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Use of diffraction analysis data |
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Use of diffraction analysis data |
Diffraction analysis deliberately limits interaction between the manner in which vessel loads are generated, such as motion of the vessel or of the surrounding fluid, and the loads themselves. For example, waves are applied to calculate load RAO data, but the vessel hull is considered fixed during the calculation to determine the values of the RAOs – its displacement and rotation in response to the applied waves is ignored. For the purposes of the diffraction calculation, the wave height is effectively assumed to be vanishingly small.
Diffraction analysis is conducted in the frequency domain; the inputs and outputs vary harmonically at specific frequencies. Limiting the interaction of input and output means that vessel response to a complex input signal can be obtained using linear combinations of the diffraction analysis results.
If further interaction effects are considered important, diffraction analysis can determine QTF data, which, as their name suggests, represent the quadratic part of the total nonlinear interaction between the vessel loading and vessel response.
OrcaFlex typically permits all possible interaction between the loads on a system and any response to those loads, usually by basing load and response calculations on the instantaneous state of the simulation. Such an approach is much easier to accommodate in a time domain analysis. Fully nonlinear behaviour can therefore be modelled, which includes linear, quadratic, cubic and higher order terms. Indeed, a frequently-asked question of time-domain analysis programs is, why does the vessel motion have higher-order components when only first order load RAOs are applied to it? The answer is that the motion is only strictly linear for infinitesimally-small waves! For waves of finite height, the vessel may respond to the loads upon it: if it translates perpendicular to the wavefront then the wave phasing will be affected, and if it yaws then the RAOs themselves (obtained in OrcaFlex by interpolation) may change. Either of these can give rise to second order, and higher, effects.
When diffraction analysis data are used in OrcaFlex, these two approaches are in conflict: the diffraction analysis approach says that the wave height is so small that the loads applied to the vessel are tiny and it therefore does not move, but the time-domain method, using full wave height, is continually updating the loads as the vessel moves in response to those very same loads. The greatest risk is that quadratic loading on a vessel is applied twice: once by use of QTF data, and once by applying the linear diffraction analysis loads using the instantaneous state of the system. We refer to this as double-counting part of the loading defined by QTF data.
OrcaFlex can follow the example set by diffraction analysis, and limit the interaction between vessel loading and response.
When OrcaFlex applies diffraction loads using these filtered responses, only the provided QTF data contributes any nonlinear load from diffraction effects. Filtering the frequency content of instantaneous response is difficult in the time domain, and it is not possible to achieve perfect separation of loading and response. For more detail, review the graphs of filter performance.
OrcaFlex can instead prevent double-counting of QTF loads by filtering the diffraction analysis results, instead of the time domain behaviour. Perfect filtering can be achieved in diffraction analysis, because it is conducted in the frequency domain, and the filtering is implemented in OrcaFlex by simply subtracting common second order loads from the input QTF data. Common second order loads are those which arise from more than one source (we use "common" here in the sense of shared, not frequently-occurring): they appear as part of the time domain analysis when linear diffraction analysis loads are applied using the instantaneous state of the system, and also contribute to the QTF data calculated in diffraction analysis.
With this subtraction of the common terms from the original QTF data, OrcaFlex can now therefore apply diffraction data using the instantaneous state of the system without incorrectly duplicating the higher-order effects. Common nonlinear effects that were previously truncated to the quadratic term present in the QTF data are now fully represented during a simulation.
Frequency domain analysis does not generate nonlinear interaction between loading and response, so there is no danger of double-counting the quadratic loading from diffraction effects. Filtering of response is also unneccessary in frequency domain analysis. However we still offer the choice of whether diffraction loads should be applied using heading frames, or frames which may rotate out of the horizontal plane.
If heading frames are not used, then vessel loads will initially be rotated away from the horizontal plane by vessel static heel and trim. Mean loads will then make a further dynamic contribution, because they will follow the vessel roll and pitch. Because vessel rotations out of the water plane are typically small, the choice of frames will usually make little difference to frequency domain analysis.
Not all vessel loads are based on diffraction analysis. For these additional vessel loads, their underlying theory also requires that limits are placed between vessel loading and response. A corresponding frequency domain model is not available, and so OrcaFlex must filter the vessel response in the time domain to provide appropriate input for the following included effects: