# Simulation of Ultrasonic Induced Cavitation and Acoustic Streaming in Liquid and Solidifying Aluminum

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Numerical Modeling

#### 2.1. General

#### 2.2. Fluid

#### 2.3. Physics

#### 2.4. Geometry and Movement

#### 2.5. Time Step Definition

## 3. Results

#### 3.1. Acoustic Pressure Wave Propagation

#### 3.2. Cavitation Development

#### 3.3. Acoustic Streaming

#### 3.3.1. Development and Propagation

#### 3.3.2. Cavitation and Mass Transport

#### 3.3.3. Solidification and Heat Transport

## 4. Discussion

#### 4.1. Acoustic Pressure Wave Propagation

#### 4.2. Cavitation Development

#### 4.3. Acoustic Streaming

#### 4.4. FLOW-3D

## 5. Summary

- The simulation tool can predict the development and distribution of pressure waves in a fluid, induced through a modeled radiator.
- Based on this, the development of the cavitation zone below and around the radiator tip can be calculated. Furthermore, information about cavitation intensity is provided. The results are consistent with the theoretical descriptions and demonstrated experimental behaviour of cavitation of previous investigations. With growing distance from the radiator surface, the pressure oscillations fall below the cavitation threshold, and most cavities are not able to survive in these regions. Furthermore, a shielding effect on acoustic field, proceeding from the cavitation zone, is measurable. However, for more accurate results, the used model may require adjustment for the application case of UST.
- Rapidly changing pressure conditions lead to calculated acoustic streaming, consistent with the qualitative descriptions and circumstances leading to acoustic streaming. Furthermore, the results are in good agreement and have the same order of magnitude as the results of other studies and experimental PIV-measurements.
- The influence of acoustic streaming on the cavitation can be calculated as well as particle transport and, for example, heat and mass transfer during solidification.
- The simulation tool is able to create a three-dimensional prediction of cavitation and acoustic streaming. The possibility of producing two- and three-dimensional results is a great advantage for analyzing, developing, and adjusting upcoming ultrasonic systems (e.g., different radiator geometries and properties).
- All parameters for the fluid and vessel geometries (as well as the ultrasonic system) are easily changeable and thus allow for preinvestigations into the influence of frequency, amplitude, etc., on the process and different fluids.

## Author Contributions

## Funding

## Conflicts of Interest

## Abbreviations

AMC | Aluminum matrix composites |

CCC | Commercial CFD-Code |

CFD | Computational fluid dynamics |

GMO | General moving object |

PIV | Particle image velocimetry |

UST | Ultrasonic treatment |

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**Figure 3.**Sound-wave development and propagation in aluminum A356 at different stages: (

**a**) 3 $\mathsf{\mu}$s, (

**b**) 25.8 $\mathsf{\mu}$s, and (

**c**) 62.5 $\mathsf{\mu}$s.

**Figure 4.**Developed cavitation zone and corresponding bubble collapse activity after a period of 0.01 s of ultrasonic treatment in A356: (

**a**) flat radiator tip and (

**b**) spherical radiator tip.

**Figure 5.**Comparison of flat and spherical radiator geometries for a period of 0.01 s of ultrasonic treatment in A356: (

**a**) development of cavitation gas volume and (

**b**) corresponding bubble collapse activity.

**Figure 6.**Analysis of shielding effect caused by cavitation cloud for t = 0.005 s: (

**a**) simulation with activated cavitation model and (

**b**) simulation without cavitation model, rest unchanged.

**Figure 7.**Analysis of shielding effect caused by cavitation cloud—pressure wave propagation in –z-direction.

**Figure 9.**Centerline velocity of acoustic streaming between radiator tip and vessel bottom (in –z-direction) for different stages of treatment.

**Figure 11.**Influence of acoustic streaming on the development and distribution of cavitation during a period of 5 s.

**Figure 12.**Influence of acoustic streaming on the distribution of particles of different size and density for a period of 5 s: (

**a**) ${\mathrm{Al}}_{2}$${\mathrm{O}}_{3}$-particles and Al-fragments and (

**b**) particles colored as a function of appearance.

**Figure 13.**Solidification process with UST of A536: (

**a**) solidification beginning, (

**b**) advanced stage, and (

**c**) shortly before complete solidification.

**Figure 14.**Solidification process without UST of A536: (

**a**) solidification beginning, (

**b**) advanced stage, and (

**c**) shortly before complete solidification.

**Figure 15.**Analysis of the influence of UST on temperature conditions: (

**a**) temperature gradient with and without UST and (

**b**) average temperature with and without UST.

**Figure 16.**Analysis of radiator caused chilling effect: (

**a**) highlighting of the enlarged region and (

**b**) temperature regime in the area around the tip.

**Figure 17.**Simulation result of acoustic streaming; rendered for the purpose of direct comparison with PIV-Analysis in [40].

**Table 1.**List of publications on the simulation of ultrasonic treatment, listed according to year of publication and calculated ultrasonic effects (AP/WP—Acoustic pressure/wave propagation, C—Cavitation, AS—Acoustic Streaming, S—Solidification). Note that most of the studies listed below are using the respective software for incorporation of individual ultrasonic-related codes.

