Gro Sagli Baarholm

Estimation of nonlinear long-term extremes of hull girder loads in ships

Abstract This paper deals with a estimation of long-term extreme value for a given return period, say D=100 yr . In principle, this response is obtained by combining the response in all the sea states. The long-term response for a linear system can be effectively obtained by determining the response for each sea state, specified by the significant wave height, H s , and the peak period, T p , in the frequency domain. However, if the response is nonlinear, time domain simulation and a long time series would be required, to limit statistical uncertainty. Therefore, the long-term analysis becomes rather complicated and time consuming. For the long-term analysis, it is crucial to introduce ways to improve the efficiency in the calculation. In this work, it is shown that, the long-term extremes can be estimated by considering only a few short-term sea states. A long-term analysis based on identifying the most important sea state, defined by the coefficient of contribution, using linear analysis is applied. An iteration procedure is thereafter used to find the nonlinear long-term extreme values. It is concluded that only a limited number of sea states is necessary to get an acceptable estimate of the nonlinear D -year response as long as the most important sea states are included, i.e., the sea state with the maximum coefficient of contribution.

Wave Sector Dependent Contour Lines

This paper is concerned with estimating the response value corresponding to given annual exceedance probability. In principle, this requires that a full long term analysis is executed. For a linear response this can easily be done. For a non-linear response quantity however, where time domain simulations are required in order to obtain the short term stochastic structure a full long term analysis will be time consuming. An approximate method to determine the long-term extremes by considering only a few short term sea states is outlined. All sea states corresponding to a certain probability of occurrence and are given by a contour line of Hs , Tp for each wave direction. The advantage of the method is that a proper estimate of the long term extreme can be obtained by considering the most unfavourable sea state along the contour line. This will make possible practical estimation of the extreme loads the structure is exposed to. The purpose of the present paper is to illustrate how to apply directional contour lines in order to obtain a characteristic design value according to requirements regarding the marginal exceedance probability.Copyright

Simplified Model for Evaluation of Fatigue From Vortex Induced Vibrations of Marine Risers

This paper presents a novel approach for approximate calculation of the fatigue damage from vortex-induced vibrations (VIV) of marine risers. The method is based on experience from a large number of laboratory tests with models of full-length risers, large-scale tests and also full-scale measurements. The method is intended to provide a conservative result and be used for screening purposes at the early design stage. The model is in particular aimed at predicting fatigue for risers that respond at very high mode orders (above 10), but may as well yield valid results for lower mode numbers. The model will, however, not be adequate for free span pipelines or other structures that normally will respond at first and second mode. The riser will be defined in terms of some key parameters like length, weight, tension, hydrodynamic diameter and stress diameter. A current profile perpendicular to the riser in one plane must be known. The program will apply a simple model for calculation of eigenfrequencies and mode shapes, and these are sorted into in-line (IL) and cross-flow (CF) bins. An effective current velocity and excitation length can be defined from the profile and will be applied to identify the dominating cross-flow response frequency and the total displacement rms value. The dominating in-line response frequency is taken as twice the cross-flow frequency, and inline response rms is taken as a given portion of the cross-flow rms value. A set of contributing modes is defined from an assumed frequency bandwidth that reflects observed bandwidths, but also modal composition for cases with discrete frequency response. A simple mode superposition technique is then used to find the set of modes that gives the identified rms values. Bending stresses will be found directly from the curvature of the mode shapes. Fatigue damage will be found from stress rms values, user defined stress concentration factor and given SN curves. The model has been implemented in a simple computer program and verified by comparing results to measurements. The ambition has not been to obtain an exact match between computed results and observations, but to verify that the model gives reasonable but conservative results in almost all cases. However, an unrealistic over prediction of the fatigue damage is not desired. The results are promising, but the need for more information from measurements and response analyses with programs like VIVANA and SHEAR7 is still obvious.Copyright

Application of Environmental Contour Lines on a Flexible Riser

This paper is concerned with estimating the response value corresponding to an annual exceedance probability. In principle, this response needs to be obtained by combining the response statistics in all sea states and wave headings. The probability distribution for a given sea state and wave direction, specified by the significant wave height, Hs , the peak period, Tp , and wave direction, β, can be obtained by frequency domain analysis for linear response. Time domain simulations are, in general, required to obtain the stochastic structure of a non-linear response quantity. To limit the statistical uncertainty, the time domain simulations must be sufficiently long. Therefore, a simplified method is necessary to improve the efficiency of the direct calculation of the long-term response value in the non-linear case. A method to determine the long-term extremes by considering only a few short term sea states is outlined. The sea states have a certain probability of occurrence and are identified by a contour line in the (Hs ,Tp ) plane. This will make possible practical estimation of the extreme loads the structure is exposed to. The contour line approach is merely suggested as a method for predicting load- and response maxima corresponding to a given annual exceedance probability without having to carry out a full long term analysis. The advantage with this concept is that the environmental and response analysis is decoupled. This is very convenient if the problem under consideration is of a very non-linear nature — in particular if characteristic values for design are to be established directly from model tests. The method is an approximate method, but seems to give results of reasonable accuracy for most problems. The purpose of the present paper is to present the contour line method applied to estimate responses on a flexible riser, lazy wave configuration, located in the North Sea.Copyright

Influence From Helical Strakes on Vortex Induced Vibrations and Static Deflection of Drilling Risers

Helical strakes are known to reduce and even eliminate the oscillation amplitude of vortex induced vibrations (VIV). This reduction will increase fatigue life, and also reduce drag magnification from cross-flow vibrations. But sections with strakes will also have a larger drag coefficient than the bare riser. Hence, the extension of a section with strakes along a riser should be large enough to reduce oscillations, but not too long in order to limit drag forces from current and waves. The optimum length and position for a given riser will therefore vary with current profile. Dynamic response from waves should also be taken into account. The purpose of the present paper is to illustrate the influence from strakes on VIV, as well as on static and dynamic response for a drilling riser. Hydrodynamic coefficients for a cylinder with helical strakes are found from experiments and applied in an empirical model for the analysis of VIV. The result from the VIV analysis is used for a second calculation of drag forces that are applied in an updated static analysis. Dynamic stresses from regular waves are also presented, but VIV are not considered for these cases. A simple study of length and position of the section with strakes is carried out for some standard current profiles. Results are presented in terms of oscillation amplitudes, fatigue damage, bending stresses and riser angles at ends. The study is based on test data for one particular strake geometry, but the analysis method as such is general, and the computer programs used in the study can easily apply other test data.Copyright