In this paper, we focus on the modeling of a fully-nonlinear, steep, irregular wave field of three-hour duration without structures in it. The fully-nonlinear effects are considered in the wave simulations using computational fluid dynamics (CFD), as well as potential theory. The overall approach for the numerical modeling is described in the paper. The Euler Overlay Method (EOM) is used to incorporate incoming waves, nonlinear effects, and CFD simulations in the numerical modeling. For computational efficiency, we also use potential theory to model the fully-nonlinear waves. Numerical damping was applied locally around the breaking region to enable simulations for large breaking waves. To compensate for energy loss in the numerical simulations, energy compensation factors of wave spectral frequency components are applied to the input wave spectrum. Results of convergence study, validation against high-order Stokes waves and fully-nonlinear irregular wave with prescribed target spectrum, as well as comparison between numerical wave crest distributions and those from multiple realizations of wave calibration tests are presented.
In wave basin model test of an offshore structure, waves that represent the given sea states have to be generated, qualified and accepted for the model test. We normally accept waves in wave calibration tests if the significant wave height, spectral peak period and spectrum match the specified target values. However, for model tests where the responses depend highly on the local wave motions (wave elevation and kinematics) such as wave impact on hull, green water impact on deck and air gap tests, additional qualification checks may be required. For instance, we may need to check wave crest probability distributions to avoid unrealistic wave crest in the test. To date, acceptance criteria of wave crest distribution calibration tests of large and steep waves of three-hour duration (full scale) have not been established. Two purposes of the work presented in the paper are: 1. to define and clarify the wave crest probability distribution of single realization (PDSR) and the probability distribution of wave crest for an ensemble of realizations (PDER) of a given sea state in order to use them appropriately; and 2. to develop semi-empirical probability distributions of nonlinear waves for both PDSR and PDER for easy, practical use. We found that in current practice ensemble and single realization distributions have the potential to be misinterpreted and misused. Clear understanding of the two kinds of distributions will help appropriate offshore design and production unit performance assessments. The semi-empirical formulas proposed in this paper were developed through regression analysis of crest distributions from a large number of sea states and realizations. Wave time series from potential flow simulations, computational fluid dynamics (CFD) simulations and model test results were used to establish the probability distributions. The nonlinear wave simulations were performed for three-hour duration assuming that they were long-crested. The sea states are assumed to be represented by JONSWAP spectrum, where a wide range of significant wave height, peak period, spectral peak parameter, and water depth were considered. Coefficients of the proposed semi-empirical probability distribution formulas, comparisons among crest distributions from numerical simulations and the semi-empirical formulas are presented in this paper.
In wave basin model test of an offshore structure, waves that represent the given sea states have to be generated, qualified and accepted for the model test. For seakeeping and stationkeeping model tests, we normally accept waves in wave calibration tests if the significant wave height, spectral peak period and spectrum match the specified target values. However, for model tests where the responses depend highly on the local wave motions (wave elevation and kinematics) such as wave impact, green water impact on deck and air gap tests, additional qualification checks may be required. For instance, we may need to check wave crest probability distributions to avoid unrealistic wave crest in the test. To date, acceptance criteria of wave crest distribution calibration tests of large and steep waves of three-hour duration (full scale) have not been established. The purpose of the work presented in the paper is to provide a semi-empirical nonlinear wave crest distribution of three-hour duration for practical use, i.e. as an acceptance criterion for wave calibration tests. The semi-empirical formulas proposed in this paper were developed through regression analysis of a large number of fully nonlinear wave crest distributions. Wave time series from potential flow simulations, computational fluid dynamics (CFD) simulations and model test results were used to establish the probability distribution. The wave simulations were performed for three-hour duration assuming that they were long-crested. The sea states are assumed to be represented by JONSWAP spectrum, where a wide range of significant wave height, peak period, spectral peak parameter, and water depth were considered. Coefficients of the proposed semi-empirical formulas, comparisons among crest distributions from wave calibration tests, numerical simulations and the semi-empirical formulas are presented in this paper.
This paper describes an analytical implementation of the component approach for motion predictions of a deepwater CALM buoy as described in the companion paper “Component Approach for Confident Predictions of Deepwater CALM Buoy Coupled Motions — Part 1: Philosophy”. The implementation of the approach starts with a “model-of-the-model” validation of the analytical tool. Emphasis is given to making an accurate analytical characterization of the model as tested. To capture the strong coupling between the buoy motions and line dynamics the analyses described herein were carried out in the time-domain. This allows a rigorous treatment of the hydrodynamic forces on the buoy as well as the non-linear mooring loads when analyzing the buoy responses in waves. Since the validation analysis is a model-of-the-model practice at model scale, the proper application of the validated tool to the full-scale system is discussed. This involves modeling of the exact full-scale system and the proper selection of the hydrodynamic coefficients for the buoy and lines. In this paper we will present the numerical modeling procedures and the results from validation work to confirm that the analytical tool is validated correctly. Detailed results from validation analysis versus model test data will be shown for system components including buoy hydrodynamics from the forced oscillation test, line tension from line oscillation test, and the motions and tensions of integrated buoy/mooring/riser system. We point out that the hydrodynamic coefficients at model scale can not be directly applied to the full-scale system analysis even though they are from model test measurements. We will present the difference between the results of the model-scale system using model scale hydrodynamic coefficients and those based on a proper range of the coefficients at full-scale. This will highlight the need to design component tests to determine appropriate full scale coefficients in order to improve the accuracy of full-scale design predictions. These results will show the advantages of adopting a component approach over the common industry practices in the areas of correct use of model test data, validation analysis and the analysis of the coupled CALM buoy system responses in waves.
For the design of offshore structures in harsh wave environments, model testing continues to be the recommended industry practice for determining wave impact forces on offshore structures. Accurate measurements of wave impacts in model tests have been a challenge for several decades. Transducers are required to accurately capture the short duration, high magnitude, and dynamic nature of impact loads. The structural model, transducers, and the transducer mountings need to be designed such that mechanical vibrations in the integrated transducer-mounting-structural model system do not contaminate the wave impact measurements. In this work, the dynamic oscillations in the measurements were controlled through the design and fabrication of transducers, their mounting and the GBS model. Wave crest probability distributions were developed that included fully nonlinear effects. These distributions were used as a benchmark to qualify the waves in the wave calibration tests. The highly stochastic nature of impact loads makes it challenging to obtain converged probability distributions of the maximum impact loads (i.e. forces or pressures) from model tests. To increase the confidence in the statistical values of wave impact loads, a large number of realizations were used for a given sea state. Variability of the maximum pressure due to wave basin effects (such as wait-time between tests) was examined with fifteen repeat tests using the same wave maker control signal. These tests provided insights into the random behavior of the impact loads.
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