Adv Multiphase v6.3 07a Solidification

The Solidification The Solidification The Solidification Model in FLUENTThe Solidification Model in FLUENT

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Fluent User Services Center

www.fluentusers.comAdvanced FLUENT TrainingMultiphase Sept. 2007

Solidification

id h f ll i bili i f d liFLUENT provides the following capabilities for modeling solidification and melting:

Calculation of liquid-solid solidification/melting in pure metals as q g pwell as in binary alloys.Modeling of continuous casting processes (i.e., pulling of solid material out of the domain).)Modeling of the thermal contact resistance between solidified material and walls (e.g., due to the presence of an air gap).Modeling of species transport with solidification/meltingModeling of species transport with solidification/melting.Postprocessing of quantities related to solidification/melting (e.g. liquid fraction and pull velocities)

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Limitation

Th lidifi i / l i d l b d l i h h dThe solidification/melting model can be used only with the segregated solver; it is not available with the coupled solvers.The solidification/melting model cannot be used for compressible flflows.Of the general multiphase models (VOF, mixture, and Eulerian), only the VOF model can be used with the solidification/melting model.With the exception of species diffusivities, you cannot specify material properties separately for the solid and liquid materials.When using the solidification/melting model in conjunction with modeling species transport with reactions, there is no mechanism to restrict the reactions to only the liquid region; i.e., the reactions are solved everywhere.




Energy Equation

h h l f h i l i d h f hThe enthalpy of the material is computed as the sum of the sensible enthalpy, h, and the latent heat, ∆H:

T

∫HhH ∆+= dTchhT p∫+=

refref

retemperatuReferenceenthalpy Referenceref

==

Th

pressureconstant at heat SpecificretemperatuReferenceref

==

pCT

<<

<

−−

=β liquidussolidus

solidus

lidli id

solidus for

for 0

TTT

TT

TTTT


> solidus

solidusliquidus

for 1 TTTT



Energy Equation

h l h b i i f hThe latent heat content can now be written in terms of the latent heat (melting heat) of the material:

Lh β=∆

For solidification/melting problems, the energy equation is

Lh β=∆

written as:( ) ( ) ( ) STkHvth

+∇⋅∇=ρ⋅∇+∂ρ∂ r

t∂




Momentum + Turbulence

h i k d h d d i i hThe momentum sink due to the reduced porosity in the mushy zone takes the following form: A

( )21 β 0010( ) ( )pullmush3

1 vvAS vv −ε+β

β−= 74 1010

001.0<<

=ε

mushA

Sinks are added to all of the turbulence equations in the mushy and solidified zones to account for the presence of solid matter:solid matter:

( )φ

ε+ββ−

= mush3

21 AS




Species EquationFor the case of multicomponent solidification with species segregationFor the case of multicomponent solidification with species segregation, the solidus and liquidus temperatures are computed using the following equations:

∑+= meltsolidus iii YmKTT

where: Ki = Partition coefficient of solute i which is the ratio

Solutes

∑+=Solutes

meltliquidus ii YmTT

where: Ki Partition coefficient of solute i, which is the ratioof the concentration in solid to that in liquid at theinterface.

Yi = Mass fraction of solute i TSl f th li id f ith t t Ymi = Slope of the liquidus surface with respect to Yi.

It is assumed that the last species material of the mixture is the solvent and that the other species are the solutes.


and that the other species are the solutes.



Species Equation

h f ll i i i i l dThe following species equation is solved:( ) ( )[ ] iii

i RJYvYvtY

+−∇=β−+βρ⋅∇+∂ρ∂ rrr

sol ,solliq ,liq 1

Diffusion flux of species i:t∂

( )[ ]1 YDYDJ β+βρ=

Average species mass fraction in a cell:

( )[ ]sol ,sol ,,liq ,liq ,, 1 imiimii YDYDJ β−+βρ−=

( ) sol ,liq , 1 iii YYY β−+β=

liq,sol, iii YKY =


q,,



Contact Resistance at Walls

h ll h fl b iThe wall heat flux can be written as:

− wTT Wall

( )β−+=

1c

w

RkLq wTT = T

L

wT T

cR kL /




Pull Velocity for Continuous Casting

Mushy zone Solidified shelly

pullvr

WallLiquid core

pull

Pulling a Solid in Continuous Casting




Pull Velocity for Continuous Casting

h i f h ll l i f h lidThe exact computation of the pull velocity for the solid material is dependent on the Young's modulus and Poisson's ratio of the solid and the forces acting on it.g

FLUENT uses a Laplacian equation to approximate the pull velocities in the solid region based on the velocities at the boundaries of the solidified region:

0∆r 0pull =∆vr




Boundary Conditions

h f ll i b d di i hFLUENT uses the following boundary conditions when computing the pull velocities:

At a velocity inlet, stationary wall, or moving wall, the specified y , y , g , pvelocity is used. At all other boundaries (including the liquid-solid interface between the liquid and solidified material), a zero-gradient velocity q ), g yis used.

The pull velocities are computed only in the solid region. N t th t FLUENT l ifi d t t lNote that FLUENT can also use a specified constant value or custom field function for the pull velocity, instead of computing it.




Setup Procedure

l b 4 d 7 d d fValues between 104 and 107 are recommended for most computations.The higher the value of the

Define Models Solidification & Melting…The higher the value of themushy zone constant, thesteeper the damping curveb d th f t thbecomes, and the faster thevelocity drops to zero asthe material solidifies. Very large values may cause the solution to oscillate as control volumes alternately solidify and melt with minor perturbations in liquid volume fraction


perturbations in liquid volume fraction.



Setup Procedure

h i l l if h l i h lidIn the Materials panel, specify the melting heat solidus temperature and liquidus temperature for the material being used in your model.g yIf you are solving for species transport, you also must specify the melting temperature of pure solvent.

Th l i h l i i l f h i i lThe solvent is the last species material of the mixture material.For each solute, you will have to specify the slope of the liquidus surface (slope of liquidus line) with respect to the concentration of h l h i i ffi i d h f diff i ithe solute , the partition coefficient, and the rate of diffusion in

solid.

It is not necessary to specify mi and Ki for the solvent.




Setup Procedure

h b d di iSet the boundary conditions.If you want to account for the presence of an air gap between a wall and an adjacent solidified region specify abetween a wall and an adjacent solidified region, specify a non-zero value, a profile, or a user-defined function for Contact Resistance under Thermal Conditions in the Wall

lpanel.If you want to specify the gradient of the surface tension with respect to the temperature at a wall boundary, you can p p y, yuse the Marangoni Stress option for the wall Shear condition.




VOF + Phase Change

l lidifi iDroplet solidificationDroplet and air at T0 = 510 K, wall at 475 K


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Adv Multiphase v6.3 07a Solidification