(VOF) Model

Multiphase Flow Modeling
with Free Surfaces Flow
Jinwon Seo
TAESUNG Software and Engineering, INC
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© 2014 ANSYS, Inc.
May 13, 2014
ANSYS Confidential
Outline
• Overview of Multiphase Flow
• Multiphase Models in ANSYS CFD
• Separated / Free Surface Flows
• Volume of Fluid (VOF) Model
• Key Concepts
• VOF Model Inputs & Requirements
• Best Practices
• VOF Model Examples
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Introduction of Multiphase Flow
Multiphase flow involves the simultaneous flow of two
or more immiscible interacting phases.
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Features of Multiphase Flows
Multiple Length Scales
Several Flow Regimes
Multiple Physics
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Flow Always Accompanied by Other Physics!
Heterogeneous
and
homogeneous
reactions
Phase change
Heat transfer
Size change
Fluid
Dynamics
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Multiphase Models in ANSYS CFD
Separated
flows
VOF model
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Dispersed
flows
Eulerian
Models
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Lagrangian
models
A Solution for Every Multiphase Problem
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Separated / Free Surface Flows
• Separated Flows
• Both phases are continuous and both are of interest
• Interface length scale is large
• Stratified flows
• Free Surface Flows
• Only liquid phase is of interest
• Open channel flows
Fluids are separated by a distinct resolvable interface
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Applications
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•
Inkjets
•
Coating
•
Tank Filling and Sloshing
•
Jet breakup
•
Open channel flows
•
Offshore transport
•
Gear lubrication
•
Piston cooling
•
Ship Hull
•
Wave Loading
© 2014 ANSYS, Inc.
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Courtesy Speedo
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Volume of Fluid (VOF) Method
• Method to track/capture the sharp interfaces
between immiscible fluids
• Shape of the interface is of interest
Volume Fraction :
Scalar indicator function between 0
and 1, for each fluid represented as
Fluid-1
Fluid-2
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Vf
f 
V
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f=1
: Fluid-1
f=0
: Fluid-2
0 < f < 1 : Interface
Applicability of VOF Model
• VOF model is used to model immiscible fluids with clearly defined interface
• Two gases cannot be modeled since they mix at the molecular level
• Liquid/liquid interfaces can be modeled as long as the two liquids are immiscible
• VOF is not appropriate if interface length is small compared to a computational
grid
• Accuracy of VOF decreases with interface length scale getting closer to the computa
tional grid scale
Interface
length larger
than grid
Interface
length scale
is smaller
than grid
VOF applicable
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VOF not applicable
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VOF Scheme Comparisons
Advantages
Explicit VOF
Sharper interface
Accurate solution
Disadvantages
Poor convergence for
skewed meshes
Poor convergence if phases
are compressible
Implicit VOF
Does not have Courant number limitation
(can be run with large time steps or in ste
ady state mode)
Can be used with poor mesh quality and f
or complex flows (e.g. compressible flows)
Numerical diffusion of inter
face does not allow accurat
e prediction of interface cur
vature
Take Away
Implicit Compressive scheme along with Bounded Second Order time
discretization scheme give sharp interface and accurate solution
(with uniform mesh size or gradual cell jumps)
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Interface scheme comparisons for VOF
Scheme
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Interface scheme
Implicit
Explicit
Accuracy
Speed
First order


Not recommende
d
Not
recommended
Second order


Not
recommended
Not
recommended
QUICK


Low
High
Modified HRIC


Medium
High
CICSAM


High
Medium
Compressive


High
Medium to High
Georeconstruct


Very high
Low to medium
BGM


Very high
Low to medium
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Interface scheme comparisons for VOF Scheme
VOF Explicit, First order time
Geo-Recon Compressive
CICSAM
VOF Implicit, Second order time
First Order
Compressive
HRIC
Take Away
Implicit Compressive scheme along with Bounded Second Order time
discretization scheme give sharp interface which is comparable to the most
accurate Geo-Reconstruct
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Interface scheme comparisons for VOF
Scheme
Explicit Schemes Comparison
Accuracy
Geo-Reconstruct > Compressive > CICSAM > HRIC
Speed
HRIC > CICSAM > Compressive > Geo-Reconstruct
Sharpness
Geo-Reconstruct > CICSAM > Compressive > HRIC
Implicit(or Steady State) Schemes Comparison
Speed
HRIC > Compressive > BGM
Sharpness
BGM > Compressive > HRIC
Stability
HRIC > Compressive > BGM
Transient Formulation Comparison
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Accuracy
Bounded Second Order > Second Order > First Order
Speed
First order > Second Order > Bounded Second Order
Stability
First order > Bounded Second Order > Second Order
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Zonal Discretization Schemes
• This option enables you to set diffusive or sharp interfac
e modeling in different cell zones based on the value of
zone dependent slope limiter. Extension of compressive
scheme.
 f  d  d
• The usage in porous medium application:
• Diffusive interface modeling in porous medium zone
• Sharp interface modeling outside the porous zone
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(Zone 1)
(Zone 2)
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(Zone 3)
Slope Limiter (Beta)
Scheme
Beta = 0
First Order Upwind
Beta = 1
Second order upwind
Beta = 2
Compressive
0 < Beta < 1 ,
1 < Beta < 2
Blended scheme
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Surface Tension
• Attractive forces between molecules in a fluid
– VOF model can include the effects of surface tension along the interface between each
pair of phases, through source term in momentum equation
• Surface tension force made of two components:
– Normal component (due to interface curvature): σκδ
– Tangential component (due to variations in the surface tension coefficient): (sσ)δ
•
Importance of surface tension effects:
– For Re >> 1, Weber number - droplet formation
U 2 L
Inertial force
We 


