Line contact: Modelling

The line contact facility enables you to model contact between pairs of lines, and it is capable of modelling all sorts of contact situations. The model works by placing penetrators at the nodes (or other points) of one of the two lines, which then contact, and penetrate, the inside or outside surface of a curved cylinder representing the other line. For example, the line contact model permits OrcaFlex to model systems where:

Line contact versus line clashing

OrcaFlex also has another way of modelling contact between lines, called line clashing. The line contact and line clashing models have different features: to help you judge which might be most suitable for your application, here are the main differences, advantages and disadvantages.

Interaction model

The line contact model is, essentially, a relationship between two distinct lines in an OrcaFlex model. One of those lines is the splined line, which has a smooth spline curve fitted between the line nodes. This spline curve allows OrcaFlex to represent the line as a smooth cylinder for the purposes of contact modelling. The other line in the relationship is the penetrating line. Penetrators at the nodes of the penetrating line interact with the splined line's contact cylinder – a flexible cylindrical elastic solid whose axis follows the spline.

Note: The splines used for line contact modelling are distinct from the splines that may be used for a line's step 1 statics method.

The penetrators are placed at some or all of the nodes of the penetrating line. By default, they are coincident with the line nodes, but their distribution along the line and offset from the line nodes may alternatively be user-defined. When contact occurs between one of these penetrators and the contact surface presented by the splined line, force and moment are applied to the penetrator, which transfers those loads to the node to which it is attached. An equal and opposite load is applied to the contact surface, and that load is transferred to the nodes at the ends of the splined line segment.

The contact between penetrating line nodes and splined line segment elastic solids is modelled in the same way as contact between lines and elastic solid shapes, following the existing shape contact model. Friction can therefore be applied to the contact during the dynamic simulation. Relative motion of the two lines will lead to rolling or sliding contact. The lines cannot be 'locked' together by this model.

To fully define the nature of the line contact relationship, you must indicate your intentions for the penetrating line to OrcaFlex through the penetrating line is data item. This may take one of three values, inside, around, or outside: these three different configurations for the penetrating line are described below.

Note: In the figures below, the deviation of the spline (dashed centreline) from the line segments (solid centreline) has been greatly exaggerated. It is expected that during practical use the segmentation will be sufficiently fine that the splines will remain close to the line segments.

Penetrating line is inside

The contained inner line is represented by the penetrating line, and the containing outer line by the splined line. When the penetrating line nodes are within the length of the containing line, their penetrators will contact the inner surface (bore) of the containing line. The bore of the containing line is the only contact surface, so the contained line nodes cannot escape other than by running off the end of the containing line.

Figure: Line contact with penetrating line inside splined line. The contact surface is the inner surface of the splined line. The penetrating line is the inner line.

Penetrating line is around

Some or all of the penetrating line nodes have penetrators which constrain the splined line. The lines do not interact at any other points. The splined line runs within the annular constraining penetrators. The splined line can move relative to the penetrators; the smooth splined shape presents the only contact surface.

Figure: Line contact with penetrating line around splined line. The contact surface is now at the outer diameter of the splined line. The splined line is the inner line.

Penetrating line is outside

Neither line is expected to be inside the another, and the nodes of the penetrating line make contact with the outer surface of the splined line cylinder. In this case it is not usually important which of the two lines is chosen to have penetrators at its nodes, and which presents the contact surface.

Figure: Line contact with penetrating line outside splined line

Offset penetrators

If specific penetrator locations are defined, then penetrators may be offset from the nodes of the penetrating line. One expected use for this facility is the representation of piggyback riser systems. Lines in this configuration are clamped together with some fixed offset, rather than being inside one another.

If the penetrating line is around method is used to model clamps placed between two lines, the penetrating line can be thought of as placing rings around the splined line. The detail of the modelling is therefore reasonably close to reality:

Figure: Around line contact with penetrators offset from line nodes

The penetrating line is inside model can also be used to place offset penetrators between the two lines to represent clamp behaviour, and is illustrated here for completeness:

Figure: Inside line contact with penetrators offset from line nodes

Splined line cylindrical solid diameter

The elastic contact cylinder of the splined line takes its diameter from the line types of the splined line segments. The line type outer contact diameter is used for outside or around contact, and the line type inner contact diameter for inside contact. At a change in the line types along the splined line, the diameter may change. This presents a discontinuity in the model, which could lead to simulations becoming unstable.

