System Identification Techniques for Prediction of Fluid Accelerations Under Irregular Waves Based on Free-Surface Elevation Measurements

2002 ◽  
Author(s):  
Witold Cies´likiewicz ◽  
Ove T. Gudmestad
Keyword(s):  
Time Series ◽  
Particle Acceleration ◽  
Free Surface ◽  
System Identification ◽  
Surface Elevation ◽  
Irregular Waves ◽  
Free Surface Elevation ◽  
Acceleration Time ◽  
Wave Kinematics ◽  
Identification Techniques

A parametric model linking the free-surface elevations with the fluid acceleration field under an irregular wave is developed. In order to estimate the parameters of the model, system identification procedures are applied based on data recorded in a wave tank. The free-surface time series are taken as input data and the output data are components of the particle acceleration vector. The particle acceleration time series were obtained by taking the numerical derivative of the measured orbital velocity time series. A simple algorithm of numerical diffrentiation is proposed. This algorithm gives very accurate values of the particle acceleration and is quite straightforward as the derivative is computed directly in time domain. A linear time-invariant model with the static nonlinearities incorporated at the input side is assumed. This paper demonstrates the results of modelling the horizontal component of the particle acceleration in comparison with the time series calculated from wave kinematics data taken in a wave flume during an earlier experiment using Laser Doppler Velocimetry. The modelled particle acceleration time series compare well with those calculated from the observed velocity time series. This proves the effectiveness of the applied approach. The system identification techniques allow for preparing the model which constructs the wave kinematics (both velocities and accelerations) using the measured time series of only the free-surface elevation. This feature of the proposed approach may be very useful in maritime engineering and oceanography.

scholarly journals Free Surface Reconstruction for Phase Accurate Irregular Wave Generation

2018 ◽  
Vol 6 (3) ◽  
pp. 105 ◽  
Author(s):  
Ankit Aggarwal ◽  
Csaba Pákozdi ◽  
Hans Bihs ◽  
Dag Myrhaug ◽  
Mayilvahanan Alagan Chella
Keyword(s):  
Free Surface ◽  
Surface Reconstruction ◽  
Deep Water ◽  
Time Domain ◽  
Present Approach ◽  
Surface Elevation ◽  
Irregular Waves ◽  
Free Surface Elevation ◽  
Irregular Wave ◽  
The Time Domain

The experimental wave paddle signal is unknown to the numerical modellers in many cases. This makes it quite challenging to numerically reproduce the time history of free surface elevation for irregular waves. In the present work, a numerical investigation is performed using a computational fluid dynamics (CFD) based model to validate and investigate a non-iterative free surface reconstruction technique for irregular waves. In the current approach, the free surface is reconstructed by spectrally composing the irregular wave train as a summation of the harmonic components coupled with the Dirichlet inlet boundary condition. The verification is performed by comparing the numerically reconstructed free surface elevation with theoretical input waves. The applicability of the present approach to generate irregular waves by reconstructing the free surface is investigated for different coastal and marine engineering problems. A numerical analysis is performed to validate the free surface reconstruction approach to generate breaking irregular waves over a submerged bar. The wave amplitudes, wave frequencies and wave phases are modelled with good accuracy in the time-domain during the higher-order energy transfers and complex processes like wave shoaling, wave breaking and wave decomposition. The present approach to generate irregular waves is also employed to model steep irregular waves in deep water. The free surface reconstruction method is able to simulate the irregular free surface profiles in deep water with low root mean square errors and high correlation coefficients. Furthermore, the irregular wave forces on a monopile are investigated in the time-domain. The amplitudes and phases of the force signal under irregular waves generated by using the current technique are modelled accurately in the time-domain. The proposed approach to numerically reproduce the free surface elevation in the time-domain provides promising and accurate results for all the benchmark cases.

scholarly journals On the Estimation of the Surface Elevation of Regular and Irregular Waves Using the Velocity Field of Bubbles

