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 joints between the elements (numElements + 1 points, the wakes too) and the drag is that at two Gauss points along each element, so that an element turning about a normal axis gets a drag moment (wet_cylinder_water::ChainJoints, 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 at the joints between the elements and the drag at 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>