To avoid such a discontinuity, OrcaFlex interpolates linearly at a change in diameter, over 10% of the segment length on each side of the node at the line type boundary:

Figure: A change in diameter is interpolated across the change in line sections.

Splined line distribution of contact loads

Contact featuring a splined line, where the splined line does not include torsion, and also uses either variable data for bend stiffness, or a stress-strain relationship for Young's modulus, can sometimes suffer difficulty in simulation convergence. A detailed explanation follows.

The nodes of the splined line receive loads arising from contact between the spline and either line contact penetrators, or supports. Generally, contact with the spline takes place between the ends of a splined line segment. Therefore, the contact load given to the line nodes at the segment ends should contain both a force, and a moment due to the offset between node and contact location.

OrcaFlex lines may choose whether or not to include torsion. Lines without torsion included cannot receive moments directly onto their nodes; instead, their neighbouring nodes must receive shear forces. These shear forces are related to the intended moment by the bending stiffness of the line types used by the line segments between the node that should receive a moment, and the neighbours receiving shear forces.

Line type bend stiffness in OrcaFlex can be discontinuous if variable data is used, or if the line type uses a stress-strain relationship for Young's modulus. The moment-curvature relationship is linearly interpolated, so the gradient, which is the bend stiffness, may suddenly change at the input data points. This can mean that the shear forces on neighbour nodes are also discontinuous, which may sometimes cause difficulty with simulation convergence.

Lines with torsion do not suffer this issue, because their nodes can receive moments directly. If you think that your model is encountering this issue, including torsion on your splined line should provide a solution.

Containment scaling

When a penetrating line is inside or around a splined line, one of the lines may protrude from the end of the other. Scaling is applied to the line contact force in this case. It may also be applied, if containment is enabled, to the contained line's interaction with the seabed and elastic solids and to the contained line's fluid kinematics.

Scaling for line contact depends on what proportion of the contact length represented by each penetrator overlaps with the length of the splined line. Scaling for the contained line's seabed contact, solid contact and fluid kinematics depends on how much of the line length represented by each of the contained line's nodes overlaps with the length of the containing line.

When OrcaFlex determines how much length from a line node or penetrator overlaps the length of another line, any angle between the two lines is ignored. The figure below shows penetrators in two cases where the assumptions made result in the same scaling factor of approximately 0.4 being used.

Figure: Scaling assumes that penetrator length is aligned with the splined line axis.

Scaled fluid loads

When a penetrating line is inside or around a splined line, then some length of the inner line (the penetrating line if it is inside, or the splined line if the penetrating line is around) might be contained inside the outer line, for part or all of the simulation. When this occurs, OrcaFlex can automatically shield the contained length of inner line from the environmental fluid forces, in the same way that the inner line's contact with elastic solids and the seabed is shielded. For a shielded length of line, OrcaFlex will instead apply fluid forces from the contents fluid and contents motion in the containing outer line. This shielding behaviour is governed by the containment enabled setting.

The containment behaviour depends on the outer line contents method, as follows:

Note: A line can be an inner line in more than one line contact relationship, but only if either (a) the outer line is the same in all those relationships, or (b) all the outer lines have the free-flooding contents method, and each inner line node is inside at most one of those outer lines at any one time. Option (b) allows contact relationships to be set up to model pull-in of a single inner line through multiple free-flooding outer lines, provided that each inner line node leaves one outer line before entering the next outer line.
Warnings: The containment modelling does not apply to any attachments to the inner line. So any attached clumps, drag chains, stiffeners or 6D buoys will experience external fluid conditions that ignore any containment effects of the inner node to which they are attached. Attachments to any contained inner node will therefore – probably wrongly – be subject to fluid loading based on the fluid density, pressure and kinematics of the sea, not those of the fluid contents of the containing line.
The line results relative velocity, normal relative velocity, axial relative velocity, Strouhal frequency, Reynolds number, seabed normal resistance and seabed normal resistance/D (when the default linear seabed resistance model is used) do not take into account line containment. They therefore report the fluid conditions or seabed interaction that the node would have experienced if it had been fully exposed to the environment. The relative velocity and seabed resistance results reported are scaled by each node's containment scaling factor in order to arrive at the conditions actually applied during the simulation. Often, the node is completely contained, and therefore the environmental velocity and seabed resistance values are scaled down to zero. These effects therefore do not affect fully contained nodes at all during the simulation.
If the outer line contents method is uniform, the inner line can protrude from the ends of the outer, but will still not be exposed to the environment, even though it is no longer inside the outer line length. This is a common source of error when modelling relatively short outer lines, such as bend stiffeners, pull tubes or riser guides. If these outer lines do not have free-flooding contents, then all of the inner line will be shielded from the environment, and its buoyancy will be calculated using the outer line's contents density.

