Liquid-Solid Phase Change Modeling Using Fluent. Anirudh and Joseph Lam 2002 Fluent Users Group Meeting
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1 Liquid-Solid Phase Change Modeling Using Fluent Anirudh and Joseph Lam 2002 Fluent Users Group Meeting
2 Solidification Model FLUENT can be used to solve fluid flow problems involving both solidification and melting for pure materials and alloys Instead of tracking the liquid-solid front explicitly, an enthalpyporosity formulation is used For pure materials, (T solidus and T liquidus are equal), a method based on specific heat is used The energy equation is written in terms of enthalpy: ( rh) +.( ruh) r =.(k T) + S t The liquid fraction, can be defined as: b = 0 if T T solidus b = 1 if T T liquidus T - Tsolidus b = T - T if T solidus < T <T liquidus, liquidus solidus 2
3 Solidification Model Other relationships between the liquid fraction and temperature (and species concentrations) are possible, but are not implemented yet The latent heat content/release can be written in terms of the latent heat and state of melting of the material, L: D H = b L Instantaneous latent heat content/release can vary between zero (for a solid) and L (for a liquid) Solution for temperature is essentially an iteration between the energy and the liquid fraction equation 3
4 Treatment of Mushy Zone in Alloys In Mushy zone, liquid fraction lies between 0 and 1 Mushy zone is modeled as a ''pseudo'' porous medium: porosity decreases from 1 to 0 as the material solidifies Appropriate momentum sink terms are added to account for the pressure drop caused by the solid material S = 2 (1 - b) A 3 ( b + e) mush r r (v - v Porosity in a solidified cell is zero: velocities takes on the solid (pull) velocity Similar sinks are also added to the turbulence equations 2 (1 - b) S = A f 3 mush ( b + e) p ) β : liquid volume fraction ε : small number to prevent division by 0 A mush : is the mushy zone constant and : the solid pull velocity v r P 4
5 Contact Resistance Due to Shrinkage T w T w l Wall T Near wall cell T Presence of an air gap between the walls and the solidified material causes an additional heat transfer resistance between the cooling walls and adjacent fluid with liquid fraction less than 1 This contact resistance is accounted for by adding appropriate resistance in the wall heat flux calculation: R c l/k w Contact Thermal ( / k + R (1 )) Resistance Near the Wall c - b q = l (T k : thermal conductivity T β : liquid volume fraction, and R c : contact resistance[m 2 K / W] - ) 5
6 Pull Velocity for Continuous Casting In continuous casting processes, the solidified material is continuously pulled out from the computational domain Solid material has a finite velocity that influences solidification front The exact computation of the pull velocity for the solid material is dependent on the E and σ of the solid and the forces acting on it In FLUENT, an approximated Laplacian equation is used: r 2 v p = 0 Appropriate Dirichlet boundary conditions are used on walls and outlets and the fluid velocity is picked up at the interface mold Solidified Shell Pull Horizontal Continuous Casting of Iron 6
7 Solidification/Melting Model Inputs Define/models/ solidification and melting... Define/materials... 7
8 Continuous Casting of Round Billet Slag (oil) Inlet Input Parameters: Parameters : Mold u u Liquid u Symmetry axis u Moving wall u u u u u u Diameter of the mold mold:: m Diameter of the nozzle: nozzle : 0.03 m Mold length length:: 0.50 m Casting speed: speed: 0.03 m/s Solidus temperature: temperature : 1490 C Liquidus temperature: temperature : 1530 C Melt superheat: superheat: 20 C Mold heat transfer coefficient: coefficient : 1270W/m2/ C Spray heat transfer coefficient: coefficient: 1080W/m2/ C Simulated length: length : 3.0 m Casting speed Schematic configuration 8
9 Continuous Casting of Round Billet Pressure-outlet Computational mesh in the upper region Input Parameters (continued): Density: 7020 kg/m 3 Viscosity: 6.2x10-3 J/kg Latent heat of fusion: 270x10 3 J/kg Specific heat: 680 J/kg/ C Thermal conductivity: 34 W/m/ C Thermal expansion coefficient: 1x10-4 /K Permeability coefficient: 5.0x10-11 m 2 Mesh size: 227x48 cells (10,896 total) Near wall treatment: enhanced wall treatment Solidification profile is obtained based on 30% liquid fraction (after Aboutalebi et al, 1995) Comparison of predicted solidified shell thickness with the experiments of Ushijima (1962) shows good agreement 9 Solidified shell thickness (mm) Distance from the meniscus (m) Expt. of Ushijima (1962) Computed profile