2020 ◽  
Vol 8 (2) ◽  
pp. 88 ◽  
Author(s):  
Diana Vargas ◽  
Ravindra Jayaratne ◽  
Edgar Mendoza ◽  
Rodolfo Silva
Keyword(s):  
Time Series ◽  
Free Surface ◽  
High Speed ◽  
Low Cost ◽  
Video Camera ◽  
Surface Elevation ◽  
Irregular Waves ◽  
Air Bubbles ◽  
Digital Video Camera ◽  
Wave Heights

This paper describes a new set of experiments focused on estimating time series of the free surface elevation of water (FSEW) from velocities recorded by submerged air bubbles under regular and irregular waves using a low-cost non-intrusive technique. The main purpose is to compute wave heights and periods using time series of velocities recorded at any depth. The velocities were taken from the tracking of a bubble curtain with only one high-speed digital video camera and a bubble generator. These experiments eliminate the need of intrusive instruments while the methodology can also be applied if the free surface is not visible or even if only part of the depth can be recorded. The estimation of the FSEW was successful for regular waves and reasonably accurate for irregular waves. Moreover, the algorithm to reconstruct the FSEW showed better results for larger wave amplitudes.

Steep Wave Loads From Irregular Waves on an Offshore Wind Turbine Foundation: Computation and Experiment

2013 ◽  
Author(s):  
Bo Terp Paulsen ◽  
Henrik Bredmose ◽  
Harry B. Bingham ◽  
Signe Schløer
Keyword(s):  
Free Surface ◽  
Potential Flow ◽  
Surface Elevation ◽  
Irregular Waves ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Free Surface Elevation ◽  
Fully Nonlinear ◽  
Flow Solver ◽  
Nonlinear Potential

Two-dimensional irregular waves on a sloping bed and their impact on a bottom mounted circular cylinder is modeled by three different numerical methods and the results are validated against laboratory experiments. We here consider the performance of a linear-, a fully nonlinear potential flow solver and a fully nonlinear Navier-Stokes/VOF solver. The validation is carried out in terms of both the free surface elevation and the inline force. Special attention is paid to the ultimate load in case of a single wave event and the general ability of the numerical models to capture the higher harmonic forcing. The test case is representative for monopile foundations at intermediate water depths. The potential flow computations are carried out in a two-dimensional vertical plane and the inline force on the cylinder is evaluated by the Morison equation. The Navier-Stokes/VOF computations are carried out in three-dimensions and the force is obtained by spatial pressure integration over the wettet area of the cylinder. In terms of both the free surface elevation and the inline force, the linear potential flow model is shown to be of limited accuracy and large deviations are generally seen when compared to the experimental measurements. The fully nonlinear Navier-Stokes/VOF computations are accurately predicting both the free surface elevation and the inline force. However, the computational cost is high relative to the potential flow solvers. Despite the fact that the nonlinear potential flow model is carried out in two-dimensions it is shown to perform just as good as the three-dimensional Navier-Stokes/VOF solver. This is observed for both the free surface elevation and the inline force, where both the ultimate load and the higher harmonic forces are accurately predicted. This shows that for moderately steep irregular waves a Morison equation combined with a fully nonlinear two-dimensional potential flow solver can be a good approximation.

Regular and Irregular Wave Propagation Analysis in a Flume with Numerical Beach Using a Navier-Stokes Based Model

2017 ◽  
Vol 372 ◽  
pp. 81-90 ◽  
Author(s):  
Rodrigo C. Lisboa ◽  
Paulo R.F. Teixeira ◽  
Eric Didier
Keyword(s):  
Wave Propagation ◽  
Free Surface ◽  
Surface Elevation ◽  
Irregular Waves ◽  
Navier Stokes ◽  
Free Surface Elevation ◽  
Irregular Wave ◽  
Damping Coefficients ◽  
Numerical Beach ◽  
Good Agreement

