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Theory, Line Theory
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Secondly, that if the chain is dragged across the seabed then an opposing friction force μR is generated, where μ is the friction coefficient and R is the seabed reaction.
The seabed interaction model used is as follows:
At any given time, OrcaFlex first calculates how much of the drag chain would be supported by the seabed. It assumes that the chain hangs vertically straight down from the line. The drag chain is then considered as being made up of two parts – the supported part and the remaining hanging part.
The hanging part of the chain is then analysed as described above.
The supported part of the chain is modelled as if it is lying on the seabed directly beneath the node to which the chain is attached. As the node moves laterally, the supported chain also moves laterally (but below the node) and so generates a friction force that is then applied to the node.
Note that the division of the drag chain into a hanging length and a supported length is done before the hanging length is analysed, and so is done with the chain vertical. This means that if current drag causes the chain to hang at an angle to the vertical then the supported length will generally have been overestimated and the hanging length correspondingly underestimated. This is an inaccuracy that cannot easily be avoided at the moment.
5.12.18 Line End Conditions
Except for Free Ends, the connection at the line end is modelled as an isotropic ball-joint with a rotational stiffness and a preferred no-moment direction. A rotational stiffness of zero simulates a freely rotating end, and a value of Infinity simulates a clamped end.
The inclusion of end stiffness allows the program to calculate the curvature and bending moment at the termination.
If the curvature is large, the calculated value is accurate only if sufficiently short segments have been used to model the line near its end.
OrcaFlex reports a value for End Force and End Ez-Angle. These are the magnitude of the end force, and the magnitude of the angle between the end force vector and the no-moment direction. Vessel motion is automatically accounted for. The end force and angle values provide the basis for the design of end fittings such as bend stiffeners.
See Modelling Line Ends.
5.12.19 Interaction with the Sea Surface
OrcaFlex Lines are subdivided into segments, and the various forces are attributed to nodes at each end. For a partially submerged segment, the hydrostatic and hydrodynamic forces are proportioned depending on how much of the segment is submerged – the Proportion Wet (PW). Proportion Wet is available as a line result variable. We also define Proportion Dry (PD) as PD = 1 - PW.
For a segment whose axis is normal to the surface, the Proportion Wet could be calculated from the intersection of the segment centreline axis with the free surface. However, this simple approach breaks down when the segment is tangent to the surface.
For this reason, OrcaFlex uses a simple but effective modification of this concept. Instead of using the centreline axis, we use the diagonal line joining the highest point on the segment circumference, at the 'dry' end, with the lowest point at the 'wet' end; see the diagonal line in the figure below. As the segment passes through the tangent position, the diagonal line switches corners but the proportion wet varies continuously. The intersection of the diagonal line with the surface continues to give the appropriate Proportion Wet result, and the hydrostatic and dynamic forces are attributed to the appropriate node.
Figure: Proportion Wet for a surface-piercing segment
This surface-piercing model enables OrcaFlex to model systems such as floating hoses, containment booms and wave suppression systems. However please note the following points when modelling such systems:
B A
Proportion Wet = B / (A+B)
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Theory, Line Theory A consequence of this model is that a hose floats in still water as a wall-sided body; in other words OrcaFlex does not take account of the variation in water plane area with draft that arises from the circular cross section.
For cases of practical dynamics, this simplification is of minor importance, but it does mean that if you check the immersion depth of a hose in still water you may find the answer slightly wrong if the hose is very buoyant, or just awash.
When modelling floating hoses, it is important to have enough segments to model the local curvature. If your hose is flexible, and the waves are short, then you will need at least ten and preferably twenty segments per wave to model the curvature properly. However a stiff hose tends to bridge the wave troughs, and fewer segments are required.
The program uses constant drag and added mass coefficients for the floating hose, and the user has to select appropriate values based on the average immersion depth. Unfortunately the literature is of limited help – if you know of any good data source, we would be very pleased to hear of it.
