Data: QTFs

QTF calculation method

OrcaWave can compute the potential load contribution to QTFs using either the direct method (analogous to diffraction load RAOs), or the indirect method (analogous to the Haskind load RAOs), or both. If both types of potential load are computed, then the preferred QTF calculation method will set the default choice for which data to import when importing results into OrcaFlex (you can change your mind at the import stage).

Free surface panelled zone

The free surface panelled zone is the portion of the free surface that is exterior to the body (or bodies) and bounded by a circle centred on the global origin (the inner circle). It must be described by panels in order to evaluate the surface forcing contribution to full QTFs. The panels can be provided in a mesh file or you can ask OrcaWave to automatically generate them.

If your free surface panelled zone is defined by a mesh file, you should provide a mesh file with the same symmetry type as the global mesh. The coordinate data in the mesh file must be given with respect to global coordinates $\GXYZ$. You must also specify the inner radius, i.e. the radius of the inner circle.

Note:

You can exclude surface forcing from the calculation by leaving the mesh file name blank. Doing so reduces the calculation time, but must be justified carefully. In general, the approximation is better at lower frequencies.

If your free surface panelled zone is automatically generated, you must specify a target panel size and the inner radius.

Notes:	Panel size should generally be similar to the body mesh.
	If you want automatically generated panels, then all body waterlines must be closed. The quality of the mesh is better if the waterline segments all have similar length, comparable to the specified panel size.

Warning:

Using OrcaWave to automatically generate panels is convenient but may lead to mesh quality issues (e.g. if a waterline has some very short segments). Using specialist software to produce a mesh will give you more control over mesh quality.

The automatically generated mesh can be saved as a WAMIT .gdf file by using the popup menu on the mesh view or mesh details pages.

Free surface quadrature zone

The free surface quadrature zone is a circular annulus, centred on the global origin, between the inner circle and outer circle. You do not need to provide panels to describe the quadrature zone, but instead define the extent of the zone and the density of collocation points.

The number of annuli defines the number of concentric annuli into which the quadrature zone is divided, each of which has a width given by the radius step. The radius of the outer circle is therefore given by the inner radius plus the product of these two values.

Note:

If the number of annuli is zero, OrcaWave does not use a quadrature zone: the surface forcing is evaluated using only panelled and asymptotic zones.

Within each concentric annulus, the surface forcing is integrated using Gaussian quadrature with the number of radial nodes and azimuthal nodes specified. The total number of collocation points for the quadrature is the product of the number of radial nodes, the number of azimuthal nodes and the number of annuli.

Note:

If the global mesh has one symmetry plane, the number of azimuthal nodes defines the number of nodes, at each radius, per half plane; similarly, if two global symmetry planes are present, it defines the number, at each radius, per quadrant.

Free surface outer circle

The outer circle is a circle centred on the global origin that defines the outer boundary of the panelled and quadrature zones. Its radius is determined by the data entered for the panelled and quadrature zones. The number of segments defines how many line segments are used to perform the line integral around the outer circle as part of the free surface forcing.

Notes:	If the global mesh has one symmetry plane, the number of segments defines the number used for half the outer circle; similarly, if two global symmetry planes are present, it defines the number used per quadrant.
	The midpoints of the outer circle line segments can be shown in the mesh view. The distance between the points should generally be similar to the panel size of the free surface panelled zone and body meshes.

Free surface asymptotic zone

The expansion order in the asymptotic zone determines how many terms are included in the asymptotic series approximations used to evaluate the surface forcing beyond the outer circle.

Note:

The accuracy of the asymptotic zone's contribution to the second-order potential depends on both the expansion order and the outer radius.

Considerations for specifying the panelled, quadrature and asymptotic zone data

Evaluating the surface forcing contribution to the second-order potential can be a significant computational burden. The data choices for the panelled, quadrature and asymptotic zones of the exterior free surface, $\SF$, will determine both the accuracy and the calculation time. Some general principles apply:

Increasing the number of panels and the number of collocation points increases the run time because each panel and collocation point is essentially an additional field point in the first-order calculation. The run time is minimised by minimising the outer radius (the extent of the panelled and quadrature zones) and minimising the number of panels and collocation points.
However, the accuracy of integration in the panelled zone improves if more, smaller, panels are used. Similarly the accuracy of integration in the quadrature zone improves if more collocation points are used.
The accuracy of the asymptotic zone integration improves as the outer radius increases and as the expansion order increases. The outer radius is the dominant effect in most cases – it must be sufficiently large to obtain accuracy, and therefore has an effect on run time.

The appropriate data to use is very problem-specific and values are best chosen by experimentation on a subset of your wave environment cases (i.e. for a subset of wave frequencies and headings). One way to estimate the accuracy of your potential load results is to compare results from a sequence of runs in which the parameters for the three zones are varied.

Note:

Comparing results from direct and indirect methods can also give an indication of accuracy, but this comparison does not demonstrate convergence with respect to outer radius, since both methods use the same outer radius approximation to evaluate a free surface integral.

A possible procedure to determine suitable data is to begin by neglecting the quadrature zone - which simplifies the situation by reducing the number of data items required. The first goal in this procedure is to fix a value for the outer radius by using a sequence of panelled zone mesh files, looking for convergence of the potential loads as the radius increases.

The theoretical error in the asymptotic zone integration gives a guide for the required outer circle radius. The error is a combination of:

Errors in the underlying asymptotics. These are $O(\textrm{e}^{-\pi R_{OC}/2 h})$ in water of depth $h$, where $R_{OC}$ is the radius of the outer circle. In water of infinite depth these errors are $O\left([\nu R_{OC}]^{-3}\right)$, where $\nu$ is the wavenumber of the longest wave.
Errors from truncating the series at a finite expansion order. These are $O\left([R_{SB}/R_{OC}]^n\right)$ where $R_{SB}$ is the maximum horizontal distance of a body surface from the global origin and $n$ is the expansion order.

After finding a value for the outer radius and a panelled zone mesh file which give satisfactory convergence in potential load results and agreement between direct and indirect methods, you can now try introducing a quadrature zone to accelerate the calculation. Try reducing the extent of the panelled zone and introducing quadrature zone annuli in such a way as to keep the outer radius fixed at your chosen value.

Integration in the quadrature zone can be appreciably faster than in the panelled zone. Accuracy can be maintained provided enough collocation points are used, and provided the inner radius is sufficiently large. You can try varying these parameters and see how they affect the potential load results and the run time.

Note:

No part of the quadrature zone should be too close to a body surface. This is because the true Rankine singularity in the Green's function is not well handled by general-purpose quadrature. Locations where the singularity is strong are better handled within the panelled zone, where OrcaWave integrates the singularity analytically.