Hydrodynamic cable

A cable object with dynamic stiffness and hydrodynamic loading.

Collaboration diagram for Hydrodynamic cable:

Author

Karl-Johan Reite

Review issues:

0223 — Cable/* makes one flow query per element per RHS, each sampling every registered lumped wake

This class simulates a cable object consisting of one or more elements. Each element is of type CableElDynStiff. Each element has methods to make it possible to use larger time steps in the integration. This is done by decreasing the stiffness of the element until the eigenfrequency of the element is low enough for the integration to be performed with the defined maximum step size.

Each element is regarded as a straight segment, responsible for calculating the forces acting on each of its ends, as well as the mass associated with each end node. The forces and mass from each element is added to the corresponding nodes of the cable, and the acceleration of each node is calculated in the OdeFcn.

The cable is influenced by:

• Internal stiffness
• Internal damping
• Hydrodynamic normal and tangential forces
• Buoyancy and gravity, with the wet fraction of each element against the wave surface (R66)
• Added mass (Ca = 1, isotropic, of the wet part)
• In waves, the Froude-Krylov and added-mass excitation (1 + Ca) rho A L f a_n normal to each element (owner ruling R104; DNV-RP-C205 Sec. 6.2, Table A-1, not checked here), left out of the analytical Jacobian as the drag is

The calculation of these forces are more thoroughly explained in CableElDynStiff.

Example configuration excerpt

<Lib
   LibName          = "marine_elements"
   SimObject        = "Cable/LumpedMass"
   Name             = "C"
   NumElements      = "7"
   Density          = "3000"
   NumericalDamping = "0"
   Diameter         = "0.1"
   E                = "117"
   DampingRatio     = "1"
   FluidRho         = "1025"
   MaxStepLength    = "0.01"
   MaxTension       = "1000"
   StepSafetyFactor = "50"
   MeanTension      = "0"
   AdaptationPeriod = "0"
   MaterialName     = "Trawl/Wire2"
   NumFaces         = "5"
   DrawScale        = "2"
/>

Input Ports

Name	Width	Description
Length	1	The length of the cable.
PosA	3	The position of end A.
PosB	3	The position of end B.
VelA	3	The velocity of end A.
VelB	3	The velocity of end B.

There is no water-velocity input port. The ambient current is taken from the Environment shared resource, which the cable queries at the mid-point of each element.

Output Ports

Name	Width	Description
ForceA	3	The force from end A of the cable.
ForceB	3	The force from end B of the cable.
PosA	3	The position of end A.
PosB	3	The position of end B.

Configuration parameters

Name	Width	Description
NumElements	1	Number of internal mass elements (Default: 2).
Density	1	The density of the cable [kg/m³].
NumericalDamping	1	Added numerical damping on each node. The damping force is calculated as \(\vec F_i = -k m_i \vec v_i\), where \(\vec F_i\) is the added damping force, \(k\) is the numerical damping factor, \(m_i\) is the node inertia and \(\vec v_i\) is the velocity of the node (Default: 0).
Diameter	1	Diameter of the cable.
E	1	The Young's modulus (elasticity) of the cable.
DampingRatio	1	The relative axial damping of the cable. 0 is no damping, 1 is critical damping (Default: 1).
FluidRho	1	The density of the ambient fluid (Default: 1025).
MaxStepLength	1	Controls the stiffness of the cable to allow integration with step lengths up to this value (Default: 0.01).
MaxTension	1	The maximum tension. If above this value, the tension is set to this this value.
StepSafetyFactor	1	A safety factor between the MaxStepLength and the one used for calculating the stiffness of the cable (Default: 50).
MeanTension	1	Tension [N] added in proportion to the stiffness reduction, as (1 - stiffness factor) * MeanTension, to correct for the decreased stiffness of the cable; the start value when AdaptationPeriod is nonzero (Default: 0).
AdaptationPeriod	1	If above zero, the cable corrects the length errors of its decreased stiffness: the mean tension starts at MeanTension and follows the element's tension with the time constant AdaptationPeriod [s], so that under a constant load it reaches the load and the strain that of the full stiffness; advanced once per integrator step, in PreOdeFcn from the step's start state, and held for every evaluation of the step (owner rulings R64, MARE-0358) (Default: 0).
MaterialName	1	The material to use for visualizing the cable (Default: Trawl/Wire2).
NumFaces	1	The number of planes to visualize the cable surface (Default: 5).
DrawScale	1	The scale of the visual appearance of the cable. This is used to make it more visible (Default: 2).

Initial conditions

This simObject does not have any initial conditions.

Full example file

<Contents>
   <OBJECTS>
      <Lib
         LibName          = "marine_elements"
         SimObject        = "Cable/LumpedMass"
         Name             = "C"
         NumElements      = "7"
         Density          = "3000"
         Diameter         = "0.1"
         E                = "117"
         MaxTension       = "1000"
      />
 
      <Lib
        LibName="environment"
        SimObject="Environment"
        Name="Env"
        Waves.Model="Component"
        Waves.NumWaves="0"
        Bathymetry.Depth="190"
        Current.Model = "Constant"
        Current.Vector = "2.5,0,0"
        />
   </OBJECTS>
 
   <INTERCONNECTIONS>
      <Connection
         C.PosA         = "0,0,0"
         C.VelA         = "0,0,0"
         C.PosB         = "0,0,18"
         C.VelB         = "0,0,0"
         C.Length       = "20"
      />
   </INTERCONNECTIONS>
 
   <INITIALIZATION>
      <InitialCondition
      />
   </INITIALIZATION>
 
   <SIMULATION>
      <Timing TStart="0" TEnd="30"/>
      <Integrator Method="RK45_i" LogStates="0" UseRSSNorm="0">
        <StepControl StepMax="0.1" StepMin="1E-060" AbsTol="0.001" RelTol="0.001"/>
      </Integrator>
   </SIMULATION>
</Contents>

This SimObject is referred to as Cable/LumpedMass