Validation hanging cable - Comparison FRyDoM / DeeplinesWind / Orcaflex

Test case

This benchmark is dedicated to a line which was pinned at both ends. The results are compared with those obtained through Orcaflex [ORCA2006] and DeeplinesWind [DLW2013]. The horizontal and vertical distances between the top and the bottom ends are 100 m and 50 m respectively and the top node is positioned at a water depth of 5 m.

Hanging cable view

The following table resumes the main properties of the cable

Properties Value
Total unstretched length 170.0 m
Outer diameter 0.396 m
Dry mass 0.165 te/m
EA 500,000 kN
EI 120.8 kNm^2

Static Analysis

In the static analysis the top node and bottom node remain fixed and no wave is considered. The cable is only submitted to its own mass and buoyancy. Top and bottom tensions of the cable are compared to Orcaflex and DeeplinesWind results in the following table.

Orcaflex Catenary DeeplinesWind FRyDoM
Top Tension (kN) 47.11 47.14 46.64 47.14
Bottom Tension (kN) 26.6 26.6 26.63 26.63
Vertical reaction, top (kN) 45.71 45.72 45.21 45.72
Horizontal reaction, top (kN) 11.4 11.47 11.47 11.47
Vertical reaction, bottom (kN) 24.04 24.03 24.03 24.03
Horizontal reaction, bottom (kN) -11.4 -11.47 -11.47 -11.47

Very good agreement is found between the tension results obtained by FRyDoM and the benchmark results from other models.

Harmonic motion in surge

The top node is animated with an harmonic motion in surge with an amplitude of 10m and a period of 27s.

The time series of the top node tension is compared to Orcaflex and DeeplinesWind results in the next figure.

Top tension surge

Fig. 82 Tension of the cable at the top node with harmonic surge motion of the top node.

Very good agreement is found between the result from FRyDoM and the tension given by Orcaflex and DeeplinesWind.

Harmonic motion in heave

The top node is animated with an harmonic motion in heave with an amplitude of 10m a and a period of 27s.

The time series of the top node tension is compared to Orcaflex and DeeplinesWind results in the next figure.

Top tension heave

Fig. 83 Tension of the cable at the top node with harmonic heave motion of the top node.

Discontinuities on the frydom results can be seen on the previous figure. This discontinuities corresponding to the part of the simulation when the cable goes out the water and cross the free surface. An element can be considerer in or out the water but not partially immersed. A progressive variation of the immersed volume of an element would help to avoid those instabilities.

Single Airy wave

The variation of the tension on the cable due to the effect of regular wave is analysed in this section. A single airy wave of amplitude 5m and with a period of 10s is considered here. Three directions are considerered : 0 deg, 45 deg and 90 deg. Time series of the end node tension compared to the results of DeeplinesWind are presented in the next figures.

Top tension airy 0

Fig. 84 Tension of the cable at the top node with a regular wave (T=10s, A=5m) with direction 0 deg.

Top tension airy 45

Fig. 85 Tension of the cable at the top node with a regular wave (T=10s, A=5m) with direction 45 deg.

Top tension airy 90

Fig. 86 Tension of the cable at the top node with a regular wave (T=10s, A=5m) with direction 90 deg.

The tension at the top point on the line when influenced by regular wave agree well with the tension values given by DeeplinesWind simulation expect on the peak and crest of the tension.

Convergence study

The dynamic cables are based on Finite Element model and BSpline functions. The cable is represented by a set of BSpline functions and its discretization can be managed by a number of control points. The influence of the number of control point on the accuracy and convergence of the simulation have been study for the harmonic surge motion test case.

A number of control points between 5 points and 70 points have been chosen. The number of control point has a direct influence on the convergence of the constraint solver. The next figure represents the evolution of the convergence ratio of the constraint solver with the number of control point.

Solver ratio conv

Fig. 87 Evolution of the ratio of convergence of the constraint solver with the number of control point for the line.

We observe that the constraint solver presents a good convergence ratio until 30 control points but this ratio decreases after this value. In this way 30 control points seems to be a maximal number of control point allowed to satisfy the convergence of the contraint solver.

The next figure shows the evolution of the accuracy of the simulation with the number of control points.

Accuracy of the simulation

Fig. 88 Evolution of the accuracy of the simulation with the number of control points.

We observe that a maximum of precision is achieved at 15 control points.

An optimal number of point control can be found from accuracy and convergence of the method. It will be 15 control points for this case.

References

[ORCA2006]
    1. Low and R. Langley, “Dynamic analysis of a flexible hanging riser in the time and frequency domain”, OMAE, 2016, UK
[DLW2013]
  1. Perdrizet, J-C Gilloteaux, D. Teixeira, G. Ferrer, L. Piriou, D. Cadiou, J-H Heurtier, C. Le Cunff, “Fully coupled floating wind turbine simulator based on nonlinear finite element method - Part II : Validation results”, OMAE, 2013, Nantes