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 seafloor contact forces.

\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 1.2). 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 bottom contact forces.

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: 1.2)
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