Ocean Engineering

JG Consultant & Ocean Engineering Services offer consulting services to modelling and analysis of environmental conditions and loads on offshore renewables. Sea states are described by irregular wave models as ocean waves that are irregular and random in nature. Furthermore, a linear irregular wave model is a sum of many small linear wave components. Short-term wave conditions are described by a stochastic method using wave spectra, or the deterministic design wave method. Statistical distributions are used to describe long-term and extreme value conditions, or scatter diagrams for governing sea state parameters.

This Figure is showing a simplified sketch of the essiential parts of an offshore renewable system, including wind, or wave and current load source as part of the input model.

The meteorological and oceanographic conditions which may influence the design loads and load effects consist of phenomena such as wind, waves, current and water level. Based on on wave data analysis, the primary purpose is to document wave loads based on concise descriptions with mathematical background.

Wave data analysis involves application of accepted time-series analysis and spectral analysis techniques, and includes the mathematical background and theory which applies to analysis of load from wave analysis.
The calculation procedures needed to establish the structural loading generally involve the following steps in which knowledge of the surface waves is essential:

establishing the wave climate in the vicinity of the structure,
estimating design wave conditions for the structure, and
selecting and applying a wave theory to determine the hydrodynamic loading on the structure.

As the fundamental properties of surface waves, induced by wind, is their irregularity, the prediction of wave parameters can be achieved only through stochastic analysis of the sea surface, which span three basic domains: time, frequency, and probability.

The wave data analysis procedure involved finding the significant wave height along with the significant wave period, assigning a Sea State value, and detailed spectral and statistical description of the wave data.

A complete physical and statistical description of the proposed operating environment is a vital component of the design process. Natural frequencies, relative geometries and scale, and other static and dynamic response characteristics are largely defined by the significant wave height and period of the seas, the direction/interaction of the sea, swell condition, and other data.

In For a linear time-invariant system, the response function can be illustrated as a floating body, moved by incident wave, as shown in the Figure below.

The transfer function, or response amplitude operator (RAO), of the linear system, is determined by the system itself.

Methods to Obtaining Wave Loads

The calculation procedures needed to establish the wave loading, generally involve the following steps in which knowledge of the surface waves is essential:

establishing the wave climate,
estimating wave conditions, and
selecting and applying a wave theory to determine the hydrodynamic loading.

Wave forces on rigid bodies are generally estimated using Morsion’s Equation, Diffraction Theory, or Froude-Krylof Theory. For very large structures (where L ~ λ), the wave ﬁeld is affected by the presence of the structure therefore diffraction theory must be used. If the structure is small but inertial forces are signiﬁcant, Froude-Krylof force estimation is employed. Froude-Krylof is based on computing the pressure force on the body surface from wave elevation effects.

Frequency Domain Analysis

In general terms, frequency domain helps study frequency contents of the discrete time domain signals as well as continuous time domain signal. It uses transformation to convert a time domain function to a frequency domain function. Then Fourier transformation can be used to convert a signal into a sum of infinite number of sinusoidal waves. In summary, it is a method used to analyze data or mathematical functions with respect to the frequency.

A linear frequency domain analysis formulation can be as shown in the Figure.

Solver for Linear Frequency Domain Analysis Formulation (Source: JG Consultant & Ocean Engineering Services)

The wave induced loads in an irregular sea can be obtained by linearly superimposing loads due to regular wave components. Analysing a large volume structure in regular incident waves is called a frequency domain analysis. Assuming steady state, with all transient effects neglected, the loads and dynamic response of the structure is oscillating harmonically with the same frequency as the incident waves.

Frequency domain analysis can be the first step in the hydrodynamic modeling process. It can be the basis for a time domain analysis where nonlinearities can be introduced.

Time Domain Analysis

In general terms, time domain is the analysis of mathematical functions, physical signals or time series of environmental data, represented by amplitude and time. In the time domain, the signal or function's value is known for all real numbers, for the case of continuous time, or at various separate instants in the case of discrete time. In a time-domain analysis, the variable is always measured against time.

Nonlinear time domain analysis is required, where the purpose of load effect analyses is to predict the response due to direct loading. This forms the basis for subsequent capacity checks according to relevant design codes.

A nonlinear time domain analysis formulation is shown in the Figure belov.

Solver for Nonlinear Time Domain Analysis Formulation (Source: JG Consultant & Ocean Engineering Services)

Some hydrodynamic load effects can be linearised and included in a frequency domain approach, while others are highly non-linear and can only be handled in time-domain. The time domain analysis takes the frequency domain results and transfers them to the time domain. It is usually used for prediction of extreme load effects. Hydrodynamic coefficients are required input, including the frequency-domain hydrodynamic added mass and damping matrices and wave-excitation force vector.

The equations of motion can be obtained by summing the forces present on each body. The steady state time-dependent form of the equation of motion for 6-degree of freedom rigid-body motions can be used.

The wave exciting forces and moments acting on the body are the Froude-Krylov force, which is the pressure in the undisturbed waves integrated over the wetted surface of the floater and the diffraction forces, which are pressures that occur due to the disturbances in the water because of the floater being present.

The hydromechanical forces and moments are divided into added mass forces due to having to accelerate the water along with the body, the damping forces due to the oscillations creating outgoing waves which carry energy away from the body and the restoring forces due to bringing the buoyancy/weight equilibrium out of balance.