Numerical simulation of casting processes: coupled mould filling and solidification using VOF and enthalpy-porosity method


Within the scope of industrial casting applications a numerical model for the simultaneous mould filling and solidification process has been formulated, implemented in a finite volume code and successfully validated using analytical and experimental data. In order to account for the developing of free surface flow and the liquid/solid phase change, respectively, the volume-of-fluid and enthalpy-porosity method have been coupled under a volume averaging framework on a fixed Eulerian grid. The coupled method captures the basic physical effects of a combined mould filling and solidification process and provides a trustful method for comprehensive casting simulations.

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A :

Surface area (\(\hbox {m}^2\))

B :

Edge length of cube (\(\hbox {m}\))

C :

Large constant in Dracy-type source term (\(\hbox {kg/m}^3 \hbox {s}\))

\(c_p\) :

Specific heat capacity (\(\hbox {J/kg K}\))

E :

Width of rectangular prism (\(\hbox {m}\))

\(F_D\) :

Darcy-type source term (\(\hbox {N/m}^3\))

\(F_{\sigma }\) :

Surface tension force (\(\hbox {N/m}^3\))

g :

Gravitational acceleration (\(\hbox {m/s}^2\))

\(\varDelta H\) :

Latent heat (\(\hbox {J}\))

h :

Specific enthalpy (\(\hbox {J/kg}\))

\(h_t\) :

Heat transfer coefficient (\(\hbox {W/m}^2 \hbox {K}\))

L :

Specific latent heat (\(\hbox {J/kg}\))

P :

Porosity function (\(\hbox {kg/m}^3 \hbox {s}\))

Pr :

Prandtl number

p :

Pressure (\(\hbox {Pa}\))

p :

Dynamic pressure (\(\hbox {Pa}\))

\({\dot{Q}}\) :

Heat flux (\(\hbox {W}\))

R :

Heat resistance (\(\hbox {K/W}\))

Re :

Reynolds number

T :

Temperature (\(\hbox {K}\))

t :

Time (\(\hbox {s}\))

U :

Velocity magnitude (\(\hbox {m/s}\))

u :

Velocity (\(\hbox {m/s}\))

\(u_r\) :

Relative velocity (\(\hbox {m/s}\))

V :

Volume (\(\hbox {m}^3\))

x :

Spatial coordinate (\(\hbox {m}\))

\(\alpha\) :

Volume fraction

\(\beta\) :

Volume expansion coefficient (\(\hbox {1/K}\))

\(\gamma\) :

Liquid fraction

\(\epsilon\) :

Small numerical constant in Darcy-type source term

\(\delta\) :

Wall thickness (\(\hbox {m}\))

\(\kappa\) :

Curvature (\(\hbox {1/m}\))

\(\lambda\) :

Heat conductivity (\(\hbox {W/m K}\))

\(\mu\) :

Dynamic viscosity (\(\hbox {kg/m s}\))

\(\nu\) :

Kinematic viscosity (\(\hbox {m}^2/\hbox {s}\))

\(\rho\) :

Density (\(\hbox {kg/m}^3\))

\(\sigma\) :

Surface tension coefficient (\(\hbox {N/m}\))


Phase change material, first phase


Air, second phase

A :


b :


c :

Pure cooling

calc :

Analytical calculation

cut :

Threshold value

D :


exp :


F :


I :


ij :

Spatial component

L :


l :


m :


S :


s :


sim :


sign :

Sign function




Computational fluid dynamics


Right-hand side




Phase change material


Polyethylene glycol


Particle image thermometry


Particle image velocimetry


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The support of the authors by the Deutsche Forschungsgemeinschaft (DFG, Grant INST 264/113-1 FUGG) is gratefully acknowledged.

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Correspondence to Johann Turnow.

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Richter, O., Turnow, J., Kornev, N. et al. Numerical simulation of casting processes: coupled mould filling and solidification using VOF and enthalpy-porosity method. Heat Mass Transfer 53, 1957–1969 (2017).

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  • Particle Image Velocimetry
  • Mushy Zone
  • Phase Change Material
  • Rectangular Prism
  • Mould Filling