Surface tension force
– For Re<<1, Capillary number - coating flows
Ca 
Surface tension effects
can be neglected
if Ca>>1 or We>>1.
U
Viscous force
 Re We 

Surface tension force
Take Away
Continuum Surface Force Model (CSF) and Continuum Surface Stress Model (CSS)
are available in ANSYS Fluent
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Turbulence Damping
•
Resolving Velocity Gradient in the vicinity of
interface
• High velocity gradients at the free surface
results in high turbulence generation
• Important to resolve interfacial instability
• Numerical damping of turbulence by adding
source term for turbulent dissipation in
interfacial cells.
• This treatment is available only for k-omega
turbulence model
No Damping
With Damping
Interfacial instability
t = 8.1s
Slug formation
t = 8.3s
Slug growth
t = 8.5s
t = 9s
Reference : Experimental investigation and CFD simulation of horizontal stratified two-phase
flow phenomena, Christophe Vall´ee , Thomas H¨ohne, Horst-Michael Prasser, Tobias
S¨uhnel Nuclear Engineering and Design 238 (2008) 637–646
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Open Channel Flows
• Characterized by Froude Number ,
Fr 
V
Inertia force

gL Gravity force
yout

Vin
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yin
• Applicable to flows where both inertia and gravity are dominant with
known depths of the liquid at the inlets or outlets
• Example – Ship moving through the sea at depth yin and speed Vin
• Prescribe yin and Vin at inlet and yout at the outlet.
Modeling Surface Gravity Waves
ANSYS CFD (Fluent) has the inbuilt capability for simulating complete wave regime.
•First order Airy wave theory
•Linear
•Small amplitude
•Shallow to deep liquid
depth
•Stokes wave theories
•Non linear
•Finite amplitude
•Intermediate to deep water
range. ( h/L > 0.1)
•Cnoidal & Solitary
•Non linear
•Finite amplitude
•Shallow water
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H - Wave height
h - Water depth
L - Wave length
Open Channel Wave BC Checking
Using a TUI command
/define/boundary-conditions/
open-channel-wave-settings
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Modeling Oblique Waves
• User can specify the Reference Wave Direction as Averaged
Flow Direction, Direction Vector or Normal to Boundary
• Now user can specify different velocity magnitude and
directions for the flow current, wave and ship .
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Wave Spectrum for Random Sea ( Beta Fe
ature)
Wave spectrum is used for simulating irregular waves
(Short and long crested waves)
– Wave spectrum available in 15.0
• Pierson-Moskowitz (Fully developed seas)
• Jonswap (Fetch limited seas)
• TMA ( Fetch limited finite depth seas)
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Multi-Fluid/Inhomogeneous VOF
• Adds interfacial sharpening schemes in Eulerian
Model Framework
–
Different Velocities and Temperatures at the
interphase
• Capable for modeling both dispersed and
separated flow regimes
– Physics in the stratified region: surface tension,
no-slip at the interface
– Physics in the dispersed region: wall lubrication,
sub-grid scale drag models based on predicted
diameter
• Anisotropic drag
– Higher drag in the interfacial normal direction for
the velocity continuity
– Lower drag in the tangential direction to allow
different shear stresses
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VOF Model Compatibility with Other Models
VOF + Solidification & Melting
• Compatible
–
–
–
–
–
Solidification and Melting Model
Moving Dynamic Mesh
Six Degrees of Freedom (6DOF) Model
System Coupling ( FSI)
Phase Change / Cavitation Model
Air entrapment during mold filling and
solidification in casting process
• Not Compatible
– Turbulent Combustion Models
– Boiling Models
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VOF + Cavitation Model
NACA 66 hydrofoil
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VOF + Solidification/Melting
Applications :
Casting
• Droplet solidification during
impingement
• Casting, air entrapment
• Effect of air convection on
solidification rate
• Shrinkage/expansion
• Welding of different metals
• Effect of arc pressure on molten pool
• Impingement of filler droplets in
welding
Air entrapment during mold filling and
solidification in casting process
Welding
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Free Surface Mass Transfer
Using UDFs for mass & heat
transfer
• Free surface evaporation
and condensation
• Direct contact
condensation
• Film boiling
• Wall condensation
Wall condensation
Equilibrium
Gas
(air + vapor species)
Liquid (water only)
Evaporation occurring at free surface
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After heating
Evaporation: Bubble growth
(pressure contours)
VOF Inputs
• Phases
• Arbitrary number of phases are allowed
• Any phase can be primary or secondary –
not important in VOF model.
• Usual practice is to have secondary phase
