Free Surface Modeling

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Free Surface Modeling
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Outline

• Engineering Applications
• Moving Boundary Methods
• Lagrangian
• Eulerian
• Flux Line-Segment Model for Advection and
  Interface Reconstruction (FLAIR)
• Hybrid Finite Element-Volume of Fluid
• Simulations

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Sample Applications

• Crystal Growth
• Molding/Casting
• Liquid Free Surfaces
• Flame Propagation

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Moving Boundary Methods

• Lagrangian Methods
• Grid is Adaptive
• Points on interface are advected
• New interface is found by fitting curve through
  advected points

• EulerianMethods
• Grid is fixed
• Fluid under interface is advected
• New interface is approximated by using volume
  fraction variable

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Some Specific Methods

• Lagrangian Type
• Moving Grid
• Front Tracking
• Eulerian Type
• Marker and Cell (MAC)
• Volume-of-Fluid (VOF)
• Surface Line Interface Calculation (SLIC)
• Hirt Nichols VOF
• Youngs VOF
• FLAIR
• Many other versions exist

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Moving Grid Methods

• Rayleigh-Taylor Instability
• Interface coincides with cell boundaries
• Distorted Grid over time

Example from Approaches to Resolving and Tracking
Interfaces and Discontinuities, Laskey et. al,
NRL Report 5999, 7/28/97
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Front Tracking Methods

• Points defined on Interface and are moved in time
• Interface location and orientation is known at
  each time step
• Method fails when interface geometry becomes
  complicated

Sample Configuration
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MAC (Marker and Cell)

• Massless Particles are injected
• Particle Trajectories are tracked
• Cannot resolve details of the inteface smaller
  than the mesh size
• Expensive in Computer time and memory

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Volume Tracking General Idea

• Define fluid volume fraction f-field
• f0 No fluid in cell
• f1 Cell filled with fluid
• 0ltflt1 Cell partially filled with fluid (i.e.
  Interface cell)
• Initial interface geometry is used to compute
  fractions

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Volume Tracking General Idea

• Interface is reconstructed using the f-field
• f-field does NOT imply a unique interface
  geometry
• interface is constructed based on some algorithm
• Volume fractions (f-field) are some-how advected
• New f-field based on amount of fluid entering,
  leaving and reamining in the cell

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Advection of Volume Fraction Field

• Fluid Advection satisfies

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Volume Tracking - Advantages/Disadvantages

• Advantages
• Interface positions are NOT stored for each
  time-step
• Large Surface Deformations
• Mergering and Breakup of Interfaces
• Easy implementation
• Disadvantages
• Interfaces are NOT exact
• Reconstruction techniques require many logical
  operations
• Resolution dependent

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SLIC (Simple Line Interface Calculation)

• Interface is Horz. or Vert.
• Assumed
• fluid resides on heavyside of interface
• Advection
• x-pass (horizontal)
• y-pass (vertical)

Original Geometry
y-pass
x-pass
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Hirt Nichols VOF

• Interface is Horz. or Vert. (piecewise constant)
  (stair stepped)
• Derivatives of the f-field determine whether the
  interface is Horz. or Vert.
• Derivatives calculated using fractional volumes
  averaged over several cells

Original Geometry
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Youngs VOF

• Interfaces - piecewise linear
• Interface has slope and is fitted within a single
  cell
• Interface slope and fluid position are determined
  from inspection of 8 neighboring cells

Original Geometry
Reconstructed