Simulation of Pancake Ice Dynamics In a Wave Field by Mark Hopkins and Hayley Shen

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Simulation of Pancake Ice DynamicsIn a Wave
Field by Mark Hopkins and Hayley Shen
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Simulation of Pancake Ice Dynamics

• Three-dimensional, discrete element ice model
• Ice floes are disks with variable aspect ratio,
  friction coef, and drag coef.
• One dimensional wave model
• Water drag and added mass
• Accurate bouyancy forces and moment

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DISCRETE ELEMENT ICE MODEL

• Computer simulation of particle systems such as
  ice accumulations
• Store position, orientation, shape, and velocity
  of each particle
• Floe orientation specified using quaternions (4
  parameter representation)
• Dynamics of system evolves from contact and body
  forces on particles (Fma at each contact)

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SIMULATION OF PANCAKE ICE DYNAMICS
Normal Contact Force Spring and
dashpot (Viscous-elastic)
Tangential Contact Force Coulomb friction
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Forces Acting on Floes
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Water Drag on Floes

• Fd -1/2Cd?wA(V-Vw) V-Vw
• Drag resolved into floe normal and tangential to
  flat surface of floe
• Use water velocity Vw at location of floe center
• Cd0.6 for normal flow
• Cd0.06 for tangential flow
• Rotational drag is similar
• Added mass coefficient 0.15

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Bouyancy Force on Floes

• Integrate dP -?wg (?-z) n dA over floe surface
• where the water surface ? is
  ? 1/2 H cos(kx-?t)
• Construct 4 dimensional look-up table
• Variables are floe normal angle to vertical,
  azimuthal angle, floe center depth, and water
  surface inclination.

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Simulation Parameters

• Domain length 600 m (6 wave lengths)
• Domain width 8.75 m
• Wave length 100 m
• Wave Amplitude 3,3.5,4,4.5,5 m
• Floe diameter 1.0 m
• Floe thickness 167 mm
• Coef of restitution 0.25
• Coef of friction 0.35

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Ice Accumulation at Barrier

Figure width 62 m
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Evolution of force on barrier as a function of
wave amplitude and time.
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Average ice drift velocity as a function of phase
angle and wave amplitude. Without collisional
dynamics
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Average ice drift velocity as a function of phase
angle and wave amplitude. With collisional
dynamics
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Ice accumulation at barrier as a function of
distance from the barrier at 1000s intervals for
H3.5 m
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Rate of thickening as a function of time and
distance from the barrier H3.5 m
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Summary

• Ice thickness reaches equilibrium