10 Cold wall 4.5 cm Melting of Pure Material: Gallium Hot wall Insulated wall 9.0 cm Material: Gallium(Pure) Property Units Value Density kg/m Specific Heat j/kg-k Therm. Cond. w/m-k 29 Viscosity kg/m-s Therm. Exp. Coeff. 1/k e-05 Melting Heat j/kg Solidus Temperature k 302 Liquidus Temperature k 302 g Insulated wall Y-Coordinate t = 5 min (current) t = 8 min (current) t = 12 min (current) t = 5 min (Exp.*) t = 8 min (Exp.*) t = 12 min (Exp.*) t = 5 min (Rep. Comp.) t = 8 min (Rep. Comp.) t = 12 min (Rep. Comp.) *(Webb and Viskanta, NHT Vol. 9, pp , 1986) Validation of Pure Metal Melting (Gallium) Ste = 0.042, Pr = 0.021, Ra = 2.2 x X-Coordinate
11 Solidification with VOF A liquid metal droplet spreads and solidifies on a cooled substrate The VOF (free surface) and phase change models in FLUENT are used together to simulate the process Results are useful for applications of liquid metal jetting, used in electronics manufacturing Also useful for printing, painting, spray gluing applications 11
12 Liquid Metal Solidification t = 50 µs solidification (black) VOF model uses single set of fluid equations tracks liquid/gas volume fraction and location and shape of gasliquid interface Phase change model uses enthalpy-porosity method tracks liquid-solid interface within the liquid phase source terms in energy equation depend on liquid fraction and available latent heat 12
13 Liquid Metal Solidification... t = 250 µs solidification (black) Solid layer is colored black Spread factor, d final /d initial = 3.2 as predicted by FLUENT is in good agreement with published numerical finding, Simulation shows that FLUENT can capture combined phenomena of free surface flows and phase change t = 750 µs t = 1.9 ms solidification (black) solidification (complete) 1 Brendon R. Holt and Albert Y. Tong, The normal incidence impact and solidification phenomena of a liquid metal droplet onto a rigid substrate, ASME FED-Vol. 234, 1995 IMECE,
14 Vibrating Mold with Solidification A 3D round billet case is studied with mold oscillations The mold stroke: 0.025m and frequency: 1Hz The average free-board is 0.15m Solidification in the mold is analyzed Free-surface of the steel is assumed shearfree and not dynamically recalculated as with a VOF analysis This is *not* a limitation but a simplification adopted here All other process parameters are same as the 2D study 14
15 Vibrating Mold with Solidification Some instantaneous solution fields Velocity vectors Pathlines Temperature Liquid Fraction 15
16 Vibrating Mold with Solidification These animations on a diameter-plane The mold water region contours are showing velocity magnitude in both cases The dynamics of the flow-fields are slower than the mold-oscillation rate In a couple of mold-cycles, no significant change in the flow-field should be expected Oscillation frequency in the actual mold can be slower Liquid Fraction Temperature 16
17 Mold Flow with Meniscus and Solidification Atmospheric Pressure SEN (V-in) A slab caster mold Flow and heat transfer Solidification Mold top is open to atmosphere Free surface at the meniscus No chemistry is considered Mold wall Open slab Wall SEN-jet (internal) Geometry Pressure Outlet 17
18 Mold Flow with Meniscus and Solidification Mold top is open to atmosphere No mold powder is considered Air on top of the mold maintains a mild recirculating flow Outlet pressure reflects the force of the support-rolls which would determine the free-board in the mold Solidified shell on mold wall develops depending on the process parameters Casting speed Incoming superheat of liquid steel The jet penetration and SEN design Mold water flow rate Velocity Vectors Liquid Fraction 18
19 Mold Flow with Meniscus and Solidification Contact resistance is automatically introduced based on the local state of solidification Similarly, pull velocity is assigned on the solidified material only Figure shows shell thickness, free surface (meniscus) and the velocity field in a slab caster mold on the wide, symmetry face 19
20 Summary of Melting/Solidification Model Features Enthalpy-Porosity formulation Accessible through GUI interface Contact resistance at walls (customizable) Marangoni convection at "walls" Solid pull velocities (both user-specified and computed) VOF-compatible Sink terms for momentum & turbulent quantities in mush & solid zones Limitation Lack of species transports model User-specified H-T curve Both species model and custom-h-t curve should be available in the next release - macro-segregation can be modeled 20
Abstract. Nomenclature. A Porosity function for momentum equations L Latent heat of melting (J/Kg) c Specific heat (J/kg-K) s Liquid fraction
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