### Abstract

The sensitivity of mesh spacing on simulations of macrosegregation, particularly 'freckles', during vertical directional solidification of a superalloy in a rectangular mold was systematically analyzed to achieve accurate predictions in finite element calculations. It was observed that a coarser mesh spacing in the x-direction horizontal tends to minimize the simulated macrosegregation, whereas a coarser mesh spacing in the y-direction vertical artificially tends to make the system appear to have more macrosegregation. When solidification conditions either lead to a well-established freckling case or to a well-established non-freckling case, the simulated results are not sensitive to the mesh spacing provided the elements are no larger than about 2d_{1} by 2 D/V and 3d_{1} by 4 D/V respectively, where d_{1} is the primary dendrite arm spacing, D is the diffusivity of the alloy solute with the smallest diffusivity in the liquid, and V is the growth rate. However, when solidification conditions are very close to the transition between freckling and no freckling, the simulated results are sensitive to the mesh spacing, especially in the y-direction. Based on the mesh sensitivity analysis from the two-dimensional simulations of rectangular castings of Rene N5, the mesh with element dimensions no larger than 2d_{1} in the x-direction and 1.5 D/V in the y-direction are recommended as the most stringent element size.

Original language | English (US) |
---|---|

Pages (from-to) | 357-370 |

Number of pages | 14 |

Journal | International Journal for Numerical Methods in Fluids |

Volume | 35 |

Issue number | 3 |

DOIs | |

State | Published - Feb 15 2001 |

### Fingerprint

### Keywords

- Dendritic single crystal
- Directional solidification
- Freckles
- Macrosegregation
- Mesh spacing

### ASJC Scopus subject areas

- Condensed Matter Physics
- Safety, Risk, Reliability and Quality
- Applied Mathematics
- Computational Theory and Mathematics
- Computer Science Applications
- Computational Mechanics
- Mechanics of Materials

### Cite this

*International Journal for Numerical Methods in Fluids*,

*35*(3), 357-370. https://doi.org/10.1002/1097-0363(20010215)35:3<357::AID-FLD99>3.0.CO;2-9

**Sensitivity of mesh spacing on simulating macrosegregation during directional solidification of a superalloy.** / Sung, P. K.; Poirier, David R; Felicelli, S. D.

Research output: Contribution to journal › Article

*International Journal for Numerical Methods in Fluids*, vol. 35, no. 3, pp. 357-370. https://doi.org/10.1002/1097-0363(20010215)35:3<357::AID-FLD99>3.0.CO;2-9

}

TY - JOUR

T1 - Sensitivity of mesh spacing on simulating macrosegregation during directional solidification of a superalloy

AU - Sung, P. K.

AU - Poirier, David R

AU - Felicelli, S. D.

PY - 2001/2/15

Y1 - 2001/2/15

N2 - The sensitivity of mesh spacing on simulations of macrosegregation, particularly 'freckles', during vertical directional solidification of a superalloy in a rectangular mold was systematically analyzed to achieve accurate predictions in finite element calculations. It was observed that a coarser mesh spacing in the x-direction horizontal tends to minimize the simulated macrosegregation, whereas a coarser mesh spacing in the y-direction vertical artificially tends to make the system appear to have more macrosegregation. When solidification conditions either lead to a well-established freckling case or to a well-established non-freckling case, the simulated results are not sensitive to the mesh spacing provided the elements are no larger than about 2d1 by 2 D/V and 3d1 by 4 D/V respectively, where d1 is the primary dendrite arm spacing, D is the diffusivity of the alloy solute with the smallest diffusivity in the liquid, and V is the growth rate. However, when solidification conditions are very close to the transition between freckling and no freckling, the simulated results are sensitive to the mesh spacing, especially in the y-direction. Based on the mesh sensitivity analysis from the two-dimensional simulations of rectangular castings of Rene N5, the mesh with element dimensions no larger than 2d1 in the x-direction and 1.5 D/V in the y-direction are recommended as the most stringent element size.

AB - The sensitivity of mesh spacing on simulations of macrosegregation, particularly 'freckles', during vertical directional solidification of a superalloy in a rectangular mold was systematically analyzed to achieve accurate predictions in finite element calculations. It was observed that a coarser mesh spacing in the x-direction horizontal tends to minimize the simulated macrosegregation, whereas a coarser mesh spacing in the y-direction vertical artificially tends to make the system appear to have more macrosegregation. When solidification conditions either lead to a well-established freckling case or to a well-established non-freckling case, the simulated results are not sensitive to the mesh spacing provided the elements are no larger than about 2d1 by 2 D/V and 3d1 by 4 D/V respectively, where d1 is the primary dendrite arm spacing, D is the diffusivity of the alloy solute with the smallest diffusivity in the liquid, and V is the growth rate. However, when solidification conditions are very close to the transition between freckling and no freckling, the simulated results are sensitive to the mesh spacing, especially in the y-direction. Based on the mesh sensitivity analysis from the two-dimensional simulations of rectangular castings of Rene N5, the mesh with element dimensions no larger than 2d1 in the x-direction and 1.5 D/V in the y-direction are recommended as the most stringent element size.

KW - Dendritic single crystal

KW - Directional solidification

KW - Freckles

KW - Macrosegregation

KW - Mesh spacing

UR - http://www.scopus.com/inward/record.url?scp=0035864598&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0035864598&partnerID=8YFLogxK

U2 - 10.1002/1097-0363(20010215)35:3<357::AID-FLD99>3.0.CO;2-9

DO - 10.1002/1097-0363(20010215)35:3<357::AID-FLD99>3.0.CO;2-9

M3 - Article

VL - 35

SP - 357

EP - 370

JO - International Journal for Numerical Methods in Fluids

JF - International Journal for Numerical Methods in Fluids

SN - 0271-2091

IS - 3

ER -