal size cylinders, the diameter ratio of the two cylinders is another important parameter for the interference coefficients.26,27 In general, the lift and drag coefficients for the trailing cylinder are less sensitive with respect to the change of the Re. The interference boundary is determined by the characteristics of the near wake of the leading riser. If the diameter of the leading riser is equal to or greater than the trailing riser, the surface roughness of the leading riser is the dominant parameter which dictates the characteristics of the near wake.

The fluctuation pressure in the wake of the leading cylinder may lead to hydroelastic instability such as galloping on the trailing riser.28,29 In order to address this problem properly, a thorough understanding of the wake flow is considered essential. The fluctuation force on the trailing riser is dependent on the variation of the following parameters:

  • longitudinal and transverse spacings (X/D1, Y/D1);

  • diameter ratio (D1/D2);

  • transverse oscillation amplitude of the leading cylinder (Ay/D1);

  • surface roughness of the leading cylinder (k/D1);

  • Re of the cross flow (UnD1/n).


          1. Multiple risers

Wake synchronization within a riser array can be a design issue30,31,32. In this case, the dynamics of the risers are coupled with the wake flow within the boundary of the array. The general practice for riser system design is to avoid the wake-induced instability problem by properly choosing the riser spacing.

      1. Load model


For the flow conditions addressed in 6.3.3.1, the general practice for modeling the hydrodynamic forces is based on the Morison formula. The formula was originally derived for calculating the hydrodynamic forces on shallow water fixed piles.33 Since the introduction of this formula, the offshore industry has extended its applicability to moveable structures, including risers. A modified form of the Morison formula is given by:

...(24)

The above formula is based on the following implicit assumptions:



  1. for the inertia force term, the diameter of the riser is small in comparison with the displacement of the relative motion between the fluid flow and the riser. The acceleration of the fluid flow is evaluated at the centerline of the riser. The higher order convective acceleration terms are neglected;

  2. the inertia, added mass and drag coefficients are time invariant. The time dependency of the hydrodynamic forces is modeled by unsteadiness of the incident flow and the body motion. The fluctuating lift and drag forces due to vortex shedding are neglected;

  3. the hydrodynamic forces are determined by the acceleration and velocity components normal to the riser centerline. The three dimensional effect due to the tangential component of the incident flow is ignored;

  4. the riser response is inline with the incident flow. The lift force is omitted.

A more precise definition of the inertia force can be made based on a Eulerian frame of reference by replacing the u/t term in Equation 24 with u/t + u u/x. However, if the hydrodynamic inertia force is evaluated by a coordinate system which moves with the riser, the u/t term should be replaced by u/t + (u -) u/x.

Derivation of higher order terms for the loading function is available in the literature.14,34,35 Since the Morison formula can be expressed in different forms, each form is associated with a set of coefficients for a specific flow condition. To maintain the accuracy of hydrodynamic loads, the Morison formula to be used in computer simulation must be consistent with that used for defining the hydrodynamic coefficients.


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