which has less presence in the domain
• Compressible phase as primary phase
• Implicit body force (Designed for flows with large
body forces)
• The force is handled in robust numerical
manner.
• Gravity acting on phases with large density
difference.
• Flows with large rotational accelerations
(such as centrifugal separators and/or
rotating machinery).
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Mesh Requirement
• Uniform mesh
• Gradual cell growth in case of non uniform mesh
• Same mesh type in the interface region
– For speed up with Explicit VOF
– For less numerical diffusion with Implicit VOF
Tet is better than Tet+hex in this case
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Best Practice: VOF Schemes
• Steady ( Only Implicit VOF available)
– Compressive – recommended for most
of the problems
– BGM – for sharper interface
– P-V Coupling: Coupled VOF ( for faster
convergence)
• Transient
– Explicit Compressive / Implicit
Compressive with Bounded second
order time discretization recommended for most of the problems
– Geo-reconstruct (available only with
Explicit) - for sharper interface
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Best Practice: VOF Schemes & Solver Settings
Explicit VOF
Generic conservative settings
Operating Conditions must set properly
for most of the VOF cases
Turn off for surface tension dominated flows
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Best Practice: VOF Schemes & Solver Settings
Explicit VOF
Generic conservative settings
•
•
•
New in R 15.0
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Use PISO algorithm
Use lower URF for Pressure and Momentum
if any divergence ( Pressure-0.2, Momentum-0.3)
If the liquid interface mesh is not uniform or the velocity is varying
• Use Variable Time stepping Method
• Use best suited courant calculation method
• Solve > set > vof-explicit-controls
0 = velocity based , 1 = flux based (default),
2 = flux averaged , 3= hybrid
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Best Practice: VOF Schemes & Solver Settings
Implicit VOF
Generic conservative settings
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Best Practice: For Speed Up
1. Use Implicit VOF, Compressive and Bounded Second
Order Time Discretization scheme
– This allows to use a larger time step size
– Use higher URFs for pressure and momentum( up to 0.8)
– NITA can be tried along with this if the phases are modeled as incompressible
2. If the solution is not accurate with Implicit VOF
– Check the solution with a smaller time step size
– Use Explicit Compressive or Geo-Reconstruct
3. Explicit VOF
– Use uniform mesh in the liquid interface regions
• Use Variable Time Stepping for non uniform mesh in the interface region
– Try with different courant calculation methods
• Solve > set > vof-explicit-controls
– NITA can be tried if the phases are modeled as incompressible
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NITA(Non Iterative Transient Advancement)
for Transient Speed-up
•
NITA can be used when the phases are modeled as incompr
essible
Computational Time in 8 CPU, Mesh count264K: ITA- 9.5 hr, NITA- 2.67 hr
ITA PISO
CPU-15,794
ITA vs NITA
NITA PISO
CPU-3,450
Water loading on a structure Sloshing in a Tank with baffles
Take Away
NITA is 3 to 5 times faster and does not compromise on accuracy
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VOF Model Examples
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Tank Filling
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Free Surface Flow around a Spinning Gear
Sliding mesh model with VOF
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Box falling
MDM (Moving Deforming Mesh) Remeshing & 6DOF (6 Degrees of Freedom)
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Slug Flow
Air Inlet
ANSYS
FLUENT
Splitter plate
Diameter: 0.078m
Length: 37m
Water Inlet
Experiment
(Reference)
Slug frequency
Reference :
Slug initiation and evolution in two-phase horizontal flow
Priscilla M. Ujang, Christopher J. Lawrence, Colin P. Hale, Geoffrey F.
Hewitt , International Journal of Multiphase Flow 32 (2006)
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Bubble Rise in Slurry
t = 0.2 s
Gas
bubble
Slurry (Water
+ Solids)
Solids
Gas
HRIC
Gas
Solids
Phase localized
Compressive
Slope limiters : Gas-Solid = 2
Gas-Fluid = 2 , Fluid-Solid = 0
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Wave Slamming
Wave interaction with a floating structure
MDM (Moving Deforming Mesh), 6DOF (6
Degrees of Freedom)and Open channel
Wave BC along with VOF model
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Wave slamming on submarine
Wave Slamming
MDM (Moving Deforming Mesh), 6DOF (6 Degrees of Freedom)and Open channel Wave BC along with VOF model
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Wave Impact Loading on an Offshore Oil Rig
Open Channel Wave BC with Solitary Wave
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