# CFD Simulation Based Investigation of Cavitation Dynamics during High Intensity Ultrasonic Treatment of A356

^{*}

## Abstract

**:**

## 1. Introduction

- Wetting: The aluminium melt inevitably contains low amounts of Al${}_{2}$O${}_{3}$, a by-product resulting from the hydrogen-absorbing reaction of aluminium and H${}_{2}$O vapour. On the surfaces of these Al${}_{2}$O${}_{3}$ particles, hydrogen deposits prevent Al${}_{2}$O${}_{3}$ from wetting. Shock waves, resulting from the collapse of cavitation bubbles near the particle, remove the hydrogen deposits and make the Al${}_{2}$O${}_{3}$ particles available as nucleation sites for heterogeneous nucleation [9,14,15,16].
- Nucleation: The released shock waves result in a change of pressure ratios close to the collapsing bubbles. This leads to an increase of the alloy’s solidification temperature, and thus to the formation of solid aluminium grains. Below liquidus temperature, a few of the grains are thermally stable and survive the drop to normal ambient pressure; they support microstructures’ refinement as available nucleation sites [5,15,16,17,18,19].
- Fragmentation: This effect takes place at temperatures below the liquidus temperature, when the alloy starts to solidify and dendrites form. Pulsating cavitation bubbles close to the dendrites and its roots bend the dendrite arms during pulsation regularly. Either during bending or through shock waves, dendrite arms break. The broken off dendrite arms henceforth are the basis for growing dendrite structures [1,16,20,21,22,23,24,25,26].

## 2. Numerical Modelling

#### 2.1. General

#### 2.2. Meshing and Geometry

#### 2.3. Fluid

#### 2.4. Cavitation Physics

## 3. Results

#### 3.1. Radiator Movement

#### 3.2. Cavitation

#### 3.2.1. Shielding Effect

#### 3.2.2. Collapsing Bubbles

## 4. Discussion

## 5. Conclusions

- The occurrence, propagation and dynamics of cavitation can be simulated.
- The software allows the analysis of pressure conditions in and around the cavitation zone during bubble lifetime, as well as during and after collapse.
- Volume fraction along the bubble-fluid interface can be evaluated.
- Tracking of collapsed bubbles is possible.
- The influence of cavitation on pressure propagation (shielding effect) is taken into account.
- Further investigations should also take the possibility of so-called two fluid simulations into account.

## Author Contributions

## Funding

## Conflicts of Interest

## Abbreviations

UST | Ultrasonic treatment |

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**Figure 2.**Analysis of calculated radiator movement: (

**a**) actually calculated radiator amplitude and (

**b**) velocity amplitude and frequency.

**Figure 3.**Development of the cavitation zone on the radiator’s surface at different times: (

**a**) cavitation volume fraction, (

**b**) pressure and (

**c**) fluid fraction.

**Figure 5.**Bubble dynamics: (

**a**) fluid fraction in and around the bubble and (

**b**) pressure conditions in the area around the bubble and after collapse.

**Figure 7.**Fluid fraction analysis on the radiator surface: (

**a**) t = 0.00027 s, (

**b**) t = 0.00037 s and (

**c**) t = 0.00097 s.

**Figure 8.**Comparison of acoustic pressure amplitudes 4 mm below the radiator with and without the activated cavitation model.

Parameter | A356 | Unit |
---|---|---|

Density | 2437 | kg/m${}^{3}$ |

Viscosity | 0.0019 | kg/m/s |

Specific heat | 1074 | J/kg/K |

Thermal conductivity | 86.9 | W/m/K |

Liquidus temperature | 881.15 | K |

Solidus temperature | 825.55 | K |

Speed of sound | 4600 | m/s |

Compressibility | 1.94 | 1/Pa |

Surface tension | 0.871 | kg/s${}^{2}$ |

**Table 2.**Parameters and values used for the calculation of hydrogen density at 973 K [32].

Parameter | Value | Unit |
---|---|---|

Gas pressure p | 101,325 | Pa |

Universal gas constant ${R}_{m}$ | 8314.41 | J/(kmol K) |

Temperature T | 973.15 | K |

Molar mass M (H${}_{2}$) | 2.016 | kg/kmol |

Model | Parameter | A356 | Unit |
---|---|---|---|

Bubble and phase change | Gamma | 1.4 | Without unit |

with adiabatic bubble and | Pressure | 101,325 | Pa |

dynamic nucleation | |||

Cavitation with empirical | Cavitation pressure | 0 | Pa |

model for cavitation control | (Cavitation threshold) | ||

active model for voids and | Surface tension coeff. | 0.871 | kg/s${}^{2}$ |

activated cavitation | Density of cav.bubbles | 0.025 | kg/m${}^{3}$ |

potential model | Cav. production coeff. | 0.02 | Without unit |

Cav. dissipation coeff. | 0.01 | Without unit | |

Surface tension model with | Surface tension coeff. | 0.871 | kg/s${}^{2}$ |

explicit numerical | Temperature dependence | 0 | kg/s${}^{2}$/K |

approximation for surface | Contact angle | 90 | Degrees |

tension pressure |

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**MDPI and ACS Style**

Riedel, E.; Bergedieck, N.; Scharf, S.
CFD Simulation Based Investigation of Cavitation Dynamics during High Intensity Ultrasonic Treatment of A356. *Metals* **2020**, *10*, 1529.
https://doi.org/10.3390/met10111529

**AMA Style**

Riedel E, Bergedieck N, Scharf S.
CFD Simulation Based Investigation of Cavitation Dynamics during High Intensity Ultrasonic Treatment of A356. *Metals*. 2020; 10(11):1529.
https://doi.org/10.3390/met10111529

**Chicago/Turabian Style**

Riedel, Eric, Niklas Bergedieck, and Stefan Scharf.
2020. "CFD Simulation Based Investigation of Cavitation Dynamics during High Intensity Ultrasonic Treatment of A356" *Metals* 10, no. 11: 1529.
https://doi.org/10.3390/met10111529