Abstract
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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Abbreviations
- 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 (\(\hbox {N/m}\))
- 1:
-
Phase change material, first phase
- 2:
-
Air, second phase
- A :
-
Ambient
- b :
-
Buoyancy
- c :
-
Pure cooling
- calc :
-
Analytical calculation
- cut :
-
Threshold value
- D :
-
Darcy-type
- exp :
-
Experiment
- F :
-
Final
- I :
-
Initial
- i, j :
-
Spatial component
- L :
-
Liquidus
- l :
-
Liquid
- m :
-
Melting
- S :
-
Solidus
- s :
-
Solid
- sim :
-
Simulation
- sign :
-
Sign function
- Al:
-
Aluminium
- CFD:
-
Computational fluid dynamics
- RHS:
-
Right-hand side
- P:
-
Profile
- PCM:
-
Phase change material
- PEG:
-
Polyethylene glycol
- PIT:
-
Particle image thermometry
- PIV:
-
Particle image velocimetry
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Acknowledgements
The support of the authors by the Deutsche Forschungsgemeinschaft (DFG, Grant INST 264/113-1 FUGG) is gratefully acknowledged.
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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). https://doi.org/10.1007/s00231-016-1954-7
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DOI: https://doi.org/10.1007/s00231-016-1954-7