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Heat and Mass Transfer

, Volume 53, Issue 6, pp 1957–1969 | Cite as

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

  • Ole Richter
  • Johann Turnow
  • Nikolai Kornev
  • Egon Hassel
Original

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.

Keywords

Particle Image Velocimetry Mushy Zone Phase Change Material Rectangular Prism Mould Filling 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

List of symbols

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 (\(\hbox {m}\))

Greek symbols

\(\alpha\)

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 (\(\hbox {N/m}\))

Subscripts

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

ij

Spatial component

L

Liquidus

l

Liquid

m

Melting

S

Solidus

s

Solid

sim

Simulation

sign

Sign function

Acronyms

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

Notes

Acknowledgements

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

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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Chair of Modeling and SimulationUniversity of RostockRostockGermany
  2. 2.Chair of Technical ThermodynamicsUniversity of RostockRostockGermany

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