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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- Wave spreading
- Wave profile and kinematics
- Wave spectrum discretization
- Wave directionality
- Regular waves
Hydrodynamic ConsiderationsWavesSea StateSite specific environmental data should be used for the design and analysis of a marine riser. The environmental conditions should be based on a suitable combination of simultaneous wind, waves and current profile likely to occur at various headings for a specified return period. In general, the maximum values of wind, wave and current do not occur simultaneously during a storm (see API RP 2A-LRFD). The return periods for waves and current should be specified. The effect of wind on riser stresses and displacement may be accounted for indirectly through the simulation of wind-induced vessel offset and slow drift movement. For a fully developed sea, a common practice is to represent the waves by the two-parameter Pierson-Moskowitz spectrum.2 For fetch-limited areas where the wave energy is concentrated in a more narrow frequency band, the JONSWAP spectrum should be considered.4 In the calculation of moments of the spectrum, a cutoff frequency three times the spectral peak frequency is recommended. This cutoff will substantially reduce the zero-crossing frequency defined as the square root of the ratio of the second-and zeroth-moments of the spectrum. The results using a cutoff frequency are in closer agreement with time-domain, zero-crossing analyses. The joint probability of occurrence of the significant wave height Hs and the mean zero crossing period TZ (or peak period Tp) is typically presented in a wave scatter diagram. Corresponding to a significant wave height in the scatter diagram, one may identify a number of sea states with different TZ. Accordingly, a family of wave spectra can be prescribed to determine the effect on riser response due to the variation of TZ. For riser fatigue analysis, the wave scatter diagram also provides the source information for deriving the total number of wave counts. Wave spreadingRiser analysis has usually been conducted based on assuming a uni‑directional sea. The effect of directional spreading can be considered as a sensitivity check in the design process. The directional spectrum is given by: S (w, q) = S (w) G (q) = S (w)  cos2n (q ‑ qo) ... (13)
where S (w) = Spectral density function, qo = Main direction of the waves, |q -qo|= 
G = Gamma function. 
The value of n should be chosen in such a way that Equation 13 will best fit the area wise wave data (see API RP 2A). Wave profile and kinematicsThe wave profile of a random, 2-dimensional sea can be represented by field measurement data or by means of synthesis of a wave spectrum. A common practice of modeling the wave profile is based on a combination of linear (Airy) waves with random phases: h(t) =  Ancos(knx-wnt+en) ...(14)
where An = Wave amplitude, obtained from the wave spectrum, S(wn) wn = Discretized frequency, en = Random phase distributed between 0 and 2p , kn = Wave number associated with frequency wn, N = Total number of discretized frequency bands. In realistic sea conditions, the wave amplitude as a function of frequency is a random and variable quantity. When attempting to match a target spectrum, each discrete wave amplitude An should be generated from a Rayleigh distribution with the expected value of [2S(wn)Dw]½ and the corresponding random phase en from a uniform distribution between 0 and 2p.3 However, normal practice is to use the expected value. The wave profile in Equation 14 is consistent with the general approach used to simulate the motions of the FPS. The velocity field induced by the incoming waves Equation 14 is determined by the gradient of the associated velocity potential. The presence of the FPS may lead to local disturbances in the wave field. Such disturbances are caused by wave diffraction and radiation from the vessel. The hydrodynamic forces acting on the vessel are usually obtained by integrating the pressure of the combined wave field. 4 The calculation of hydrodynamic forces on a riser is in general based on the kinematics of the incoming waves. Wave kinematics can include contributions from the diffraction and radiation wave potentials induced by the vessel, but non-linear waves can only be handled wave-component by wave-component. Nonlinear aspects of steep waves should be considered for calculating the impact velocity on the riser. Technology for modeling the higher-order dispersion of irregular waves in the time-domain includes the use of the third order Stokes wave theory and the Green-Naghdi theory of fluid sheets. 5,6,7 In practice the use of linear wave theory is sufficiently accurate in determining the kinematics (velocity and acceleration field) of incoming waves. At the free surface level, simple techniques like the linear (Wheeler) stretching of the Airy potential to the actual wave elevation can be applied (API RP 2A-WSD, Commentary on Wave Forces). Wave spectrum discretizationSince the flexural periods of a riser may be located in the wave frequency range, a sufficiently large number N of the discretized wave frequencies should be used to generate sufficient wave energy at and around the resonant frequencies. The effect of multi-directional waves should be accounted for during the fatigue analysis of a riser. The operational wave conditions should be specified on an annual basis in which the probability of occurrence of the significant wave height is distributed at various headings. Riser clearance should be determined by the most severe condition for each sector. Regular wavesA traditional approach for designing a shallow water riser is based on regular waves. The wave height is normally set equal to the maximum height of the design sea state. The types of wave profile to be chosen may range from Airy waves to higher order Stokes waves. Such an approach is valid if the riser response to the sea state is quasi-static. More sophisticated analytical techniques such as spectral analysis in the frequency domain or time-domain simulation with irregular waves should be considered if the natural periods of the riser are within the frequency range of the wave spectrum. This is usually the case with deepwater risers. 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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