Author(s) | Year | Fluid/Alloy | Software | AP/WP | C | AS | S | Reference |
---|---|---|---|---|---|---|---|---|

Dahlem et al. | 1999 | Water | Sysnoise /Fluent CFD | X | X | [49] | ||

Kumar et al. | 2006 | Water | Other CFD-Code | X | [50] | |||

Klima et al. | 2007 | Water | FEM LAB 3.1 | X | [51] | |||

Trujillo & Knoerzer | 2009 | Unclear | COMSOL Multiphysics | X | [35] | |||

Nastac | 2011 | Aluminum (A356) | Other CFD-Code | X | X | X | [52] | |

Shu et al. | 2012 | Succinonitril | COMSOL Multiphysics | X | [17] | |||

Jamshidi et al. | 2012 | Water | COMSOL Multiphysics | X | X | [53] | ||

Ishiwata et al. | 2012 | Aluminum | Other CFD-Code | X | [39] | |||

Schenker et al. | 2012 | Water | Fluent | X | [38] | |||

Xu et al. | 2013 | Water | COMSOL Multiphysics | X | X | [54] | ||

Jamshidi | 2013 | Water | COMSOL Multiphysics | X | [55] | |||

Huang et al. | 2014 | Pure aluminum | COMSOL Multiphysics | X | [8] | |||

Jamshidi et al. | 2014 | Water | FVM-Code | X | X | [56] | ||

Zhang & Nastac | 2014 | Aluminum (6061) | ANSYS Fluent | X | [57] | |||

Kang et al. | 2015 | Water/aluminum/steel | ANSYS Fluent | X | X | [58] | ||

Sajjadi et al. | 2015 | Water | ANSYS Fluent | X | X | [43] | ||

Zhang et al. | 2015 | Stainless steel | ANSYS Fluent | X | X | [37] | ||

Sajjadi et al. | 2015 | Water | Other CFD-Code | X | X | X | [43] | |

Lebon et al. | 2015 | Water/aluminum | Other CFD-Code | X | X | [59] | ||

Žnidarčič | 2015 | Water | ANSYS Fluent | X | [45] | |||

Jamshidi et al. | 2016 | Adipic acid | Other code | X | X | X | [60] | |

Lebon et al. | 2016 | Water/aluminum | Other CFD-Code | X | X | [61] | ||

Wang et al. | 2016 | Succinonitril | Other code | X | [62] | |||

Mottyll & Skoda | 2016 | Water | ANSYS ICEM CFD | X | [46] | |||

Jia et al. | 2016 | Aluminum (A356) | ANSYS Fluent | X | [21] | |||

Rubinette et al. | 2016 | Aluminum/water | COMSOL Multiphysics | X | [42] | |||

Rahimi et al. | 2017 | Water | Other CFD-Code | X | X | X | [63] | |

Lebon et al. | 2017 | Aluminum | Other code | X | [44] | |||

Wang et al. | 2017 | Aluminum (AlCu2) | ProCAST (FEM) | X | X | [47] | ||

Louisnard | 2017 | Water | COMSOL | X | [36] | |||

Sajjadi et al. | 2017 | Water/glycerol | ANSYS Fluent | X | x | [64] | ||

Lebon et al. | 2018 | Water/aluminum a.o. | Other code | X | [65] | |||

Fang et al. | 2018 | Water | OpenFOAM | X | X | [66] | ||

Tzanakis et al. | 2018 | Water | OpenFOAM | X | [40] | |||

Lebon et al. | 2019 | Water/aluminum | OpenFOAM | X | X | [67] | ||

Lebon et al. | 2019 | Aluminum | OpenFOAM | X | X | X | [68] | |

Lebon et al. | 2019 | Aluminum | OpenFOAM | X | X | X | [41] | |

Riedel et al. | 2019 | Aluminum (A356) | FLOW-3D | X | X | [48] | ||

Komarov & Yamamoto | 2019 | Water/aluminum (AlSi17) | Other code | X | X | [69] |

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

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

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/${\mathrm{s}}^{2}$ |

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/${\mathrm{s}}^{2}$ |

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

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/${\mathrm{s}}^{2}$ |

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

approximation for surface | Contact angle | 90 | Degrees(s) |

tension pressure |

**Table 4.**Parameters and values used for calculation of hydrogen density at 973 K [72].

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 (${\mathrm{H}}_{2}$) | 2.016 | kg/kmol |

Simulation | Maximum Time Step [s] |
---|---|

Pressure | $3.91\times {10}^{-7}$ |

Cavitation | $1.56\times {10}^{-6}$ |

Acoustic Streaming | $1.25\times {10}^{-5}$ |

UST + solidification | $1.25\times {10}^{-5}$ |

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**MDPI and ACS Style**

Riedel, E.; Liepe, M.; Scharf, S. Simulation of Ultrasonic Induced Cavitation and Acoustic Streaming in Liquid and Solidifying Aluminum. *Metals* **2020**, *10*, 476.
https://doi.org/10.3390/met10040476

**AMA Style**

Riedel E, Liepe M, Scharf S. Simulation of Ultrasonic Induced Cavitation and Acoustic Streaming in Liquid and Solidifying Aluminum. *Metals*. 2020; 10(4):476.
https://doi.org/10.3390/met10040476

**Chicago/Turabian Style**

Riedel, Eric, Martin Liepe, and Stefan Scharf. 2020. "Simulation of Ultrasonic Induced Cavitation and Acoustic Streaming in Liquid and Solidifying Aluminum" *Metals* 10, no. 4: 476.
https://doi.org/10.3390/met10040476