5.12.20 Interaction with Seabed and Shapes
Nodes are also subjected to reaction forces from the seabed and any Shapes with which they come into contact. The contact occurs at the outer edge of the line, as specified by the contact diameter. The reaction force is given by:
Reaction = KAd where
K = stiffness of the seabed or shape,
d = depth of penetration, allowing for the contact diameter,
A = contact area, which is taken to be contact diameter multiplied by the length of line represented by the node.
In addition, when the explicit solver is in use, nodes experience a damping force. For details see Seabed Theory and Shapes Theory.
Finally, friction forces can also be included.
5.12.21 Clashing
OrcaFlex provides two different ways of modelling contact between lines: the Line Contact model and the Line Clashing model. The clashing model is described below. For a summary of the differences, advantages and disadvantages of the two models see Line Contact versus Line Clashing.
Line Clashing Data
To include clash modelling between two lines, you must set Clash Check to "Yes" and set the Contact Stiffness to a non-zero value, for both lines. You can also specify the Contact Damping value.
The facility to suppress clash modelling (by setting Clash Check to "No") has been included because the clashing algorithm is time consuming. It is therefore best to suppress clash modelling on all sections that will never clash with other lines, or if you are not interested in the effects of clashing.
OrcaFlex assumes constant spring stiffness and damping values, and neglects friction. The force algorithm is described below. It pushes lines apart again if they try to pass through another, and it permits lines to separate again after contact. Multiple contact points along the line length are allowed for.
Clashing behaviour can be difficult to understand and it is not always obvious what the results mean and how they should be used in practice. This is a developing area and we would appreciate feedback from users. The following notes expand on the way the calculations are carried out by the software and give our suggestions on interpretation.
Note: Line clashing is not modelled during statics.
Calculating the Clash Force
OrcaFlex checks for clashing between any two line segments for which clash checking is enabled and the contact stiffness is non-zero (for both segments involved). The two segments do not need to be in different lines - a line can clash with itself.
The clash check between segment S1 (on line L1) and segment S2 (on a different line L2) is done as follows. Let the radii of the two segments be r1 and r2 (as defined by the line type contact diameter). First OrcaFlex calculates the shortest separation distance, d, between the centrelines of the two segments. If d ≥ (r1 + r2) then the lines are not in contact and no contact force is applied.
If d < (r1 + r2) then the lines are in contact. In this case OrcaFlex applies equal and opposite clash contact forces to the 2 segments to push them apart, as follows. Let p1 and p2 be the two points of closest proximity – i.e. p1 is on the centreline of segment S1 and p2 is on the centreline of segment S2, and these are the two points that are minimum
Theory, Line Theory
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distance d apart. Also, let u be the unit vector in the direction from p1 towards p2. Then the magnitude of the clash contact force applied is given by:
F = (Stiffness Term) + (Damping Term)
where the two terms on the right are documented below. A force of this magnitude F is applied to segment S1, at p1, in direction -u. And the equal and opposite force is applied to segment S2, at p2, in direction +u.
The stiffness term is given by:
Stiffness Term = k(d - [r1 + r2])
where k = 1 / (1/k1 + 1/k2) is the combined contact stiffness of the segments. Here k1 and k2 are the contact stiffnesses of the two segments, as specified in the Line Types data.
The damping term is based on the rate of penetration, v, which is the u-direction component of p1's velocity relative to p2. If v≤0 then the two segments are moving apart and then no damping force is applied. If v>0 then the penetration is increasing and the damping term is then given by:
Damping Term = cv
where c is the combined contact damping value of the two segments, which is given by:
c = 0 if c1=0 or c2=0
c = 1 / (1/c1 + 1/c2) otherwise.
Here c1 and c2 are the contact damping values of the two segments, as specified in the Line Types data.
How the Clash Force is Applied and Reported
In general, clashing will take place between one segment of one line and one segment of another (the probability of a clash occurring exactly at a node is very small unless you take special measures to make it happen). OrcaFlex determines the force as just described, and reports the force as a segment variable – i.e. when you ask for the clash force at a particular arc length along the line, the force reported is the clash force for the segment which contains the specified point.