Note that you should take care if any VIV modelling, wake interference or lift forces due to seabed proximity are specified for an inner line section for which containment might occur. Specifically:

Penetrator discretisation

Penetrator discretisation is intended to be used when the line contact penetrators and the spline have the same, or very similar, diameters – for example a centralised pipe, where the centralisers are in an interference fit with the outer pipe. In such a case the true contact force occurs simultaneously at all points on the circumference of the penetrator and so is ill-defined by a single penetrator, which can only represent contact at a single point. This results in a singularity in the force model which can lead to noisy or unstable simulations. By discretising the original penetrator into multiple smaller penetrators, placed around the original contact surface, the contact can be robustly defined. Penetrator discretisation is only available for penetrators from inside or around relationships.

If a line contact relationship has a penetrator discretisation count greater than one, OrcaFlex generates that number of penetrators in place of what would otherwise be a single penetrator. The new set of discretised penetrators are each given a contact diameter $d_\mathrm{d}$ and area $a_\mathrm{d}$, which are scaled from the original single penetrator's diameter and area $d_\mathrm{o}$ and $a_\mathrm{o}$ by the penetrator discretisation scale $s$, i.e. \begin{align} d_\mathrm{d} &= s\, d_\mathrm{o} \\ a_\mathrm{d} &= s\, a_\mathrm{o} \end{align} The discretised penetrator contact length is not scaled. For the default value '~', the contact length $l$ is calculated as contact area divided by contact diameter, so is invariant under the above scaling \begin{equation} l = a_\mathrm{d}/d_\mathrm{d} = a_\mathrm{o}/d_\mathrm{o} \end{equation} The discretised penetrators are evenly distributed in such a way as to best represent the original single penetrator's contact surface. This is most easily described pictorially: the below figure illustrates an original single penetrator, drawn in black, from an inside penetrating line, and a discretisation into multiple penetrators, drawn in blue, using a penetrator discretisation count of 3 and a penetrator discretisation scale of 0.4.

Figure: Inside penetrator discretisation using count=3 and scale=0.4.

The discretisation of an around penetrator is illustrated below. Again, the original penetrator is drawn in black and the discretised penetrators in blue. This example has a penetrator discretisation count of 3 and a penetrator discretisation scale of 1.6.

Figure: Around penetrator discretisation using count=3 and scale=1.6.

Using penetrator discretisation

Usually, when discretising an inside penetrator, you will choose a penetrator discretisation scale less than one; conversely for an around penetrator, a scale value greater than one is appropriate. Using a larger number of discretised penetrators will result in a better representation of the true physical contact surface being modelled but this has an associated computational cost. If you are confident that there is only going to be a single point of contact, at any given penetrator location, then penetrator discretisation is not required since the contact surface is well-defined by a single penetrator.

In some cases, you can expect to see quite different model behaviour for different count and scale values. This is simply because the representation of the physical system has changed. One such change that can be significant is the effective stiffness between the penetrating line and the splined line: the reaction force a penetrator feels, when it penetrates the spline, is proportional to the penetrator contact area which is scaled by the penetrator discretisation scale, in other words, the reaction force is directly proportional to the penetrator discretisation scale. Another reason for the change in effective stiffness is that the penetrator discretisation count defines the number of discretised penetrators and their distribution around the contact surface: this count therefore determines how many penetrators will come into simultaneous contact with the spline, directly influencing the stiffness of the overall contact between the two lines.

You should use a penetrator discretisation count and scale that will ensure a well-defined contact surface. You can then adjust the contact relationship's normal stiffness value to meet the desired level of effective stiffness between the penetrating line and the splined line.