Transcript Free Surface Modeling - University of Toronto

Free Surface Modeling
Outline

Engineering Applications

Moving Boundary Methods
– Lagrangian
– Eulerian
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Flux Line-Segment Model for Advection and
Interface Reconstruction (FLAIR)
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Hybrid Finite Element-Volume of Fluid
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Simulations
Sample Applications
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Crystal Growth
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Molding/Casting
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Liquid Free Surfaces
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Flame Propagation
Moving Boundary Methods
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Lagrangian Methods
– Grid is Adaptive
– Points on interface are
advected
– New interface is found by
fitting curve through
advected points
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EulerianMethods
– Grid is fixed
– Fluid under interface is
advected
– New interface is
approximated by using
volume fraction variable
Some Specific Methods
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Lagrangian Type
– Moving Grid
– Front Tracking
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Eulerian Type
– Marker and Cell (MAC)
– Volume-of-Fluid (VOF)
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Surface Line Interface Calculation (SLIC)
Hirt & Nichols VOF
Young’s VOF
FLAIR
Many other versions exist
Moving Grid Methods
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Rayleigh-Taylor
Instability
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Interface coincides
with cell boundaries
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Distorted Grid over
time
Example from Approaches to Resolving and Tracking Interfaces and Discontinuities, Laskey et. al, NRL Report 5999, 7/28/97
Front Tracking Methods
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Points defined on Interface
and are moved in time
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Interface location and
orientation is known at each
time step
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Method fails when interface
geometry becomes
complicated
Sample Configuration
MAC (Marker and Cell)
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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
Volume Tracking: General Idea
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Define “fluid volume fraction” : f-field
– f=0: No fluid in cell
– f=1: Cell filled with fluid
– 0<f<1: Cell partially filled with fluid (i.e. Interface cell)
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Initial interface geometry is used to compute
fractions
1
1
1
1
1
1
1
1
.92
.09
0
1
.85
.35
0
0
.31
.09
0
0
0
0
0
0
0
0
.68
0
.42
0
Volume Tracking: General Idea
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Interface is reconstructed using the “f-field”
– f-field does NOT imply a unique interface geometry
– interface is constructed based on some algorithm
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Volume fractions (f-field) are some-how advected
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New f-field based on amount of fluid entering,
leaving and reamining in the cell
Advection of Volume Fraction Field
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Fluid Advection satisfies:
F
 U   F  0
t
Volume Tracking Advantages/Disadvantages
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Advantages
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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
SLIC (Simple Line Interface Calculation)
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Interface is Horz. or Vert.
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Assumed:
– fluid resides on heavyside
of interface
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Original Geometry
Advection:
– x-pass (horizontal)
– y-pass (vertical)
x-pass
y-pass
Hirt & Nichol’s VOF
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Interface is Horz. or Vert.
(piecewise constant)
(stair stepped)
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Derivatives of the f-field
determine whether the
interface is Horz. or Vert.
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Derivatives calculated using
fractional volumes averaged
over several cells
Original Geometry
Reconstructed
Young’s VOF
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Interfaces - piecewise linear
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Interface has slope and is
fitted within a single cell
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Original Geometry
Interface slope and fluid
position are determined
from inspection of 8
neighboring cells
Reconstructed