# A study on development of the three-dimensional

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## Abstract

A three dimensional model was developed to analyze the mold filling and solidification in the casting processes. The model uses the VOF method for the calculation of the free surface and the modified Equivalent Specific Heat method for the treatment of the latent heat evolution. The solution procedure is based on the SIMPLER algorithm. The complete model has been validated using the exact solutions for phase change heat transfer and the experimental results of broken water column. The three-dimensional model has been applied to the benchmark test and the results were compared to those from experiment, a two-dimensional analysis, and another three dimensional numerical model.

## Key Words

Mold Filling Solidification Free Surface Phase Change SIMPLER VOF Equivalent Specific Heat## Nomenclature

*a*Thermal diffusion coefficient

*a*coefficients for discretized equations

*A*Area

*b*Source term

*C*_{f}Wall friction variation

*C*_{p}Specific heat

*D*_{h}Hydraulic diameter

*f*Fraction

*F*Volume fraction

- Φ
Dependent variable

- Γ
Diffusion coefficient

*g*Gravitational force

*h*Heat transfer coefficient

- ΔH
Release of latent heat

*k*Thermal conductivity

*L*Latent heat

- Λ
Darcy friction factor

*p*Pressure

*q*Heat flux

*R*Thermal resistance

*p*Density

*S,S*_{c},*S*_{p}Linearized source term

*t*Time

*T*Temperature

*T*_{p}Initial temperature

*T*_{f}Interface temperature

*τw,τ*Shear stress

*u, V*Velocity components

*V*Volume

*x, y, z*Index for Cartesian coordinate

## Subscripts

*A,D,AD*Acceptor, donor, interface

*av*Average

*i,p,e,w,n,s,t,b*Directions

*nb*Neighbor

*S,l,m*Solid, liquid, mold

*sol,liq*Ssolidus, liquidus

## Superscripts

*n,n+1*Previous (or present) and the next

*old*Previous (or present) time stage

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