# On the CFD Modelling of Slamming of the Metal Melt in High-Pressure Die Casting Involving Lost Cores

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## Abstract

**:**

## 1. Introduction

## 2. Model Equations and Simulation Methodology

#### 2.1. Model Equations

**U**=

**0**), at ambient temperature (T = ${T}_{amb}$) and at atmospheric pressure (p = ${p}_{amb}$). The initial conditions for the turbulence model are set via the length scale of the largest eddies and the turbulence intensity. Those quantities were set to 2 mm and 5 %, respectively.

#### 2.2. Simulation Methodology

## 3. Results and Discussion

#### 3.1. The Concept of the Dimensionless Slamming Factor

#### 3.2. Determining the Slamming Factor with Respect to Mesh Resolution

#### 3.3. Effect of Turbulence

#### 3.4. Effect of Courant Number

#### 3.5. Response of the Core to the Spike-Like Force Impact

## 4. Conclusions

## Author Contributions

## Funding

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Appendix A. The Menter SST k-ω Model (Menter 1994)

## References

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**Figure 1.**The geometry for investigating the slamming on a salt core in channel; all dimensions are in mm.

**Figure 2.**An example of a computational grid created with the utilities blockMesh and mirrorMesh for a mesh spacing of 2 mm.

**Figure 3.**Pressure Implicit with Splitting of Operator (PISO) algorithm before and after the adjustments.

**Figure 5.**Phase distribution of the melt at impact and immediately afterwards: (

**a**) $\frac{t\xb7U}{R}$ = 0.2; (

**b**) $\frac{t\xb7U}{R}$ = 0.205; (

**c**) $\frac{t\xb7U}{R}$ = 0.21. Here, $U={U}_{in}$ with ${U}_{in}$ = 20 ms${}^{-1}$.

**Figure 6.**The pressure field at the times of impact and immediately afterwards: (

**a**) $\frac{t\xb7U}{R}$ = 0.2; (

**b**) $\frac{t\xb7U}{R}$ = 0.205; (

**c**) $\frac{t\xb7U}{R}$ = 0.21. Here, $U={U}_{in}$ with ${U}_{in}$ = 20 ms${}^{-1}$.

**Figure 7.**The velocity magnitude field at the times of impact and immediately afterwards: (

**a**) $\frac{t\xb7U}{R}$ = 0.2; (

**b**) $\frac{t\xb7U}{R}$ = 0.205; (

**c**) $\frac{t\xb7U}{R}$ = 0.21. Here, $U={U}_{in}$ with ${U}_{in}$ = 20 ms${}^{-1}$.

**Figure 9.**Comparison of the computed result with reference studies in previously published articles; mesh cell spacing 0.025 mm.

**Figure 10.**Influence of the selected turbulence model on the computed result for the slamming factor.

**Figure 11.**Results of the time step size $\Delta t$ study: (

**a**) Results for ${F}_{stat}$; (

**b**) Results for ${F}_{max}$.

**Table 1.**Boundary conditions for the presented model. $\mathbf{n}$ denotes the outward unit normal vector.

Boundary | $\mathit{\gamma}$ | U/ms${}^{-1}$ | p/Pa | T/K | ||||
---|---|---|---|---|---|---|---|---|

inlet | $\gamma $ | = 1 | $\mathbf{U}$ | = ${U}_{in}{\mathbf{e}}_{\mathbf{x}}$ | $\mathbf{n}\xb7\nabla p$ | = 0 | T | = ${T}_{melt}$ |

outlet | $\mathbf{n}\xb7\nabla \gamma $ | = 0 | $(\mathbf{n}\xb7\nabla )\mathbf{U}$ | = 0 | p | = ${p}_{amb}$ | $\mathbf{n}\xb7\nabla T$ | = 0 |

salt core | $\mathbf{n}\xb7\nabla \gamma $ | = 0 | $\mathbf{U}$ | = 0 | $\mathbf{n}\xb7\nabla p$ | = $\rho (\mathbf{g}\xb7\mathbf{n})$ | $\mathbf{n}\xb7\nabla T$ | = 0 |

wall | $\mathbf{n}\xb7\nabla \gamma $ | = 0 | $\mathbf{U}$ | = 0 | $\mathbf{n}\xb7\nabla p$ | = $\rho (\mathbf{g}\xb7\mathbf{n})$ | $\mathbf{n}\xb7\nabla T$ | = 0 |

${\mathit{c}}_{{\mathit{v}}_{\mathit{g}}}$ | 720 J kg${}^{-1}$ K${}^{-1}$ |
---|---|

${c}_{{v}_{l}}$ | 1000 J kg${}^{-1}$ K${}^{-1}$ |

${k}_{g}$ | 0.026 W m${}^{-1}$K${}^{-1}$ |

${k}_{l}$ | 70 W m${}^{-1}$K${}^{-1}$ |

M | 0.028 kg mol${}^{-1}$ |

${T}_{amb}$ | 293 K |

${p}_{amb}$ | ${10}^{5}$ Pa |

${T}_{melt}$ | 823 K |

${U}_{in}$ | 10, 20 m s${}^{-1}$ |

${\mu}_{g}$ | 1.8$\times {10}^{-5}$ Pa s |

${\mu}_{l}$ | 1.62$\times {10}^{-3}$ Pa s |

${\rho}_{l}$ | 2520 kg m${}^{-3}$ |

$\sigma $ | 0.629 N m${}^{-1}$ |

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**MDPI and ACS Style**

Kohlstädt, S.; Vynnycky, M.; Goeke, S. On the CFD Modelling of Slamming of the Metal Melt in High-Pressure Die Casting Involving Lost Cores. *Metals* **2021**, *11*, 78.
https://doi.org/10.3390/met11010078

**AMA Style**

Kohlstädt S, Vynnycky M, Goeke S. On the CFD Modelling of Slamming of the Metal Melt in High-Pressure Die Casting Involving Lost Cores. *Metals*. 2021; 11(1):78.
https://doi.org/10.3390/met11010078

**Chicago/Turabian Style**

Kohlstädt, Sebastian, Michael Vynnycky, and Stephan Goeke. 2021. "On the CFD Modelling of Slamming of the Metal Melt in High-Pressure Die Casting Involving Lost Cores" *Metals* 11, no. 1: 78.
https://doi.org/10.3390/met11010078