6 DOF cable

Class containing a cable with six degrees of freedom.

Collaboration diagram for 6 DOF cable:

Author

Jørgen Haavind Jensen

Date

21.06.2011 JHJ: Initial version.

Hydrodynamics

The simulation must include an Environment (fhsim_environment): a model without one is a setup error (MARE-0315). Each element is a cylinder loaded by the water on its wet part, as RbCable/Cable loads it (wet_cylinder_water::FixedDragLoadOnElement, the wet-cylinder law of fhsim_environment, MARE-0227, MARE-0315):

• the wet fraction f of the element against the wave surface over its two ends; a dry element has no water load (the air is not modelled), and an element whose centre is at the surface is half wet;
• the buoyancy \(\rho g f \pi r^2 L\);
• the drag on the velocity relative to the environment's particle velocity at the element's centre (current, waves and wakes), \(-\rho r L f (\pi C_t |V_t| V_t + C_n |V_n| V_n)\) with the tangential and normal parts of the relative velocity as vectors, so it does not depend on the orientation of the global axes;
• in waves the Morison inertia force \((1 + C_a) \rho f \pi r^2 L\, a_n\) normal to the axis, from the mean wave acceleration at the element's ends: the Froude-Krylov part and the added-mass part;
• the added mass: each element carries \(m_a = C_a \rho f \pi r^2 L\) normal to its axis in its translational inertia, \(m I + m_a (I - N N^T)\), N the axis ( \(C_a\) = 1, DNV-RP-C205 (2021) Table A-1; MARE-0374, owner ruling R2, as RbCable/Cable since MARE-0314). Nothing is added along the axis or to the moment of inertia, and the change of f in time is not included. The turning added mass gives the Coriolis force \(-\dot A (v - u)\) on the velocity relative to the water (MARE-0323).

The other objects' wakes are taken once per integrator step, in PreOdeFcn, at the element centres of the step start and held for the step, at the non-casting cutoff tier; the current and the waves stay live (ExternalWakeUpdate, fhsim_environment's ElementFlowInteraction, MARE-0223).

With gaussPointDrag (MARE-0396) the water is taken at the two Gauss points of each element (2 numElements points, the wakes too) and the drag is that at them, so that an element turning about a normal axis gets a drag moment (wet_cylinder_water::ElementGaussPoints, environment::wet_cylinder::GaussPointDragLoad). The centre is not queried.

Example configuration excerpt

<Lib
  LibName            = "marine_elements"
  SimObject          = "RbCable/6DofCable"
  Name               = "C"
  Length             = "20"
  numElements        = "7"
  Alpha              = "1.0"
      Beta               = "1.0"
      Epsilon            = "0.0001"
      Weight             = "200"
      Radius             = "0.01"
      Damping_Tangential = "0.01"
      Damping_Normal     = "1.2"
/>

Input Ports

Name	Width	Description
posA	3	Position of end point A.
posB	3	Position of end point B.
velA	3	Velocity of end point A.
velB	3	Velocity of end point B.

Output Ports

Name	Width	Description
forceA	3	The force acting on end point A.
forceB	3	The force acting on end point B.

Configuration parameters

Name	Width	Description
Length	1	Length of cable
numElements	1	Number of internal mass elements.
Alpha	1	...
Beta	1	...
Epsilon	1	...
Weight	1	Weight of the cable.
Radius	1	Radius of the cable.
Damping_Tangential	1	Tangential damping coefficient.
Damping_Normal	1	Normal damping coefficient.
ExternalWakeUpdate	1	How the other objects' wakes reach the element centres; listed in fhsim_environment's doc/user/wake-parameters.md. (Default: Step)
gaussPointDrag	1	Boolean. Takes the water and the drag at the two Gauss points along each element, so that an element turning about a normal axis gets a drag moment (MARE-0396). Off: the drag on the water at the element centre (Default: true; owner ruling 2026-10-22)

Initial conditions

Name	Width	Description
pos<i>	3	Position of point \(i \in {0\cdots\text{numElements}-1}\).
vel<i>	3	Velocity of point \(i \in {0\cdots\text{numElements}-1}\).
theta<i>	4	Orientation in quaternion of point \(i \in {0\cdots\text{numElements}-1}\)..
omega<i>	3	Angular velocity in rad per second of point \(i \in {0\cdots\text{numElements}-1}\)..

Full example file

<Contents>
   <OBJECTS>
      <Lib
        LibName="environment"
        SimObject="Environment"
        Name="Env"
        Waves.Model="Component"
        Waves.NumWaves="0"
        Bathymetry.Depth="500"
        Current.Model = "Constant"
        Current.Vector = "1,0,0"
        />
      <Lib
         LibName            = "marine_elements"
         SimObject          = "RbCable/6DofCable"
         Name               = "C"
         Length             = "20"
         numElements        = "7"
         Alpha              = "1"
         Beta               = "1"
         Epsilon            = "1e-6"
         Weight             = "200"
         Radius             = "0.01"
         Damping_Tangential = "0.01"
         Damping_Normal     = "1.2"
      />
   </OBJECTS>
 
   <INTERCONNECTIONS>
      <Connection
         C.posA = "0,0,0"
         C.posB = "0,0.1,5.0"   
         C.velA = "0,0,0"
         C.velB = "0,0,0"
      />
   </INTERCONNECTIONS>
 
   <INITIALIZATION>
      <InitialCondition
      />
   </INITIALIZATION>
 
   <SIMULATION>
      <Timing TStart="0" TEnd="10"/>
      <Integrator Method="RK45_i" NumCores="1" LogStates="0" UseRSSNorm="0">
        <StepControl Step="1e-4" StepMax="100" StepMin="1e-6" AbsTol="1e-7" RelTol="1e-7"/>
      </Integrator>
      <!-- TODO migrate_v3: FileOutput="objects:states" -> configure via <OBSERVERS> section -->
   </SIMULATION>
</Contents>