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
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- Equivalent static load
- Vortex induced fluctuating loads
- Spanwise correlation
- Effect of riser oscillation
- Vortex induced loads on flexible risers
Static loadFigure 35 shows the drag coefficient of a stationary smooth circular cylinder in four flow regimes as a function of the Re. The occurrence of drag force is a result of pressure deficit at the downstream side of the riser cross section. In subcritical Re flow, the drag coefficient is in the range of 1.0 to 1.2. Scattered data had been found in the supercritical flow regime in which the flow field and pressure fluctuation are sensitive to small external disturbance. Accordingly, a conservative approach should be taken to estimate the drag force by using the upper bound value of Cd. In the critical flow regime, transition of boundary layer may occur on only one side of the riser cross section. The corresponding asymmetric flow pattern is accompanied with a sizable steady lift force.15 Outside the critical flow regime, the steady lift force is less significant, and therefore it is often neglected in riser analysis. Equivalent static loadThe slow drift movement of the surface vessel can induce a quasi‑steady current load on the attached riser. For time-domain simulation, the vessel slow drift movement should be prescribed as the boundary condition at the attachment point of the riser. For frequency-domain simulation, however, the effect of slow drift movement is approximated by an equivalent static current load on the riser. If a background current is also included in the frequency domain simulation, the combined static load should be computed based on the superposition of velocity vectors of the current and slow drift movement at the mean position of the riser. Vortex induced fluctuating loadsIn the subcritical flow regime, the vortex induced hydrodynamic forces are concentrated in a narrow bandwidth of frequency. The dominant vortex shedding frequency is represented by the Strouhal number (St) which is in the range of 0.18 to 0.2. The phenomenon of alternate shedding of vortices over the cross section of the riser, leads to the coupled dynamic lift and drag forces. One cycle of lift oscillation corresponds to two cycles of drag. The probability density of the lift fluctuation should be approximated by a Gaussian distribution.19 The coefficients for the mean and fluctuating lift and drag forces are defined by the following relationship:  ...(20)
 ...(21)
 ...(22)
 ...(23)
In some references, the standard deviation s() is represented by the root-mean-square value.20 The variations of CL and Cd for a smooth stationary circular cylinder are reproduced in Figure 36. In the critical flow regime, vortex shedding is dominant on one side of the riser cross section. The wake is less organized after the occurrence of boundary layer transition. Scattered values for the Strouhal number (see Section 6.9) were found in the range of 0.2 to 0.45.21 In supercritical Re flow, the fluctuation of pressure is stochastic in nature. The characteristics of the near wake is strongly dependent on the turbulent intensity in the boundary layer. For a smooth circular cylinder, the wake is disorganized but not fully mixed with turbulence. The spectra of the lift and drag fluctuation may demonstrate multiple distinct energy bands. Because of this nature, the lift and drag should not be characterized by a single frequency. In the high end of the supercritical flow regime, the boundary layer would have gone through another stage of transition.19 It is believed that a hysteresis process may exist in this flow regime. After this flow regime, the phenomenon of regular vortex shedding reappears in the turbulent wake.15 Spanwise correlationThe correlation of vortex formation in the spanwise (i.e. axial) direction is an important factor contributing to the low frequency component of the hydrodynamic forces. For the time being, the subject remains a research topic. Observed data suggests that the spatial‑temporal perturbation of the excitation forces would lead to the modulation of amplitude and frequency (i.e. beats) for the lift forces over a finite segment of a cylinder.19 The coupled drag force consists of both a low frequency component corresponding to the beat frequency of the lift force and a high frequency component corresponding to the vortex excitation. Effect of riser oscillationThe oscillation of the riser has a tendency to change the characteristics of the surrounding flow. The spanwise correlation of vortex formation can be enhanced due to small amplitude transverse oscillation of the riser. The phenomenon of vortex formation in the near wake, as well as the added mass and damping coefficients of the riser cross section, are governed by three dimensionless parameters including the amplitude ratio (Ay/D), the reduced velocity (Un/fD) and Re.22 When the vortex shedding period is close to one of the flexural bending periods of the riser, the lock‑on condition is likely to occur. Under this condition, the dynamic equilibrium can be described by a closed feedback loop in which the hydrodynamic excitation, added mass and damping are dependent on the response amplitude of the riser. The oscillating amplitude tends to be self-limiting as a consequence of the dynamic interplay of the fluid‑structure interaction. The vortex shedding frequency is locked onto the nearest modal frequency of the riser. Corresponding to a non‑uniform current profile, the vortex shedding frequency is not a constant along the riser. Accordingly, the lock‑on phenomenon may not occur on the whole length of the riser. Outside the lock‑on region, the oscillatory drag forces contribute to the viscous damping. The interaction of the riser oscillation and the near wake is imposed implicitly in the added mass and damping coefficients. It should be pointed out that the value of the added mass and damping coefficients for in‑line and transverse oscillations may not be identical due to the asymmetry of the flow pattern. Furthermore, the transverse oscillation of the riser can also change the mean drag forces. For the lock-on condition, the augmentation of the mean in-line drag is in the range of 1.0 to 3.0 times or even higher in some cases in comparison with a stationary cylinder.23 The mean in-line drag coefficient of an oscillating cylinder should be deduced in conjunction with either measurements or numerical simulation of the hydrodynamic forces. Vortex induced loads on flexible risersThe effects of vortex-induced vibration on flexible risrs should be checked in a particular case. See API RP 17B for further explanation. 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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