If multiple clashes occur simultaneously on the same segment then the Line Clash Force reported is the magnitude of the vector sum of the clash forces involved.
In the OrcaFlex model, all forces act at the nodes, so the clash force has to be divided between the two nodes at the ends of the segment in which the force acts. The force is divided in such a way that the moments of the two forces about the contact point are equal and opposite.
Interpreting the Results
Contact between lines can be a violent impact at high relative velocity, or a gentle drift of one line against another, or anything in between. We need to view the results in different ways for different sorts of contact. The following notes give some general guidance based on our experience, but in difficult cases it is essential that users develop their own understanding of the underlying physics, and confirm it by sensitivity analysis.
OrcaFlex provides three measures of the severity of a clash event:
Clash force.
Clash impulse (integral of contact force times time – a measure of momentum transfer).
Clash energy (calculated by integrating the magnitude of clash force with respect to depth of penetration).
There are 3 types of OrcaFlex results which can be used for analysing clashing:
1. Time Histories of Clash force and Clash impulse.
2. Range Graphs of Clash force.
3. The Line Clashing Report contains Clash force, Clash impulse and Clash energy, together with a host of other details about clash events.
Low Speed Contact
Where one line drifts quite slowly against another as a result of weight or drag forces, then the contact is essentially quasi-static. The clash force at the point of contact is the best measure of what is happening, and will be insensitive to segmentation and contact stiffness.
High Speed Impact
The case of violent impact at high speed is much more complicated. Contact forces arrest the relative movement of the lines over a very short time interval. Momentum is transferred from the faster moving to the slower moving line.
Kinetic energy at the moment of impact is converted partly to local strain energy at the point of contact, and partly to axial and bending strain energy elsewhere in the lines.
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Theory, 6D Buoy Theory If the discretisation of the lines is sufficiently fine, the contact stiffness value is correct, and contact damping is small, then OrcaFlex models the impact correctly, and all the reported results (force, impulse, energy) are correct. In practice, however, contact stiffness is rarely known with any precision, and it may not be practicable to discretise the line sufficiently to represent the deformation of the line axially, or particularly in bending, following a violent impact. (Deformation of the colliding cross sections is represented by the contact stiffness.) Under these circumstances, we need a measure of clash severity which is both meaningful for engineering purposes, and insensitive to discretisation and contact stiffness. Of the three measures available: Maximum clash force reduces with reducing contact stiffness and is usually the least reliable measure.
Impulse is generally insensitive to changes in contact stiffness, though this may be masked where the change in stiffness causes a change in the character of the impact. (For example, a high contact stiffness may give rise to a single impact followed by a large rebound. Reducing stiffness can reduce the rebound to such an extent that the single impact is replaced by a double impact.) Impulse is also fairly insensitive to changes in segmentation.
Unfortunately, however, impulse is not a convenient measure for engineering purposes.
Energy is the most convenient practical measure of potential damage. This may be sensitive to contact stiffness, where there is a fairly equal distribution of strain energy between contact and other elastic deformations of the system, but if contact strain energy is the dominant component, then sensitivity is reduced. Contact strain energy is also sensitive to discretisation: longer segments give higher values of contact strain energy. This means that the reported strain energy for a coarsely segmented model is generally conservative. In practical cases, it may be possible to reduce segment length sufficiently to show that contact strain energy is below damaging levels, without needing to go to the very fine discretisation which might be required for an accurate value.
Sensitivity to time step
Clash events are often intermittent and short lived. Consequently, simulations of clash events can be sensitive to the choice of time step.
For explicit integration this is usually not an issue because use of the explicit solver typically necessitates the use of short time steps. However, when implicit integration is used, you should take extra caution when interpreting clashing results because of the longer time steps allowed by the implicit solver. We recommend that you carry out sensitivity studies to show that the time step in use is sufficiently short.
Damping
Linear damping is included in the OrcaFlex contact model, and contributes to the reported clash force, impulse and energy results.