Tutorial 2 — A spread mooring and its output channels

Goal: model the three-line chain mooring of the IEA-15MW VolturnUS-S semi-submersible, request node-level channels and per-line files, and compute the system’s restoring force for a platform offset.

Deck: examples/spread_3line_chain.dat · Route: EI = 0 cable path, static · Run time: < 1 s

The deck

The line type and options are those of Tutorial 1 scaled to the reference platform: an R4 studless chain (volume-equivalent diameter 0.333 m, 685 kg/m, EA = 3.27e9 N), 850 m per line, 200 m water depth, and a stiffer seabed (kBot = 3.0e6). What is new is the topology:

--------------------- POINTS -------------------------------------------
ID    Type      X         Y         Z         Mass    Vol     CdA    Ca
1     Fixed     837.6     0.0       -200.0    0       0       0      0
2     Coupled   58.0      0.0       -14.0     0       0       0      0
3     Fixed    -418.8     725.383   -200.0    0       0       0      0
4     Coupled  -29.0      50.229    -14.0     0       0       0      0
5     Fixed    -418.8    -725.383   -200.0    0       0       0      0
6     Coupled  -29.0     -50.229    -14.0     0       0       0      0
--------------------- LINES --------------------------------------------
ID    NodeA   NodeB   Outputs
1     2       1       -
2     4       3       -
3     6       5       -
--------------------- SECTIONS -----------------------------------------
LineID   LineType   Length   NumSegs
1        chain      850.0    50
2        chain      850.0    50
3        chain      850.0    50

Three fairleads sit on a 58 m radius, 14 m below the still-water line, at azimuths 0°, 120°, and 240°; three anchors lie on the seabed at 837.6 m radius. Each line runs from its fairlead (End A) to its anchor (End B). Every SECTIONS row names the line it belongs to by LineID; a composite line (chain–polyester–chain, say) is one LINES row with several ordered SECTIONS rows — see examples/composite_chain_poly_chain.dat.

Add channels and per-line files

Copy the deck to my_spread.dat. In LINES, change line 1’s Outputs flag from - to pt; at the end of OUTPUTS, add three channels:

1     2       1       pt
...
"FairDecl1"
"Ten1N26"
"L1N26pz"

p writes node positions and t segment tensions for line 1 to separate files. FairDecl1 is the declination (angle from vertical-up), Ten1N26 the tension at node 26 of line 1 (nodes are numbered 1…51 from End A), and L1N26pz that node’s z coordinate. The full vocabulary is in Output files and channels.

New-Item -ItemType Directory -Force results | Out-Null   # already there after the quickstart
Copy-Item .\examples\spread_3line_chain.dat .\my_spread.dat
# edit my_spread.dat as above, then:
.\CableDyn_driver.exe .\my_spread.dat .\results\spread

   Created CableDyn model: 3 line object(s), 6 point(s), 3 section(s) [EI=0: 3, finite-EI: 0].
   Initial conditions: Newton static equilibrium with load continuation completed.
   Fairlead convention: force is on End A toward End B; inclinations are signed below horizontal.
   Line 1 fairlead effective tension:  2.43712E+006 N
      force [Fx, Fy, Fz]: [ 1.35070E+006,  0.00000E+000, -2.02858E+006] N, inclination=   56.343 deg
      line tangent: inclination=   55.685 deg, declination=  145.685 deg, azimuth=    0.000 deg
   Line 2 fairlead effective tension:  2.43715E+006 N
      force [Fx, Fy, Fz]: [-6.75364E+005,  1.16977E+006, -2.02860E+006] N, inclination=   56.343 deg
      line tangent: inclination=   55.684 deg, declination=  145.684 deg, azimuth=  120.000 deg
   Line 3 fairlead effective tension:  2.43715E+006 N
      force [Fx, Fy, Fz]: [-6.75364E+005, -1.16977E+006, -2.02860E+006] N, inclination=   56.343 deg
      line tangent: inclination=   55.684 deg, declination=  145.684 deg, azimuth=  240.000 deg
  CableDyn initialization completed.
CableDyn_driver: converged run written to .\results\spread.out

The run writes four files:

File

Contents

spread.out

the 15 requested channels at t = 0

spread.static.out

the nodal profile of all three lines (LineID column)

spread.Line1.p.out

line 1 node positions Node X(m) Y(m) Z(m), End A → End B

spread.Line1.t.out

line 1 segment tensions Segment Tension(N), End A → End B

The last three channels of spread.out are:

FairDecl1        Ten1N26          L1N26pz
1.4568478E+002   1.3507024E+006  -2.0000585E+002

Node 26 (mid-line) sits on the seabed (z = -200.006 m) and carries exactly the horizontal tension 1.351 MN, which equals the fairlead’s Fx above: on a frictionless seabed the grounded chain transmits the horizontal load unchanged to the anchor.

Interpret the fairlead report

The console block is printed for every line, whether or not you request channels. Its force is the load the line applies to its End A, directed along the line toward End B. The three lines are identical, so the vertical loads add (3 × 2.029 MN = 6.09 MN, the mooring’s contribution to the platform’s vertical equilibrium) while the horizontal loads cancel. Declination is measured from vertical-up (145.7° = 55.7° below horizontal); azimuth from +X toward +Y. These conventions are defined once in Conventions.

Exercises

  1. Restoring force. Surge the platform 10 m: add 10 to the X of points 2, 4, and 6 and rerun. The console forces become Fx = +0.968 MN (line 1, now slacker) and -0.820 MN (lines 2 and 3). Their sum, -0.671 MN, is the mooring restoring force on the platform — an average stiffness of about 67 kN/m over the first 10 m. Repeat at 20 m to see the stiffening.

  2. Four lines. Run examples/spread_4line_chain.dat and check that the four fairlead azimuths and tensions are symmetric.

  3. Composite line. Run examples/composite_chain_poly_chain.dat and plot Tension against ArcLength from its .static.out: the slope changes where the submerged weight per metre changes at the section boundaries.

Next: Tutorial 3 — A lazy-wave power cable.