Center weight mass

Simulation of a center weight for double trawl systems.

Collaboration diagram for Center weight mass:

Author

Karl-Johan Reite

Date

01.01.2006 KJR: Initial version.

26.05.2011 KJR: Rewritten to new version of FhSim.

A submerged mass object acted on by its submerged weight, three external forces, quadratic hydrodynamic drag and the seafloor contact force.

\begin{eqnarray*} \dot{\vec{x_1}} &=& \vec{x_2} \\ \dot{\vec{x_2}} &=& \frac{\sum \vec{F}}{m} \end{eqnarray*}

, where

• \(\vec{x_1}\) is the position of the center weight object
• \(\vec{x_2}\) is the velocity of the center weight object
• \(\sum \vec{F}\) is the sum of the forces acting on the center weight object
• \(m\) is the mass of the center weight object

The weight is modelled as a sphere whose radius r follows from Mass and Density. The drag acts on the velocity relative to the water, so the weight is swept by currents and waves; it is environment::sphere_hydro's quadratic law on a free sphere of diameter 2r:

\begin{eqnarray*} \vec{v}_r &=& \vec{x_2} - \vec{v}_w \\ \vec{F}_d &=& -\frac{1}{2} \rho \, \pi r^2 \, C_d \, |\vec{v}_r| \, \vec{v}_r \end{eqnarray*}

, where \(\vec{v}_w\) is the water velocity at the position of the weight, \(\rho\) = Rho the water density (default 1025 kg/m \(^3\), also the density of the buoyancy) and \(C_d\) = DragCoefficient the drag coefficient (default: the environment's sphere default, 0.5). Everything is expressed in the NED frame; the weight has no orientation. An Environment and a seafloor forces element are required shared resources — the former supplies \(\vec{v}_w\), the latter the soil load on the weight: environment::SeafloorForcesInterface::Sphere with the diameter 2r at the position, the force acting at the centre. The weight holds no soil parameter (the soil is the environment's).

Wake

With CastWake the weight casts a lumped wake that the other objects feel, through an environment::wake::BodyFlowInteraction and an environment::sphere_hydro::SphereCaster (fhsim_environment ADR 0002). The weight reads its own water velocity \(\vec{v}_w\) through it: the current with every other object's wake, never its own, plus the waves. It meets the other objects' wakes with or without CastWake.

The weight is always fully submerged: its submerged weight is constant, and it gets neither the wave surface (owner ruling R66) nor the wave excitation (R67). It is the centre clump of a double trawl, towed on or near the seabed, not a body of the wave zone (R110).

Example configuration excerpt

<Lib
   LibName                   = "fishery"
   SimObject                 = "Trawl/CenterWeight"
   Name                      = "C"
   Mass                      = "1000"
   Material                  = "Simple/Green"
   Density                   = "7500"
/>

Input Ports

Name	Width	Description
Force1	3	A force acting on the center weight.
Force2	3	A force acting on the center weight.
Force3	3	A force acting on the center weight.

Output Ports

Name	Width	Description
Pos	3	Position.
Vel	3	Velocity.

Configuration parameters

Name	Width	Description
Mass	1	The mass of the center weight object.
Density	1	The density of the center weight object.
Material	1	The visualization material of the center weight, specified by its name.
Mesh	1	The visualization mesh (geometry) of the center weight, specified by its filename (Default: fhSphere.mesh).
Scale	1	The scale of the center weight, related to the mesh. (Default: 1)
Rho	1	Water density [kg/m^3], > 0: the drag, the buoyancy and the wake. (Default: 1025)
DragCoefficient	1	Drag coefficient C_d of the sphere on its frontal area π r² [-], >= 0. (Default: the environment's sphere default, 0.5)
CastWake	1	The weight casts a lumped wake; the other wake parameters (Wake*, ExternalWakeUpdate) are listed in fhsim_environment's doc/user/wake-parameters.md. (Default: false)

Initial conditions

Name	Width	Description
Pos	3	Initial Position.
Vel	3	Initial Velocity.

Full example file

<Contents>
   <OBJECTS>
      <Lib
         LibName                   = "environment"
         SimObject                 = "Environment"
         Name                      = "Env"
         Waves.NumWaves            = "0"
         Bathymetry.Depth          = "55"
         Current.Model             = "Constant"
         Current.Vector            = "2.5,0,0"
      />
      <Lib 
         LibName                   = "fishery"
         SimObject                 = "Trawl/CenterWeight"
         Name                      = "C"
         Mass                      = "1000"
         Material                  = "Simple/Green"
         Density                   = "7500"
      />
   </OBJECTS>
   
   <INTERCONNECTIONS>
      <Connection
         C.Force1       = "10,10,10"
         C.Force2       = "10,10,10"
         C.Force3       = "10,10,10"
      />
   </INTERCONNECTIONS>
   
   <INITIALIZATION>
      <InitialCondition
         C.Pos = "0,0,-5"
         C.Vel = "0,0,0"
      />
   </INITIALIZATION>
   
   <SIMULATION>
      <Timing TStart="0" TEnd="30"/>
      <Integrator Method="RK45_i" NumCores="1" LogStates="1" UseRSSNorm="0">
        <StepControl StepMax="0.002" StepMin="0.00000001" AbsTol="1e-3" RelTol="1e-3"/>
      </Integrator>
      <!-- TODO migrate_v3: FileOutput="objects:all" -> configure via <OBSERVERS> section -->
   </SIMULATION>
</Contents>

This SimObject is referred to as Trawl/CenterWeight