This paper describes the analysis of the propagation of regular and irregular waves in a flume by using Fluent® model, which is based on the Navier-Stokes (NS) equations and employs the finite volume method and the Volume of Fluid (VoF) technique to deal with two-phase flows (air and water). At the end of the flume, a numerical beach is used to suppress wave reflections. The methodology consists of adding a damping sink term to the momentum equation. In this study, this term is calibrated for three cases of regular incident waves (H = 1 m, T = 5, 7.5, and 12 s) by varying the linear and quadratic damping coefficients of the formulation. In general, while lower values of damping coefficients cause residuals on the free surface elevation due to wave interactions with the outlet boundary, reflection occurs on the numerical beach when higher values are used. A range of optimal damping coefficients are found considering one of them null. In one of these cases, temporal series of free surface elevation are compared with theoretical ones and very good agreement is reached. Afterwards, an irregular wave propagation, characterized by a JONSWAP spectrum, is investigated. Several gauges along the flume are evaluated and good agreement between the spectrum obtained numerically and the ones imposed at beginning of the flume is verified. This study shows the capacity of NS models, such as Fluent®, to simulate adequately regular and irregular wave propagations in a flume with numerical beach to avoid reflections.

Estimation of Wave Loads due to Green Water Events in 10000-Year Conditions on a TLP Deck Structure

2016 ◽  
Author(s):  
Csaba Pakozdi ◽  
Anders Östman ◽  
Guomin Ji ◽  
Carl Trygve Stansberg ◽  
Ola Reum ◽  
...  
Keyword(s):  
Time Series ◽  
Free Surface ◽  
Model Test ◽  
Extreme Events ◽  
Structural Design ◽  
Surface Elevation ◽  
Green Water ◽  
Free Surface Elevation ◽  
Numerical Wave ◽  
Steep Wave

In order to provide qualitative and quantitative information on the hydrodynamics loads during green water events on a module on the deck of a TLP in 10000-year conditions, MARINTEK has carried out CFD simulations. This paper presents extreme wave events and corresponding hydrodynamics loads on the module which can be directly linked to the extreme events observed in model tests. This means that the simulated extreme events can be related to a probability of occurrence, found from the model test. A prerequisite for the structural design is that reliable estimates of hydrodynamic loads during a green water event can be made. Measured time series of waves from existing model test data are compared with CFD generated synthetic numerical waves. The selection of steep wave events are based on two physical parameters: the wave crest height and the rise velocity (time derivative of the free surface elevation at a given location). These parameters are relevant for green water and corresponding loads. The comparison of the measured free surface elevation of the calibrated waves with the time series of the numerical waves, as well as the measured and simulated relative wave probes time series shows that the applied numerical wave events have similar physical conditions as those observed in the model test. In a new procedure developed by MARINTEK one identifies observed steep wave events, which are similar to existing numerical wave events, instead of trying to reproduce measured events. This procedure reduces the computational time, as well as computational costs, to an industrially acceptable level. Traditional load estimation is not able to provide such reliable detailed local load history for structural design purpose at areas exposed to wave impacts. Therefore, topside modules are currently not installed in such areas. This new procedure, where CFD simulates realistic breaking waves with coupling to structural analysis tools, offers new possibilities for the design of structures subject to risk of green water loading.

scholarly journals Similarity and Froude Number Similitude in Kinematic and Hydrodynamic Features of Solitary Waves over Horizontal Bed

Processes ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 1420
Author(s):  
Chang Lin ◽  
Ming-Jer Kao ◽  
James Yang ◽  
Rajkumar Venkatesh Raikar ◽  
Juan-Ming Yuan ◽  
...  
Keyword(s):  
Free Surface ◽  
Froude Number ◽  
Solitary Waves ◽  
High Speed ◽  
Surface Elevation ◽  
Free Surface Elevation ◽  
Wave Kinematics ◽  
Wave Celerity ◽  
Image Velocimetry ◽  
Wave Heights

This study presents, experimentally, similarity and Froude number similitude (FNS) in the dimensionless features of two solitary waves propagating over a horizontal bed, using two wave gauges and a high-speed particle image velocimetry (HSPIV). The two waves have distinct wave heights H0 (2.9 and 5.8 cm) and still water depths h0 (8.0 and 16.0 cm) but identical H0/h0 (0.363). Together with the geometric features of free surface elevation and wavelength, the kinematic characteristics of horizontal and vertical velocities, as well as wave celerity, are elucidated. Illustration of the hydrodynamic features of local and convective accelerations are also made in this study. Both similarity and FNS hold true for the dimensionless free surface elevation (FSE), wavelength and celerity, horizontal and vertical velocities, and local and convective accelerations in the horizontal and vertical directions. The similarities and FNSs indicate that gravity dominates and governs the wave kinematics and hydrodynamics.

