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
Condition 3. Riser oscillating in waves
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Condition 3. Riser oscillating in wavesIn this case, the riser oscillation may be caused by the excitation of the waves and/or the movement transmitted from the surface vessel through the upper riser termination. The hydrodynamic loading function may be expressed in terms of a pressure force acting on the volume occupied by the riser, an added mass force due to the perturbation of the flow field by the motions of the riser and a drag force proportional to the square of the relative velocity of the riser and the incident flow. The velocity field of the ambient flow is typically expressed in a global coordinate system. Referring to the Eulerian frame of reference, the acceleration of the ambient flow is given by:  ...(19)
where DV/Dt denotes the material derivatives of the velocity vector V(x1, x2, x3, t) and Ñ denotes the gradient differential operator. The leading order term ¶V/¶t represents the acceleration of the unsteady flow evaluated at a fixed point in the flow field. The convective acceleration term  , which produces the second harmonics of the pressure force, is due to the non-uniformity of the wave particle motions. In order to calculate the hydrodynamic forces in terms of local coordinates, the transformation of the incident flow velocity and its derivatives requires the information of the instantaneous position and direction cosines of the riser's longitudinal axis.
Introducing the velocity components (u, v, w) of the incident flow in the body-fixed local coordinate system (x, y, z) as shown in Figure 34, a higher-order convective term due to the interaction of the riser's rotational motions and the tangential velocity component (w) of the incident flow can be expressed14 as (u -  ) ¶w/¶z - w ¶/¶z. This high order term is often omitted in riser analysis because its magnitude is within the error bound of the leading order term CarA. Thus, unless a higher degree of accuracy is provided for the added mass coefficient Ca, the overall accuracy of the hydrodynamic forces may not be improved by including this term in the computation.
In general, the diameter of a riser is small in comparison with the displacement of wave particle motions, and it suffices to evaluate the pressure force based on the acceleration of the incident flow at the longitudinal axis of the riser. Care must be taken if the riser diameter is large enough such that Du/Dt can no longer be treated as a constant over the riser cross section. Under this condition, Du/Dt should be taken as an averaged value over the cross section, at each time step. Within the context of viscous fluid flow, the perturbation pressure force due to the presence of a stationary cylinder in waves is in general not equal to the added mass force of an oscillating cylinder in calm water; even though the respective KC numbers are identical. Except for the following two limiting cases, the principle of flow superposition is not applicable for evaluating the fluid forces. Case 1: At low KC number (KC < 5 or the relative displacement less than one), the fluid motion can be described by potential flow. The classical solution indicates that the perturbation term of a stationary cylinder is equal to the added mass term of an oscillating cylinder. Case 2: At high KC number (KC > 90, or the relative displacement greater than 15), the flow condition reaches post-critical steady-state. The fluid forces would be practically the same regardless whether the body or the fluid is moving. For these two limiting cases, it is valid to set Ca=CM - 1 and the inertia and added mass terms become rADu/Dt+(CM-1)rA(Du/Dt- ), in which the coefficient CM can be referred to the value for a stationary cylinder.
For the intermediate KC numbers, it is appropriate to express the inertia and added mass terms in the following form: CMrADu/Dt-CarA  , where the coefficients CM and Ca are to be obtained in conjunction with the variation of four independent parameters: (1) the phase angle between and u, (2) the motion amplitude (Ax/D), (3) the KC number based on the maximum wave particle velocity normal to the riser axis (umax T/D), (4) the ratio of Re to KC numbers (Re/KCºb). In other words, the fluid forces are determined by the history of the relative motions between the fluid and the riser. Until such a data base for the relative motions of a cylinder in waves is developed, the value of CM, Ca and Cd may be determined by linear interpolation of the coefficients as obtained for the two limiting cases. See Table 4. Note that this will result in Ca= CM -1 for all KCs. The KC number to be used for interpolation should be based on the maximum relative velocity and Tp. Such a crude approximation would not lead to significant error for the total loading of a drag dominant flow regime at high KC number.
The actual added mass and drag coefficients may change from one cycle to another in a random sea because of the rapid change of the flow field. The use of time invariant CM , Ca and Cd to close-fit a force measurement record leads to the filtration of the time-varying components in these coefficients. As an engineering approximation, this approach preserves only the leading order quantities of the hydrodynamic loads. In random waves, the vortex induced lift forces are less significant than those measured under two-dimensional sinusoidal flow conditions, and they are not correlated along the riser length. Because of this nature, these forces are neglected in riser analysis. Directory: standards standards -> Request for proposal contract form for the transit industry standards -> Indiana Academic Standards Resource Guide Grade 8 United States History – Growth and Development (to 1877) Updated April 2016 standards -> Us history Dictionary Based on the sc state Standards standards -> Integrating Standards Education into the Business School Curriculum standards -> Use of Sprint U301 3G/4g mobile Broadband usb device Installation standards -> International organisation for standardisation organisation internationale de normalisation standards -> Standards of Excellence standards -> Common Core State Standards for Mathematics (ccssm) Download 2.34 Mb. Share with your friends:
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