scholarly journals Experimental and Numerical Study of the Free Surface Elevation Over the Pontoons of a Semisubmersible Platform in Waves

2018 ◽  
Author(s):  
João Pessoa ◽  
Carl Trygve Stansberg ◽  
Nuno Fonseca ◽  
Manuel Laranjinha
Keyword(s):  
Experimental Data ◽  
Free Surface ◽  
Linear Theory ◽  
Air Gap ◽  
Surface Elevation ◽  
Irregular Waves ◽  
Diffraction Radiation ◽  
Free Surface Elevation ◽  
Numerical Computations ◽  
Radiation Theory

The region over the pontoons, especially in the vicinity of columns, is typically a critical area in terms of upwell when analyzing the air gap of semisubmersible platforms. There is indication that numerical computations using potential flow theory may in some cases overestimate the free surface elevation in this region. To assess the possibility, experimental data is compared to numerical computations in three locations under the deck box: one location over the pontoons, one location in the vicinity of the pontoons and one location between the pontoons. The data was acquired in FORCE’s towing tank facility, in Lyngby, Denmark, by relative wave gauges fixed to the moored semisubmersible platform. The experimental data is treated in order to remove the global motions from the upwell signal. The resulting free surface elevation, which includes contributions from incident, diffracted and radiated wave fields, is compared to the disturbed free surface elevation calculated with linear diffraction-radiation theory. The study is initially conducted in irregular waves, where simulation statistics in 4 different sea states are compared to the experiments and the observed nonlinear effects are discussed. The extreme crest heights are compared with non-Gaussian models as defined in DNVGL-OTG-13 and as defined by Stansberg (2014). The study is then extended to regular waves. In a first stage we estimate the first harmonic components by removing all higher order effects, and compare the results to linear theory. For these band-pass filtered signals it is shown that results calculated with linear theory tend to overestimate free surface elevation in the location over the pontoons, but seem to correlate well with the experiments in the other locations. In a second stage the experimental crest heights are compared with non-linear models as defined in DNVGL-OTG-13 and as defined by Stansberg (2014). It is shown in this case study that the maximum free surface elevation over the pontoons in front of upwave columns can be severely overestimated if calculated with the current state of the art numerical models, which are based on linear diffraction-radiation theory. We explain the observed discrepancy in this case primarily by a very high linear predicted amplification induced by the shallow pontoon, with resulting high local steepness leading to local breaking and dissipation. Therefore, such pontoon effects should be addressed in semisubmersible platform air-gap analysis. The work also highlights the importance of having good experimental data available when preforming such analysis.

scholarly journals SPECTRAL DESCRIPTION OF ENERGY DISSIPATION IN BREAKING WAVE GROUPS

2011 ◽  
Vol 1 (32) ◽  
pp. 19
Author(s):  
James Kaihatu ◽  
Hoda M. El Safty
Keyword(s):  
Time Series ◽  
Free Surface ◽  
Spectral Density ◽  
Dissipation Rate ◽  
Long Waves ◽  
Surface Elevation ◽  
Breaking Wave ◽  
Random Waves ◽  
Free Surface Elevation ◽  
Wave Groups

The dissipation characteristics of laboratory breaking wave groups and random waves are studied. A time-domain eddy viscosity model is used to represent the breaking wave, and the instantaneous dissipation time series deduced from measurements of free surface elevation. Fourier series of these time series yields the dissipation rate as a function of frequency, the frequency dependence of which has been shown to be the inverse of that of the spectral density of free surface elevation for random waves. It is shown that the inverse relationship between the dissipation rate and the free surface spectral density does not appear to hold for wave groups, likely due to the presence of generated long waves in the dissipation time series. These long waves introduce a periodicity into the dissipation time series and inhibit any true randomness from developing. The overall bulk dissipation is calculated from the dissipation rate for both the wave groups and random waves. It appears that, overall, the wave groups undergo a greater degree of dissipation than equivalent random waves.

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